LMFDB - Embedded newform 576.2.y.a.47.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,2,Mod(47,576)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
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			47.17
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.32549	+	1.11494i	0.765270	+	0.643709i
$3$	1.32549	+	1.11494i	0.765270	+	0.643709i
$4$		0			0
$5$	0.323102	−	1.20583i	0.144496	−	0.539266i	−0.855282	−	0.518164i	$-0.826616\pi$
$5$	0.323102	−	1.20583i	0.144496	−	0.539266i	0.999777	−	0.0211020i	$-0.00671747\pi$
$6$		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
$11$	0.823794	+	3.07444i	0.248383	+	0.926979i	0.971653	+	0.236413i	$0.0759719\pi$
$11$	0.823794	+	3.07444i	0.248383	+	0.926979i	−0.723269	+	0.690566i	$0.757361\pi$
$12$		0			0
$13$	−0.740984	+	2.76539i	−0.205512	+	0.766982i	0.783781	+	0.621038i	$0.213289\pi$
$13$	−0.740984	+	2.76539i	−0.205512	+	0.766982i	−0.989293	+	0.145944i	$0.953378\pi$
$14$		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	−0.0558614	−	0.998439i	$-0.517791\pi$
$19$	4.10860	−	4.10860i	0.942577	−	0.942577i	0.998439	+	0.0558614i	$0.0177905\pi$
$20$		0			0
$21$	−0.456792	+	0.165636i	−0.0996802	+	0.0361448i
$22$		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
$27$	−2.61431	+	4.49059i	−0.503123	+	0.864215i
$28$		0			0
$29$	−1.02626	−	3.83006i	−0.190572	−	0.711224i	−0.993369	−	0.114972i	$-0.963322\pi$
$29$	−1.02626	−	3.83006i	−0.190572	−	0.711224i	0.802797	−	0.596253i	$-0.203344\pi$
$30$		0			0
$31$	8.81101	−	5.08704i	1.58250	−	0.913659i	0.588012	−	0.808852i	$-0.299911\pi$
$31$	8.81101	−	5.08704i	1.58250	−	0.913659i	0.994493	−	0.104807i	$-0.0334225\pi$
$32$		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	−0.546519	−	0.837447i	$-0.684047\pi$
$37$	1.76964	−	1.76964i	0.290928	−	0.290928i	0.837447	+	0.546519i	$0.184047\pi$
$38$		0			0
$39$	−4.06540	+	2.83934i	−0.650985	+	0.454658i
$40$		0			0
$41$	−2.66819	−	4.62144i	−0.416701	−	0.721747i	0.578904	−	0.815395i	$-0.303480\pi$
$41$	−2.66819	−	4.62144i	−0.416701	−	0.721747i	−0.995605	+	0.0936482i	$0.970147\pi$
$42$		0			0
$43$	−6.89490	+	1.84748i	−1.05146	+	0.281738i	−0.742856	−	0.669452i	$-0.766529\pi$
$43$	−6.89490	+	1.84748i	−1.05146	+	0.281738i	−0.308606	+	0.951190i	$0.599862\pi$
$44$		0			0
$45$	3.73007	+	0.335387i	0.556046	+	0.0499965i
$46$		0			0
$47$	−5.48486	+	9.50006i	−0.800049	+	1.38573i	0.119534	+	0.992830i	$0.461860\pi$
$47$	−5.48486	+	9.50006i	−0.800049	+	1.38573i	−0.919583	+	0.392896i	$0.871473\pi$
$48$		0			0
$49$	3.46065	+	5.99402i	0.494379	+	0.856289i
$50$		0			0
$51$	−4.14791	+	4.93123i	−0.580824	+	0.690510i
$52$		0			0
$53$	−8.58403	−	8.58403i	−1.17911	−	1.17911i	−0.979972	−	0.199135i	$-0.936187\pi$
$53$	−8.58403	−	8.58403i	−1.17911	−	1.17911i	−0.199135	−	0.979972i	$-0.563813\pi$
$54$		0			0
$55$	3.97344			0.535778
$56$		0			0
$57$	10.0267	−	0.865067i	1.32807	−	0.114581i
$58$		0			0
$59$	−5.38532	−	1.44299i	−0.701109	−	0.187862i	−0.109382	−	0.994000i	$-0.534887\pi$
$59$	−5.38532	−	1.44299i	−0.701109	−	0.187862i	−0.591727	+	0.806138i	$0.701554\pi$
$60$		0			0
$61$	−6.23168	+	1.66977i	−0.797885	+	0.213793i	−0.634655	−	0.772796i	$-0.718858\pi$
$61$	−6.23168	+	1.66977i	−0.797885	+	0.213793i	−0.163230	+	0.986588i	$0.552191\pi$
$62$		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
$67$	−3.75640	−	1.00652i	−0.458918	−	0.122967i	0.0219514	−	0.999759i	$-0.493012\pi$
$67$	−3.75640	−	1.00652i	−0.458918	−	0.122967i	−0.480869	+	0.876792i	$0.659679\pi$
$68$		0			0
$69$	3.10336	+	0.551057i	0.373600	+	0.0663395i
$70$		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	$-0.816725\pi$
$73$		−	9.30419i		−	1.08897i	0.838770	−	0.544487i	$-0.183275\pi$
$74$		0			0
$75$	2.03203	+	5.60393i	0.234639	+	0.647086i
$76$		0			0
$77$	−0.862479	−	0.231101i	−0.0982886	−	0.0263364i
$78$		0			0
$79$	8.70990	+	5.02866i	0.979940	+	0.565769i	0.902252	−	0.431209i	$-0.141913\pi$
$79$	8.70990	+	5.02866i	0.979940	+	0.565769i	0.0776882	+	0.996978i	$0.475246\pi$
$80$		0			0
$81$	−8.47195	+	3.03744i	−0.941328	+	0.337493i
$82$		0			0
$83$	−2.19703	+	0.588691i	−0.241155	+	0.0646173i	−0.377372	−	0.926062i	$-0.623172\pi$
$83$	−2.19703	+	0.588691i	−0.241155	+	0.0646173i	0.136217	+	0.990679i	$0.456506\pi$
$84$		0			0
$85$	4.48608	+	1.20204i	0.486584	+	0.130380i
$86$		0			0
$87$	2.90998	−	6.22091i	0.311982	−	0.666952i
$88$		0			0
$89$	1.87637			0.198895			0.0994475	−	0.995043i	$-0.468292\pi$
$89$	1.87637			0.198895			0.0994475	+	0.995043i	$0.468292\pi$
$90$		0			0
$91$	−0.567911	−	0.567911i	−0.0595332	−	0.0595332i
$92$		0			0
$93$	17.3506	+	3.08091i	1.79917	+	0.319476i
$94$		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
$99$	−8.66374	+	4.01461i	−0.870739	+	0.403484i
$100$		0			0
$101$	−15.6211	+	4.18566i	−1.55436	+	0.416488i	−0.930871	−	0.365347i	$-0.880950\pi$
$101$	−15.6211	+	4.18566i	−1.55436	+	0.416488i	−0.623485	+	0.781836i	$0.714284\pi$
$102$		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	$-0.616106\pi$
$107$	5.97359	−	5.97359i	0.577489	−	0.577489i	0.934211	+	0.356722i	$0.116106\pi$
$108$		0			0
$109$	−3.40913	−	3.40913i	−0.326536	−	0.326536i	0.524732	−	0.851268i	$-0.324166\pi$
$109$	−3.40913	−	3.40913i	−0.326536	−	0.326536i	−0.851268	+	0.524732i	$0.824166\pi$
$110$		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
$115$	−0.587966	−	2.19432i	−0.0548281	−	0.204621i
$116$		0			0
$117$	−8.55432	−	0.769157i	−0.790847	−	0.0711086i
$118$		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
$123$	1.61596	−	9.10052i	0.145706	−	0.820566i
$124$		0			0
$125$	7.45164	−	7.45164i	0.666495	−	0.666495i
$126$		0			0
$127$			3.63934i			0.322939i	0.986878	+	0.161470i	$0.0516234\pi$
$127$			3.63934i			0.322939i	−0.986878	+	0.161470i	$0.948377\pi$
$128$		0			0
$129$	−11.1989	−	5.23856i	−0.986010	−	0.461229i
$130$		0			0
$131$	4.01630	−	14.9890i	0.350906	−	1.30960i	−0.534653	−	0.845072i	$-0.679558\pi$
$131$	4.01630	−	14.9890i	0.350906	−	1.30960i	0.885559	−	0.464527i	$-0.153776\pi$
$132$		0			0
$133$	0.421878	+	1.57447i	0.0365815	+	0.136524i
$134$		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	$0.515325\pi$
$137$	−10.4065	+	18.0245i	−0.889085	+	1.53994i	−0.840959	+	0.541099i	$0.818008\pi$
$138$		0			0
$139$	0.214907	−	0.802043i	0.0182282	−	0.0680284i	−0.956213	−	0.292673i	$-0.905455\pi$
$139$	0.214907	−	0.802043i	0.0182282	−	0.0680284i	0.974441	+	0.224644i	$0.0721220\pi$
$140$		0			0
$141$	−17.8621	+	6.47693i	−1.50426	+	0.545456i
$142$		0			0
$143$	−9.11246			−0.762022
$144$		0			0
$145$	−4.95000			−0.411076
$146$		0			0
$147$	−2.09591	+	11.8034i	−0.172868	+	0.973529i
$148$		0			0
$149$	1.37640	−	5.13681i	0.112759	−	0.420824i	−0.886350	−	0.463015i	$-0.846767\pi$
$149$	1.37640	−	5.13681i	0.112759	−	0.420824i	0.999110	+	0.0421919i	$0.0134341\pi$
$150$		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
$155$	−3.28727	−	12.2683i	−0.264040	−	0.985410i
$156$		0			0
$157$	1.51093	−	5.63885i	0.120585	−	0.450029i	−0.879059	−	0.476713i	$-0.841828\pi$
$157$	1.51093	−	5.63885i	0.120585	−	0.450029i	0.999644	+	0.0266838i	$0.00849471\pi$
$158$		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	−0.0163656	−	0.999866i	$-0.505210\pi$
$163$	12.5565	−	12.5565i	0.983500	−	0.983500i	0.999866	+	0.0163656i	$0.00520958\pi$
$164$		0			0
$165$	5.26674	+	4.43013i	0.410015	+	0.344885i
$166$		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
$171$	14.2548	+	10.0325i	1.09009	+	0.767206i
$172$		0			0
$173$	−0.640380	−	2.38993i	−0.0486872	−	0.181703i	0.937300	−	0.348523i	$-0.113317\pi$
$173$	−0.640380	−	2.38993i	−0.0486872	−	0.181703i	−0.985987	+	0.166820i	$0.946650\pi$
$174$		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	$-0.0818111\pi$
$179$	9.53870	+	9.53870i	0.712956	+	0.712956i	−0.254197	+	0.967153i	$0.581811\pi$
$180$		0			0
$181$	−6.83874	+	6.83874i	−0.508320	+	0.508320i	−0.914010	−	0.405691i	$-0.867031\pi$
$181$	−6.83874	+	6.83874i	−0.508320	+	0.508320i	0.405691	+	0.914010i	$0.367031\pi$
$182$		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
$187$	−11.4379	+	3.06477i	−0.836421	+	0.224118i
$188$		0			0
$189$	−0.724281	−	1.26502i	−0.0526837	−	0.0920164i
$190$		0			0
$191$	−7.08629	+	12.2738i	−0.512746	+	0.888102i	0.487145	+	0.873321i	$0.338038\pi$
$191$	−7.08629	+	12.2738i	−0.512746	+	0.888102i	−0.999891	+	0.0147810i	$0.995295\pi$
$192$		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
$195$	2.11023	+	5.81960i	0.151117	+	0.416750i
$196$		0			0
$197$	8.02294	+	8.02294i	0.571611	+	0.571611i	0.932578	−	0.360968i	$-0.117553\pi$
$197$	8.02294	+	8.02294i	0.571611	+	0.571611i	−0.360968	+	0.932578i	$0.617553\pi$
$198$		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
$203$	1.07445	+	0.287899i	0.0754119	+	0.0202066i
$204$		0			0
$205$	−6.43478	+	1.72420i	−0.449425	+	0.120423i
$206$		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
$211$	−16.3108	−	4.37047i	−1.12288	−	0.300875i	−0.350833	−	0.936438i	$-0.614101\pi$
$211$	−16.3108	−	4.37047i	−1.12288	−	0.300875i	−0.772049	+	0.635563i	$0.780768\pi$
$212$		0			0
$213$	11.9084	−	14.1573i	0.815951	−	0.970039i
$214$		0			0
$215$			8.91103i			0.607727i
$216$		0			0
$217$			2.85415i			0.193753i
$218$		0			0
$219$	10.3736	−	12.3326i	0.700982	−	0.833359i
$220$		0			0
$221$	−10.2881	−	2.75669i	−0.692054	−	0.185435i
$222$		0			0
$223$	−12.3586	−	7.13522i	−0.827591	−	0.477810i	0.0254364	−	0.999676i	$-0.491902\pi$
$223$	−12.3586	−	7.13522i	−0.827591	−	0.477810i	−0.853027	+	0.521867i	$0.825236\pi$
$224$		0			0
$225$	−3.55460	+	9.69352i	−0.236973	+	0.646235i
$226$		0			0
$227$	8.50557	−	2.27906i	0.564535	−	0.151267i	0.0347459	−	0.999396i	$-0.488938\pi$
$227$	8.50557	−	2.27906i	0.564535	−	0.151267i	0.529789	+	0.848130i	$0.322271\pi$
$228$		0			0
$229$	24.0786	+	6.45185i	1.59116	+	0.426350i	0.942358	−	0.334606i	$-0.108603\pi$
$229$	24.0786	+	6.45185i	1.59116	+	0.426350i	0.648803	+	0.760957i	$0.275270\pi$
$230$		0			0
$231$	−0.885543	−	1.26793i	−0.0582644	−	0.0834237i
$232$		0			0
$233$	6.51295			0.426678			0.213339	−	0.976978i	$-0.431566\pi$
$233$	6.51295			0.426678			0.213339	+	0.976978i	$0.431566\pi$
$234$		0			0
$235$	9.68332	+	9.68332i	0.631670	+	0.631670i
$236$		0			0
$237$	5.93822	+	16.3764i	0.385729	+	1.06376i
$238$		0			0
$239$	−2.36907	−	4.10336i	−0.153243	−	0.265424i	0.779175	−	0.626806i	$-0.215638\pi$
$239$	−2.36907	−	4.10336i	−0.153243	−	0.265424i	−0.932418	+	0.361382i	$0.882305\pi$
$240$		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
$243$	−14.6160	−	5.41961i	−0.937618	−	0.347668i
$244$		0			0
$245$	8.34594	−	2.23629i	0.533203	−	0.142871i
$246$		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	$-0.650427\pi$
$251$	6.89508	−	6.89508i	0.435213	−	0.435213i	0.890397	+	0.455184i	$0.150427\pi$
$252$		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
$259$	0.181710	+	0.678152i	0.0112909	+	0.0421383i
$260$		0			0
$261$	10.7931	−	5.00130i	0.668074	−	0.309572i
$262$		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
$267$	2.48711	+	2.09204i	0.152209	+	0.128031i
$268$		0			0
$269$	12.3633	−	12.3633i	0.753802	−	0.753802i	−0.221384	−	0.975187i	$-0.571058\pi$
$269$	12.3633	−	12.3633i	0.753802	−	0.753802i	0.975187	+	0.221384i	$0.0710575\pi$
$270$		0			0
$271$			27.2658i			1.65628i	0.560523	+	0.828139i	$0.310600\pi$
$271$			27.2658i			1.65628i	−0.560523	+	0.828139i	$0.689400\pi$
$272$		0			0
$273$	−0.119574	−	1.38594i	−0.00723694	−	0.0838811i
$274$		0			0
$275$	−2.83514	+	10.5809i	−0.170966	+	0.638053i
$276$		0			0
$277$	4.47587	+	16.7042i	0.268929	+	1.00366i	0.959801	+	0.280680i	$0.0905601\pi$
$277$	4.47587	+	16.7042i	0.268929	+	1.00366i	−0.690872	+	0.722977i	$0.742773\pi$
$278$		0			0
$279$	19.5630	+	23.4285i	1.17121	+	1.40263i
$280$		0			0
$281$	7.04702	−	12.2058i	0.420390	−	0.728137i	−0.575588	−	0.817740i	$-0.695227\pi$
$281$	7.04702	−	12.2058i	0.420390	−	0.728137i	0.995978	+	0.0896034i	$0.0285600\pi$
$282$		0			0
$283$	0.168478	−	0.628767i	0.0100149	−	0.0373763i	−0.960738	−	0.277459i	$-0.910508\pi$
$283$	0.168478	−	0.628767i	0.0100149	−	0.0373763i	0.970753	+	0.240082i	$0.0771745\pi$
$284$		0			0
$285$	2.19653	−	12.3701i	0.130111	−	0.732740i
$286$		0			0
$287$	1.49702			0.0883665
$288$		0			0
$289$	3.15927			0.185839
$290$		0			0
$291$	29.9306	−	10.8531i	1.75456	−	0.636218i
$292$		0			0
$293$	−2.16816	+	8.09169i	−0.126665	+	0.472722i	−0.999894	−	0.0145900i	$-0.995356\pi$
$293$	−2.16816	+	8.09169i	−0.126665	+	0.472722i	0.873228	+	0.487312i	$0.162022\pi$
$294$		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
$299$	1.34841	+	5.03233i	0.0779804	+	0.291027i
$300$		0			0
$301$	0.518278	−	1.93424i	0.0298730	−	0.111488i
$302$		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	−0.934315	−	0.356449i	$-0.883987\pi$
$307$	−10.1250	+	10.1250i	−0.577865	+	0.577865i	0.356449	+	0.934315i	$0.383987\pi$
$308$		0			0
$309$	0.0370275	−	0.208526i	0.00210642	−	0.0118626i
$310$		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	0.753038	−	0.657977i	$-0.228588\pi$
$313$	9.90266	+	5.71730i	0.559732	+	0.323161i	−0.193306	+	0.981138i	$0.561921\pi$
$314$		0			0
$315$	−0.604683	+	0.859168i	−0.0340700	+	0.0484086i
$316$		0			0
$317$	7.06533	+	26.3682i	0.396828	+	1.48098i	0.818644	+	0.574302i	$0.194726\pi$
$317$	7.06533	+	26.3682i	0.396828	+	1.48098i	−0.421815	+	0.906682i	$0.638607\pi$
$318$		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
$331$	11.1026	−	2.97493i	0.610254	−	0.163517i	0.0595605	−	0.998225i	$-0.481030\pi$
$331$	11.1026	−	2.97493i	0.610254	−	0.163517i	0.550693	+	0.834708i	$0.314363\pi$
$332$		0			0
$333$	6.13978	+	4.32118i	0.336458	+	0.236799i
$334$		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
$339$	3.76766	+	0.669016i	0.204631	+	0.0363360i
$340$		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
$347$	−3.10690	−	0.832493i	−0.166787	−	0.0446905i	0.174459	−	0.984664i	$-0.444182\pi$
$347$	−3.10690	−	0.832493i	−0.166787	−	0.0446905i	−0.341246	+	0.939974i	$0.610849\pi$
$348$		0			0
$349$	−32.0100	+	8.57705i	−1.71346	+	0.459119i	−0.976268	−	0.216568i	$-0.930514\pi$
$349$	−32.0100	+	8.57705i	−1.71346	+	0.459119i	−0.737188	+	0.675687i	$0.763847\pi$
$350$		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
$355$	−12.8793	−	3.45099i	−0.683561	−	0.183160i
$356$		0			0
$357$	−0.616220	−	1.69941i	−0.0326138	−	0.0899423i
$358$		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
$363$	1.48225	+	0.263201i	0.0777981	+	0.0138145i
$364$		0			0
$365$	−11.2193	−	3.00621i	−0.587246	−	0.157352i
$366$		0			0
$367$	−1.27977	−	0.738875i	−0.0668034	−	0.0385690i	0.466226	−	0.884666i	$-0.345613\pi$
$367$	−1.27977	−	0.738875i	−0.0668034	−	0.0385690i	−0.533030	+	0.846097i	$0.678947\pi$
$368$		0			0
$369$	12.2884	−	10.2609i	0.639710	−	0.534162i
$370$		0			0
$371$	3.28952	−	0.881424i	0.170783	−	0.0457612i
$372$		0			0
$373$	−31.6496	−	8.48049i	−1.63876	−	0.439103i	−0.682322	−	0.731052i	$-0.739030\pi$
$373$	−31.6496	−	8.48049i	−1.63876	−	0.439103i	−0.956434	+	0.291948i	$0.905696\pi$
$374$		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	0.0108880	−	0.999941i	$-0.496534\pi$
$379$	−19.2548	−	19.2548i	−0.989053	−	0.989053i	−0.999941	+	0.0108880i	$0.996534\pi$
$380$		0			0
$381$	−4.05763	+	4.82390i	−0.207879	+	0.247136i
$382$		0			0
$383$	−3.99635	−	6.92189i	−0.204204	−	0.353692i	0.745675	−	0.666310i	$-0.232127\pi$
$383$	−3.99635	−	6.92189i	−0.204204	−	0.353692i	−0.949879	+	0.312618i	$0.898794\pi$
$384$		0			0
$385$	−0.557338	+	0.965338i	−0.0284046	+	0.0491982i
$386$		0			0
$387$	−9.00336	−	19.4297i	−0.457667	−	0.987669i
$388$		0			0
$389$	−8.25574	+	2.21212i	−0.418583	+	0.112159i	−0.461962	−	0.886900i	$-0.652854\pi$
$389$	−8.25574	+	2.21212i	−0.418583	+	0.112159i	0.0433793	+	0.999059i	$0.486188\pi$
$390$		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	0.993936	+	0.109957i	$0.0350713\pi$
$397$	21.9949	+	21.9949i	1.10389	+	1.10389i	0.109957	+	0.993936i	$0.464929\pi$
$398$		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
$403$	7.53883	+	28.1353i	0.375536	+	1.40152i
$404$		0			0
$405$	0.925337	+	11.1972i	0.0459803	+	0.556392i
$406$		0			0
$407$	6.89849	+	3.98284i	0.341945	+	0.197422i
$408$		0			0
$409$	−21.0100	+	12.1301i	−1.03888	+	0.599797i	−0.919515	−	0.393054i	$-0.871419\pi$
$409$	−21.0100	+	12.1301i	−1.03888	+	0.599797i	−0.119363	+	0.992851i	$0.538085\pi$
$410$		0			0
$411$	−33.8899	+	12.2887i	−1.67166	+	0.606159i
$412$		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
$419$	−2.95796	+	11.0392i	−0.144506	+	0.539302i	0.855271	+	0.518180i	$0.173390\pi$
$419$	−2.95796	+	11.0392i	−0.144506	+	0.539302i	−0.999777	+	0.0211217i	$0.993276\pi$
$420$		0			0
$421$	−4.47753	−	16.7104i	−0.218221	−	0.814413i	−0.985008	−	0.172511i	$-0.944812\pi$
$421$	−4.47753	−	16.7104i	−0.218221	−	0.814413i	0.766786	−	0.641903i	$-0.221855\pi$
$422$		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
$427$	0.468425	−	1.74819i	0.0226687	−	0.0846006i
$428$		0			0
$429$	−12.0784	−	10.1598i	−0.583153	−	0.490520i
$430$		0			0
$431$	33.7821			1.62723			0.813613	−	0.581407i	$-0.197498\pi$
$431$	33.7821			1.62723			0.813613	+	0.581407i	$0.197498\pi$
$432$		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
$435$	−6.56117	−	5.51894i	−0.314584	−	0.264613i
$436$		0			0
$437$	2.73664	−	10.2133i	0.130911	−	0.488567i
$438$		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
$443$	2.35908	+	8.80422i	0.112083	+	0.418301i	0.999052	−	0.0435282i	$-0.0138598\pi$
$443$	2.35908	+	8.80422i	0.112083	+	0.418301i	−0.886969	+	0.461830i	$0.847193\pi$
$444$		0			0
$445$	0.606260	−	2.26259i	0.0287395	−	0.107257i
$446$		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
$453$	4.99847	−	1.81248i	0.234848	−	0.0851579i
$454$		0			0
$455$	−0.868300	+	0.501313i	−0.0407065	+	0.0235019i
$456$		0			0
$457$	−1.90950	−	1.10245i	−0.0893226	−	0.0515704i	0.454673	−	0.890658i	$-0.349756\pi$
$457$	−1.90950	−	1.10245i	−0.0893226	−	0.0515704i	−0.543996	+	0.839088i	$0.683089\pi$
$458$		0			0
$459$	−16.7064	−	9.72604i	−0.779788	−	0.453972i
$460$		0			0
$461$	−5.14058	−	19.1849i	−0.239421	−	0.893531i	−0.976106	−	0.217295i	$-0.930277\pi$
$461$	−5.14058	−	19.1849i	−0.239421	−	0.893531i	0.736685	−	0.676236i	$-0.236390\pi$
$462$		0			0
$463$	−1.39347	+	0.804523i	−0.0647602	+	0.0373893i	−0.532031	−	0.846725i	$-0.678571\pi$
$463$	−1.39347	+	0.804523i	−0.0647602	+	0.0373893i	0.467270	+	0.884115i	$0.345238\pi$
$464$		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	$-0.355489\pi$
$467$	−9.94383	−	9.94383i	−0.460145	−	0.460145i	−0.898703	+	0.438558i	$0.855489\pi$
$468$		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
$475$	19.3156	−	5.17561i	0.886262	−	0.237473i
$476$		0			0
$477$	20.9608	−	29.7823i	0.959729	−	1.36364i
$478$		0			0
$479$	14.3867	−	24.9185i	0.657346	−	1.13856i	−0.323955	−	0.946073i	$-0.605013\pi$
$479$	14.3867	−	24.9185i	0.657346	−	1.13856i	0.981300	−	0.192483i	$-0.0616542\pi$
$480$		0			0
$481$	3.58248	+	6.20504i	0.163347	+	0.282925i
$482$		0			0
$483$	−0.569174	+	0.676659i	−0.0258983	+	0.0307891i
$484$		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
$491$	−5.26076	−	1.40962i	−0.237415	−	0.0636152i	0.138150	−	0.990411i	$-0.455885\pi$
$491$	−5.26076	−	1.40962i	−0.237415	−	0.0636152i	−0.375565	+	0.926796i	$0.622551\pi$
$492$		0			0
$493$	14.2490	−	3.81801i	0.641744	−	0.171955i
$494$		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
$499$	−17.2217	−	4.61454i	−0.770950	−	0.206575i	−0.148159	−	0.988964i	$-0.547335\pi$
$499$	−17.2217	−	4.61454i	−0.770950	−	0.206575i	−0.622791	+	0.782388i	$0.714001\pi$
$500$		0			0
$501$	−23.7946	−	4.22516i	−1.06306	−	0.188766i
$502$		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
$507$	2.83620	+	7.82166i	0.125960	+	0.347372i
$508$		0			0
$509$	10.6256	+	2.84712i	0.470971	+	0.126196i	0.486495	−	0.873683i	$-0.338275\pi$
$509$	10.6256	+	2.84712i	0.470971	+	0.126196i	−0.0155245	+	0.999879i	$0.504942\pi$
$510$		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
$515$	−0.147444	+	0.0395075i	−0.00649716	+	0.00174091i
$516$		0			0
$517$	−33.7258	−	9.03680i	−1.48326	−	0.397438i
$518$		0			0
$519$	1.81581	−	3.88180i	0.0797050	−	0.170392i
$520$		0			0
$521$	8.17552			0.358176			0.179088	−	0.983833i	$-0.442685\pi$
$521$	8.17552			0.358176			0.179088	+	0.983833i	$0.442685\pi$
$522$		0			0
$523$	11.4305	+	11.4305i	0.499820	+	0.499820i	0.911382	−	0.411562i	$-0.135017\pi$
$523$	11.4305	+	11.4305i	0.499820	+	0.499820i	−0.411562	+	0.911382i	$0.635017\pi$
$524$		0			0
$525$	−1.64649	−	0.292364i	−0.0718586	−	0.0127598i
$526$		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
$531$	1.49786	−	16.6587i	0.0650014	−	0.722925i
$532$		0			0
$533$	14.7572	−	3.95417i	0.639204	−	0.171274i
$534$		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	0.887706	−	0.460411i	$-0.152298\pi$
$541$	9.93863	+	9.93863i	0.427295	+	0.427295i	−0.460411	+	0.887706i	$0.652298\pi$
$542$		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
$547$	0.754938	+	2.81747i	0.0322788	+	0.120466i	0.980185	−	0.198082i	$-0.0634713\pi$
$547$	0.754938	+	2.81747i	0.0322788	+	0.120466i	−0.947907	+	0.318548i	$0.896805\pi$
$548$		0			0
$549$	−8.13733	−	17.5608i	−0.347293	−	0.749476i
$550$		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
$555$	0.946083	−	5.32800i	0.0401590	−	0.226161i
$556$		0			0
$557$	−11.5964	+	11.5964i	−0.491356	+	0.491356i	−0.908733	−	0.417377i	$-0.862949\pi$
$557$	−11.5964	+	11.5964i	−0.491356	+	0.491356i	0.417377	+	0.908733i	$0.362949\pi$
$558$		0			0
$559$		−	20.4360i		−	0.864352i
$560$		0			0
$561$	−18.5778	−	8.69021i	−0.784356	−	0.366901i
$562$		0			0
$563$	1.99011	−	7.42718i	0.0838730	−	0.313018i	−0.911225	−	0.411908i	$-0.864862\pi$
$563$	1.99011	−	7.42718i	0.0838730	−	0.313018i	0.995098	+	0.0988898i	$0.0315291\pi$
$564$		0			0
$565$	−0.713826	−	2.66403i	−0.0300309	−	0.112077i
$566$		0			0
$567$	0.450388	−	2.48429i	0.0189145	−	0.104330i
$568$		0			0
$569$	11.7897	−	20.4204i	0.494250	−	0.856066i	−0.505728	−	0.862693i	$-0.668776\pi$
$569$	11.7897	−	20.4204i	0.494250	−	0.856066i	0.999978	+	0.00662697i	$0.00210945\pi$
$570$		0			0
$571$	−1.99940	+	7.46185i	−0.0836722	+	0.312269i	−0.995059	−	0.0992811i	$-0.968346\pi$
$571$	−1.99940	+	7.46185i	−0.0836722	+	0.312269i	0.911387	+	0.411550i	$0.135012\pi$
$572$		0			0
$573$	−23.0773	+	8.36802i	−0.964069	+	0.349579i
$574$		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
$579$	3.91859	−	22.0681i	0.162851	−	0.917119i
$580$		0			0
$581$	0.165147	−	0.616336i	0.00685144	−	0.0255699i
$582$		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
$587$	11.7964	+	44.0249i	0.486891	+	1.81710i	0.571388	+	0.820680i	$0.306405\pi$
$587$	11.7964	+	44.0249i	0.486891	+	1.81710i	−0.0844969	+	0.996424i	$0.526928\pi$
$588$		0			0
$589$	15.3003	−	57.1015i	0.630438	−	2.35283i
$590$		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
$597$	−14.4742	−	12.1750i	−0.592390	−	0.498290i
$598$		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	0.799316	−	0.600912i	$-0.205196\pi$
$601$	16.6353	+	9.60440i	0.678569	+	0.391772i	−0.120747	+	0.992683i	$0.538529\pi$
$602$		0			0
$603$	1.04479	−	11.6199i	0.0425473	−	0.473197i
$604$		0			0
$605$	−0.280829	−	1.04807i	−0.0114173	−	0.0426101i
$606$		0			0
$607$	−12.1261	+	7.00100i	−0.492183	+	0.284162i	−0.725480	−	0.688244i	$-0.758382\pi$
$607$	−12.1261	+	7.00100i	−0.492183	+	0.284162i	0.233297	+	0.972406i	$0.425049\pi$
$608$		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	−0.248478	−	0.968637i	$-0.579930\pi$
$613$	17.8303	−	17.8303i	0.720159	−	0.720159i	0.968637	+	0.248478i	$0.0799304\pi$
$614$		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	$0.271136\pi$
$617$	24.3668	+	42.2045i	0.980970	+	1.69909i	0.322340	+	0.946624i	$0.395531\pi$
$618$		0			0
$619$	−11.1877	+	2.99775i	−0.449673	+	0.120490i	−0.476547	−	0.879149i	$-0.658112\pi$
$619$	−11.1877	+	2.99775i	−0.449673	+	0.120490i	0.0268731	+	0.999639i	$0.491445\pi$
$620$		0			0
$621$	−0.0341372	+	9.45565i	−0.00136988	+	0.379442i
$622$		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
$627$	10.9196	+	30.1139i	0.436085	+	1.20264i
$628$		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
$635$	4.38844	+	1.17588i	0.174150	+	0.0466633i
$636$		0			0
$637$	−19.1401	+	5.12858i	−0.758359	+	0.203202i
$638$		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
$643$	19.5010	+	5.22528i	0.769044	+	0.206065i	0.621949	−	0.783058i	$-0.286341\pi$
$643$	19.5010	+	5.22528i	0.769044	+	0.206065i	0.147095	+	0.989122i	$0.453008\pi$
$644$		0			0
$645$	−9.93523	+	11.8115i	−0.391199	+	0.465076i
$646$		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
$651$	−3.18220	+	3.78315i	−0.124720	+	0.148273i
$652$		0			0
$653$	0.854532	+	0.228971i	0.0334404	+	0.00896033i	0.275500	−	0.961301i	$-0.411156\pi$
$653$	0.854532	+	0.228971i	0.0334404	+	0.00896033i	−0.242060	+	0.970261i	$0.577823\pi$
$654$		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
$659$	−48.6567	+	13.0375i	−1.89539	+	0.507869i	−0.897653	+	0.440704i	$0.854729\pi$
$659$	−48.6567	+	13.0375i	−1.89539	+	0.507869i	−0.997742	+	0.0671656i	$0.978604\pi$
$660$		0			0
$661$	26.7677	+	7.17239i	1.04114	+	0.278974i	0.738587	−	0.674158i	$-0.235493\pi$
$661$	26.7677	+	7.17239i	1.04114	+	0.278974i	0.302557	+	0.953131i	$0.402160\pi$
$662$		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
$669$	−8.42580	−	23.2367i	−0.325760	−	0.898381i
$670$		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
$675$	−15.5192	+	8.88549i	−0.597336	+	0.342003i
$676$		0			0
$677$	10.0436	−	2.69118i	0.386007	−	0.103430i	−0.0605961	−	0.998162i	$-0.519300\pi$
$677$	10.0436	−	2.69118i	0.386007	−	0.103430i	0.446603	+	0.894732i	$0.352633\pi$
$678$		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	$-0.829911\pi$
$683$	−9.18142	+	9.18142i	−0.351317	+	0.351317i	0.509282	+	0.860600i	$0.329911\pi$
$684$		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
$691$	6.53111	+	24.3744i	0.248455	+	0.927247i	0.971615	+	0.236567i	$0.0760221\pi$
$691$	6.53111	+	24.3744i	0.248455	+	0.927247i	−0.723160	+	0.690680i	$0.757311\pi$
$692$		0			0
$693$	0.239887	−	2.66795i	0.00911256	−	0.101347i
$694$		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
$699$	8.63283	+	7.26153i	0.326524	+	0.274656i
$700$		0			0
$701$	−32.8695	+	32.8695i	−1.24146	+	1.24146i	−0.282069	+	0.959394i	$0.591021\pi$
$701$	−32.8695	+	32.8695i	−1.24146	+	1.24146i	−0.959394	+	0.282069i	$0.908979\pi$
$702$		0			0
$703$		−	14.5415i		−	0.548443i
$704$		0			0
$705$	2.03883	+	23.6314i	0.0767867	+	0.890011i
$706$		0			0
$707$	1.17421	−	4.38221i	0.0441607	−	0.164810i
$708$		0			0
$709$	−11.0318	−	41.1714i	−0.414310	−	1.54622i	−0.786215	−	0.617953i	$-0.787962\pi$
$709$	−11.0318	−	41.1714i	−0.414310	−	1.54622i	0.371905	−	0.928271i	$-0.378705\pi$
$710$		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
$715$	−2.94426	+	10.9881i	−0.110109	+	0.410932i
$716$		0			0
$717$	1.43481	−	8.08031i	0.0535838	−	0.301765i
$718$		0			0
$719$	−8.84226			−0.329761			−0.164880	−	0.986314i	$-0.552724\pi$
$719$	−8.84226			−0.329761			−0.164880	+	0.986314i	$0.552724\pi$
$720$		0			0
$721$	0.0343022			0.00127748
$722$		0			0
$723$	24.2229	−	8.78340i	0.900858	−	0.326658i
$724$		0			0
$725$	3.53195	−	13.1814i	0.131173	−	0.489545i
$726$		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
$731$	−6.87321	−	25.6512i	−0.254215	−	0.948743i
$732$		0			0
$733$	7.73423	−	28.8645i	0.285670	−	1.06614i	−0.662678	−	0.748905i	$-0.730580\pi$
$733$	7.73423	−	28.8645i	0.285670	−	1.06614i	0.948348	−	0.317232i	$-0.102753\pi$
$734$		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	−0.822921	−	0.568156i	$-0.807657\pi$
$739$	−6.92568	+	6.92568i	−0.254765	+	0.254765i	0.568156	+	0.822921i	$0.307657\pi$
$740$		0			0
$741$	−5.03740	+	28.3688i	−0.185053	+	1.04215i
$742$		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
$747$	−2.86888	−	6.19119i	−0.104967	−	0.226524i
$748$		0			0
$749$	0.613380	+	2.28916i	0.0224124	+	0.0836442i
$750$		0			0
$751$	−7.35037	+	4.24374i	−0.268219	+	0.154856i	−0.628078	−	0.778151i	$-0.716158\pi$
$751$	−7.35037	+	4.24374i	−0.268219	+	0.154856i	0.359859	+	0.933007i	$0.382825\pi$
$752$		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	−0.927682	−	0.373372i	$-0.878201\pi$
$757$	−15.2511	+	15.2511i	−0.554309	+	0.554309i	0.373372	+	0.927682i	$0.378201\pi$
$758$		0			0
$759$	0.862335	+	9.99505i	0.0313008	+	0.362797i
$760$		0			0
$761$	−1.63439	−	2.83084i	−0.0592465	−	0.102618i	0.834881	−	0.550431i	$-0.185536\pi$
$761$	−1.63439	−	2.83084i	−0.0592465	−	0.102618i	−0.894127	+	0.447813i	$0.852203\pi$
$762$		0			0
$763$	1.30643	−	0.350056i	0.0472959	−	0.0126729i
$764$		0			0
$765$	−1.24774	+	13.8770i	−0.0451123	+	0.501725i
$766$		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
$771$	4.28176	+	0.760304i	0.154204	+	0.0273817i
$772$		0			0
$773$	−20.0548	−	20.0548i	−0.721320	−	0.721320i	0.247554	−	0.968874i	$-0.420373\pi$
$773$	−20.0548	−	20.0548i	−0.721320	−	0.721320i	−0.968874	+	0.247554i	$0.920373\pi$
$774$		0			0
$775$	35.0148			1.25777
$776$		0			0
$777$	−0.515242	+	1.10148i	−0.0184842	+	0.0395153i
$778$		0			0
$779$	−29.9501	−	8.02512i	−1.07308	−	0.287530i
$780$		0			0
$781$	32.8375	−	8.79878i	1.17502	−	0.314845i
$782$		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
$787$	9.14785	+	2.45116i	0.326086	+	0.0873744i	0.418148	−	0.908379i	$-0.362679\pi$
$787$	9.14785	+	2.45116i	0.326086	+	0.0873744i	−0.0920625	+	0.995753i	$0.529346\pi$
$788$		0			0
$789$	2.14568	+	5.91736i	0.0763883	+	0.210664i
$790$		0			0
$791$			0.619775i			0.0220367i
$792$		0			0
$793$		−	18.4703i		−	0.655900i
$794$		0			0
$795$	−25.8446	−	4.58917i	−0.916613	−	0.162761i
$796$		0			0
$797$	26.8654	+	7.19855i	0.951620	+	0.254986i	0.701050	−	0.713112i	$-0.252715\pi$
$797$	26.8654	+	7.19855i	0.951620	+	0.254986i	0.250571	+	0.968098i	$0.419382\pi$
$798$		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
$803$	28.6052	−	7.66474i	1.00946	−	0.270483i
$804$		0			0
$805$	0.615577	+	0.164943i	0.0216962	+	0.00581349i
$806$		0			0
$807$	30.1716	−	2.60309i	1.06209	−	0.0916332i
$808$		0			0
$809$	−48.8492			−1.71745			−0.858724	−	0.512439i	$-0.828742\pi$
$809$	−48.8492			−1.71745			−0.858724	+	0.512439i	$0.828742\pi$
$810$		0			0
$811$	5.86383	+	5.86383i	0.205907	+	0.205907i	0.802525	−	0.596618i	$-0.203489\pi$
$811$	5.86383	+	5.86383i	0.205907	+	0.205907i	−0.596618	+	0.802525i	$0.703489\pi$
$812$		0			0
$813$	−30.3996	+	36.1404i	−1.06616	+	1.26750i
$814$		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
$819$	1.38675	−	1.97037i	0.0484568	−	0.0688502i
$820$		0			0
$821$	−3.09154	+	0.828375i	−0.107895	+	0.0289105i	−0.312363	−	0.949963i	$-0.601120\pi$
$821$	−3.09154	+	0.828375i	−0.107895	+	0.0289105i	0.204467	+	0.978873i	$0.434454\pi$
$822$		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	$-0.851263\pi$
$827$	−12.7209	+	12.7209i	−0.442348	+	0.442348i	0.450453	+	0.892800i	$0.351263\pi$
$828$		0			0
$829$	−10.4132	−	10.4132i	−0.361665	−	0.361665i	0.502761	−	0.864425i	$-0.332318\pi$
$829$	−10.4132	−	10.4132i	−0.361665	−	0.361665i	−0.864425	+	0.502761i	$0.832318\pi$
$830$		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
$835$	4.50815	+	16.8246i	0.156011	+	0.582241i
$836$		0			0
$837$	−0.190858	+	52.8657i	−0.00659702	+	1.82731i
$838$		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
$843$	22.9494	−	8.32164i	0.790420	−	0.286613i
$844$		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
$851$	1.17872	−	4.39903i	0.0404059	−	0.150797i
$852$		0			0
$853$	7.61221	+	28.4092i	0.260637	+	0.972711i	0.964867	+	0.262739i	$0.0846258\pi$
$853$	7.61221	+	28.4092i	0.260637	+	0.972711i	−0.704230	+	0.709972i	$0.748708\pi$
$854$		0			0
$855$	16.7033	−	13.9474i	0.571241	−	0.476990i
$856$		0			0
$857$	−14.3783	+	24.9039i	−0.491152	+	0.850700i	−0.999948	−	0.0101867i	$-0.996757\pi$
$857$	−14.3783	+	24.9039i	−0.491152	+	0.850700i	0.508796	+	0.860887i	$0.330091\pi$
$858$		0			0
$859$	2.48122	−	9.26004i	0.0846582	−	0.315949i	−0.910591	−	0.413308i	$-0.864373\pi$
$859$	2.48122	−	9.26004i	0.0846582	−	0.315949i	0.995249	+	0.0973599i	$0.0310398\pi$
$860$		0			0
$861$	1.98429	+	1.66909i	0.0676243	+	0.0568823i
$862$		0			0
$863$	38.6895			1.31700			0.658502	−	0.752579i	$-0.271190\pi$
$863$	38.6895			1.31700			0.658502	+	0.752579i	$0.271190\pi$
$864$		0			0
$865$	−3.08877			−0.105021
$866$		0			0
$867$	4.18757	+	3.52238i	0.142217	+	0.119626i
$868$		0			0
$869$	−8.28517	+	30.9207i	−0.281055	+	1.04891i
$870$		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
$875$	0.765148	+	2.85557i	0.0258667	+	0.0965360i
$876$		0			0
$877$	−9.07397	+	33.8645i	−0.306406	+	1.14352i	0.625322	+	0.780367i	$0.284968\pi$
$877$	−9.07397	+	33.8645i	−0.306406	+	1.14352i	−0.931728	+	0.363157i	$0.881699\pi$
$878$		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	0.213292	−	0.976988i	$-0.431581\pi$
$883$	35.3696	−	35.3696i	1.19028	−	1.19028i	0.976988	−	0.213292i	$-0.0684187\pi$
$884$		0			0
$885$	−11.3331	+	4.10946i	−0.380957	+	0.138138i
$886$		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
$891$	−16.3176	−	23.5443i	−0.546659	−	0.788764i
$892$		0			0
$893$	16.4968	+	61.5670i	0.552045	+	2.06026i
$894$		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
$907$	26.5046	−	7.10188i	0.880070	−	0.235814i	0.209633	−	0.977780i	$-0.432773\pi$
$907$	26.5046	−	7.10188i	0.880070	−	0.235814i	0.670437	+	0.741966i	$0.266106\pi$
$908$		0			0
$909$	−20.3980	−	44.0200i	−0.676560	−	1.46005i
$910$		0			0
$911$	23.4177	−	40.5606i	0.775863	−	1.34383i	−0.158445	−	0.987368i	$-0.550648\pi$
$911$	23.4177	−	40.5606i	0.775863	−	1.34383i	0.934308	−	0.356466i	$-0.116018\pi$
$912$		0			0
$913$	−3.61980	−	6.26967i	−0.119798	−	0.207496i
$914$		0			0
$915$	−8.97957	+	10.6753i	−0.296855	+	0.352915i
$916$		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
$923$	29.5366	+	7.91430i	0.972209	+	0.260503i
$924$		0			0
$925$	8.31957	−	2.22922i	0.273546	−	0.0732964i
$926$		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
$931$	38.8455	+	10.4086i	1.27311	+	0.341128i
$932$		0			0
$933$	27.1451	+	4.82010i	0.888689	+	0.157803i
$934$		0			0
$935$			14.7824i			0.483437i
$936$		0			0
$937$		−	41.2133i		−	1.34638i	−0.739470	−	0.673189i	$-0.764924\pi$
$937$		−	41.2133i		−	1.34638i	0.739470	−	0.673189i	$-0.235076\pi$
$938$		0			0
$939$	6.75142	+	18.6191i	0.220324	+	0.607610i
$940$		0			0
$941$	12.0368	+	3.22526i	0.392390	+	0.105141i	0.449619	−	0.893221i	$-0.351560\pi$
$941$	12.0368	+	3.22526i	0.392390	+	0.105141i	−0.0572290	+	0.998361i	$0.518227\pi$
$942$		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
$947$	−14.8120	+	3.96886i	−0.481325	+	0.128971i	−0.491320	−	0.870979i	$-0.663485\pi$
$947$	−14.8120	+	3.96886i	−0.481325	+	0.128971i	0.00999447	+	0.999950i	$0.496819\pi$
$948$		0			0
$949$	25.7297	+	6.89426i	0.835222	+	0.223797i
$950$		0			0
$951$	−20.0338	+	42.8281i	−0.649642	+	1.38879i
$952$		0			0
$953$	−20.0192			−0.648486			−0.324243	−	0.945974i	$-0.605110\pi$
$953$	−20.0192			−0.648486			−0.324243	+	0.945974i	$0.605110\pi$
$954$		0			0
$955$	12.5106	+	12.5106i	0.404833	+	0.404833i
$956$		0			0
$957$	21.5231	+	3.82181i	0.695742	+	0.123541i
$958$		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
$963$	20.7254	+	14.5865i	0.667866	+	0.470045i
$964$		0			0
$965$	−15.6039	+	4.18105i	−0.502307	+	0.134593i
$966$		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	$-0.839594\pi$
$971$	−12.2406	+	12.2406i	−0.392820	+	0.392820i	0.482871	+	0.875691i	$0.339594\pi$
$972$		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
$979$	1.54575	+	5.76880i	0.0494022	+	0.184372i
$980$		0			0
$981$	8.32455	−	11.8280i	0.265782	−	0.377639i
$982$		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
$987$	0.931885	−	5.24804i	0.0296622	−	0.167047i
$988$		0			0
$989$	−9.18504	+	9.18504i	−0.292067	+	0.292067i
$990$		0			0
$991$			21.1610i			0.672200i	0.941826	+	0.336100i	$0.109108\pi$
$991$			21.1610i			0.672200i	−0.941826	+	0.336100i	$0.890892\pi$
$992$		0			0
$993$	18.0332	+	8.43546i	0.572266	+	0.267691i
$994$		0			0
$995$	−3.52825	+	13.1676i	−0.111853	+	0.417441i
$996$		0			0
$997$	−3.41563	−	12.7473i	−0.108174	−	0.403712i	0.890512	−	0.454960i	$-0.150347\pi$
$997$	−3.41563	−	12.7473i	−0.108174	−	0.403712i	−0.998686	+	0.0512486i	$0.983680\pi$
$998$		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.47.17		88
3.2	odd	2		1728.2.z.a.1007.7		88
4.3	odd	2		144.2.u.a.83.22	yes	88
9.4	even	3		1728.2.z.a.1583.7		88
9.5	odd	6	inner	576.2.y.a.239.6		88
12.11	even	2		432.2.v.a.35.1		88
16.5	even	4		144.2.u.a.11.16	✓	88
16.11	odd	4	inner	576.2.y.a.335.6		88
36.23	even	6		144.2.u.a.131.16	yes	88
36.31	odd	6		432.2.v.a.179.7		88
48.5	odd	4		432.2.v.a.251.7		88
48.11	even	4		1728.2.z.a.143.7		88
144.5	odd	12		144.2.u.a.59.22	yes	88
144.59	even	12	inner	576.2.y.a.527.17		88
144.85	even	12		432.2.v.a.395.1		88
144.139	odd	12		1728.2.z.a.719.7		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.16	✓	88	16.5	even	4
144.2.u.a.59.22	yes	88	144.5	odd	12
144.2.u.a.83.22	yes	88	4.3	odd	2
144.2.u.a.131.16	yes	88	36.23	even	6
432.2.v.a.35.1		88	12.11	even	2
432.2.v.a.179.7		88	36.31	odd	6
432.2.v.a.251.7		88	48.5	odd	4
432.2.v.a.395.1		88	144.85	even	12
576.2.y.a.47.17		88	1.1	even	1	trivial
576.2.y.a.239.6		88	9.5	odd	6	inner
576.2.y.a.335.6		88	16.11	odd	4	inner
576.2.y.a.527.17		88	144.59	even	12	inner
1728.2.z.a.143.7		88	48.11	even	4
1728.2.z.a.719.7		88	144.139	odd	12
1728.2.z.a.1007.7		88	3.2	odd	2
1728.2.z.a.1583.7		88	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

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