LMFDB - Embedded newform 576.2.y.a.335.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.6
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11494 + 1.32549i) q^{3} +(1.20583 + 0.323102i) q^{5} +(-0.140266 + 0.242948i) q^{7} +(-0.513832 - 2.95567i) q^{9} +O(q^{10})$	\(q+(-1.11494 + 1.32549i) q^{3} +(1.20583 + 0.323102i) q^{5} +(-0.140266 + 0.242948i) q^{7} +(-0.513832 - 2.95567i) q^{9} +(3.07444 - 0.823794i) q^{11} +(2.76539 + 0.740984i) q^{13} +(-1.77270 + 1.23808i) q^{15} +3.72031i q^{17} +(4.10860 + 4.10860i) q^{19} +(-0.165636 - 0.456792i) q^{21} +(1.57595 - 0.909876i) q^{23} +(-2.98049 - 1.72078i) q^{25} +(4.49059 + 2.61431i) q^{27} +(-3.83006 + 1.02626i) q^{29} +(-8.81101 + 5.08704i) q^{31} +(-2.33588 + 4.99361i) q^{33} +(-0.247635 + 0.247635i) q^{35} +(1.76964 + 1.76964i) q^{37} +(-4.06540 + 2.83934i) q^{39} +(2.66819 + 4.62144i) q^{41} +(1.84748 + 6.89490i) q^{43} +(0.335387 - 3.73007i) q^{45} +(5.48486 - 9.50006i) q^{47} +(3.46065 + 5.99402i) q^{49} +(-4.93123 - 4.14791i) q^{51} +(8.58403 - 8.58403i) q^{53} +3.97344 q^{55} +(-10.0267 + 0.865067i) q^{57} +(-1.44299 + 5.38532i) q^{59} +(1.66977 + 6.23168i) q^{61} +(0.790146 + 0.289745i) q^{63} +(3.09519 + 1.78701i) q^{65} +(1.00652 - 3.75640i) q^{67} +(-0.551057 + 3.10336i) q^{69} -10.6808i q^{71} +9.30419i q^{73} +(5.60393 - 2.03203i) q^{75} +(-0.231101 + 0.862479i) q^{77} +(-8.70990 - 5.02866i) q^{79} +(-8.47195 + 3.03744i) q^{81} +(-0.588691 - 2.19703i) q^{83} +(-1.20204 + 4.48608i) q^{85} +(2.90998 - 6.22091i) q^{87} -1.87637 q^{89} +(-0.567911 + 0.567911i) q^{91} +(3.08091 - 17.3506i) q^{93} +(3.62679 + 6.28179i) q^{95} +(9.19070 - 15.9188i) q^{97} +(-4.01461 - 8.66374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.11494	+	1.32549i	−0.643709	+	0.765270i
$3$	−1.11494	+	1.32549i	−0.643709	+	0.765270i
$4$		0			0
$5$	1.20583	+	0.323102i	0.539266	+	0.144496i	0.518164	−	0.855282i	$-0.326616\pi$
$5$	1.20583	+	0.323102i	0.539266	+	0.144496i	0.0211020	+	0.999777i	$0.493283\pi$
$6$		0			0
$7$	−0.140266	+	0.242948i	−0.0530156	+	0.0918256i	−0.891315	−	0.453384i	$-0.850217\pi$
$7$	−0.140266	+	0.242948i	−0.0530156	+	0.0918256i	0.838300	+	0.545210i	$0.183550\pi$
$8$		0			0
$9$	−0.513832	−	2.95567i	−0.171277	−	0.985223i
$10$		0			0
$11$	3.07444	−	0.823794i	0.926979	−	0.248383i	0.236413	−	0.971653i	$-0.424028\pi$
$11$	3.07444	−	0.823794i	0.926979	−	0.248383i	0.690566	+	0.723269i	$0.257361\pi$
$12$		0			0
$13$	2.76539	+	0.740984i	0.766982	+	0.205512i	0.621038	−	0.783781i	$-0.286711\pi$
$13$	2.76539	+	0.740984i	0.766982	+	0.205512i	0.145944	+	0.989293i	$0.453378\pi$
$14$		0			0
$15$	−1.77270	+	1.23808i	−0.457708	+	0.319671i
$16$		0			0
$17$			3.72031i			0.902309i	0.892446	+	0.451154i	$0.148988\pi$
$17$			3.72031i			0.902309i	−0.892446	+	0.451154i	$0.851012\pi$
$18$		0			0
$19$	4.10860	+	4.10860i	0.942577	+	0.942577i	0.998439	−	0.0558614i	$-0.0177905\pi$
$19$	4.10860	+	4.10860i	0.942577	+	0.942577i	−0.0558614	+	0.998439i	$0.517791\pi$
$20$		0			0
$21$	−0.165636	−	0.456792i	−0.0361448	−	0.0996802i
$22$		0			0
$23$	1.57595	−	0.909876i	0.328609	−	0.189722i	−0.326615	−	0.945158i	$-0.605908\pi$
$23$	1.57595	−	0.909876i	0.328609	−	0.189722i	0.655223	+	0.755435i	$0.272575\pi$
$24$		0			0
$25$	−2.98049	−	1.72078i	−0.596097	−	0.344157i
$26$		0			0
$27$	4.49059	+	2.61431i	0.864215	+	0.503123i
$28$		0			0
$29$	−3.83006	+	1.02626i	−0.711224	+	0.190572i	−0.596253	−	0.802797i	$-0.703344\pi$
$29$	−3.83006	+	1.02626i	−0.711224	+	0.190572i	−0.114972	+	0.993369i	$0.536678\pi$
$30$		0			0
$31$	−8.81101	+	5.08704i	−1.58250	+	0.913659i	−0.588012	+	0.808852i	$0.700089\pi$
$31$	−8.81101	+	5.08704i	−1.58250	+	0.913659i	−0.994493	+	0.104807i	$0.966578\pi$
$32$		0			0
$33$	−2.33588	+	4.99361i	−0.406625	+	0.869276i
$34$		0			0
$35$	−0.247635	+	0.247635i	−0.0418579	+	0.0418579i
$36$		0			0
$37$	1.76964	+	1.76964i	0.290928	+	0.290928i	0.837447	−	0.546519i	$-0.184047\pi$
$37$	1.76964	+	1.76964i	0.290928	+	0.290928i	−0.546519	+	0.837447i	$0.684047\pi$
$38$		0			0
$39$	−4.06540	+	2.83934i	−0.650985	+	0.454658i
$40$		0			0
$41$	2.66819	+	4.62144i	0.416701	+	0.721747i	0.995605	−	0.0936482i	$-0.0298529\pi$
$41$	2.66819	+	4.62144i	0.416701	+	0.721747i	−0.578904	+	0.815395i	$0.696520\pi$
$42$		0			0
$43$	1.84748	+	6.89490i	0.281738	+	1.05146i	0.951190	+	0.308606i	$0.0998625\pi$
$43$	1.84748	+	6.89490i	0.281738	+	1.05146i	−0.669452	+	0.742856i	$0.733471\pi$
$44$		0			0
$45$	0.335387	−	3.73007i	0.0499965	−	0.556046i
$46$		0			0
$47$	5.48486	−	9.50006i	0.800049	−	1.38573i	−0.119534	−	0.992830i	$-0.538140\pi$
$47$	5.48486	−	9.50006i	0.800049	−	1.38573i	0.919583	−	0.392896i	$-0.128527\pi$
$48$		0			0
$49$	3.46065	+	5.99402i	0.494379	+	0.856289i
$50$		0			0
$51$	−4.93123	−	4.14791i	−0.690510	−	0.580824i
$52$		0			0
$53$	8.58403	−	8.58403i	1.17911	−	1.17911i	0.199135	−	0.979972i	$-0.436187\pi$
$53$	8.58403	−	8.58403i	1.17911	−	1.17911i	0.979972	−	0.199135i	$-0.0638133\pi$
$54$		0			0
$55$	3.97344			0.535778
$56$		0			0
$57$	−10.0267	+	0.865067i	−1.32807	+	0.114581i
$58$		0			0
$59$	−1.44299	+	5.38532i	−0.187862	+	0.701109i	0.806138	+	0.591727i	$0.201554\pi$
$59$	−1.44299	+	5.38532i	−0.187862	+	0.701109i	−0.994000	+	0.109382i	$0.965113\pi$
$60$		0			0
$61$	1.66977	+	6.23168i	0.213793	+	0.797885i	0.986588	+	0.163230i	$0.0521911\pi$
$61$	1.66977	+	6.23168i	0.213793	+	0.797885i	−0.772796	+	0.634655i	$0.781142\pi$
$62$		0			0
$63$	0.790146	+	0.289745i	0.0995491	+	0.0365045i
$64$		0			0
$65$	3.09519	+	1.78701i	0.383911	+	0.221651i
$66$		0			0
$67$	1.00652	−	3.75640i	0.122967	−	0.458918i	−0.876792	−	0.480869i	$-0.840321\pi$
$67$	1.00652	−	3.75640i	0.122967	−	0.458918i	0.999759	+	0.0219514i	$0.00698792\pi$
$68$		0			0
$69$	−0.551057	+	3.10336i	−0.0663395	+	0.373600i
$70$		0			0
$71$		−	10.6808i		−	1.26758i	−0.773506	−	0.633789i	$-0.781499\pi$
$71$		−	10.6808i		−	1.26758i	0.773506	−	0.633789i	$-0.218501\pi$
$72$		0			0
$73$			9.30419i			1.08897i	0.838770	+	0.544487i	$0.183275\pi$
$73$			9.30419i			1.08897i	−0.838770	+	0.544487i	$0.816725\pi$
$74$		0			0
$75$	5.60393	−	2.03203i	0.647086	−	0.234639i
$76$		0			0
$77$	−0.231101	+	0.862479i	−0.0263364	+	0.0982886i
$78$		0			0
$79$	−8.70990	−	5.02866i	−0.979940	−	0.565769i	−0.0776882	−	0.996978i	$-0.524754\pi$
$79$	−8.70990	−	5.02866i	−0.979940	−	0.565769i	−0.902252	+	0.431209i	$0.858087\pi$
$80$		0			0
$81$	−8.47195	+	3.03744i	−0.941328	+	0.337493i
$82$		0			0
$83$	−0.588691	−	2.19703i	−0.0646173	−	0.241155i	0.926062	−	0.377372i	$-0.123172\pi$
$83$	−0.588691	−	2.19703i	−0.0646173	−	0.241155i	−0.990679	+	0.136217i	$0.956506\pi$
$84$		0			0
$85$	−1.20204	+	4.48608i	−0.130380	+	0.486584i
$86$		0			0
$87$	2.90998	−	6.22091i	0.311982	−	0.666952i
$88$		0			0
$89$	−1.87637			−0.198895			−0.0994475	−	0.995043i	$-0.531708\pi$
$89$	−1.87637			−0.198895			−0.0994475	+	0.995043i	$0.531708\pi$
$90$		0			0
$91$	−0.567911	+	0.567911i	−0.0595332	+	0.0595332i
$92$		0			0
$93$	3.08091	−	17.3506i	0.319476	−	1.79917i
$94$		0			0
$95$	3.62679	+	6.28179i	0.372101	+	0.644498i
$96$		0			0
$97$	9.19070	−	15.9188i	0.933175	−	1.61631i	0.155317	−	0.987865i	$-0.450360\pi$
$97$	9.19070	−	15.9188i	0.933175	−	1.61631i	0.777857	−	0.628441i	$-0.216307\pi$
$98$		0			0
$99$	−4.01461	−	8.66374i	−0.403484	−	0.870739i
$100$		0			0
$101$	−4.18566	−	15.6211i	−0.416488	−	1.55436i	−0.781836	−	0.623485i	$-0.785716\pi$
$101$	−4.18566	−	15.6211i	−0.416488	−	1.55436i	0.365347	−	0.930871i	$-0.380950\pi$
$102$		0			0
$103$	−0.0611378	−	0.105894i	−0.00602409	−	0.0104340i	0.862998	−	0.505208i	$-0.168584\pi$
$103$	−0.0611378	−	0.105894i	−0.00602409	−	0.0104340i	−0.869022	+	0.494774i	$0.835251\pi$
$104$		0			0
$105$	−0.0521396	−	0.604333i	−0.00508830	−	0.0589769i
$106$		0			0
$107$	−5.97359	−	5.97359i	−0.577489	−	0.577489i	0.356722	−	0.934211i	$-0.383894\pi$
$107$	−5.97359	−	5.97359i	−0.577489	−	0.577489i	−0.934211	+	0.356722i	$0.883894\pi$
$108$		0			0
$109$	−3.40913	+	3.40913i	−0.326536	+	0.326536i	−0.851268	−	0.524732i	$-0.824166\pi$
$109$	−3.40913	+	3.40913i	−0.326536	+	0.326536i	0.524732	+	0.851268i	$0.324166\pi$
$110$		0			0
$111$	−4.31868	+	0.372599i	−0.409911	+	0.0353655i
$112$		0			0
$113$	1.91330	−	1.10464i	0.179988	−	0.103916i	−0.407299	−	0.913295i	$-0.633529\pi$
$113$	1.91330	−	1.10464i	0.179988	−	0.103916i	0.587287	+	0.809379i	$0.300196\pi$
$114$		0			0
$115$	2.19432	−	0.587966i	0.204621	−	0.0548281i
$116$		0			0
$117$	0.769157	−	8.55432i	0.0711086	−	0.790847i
$118$		0			0
$119$	−0.903842	−	0.521833i	−0.0828551	−	0.0478364i
$120$		0			0
$121$	−0.752719	+	0.434583i	−0.0684290	+	0.0395075i
$122$		0			0
$123$	−9.10052	−	1.61596i	−0.820566	−	0.145706i
$124$		0			0
$125$	−7.45164	−	7.45164i	−0.666495	−	0.666495i
$126$		0			0
$127$		−	3.63934i		−	0.322939i	−0.986878	−	0.161470i	$-0.948377\pi$
$127$		−	3.63934i		−	0.322939i	0.986878	−	0.161470i	$-0.0516234\pi$
$128$		0			0
$129$	−11.1989	−	5.23856i	−0.986010	−	0.461229i
$130$		0			0
$131$	14.9890	+	4.01630i	1.30960	+	0.350906i	0.845072	−	0.534653i	$-0.179558\pi$
$131$	14.9890	+	4.01630i	1.30960	+	0.350906i	0.464527	+	0.885559i	$0.346224\pi$
$132$		0			0
$133$	−1.57447	+	0.421878i	−0.136524	+	0.0365815i
$134$		0			0
$135$	4.57022	+	4.60334i	0.393342	+	0.396192i
$136$		0			0
$137$	10.4065	−	18.0245i	0.889085	−	1.53994i	0.0481263	−	0.998841i	$-0.484675\pi$
$137$	10.4065	−	18.0245i	0.889085	−	1.53994i	0.840959	−	0.541099i	$-0.181992\pi$
$138$		0			0
$139$	−0.802043	−	0.214907i	−0.0680284	−	0.0182282i	0.224644	−	0.974441i	$-0.427878\pi$
$139$	−0.802043	−	0.214907i	−0.0680284	−	0.0182282i	−0.292673	+	0.956213i	$0.594545\pi$
$140$		0			0
$141$	6.47693	+	17.8621i	0.545456	+	1.50426i
$142$		0			0
$143$	9.11246			0.762022
$144$		0			0
$145$	−4.95000			−0.411076
$146$		0			0
$147$	−11.8034	−	2.09591i	−0.973529	−	0.172868i
$148$		0			0
$149$	5.13681	+	1.37640i	0.420824	+	0.112759i	0.463015	−	0.886350i	$-0.346767\pi$
$149$	5.13681	+	1.37640i	0.420824	+	0.112759i	−0.0421919	+	0.999110i	$0.513434\pi$
$150$		0			0
$151$	1.53487	−	2.65847i	0.124906	−	0.216343i	−0.796790	−	0.604256i	$-0.793471\pi$
$151$	1.53487	−	2.65847i	0.124906	−	0.216343i	0.921696	+	0.387913i	$0.126804\pi$
$152$		0			0
$153$	10.9960	−	1.91162i	0.888975	−	0.154545i
$154$		0			0
$155$	−12.2683	+	3.28727i	−0.985410	+	0.264040i
$156$		0			0
$157$	−5.63885	−	1.51093i	−0.450029	−	0.120585i	0.0266838	−	0.999644i	$-0.491505\pi$
$157$	−5.63885	−	1.51093i	−0.450029	−	0.120585i	−0.476713	+	0.879059i	$0.658172\pi$
$158$		0			0
$159$	1.80737	+	20.9487i	0.143334	+	1.66134i
$160$		0			0
$161$			0.510499i			0.0402329i
$162$		0			0
$163$	12.5565	+	12.5565i	0.983500	+	0.983500i	0.999866	−	0.0163656i	$-0.00520958\pi$
$163$	12.5565	+	12.5565i	0.983500	+	0.983500i	−0.0163656	+	0.999866i	$0.505210\pi$
$164$		0			0
$165$	−4.43013	+	5.26674i	−0.344885	+	0.410015i
$166$		0			0
$167$	−12.0834	+	6.97635i	−0.935041	+	0.539846i	−0.888402	−	0.459066i	$-0.848184\pi$
$167$	−12.0834	+	6.97635i	−0.935041	+	0.539846i	−0.0466388	+	0.998912i	$0.514851\pi$
$168$		0			0
$169$	−4.16000	−	2.40178i	−0.320000	−	0.184752i
$170$		0			0
$171$	10.0325	−	14.2548i	0.767206	−	1.09009i
$172$		0			0
$173$	−2.38993	+	0.640380i	−0.181703	+	0.0486872i	−0.348523	−	0.937300i	$-0.613317\pi$
$173$	−2.38993	+	0.640380i	−0.181703	+	0.0486872i	0.166820	+	0.985987i	$0.446650\pi$
$174$		0			0
$175$	0.836121	−	0.482735i	0.0632048	−	0.0364913i
$176$		0			0
$177$	−5.52933	−	7.91696i	−0.415610	−	0.595075i
$178$		0			0
$179$	−9.53870	+	9.53870i	−0.712956	+	0.712956i	−0.967153	−	0.254197i	$-0.918189\pi$
$179$	−9.53870	+	9.53870i	−0.712956	+	0.712956i	0.254197	+	0.967153i	$0.418189\pi$
$180$		0			0
$181$	−6.83874	−	6.83874i	−0.508320	−	0.508320i	0.405691	−	0.914010i	$-0.367031\pi$
$181$	−6.83874	−	6.83874i	−0.508320	−	0.508320i	−0.914010	+	0.405691i	$0.867031\pi$
$182$		0			0
$183$	−10.1217	−	4.73466i	−0.748218	−	0.349996i
$184$		0			0
$185$	1.56212	+	2.70567i	0.114849	+	0.198925i
$186$		0			0
$187$	3.06477	+	11.4379i	0.224118	+	0.836421i
$188$		0			0
$189$	−1.26502	+	0.724281i	−0.0920164	+	0.0526837i
$190$		0			0
$191$	7.08629	−	12.2738i	0.512746	−	0.888102i	−0.487145	−	0.873321i	$-0.661962\pi$
$191$	7.08629	−	12.2738i	0.512746	−	0.888102i	0.999891	−	0.0147810i	$-0.00470512\pi$
$192$		0			0
$193$	−6.47017	−	11.2067i	−0.465733	−	0.806673i	0.533501	−	0.845799i	$-0.320876\pi$
$193$	−6.47017	−	11.2067i	−0.465733	−	0.806673i	−0.999234	+	0.0391263i	$0.987543\pi$
$194$		0			0
$195$	−5.81960	+	2.11023i	−0.416750	+	0.151117i
$196$		0			0
$197$	−8.02294	+	8.02294i	−0.571611	+	0.571611i	−0.932578	−	0.360968i	$-0.882447\pi$
$197$	−8.02294	+	8.02294i	−0.571611	+	0.571611i	0.360968	+	0.932578i	$0.382447\pi$
$198$		0			0
$199$	−10.9199			−0.774093			−0.387046	−	0.922060i	$-0.626505\pi$
$199$	−10.9199			−0.774093			−0.387046	+	0.922060i	$0.626505\pi$
$200$		0			0
$201$	3.85685	+	5.52229i	0.272041	+	0.389512i
$202$		0			0
$203$	0.287899	−	1.07445i	0.0202066	−	0.0754119i
$204$		0			0
$205$	1.72420	+	6.43478i	0.120423	+	0.449425i
$206$		0			0
$207$	−3.49907	−	4.19047i	−0.243202	−	0.291258i
$208$		0			0
$209$	16.0163	+	9.24701i	1.10787	+	0.639629i
$210$		0			0
$211$	4.37047	−	16.3108i	0.300875	−	1.12288i	−0.635563	−	0.772049i	$-0.719232\pi$
$211$	4.37047	−	16.3108i	0.300875	−	1.12288i	0.936438	−	0.350833i	$-0.114101\pi$
$212$		0			0
$213$	14.1573	+	11.9084i	0.970039	+	0.815951i
$214$		0			0
$215$			8.91103i			0.607727i
$216$		0			0
$217$		−	2.85415i		−	0.193753i
$218$		0			0
$219$	−12.3326	−	10.3736i	−0.833359	−	0.700982i
$220$		0			0
$221$	−2.75669	+	10.2881i	−0.185435	+	0.692054i
$222$		0			0
$223$	12.3586	+	7.13522i	0.827591	+	0.477810i	0.853027	−	0.521867i	$-0.174764\pi$
$223$	12.3586	+	7.13522i	0.827591	+	0.477810i	−0.0254364	+	0.999676i	$0.508098\pi$
$224$		0			0
$225$	−3.55460	+	9.69352i	−0.236973	+	0.646235i
$226$		0			0
$227$	2.27906	+	8.50557i	0.151267	+	0.564535i	0.999396	+	0.0347459i	$0.0110622\pi$
$227$	2.27906	+	8.50557i	0.151267	+	0.564535i	−0.848130	+	0.529789i	$0.822271\pi$
$228$		0			0
$229$	−6.45185	+	24.0786i	−0.426350	+	1.59116i	0.334606	+	0.942358i	$0.391397\pi$
$229$	−6.45185	+	24.0786i	−0.426350	+	1.59116i	−0.760957	+	0.648803i	$0.775270\pi$
$230$		0			0
$231$	−0.885543	−	1.26793i	−0.0582644	−	0.0834237i
$232$		0			0
$233$	−6.51295			−0.426678			−0.213339	−	0.976978i	$-0.568434\pi$
$233$	−6.51295			−0.426678			−0.213339	+	0.976978i	$0.568434\pi$
$234$		0			0
$235$	9.68332	−	9.68332i	0.631670	−	0.631670i
$236$		0			0
$237$	16.3764	−	5.93822i	1.06376	−	0.385729i
$238$		0			0
$239$	2.36907	+	4.10336i	0.153243	+	0.265424i	0.932418	−	0.361382i	$-0.117695\pi$
$239$	2.36907	+	4.10336i	0.153243	+	0.265424i	−0.779175	+	0.626806i	$0.784362\pi$
$240$		0			0
$241$	7.43805	−	12.8831i	0.479127	−	0.829872i	−0.520586	−	0.853809i	$-0.674287\pi$
$241$	7.43805	−	12.8831i	0.479127	−	0.829872i	0.999713	+	0.0239367i	$0.00762000\pi$
$242$		0			0
$243$	5.41961	−	14.6160i	0.347668	−	0.937618i
$244$		0			0
$245$	2.23629	+	8.34594i	0.142871	+	0.533203i
$246$		0			0
$247$	8.31748	+	14.4063i	0.529228	+	0.916650i
$248$		0			0
$249$	3.56848	+	1.66924i	0.226143	+	0.105784i
$250$		0			0
$251$	−6.89508	−	6.89508i	−0.435213	−	0.435213i	0.455184	−	0.890397i	$-0.349573\pi$
$251$	−6.89508	−	6.89508i	−0.435213	−	0.435213i	−0.890397	+	0.455184i	$0.849573\pi$
$252$		0			0
$253$	4.09562	−	4.09562i	0.257489	−	0.257489i
$254$		0			0
$255$	−4.60604	−	6.59499i	−0.288442	−	0.412994i
$256$		0			0
$257$	2.17437	−	1.25537i	0.135633	−	0.0783080i	−0.430648	−	0.902520i	$-0.641715\pi$
$257$	2.17437	−	1.25537i	0.135633	−	0.0783080i	0.566281	+	0.824212i	$0.308382\pi$
$258$		0			0
$259$	−0.678152	+	0.181710i	−0.0421383	+	0.0112909i
$260$		0			0
$261$	5.00130	+	10.7931i	0.309572	+	0.668074i
$262$		0			0
$263$	3.14718	+	1.81703i	0.194064	+	0.112043i	0.593884	−	0.804551i	$-0.297594\pi$
$263$	3.14718	+	1.81703i	0.194064	+	0.112043i	−0.399820	+	0.916594i	$0.630927\pi$
$264$		0			0
$265$	13.1244	−	7.57740i	0.806228	−	0.465476i
$266$		0			0
$267$	2.09204	−	2.48711i	0.128031	−	0.152209i
$268$		0			0
$269$	−12.3633	−	12.3633i	−0.753802	−	0.753802i	0.221384	−	0.975187i	$-0.428942\pi$
$269$	−12.3633	−	12.3633i	−0.753802	−	0.753802i	−0.975187	+	0.221384i	$0.928942\pi$
$270$		0			0
$271$		−	27.2658i		−	1.65628i	−0.560523	−	0.828139i	$-0.689400\pi$
$271$		−	27.2658i		−	1.65628i	0.560523	−	0.828139i	$-0.310600\pi$
$272$		0			0
$273$	−0.119574	−	1.38594i	−0.00723694	−	0.0838811i
$274$		0			0
$275$	−10.5809	−	2.83514i	−0.638053	−	0.170966i
$276$		0			0
$277$	−16.7042	+	4.47587i	−1.00366	+	0.268929i	−0.722977	−	0.690872i	$-0.757227\pi$
$277$	−16.7042	+	4.47587i	−1.00366	+	0.268929i	−0.280680	+	0.959801i	$0.590560\pi$
$278$		0			0
$279$	19.5630	+	23.4285i	1.17121	+	1.40263i
$280$		0			0
$281$	−7.04702	+	12.2058i	−0.420390	+	0.728137i	−0.995978	−	0.0896034i	$-0.971440\pi$
$281$	−7.04702	+	12.2058i	−0.420390	+	0.728137i	0.575588	+	0.817740i	$0.304773\pi$
$282$		0			0
$283$	−0.628767	−	0.168478i	−0.0373763	−	0.0100149i	0.240082	−	0.970753i	$-0.422826\pi$
$283$	−0.628767	−	0.168478i	−0.0373763	−	0.0100149i	−0.277459	+	0.960738i	$0.589492\pi$
$284$		0			0
$285$	−12.3701	−	2.19653i	−0.732740	−	0.130111i
$286$		0			0
$287$	−1.49702			−0.0883665
$288$		0			0
$289$	3.15927			0.185839
$290$		0			0
$291$	10.8531	+	29.9306i	0.636218	+	1.75456i
$292$		0			0
$293$	−8.09169	−	2.16816i	−0.472722	−	0.126665i	0.0145900	−	0.999894i	$-0.495356\pi$
$293$	−8.09169	−	2.16816i	−0.472722	−	0.126665i	−0.487312	+	0.873228i	$0.662022\pi$
$294$		0			0
$295$	−3.48002	+	6.02757i	−0.202615	+	0.350939i
$296$		0			0
$297$	15.9597	+	4.33821i	0.926077	+	0.251728i
$298$		0			0
$299$	5.03233	−	1.34841i	0.291027	−	0.0779804i
$300$		0			0
$301$	−1.93424	−	0.518278i	−0.111488	−	0.0298730i
$302$		0			0
$303$	25.3723	+	11.8685i	1.45760	+	0.681827i
$304$		0			0
$305$			8.05388i			0.461164i
$306$		0			0
$307$	−10.1250	−	10.1250i	−0.577865	−	0.577865i	0.356449	−	0.934315i	$-0.383987\pi$
$307$	−10.1250	−	10.1250i	−0.577865	−	0.577865i	−0.934315	+	0.356449i	$0.883987\pi$
$308$		0			0
$309$	0.208526	+	0.0370275i	0.0118626	+	0.00210642i
$310$		0			0
$311$	13.7848	−	7.95868i	0.781667	−	0.451295i	−0.0553539	−	0.998467i	$-0.517629\pi$
$311$	13.7848	−	7.95868i	0.781667	−	0.451295i	0.837021	+	0.547171i	$0.184295\pi$
$312$		0			0
$313$	−9.90266	−	5.71730i	−0.559732	−	0.323161i	0.193306	−	0.981138i	$-0.438079\pi$
$313$	−9.90266	−	5.71730i	−0.559732	−	0.323161i	−0.753038	+	0.657977i	$0.771412\pi$
$314$		0			0
$315$	0.859168	+	0.604683i	0.0484086	+	0.0340700i
$316$		0			0
$317$	26.3682	−	7.06533i	1.48098	−	0.396828i	0.574302	−	0.818644i	$-0.305274\pi$
$317$	26.3682	−	7.06533i	1.48098	−	0.396828i	0.906682	+	0.421815i	$0.138607\pi$
$318$		0			0
$319$	−10.9299	+	6.31036i	−0.611955	+	0.353313i
$320$		0			0
$321$	14.5781	−	1.25774i	0.813670	−	0.0702004i
$322$		0			0
$323$	−15.2853	+	15.2853i	−0.850495	+	0.850495i
$324$		0			0
$325$	−6.96714	−	6.96714i	−0.386467	−	0.386467i
$326$		0			0
$327$	−0.717795	−	8.31973i	−0.0396941	−	0.460082i
$328$		0			0
$329$	1.53868	+	2.66507i	0.0848301	+	0.146930i
$330$		0			0
$331$	−2.97493	−	11.1026i	−0.163517	−	0.610254i	−0.998225	−	0.0595605i	$-0.981030\pi$
$331$	−2.97493	−	11.1026i	−0.163517	−	0.610254i	0.834708	−	0.550693i	$-0.185637\pi$
$332$		0			0
$333$	4.32118	−	6.13978i	0.236799	−	0.336458i
$334$		0			0
$335$	2.42740	−	4.20439i	0.132623	−	0.229710i
$336$		0			0
$337$	4.37194	+	7.57242i	0.238155	+	0.412496i	0.960185	−	0.279366i	$-0.0901242\pi$
$337$	4.37194	+	7.57242i	0.238155	+	0.412496i	−0.722030	+	0.691862i	$0.756791\pi$
$338$		0			0
$339$	−0.669016	+	3.76766i	−0.0363360	+	0.204631i
$340$		0			0
$341$	−22.8983	+	22.8983i	−1.24001	+	1.24001i
$342$		0			0
$343$	−3.90537			−0.210870
$344$		0			0
$345$	−1.66719	+	3.56409i	−0.0897583	+	0.191884i
$346$		0			0
$347$	−0.832493	+	3.10690i	−0.0446905	+	0.166787i	−0.984664	−	0.174459i	$-0.944182\pi$
$347$	−0.832493	+	3.10690i	−0.0446905	+	0.166787i	0.939974	+	0.341246i	$0.110849\pi$
$348$		0			0
$349$	8.57705	+	32.0100i	0.459119	+	1.71346i	0.675687	+	0.737188i	$0.263847\pi$
$349$	8.57705	+	32.0100i	0.459119	+	1.71346i	−0.216568	+	0.976268i	$0.569486\pi$
$350$		0			0
$351$	10.4811	+	10.5570i	0.559439	+	0.563493i
$352$		0			0
$353$	−7.18886	−	4.15049i	−0.382624	−	0.220908i	0.296335	−	0.955084i	$-0.404235\pi$
$353$	−7.18886	−	4.15049i	−0.382624	−	0.220908i	−0.678959	+	0.734176i	$0.737569\pi$
$354$		0			0
$355$	3.45099	−	12.8793i	0.183160	−	0.683561i
$356$		0			0
$357$	1.69941	−	0.616220i	0.0899423	−	0.0326138i
$358$		0			0
$359$			17.1616i			0.905754i	0.891573	+	0.452877i	$0.149602\pi$
$359$			17.1616i			0.905754i	−0.891573	+	0.452877i	$0.850398\pi$
$360$		0			0
$361$			14.7612i			0.776903i
$362$		0			0
$363$	0.263201	−	1.48225i	0.0138145	−	0.0777981i
$364$		0			0
$365$	−3.00621	+	11.2193i	−0.157352	+	0.587246i
$366$		0			0
$367$	1.27977	+	0.738875i	0.0668034	+	0.0385690i	0.533030	−	0.846097i	$-0.321053\pi$
$367$	1.27977	+	0.738875i	0.0668034	+	0.0385690i	−0.466226	+	0.884666i	$0.654387\pi$
$368$		0			0
$369$	12.2884	−	10.2609i	0.639710	−	0.534162i
$370$		0			0
$371$	0.881424	+	3.28952i	0.0457612	+	0.170783i
$372$		0			0
$373$	8.48049	−	31.6496i	0.439103	−	1.63876i	−0.291948	−	0.956434i	$-0.594304\pi$
$373$	8.48049	−	31.6496i	0.439103	−	1.63876i	0.731052	−	0.682322i	$-0.239030\pi$
$374$		0			0
$375$	18.1852	−	1.56895i	0.939078	−	0.0810200i
$376$		0			0
$377$	−11.3521			−0.584661
$378$		0			0
$379$	−19.2548	+	19.2548i	−0.989053	+	0.989053i	−0.999941	−	0.0108880i	$-0.996534\pi$
$379$	−19.2548	+	19.2548i	−0.989053	+	0.989053i	0.0108880	+	0.999941i	$0.496534\pi$
$380$		0			0
$381$	4.82390	+	4.05763i	0.247136	+	0.207879i
$382$		0			0
$383$	3.99635	+	6.92189i	0.204204	+	0.353692i	0.949879	−	0.312618i	$-0.101206\pi$
$383$	3.99635	+	6.92189i	0.204204	+	0.353692i	−0.745675	+	0.666310i	$0.767873\pi$
$384$		0			0
$385$	−0.557338	+	0.965338i	−0.0284046	+	0.0491982i
$386$		0			0
$387$	19.4297	−	9.00336i	0.987669	−	0.457667i
$388$		0			0
$389$	−2.21212	−	8.25574i	−0.112159	−	0.418583i	0.886900	−	0.461962i	$-0.152854\pi$
$389$	−2.21212	−	8.25574i	−0.112159	−	0.418583i	−0.999059	+	0.0433793i	$0.986188\pi$
$390$		0			0
$391$	3.38502	+	5.86303i	0.171188	+	0.296506i
$392$		0			0
$393$	−22.0354	+	15.3899i	−1.11154	+	0.776316i
$394$		0			0
$395$	−8.87792	−	8.87792i	−0.446697	−	0.446697i
$396$		0			0
$397$	21.9949	−	21.9949i	1.10389	−	1.10389i	0.109957	−	0.993936i	$-0.464929\pi$
$397$	21.9949	−	21.9949i	1.10389	−	1.10389i	0.993936	−	0.109957i	$-0.0350713\pi$
$398$		0			0
$399$	1.19624	−	2.55731i	0.0598870	−	0.128026i
$400$		0			0
$401$	−15.4215	+	8.90359i	−0.770111	+	0.444624i	−0.832914	−	0.553402i	$-0.813329\pi$
$401$	−15.4215	+	8.90359i	−0.770111	+	0.444624i	0.0628030	+	0.998026i	$0.479996\pi$
$402$		0			0
$403$	−28.1353	+	7.53883i	−1.40152	+	0.375536i
$404$		0			0
$405$	−11.1972	+	0.925337i	−0.556392	+	0.0459803i
$406$		0			0
$407$	6.89849	+	3.98284i	0.341945	+	0.197422i
$408$		0			0
$409$	21.0100	−	12.1301i	1.03888	−	0.599797i	0.119363	−	0.992851i	$-0.461915\pi$
$409$	21.0100	−	12.1301i	1.03888	−	0.599797i	0.919515	+	0.393054i	$0.128581\pi$
$410$		0			0
$411$	12.2887	+	33.8899i	0.606159	+	1.67166i
$412$		0			0
$413$	−1.10595	−	1.10595i	−0.0544202	−	0.0544202i
$414$		0			0
$415$		−	2.83946i		−	0.139383i
$416$		0			0
$417$	1.17908	−	0.823490i	0.0577399	−	0.0403265i
$418$		0			0
$419$	−11.0392	−	2.95796i	−0.539302	−	0.144506i	−0.0211217	−	0.999777i	$-0.506724\pi$
$419$	−11.0392	−	2.95796i	−0.539302	−	0.144506i	−0.518180	+	0.855271i	$0.673390\pi$
$420$		0			0
$421$	16.7104	−	4.47753i	0.814413	−	0.218221i	0.172511	−	0.985008i	$-0.444812\pi$
$421$	16.7104	−	4.47753i	0.814413	−	0.218221i	0.641903	+	0.766786i	$0.278145\pi$
$422$		0			0
$423$	−30.8973	−	11.3300i	−1.50228	−	0.550883i
$424$		0			0
$425$	6.40186	−	11.0883i	0.310536	−	0.537864i
$426$		0			0
$427$	−1.74819	−	0.468425i	−0.0846006	−	0.0226687i
$428$		0			0
$429$	−10.1598	+	12.0784i	−0.490520	+	0.583153i
$430$		0			0
$431$	−33.7821			−1.62723			−0.813613	−	0.581407i	$-0.802502\pi$
$431$	−33.7821			−1.62723			−0.813613	+	0.581407i	$0.802502\pi$
$432$		0			0
$433$	−32.7436			−1.57356			−0.786779	−	0.617235i	$-0.788253\pi$
$433$	−32.7436			−1.57356			−0.786779	+	0.617235i	$0.788253\pi$
$434$		0			0
$435$	5.51894	−	6.56117i	0.264613	−	0.314584i
$436$		0			0
$437$	10.2133	+	2.73664i	0.488567	+	0.130911i
$438$		0			0
$439$	14.7258	−	25.5058i	0.702824	−	1.21733i	−0.264647	−	0.964345i	$-0.585255\pi$
$439$	14.7258	−	25.5058i	0.702824	−	1.21733i	0.967471	−	0.252982i	$-0.0814113\pi$
$440$		0			0
$441$	15.9382	−	13.3085i	0.758960	−	0.633736i
$442$		0			0
$443$	8.80422	−	2.35908i	0.418301	−	0.112083i	−0.0435282	−	0.999052i	$-0.513860\pi$
$443$	8.80422	−	2.35908i	0.418301	−	0.112083i	0.461830	+	0.886969i	$0.347193\pi$
$444$		0			0
$445$	−2.26259	−	0.606260i	−0.107257	−	0.0287395i
$446$		0			0
$447$	−7.55162	+	5.27417i	−0.357179	+	0.249460i
$448$		0			0
$449$		−	2.79179i		−	0.131753i	−0.997828	−	0.0658765i	$-0.979016\pi$
$449$		−	2.79179i		−	0.131753i	0.997828	−	0.0658765i	$-0.0209843\pi$
$450$		0			0
$451$	12.0103	+	12.0103i	0.565543	+	0.565543i
$452$		0			0
$453$	1.81248	+	4.99847i	0.0851579	+	0.234848i
$454$		0			0
$455$	−0.868300	+	0.501313i	−0.0407065	+	0.0235019i
$456$		0			0
$457$	1.90950	+	1.10245i	0.0893226	+	0.0515704i	0.543996	−	0.839088i	$-0.316911\pi$
$457$	1.90950	+	1.10245i	0.0893226	+	0.0515704i	−0.454673	+	0.890658i	$0.650244\pi$
$458$		0			0
$459$	−9.72604	+	16.7064i	−0.453972	+	0.779788i
$460$		0			0
$461$	−19.1849	+	5.14058i	−0.893531	+	0.239421i	−0.676236	−	0.736685i	$-0.736390\pi$
$461$	−19.1849	+	5.14058i	−0.893531	+	0.239421i	−0.217295	+	0.976106i	$0.569723\pi$
$462$		0			0
$463$	1.39347	−	0.804523i	0.0647602	−	0.0373893i	−0.467270	−	0.884115i	$-0.654762\pi$
$463$	1.39347	−	0.804523i	0.0647602	−	0.0373893i	0.532031	+	0.846725i	$0.321429\pi$
$464$		0			0
$465$	9.32109	−	19.9265i	0.432255	−	0.924070i
$466$		0			0
$467$	9.94383	−	9.94383i	0.460145	−	0.460145i	−0.438558	−	0.898703i	$-0.644511\pi$
$467$	9.94383	−	9.94383i	0.460145	−	0.460145i	0.898703	+	0.438558i	$0.144511\pi$
$468$		0			0
$469$	0.771428	+	0.771428i	0.0356213	+	0.0356213i
$470$		0			0
$471$	8.28968	−	5.78964i	0.381968	−	0.266772i
$472$		0			0
$473$	11.3600	+	19.6760i	0.522331	+	0.904704i
$474$		0			0
$475$	−5.17561	−	19.3156i	−0.237473	−	0.886262i
$476$		0			0
$477$	−29.7823	−	20.9608i	−1.36364	−	0.959729i
$478$		0			0
$479$	−14.3867	+	24.9185i	−0.657346	+	1.13856i	0.323955	+	0.946073i	$0.394987\pi$
$479$	−14.3867	+	24.9185i	−0.657346	+	1.13856i	−0.981300	+	0.192483i	$0.938346\pi$
$480$		0			0
$481$	3.58248	+	6.20504i	0.163347	+	0.282925i
$482$		0			0
$483$	−0.676659	−	0.569174i	−0.0307891	−	0.0258983i
$484$		0			0
$485$	16.2259	−	16.2259i	0.736778	−	0.736778i
$486$		0			0
$487$	−43.0194			−1.94939			−0.974697	−	0.223530i	$-0.928242\pi$
$487$	−43.0194			−1.94939			−0.974697	+	0.223530i	$0.928242\pi$
$488$		0			0
$489$	−30.6432	+	2.64377i	−1.38573	+	0.119556i
$490$		0			0
$491$	−1.40962	+	5.26076i	−0.0636152	+	0.237415i	−0.990411	−	0.138150i	$-0.955885\pi$
$491$	−1.40962	+	5.26076i	−0.0636152	+	0.237415i	0.926796	+	0.375565i	$0.122551\pi$
$492$		0			0
$493$	−3.81801	−	14.2490i	−0.171955	−	0.641744i
$494$		0			0
$495$	−2.04168	−	11.7442i	−0.0917667	−	0.527861i
$496$		0			0
$497$	2.59488	+	1.49815i	0.116396	+	0.0672013i
$498$		0			0
$499$	4.61454	−	17.2217i	0.206575	−	0.770950i	−0.782388	−	0.622791i	$-0.785999\pi$
$499$	4.61454	−	17.2217i	0.206575	−	0.770950i	0.988964	−	0.148159i	$-0.0473347\pi$
$500$		0			0
$501$	4.22516	−	23.7946i	0.188766	−	1.06306i
$502$		0			0
$503$		−	0.254767i		−	0.0113595i	−0.999984	−	0.00567974i	$-0.998192\pi$
$503$		−	0.254767i		−	0.0113595i	0.999984	−	0.00567974i	$-0.00180793\pi$
$504$		0			0
$505$		−	20.1888i		−	0.898391i
$506$		0			0
$507$	7.82166	−	2.83620i	0.347372	−	0.125960i
$508$		0			0
$509$	2.84712	−	10.6256i	0.126196	−	0.470971i	−0.873683	−	0.486495i	$-0.838275\pi$
$509$	2.84712	−	10.6256i	0.126196	−	0.470971i	0.999879	+	0.0155245i	$0.00494181\pi$
$510$		0			0
$511$	−2.26043	−	1.30506i	−0.0999956	−	0.0577325i
$512$		0			0
$513$	7.70890	+	29.1912i	0.340356	+	1.28882i
$514$		0			0
$515$	−0.0395075	−	0.147444i	−0.00174091	−	0.00649716i
$516$		0			0
$517$	9.03680	−	33.7258i	0.397438	−	1.48326i
$518$		0			0
$519$	1.81581	−	3.88180i	0.0797050	−	0.170392i
$520$		0			0
$521$	−8.17552			−0.358176			−0.179088	−	0.983833i	$-0.557315\pi$
$521$	−8.17552			−0.358176			−0.179088	+	0.983833i	$0.557315\pi$
$522$		0			0
$523$	11.4305	−	11.4305i	0.499820	−	0.499820i	−0.411562	−	0.911382i	$-0.635017\pi$
$523$	11.4305	−	11.4305i	0.499820	−	0.499820i	0.911382	+	0.411562i	$0.135017\pi$
$524$		0			0
$525$	−0.292364	+	1.64649i	−0.0127598	+	0.0718586i
$526$		0			0
$527$	−18.9254	−	32.7797i	−0.824403	−	1.42791i
$528$		0			0
$529$	−9.84425	+	17.0507i	−0.428011	+	0.741337i
$530$		0			0
$531$	16.6587	+	1.49786i	0.722925	+	0.0650014i
$532$		0			0
$533$	3.95417	+	14.7572i	0.171274	+	0.639204i
$534$		0			0
$535$	−5.27308	−	9.13325i	−0.227975	−	0.394865i
$536$		0			0
$537$	−2.00838	−	23.2785i	−0.0866679	−	1.00454i
$538$		0			0
$539$	15.5774	+	15.5774i	0.670967	+	0.670967i
$540$		0			0
$541$	9.93863	−	9.93863i	0.427295	−	0.427295i	−0.460411	−	0.887706i	$-0.652298\pi$
$541$	9.93863	−	9.93863i	0.427295	−	0.427295i	0.887706	+	0.460411i	$0.152298\pi$
$542$		0			0
$543$	16.6894	−	1.43990i	0.716212	−	0.0617920i
$544$		0			0
$545$	−5.21235	+	3.00935i	−0.223273	+	0.128906i
$546$		0			0
$547$	−2.81747	+	0.754938i	−0.120466	+	0.0322788i	−0.318548	−	0.947907i	$-0.603195\pi$
$547$	−2.81747	+	0.754938i	−0.120466	+	0.0322788i	0.198082	+	0.980185i	$0.436529\pi$
$548$		0			0
$549$	17.5608	−	8.13733i	0.749476	−	0.347293i
$550$		0			0
$551$	−19.9527	−	11.5197i	−0.850012	−	0.490755i
$552$		0			0
$553$	2.44341	−	1.41070i	0.103904	−	0.0599891i
$554$		0			0
$555$	−5.32800	−	0.946083i	−0.226161	−	0.0401590i
$556$		0			0
$557$	11.5964	+	11.5964i	0.491356	+	0.491356i	0.908733	−	0.417377i	$-0.137051\pi$
$557$	11.5964	+	11.5964i	0.491356	+	0.491356i	−0.417377	+	0.908733i	$0.637051\pi$
$558$		0			0
$559$			20.4360i			0.864352i
$560$		0			0
$561$	−18.5778	−	8.69021i	−0.784356	−	0.366901i
$562$		0			0
$563$	7.42718	+	1.99011i	0.313018	+	0.0838730i	0.411908	−	0.911225i	$-0.364862\pi$
$563$	7.42718	+	1.99011i	0.313018	+	0.0838730i	−0.0988898	+	0.995098i	$0.531529\pi$
$564$		0			0
$565$	2.66403	−	0.713826i	0.112077	−	0.0300309i
$566$		0			0
$567$	0.450388	−	2.48429i	0.0189145	−	0.104330i
$568$		0			0
$569$	−11.7897	+	20.4204i	−0.494250	+	0.856066i	−0.999978	−	0.00662697i	$-0.997891\pi$
$569$	−11.7897	+	20.4204i	−0.494250	+	0.856066i	0.505728	+	0.862693i	$0.331224\pi$
$570$		0			0
$571$	7.46185	+	1.99940i	0.312269	+	0.0836722i	0.411550	−	0.911387i	$-0.364988\pi$
$571$	7.46185	+	1.99940i	0.312269	+	0.0836722i	−0.0992811	+	0.995059i	$0.531654\pi$
$572$		0			0
$573$	8.36802	+	23.0773i	0.349579	+	0.964069i
$574$		0			0
$575$	−6.26280			−0.261177
$576$		0			0
$577$	16.4238			0.683733			0.341866	−	0.939749i	$-0.388941\pi$
$577$	16.4238			0.683733			0.341866	+	0.939749i	$0.388941\pi$
$578$		0			0
$579$	22.0681	+	3.91859i	0.917119	+	0.162851i
$580$		0			0
$581$	0.616336	+	0.165147i	0.0255699	+	0.00685144i
$582$		0			0
$583$	19.3196	−	33.4626i	0.800137	−	1.38588i
$584$		0			0
$585$	3.69140	−	10.0666i	0.152621	−	0.416202i
$586$		0			0
$587$	44.0249	−	11.7964i	1.81710	−	0.486891i	0.820680	−	0.571388i	$-0.193595\pi$
$587$	44.0249	−	11.7964i	1.81710	−	0.486891i	0.996424	+	0.0844969i	$0.0269283\pi$
$588$		0			0
$589$	−57.1015	−	15.3003i	−2.35283	−	0.630438i
$590$		0			0
$591$	−1.68923	−	19.5794i	−0.0694858	−	0.805388i
$592$		0			0
$593$		−	9.66931i		−	0.397071i	−0.980094	−	0.198535i	$-0.936382\pi$
$593$		−	9.66931i		−	0.397071i	0.980094	−	0.198535i	$-0.0636185\pi$
$594$		0			0
$595$	−0.921278	−	0.921278i	−0.0377687	−	0.0377687i
$596$		0			0
$597$	12.1750	−	14.4742i	0.498290	−	0.592390i
$598$		0			0
$599$	8.99479	−	5.19314i	0.367517	−	0.212186i	−0.304856	−	0.952398i	$-0.598608\pi$
$599$	8.99479	−	5.19314i	0.367517	−	0.212186i	0.672373	+	0.740212i	$0.265275\pi$
$600$		0			0
$601$	−16.6353	−	9.60440i	−0.678569	−	0.391772i	0.120747	−	0.992683i	$-0.461471\pi$
$601$	−16.6353	−	9.60440i	−0.678569	−	0.391772i	−0.799316	+	0.600912i	$0.794804\pi$
$602$		0			0
$603$	−11.6199	−	1.04479i	−0.473197	−	0.0425473i
$604$		0			0
$605$	−1.04807	+	0.280829i	−0.0426101	+	0.0114173i
$606$		0			0
$607$	12.1261	−	7.00100i	0.492183	−	0.284162i	−0.233297	−	0.972406i	$-0.574951\pi$
$607$	12.1261	−	7.00100i	0.492183	−	0.284162i	0.725480	+	0.688244i	$0.241618\pi$
$608$		0			0
$609$	1.10319	+	1.57955i	0.0447033	+	0.0640068i
$610$		0			0
$611$	22.2072	−	22.2072i	0.898406	−	0.898406i
$612$		0			0
$613$	17.8303	+	17.8303i	0.720159	+	0.720159i	0.968637	−	0.248478i	$-0.0799304\pi$
$613$	17.8303	+	17.8303i	0.720159	+	0.720159i	−0.248478	+	0.968637i	$0.579930\pi$
$614$		0			0
$615$	−10.4516	−	4.88898i	−0.421449	−	0.197143i
$616$		0			0
$617$	−24.3668	−	42.2045i	−0.980970	−	1.69909i	−0.658630	−	0.752467i	$-0.728864\pi$
$617$	−24.3668	−	42.2045i	−0.980970	−	1.69909i	−0.322340	−	0.946624i	$-0.604469\pi$
$618$		0			0
$619$	2.99775	+	11.1877i	0.120490	+	0.449673i	0.999639	−	0.0268731i	$-0.00855501\pi$
$619$	2.99775	+	11.1877i	0.120490	+	0.449673i	−0.879149	+	0.476547i	$0.841888\pi$
$620$		0			0
$621$	9.45565	+	0.0341372i	0.379442	+	0.00136988i
$622$		0			0
$623$	0.263191	−	0.455861i	0.0105445	−	0.0182637i
$624$		0			0
$625$	2.02612	+	3.50934i	0.0810447	+	0.140374i
$626$		0			0
$627$	−30.1139	+	10.9196i	−1.20264	+	0.436085i
$628$		0			0
$629$	−6.58363	+	6.58363i	−0.262506	+	0.262506i
$630$		0			0
$631$	−1.63509			−0.0650918			−0.0325459	−	0.999470i	$-0.510362\pi$
$631$	−1.63509			−0.0650918			−0.0325459	+	0.999470i	$0.510362\pi$
$632$		0			0
$633$	16.7470	+	23.9785i	0.665632	+	0.953060i
$634$		0			0
$635$	1.17588	−	4.38844i	0.0466633	−	0.174150i
$636$		0			0
$637$	5.12858	+	19.1401i	0.203202	+	0.758359i
$638$		0			0
$639$	−31.5689	+	5.48814i	−1.24885	+	0.217107i
$640$		0			0
$641$	−33.5608	−	19.3763i	−1.32557	−	0.765319i	−0.340960	−	0.940078i	$-0.610752\pi$
$641$	−33.5608	−	19.3763i	−1.32557	−	0.765319i	−0.984611	+	0.174759i	$0.944085\pi$
$642$		0			0
$643$	−5.22528	+	19.5010i	−0.206065	+	0.769044i	0.783058	+	0.621949i	$0.213659\pi$
$643$	−5.22528	+	19.5010i	−0.206065	+	0.769044i	−0.989122	+	0.147095i	$0.953008\pi$
$644$		0			0
$645$	−11.8115	−	9.93523i	−0.465076	−	0.391199i
$646$		0			0
$647$		−	28.2882i		−	1.11212i	−0.831141	−	0.556062i	$-0.812312\pi$
$647$		−	28.2882i		−	1.11212i	0.831141	−	0.556062i	$-0.187688\pi$
$648$		0			0
$649$			17.7456i			0.696575i
$650$		0			0
$651$	3.78315	+	3.18220i	0.148273	+	0.124720i
$652$		0			0
$653$	0.228971	−	0.854532i	0.00896033	−	0.0334404i	−0.961301	−	0.275500i	$-0.911156\pi$
$653$	0.228971	−	0.854532i	0.00896033	−	0.0334404i	0.970261	+	0.242060i	$0.0778231\pi$
$654$		0			0
$655$	16.7766	+	9.68599i	0.655517	+	0.378463i
$656$		0			0
$657$	27.5001	−	4.78079i	1.07288	−	0.186517i
$658$		0			0
$659$	−13.0375	−	48.6567i	−0.507869	−	1.89539i	−0.440704	−	0.897653i	$-0.645271\pi$
$659$	−13.0375	−	48.6567i	−0.507869	−	1.89539i	−0.0671656	−	0.997742i	$-0.521396\pi$
$660$		0			0
$661$	−7.17239	+	26.7677i	−0.278974	+	1.04114i	0.674158	+	0.738587i	$0.264507\pi$
$661$	−7.17239	+	26.7677i	−0.278974	+	1.04114i	−0.953131	+	0.302557i	$0.902160\pi$
$662$		0			0
$663$	−10.5632	−	15.1246i	−0.410242	−	0.587390i
$664$		0			0
$665$	−2.03486			−0.0789086
$666$		0			0
$667$	−5.10222	+	5.10222i	−0.197559	+	0.197559i
$668$		0			0
$669$	−23.2367	+	8.42580i	−0.898381	+	0.325760i
$670$		0			0
$671$	10.2672	+	17.7834i	0.396363	+	0.686520i
$672$		0			0
$673$	−16.5237	+	28.6198i	−0.636941	+	1.10321i	0.349160	+	0.937063i	$0.386467\pi$
$673$	−16.5237	+	28.6198i	−0.636941	+	1.10321i	−0.986100	+	0.166150i	$0.946866\pi$
$674$		0			0
$675$	−8.88549	−	15.5192i	−0.342003	−	0.597336i
$676$		0			0
$677$	2.69118	+	10.0436i	0.103430	+	0.386007i	0.998162	−	0.0605961i	$-0.0193002\pi$
$677$	2.69118	+	10.0436i	0.103430	+	0.386007i	−0.894732	+	0.446603i	$0.852633\pi$
$678$		0			0
$679$	2.57829	+	4.46572i	0.0989455	+	0.171379i
$680$		0			0
$681$	−13.8150	−	6.46231i	−0.529393	−	0.247636i
$682$		0			0
$683$	9.18142	+	9.18142i	0.351317	+	0.351317i	0.860600	−	0.509282i	$-0.170089\pi$
$683$	9.18142	+	9.18142i	0.351317	+	0.351317i	−0.509282	+	0.860600i	$0.670089\pi$
$684$		0			0
$685$	18.3723	−	18.3723i	0.701968	−	0.701968i
$686$		0			0
$687$	−24.7225	−	35.3980i	−0.943223	−	1.35052i
$688$		0			0
$689$	30.0988	−	17.3776i	1.14667	−	0.662033i
$690$		0			0
$691$	−24.3744	+	6.53111i	−0.927247	+	0.248455i	−0.690680	−	0.723160i	$-0.742689\pi$
$691$	−24.3744	+	6.53111i	−0.927247	+	0.248455i	−0.236567	+	0.971615i	$0.576022\pi$
$692$		0			0
$693$	2.66795	+	0.239887i	0.101347	+	0.00911256i
$694$		0			0
$695$	−0.897694	−	0.518284i	−0.0340515	−	0.0196596i
$696$		0			0
$697$	−17.1932	+	9.92649i	−0.651239	+	0.375993i
$698$		0			0
$699$	7.26153	−	8.63283i	0.274656	−	0.326524i
$700$		0			0
$701$	32.8695	+	32.8695i	1.24146	+	1.24146i	0.959394	+	0.282069i	$0.0910207\pi$
$701$	32.8695	+	32.8695i	1.24146	+	1.24146i	0.282069	+	0.959394i	$0.408979\pi$
$702$		0			0
$703$			14.5415i			0.548443i
$704$		0			0
$705$	2.03883	+	23.6314i	0.0767867	+	0.890011i
$706$		0			0
$707$	4.38221	+	1.17421i	0.164810	+	0.0441607i
$708$		0			0
$709$	41.1714	−	11.0318i	1.54622	−	0.414310i	0.617953	−	0.786215i	$-0.287962\pi$
$709$	41.1714	−	11.0318i	1.54622	−	0.414310i	0.928271	+	0.371905i	$0.121295\pi$
$710$		0			0
$711$	−10.3876	+	28.3275i	−0.389567	+	1.06236i
$712$		0			0
$713$	−9.25715	+	16.0339i	−0.346683	+	0.600473i
$714$		0			0
$715$	10.9881	+	2.94426i	0.410932	+	0.110109i
$716$		0			0
$717$	−8.08031	−	1.43481i	−0.301765	−	0.0535838i
$718$		0			0
$719$	8.84226			0.329761			0.164880	−	0.986314i	$-0.447276\pi$
$719$	8.84226			0.329761			0.164880	+	0.986314i	$0.447276\pi$
$720$		0			0
$721$	0.0343022			0.00127748
$722$		0			0
$723$	8.78340	+	24.2229i	0.326658	+	0.900858i
$724$		0			0
$725$	13.1814	+	3.53195i	0.489545	+	0.131173i
$726$		0			0
$727$	−11.4146	+	19.7707i	−0.423344	+	0.733254i	−0.996264	−	0.0863576i	$-0.972477\pi$
$727$	−11.4146	+	19.7707i	−0.423344	+	0.733254i	0.572920	+	0.819611i	$0.305811\pi$
$728$		0			0
$729$	13.3308	+	23.4796i	0.493734	+	0.869613i
$730$		0			0
$731$	−25.6512	+	6.87321i	−0.948743	+	0.254215i
$732$		0			0
$733$	−28.8645	−	7.73423i	−1.06614	−	0.285670i	−0.317232	−	0.948348i	$-0.602753\pi$
$733$	−28.8645	−	7.73423i	−1.06614	−	0.285670i	−0.748905	+	0.662678i	$0.769420\pi$
$734$		0			0
$735$	−13.5558	−	6.34103i	−0.500012	−	0.233892i
$736$		0			0
$737$		−	12.3780i		−	0.455950i
$738$		0			0
$739$	−6.92568	−	6.92568i	−0.254765	−	0.254765i	0.568156	−	0.822921i	$-0.307657\pi$
$739$	−6.92568	−	6.92568i	−0.254765	−	0.254765i	−0.822921	+	0.568156i	$0.807657\pi$
$740$		0			0
$741$	−28.3688	−	5.03740i	−1.04215	−	0.185053i
$742$		0			0
$743$	−27.7583	+	16.0262i	−1.01835	+	0.587946i	−0.913626	−	0.406555i	$-0.866730\pi$
$743$	−27.7583	+	16.0262i	−1.01835	+	0.587946i	−0.104726	+	0.994501i	$0.533397\pi$
$744$		0			0
$745$	5.74942	+	3.31943i	0.210642	+	0.121614i
$746$		0			0
$747$	−6.19119	+	2.86888i	−0.226524	+	0.104967i
$748$		0			0
$749$	2.28916	−	0.613380i	0.0836442	−	0.0224124i
$750$		0			0
$751$	7.35037	−	4.24374i	0.268219	−	0.154856i	−0.359859	−	0.933007i	$-0.617175\pi$
$751$	7.35037	−	4.24374i	0.268219	−	0.154856i	0.628078	+	0.778151i	$0.283842\pi$
$752$		0			0
$753$	16.8269	−	1.45176i	0.613207	−	0.0529051i
$754$		0			0
$755$	2.70975	−	2.70975i	0.0986179	−	0.0986179i
$756$		0			0
$757$	−15.2511	−	15.2511i	−0.554309	−	0.554309i	0.373372	−	0.927682i	$-0.378201\pi$
$757$	−15.2511	−	15.2511i	−0.554309	−	0.554309i	−0.927682	+	0.373372i	$0.878201\pi$
$758$		0			0
$759$	0.862335	+	9.99505i	0.0313008	+	0.362797i
$760$		0			0
$761$	1.63439	+	2.83084i	0.0592465	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$761$	1.63439	+	2.83084i	0.0592465	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$762$		0			0
$763$	−0.350056	−	1.30643i	−0.0126729	−	0.0472959i
$764$		0			0
$765$	13.8770	+	1.24774i	0.501725	+	0.0451123i
$766$		0			0
$767$	−7.98088	+	13.8233i	−0.288173	+	0.499130i
$768$		0			0
$769$	19.1814	+	33.2232i	0.691701	+	1.19806i	0.971280	+	0.237938i	$0.0764716\pi$
$769$	19.1814	+	33.2232i	0.691701	+	1.19806i	−0.279580	+	0.960123i	$0.590195\pi$
$770$		0			0
$771$	−0.760304	+	4.28176i	−0.0273817	+	0.154204i
$772$		0			0
$773$	20.0548	−	20.0548i	0.721320	−	0.721320i	−0.247554	−	0.968874i	$-0.579627\pi$
$773$	20.0548	−	20.0548i	0.721320	−	0.721320i	0.968874	+	0.247554i	$0.0796267\pi$
$774$		0			0
$775$	35.0148			1.25777
$776$		0			0
$777$	0.515242	−	1.10148i	0.0184842	−	0.0395153i
$778$		0			0
$779$	−8.02512	+	29.9501i	−0.287530	+	1.07308i
$780$		0			0
$781$	−8.79878	−	32.8375i	−0.314845	−	1.17502i
$782$		0			0
$783$	−19.8822	−	5.40442i	−0.710532	−	0.193138i
$784$		0			0
$785$	−6.31134	−	3.64385i	−0.225261	−	0.130055i
$786$		0			0
$787$	−2.45116	+	9.14785i	−0.0873744	+	0.326086i	−0.995753	−	0.0920625i	$-0.970654\pi$
$787$	−2.45116	+	9.14785i	−0.0873744	+	0.326086i	0.908379	+	0.418148i	$0.137321\pi$
$788$		0			0
$789$	−5.91736	+	2.14568i	−0.210664	+	0.0763883i
$790$		0			0
$791$			0.619775i			0.0220367i
$792$		0			0
$793$			18.4703i			0.655900i
$794$		0			0
$795$	−4.58917	+	25.8446i	−0.162761	+	0.916613i
$796$		0			0
$797$	7.19855	−	26.8654i	0.254986	−	0.951620i	−0.713112	−	0.701050i	$-0.752715\pi$
$797$	7.19855	−	26.8654i	0.254986	−	0.951620i	0.968098	−	0.250571i	$-0.0806182\pi$
$798$		0			0
$799$	35.3432	+	20.4054i	1.25035	+	0.721891i
$800$		0			0
$801$	0.964141	+	5.54594i	0.0340662	+	0.195956i
$802$		0			0
$803$	7.66474	+	28.6052i	0.270483	+	1.00946i
$804$		0			0
$805$	−0.164943	+	0.615577i	−0.00581349	+	0.0216962i
$806$		0			0
$807$	30.1716	−	2.60309i	1.06209	−	0.0916332i
$808$		0			0
$809$	48.8492			1.71745			0.858724	−	0.512439i	$-0.171258\pi$
$809$	48.8492			1.71745			0.858724	+	0.512439i	$0.171258\pi$
$810$		0			0
$811$	5.86383	−	5.86383i	0.205907	−	0.205907i	−0.596618	−	0.802525i	$-0.703489\pi$
$811$	5.86383	−	5.86383i	0.205907	−	0.205907i	0.802525	+	0.596618i	$0.203489\pi$
$812$		0			0
$813$	36.1404	+	30.3996i	1.26750	+	1.06616i
$814$		0			0
$815$	11.0840	+	19.1981i	0.388256	+	0.672480i
$816$		0			0
$817$	−20.7378	+	35.9189i	−0.725524	+	1.25664i
$818$		0			0
$819$	1.97037	+	1.38675i	0.0688502	+	0.0484568i
$820$		0			0
$821$	−0.828375	−	3.09154i	−0.0289105	−	0.107895i	0.949963	−	0.312363i	$-0.101120\pi$
$821$	−0.828375	−	3.09154i	−0.0289105	−	0.107895i	−0.978873	+	0.204467i	$0.934454\pi$
$822$		0			0
$823$	20.9908	+	36.3572i	0.731695	+	1.26733i	0.956158	+	0.292850i	$0.0946037\pi$
$823$	20.9908	+	36.3572i	0.731695	+	1.26733i	−0.224464	+	0.974482i	$0.572063\pi$
$824$		0			0
$825$	15.5550	−	10.8638i	0.541555	−	0.378231i
$826$		0			0
$827$	12.7209	+	12.7209i	0.442348	+	0.442348i	0.892800	−	0.450453i	$-0.148737\pi$
$827$	12.7209	+	12.7209i	0.442348	+	0.442348i	−0.450453	+	0.892800i	$0.648737\pi$
$828$		0			0
$829$	−10.4132	+	10.4132i	−0.361665	+	0.361665i	−0.864425	−	0.502761i	$-0.832318\pi$
$829$	−10.4132	+	10.4132i	−0.361665	+	0.361665i	0.502761	+	0.864425i	$0.332318\pi$
$830$		0			0
$831$	12.6914	−	27.1315i	0.440260	−	0.941181i
$832$		0			0
$833$	−22.2996	+	12.8747i	−0.772637	+	0.446082i
$834$		0			0
$835$	−16.8246	+	4.50815i	−0.582241	+	0.156011i
$836$		0			0
$837$	−52.8657	−	0.190858i	−1.82731	−	0.00659702i
$838$		0			0
$839$	25.7863	+	14.8877i	0.890241	+	0.513981i	0.874021	−	0.485888i	$-0.161504\pi$
$839$	25.7863	+	14.8877i	0.890241	+	0.513981i	0.0162196	+	0.999868i	$0.494837\pi$
$840$		0			0
$841$	−11.4986	+	6.63872i	−0.396503	+	0.228921i
$842$		0			0
$843$	−8.32164	−	22.9494i	−0.286613	−	0.790420i
$844$		0			0
$845$	−4.24025	−	4.24025i	−0.145869	−	0.145869i
$846$		0			0
$847$		−	0.243829i		−	0.00837805i
$848$		0			0
$849$	0.924350	−	0.645580i	0.0317236	−	0.0221563i
$850$		0			0
$851$	4.39903	+	1.17872i	0.150797	+	0.0404059i
$852$		0			0
$853$	−28.4092	+	7.61221i	−0.972711	+	0.260637i	−0.709972	−	0.704230i	$-0.751292\pi$
$853$	−28.4092	+	7.61221i	−0.972711	+	0.260637i	−0.262739	+	0.964867i	$0.584626\pi$
$854$		0			0
$855$	16.7033	−	13.9474i	0.571241	−	0.476990i
$856$		0			0
$857$	14.3783	−	24.9039i	0.491152	−	0.850700i	−0.508796	−	0.860887i	$-0.669909\pi$
$857$	14.3783	−	24.9039i	0.491152	−	0.850700i	0.999948	+	0.0101867i	$0.00324259\pi$
$858$		0			0
$859$	−9.26004	−	2.48122i	−0.315949	−	0.0846582i	0.0973599	−	0.995249i	$-0.468960\pi$
$859$	−9.26004	−	2.48122i	−0.315949	−	0.0846582i	−0.413308	+	0.910591i	$0.635627\pi$
$860$		0			0
$861$	1.66909	−	1.98429i	0.0568823	−	0.0676243i
$862$		0			0
$863$	−38.6895			−1.31700			−0.658502	−	0.752579i	$-0.728810\pi$
$863$	−38.6895			−1.31700			−0.658502	+	0.752579i	$0.728810\pi$
$864$		0			0
$865$	−3.08877			−0.105021
$866$		0			0
$867$	−3.52238	+	4.18757i	−0.119626	+	0.142217i
$868$		0			0
$869$	−30.9207	−	8.28517i	−1.04891	−	0.281055i
$870$		0			0
$871$	5.56687	−	9.64210i	0.188626	−	0.326710i
$872$		0			0
$873$	−51.7731	−	18.9851i	−1.75225	−	0.642548i
$874$		0			0
$875$	2.85557	−	0.765148i	0.0965360	−	0.0258667i
$876$		0			0
$877$	33.8645	+	9.07397i	1.14352	+	0.306406i	0.780367	−	0.625322i	$-0.215032\pi$
$877$	33.8645	+	9.07397i	1.14352	+	0.306406i	0.363157	+	0.931728i	$0.381699\pi$
$878$		0			0
$879$	11.8956	−	8.30807i	0.401228	−	0.280224i
$880$		0			0
$881$		−	15.5358i		−	0.523415i	−0.965147	−	0.261708i	$-0.915714\pi$
$881$		−	15.5358i		−	0.523415i	0.965147	−	0.261708i	$-0.0842856\pi$
$882$		0			0
$883$	35.3696	+	35.3696i	1.19028	+	1.19028i	0.976988	+	0.213292i	$0.0684187\pi$
$883$	35.3696	+	35.3696i	1.19028	+	1.19028i	0.213292	+	0.976988i	$0.431581\pi$
$884$		0			0
$885$	−4.10946	−	11.3331i	−0.138138	−	0.380957i
$886$		0			0
$887$	22.5037	−	12.9925i	0.755599	−	0.436246i	−0.0721141	−	0.997396i	$-0.522975\pi$
$887$	22.5037	−	12.9925i	0.755599	−	0.436246i	0.827714	+	0.561151i	$0.189641\pi$
$888$		0			0
$889$	0.884169	+	0.510475i	0.0296541	+	0.0171208i
$890$		0			0
$891$	−23.5443	+	16.3176i	−0.788764	+	0.546659i
$892$		0			0
$893$	61.5670	−	16.4968i	2.06026	−	0.552045i
$894$		0			0
$895$	−14.5841	+	8.42011i	−0.487492	+	0.281453i
$896$		0			0
$897$	−3.82343	+	8.17367i	−0.127661	+	0.272911i
$898$		0			0
$899$	28.5261	−	28.5261i	0.951398	−	0.951398i
$900$		0			0
$901$	31.9353	+	31.9353i	1.06392	+	1.06392i
$902$		0			0
$903$	2.84352	−	1.98596i	0.0946266	−	0.0660887i
$904$		0			0
$905$	−6.03678	−	10.4560i	−0.200669	−	0.347569i
$906$		0			0
$907$	−7.10188	−	26.5046i	−0.235814	−	0.880070i	−0.977780	−	0.209633i	$-0.932773\pi$
$907$	−7.10188	−	26.5046i	−0.235814	−	0.880070i	0.741966	−	0.670437i	$-0.233894\pi$
$908$		0			0
$909$	−44.0200	+	20.3980i	−1.46005	+	0.676560i
$910$		0			0
$911$	−23.4177	+	40.5606i	−0.775863	+	1.34383i	0.158445	+	0.987368i	$0.449352\pi$
$911$	−23.4177	+	40.5606i	−0.775863	+	1.34383i	−0.934308	+	0.356466i	$0.883982\pi$
$912$		0			0
$913$	−3.61980	−	6.26967i	−0.119798	−	0.207496i
$914$		0			0
$915$	−10.6753	−	8.97957i	−0.352915	−	0.296855i
$916$		0			0
$917$	−3.07820	+	3.07820i	−0.101651	+	0.101651i
$918$		0			0
$919$	0.421071			0.0138899			0.00694493	−	0.999976i	$-0.497789\pi$
$919$	0.421071			0.0138899			0.00694493	+	0.999976i	$0.497789\pi$
$920$		0			0
$921$	24.7093	−	2.13183i	0.814200	−	0.0702461i
$922$		0			0
$923$	7.91430	−	29.5366i	0.260503	−	0.972209i
$924$		0			0
$925$	−2.22922	−	8.31957i	−0.0732964	−	0.273546i
$926$		0			0
$927$	−0.281572	+	0.235115i	−0.00924805	+	0.00772218i
$928$		0			0
$929$	−5.41100	−	3.12404i	−0.177529	−	0.102496i	0.408602	−	0.912713i	$-0.366016\pi$
$929$	−5.41100	−	3.12404i	−0.177529	−	0.102496i	−0.586131	+	0.810216i	$0.699350\pi$
$930$		0			0
$931$	−10.4086	+	38.8455i	−0.341128	+	1.27311i
$932$		0			0
$933$	−4.82010	+	27.1451i	−0.157803	+	0.888689i
$934$		0			0
$935$			14.7824i			0.483437i
$936$		0			0
$937$			41.2133i			1.34638i	0.739470	+	0.673189i	$0.235076\pi$
$937$			41.2133i			1.34638i	−0.739470	+	0.673189i	$0.764924\pi$
$938$		0			0
$939$	18.6191	−	6.75142i	0.607610	−	0.220324i
$940$		0			0
$941$	3.22526	−	12.0368i	0.105141	−	0.392390i	−0.893221	−	0.449619i	$-0.851560\pi$
$941$	3.22526	−	12.0368i	0.105141	−	0.392390i	0.998361	+	0.0572290i	$0.0182265\pi$
$942$		0			0
$943$	8.40987	+	4.85544i	0.273863	+	0.158115i
$944$		0			0
$945$	−1.75942	+	0.464633i	−0.0572339	+	0.0151145i
$946$		0			0
$947$	−3.96886	−	14.8120i	−0.128971	−	0.481325i	0.870979	−	0.491320i	$-0.163485\pi$
$947$	−3.96886	−	14.8120i	−0.128971	−	0.481325i	−0.999950	+	0.00999447i	$0.996819\pi$
$948$		0			0
$949$	−6.89426	+	25.7297i	−0.223797	+	0.835222i
$950$		0			0
$951$	−20.0338	+	42.8281i	−0.649642	+	1.38879i
$952$		0			0
$953$	20.0192			0.648486			0.324243	−	0.945974i	$-0.394890\pi$
$953$	20.0192			0.648486			0.324243	+	0.945974i	$0.394890\pi$
$954$		0			0
$955$	12.5106	−	12.5106i	0.404833	−	0.404833i
$956$		0			0
$957$	3.82181	−	21.5231i	0.123541	−	0.695742i
$958$		0			0
$959$	2.91935	+	5.05646i	0.0942707	+	0.163282i
$960$		0			0
$961$	36.2559	−	62.7971i	1.16955	−	2.02571i
$962$		0			0
$963$	−14.5865	+	20.7254i	−0.470045	+	0.667866i
$964$		0			0
$965$	−4.18105	−	15.6039i	−0.134593	−	0.502307i
$966$		0			0
$967$	16.3485	+	28.3164i	0.525732	+	0.910594i	0.999551	+	0.0299719i	$0.00954179\pi$
$967$	16.3485	+	28.3164i	0.525732	+	0.910594i	−0.473819	+	0.880622i	$0.657125\pi$
$968$		0			0
$969$	−3.21832	−	37.3025i	−0.103387	−	1.19833i
$970$		0			0
$971$	12.2406	+	12.2406i	0.392820	+	0.392820i	0.875691	−	0.482871i	$-0.160406\pi$
$971$	12.2406	+	12.2406i	0.392820	+	0.392820i	−0.482871	+	0.875691i	$0.660406\pi$
$972$		0			0
$973$	0.164710	−	0.164710i	0.00528037	−	0.00528037i
$974$		0			0
$975$	17.0028	−	1.46693i	0.544524	−	0.0469795i
$976$		0			0
$977$	34.1771	−	19.7322i	1.09342	−	0.631288i	0.158938	−	0.987289i	$-0.449193\pi$
$977$	34.1771	−	19.7322i	1.09342	−	0.631288i	0.934486	+	0.356000i	$0.115860\pi$
$978$		0			0
$979$	−5.76880	+	1.54575i	−0.184372	+	0.0494022i
$980$		0			0
$981$	11.8280	+	8.32455i	0.377639	+	0.265782i
$982$		0			0
$983$	−3.78032	−	2.18257i	−0.120574	−	0.0696132i	0.438500	−	0.898731i	$-0.355510\pi$
$983$	−3.78032	−	2.18257i	−0.120574	−	0.0696132i	−0.559074	+	0.829118i	$0.688843\pi$
$984$		0			0
$985$	−12.2666	+	7.08211i	−0.390845	+	0.225655i
$986$		0			0
$987$	−5.24804	−	0.931885i	−0.167047	−	0.0296622i
$988$		0			0
$989$	9.18504	+	9.18504i	0.292067	+	0.292067i
$990$		0			0
$991$		−	21.1610i		−	0.672200i	−0.941826	−	0.336100i	$-0.890892\pi$
$991$		−	21.1610i		−	0.672200i	0.941826	−	0.336100i	$-0.109108\pi$
$992$		0			0
$993$	18.0332	+	8.43546i	0.572266	+	0.267691i
$994$		0			0
$995$	−13.1676	−	3.52825i	−0.417441	−	0.111853i
$996$		0			0
$997$	12.7473	−	3.41563i	0.403712	−	0.108174i	−0.0512486	−	0.998686i	$-0.516320\pi$
$997$	12.7473	−	3.41563i	0.403712	−	0.108174i	0.454960	+	0.890512i	$0.349653\pi$
$998$		0			0
$999$	3.32036	+	12.5731i	0.105051	+	0.397796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.6		88
3.2	odd	2		1728.2.z.a.143.7		88
4.3	odd	2		144.2.u.a.11.16	✓	88
9.4	even	3		1728.2.z.a.719.7		88
9.5	odd	6	inner	576.2.y.a.527.17		88
12.11	even	2		432.2.v.a.251.7		88
16.3	odd	4	inner	576.2.y.a.47.17		88
16.13	even	4		144.2.u.a.83.22	yes	88
36.23	even	6		144.2.u.a.59.22	yes	88
36.31	odd	6		432.2.v.a.395.1		88
48.29	odd	4		432.2.v.a.35.1		88
48.35	even	4		1728.2.z.a.1007.7		88
144.13	even	12		432.2.v.a.179.7		88
144.67	odd	12		1728.2.z.a.1583.7		88
144.77	odd	12		144.2.u.a.131.16	yes	88
144.131	even	12	inner	576.2.y.a.239.6		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.16	✓	88	4.3	odd	2
144.2.u.a.59.22	yes	88	36.23	even	6
144.2.u.a.83.22	yes	88	16.13	even	4
144.2.u.a.131.16	yes	88	144.77	odd	12
432.2.v.a.35.1		88	48.29	odd	4
432.2.v.a.179.7		88	144.13	even	12
432.2.v.a.251.7		88	12.11	even	2
432.2.v.a.395.1		88	36.31	odd	6
576.2.y.a.47.17		88	16.3	odd	4	inner
576.2.y.a.239.6		88	144.131	even	12	inner
576.2.y.a.335.6		88	1.1	even	1	trivial
576.2.y.a.527.17		88	9.5	odd	6	inner
1728.2.z.a.143.7		88	3.2	odd	2
1728.2.z.a.719.7		88	9.4	even	3
1728.2.z.a.1007.7		88	48.35	even	4
1728.2.z.a.1583.7		88	144.67	odd	12

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.11494 + 1.32549i) q^{3} +(1.20583 + 0.323102i) q^{5} +(-0.140266 + 0.242948i) q^{7} +(-0.513832 - 2.95567i) q^{9} +O(q^{10})\)	\(q+(-1.11494 + 1.32549i) q^{3} +(1.20583 + 0.323102i) q^{5} +(-0.140266 + 0.242948i) q^{7} +(-0.513832 - 2.95567i) q^{9} +(3.07444 - 0.823794i) q^{11} +(2.76539 + 0.740984i) q^{13} +(-1.77270 + 1.23808i) q^{15} +3.72031i q^{17} +(4.10860 + 4.10860i) q^{19} +(-0.165636 - 0.456792i) q^{21} +(1.57595 - 0.909876i) q^{23} +(-2.98049 - 1.72078i) q^{25} +(4.49059 + 2.61431i) q^{27} +(-3.83006 + 1.02626i) q^{29} +(-8.81101 + 5.08704i) q^{31} +(-2.33588 + 4.99361i) q^{33} +(-0.247635 + 0.247635i) q^{35} +(1.76964 + 1.76964i) q^{37} +(-4.06540 + 2.83934i) q^{39} +(2.66819 + 4.62144i) q^{41} +(1.84748 + 6.89490i) q^{43} +(0.335387 - 3.73007i) q^{45} +(5.48486 - 9.50006i) q^{47} +(3.46065 + 5.99402i) q^{49} +(-4.93123 - 4.14791i) q^{51} +(8.58403 - 8.58403i) q^{53} +3.97344 q^{55} +(-10.0267 + 0.865067i) q^{57} +(-1.44299 + 5.38532i) q^{59} +(1.66977 + 6.23168i) q^{61} +(0.790146 + 0.289745i) q^{63} +(3.09519 + 1.78701i) q^{65} +(1.00652 - 3.75640i) q^{67} +(-0.551057 + 3.10336i) q^{69} -10.6808i q^{71} +9.30419i q^{73} +(5.60393 - 2.03203i) q^{75} +(-0.231101 + 0.862479i) q^{77} +(-8.70990 - 5.02866i) q^{79} +(-8.47195 + 3.03744i) q^{81} +(-0.588691 - 2.19703i) q^{83} +(-1.20204 + 4.48608i) q^{85} +(2.90998 - 6.22091i) q^{87} -1.87637 q^{89} +(-0.567911 + 0.567911i) q^{91} +(3.08091 - 17.3506i) q^{93} +(3.62679 + 6.28179i) q^{95} +(9.19070 - 15.9188i) q^{97} +(-4.01461 - 8.66374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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