LMFDB - Embedded newform 432.2.u.a.385.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			385.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	432.385
Dual form			432.2.u.a.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11334 + 1.32683i) q^{3} +(0.439693 + 2.49362i) q^{5} +(1.79813 + 1.50881i) q^{7} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$	\(q+(1.11334 + 1.32683i) q^{3} +(0.439693 + 2.49362i) q^{5} +(1.79813 + 1.50881i) q^{7} +(-0.520945 + 2.95442i) q^{9} +(0.745100 - 4.22567i) q^{11} +(-0.713011 - 0.259515i) q^{13} +(-2.81908 + 3.35965i) q^{15} +(-2.46064 - 4.26195i) q^{17} +(-3.62449 + 6.27779i) q^{19} +4.06564i q^{21} +(0.233956 - 0.196312i) q^{23} +(-1.32635 + 0.482753i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(2.91875 - 1.06234i) q^{29} +(6.58512 - 5.52557i) q^{31} +(6.43629 - 3.71599i) q^{33} +(-2.97178 + 5.14728i) q^{35} +(3.78699 + 6.55926i) q^{37} +(-0.449493 - 1.23497i) q^{39} +(-4.60607 - 1.67647i) q^{41} +(0.283119 - 1.60565i) q^{43} -7.59627 q^{45} +(1.39053 + 1.16679i) q^{47} +(-0.258770 - 1.46756i) q^{49} +(2.91534 - 8.00984i) q^{51} +0.573978 q^{53} +10.8648 q^{55} +(-12.3648 + 2.18025i) q^{57} +(-0.950837 - 5.39246i) q^{59} +(8.46451 + 7.10257i) q^{61} +(-5.39440 + 4.52644i) q^{63} +(0.333626 - 1.89209i) q^{65} +(0.0393628 + 0.0143269i) q^{67} +(0.520945 + 0.0918566i) q^{69} +(-2.10220 - 3.64111i) q^{71} +(5.54576 - 9.60554i) q^{73} +(-2.11721 - 1.22237i) q^{75} +(7.71554 - 6.47410i) q^{77} +(-6.92989 + 2.52227i) q^{79} +(-8.45723 - 3.07818i) q^{81} +(6.41147 - 2.33359i) q^{83} +(9.54576 - 8.00984i) q^{85} +(4.65910 + 2.68993i) q^{87} +(-3.96064 + 6.86002i) q^{89} +(-0.890530 - 1.54244i) q^{91} +(14.6630 + 2.58548i) q^{93} +(-17.2481 - 6.27779i) q^{95} +(-0.570108 + 3.23324i) q^{97} +(12.0963 + 4.40268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q - 3 * q^5 - 3 * q^7	$ 6 q - 3 q^{5} - 3 q^{7} + 3 q^{11} - 12 q^{13} - 6 q^{17} - 9 q^{19} + 6 q^{23} - 9 q^{25} - 27 q^{27} + 15 q^{29} + 18 q^{31} - 9 q^{33} - 3 q^{35} + 15 q^{37} - 3 q^{41} + 18 q^{43} - 18 q^{45} - 9 q^{47} + 21 q^{49} - 27 q^{51} - 12 q^{53} + 18 q^{55} - 27 q^{57} + 6 q^{59} + 18 q^{61} + 9 q^{63} + 21 q^{65} + 9 q^{67} - 12 q^{71} + 3 q^{73} + 18 q^{75} + 39 q^{77} - 33 q^{79} + 18 q^{83} + 27 q^{85} - 9 q^{87} - 15 q^{89} + 12 q^{91} + 27 q^{93} - 21 q^{95} - 12 q^{97} + 45 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 3 * q^7 + 3 * q^11 - 12 * q^13 - 6 * q^17 - 9 * q^19 + 6 * q^23 - 9 * q^25 - 27 * q^27 + 15 * q^29 + 18 * q^31 - 9 * q^33 - 3 * q^35 + 15 * q^37 - 3 * q^41 + 18 * q^43 - 18 * q^45 - 9 * q^47 + 21 * q^49 - 27 * q^51 - 12 * q^53 + 18 * q^55 - 27 * q^57 + 6 * q^59 + 18 * q^61 + 9 * q^63 + 21 * q^65 + 9 * q^67 - 12 * q^71 + 3 * q^73 + 18 * q^75 + 39 * q^77 - 33 * q^79 + 18 * q^83 + 27 * q^85 - 9 * q^87 - 15 * q^89 + 12 * q^91 + 27 * q^93 - 21 * q^95 - 12 * q^97 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$4$		0			0
$5$	0.439693	+	2.49362i	0.196637	+	1.11518i	0.910069	+	0.414457i	$0.136028\pi$
$5$	0.439693	+	2.49362i	0.196637	+	1.11518i	−0.713432	+	0.700724i	$0.752860\pi$
$6$		0			0
$7$	1.79813	+	1.50881i	0.679631	+	0.570278i	0.915898	−	0.401410i	$-0.131480\pi$
$7$	1.79813	+	1.50881i	0.679631	+	0.570278i	−0.236268	+	0.971688i	$0.575924\pi$
$8$		0			0
$9$	−0.520945	+	2.95442i	−0.173648	+	0.984808i
$10$		0			0
$11$	0.745100	−	4.22567i	0.224656	−	1.27409i	−0.638685	−	0.769468i	$-0.720521\pi$
$11$	0.745100	−	4.22567i	0.224656	−	1.27409i	0.863342	−	0.504620i	$-0.168367\pi$
$12$		0			0
$13$	−0.713011	−	0.259515i	−0.197754	−	0.0719765i	0.241245	−	0.970464i	$-0.422444\pi$
$13$	−0.713011	−	0.259515i	−0.197754	−	0.0719765i	−0.438998	+	0.898488i	$0.644667\pi$
$14$		0			0
$15$	−2.81908	+	3.35965i	−0.727883	+	0.867457i
$16$		0			0
$17$	−2.46064	−	4.26195i	−0.596792	−	1.03367i	−0.993291	−	0.115639i	$-0.963108\pi$
$17$	−2.46064	−	4.26195i	−0.596792	−	1.03367i	0.396499	−	0.918035i	$-0.370225\pi$
$18$		0			0
$19$	−3.62449	+	6.27779i	−0.831514	+	1.44022i	0.0653235	+	0.997864i	$0.479192\pi$
$19$	−3.62449	+	6.27779i	−0.831514	+	1.44022i	−0.896837	+	0.442360i	$0.854141\pi$
$20$		0			0
$21$			4.06564i			0.887195i
$22$		0			0
$23$	0.233956	−	0.196312i	0.0487831	−	0.0409339i	−0.618070	−	0.786123i	$-0.712085\pi$
$23$	0.233956	−	0.196312i	0.0487831	−	0.0409339i	0.666853	+	0.745189i	$0.267641\pi$
$24$		0			0
$25$	−1.32635	+	0.482753i	−0.265270	+	0.0965505i
$26$		0			0
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$		0			0
$29$	2.91875	−	1.06234i	0.541998	−	0.197271i	−0.0564897	−	0.998403i	$-0.517991\pi$
$29$	2.91875	−	1.06234i	0.541998	−	0.197271i	0.598488	+	0.801132i	$0.295769\pi$
$30$		0			0
$31$	6.58512	−	5.52557i	1.18272	−	0.992422i	0.182766	−	0.983156i	$-0.441495\pi$
$31$	6.58512	−	5.52557i	1.18272	−	0.992422i	0.999957	−	0.00926586i	$-0.00294946\pi$
$32$		0			0
$33$	6.43629	−	3.71599i	1.12041	−	0.646871i
$34$		0			0
$35$	−2.97178	+	5.14728i	−0.502323	+	0.870049i
$36$		0			0
$37$	3.78699	+	6.55926i	0.622577	+	1.07834i	0.989004	+	0.147888i	$0.0472477\pi$
$37$	3.78699	+	6.55926i	0.622577	+	1.07834i	−0.366427	+	0.930447i	$0.619419\pi$
$38$		0			0
$39$	−0.449493	−	1.23497i	−0.0719765	−	0.197754i
$40$		0			0
$41$	−4.60607	−	1.67647i	−0.719347	−	0.261821i	−0.0436983	−	0.999045i	$-0.513914\pi$
$41$	−4.60607	−	1.67647i	−0.719347	−	0.261821i	−0.675648	+	0.737224i	$0.736136\pi$
$42$		0			0
$43$	0.283119	−	1.60565i	0.0431752	−	0.244859i	−0.955580	−	0.294730i	$-0.904770\pi$
$43$	0.283119	−	1.60565i	0.0431752	−	0.244859i	0.998756	+	0.0498718i	$0.0158813\pi$
$44$		0			0
$45$	−7.59627			−1.13238
$46$		0			0
$47$	1.39053	+	1.16679i	0.202830	+	0.170194i	0.738545	−	0.674205i	$-0.235513\pi$
$47$	1.39053	+	1.16679i	0.202830	+	0.170194i	−0.535715	+	0.844399i	$0.679958\pi$
$48$		0			0
$49$	−0.258770	−	1.46756i	−0.0369672	−	0.209651i
$50$		0			0
$51$	2.91534	−	8.00984i	0.408230	−	1.12160i
$52$		0			0
$53$	0.573978			0.0788419			0.0394210	−	0.999223i	$-0.487449\pi$
$53$	0.573978			0.0788419			0.0394210	+	0.999223i	$0.487449\pi$
$54$		0			0
$55$	10.8648			1.46501
$56$		0			0
$57$	−12.3648	+	2.18025i	−1.63776	+	0.288782i
$58$		0			0
$59$	−0.950837	−	5.39246i	−0.123788	−	0.702039i	−0.982020	−	0.188777i	$-0.939548\pi$
$59$	−0.950837	−	5.39246i	−0.123788	−	0.702039i	0.858232	−	0.513263i	$-0.171563\pi$
$60$		0			0
$61$	8.46451	+	7.10257i	1.08377	+	0.909390i	0.996228	−	0.0867707i	$-0.0276547\pi$
$61$	8.46451	+	7.10257i	1.08377	+	0.909390i	0.0875408	+	0.996161i	$0.472099\pi$
$62$		0			0
$63$	−5.39440	+	4.52644i	−0.679631	+	0.570278i
$64$		0			0
$65$	0.333626	−	1.89209i	0.0413812	−	0.234684i
$66$		0			0
$67$	0.0393628	+	0.0143269i	0.00480894	+	0.00175031i	0.344423	−	0.938814i	$-0.388074\pi$
$67$	0.0393628	+	0.0143269i	0.00480894	+	0.00175031i	−0.339615	+	0.940565i	$0.610297\pi$
$68$		0			0
$69$	0.520945	+	0.0918566i	0.0627144	+	0.0110582i
$70$		0			0
$71$	−2.10220	−	3.64111i	−0.249485	−	0.432120i	0.713898	−	0.700250i	$-0.246928\pi$
$71$	−2.10220	−	3.64111i	−0.249485	−	0.432120i	−0.963383	+	0.268129i	$0.913595\pi$
$72$		0			0
$73$	5.54576	−	9.60554i	0.649082	−	1.12424i	−0.334260	−	0.942481i	$-0.608487\pi$
$73$	5.54576	−	9.60554i	0.649082	−	1.12424i	0.983342	−	0.181762i	$-0.0581802\pi$
$74$		0			0
$75$	−2.11721	−	1.22237i	−0.244474	−	0.141147i
$76$		0			0
$77$	7.71554	−	6.47410i	0.879267	−	0.737793i
$78$		0			0
$79$	−6.92989	+	2.52227i	−0.779674	+	0.283778i	−0.701037	−	0.713125i	$-0.747279\pi$
$79$	−6.92989	+	2.52227i	−0.779674	+	0.283778i	−0.0786372	+	0.996903i	$0.525057\pi$
$80$		0			0
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$		0			0
$83$	6.41147	−	2.33359i	0.703751	−	0.256144i	0.0347393	−	0.999396i	$-0.488940\pi$
$83$	6.41147	−	2.33359i	0.703751	−	0.256144i	0.669011	+	0.743252i	$0.266718\pi$
$84$		0			0
$85$	9.54576	−	8.00984i	1.03538	−	0.868789i
$86$		0			0
$87$	4.65910	+	2.68993i	0.499508	+	0.288391i
$88$		0			0
$89$	−3.96064	+	6.86002i	−0.419827	+	0.727161i	−0.995922	−	0.0902216i	$-0.971242\pi$
$89$	−3.96064	+	6.86002i	−0.419827	+	0.727161i	0.576095	+	0.817383i	$0.304576\pi$
$90$		0			0
$91$	−0.890530	−	1.54244i	−0.0933529	−	0.161692i
$92$		0			0
$93$	14.6630	+	2.58548i	1.52048	+	0.268102i
$94$		0			0
$95$	−17.2481	−	6.27779i	−1.76962	−	0.644088i
$96$		0			0
$97$	−0.570108	+	3.23324i	−0.0578857	+	0.328286i	−0.999975	−	0.00707624i	$-0.997748\pi$
$97$	−0.570108	+	3.23324i	−0.0578857	+	0.328286i	0.942089	+	0.335362i	$0.108859\pi$
$98$		0			0
$99$	12.0963	+	4.40268i	1.21572	+	0.442486i
$100$		0			0
$101$	−9.18732	−	7.70908i	−0.914172	−	0.767082i	0.0587358	−	0.998274i	$-0.481293\pi$
$101$	−9.18732	−	7.70908i	−0.914172	−	0.767082i	−0.972908	+	0.231192i	$0.925737\pi$
$102$		0			0
$103$	−0.418748	−	2.37484i	−0.0412605	−	0.234000i	0.957203	−	0.289418i	$-0.0934618\pi$
$103$	−0.418748	−	2.37484i	−0.0412605	−	0.234000i	−0.998463	+	0.0554184i	$0.982351\pi$
$104$		0			0
$105$	−10.1382	+	1.78763i	−0.989383	+	0.174455i
$106$		0			0
$107$	2.42602			0.234532			0.117266	−	0.993101i	$-0.462587\pi$
$107$	2.42602			0.234532			0.117266	+	0.993101i	$0.462587\pi$
$108$		0			0
$109$	−2.32770			−0.222953			−0.111476	−	0.993767i	$-0.535558\pi$
$109$	−2.32770			−0.222953			−0.111476	+	0.993767i	$0.535558\pi$
$110$		0			0
$111$	−4.48680	+	12.3274i	−0.425868	+	1.17006i
$112$		0			0
$113$	−2.96198	−	16.7982i	−0.278640	−	1.58024i	−0.727157	−	0.686471i	$-0.759159\pi$
$113$	−2.96198	−	16.7982i	−0.278640	−	1.58024i	0.448518	−	0.893774i	$-0.351952\pi$
$114$		0			0
$115$	0.592396	+	0.497079i	0.0552412	+	0.0463529i
$116$		0			0
$117$	1.13816	−	1.97134i	0.105223	−	0.182251i
$118$		0			0
$119$	2.00593	−	11.3762i	0.183883	−	1.04285i
$120$		0			0
$121$	−6.96451	−	2.53487i	−0.633137	−	0.230443i
$122$		0			0
$123$	−2.90373	−	7.97794i	−0.261821	−	0.719347i
$124$		0			0
$125$	4.54323	+	7.86911i	0.406359	+	0.703835i
$126$		0			0
$127$	6.32295	−	10.9517i	0.561071	−	0.971803i	−0.436332	−	0.899786i	$-0.643723\pi$
$127$	6.32295	−	10.9517i	0.561071	−	0.971803i	0.997403	−	0.0720178i	$-0.0229438\pi$
$128$		0			0
$129$	2.44562	−	1.41198i	0.215325	−	0.124318i
$130$		0			0
$131$	3.97565	−	3.33597i	0.347354	−	0.291465i	−0.452372	−	0.891829i	$-0.649422\pi$
$131$	3.97565	−	3.33597i	0.347354	−	0.291465i	0.799727	+	0.600364i	$0.204978\pi$
$132$		0			0
$133$	−15.9893	+	5.81964i	−1.38645	+	0.504627i
$134$		0			0
$135$	−8.45723	−	10.0789i	−0.727883	−	0.867457i
$136$		0			0
$137$	16.0817	−	5.85327i	1.37395	−	0.500078i	0.453614	−	0.891198i	$-0.350134\pi$
$137$	16.0817	−	5.85327i	1.37395	−	0.500078i	0.920340	+	0.391120i	$0.127912\pi$
$138$		0			0
$139$	−9.34389	+	7.84046i	−0.792539	+	0.665019i	−0.946372	−	0.323078i	$-0.895282\pi$
$139$	−9.34389	+	7.84046i	−0.792539	+	0.665019i	0.153834	+	0.988097i	$0.450838\pi$
$140$		0			0
$141$			3.14403i			0.264775i
$142$		0			0
$143$	−1.62789	+	2.81959i	−0.136131	+	0.235786i
$144$		0			0
$145$	3.93242	+	6.81115i	0.326570	+	0.565635i
$146$		0			0
$147$	1.65910	−	1.97724i	0.136840	−	0.163080i
$148$		0			0
$149$	−7.23783	−	2.63435i	−0.592946	−	0.215815i	0.0280788	−	0.999606i	$-0.491061\pi$
$149$	−7.23783	−	2.63435i	−0.592946	−	0.215815i	−0.621025	+	0.783791i	$0.713283\pi$
$150$		0			0
$151$	0.135630	−	0.769193i	0.0110374	−	0.0625961i	−0.978792	−	0.204858i	$-0.934327\pi$
$151$	0.135630	−	0.769193i	0.0110374	−	0.0625961i	0.989829	+	0.142262i	$0.0454377\pi$
$152$		0			0
$153$	13.8735	−	5.04952i	1.12160	−	0.408230i
$154$		0			0
$155$	16.6741	+	13.9912i	1.33930	+	1.12380i
$156$		0			0
$157$	−1.80793	−	10.2533i	−0.144289	−	0.818302i	−0.967935	−	0.251199i	$-0.919175\pi$
$157$	−1.80793	−	10.2533i	−0.144289	−	0.818302i	0.823647	−	0.567103i	$-0.191936\pi$
$158$		0			0
$159$	0.639033	+	0.761570i	0.0506786	+	0.0603964i
$160$		0			0
$161$	0.716881			0.0564982
$162$		0			0
$163$	10.5740			0.828218			0.414109	−	0.910227i	$-0.364093\pi$
$163$	10.5740			0.828218			0.414109	+	0.910227i	$0.364093\pi$
$164$		0			0
$165$	12.0963	+	14.4158i	0.941693	+	1.12227i
$166$		0			0
$167$	−0.260992	−	1.48016i	−0.0201962	−	0.114538i	0.973043	−	0.230623i	$-0.0740765\pi$
$167$	−0.260992	−	1.48016i	−0.0201962	−	0.114538i	−0.993239	+	0.116085i	$0.962965\pi$
$168$		0			0
$169$	−9.51754	−	7.98617i	−0.732119	−	0.614320i
$170$		0			0
$171$	−16.6591	−	13.9786i	−1.27395	−	1.06897i
$172$		0			0
$173$	−1.93629	+	10.9812i	−0.147213	+	0.834888i	0.818350	+	0.574720i	$0.194889\pi$
$173$	−1.93629	+	10.9812i	−0.147213	+	0.834888i	−0.965563	+	0.260168i	$0.916222\pi$
$174$		0			0
$175$	−3.11334	−	1.13316i	−0.235346	−	0.0856591i
$176$		0			0
$177$	6.09627	−	7.26525i	0.458223	−	0.546089i
$178$		0			0
$179$	3.90420	+	6.76227i	0.291814	+	0.505436i	0.974239	−	0.225520i	$-0.0724080\pi$
$179$	3.90420	+	6.76227i	0.291814	+	0.505436i	−0.682425	+	0.730956i	$0.739075\pi$
$180$		0			0
$181$	−5.23783	+	9.07218i	−0.389325	+	0.674330i	−0.992359	−	0.123385i	$-0.960625\pi$
$181$	−5.23783	+	9.07218i	−0.389325	+	0.674330i	0.603034	+	0.797715i	$0.293958\pi$
$182$		0			0
$183$			19.1385i			1.41476i
$184$		0			0
$185$	−14.6912	+	12.3274i	−1.08012	+	0.906326i
$186$		0			0
$187$	−19.8430	+	7.22227i	−1.45107	+	0.528144i
$188$		0			0
$189$	−12.0116	−	2.11797i	−0.873716	−	0.154060i
$190$		0			0
$191$	−11.4918	+	4.18269i	−0.831521	+	0.302649i	−0.722483	−	0.691389i	$-0.756999\pi$
$191$	−11.4918	+	4.18269i	−0.831521	+	0.302649i	−0.109038	+	0.994038i	$0.534777\pi$
$192$		0			0
$193$	−12.5385	+	10.5210i	−0.902540	+	0.757321i	−0.970685	−	0.240354i	$-0.922736\pi$
$193$	−12.5385	+	10.5210i	−0.902540	+	0.757321i	0.0681452	+	0.997675i	$0.478292\pi$
$194$		0			0
$195$	2.88191	−	1.66387i	0.206378	−	0.119152i
$196$		0			0
$197$	−9.49794	+	16.4509i	−0.676700	+	1.17208i	0.299269	+	0.954169i	$0.403257\pi$
$197$	−9.49794	+	16.4509i	−0.676700	+	1.17208i	−0.975969	+	0.217910i	$0.930076\pi$
$198$		0			0
$199$	11.5214	+	19.9557i	0.816731	+	1.41462i	0.908078	+	0.418801i	$0.137549\pi$
$199$	11.5214	+	19.9557i	0.816731	+	1.41462i	−0.0913469	+	0.995819i	$0.529117\pi$
$200$		0			0
$201$	0.0248149	+	0.0681784i	0.00175031	+	0.00480894i
$202$		0			0
$203$	6.85117	+	2.49362i	0.480858	+	0.175018i
$204$		0			0
$205$	2.15523	−	12.2229i	0.150528	−	0.853685i
$206$		0			0
$207$	0.458111	+	0.793471i	0.0318409	+	0.0551501i
$208$		0			0
$209$	23.8273	+	19.9935i	1.64817	+	1.38298i
$210$		0			0
$211$	−3.03849	−	17.2321i	−0.209178	−	1.18631i	−0.890728	−	0.454536i	$-0.849805\pi$
$211$	−3.03849	−	17.2321i	−0.209178	−	1.18631i	0.681550	−	0.731771i	$-0.261306\pi$
$212$		0			0
$213$	2.49067	−	6.84305i	0.170658	−	0.468878i
$214$		0			0
$215$	4.12836			0.281552
$216$		0			0
$217$	20.1780			1.36977
$218$		0			0
$219$	18.9192	−	3.33597i	1.27844	−	0.225424i
$220$		0			0
$221$	0.648423	+	3.67739i	0.0436176	+	0.247368i
$222$		0			0
$223$	3.23190	+	2.71188i	0.216424	+	0.181601i	0.744554	−	0.667562i	$-0.232662\pi$
$223$	3.23190	+	2.71188i	0.216424	+	0.181601i	−0.528130	+	0.849163i	$0.677107\pi$
$224$		0			0
$225$	−0.735300	−	4.17009i	−0.0490200	−	0.278006i
$226$		0			0
$227$	−2.77244	+	15.7233i	−0.184013	+	1.04359i	0.743203	+	0.669066i	$0.233306\pi$
$227$	−2.77244	+	15.7233i	−0.184013	+	1.04359i	−0.927216	+	0.374526i	$0.877806\pi$
$228$		0			0
$229$	16.7713	+	6.10424i	1.10828	+	0.403379i	0.830361	−	0.557226i	$-0.188134\pi$
$229$	16.7713	+	6.10424i	1.10828	+	0.403379i	0.277915	+	0.960606i	$0.410357\pi$
$230$		0			0
$231$	17.1800	+	3.02931i	1.13036	+	0.199314i
$232$		0			0
$233$	0.368241	+	0.637812i	0.0241243	+	0.0417844i	0.877835	−	0.478962i	$-0.158987\pi$
$233$	0.368241	+	0.637812i	0.0241243	+	0.0417844i	−0.853711	+	0.520747i	$0.825654\pi$
$234$		0			0
$235$	−2.29813	+	3.98048i	−0.149914	+	0.259658i
$236$		0			0
$237$	−11.0620	−	6.38662i	−0.718551	−	0.414856i
$238$		0			0
$239$	2.20187	−	1.84759i	0.142427	−	0.119510i	−0.568791	−	0.822482i	$-0.692589\pi$
$239$	2.20187	−	1.84759i	0.142427	−	0.119510i	0.711218	+	0.702972i	$0.248144\pi$
$240$		0			0
$241$	−2.05051	+	0.746324i	−0.132085	+	0.0480749i	−0.407217	−	0.913332i	$-0.633501\pi$
$241$	−2.05051	+	0.746324i	−0.132085	+	0.0480749i	0.275132	+	0.961406i	$0.411278\pi$
$242$		0			0
$243$	−5.33157	−	14.6484i	−0.342020	−	0.939693i
$244$		0			0
$245$	3.54576	−	1.29055i	0.226530	−	0.0824503i
$246$		0			0
$247$	4.21348	−	3.53553i	0.268097	−	0.224960i
$248$		0			0
$249$	10.2344	+	5.90885i	0.648580	+	0.374458i
$250$		0			0
$251$	−13.0189	+	22.5494i	−0.821745	+	1.42330i	0.0826372	+	0.996580i	$0.473666\pi$
$251$	−13.0189	+	22.5494i	−0.821745	+	1.42330i	−0.904382	+	0.426724i	$0.859668\pi$
$252$		0			0
$253$	−0.655230	−	1.13489i	−0.0411939	−	0.0713500i
$254$		0			0
$255$	21.2554	+	3.74789i	1.33106	+	0.234702i
$256$		0			0
$257$	−9.38965	−	3.41755i	−0.585710	−	0.213181i	0.0321313	−	0.999484i	$-0.489771\pi$
$257$	−9.38965	−	3.41755i	−0.585710	−	0.213181i	−0.617842	+	0.786302i	$0.711993\pi$
$258$		0			0
$259$	−3.08718	+	17.5083i	−0.191828	+	1.08791i
$260$		0			0
$261$	1.61809	+	9.17664i	0.100157	+	0.568020i
$262$		0			0
$263$	−11.6612	−	9.78487i	−0.719058	−	0.603361i	0.208067	−	0.978115i	$-0.433283\pi$
$263$	−11.6612	−	9.78487i	−0.719058	−	0.603361i	−0.927125	+	0.374753i	$0.877727\pi$
$264$		0			0
$265$	0.252374	+	1.43128i	0.0155032	+	0.0879230i
$266$		0			0
$267$	−13.5116	+	2.38246i	−0.826897	+	0.145804i
$268$		0			0
$269$	30.5476			1.86252			0.931259	−	0.364358i	$-0.118711\pi$
$269$	30.5476			1.86252			0.931259	+	0.364358i	$0.118711\pi$
$270$		0			0
$271$	−25.8307			−1.56910			−0.784551	−	0.620064i	$-0.787107\pi$
$271$	−25.8307			−1.56910			−0.784551	+	0.620064i	$0.787107\pi$
$272$		0			0
$273$	1.05509	−	2.89884i	0.0638571	−	0.175446i
$274$		0			0
$275$	1.05169	+	5.96443i	0.0634192	+	0.359668i
$276$		0			0
$277$	−17.1860	−	14.4207i	−1.03261	−	0.866459i	−0.0414465	−	0.999141i	$-0.513197\pi$
$277$	−17.1860	−	14.4207i	−1.03261	−	0.866459i	−0.991159	+	0.132682i	$0.957641\pi$
$278$		0			0
$279$	12.8944	+	22.3338i	0.771968	+	1.33709i
$280$		0			0
$281$	1.01485	−	5.75552i	0.0605410	−	0.343345i	−0.939459	−	0.342662i	$-0.888671\pi$
$281$	1.01485	−	5.75552i	0.0605410	−	0.343345i	1.00000		0.000683195i	$-0.000217468\pi$
$282$		0			0
$283$	−6.96451	−	2.53487i	−0.413997	−	0.150683i	0.126620	−	0.991951i	$-0.459587\pi$
$283$	−6.96451	−	2.53487i	−0.413997	−	0.150683i	−0.540617	+	0.841269i	$0.681809\pi$
$284$		0			0
$285$	−10.8735	−	29.8746i	−0.644088	−	1.76962i
$286$		0			0
$287$	−5.75284	−	9.96421i	−0.339579	−	0.588169i
$288$		0			0
$289$	−3.60947	+	6.25179i	−0.212322	+	0.367752i
$290$		0			0
$291$	−4.92468	+	2.84326i	−0.288690	+	0.166675i
$292$		0			0
$293$	−6.79994	+	5.70583i	−0.397257	+	0.333338i	−0.819432	−	0.573176i	$-0.805711\pi$
$293$	−6.79994	+	5.70583i	−0.397257	+	0.333338i	0.422175	+	0.906514i	$0.361267\pi$
$294$		0			0
$295$	13.0287	−	4.74205i	0.758559	−	0.276093i
$296$		0			0
$297$	7.62567	+	20.9513i	0.442486	+	1.21572i
$298$		0			0
$299$	−0.217759	+	0.0792577i	−0.0125933	+	0.00458359i
$300$		0			0
$301$	2.93170	−	2.45999i	0.168981	−	0.141792i
$302$		0			0
$303$		−	20.7728i		−	1.19337i
$304$		0			0
$305$	−13.9893	+	24.2302i	−0.801026	+	1.38742i
$306$		0			0
$307$	−8.04963	−	13.9424i	−0.459417	−	0.795733i	0.539514	−	0.841977i	$-0.318608\pi$
$307$	−8.04963	−	13.9424i	−0.459417	−	0.795733i	−0.998930	+	0.0462440i	$0.985275\pi$
$308$		0			0
$309$	2.68479	−	3.19961i	0.152733	−	0.182020i
$310$		0			0
$311$	12.7699	+	4.64787i	0.724115	+	0.263556i	0.677672	−	0.735364i	$-0.262989\pi$
$311$	12.7699	+	4.64787i	0.724115	+	0.263556i	0.0464436	+	0.998921i	$0.485211\pi$
$312$		0			0
$313$	−3.73442	+	21.1790i	−0.211082	+	1.19711i	0.676495	+	0.736447i	$0.263498\pi$
$313$	−3.73442	+	21.1790i	−0.211082	+	1.19711i	−0.887577	+	0.460659i	$0.847613\pi$
$314$		0			0
$315$	−13.6591	−	11.4613i	−0.769603	−	0.645774i
$316$		0			0
$317$	−16.1578	−	13.5580i	−0.907510	−	0.761491i	0.0641337	−	0.997941i	$-0.479572\pi$
$317$	−16.1578	−	13.5580i	−0.907510	−	0.761491i	−0.971644	+	0.236450i	$0.924016\pi$
$318$		0			0
$319$	−2.31433	−	13.1252i	−0.129578	−	0.734871i
$320$		0			0
$321$	2.70099	+	3.21891i	0.150755	+	0.179662i
$322$		0			0
$323$	35.6742			1.98496
$324$		0			0
$325$	1.07098			0.0594076
$326$		0			0
$327$	−2.59152	−	3.08845i	−0.143311	−	0.170792i
$328$		0			0
$329$	0.739885	+	4.19610i	0.0407912	+	0.231338i
$330$		0			0
$331$	−12.5929	−	10.5667i	−0.692166	−	0.580797i	0.227367	−	0.973809i	$-0.426988\pi$
$331$	−12.5929	−	10.5667i	−0.692166	−	0.580797i	−0.919533	+	0.393013i	$0.871433\pi$
$332$		0			0
$333$	−21.3516	+	7.77136i	−1.17006	+	0.425868i
$334$		0			0
$335$	−0.0184183	+	0.104455i	−0.00100630	+	0.00570701i
$336$		0			0
$337$	−9.91534	−	3.60889i	−0.540123	−	0.196589i	0.0575296	−	0.998344i	$-0.481678\pi$
$337$	−9.91534	−	3.60889i	−0.540123	−	0.196589i	−0.597653	+	0.801755i	$0.703900\pi$
$338$		0			0
$339$	18.9907	−	22.6322i	1.03143	−	1.22921i
$340$		0			0
$341$	−18.4427	−	31.9437i	−0.998727	−	1.72985i
$342$		0			0
$343$	9.96451	−	17.2590i	0.538033	−	0.931900i
$344$		0			0
$345$			1.33943i			0.0721123i
$346$		0			0
$347$	−21.7251	+	18.2295i	−1.16626	+	0.978612i	−0.999972	−	0.00746500i	$-0.997624\pi$
$347$	−21.7251	+	18.2295i	−1.16626	+	0.978612i	−0.166292	+	0.986077i	$0.553179\pi$
$348$		0			0
$349$	−14.7554	+	5.37051i	−0.789837	+	0.287477i	−0.705268	−	0.708941i	$-0.749173\pi$
$349$	−14.7554	+	5.37051i	−0.789837	+	0.287477i	−0.0845685	+	0.996418i	$0.526951\pi$
$350$		0			0
$351$	3.88279	−	0.684640i	0.207248	−	0.0365434i
$352$		0			0
$353$	1.93969	−	0.705990i	0.103239	−	0.0375761i	−0.289884	−	0.957062i	$-0.593617\pi$
$353$	1.93969	−	0.705990i	0.103239	−	0.0375761i	0.393123	+	0.919486i	$0.371395\pi$
$354$		0			0
$355$	8.15523	−	6.84305i	0.432835	−	0.363191i
$356$		0			0
$357$	17.3275	−	10.0041i	0.917070	−	0.529471i
$358$		0			0
$359$	−17.4820	+	30.2798i	−0.922667	+	1.59811i	−0.127397	+	0.991852i	$0.540662\pi$
$359$	−17.4820	+	30.2798i	−0.922667	+	1.59811i	−0.795271	+	0.606255i	$0.792671\pi$
$360$		0			0
$361$	−16.7738	−	29.0530i	−0.882831	−	1.52911i
$362$		0			0
$363$	−4.39053	−	12.0629i	−0.230443	−	0.633137i
$364$		0			0
$365$	26.3910	+	9.60554i	1.38137	+	0.502777i
$366$		0			0
$367$	0.0773815	−	0.438852i	0.00403928	−	0.0229079i	−0.982722	−	0.185090i	$-0.940742\pi$
$367$	0.0773815	−	0.438852i	0.00403928	−	0.0229079i	0.986761	+	0.162182i	$0.0518533\pi$
$368$		0			0
$369$	7.35251	−	12.7349i	0.382756	−	0.662954i
$370$		0			0
$371$	1.03209	+	0.866025i	0.0535834	+	0.0449618i
$372$		0			0
$373$	−3.83110	−	21.7272i	−0.198367	−	1.12499i	−0.907542	−	0.419962i	$-0.862044\pi$
$373$	−3.83110	−	21.7272i	−0.198367	−	1.12499i	0.709175	−	0.705032i	$-0.249068\pi$
$374$		0			0
$375$	−5.38279	+	14.7891i	−0.277966	+	0.763705i
$376$		0			0
$377$	−2.35679			−0.121381
$378$		0			0
$379$	−13.1138			−0.673611			−0.336806	−	0.941574i	$-0.609346\pi$
$379$	−13.1138			−0.673611			−0.336806	+	0.941574i	$0.609346\pi$
$380$		0			0
$381$	21.5706	−	3.80347i	1.10509	−	0.194858i
$382$		0			0
$383$	−2.79767	−	15.8664i	−0.142954	−	0.810733i	−0.968987	−	0.247111i	$-0.920519\pi$
$383$	−2.79767	−	15.8664i	−0.142954	−	0.810733i	0.826033	−	0.563622i	$-0.190592\pi$
$384$		0			0
$385$	19.5364	+	16.3930i	0.995668	+	0.835465i
$386$		0			0
$387$	4.59627	+	1.67290i	0.233641	+	0.0850385i
$388$		0			0
$389$	0.0984882	−	0.558554i	0.00499355	−	0.0283198i	−0.982209	−	0.187790i	$-0.939868\pi$
$389$	0.0984882	−	0.558554i	0.00499355	−	0.0283198i	0.987203	+	0.159470i	$0.0509786\pi$
$390$		0			0
$391$	−1.41235	−	0.514054i	−0.0714257	−	0.0259968i
$392$		0			0
$393$	8.85251	+	1.56094i	0.446550	+	0.0787388i
$394$		0			0
$395$	−9.33662	−	16.1715i	−0.469776	−	0.813676i
$396$		0			0
$397$	−18.0107	+	31.1955i	−0.903933	+	1.56566i	−0.0815894	+	0.996666i	$0.526000\pi$
$397$	−18.0107	+	31.1955i	−0.903933	+	1.56566i	−0.822343	+	0.568992i	$0.807334\pi$
$398$		0			0
$399$	−25.5232	−	14.7358i	−1.27776	−	0.737715i
$400$		0			0
$401$	27.5724	−	23.1360i	1.37690	−	1.15536i	0.406556	−	0.913626i	$-0.366730\pi$
$401$	27.5724	−	23.1360i	1.37690	−	1.15536i	0.970344	−	0.241730i	$-0.0777147\pi$
$402$		0			0
$403$	−6.12923	+	2.23086i	−0.305319	+	0.111127i
$404$		0			0
$405$	3.95723	−	22.4426i	0.196637	−	1.11518i
$406$		0			0
$407$	30.5390	−	11.1153i	1.51376	−	0.550963i
$408$		0			0
$409$	9.71032	−	8.14793i	0.480145	−	0.402889i	−0.370334	−	0.928899i	$-0.620757\pi$
$409$	9.71032	−	8.14793i	0.480145	−	0.402889i	0.850479	+	0.526009i	$0.176312\pi$
$410$		0			0
$411$	25.6707	+	14.8210i	1.26624	+	0.731066i
$412$		0			0
$413$	6.42649	−	11.1310i	0.316227	−	0.547721i
$414$		0			0
$415$	8.63816	+	14.9617i	0.424030	+	0.734442i
$416$		0			0
$417$	−20.8059	−	3.66864i	−1.01887	−	0.179654i
$418$		0			0
$419$	13.3991	+	4.87689i	0.654591	+	0.238252i	0.647899	−	0.761726i	$-0.275648\pi$
$419$	13.3991	+	4.87689i	0.654591	+	0.238252i	0.00669178	+	0.999978i	$0.497870\pi$
$420$		0			0
$421$	0.546637	−	3.10013i	0.0266414	−	0.151091i	−0.968585	−	0.248682i	$-0.920003\pi$
$421$	0.546637	−	3.10013i	0.0266414	−	0.151091i	0.995227	+	0.0975909i	$0.0311137\pi$
$422$		0			0
$423$	−4.17159	+	3.50038i	−0.202830	+	0.170194i
$424$		0			0
$425$	5.32114	+	4.46496i	0.258113	+	0.216583i
$426$		0			0
$427$	4.50387	+	25.5427i	0.217958	+	1.23610i
$428$		0			0
$429$	−5.55350	+	0.979232i	−0.268126	+	0.0472778i
$430$		0			0
$431$	−15.4911			−0.746182			−0.373091	−	0.927795i	$-0.621702\pi$
$431$	−15.4911			−0.746182			−0.373091	+	0.927795i	$0.621702\pi$
$432$		0			0
$433$	−2.22844			−0.107092			−0.0535459	−	0.998565i	$-0.517052\pi$
$433$	−2.22844			−0.107092			−0.0535459	+	0.998565i	$0.517052\pi$
$434$		0			0
$435$	−4.65910	+	12.8008i	−0.223387	+	0.613750i
$436$		0			0
$437$	0.384438	+	2.18025i	0.0183901	+	0.104296i
$438$		0			0
$439$	−13.1570	−	11.0401i	−0.627951	−	0.526914i	0.272340	−	0.962201i	$-0.412202\pi$
$439$	−13.1570	−	11.0401i	−0.627951	−	0.526914i	−0.900292	+	0.435287i	$0.856647\pi$
$440$		0			0
$441$	4.47060			0.212886
$442$		0			0
$443$	4.10173	−	23.2621i	0.194879	−	1.10521i	−0.717712	−	0.696340i	$-0.754810\pi$
$443$	4.10173	−	23.2621i	0.194879	−	1.10521i	0.912591	−	0.408874i	$-0.134078\pi$
$444$		0			0
$445$	−18.8478	−	6.86002i	−0.893470	−	0.325196i
$446$		0			0
$447$	−4.56283	−	12.5363i	−0.215815	−	0.592946i
$448$		0			0
$449$	10.1295	+	17.5449i	0.478042	+	0.827994i	0.999683	−	0.0251715i	$-0.00801318\pi$
$449$	10.1295	+	17.5449i	0.478042	+	0.827994i	−0.521641	+	0.853165i	$0.674680\pi$
$450$		0			0
$451$	−10.5162	+	18.2146i	−0.495188	+	0.857691i
$452$		0			0
$453$	1.17159	−	0.676417i	0.0550460	−	0.0317808i
$454$		0			0
$455$	3.45471	−	2.89884i	0.161959	−	0.135900i
$456$		0			0
$457$	38.1143	−	13.8725i	1.78291	−	0.648926i	0.783282	−	0.621666i	$-0.213544\pi$
$457$	38.1143	−	13.8725i	1.78291	−	0.648926i	0.999628	−	0.0272600i	$-0.00867822\pi$
$458$		0			0
$459$	22.1457	+	12.7858i	1.03367	+	0.596792i
$460$		0			0
$461$	−12.8824	+	4.68880i	−0.599992	+	0.218379i	−0.624119	−	0.781330i	$-0.714542\pi$
$461$	−12.8824	+	4.68880i	−0.599992	+	0.218379i	0.0241264	+	0.999709i	$0.492320\pi$
$462$		0			0
$463$	−4.14022	+	3.47405i	−0.192412	+	0.161453i	−0.733904	−	0.679253i	$-0.762304\pi$
$463$	−4.14022	+	3.47405i	−0.192412	+	0.161453i	0.541492	+	0.840706i	$0.317860\pi$
$464$		0			0
$465$			37.7007i			1.74833i
$466$		0			0
$467$	15.7451	−	27.2713i	0.728596	−	1.26197i	−0.228880	−	0.973455i	$-0.573506\pi$
$467$	15.7451	−	27.2713i	0.728596	−	1.26197i	0.957477	−	0.288511i	$-0.0931603\pi$
$468$		0			0
$469$	0.0491630	+	0.0851529i	0.00227014	+	0.00393199i
$470$		0			0
$471$	11.5915	−	13.8142i	0.534109	−	0.636526i
$472$		0			0
$473$	−6.57398	−	2.39273i	−0.302272	−	0.110018i
$474$		0			0
$475$	1.77672	−	10.0763i	0.0815216	−	0.462332i
$476$		0			0
$477$	−0.299011	+	1.69577i	−0.0136908	+	0.0776441i
$478$		0			0
$479$	16.0667	+	13.4816i	0.734106	+	0.615988i	0.931248	−	0.364387i	$-0.118721\pi$
$479$	16.0667	+	13.4816i	0.734106	+	0.615988i	−0.197141	+	0.980375i	$0.563166\pi$
$480$		0			0
$481$	−0.997941	−	5.65960i	−0.0455022	−	0.258056i
$482$		0			0
$483$	0.798133	+	0.951178i	0.0363163	+	0.0432801i
$484$		0			0
$485$	−8.31315			−0.377481
$486$		0			0
$487$	15.4492			0.700072			0.350036	−	0.936736i	$-0.386169\pi$
$487$	15.4492			0.700072			0.350036	+	0.936736i	$0.386169\pi$
$488$		0			0
$489$	11.7724	+	14.0298i	0.532368	+	0.634452i
$490$		0			0
$491$	−2.75443	−	15.6212i	−0.124306	−	0.704973i	−0.981718	−	0.190343i	$-0.939040\pi$
$491$	−2.75443	−	15.6212i	−0.124306	−	0.704973i	0.857412	−	0.514631i	$-0.172071\pi$
$492$		0			0
$493$	−11.7096	−	9.82553i	−0.527374	−	0.442519i
$494$		0			0
$495$	−5.65998	+	32.0993i	−0.254397	+	1.44276i
$496$		0			0
$497$	1.71373	−	9.71902i	0.0768711	−	0.435958i
$498$		0			0
$499$	−7.03596	−	2.56088i	−0.314973	−	0.114641i	0.179696	−	0.983722i	$-0.442489\pi$
$499$	−7.03596	−	2.56088i	−0.314973	−	0.114641i	−0.494669	+	0.869081i	$0.664711\pi$
$500$		0			0
$501$	1.67334	−	1.99421i	0.0747595	−	0.0890949i
$502$		0			0
$503$	−10.0667	−	17.4360i	−0.448852	−	0.777435i	0.549459	−	0.835520i	$-0.314834\pi$
$503$	−10.0667	−	17.4360i	−0.448852	−	0.777435i	−0.998312	+	0.0580857i	$0.981500\pi$
$504$		0			0
$505$	15.1839	−	26.2993i	0.675675	−	1.17030i
$506$		0			0
$507$		−	21.5195i		−	0.955713i
$508$		0			0
$509$	−28.7900	+	24.1577i	−1.27609	+	1.07077i	−0.282324	+	0.959319i	$0.591105\pi$
$509$	−28.7900	+	24.1577i	−1.27609	+	1.07077i	−0.993770	+	0.111450i	$0.964450\pi$
$510$		0			0
$511$	24.4650	−	8.90452i	1.08227	−	0.393913i
$512$		0			0
$513$		−	37.6668i		−	1.66303i
$514$		0			0
$515$	5.73783	−	2.08840i	0.252839	−	0.0920258i
$516$		0			0
$517$	5.96657	−	5.00654i	0.262409	−	0.220188i
$518$		0			0
$519$	−16.7260	+	9.65674i	−0.734188	+	0.423884i
$520$		0			0
$521$	−13.9645	+	24.1872i	−0.611796	+	1.05966i	0.379141	+	0.925339i	$0.376219\pi$
$521$	−13.9645	+	24.1872i	−0.611796	+	1.05966i	−0.990938	+	0.134323i	$0.957114\pi$
$522$		0			0
$523$	3.64677	+	6.31640i	0.159462	+	0.276197i	0.934675	−	0.355504i	$-0.115691\pi$
$523$	3.64677	+	6.31640i	0.159462	+	0.276197i	−0.775213	+	0.631700i	$0.782357\pi$
$524$		0			0
$525$	−1.96270	−	5.39246i	−0.0856591	−	0.235346i
$526$		0			0
$527$	−39.7533	−	14.4690i	−1.73168	−	0.630280i
$528$		0			0
$529$	−3.97771	+	22.5587i	−0.172944	+	0.980814i
$530$		0			0
$531$	16.4270			0.712869
$532$		0			0
$533$	2.84911	+	2.39068i	0.123409	+	0.103552i
$534$		0			0
$535$	1.06670	+	6.04958i	0.0461176	+	0.261546i
$536$		0			0
$537$	−4.62567	+	12.7089i	−0.199612	+	0.548430i
$538$		0			0
$539$	−6.39424			−0.275419
$540$		0			0
$541$	−2.88444			−0.124012			−0.0620058	−	0.998076i	$-0.519750\pi$
$541$	−2.88444			−0.124012			−0.0620058	+	0.998076i	$0.519750\pi$
$542$		0			0
$543$	−17.8687	+	3.15074i	−0.766820	+	0.135211i
$544$		0			0
$545$	−1.02347	−	5.80439i	−0.0438407	−	0.248633i
$546$		0			0
$547$	8.57263	+	7.19329i	0.366539	+	0.307563i	0.807391	−	0.590017i	$-0.200879\pi$
$547$	8.57263	+	7.19329i	0.366539	+	0.307563i	−0.440851	+	0.897580i	$0.645323\pi$
$548$		0			0
$549$	−25.3935	+	21.3077i	−1.08377	+	0.909390i
$550$		0			0
$551$	−3.90983	+	22.1737i	−0.166564	+	0.944632i
$552$		0			0
$553$	−16.2665	−	5.92053i	−0.691722	−	0.251766i
$554$		0			0
$555$	−32.7126	−	5.76811i	−1.38857	−	0.244843i
$556$		0			0
$557$	−16.6741	−	28.8804i	−0.706505	−	1.22370i	−0.966146	−	0.257997i	$-0.916937\pi$
$557$	−16.6741	−	28.8804i	−0.706505	−	1.22370i	0.259641	−	0.965705i	$-0.416396\pi$
$558$		0			0
$559$	−0.618555	+	1.07137i	−0.0261621	+	0.0453141i
$560$		0			0
$561$	−31.6747	−	18.2874i	−1.33731	−	0.772096i
$562$		0			0
$563$	−14.1668	+	11.8874i	−0.597061	+	0.500994i	−0.890500	−	0.454984i	$-0.849645\pi$
$563$	−14.1668	+	11.8874i	−0.597061	+	0.500994i	0.293438	+	0.955978i	$0.405200\pi$
$564$		0			0
$565$	40.5861	−	14.7721i	1.70747	−	0.621468i
$566$		0			0
$567$	−10.5628	−	18.2954i	−0.443597	−	0.768333i
$568$		0			0
$569$	−27.5638	+	10.0324i	−1.15553	+	0.420580i	−0.847500	−	0.530796i	$-0.821893\pi$
$569$	−27.5638	+	10.0324i	−1.15553	+	0.420580i	−0.308033	+	0.951376i	$0.599671\pi$
$570$		0			0
$571$	−1.50387	+	1.26190i	−0.0629350	+	0.0528087i	−0.673713	−	0.738993i	$-0.735301\pi$
$571$	−1.50387	+	1.26190i	−0.0629350	+	0.0528087i	0.610778	+	0.791802i	$0.290857\pi$
$572$		0			0
$573$	−18.3441	−	10.5909i	−0.766334	−	0.442443i
$574$		0			0
$575$	−0.215537	+	0.373321i	−0.00898852	+	0.0155686i
$576$		0			0
$577$	5.52956	+	9.57748i	0.230199	+	0.398716i	0.957866	−	0.287214i	$-0.0927291\pi$
$577$	5.52956	+	9.57748i	0.230199	+	0.398716i	−0.727668	+	0.685930i	$0.759396\pi$
$578$		0			0
$579$	−27.9192	−	4.92291i	−1.16028	−	0.204589i
$580$		0			0
$581$	15.0496	+	5.47762i	0.624364	+	0.227250i
$582$		0			0
$583$	0.427671	−	2.42544i	0.0177123	−	0.100452i
$584$		0			0
$585$	5.41622	+	1.97134i	0.223933	+	0.0815050i
$586$		0			0
$587$	−25.3917	−	21.3062i	−1.04803	−	0.879400i	−0.0551433	−	0.998478i	$-0.517562\pi$
$587$	−25.3917	−	21.3062i	−1.04803	−	0.879400i	−0.992885	+	0.119078i	$0.962006\pi$
$588$		0			0
$589$	10.8207	+	61.3674i	0.445860	+	2.52860i
$590$		0			0
$591$	−32.4020	+	5.71334i	−1.33284	+	0.235016i
$592$		0			0
$593$	14.8283			0.608926			0.304463	−	0.952524i	$-0.401523\pi$
$593$	14.8283			0.608926			0.304463	+	0.952524i	$0.401523\pi$
$594$		0			0
$595$	29.2499			1.19913
$596$		0			0
$597$	−13.6505	+	37.5044i	−0.558677	+	1.53495i
$598$		0			0
$599$	8.20930	+	46.5573i	0.335423	+	1.90228i	0.423016	+	0.906122i	$0.360971\pi$
$599$	8.20930	+	46.5573i	0.335423	+	1.90228i	−0.0875932	+	0.996156i	$0.527918\pi$
$600$		0			0
$601$	28.1996	+	23.6623i	1.15029	+	0.965206i	0.999726	−	0.0233949i	$-0.00744749\pi$
$601$	28.1996	+	23.6623i	1.15029	+	0.965206i	0.150561	+	0.988601i	$0.451892\pi$
$602$		0			0
$603$	−0.0628336	+	0.108831i	−0.00255878	+	0.00443194i
$604$		0			0
$605$	3.25877	−	18.4814i	0.132488	−	0.751376i
$606$		0			0
$607$	38.8764	+	14.1499i	1.57795	+	0.574326i	0.974756	−	0.223272i	$-0.0716738\pi$
$607$	38.8764	+	14.1499i	1.57795	+	0.574326i	0.603190	+	0.797597i	$0.293896\pi$
$608$		0			0
$609$	4.31908	+	11.8666i	0.175018	+	0.480858i
$610$		0			0
$611$	−0.688663	−	1.19280i	−0.0278603	−	0.0482555i
$612$		0			0
$613$	20.6755	−	35.8109i	0.835074	−	1.44639i	−0.0588963	−	0.998264i	$-0.518758\pi$
$613$	20.6755	−	35.8109i	0.835074	−	1.44639i	0.893970	−	0.448126i	$-0.147909\pi$
$614$		0			0
$615$	18.6172	−	10.7487i	0.750718	−	0.433427i
$616$		0			0
$617$	18.7867	−	15.7639i	0.756326	−	0.634633i	−0.180842	−	0.983512i	$-0.557882\pi$
$617$	18.7867	−	15.7639i	0.756326	−	0.634633i	0.937168	+	0.348880i	$0.113438\pi$
$618$		0			0
$619$	37.2768	−	13.5676i	1.49828	−	0.545329i	0.542666	−	0.839949i	$-0.317415\pi$
$619$	37.2768	−	13.5676i	1.49828	−	0.545329i	0.955615	+	0.294619i	$0.0951929\pi$
$620$		0			0
$621$	−0.542766	+	1.49124i	−0.0217805	+	0.0598413i
$622$		0			0
$623$	−17.4722	+	6.35938i	−0.700011	+	0.254783i
$624$		0			0
$625$	−23.0312	+	19.3255i	−0.921248	+	0.773019i
$626$		0			0
$627$			53.8742i			2.15153i
$628$		0			0
$629$	18.6368	−	32.2799i	0.743098	−	1.28708i
$630$		0			0
$631$	−16.6596	−	28.8552i	−0.663207	−	1.14871i	−0.979768	−	0.200136i	$-0.935862\pi$
$631$	−16.6596	−	28.8552i	−0.663207	−	1.14871i	0.316561	−	0.948572i	$-0.397472\pi$
$632$		0			0
$633$	19.4812	−	23.2168i	0.774307	−	0.922783i
$634$		0			0
$635$	30.0895	+	10.9517i	1.19406	+	0.434604i
$636$		0			0
$637$	−0.196347	+	1.11354i	−0.00777957	+	0.0441201i
$638$		0			0
$639$	11.8525	−	4.31396i	0.468878	−	0.170658i
$640$		0			0
$641$	5.55690	+	4.66280i	0.219485	+	0.184169i	0.745900	−	0.666058i	$-0.232020\pi$
$641$	5.55690	+	4.66280i	0.219485	+	0.184169i	−0.526415	+	0.850228i	$0.676464\pi$
$642$		0			0
$643$	1.34120	+	7.60635i	0.0528919	+	0.299965i	0.999766	−	0.0216400i	$-0.00688876\pi$
$643$	1.34120	+	7.60635i	0.0528919	+	0.299965i	−0.946874	+	0.321605i	$0.895778\pi$
$644$		0			0
$645$	4.59627	+	5.47762i	0.180978	+	0.215681i
$646$		0			0
$647$	40.9469			1.60979			0.804894	−	0.593419i	$-0.202222\pi$
$647$	40.9469			1.60979			0.804894	+	0.593419i	$0.202222\pi$
$648$		0			0
$649$	−23.4953			−0.922269
$650$		0			0
$651$	22.4650	+	26.7727i	0.880472	+	1.04931i
$652$		0			0
$653$	3.45171	+	19.5756i	0.135076	+	0.766054i	0.974807	+	0.223051i	$0.0716017\pi$
$653$	3.45171	+	19.5756i	0.135076	+	0.766054i	−0.839731	+	0.543003i	$0.817287\pi$
$654$		0			0
$655$	10.0667	+	8.44697i	0.393339	+	0.330050i
$656$		0			0
$657$	25.4898	+	21.3885i	0.994451	+	0.834444i
$658$		0			0
$659$	−2.98499	+	16.9287i	−0.116279	+	0.659448i	0.869831	+	0.493350i	$0.164228\pi$
$659$	−2.98499	+	16.9287i	−0.116279	+	0.659448i	−0.986109	+	0.166098i	$0.946883\pi$
$660$		0			0
$661$	32.3276	+	11.7663i	1.25740	+	0.457655i	0.882895	−	0.469571i	$-0.155591\pi$
$661$	32.3276	+	11.7663i	1.25740	+	0.457655i	0.374503	+	0.927226i	$0.377813\pi$
$662$		0			0
$663$	−4.15735	+	4.95453i	−0.161458	+	0.192418i
$664$		0			0
$665$	−21.5424	−	37.3125i	−0.835377	−	1.44691i
$666$		0			0
$667$	0.474308	−	0.821525i	0.0183653	−	0.0318096i
$668$		0			0
$669$			7.30742i			0.282521i
$670$		0			0
$671$	36.3200	−	30.4761i	1.40212	−	1.17652i
$672$		0			0
$673$	−22.4513	+	8.17161i	−0.865434	+	0.314992i	−0.736317	−	0.676637i	$-0.763437\pi$
$673$	−22.4513	+	8.17161i	−0.865434	+	0.314992i	−0.129117	+	0.991629i	$0.541214\pi$
$674$		0			0
$675$	4.71436	−	5.61835i	0.181456	−	0.216250i
$676$		0			0
$677$	−32.6238	+	11.8741i	−1.25383	+	0.456358i	−0.881695	−	0.471819i	$-0.843597\pi$
$677$	−32.6238	+	11.8741i	−1.25383	+	0.456358i	−0.372138	+	0.928177i	$0.621375\pi$
$678$		0			0
$679$	−5.90348	+	4.95361i	−0.226555	+	0.190102i
$680$		0			0
$681$	−23.9488	+	13.8268i	−0.917719	+	0.529845i
$682$		0			0
$683$	−19.5030	+	33.7802i	−0.746261	+	1.29256i	0.203342	+	0.979108i	$0.434820\pi$
$683$	−19.5030	+	33.7802i	−0.746261	+	1.29256i	−0.949603	+	0.313455i	$0.898514\pi$
$684$		0			0
$685$	21.6668	+	37.5281i	0.827847	+	1.43387i
$686$		0			0
$687$	10.5729	+	29.0487i	0.403379	+	1.10828i
$688$		0			0
$689$	−0.409253	−	0.148956i	−0.0155913	−	0.00567476i
$690$		0			0
$691$	−4.39780	+	24.9412i	−0.167300	+	0.948807i	0.779361	+	0.626576i	$0.215544\pi$
$691$	−4.39780	+	24.9412i	−0.167300	+	0.948807i	−0.946661	+	0.322232i	$0.895567\pi$
$692$		0			0
$693$	15.1079	+	26.1676i	0.573901	+	0.994025i
$694$		0			0
$695$	−23.6596	−	19.8527i	−0.897459	−	0.753057i
$696$		0			0
$697$	4.18883	+	23.7560i	0.158663	+	0.899823i
$698$		0			0
$699$	−0.436289	+	1.19869i	−0.0165020	+	0.0453388i
$700$		0			0
$701$	42.3054			1.59785			0.798927	−	0.601429i	$-0.205402\pi$
$701$	42.3054			1.59785			0.798927	+	0.601429i	$0.205402\pi$
$702$		0			0
$703$	−54.9035			−2.07073
$704$		0			0
$705$	−7.84002	+	1.38241i	−0.295272	+	0.0520645i
$706$		0			0
$707$	−4.88847	−	27.7239i	−0.183850	−	1.04266i
$708$		0			0
$709$	−36.7098	−	30.8032i	−1.37867	−	1.15684i	−0.969703	−	0.244288i	$-0.921446\pi$
$709$	−36.7098	−	30.8032i	−1.37867	−	1.15684i	−0.408964	−	0.912551i	$-0.634110\pi$
$710$		0			0
$711$	−3.84178	−	21.7878i	−0.144078	−	0.817106i
$712$		0			0
$713$	0.455889	−	2.58548i	0.0170732	−	0.0968269i
$714$		0			0
$715$	−7.74675	−	2.81959i	−0.289712	−	0.105447i
$716$		0			0
$717$	4.90286	+	0.864506i	0.183101	+	0.0322856i
$718$		0			0
$719$	6.15451	+	10.6599i	0.229525	+	0.397548i	0.957667	−	0.287877i	$-0.0929495\pi$
$719$	6.15451	+	10.6599i	0.229525	+	0.397548i	−0.728143	+	0.685426i	$0.759616\pi$
$720$		0			0
$721$	2.83022	−	4.90209i	0.105403	−	0.182563i
$722$		0			0
$723$	−3.27316	−	1.88976i	−0.121730	−	0.0702808i
$724$		0			0
$725$	−3.35844	+	2.81807i	−0.124729	+	0.104660i
$726$		0			0
$727$	−16.3542	+	5.95243i	−0.606542	+	0.220763i	−0.626990	−	0.779028i	$-0.715713\pi$
$727$	−16.3542	+	5.95243i	−0.606542	+	0.220763i	0.0204474	+	0.999791i	$0.493491\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$		0			0
$731$	−7.53983	+	2.74427i	−0.278871	+	0.101501i
$732$		0			0
$733$	11.0266	−	9.25244i	0.407278	−	0.341747i	−0.416021	−	0.909355i	$-0.636576\pi$
$733$	11.0266	−	9.25244i	0.407278	−	0.341747i	0.823299	+	0.567608i	$0.192131\pi$
$734$		0			0
$735$	5.65998	+	3.26779i	0.208771	+	0.120534i
$736$		0			0
$737$	0.0898700	−	0.155659i	0.00331041	−	0.00573379i
$738$		0			0
$739$	−6.82383	−	11.8192i	−0.251018	−	0.434777i	0.712788	−	0.701380i	$-0.247432\pi$
$739$	−6.82383	−	11.8192i	−0.251018	−	0.434777i	−0.963806	+	0.266603i	$0.914099\pi$
$740$		0			0
$741$	9.38207	+	1.65431i	0.344659	+	0.0607727i
$742$		0			0
$743$	−17.2459	−	6.27698i	−0.632690	−	0.230280i	0.00571190	−	0.999984i	$-0.498182\pi$
$743$	−17.2459	−	6.27698i	−0.632690	−	0.230280i	−0.638402	+	0.769703i	$0.720404\pi$
$744$		0			0
$745$	3.38666	−	19.2067i	0.124078	−	0.703679i
$746$		0			0
$747$	3.55438	+	20.1579i	0.130048	+	0.737538i
$748$		0			0
$749$	4.36231	+	3.66041i	0.159395	+	0.133749i
$750$		0			0
$751$	7.01460	+	39.7818i	0.255967	+	1.45166i	0.793579	+	0.608467i	$0.208215\pi$
$751$	7.01460	+	39.7818i	0.255967	+	1.45166i	−0.537613	+	0.843192i	$0.680674\pi$
$752$		0			0
$753$	−44.4136	+	7.83131i	−1.61852	+	0.285389i
$754$		0			0
$755$	1.97771			0.0719763
$756$		0			0
$757$	3.71595			0.135058			0.0675292	−	0.997717i	$-0.478488\pi$
$757$	3.71595			0.135058			0.0675292	+	0.997717i	$0.478488\pi$
$758$		0			0
$759$	0.776311	−	2.13290i	0.0281783	−	0.0774193i
$760$		0			0
$761$	−6.41147	−	36.3613i	−0.232416	−	1.31810i	−0.847988	−	0.530015i	$-0.822186\pi$
$761$	−6.41147	−	36.3613i	−0.232416	−	1.31810i	0.615573	−	0.788080i	$-0.288925\pi$
$762$		0			0
$763$	−4.18551	−	3.51206i	−0.151526	−	0.127145i
$764$		0			0
$765$	18.6917	+	32.3749i	0.675798	+	1.17052i
$766$		0			0
$767$	−0.721467	+	4.09164i	−0.0260507	+	0.147741i
$768$		0			0
$769$	25.5501	+	9.29947i	0.921360	+	0.335348i	0.758779	−	0.651348i	$-0.225796\pi$
$769$	25.5501	+	9.29947i	0.921360	+	0.335348i	0.162581	+	0.986695i	$0.448018\pi$
$770$		0			0
$771$	−5.91938	−	16.2634i	−0.213181	−	0.585710i
$772$		0			0
$773$	0.869585	+	1.50617i	0.0312768	+	0.0541730i	0.881240	−	0.472669i	$-0.156709\pi$
$773$	0.869585	+	1.50617i	0.0312768	+	0.0541730i	−0.849963	+	0.526842i	$0.823376\pi$
$774$		0			0
$775$	−6.06670	+	10.5078i	−0.217922	+	0.377453i
$776$		0			0
$777$	−26.6676	+	15.3965i	−0.956693	+	0.552347i
$778$		0			0
$779$	27.2192	−	22.8396i	0.975228	−	0.818313i
$780$		0			0
$781$	−16.9525	+	6.17020i	−0.606608	+	0.220787i
$782$		0			0
$783$	−10.3743	+	12.3636i	−0.370748	+	0.441841i
$784$		0			0
$785$	24.7729	−	9.01660i	0.884183	−	0.321816i
$786$		0			0
$787$	17.7271	−	14.8748i	0.631905	−	0.530231i	−0.269616	−	0.962968i	$-0.586897\pi$
$787$	17.7271	−	14.8748i	0.631905	−	0.530231i	0.901520	+	0.432737i	$0.142452\pi$
$788$		0			0
$789$		−	26.3663i		−	0.938663i
$790$		0			0
$791$	20.0194	−	34.6745i	0.711806	−	1.23288i
$792$		0			0
$793$	−4.19207	−	7.26087i	−0.148865	−	0.257841i
$794$		0			0
$795$	−1.61809	+	1.92836i	−0.0573877	+	0.0683920i
$796$		0			0
$797$	−2.32295	−	0.845484i	−0.0822830	−	0.0299486i	0.300551	−	0.953766i	$-0.402830\pi$
$797$	−2.32295	−	0.845484i	−0.0822830	−	0.0299486i	−0.382834	+	0.923817i	$0.625052\pi$
$798$		0			0
$799$	1.55122	−	8.79742i	0.0548783	−	0.311230i
$800$		0			0
$801$	−18.2041	−	15.2751i	−0.643212	−	0.539719i
$802$		0			0
$803$	−36.4577	−	30.5916i	−1.28656	−	1.07956i
$804$		0			0
$805$	0.315207	+	1.78763i	0.0111096	+	0.0630057i
$806$		0			0
$807$	34.0099	+	40.5314i	1.19720	+	1.42677i
$808$		0			0
$809$	1.04870			0.0368702			0.0184351	−	0.999830i	$-0.494132\pi$
$809$	1.04870			0.0368702			0.0184351	+	0.999830i	$0.494132\pi$
$810$		0			0
$811$	21.3087			0.748250			0.374125	−	0.927378i	$-0.377943\pi$
$811$	21.3087			0.748250			0.374125	+	0.927378i	$0.377943\pi$
$812$		0			0
$813$	−28.7584	−	34.2729i	−1.00860	−	1.20200i
$814$		0			0
$815$	4.64930	+	26.3675i	0.162858	+	0.923613i
$816$		0			0
$817$	9.05375	+	7.59700i	0.316751	+	0.265785i
$818$		0			0
$819$	5.02094	−	1.82747i	0.175446	−	0.0638571i
$820$		0			0
$821$	−8.53209	+	48.3879i	−0.297772	+	1.68875i	0.357946	+	0.933742i	$0.383477\pi$
$821$	−8.53209	+	48.3879i	−0.297772	+	1.68875i	−0.655718	+	0.755006i	$0.727634\pi$
$822$		0			0
$823$	3.19207	+	1.16182i	0.111268	+	0.0404984i	0.397054	−	0.917795i	$-0.370032\pi$
$823$	3.19207	+	1.16182i	0.111268	+	0.0404984i	−0.285786	+	0.958293i	$0.592255\pi$
$824$		0			0
$825$	−6.74288	+	8.03585i	−0.234757	+	0.279772i
$826$		0			0
$827$	−23.8359	−	41.2850i	−0.828856	−	1.43562i	−0.898937	−	0.438079i	$-0.855659\pi$
$827$	−23.8359	−	41.2850i	−0.828856	−	1.43562i	0.0700811	−	0.997541i	$-0.477674\pi$
$828$		0			0
$829$	−1.71570	+	2.97168i	−0.0595887	+	0.103211i	−0.894281	−	0.447506i	$-0.852312\pi$
$829$	−1.71570	+	2.97168i	−0.0595887	+	0.103211i	0.834692	+	0.550717i	$0.185646\pi$
$830$		0			0
$831$		−	38.8580i		−	1.34797i
$832$		0			0
$833$	−5.61793	+	4.71400i	−0.194650	+	0.163330i
$834$		0			0
$835$	3.57620	−	1.30163i	0.123759	−	0.0450448i
$836$		0			0
$837$	−15.2772	+	41.9737i	−0.528057	+	1.45082i
$838$		0			0
$839$	−23.7288	+	8.63658i	−0.819209	+	0.298168i	−0.717422	−	0.696639i	$-0.754678\pi$
$839$	−23.7288	+	8.63658i	−0.819209	+	0.298168i	−0.101787	+	0.994806i	$0.532456\pi$
$840$		0			0
$841$	−14.8248	+	12.4395i	−0.511199	+	0.428947i
$842$		0			0
$843$	8.76645	−	5.06132i	0.301933	−	0.174321i
$844$		0			0
$845$	15.7297	−	27.2446i	0.541117	−	0.937243i
$846$		0			0
$847$	−8.69846	−	15.0662i	−0.298883	−	0.517680i
$848$		0			0
$849$	−4.39053	−	12.0629i	−0.150683	−	0.413997i
$850$		0			0
$851$	2.17365	+	0.791143i	0.0745117	+	0.0271200i
$852$		0			0
$853$	6.88144	−	39.0266i	0.235616	−	1.33625i	−0.605696	−	0.795696i	$-0.707105\pi$
$853$	6.88144	−	39.0266i	0.235616	−	1.33625i	0.841312	−	0.540550i	$-0.181784\pi$
$854$		0			0
$855$	27.5326	−	47.6878i	0.941594	−	1.63089i
$856$		0			0
$857$	−21.3136	−	17.8842i	−0.728059	−	0.610914i	0.201543	−	0.979480i	$-0.435405\pi$
$857$	−21.3136	−	17.8842i	−0.728059	−	0.610914i	−0.929602	+	0.368566i	$0.879849\pi$
$858$		0			0
$859$	−1.45987	−	8.27931i	−0.0498100	−	0.282486i	0.949721	−	0.313096i	$-0.101366\pi$
$859$	−1.45987	−	8.27931i	−0.0498100	−	0.282486i	−0.999531	+	0.0306097i	$0.990255\pi$
$860$		0			0
$861$	6.81592	−	18.7266i	0.232286	−	0.638201i
$862$		0			0
$863$	41.9436			1.42778			0.713888	−	0.700260i	$-0.246933\pi$
$863$	41.9436			1.42778			0.713888	+	0.700260i	$0.246933\pi$
$864$		0			0
$865$	−28.2344			−0.959999
$866$		0			0
$867$	−12.3136	+	2.17122i	−0.418192	+	0.0737386i
$868$		0			0
$869$	5.49484	+	31.1628i	0.186400	+	1.05713i
$870$		0			0
$871$	−0.0243481	−	0.0204305i	−0.000825004	−	0.000692260i
$872$		0			0
$873$	−9.25537	−	3.36868i	−0.313247	−	0.114012i
$874$		0			0
$875$	−3.70368	+	21.0046i	−0.125207	+	0.710085i
$876$		0			0
$877$	43.7156	+	15.9112i	1.47617	+	0.537282i	0.949768	−	0.312953i	$-0.101318\pi$
$877$	43.7156	+	15.9112i	1.47617	+	0.537282i	0.526402	+	0.850236i	$0.323541\pi$
$878$		0			0
$879$	−15.1413	−	2.66982i	−0.510704	−	0.0900508i
$880$		0			0
$881$	−5.84611	−	10.1258i	−0.196961	−	0.341146i	0.750581	−	0.660779i	$-0.229774\pi$
$881$	−5.84611	−	10.1258i	−0.196961	−	0.341146i	−0.947541	+	0.319633i	$0.896440\pi$
$882$		0			0
$883$	−4.41400	+	7.64527i	−0.148543	+	0.257284i	−0.930689	−	0.365811i	$-0.880792\pi$
$883$	−4.41400	+	7.64527i	−0.148543	+	0.257284i	0.782146	+	0.623095i	$0.214125\pi$
$884$		0			0
$885$	20.7973	+	12.0073i	0.699092	+	0.403621i
$886$		0			0
$887$	3.21554	−	2.69816i	0.107967	−	0.0905952i	−0.587206	−	0.809438i	$-0.699772\pi$
$887$	3.21554	−	2.69816i	0.107967	−	0.0905952i	0.695173	+	0.718842i	$0.255328\pi$
$888$		0			0
$889$	27.8935	−	10.1524i	0.935519	−	0.340501i
$890$		0			0
$891$	−19.3089	+	33.4439i	−0.646871	+	1.12041i
$892$		0			0
$893$	−12.3648	+	4.50043i	−0.413774	+	0.150601i
$894$		0			0
$895$	−15.1459	+	12.7089i	−0.506271	+	0.424812i
$896$		0			0
$897$	−0.347601	−	0.200688i	−0.0116061	−	0.00670076i
$898$		0			0
$899$	13.3503	−	23.1234i	0.445257	−	0.771208i
$900$		0			0
$901$	−1.41235	−	2.44626i	−0.0470522	−	0.0814969i
$902$		0			0
$903$	6.52797	+	1.15106i	0.217237	+	0.0383048i
$904$		0			0
$905$	−24.9256	−	9.07218i	−0.828555	−	0.301569i
$906$		0			0
$907$	8.68732	−	49.2682i	0.288458	−	1.63592i	−0.404209	−	0.914667i	$-0.632453\pi$
$907$	8.68732	−	49.2682i	0.288458	−	1.63592i	0.692666	−	0.721258i	$-0.256436\pi$
$908$		0			0
$909$	27.5620	−	23.1272i	0.914172	−	0.767082i
$910$		0			0
$911$	12.3532	+	10.3656i	0.409281	+	0.343427i	0.824068	−	0.566491i	$-0.191700\pi$
$911$	12.3532	+	10.3656i	0.409281	+	0.343427i	−0.414787	+	0.909918i	$0.636144\pi$
$912$		0			0
$913$	−5.08378	−	28.8315i	−0.168248	−	0.954185i
$914$		0			0
$915$	−47.7242	+	8.41507i	−1.57771	+	0.278194i
$916$		0			0
$917$	12.1821			0.402289
$918$		0			0
$919$	43.4023			1.43171			0.715855	−	0.698249i	$-0.246037\pi$
$919$	43.4023			1.43171			0.715855	+	0.698249i	$0.246037\pi$
$920$		0			0
$921$	9.53714	−	26.2031i	0.314259	−	0.863421i
$922$		0			0
$923$	0.553967	+	3.14170i	0.0182340	+	0.103410i
$924$		0			0
$925$	−8.18938	−	6.87170i	−0.269265	−	0.225940i
$926$		0			0
$927$	7.23442			0.237610
$928$		0			0
$929$	3.74691	−	21.2498i	0.122932	−	0.697183i	−0.859582	−	0.510997i	$-0.829276\pi$
$929$	3.74691	−	21.2498i	0.122932	−	0.697183i	0.982515	−	0.186186i	$-0.0596126\pi$
$930$		0			0
$931$	10.1509	+	3.69464i	0.332684	+	0.121087i
$932$		0			0
$933$	8.05035	+	22.1181i	0.263556	+	0.724115i
$934$		0			0
$935$	−26.7344	−	46.3054i	−0.874309	−	1.51435i
$936$		0			0
$937$	8.94625	−	15.4954i	0.292261	−	0.506211i	−0.682083	−	0.731275i	$-0.738926\pi$
$937$	8.94625	−	15.4954i	0.292261	−	0.506211i	0.974344	+	0.225064i	$0.0722590\pi$
$938$		0			0
$939$	−32.2585	+	18.6245i	−1.05272	+	0.607786i
$940$		0			0
$941$	23.8739	−	20.0326i	0.778268	−	0.653044i	−0.164544	−	0.986370i	$-0.552615\pi$
$941$	23.8739	−	20.0326i	0.778268	−	0.653044i	0.942812	+	0.333326i	$0.108171\pi$
$942$		0			0
$943$	−1.40673	+	0.512007i	−0.0458093	+	0.0166732i
$944$		0			0
$945$		−	30.8837i		−	1.00465i
$946$		0			0
$947$	−38.0412	+	13.8459i	−1.23617	+	0.449930i	−0.875707	−	0.482843i	$-0.839604\pi$
$947$	−38.0412	+	13.8459i	−1.23617	+	0.449930i	−0.360465	+	0.932773i	$0.617382\pi$
$948$		0			0
$949$	−6.44697	+	5.40965i	−0.209277	+	0.175605i
$950$		0			0
$951$		−	36.5332i		−	1.18467i
$952$		0			0
$953$	−23.7040	+	41.0565i	−0.767847	+	1.32995i	0.170881	+	0.985292i	$0.445339\pi$
$953$	−23.7040	+	41.0565i	−0.767847	+	1.32995i	−0.938728	+	0.344659i	$0.887995\pi$
$954$		0			0
$955$	−15.4829	−	26.8172i	−0.501016	−	0.867785i
$956$		0			0
$957$	14.8383	−	17.6836i	0.479653	−	0.571628i
$958$		0			0
$959$	37.7486	+	13.7394i	1.21896	+	0.443667i
$960$		0			0
$961$	7.44878	−	42.2441i	0.240283	−	1.36271i
$962$		0			0
$963$	−1.26382	+	7.16750i	−0.0407261	+	0.230969i
$964$		0			0
$965$	−31.7486	−	26.6402i	−1.02202	−	0.857579i
$966$		0			0
$967$	−1.95817	−	11.1053i	−0.0629704	−	0.357123i	−0.999970	−	0.00779154i	$-0.997520\pi$
$967$	−1.95817	−	11.1053i	−0.0629704	−	0.357123i	0.936999	−	0.349331i	$-0.113591\pi$
$968$		0			0
$969$	39.7175	+	47.3335i	1.27591	+	1.52057i
$970$		0			0
$971$	−7.23442			−0.232164			−0.116082	−	0.993240i	$-0.537033\pi$
$971$	−7.23442			−0.232164			−0.116082	+	0.993240i	$0.537033\pi$
$972$		0			0
$973$	−28.6313			−0.917879
$974$		0			0
$975$	1.19237	+	1.42101i	0.0381864	+	0.0455088i
$976$		0			0
$977$	3.95646	+	22.4382i	0.126578	+	0.717862i	0.980358	+	0.197227i	$0.0631936\pi$
$977$	3.95646	+	22.4382i	0.126578	+	0.717862i	−0.853779	+	0.520635i	$0.825695\pi$
$978$		0			0
$979$	26.0371	+	21.8478i	0.832151	+	0.698257i
$980$		0			0
$981$	1.21260	−	6.87700i	0.0387154	−	0.219566i
$982$		0			0
$983$	0.254738	−	1.44469i	0.00812488	−	0.0460785i	−0.980476	−	0.196640i	$-0.936997\pi$
$983$	0.254738	−	1.44469i	0.00812488	−	0.0460785i	0.988601	+	0.150561i	$0.0481081\pi$
$984$		0			0
$985$	−45.1985	−	16.4509i	−1.44014	−	0.524170i
$986$		0			0
$987$	−4.74376	+	5.65339i	−0.150995	+	0.179949i
$988$		0			0
$989$	−0.248970	−	0.431229i	−0.00791680	−	0.0137123i
$990$		0			0
$991$	−1.94475	+	3.36840i	−0.0617769	+	0.107001i	−0.895260	−	0.445545i	$-0.853010\pi$
$991$	−1.94475	+	3.36840i	−0.0617769	+	0.107001i	0.833483	+	0.552545i	$0.186343\pi$
$992$		0			0
$993$		−	28.4729i		−	0.903559i
$994$		0			0
$995$	−44.6960	+	37.5044i	−1.41696	+	1.18897i
$996$		0			0
$997$	17.9884	−	6.54726i	0.569700	−	0.207354i	−0.0410778	−	0.999156i	$-0.513079\pi$
$997$	17.9884	−	6.54726i	0.569700	−	0.207354i	0.610778	+	0.791802i	$0.290857\pi$
$998$		0			0
$999$	−34.0829	−	19.6778i	−1.07834	−	0.622577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.a.385.1		6
4.3	odd	2		54.2.e.a.7.1	✓	6
12.11	even	2		162.2.e.a.19.1		6
27.4	even	9	inner	432.2.u.a.193.1		6
36.7	odd	6		486.2.e.b.379.1		6
36.11	even	6		486.2.e.c.379.1		6
36.23	even	6		486.2.e.a.217.1		6
36.31	odd	6		486.2.e.d.217.1		6
108.7	odd	18		1458.2.c.d.487.1		6
108.11	even	18		1458.2.c.a.973.3		6
108.23	even	18		162.2.e.a.145.1		6
108.31	odd	18		54.2.e.a.31.1	yes	6
108.43	odd	18		1458.2.c.d.973.1		6
108.47	even	18		1458.2.c.a.487.3		6
108.59	even	18		486.2.e.a.271.1		6
108.67	odd	18		486.2.e.b.109.1		6
108.79	odd	18		1458.2.a.a.1.3		3
108.83	even	18		1458.2.a.d.1.1		3
108.95	even	18		486.2.e.c.109.1		6
108.103	odd	18		486.2.e.d.271.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.a.7.1	✓	6	4.3	odd	2
54.2.e.a.31.1	yes	6	108.31	odd	18
162.2.e.a.19.1		6	12.11	even	2
162.2.e.a.145.1		6	108.23	even	18
432.2.u.a.193.1		6	27.4	even	9	inner
432.2.u.a.385.1		6	1.1	even	1	trivial
486.2.e.a.217.1		6	36.23	even	6
486.2.e.a.271.1		6	108.59	even	18
486.2.e.b.109.1		6	108.67	odd	18
486.2.e.b.379.1		6	36.7	odd	6
486.2.e.c.109.1		6	108.95	even	18
486.2.e.c.379.1		6	36.11	even	6
486.2.e.d.217.1		6	36.31	odd	6
486.2.e.d.271.1		6	108.103	odd	18
1458.2.a.a.1.3		3	108.79	odd	18
1458.2.a.d.1.1		3	108.83	even	18
1458.2.c.a.487.3		6	108.47	even	18
1458.2.c.a.973.3		6	108.11	even	18
1458.2.c.d.487.1		6	108.7	odd	18
1458.2.c.d.973.1		6	108.43	odd	18

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.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11334 + 1.32683i) q^{3} +(0.439693 + 2.49362i) q^{5} +(1.79813 + 1.50881i) q^{7} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\)	\(q+(1.11334 + 1.32683i) q^{3} +(0.439693 + 2.49362i) q^{5} +(1.79813 + 1.50881i) q^{7} +(-0.520945 + 2.95442i) q^{9} +(0.745100 - 4.22567i) q^{11} +(-0.713011 - 0.259515i) q^{13} +(-2.81908 + 3.35965i) q^{15} +(-2.46064 - 4.26195i) q^{17} +(-3.62449 + 6.27779i) q^{19} +4.06564i q^{21} +(0.233956 - 0.196312i) q^{23} +(-1.32635 + 0.482753i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(2.91875 - 1.06234i) q^{29} +(6.58512 - 5.52557i) q^{31} +(6.43629 - 3.71599i) q^{33} +(-2.97178 + 5.14728i) q^{35} +(3.78699 + 6.55926i) q^{37} +(-0.449493 - 1.23497i) q^{39} +(-4.60607 - 1.67647i) q^{41} +(0.283119 - 1.60565i) q^{43} -7.59627 q^{45} +(1.39053 + 1.16679i) q^{47} +(-0.258770 - 1.46756i) q^{49} +(2.91534 - 8.00984i) q^{51} +0.573978 q^{53} +10.8648 q^{55} +(-12.3648 + 2.18025i) q^{57} +(-0.950837 - 5.39246i) q^{59} +(8.46451 + 7.10257i) q^{61} +(-5.39440 + 4.52644i) q^{63} +(0.333626 - 1.89209i) q^{65} +(0.0393628 + 0.0143269i) q^{67} +(0.520945 + 0.0918566i) q^{69} +(-2.10220 - 3.64111i) q^{71} +(5.54576 - 9.60554i) q^{73} +(-2.11721 - 1.22237i) q^{75} +(7.71554 - 6.47410i) q^{77} +(-6.92989 + 2.52227i) q^{79} +(-8.45723 - 3.07818i) q^{81} +(6.41147 - 2.33359i) q^{83} +(9.54576 - 8.00984i) q^{85} +(4.65910 + 2.68993i) q^{87} +(-3.96064 + 6.86002i) q^{89} +(-0.890530 - 1.54244i) q^{91} +(14.6630 + 2.58548i) q^{93} +(-17.2481 - 6.27779i) q^{95} +(-0.570108 + 3.23324i) q^{97} +(12.0963 + 4.40268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q - 3 * q^5 - 3 * q^7	\( 6 q - 3 q^{5} - 3 q^{7} + 3 q^{11} - 12 q^{13} - 6 q^{17} - 9 q^{19} + 6 q^{23} - 9 q^{25} - 27 q^{27} + 15 q^{29} + 18 q^{31} - 9 q^{33} - 3 q^{35} + 15 q^{37} - 3 q^{41} + 18 q^{43} - 18 q^{45} - 9 q^{47} + 21 q^{49} - 27 q^{51} - 12 q^{53} + 18 q^{55} - 27 q^{57} + 6 q^{59} + 18 q^{61} + 9 q^{63} + 21 q^{65} + 9 q^{67} - 12 q^{71} + 3 q^{73} + 18 q^{75} + 39 q^{77} - 33 q^{79} + 18 q^{83} + 27 q^{85} - 9 q^{87} - 15 q^{89} + 12 q^{91} + 27 q^{93} - 21 q^{95} - 12 q^{97} + 45 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 3 * q^7 + 3 * q^11 - 12 * q^13 - 6 * q^17 - 9 * q^19 + 6 * q^23 - 9 * q^25 - 27 * q^27 + 15 * q^29 + 18 * q^31 - 9 * q^33 - 3 * q^35 + 15 * q^37 - 3 * q^41 + 18 * q^43 - 18 * q^45 - 9 * q^47 + 21 * q^49 - 27 * q^51 - 12 * q^53 + 18 * q^55 - 27 * q^57 + 6 * q^59 + 18 * q^61 + 9 * q^63 + 21 * q^65 + 9 * q^67 - 12 * q^71 + 3 * q^73 + 18 * q^75 + 39 * q^77 - 33 * q^79 + 18 * q^83 + 27 * q^85 - 9 * q^87 - 15 * q^89 + 12 * q^91 + 27 * q^93 - 21 * q^95 - 12 * q^97 + 45 * q^99

Introduction

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