LMFDB - Embedded newform 432.2.l.b.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	432.107
Dual form			432.2.l.b.323.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900149 - 1.09075i) q^{2} +(-0.379462 + 1.96367i) q^{4} +(1.29039 - 1.29039i) q^{5} -3.83003 q^{7} +(2.48344 - 1.35370i) q^{8} +O(q^{10})$	\(q+(-0.900149 - 1.09075i) q^{2} +(-0.379462 + 1.96367i) q^{4} +(1.29039 - 1.29039i) q^{5} -3.83003 q^{7} +(2.48344 - 1.35370i) q^{8} +(-2.56904 - 0.245948i) q^{10} +(-1.73926 - 1.73926i) q^{11} +(0.145981 - 0.145981i) q^{13} +(3.44760 + 4.17760i) q^{14} +(-3.71202 - 1.49028i) q^{16} +2.19496i q^{17} +(-4.91334 - 4.91334i) q^{19} +(2.04426 + 3.02357i) q^{20} +(-0.331501 + 3.46269i) q^{22} -9.44891i q^{23} +1.66976i q^{25} +(-0.290633 - 0.0278238i) q^{26} +(1.45335 - 7.52093i) q^{28} +(-5.42030 - 5.42030i) q^{29} +4.73544i q^{31} +(1.71585 + 5.39035i) q^{32} +(2.39415 - 1.97579i) q^{34} +(-4.94226 + 4.94226i) q^{35} +(0.955378 + 0.955378i) q^{37} +(-0.936477 + 9.78196i) q^{38} +(1.45782 - 4.95143i) q^{40} -7.05050 q^{41} +(-1.66838 + 1.66838i) q^{43} +(4.07532 - 2.75535i) q^{44} +(-10.3064 + 8.50543i) q^{46} -4.20126 q^{47} +7.66916 q^{49} +(1.82129 - 1.50304i) q^{50} +(0.231265 + 0.342053i) q^{52} +(3.96958 - 3.96958i) q^{53} -4.48866 q^{55} +(-9.51167 + 5.18472i) q^{56} +(-1.03310 + 10.7913i) q^{58} +(5.64431 + 5.64431i) q^{59} +(0.214341 - 0.214341i) q^{61} +(5.16517 - 4.26260i) q^{62} +(4.33499 - 6.72368i) q^{64} -0.376746i q^{65} +(3.96018 + 3.96018i) q^{67} +(-4.31018 - 0.832904i) q^{68} +(9.83952 + 0.941987i) q^{70} +0.302489i q^{71} +1.89455i q^{73} +(0.182094 - 1.90206i) q^{74} +(11.5126 - 7.78376i) q^{76} +(6.66142 + 6.66142i) q^{77} -14.5211i q^{79} +(-6.71302 + 2.86692i) q^{80} +(6.34650 + 7.69032i) q^{82} +(6.41307 - 6.41307i) q^{83} +(2.83236 + 2.83236i) q^{85} +(3.32156 + 0.317990i) q^{86} +(-6.67379 - 1.96492i) q^{88} -16.5738 q^{89} +(-0.559112 + 0.559112i) q^{91} +(18.5546 + 3.58551i) q^{92} +(3.78177 + 4.58252i) q^{94} -12.6803 q^{95} +17.2736 q^{97} +(-6.90339 - 8.36512i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) $ 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.900149	−	1.09075i	−0.636502	−	0.771275i
$2$	−0.900149	−	1.09075i	−0.636502	−	0.771275i
$3$		0			0
$3$		0			0
$4$	−0.379462	+	1.96367i	−0.189731	+	0.981836i
$5$	1.29039	−	1.29039i	0.577082	−	0.577082i	−0.357016	−	0.934098i	$-0.616206\pi$
$5$	1.29039	−	1.29039i	0.577082	−	0.577082i	0.934098	+	0.357016i	$0.116206\pi$
$6$		0			0
$7$	−3.83003			−1.44762			−0.723808	−	0.690001i	$-0.757610\pi$
$7$	−3.83003			−1.44762			−0.723808	+	0.690001i	$0.757610\pi$
$8$	2.48344	−	1.35370i	0.878030	−	0.478605i
$9$		0			0
$10$	−2.56904	−	0.245948i	−0.812403	−	0.0777754i
$11$	−1.73926	−	1.73926i	−0.524407	−	0.524407i	0.394493	−	0.918899i	$-0.370920\pi$
$11$	−1.73926	−	1.73926i	−0.524407	−	0.524407i	−0.918899	+	0.394493i	$0.870920\pi$
$12$		0			0
$13$	0.145981	−	0.145981i	0.0404879	−	0.0404879i	−0.686573	−	0.727061i	$-0.740886\pi$
$13$	0.145981	−	0.145981i	0.0404879	−	0.0404879i	0.727061	+	0.686573i	$0.240886\pi$
$14$	3.44760	+	4.17760i	0.921410	+	1.11651i
$15$		0			0
$16$	−3.71202	−	1.49028i	−0.928004	−	0.372570i
$17$			2.19496i			0.532355i	0.963924	+	0.266178i	$0.0857608\pi$
$17$			2.19496i			0.532355i	−0.963924	+	0.266178i	$0.914239\pi$
$18$		0			0
$19$	−4.91334	−	4.91334i	−1.12720	−	1.12720i	−0.990631	−	0.136567i	$-0.956393\pi$
$19$	−4.91334	−	4.91334i	−1.12720	−	1.12720i	−0.136567	−	0.990631i	$-0.543607\pi$
$20$	2.04426	+	3.02357i	0.457110	+	0.676090i
$21$		0			0
$22$	−0.331501	+	3.46269i	−0.0706762	+	0.738248i
$23$		−	9.44891i		−	1.97023i	−0.171884	−	0.985117i	$-0.554985\pi$
$23$		−	9.44891i		−	1.97023i	0.171884	−	0.985117i	$-0.445015\pi$
$24$		0			0
$25$			1.66976i			0.333953i
$26$	−0.290633	−	0.0278238i	−0.0569979	−	0.00545670i
$27$		0			0
$28$	1.45335	−	7.52093i	0.274658	−	1.42132i
$29$	−5.42030	−	5.42030i	−1.00652	−	1.00652i	−0.999979	−	0.00654528i	$-0.997917\pi$
$29$	−5.42030	−	5.42030i	−1.00652	−	1.00652i	−0.00654528	−	0.999979i	$-0.502083\pi$
$30$		0			0
$31$			4.73544i			0.850509i	0.905074	+	0.425255i	$0.139815\pi$
$31$			4.73544i			0.850509i	−0.905074	+	0.425255i	$0.860185\pi$
$32$	1.71585	+	5.39035i	0.303322	+	0.952888i
$33$		0			0
$34$	2.39415	−	1.97579i	0.410593	−	0.338845i
$35$	−4.94226	+	4.94226i	−0.835394	+	0.835394i
$36$		0			0
$37$	0.955378	+	0.955378i	0.157063	+	0.157063i	0.781264	−	0.624201i	$-0.214575\pi$
$37$	0.955378	+	0.955378i	0.157063	+	0.157063i	−0.624201	+	0.781264i	$0.714575\pi$
$38$	−0.936477	+	9.78196i	−0.151917	+	1.58684i
$39$		0			0
$40$	1.45782	−	4.95143i	0.230501	−	0.782890i
$41$	−7.05050			−1.10110			−0.550551	−	0.834801i	$-0.685583\pi$
$41$	−7.05050			−1.10110			−0.550551	+	0.834801i	$0.685583\pi$
$42$		0			0
$43$	−1.66838	+	1.66838i	−0.254425	+	0.254425i	−0.822782	−	0.568357i	$-0.807579\pi$
$43$	−1.66838	+	1.66838i	−0.254425	+	0.254425i	0.568357	+	0.822782i	$0.307579\pi$
$44$	4.07532	−	2.75535i	0.614378	−	0.415385i
$45$		0			0
$46$	−10.3064	+	8.50543i	−1.51959	+	1.25406i
$47$	−4.20126			−0.612817			−0.306409	−	0.951900i	$-0.599127\pi$
$47$	−4.20126			−0.612817			−0.306409	+	0.951900i	$0.599127\pi$
$48$		0			0
$49$	7.66916			1.09559
$50$	1.82129	−	1.50304i	0.257569	−	0.212561i
$51$		0			0
$52$	0.231265	+	0.342053i	0.0320706	+	0.0474343i
$53$	3.96958	−	3.96958i	0.545264	−	0.545264i	−0.379803	−	0.925067i	$-0.624008\pi$
$53$	3.96958	−	3.96958i	0.545264	−	0.545264i	0.925067	+	0.379803i	$0.124008\pi$
$54$		0			0
$55$	−4.48866			−0.605251
$56$	−9.51167	+	5.18472i	−1.27105	+	0.692837i
$57$		0			0
$58$	−1.03310	+	10.7913i	−0.135653	+	1.41696i
$59$	5.64431	+	5.64431i	0.734827	+	0.734827i	0.971572	−	0.236745i	$-0.0760807\pi$
$59$	5.64431	+	5.64431i	0.734827	+	0.734827i	−0.236745	+	0.971572i	$0.576081\pi$
$60$		0			0
$61$	0.214341	−	0.214341i	0.0274436	−	0.0274436i	−0.693252	−	0.720695i	$-0.743823\pi$
$61$	0.214341	−	0.214341i	0.0274436	−	0.0274436i	0.720695	+	0.693252i	$0.243823\pi$
$62$	5.16517	−	4.26260i	0.655977	−	0.541351i
$63$		0			0
$64$	4.33499	−	6.72368i	0.541874	−	0.840460i
$65$		−	0.376746i		−	0.0467296i
$66$		0			0
$67$	3.96018	+	3.96018i	0.483813	+	0.483813i	0.906347	−	0.422534i	$-0.138859\pi$
$67$	3.96018	+	3.96018i	0.483813	+	0.483813i	−0.422534	+	0.906347i	$0.638859\pi$
$68$	−4.31018	−	0.832904i	−0.522686	−	0.101004i
$69$		0			0
$70$	9.83952	+	0.941987i	1.17605	+	0.112589i
$71$			0.302489i			0.0358989i	0.999839	+	0.0179494i	$0.00571379\pi$
$71$			0.302489i			0.0358989i	−0.999839	+	0.0179494i	$0.994286\pi$
$72$		0			0
$73$			1.89455i			0.221740i	0.993835	+	0.110870i	$0.0353637\pi$
$73$			1.89455i			0.221740i	−0.993835	+	0.110870i	$0.964636\pi$
$74$	0.182094	−	1.90206i	0.0211680	−	0.221110i
$75$		0			0
$76$	11.5126	−	7.78376i	1.32059	−	0.892859i
$77$	6.66142	+	6.66142i	0.759140	+	0.759140i
$78$		0			0
$79$		−	14.5211i		−	1.63375i	−0.576814	−	0.816876i	$-0.695704\pi$
$79$		−	14.5211i		−	1.63375i	0.576814	−	0.816876i	$-0.304296\pi$
$80$	−6.71302	+	2.86692i	−0.750538	+	0.320531i
$81$		0			0
$82$	6.34650	+	7.69032i	0.700854	+	0.849253i
$83$	6.41307	−	6.41307i	0.703926	−	0.703926i	−0.261325	−	0.965251i	$-0.584159\pi$
$83$	6.41307	−	6.41307i	0.703926	−	0.703926i	0.965251	+	0.261325i	$0.0841594\pi$
$84$		0			0
$85$	2.83236	+	2.83236i	0.307213	+	0.307213i
$86$	3.32156	+	0.317990i	0.358173	+	0.0342898i
$87$		0			0
$88$	−6.67379	−	1.96492i	−0.711429	−	0.209461i
$89$	−16.5738			−1.75682			−0.878410	−	0.477908i	$-0.841395\pi$
$89$	−16.5738			−1.75682			−0.878410	+	0.477908i	$0.841395\pi$
$90$		0			0
$91$	−0.559112	+	0.559112i	−0.0586109	+	0.0586109i
$92$	18.5546	+	3.58551i	1.93445	+	0.373815i
$93$		0			0
$94$	3.78177	+	4.58252i	0.390059	+	0.472651i
$95$	−12.6803			−1.30097
$96$		0			0
$97$	17.2736			1.75387			0.876934	−	0.480611i	$-0.159585\pi$
$97$	17.2736			1.75387			0.876934	+	0.480611i	$0.159585\pi$
$98$	−6.90339	−	8.36512i	−0.697347	−	0.845004i
$99$		0			0
$100$	−3.27887	−	0.633612i	−0.327887	−	0.0633612i
$101$	11.3262	−	11.3262i	1.12699	−	1.12699i	0.136332	−	0.990663i	$-0.456469\pi$
$101$	11.3262	−	11.3262i	1.12699	−	1.12699i	0.990663	−	0.136332i	$-0.0435313\pi$
$102$		0			0
$103$	1.09302			0.107698			0.0538490	−	0.998549i	$-0.482851\pi$
$103$	1.09302			0.107698			0.0538490	+	0.998549i	$0.482851\pi$
$104$	0.164921	−	0.560150i	0.0161719	−	0.0549273i
$105$		0			0
$106$	−7.90303	−	0.756597i	−0.767610	−	0.0734872i
$107$	11.1443	+	11.1443i	1.07736	+	1.07736i	0.996745	+	0.0806138i	$0.0256880\pi$
$107$	11.1443	+	11.1443i	1.07736	+	1.07736i	0.0806138	+	0.996745i	$0.474312\pi$
$108$		0			0
$109$	11.4668	−	11.4668i	1.09832	−	1.09832i	0.103711	−	0.994608i	$-0.466928\pi$
$109$	11.4668	−	11.4668i	1.09832	−	1.09832i	0.994608	−	0.103711i	$-0.0330715\pi$
$110$	4.04047	+	4.89600i	0.385244	+	0.466815i
$111$		0			0
$112$	14.2171	+	5.70782i	1.34339	+	0.539338i
$113$		−	12.8436i		−	1.20822i	−0.796901	−	0.604110i	$-0.793529\pi$
$113$		−	12.8436i		−	1.20822i	0.796901	−	0.604110i	$-0.206471\pi$
$114$		0			0
$115$	−12.1928	−	12.1928i	−1.13699	−	1.13699i
$116$	12.7005	−	8.58689i	1.17921	−	0.797272i
$117$		0			0
$118$	1.07580	−	11.2372i	0.0990352	−	1.03447i
$119$		−	8.40676i		−	0.770646i
$120$		0			0
$121$		−	4.94995i		−	0.449995i
$122$	−0.426731	−	0.0408531i	−0.0386344	−	0.00369867i
$123$		0			0
$124$	−9.29884	−	1.79692i	−0.835061	−	0.161368i
$125$	8.60663	+	8.60663i	0.769800	+	0.769800i
$126$		0			0
$127$			10.1231i			0.898278i	0.893462	+	0.449139i	$0.148269\pi$
$127$			10.1231i			0.898278i	−0.893462	+	0.449139i	$0.851731\pi$
$128$	−11.2360	+	1.32393i	−0.993130	+	0.117020i
$129$		0			0
$130$	−0.410935	+	0.339128i	−0.0360414	+	0.0297435i
$131$	2.52933	−	2.52933i	0.220989	−	0.220989i	−0.587926	−	0.808915i	$-0.700055\pi$
$131$	2.52933	−	2.52933i	0.220989	−	0.220989i	0.808915	+	0.587926i	$0.200055\pi$
$132$		0			0
$133$	18.8183	+	18.8183i	1.63175	+	1.63175i
$134$	0.754805	−	7.88431i	0.0652052	−	0.681101i
$135$		0			0
$136$	2.97131	+	5.45105i	0.254788	+	0.467424i
$137$	−1.35887			−0.116096			−0.0580479	−	0.998314i	$-0.518488\pi$
$137$	−1.35887			−0.116096			−0.0580479	+	0.998314i	$0.518488\pi$
$138$		0			0
$139$	−8.78047	+	8.78047i	−0.744750	+	0.744750i	−0.973488	−	0.228738i	$-0.926540\pi$
$139$	−8.78047	+	8.78047i	−0.744750	+	0.744750i	0.228738	+	0.973488i	$0.426540\pi$
$140$	−7.82957	−	11.5804i	−0.661719	−	0.978720i
$141$		0			0
$142$	0.329940	−	0.272285i	0.0276879	−	0.0228497i
$143$	−0.507798			−0.0424642
$144$		0			0
$145$	−13.9886			−1.16169
$146$	2.06647	−	1.70537i	0.171022	−	0.141138i
$147$		0			0
$148$	−2.23858	+	1.51352i	−0.184010	+	0.124410i
$149$	−2.19665	+	2.19665i	−0.179957	+	0.179957i	−0.791337	−	0.611380i	$-0.790615\pi$
$149$	−2.19665	+	2.19665i	−0.179957	+	0.179957i	0.611380	+	0.791337i	$0.290615\pi$
$150$		0			0
$151$	−16.2173			−1.31974			−0.659872	−	0.751378i	$-0.729389\pi$
$151$	−16.2173			−1.31974			−0.659872	+	0.751378i	$0.729389\pi$
$152$	−18.8532	−	5.55082i	−1.52920	−	0.450231i
$153$		0			0
$154$	1.26966	−	13.2622i	0.102312	−	1.06870i
$155$	6.11058	+	6.11058i	0.490814	+	0.490814i
$156$		0			0
$157$	1.57749	−	1.57749i	0.125898	−	0.125898i	−0.641350	−	0.767248i	$-0.721626\pi$
$157$	1.57749	−	1.57749i	0.125898	−	0.125898i	0.767248	+	0.641350i	$0.221626\pi$
$158$	−15.8389	+	13.0712i	−1.26007	+	1.03989i
$159$		0			0
$160$	9.16980	+	4.74155i	0.724936	+	0.374853i
$161$			36.1897i			2.85214i
$162$		0			0
$163$	6.17632	+	6.17632i	0.483767	+	0.483767i	0.906332	−	0.422565i	$-0.138870\pi$
$163$	6.17632	+	6.17632i	0.483767	+	0.483767i	−0.422565	+	0.906332i	$0.638870\pi$
$164$	2.67540	−	13.8449i	0.208914	−	1.08110i
$165$		0			0
$166$	−12.7678	−	1.22232i	−0.990971	−	0.0948707i
$167$		−	10.1994i		−	0.789255i	−0.918841	−	0.394628i	$-0.870874\pi$
$167$		−	10.1994i		−	0.789255i	0.918841	−	0.394628i	$-0.129126\pi$
$168$		0			0
$169$			12.9574i			0.996721i
$170$	0.539844	−	5.63894i	0.0414042	−	0.432487i
$171$		0			0
$172$	−2.64306	−	3.90923i	−0.201531	−	0.298076i
$173$	8.47299	+	8.47299i	0.644189	+	0.644189i	0.951583	−	0.307393i	$-0.0994567\pi$
$173$	8.47299	+	8.47299i	0.644189	+	0.644189i	−0.307393	+	0.951583i	$0.599457\pi$
$174$		0			0
$175$		−	6.39525i		−	0.483435i
$176$	3.86418	+	9.04815i	0.291273	+	0.682030i
$177$		0			0
$178$	14.9189	+	18.0778i	1.11822	+	1.35499i
$179$	−11.7516	+	11.7516i	−0.878359	+	0.878359i	−0.993365	−	0.115006i	$-0.963311\pi$
$179$	−11.7516	+	11.7516i	−0.878359	+	0.878359i	0.115006	+	0.993365i	$0.463311\pi$
$180$		0			0
$181$	−4.75300	−	4.75300i	−0.353288	−	0.353288i	0.508044	−	0.861331i	$-0.330369\pi$
$181$	−4.75300	−	4.75300i	−0.353288	−	0.353288i	−0.861331	+	0.508044i	$0.830369\pi$
$182$	1.11314	+	0.106566i	0.0825111	+	0.00789920i
$183$		0			0
$184$	−12.7910	−	23.4658i	−0.942965	−	1.72993i
$185$	2.46563			0.181277
$186$		0			0
$187$	3.81760	−	3.81760i	0.279171	−	0.279171i
$188$	1.59422	−	8.24991i	0.116271	−	0.601686i
$189$		0			0
$190$	11.4142	+	13.8310i	0.828071	+	1.00341i
$191$	11.3623			0.822144			0.411072	−	0.911603i	$-0.365154\pi$
$191$	11.3623			0.822144			0.411072	+	0.911603i	$0.365154\pi$
$192$		0			0
$193$	−17.8411			−1.28423			−0.642114	−	0.766609i	$-0.721942\pi$
$193$	−17.8411			−1.28423			−0.642114	+	0.766609i	$0.721942\pi$
$194$	−15.5488	−	18.8411i	−1.11634	−	1.35272i
$195$		0			0
$196$	−2.91016	+	15.0597i	−0.207868	+	1.07569i
$197$	6.93546	−	6.93546i	0.494131	−	0.494131i	−0.415474	−	0.909605i	$-0.636384\pi$
$197$	6.93546	−	6.93546i	0.494131	−	0.494131i	0.909605	+	0.415474i	$0.136384\pi$
$198$		0			0
$199$	17.9531			1.27266			0.636331	−	0.771416i	$-0.280451\pi$
$199$	17.9531			1.27266			0.636331	+	0.771416i	$0.280451\pi$
$200$	2.26036	+	4.14676i	0.159831	+	0.293220i
$201$		0			0
$202$	−22.5492	−	2.15875i	−1.58656	−	0.151889i
$203$	20.7599	+	20.7599i	1.45706	+	1.45706i
$204$		0			0
$205$	−9.09793	+	9.09793i	−0.635427	+	0.635427i
$206$	−0.983877	−	1.19220i	−0.0685499	−	0.0830648i
$207$		0			0
$208$	−0.759437	+	0.324332i	−0.0526575	+	0.0224883i
$209$			17.0912i			1.18222i
$210$		0			0
$211$	5.74398	+	5.74398i	0.395432	+	0.395432i	0.876618	−	0.481186i	$-0.159794\pi$
$211$	5.74398	+	5.74398i	0.395432	+	0.395432i	−0.481186	+	0.876618i	$0.659794\pi$
$212$	6.28865	+	9.30126i	0.431906	+	0.638813i
$213$		0			0
$214$	2.12409	−	22.1871i	0.145200	−	1.51668i
$215$			4.30573i			0.293648i
$216$		0			0
$217$		−	18.1369i		−	1.23121i
$218$	−22.8292	−	2.18555i	−1.54619	−	0.148024i
$219$		0			0
$220$	1.70328	−	8.81426i	0.114835	−	0.594258i
$221$	0.320422	+	0.320422i	0.0215539	+	0.0215539i
$222$		0			0
$223$		−	6.88159i		−	0.460825i	−0.973093	−	0.230413i	$-0.925992\pi$
$223$		−	6.88159i		−	0.460825i	0.973093	−	0.230413i	$-0.0740076\pi$
$224$	−6.57176	−	20.6452i	−0.439094	−	1.37942i
$225$		0			0
$226$	−14.0091	+	11.5611i	−0.931871	+	0.769034i
$227$	−12.7921	+	12.7921i	−0.849041	+	0.849041i	−0.990014	−	0.140972i	$-0.954977\pi$
$227$	−12.7921	+	12.7921i	−0.849041	+	0.849041i	0.140972	+	0.990014i	$0.454977\pi$
$228$		0			0
$229$	−19.4425	−	19.4425i	−1.28479	−	1.28479i	−0.937907	−	0.346887i	$-0.887239\pi$
$229$	−19.4425	−	19.4425i	−1.28479	−	1.28479i	−0.346887	−	0.937907i	$-0.612761\pi$
$230$	−2.32394	+	24.2747i	−0.153236	+	1.60062i
$231$		0			0
$232$	−20.7985	−	6.12355i	−1.36549	−	0.402031i
$233$	7.38023			0.483495			0.241747	−	0.970339i	$-0.422279\pi$
$233$	7.38023			0.483495			0.241747	+	0.970339i	$0.422279\pi$
$234$		0			0
$235$	−5.42129	+	5.42129i	−0.353646	+	0.353646i
$236$	−13.2254	+	8.94177i	−0.860899	+	0.582060i
$237$		0			0
$238$	−9.16966	+	7.56734i	−0.594381	+	0.490518i
$239$	−17.8252			−1.15302			−0.576508	−	0.817092i	$-0.695585\pi$
$239$	−17.8252			−1.15302			−0.576508	+	0.817092i	$0.695585\pi$
$240$		0			0
$241$	−8.04278			−0.518081			−0.259040	−	0.965866i	$-0.583406\pi$
$241$	−8.04278			−0.518081			−0.259040	+	0.965866i	$0.583406\pi$
$242$	−5.39915	+	4.45569i	−0.347070	+	0.286423i
$243$		0			0
$244$	0.339561	+	0.502230i	0.0217382	+	0.0321520i
$245$	9.89624	−	9.89624i	0.632248	−	0.632248i
$246$		0			0
$247$	−1.43451			−0.0912757
$248$	6.41036	+	11.7602i	0.407058	+	0.746773i
$249$		0			0
$250$	1.64041	−	17.1349i	0.103749	−	1.08371i
$251$	−12.7562	−	12.7562i	−0.805163	−	0.805163i	0.178734	−	0.983897i	$-0.442800\pi$
$251$	−12.7562	−	12.7562i	−0.805163	−	0.805163i	−0.983897	+	0.178734i	$0.942800\pi$
$252$		0			0
$253$	−16.4341	+	16.4341i	−1.03320	+	1.03320i
$254$	11.0417	−	9.11228i	0.692820	−	0.571755i
$255$		0			0
$256$	11.5581	+	11.0639i	0.722383	+	0.691493i
$257$		−	6.97550i		−	0.435120i	−0.976047	−	0.217560i	$-0.930190\pi$
$257$		−	6.97550i		−	0.435120i	0.976047	−	0.217560i	$-0.0698098\pi$
$258$		0			0
$259$	−3.65913	−	3.65913i	−0.227367	−	0.227367i
$260$	0.739806	+	0.142961i	0.0458808	+	0.00886607i
$261$		0			0
$262$	−5.03564	−	0.482088i	−0.311103	−	0.0297835i
$263$		−	15.2610i		−	0.941036i	−0.882390	−	0.470518i	$-0.844067\pi$
$263$		−	15.2610i		−	0.941036i	0.882390	−	0.470518i	$-0.155933\pi$
$264$		0			0
$265$		−	10.2447i		−	0.629324i
$266$	3.58674	−	37.4652i	0.219917	−	2.29714i
$267$		0			0
$268$	−9.27924	+	6.27376i	−0.566820	+	0.383231i
$269$	−9.11506	−	9.11506i	−0.555755	−	0.555755i	0.372341	−	0.928096i	$-0.378555\pi$
$269$	−9.11506	−	9.11506i	−0.555755	−	0.555755i	−0.928096	+	0.372341i	$0.878555\pi$
$270$		0			0
$271$			3.90936i			0.237477i	0.992926	+	0.118738i	$0.0378850\pi$
$271$			3.90936i			0.237477i	−0.992926	+	0.118738i	$0.962115\pi$
$272$	3.27110	−	8.14772i	0.198340	−	0.494028i
$273$		0			0
$274$	1.22318	+	1.48218i	0.0738952	+	0.0895419i
$275$	2.90415	−	2.90415i	0.175127	−	0.175127i
$276$		0			0
$277$	−10.9862	−	10.9862i	−0.660097	−	0.660097i	0.295306	−	0.955403i	$-0.404579\pi$
$277$	−10.9862	−	10.9862i	−0.660097	−	0.660097i	−0.955403	+	0.295306i	$0.904579\pi$
$278$	17.4810	+	1.67355i	1.04844	+	0.100373i
$279$		0			0
$280$	−5.58348	+	18.9641i	−0.333677	+	1.13332i
$281$	−30.1111			−1.79628			−0.898140	−	0.439710i	$-0.855081\pi$
$281$	−30.1111			−1.79628			−0.898140	+	0.439710i	$0.855081\pi$
$282$		0			0
$283$	14.5914	−	14.5914i	0.867370	−	0.867370i	−0.124810	−	0.992181i	$-0.539832\pi$
$283$	14.5914	−	14.5914i	0.867370	−	0.867370i	0.992181	+	0.124810i	$0.0398323\pi$
$284$	−0.593990	−	0.114783i	−0.0352468	−	0.00681114i
$285$		0			0
$286$	0.457094	+	0.553880i	0.0270285	+	0.0327516i
$287$	27.0036			1.59397
$288$		0			0
$289$	12.1822			0.716598
$290$	12.5919	+	15.2581i	0.739420	+	0.895986i
$291$		0			0
$292$	−3.72027	−	0.718909i	−0.217712	−	0.0420710i
$293$	1.57484	−	1.57484i	0.0920031	−	0.0920031i	−0.659607	−	0.751610i	$-0.729277\pi$
$293$	1.57484	−	1.57484i	0.0920031	−	0.0920031i	0.751610	+	0.659607i	$0.229277\pi$
$294$		0			0
$295$	14.5668			0.848110
$296$	3.66592	+	1.07933i	0.213077	+	0.0627349i
$297$		0			0
$298$	4.37331	+	0.418679i	0.253339	+	0.0242534i
$299$	−1.37936	−	1.37936i	−0.0797706	−	0.0797706i
$300$		0			0
$301$	6.38993	−	6.38993i	0.368310	−	0.368310i
$302$	14.5980	+	17.6890i	0.840019	+	1.01789i
$303$		0			0
$304$	10.9162	+	25.5607i	0.626084	+	1.46600i
$305$		−	0.553169i		−	0.0316744i
$306$		0			0
$307$	12.4023	+	12.4023i	0.707837	+	0.707837i	0.966080	−	0.258243i	$-0.0831436\pi$
$307$	12.4023	+	12.4023i	0.707837	+	0.707837i	−0.258243	+	0.966080i	$0.583144\pi$
$308$	−15.6086	+	10.5531i	−0.889383	+	0.601318i
$309$		0			0
$310$	1.16467	−	12.1655i	0.0661487	−	0.690956i
$311$			6.47936i			0.367411i	0.982981	+	0.183705i	$0.0588093\pi$
$311$			6.47936i			0.367411i	−0.982981	+	0.183705i	$0.941191\pi$
$312$		0			0
$313$			17.9430i			1.01420i	0.861888	+	0.507099i	$0.169282\pi$
$313$			17.9430i			1.01420i	−0.861888	+	0.507099i	$0.830718\pi$
$314$	−3.14063	−	0.300668i	−0.177236	−	0.0169677i
$315$		0			0
$316$	28.5147	+	5.51021i	1.60408	+	0.309974i
$317$	−5.79302	−	5.79302i	−0.325368	−	0.325368i	0.525454	−	0.850822i	$-0.323896\pi$
$317$	−5.79302	−	5.79302i	−0.325368	−	0.325368i	−0.850822	+	0.525454i	$0.823896\pi$
$318$		0			0
$319$			18.8546i			1.05566i
$320$	−3.08235	−	14.2700i	−0.172309	−	0.797720i
$321$		0			0
$322$	39.4738	−	32.5761i	2.19979	−	1.81539i
$323$	10.7846	−	10.7846i	0.600070	−	0.600070i
$324$		0			0
$325$	0.243754	+	0.243754i	0.0135210	+	0.0135210i
$326$	1.17720	−	12.2964i	0.0651990	−	0.681036i
$327$		0			0
$328$	−17.5095	+	9.54426i	−0.966802	+	0.526994i
$329$	16.0910			0.887125
$330$		0			0
$331$	3.59554	−	3.59554i	0.197629	−	0.197629i	−0.601354	−	0.798983i	$-0.705372\pi$
$331$	3.59554	−	3.59554i	0.197629	−	0.197629i	0.798983	+	0.601354i	$0.205372\pi$
$332$	10.1596	+	15.0267i	0.557583	+	0.824697i
$333$		0			0
$334$	−11.1250	+	9.18101i	−0.608733	+	0.502362i
$335$	10.2204			0.558400
$336$		0			0
$337$	−17.1100			−0.932039			−0.466019	−	0.884775i	$-0.654312\pi$
$337$	−17.1100			−0.932039			−0.466019	+	0.884775i	$0.654312\pi$
$338$	14.1332	−	11.6636i	0.768747	−	0.634415i
$339$		0			0
$340$	−6.63660	+	4.48705i	−0.359920	+	0.243345i
$341$	8.23615	−	8.23615i	0.446013	−	0.446013i
$342$		0			0
$343$	−2.56289			−0.138383
$344$	−1.88484	+	6.40180i	−0.101624	+	0.345162i
$345$		0			0
$346$	1.61494	−	16.8688i	0.0868197	−	0.906875i
$347$	17.9127	+	17.9127i	0.961606	+	0.961606i	0.999290	−	0.0376842i	$-0.0119981\pi$
$347$	17.9127	+	17.9127i	0.961606	+	0.961606i	−0.0376842	+	0.999290i	$0.511998\pi$
$348$		0			0
$349$	1.43838	−	1.43838i	0.0769946	−	0.0769946i	−0.667561	−	0.744555i	$-0.732662\pi$
$349$	1.43838	−	1.43838i	0.0769946	−	0.0769946i	0.744555	+	0.667561i	$0.232662\pi$
$350$	−6.97560	+	5.75668i	−0.372862	+	0.307707i
$351$		0			0
$352$	6.39091	−	12.3595i	0.340637	−	0.658765i
$353$		−	4.64804i		−	0.247390i	−0.992320	−	0.123695i	$-0.960526\pi$
$353$		−	4.64804i		−	0.247390i	0.992320	−	0.123695i	$-0.0394745\pi$
$354$		0			0
$355$	0.390331	+	0.390331i	0.0207166	+	0.0207166i
$356$	6.28914	−	32.5455i	0.333324	−	1.72491i
$357$		0			0
$358$	23.3963	+	2.23985i	1.23653	+	0.118380i
$359$		−	4.63171i		−	0.244453i	−0.992502	−	0.122226i	$-0.960997\pi$
$359$		−	4.63171i		−	0.244453i	0.992502	−	0.122226i	$-0.0390034\pi$
$360$		0			0
$361$			29.2819i			1.54115i
$362$	−0.905915	+	9.46273i	−0.0476139	+	0.497350i
$363$		0			0
$364$	−0.885751	−	1.31008i	−0.0464260	−	0.0686666i
$365$	2.44471	+	2.44471i	0.127962	+	0.127962i
$366$		0			0
$367$			13.8249i			0.721655i	0.932633	+	0.360827i	$0.117506\pi$
$367$			13.8249i			0.721655i	−0.932633	+	0.360827i	$0.882494\pi$
$368$	−14.0815	+	35.0745i	−0.734050	+	1.82839i
$369$		0			0
$370$	−2.21943	−	2.68938i	−0.115383	−	0.139814i
$371$	−15.2036	+	15.2036i	−0.789333	+	0.789333i
$372$		0			0
$373$	−11.5214	−	11.5214i	−0.596557	−	0.596557i	0.342838	−	0.939395i	$-0.388612\pi$
$373$	−11.5214	−	11.5214i	−0.596557	−	0.596557i	−0.939395	+	0.342838i	$0.888612\pi$
$374$	−7.60045	−	0.727630i	−0.393010	−	0.0376248i
$375$		0			0
$376$	−10.4336	+	5.68725i	−0.538072	+	0.293298i
$377$	−1.58252			−0.0815040
$378$		0			0
$379$	13.5115	−	13.5115i	0.694040	−	0.694040i	−0.269078	−	0.963118i	$-0.586719\pi$
$379$	13.5115	−	13.5115i	0.694040	−	0.694040i	0.963118	+	0.269078i	$0.0867190\pi$
$380$	4.81170	−	24.9000i	0.246835	−	1.27734i
$381$		0			0
$382$	−10.2277	−	12.3934i	−0.523296	−	0.634100i
$383$	−29.3220			−1.49829			−0.749143	−	0.662409i	$-0.769534\pi$
$383$	−29.3220			−1.49829			−0.749143	+	0.662409i	$0.769534\pi$
$384$		0			0
$385$	17.1917			0.876172
$386$	16.0596	+	19.4601i	0.817413	+	0.990493i
$387$		0			0
$388$	−6.55468	+	33.9197i	−0.332764	+	1.72201i
$389$	−2.87475	+	2.87475i	−0.145756	+	0.145756i	−0.776219	−	0.630463i	$-0.782865\pi$
$389$	−2.87475	+	2.87475i	−0.145756	+	0.145756i	0.630463	+	0.776219i	$0.282865\pi$
$390$		0			0
$391$	20.7400			1.04886
$392$	19.0459	−	10.3817i	0.961964	−	0.524357i
$393$		0			0
$394$	−13.8078	−	1.32189i	−0.695626	−	0.0665958i
$395$	−18.7380	−	18.7380i	−0.942809	−	0.942809i
$396$		0			0
$397$	1.67071	−	1.67071i	0.0838504	−	0.0838504i	−0.663938	−	0.747788i	$-0.731116\pi$
$397$	1.67071	−	1.67071i	0.0838504	−	0.0838504i	0.747788	+	0.663938i	$0.231116\pi$
$398$	−16.1605	−	19.5823i	−0.810052	−	0.981573i
$399$		0			0
$400$	2.48841	−	6.19819i	0.124421	−	0.309909i
$401$		−	23.4088i		−	1.16898i	−0.811402	−	0.584489i	$-0.801295\pi$
$401$		−	23.4088i		−	1.16898i	0.811402	−	0.584489i	$-0.198705\pi$
$402$		0			0
$403$	0.691284	+	0.691284i	0.0344353	+	0.0344353i
$404$	17.9430	+	26.5387i	0.892698	+	1.32035i
$405$		0			0
$406$	3.95681	−	41.3309i	0.196373	−	2.05122i
$407$		−	3.32330i		−	0.164730i
$408$		0			0
$409$		−	29.8272i		−	1.47486i	−0.675425	−	0.737429i	$-0.736040\pi$
$409$		−	29.8272i		−	1.47486i	0.675425	−	0.737429i	$-0.263960\pi$
$410$	18.1130	+	1.73405i	0.894539	+	0.0856388i
$411$		0			0
$412$	−0.414758	+	2.14632i	−0.0204337	+	0.105742i
$413$	−21.6179	−	21.6179i	−1.06375	−	1.06375i
$414$		0			0
$415$		−	16.5508i		−	0.812446i
$416$	1.03737	+	0.536407i	0.0508613	+	0.0262995i
$417$		0			0
$418$	18.6421	−	15.3846i	0.911817	−	0.752485i
$419$	20.9053	−	20.9053i	1.02129	−	1.02129i	0.0215246	−	0.999768i	$-0.493148\pi$
$419$	20.9053	−	20.9053i	1.02129	−	1.02129i	0.999768	−	0.0215246i	$-0.00685204\pi$
$420$		0			0
$421$	15.8394	+	15.8394i	0.771965	+	0.771965i	0.978450	−	0.206485i	$-0.0662024\pi$
$421$	15.8394	+	15.8394i	0.771965	+	0.771965i	−0.206485	+	0.978450i	$0.566202\pi$
$422$	1.09480	−	11.4357i	0.0532938	−	0.556680i
$423$		0			0
$424$	4.48461	−	15.2319i	0.217792	−	0.739724i
$425$	−3.66506			−0.177781
$426$		0			0
$427$	−0.820933	+	0.820933i	−0.0397278	+	0.0397278i
$428$	−26.1126	+	17.6549i	−1.26220	+	0.853381i
$429$		0			0
$430$	4.69646	−	3.87580i	0.226484	−	0.186907i
$431$	−7.04726			−0.339454			−0.169727	−	0.985491i	$-0.554289\pi$
$431$	−7.04726			−0.339454			−0.169727	+	0.985491i	$0.554289\pi$
$432$		0			0
$433$	9.05113			0.434970			0.217485	−	0.976064i	$-0.430215\pi$
$433$	9.05113			0.434970			0.217485	+	0.976064i	$0.430215\pi$
$434$	−19.7828	+	16.3259i	−0.949603	+	0.783668i
$435$		0			0
$436$	18.1658	+	26.8682i	0.869983	+	1.28675i
$437$	−46.4257	+	46.4257i	−2.22084	+	2.22084i
$438$		0			0
$439$	15.0613			0.718837			0.359419	−	0.933176i	$-0.382975\pi$
$439$	15.0613			0.718837			0.359419	+	0.933176i	$0.382975\pi$
$440$	−11.1473	+	6.07631i	−0.531429	+	0.289677i
$441$		0			0
$442$	0.0610721	−	0.637928i	0.00290490	−	0.0303431i
$443$	−9.49261	−	9.49261i	−0.451008	−	0.451008i	0.444681	−	0.895689i	$-0.353317\pi$
$443$	−9.49261	−	9.49261i	−0.451008	−	0.451008i	−0.895689	+	0.444681i	$0.853317\pi$
$444$		0			0
$445$	−21.3868	+	21.3868i	−1.01383	+	1.01383i
$446$	−7.50608	+	6.19446i	−0.355423	+	0.293316i
$447$		0			0
$448$	−16.6032	+	25.7519i	−0.784426	+	1.21666i
$449$		−	18.6363i		−	0.879499i	−0.898120	−	0.439750i	$-0.855067\pi$
$449$		−	18.6363i		−	0.879499i	0.898120	−	0.439750i	$-0.144933\pi$
$450$		0			0
$451$	12.2627	+	12.2627i	0.577426	+	0.577426i
$452$	25.2205	+	4.87365i	1.18627	+	0.229237i
$453$		0			0
$454$	25.4678	+	2.43816i	1.19526	+	0.114428i
$455$			1.44295i			0.0676466i
$456$		0			0
$457$		−	18.9194i		−	0.885012i	−0.896765	−	0.442506i	$-0.854089\pi$
$457$		−	18.9194i		−	0.885012i	0.896765	−	0.442506i	$-0.145911\pi$
$458$	−3.70571	+	38.7079i	−0.173156	+	1.80870i
$459$		0			0
$460$	28.5694	−	19.3160i	1.33206	−	0.900613i
$461$	12.0421	+	12.0421i	0.560857	+	0.560857i	0.929551	−	0.368694i	$-0.120195\pi$
$461$	12.0421	+	12.0421i	0.560857	+	0.560857i	−0.368694	+	0.929551i	$0.620195\pi$
$462$		0			0
$463$			16.2188i			0.753753i	0.926263	+	0.376877i	$0.123002\pi$
$463$			16.2188i			0.753753i	−0.926263	+	0.376877i	$0.876998\pi$
$464$	12.0425	+	28.1980i	0.559058	+	1.30906i
$465$		0			0
$466$	−6.64331	−	8.04997i	−0.307745	−	0.372908i
$467$	3.53705	−	3.53705i	0.163675	−	0.163675i	−0.620518	−	0.784193i	$-0.713077\pi$
$467$	3.53705	−	3.53705i	0.163675	−	0.163675i	0.784193	+	0.620518i	$0.213077\pi$
$468$		0			0
$469$	−15.1676	−	15.1676i	−0.700376	−	0.700376i
$470$	10.7932	+	1.03329i	0.497855	+	0.0476622i
$471$		0			0
$472$	21.6580	+	6.37663i	0.996892	+	0.293508i
$473$	5.80348			0.266844
$474$		0			0
$475$	8.20412	−	8.20412i	0.376431	−	0.376431i
$476$	16.5081	+	3.19005i	0.756648	+	0.146216i
$477$		0			0
$478$	16.0453	+	19.4428i	0.733896	+	0.889292i
$479$	−28.5702			−1.30540			−0.652702	−	0.757614i	$-0.726365\pi$
$479$	−28.5702			−1.30540			−0.652702	+	0.757614i	$0.726365\pi$
$480$		0			0
$481$	0.278934			0.0127183
$482$	7.23970	+	8.77265i	0.329759	+	0.399583i
$483$		0			0
$484$	9.72008	+	1.87832i	0.441822	+	0.0853782i
$485$	22.2898	−	22.2898i	1.01213	−	1.01213i
$486$		0			0
$487$	−8.23365			−0.373102			−0.186551	−	0.982445i	$-0.559731\pi$
$487$	−8.23365			−0.373102			−0.186551	+	0.982445i	$0.559731\pi$
$488$	0.242151	−	0.822458i	0.0109616	−	0.0372309i
$489$		0			0
$490$	−19.7024	−	1.88621i	−0.890064	−	0.0852103i
$491$	−26.7582	−	26.7582i	−1.20758	−	1.20758i	−0.971809	−	0.235771i	$-0.924239\pi$
$491$	−26.7582	−	26.7582i	−1.20758	−	1.20758i	−0.235771	−	0.971809i	$-0.575761\pi$
$492$		0			0
$493$	11.8973	−	11.8973i	0.535828	−	0.535828i
$494$	1.29127	+	1.56469i	0.0580971	+	0.0703987i
$495$		0			0
$496$	7.05712	−	17.5780i	0.316874	−	0.789276i
$497$		−	1.15854i		−	0.0519678i
$498$		0			0
$499$	8.54782	+	8.54782i	0.382653	+	0.382653i	0.872057	−	0.489404i	$-0.162786\pi$
$499$	8.54782	+	8.54782i	0.382653	+	0.382653i	−0.489404	+	0.872057i	$0.662786\pi$
$500$	−20.1665	+	13.6347i	−0.901873	+	0.609762i
$501$		0			0
$502$	−2.43131	+	25.3963i	−0.108515	+	1.13349i
$503$			5.19075i			0.231444i	0.993282	+	0.115722i	$0.0369182\pi$
$503$			5.19075i			0.231444i	−0.993282	+	0.115722i	$0.963082\pi$
$504$		0			0
$505$		−	29.2304i		−	1.30074i
$506$	32.7186	+	3.13232i	1.45452	+	0.139249i
$507$		0			0
$508$	−19.8784	−	3.84133i	−0.881962	−	0.170431i
$509$	15.3416	+	15.3416i	0.680003	+	0.680003i	0.960001	−	0.279998i	$-0.0903338\pi$
$509$	15.3416	+	15.3416i	0.680003	+	0.680003i	−0.279998	+	0.960001i	$0.590334\pi$
$510$		0			0
$511$		−	7.25617i		−	0.320994i
$512$	1.66386	−	22.5662i	0.0735331	−	0.997293i
$513$		0			0
$514$	−7.60852	+	6.27900i	−0.335597	+	0.276955i
$515$	1.41042	−	1.41042i	0.0621506	−	0.0621506i
$516$		0			0
$517$	7.30709	+	7.30709i	0.321366	+	0.321366i
$518$	−0.697425	+	7.28495i	−0.0306431	+	0.320082i
$519$		0			0
$520$	−0.510002	−	0.935629i	−0.0223651	−	0.0410300i
$521$	−24.1468			−1.05789			−0.528946	−	0.848656i	$-0.677412\pi$
$521$	−24.1468			−1.05789			−0.528946	+	0.848656i	$0.677412\pi$
$522$		0			0
$523$	8.27158	−	8.27158i	0.361691	−	0.361691i	−0.502744	−	0.864435i	$-0.667676\pi$
$523$	8.27158	−	8.27158i	0.361691	−	0.361691i	0.864435	+	0.502744i	$0.167676\pi$
$524$	4.00700	+	5.92657i	0.175046	+	0.258903i
$525$		0			0
$526$	−16.6459	+	13.7372i	−0.725798	+	0.598971i
$527$	−10.3941			−0.452773
$528$		0			0
$529$	−66.2819			−2.88182
$530$	−11.1743	+	9.22172i	−0.485382	+	0.400566i
$531$		0			0
$532$	−44.0937	+	29.8121i	−1.91171	+	1.29252i
$533$	−1.02924	+	1.02924i	−0.0445813	+	0.0445813i
$534$		0			0
$535$	28.7611			1.24345
$536$	15.1958	+	4.47399i	0.656358	+	0.193247i
$537$		0			0
$538$	−1.73732	+	18.1471i	−0.0749011	+	0.782379i
$539$	−13.3387	−	13.3387i	−0.574537	−	0.574537i
$540$		0			0
$541$	−13.3477	+	13.3477i	−0.573864	+	0.573864i	−0.933206	−	0.359342i	$-0.883001\pi$
$541$	−13.3477	+	13.3477i	−0.573864	+	0.573864i	0.359342	+	0.933206i	$0.383001\pi$
$542$	4.26412	−	3.51901i	0.183160	−	0.151154i
$543$		0			0
$544$	−11.8316	+	3.76622i	−0.507275	+	0.161475i
$545$		−	29.5933i		−	1.26764i
$546$		0			0
$547$	3.47695	+	3.47695i	0.148664	+	0.148664i	0.777521	−	0.628857i	$-0.216477\pi$
$547$	3.47695	+	3.47695i	0.148664	+	0.148664i	−0.628857	+	0.777521i	$0.716477\pi$
$548$	0.515639	−	2.66837i	0.0220270	−	0.113987i
$549$		0			0
$550$	−5.78187	−	0.553528i	−0.246540	−	0.0236025i
$551$			53.2635i			2.26910i
$552$		0			0
$553$			55.6163i			2.36505i
$554$	−2.09396	+	21.8724i	−0.0889637	+	0.929270i
$555$		0			0
$556$	−13.9101	−	20.5738i	−0.589920	−	0.872524i
$557$	−0.755563	−	0.755563i	−0.0320142	−	0.0320142i	0.690918	−	0.722933i	$-0.257206\pi$
$557$	−0.755563	−	0.755563i	−0.0320142	−	0.0320142i	−0.722933	+	0.690918i	$0.757206\pi$
$558$		0			0
$559$			0.487102i			0.0206022i
$560$	25.7111	−	10.9804i	1.08649	−	0.464006i
$561$		0			0
$562$	27.1045	+	32.8437i	1.14334	+	1.38543i
$563$	18.5500	−	18.5500i	0.781790	−	0.781790i	−0.198343	−	0.980133i	$-0.563556\pi$
$563$	18.5500	−	18.5500i	0.781790	−	0.781790i	0.980133	+	0.198343i	$0.0635559\pi$
$564$		0			0
$565$	−16.5733	−	16.5733i	−0.697242	−	0.697242i
$566$	−29.0500	−	2.78111i	−1.22106	−	0.116899i
$567$		0			0
$568$	0.409480	+	0.751215i	0.0171814	+	0.0315203i
$569$	25.3411			1.06235			0.531177	−	0.847261i	$-0.321750\pi$
$569$	25.3411			1.06235			0.531177	+	0.847261i	$0.321750\pi$
$570$		0			0
$571$	−9.68841	+	9.68841i	−0.405447	+	0.405447i	−0.880148	−	0.474700i	$-0.842557\pi$
$571$	−9.68841	+	9.68841i	−0.405447	+	0.405447i	0.474700	+	0.880148i	$0.342557\pi$
$572$	0.192690	−	0.997149i	0.00805679	−	0.0416929i
$573$		0			0
$574$	−24.3073	−	29.4542i	−1.01457	−	1.22939i
$575$	15.7774			0.657965
$576$		0			0
$577$	−19.1525			−0.797328			−0.398664	−	0.917097i	$-0.630526\pi$
$577$	−19.1525			−0.797328			−0.398664	+	0.917097i	$0.630526\pi$
$578$	−10.9658	−	13.2877i	−0.456116	−	0.552694i
$579$		0			0
$580$	5.30817	−	27.4691i	0.220410	−	1.14059i
$581$	−24.5623	+	24.5623i	−1.01901	+	1.01901i
$582$		0			0
$583$	−13.8083			−0.571880
$584$	2.56465	+	4.70500i	0.106126	+	0.194694i
$585$		0			0
$586$	−3.13534	−	0.300162i	−0.129520	−	0.0123996i
$587$	−8.11398	−	8.11398i	−0.334900	−	0.334900i	0.519544	−	0.854444i	$-0.326102\pi$
$587$	−8.11398	−	8.11398i	−0.334900	−	0.334900i	−0.854444	+	0.519544i	$0.826102\pi$
$588$		0			0
$589$	23.2668	−	23.2668i	0.958692	−	0.958692i
$590$	−13.1123	−	15.8887i	−0.539824	−	0.654127i
$591$		0			0
$592$	−2.12260	−	4.97016i	−0.0872383	−	0.204272i
$593$		−	0.597008i		−	0.0245162i	−0.999925	−	0.0122581i	$-0.996098\pi$
$593$		−	0.597008i		−	0.0245162i	0.999925	−	0.0122581i	$-0.00390197\pi$
$594$		0			0
$595$	−10.8480	−	10.8480i	−0.444726	−	0.444726i
$596$	−3.47996	−	5.14705i	−0.142545	−	0.210832i
$597$		0			0
$598$	−0.262905	+	2.74617i	−0.0107510	+	0.112299i
$599$		−	7.70925i		−	0.314991i	−0.987520	−	0.157496i	$-0.949658\pi$
$599$		−	7.70925i		−	0.314991i	0.987520	−	0.157496i	$-0.0503421\pi$
$600$		0			0
$601$			10.1359i			0.413453i	0.978399	+	0.206727i	$0.0662811\pi$
$601$			10.1359i			0.413453i	−0.978399	+	0.206727i	$0.933719\pi$
$602$	−12.7217	−	1.21791i	−0.518498	−	0.0496384i
$603$		0			0
$604$	6.15385	−	31.8454i	0.250396	−	1.29577i
$605$	−6.38739	−	6.38739i	−0.259684	−	0.259684i
$606$		0			0
$607$		−	7.07480i		−	0.287157i	−0.989639	−	0.143579i	$-0.954139\pi$
$607$		−	7.07480i		−	0.287157i	0.989639	−	0.143579i	$-0.0458610\pi$
$608$	18.0541	−	34.9152i	0.732189	−	1.41600i
$609$		0			0
$610$	−0.603368	+	0.497935i	−0.0244297	+	0.0201608i
$611$	−0.613305	+	0.613305i	−0.0248117	+	0.0248117i
$612$		0			0
$613$	3.83757	+	3.83757i	0.154998	+	0.154998i	0.780346	−	0.625348i	$-0.215043\pi$
$613$	3.83757	+	3.83757i	0.154998	+	0.154998i	−0.625348	+	0.780346i	$0.715043\pi$
$614$	2.36386	−	24.6917i	0.0953977	−	0.996476i
$615$		0			0
$616$	25.5608	+	7.52570i	1.02988	+	0.303219i
$617$	17.7142			0.713146			0.356573	−	0.934267i	$-0.383945\pi$
$617$	17.7142			0.713146			0.356573	+	0.934267i	$0.383945\pi$
$618$		0			0
$619$	4.23945	−	4.23945i	0.170398	−	0.170398i	−0.616756	−	0.787154i	$-0.711554\pi$
$619$	4.23945	−	4.23945i	0.170398	−	0.170398i	0.787154	+	0.616756i	$0.211554\pi$
$620$	−14.3179	+	9.68044i	−0.575021	+	0.388776i
$621$		0			0
$622$	7.06735	−	5.83239i	0.283375	−	0.233858i
$623$	63.4782			2.54320
$624$		0			0
$625$	13.8631			0.554523
$626$	19.5713	−	16.1514i	0.782226	−	0.645539i
$627$		0			0
$628$	2.49908	+	3.69628i	0.0997242	+	0.147498i
$629$	−2.09701	+	2.09701i	−0.0836134	+	0.0836134i
$630$		0			0
$631$	6.62133			0.263591			0.131795	−	0.991277i	$-0.457926\pi$
$631$	6.62133			0.263591			0.131795	+	0.991277i	$0.457926\pi$
$632$	−19.6572	−	36.0623i	−0.781922	−	1.43448i
$633$		0			0
$634$	−1.10414	+	11.5333i	−0.0438511	+	0.458046i
$635$	13.0628	+	13.0628i	0.518380	+	0.518380i
$636$		0			0
$637$	1.11955	−	1.11955i	0.0443583	−	0.0443583i
$638$	20.5656	−	16.9720i	0.814201	−	0.671927i
$639$		0			0
$640$	−12.7905	+	16.2072i	−0.505587	+	0.640647i
$641$			35.3591i			1.39660i	0.715805	+	0.698300i	$0.246060\pi$
$641$			35.3591i			1.39660i	−0.715805	+	0.698300i	$0.753940\pi$
$642$		0			0
$643$	−11.5700	−	11.5700i	−0.456278	−	0.456278i	0.441154	−	0.897432i	$-0.354569\pi$
$643$	−11.5700	−	11.5700i	−0.456278	−	0.456278i	−0.897432	+	0.441154i	$0.854569\pi$
$644$	−71.0646	−	13.7326i	−2.80034	−	0.541141i
$645$		0			0
$646$	−21.4710	−	2.05553i	−0.844765	−	0.0808736i
$647$		−	19.7289i		−	0.775624i	−0.921738	−	0.387812i	$-0.873231\pi$
$647$		−	19.7289i		−	0.775624i	0.921738	−	0.387812i	$-0.126769\pi$
$648$		0			0
$649$		−	19.6338i		−	0.770696i
$650$	0.0464591	−	0.485289i	0.00182228	−	0.0190346i
$651$		0			0
$652$	−14.4720	+	9.78459i	−0.566766	+	0.383194i
$653$	−6.28888	−	6.28888i	−0.246103	−	0.246103i	0.573266	−	0.819369i	$-0.305676\pi$
$653$	−6.28888	−	6.28888i	−0.246103	−	0.246103i	−0.819369	+	0.573266i	$0.805676\pi$
$654$		0			0
$655$		−	6.52768i		−	0.255057i
$656$	26.1716	+	10.5072i	1.02183	+	0.410238i
$657$		0			0
$658$	−14.4843	−	17.5512i	−0.564656	−	0.684217i
$659$	17.1950	−	17.1950i	0.669821	−	0.669821i	−0.287853	−	0.957675i	$-0.592942\pi$
$659$	17.1950	−	17.1950i	0.669821	−	0.669821i	0.957675	+	0.287853i	$0.0929415\pi$
$660$		0			0
$661$	11.3184	+	11.3184i	0.440236	+	0.440236i	0.892091	−	0.451855i	$-0.149238\pi$
$661$	11.3184	+	11.3184i	0.440236	+	0.440236i	−0.451855	+	0.892091i	$0.649238\pi$
$662$	−7.15836	−	0.685306i	−0.278218	−	0.0266352i
$663$		0			0
$664$	7.24513	−	24.6079i	0.281166	−	0.954971i
$665$	48.5660			1.88331
$666$		0			0
$667$	−51.2159	+	51.2159i	−1.98309	+	1.98309i
$668$	20.0283	+	3.87030i	0.774919	+	0.149746i
$669$		0			0
$670$	−9.19988	−	11.1479i	−0.355422	−	0.430680i
$671$	−0.745590			−0.0287832
$672$		0			0
$673$	35.7094			1.37650			0.688249	−	0.725475i	$-0.258380\pi$
$673$	35.7094			1.37650			0.688249	+	0.725475i	$0.258380\pi$
$674$	15.4015	+	18.6627i	0.593244	+	0.718859i
$675$		0			0
$676$	−25.4440	−	4.91684i	−0.978617	−	0.189109i
$677$	−24.2656	+	24.2656i	−0.932602	+	0.932602i	−0.997868	−	0.0652662i	$-0.979210\pi$
$677$	−24.2656	+	24.2656i	−0.932602	+	0.932602i	0.0652662	+	0.997868i	$0.479210\pi$
$678$		0			0
$679$	−66.1585			−2.53893
$680$	10.8682	+	3.19984i	0.416776	+	0.122708i
$681$		0			0
$682$	−16.3973	−	1.56980i	−0.627887	−	0.0601108i
$683$	−23.8920	−	23.8920i	−0.914202	−	0.914202i	0.0823975	−	0.996600i	$-0.473742\pi$
$683$	−23.8920	−	23.8920i	−0.914202	−	0.914202i	−0.996600	+	0.0823975i	$0.973742\pi$
$684$		0			0
$685$	−1.75348	+	1.75348i	−0.0669969	+	0.0669969i
$686$	2.30698	+	2.79547i	0.0880811	+	0.106731i
$687$		0			0
$688$	8.67938	−	3.70669i	0.330898	−	0.141316i
$689$		−	1.15897i		−	0.0441531i
$690$		0			0
$691$	−2.79047	−	2.79047i	−0.106154	−	0.106154i	0.652035	−	0.758189i	$-0.273916\pi$
$691$	−2.79047	−	2.79047i	−0.106154	−	0.106154i	−0.758189	+	0.652035i	$0.773916\pi$
$692$	−19.8533	+	13.4230i	−0.754711	+	0.510265i
$693$		0			0
$694$	3.41414	−	35.6624i	0.129599	−	1.35373i
$695$			22.6605i			0.859563i
$696$		0			0
$697$		−	15.4755i		−	0.586178i
$698$	−2.86366	−	0.274153i	−0.108391	−	0.0103768i
$699$		0			0
$700$	12.5582	+	2.42676i	0.474654	+	0.0917228i
$701$	−20.9991	−	20.9991i	−0.793127	−	0.793127i	0.188874	−	0.982001i	$-0.439516\pi$
$701$	−20.9991	−	20.9991i	−0.793127	−	0.793127i	−0.982001	+	0.188874i	$0.939516\pi$
$702$		0			0
$703$		−	9.38820i		−	0.354083i
$704$	−19.2339	+	4.15455i	−0.724905	+	0.156580i
$705$		0			0
$706$	−5.06984	+	4.18393i	−0.190806	+	0.157464i
$707$	−43.3796	+	43.3796i	−1.63146	+	1.63146i
$708$		0			0
$709$	13.8356	+	13.8356i	0.519605	+	0.519605i	0.917452	−	0.397847i	$-0.130242\pi$
$709$	13.8356	+	13.8356i	0.519605	+	0.519605i	−0.397847	+	0.917452i	$0.630242\pi$
$710$	0.0743965	−	0.777108i	0.00279205	−	0.0291643i
$711$		0			0
$712$	−41.1601	+	22.4360i	−1.54254	+	0.840823i
$713$	44.7447			1.67570
$714$		0			0
$715$	−0.655260	+	0.655260i	−0.0245053	+	0.0245053i
$716$	−18.6171	−	27.5357i	−0.695752	−	1.02906i
$717$		0			0
$718$	−5.05203	+	4.16923i	−0.188540	+	0.155594i
$719$	38.6642			1.44193			0.720965	−	0.692971i	$-0.243699\pi$
$719$	38.6642			1.44193			0.720965	+	0.692971i	$0.243699\pi$
$720$		0			0
$721$	−4.18628			−0.155905
$722$	31.9391	−	26.3580i	1.18865	−	0.980945i
$723$		0			0
$724$	11.1369	−	7.52975i	0.413900	−	0.279841i
$725$	9.05061	−	9.05061i	0.336131	−	0.336131i
$726$		0			0
$727$	−20.7932			−0.771179			−0.385589	−	0.922670i	$-0.626002\pi$
$727$	−20.7932			−0.771179			−0.385589	+	0.922670i	$0.626002\pi$
$728$	−0.631654	+	2.14539i	−0.0234107	+	0.0795136i
$729$		0			0
$730$	0.465959	−	4.86717i	0.0172459	−	0.180142i
$731$	−3.66201	−	3.66201i	−0.135444	−	0.135444i
$732$		0			0
$733$	−17.6516	+	17.6516i	−0.651978	+	0.651978i	−0.953469	−	0.301491i	$-0.902516\pi$
$733$	−17.6516	+	17.6516i	−0.651978	+	0.651978i	0.301491	+	0.953469i	$0.402516\pi$
$734$	15.0795	−	12.4445i	0.556595	−	0.459334i
$735$		0			0
$736$	50.9329	−	16.2129i	1.87741	−	0.597616i
$737$		−	13.7756i		−	0.507430i
$738$		0			0
$739$	−13.3427	−	13.3427i	−0.490821	−	0.490821i	0.417744	−	0.908565i	$-0.362821\pi$
$739$	−13.3427	−	13.3427i	−0.490821	−	0.490821i	−0.908565	+	0.417744i	$0.862821\pi$
$740$	−0.935614	+	4.84169i	−0.0343938	+	0.177984i
$741$		0			0
$742$	30.2689	+	2.89779i	1.11120	+	0.106381i
$743$			10.2617i			0.376465i	0.982125	+	0.188232i	$0.0602758\pi$
$743$			10.2617i			0.376465i	−0.982125	+	0.188232i	$0.939724\pi$
$744$		0			0
$745$			5.66910i			0.207700i
$746$	−2.19597	+	22.9380i	−0.0804002	+	0.839820i
$747$		0			0
$748$	6.04788	+	8.94515i	0.221132	+	0.327067i
$749$	−42.6830	−	42.6830i	−1.55960	−	1.55960i
$750$		0			0
$751$		−	44.8995i		−	1.63840i	−0.573504	−	0.819202i	$-0.694416\pi$
$751$		−	44.8995i		−	1.63840i	0.573504	−	0.819202i	$-0.305584\pi$
$752$	15.5952	+	6.26106i	0.568697	+	0.228317i
$753$		0			0
$754$	1.42451	+	1.72613i	0.0518774	+	0.0628620i
$755$	−20.9267	+	20.9267i	−0.761600	+	0.761600i
$756$		0			0
$757$	4.92663	+	4.92663i	0.179061	+	0.179061i	0.790947	−	0.611885i	$-0.209589\pi$
$757$	4.92663	+	4.92663i	0.179061	+	0.179061i	−0.611885	+	0.790947i	$0.709589\pi$
$758$	−26.9001	−	2.57528i	−0.977054	−	0.0935383i
$759$		0			0
$760$	−31.4908	+	17.1653i	−1.14229	+	0.622652i
$761$	−4.23076			−0.153365			−0.0766825	−	0.997056i	$-0.524433\pi$
$761$	−4.23076			−0.153365			−0.0766825	+	0.997056i	$0.524433\pi$
$762$		0			0
$763$	−43.9181	+	43.9181i	−1.58994	+	1.58994i
$764$	−4.31155	+	22.3118i	−0.155986	+	0.807211i
$765$		0			0
$766$	26.3942	+	31.9829i	0.953661	+	1.15559i
$767$	1.64792			0.0595031
$768$		0			0
$769$	37.8600			1.36527			0.682634	−	0.730760i	$-0.260834\pi$
$769$	37.8600			1.36527			0.682634	+	0.730760i	$0.260834\pi$
$770$	−15.4751	−	18.7518i	−0.557685	−	0.675770i
$771$		0			0
$772$	6.77001	−	35.0340i	0.243658	−	1.26090i
$773$	−5.52284	+	5.52284i	−0.198643	+	0.198643i	−0.799418	−	0.600775i	$-0.794859\pi$
$773$	−5.52284	+	5.52284i	−0.198643	+	0.198643i	0.600775	+	0.799418i	$0.294859\pi$
$774$		0			0
$775$	−7.90706			−0.284030
$776$	42.8980	−	23.3833i	1.53995	−	0.839411i
$777$		0			0
$778$	5.72333	+	0.547924i	0.205191	+	0.0196440i
$779$	34.6415	+	34.6415i	1.24116	+	1.24116i
$780$		0			0
$781$	0.526107	−	0.526107i	0.0188256	−	0.0188256i
$782$	−18.6691	−	22.6221i	−0.667604	−	0.808964i
$783$		0			0
$784$	−28.4680	−	11.4292i	−1.01672	−	0.408185i
$785$		−	4.07118i		−	0.145307i
$786$		0			0
$787$	12.1992	+	12.1992i	0.434855	+	0.434855i	0.890276	−	0.455421i	$-0.150511\pi$
$787$	12.1992	+	12.1992i	0.434855	+	0.434855i	−0.455421	+	0.890276i	$0.650511\pi$
$788$	10.9872	+	16.2507i	0.391404	+	0.578908i
$789$		0			0
$790$	−3.57143	+	37.3053i	−0.127066	+	1.32726i
$791$			49.1913i			1.74904i
$792$		0			0
$793$		−	0.0625795i		−	0.00222226i
$794$	−3.32621	−	0.318435i	−0.118043	−	0.0113008i
$795$		0			0
$796$	−6.81253	+	35.2540i	−0.241464	+	1.24955i
$797$	24.4867	+	24.4867i	0.867365	+	0.867365i	0.992180	−	0.124815i	$-0.0398337\pi$
$797$	24.4867	+	24.4867i	0.867365	+	0.867365i	−0.124815	+	0.992180i	$0.539834\pi$
$798$		0			0
$799$		−	9.22160i		−	0.326237i
$800$	−9.00060	+	2.86506i	−0.318219	+	0.101295i
$801$		0			0
$802$	−25.5330	+	21.0714i	−0.901603	+	0.744056i
$803$	3.29511	−	3.29511i	0.116282	−	0.116282i
$804$		0			0
$805$	46.6989	+	46.6989i	1.64592	+	1.64592i
$806$	0.131758	−	1.37628i	0.00464097	−	0.0484772i
$807$		0			0
$808$	12.7957	−	43.4601i	0.450150	−	1.52892i
$809$	9.37507			0.329610			0.164805	−	0.986326i	$-0.447301\pi$
$809$	9.37507			0.329610			0.164805	+	0.986326i	$0.447301\pi$
$810$		0			0
$811$	34.4142	−	34.4142i	1.20845	−	1.20845i	0.236915	−	0.971530i	$-0.423864\pi$
$811$	34.4142	−	34.4142i	1.20845	−	1.20845i	0.971530	−	0.236915i	$-0.0761363\pi$
$812$	−48.6433	+	32.8881i	−1.70704	+	1.15414i
$813$		0			0
$814$	−3.62488	+	2.99147i	−0.127052	+	0.104851i
$815$	15.9398			0.558347
$816$		0			0
$817$	16.3946			0.573574
$818$	−32.5339	+	26.8489i	−1.13752	+	0.938750i
$819$		0			0
$820$	−14.4130	−	21.3177i	−0.503325	−	0.744445i
$821$	−6.68645	+	6.68645i	−0.233359	+	0.233359i	−0.814093	−	0.580734i	$-0.802765\pi$
$821$	−6.68645	+	6.68645i	−0.233359	+	0.233359i	0.580734	+	0.814093i	$0.302765\pi$
$822$		0			0
$823$	33.1046			1.15395			0.576977	−	0.816760i	$-0.304232\pi$
$823$	33.1046			1.15395			0.576977	+	0.816760i	$0.304232\pi$
$824$	2.71444	−	1.47961i	0.0945621	−	0.0515448i
$825$		0			0
$826$	−4.12034	+	43.0390i	−0.143365	+	1.49752i
$827$	−21.6578	−	21.6578i	−0.753114	−	0.753114i	0.221945	−	0.975059i	$-0.428759\pi$
$827$	−21.6578	−	21.6578i	−0.753114	−	0.753114i	−0.975059	+	0.221945i	$0.928759\pi$
$828$		0			0
$829$	22.9488	−	22.9488i	0.797046	−	0.797046i	−0.185582	−	0.982629i	$-0.559417\pi$
$829$	22.9488	−	22.9488i	0.797046	−	0.797046i	0.982629	+	0.185582i	$0.0594171\pi$
$830$	−18.0527	+	14.8982i	−0.626620	+	0.517123i
$831$		0			0
$832$	−0.348703	−	1.61436i	−0.0120891	−	0.0559677i
$833$			16.8335i			0.583245i
$834$		0			0
$835$	−13.1613	−	13.1613i	−0.455465	−	0.455465i
$836$	−33.5614	−	6.48545i	−1.16075	−	0.224304i
$837$		0			0
$838$	−41.6204	−	3.98453i	−1.43775	−	0.137643i
$839$			48.8903i			1.68788i	0.536437	+	0.843940i	$0.319770\pi$
$839$			48.8903i			1.68788i	−0.536437	+	0.843940i	$0.680230\pi$
$840$		0			0
$841$			29.7592i			1.02618i
$842$	3.01897	−	31.5346i	0.104041	−	1.08675i
$843$		0			0
$844$	−13.4589	+	9.09967i	−0.463275	+	0.313224i
$845$	16.7201	+	16.7201i	0.575190	+	0.575190i
$846$		0			0
$847$			18.9585i			0.651421i
$848$	−20.6509	+	8.81936i	−0.709156	+	0.302858i
$849$		0			0
$850$	3.29910	+	3.99765i	0.113158	+	0.137118i
$851$	9.02728	−	9.02728i	0.309451	−	0.309451i
$852$		0			0
$853$	−24.8251	−	24.8251i	−0.849994	−	0.849994i	0.140138	−	0.990132i	$-0.455245\pi$
$853$	−24.8251	−	24.8251i	−0.849994	−	0.849994i	−0.990132	+	0.140138i	$0.955245\pi$
$854$	1.63439	+	0.156469i	0.0559278	+	0.00535425i
$855$		0			0
$856$	42.7623	+	12.5902i	1.46158	+	0.430324i
$857$	23.3809			0.798677			0.399339	−	0.916804i	$-0.369240\pi$
$857$	23.3809			0.798677			0.399339	+	0.916804i	$0.369240\pi$
$858$		0			0
$859$	12.4770	−	12.4770i	0.425711	−	0.425711i	−0.461453	−	0.887164i	$-0.652672\pi$
$859$	12.4770	−	12.4770i	0.425711	−	0.425711i	0.887164	+	0.461453i	$0.152672\pi$
$860$	−8.45503	−	1.63386i	−0.288314	−	0.0557142i
$861$		0			0
$862$	6.34358	+	7.68678i	0.216063	+	0.261813i
$863$	35.1333			1.19595			0.597976	−	0.801514i	$-0.295972\pi$
$863$	35.1333			1.19595			0.597976	+	0.801514i	$0.295972\pi$
$864$		0			0
$865$	21.8670			0.743500
$866$	−8.14737	−	9.87251i	−0.276859	−	0.335481i
$867$		0			0
$868$	35.6149	+	6.88226i	1.20885	+	0.233599i
$869$	−25.2560	+	25.2560i	−0.856750	+	0.856750i
$870$		0			0
$871$	1.15622			0.0391771
$872$	12.9545	−	43.9997i	0.438696	−	1.49002i
$873$		0			0
$874$	92.4289	+	8.84869i	3.12645	+	0.299311i
$875$	−32.9637	−	32.9637i	−1.11438	−	1.11438i
$876$		0			0
$877$	36.3245	−	36.3245i	1.22659	−	1.22659i	0.261344	−	0.965246i	$-0.415834\pi$
$877$	36.3245	−	36.3245i	1.22659	−	1.22659i	0.965246	−	0.261344i	$-0.0841658\pi$
$878$	−13.5574	−	16.4281i	−0.457541	−	0.554421i
$879$		0			0
$880$	16.6620	+	6.68936i	0.561676	+	0.225498i
$881$			29.5584i			0.995849i	0.867221	+	0.497924i	$0.165904\pi$
$881$			29.5584i			0.995849i	−0.867221	+	0.497924i	$0.834096\pi$
$882$		0			0
$883$	−12.2911	−	12.2911i	−0.413628	−	0.413628i	0.469373	−	0.883000i	$-0.344480\pi$
$883$	−12.2911	−	12.2911i	−0.413628	−	0.413628i	−0.883000	+	0.469373i	$0.844480\pi$
$884$	−0.750792	+	0.507616i	−0.0252519	+	0.0170730i
$885$		0			0
$886$	−1.80928	+	18.8988i	−0.0607839	+	0.634918i
$887$			10.9909i			0.369038i	0.982829	+	0.184519i	$0.0590727\pi$
$887$			10.9909i			0.369038i	−0.982829	+	0.184519i	$0.940927\pi$
$888$		0			0
$889$		−	38.7717i		−	1.30036i
$890$	42.5788	+	4.07629i	1.42725	+	0.136637i
$891$		0			0
$892$	13.5132	+	2.61130i	0.452455	+	0.0874329i
$893$	20.6423	+	20.6423i	0.690767	+	0.690767i
$894$		0			0
$895$			30.3285i			1.01377i
$896$	43.0342	−	5.07070i	1.43767	−	0.169400i
$897$		0			0
$898$	−20.3275	+	16.7754i	−0.678336	+	0.559803i
$899$	25.6675	−	25.6675i	0.856058	−	0.856058i
$900$		0			0
$901$	8.71306	+	8.71306i	0.290274	+	0.290274i
$902$	2.33725	−	24.4137i	0.0778218	−	0.812887i
$903$		0			0
$904$	−17.3863	−	31.8963i	−0.578261	−	1.06085i
$905$	−12.2665			−0.407752
$906$		0			0
$907$	19.8302	−	19.8302i	0.658452	−	0.658452i	−0.296562	−	0.955014i	$-0.595840\pi$
$907$	19.8302	−	19.8302i	0.658452	−	0.658452i	0.955014	+	0.296562i	$0.0958401\pi$
$908$	−20.2654	−	29.9736i	−0.672530	−	0.994709i
$909$		0			0
$910$	1.57390	−	1.29887i	0.0521742	−	0.0430572i
$911$	−27.0177			−0.895136			−0.447568	−	0.894250i	$-0.647710\pi$
$911$	−27.0177			−0.895136			−0.447568	+	0.894250i	$0.647710\pi$
$912$		0			0
$913$	−22.3080			−0.738287
$914$	−20.6363	+	17.0303i	−0.682588	+	0.563312i
$915$		0			0
$916$	45.5563	−	30.8009i	1.50522	−	1.01769i
$917$	−9.68743	+	9.68743i	−0.319907	+	0.319907i
$918$		0			0
$919$	−29.8432			−0.984436			−0.492218	−	0.870472i	$-0.663814\pi$
$919$	−29.8432			−0.984436			−0.492218	+	0.870472i	$0.663814\pi$
$920$	−46.7856	−	13.7748i	−1.54248	−	0.454141i
$921$		0			0
$922$	2.29521	−	23.9746i	0.0755887	−	0.789561i
$923$	0.0441577	+	0.0441577i	0.00145347	+	0.00145347i
$924$		0			0
$925$	−1.59525	+	1.59525i	−0.0524516	+	0.0524516i
$926$	17.6907	−	14.5994i	0.581351	−	0.479765i
$927$		0			0
$928$	19.9169	−	38.5177i	0.653803	−	1.26441i
$929$			1.72307i			0.0565319i	0.999600	+	0.0282660i	$0.00899854\pi$
$929$			1.72307i			0.0565319i	−0.999600	+	0.0282660i	$0.991001\pi$
$930$		0			0
$931$	−37.6812	−	37.6812i	−1.23495	−	1.23495i
$932$	−2.80052	+	14.4923i	−0.0917340	+	0.474713i
$933$		0			0
$934$	−7.04190	−	0.674157i	−0.230418	−	0.0220591i
$935$		−	9.85243i		−	0.322209i
$936$		0			0
$937$			56.5376i			1.84700i	0.383594	+	0.923502i	$0.374686\pi$
$937$			56.5376i			1.84700i	−0.383594	+	0.923502i	$0.625314\pi$
$938$	−2.89093	+	30.1972i	−0.0943922	+	0.985973i
$939$		0			0
$940$	−8.58846	−	12.7028i	−0.280125	−	0.414320i
$941$	11.8657	+	11.8657i	0.386810	+	0.386810i	0.873548	−	0.486738i	$-0.161813\pi$
$941$	11.8657	+	11.8657i	0.386810	+	0.386810i	−0.486738	+	0.873548i	$0.661813\pi$
$942$		0			0
$943$			66.6195i			2.16943i
$944$	−12.5402	−	29.3634i	−0.408148	−	0.955696i
$945$		0			0
$946$	−5.22400	−	6.33013i	−0.169847	−	0.205810i
$947$	−1.98996	+	1.98996i	−0.0646651	+	0.0646651i	−0.738700	−	0.674035i	$-0.764560\pi$
$947$	−1.98996	+	1.98996i	−0.0646651	+	0.0646651i	0.674035	+	0.738700i	$0.264560\pi$
$948$		0			0
$949$	0.276568	+	0.276568i	0.00897777	+	0.00897777i
$950$	−16.3336	−	1.56369i	−0.529930	−	0.0507329i
$951$		0			0
$952$	−11.3802	−	20.8777i	−0.368835	−	0.676651i
$953$	−8.71035			−0.282156			−0.141078	−	0.989998i	$-0.545057\pi$
$953$	−8.71035			−0.282156			−0.141078	+	0.989998i	$0.545057\pi$
$954$		0			0
$955$	14.6618	−	14.6618i	0.474445	−	0.474445i
$956$	6.76399	−	35.0028i	0.218763	−	1.13207i
$957$		0			0
$958$	25.7174	+	31.1629i	0.830892	+	1.00683i
$959$	5.20451			0.168062
$960$		0			0
$961$	8.57565			0.276634
$962$	−0.251082	−	0.304247i	−0.00809522	−	0.00980931i
$963$		0			0
$964$	3.05193	−	15.7934i	0.0982961	−	0.508671i
$965$	−23.0220	+	23.0220i	−0.741105	+	0.741105i
$966$		0			0
$967$	−30.5560			−0.982616			−0.491308	−	0.870986i	$-0.663481\pi$
$967$	−30.5560			−0.982616			−0.491308	+	0.870986i	$0.663481\pi$
$968$	−6.70075	−	12.2929i	−0.215370	−	0.395109i
$969$		0			0
$970$	−44.3766	−	4.24840i	−1.42485	−	0.136408i
$971$	32.2694	+	32.2694i	1.03557	+	1.03557i	0.999344	+	0.0362294i	$0.0115347\pi$
$971$	32.2694	+	32.2694i	1.03557	+	1.03557i	0.0362294	+	0.999344i	$0.488465\pi$
$972$		0			0
$973$	33.6295	−	33.6295i	1.07811	−	1.07811i
$974$	7.41151	+	8.98084i	0.237480	+	0.287765i
$975$		0			0
$976$	−1.11507	+	0.476209i	−0.0356924	+	0.0152431i
$977$		−	44.4631i		−	1.42250i	−0.702940	−	0.711250i	$-0.748130\pi$
$977$		−	44.4631i		−	1.42250i	0.702940	−	0.711250i	$-0.251870\pi$
$978$		0			0
$979$	28.8262	+	28.8262i	0.921288	+	0.921288i
$980$	15.6777	+	23.1882i	0.500806	+	0.740721i
$981$		0			0
$982$	−5.10007	+	53.2728i	−0.162750	+	1.70000i
$983$		−	0.290162i		−	0.00925472i	−0.999989	−	0.00462736i	$-0.998527\pi$
$983$		−	0.290162i		−	0.00925472i	0.999989	−	0.00462736i	$-0.00147294\pi$
$984$		0			0
$985$		−	17.8990i		−	0.570308i
$986$	−23.6863	−	2.26761i	−0.754327	−	0.0722155i
$987$		0			0
$988$	0.544343	−	2.81691i	0.0173178	−	0.0896177i
$989$	15.7643	+	15.7643i	0.501277	+	0.501277i
$990$		0			0
$991$		−	40.4466i		−	1.28483i	−0.766357	−	0.642415i	$-0.777933\pi$
$991$		−	40.4466i		−	1.28483i	0.766357	−	0.642415i	$-0.222067\pi$
$992$	−25.5257	+	8.12530i	−0.810440	+	0.257978i
$993$		0			0
$994$	−1.26368	+	1.04286i	−0.0400815	+	0.0330776i
$995$	23.1666	−	23.1666i	0.734431	−	0.734431i
$996$		0			0
$997$	−7.79492	−	7.79492i	−0.246867	−	0.246867i	0.572816	−	0.819684i	$-0.305851\pi$
$997$	−7.79492	−	7.79492i	−0.246867	−	0.246867i	−0.819684	+	0.572816i	$0.805851\pi$
$998$	1.62920	−	17.0178i	0.0515716	−	0.538690i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.b.107.5	✓	32
3.2	odd	2	inner	432.2.l.b.107.12	yes	32
4.3	odd	2		1728.2.l.b.1295.12		32
12.11	even	2		1728.2.l.b.1295.5		32
16.3	odd	4	inner	432.2.l.b.323.12	yes	32
16.13	even	4		1728.2.l.b.431.5		32
48.29	odd	4		1728.2.l.b.431.12		32
48.35	even	4	inner	432.2.l.b.323.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.b.107.5	✓	32	1.1	even	1	trivial
432.2.l.b.107.12	yes	32	3.2	odd	2	inner
432.2.l.b.323.5	yes	32	48.35	even	4	inner
432.2.l.b.323.12	yes	32	16.3	odd	4	inner
1728.2.l.b.431.5		32	16.13	even	4
1728.2.l.b.431.12		32	48.29	odd	4
1728.2.l.b.1295.5		32	12.11	even	2
1728.2.l.b.1295.12		32	4.3	odd	2

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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900149 - 1.09075i) q^{2} +(-0.379462 + 1.96367i) q^{4} +(1.29039 - 1.29039i) q^{5} -3.83003 q^{7} +(2.48344 - 1.35370i) q^{8} +O(q^{10})\)	\(q+(-0.900149 - 1.09075i) q^{2} +(-0.379462 + 1.96367i) q^{4} +(1.29039 - 1.29039i) q^{5} -3.83003 q^{7} +(2.48344 - 1.35370i) q^{8} +(-2.56904 - 0.245948i) q^{10} +(-1.73926 - 1.73926i) q^{11} +(0.145981 - 0.145981i) q^{13} +(3.44760 + 4.17760i) q^{14} +(-3.71202 - 1.49028i) q^{16} +2.19496i q^{17} +(-4.91334 - 4.91334i) q^{19} +(2.04426 + 3.02357i) q^{20} +(-0.331501 + 3.46269i) q^{22} -9.44891i q^{23} +1.66976i q^{25} +(-0.290633 - 0.0278238i) q^{26} +(1.45335 - 7.52093i) q^{28} +(-5.42030 - 5.42030i) q^{29} +4.73544i q^{31} +(1.71585 + 5.39035i) q^{32} +(2.39415 - 1.97579i) q^{34} +(-4.94226 + 4.94226i) q^{35} +(0.955378 + 0.955378i) q^{37} +(-0.936477 + 9.78196i) q^{38} +(1.45782 - 4.95143i) q^{40} -7.05050 q^{41} +(-1.66838 + 1.66838i) q^{43} +(4.07532 - 2.75535i) q^{44} +(-10.3064 + 8.50543i) q^{46} -4.20126 q^{47} +7.66916 q^{49} +(1.82129 - 1.50304i) q^{50} +(0.231265 + 0.342053i) q^{52} +(3.96958 - 3.96958i) q^{53} -4.48866 q^{55} +(-9.51167 + 5.18472i) q^{56} +(-1.03310 + 10.7913i) q^{58} +(5.64431 + 5.64431i) q^{59} +(0.214341 - 0.214341i) q^{61} +(5.16517 - 4.26260i) q^{62} +(4.33499 - 6.72368i) q^{64} -0.376746i q^{65} +(3.96018 + 3.96018i) q^{67} +(-4.31018 - 0.832904i) q^{68} +(9.83952 + 0.941987i) q^{70} +0.302489i q^{71} +1.89455i q^{73} +(0.182094 - 1.90206i) q^{74} +(11.5126 - 7.78376i) q^{76} +(6.66142 + 6.66142i) q^{77} -14.5211i q^{79} +(-6.71302 + 2.86692i) q^{80} +(6.34650 + 7.69032i) q^{82} +(6.41307 - 6.41307i) q^{83} +(2.83236 + 2.83236i) q^{85} +(3.32156 + 0.317990i) q^{86} +(-6.67379 - 1.96492i) q^{88} -16.5738 q^{89} +(-0.559112 + 0.559112i) q^{91} +(18.5546 + 3.58551i) q^{92} +(3.78177 + 4.58252i) q^{94} -12.6803 q^{95} +17.2736 q^{97} +(-6.90339 - 8.36512i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

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