LMFDB - Embedded newform 432.2.be.a.335.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			335.4
Character	$\chi$	$=$	432.335
Dual form			432.2.be.a.383.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.265485 - 1.71158i) q^{3} +(0.601308 - 1.65208i) q^{5} +(-3.31695 - 0.584867i) q^{7} +(-2.85904 - 0.908799i) q^{9} +O(q^{10})$	\(q+(0.265485 - 1.71158i) q^{3} +(0.601308 - 1.65208i) q^{5} +(-3.31695 - 0.584867i) q^{7} +(-2.85904 - 0.908799i) q^{9} +(-1.91444 + 0.696801i) q^{11} +(3.10802 - 2.60794i) q^{13} +(-2.66804 - 1.46779i) q^{15} +(-2.93090 + 1.69216i) q^{17} +(-2.04178 - 1.17882i) q^{19} +(-1.88165 + 5.52196i) q^{21} +(-0.695477 - 3.94425i) q^{23} +(1.46242 + 1.22712i) q^{25} +(-2.31452 + 4.65220i) q^{27} +(1.89297 - 2.25596i) q^{29} +(4.69332 - 0.827559i) q^{31} +(0.684376 + 3.46172i) q^{33} +(-2.96076 + 5.12818i) q^{35} +(4.41679 + 7.65010i) q^{37} +(-3.63857 - 6.01200i) q^{39} +(-6.67751 - 7.95795i) q^{41} +(-1.29292 - 3.55227i) q^{43} +(-3.22057 + 4.17689i) q^{45} +(2.19570 - 12.4524i) q^{47} +(4.08223 + 1.48581i) q^{49} +(2.11816 + 5.46573i) q^{51} -10.0071i q^{53} +3.58181i q^{55} +(-2.55971 + 3.18171i) q^{57} +(-6.19943 - 2.25641i) q^{59} +(-0.0727139 + 0.412381i) q^{61} +(8.95174 + 4.68660i) q^{63} +(-2.43965 - 6.70287i) q^{65} +(7.81114 + 9.30896i) q^{67} +(-6.93555 + 0.143229i) q^{69} +(7.57186 + 13.1148i) q^{71} +(5.87873 - 10.1823i) q^{73} +(2.48857 - 2.17728i) q^{75} +(6.75765 - 1.19156i) q^{77} +(5.00952 - 5.97012i) q^{79} +(7.34817 + 5.19658i) q^{81} +(12.5809 + 10.5566i) q^{83} +(1.03320 + 5.85959i) q^{85} +(-3.35870 - 3.83890i) q^{87} +(-2.81064 - 1.62273i) q^{89} +(-11.8344 + 6.83262i) q^{91} +(-0.170430 - 8.25272i) q^{93} +(-3.17524 + 2.66435i) q^{95} +(10.7401 - 3.90906i) q^{97} +(6.10672 - 0.252332i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^5 - 12 * q^9	$ 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) $ 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.265485	−	1.71158i	0.153278	−	0.988183i
$3$	0.265485	−	1.71158i	0.153278	−	0.988183i
$4$		0			0
$5$	0.601308	−	1.65208i	0.268913	−	0.738833i	−0.729577	−	0.683899i	$-0.760283\pi$
$5$	0.601308	−	1.65208i	0.268913	−	0.738833i	0.998490	−	0.0549340i	$-0.0174948\pi$
$6$		0			0
$7$	−3.31695	−	0.584867i	−1.25369	−	0.221059i	−0.492916	−	0.870077i	$-0.664069\pi$
$7$	−3.31695	−	0.584867i	−1.25369	−	0.221059i	−0.760773	+	0.649018i	$0.775180\pi$
$8$		0			0
$9$	−2.85904	−	0.908799i	−0.953012	−	0.302933i
$10$		0			0
$11$	−1.91444	+	0.696801i	−0.577227	+	0.210093i	−0.614102	−	0.789227i	$-0.710482\pi$
$11$	−1.91444	+	0.696801i	−0.577227	+	0.210093i	0.0368755	+	0.999320i	$0.488260\pi$
$12$		0			0
$13$	3.10802	−	2.60794i	0.862010	−	0.723312i	−0.100390	−	0.994948i	$-0.532009\pi$
$13$	3.10802	−	2.60794i	0.862010	−	0.723312i	0.962400	+	0.271636i	$0.0875647\pi$
$14$		0			0
$15$	−2.66804	−	1.46779i	−0.688884	−	0.378982i
$16$		0			0
$17$	−2.93090	+	1.69216i	−0.710848	+	0.410408i	−0.811375	−	0.584526i	$-0.801280\pi$
$17$	−2.93090	+	1.69216i	−0.710848	+	0.410408i	0.100527	+	0.994934i	$0.467947\pi$
$18$		0			0
$19$	−2.04178	−	1.17882i	−0.468416	−	0.270440i	0.247160	−	0.968975i	$-0.420503\pi$
$19$	−2.04178	−	1.17882i	−0.468416	−	0.270440i	−0.715576	+	0.698534i	$0.753836\pi$
$20$		0			0
$21$	−1.88165	+	5.52196i	−0.410610	+	1.20499i
$22$		0			0
$23$	−0.695477	−	3.94425i	−0.145017	−	0.822433i	−0.967353	−	0.253431i	$-0.918441\pi$
$23$	−0.695477	−	3.94425i	−0.145017	−	0.822433i	0.822336	−	0.569002i	$-0.192670\pi$
$24$		0			0
$25$	1.46242	+	1.22712i	0.292485	+	0.245424i
$26$		0			0
$27$	−2.31452	+	4.65220i	−0.445429	+	0.895317i
$28$		0			0
$29$	1.89297	−	2.25596i	0.351516	−	0.418921i	−0.561094	−	0.827752i	$-0.689619\pi$
$29$	1.89297	−	2.25596i	0.351516	−	0.418921i	0.912610	+	0.408832i	$0.134064\pi$
$30$		0			0
$31$	4.69332	−	0.827559i	0.842946	−	0.148634i	0.264531	−	0.964377i	$-0.414783\pi$
$31$	4.69332	−	0.827559i	0.842946	−	0.148634i	0.578414	+	0.815743i	$0.303672\pi$
$32$		0			0
$33$	0.684376	+	3.46172i	0.119135	+	0.602608i
$34$		0			0
$35$	−2.96076	+	5.12818i	−0.500459	+	0.866821i
$36$		0			0
$37$	4.41679	+	7.65010i	0.726115	+	1.25767i	0.958513	+	0.285047i	$0.0920093\pi$
$37$	4.41679	+	7.65010i	0.726115	+	1.25767i	−0.232398	+	0.972621i	$0.574657\pi$
$38$		0			0
$39$	−3.63857	−	6.01200i	−0.582638	−	0.962691i
$40$		0			0
$41$	−6.67751	−	7.95795i	−1.04285	−	1.24282i	−0.969390	−	0.245525i	$-0.921040\pi$
$41$	−6.67751	−	7.95795i	−1.04285	−	1.24282i	−0.0734622	−	0.997298i	$-0.523405\pi$
$42$		0			0
$43$	−1.29292	−	3.55227i	−0.197169	−	0.541717i	0.801226	−	0.598362i	$-0.204182\pi$
$43$	−1.29292	−	3.55227i	−0.197169	−	0.541717i	−0.998394	+	0.0566457i	$0.981959\pi$
$44$		0			0
$45$	−3.22057	+	4.17689i	−0.480094	+	0.622654i
$46$		0			0
$47$	2.19570	−	12.4524i	0.320276	−	1.81637i	−0.220706	−	0.975340i	$-0.570836\pi$
$47$	2.19570	−	12.4524i	0.320276	−	1.81637i	0.540982	−	0.841034i	$-0.318053\pi$
$48$		0			0
$49$	4.08223	+	1.48581i	0.583175	+	0.212258i
$50$		0			0
$51$	2.11816	+	5.46573i	0.296601	+	0.765355i
$52$		0			0
$53$		−	10.0071i		−	1.37457i	−0.726386	−	0.687287i	$-0.758801\pi$
$53$		−	10.0071i		−	1.37457i	0.726386	−	0.687287i	$-0.241199\pi$
$54$		0			0
$55$			3.58181i			0.482971i
$56$		0			0
$57$	−2.55971	+	3.18171i	−0.339042	+	0.421428i
$58$		0			0
$59$	−6.19943	−	2.25641i	−0.807097	−	0.293759i	−0.0946731	−	0.995508i	$-0.530181\pi$
$59$	−6.19943	−	2.25641i	−0.807097	−	0.293759i	−0.712424	+	0.701749i	$0.752403\pi$
$60$		0			0
$61$	−0.0727139	+	0.412381i	−0.00931006	+	0.0528000i	−0.989109	−	0.147186i	$-0.952978\pi$
$61$	−0.0727139	+	0.412381i	−0.00931006	+	0.0528000i	0.979799	+	0.199986i	$0.0640896\pi$
$62$		0			0
$63$	8.95174	+	4.68660i	1.12781	+	0.590456i
$64$		0			0
$65$	−2.43965	−	6.70287i	−0.302601	−	0.831389i
$66$		0			0
$67$	7.81114	+	9.30896i	0.954283	+	1.13727i	0.990443	+	0.137924i	$0.0440430\pi$
$67$	7.81114	+	9.30896i	0.954283	+	1.13727i	−0.0361600	+	0.999346i	$0.511513\pi$
$68$		0			0
$69$	−6.93555	+	0.143229i	−0.834942	+	0.0172427i
$70$		0			0
$71$	7.57186	+	13.1148i	0.898615	+	1.55645i	0.829266	+	0.558854i	$0.188759\pi$
$71$	7.57186	+	13.1148i	0.898615	+	1.55645i	0.0693485	+	0.997592i	$0.477908\pi$
$72$		0			0
$73$	5.87873	−	10.1823i	0.688054	−	1.19174i	−0.284413	−	0.958702i	$-0.591799\pi$
$73$	5.87873	−	10.1823i	0.688054	−	1.19174i	0.972467	−	0.233042i	$-0.0748681\pi$
$74$		0			0
$75$	2.48857	−	2.17728i	0.287355	−	0.251410i
$76$		0			0
$77$	6.75765	−	1.19156i	0.770106	−	0.135790i
$78$		0			0
$79$	5.00952	−	5.97012i	0.563615	−	0.671691i	−0.406692	−	0.913565i	$-0.633318\pi$
$79$	5.00952	−	5.97012i	0.563615	−	0.671691i	0.970308	+	0.241875i	$0.0777623\pi$
$80$		0			0
$81$	7.34817	+	5.19658i	0.816463	+	0.577398i
$82$		0			0
$83$	12.5809	+	10.5566i	1.38093	+	1.15874i	0.968866	+	0.247587i	$0.0796374\pi$
$83$	12.5809	+	10.5566i	1.38093	+	1.15874i	0.412067	+	0.911154i	$0.364807\pi$
$84$		0			0
$85$	1.03320	+	5.85959i	0.112067	+	0.635562i
$86$		0			0
$87$	−3.35870	−	3.83890i	−0.360091	−	0.411574i
$88$		0			0
$89$	−2.81064	−	1.62273i	−0.297928	−	0.172009i	0.343584	−	0.939122i	$-0.388359\pi$
$89$	−2.81064	−	1.62273i	−0.297928	−	0.172009i	−0.641512	+	0.767113i	$0.721692\pi$
$90$		0			0
$91$	−11.8344	+	6.83262i	−1.24059	+	0.716253i
$92$		0			0
$93$	−0.170430	−	8.25272i	−0.0176728	−	0.855767i
$94$		0			0
$95$	−3.17524	+	2.66435i	−0.325773	+	0.273356i
$96$		0			0
$97$	10.7401	−	3.90906i	1.09049	−	0.396905i	0.266686	−	0.963783i	$-0.414071\pi$
$97$	10.7401	−	3.90906i	1.09049	−	0.396905i	0.823802	+	0.566878i	$0.191849\pi$
$98$		0			0
$99$	6.10672	−	0.252332i	0.613748	−	0.0253603i
$100$		0			0
$101$	−5.82407	−	1.02694i	−0.579516	−	0.102184i	−0.123796	−	0.992308i	$-0.539507\pi$
$101$	−5.82407	−	1.02694i	−0.579516	−	0.102184i	−0.455720	+	0.890123i	$0.650618\pi$
$102$		0			0
$103$	1.09855	−	3.01824i	0.108243	−	0.297396i	−0.873731	−	0.486409i	$-0.838307\pi$
$103$	1.09855	−	3.01824i	0.108243	−	0.297396i	0.981975	+	0.189013i	$0.0605288\pi$
$104$		0			0
$105$	7.99127	+	6.42904i	0.779868	+	0.627410i
$106$		0			0
$107$	2.38343			0.230415			0.115208	−	0.993341i	$-0.463247\pi$
$107$	2.38343			0.230415			0.115208	+	0.993341i	$0.463247\pi$
$108$		0			0
$109$	−4.67235			−0.447530			−0.223765	−	0.974643i	$-0.571835\pi$
$109$	−4.67235			−0.447530			−0.223765	+	0.974643i	$0.571835\pi$
$110$		0			0
$111$	14.2664	−	5.52871i	1.35410	−	0.524762i
$112$		0			0
$113$	−5.25158	+	14.4286i	−0.494027	+	1.35733i	0.402938	+	0.915227i	$0.367989\pi$
$113$	−5.25158	+	14.4286i	−0.494027	+	1.35733i	−0.896965	+	0.442101i	$0.854233\pi$
$114$		0			0
$115$	−6.93441	−	1.22272i	−0.646637	−	0.114020i
$116$		0			0
$117$	−11.2560	+	4.63162i	−1.04062	+	0.428194i
$118$		0			0
$119$	10.7113	−	3.89861i	0.981907	−	0.357385i
$120$		0			0
$121$	−5.24692	+	4.40269i	−0.476993	+	0.400245i
$122$		0			0
$123$	−15.3935	+	9.31641i	−1.38798	+	0.840032i
$124$		0			0
$125$	10.5195	−	6.07343i	0.940892	−	0.543224i
$126$		0			0
$127$	7.33037	+	4.23219i	0.650465	+	0.375546i	0.788634	−	0.614863i	$-0.210789\pi$
$127$	7.33037	+	4.23219i	0.650465	+	0.375546i	−0.138169	+	0.990409i	$0.544122\pi$
$128$		0			0
$129$	−6.42326	+	1.26987i	−0.565537	+	0.111806i
$130$		0			0
$131$	−0.590649	−	3.34974i	−0.0516053	−	0.292668i	0.948072	−	0.318054i	$-0.103029\pi$
$131$	−0.590649	−	3.34974i	−0.0516053	−	0.292668i	−0.999678	+	0.0253865i	$0.991918\pi$
$132$		0			0
$133$	6.08302	+	5.10426i	0.527464	+	0.442595i
$134$		0			0
$135$	6.29408	+	6.62118i	0.541708	+	0.569860i
$136$		0			0
$137$	−3.87409	+	4.61696i	−0.330986	+	0.394454i	−0.905713	−	0.423891i	$-0.860664\pi$
$137$	−3.87409	+	4.61696i	−0.330986	+	0.394454i	0.574727	+	0.818345i	$0.305108\pi$
$138$		0			0
$139$	18.5190	−	3.26539i	1.57076	−	0.276967i	0.680612	−	0.732644i	$-0.261714\pi$
$139$	18.5190	−	3.26539i	1.57076	−	0.276967i	0.890145	+	0.455677i	$0.150603\pi$
$140$		0			0
$141$	−20.7305	−	7.06406i	−1.74582	−	0.594901i
$142$		0			0
$143$	−4.13292	+	7.15842i	−0.345612	+	0.598617i
$144$		0			0
$145$	−2.58876	−	4.48387i	−0.214985	−	0.372365i
$146$		0			0
$147$	3.62686	−	6.59261i	0.299138	−	0.543749i
$148$		0			0
$149$	−0.977398	−	1.16482i	−0.0800716	−	0.0954256i	0.724521	−	0.689252i	$-0.242061\pi$
$149$	−0.977398	−	1.16482i	−0.0800716	−	0.0954256i	−0.804593	+	0.593827i	$0.797616\pi$
$150$		0			0
$151$	−5.98184	−	16.4350i	−0.486795	−	1.33746i	−0.903567	−	0.428447i	$-0.859061\pi$
$151$	−5.98184	−	16.4350i	−0.486795	−	1.33746i	0.416771	−	0.909011i	$-0.363162\pi$
$152$		0			0
$153$	9.91738	−	2.17433i	0.801773	−	0.175785i
$154$		0			0
$155$	1.45494	−	8.25137i	0.116863	−	0.662766i
$156$		0			0
$157$	2.00637	+	0.730259i	0.160126	+	0.0582810i	0.420839	−	0.907135i	$-0.361736\pi$
$157$	2.00637	+	0.730259i	0.160126	+	0.0582810i	−0.260714	+	0.965416i	$0.583958\pi$
$158$		0			0
$159$	−17.1279	−	2.65672i	−1.35833	−	0.210692i
$160$		0			0
$161$			13.4896i			1.06313i
$162$		0			0
$163$			23.0331i			1.80409i	0.431640	+	0.902046i	$0.357935\pi$
$163$			23.0331i			1.80409i	−0.431640	+	0.902046i	$0.642065\pi$
$164$		0			0
$165$	6.13056	+	0.950916i	0.477264	+	0.0740287i
$166$		0			0
$167$	−22.1988	−	8.07970i	−1.71779	−	0.625226i	−0.720150	−	0.693819i	$-0.755927\pi$
$167$	−22.1988	−	8.07970i	−1.71779	−	0.625226i	−0.997645	+	0.0685925i	$0.978149\pi$
$168$		0			0
$169$	0.601020	−	3.40855i	0.0462323	−	0.262196i
$170$		0			0
$171$	4.76620	+	5.22586i	0.364481	+	0.399631i
$172$		0			0
$173$	1.26759	+	3.48267i	0.0963728	+	0.264782i	0.978506	−	0.206218i	$-0.0661155\pi$
$173$	1.26759	+	3.48267i	0.0963728	+	0.264782i	−0.882133	+	0.471000i	$0.843893\pi$
$174$		0			0
$175$	−4.13308	−	4.92561i	−0.312432	−	0.372341i
$176$		0			0
$177$	−5.50789	+	10.0118i	−0.413998	+	0.752533i
$178$		0			0
$179$	−4.88951	−	8.46888i	−0.365459	−	0.632994i	0.623391	−	0.781911i	$-0.285755\pi$
$179$	−4.88951	−	8.46888i	−0.365459	−	0.632994i	−0.988850	+	0.148917i	$0.952421\pi$
$180$		0			0
$181$	−2.23147	+	3.86501i	−0.165864	+	0.287284i	−0.936962	−	0.349432i	$-0.886374\pi$
$181$	−2.23147	+	3.86501i	−0.165864	+	0.287284i	0.771098	+	0.636716i	$0.219708\pi$
$182$		0			0
$183$	0.686520	+	0.233937i	0.0507490	+	0.0172931i
$184$		0			0
$185$	15.2944	−	2.69682i	1.12447	−	0.198274i
$186$		0			0
$187$	4.43195	−	5.28179i	0.324096	−	0.386243i
$188$		0			0
$189$	10.3981	−	14.0774i	0.756347	−	1.02398i
$190$		0			0
$191$	−1.11424	−	0.934959i	−0.0806236	−	0.0676513i	0.601585	−	0.798809i	$-0.294536\pi$
$191$	−1.11424	−	0.934959i	−0.0806236	−	0.0676513i	−0.682209	+	0.731157i	$0.738980\pi$
$192$		0			0
$193$	−2.89413	−	16.4134i	−0.208324	−	1.18146i	−0.892122	−	0.451794i	$-0.850784\pi$
$193$	−2.89413	−	16.4134i	−0.208324	−	1.18146i	0.683798	−	0.729671i	$-0.260327\pi$
$194$		0			0
$195$	−12.1202	+	2.39615i	−0.867947	+	0.171592i
$196$		0			0
$197$	0.492249	+	0.284200i	0.0350713	+	0.0202484i	0.517433	−	0.855724i	$-0.326888\pi$
$197$	0.492249	+	0.284200i	0.0350713	+	0.0202484i	−0.482362	+	0.875972i	$0.660221\pi$
$198$		0			0
$199$	−13.9651	+	8.06276i	−0.989960	+	0.571554i	−0.905262	−	0.424853i	$-0.860326\pi$
$199$	−13.9651	+	8.06276i	−0.989960	+	0.571554i	−0.0846975	+	0.996407i	$0.526992\pi$
$200$		0			0
$201$	18.0068	−	10.8980i	1.27010	−	0.768688i
$202$		0			0
$203$	−7.59833	+	6.37575i	−0.533298	+	0.447490i
$204$		0			0
$205$	−17.1624	+	6.24661i	−1.19868	+	0.436282i
$206$		0			0
$207$	−1.59614	+	11.9088i	−0.110939	+	0.827719i
$208$		0			0
$209$	4.73027	+	0.834075i	0.327200	+	0.0576942i
$210$		0			0
$211$	2.10308	−	5.77817i	0.144782	−	0.397786i	−0.846012	−	0.533164i	$-0.821003\pi$
$211$	2.10308	−	5.77817i	0.144782	−	0.397786i	0.990794	+	0.135378i	$0.0432250\pi$
$212$		0			0
$213$	24.4574	−	9.47808i	1.67579	−	0.649427i
$214$		0			0
$215$	−6.64609			−0.453259
$216$		0			0
$217$	−16.0515			−1.08965
$218$		0			0
$219$	−15.8671	−	12.7652i	−1.07220	−	0.862591i
$220$		0			0
$221$	−4.69626	+	12.9029i	−0.315905	+	0.867941i
$222$		0			0
$223$	6.78099	+	1.19567i	0.454088	+	0.0800680i	0.396015	−	0.918244i	$-0.370393\pi$
$223$	6.78099	+	1.19567i	0.454088	+	0.0800680i	0.0580739	+	0.998312i	$0.481504\pi$
$224$		0			0
$225$	−3.06592	−	4.83743i	−0.204394	−	0.322495i
$226$		0			0
$227$	19.2009	−	6.98854i	1.27441	−	0.463846i	0.385827	−	0.922571i	$-0.373916\pi$
$227$	19.2009	−	6.98854i	1.27441	−	0.463846i	0.888578	+	0.458725i	$0.151694\pi$
$228$		0			0
$229$	−3.69275	+	3.09858i	−0.244024	+	0.204760i	−0.756594	−	0.653885i	$-0.773138\pi$
$229$	−3.69275	+	3.09858i	−0.244024	+	0.204760i	0.512570	+	0.858645i	$0.328693\pi$
$230$		0			0
$231$	−0.245393	−	11.8826i	−0.0161456	−	0.781819i
$232$		0			0
$233$	−5.70605	+	3.29439i	−0.373816	+	0.215823i	−0.675124	−	0.737704i	$-0.735910\pi$
$233$	−5.70605	+	3.29439i	−0.373816	+	0.215823i	0.301308	+	0.953527i	$0.402577\pi$
$234$		0			0
$235$	−19.2521	−	11.1152i	−1.25587	−	0.725077i
$236$		0			0
$237$	−8.88840	−	10.1592i	−0.577364	−	0.659910i
$238$		0			0
$239$	−1.78098	−	10.1005i	−0.115202	−	0.653344i	−0.986650	−	0.162856i	$-0.947930\pi$
$239$	−1.78098	−	10.1005i	−0.115202	−	0.653344i	0.871448	−	0.490488i	$-0.163182\pi$
$240$		0			0
$241$	−16.6341	−	13.9577i	−1.07150	−	0.899092i	−0.0763084	−	0.997084i	$-0.524313\pi$
$241$	−16.6341	−	13.9577i	−1.07150	−	0.899092i	−0.995187	+	0.0979927i	$0.968758\pi$
$242$		0			0
$243$	10.8452	−	11.1974i	0.695720	−	0.718313i
$244$		0			0
$245$	4.90935	−	5.85074i	0.313647	−	0.373790i
$246$		0			0
$247$	−9.42018	+	1.66103i	−0.599392	+	0.105689i
$248$		0			0
$249$	21.4086	−	18.7306i	1.35671	−	1.18701i
$250$		0			0
$251$	−7.00303	+	12.1296i	−0.442027	+	0.765614i	−0.997840	−	0.0656939i	$-0.979074\pi$
$251$	−7.00303	+	12.1296i	−0.442027	+	0.765614i	0.555813	+	0.831308i	$0.312407\pi$
$252$		0			0
$253$	4.07981	+	7.06644i	0.256495	+	0.444263i
$254$		0			0
$255$	10.3035	−	0.212781i	0.645229	−	0.0133249i
$256$		0			0
$257$	−16.2302	−	19.3424i	−1.01241	−	1.20655i	−0.978313	−	0.207130i	$-0.933588\pi$
$257$	−16.2302	−	19.3424i	−1.01241	−	1.20655i	−0.0341011	−	0.999418i	$-0.510857\pi$
$258$		0			0
$259$	−10.1760	−	27.9582i	−0.632303	−	1.73724i
$260$		0			0
$261$	−7.46229	+	4.72953i	−0.461904	+	0.292750i
$262$		0			0
$263$	0.542765	−	3.07817i	0.0334683	−	0.189808i	−0.963490	−	0.267744i	$-0.913722\pi$
$263$	0.542765	−	3.07817i	0.0334683	−	0.189808i	0.996958	+	0.0779359i	$0.0248330\pi$
$264$		0			0
$265$	−16.5325	−	6.01732i	−1.01558	−	0.369641i
$266$		0			0
$267$	−3.52362	+	4.37984i	−0.215642	+	0.268042i
$268$		0			0
$269$			21.1146i			1.28738i	0.765287	+	0.643689i	$0.222597\pi$
$269$			21.1146i			1.28738i	−0.765287	+	0.643689i	$0.777403\pi$
$270$		0			0
$271$		−	1.60064i		−	0.0972320i	−0.998818	−	0.0486160i	$-0.984519\pi$
$271$		−	1.60064i		−	0.0972320i	0.998818	−	0.0486160i	$-0.0154811\pi$
$272$		0			0
$273$	8.55273	+	22.0696i	0.517635	+	1.33571i
$274$		0			0
$275$	−3.65479	−	1.33023i	−0.220392	−	0.0802161i
$276$		0			0
$277$	−1.63119	+	9.25096i	−0.0980090	+	0.555836i	0.895775	+	0.444508i	$0.146622\pi$
$277$	−1.63119	+	9.25096i	−0.0980090	+	0.555836i	−0.993784	+	0.111328i	$0.964490\pi$
$278$		0			0
$279$	−14.1705	−	1.89927i	−0.848363	−	0.113706i
$280$		0			0
$281$	8.00459	+	21.9924i	0.477514	+	1.31196i	0.911597	+	0.411085i	$0.134850\pi$
$281$	8.00459	+	21.9924i	0.477514	+	1.31196i	−0.434083	+	0.900873i	$0.642928\pi$
$282$		0			0
$283$	12.4967	+	14.8930i	0.742853	+	0.885297i	0.996635	−	0.0819641i	$-0.0261193\pi$
$283$	12.4967	+	14.8930i	0.742853	+	0.885297i	−0.253783	+	0.967261i	$0.581675\pi$
$284$		0			0
$285$	3.71727	+	6.14204i	0.220192	+	0.363823i
$286$		0			0
$287$	17.4946	+	30.3016i	1.03267	+	1.78865i
$288$		0			0
$289$	−2.77321	+	4.80334i	−0.163130	+	0.282549i
$290$		0			0
$291$	−3.83936	−	19.4203i	−0.225067	−	1.13844i
$292$		0			0
$293$	31.0155	−	5.46886i	1.81194	−	0.319494i	0.837894	−	0.545833i	$-0.183787\pi$
$293$	31.0155	−	5.46886i	1.81194	−	0.319494i	0.974049	+	0.226339i	$0.0726756\pi$
$294$		0			0
$295$	−7.45554	+	8.88516i	−0.434078	+	0.517314i
$296$		0			0
$297$	1.18935	−	10.5191i	0.0690133	−	0.610383i
$298$		0			0
$299$	−12.4479	−	10.4450i	−0.719882	−	0.604052i
$300$		0			0
$301$	2.21095	+	12.5389i	0.127437	+	0.722730i
$302$		0			0
$303$	−3.30390	+	9.69574i	−0.189804	+	0.557006i
$304$		0			0
$305$	0.637563	+	0.368097i	0.0365068	+	0.0210772i
$306$		0			0
$307$	−1.54525	+	0.892151i	−0.0881921	+	0.0509177i	−0.543447	−	0.839443i	$-0.682881\pi$
$307$	−1.54525	+	0.892151i	−0.0881921	+	0.0509177i	0.455255	+	0.890361i	$0.349548\pi$
$308$		0			0
$309$	−4.87431	−	2.68155i	−0.277290	−	0.152548i
$310$		0			0
$311$	−8.43637	+	7.07896i	−0.478383	+	0.401411i	−0.849841	−	0.527039i	$-0.823302\pi$
$311$	−8.43637	+	7.07896i	−0.478383	+	0.401411i	0.371458	+	0.928450i	$0.378858\pi$
$312$		0			0
$313$	−18.0684	+	6.57635i	−1.02129	+	0.371718i	−0.797757	−	0.602980i	$-0.793980\pi$
$313$	−18.0684	+	6.57635i	−1.02129	+	0.371718i	−0.223529	+	0.974697i	$0.571758\pi$
$314$		0			0
$315$	13.1254	−	11.9709i	0.739532	−	0.674485i
$316$		0			0
$317$	21.7504	+	3.83518i	1.22162	+	0.215405i	0.747024	−	0.664797i	$-0.231482\pi$
$317$	21.7504	+	3.83518i	1.22162	+	0.215405i	0.474600	+	0.880202i	$0.342593\pi$
$318$		0			0
$319$	−2.05204	+	5.63793i	−0.114892	+	0.315663i
$320$		0			0
$321$	0.632766	−	4.07945i	0.0353176	−	0.227693i
$322$		0			0
$323$	7.97900			0.443963
$324$		0			0
$325$	7.74549			0.429643
$326$		0			0
$327$	−1.24044	+	7.99712i	−0.0685964	+	0.442242i
$328$		0			0
$329$	−14.5661	+	40.0199i	−0.803052	+	2.20637i
$330$		0			0
$331$	−13.3244	−	2.34946i	−0.732377	−	0.129138i	−0.204991	−	0.978764i	$-0.565717\pi$
$331$	−13.3244	−	2.34946i	−0.732377	−	0.129138i	−0.527386	+	0.849626i	$0.676828\pi$
$332$		0			0
$333$	−5.67534	−	25.8859i	−0.311007	−	1.41854i
$334$		0			0
$335$	20.0760	−	7.30708i	1.09687	−	0.399229i
$336$		0			0
$337$	10.8570	−	9.11008i	0.591417	−	0.496258i	−0.297257	−	0.954798i	$-0.596072\pi$
$337$	10.8570	−	9.11008i	0.591417	−	0.496258i	0.888674	+	0.458540i	$0.151627\pi$
$338$		0			0
$339$	23.3015	+	12.8191i	1.26557	+	0.696238i
$340$		0			0
$341$	−8.40846	+	4.85463i	−0.455344	+	0.262893i
$342$		0			0
$343$	7.74659	+	4.47250i	0.418277	+	0.241492i
$344$		0			0
$345$	−3.93378	+	11.5442i	−0.211787	+	0.621519i
$346$		0			0
$347$	−2.54597	−	14.4389i	−0.136675	−	0.775121i	−0.973679	−	0.227924i	$-0.926806\pi$
$347$	−2.54597	−	14.4389i	−0.136675	−	0.775121i	0.837004	−	0.547196i	$-0.184305\pi$
$348$		0			0
$349$	−8.88139	−	7.45237i	−0.475410	−	0.398916i	0.373354	−	0.927689i	$-0.378208\pi$
$349$	−8.88139	−	7.45237i	−0.475410	−	0.398916i	−0.848763	+	0.528773i	$0.822652\pi$
$350$		0			0
$351$	4.93910	+	20.4953i	0.263630	+	1.09396i
$352$		0			0
$353$	−12.3110	+	14.6717i	−0.655249	+	0.780895i	−0.986696	−	0.162579i	$-0.948019\pi$
$353$	−12.3110	+	14.6717i	−0.655249	+	0.780895i	0.331447	+	0.943474i	$0.392463\pi$
$354$		0			0
$355$	26.2198	−	4.62326i	1.39160	−	0.245377i
$356$		0			0
$357$	−3.82909	−	19.3684i	−0.202657	−	1.02508i
$358$		0			0
$359$	1.56411	−	2.70911i	0.0825504	−	0.142982i	−0.821794	−	0.569784i	$-0.807027\pi$
$359$	1.56411	−	2.70911i	0.0825504	−	0.142982i	0.904345	+	0.426803i	$0.140360\pi$
$360$		0			0
$361$	−6.72076	−	11.6407i	−0.353724	−	0.612668i
$362$		0			0
$363$	6.14259	+	10.1494i	0.322403	+	0.532705i
$364$		0			0
$365$	−13.2870	−	15.8348i	−0.695473	−	0.828833i
$366$		0			0
$367$	11.9355	+	32.7926i	0.623030	+	1.71176i	0.699446	+	0.714686i	$0.253430\pi$
$367$	11.9355	+	32.7926i	0.623030	+	1.71176i	−0.0764152	+	0.997076i	$0.524347\pi$
$368$		0			0
$369$	11.8591	+	28.8206i	0.617358	+	1.50034i
$370$		0			0
$371$	−5.85280	+	33.1929i	−0.303862	+	1.72329i
$372$		0			0
$373$	−17.5314	−	6.38090i	−0.907740	−	0.330391i	−0.154390	−	0.988010i	$-0.549341\pi$
$373$	−17.5314	−	6.38090i	−0.907740	−	0.330391i	−0.753350	+	0.657619i	$0.771564\pi$
$374$		0			0
$375$	−7.60242	−	19.6174i	−0.392587	−	1.01304i
$376$		0			0
$377$		−	11.9483i		−	0.615369i
$378$		0			0
$379$		−	4.52212i		−	0.232285i	−0.993233	−	0.116143i	$-0.962947\pi$
$379$		−	4.52212i		−	0.232285i	0.993233	−	0.116143i	$-0.0370530\pi$
$380$		0			0
$381$	9.18985	−	11.4230i	0.470810	−	0.585216i
$382$		0			0
$383$	7.58521	+	2.76079i	0.387586	+	0.141070i	0.528461	−	0.848958i	$-0.322769\pi$
$383$	7.58521	+	2.76079i	0.387586	+	0.141070i	−0.140875	+	0.990027i	$0.544991\pi$
$384$		0			0
$385$	2.09488	−	11.8807i	0.106765	−	0.605495i
$386$		0			0
$387$	0.468205	+	11.3311i	0.0238002	+	0.575991i
$388$		0			0
$389$	2.93943	+	8.07603i	0.149035	+	0.409471i	0.991636	−	0.129068i	$-0.0411986\pi$
$389$	2.93943	+	8.07603i	0.149035	+	0.409471i	−0.842600	+	0.538539i	$0.818976\pi$
$390$		0			0
$391$	8.71266	+	10.3833i	0.440618	+	0.525109i
$392$		0			0
$393$	−5.89016	+	0.121640i	−0.297119	+	0.00613593i
$394$		0			0
$395$	−6.85085	−	11.8660i	−0.344704	−	0.597044i
$396$		0			0
$397$	−8.36056	+	14.4809i	−0.419605	+	0.726776i	−0.995900	−	0.0904653i	$-0.971165\pi$
$397$	−8.36056	+	14.4809i	−0.419605	+	0.726776i	0.576295	+	0.817242i	$0.304498\pi$
$398$		0			0
$399$	10.3513	−	9.05649i	0.518214	−	0.453391i
$400$		0			0
$401$	10.7406	−	1.89386i	0.536360	−	0.0945747i	0.101094	−	0.994877i	$-0.467766\pi$
$401$	10.7406	−	1.89386i	0.536360	−	0.0945747i	0.435266	+	0.900302i	$0.356654\pi$
$402$		0			0
$403$	12.4287	−	14.8120i	0.619119	−	0.737837i
$404$		0			0
$405$	13.0037	−	9.01502i	0.646158	−	0.447960i
$406$		0			0
$407$	−13.7863	−	11.5681i	−0.683361	−	0.573408i
$408$		0			0
$409$	−1.98786	−	11.2737i	−0.0982932	−	0.557449i	−0.993688	−	0.112176i	$-0.964218\pi$
$409$	−1.98786	−	11.2737i	−0.0982932	−	0.557449i	0.895395	−	0.445273i	$-0.146893\pi$
$410$		0			0
$411$	6.87380	+	7.85656i	0.339060	+	0.387536i
$412$		0			0
$413$	19.2435	+	11.1102i	0.946911	+	0.546699i
$414$		0			0
$415$	25.0054	−	14.4369i	1.22747	−	0.708678i
$416$		0			0
$417$	−0.672485	−	32.5636i	−0.0329317	−	1.59465i
$418$		0			0
$419$	29.6189	−	24.8532i	1.44698	−	1.21416i	0.512226	−	0.858851i	$-0.328821\pi$
$419$	29.6189	−	24.8532i	1.44698	−	1.21416i	0.934750	−	0.355306i	$-0.115623\pi$
$420$		0			0
$421$	22.9468	−	8.35196i	1.11836	−	0.407050i	0.284306	−	0.958733i	$-0.408237\pi$
$421$	22.9468	−	8.35196i	1.11836	−	0.407050i	0.834053	+	0.551684i	$0.186014\pi$
$422$		0			0
$423$	−17.5944	+	33.6065i	−0.855467	+	1.63400i
$424$		0			0
$425$	−6.36270	−	1.12192i	−0.308636	−	0.0544209i
$426$		0			0
$427$	0.482377	−	1.32532i	0.0233438	−	0.0641367i
$428$		0			0
$429$	11.1550	+	8.97429i	0.538569	+	0.433283i
$430$		0			0
$431$	1.83273			0.0882794			0.0441397	−	0.999025i	$-0.485945\pi$
$431$	1.83273			0.0882794			0.0441397	+	0.999025i	$0.485945\pi$
$432$		0			0
$433$	24.3880			1.17201			0.586006	−	0.810306i	$-0.300699\pi$
$433$	24.3880			1.17201			0.586006	+	0.810306i	$0.300699\pi$
$434$		0			0
$435$	−8.36179	+	3.24048i	−0.400917	+	0.155369i
$436$		0			0
$437$	−3.22955	+	8.87312i	−0.154490	+	0.424459i
$438$		0			0
$439$	−6.79585	−	1.19829i	−0.324348	−	0.0571913i	0.00910346	−	0.999959i	$-0.497102\pi$
$439$	−6.79585	−	1.19829i	−0.324348	−	0.0571913i	−0.333452	+	0.942767i	$0.608213\pi$
$440$		0			0
$441$	−10.3209	−	7.95791i	−0.491473	−	0.378948i
$442$		0			0
$443$	−12.8196	+	4.66594i	−0.609076	+	0.221686i	−0.628099	−	0.778133i	$-0.716167\pi$
$443$	−12.8196	+	4.66594i	−0.609076	+	0.221686i	0.0190226	+	0.999819i	$0.493945\pi$
$444$		0			0
$445$	−4.37094	+	3.66765i	−0.207202	+	0.173863i
$446$		0			0
$447$	−2.25317	+	1.36366i	−0.106571	+	0.0644987i
$448$		0			0
$449$	−2.16633	+	1.25073i	−0.102235	+	0.0590255i	−0.550246	−	0.835003i	$-0.685466\pi$
$449$	−2.16633	+	1.25073i	−0.102235	+	0.0590255i	0.448011	+	0.894028i	$0.352133\pi$
$450$		0			0
$451$	18.3288	+	10.5822i	0.863071	+	0.498294i
$452$		0			0
$453$	−29.7179	+	5.87518i	−1.39627	+	0.276040i
$454$		0			0
$455$	4.17189	+	23.6600i	0.195581	+	1.10920i
$456$		0			0
$457$	12.1416	+	10.1880i	0.567961	+	0.476576i	0.880969	−	0.473175i	$-0.156892\pi$
$457$	12.1416	+	10.1880i	0.567961	+	0.476576i	−0.313008	+	0.949751i	$0.601337\pi$
$458$		0			0
$459$	−1.08864	−	17.5517i	−0.0508133	−	0.819242i
$460$		0			0
$461$	13.3795	−	15.9451i	0.623147	−	0.742637i	−0.358461	−	0.933545i	$-0.616699\pi$
$461$	13.3795	−	15.9451i	0.623147	−	0.742637i	0.981608	+	0.190907i	$0.0611430\pi$
$462$		0			0
$463$	−4.07709	+	0.718900i	−0.189478	+	0.0334101i	−0.267582	−	0.963535i	$-0.586225\pi$
$463$	−4.07709	+	0.718900i	−0.189478	+	0.0334101i	0.0781036	+	0.996945i	$0.475113\pi$
$464$		0			0
$465$	−13.7366	−	4.68086i	−0.637021	−	0.217070i
$466$		0			0
$467$	1.51667	−	2.62696i	0.0701833	−	0.121561i	−0.828798	−	0.559548i	$-0.810975\pi$
$467$	1.51667	−	2.62696i	0.0701833	−	0.121561i	0.898982	+	0.437987i	$0.144308\pi$
$468$		0			0
$469$	−20.4646	−	35.4458i	−0.944970	−	1.63674i
$470$		0			0
$471$	1.78256	−	3.24019i	0.0821360	−	0.149300i
$472$		0			0
$473$	4.95045	+	5.89972i	0.227622	+	0.271269i
$474$		0			0
$475$	−1.53939	−	4.22944i	−0.0706321	−	0.194060i
$476$		0			0
$477$	−9.09441	+	28.6105i	−0.416404	+	1.30999i
$478$		0			0
$479$	0.400967	−	2.27400i	0.0183207	−	0.103902i	−0.974276	−	0.225357i	$-0.927645\pi$
$479$	0.400967	−	2.27400i	0.0183207	−	0.103902i	0.992597	+	0.121456i	$0.0387562\pi$
$480$		0			0
$481$	33.6784	+	12.2579i	1.53560	+	0.558914i
$482$		0			0
$483$	23.0886	+	3.58129i	1.05057	+	0.162955i
$484$		0			0
$485$		−	20.0940i		−	0.912421i
$486$		0			0
$487$		−	10.8187i		−	0.490242i	−0.969492	−	0.245121i	$-0.921172\pi$
$487$		−	10.8187i		−	0.490242i	0.969492	−	0.245121i	$-0.0788277\pi$
$488$		0			0
$489$	39.4231	+	6.11495i	1.78277	+	0.276527i
$490$		0			0
$491$	37.8763	+	13.7858i	1.70933	+	0.622146i	0.996833	−	0.0795275i	$-0.0253411\pi$
$491$	37.8763	+	13.7858i	1.70933	+	0.622146i	0.712499	+	0.701673i	$0.247563\pi$
$492$		0			0
$493$	−1.73068	+	9.81519i	−0.0779461	+	0.442054i
$494$		0			0
$495$	3.25515	−	10.2405i	0.146308	−	0.460277i
$496$		0			0
$497$	−17.4450	−	47.9298i	−0.782516	−	2.14995i
$498$		0			0
$499$	−12.0797	−	14.3960i	−0.540760	−	0.644452i	0.424598	−	0.905382i	$-0.360415\pi$
$499$	−12.0797	−	14.3960i	−0.540760	−	0.644452i	−0.965358	+	0.260930i	$0.915971\pi$
$500$		0			0
$501$	−19.7225	+	35.8501i	−0.881138	+	1.60166i
$502$		0			0
$503$	4.44979	+	7.70726i	0.198406	+	0.343650i	0.948012	−	0.318235i	$-0.103090\pi$
$503$	4.44979	+	7.70726i	0.198406	+	0.343650i	−0.749606	+	0.661885i	$0.769757\pi$
$504$		0			0
$505$	−5.19865	+	9.00432i	−0.231337	+	0.400687i
$506$		0			0
$507$	−5.67446	−	1.93361i	−0.252012	−	0.0858748i
$508$		0			0
$509$	16.1048	−	2.83970i	0.713831	−	0.125868i	0.195073	−	0.980789i	$-0.437506\pi$
$509$	16.1048	−	2.83970i	0.713831	−	0.125868i	0.518758	+	0.854921i	$0.326395\pi$
$510$		0			0
$511$	−25.4547	+	30.3358i	−1.12605	+	1.34198i
$512$		0			0
$513$	10.2098	−	6.77037i	0.450776	−	0.298919i
$514$		0			0
$515$	−4.32580	−	3.62978i	−0.190618	−	0.159947i
$516$		0			0
$517$	4.47332	+	25.3695i	0.196736	+	1.11575i
$518$		0			0
$519$	6.29740	−	1.24498i	0.276425	−	0.0546488i
$520$		0			0
$521$	5.28398	+	3.05071i	0.231495	+	0.133654i	0.611262	−	0.791429i	$-0.290662\pi$
$521$	5.28398	+	3.05071i	0.231495	+	0.133654i	−0.379766	+	0.925082i	$0.623996\pi$
$522$		0			0
$523$	−26.2053	+	15.1297i	−1.14588	+	0.661574i	−0.947880	−	0.318628i	$-0.896778\pi$
$523$	−26.2053	+	15.1297i	−1.14588	+	0.661574i	−0.198000	+	0.980202i	$0.563445\pi$
$524$		0			0
$525$	−9.52787	+	5.76644i	−0.415830	+	0.251668i
$526$		0			0
$527$	−12.3553	+	10.3673i	−0.538206	+	0.451608i
$528$		0			0
$529$	6.53952	−	2.38019i	0.284327	−	0.103487i
$530$		0			0
$531$	15.6738	+	12.0852i	0.680184	+	0.524453i
$532$		0			0
$533$	−41.5077	−	7.31893i	−1.79790	−	0.317018i
$534$		0			0
$535$	1.43318	−	3.93763i	0.0619617	−	0.170238i
$536$		0			0
$537$	−15.7933	+	6.12044i	−0.681530	+	0.264117i
$538$		0			0
$539$	−8.85051			−0.381218
$540$		0			0
$541$	−7.88737			−0.339105			−0.169552	−	0.985521i	$-0.554232\pi$
$541$	−7.88737			−0.339105			−0.169552	+	0.985521i	$0.554232\pi$
$542$		0			0
$543$	6.02287	+	4.84545i	0.258466	+	0.207938i
$544$		0			0
$545$	−2.80952	+	7.71910i	−0.120347	+	0.330650i
$546$		0			0
$547$	18.7310	+	3.30278i	0.800878	+	0.141216i	0.559084	−	0.829111i	$-0.311153\pi$
$547$	18.7310	+	3.30278i	0.800878	+	0.141216i	0.241794	+	0.970327i	$0.422264\pi$
$548$		0			0
$549$	0.582663	−	1.11293i	0.0248675	−	0.0474987i
$550$		0			0
$551$	−6.52440	+	2.37469i	−0.277949	+	0.101165i
$552$		0			0
$553$	−20.1081	+	16.8727i	−0.855081	+	0.717499i
$554$		0			0
$555$	−0.555391	−	26.8936i	−0.0235750	−	1.14157i
$556$		0			0
$557$	3.52729	−	2.03648i	0.149456	−	0.0862886i	−0.423407	−	0.905940i	$-0.639166\pi$
$557$	3.52729	−	2.03648i	0.149456	−	0.0862886i	0.572863	+	0.819651i	$0.305833\pi$
$558$		0			0
$559$	−13.2825	−	7.66868i	−0.561792	−	0.324351i
$560$		0			0
$561$	−7.86362	−	8.98789i	−0.332002	−	0.379469i
$562$		0			0
$563$	1.67761	+	9.51422i	0.0707030	+	0.400976i	0.999535	+	0.0304766i	$0.00970249\pi$
$563$	1.67761	+	9.51422i	0.0707030	+	0.400976i	−0.928833	+	0.370500i	$0.879186\pi$
$564$		0			0
$565$	20.6794	+	17.3521i	0.869989	+	0.730007i
$566$		0			0
$567$	−21.3342	−	21.5345i	−0.895951	−	0.904364i
$568$		0			0
$569$	−18.7820	+	22.3835i	−0.787382	+	0.938365i	−0.999242	−	0.0389352i	$-0.987603\pi$
$569$	−18.7820	+	22.3835i	−0.787382	+	0.938365i	0.211860	+	0.977300i	$0.432048\pi$
$570$		0			0
$571$	−29.7351	+	5.24311i	−1.24438	+	0.219417i	−0.756791	−	0.653657i	$-0.773234\pi$
$571$	−29.7351	+	5.24311i	−1.24438	+	0.219417i	−0.487587	+	0.873075i	$0.662123\pi$
$572$		0			0
$573$	−1.89607	+	1.65890i	−0.0792096	+	0.0693015i
$574$		0			0
$575$	3.82298	−	6.62160i	0.159429	−	0.276140i
$576$		0			0
$577$	11.3102	+	19.5898i	0.470848	+	0.815532i	0.999444	−	0.0333411i	$-0.0106148\pi$
$577$	11.3102	+	19.5898i	0.470848	+	0.815532i	−0.528596	+	0.848873i	$0.677281\pi$
$578$		0			0
$579$	−28.8613	+	0.596026i	−1.19944	+	0.0247700i
$580$		0			0
$581$	−35.5560	−	42.3739i	−1.47511	−	1.75797i
$582$		0			0
$583$	6.97292	+	19.1580i	0.288789	+	0.793441i
$584$		0			0
$585$	0.883468	+	21.3809i	0.0365269	+	0.883992i
$586$		0			0
$587$	−2.91625	+	16.5389i	−0.120367	+	0.682633i	0.863586	+	0.504202i	$0.168213\pi$
$587$	−2.91625	+	16.5389i	−0.120367	+	0.682633i	−0.983952	+	0.178431i	$0.942898\pi$
$588$		0			0
$589$	−10.5583	−	3.84290i	−0.435046	−	0.158344i
$590$		0			0
$591$	0.617118	−	0.767075i	0.0253848	−	0.0315533i
$592$		0			0
$593$		−	29.7423i		−	1.22137i	−0.791874	−	0.610685i	$-0.790894\pi$
$593$		−	29.7423i		−	1.22137i	0.791874	−	0.610685i	$-0.209106\pi$
$594$		0			0
$595$		−	20.0403i		−	0.821570i
$596$		0			0
$597$	10.0926	+	26.0430i	0.413061	+	1.06587i
$598$		0			0
$599$	−37.6477	−	13.7027i	−1.53824	−	0.559875i	−0.572621	−	0.819820i	$-0.694073\pi$
$599$	−37.6477	−	13.7027i	−1.53824	−	0.559875i	−0.965624	+	0.259945i	$0.916296\pi$
$600$		0			0
$601$	0.169116	−	0.959102i	0.00689837	−	0.0391226i	−0.981164	−	0.193175i	$-0.938121\pi$
$601$	0.169116	−	0.959102i	0.00689837	−	0.0391226i	0.988063	+	0.154053i	$0.0492325\pi$
$602$		0			0
$603$	−13.8724	−	33.7134i	−0.564926	−	1.37292i
$604$		0			0
$605$	4.11858	+	11.3157i	0.167444	+	0.460049i
$606$		0			0
$607$	−26.7728	−	31.9065i	−1.08667	−	1.29505i	−0.952651	−	0.304067i	$-0.901655\pi$
$607$	−26.7728	−	31.9065i	−1.08667	−	1.29505i	−0.134022	−	0.990978i	$-0.542789\pi$
$608$		0			0
$609$	8.89539	+	14.6978i	0.360459	+	0.595586i
$610$		0			0
$611$	−25.6509	−	44.4287i	−1.03772	−	1.79739i
$612$		0			0
$613$	11.4932	−	19.9068i	0.464207	−	0.804029i	−0.534959	−	0.844878i	$-0.679673\pi$
$613$	11.4932	−	19.9068i	0.464207	−	0.804029i	0.999165	+	0.0408488i	$0.0130062\pi$
$614$		0			0
$615$	6.13523	+	31.0333i	0.247396	+	1.25138i
$616$		0			0
$617$	40.0276	−	7.05794i	1.61145	−	0.284142i	0.705877	−	0.708334i	$-0.250553\pi$
$617$	40.0276	−	7.05794i	1.61145	−	0.284142i	0.905572	+	0.424192i	$0.139442\pi$
$618$		0			0
$619$	17.5190	−	20.8783i	0.704147	−	0.839169i	−0.288842	−	0.957377i	$-0.593270\pi$
$619$	17.5190	−	20.8783i	0.704147	−	0.839169i	0.992989	+	0.118207i	$0.0377148\pi$
$620$		0			0
$621$	19.9591	+	5.89353i	0.800933	+	0.236499i
$622$		0			0
$623$	8.37368	+	7.02635i	0.335484	+	0.281505i
$624$		0			0
$625$	−2.05082	−	11.6308i	−0.0820328	−	0.465231i
$626$		0			0
$627$	2.68341	−	7.87482i	0.107165	−	0.314490i
$628$		0			0
$629$	−25.8903	−	14.9478i	−1.03231	−	0.596007i
$630$		0			0
$631$	34.4360	−	19.8817i	1.37088	−	0.791476i	0.379839	−	0.925053i	$-0.375980\pi$
$631$	34.4360	−	19.8817i	1.37088	−	0.791476i	0.991039	+	0.133577i	$0.0426462\pi$
$632$		0			0
$633$	−9.33149	−	5.13362i	−0.370893	−	0.204043i
$634$		0			0
$635$	11.3997	−	9.56551i	0.452384	−	0.379596i
$636$		0			0
$637$	16.5625	−	6.02827i	0.656232	−	0.238849i
$638$		0			0
$639$	−9.72945	−	44.3771i	−0.384891	−	1.75553i
$640$		0			0
$641$	16.0784	+	2.83506i	0.635060	+	0.111978i	0.481904	−	0.876224i	$-0.339945\pi$
$641$	16.0784	+	2.83506i	0.635060	+	0.111978i	0.153156	+	0.988202i	$0.451056\pi$
$642$		0			0
$643$	−12.5805	+	34.5646i	−0.496126	+	1.36309i	0.398865	+	0.917010i	$0.369404\pi$
$643$	−12.5805	+	34.5646i	−0.496126	+	1.36309i	−0.894991	+	0.446084i	$0.852818\pi$
$644$		0			0
$645$	−1.76444	+	11.3753i	−0.0694746	+	0.447903i
$646$		0			0
$647$	16.3460			0.642627			0.321314	−	0.946973i	$-0.395876\pi$
$647$	16.3460			0.642627			0.321314	+	0.946973i	$0.395876\pi$
$648$		0			0
$649$	13.4407			0.527595
$650$		0			0
$651$	−4.26144	+	27.4735i	−0.167019	+	1.07677i
$652$		0			0
$653$	−14.5391	+	39.9459i	−0.568960	+	1.56320i	0.237172	+	0.971468i	$0.423779\pi$
$653$	−14.5391	+	39.9459i	−0.568960	+	1.56320i	−0.806132	+	0.591736i	$0.798443\pi$
$654$		0			0
$655$	−5.88920	−	1.03842i	−0.230110	−	0.0405746i
$656$		0			0
$657$	−26.0612	+	23.7689i	−1.01674	+	0.927312i
$658$		0			0
$659$	−38.5139	+	14.0179i	−1.50029	+	0.546060i	−0.956135	−	0.292926i	$-0.905371\pi$
$659$	−38.5139	+	14.0179i	−1.50029	+	0.546060i	−0.544153	+	0.838986i	$0.683149\pi$
$660$		0			0
$661$	24.6279	−	20.6653i	0.957916	−	0.803787i	−0.0226971	−	0.999742i	$-0.507225\pi$
$661$	24.6279	−	20.6653i	0.957916	−	0.803787i	0.980613	+	0.195956i	$0.0627809\pi$
$662$		0			0
$663$	20.8376	+	11.4636i	0.809263	+	0.445208i
$664$		0			0
$665$	12.0904	−	6.98040i	0.468846	−	0.270688i
$666$		0			0
$667$	−10.2146	−	5.89739i	−0.395510	−	0.228348i
$668$		0			0
$669$	3.84674	−	11.2888i	0.148724	−	0.436450i
$670$		0			0
$671$	−0.148141	−	0.840148i	−0.00571891	−	0.0324335i
$672$		0			0
$673$	14.3659	+	12.0545i	0.553767	+	0.464665i	0.876214	−	0.481922i	$-0.160061\pi$
$673$	14.3659	+	12.0545i	0.553767	+	0.464665i	−0.322447	+	0.946587i	$0.604506\pi$
$674$		0			0
$675$	−9.09361	+	3.96331i	−0.350013	+	0.152548i
$676$		0			0
$677$	29.7738	−	35.4831i	1.14430	−	1.36373i	0.223027	−	0.974812i	$-0.428406\pi$
$677$	29.7738	−	35.4831i	1.14430	−	1.36373i	0.921275	−	0.388913i	$-0.127149\pi$
$678$		0			0
$679$	−37.9105	+	6.68465i	−1.45487	+	0.256533i
$680$		0			0
$681$	−6.86393	−	34.7192i	−0.263026	−	1.33044i
$682$		0			0
$683$	11.4472	−	19.8272i	0.438016	−	0.758666i	−0.559520	−	0.828817i	$-0.689015\pi$
$683$	11.4472	−	19.8272i	0.438016	−	0.758666i	0.997536	+	0.0701505i	$0.0223480\pi$
$684$		0			0
$685$	5.29807	+	9.17653i	0.202429	+	0.350617i
$686$		0			0
$687$	4.32312	+	7.14307i	0.164937	+	0.272525i
$688$		0			0
$689$	−26.0978	−	31.1021i	−0.994247	−	1.18490i
$690$		0			0
$691$	7.74396	+	21.2764i	0.294594	+	0.809391i	0.995380	+	0.0960186i	$0.0306108\pi$
$691$	7.74396	+	21.2764i	0.294594	+	0.809391i	−0.700785	+	0.713372i	$0.747167\pi$
$692$		0			0
$693$	−20.4032	−	2.73465i	−0.775055	−	0.103881i
$694$		0			0
$695$	5.74091	−	32.5583i	0.217765	−	1.23501i
$696$		0			0
$697$	33.0372	+	12.0246i	1.25137	+	0.455463i
$698$		0			0
$699$	4.12375	+	10.6410i	0.155975	+	0.402480i
$700$		0			0
$701$			4.91265i			0.185548i	0.995687	+	0.0927741i	$0.0295735\pi$
$701$			4.91265i			0.185548i	−0.995687	+	0.0927741i	$0.970427\pi$
$702$		0			0
$703$		−	20.8264i		−	0.785482i
$704$		0			0
$705$	−24.1358	+	30.0007i	−0.909006	+	1.12989i
$706$		0			0
$707$	18.7175	+	6.81261i	0.703944	+	0.256215i
$708$		0			0
$709$	2.99743	−	16.9993i	0.112571	−	0.638421i	−0.875354	−	0.483483i	$-0.839371\pi$
$709$	2.99743	−	16.9993i	0.112571	−	0.638421i	0.987924	−	0.154937i	$-0.0495176\pi$
$710$		0			0
$711$	−19.7480	+	12.5161i	−0.740609	+	0.469391i
$712$		0			0
$713$	−6.52820	−	17.9361i	−0.244483	−	0.671712i
$714$		0			0
$715$	9.34114	+	11.1323i	0.349339	+	0.416326i
$716$		0			0
$717$	−17.7606	+	0.366781i	−0.663281	+	0.0136977i
$718$		0			0
$719$	−13.2483	−	22.9467i	−0.494077	−	0.855767i	0.505900	−	0.862592i	$-0.331161\pi$
$719$	−13.2483	−	22.9467i	−0.494077	−	0.855767i	−0.999977	+	0.00682566i	$0.997827\pi$
$720$		0			0
$721$	−5.40910	+	9.36883i	−0.201445	+	0.348913i
$722$		0			0
$723$	−28.3058	+	24.7651i	−1.05270	+	0.921023i
$724$		0			0
$725$	5.53665	−	0.976262i	0.205626	−	0.0362574i
$726$		0			0
$727$	12.7022	−	15.1379i	0.471098	−	0.561433i	−0.477208	−	0.878791i	$-0.658351\pi$
$727$	12.7022	−	15.1379i	0.471098	−	0.561433i	0.948306	+	0.317357i	$0.102795\pi$
$728$		0			0
$729$	−16.2860	−	21.5352i	−0.603186	−	0.797601i
$730$		0			0
$731$	9.80043	+	8.22354i	0.362482	+	0.304159i
$732$		0			0
$733$	−2.32265	−	13.1724i	−0.0857892	−	0.486535i	−0.997184	−	0.0750004i	$-0.976104\pi$
$733$	−2.32265	−	13.1724i	−0.0857892	−	0.486535i	0.911394	−	0.411534i	$-0.135007\pi$
$734$		0			0
$735$	−8.71067	−	9.95605i	−0.321298	−	0.367234i
$736$		0			0
$737$	−21.4405	−	12.3787i	−0.789770	−	0.455974i
$738$		0			0
$739$	18.2507	−	10.5370i	0.671363	−	0.387611i	−0.125230	−	0.992128i	$-0.539967\pi$
$739$	18.2507	−	10.5370i	0.671363	−	0.387611i	0.796593	+	0.604516i	$0.206634\pi$
$740$		0			0
$741$	0.342078	+	16.5644i	0.0125665	+	0.608509i
$742$		0			0
$743$	−25.5261	+	21.4190i	−0.936463	+	0.785786i	−0.976966	−	0.213394i	$-0.931548\pi$
$743$	−25.5261	+	21.4190i	−0.936463	+	0.785786i	0.0405033	+	0.999179i	$0.487104\pi$
$744$		0			0
$745$	−2.51209	+	0.914326i	−0.0920358	+	0.0334983i
$746$		0			0
$747$	−26.3754	−	41.6153i	−0.965024	−	1.52262i
$748$		0			0
$749$	−7.90573	−	1.39399i	−0.288869	−	0.0509354i
$750$		0			0
$751$	13.9383	−	38.2951i	0.508615	−	1.39741i	−0.374051	−	0.927408i	$-0.622031\pi$
$751$	13.9383	−	38.2951i	0.508615	−	1.39741i	0.882666	−	0.470001i	$-0.155746\pi$
$752$		0			0
$753$	18.9016	+	15.2065i	0.688814	+	0.554156i
$754$		0			0
$755$	−30.7488			−1.11906
$756$		0			0
$757$	52.2535			1.89919			0.949593	−	0.313487i	$-0.101497\pi$
$757$	52.2535			1.89919			0.949593	+	0.313487i	$0.101497\pi$
$758$		0			0
$759$	13.1779	−	5.10690i	0.478328	−	0.185369i
$760$		0			0
$761$	9.53784	−	26.2050i	0.345746	−	0.949930i	−0.637948	−	0.770080i	$-0.720216\pi$
$761$	9.53784	−	26.2050i	0.345746	−	0.949930i	0.983694	−	0.179851i	$-0.0575614\pi$
$762$		0			0
$763$	15.4979	+	2.73271i	0.561063	+	0.0989306i
$764$		0			0
$765$	2.37123	−	17.6918i	0.0857319	−	0.639647i
$766$		0			0
$767$	−25.1525	+	9.15477i	−0.908205	+	0.330560i
$768$		0			0
$769$	8.86910	−	7.44206i	0.319828	−	0.268368i	−0.468712	−	0.883351i	$-0.655282\pi$
$769$	8.86910	−	7.44206i	0.319828	−	0.268368i	0.788540	+	0.614983i	$0.210837\pi$
$770$		0			0
$771$	−37.4151	+	22.6443i	−1.34747	+	0.815514i
$772$		0			0
$773$	2.47753	−	1.43040i	0.0891105	−	0.0514480i	−0.454783	−	0.890603i	$-0.650283\pi$
$773$	2.47753	−	1.43040i	0.0891105	−	0.0514480i	0.543893	+	0.839155i	$0.316950\pi$
$774$		0			0
$775$	7.87914	+	4.54902i	0.283027	+	0.163406i
$776$		0			0
$777$	−50.5544	+	9.99451i	−1.81363	+	0.358551i
$778$		0			0
$779$	4.25300	+	24.1200i	0.152380	+	0.864187i
$780$		0			0
$781$	−23.6343	−	19.8316i	−0.845703	−	0.709629i
$782$		0			0
$783$	6.11385	+	14.0279i	0.218491	+	0.501318i
$784$		0			0
$785$	2.41289	−	2.87557i	0.0861198	−	0.102634i
$786$		0			0
$787$	−20.8499	+	3.67640i	−0.743219	+	0.131050i	−0.532420	−	0.846480i	$-0.678717\pi$
$787$	−20.8499	+	3.67640i	−0.743219	+	0.131050i	−0.210798	+	0.977530i	$0.567606\pi$
$788$		0			0
$789$	−5.12445	−	1.74620i	−0.182435	−	0.0621662i
$790$		0			0
$791$	25.8580	−	44.7874i	0.919406	−	1.59246i
$792$		0			0
$793$	0.849468	+	1.47132i	0.0301655	+	0.0522482i
$794$		0			0
$795$	−14.6883	+	26.6992i	−0.520939	+	0.946922i
$796$		0			0
$797$	−17.6420	−	21.0249i	−0.624911	−	0.744740i	0.356996	−	0.934106i	$-0.383801\pi$
$797$	−17.6420	−	21.0249i	−0.624911	−	0.744740i	−0.981907	+	0.189366i	$0.939357\pi$
$798$		0			0
$799$	14.6361	+	40.2123i	0.517788	+	1.42261i
$800$		0			0
$801$	6.56100	+	7.19374i	0.231822	+	0.254178i
$802$		0			0
$803$	−4.15950	+	23.5897i	−0.146786	+	0.832462i
$804$		0			0
$805$	22.2860	+	8.11142i	0.785477	+	0.285890i
$806$		0			0
$807$	36.1394	+	5.60560i	1.27217	+	0.197327i
$808$		0			0
$809$			41.4523i			1.45738i	0.684842	+	0.728692i	$0.259871\pi$
$809$			41.4523i			1.45738i	−0.684842	+	0.728692i	$0.740129\pi$
$810$		0			0
$811$			42.2247i			1.48271i	0.671113	+	0.741355i	$0.265816\pi$
$811$			42.2247i			1.48271i	−0.671113	+	0.741355i	$0.734184\pi$
$812$		0			0
$813$	−2.73963	−	0.424946i	−0.0960831	−	0.0149035i
$814$		0			0
$815$	38.0525	+	13.8500i	1.33292	+	0.485144i
$816$		0			0
$817$	−1.54764	+	8.77708i	−0.0541449	+	0.307071i
$818$		0			0
$819$	40.0446	−	8.77956i	1.39927	−	0.306783i
$820$		0			0
$821$	10.9108	+	29.9771i	0.380789	+	1.04621i	0.971025	+	0.238978i	$0.0768122\pi$
$821$	10.9108	+	29.9771i	0.380789	+	1.04621i	−0.590237	+	0.807230i	$0.700966\pi$
$822$		0			0
$823$	−27.8560	−	33.1975i	−0.970999	−	1.15719i	−0.987546	−	0.157329i	$-0.949712\pi$
$823$	−27.8560	−	33.1975i	−0.970999	−	1.15719i	0.0165468	−	0.999863i	$-0.494733\pi$
$824$		0			0
$825$	−3.24710	+	5.90231i	−0.113049	+	0.205492i
$826$		0			0
$827$	−1.71924	−	2.97781i	−0.0597839	−	0.103549i	0.834584	−	0.550880i	$-0.185708\pi$
$827$	−1.71924	−	2.97781i	−0.0597839	−	0.103549i	−0.894368	+	0.447331i	$0.852374\pi$
$828$		0			0
$829$	−3.02819	+	5.24497i	−0.105173	+	0.182165i	−0.913809	−	0.406144i	$-0.866873\pi$
$829$	−3.02819	+	5.24497i	−0.105173	+	0.182165i	0.808636	+	0.588310i	$0.200206\pi$
$830$		0			0
$831$	15.4007	+	5.24792i	0.534246	+	0.182048i
$832$		0			0
$833$	−14.4788	+	2.55301i	−0.501662	+	0.0884565i
$834$		0			0
$835$	−26.6966	+	31.8158i	−0.923875	+	1.10103i
$836$		0			0
$837$	−7.01280	+	23.7497i	−0.242398	+	0.820910i
$838$		0			0
$839$	11.3788	+	9.54796i	0.392840	+	0.329632i	0.817718	−	0.575618i	$-0.195239\pi$
$839$	11.3788	+	9.54796i	0.392840	+	0.329632i	−0.424878	+	0.905251i	$0.639683\pi$
$840$		0			0
$841$	3.52980	+	20.0185i	0.121717	+	0.690293i
$842$		0			0
$843$	39.7670	−	7.86186i	1.36965	−	0.270777i
$844$		0			0
$845$	−5.26980	−	3.04252i	−0.181287	−	0.104666i
$846$		0			0
$847$	19.9788	−	11.5347i	0.686478	−	0.396339i
$848$		0			0
$849$	28.8083	−	17.4353i	0.988699	−	0.598378i
$850$		0			0
$851$	27.1021	−	22.7414i	0.929048	−	0.779564i
$852$		0			0
$853$	−13.5897	+	4.94624i	−0.465302	+	0.169356i	−0.564023	−	0.825759i	$-0.690747\pi$
$853$	−13.5897	+	4.94624i	−0.465302	+	0.169356i	0.0987209	+	0.995115i	$0.468525\pi$
$854$		0			0
$855$	11.4995	−	4.73180i	0.393274	−	0.161824i
$856$		0			0
$857$	42.4672	+	7.48812i	1.45065	+	0.255789i	0.842786	−	0.538249i	$-0.180914\pi$
$857$	42.4672	+	7.48812i	1.45065	+	0.255789i	0.607867	+	0.794039i	$0.292025\pi$
$858$		0			0
$859$	1.46996	−	4.03868i	0.0501544	−	0.137798i	−0.912086	−	0.409999i	$-0.865529\pi$
$859$	1.46996	−	4.03868i	0.0501544	−	0.137798i	0.962241	+	0.272201i	$0.0877514\pi$
$860$		0			0
$861$	56.5082	−	21.8989i	1.92580	−	0.746312i
$862$		0			0
$863$	6.00632			0.204458			0.102229	−	0.994761i	$-0.467403\pi$
$863$	6.00632			0.204458			0.102229	+	0.994761i	$0.467403\pi$
$864$		0			0
$865$	6.51586			0.221546
$866$		0			0
$867$	7.48507	+	6.02179i	0.254206	+	0.204511i
$868$		0			0
$869$	−5.43047	+	14.9201i	−0.184216	+	0.506130i
$870$		0			0
$871$	48.5544	+	8.56145i	1.64520	+	0.290094i
$872$		0			0
$873$	−34.2588	+	1.41559i	−1.15948	+	0.0479103i
$874$		0			0
$875$	−38.4448	+	13.9928i	−1.29967	+	0.473041i
$876$		0			0
$877$	1.42320	−	1.19421i	0.0480580	−	0.0403255i	−0.618442	−	0.785830i	$-0.712236\pi$
$877$	1.42320	−	1.19421i	0.0480580	−	0.0403255i	0.666500	+	0.745505i	$0.267792\pi$
$878$		0			0
$879$	−1.12627	−	54.5374i	−0.0379883	−	1.83950i
$880$		0			0
$881$	−6.71329	+	3.87592i	−0.226177	+	0.130583i	−0.608807	−	0.793318i	$-0.708352\pi$
$881$	−6.71329	+	3.87592i	−0.226177	+	0.130583i	0.382630	+	0.923902i	$0.375018\pi$
$882$		0			0
$883$	9.22295	+	5.32487i	0.310377	+	0.179196i	0.647095	−	0.762409i	$-0.275984\pi$
$883$	9.22295	+	5.32487i	0.310377	+	0.179196i	−0.336718	+	0.941605i	$0.609317\pi$
$884$		0			0
$885$	13.2284	+	15.1197i	0.444667	+	0.508242i
$886$		0			0
$887$	3.81854	+	21.6560i	0.128214	+	0.727138i	0.979347	+	0.202188i	$0.0648051\pi$
$887$	3.81854	+	21.6560i	0.128214	+	0.727138i	−0.851133	+	0.524951i	$0.824084\pi$
$888$		0			0
$889$	−21.8392	−	18.3252i	−0.732463	−	0.614609i
$890$		0			0
$891$	−17.6886	−	4.82835i	−0.592592	−	0.161756i
$892$		0			0
$893$	−19.1623	+	22.8368i	−0.641243	+	0.764203i
$894$		0			0
$895$	−16.9314	+	2.98546i	−0.565953	+	0.0997928i
$896$		0			0
$897$	−21.1823	+	18.5326i	−0.707256	+	0.618787i
$898$		0			0
$899$	7.01739	−	12.1545i	0.234043	−	0.405375i
$900$		0			0
$901$	16.9335	+	29.3297i	0.564137	+	0.977114i
$902$		0			0
$903$	22.0483	−	0.455329i	0.733723	−	0.0151524i
$904$		0			0
$905$	5.04352	+	6.01063i	0.167652	+	0.199800i
$906$		0			0
$907$	−7.63320	−	20.9721i	−0.253456	−	0.696366i	−0.999535	−	0.0305073i	$-0.990288\pi$
$907$	−7.63320	−	20.9721i	−0.253456	−	0.696366i	0.746078	−	0.665858i	$-0.231935\pi$
$908$		0			0
$909$	15.7179	+	8.22897i	0.521331	+	0.272938i
$910$		0			0
$911$	−2.00814	+	11.3887i	−0.0665327	+	0.377326i	0.933301	+	0.359095i	$0.116915\pi$
$911$	−2.00814	+	11.3887i	−0.0665327	+	0.377326i	−0.999834	+	0.0182309i	$0.994197\pi$
$912$		0			0
$913$	−31.4413	−	11.4437i	−1.04055	−	0.378731i
$914$		0			0
$915$	0.799293	−	0.993518i	0.0264238	−	0.0328447i
$916$		0			0
$917$			11.4564i			0.378322i
$918$		0			0
$919$		−	35.4086i		−	1.16802i	−0.811746	−	0.584011i	$-0.801483\pi$
$919$		−	35.4086i		−	1.16802i	0.811746	−	0.584011i	$-0.198517\pi$
$920$		0			0
$921$	1.11675	+	2.88168i	0.0367981	+	0.0949545i
$922$		0			0
$923$	57.7362	+	21.0143i	1.90041	+	0.691693i
$924$		0			0
$925$	−2.92837	+	16.6076i	−0.0962842	+	0.546055i
$926$		0			0
$927$	−5.88376	+	7.63088i	−0.193248	+	0.250631i
$928$		0			0
$929$	−4.75085	−	13.0528i	−0.155870	−	0.428250i	0.837036	−	0.547147i	$-0.184286\pi$
$929$	−4.75085	−	13.0528i	−0.155870	−	0.428250i	−0.992907	+	0.118897i	$0.962064\pi$
$930$		0			0
$931$	−6.58350	−	7.84591i	−0.215765	−	0.257139i
$932$		0			0
$933$	9.87650	+	16.3189i	0.323342	+	0.534257i
$934$		0			0
$935$	−6.06098	−	10.4979i	−0.198215	−	0.343319i
$936$		0			0
$937$	2.62506	−	4.54673i	0.0857569	−	0.148535i	−0.819957	−	0.572426i	$-0.806002\pi$
$937$	2.62506	−	4.54673i	0.0857569	−	0.148535i	0.905714	+	0.423890i	$0.139336\pi$
$938$		0			0
$939$	6.45909	+	32.6715i	0.210785	+	1.06619i
$940$		0			0
$941$	24.7575	−	4.36542i	0.807072	−	0.142309i	0.245135	−	0.969489i	$-0.421168\pi$
$941$	24.7575	−	4.36542i	0.807072	−	0.142309i	0.561936	+	0.827180i	$0.310057\pi$
$942$		0			0
$943$	−26.7441	+	31.8724i	−0.870907	+	1.03791i
$944$		0			0
$945$	−17.0046	−	25.6433i	−0.553160	−	0.834177i
$946$		0			0
$947$	26.3507	+	22.1108i	0.856282	+	0.718506i	0.961164	−	0.275979i	$-0.0890021\pi$
$947$	26.3507	+	22.1108i	0.856282	+	0.718506i	−0.104882	+	0.994485i	$0.533447\pi$
$948$		0			0
$949$	−8.28350	−	46.9781i	−0.268894	−	1.52497i
$950$		0			0
$951$	12.3386	−	36.2094i	0.400108	−	1.17417i
$952$		0			0
$953$	−6.30853	−	3.64223i	−0.204353	−	0.117984i	0.394331	−	0.918968i	$-0.370976\pi$
$953$	−6.30853	−	3.64223i	−0.204353	−	0.117984i	−0.598684	+	0.800985i	$0.704310\pi$
$954$		0			0
$955$	−2.21463	+	1.27862i	−0.0716637	+	0.0413751i
$956$		0			0
$957$	9.10500	+	5.00902i	0.294323	+	0.161919i
$958$		0			0
$959$	15.5505	−	13.0484i	0.502151	−	0.421355i
$960$		0			0
$961$	−7.78805	+	2.83462i	−0.251227	+	0.0914393i
$962$		0			0
$963$	−6.81432	−	2.16606i	−0.219589	−	0.0698005i
$964$		0			0
$965$	−28.8566	−	5.08819i	−0.928926	−	0.163795i
$966$		0			0
$967$	−16.9994	+	46.7055i	−0.546664	+	1.50195i	0.291524	+	0.956564i	$0.405838\pi$
$967$	−16.9994	+	46.7055i	−0.546664	+	1.50195i	−0.838187	+	0.545383i	$0.816384\pi$
$968$		0			0
$969$	2.11831	−	13.6567i	0.0680498	−	0.438717i
$970$		0			0
$971$	−10.4064			−0.333956			−0.166978	−	0.985961i	$-0.553401\pi$
$971$	−10.4064			−0.333956			−0.166978	+	0.985961i	$0.553401\pi$
$972$		0			0
$973$	−63.3362			−2.03047
$974$		0			0
$975$	2.05631	−	13.2571i	0.0658547	−	0.424566i
$976$		0			0
$977$	5.41567	−	14.8794i	0.173263	−	0.476036i	−0.822417	−	0.568885i	$-0.807375\pi$
$977$	5.41567	−	14.8794i	0.173263	−	0.476036i	0.995680	+	0.0928489i	$0.0295974\pi$
$978$		0			0
$979$	6.51154	+	1.14816i	0.208110	+	0.0366954i
$980$		0			0
$981$	13.3584	+	4.24623i	0.426501	+	0.135572i
$982$		0			0
$983$	−11.6932	+	4.25598i	−0.372956	+	0.135745i	−0.521696	−	0.853132i	$-0.674700\pi$
$983$	−11.6932	+	4.25598i	−0.372956	+	0.135745i	0.148740	+	0.988876i	$0.452478\pi$
$984$		0			0
$985$	0.765516	−	0.642344i	0.0243914	−	0.0204668i
$986$		0			0
$987$	64.6303	+	35.5557i	2.05721	+	1.13175i
$988$		0			0
$989$	−13.1119	+	7.57013i	−0.416933	+	0.240716i
$990$		0			0
$991$	31.3417	+	18.0951i	0.995601	+	0.574811i	0.906944	−	0.421251i	$-0.138409\pi$
$991$	31.3417	+	18.0951i	0.995601	+	0.574811i	0.0886575	+	0.996062i	$0.471742\pi$
$992$		0			0
$993$	−7.55873	+	22.1821i	−0.239869	+	0.703929i
$994$		0			0
$995$	4.92299	+	27.9197i	0.156069	+	0.885113i
$996$		0			0
$997$	20.8072	+	17.4593i	0.658971	+	0.552942i	0.909778	−	0.415095i	$-0.136252\pi$
$997$	20.8072	+	17.4593i	0.658971	+	0.552942i	−0.250807	+	0.968037i	$0.580696\pi$
$998$		0			0
$999$	−45.8125	+	2.84151i	−1.44944	+	0.0899014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.335.4	yes	36
4.3	odd	2	inner	432.2.be.a.335.3	✓	36
27.5	odd	18	inner	432.2.be.a.383.3	yes	36
108.59	even	18	inner	432.2.be.a.383.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.335.3	✓	36	4.3	odd	2	inner
432.2.be.a.335.4	yes	36	1.1	even	1	trivial
432.2.be.a.383.3	yes	36	27.5	odd	18	inner
432.2.be.a.383.4	yes	36	108.59	even	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.265485 - 1.71158i) q^{3} +(0.601308 - 1.65208i) q^{5} +(-3.31695 - 0.584867i) q^{7} +(-2.85904 - 0.908799i) q^{9} +O(q^{10})\)	\(q+(0.265485 - 1.71158i) q^{3} +(0.601308 - 1.65208i) q^{5} +(-3.31695 - 0.584867i) q^{7} +(-2.85904 - 0.908799i) q^{9} +(-1.91444 + 0.696801i) q^{11} +(3.10802 - 2.60794i) q^{13} +(-2.66804 - 1.46779i) q^{15} +(-2.93090 + 1.69216i) q^{17} +(-2.04178 - 1.17882i) q^{19} +(-1.88165 + 5.52196i) q^{21} +(-0.695477 - 3.94425i) q^{23} +(1.46242 + 1.22712i) q^{25} +(-2.31452 + 4.65220i) q^{27} +(1.89297 - 2.25596i) q^{29} +(4.69332 - 0.827559i) q^{31} +(0.684376 + 3.46172i) q^{33} +(-2.96076 + 5.12818i) q^{35} +(4.41679 + 7.65010i) q^{37} +(-3.63857 - 6.01200i) q^{39} +(-6.67751 - 7.95795i) q^{41} +(-1.29292 - 3.55227i) q^{43} +(-3.22057 + 4.17689i) q^{45} +(2.19570 - 12.4524i) q^{47} +(4.08223 + 1.48581i) q^{49} +(2.11816 + 5.46573i) q^{51} -10.0071i q^{53} +3.58181i q^{55} +(-2.55971 + 3.18171i) q^{57} +(-6.19943 - 2.25641i) q^{59} +(-0.0727139 + 0.412381i) q^{61} +(8.95174 + 4.68660i) q^{63} +(-2.43965 - 6.70287i) q^{65} +(7.81114 + 9.30896i) q^{67} +(-6.93555 + 0.143229i) q^{69} +(7.57186 + 13.1148i) q^{71} +(5.87873 - 10.1823i) q^{73} +(2.48857 - 2.17728i) q^{75} +(6.75765 - 1.19156i) q^{77} +(5.00952 - 5.97012i) q^{79} +(7.34817 + 5.19658i) q^{81} +(12.5809 + 10.5566i) q^{83} +(1.03320 + 5.85959i) q^{85} +(-3.35870 - 3.83890i) q^{87} +(-2.81064 - 1.62273i) q^{89} +(-11.8344 + 6.83262i) q^{91} +(-0.170430 - 8.25272i) q^{93} +(-3.17524 + 2.66435i) q^{95} +(10.7401 - 3.90906i) q^{97} +(6.10672 - 0.252332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^5 - 12 * q^9	\( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) \) 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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