LMFDB - Embedded newform 736.2.x.a.593.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [736,2,Mod(49,736)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(736, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("736.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 736 = 2^{5} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	736.x (of order $22$, degree $10$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.87698958877$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			593.5
Character	$\chi$	$=$	736.593
Dual form			736.2.x.a.561.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.56187 - 1.35337i) q^{3} +(1.30771 + 0.188020i) q^{5} +(-1.93127 - 4.22889i) q^{7} +(0.180888 + 1.25811i) q^{9} +(0.917064 + 3.12323i) q^{11} +(-4.99596 - 2.28158i) q^{13} +(-1.78801 - 2.06347i) q^{15} +(3.05609 - 1.96403i) q^{17} +(-1.11353 + 1.73268i) q^{19} +(-2.70685 + 9.21868i) q^{21} +(4.20285 + 2.30999i) q^{23} +(-3.12272 - 0.916913i) q^{25} +(-1.93179 + 3.00592i) q^{27} +(-0.0805869 - 0.125396i) q^{29} +(-5.26595 - 6.07723i) q^{31} +(2.79455 - 6.11921i) q^{33} +(-1.73042 - 5.89326i) q^{35} +(-6.57274 + 0.945018i) q^{37} +(4.71523 + 10.3249i) q^{39} +(-0.661733 + 4.60245i) q^{41} +(4.20419 + 3.64295i) q^{43} +1.67924i q^{45} -2.17073 q^{47} +(-9.56965 + 11.0440i) q^{49} +(-7.43128 - 1.06846i) q^{51} +(-1.56586 + 0.715106i) q^{53} +(0.612021 + 4.25670i) q^{55} +(4.08414 - 1.19921i) q^{57} +(-10.3139 - 4.71020i) q^{59} +(0.788289 - 0.683056i) q^{61} +(4.97104 - 3.19469i) q^{63} +(-6.10427 - 3.92298i) q^{65} +(1.96238 - 6.68327i) q^{67} +(-3.43804 - 9.29591i) q^{69} +(-4.09570 - 1.20261i) q^{71} +(-5.31849 - 3.41799i) q^{73} +(3.63636 + 5.65829i) q^{75} +(11.4367 - 9.90995i) q^{77} +(-3.36807 + 7.37505i) q^{79} +(10.7440 - 3.15472i) q^{81} +(-3.79551 + 0.545712i) q^{83} +(4.36575 - 1.99377i) q^{85} +(-0.0438403 + 0.304916i) q^{87} +(-5.49693 + 6.34379i) q^{89} +25.5337i q^{91} +16.6186i q^{93} +(-1.78195 + 2.05647i) q^{95} +(2.47737 - 17.2305i) q^{97} +(-3.76347 + 1.71872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 22 q^{7} + 22 q^{15} - 18 q^{17} + 16 q^{23} - 4 q^{25} + 34 q^{31} - 30 q^{33} + 18 q^{39} - 18 q^{41} + 40 q^{47} - 28 q^{49} + 38 q^{55} - 30 q^{57} - 18 q^{63} - 38 q^{65} + 26 q^{71} - 18 q^{73}+ \cdots - 18 q^{97}+O(q^{100}) $ 220 * q + 22 * q^7 + 22 * q^15 - 18 * q^17 + 16 * q^23 - 4 * q^25 + 34 * q^31 - 30 * q^33 + 18 * q^39 - 18 * q^41 + 40 * q^47 - 28 * q^49 + 38 * q^55 - 30 * q^57 - 18 * q^63 - 38 * q^65 + 26 * q^71 - 18 * q^73 + 22 * q^79 - 52 * q^81 + 42 * q^87 - 2 * q^89 + 78 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/736\mathbb{Z}\right)^\times$.

$n$	$97$	$415$	$645$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.56187	−	1.35337i	−0.901746	−	0.781367i	0.0746827	−	0.997207i	$-0.476206\pi$
$3$	−1.56187	−	1.35337i	−0.901746	−	0.781367i	−0.976429	+	0.215840i	$0.930751\pi$
$4$		0			0
$5$	1.30771	+	0.188020i	0.584824	+	0.0840851i	0.428375	−	0.903601i	$-0.359086\pi$
$5$	1.30771	+	0.188020i	0.584824	+	0.0840851i	0.156449	+	0.987686i	$0.449995\pi$
$6$		0			0
$7$	−1.93127	−	4.22889i	−0.729950	−	1.59837i	−0.799412	−	0.600784i	$-0.794855\pi$
$7$	−1.93127	−	4.22889i	−0.729950	−	1.59837i	0.0694612	−	0.997585i	$-0.477872\pi$
$8$		0			0
$9$	0.180888	+	1.25811i	0.0602961	+	0.419369i
$10$		0			0
$11$	0.917064	+	3.12323i	0.276505	+	0.941690i	0.974274	+	0.225367i	$0.0723581\pi$
$11$	0.917064	+	3.12323i	0.276505	+	0.941690i	−0.697769	+	0.716323i	$0.745824\pi$
$12$		0			0
$13$	−4.99596	−	2.28158i	−1.38563	−	0.632796i	−0.423628	−	0.905836i	$-0.639244\pi$
$13$	−4.99596	−	2.28158i	−1.38563	−	0.632796i	−0.962003	+	0.273040i	$0.911971\pi$
$14$		0			0
$15$	−1.78801	−	2.06347i	−0.461662	−	0.532786i
$16$		0			0
$17$	3.05609	−	1.96403i	0.741211	−	0.476348i	−0.114746	−	0.993395i	$-0.536605\pi$
$17$	3.05609	−	1.96403i	0.741211	−	0.476348i	0.855957	+	0.517047i	$0.172969\pi$
$18$		0			0
$19$	−1.11353	+	1.73268i	−0.255460	+	0.397504i	−0.945168	−	0.326583i	$-0.894103\pi$
$19$	−1.11353	+	1.73268i	−0.255460	+	0.397504i	0.689708	+	0.724088i	$0.257739\pi$
$20$		0			0
$21$	−2.70685	+	9.21868i	−0.590683	+	2.01168i
$22$		0			0
$23$	4.20285	+	2.30999i	0.876355	+	0.481666i
$23$	4.20285	+	2.30999i	0.876355	+	0.481666i
$24$		0			0
$25$	−3.12272	−	0.916913i	−0.624544	−	0.183383i
$26$		0			0
$27$	−1.93179	+	3.00592i	−0.371773	+	0.578490i
$28$		0			0
$29$	−0.0805869	−	0.125396i	−0.0149646	−	0.0232854i	0.833691	−	0.552232i	$-0.186224\pi$
$29$	−0.0805869	−	0.125396i	−0.0149646	−	0.0232854i	−0.848655	+	0.528946i	$0.822587\pi$
$30$		0			0
$31$	−5.26595	−	6.07723i	−0.945793	−	1.09150i	−0.995690	−	0.0927488i	$-0.970435\pi$
$31$	−5.26595	−	6.07723i	−0.945793	−	1.09150i	0.0498967	−	0.998754i	$-0.484111\pi$
$32$		0			0
$33$	2.79455	−	6.11921i	0.486468	−	1.06522i
$34$		0			0
$35$	−1.73042	−	5.89326i	−0.292494	−	0.996143i
$36$		0			0
$37$	−6.57274	+	0.945018i	−1.08055	+	0.155360i	−0.659521	−	0.751686i	$-0.729241\pi$
$37$	−6.57274	+	0.945018i	−1.08055	+	0.155360i	−0.421031	+	0.907046i	$0.638332\pi$
$38$		0			0
$39$	4.71523	+	10.3249i	0.755040	+	1.65331i
$40$		0			0
$41$	−0.661733	+	4.60245i	−0.103345	+	0.718783i	0.870599	+	0.491994i	$0.163732\pi$
$41$	−0.661733	+	4.60245i	−0.103345	+	0.718783i	−0.973944	+	0.226789i	$0.927177\pi$
$42$		0			0
$43$	4.20419	+	3.64295i	0.641133	+	0.555545i	0.913597	−	0.406621i	$-0.133293\pi$
$43$	4.20419	+	3.64295i	0.641133	+	0.555545i	−0.272464	+	0.962166i	$0.587839\pi$
$44$		0			0
$45$			1.67924i			0.250327i
$46$		0			0
$47$	−2.17073			−0.316633			−0.158317	−	0.987388i	$-0.550607\pi$
$47$	−2.17073			−0.316633			−0.158317	+	0.987388i	$0.550607\pi$
$48$		0			0
$49$	−9.56965	+	11.0440i	−1.36709	+	1.57771i
$50$		0			0
$51$	−7.43128	−	1.06846i	−1.04059	−	0.149614i
$52$		0			0
$53$	−1.56586	+	0.715106i	−0.215088	+	0.0982273i	−0.520045	−	0.854139i	$-0.674085\pi$
$53$	−1.56586	+	0.715106i	−0.215088	+	0.0982273i	0.304958	+	0.952366i	$0.401358\pi$
$54$		0			0
$55$	0.612021	+	4.25670i	0.0825249	+	0.573973i
$56$		0			0
$57$	4.08414	−	1.19921i	0.540957	−	0.158839i
$58$		0			0
$59$	−10.3139	−	4.71020i	−1.34275	−	0.613215i	−0.391089	−	0.920353i	$-0.627902\pi$
$59$	−10.3139	−	4.71020i	−1.34275	−	0.613215i	−0.951665	+	0.307137i	$0.900629\pi$
$60$		0			0
$61$	0.788289	−	0.683056i	0.100930	−	0.0874564i	−0.602934	−	0.797791i	$-0.706002\pi$
$61$	0.788289	−	0.683056i	0.100930	−	0.0874564i	0.703864	+	0.710335i	$0.251456\pi$
$62$		0			0
$63$	4.97104	−	3.19469i	0.626292	−	0.402494i
$64$		0			0
$65$	−6.10427	−	3.92298i	−0.757142	−	0.486585i
$66$		0			0
$67$	1.96238	−	6.68327i	0.239743	−	0.816491i	−0.748438	−	0.663204i	$-0.769196\pi$
$67$	1.96238	−	6.68327i	0.239743	−	0.816491i	0.988182	−	0.153287i	$-0.0489858\pi$
$68$		0			0
$69$	−3.43804	−	9.29591i	−0.413892	−	1.11910i
$70$		0			0
$71$	−4.09570	−	1.20261i	−0.486071	−	0.142723i	0.0295097	−	0.999564i	$-0.490605\pi$
$71$	−4.09570	−	1.20261i	−0.486071	−	0.142723i	−0.515580	+	0.856841i	$0.672424\pi$
$72$		0			0
$73$	−5.31849	−	3.41799i	−0.622482	−	0.400045i	0.191037	−	0.981583i	$-0.438815\pi$
$73$	−5.31849	−	3.41799i	−0.622482	−	0.400045i	−0.813519	+	0.581538i	$0.802451\pi$
$74$		0			0
$75$	3.63636	+	5.65829i	0.419891	+	0.653363i
$76$		0			0
$77$	11.4367	−	9.90995i	1.30333	−	1.12934i
$78$		0			0
$79$	−3.36807	+	7.37505i	−0.378938	+	0.829758i	0.620041	+	0.784570i	$0.287116\pi$
$79$	−3.36807	+	7.37505i	−0.378938	+	0.829758i	−0.998978	+	0.0451884i	$0.985611\pi$
$80$		0			0
$81$	10.7440	−	3.15472i	1.19378	−	0.350525i
$82$		0			0
$83$	−3.79551	+	0.545712i	−0.416611	+	0.0598996i	−0.347433	−	0.937705i	$-0.612947\pi$
$83$	−3.79551	+	0.545712i	−0.416611	+	0.0598996i	−0.0691778	+	0.997604i	$0.522038\pi$
$84$		0			0
$85$	4.36575	−	1.99377i	0.473532	−	0.216255i
$86$		0			0
$87$	−0.0438403	+	0.304916i	−0.00470017	+	0.0326904i
$88$		0			0
$89$	−5.49693	+	6.34379i	−0.582673	+	0.672440i	−0.968177	−	0.250266i	$-0.919482\pi$
$89$	−5.49693	+	6.34379i	−0.582673	+	0.672440i	0.385504	+	0.922706i	$0.374027\pi$
$90$		0			0
$91$			25.5337i			2.67666i
$92$		0			0
$93$			16.6186i			1.72327i
$94$		0			0
$95$	−1.78195	+	2.05647i	−0.182824	+	0.210990i
$96$		0			0
$97$	2.47737	−	17.2305i	0.251538	−	1.74949i	−0.337447	−	0.941344i	$-0.609563\pi$
$97$	2.47737	−	17.2305i	0.251538	−	1.74949i	0.588986	−	0.808144i	$-0.299527\pi$
$98$		0			0
$99$	−3.76347	+	1.71872i	−0.378243	+	0.172738i
$100$		0			0
$101$	6.37368	−	0.916397i	0.634205	−	0.0911849i	0.182288	−	0.983245i	$-0.441650\pi$
$101$	6.37368	−	0.916397i	0.634205	−	0.0911849i	0.451917	+	0.892060i	$0.350740\pi$
$102$		0			0
$103$	11.7000	−	3.43544i	1.15284	−	0.338504i	0.351194	−	0.936303i	$-0.385776\pi$
$103$	11.7000	−	3.43544i	1.15284	−	0.338504i	0.801646	+	0.597798i	$0.203958\pi$
$104$		0			0
$105$	−5.27306	+	11.5464i	−0.514598	+	1.12681i
$106$		0			0
$107$	9.79025	−	8.48330i	0.946459	−	0.820112i	−0.0373552	−	0.999302i	$-0.511893\pi$
$107$	9.79025	−	8.48330i	0.946459	−	0.820112i	0.983814	+	0.179191i	$0.0573479\pi$
$108$		0			0
$109$	−0.511817	−	0.796403i	−0.0490232	−	0.0762816i	0.815877	−	0.578226i	$-0.196255\pi$
$109$	−0.511817	−	0.796403i	−0.0490232	−	0.0762816i	−0.864900	+	0.501944i	$0.832618\pi$
$110$		0			0
$111$	11.5447	+	7.41934i	1.09578	+	0.704213i
$112$		0			0
$113$	5.20573	+	1.52854i	0.489714	+	0.143793i	0.517261	−	0.855828i	$-0.326952\pi$
$113$	5.20573	+	1.52854i	0.489714	+	0.143793i	−0.0275476	+	0.999620i	$0.508770\pi$
$114$		0			0
$115$	5.06177	+	3.81101i	0.472013	+	0.355378i
$116$		0			0
$117$	1.96676	−	6.69816i	0.181827	−	0.619245i
$118$		0			0
$119$	−14.2078	−	9.13079i	−1.30243	−	0.837019i
$120$		0			0
$121$	0.340219	−	0.218645i	0.0309290	−	0.0198768i
$122$		0			0
$123$	7.26235	−	6.29287i	0.654824	−	0.567409i
$124$		0			0
$125$	−9.92003	−	4.53032i	−0.887274	−	0.405205i
$126$		0			0
$127$	−0.354005	+	0.103945i	−0.0314129	+	0.00922366i	−0.297401	−	0.954753i	$-0.596120\pi$
$127$	−0.354005	+	0.103945i	−0.0314129	+	0.00922366i	0.265988	+	0.963976i	$0.414302\pi$
$128$		0			0
$129$	−1.63614	−	11.3796i	−0.144054	−	1.00192i
$130$		0			0
$131$	3.04328	−	1.38982i	0.265893	−	0.121429i	−0.278008	−	0.960579i	$-0.589674\pi$
$131$	3.04328	−	1.38982i	0.265893	−	0.121429i	0.543901	+	0.839150i	$0.316947\pi$
$132$		0			0
$133$	9.47783	+	1.36271i	0.821832	+	0.118162i
$134$		0			0
$135$	−3.09139	+	3.56765i	−0.266064	+	0.307055i
$136$		0			0
$137$	12.1856			1.04108			0.520542	−	0.853836i	$-0.325730\pi$
$137$	12.1856			1.04108			0.520542	+	0.853836i	$0.325730\pi$
$138$		0			0
$139$		−	10.9900i		−	0.932160i	−0.884743	−	0.466080i	$-0.845666\pi$
$139$		−	10.9900i		−	0.932160i	0.884743	−	0.466080i	$-0.154334\pi$
$140$		0			0
$141$	3.39040	+	2.93780i	0.285523	+	0.247407i
$142$		0			0
$143$	2.54429	−	17.6959i	0.212764	−	1.47981i
$144$		0			0
$145$	−0.0818072	−	0.179133i	−0.00679372	−	0.0148762i
$146$		0			0
$147$	29.8931	−	4.29798i	2.46554	−	0.354491i
$148$		0			0
$149$	1.30512	+	4.44483i	0.106920	+	0.364135i	0.995520	−	0.0945465i	$-0.0301401\pi$
$149$	1.30512	+	4.44483i	0.106920	+	0.364135i	−0.888601	+	0.458681i	$0.848322\pi$
$150$		0			0
$151$	7.15579	−	15.6690i	0.582330	−	1.27512i	−0.357638	−	0.933860i	$-0.616418\pi$
$151$	7.15579	−	15.6690i	0.582330	−	1.27512i	0.939968	−	0.341264i	$-0.110855\pi$
$152$		0			0
$153$	3.02377	+	3.48962i	0.244457	+	0.282119i
$154$		0			0
$155$	−5.74368	−	8.93734i	−0.461344	−	0.717865i
$156$		0			0
$157$	2.38160	−	3.70585i	0.190073	−	0.295759i	−0.733118	−	0.680102i	$-0.761936\pi$
$157$	2.38160	−	3.70585i	0.190073	−	0.295759i	0.923190	+	0.384343i	$0.125572\pi$
$158$		0			0
$159$	3.41348	+	1.00229i	0.270706	+	0.0794865i
$160$		0			0
$161$	1.65185	−	22.2346i	0.130184	−	1.75233i
$162$		0			0
$163$	6.69156	−	22.7894i	0.524123	−	1.78500i	−0.0901744	−	0.995926i	$-0.528742\pi$
$163$	6.69156	−	22.7894i	0.524123	−	1.78500i	0.614298	−	0.789074i	$-0.289439\pi$
$164$		0			0
$165$	4.80498	−	7.47670i	0.374067	−	0.582060i
$166$		0			0
$167$	−4.10239	+	2.63645i	−0.317453	+	0.204014i	−0.689657	−	0.724136i	$-0.742239\pi$
$167$	−4.10239	+	2.63645i	−0.317453	+	0.204014i	0.372204	+	0.928151i	$0.378602\pi$
$168$		0			0
$169$	11.2408	+	12.9726i	0.864680	+	0.997894i
$170$		0			0
$171$	−2.38132	−	1.08751i	−0.182104	−	0.0831641i
$172$		0			0
$173$	−3.43944	−	11.7137i	−0.261496	−	0.890573i	−0.980658	−	0.195731i	$-0.937292\pi$
$173$	−3.43944	−	11.7137i	−0.261496	−	0.890573i	0.719162	−	0.694843i	$-0.244526\pi$
$174$		0			0
$175$	2.15328	+	14.9764i	0.162773	+	1.13211i
$176$		0			0
$177$	9.73433	+	21.3152i	0.731677	+	1.60215i
$178$		0			0
$179$	−21.0854	−	3.03163i	−1.57600	−	0.226594i	−0.701876	−	0.712299i	$-0.747654\pi$
$179$	−21.0854	−	3.03163i	−1.57600	−	0.226594i	−0.874123	+	0.485705i	$0.838563\pi$
$180$		0			0
$181$	11.6255	+	10.0735i	0.864115	+	0.748760i	0.969349	−	0.245688i	$-0.0790137\pi$
$181$	11.6255	+	10.0735i	0.864115	+	0.748760i	−0.105234	+	0.994447i	$0.533559\pi$
$182$		0			0
$183$	−2.15563			−0.159349
$184$		0			0
$185$	−8.77290			−0.644997
$186$		0			0
$187$	8.93675	+	7.74374i	0.653520	+	0.566278i
$188$		0			0
$189$	16.4425	+	2.36408i	1.19602	+	0.171961i
$190$		0			0
$191$	7.99315	+	17.5026i	0.578364	+	1.26644i	0.942223	+	0.334986i	$0.108732\pi$
$191$	7.99315	+	17.5026i	0.578364	+	1.26644i	−0.363859	+	0.931454i	$0.618541\pi$
$192$		0			0
$193$	−0.0340978	−	0.237156i	−0.00245442	−	0.0170708i	0.988557	−	0.150845i	$-0.0481994\pi$
$193$	−0.0340978	−	0.237156i	−0.00245442	−	0.0170708i	−0.991012	+	0.133774i	$0.957290\pi$
$194$		0			0
$195$	4.22485	+	14.3885i	0.302548	+	1.03038i
$196$		0			0
$197$	−12.9836	−	5.92940i	−0.925042	−	0.422452i	−0.104816	−	0.994492i	$-0.533425\pi$
$197$	−12.9836	−	5.92940i	−0.925042	−	0.422452i	−0.820226	+	0.572039i	$0.806153\pi$
$198$		0			0
$199$	−10.3270	−	11.9180i	−0.732064	−	0.844847i	0.260638	−	0.965436i	$-0.416067\pi$
$199$	−10.3270	−	11.9180i	−0.732064	−	0.844847i	−0.992702	+	0.120590i	$0.961522\pi$
$200$		0			0
$201$	−12.1099	+	7.78257i	−0.854167	+	0.548940i
$202$		0			0
$203$	−0.374649	+	0.582966i	−0.0262952	+	0.0409162i
$204$		0			0
$205$	−1.73071	+	5.89424i	−0.120878	+	0.411672i
$206$		0			0
$207$	−2.14596	+	5.70548i	−0.149155	+	0.396558i
$208$		0			0
$209$	−6.43274	−	1.88882i	−0.444962	−	0.130653i
$210$		0			0
$211$	6.22132	−	9.68056i	0.428293	−	0.666437i	−0.558299	−	0.829640i	$-0.688546\pi$
$211$	6.22132	−	9.68056i	0.428293	−	0.666437i	0.986593	+	0.163202i	$0.0521823\pi$
$212$		0			0
$213$	4.76939	+	7.42131i	0.326793	+	0.508500i
$214$		0			0
$215$	4.81290	+	5.55439i	0.328237	+	0.378806i
$216$		0			0
$217$	−15.5300	+	34.0059i	−1.05424	+	2.30847i
$218$		0			0
$219$	3.68100	+	12.5363i	0.248739	+	0.847127i
$220$		0			0
$221$	−19.7492	+	2.83951i	−1.32848	+	0.191006i
$222$		0			0
$223$	−2.23447	−	4.89280i	−0.149631	−	0.327646i	0.819943	−	0.572445i	$-0.194005\pi$
$223$	−2.23447	−	4.89280i	−0.149631	−	0.327646i	−0.969574	+	0.244799i	$0.921278\pi$
$224$		0			0
$225$	0.588710	−	4.09457i	0.0392473	−	0.272971i
$226$		0			0
$227$	−5.60075	−	4.85307i	−0.371735	−	0.322110i	0.448880	−	0.893592i	$-0.351823\pi$
$227$	−5.60075	−	4.85307i	−0.371735	−	0.322110i	−0.820614	+	0.571482i	$0.806369\pi$
$228$		0			0
$229$		−	9.88644i		−	0.653314i	−0.945143	−	0.326657i	$-0.894078\pi$
$229$		−	9.88644i		−	0.653314i	0.945143	−	0.326657i	$-0.105922\pi$
$230$		0			0
$231$	−31.2744			−2.05771
$232$		0			0
$233$	−5.26267	+	6.07344i	−0.344769	+	0.397884i	−0.901479	−	0.432822i	$-0.857518\pi$
$233$	−5.26267	+	6.07344i	−0.344769	+	0.397884i	0.556710	+	0.830707i	$0.312063\pi$
$234$		0			0
$235$	−2.83868	−	0.408140i	−0.185175	−	0.0266241i
$236$		0			0
$237$	15.2417	−	6.96063i	0.990052	−	0.452141i
$238$		0			0
$239$	−0.292625	−	2.03525i	−0.0189284	−	0.131650i	0.978166	−	0.207825i	$-0.0666383\pi$
$239$	−0.292625	−	2.03525i	−0.0189284	−	0.131650i	−0.997094	+	0.0761750i	$0.975729\pi$
$240$		0			0
$241$	−8.25098	+	2.42271i	−0.531492	+	0.156060i	−0.536457	−	0.843927i	$-0.680238\pi$
$241$	−8.25098	+	2.42271i	−0.531492	+	0.156060i	0.00496497	+	0.999988i	$0.498420\pi$
$242$		0			0
$243$	−11.2995	−	5.16030i	−0.724862	−	0.331033i
$244$		0			0
$245$	−14.5908	+	12.6430i	−0.932171	+	0.807731i
$246$		0			0
$247$	9.51638	−	6.11581i	0.605513	−	0.389140i
$248$		0			0
$249$	6.66664	+	4.28439i	0.422481	+	0.271512i
$250$		0			0
$251$	0.580420	−	1.97673i	0.0366358	−	0.124770i	−0.939145	−	0.343521i	$-0.888380\pi$
$251$	0.580420	−	1.97673i	0.0366358	−	0.124770i	0.975781	+	0.218751i	$0.0701984\pi$
$252$		0			0
$253$	−3.36035	+	15.2449i	−0.211263	+	0.958438i
$254$		0			0
$255$	−9.51704	−	2.79446i	−0.595980	−	0.174996i
$256$		0			0
$257$	20.1251	+	12.9336i	1.25537	+	0.806777i	0.987643	−	0.156718i	$-0.0500913\pi$
$257$	20.1251	+	12.9336i	1.25537	+	0.806777i	0.267726	+	0.963495i	$0.413728\pi$
$258$		0			0
$259$	16.6901	+	25.9703i	1.03707	+	1.61372i
$260$		0			0
$261$	0.143184	−	0.124070i	0.00886286	−	0.00767971i
$262$		0			0
$263$	−11.1950	+	24.5137i	−0.690316	+	1.51158i	0.161014	+	0.986952i	$0.448524\pi$
$263$	−11.1950	+	24.5137i	−0.690316	+	1.51158i	−0.851330	+	0.524630i	$0.824204\pi$
$264$		0			0
$265$	−2.18214	+	0.640735i	−0.134048	+	0.0393601i
$266$		0			0
$267$	17.1710	−	2.46881i	1.05085	−	0.151089i
$268$		0			0
$269$	−1.55248	+	0.708995i	−0.0946565	+	0.0432282i	−0.462181	−	0.886786i	$-0.652933\pi$
$269$	−1.55248	+	0.708995i	−0.0946565	+	0.0432282i	0.367524	+	0.930014i	$0.380206\pi$
$270$		0			0
$271$	−2.41340	+	16.7856i	−0.146604	+	1.01965i	0.775123	+	0.631810i	$0.217688\pi$
$271$	−2.41340	+	16.7856i	−0.146604	+	1.01965i	−0.921727	+	0.387840i	$0.873221\pi$
$272$		0			0
$273$	34.5565	−	39.8803i	2.09145	−	2.41367i
$274$		0			0
$275$		−	10.5938i		−	0.638833i
$276$		0			0
$277$			3.87012i			0.232533i	0.993218	+	0.116266i	$0.0370926\pi$
$277$			3.87012i			0.232533i	−0.993218	+	0.116266i	$0.962907\pi$
$278$		0			0
$279$	6.69325	−	7.72443i	0.400715	−	0.462449i
$280$		0			0
$281$	3.83410	−	26.6668i	0.228723	−	1.59081i	−0.474773	−	0.880108i	$-0.657470\pi$
$281$	3.83410	−	26.6668i	0.228723	−	1.59081i	0.703497	−	0.710699i	$-0.251621\pi$
$282$		0			0
$283$	5.15847	−	2.35579i	0.306639	−	0.140037i	−0.256152	−	0.966636i	$-0.582455\pi$
$283$	5.15847	−	2.35579i	0.306639	−	0.140037i	0.562791	+	0.826599i	$0.309728\pi$
$284$		0			0
$285$	5.56633	−	0.800318i	0.329721	−	0.0474067i
$286$		0			0
$287$	20.7412	−	6.09018i	1.22432	−	0.359492i
$288$		0			0
$289$	−1.57977	+	3.45922i	−0.0929279	+	0.203484i
$290$		0			0
$291$	−27.1885	+	23.5589i	−1.59382	+	1.38105i
$292$		0			0
$293$	−12.0938	−	18.8183i	−0.706528	−	1.09938i	−0.990091	−	0.140426i	$-0.955153\pi$
$293$	−12.0938	−	18.8183i	−0.706528	−	1.09938i	0.283563	−	0.958954i	$-0.408483\pi$
$294$		0			0
$295$	−12.6019	−	8.09878i	−0.733713	−	0.471529i
$296$		0			0
$297$	−11.1598	−	3.27680i	−0.647556	−	0.190139i
$298$		0			0
$299$	−15.7269	−	21.1297i	−0.909508	−	1.22196i
$300$		0			0
$301$	7.28621	−	24.8146i	0.419970	−	1.43029i
$302$		0			0
$303$	−11.1951	−	7.19464i	−0.643141	−	0.413322i
$304$		0			0
$305$	1.15928	−	0.745024i	0.0663802	−	0.0426599i
$306$		0			0
$307$	−9.52161	+	8.25053i	−0.543427	+	0.470882i	−0.882786	−	0.469774i	$-0.844335\pi$
$307$	−9.52161	+	8.25053i	−0.543427	+	0.470882i	0.339359	+	0.940657i	$0.389790\pi$
$308$		0			0
$309$	−22.9234	−	10.4688i	−1.30407	−	0.595547i
$310$		0			0
$311$	27.9339	−	8.20213i	1.58398	−	0.465100i	0.632952	−	0.774191i	$-0.281843\pi$
$311$	27.9339	−	8.20213i	1.58398	−	0.465100i	0.951032	+	0.309091i	$0.100025\pi$
$312$		0			0
$313$	0.965667	+	6.71636i	0.0545827	+	0.379631i	0.998742	+	0.0501420i	$0.0159674\pi$
$313$	0.965667	+	6.71636i	0.0545827	+	0.379631i	−0.944159	+	0.329489i	$0.893124\pi$
$314$		0			0
$315$	7.10133	−	3.24307i	0.400115	−	0.182726i
$316$		0			0
$317$	3.80052	+	0.546432i	0.213458	+	0.0306907i	0.248214	−	0.968705i	$-0.420156\pi$
$317$	3.80052	+	0.546432i	0.213458	+	0.0306907i	−0.0347559	+	0.999396i	$0.511065\pi$
$318$		0			0
$319$	0.317737	−	0.366688i	0.0177898	−	0.0205306i
$320$		0			0
$321$	−26.7721			−1.49427
$322$		0			0
$323$			7.48223i			0.416323i
$324$		0			0
$325$	13.5090	+	11.7056i	0.749343	+	0.649309i
$326$		0			0
$327$	−0.278435	+	1.93656i	−0.0153975	+	0.107092i
$328$		0			0
$329$	4.19226	+	9.17976i	0.231127	+	0.506097i
$330$		0			0
$331$	−32.6993	+	4.70145i	−1.79732	+	0.258415i	−0.958315	−	0.285714i	$-0.907769\pi$
$331$	−32.6993	+	4.70145i	−1.79732	+	0.258415i	−0.839002	+	0.544129i	$0.816860\pi$
$332$		0			0
$333$	−2.37786	−	8.09826i	−0.130306	−	0.443782i
$334$		0			0
$335$	3.82281	−	8.37079i	0.208863	−	0.457345i
$336$		0			0
$337$	−15.6826	−	18.0987i	−0.854286	−	0.985899i	0.145708	−	0.989328i	$-0.453454\pi$
$337$	−15.6826	−	18.0987i	−0.854286	−	0.985899i	−0.999994	+	0.00342903i	$0.998909\pi$
$338$		0			0
$339$	−6.06199	−	9.43264i	−0.329242	−	0.512311i
$340$		0			0
$341$	14.1514	−	22.0200i	0.766341	−	1.19245i
$342$		0			0
$343$	33.9604	+	9.97168i	1.83369	+	0.538420i
$344$		0			0
$345$	−2.74814	−	12.8027i	−0.147955	−	0.689277i
$346$		0			0
$347$	−4.06310	+	13.8376i	−0.218118	+	0.742843i	0.775629	+	0.631189i	$0.217433\pi$
$347$	−4.06310	+	13.8376i	−0.218118	+	0.742843i	−0.993747	+	0.111654i	$0.964385\pi$
$348$		0			0
$349$	−20.1194	+	31.3063i	−1.07696	+	1.67579i	−0.463382	+	0.886158i	$0.653364\pi$
$349$	−20.1194	+	31.3063i	−1.07696	+	1.67579i	−0.613582	+	0.789631i	$0.710272\pi$
$350$		0			0
$351$	16.5094	−	10.6099i	0.881207	−	0.566317i
$352$		0			0
$353$	−9.04476	−	10.4382i	−0.481404	−	0.555570i	0.462144	−	0.886805i	$-0.347080\pi$
$353$	−9.04476	−	10.4382i	−0.481404	−	0.555570i	−0.943548	+	0.331235i	$0.892535\pi$
$354$		0			0
$355$	−5.12987	−	2.34273i	−0.272265	−	0.124339i
$356$		0			0
$357$	9.83340	+	33.4895i	0.520439	+	1.77245i
$358$		0			0
$359$	1.35324	+	9.41201i	0.0714214	+	0.496747i	0.993864	+	0.110612i	$0.0352811\pi$
$359$	1.35324	+	9.41201i	0.0714214	+	0.496747i	−0.922442	+	0.386135i	$0.873810\pi$
$360$		0			0
$361$	6.13064	+	13.4242i	0.322665	+	0.706539i
$362$		0			0
$363$	−0.827285	−	0.118946i	−0.0434212	−	0.00624303i
$364$		0			0
$365$	−6.31238	−	5.46971i	−0.330405	−	0.286298i
$366$		0			0
$367$	−15.5644			−0.812455			−0.406228	−	0.913772i	$-0.633156\pi$
$367$	−15.5644			−0.812455			−0.406228	+	0.913772i	$0.633156\pi$
$368$		0			0
$369$	−5.91007			−0.307666
$370$		0			0
$371$	6.04820	+	5.24079i	0.314007	+	0.272088i
$372$		0			0
$373$	−14.9484	−	2.14926i	−0.774001	−	0.111285i	−0.256014	−	0.966673i	$-0.582409\pi$
$373$	−14.9484	−	2.14926i	−0.774001	−	0.111285i	−0.517987	+	0.855388i	$0.673318\pi$
$374$		0			0
$375$	9.36260	+	20.5012i	0.483482	+	1.05868i
$376$		0			0
$377$	0.116509	+	0.810338i	0.00600052	+	0.0417345i
$378$		0			0
$379$	−2.43021	−	8.27655i	−0.124832	−	0.425138i	0.873234	−	0.487301i	$-0.162018\pi$
$379$	−2.43021	−	8.27655i	−0.124832	−	0.425138i	−0.998066	+	0.0621628i	$0.980200\pi$
$380$		0			0
$381$	0.693587	+	0.316751i	0.0355335	+	0.0162276i
$382$		0			0
$383$	−16.7291	−	19.3064i	−0.854815	−	0.986509i	0.145181	−	0.989405i	$-0.453623\pi$
$383$	−16.7291	−	19.3064i	−0.854815	−	0.986509i	−0.999996	+	0.00289649i	$0.999078\pi$
$384$		0			0
$385$	16.8191	−	10.8090i	0.857181	−	0.550877i
$386$		0			0
$387$	−3.82273	+	5.94828i	−0.194320	+	0.302368i
$388$		0			0
$389$	0.0160683	−	0.0547237i	0.000814697	−	0.00277460i	−0.959085	−	0.283120i	$-0.908631\pi$
$389$	0.0160683	−	0.0547237i	0.000814697	−	0.00277460i	0.959899	+	0.280345i	$0.0904489\pi$
$390$		0			0
$391$	17.3812	−	1.19499i	0.879004	−	0.0604333i
$392$		0			0
$393$	−6.63415	−	1.94796i	−0.334649	−	0.0982617i
$394$		0			0
$395$	−5.79111	+	9.01114i	−0.291382	+	0.453400i
$396$		0			0
$397$	−0.621609	−	0.967242i	−0.0311976	−	0.0485445i	0.825304	−	0.564688i	$-0.191003\pi$
$397$	−0.621609	−	0.967242i	−0.0311976	−	0.0485445i	−0.856502	+	0.516144i	$0.827367\pi$
$398$		0			0
$399$	−12.9589	−	14.9554i	−0.648756	−	0.748704i
$400$		0			0
$401$	14.9916	−	32.8270i	0.748645	−	1.63930i	−0.0201400	−	0.999797i	$-0.506411\pi$
$401$	14.9916	−	32.8270i	0.748645	−	1.63930i	0.768785	−	0.639507i	$-0.220862\pi$
$402$		0			0
$403$	12.4428	+	42.3763i	0.619820	+	2.11091i
$404$		0			0
$405$	14.6432	−	2.10537i	0.727624	−	0.104617i
$406$		0			0
$407$	−8.97913	−	19.6616i	−0.445079	−	0.974587i
$408$		0			0
$409$	1.60020	−	11.1297i	0.0791250	−	0.550327i	−0.911243	−	0.411869i	$-0.864876\pi$
$409$	1.60020	−	11.1297i	0.0791250	−	0.550327i	0.990368	−	0.138458i	$-0.0442146\pi$
$410$		0			0
$411$	−19.0323	−	16.4916i	−0.938793	−	0.813469i
$412$		0			0
$413$			52.7129i			2.59383i
$414$		0			0
$415$	−5.06602			−0.248681
$416$		0			0
$417$	−14.8735	+	17.1650i	−0.728359	+	0.840572i
$418$		0			0
$419$	14.4310	+	2.07486i	0.704998	+	0.101363i	0.485484	−	0.874246i	$-0.338643\pi$
$419$	14.4310	+	2.07486i	0.704998	+	0.101363i	0.219515	+	0.975609i	$0.429553\pi$
$420$		0			0
$421$	26.0719	−	11.9066i	1.27067	−	0.580294i	0.338039	−	0.941132i	$-0.390237\pi$
$421$	26.0719	−	11.9066i	1.27067	−	0.580294i	0.932629	+	0.360838i	$0.117509\pi$
$422$		0			0
$423$	−0.392659	−	2.73101i	−0.0190918	−	0.132786i
$424$		0			0
$425$	−11.3442	+	3.33095i	−0.550273	+	0.161575i
$426$		0			0
$427$	−4.41096	−	2.01442i	−0.213462	−	0.0974846i
$428$		0			0
$429$	−27.9229	+	24.1953i	−1.34813	+	1.16816i
$430$		0			0
$431$	−3.90268	+	2.50810i	−0.187986	+	0.120811i	−0.631248	−	0.775581i	$-0.717457\pi$
$431$	−3.90268	+	2.50810i	−0.187986	+	0.120811i	0.443263	+	0.896392i	$0.353821\pi$
$432$		0			0
$433$	−22.3385	−	14.3561i	−1.07352	−	0.689909i	−0.120468	−	0.992717i	$-0.538439\pi$
$433$	−22.3385	−	14.3561i	−1.07352	−	0.689909i	−0.953051	+	0.302808i	$0.902076\pi$
$434$		0			0
$435$	−0.114660	+	0.390498i	−0.00549755	+	0.0187229i
$436$		0			0
$437$	−8.68246	+	4.70997i	−0.415338	+	0.225308i
$438$		0			0
$439$	−4.16419	−	1.22272i	−0.198746	−	0.0583570i	0.180845	−	0.983512i	$-0.442117\pi$
$439$	−4.16419	−	1.22272i	−0.198746	−	0.0583570i	−0.379590	+	0.925155i	$0.623935\pi$
$440$		0			0
$441$	−15.6255	−	10.0419i	−0.744072	−	0.478186i
$442$		0			0
$443$	−7.36742	−	11.4639i	−0.350037	−	0.544668i	0.620935	−	0.783862i	$-0.286753\pi$
$443$	−7.36742	−	11.4639i	−0.350037	−	0.544668i	−0.970972	+	0.239194i	$0.923117\pi$
$444$		0			0
$445$	−8.38113	+	7.26229i	−0.397304	+	0.344266i
$446$		0			0
$447$	3.97707	−	8.70856i	0.188109	−	0.411901i
$448$		0			0
$449$	28.3201	−	8.31554i	1.33651	−	0.392435i	0.466087	−	0.884739i	$-0.345663\pi$
$449$	28.3201	−	8.31554i	1.33651	−	0.392435i	0.870423	+	0.492304i	$0.163845\pi$
$450$		0			0
$451$	−14.9814	+	2.15400i	−0.705446	+	0.101428i
$452$		0			0
$453$	−32.3823	+	14.7885i	−1.52145	+	0.694825i
$454$		0			0
$455$	−4.80084	+	33.3906i	−0.225067	+	1.56537i
$456$		0			0
$457$	6.07553	−	7.01153i	0.284201	−	0.327986i	−0.595642	−	0.803250i	$-0.703102\pi$
$457$	6.07553	−	7.01153i	0.284201	−	0.327986i	0.879843	+	0.475265i	$0.157648\pi$
$458$		0			0
$459$			12.9805i			0.605877i
$460$		0			0
$461$		−	40.6482i		−	1.89318i	−0.322446	−	0.946588i	$-0.604505\pi$
$461$		−	40.6482i		−	1.89318i	0.322446	−	0.946588i	$-0.395495\pi$
$462$		0			0
$463$	−3.09248	+	3.56891i	−0.143720	+	0.165861i	−0.823046	−	0.567975i	$-0.807727\pi$
$463$	−3.09248	+	3.56891i	−0.143720	+	0.165861i	0.679326	+	0.733837i	$0.262272\pi$
$464$		0			0
$465$	−3.12463	+	21.7323i	−0.144901	+	1.00781i
$466$		0			0
$467$	33.1508	−	15.1394i	1.53403	−	0.700570i	0.543701	−	0.839279i	$-0.317022\pi$
$467$	33.1508	−	15.1394i	1.53403	−	0.700570i	0.990333	+	0.138709i	$0.0442951\pi$
$468$		0			0
$469$	−32.0527	+	4.60848i	−1.48005	+	0.212800i
$470$		0			0
$471$	−8.73513	+	2.56486i	−0.402493	+	0.118183i
$472$		0			0
$473$	−7.52227	+	16.4715i	−0.345874	+	0.757359i
$474$		0			0
$475$	5.06595	−	4.38967i	0.232442	−	0.201412i
$476$		0			0
$477$	−1.18292	−	1.84067i	−0.0541624	−	0.0842783i
$478$		0			0
$479$	16.2540	+	10.4458i	0.742664	+	0.477281i	0.856454	−	0.516224i	$-0.172663\pi$
$479$	16.2540	+	10.4458i	0.742664	+	0.477281i	−0.113790	+	0.993505i	$0.536299\pi$
$480$		0			0
$481$	34.9933	+	10.2750i	1.59556	+	0.468498i
$482$		0			0
$483$	−32.6715	+	32.4920i	−1.48661	+	1.47844i
$484$		0			0
$485$	6.47934	−	22.0666i	0.294212	−	1.00199i
$486$		0			0
$487$	5.12181	+	3.29159i	0.232091	+	0.149156i	0.651518	−	0.758633i	$-0.274132\pi$
$487$	5.12181	+	3.29159i	0.232091	+	0.149156i	−0.419427	+	0.907789i	$0.637769\pi$
$488$		0			0
$489$	−41.2937	+	26.5379i	−1.86737	+	1.20008i
$490$		0			0
$491$	18.0637	−	15.6523i	0.815202	−	0.706376i	−0.143852	−	0.989599i	$-0.545949\pi$
$491$	18.0637	−	15.6523i	0.815202	−	0.706376i	0.959054	+	0.283223i	$0.0914036\pi$
$492$		0			0
$493$	−0.492562	−	0.224946i	−0.0221839	−	0.0101310i
$494$		0			0
$495$	−5.24467	+	1.53997i	−0.235730	+	0.0692167i
$496$		0			0
$497$	2.82421	+	19.6428i	0.126683	+	0.881101i
$498$		0			0
$499$	13.1259	−	5.99439i	0.587595	−	0.268346i	−0.0993528	−	0.995052i	$-0.531677\pi$
$499$	13.1259	−	5.99439i	0.587595	−	0.268346i	0.686948	+	0.726706i	$0.258950\pi$
$500$		0			0
$501$	9.97549	+	1.43426i	0.445672	+	0.0640780i
$502$		0			0
$503$	−2.25594	+	2.60350i	−0.100588	+	0.116084i	−0.803811	−	0.594884i	$-0.797198\pi$
$503$	−2.25594	+	2.60350i	−0.100588	+	0.116084i	0.703224	+	0.710969i	$0.251743\pi$
$504$		0			0
$505$	8.50721			0.378566
$506$		0			0
$507$		−	35.4745i		−	1.57548i
$508$		0			0
$509$	−19.8545	−	17.2040i	−0.880036	−	0.762555i	0.0924012	−	0.995722i	$-0.470546\pi$
$509$	−19.8545	−	17.2040i	−0.880036	−	0.762555i	−0.972437	+	0.233167i	$0.925091\pi$
$510$		0			0
$511$	−4.18285	+	29.0923i	−0.185038	+	1.28697i
$512$		0			0
$513$	−3.05721	−	6.69435i	−0.134979	−	0.295563i
$514$		0			0
$515$	15.9462	−	2.29271i	0.702672	−	0.101029i
$516$		0			0
$517$	−1.99070	−	6.77969i	−0.0875507	−	0.298170i
$518$		0			0
$519$	−10.4809	+	22.9501i	−0.460062	+	1.00740i
$520$		0			0
$521$	11.2878	+	13.0268i	0.494528	+	0.570716i	0.947070	−	0.321027i	$-0.104028\pi$
$521$	11.2878	+	13.0268i	0.494528	+	0.570716i	−0.452542	+	0.891743i	$0.649483\pi$
$522$		0			0
$523$	−11.1856	−	17.4052i	−0.489114	−	0.761076i	0.505709	−	0.862704i	$-0.331231\pi$
$523$	−11.1856	−	17.4052i	−0.489114	−	0.761076i	−0.994822	+	0.101629i	$0.967595\pi$
$524$		0			0
$525$	16.9055	−	26.3054i	0.737815	−	1.14806i
$526$		0			0
$527$	−28.0291	−	8.23009i	−1.22097	−	0.358508i
$528$		0			0
$529$	12.3279	+	19.4171i	0.535996	+	0.844221i
$530$		0			0
$531$	4.06026	−	13.8280i	0.176200	−	0.600084i
$532$		0			0
$533$	13.8069	−	21.4839i	0.598041	−	0.930570i
$534$		0			0
$535$	14.3978	−	9.25291i	0.622472	−	0.400038i
$536$		0			0
$537$	28.8298	+	33.2713i	1.24410	+	1.43576i
$538$		0			0
$539$	−43.2689	−	19.7602i	−1.86372	−	0.851133i
$540$		0			0
$541$	9.69721	+	33.0257i	0.416916	+	1.41988i	0.853910	+	0.520420i	$0.174225\pi$
$541$	9.69721	+	33.0257i	0.416916	+	1.41988i	−0.436995	+	0.899464i	$0.643957\pi$
$542$		0			0
$543$	−4.52429	−	31.4671i	−0.194156	−	1.35038i
$544$		0			0
$545$	−0.519567	−	1.13769i	−0.0222558	−	0.0487335i
$546$		0			0
$547$	18.3778	+	2.64233i	0.785778	+	0.112978i	0.523513	−	0.852018i	$-0.324621\pi$
$547$	18.3778	+	2.64233i	0.785778	+	0.112978i	0.262265	+	0.964996i	$0.415530\pi$
$548$		0			0
$549$	1.00195	+	0.868194i	0.0427622	+	0.0370536i
$550$		0			0
$551$	0.307006			0.0130789
$552$		0			0
$553$	37.6929			1.60287
$554$		0			0
$555$	13.7021	+	11.8730i	0.581623	+	0.503979i
$556$		0			0
$557$	5.93872	+	0.853859i	0.251632	+	0.0361792i	0.266976	−	0.963703i	$-0.413975\pi$
$557$	5.93872	+	0.853859i	0.251632	+	0.0361792i	−0.0153447	+	0.999882i	$0.504885\pi$
$558$		0			0
$559$	−12.6923	−	27.7922i	−0.536827	−	1.17549i
$560$		0			0
$561$	−3.47792	−	24.1894i	−0.146838	−	1.02128i
$562$		0			0
$563$	6.62086	+	22.5486i	0.279036	+	0.950310i	0.973097	+	0.230394i	$0.0740015\pi$
$563$	6.62086	+	22.5486i	0.279036	+	0.950310i	−0.694061	+	0.719916i	$0.744180\pi$
$564$		0			0
$565$	6.52017	+	2.97766i	0.274306	+	0.125271i
$566$		0			0
$567$	−34.0905	−	39.3425i	−1.43167	−	1.65223i
$568$		0			0
$569$	−10.6530	+	6.84627i	−0.446597	+	0.287011i	−0.744546	−	0.667571i	$-0.767334\pi$
$569$	−10.6530	+	6.84627i	−0.446597	+	0.287011i	0.297949	+	0.954582i	$0.403698\pi$
$570$		0			0
$571$	−6.38252	+	9.93140i	−0.267100	+	0.415616i	−0.948733	−	0.316078i	$-0.897634\pi$
$571$	−6.38252	+	9.93140i	−0.267100	+	0.415616i	0.681633	+	0.731694i	$0.261270\pi$
$572$		0			0
$573$	11.2031	−	38.1544i	0.468018	−	1.59392i
$574$		0			0
$575$	−11.0063	−	11.0671i	−0.458993	−	0.461530i
$576$		0			0
$577$	−9.21953	−	2.70710i	−0.383814	−	0.112698i	0.0841328	−	0.996455i	$-0.473188\pi$
$577$	−9.21953	−	2.70710i	−0.383814	−	0.112698i	−0.467947	+	0.883757i	$0.655006\pi$
$578$		0			0
$579$	−0.267702	+	0.416553i	−0.0111253	+	0.0173114i
$580$		0			0
$581$	9.63789	+	14.9969i	0.399847	+	0.622174i
$582$		0			0
$583$	−3.66944	−	4.23475i	−0.151973	−	0.175386i
$584$		0			0
$585$	3.83133	−	8.38944i	0.158406	−	0.346861i
$586$		0			0
$587$	7.35050	+	25.0335i	0.303388	+	1.03324i	0.960229	+	0.279215i	$0.0900741\pi$
$587$	7.35050	+	25.0335i	0.303388	+	1.03324i	−0.656841	+	0.754029i	$0.728108\pi$
$588$		0			0
$589$	16.3937	−	2.35706i	0.675490	−	0.0971208i
$590$		0			0
$591$	12.2540	+	26.8325i	0.504062	+	1.10374i
$592$		0			0
$593$	−1.45857	+	10.1446i	−0.0598962	+	0.416587i	0.937709	+	0.347422i	$0.112943\pi$
$593$	−1.45857	+	10.1446i	−0.0598962	+	0.416587i	−0.997605	+	0.0691654i	$0.977966\pi$
$594$		0			0
$595$	−16.8629	−	14.6118i	−0.691310	−	0.599023i
$596$		0			0
$597$			32.5907i			1.33385i
$598$		0			0
$599$	16.7339			0.683730			0.341865	−	0.939749i	$-0.388941\pi$
$599$	16.7339			0.683730			0.341865	+	0.939749i	$0.388941\pi$
$600$		0			0
$601$	6.25738	−	7.22140i	0.255244	−	0.294567i	−0.613637	−	0.789588i	$-0.710294\pi$
$601$	6.25738	−	7.22140i	0.255244	−	0.294567i	0.868881	+	0.495021i	$0.164840\pi$
$602$		0			0
$603$	8.76323	+	1.25996i	0.356866	+	0.0513096i
$604$		0			0
$605$	0.486016	−	0.221956i	0.0197594	−	0.00902380i
$606$		0			0
$607$	2.94818	+	20.5050i	0.119663	+	0.832274i	0.957928	+	0.287010i	$0.0926613\pi$
$607$	2.94818	+	20.5050i	0.119663	+	0.832274i	−0.838265	+	0.545263i	$0.816430\pi$
$608$		0			0
$609$	1.37412	−	0.403478i	0.0556822	−	0.0163498i
$610$		0			0
$611$	10.8449	+	4.95269i	0.438737	+	0.200364i
$612$		0			0
$613$	−25.3969	+	22.0066i	−1.02577	+	0.888837i	−0.993859	−	0.110653i	$-0.964706\pi$
$613$	−25.3969	+	22.0066i	−1.02577	+	0.888837i	−0.0319138	+	0.999491i	$0.510160\pi$
$614$		0			0
$615$	10.6802	−	6.86376i	0.430668	−	0.276773i
$616$		0			0
$617$	−0.327411	−	0.210414i	−0.0131811	−	0.00847095i	0.534034	−	0.845463i	$-0.320676\pi$
$617$	−0.327411	−	0.210414i	−0.0131811	−	0.00847095i	−0.547215	+	0.836992i	$0.684312\pi$
$618$		0			0
$619$	−6.75022	+	22.9892i	−0.271314	+	0.924012i	0.705281	+	0.708928i	$0.250821\pi$
$619$	−6.75022	+	22.9892i	−0.271314	+	0.924012i	−0.976595	+	0.215084i	$0.930997\pi$
$620$		0			0
$621$	−15.0627	+	8.17104i	−0.604444	+	0.327892i
$622$		0			0
$623$	37.4432	+	10.9943i	1.50013	+	0.440478i
$624$		0			0
$625$	1.56881	+	1.00821i	0.0627524	+	0.0403285i
$626$		0			0
$627$	7.49083	+	11.6560i	0.299155	+	0.465494i
$628$		0			0
$629$	−18.2309	+	15.7971i	−0.726912	+	0.629873i
$630$		0			0
$631$	3.94336	−	8.63475i	0.156983	−	0.343744i	−0.814756	−	0.579804i	$-0.803129\pi$
$631$	3.94336	−	8.63475i	0.156983	−	0.343744i	0.971738	+	0.236060i	$0.0758563\pi$
$632$		0			0
$633$	−22.8183	+	6.70004i	−0.906944	+	0.266303i
$634$		0			0
$635$	−0.482479	+	0.0693701i	−0.0191466	+	0.00275287i
$636$		0			0
$637$	73.0073	−	33.3413i	2.89265	−	1.32103i
$638$		0			0
$639$	0.772142	−	5.37037i	0.0305455	−	0.212448i
$640$		0			0
$641$	−27.2887	+	31.4928i	−1.07784	+	1.24389i	−0.109569	+	0.993979i	$0.534947\pi$
$641$	−27.2887	+	31.4928i	−1.07784	+	1.24389i	−0.968269	+	0.249912i	$0.919598\pi$
$642$		0			0
$643$		−	30.8155i		−	1.21524i	−0.794226	−	0.607622i	$-0.792123\pi$
$643$		−	30.8155i		−	1.21524i	0.794226	−	0.607622i	$-0.207877\pi$
$644$		0			0
$645$		−	15.1889i		−	0.598061i
$646$		0			0
$647$	5.78546	−	6.67678i	0.227450	−	0.262491i	−0.630541	−	0.776156i	$-0.717167\pi$
$647$	5.78546	−	6.67678i	0.227450	−	0.262491i	0.857991	+	0.513665i	$0.171712\pi$
$648$		0			0
$649$	5.25254	−	36.5322i	0.206180	−	1.43402i
$650$		0			0
$651$	70.2782	−	32.0950i	2.75442	−	1.25790i
$652$		0			0
$653$	21.6363	−	3.11084i	0.846695	−	0.121736i	0.294706	−	0.955588i	$-0.404778\pi$
$653$	21.6363	−	3.11084i	0.846695	−	0.121736i	0.551989	+	0.833851i	$0.313869\pi$
$654$		0			0
$655$	4.24104	−	1.24528i	0.165711	−	0.0486571i
$656$		0			0
$657$	3.33814	−	7.30950i	0.130233	−	0.285171i
$658$		0			0
$659$	−25.9938	+	22.5237i	−1.01257	+	0.877400i	−0.992481	−	0.122398i	$-0.960942\pi$
$659$	−25.9938	+	22.5237i	−1.01257	+	0.877400i	−0.0200929	+	0.999798i	$0.506396\pi$
$660$		0			0
$661$	−10.4877	−	16.3191i	−0.407923	−	0.634740i	0.575130	−	0.818062i	$-0.304951\pi$
$661$	−10.4877	−	16.3191i	−0.407923	−	0.634740i	−0.983053	+	0.183322i	$0.941315\pi$
$662$		0			0
$663$	34.6886	+	22.2930i	1.34719	+	0.865789i
$664$		0			0
$665$	12.1380	+	3.56404i	0.470692	+	0.138208i
$666$		0			0
$667$	−0.0490322	−	0.713174i	−0.00189853	−	0.0276142i
$668$		0			0
$669$	−3.13181	+	10.6660i	−0.121083	+	0.412370i
$670$		0			0
$671$	2.85625	+	1.83560i	0.110264	+	0.0708627i
$672$		0			0
$673$	−7.38986	+	4.74918i	−0.284858	+	0.183067i	−0.675265	−	0.737575i	$-0.735971\pi$
$673$	−7.38986	+	4.74918i	−0.284858	+	0.183067i	0.390407	+	0.920642i	$0.372334\pi$
$674$		0			0
$675$	8.78861	−	7.61537i	0.338274	−	0.293116i
$676$		0			0
$677$	34.3339	+	15.6798i	1.31956	+	0.602623i	0.945754	−	0.324884i	$-0.105325\pi$
$677$	34.3339	+	15.6798i	1.31956	+	0.602623i	0.373806	+	0.927507i	$0.378052\pi$
$678$		0			0
$679$	−77.6501	+	22.8001i	−2.97994	+	0.874988i
$680$		0			0
$681$	2.17964	+	15.1597i	0.0835241	+	0.580923i
$682$		0			0
$683$	−0.384910	+	0.175782i	−0.0147282	+	0.00672613i	−0.422765	−	0.906239i	$-0.638941\pi$
$683$	−0.384910	+	0.175782i	−0.0147282	+	0.00672613i	0.408037	+	0.912965i	$0.366213\pi$
$684$		0			0
$685$	15.9352	+	2.29113i	0.608851	+	0.0875396i
$686$		0			0
$687$	−13.3800	+	15.4413i	−0.510479	+	0.589124i
$688$		0			0
$689$	9.45456			0.360190
$690$		0			0
$691$		−	12.7118i		−	0.483581i	−0.970328	−	0.241791i	$-0.922265\pi$
$691$		−	12.7118i		−	0.483581i	0.970328	−	0.241791i	$-0.0777347\pi$
$692$		0			0
$693$	14.5365	+	12.5960i	0.552197	+	0.478482i
$694$		0			0
$695$	2.06634	−	14.3717i	0.0783807	−	0.545150i
$696$		0			0
$697$	7.01705	+	15.3652i	0.265790	+	0.581998i
$698$		0			0
$699$	16.4392	−	2.36360i	0.621788	−	0.0893996i
$700$		0			0
$701$	−2.44522	−	8.32764i	−0.0923545	−	0.314531i	0.900340	−	0.435188i	$-0.143318\pi$
$701$	−2.44522	−	8.32764i	−0.0923545	−	0.314531i	−0.992694	+	0.120657i	$0.961500\pi$
$702$		0			0
$703$	5.68151	−	12.4408i	0.214282	−	0.469212i
$704$		0			0
$705$	3.88128	+	4.47924i	0.146178	+	0.168698i
$706$		0			0
$707$	−16.1846	−	25.1838i	−0.608685	−	0.947133i
$708$		0			0
$709$	−12.5474	+	19.5241i	−0.471227	+	0.733244i	−0.992777	−	0.119977i	$-0.961718\pi$
$709$	−12.5474	+	19.5241i	−0.471227	+	0.733244i	0.521550	+	0.853221i	$0.325354\pi$
$710$		0			0
$711$	−9.88784	−	2.90333i	−0.370823	−	0.108883i
$712$		0			0
$713$	−8.09367	−	37.7060i	−0.303110	−	1.41210i
$714$		0			0
$715$	6.65436	−	22.6627i	0.248859	−	0.847536i
$716$		0			0
$717$	−2.29740	+	3.57483i	−0.0857981	+	0.133504i
$718$		0			0
$719$	−15.8128	+	10.1623i	−0.589718	+	0.378988i	−0.801203	−	0.598393i	$-0.795806\pi$
$719$	−15.8128	+	10.1623i	−0.589718	+	0.378988i	0.211485	+	0.977381i	$0.432170\pi$
$720$		0			0
$721$	−37.1240	−	42.8434i	−1.38257	−	1.59557i
$722$		0			0
$723$	16.1658	+	7.38266i	0.601212	+	0.274564i
$724$		0			0
$725$	0.136673	+	0.465467i	0.00507592	+	0.0172870i
$726$		0			0
$727$	−0.884465	−	6.15159i	−0.0328030	−	0.228150i	0.966825	−	0.255441i	$-0.0822208\pi$
$727$	−0.884465	−	6.15159i	−0.0328030	−	0.228150i	−0.999628	+	0.0272916i	$0.991312\pi$
$728$		0			0
$729$	−3.29039	−	7.20496i	−0.121866	−	0.266850i
$730$		0			0
$731$	20.0033	+	2.87604i	0.739847	+	0.106374i
$732$		0			0
$733$	−25.4249	−	22.0308i	−0.939092	−	0.813728i	0.0435862	−	0.999050i	$-0.486122\pi$
$733$	−25.4249	−	22.0308i	−0.939092	−	0.813728i	−0.982678	+	0.185322i	$0.940667\pi$
$734$		0			0
$735$	39.8995			1.47172
$736$		0			0
$737$	22.6730			0.835172
$738$		0			0
$739$	27.6796	+	23.9845i	1.01821	+	0.882285i	0.993085	−	0.117399i	$-0.0374558\pi$
$739$	27.6796	+	23.9845i	1.01821	+	0.882285i	0.0251263	+	0.999684i	$0.492001\pi$
$740$		0			0
$741$	−23.1403	−	3.32707i	−0.850080	−	0.122223i
$742$		0			0
$743$	−9.03031	−	19.7736i	−0.331290	−	0.725424i	0.668544	−	0.743673i	$-0.266918\pi$
$743$	−9.03031	−	19.7736i	−0.331290	−	0.725424i	−0.999833	+	0.0182494i	$0.994191\pi$
$744$		0			0
$745$	0.870998	+	6.05793i	0.0319109	+	0.221945i
$746$		0			0
$747$	−1.37313	−	4.67644i	−0.0502400	−	0.171102i
$748$		0			0
$749$	−54.7825	−	25.0183i	−2.00171	−	0.914150i
$750$		0			0
$751$	21.7012	+	25.0445i	0.791887	+	0.913886i	0.997907	−	0.0646614i	$-0.0205967\pi$
$751$	21.7012	+	25.0445i	0.791887	+	0.913886i	−0.206020	+	0.978548i	$0.566051\pi$
$752$		0			0
$753$	−3.58178	+	2.30187i	−0.130527	+	0.0838848i
$754$		0			0
$755$	12.3038	−	19.1450i	0.447780	−	0.696759i
$756$		0			0
$757$	0.442918	−	1.50844i	0.0160981	−	0.0548252i	−0.951052	−	0.309030i	$-0.899996\pi$
$757$	0.442918	−	1.50844i	0.0160981	−	0.0548252i	0.967150	+	0.254205i	$0.0818138\pi$
$758$		0			0
$759$	25.8804	−	19.2627i	0.939398	−	0.699193i
$760$		0			0
$761$	30.3793	+	8.92016i	1.10125	+	0.323356i	0.781348	−	0.624096i	$-0.214533\pi$
$761$	30.3793	+	8.92016i	1.10125	+	0.323356i	0.319900	+	0.947451i	$0.396351\pi$
$762$		0			0
$763$	−2.37944	+	3.70248i	−0.0861416	+	0.134039i
$764$		0			0
$765$	3.29809	+	5.13193i	0.119243	+	0.185545i
$766$		0			0
$767$	40.7811	+	47.0639i	1.47252	+	1.69938i
$768$		0			0
$769$	1.12104	−	2.45473i	0.0404257	−	0.0885199i	−0.888342	−	0.459183i	$-0.848142\pi$
$769$	1.12104	−	2.45473i	0.0404257	−	0.0885199i	0.928767	+	0.370663i	$0.120870\pi$
$770$		0			0
$771$	−13.9289	−	47.4373i	−0.501635	−	1.70841i
$772$		0			0
$773$	53.4426	−	7.68389i	1.92220	−	0.276370i	0.927064	−	0.374903i	$-0.122324\pi$
$773$	53.4426	−	7.68389i	1.92220	−	0.276370i	0.995134	+	0.0985331i	$0.0314150\pi$
$774$		0			0
$775$	10.8718	+	23.8059i	0.390526	+	0.855133i
$776$		0			0
$777$	9.07961	−	63.1501i	0.325729	−	2.26550i
$778$		0			0
$779$	−7.23773	−	6.27153i	−0.259318	−	0.224701i
$780$		0			0
$781$		−	13.8947i		−	0.497191i
$782$		0			0
$783$	0.532607			0.0190338
$784$		0			0
$785$	3.81121	−	4.39837i	0.136028	−	0.156985i
$786$		0			0
$787$	20.7182	+	2.97883i	0.738524	+	0.106184i	0.501303	−	0.865272i	$-0.332854\pi$
$787$	20.7182	+	2.97883i	0.738524	+	0.106184i	0.237221	+	0.971456i	$0.423763\pi$
$788$		0			0
$789$	50.6613	−	23.1363i	1.80359	−	0.823672i
$790$		0			0
$791$	−3.58963	−	24.9664i	−0.127633	−	0.887704i
$792$		0			0
$793$	−5.49671	+	1.61398i	−0.195194	+	0.0573141i
$794$		0			0
$795$	4.27538	+	1.95250i	0.151632	+	0.0692480i
$796$		0			0
$797$	−12.1025	+	10.4869i	−0.428692	+	0.371464i	−0.842316	−	0.538984i	$-0.818808\pi$
$797$	−12.1025	+	10.4869i	−0.428692	+	0.371464i	0.413624	+	0.910448i	$0.364263\pi$
$798$		0			0
$799$	−6.63395	+	4.26338i	−0.234692	+	0.150828i
$800$		0			0
$801$	−8.97549	−	5.76820i	−0.317133	−	0.203809i
$802$		0			0
$803$	5.79777	−	19.7454i	0.204599	−	0.696800i
$804$		0			0
$805$	6.34068	−	28.7657i	0.223480	−	1.01386i
$806$		0			0
$807$	3.38431	+	0.993722i	0.119133	+	0.0349807i
$808$		0			0
$809$	−47.3775	−	30.4477i	−1.66571	−	1.07048i	−0.909067	−	0.416650i	$-0.863204\pi$
$809$	−47.3775	−	30.4477i	−1.66571	−	1.07048i	−0.756638	−	0.653834i	$-0.773160\pi$
$810$		0			0
$811$	14.6119	+	22.7366i	0.513094	+	0.798390i	0.997054	−	0.0767001i	$-0.0244384\pi$
$811$	14.6119	+	22.7366i	0.513094	+	0.798390i	−0.483960	+	0.875090i	$0.660802\pi$
$812$		0			0
$813$	26.4865	−	22.9506i	0.928920	−	0.804914i
$814$		0			0
$815$	13.0355	−	28.5437i	0.456612	−	0.999841i
$816$		0			0
$817$	−10.9936	+	3.22800i	−0.384616	+	0.112933i
$818$		0			0
$819$	−32.1241	+	4.61875i	−1.12251	+	0.161392i
$820$		0			0
$821$	−7.42725	+	3.39191i	−0.259213	+	0.118378i	−0.540783	−	0.841162i	$-0.681872\pi$
$821$	−7.42725	+	3.39191i	−0.259213	+	0.118378i	0.281570	+	0.959541i	$0.409145\pi$
$822$		0			0
$823$	2.42519	−	16.8675i	0.0845367	−	0.587966i	−0.902888	−	0.429876i	$-0.858557\pi$
$823$	2.42519	−	16.8675i	0.0845367	−	0.587966i	0.987425	−	0.158090i	$-0.0505336\pi$
$824$		0			0
$825$	−14.3374	+	16.5462i	−0.499163	+	0.576065i
$826$		0			0
$827$			45.1316i			1.56938i	0.619889	+	0.784690i	$0.287178\pi$
$827$			45.1316i			1.56938i	−0.619889	+	0.784690i	$0.712822\pi$
$828$		0			0
$829$			14.7254i			0.511435i	0.966752	+	0.255717i	$0.0823117\pi$
$829$			14.7254i			0.511435i	−0.966752	+	0.255717i	$0.917688\pi$
$830$		0			0
$831$	5.23769	−	6.04462i	0.181693	−	0.209685i
$832$		0			0
$833$	−7.55504	+	52.5465i	−0.261767	+	1.82063i
$834$		0			0
$835$	−5.86043	+	2.67637i	−0.202809	+	0.0926196i
$836$		0			0
$837$	28.4404	−	4.08911i	0.983044	−	0.141340i
$838$		0			0
$839$	33.3829	−	9.80209i	1.15250	−	0.338406i	0.350989	−	0.936380i	$-0.385846\pi$
$839$	33.3829	−	9.80209i	1.15250	−	0.338406i	0.801516	+	0.597974i	$0.204027\pi$
$840$		0			0
$841$	12.0378	−	26.3591i	0.415097	−	0.908935i
$842$		0			0
$843$	−42.0783	+	36.4611i	−1.44926	+	1.25579i
$844$		0			0
$845$	12.2606	+	19.0779i	0.421778	+	0.656299i
$846$		0			0
$847$	−1.58168	−	1.01648i	−0.0543471	−	0.0349268i
$848$		0			0
$849$	−11.2451	−	3.30186i	−0.385931	−	0.113320i
$850$		0			0
$851$	−29.8072	−	11.2112i	−1.02178	−	0.384315i
$852$		0			0
$853$	10.6935	−	36.4189i	0.366140	−	1.24696i	−0.546245	−	0.837626i	$-0.683943\pi$
$853$	10.6935	−	36.4189i	0.366140	−	1.24696i	0.912385	−	0.409333i	$-0.134239\pi$
$854$		0			0
$855$	−2.90960	−	1.86988i	−0.0995061	−	0.0639487i
$856$		0			0
$857$	−11.0369	+	7.09297i	−0.377012	+	0.242291i	−0.715399	−	0.698716i	$-0.753755\pi$
$857$	−11.0369	+	7.09297i	−0.377012	+	0.242291i	0.338387	+	0.941007i	$0.390119\pi$
$858$		0			0
$859$	26.2081	−	22.7094i	0.894207	−	0.774835i	−0.0808644	−	0.996725i	$-0.525768\pi$
$859$	26.2081	−	22.7094i	0.894207	−	0.774835i	0.975072	+	0.221890i	$0.0712226\pi$
$860$		0			0
$861$	−40.6374	−	18.5585i	−1.38492	−	0.632471i
$862$		0			0
$863$	1.51809	−	0.445751i	0.0516763	−	0.0151735i	−0.255792	−	0.966732i	$-0.582336\pi$
$863$	1.51809	−	0.445751i	0.0516763	−	0.0151735i	0.307469	+	0.951558i	$0.400518\pi$
$864$		0			0
$865$	−2.29538	−	15.9647i	−0.0780453	−	0.542817i
$866$		0			0
$867$	7.14901	−	3.26484i	0.242793	−	0.110880i
$868$		0			0
$869$	−26.1227	−	3.75588i	−0.886153	−	0.127410i
$870$		0			0
$871$	−25.0524	+	28.9120i	−0.848868	+	0.979646i
$872$		0			0
$873$	22.1259			0.748847
$874$		0			0
$875$			50.6999i			1.71397i
$876$		0			0
$877$	32.3282	+	28.0125i	1.09165	+	0.945916i	0.998761	−	0.0497609i	$-0.0158459\pi$
$877$	32.3282	+	28.0125i	1.09165	+	0.945916i	0.0928841	+	0.995677i	$0.470391\pi$
$878$		0			0
$879$	−6.57918	+	45.7592i	−0.221910	+	1.54342i
$880$		0			0
$881$	−4.90329	−	10.7367i	−0.165196	−	0.361729i	0.808872	−	0.587985i	$-0.200079\pi$
$881$	−4.90329	−	10.7367i	−0.165196	−	0.361729i	−0.974068	+	0.226256i	$0.927351\pi$
$882$		0			0
$883$	−35.2810	+	5.07264i	−1.18730	+	0.170708i	−0.707528	−	0.706685i	$-0.750190\pi$
$883$	−35.2810	+	5.07264i	−1.18730	+	0.170708i	−0.479772	+	0.877393i	$0.659281\pi$
$884$		0			0
$885$	8.72197	+	29.7043i	0.293186	+	0.998499i
$886$		0			0
$887$	−1.46551	+	3.20901i	−0.0492069	+	0.107748i	−0.932639	−	0.360812i	$-0.882500\pi$
$887$	−1.46551	+	3.20901i	−0.0492069	+	0.107748i	0.883432	+	0.468560i	$0.155227\pi$
$888$		0			0
$889$	1.12325	+	1.29630i	0.0376727	+	0.0434766i
$890$		0			0
$891$	19.7059	+	30.6629i	0.660171	+	1.02725i
$892$		0			0
$893$	2.41716	−	3.76118i	0.0808873	−	0.125863i
$894$		0			0
$895$	−27.0036	−	7.92896i	−0.902629	−	0.265036i
$896$		0			0
$897$	−4.03302	+	54.2861i	−0.134659	+	1.81256i
$898$		0			0
$899$	−0.337692	+	1.15007i	−0.0112627	+	0.0383571i
$900$		0			0
$901$	−3.38093	+	5.26083i	−0.112635	+	0.175264i
$902$		0			0
$903$	−44.9633	+	28.8962i	−1.49629	+	0.961605i
$904$		0			0
$905$	13.3087	+	15.3591i	0.442396	+	0.510552i
$906$		0			0
$907$	−38.3392	−	17.5089i	−1.27303	−	0.581374i	−0.339748	−	0.940516i	$-0.610342\pi$
$907$	−38.3392	−	17.5089i	−1.27303	−	0.581374i	−0.933283	+	0.359143i	$0.883069\pi$
$908$		0			0
$909$	2.30585	+	7.85300i	0.0764802	+	0.260468i
$910$		0			0
$911$	−0.654460	−	4.55187i	−0.0216832	−	0.150810i	0.976103	−	0.217306i	$-0.0697271\pi$
$911$	−0.654460	−	4.55187i	−0.0216832	−	0.150810i	−0.997787	+	0.0664962i	$0.978818\pi$
$912$		0			0
$913$	−5.18511	−	11.3538i	−0.171602	−	0.375756i
$914$		0			0
$915$	−2.81894	−	0.405302i	−0.0931911	−	0.0133989i
$916$		0			0
$917$	−11.7548	−	10.1856i	−0.388177	−	0.336357i
$918$		0			0
$919$	−12.9923			−0.428576			−0.214288	−	0.976771i	$-0.568743\pi$
$919$	−12.9923			−0.428576			−0.214288	+	0.976771i	$0.568743\pi$
$920$		0			0
$921$	26.0375			0.857966
$922$		0			0
$923$	17.7181	+	15.3528i	0.583199	+	0.505345i
$924$		0			0
$925$	21.3913	+	3.07561i	0.703342	+	0.101125i
$926$		0			0
$927$	6.43855	+	14.0985i	0.211470	+	0.463054i
$928$		0			0
$929$	7.60157	+	52.8701i	0.249399	+	1.73461i	0.601698	+	0.798724i	$0.294491\pi$
$929$	7.60157	+	52.8701i	0.249399	+	1.73461i	−0.352299	+	0.935888i	$0.614600\pi$
$930$		0			0
$931$	−8.47961	−	28.8789i	−0.277908	−	0.946468i
$932$		0			0
$933$	−54.7296	−	24.9942i	−1.79177	−	0.818272i
$934$		0			0
$935$	10.2307	+	11.8068i	0.334579	+	0.386125i
$936$		0			0
$937$	24.1611	−	15.5274i	0.789309	−	0.507258i	−0.0828019	−	0.996566i	$-0.526387\pi$
$937$	24.1611	−	15.5274i	0.789309	−	0.507258i	0.872111	+	0.489308i	$0.162751\pi$
$938$		0			0
$939$	7.58146	−	11.7970i	0.247412	−	0.384980i
$940$		0			0
$941$	−12.9281	+	44.0289i	−0.421442	+	1.43530i	0.426150	+	0.904653i	$0.359870\pi$
$941$	−12.9281	+	44.0289i	−0.421442	+	1.43530i	−0.847592	+	0.530648i	$0.821948\pi$
$942$		0			0
$943$	−13.4128	+	17.8148i	−0.436780	+	0.580131i
$944$		0			0
$945$	21.0575	+	6.18304i	0.685000	+	0.201134i
$946$		0			0
$947$	−3.34638	+	5.20708i	−0.108743	+	0.169207i	−0.891360	−	0.453296i	$-0.850248\pi$
$947$	−3.34638	+	5.20708i	−0.108743	+	0.169207i	0.782617	+	0.622503i	$0.213884\pi$
$948$		0			0
$949$	18.7726	+	29.2107i	0.609383	+	0.948219i
$950$		0			0
$951$	−5.19639	−	5.99695i	−0.168505	−	0.194465i
$952$		0			0
$953$	0.189560	−	0.415079i	0.00614046	−	0.0134457i	−0.906537	−	0.422127i	$-0.861284\pi$
$953$	0.189560	−	0.415079i	0.00614046	−	0.0134457i	0.912677	+	0.408681i	$0.134011\pi$
$954$		0			0
$955$	7.16187	+	24.3911i	0.231753	+	0.789277i
$956$		0			0
$957$	−0.992526	+	0.142704i	−0.0320838	+	0.00461296i
$958$		0			0
$959$	−23.5336	−	51.5314i	−0.759940	−	1.66404i
$960$		0			0
$961$	−4.79074	+	33.3204i	−0.154540	+	1.07485i
$962$		0			0
$963$	12.4438	+	10.7826i	0.400997	+	0.347466i
$964$		0			0
$965$		−	0.316541i		−	0.0101898i
$966$		0			0
$967$	−1.19554			−0.0384460			−0.0192230	−	0.999815i	$-0.506119\pi$
$967$	−1.19554			−0.0384460			−0.0192230	+	0.999815i	$0.506119\pi$
$968$		0			0
$969$	10.1262	−	11.6863i	0.325301	−	0.375417i
$970$		0			0
$971$	−40.0490	−	5.75818i	−1.28523	−	0.184789i	−0.534373	−	0.845249i	$-0.679452\pi$
$971$	−40.0490	−	5.75818i	−1.28523	−	0.184789i	−0.750861	+	0.660460i	$0.770361\pi$
$972$		0			0
$973$	−46.4755	+	21.2246i	−1.48994	+	0.680431i
$974$		0			0
$975$	−5.25728	−	36.5652i	−0.168368	−	1.17102i
$976$		0			0
$977$	−16.9005	+	4.96244i	−0.540695	+	0.158762i	−0.540666	−	0.841238i	$-0.681828\pi$
$977$	−16.9005	+	4.96244i	−0.540695	+	0.158762i	−2.93991e−5		1.00000i	$0.500009\pi$
$978$		0			0
$979$	−24.8542	−	11.3505i	−0.794342	−	0.362764i
$980$		0			0
$981$	0.909378	−	0.787980i	0.0290342	−	0.0251583i
$982$		0			0
$983$	−11.2551	+	7.23324i	−0.358983	+	0.230705i	−0.707683	−	0.706530i	$-0.750260\pi$
$983$	−11.2551	+	7.23324i	−0.358983	+	0.230705i	0.348700	+	0.937234i	$0.386623\pi$
$984$		0			0
$985$	−15.8639	−	10.1951i	−0.505465	−	0.324843i
$986$		0			0
$987$	5.87584	−	20.0113i	0.187030	−	0.636966i
$988$		0			0
$989$	9.25441	+	25.0224i	0.294273	+	0.795666i
$990$		0			0
$991$	21.3180	+	6.25952i	0.677188	+	0.198840i	0.602201	−	0.798344i	$-0.294290\pi$
$991$	21.3180	+	6.25952i	0.677188	+	0.198840i	0.0749864	+	0.997185i	$0.476109\pi$
$992$		0			0
$993$	57.4349	+	36.9111i	1.82264	+	1.17134i
$994$		0			0
$995$	−11.2639	−	17.5270i	−0.357090	−	0.555643i
$996$		0			0
$997$	−16.5153	+	14.3106i	−0.523046	+	0.453222i	−0.875925	−	0.482447i	$-0.839748\pi$
$997$	−16.5153	+	14.3106i	−0.523046	+	0.453222i	0.352879	+	0.935669i	$0.385203\pi$
$998$		0			0
$999$	9.85651	−	21.5827i	0.311846	−	0.682848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	736.2.x.a.593.5		220
4.3	odd	2		184.2.p.a.133.13	yes	220
8.3	odd	2		184.2.p.a.133.9	yes	220
8.5	even	2	inner	736.2.x.a.593.18		220
23.9	even	11	inner	736.2.x.a.561.18		220
92.55	odd	22		184.2.p.a.101.9	✓	220
184.101	even	22	inner	736.2.x.a.561.5		220
184.147	odd	22		184.2.p.a.101.13	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.p.a.101.9	✓	220	92.55	odd	22
184.2.p.a.101.13	yes	220	184.147	odd	22
184.2.p.a.133.9	yes	220	8.3	odd	2
184.2.p.a.133.13	yes	220	4.3	odd	2
736.2.x.a.561.5		220	184.101	even	22	inner
736.2.x.a.561.18		220	23.9	even	11	inner
736.2.x.a.593.5		220	1.1	even	1	trivial
736.2.x.a.593.18		220	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	736.x (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.56187 - 1.35337i) q^{3} +(1.30771 + 0.188020i) q^{5} +(-1.93127 - 4.22889i) q^{7} +(0.180888 + 1.25811i) q^{9} +(0.917064 + 3.12323i) q^{11} +(-4.99596 - 2.28158i) q^{13} +(-1.78801 - 2.06347i) q^{15} +(3.05609 - 1.96403i) q^{17} +(-1.11353 + 1.73268i) q^{19} +(-2.70685 + 9.21868i) q^{21} +(4.20285 + 2.30999i) q^{23} +(-3.12272 - 0.916913i) q^{25} +(-1.93179 + 3.00592i) q^{27} +(-0.0805869 - 0.125396i) q^{29} +(-5.26595 - 6.07723i) q^{31} +(2.79455 - 6.11921i) q^{33} +(-1.73042 - 5.89326i) q^{35} +(-6.57274 + 0.945018i) q^{37} +(4.71523 + 10.3249i) q^{39} +(-0.661733 + 4.60245i) q^{41} +(4.20419 + 3.64295i) q^{43} +1.67924i q^{45} -2.17073 q^{47} +(-9.56965 + 11.0440i) q^{49} +(-7.43128 - 1.06846i) q^{51} +(-1.56586 + 0.715106i) q^{53} +(0.612021 + 4.25670i) q^{55} +(4.08414 - 1.19921i) q^{57} +(-10.3139 - 4.71020i) q^{59} +(0.788289 - 0.683056i) q^{61} +(4.97104 - 3.19469i) q^{63} +(-6.10427 - 3.92298i) q^{65} +(1.96238 - 6.68327i) q^{67} +(-3.43804 - 9.29591i) q^{69} +(-4.09570 - 1.20261i) q^{71} +(-5.31849 - 3.41799i) q^{73} +(3.63636 + 5.65829i) q^{75} +(11.4367 - 9.90995i) q^{77} +(-3.36807 + 7.37505i) q^{79} +(10.7440 - 3.15472i) q^{81} +(-3.79551 + 0.545712i) q^{83} +(4.36575 - 1.99377i) q^{85} +(-0.0438403 + 0.304916i) q^{87} +(-5.49693 + 6.34379i) q^{89} +25.5337i q^{91} +16.6186i q^{93} +(-1.78195 + 2.05647i) q^{95} +(2.47737 - 17.2305i) q^{97} +(-3.76347 + 1.71872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 22 q^{7} + 22 q^{15} - 18 q^{17} + 16 q^{23} - 4 q^{25} + 34 q^{31} - 30 q^{33} + 18 q^{39} - 18 q^{41} + 40 q^{47} - 28 q^{49} + 38 q^{55} - 30 q^{57} - 18 q^{63} - 38 q^{65} + 26 q^{71} - 18 q^{73}+ \cdots - 18 q^{97}+O(q^{100}) \) 220 * q + 22 * q^7 + 22 * q^15 - 18 * q^17 + 16 * q^23 - 4 * q^25 + 34 * q^31 - 30 * q^33 + 18 * q^39 - 18 * q^41 + 40 * q^47 - 28 * q^49 + 38 * q^55 - 30 * q^57 - 18 * q^63 - 38 * q^65 + 26 * q^71 - 18 * q^73 + 22 * q^79 - 52 * q^81 + 42 * q^87 - 2 * q^89 + 78 * q^95 - 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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