LMFDB - Embedded newform 432.2.v.a.179.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(35,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, 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("432.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (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:	$3.44953736732$
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			179.7
Character	$\chi$	$=$	432.179
Dual form			432.2.v.a.251.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.717593 + 1.21863i) q^{2} +(-0.970121 - 1.74896i) q^{4} +(-1.20583 + 0.323102i) q^{5} +(0.140266 + 0.242948i) q^{7} +(2.82749 + 0.0728225i) q^{8} +(0.471556 - 1.70132i) q^{10} +(3.07444 + 0.823794i) q^{11} +(2.76539 - 0.740984i) q^{13} +(-0.396717 - 0.00340517i) q^{14} +(-2.11773 + 3.39341i) q^{16} +3.72031i q^{17} +(-4.10860 + 4.10860i) q^{19} +(1.73490 + 1.79551i) q^{20} +(-3.21010 + 3.15546i) q^{22} +(1.57595 + 0.909876i) q^{23} +(-2.98049 + 1.72078i) q^{25} +(-1.08144 + 3.90172i) q^{26} +(0.288831 - 0.481009i) q^{28} +(3.83006 + 1.02626i) q^{29} +(8.81101 + 5.08704i) q^{31} +(-2.61564 - 5.01582i) q^{32} +(-4.53369 - 2.66967i) q^{34} +(-0.247635 - 0.247635i) q^{35} +(1.76964 - 1.76964i) q^{37} +(-2.05856 - 7.95516i) q^{38} +(-3.43301 + 0.825757i) q^{40} +(-2.66819 + 4.62144i) q^{41} +(-1.84748 + 6.89490i) q^{43} +(-1.54180 - 6.17626i) q^{44} +(-2.23969 + 1.26758i) q^{46} +(5.48486 + 9.50006i) q^{47} +(3.46065 - 5.99402i) q^{49} +(0.0417747 - 4.86693i) q^{50} +(-3.97872 - 4.11772i) q^{52} +(-8.58403 - 8.58403i) q^{53} -3.97344 q^{55} +(0.378909 + 0.697147i) q^{56} +(-3.99906 + 3.93099i) q^{58} +(-1.44299 - 5.38532i) q^{59} +(1.66977 - 6.23168i) q^{61} +(-12.5219 + 7.08695i) q^{62} +(7.98939 + 0.411810i) q^{64} +(-3.09519 + 1.78701i) q^{65} +(-1.00652 - 3.75640i) q^{67} +(6.50668 - 3.60915i) q^{68} +(0.479476 - 0.124074i) q^{70} +10.6808i q^{71} -9.30419i q^{73} +(0.886658 + 3.42643i) q^{74} +(11.1716 + 3.19994i) q^{76} +(0.231101 + 0.862479i) q^{77} +(8.70990 - 5.02866i) q^{79} +(1.45721 - 4.77613i) q^{80} +(-3.71715 - 6.56784i) q^{82} +(-0.588691 + 2.19703i) q^{83} +(-1.20204 - 4.48608i) q^{85} +(-7.07659 - 7.19913i) q^{86} +(8.63296 + 2.55316i) q^{88} +1.87637 q^{89} +(0.567911 + 0.567911i) q^{91} +(0.0624738 - 3.63897i) q^{92} +(-15.5130 - 0.133153i) q^{94} +(3.62679 - 6.28179i) q^{95} +(9.19070 + 15.9188i) q^{97} +(4.82116 + 8.51852i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.717593	+	1.21863i	−0.507415	+	0.861702i
$2$	−0.717593	+	1.21863i	−0.507415	+	0.861702i
$3$		0			0
$3$		0			0
$4$	−0.970121	−	1.74896i	−0.485061	−	0.874481i
$5$	−1.20583	+	0.323102i	−0.539266	+	0.144496i	−0.518164	−	0.855282i	$-0.673384\pi$
$5$	−1.20583	+	0.323102i	−0.539266	+	0.144496i	−0.0211020	+	0.999777i	$0.506717\pi$
$6$		0			0
$7$	0.140266	+	0.242948i	0.0530156	+	0.0918256i	0.891315	−	0.453384i	$-0.149783\pi$
$7$	0.140266	+	0.242948i	0.0530156	+	0.0918256i	−0.838300	+	0.545210i	$0.816450\pi$
$8$	2.82749	+	0.0728225i	0.999669	+	0.0257466i
$9$		0			0
$10$	0.471556	−	1.70132i	0.149119	−	0.538005i
$11$	3.07444	+	0.823794i	0.926979	+	0.248383i	0.690566	−	0.723269i	$-0.257361\pi$
$11$	3.07444	+	0.823794i	0.926979	+	0.248383i	0.236413	+	0.971653i	$0.424028\pi$
$12$		0			0
$13$	2.76539	−	0.740984i	0.766982	−	0.205512i	0.145944	−	0.989293i	$-0.453378\pi$
$13$	2.76539	−	0.740984i	0.766982	−	0.205512i	0.621038	+	0.783781i	$0.286711\pi$
$14$	−0.396717	−	0.00340517i	−0.106027	−	0.000910071i
$15$		0			0
$16$	−2.11773	+	3.39341i	−0.529432	+	0.848352i
$17$			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	$-0.982209\pi$
$19$	−4.10860	+	4.10860i	−0.942577	+	0.942577i	0.0558614	+	0.998439i	$0.482209\pi$
$20$	1.73490	+	1.79551i	0.387935	+	0.401488i
$21$		0			0
$22$	−3.21010	+	3.15546i	−0.684395	+	0.672747i
$23$	1.57595	+	0.909876i	0.328609	+	0.189722i	0.655223	−	0.755435i	$-0.272575\pi$
$23$	1.57595	+	0.909876i	0.328609	+	0.189722i	−0.326615	+	0.945158i	$0.605908\pi$
$24$		0			0
$25$	−2.98049	+	1.72078i	−0.596097	+	0.344157i
$26$	−1.08144	+	3.90172i	−0.212088	+	0.765189i
$27$		0			0
$28$	0.288831	−	0.481009i	0.0545840	−	0.0909021i
$29$	3.83006	+	1.02626i	0.711224	+	0.190572i	0.596253	−	0.802797i	$-0.296656\pi$
$29$	3.83006	+	1.02626i	0.711224	+	0.190572i	0.114972	+	0.993369i	$0.463322\pi$
$30$		0			0
$31$	8.81101	+	5.08704i	1.58250	+	0.913659i	0.994493	+	0.104807i	$0.0334225\pi$
$31$	8.81101	+	5.08704i	1.58250	+	0.913659i	0.588012	+	0.808852i	$0.299911\pi$
$32$	−2.61564	−	5.01582i	−0.462385	−	0.886679i
$33$		0			0
$34$	−4.53369	−	2.66967i	−0.777521	−	0.457845i
$35$	−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	$0.184047\pi$
$38$	−2.05856	−	7.95516i	−0.333943	−	1.29050i
$39$		0			0
$40$	−3.43301	+	0.825757i	−0.542807	+	0.130564i
$41$	−2.66819	+	4.62144i	−0.416701	+	0.721747i	−0.995605	−	0.0936482i	$-0.970147\pi$
$41$	−2.66819	+	4.62144i	−0.416701	+	0.721747i	0.578904	+	0.815395i	$0.303480\pi$
$42$		0			0
$43$	−1.84748	+	6.89490i	−0.281738	+	1.05146i	0.669452	+	0.742856i	$0.266529\pi$
$43$	−1.84748	+	6.89490i	−0.281738	+	1.05146i	−0.951190	+	0.308606i	$0.900138\pi$
$44$	−1.54180	−	6.17626i	−0.232435	−	0.931106i
$45$		0			0
$46$	−2.23969	+	1.26758i	−0.330225	+	0.186895i
$47$	5.48486	+	9.50006i	0.800049	+	1.38573i	0.919583	+	0.392896i	$0.128527\pi$
$47$	5.48486	+	9.50006i	0.800049	+	1.38573i	−0.119534	+	0.992830i	$0.538140\pi$
$48$		0			0
$49$	3.46065	−	5.99402i	0.494379	−	0.856289i
$50$	0.0417747	−	4.86693i	0.00590783	−	0.688288i
$51$		0			0
$52$	−3.97872	−	4.11772i	−0.551749	−	0.571025i
$53$	−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
$56$	0.378909	+	0.697147i	0.0506338	+	0.0931602i
$57$		0			0
$58$	−3.99906	+	3.93099i	−0.525102	+	0.516164i
$59$	−1.44299	−	5.38532i	−0.187862	−	0.701109i	−0.994000	−	0.109382i	$-0.965113\pi$
$59$	−1.44299	−	5.38532i	−0.187862	−	0.701109i	0.806138	−	0.591727i	$-0.201554\pi$
$60$		0			0
$61$	1.66977	−	6.23168i	0.213793	−	0.797885i	−0.772796	−	0.634655i	$-0.781142\pi$
$61$	1.66977	−	6.23168i	0.213793	−	0.797885i	0.986588	−	0.163230i	$-0.0521911\pi$
$62$	−12.5219	+	7.08695i	−1.59029	+	0.900043i
$63$		0			0
$64$	7.98939	+	0.411810i	0.998674	+	0.0514762i
$65$	−3.09519	+	1.78701i	−0.383911	+	0.221651i
$66$		0			0
$67$	−1.00652	−	3.75640i	−0.122967	−	0.458918i	0.876792	−	0.480869i	$-0.159679\pi$
$67$	−1.00652	−	3.75640i	−0.122967	−	0.458918i	−0.999759	+	0.0219514i	$0.993012\pi$
$68$	6.50668	−	3.60915i	0.789051	−	0.437674i
$69$		0			0
$70$	0.479476	−	0.124074i	0.0573083	−	0.0148297i
$71$			10.6808i			1.26758i	0.773506	+	0.633789i	$0.218501\pi$
$71$			10.6808i			1.26758i	−0.773506	+	0.633789i	$0.781499\pi$
$72$		0			0
$73$		−	9.30419i		−	1.08897i	−0.838770	−	0.544487i	$-0.816725\pi$
$73$		−	9.30419i		−	1.08897i	0.838770	−	0.544487i	$-0.183275\pi$
$74$	0.886658	+	3.42643i	0.103072	+	0.398314i
$75$		0			0
$76$	11.1716	+	3.19994i	1.28147	+	0.367058i
$77$	0.231101	+	0.862479i	0.0263364	+	0.0982886i
$78$		0			0
$79$	8.70990	−	5.02866i	0.979940	−	0.565769i	0.0776882	−	0.996978i	$-0.475246\pi$
$79$	8.70990	−	5.02866i	0.979940	−	0.565769i	0.902252	+	0.431209i	$0.141913\pi$
$80$	1.45721	−	4.77613i	0.162921	−	0.533988i
$81$		0			0
$82$	−3.71715	−	6.56784i	−0.410491	−	0.725297i
$83$	−0.588691	+	2.19703i	−0.0646173	+	0.241155i	−0.990679	−	0.136217i	$-0.956506\pi$
$83$	−0.588691	+	2.19703i	−0.0646173	+	0.241155i	0.926062	+	0.377372i	$0.123172\pi$
$84$		0			0
$85$	−1.20204	−	4.48608i	−0.130380	−	0.486584i
$86$	−7.07659	−	7.19913i	−0.763089	−	0.776302i
$87$		0			0
$88$	8.63296	+	2.55316i	0.920277	+	0.272168i
$89$	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
$92$	0.0624738	−	3.63897i	0.00651335	−	0.379389i
$93$		0			0
$94$	−15.5130	−	0.133153i	−1.60004	−	0.0137337i
$95$	3.62679	−	6.28179i	0.372101	−	0.644498i
$96$		0			0
$97$	9.19070	+	15.9188i	0.933175	+	1.61631i	0.777857	+	0.628441i	$0.216307\pi$
$97$	9.19070	+	15.9188i	0.933175	+	1.61631i	0.155317	+	0.987865i	$0.450360\pi$
$98$	4.82116	+	8.51852i	0.487011	+	0.860501i
$99$		0			0
$100$	5.90102	+	3.54338i	0.590102	+	0.354338i
$101$	4.18566	−	15.6211i	0.416488	−	1.55436i	−0.365347	−	0.930871i	$-0.619050\pi$
$101$	4.18566	−	15.6211i	0.416488	−	1.55436i	0.781836	−	0.623485i	$-0.214284\pi$
$102$		0			0
$103$	0.0611378	−	0.105894i	0.00602409	−	0.0104340i	−0.862998	−	0.505208i	$-0.831416\pi$
$103$	0.0611378	−	0.105894i	0.00602409	−	0.0104340i	0.869022	+	0.494774i	$0.164749\pi$
$104$	7.87308	−	1.89374i	0.772019	−	0.185697i
$105$		0			0
$106$	16.6206	−	4.30092i	1.61434	−	0.417743i
$107$	−5.97359	+	5.97359i	−0.577489	+	0.577489i	−0.934211	−	0.356722i	$-0.883894\pi$
$107$	−5.97359	+	5.97359i	−0.577489	+	0.577489i	0.356722	+	0.934211i	$0.383894\pi$
$108$		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	$0.824166\pi$
$110$	2.85131	−	4.84215i	0.271862	−	0.461681i
$111$		0			0
$112$	−1.12147	−	0.0385180i	−0.105969	−	0.00363961i
$113$	−1.91330	−	1.10464i	−0.179988	−	0.103916i	0.407299	−	0.913295i	$-0.366471\pi$
$113$	−1.91330	−	1.10464i	−0.179988	−	0.103916i	−0.587287	+	0.809379i	$0.699804\pi$
$114$		0			0
$115$	−2.19432	−	0.587966i	−0.204621	−	0.0548281i
$116$	−1.92073	−	7.69422i	−0.178335	−	0.714391i
$117$		0			0
$118$	7.59820	+	2.10599i	0.699471	+	0.193872i
$119$	−0.903842	+	0.521833i	−0.0828551	+	0.0478364i
$120$		0			0
$121$	−0.752719	−	0.434583i	−0.0684290	−	0.0395075i
$122$	6.39590	+	6.50664i	0.579057	+	0.589084i
$123$		0			0
$124$	0.349286	−	20.3452i	0.0313668	−	1.82705i
$125$	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	$-0.0516234\pi$
$128$	−6.23498	+	9.44061i	−0.551099	+	0.834440i
$129$		0			0
$130$	0.0433824	−	5.05424i	0.00380489	−	0.443286i
$131$	14.9890	−	4.01630i	1.30960	−	0.350906i	0.464527	−	0.885559i	$-0.346224\pi$
$131$	14.9890	−	4.01630i	1.30960	−	0.350906i	0.845072	+	0.534653i	$0.179558\pi$
$132$		0			0
$133$	−1.57447	−	0.421878i	−0.136524	−	0.0365815i
$134$	5.29994	+	1.46899i	0.457845	+	0.126901i
$135$		0			0
$136$	−0.270922	+	10.5191i	−0.0232314	+	0.902009i
$137$	−10.4065	−	18.0245i	−0.889085	−	1.53994i	−0.840959	−	0.541099i	$-0.818008\pi$
$137$	−10.4065	−	18.0245i	−0.889085	−	1.53994i	−0.0481263	−	0.998841i	$-0.515325\pi$
$138$		0			0
$139$	0.802043	−	0.214907i	0.0680284	−	0.0182282i	−0.224644	−	0.974441i	$-0.572122\pi$
$139$	0.802043	−	0.214907i	0.0680284	−	0.0182282i	0.292673	+	0.956213i	$0.405455\pi$
$140$	−0.192868	+	0.673339i	−0.0163003	+	0.0569075i
$141$		0			0
$142$	−13.0159	−	7.66446i	−1.09227	−	0.643187i
$143$	9.11246			0.762022
$144$		0			0
$145$	−4.95000			−0.411076
$146$	11.3384	+	6.67662i	0.938370	+	0.552561i
$147$		0			0
$148$	−4.81181	−	1.37827i	−0.395528	−	0.113293i
$149$	−5.13681	+	1.37640i	−0.420824	+	0.112759i	−0.463015	−	0.886350i	$-0.653233\pi$
$149$	−5.13681	+	1.37640i	−0.420824	+	0.112759i	0.0421919	+	0.999110i	$0.486566\pi$
$150$		0			0
$151$	−1.53487	−	2.65847i	−0.124906	−	0.216343i	0.796790	−	0.604256i	$-0.206529\pi$
$151$	−1.53487	−	2.65847i	−0.124906	−	0.216343i	−0.921696	+	0.387913i	$0.873196\pi$
$152$	−11.9162	+	11.3178i	−0.966533	+	0.917996i
$153$		0			0
$154$	−1.21688	−	0.337283i	−0.0980590	−	0.0271790i
$155$	−12.2683	−	3.28727i	−0.985410	−	0.264040i
$156$		0			0
$157$	−5.63885	+	1.51093i	−0.450029	+	0.120585i	−0.476713	−	0.879059i	$-0.658172\pi$
$157$	−5.63885	+	1.51093i	−0.450029	+	0.120585i	0.0266838	+	0.999644i	$0.491505\pi$
$158$	−0.122079	+	14.2227i	−0.00971205	+	1.13150i
$159$		0			0
$160$	4.77465	+	5.20312i	0.377470	+	0.411343i
$161$			0.510499i			0.0402329i
$162$		0			0
$163$	−12.5565	+	12.5565i	−0.983500	+	0.983500i	−0.999866	−	0.0163656i	$-0.994790\pi$
$163$	−12.5565	+	12.5565i	−0.983500	+	0.983500i	0.0163656	+	0.999866i	$0.494790\pi$
$164$	10.6712	+	0.183203i	0.833279	+	0.0143057i
$165$		0			0
$166$	−2.25492	−	2.29397i	−0.175016	−	0.178046i
$167$	−12.0834	−	6.97635i	−0.935041	−	0.539846i	−0.0466388	−	0.998912i	$-0.514851\pi$
$167$	−12.0834	−	6.97635i	−0.935041	−	0.539846i	−0.888402	+	0.459066i	$0.848184\pi$
$168$		0			0
$169$	−4.16000	+	2.40178i	−0.320000	+	0.184752i
$170$	6.32945	+	1.75433i	0.485447	+	0.134551i
$171$		0			0
$172$	13.8512	−	3.45771i	1.05614	−	0.263648i
$173$	2.38993	+	0.640380i	0.181703	+	0.0486872i	0.348523	−	0.937300i	$-0.386683\pi$
$173$	2.38993	+	0.640380i	0.181703	+	0.0486872i	−0.166820	+	0.985987i	$0.553350\pi$
$174$		0			0
$175$	−0.836121	−	0.482735i	−0.0632048	−	0.0364913i
$176$	−9.30631	+	8.68827i	−0.701489	+	0.654903i
$177$		0			0
$178$	−1.34647	+	2.28661i	−0.100922	+	0.171388i
$179$	−9.53870	−	9.53870i	−0.712956	−	0.712956i	0.254197	−	0.967153i	$-0.418189\pi$
$179$	−9.53870	−	9.53870i	−0.712956	−	0.712956i	−0.967153	+	0.254197i	$0.918189\pi$
$180$		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	$0.367031\pi$
$182$	−1.09960	+	0.284545i	−0.0815079	+	0.0210919i
$183$		0			0
$184$	4.38973	+	2.68743i	0.323615	+	0.198120i
$185$	−1.56212	+	2.70567i	−0.114849	+	0.198925i
$186$		0			0
$187$	−3.06477	+	11.4379i	−0.224118	+	0.836421i
$188$	11.2943	−	18.8090i	0.823718	−	1.37179i
$189$		0			0
$190$	5.05262	+	8.92748i	0.366555	+	0.647668i
$191$	7.08629	+	12.2738i	0.512746	+	0.888102i	0.999891	+	0.0147810i	$0.00470512\pi$
$191$	7.08629	+	12.2738i	0.512746	+	0.888102i	−0.487145	+	0.873321i	$0.661962\pi$
$192$		0			0
$193$	−6.47017	+	11.2067i	−0.465733	+	0.806673i	−0.999234	−	0.0391263i	$-0.987543\pi$
$193$	−6.47017	+	11.2067i	−0.465733	+	0.806673i	0.533501	+	0.845799i	$0.320876\pi$
$194$	−25.9943	−	0.223119i	−1.86628	−	0.0160190i
$195$		0			0
$196$	−13.8406	−	0.237615i	−0.988612	−	0.0169725i
$197$	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	$-0.373495\pi$
$199$	10.9199			0.774093			0.387046	+	0.922060i	$0.373495\pi$
$200$	−8.55260	+	4.64845i	−0.604760	+	0.328695i
$201$		0			0
$202$	16.0327	+	16.3103i	1.12806	+	1.14759i
$203$	0.287899	+	1.07445i	0.0202066	+	0.0754119i
$204$		0			0
$205$	1.72420	−	6.43478i	0.120423	−	0.449425i
$206$	0.0851733	+	0.150493i	0.00593431	+	0.0104853i
$207$		0			0
$208$	−3.34189	+	10.9533i	−0.231718	+	0.759475i
$209$	−16.0163	+	9.24701i	−1.10787	+	0.639629i
$210$		0			0
$211$	−4.37047	−	16.3108i	−0.300875	−	1.12288i	−0.936438	−	0.350833i	$-0.885899\pi$
$211$	−4.37047	−	16.3108i	−0.300875	−	1.12288i	0.635563	−	0.772049i	$-0.280768\pi$
$212$	−6.68559	+	23.3407i	−0.459168	+	1.60304i
$213$		0			0
$214$	−2.99300	−	11.5662i	−0.204597	−	0.790650i
$215$		−	8.91103i		−	0.607727i
$216$		0			0
$217$			2.85415i			0.193753i
$218$	6.60085	−	1.70811i	0.447066	−	0.115688i
$219$		0			0
$220$	3.85472	+	6.94939i	0.259885	+	0.468528i
$221$	2.75669	+	10.2881i	0.185435	+	0.692054i
$222$		0			0
$223$	−12.3586	+	7.13522i	−0.827591	+	0.477810i	−0.853027	−	0.521867i	$-0.825236\pi$
$223$	−12.3586	+	7.13522i	−0.827591	+	0.477810i	0.0254364	+	0.999676i	$0.491902\pi$
$224$	0.851696	−	1.33901i	0.0569063	−	0.0894666i
$225$		0			0
$226$	2.71912	−	1.53892i	0.180873	−	0.102367i
$227$	2.27906	−	8.50557i	0.151267	−	0.564535i	−0.848130	−	0.529789i	$-0.822271\pi$
$227$	2.27906	−	8.50557i	0.151267	−	0.564535i	0.999396	−	0.0347459i	$-0.0110622\pi$
$228$		0			0
$229$	−6.45185	−	24.0786i	−0.426350	−	1.59116i	−0.760957	−	0.648803i	$-0.775270\pi$
$229$	−6.45185	−	24.0786i	−0.426350	−	1.59116i	0.334606	−	0.942358i	$-0.391397\pi$
$230$	2.29114	−	2.25214i	0.151073	−	0.148502i
$231$		0			0
$232$	10.7547	+	3.18066i	0.706082	+	0.208820i
$233$	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
$236$	−8.01884	+	7.74815i	−0.521982	+	0.504362i
$237$		0			0
$238$	0.0126683	−	1.47591i	0.000821165	−	0.0956693i
$239$	2.36907	−	4.10336i	0.153243	−	0.265424i	−0.779175	−	0.626806i	$-0.784362\pi$
$239$	2.36907	−	4.10336i	0.153243	−	0.265424i	0.932418	+	0.361382i	$0.117695\pi$
$240$		0			0
$241$	7.43805	+	12.8831i	0.479127	+	0.829872i	0.999713	−	0.0239367i	$-0.00762000\pi$
$241$	7.43805	+	12.8831i	0.479127	+	0.829872i	−0.520586	+	0.853809i	$0.674287\pi$
$242$	1.06974	−	0.605434i	0.0687656	−	0.0389187i
$243$		0			0
$244$	−12.5188	+	3.12512i	−0.801437	+	0.200065i
$245$	−2.23629	+	8.34594i	−0.142871	+	0.533203i
$246$		0			0
$247$	−8.31748	+	14.4063i	−0.529228	+	0.916650i
$248$	24.5426	+	15.0252i	1.55846	+	0.954101i
$249$		0			0
$250$	3.73355	+	14.4280i	0.236131	+	0.912510i
$251$	−6.89508	+	6.89508i	−0.435213	+	0.435213i	−0.890397	−	0.455184i	$-0.849573\pi$
$251$	−6.89508	+	6.89508i	−0.435213	+	0.435213i	0.455184	+	0.890397i	$0.349573\pi$
$252$		0			0
$253$	4.09562	+	4.09562i	0.257489	+	0.257489i
$254$	4.43501	+	2.61156i	0.278277	+	0.163864i
$255$		0			0
$256$	−7.03044	−	14.3726i	−0.439403	−	0.898290i
$257$	−2.17437	−	1.25537i	−0.135633	−	0.0783080i	0.430648	−	0.902520i	$-0.358285\pi$
$257$	−2.17437	−	1.25537i	−0.135633	−	0.0783080i	−0.566281	+	0.824212i	$0.691618\pi$
$258$		0			0
$259$	0.678152	+	0.181710i	0.0421383	+	0.0112909i
$260$	6.12812	+	3.67975i	0.380050	+	0.228209i
$261$		0			0
$262$	−5.86164	+	21.1482i	−0.362133	+	1.30654i
$263$	3.14718	−	1.81703i	0.194064	−	0.112043i	−0.399820	−	0.916594i	$-0.630927\pi$
$263$	3.14718	−	1.81703i	0.194064	−	0.112043i	0.593884	+	0.804551i	$0.297594\pi$
$264$		0			0
$265$	13.1244	+	7.57740i	0.806228	+	0.465476i
$266$	1.64394	−	1.61596i	0.100797	−	0.0990810i
$267$		0			0
$268$	−5.59335	+	5.40454i	−0.341668	+	0.330135i
$269$	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	$-0.689400\pi$
$271$		−	27.2658i		−	1.65628i	0.560523	−	0.828139i	$-0.310600\pi$
$272$	−12.6245	−	7.87862i	−0.765475	−	0.477711i
$273$		0			0
$274$	29.4329	+	0.252633i	1.77810	+	0.0152621i
$275$	−10.5809	+	2.83514i	−0.638053	+	0.170966i
$276$		0			0
$277$	−16.7042	−	4.47587i	−1.00366	−	0.268929i	−0.280680	−	0.959801i	$-0.590560\pi$
$277$	−16.7042	−	4.47587i	−1.00366	−	0.268929i	−0.722977	+	0.690872i	$0.757227\pi$
$278$	−0.313648	+	1.13161i	−0.0188114	+	0.0678694i
$279$		0			0
$280$	−0.682151	−	0.718217i	−0.0407663	−	0.0429217i
$281$	7.04702	+	12.2058i	0.420390	+	0.728137i	0.995978	−	0.0896034i	$-0.0285600\pi$
$281$	7.04702	+	12.2058i	0.420390	+	0.728137i	−0.575588	+	0.817740i	$0.695227\pi$
$282$		0			0
$283$	0.628767	−	0.168478i	0.0373763	−	0.0100149i	−0.240082	−	0.970753i	$-0.577174\pi$
$283$	0.628767	−	0.168478i	0.0373763	−	0.0100149i	0.277459	+	0.960738i	$0.410508\pi$
$284$	18.6803	−	10.3617i	1.10847	−	0.614852i
$285$		0			0
$286$	−6.53903	+	11.1047i	−0.386661	+	0.656636i
$287$	−1.49702			−0.0883665
$288$		0			0
$289$	3.15927			0.185839
$290$	3.55209	−	6.03223i	0.208586	−	0.354225i
$291$		0			0
$292$	−16.2727	+	9.02619i	−0.952286	+	0.528218i
$293$	8.09169	−	2.16816i	0.472722	−	0.126665i	−0.0145900	−	0.999894i	$-0.504644\pi$
$293$	8.09169	−	2.16816i	0.472722	−	0.126665i	0.487312	+	0.873228i	$0.337978\pi$
$294$		0			0
$295$	3.48002	+	6.02757i	0.202615	+	0.350939i
$296$	5.13252	−	4.87478i	0.298322	−	0.283341i
$297$		0			0
$298$	2.00881	−	7.24757i	0.116367	−	0.419840i
$299$	5.03233	+	1.34841i	0.291027	+	0.0779804i
$300$		0			0
$301$	−1.93424	+	0.518278i	−0.111488	+	0.0298730i
$302$	4.34110	+	0.0372612i	0.249802	+	0.00214414i
$303$		0			0
$304$	−5.24125	−	22.6431i	−0.300606	−	1.29867i
$305$			8.05388i			0.461164i
$306$		0			0
$307$	10.1250	−	10.1250i	0.577865	−	0.577865i	−0.356449	−	0.934315i	$-0.616013\pi$
$307$	10.1250	−	10.1250i	0.577865	−	0.577865i	0.934315	+	0.356449i	$0.116013\pi$
$308$	1.28425	−	1.24090i	0.0731768	−	0.0707066i
$309$		0			0
$310$	12.8096	−	12.5916i	0.727535	−	0.715152i
$311$	13.7848	+	7.95868i	0.781667	+	0.451295i	0.837021	−	0.547171i	$-0.184295\pi$
$311$	13.7848	+	7.95868i	0.781667	+	0.451295i	−0.0553539	+	0.998467i	$0.517629\pi$
$312$		0			0
$313$	−9.90266	+	5.71730i	−0.559732	+	0.323161i	−0.753038	−	0.657977i	$-0.771412\pi$
$313$	−9.90266	+	5.71730i	−0.559732	+	0.323161i	0.193306	+	0.981138i	$0.438079\pi$
$314$	2.20514	−	7.95591i	0.124443	−	0.448978i
$315$		0			0
$316$	−17.2446	−	10.3549i	−0.970084	−	0.582507i
$317$	−26.3682	−	7.06533i	−1.48098	−	0.396828i	−0.574302	−	0.818644i	$-0.694726\pi$
$317$	−26.3682	−	7.06533i	−1.48098	−	0.396828i	−0.906682	+	0.421815i	$0.861393\pi$
$318$		0			0
$319$	10.9299	+	6.31036i	0.611955	+	0.353313i
$320$	−9.76694	+	2.08482i	−0.545989	+	0.116545i
$321$		0			0
$322$	−0.622109	−	0.366330i	−0.0346688	−	0.0204148i
$323$	−15.2853	−	15.2853i	−0.850495	−	0.850495i
$324$		0			0
$325$	−6.96714	+	6.96714i	−0.386467	+	0.386467i
$326$	−6.29128	−	24.3122i	−0.348442	−	1.34653i
$327$		0			0
$328$	−7.88082	+	12.8728i	−0.435145	+	0.710779i
$329$	−1.53868	+	2.66507i	−0.0848301	+	0.146930i
$330$		0			0
$331$	2.97493	−	11.1026i	0.163517	−	0.610254i	−0.834708	−	0.550693i	$-0.814363\pi$
$331$	2.97493	−	11.1026i	0.163517	−	0.610254i	0.998225	−	0.0595605i	$-0.0189699\pi$
$332$	4.41362	−	1.10178i	0.242229	−	0.0604682i
$333$		0			0
$334$	17.1726	−	9.71902i	0.939640	−	0.531801i
$335$	2.42740	+	4.20439i	0.132623	+	0.229710i
$336$		0			0
$337$	4.37194	−	7.57242i	0.238155	−	0.412496i	−0.722030	−	0.691862i	$-0.756791\pi$
$337$	4.37194	−	7.57242i	0.238155	−	0.412496i	0.960185	+	0.279366i	$0.0901242\pi$
$338$	0.0583068	−	6.79300i	0.00317147	−	0.369490i
$339$		0			0
$340$	−6.67986	+	6.45437i	−0.362266	+	0.350037i
$341$	22.8983	+	22.8983i	1.24001	+	1.24001i
$342$		0			0
$343$	3.90537			0.210870
$344$	−5.72584	+	19.3607i	−0.308717	+	1.04386i
$345$		0			0
$346$	−2.49538	+	2.45291i	−0.134153	+	0.131869i
$347$	−0.832493	−	3.10690i	−0.0446905	−	0.166787i	0.939974	−	0.341246i	$-0.110849\pi$
$347$	−0.832493	−	3.10690i	−0.0446905	−	0.166787i	−0.984664	+	0.174459i	$0.944182\pi$
$348$		0			0
$349$	8.57705	−	32.0100i	0.459119	−	1.71346i	−0.216568	−	0.976268i	$-0.569486\pi$
$349$	8.57705	−	32.0100i	0.459119	−	1.71346i	0.675687	−	0.737188i	$-0.263847\pi$
$350$	1.18827	−	0.672516i	0.0635157	−	0.0359475i
$351$		0			0
$352$	−3.90965	−	17.5756i	−0.208385	−	0.936782i
$353$	7.18886	−	4.15049i	0.382624	−	0.220908i	−0.296335	−	0.955084i	$-0.595765\pi$
$353$	7.18886	−	4.15049i	0.382624	−	0.220908i	0.678959	+	0.734176i	$0.262431\pi$
$354$		0			0
$355$	−3.45099	−	12.8793i	−0.183160	−	0.683561i
$356$	−1.82031	−	3.28170i	−0.0964762	−	0.173930i
$357$		0			0
$358$	18.4691	−	4.77925i	0.976120	−	0.252591i
$359$		−	17.1616i		−	0.905754i	−0.891573	−	0.452877i	$-0.850398\pi$
$359$		−	17.1616i		−	0.905754i	0.891573	−	0.452877i	$-0.149602\pi$
$360$		0			0
$361$		−	14.7612i		−	0.776903i
$362$	−3.42647	−	13.2413i	−0.180091	−	0.695949i
$363$		0			0
$364$	0.442312	−	1.54420i	0.0231834	−	0.0809379i
$365$	3.00621	+	11.2193i	0.157352	+	0.587246i
$366$		0			0
$367$	−1.27977	+	0.738875i	−0.0668034	+	0.0385690i	−0.533030	−	0.846097i	$-0.678947\pi$
$367$	−1.27977	+	0.738875i	−0.0668034	+	0.0385690i	0.466226	+	0.884666i	$0.345613\pi$
$368$	−6.42502	+	3.42097i	−0.334927	+	0.178331i
$369$		0			0
$370$	−2.17625	−	3.84522i	−0.113138	−	0.199903i
$371$	0.881424	−	3.28952i	0.0457612	−	0.170783i
$372$		0			0
$373$	8.48049	+	31.6496i	0.439103	+	1.63876i	0.731052	+	0.682322i	$0.239030\pi$
$373$	8.48049	+	31.6496i	0.439103	+	1.63876i	−0.291948	+	0.956434i	$0.594304\pi$
$374$	−11.7393	−	11.9426i	−0.607025	−	0.617536i
$375$		0			0
$376$	14.8166	+	27.2607i	0.764106	+	1.40587i
$377$	11.3521			0.584661
$378$		0			0
$379$	19.2548	+	19.2548i	0.989053	+	0.989053i	0.999941	−	0.0108880i	$-0.00346583\pi$
$379$	19.2548	+	19.2548i	0.989053	+	0.989053i	−0.0108880	+	0.999941i	$0.503466\pi$
$380$	−14.5050	−	0.249022i	−0.744092	−	0.0127746i
$381$		0			0
$382$	−20.0423	−	0.172031i	−1.02545	−	0.00880186i
$383$	3.99635	−	6.92189i	0.204204	−	0.353692i	−0.745675	−	0.666310i	$-0.767873\pi$
$383$	3.99635	−	6.92189i	0.204204	−	0.353692i	0.949879	+	0.312618i	$0.101206\pi$
$384$		0			0
$385$	−0.557338	−	0.965338i	−0.0284046	−	0.0491982i
$386$	−9.01383	−	15.9266i	−0.458792	−	0.810641i
$387$		0			0
$388$	18.9252	−	31.5173i	0.960782	−	1.60005i
$389$	2.21212	−	8.25574i	0.112159	−	0.418583i	−0.886900	−	0.461962i	$-0.847146\pi$
$389$	2.21212	−	8.25574i	0.112159	−	0.418583i	0.999059	+	0.0433793i	$0.0138124\pi$
$390$		0			0
$391$	−3.38502	+	5.86303i	−0.171188	+	0.296506i
$392$	10.2215	−	16.6960i	0.516261	−	0.843277i
$393$		0			0
$394$	−15.5342	+	4.01980i	−0.782602	+	0.202514i
$395$	−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	$0.464929\pi$
$398$	−7.83606	+	13.3073i	−0.392786	+	0.667037i
$399$		0			0
$400$	0.472540	−	13.7582i	0.0236270	−	0.687908i
$401$	15.4215	+	8.90359i	0.770111	+	0.444624i	0.832914	−	0.553402i	$-0.186671\pi$
$401$	15.4215	+	8.90359i	0.770111	+	0.444624i	−0.0628030	+	0.998026i	$0.520004\pi$
$402$		0			0
$403$	28.1353	+	7.53883i	1.40152	+	0.375536i
$404$	−31.3813	+	7.83379i	−1.56128	+	0.389746i
$405$		0			0
$406$	−1.51596	−	0.420178i	−0.0752357	−	0.0208531i
$407$	6.89849	−	3.98284i	0.341945	−	0.197422i
$408$		0			0
$409$	21.0100	+	12.1301i	1.03888	+	0.599797i	0.919515	−	0.393054i	$-0.128581\pi$
$409$	21.0100	+	12.1301i	1.03888	+	0.599797i	0.119363	+	0.992851i	$0.461915\pi$
$410$	6.60436	+	6.71871i	0.326166	+	0.331814i
$411$		0			0
$412$	−0.244515	−	0.00419784i	−0.0120464	−	0.000206813i
$413$	1.10595	−	1.10595i	0.0544202	−	0.0544202i
$414$		0			0
$415$		−	2.83946i		−	0.139383i
$416$	−10.9499	−	11.9325i	−0.536864	−	0.585041i
$417$		0			0
$418$	0.224485	−	26.1535i	0.0109799	−	1.27921i
$419$	−11.0392	+	2.95796i	−0.539302	+	0.144506i	−0.518180	−	0.855271i	$-0.673390\pi$
$419$	−11.0392	+	2.95796i	−0.539302	+	0.144506i	−0.0211217	+	0.999777i	$0.506724\pi$
$420$		0			0
$421$	16.7104	+	4.47753i	0.814413	+	0.218221i	0.641903	−	0.766786i	$-0.278145\pi$
$421$	16.7104	+	4.47753i	0.814413	+	0.218221i	0.172511	+	0.985008i	$0.444812\pi$
$422$	23.0131	+	6.37853i	1.12026	+	0.310502i
$423$		0			0
$424$	−23.6461	−	24.8964i	−1.14836	−	1.20907i
$425$	−6.40186	−	11.0883i	−0.310536	−	0.537864i
$426$		0			0
$427$	1.74819	−	0.468425i	0.0846006	−	0.0226687i
$428$	16.2427	+	4.65247i	0.785120	+	0.224886i
$429$		0			0
$430$	10.8593	+	6.39449i	0.523680	+	0.308370i
$431$	−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	$0.788253\pi$
$434$	−3.47816	−	2.04812i	−0.166957	−	0.0983129i
$435$		0			0
$436$	−2.65517	+	9.26972i	−0.127160	+	0.443939i
$437$	−10.2133	+	2.73664i	−0.488567	+	0.130911i
$438$		0			0
$439$	−14.7258	−	25.5058i	−0.702824	−	1.21733i	−0.967471	−	0.252982i	$-0.918589\pi$
$439$	−14.7258	−	25.5058i	−0.702824	−	1.21733i	0.264647	−	0.964345i	$-0.414745\pi$
$440$	−11.2349	−	0.289356i	−0.535601	−	0.0137945i
$441$		0			0
$442$	−14.5156	−	4.02329i	−0.690437	−	0.191368i
$443$	8.80422	+	2.35908i	0.418301	+	0.112083i	0.461830	−	0.886969i	$-0.347193\pi$
$443$	8.80422	+	2.35908i	0.418301	+	0.112083i	−0.0435282	+	0.999052i	$0.513860\pi$
$444$		0			0
$445$	−2.26259	+	0.606260i	−0.107257	+	0.0287395i
$446$	0.173218	−	20.1807i	0.00820213	−	0.955584i
$447$		0			0
$448$	1.02059	+	1.99877i	0.0482184	+	0.0944329i
$449$		−	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
$452$	−0.0758469	+	4.41792i	−0.00356754	+	0.207802i
$453$		0			0
$454$	8.72971	+	8.88087i	0.409706	+	0.416800i
$455$	−0.868300	−	0.501313i	−0.0407065	−	0.0235019i
$456$		0			0
$457$	1.90950	−	1.10245i	0.0893226	−	0.0515704i	−0.454673	−	0.890658i	$-0.650244\pi$
$457$	1.90950	−	1.10245i	0.0893226	−	0.0515704i	0.543996	+	0.839088i	$0.316911\pi$
$458$	33.9728	+	9.41623i	1.58744	+	0.439992i
$459$		0			0
$460$	1.10043	+	4.40818i	0.0513076	+	0.205532i
$461$	19.1849	+	5.14058i	0.893531	+	0.239421i	0.676236	−	0.736685i	$-0.263610\pi$
$461$	19.1849	+	5.14058i	0.893531	+	0.239421i	0.217295	+	0.976106i	$0.430277\pi$
$462$		0			0
$463$	−1.39347	−	0.804523i	−0.0647602	−	0.0373893i	0.467270	−	0.884115i	$-0.345238\pi$
$463$	−1.39347	−	0.804523i	−0.0647602	−	0.0373893i	−0.532031	+	0.846725i	$0.678571\pi$
$464$	−11.5936	+	10.8236i	−0.538217	+	0.502474i
$465$		0			0
$466$	−4.67365	+	7.93688i	−0.216503	+	0.367669i
$467$	9.94383	+	9.94383i	0.460145	+	0.460145i	0.898703	−	0.438558i	$-0.144511\pi$
$467$	9.94383	+	9.94383i	0.460145	+	0.460145i	−0.438558	+	0.898703i	$0.644511\pi$
$468$		0			0
$469$	0.771428	−	0.771428i	0.0356213	−	0.0356213i
$470$	18.7491	−	4.85171i	0.864831	−	0.223793i
$471$		0			0
$472$	−3.68787	−	15.3320i	−0.169748	−	0.705713i
$473$	−11.3600	+	19.6760i	−0.522331	+	0.904704i
$474$		0			0
$475$	5.17561	−	19.3156i	0.237473	−	0.886262i
$476$	1.78950	+	1.07454i	0.0820217	+	0.0492516i
$477$		0			0
$478$	3.30045	+	5.83157i	0.150959	+	0.266730i
$479$	−14.3867	−	24.9185i	−0.657346	−	1.13856i	−0.981300	−	0.192483i	$-0.938346\pi$
$479$	−14.3867	−	24.9185i	−0.657346	−	1.13856i	0.323955	−	0.946073i	$-0.394987\pi$
$480$		0			0
$481$	3.58248	−	6.20504i	0.163347	−	0.282925i
$482$	−21.0372	−	0.180570i	−0.958219	−	0.00822475i
$483$		0			0
$484$	−0.0298393	+	1.73808i	−0.00135633	+	0.0790034i
$485$	−16.2259	−	16.2259i	−0.736778	−	0.736778i
$486$		0			0
$487$	43.0194			1.94939			0.974697	−	0.223530i	$-0.0717581\pi$
$487$	43.0194			1.94939			0.974697	+	0.223530i	$0.0717581\pi$
$488$	5.17507	−	17.4984i	0.234265	−	0.792116i
$489$		0			0
$490$	−8.56588	−	8.71420i	−0.386967	−	0.393667i
$491$	−1.40962	−	5.26076i	−0.0636152	−	0.237415i	0.926796	−	0.375565i	$-0.122551\pi$
$491$	−1.40962	−	5.26076i	−0.0636152	−	0.237415i	−0.990411	+	0.138150i	$0.955885\pi$
$492$		0			0
$493$	−3.81801	+	14.2490i	−0.171955	+	0.641744i
$494$	−11.5874	−	20.4738i	−0.521341	−	0.921159i
$495$		0			0
$496$	−35.9217	+	19.1264i	−1.61293	+	0.858800i
$497$	−2.59488	+	1.49815i	−0.116396	+	0.0672013i
$498$		0			0
$499$	−4.61454	−	17.2217i	−0.206575	−	0.770950i	−0.988964	−	0.148159i	$-0.952665\pi$
$499$	−4.61454	−	17.2217i	−0.206575	−	0.770950i	0.782388	−	0.622791i	$-0.214001\pi$
$500$	−20.2616	−	5.80364i	−0.906128	−	0.259547i
$501$		0			0
$502$	−3.45469	−	13.3504i	−0.154191	−	0.595858i
$503$			0.254767i			0.0113595i	0.999984	+	0.00567974i	$0.00180793\pi$
$503$			0.254767i			0.0113595i	−0.999984	+	0.00567974i	$0.998192\pi$
$504$		0			0
$505$			20.1888i			0.898391i
$506$	−7.93004	+	2.05206i	−0.352533	+	0.0912252i
$507$		0			0
$508$	−6.36506	+	3.53060i	−0.282404	+	0.156645i
$509$	−2.84712	−	10.6256i	−0.126196	−	0.470971i	0.873683	−	0.486495i	$-0.161725\pi$
$509$	−2.84712	−	10.6256i	−0.126196	−	0.470971i	−0.999879	+	0.0155245i	$0.995058\pi$
$510$		0			0
$511$	2.26043	−	1.30506i	0.0999956	−	0.0577325i
$512$	22.5599	+	1.74619i	0.997018	+	0.0771716i
$513$		0			0
$514$	3.09015	−	1.74891i	0.136301	−	0.0771410i
$515$	−0.0395075	+	0.147444i	−0.00174091	+	0.00649716i
$516$		0			0
$517$	9.03680	+	33.7258i	0.397438	+	1.48326i
$518$	−0.708074	+	0.696023i	−0.0311110	+	0.0305815i
$519$		0			0
$520$	−8.88175	+	4.82735i	−0.389491	+	0.211693i
$521$	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	0.411562	−	0.911382i	$-0.364983\pi$
$523$	−11.4305	−	11.4305i	−0.499820	−	0.499820i	−0.911382	+	0.411562i	$0.864983\pi$
$524$	−21.5655	−	22.3189i	−0.942095	−	0.975008i
$525$		0			0
$526$	−0.0441112	+	5.13914i	−0.00192334	+	0.224077i
$527$	−18.9254	+	32.7797i	−0.824403	+	1.42791i
$528$		0			0
$529$	−9.84425	−	17.0507i	−0.428011	−	0.741337i
$530$	−18.6521	+	10.5564i	−0.810193	+	0.458539i
$531$		0			0
$532$	0.789579	+	3.16296i	0.0342326	+	0.137132i
$533$	−3.95417	+	14.7572i	−0.171274	+	0.639204i
$534$		0			0
$535$	5.27308	−	9.13325i	0.227975	−	0.394865i
$536$	−2.57239	−	10.6945i	−0.111110	−	0.461931i
$537$		0			0
$538$	6.19447	+	23.9381i	0.267063	+	1.03204i
$539$	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	$0.652298\pi$
$542$	33.2269	+	19.5657i	1.42722	+	0.840420i
$543$		0			0
$544$	18.6604	−	9.73101i	0.800058	−	0.417214i
$545$	5.21235	+	3.00935i	0.223273	+	0.128906i
$546$		0			0
$547$	2.81747	+	0.754938i	0.120466	+	0.0322788i	0.318548	−	0.947907i	$-0.396805\pi$
$547$	2.81747	+	0.754938i	0.120466	+	0.0322788i	−0.198082	+	0.980185i	$0.563471\pi$
$548$	−21.4287	+	35.6865i	−0.915388	+	1.52445i
$549$		0			0
$550$	4.13779	−	14.9287i	0.176436	−	0.636562i
$551$	−19.9527	+	11.5197i	−0.850012	+	0.490755i
$552$		0			0
$553$	2.44341	+	1.41070i	0.103904	+	0.0599891i
$554$	17.4412	−	17.1444i	0.741007	−	0.728395i
$555$		0			0
$556$	−1.15394	−	1.19426i	−0.0489380	−	0.0506477i
$557$	−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
$560$	1.36475	−	0.315902i	0.0576711	−	0.0133493i
$561$		0			0
$562$	−19.9312	−	0.171077i	−0.840749	−	0.00721646i
$563$	7.42718	−	1.99011i	0.313018	−	0.0838730i	−0.0988898	−	0.995098i	$-0.531529\pi$
$563$	7.42718	−	1.99011i	0.313018	−	0.0838730i	0.411908	+	0.911225i	$0.364862\pi$
$564$		0			0
$565$	2.66403	+	0.713826i	0.112077	+	0.0300309i
$566$	−0.245887	+	0.887133i	−0.0103354	+	0.0372890i
$567$		0			0
$568$	−0.777802	+	30.1998i	−0.0326359	+	1.26716i
$569$	11.7897	+	20.4204i	0.494250	+	0.856066i	0.999978	−	0.00662697i	$-0.00210945\pi$
$569$	11.7897	+	20.4204i	0.494250	+	0.856066i	−0.505728	+	0.862693i	$0.668776\pi$
$570$		0			0
$571$	−7.46185	+	1.99940i	−0.312269	+	0.0836722i	−0.411550	−	0.911387i	$-0.635012\pi$
$571$	−7.46185	+	1.99940i	−0.312269	+	0.0836722i	0.0992811	+	0.995059i	$0.468346\pi$
$572$	−8.84019	−	15.9373i	−0.369627	−	0.666373i
$573$		0			0
$574$	1.07425	−	1.82432i	0.0448385	−	0.0761456i
$575$	−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	$0.388941\pi$
$578$	−2.26707	+	3.84998i	−0.0942976	+	0.160138i
$579$		0			0
$580$	4.80210	+	8.65737i	0.199397	+	0.359478i
$581$	−0.616336	+	0.165147i	−0.0255699	+	0.00685144i
$582$		0			0
$583$	−19.3196	−	33.4626i	−0.800137	−	1.38588i
$584$	0.677554	−	26.3075i	0.0280374	−	1.08861i
$585$		0			0
$586$	−3.16435	+	11.4166i	−0.130718	+	0.471617i
$587$	44.0249	+	11.7964i	1.81710	+	0.486891i	0.996424	−	0.0844969i	$-0.0269283\pi$
$587$	44.0249	+	11.7964i	1.81710	+	0.486891i	0.820680	+	0.571388i	$0.193595\pi$
$588$		0			0
$589$	−57.1015	+	15.3003i	−2.35283	+	0.630438i
$590$	−9.84262	−	0.0844828i	−0.405214	−	0.00347810i
$591$		0			0
$592$	2.25750	+	9.75275i	0.0927825	+	0.400836i
$593$		−	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
$596$	7.39060	+	7.64880i	0.302731	+	0.313307i
$597$		0			0
$598$	−5.25437	+	5.16494i	−0.214867	+	0.211210i
$599$	8.99479	+	5.19314i	0.367517	+	0.212186i	0.672373	−	0.740212i	$-0.265275\pi$
$599$	8.99479	+	5.19314i	0.367517	+	0.212186i	−0.304856	+	0.952398i	$0.598608\pi$
$600$		0			0
$601$	−16.6353	+	9.60440i	−0.678569	+	0.391772i	−0.799316	−	0.600912i	$-0.794804\pi$
$601$	−16.6353	+	9.60440i	−0.678569	+	0.391772i	0.120747	+	0.992683i	$0.461471\pi$
$602$	0.756407	−	2.72903i	0.0308288	−	0.111227i
$603$		0			0
$604$	−3.16055	+	5.26345i	−0.128601	+	0.214167i
$605$	1.04807	+	0.280829i	0.0426101	+	0.0114173i
$606$		0			0
$607$	−12.1261	−	7.00100i	−0.492183	−	0.284162i	0.233297	−	0.972406i	$-0.425049\pi$
$607$	−12.1261	−	7.00100i	−0.492183	−	0.284162i	−0.725480	+	0.688244i	$0.758382\pi$
$608$	31.3546	+	9.86134i	1.27160	+	0.399930i
$609$		0			0
$610$	−9.81470	−	5.77941i	−0.397386	−	0.234001i
$611$	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	$0.0799304\pi$
$614$	5.07302	+	19.6043i	0.204730	+	0.791165i
$615$		0			0
$616$	0.590627	+	2.45548i	0.0237970	+	0.0989341i
$617$	24.3668	−	42.2045i	0.980970	−	1.69909i	0.322340	−	0.946624i	$-0.395531\pi$
$617$	24.3668	−	42.2045i	0.980970	−	1.69909i	0.658630	−	0.752467i	$-0.271136\pi$
$618$		0			0
$619$	−2.99775	+	11.1877i	−0.120490	+	0.449673i	−0.999639	−	0.0268731i	$-0.991445\pi$
$619$	−2.99775	+	11.1877i	−0.120490	+	0.449673i	0.879149	+	0.476547i	$0.158112\pi$
$620$	6.15239	+	24.6457i	0.247086	+	0.989797i
$621$		0			0
$622$	−19.5906	+	11.0875i	−0.785511	+	0.444570i
$623$	0.263191	+	0.455861i	0.0105445	+	0.0182637i
$624$		0			0
$625$	2.02612	−	3.50934i	0.0810447	−	0.140374i
$626$	0.138796	−	16.1704i	0.00554742	−	0.646299i
$627$		0			0
$628$	8.11292	+	8.39635i	0.323741	+	0.335051i
$629$	6.58363	+	6.58363i	0.262506	+	0.262506i
$630$		0			0
$631$	1.63509			0.0650918			0.0325459	−	0.999470i	$-0.489638\pi$
$631$	1.63509			0.0650918			0.0325459	+	0.999470i	$0.489638\pi$
$632$	24.9934	−	13.5842i	0.994182	−	0.540351i
$633$		0			0
$634$	27.5316	−	27.0630i	1.09342	−	1.07481i
$635$	1.17588	+	4.38844i	0.0466633	+	0.174150i
$636$		0			0
$637$	5.12858	−	19.1401i	0.203202	−	0.758359i
$638$	−15.5332	+	8.79120i	−0.614965	+	0.348047i
$639$		0			0
$640$	4.46806	−	13.3983i	0.176616	−	0.529616i
$641$	33.5608	−	19.3763i	1.32557	−	0.765319i	0.340960	−	0.940078i	$-0.389248\pi$
$641$	33.5608	−	19.3763i	1.32557	−	0.765319i	0.984611	+	0.174759i	$0.0559148\pi$
$642$		0			0
$643$	5.22528	+	19.5010i	0.206065	+	0.769044i	0.989122	+	0.147095i	$0.0469924\pi$
$643$	5.22528	+	19.5010i	0.206065	+	0.769044i	−0.783058	+	0.621949i	$0.786341\pi$
$644$	0.892842	−	0.495245i	0.0351829	−	0.0195154i
$645$		0			0
$646$	29.5957	−	7.65850i	1.16443	−	0.301320i
$647$			28.2882i			1.11212i	0.831141	+	0.556062i	$0.187688\pi$
$647$			28.2882i			1.11212i	−0.831141	+	0.556062i	$0.812312\pi$
$648$		0			0
$649$		−	17.7456i		−	0.696575i
$650$	−3.49080	−	13.4899i	−0.136920	−	0.529119i
$651$		0			0
$652$	34.1421	+	9.77950i	1.33711	+	0.382995i
$653$	−0.228971	−	0.854532i	−0.00896033	−	0.0334404i	0.961301	−	0.275500i	$-0.0888436\pi$
$653$	−0.228971	−	0.854532i	−0.00896033	−	0.0334404i	−0.970261	+	0.242060i	$0.922177\pi$
$654$		0			0
$655$	−16.7766	+	9.68599i	−0.655517	+	0.378463i
$656$	−10.0319	−	18.8412i	−0.391681	−	0.735625i
$657$		0			0
$658$	−2.14359	−	3.78752i	−0.0835659	−	0.147653i
$659$	−13.0375	+	48.6567i	−0.507869	+	1.89539i	−0.0671656	+	0.997742i	$0.521396\pi$
$659$	−13.0375	+	48.6567i	−0.507869	+	1.89539i	−0.440704	+	0.897653i	$0.645271\pi$
$660$		0			0
$661$	−7.17239	−	26.7677i	−0.278974	−	1.04114i	−0.953131	−	0.302557i	$-0.902160\pi$
$661$	−7.17239	−	26.7677i	−0.278974	−	1.04114i	0.674158	−	0.738587i	$-0.264507\pi$
$662$	11.3952	+	11.5925i	0.442886	+	0.450555i
$663$		0			0
$664$	−1.82451	+	6.16920i	−0.0708048	+	0.239411i
$665$	2.03486			0.0789086
$666$		0			0
$667$	5.10222	+	5.10222i	0.197559	+	0.197559i
$668$	−0.479010	+	27.9013i	−0.0185334	+	1.07953i
$669$		0			0
$670$	−6.86548	−	0.0589290i	−0.265237	−	0.00227663i
$671$	10.2672	−	17.7834i	0.396363	−	0.686520i
$672$		0			0
$673$	−16.5237	−	28.6198i	−0.636941	−	1.10321i	−0.986100	−	0.166150i	$-0.946866\pi$
$673$	−16.5237	−	28.6198i	−0.636941	−	1.10321i	0.349160	−	0.937063i	$-0.386467\pi$
$674$	6.09071	+	10.7617i	0.234605	+	0.414525i
$675$		0			0
$676$	8.23631	+	4.94566i	0.316781	+	0.190218i
$677$	−2.69118	+	10.0436i	−0.103430	+	0.386007i	−0.998162	−	0.0605961i	$-0.980700\pi$
$677$	−2.69118	+	10.0436i	−0.103430	+	0.386007i	0.894732	+	0.446603i	$0.147367\pi$
$678$		0			0
$679$	−2.57829	+	4.46572i	−0.0989455	+	0.171379i
$680$	−3.07207	−	12.7719i	−0.117809	−	0.489779i
$681$		0			0
$682$	−44.3362	+	11.4729i	−1.69772	+	0.439320i
$683$	9.18142	−	9.18142i	0.351317	−	0.351317i	−0.509282	−	0.860600i	$-0.670089\pi$
$683$	9.18142	−	9.18142i	0.351317	−	0.351317i	0.860600	+	0.509282i	$0.170089\pi$
$684$		0			0
$685$	18.3723	+	18.3723i	0.701968	+	0.701968i
$686$	−2.80247	+	4.75920i	−0.106999	+	0.181707i
$687$		0			0
$688$	−19.4847	−	20.8708i	−0.742848	−	0.795691i
$689$	−30.0988	−	17.3776i	−1.14667	−	0.662033i
$690$		0			0
$691$	24.3744	+	6.53111i	0.927247	+	0.248455i	0.690680	−	0.723160i	$-0.257311\pi$
$691$	24.3744	+	6.53111i	0.927247	+	0.248455i	0.236567	+	0.971615i	$0.423978\pi$
$692$	−1.19852	−	4.80114i	−0.0455610	−	0.182512i
$693$		0			0
$694$	4.38356	+	1.21499i	0.166398	+	0.0461204i
$695$	−0.897694	+	0.518284i	−0.0340515	+	0.0196596i
$696$		0			0
$697$	−17.1932	−	9.92649i	−0.651239	−	0.375993i
$698$	32.8535	+	33.4224i	1.24352	+	1.26506i
$699$		0			0
$700$	−0.0331455	+	1.93066i	−0.00125278	+	0.0729719i
$701$	−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
$704$	24.2237	+	7.84770i	0.912965	+	0.295771i
$705$		0			0
$706$	−0.100760	+	11.7389i	−0.00379213	+	0.441800i
$707$	4.38221	−	1.17421i	0.164810	−	0.0441607i
$708$		0			0
$709$	41.1714	+	11.0318i	1.54622	+	0.414310i	0.928271	−	0.371905i	$-0.121295\pi$
$709$	41.1714	+	11.0318i	1.54622	+	0.414310i	0.617953	+	0.786215i	$0.287962\pi$
$710$	18.1715	+	5.03659i	0.681964	+	0.189020i
$711$		0			0
$712$	5.30542	+	0.136642i	0.198829	+	0.00512088i
$713$	9.25715	+	16.0339i	0.346683	+	0.600473i
$714$		0			0
$715$	−10.9881	+	2.94426i	−0.410932	+	0.110109i
$716$	−7.42912	+	25.9365i	−0.277639	+	0.969293i
$717$		0			0
$718$	20.9136	+	12.3150i	0.780490	+	0.459593i
$719$	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
$722$	17.9884	+	10.5925i	0.669459	+	0.394212i
$723$		0			0
$724$	18.5951	+	5.32629i	0.691082	+	0.197950i
$725$	−13.1814	+	3.53195i	−0.489545	+	0.131173i
$726$		0			0
$727$	11.4146	+	19.7707i	0.423344	+	0.733254i	0.996264	−	0.0863576i	$-0.0275228\pi$
$727$	11.4146	+	19.7707i	0.423344	+	0.733254i	−0.572920	+	0.819611i	$0.694189\pi$
$728$	1.56441	+	1.64712i	0.0579807	+	0.0610463i
$729$		0			0
$730$	−15.8294	−	4.38744i	−0.585873	−	0.162387i
$731$	−25.6512	−	6.87321i	−0.948743	−	0.254215i
$732$		0			0
$733$	−28.8645	+	7.73423i	−1.06614	+	0.285670i	−0.748905	−	0.662678i	$-0.769420\pi$
$733$	−28.8645	+	7.73423i	−1.06614	+	0.285670i	−0.317232	+	0.948348i	$0.602753\pi$
$734$	0.0179373	−	2.08978i	0.000662079	−	0.0771351i
$735$		0			0
$736$	0.441643	−	10.2846i	0.0162792	−	0.379095i
$737$		−	12.3780i		−	0.455950i
$738$		0			0
$739$	6.92568	−	6.92568i	0.254765	−	0.254765i	−0.568156	−	0.822921i	$-0.692343\pi$
$739$	6.92568	−	6.92568i	0.254765	−	0.254765i	0.822921	+	0.568156i	$0.192343\pi$
$740$	6.24756	+	0.107258i	0.229665	+	0.00394289i
$741$		0			0
$742$	3.37620	+	3.43467i	0.123944	+	0.126091i
$743$	−27.7583	−	16.0262i	−1.01835	−	0.587946i	−0.104726	−	0.994501i	$-0.533397\pi$
$743$	−27.7583	−	16.0262i	−1.01835	−	0.587946i	−0.913626	+	0.406555i	$0.866730\pi$
$744$		0			0
$745$	5.74942	−	3.31943i	0.210642	−	0.121614i
$746$	−44.6548	−	12.3770i	−1.63493	−	0.453153i
$747$		0			0
$748$	22.9776	−	5.73597i	0.840145	−	0.209728i
$749$	−2.28916	−	0.613380i	−0.0836442	−	0.0224124i
$750$		0			0
$751$	−7.35037	−	4.24374i	−0.268219	−	0.154856i	0.359859	−	0.933007i	$-0.382825\pi$
$751$	−7.35037	−	4.24374i	−0.268219	−	0.154856i	−0.628078	+	0.778151i	$0.716158\pi$
$752$	−43.8530	−	1.50618i	−1.59916	−	0.0549248i
$753$		0			0
$754$	−8.14615	+	13.8340i	−0.296665	+	0.503803i
$755$	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	$0.378201\pi$
$758$	−37.2816	+	9.64738i	−1.35413	+	0.350409i
$759$		0			0
$760$	10.7122	−	17.4976i	0.388571	−	0.634704i
$761$	−1.63439	+	2.83084i	−0.0592465	+	0.102618i	−0.894127	−	0.447813i	$-0.852203\pi$
$761$	−1.63439	+	2.83084i	−0.0592465	+	0.102618i	0.834881	+	0.550431i	$0.185536\pi$
$762$		0			0
$763$	0.350056	−	1.30643i	0.0126729	−	0.0472959i
$764$	14.5919	−	24.3007i	0.527915	−	0.879170i
$765$		0			0
$766$	5.56747	+	9.83718i	0.201161	+	0.355432i
$767$	−7.98088	−	13.8233i	−0.288173	−	0.499130i
$768$		0			0
$769$	19.1814	−	33.2232i	0.691701	−	1.19806i	−0.279580	−	0.960123i	$-0.590195\pi$
$769$	19.1814	−	33.2232i	0.691701	−	1.19806i	0.971280	−	0.237938i	$-0.0764716\pi$
$770$	1.57633	+	0.0135302i	0.0568071	+	0.000487596i
$771$		0			0
$772$	25.8769	+	0.444254i	0.931328	+	0.0159891i
$773$	−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
$776$	24.8274	+	45.6794i	0.891251	+	1.63980i
$777$		0			0
$778$	8.47329	+	8.62001i	0.303782	+	0.309042i
$779$	−8.02512	−	29.9501i	−0.287530	−	1.07308i
$780$		0			0
$781$	−8.79878	+	32.8375i	−0.314845	+	1.17502i
$782$	−4.71580	−	8.33236i	−0.168637	−	0.297965i
$783$		0			0
$784$	13.0114	+	24.4371i	0.464694	+	0.872754i
$785$	6.31134	−	3.64385i	0.225261	−	0.130055i
$786$		0			0
$787$	2.45116	+	9.14785i	0.0873744	+	0.326086i	0.995753	−	0.0920625i	$-0.0293460\pi$
$787$	2.45116	+	9.14785i	0.0873744	+	0.326086i	−0.908379	+	0.418148i	$0.862679\pi$
$788$	6.24859	−	21.8150i	0.222597	−	0.777128i
$789$		0			0
$790$	−4.44818	−	17.1896i	−0.158259	−	0.611580i
$791$		−	0.619775i		−	0.0220367i
$792$		0			0
$793$		−	18.4703i		−	0.655900i
$794$	−42.5871	+	11.0203i	−1.51136	+	0.391095i
$795$		0			0
$796$	−10.5936	−	19.0985i	−0.375482	−	0.676929i
$797$	−7.19855	−	26.8654i	−0.254986	−	0.951620i	−0.968098	−	0.250571i	$-0.919382\pi$
$797$	−7.19855	−	26.8654i	−0.254986	−	0.951620i	0.713112	−	0.701050i	$-0.247285\pi$
$798$		0			0
$799$	−35.3432	+	20.4054i	−1.25035	+	0.721891i
$800$	16.4270	+	10.4486i	0.580783	+	0.369414i
$801$		0			0
$802$	−21.9165	+	12.4039i	−0.773899	+	0.437998i
$803$	7.66474	−	28.6052i	0.270483	−	1.00946i
$804$		0			0
$805$	−0.164943	−	0.615577i	−0.00581349	−	0.0216962i
$806$	−29.3768	+	28.8767i	−1.03475	+	1.01714i
$807$		0			0
$808$	12.9725	−	43.8636i	0.456370	−	1.54312i
$809$	−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	0.596618	−	0.802525i	$-0.296511\pi$
$811$	−5.86383	−	5.86383i	−0.205907	−	0.205907i	−0.802525	+	0.596618i	$0.796511\pi$
$812$	1.59988	−	1.54587i	0.0561448	−	0.0542496i
$813$		0			0
$814$	−0.0966897	+	11.2648i	−0.00338897	+	0.394830i
$815$	11.0840	−	19.1981i	0.388256	−	0.672480i
$816$		0			0
$817$	−20.7378	−	35.9189i	−0.725524	−	1.25664i
$818$	−29.8588	+	16.8990i	−1.04399	+	0.590858i
$819$		0			0
$820$	−12.9269	+	3.22697i	−0.451426	+	0.112691i
$821$	0.828375	−	3.09154i	0.0289105	−	0.107895i	−0.949963	−	0.312363i	$-0.898880\pi$
$821$	0.828375	−	3.09154i	0.0289105	−	0.107895i	0.978873	+	0.204467i	$0.0655462\pi$
$822$		0			0
$823$	−20.9908	+	36.3572i	−0.731695	+	1.26733i	0.224464	+	0.974482i	$0.427937\pi$
$823$	−20.9908	+	36.3572i	−0.731695	+	1.26733i	−0.956158	+	0.292850i	$0.905396\pi$
$824$	0.180578	−	0.294961i	0.00629073	−	0.0102755i
$825$		0			0
$826$	0.554122	+	2.14136i	0.0192804	+	0.0745076i
$827$	12.7209	−	12.7209i	0.442348	−	0.442348i	−0.450453	−	0.892800i	$-0.648737\pi$
$827$	12.7209	−	12.7209i	0.442348	−	0.442348i	0.892800	+	0.450453i	$0.148737\pi$
$828$		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	$0.832318\pi$
$830$	3.46025	+	2.03757i	0.120107	+	0.0707252i
$831$		0			0
$832$	22.3989	−	4.78120i	0.776544	−	0.165758i
$833$	22.2996	+	12.8747i	0.772637	+	0.446082i
$834$		0			0
$835$	16.8246	+	4.50815i	0.582241	+	0.156011i
$836$	31.7104	+	19.0411i	1.09673	+	0.658552i
$837$		0			0
$838$	4.31702	−	15.5754i	0.149129	−	0.538042i
$839$	25.7863	−	14.8877i	0.890241	−	0.513981i	0.0162196	−	0.999868i	$-0.494837\pi$
$839$	25.7863	−	14.8877i	0.890241	−	0.513981i	0.874021	+	0.485888i	$0.161504\pi$
$840$		0			0
$841$	−11.4986	−	6.63872i	−0.396503	−	0.228921i
$842$	−17.4477	+	17.1507i	−0.601287	+	0.591053i
$843$		0			0
$844$	−24.2871	+	23.4672i	−0.835996	+	0.807775i
$845$	4.24025	−	4.24025i	0.145869	−	0.145869i
$846$		0			0
$847$		−	0.243829i		−	0.00837805i
$848$	47.3078	−	10.9505i	1.62456	−	0.376040i
$849$		0			0
$850$	18.1065	+	0.155415i	0.621048	+	0.00533069i
$851$	4.39903	−	1.17872i	0.150797	−	0.0404059i
$852$		0			0
$853$	−28.4092	−	7.61221i	−0.972711	−	0.260637i	−0.262739	−	0.964867i	$-0.584626\pi$
$853$	−28.4092	−	7.61221i	−0.972711	−	0.260637i	−0.709972	+	0.704230i	$0.751292\pi$
$854$	−0.683648	+	2.46653i	−0.0233940	+	0.0844029i
$855$		0			0
$856$	−17.3253	+	16.4553i	−0.592166	+	0.562429i
$857$	−14.3783	−	24.9039i	−0.491152	−	0.850700i	0.508796	−	0.860887i	$-0.330091\pi$
$857$	−14.3783	−	24.9039i	−0.491152	−	0.850700i	−0.999948	+	0.0101867i	$0.996757\pi$
$858$		0			0
$859$	9.26004	−	2.48122i	0.315949	−	0.0846582i	−0.0973599	−	0.995249i	$-0.531040\pi$
$859$	9.26004	−	2.48122i	0.315949	−	0.0846582i	0.413308	+	0.910591i	$0.364373\pi$
$860$	−15.5850	+	8.64478i	−0.531446	+	0.294784i
$861$		0			0
$862$	24.2418	−	41.1679i	0.825678	−	1.40218i
$863$	−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
$866$	23.4966	−	39.9024i	0.798446	−	1.35594i
$867$		0			0
$868$	4.99181	−	2.76888i	0.169433	−	0.0939818i
$869$	30.9207	−	8.28517i	1.04891	−	0.281055i
$870$		0			0
$871$	−5.56687	−	9.64210i	−0.188626	−	0.326710i
$872$	−9.39103	−	9.88755i	−0.318020	−	0.334835i
$873$		0			0
$874$	3.99402	−	14.4100i	0.135100	−	0.487425i
$875$	2.85557	+	0.765148i	0.0965360	+	0.0258667i
$876$		0			0
$877$	33.8645	−	9.07397i	1.14352	−	0.306406i	0.363157	−	0.931728i	$-0.381699\pi$
$877$	33.8645	−	9.07397i	1.14352	−	0.306406i	0.780367	+	0.625322i	$0.215032\pi$
$878$	41.6493	+	0.357492i	1.40560	+	0.0120648i
$879$		0			0
$880$	8.41467	−	13.4835i	0.283658	−	0.454529i
$881$		−	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	$0.568419\pi$
$883$	−35.3696	+	35.3696i	−1.19028	+	1.19028i	−0.976988	+	0.213292i	$0.931581\pi$
$884$	15.3192	−	14.8021i	0.515240	−	0.497848i
$885$		0			0
$886$	−9.19270	+	9.03623i	−0.308835	+	0.303578i
$887$	22.5037	+	12.9925i	0.755599	+	0.436246i	0.827714	−	0.561151i	$-0.189641\pi$
$887$	22.5037	+	12.9925i	0.755599	+	0.436246i	−0.0721141	+	0.997396i	$0.522975\pi$
$888$		0			0
$889$	0.884169	−	0.510475i	0.0296541	−	0.0171208i
$890$	0.884814	−	3.19231i	0.0296590	−	0.107007i
$891$		0			0
$892$	24.4685	+	14.6926i	0.819267	+	0.491945i
$893$	−61.5670	−	16.4968i	−2.06026	−	0.552045i
$894$		0			0
$895$	14.5841	+	8.42011i	0.487492	+	0.281453i
$896$	−3.16813	−	0.190577i	−0.105840	−	0.00636674i
$897$		0			0
$898$	3.40217	+	2.00337i	0.113532	+	0.0668534i
$899$	28.5261	+	28.5261i	0.951398	+	0.951398i
$900$		0			0
$901$	31.9353	−	31.9353i	1.06392	−	1.06392i
$902$	−6.01762	−	23.2546i	−0.200365	−	0.774295i
$903$		0			0
$904$	−5.32939	−	3.26270i	−0.177253	−	0.108516i
$905$	6.03678	−	10.4560i	0.200669	−	0.347569i
$906$		0			0
$907$	7.10188	−	26.5046i	0.235814	−	0.880070i	−0.741966	−	0.670437i	$-0.766106\pi$
$907$	7.10188	−	26.5046i	0.235814	−	0.880070i	0.977780	−	0.209633i	$-0.0672268\pi$
$908$	−17.0869	+	4.26545i	−0.567048	+	0.141554i
$909$		0			0
$910$	1.23400	−	0.698398i	0.0409067	−	0.0231517i
$911$	−23.4177	−	40.5606i	−0.775863	−	1.34383i	−0.934308	−	0.356466i	$-0.883982\pi$
$911$	−23.4177	−	40.5606i	−0.775863	−	1.34383i	0.158445	−	0.987368i	$-0.449352\pi$
$912$		0			0
$913$	−3.61980	+	6.26967i	−0.119798	+	0.207496i
$914$	−0.0267637	+	3.11809i	−0.000885264	+	0.103137i
$915$		0			0
$916$	−35.8535	+	34.6432i	−1.18463	+	1.14464i
$917$	3.07820	+	3.07820i	0.101651	+	0.101651i
$918$		0			0
$919$	−0.421071			−0.0138899			−0.00694493	−	0.999976i	$-0.502211\pi$
$919$	−0.421071			−0.0138899			−0.00694493	+	0.999976i	$0.502211\pi$
$920$	−6.16160	−	1.82226i	−0.203142	−	0.0600783i
$921$		0			0
$922$	−20.0314	+	19.6905i	−0.659700	+	0.648472i
$923$	7.91430	+	29.5366i	0.260503	+	0.972209i
$924$		0			0
$925$	−2.22922	+	8.31957i	−0.0732964	+	0.273546i
$926$	1.98036	−	1.12081i	0.0650788	−	0.0368321i
$927$		0			0
$928$	−4.87053	−	21.8952i	−0.159883	−	0.718745i
$929$	5.41100	−	3.12404i	0.177529	−	0.102496i	−0.408602	−	0.912713i	$-0.633984\pi$
$929$	5.41100	−	3.12404i	0.177529	−	0.102496i	0.586131	+	0.810216i	$0.300650\pi$
$930$		0			0
$931$	10.4086	+	38.8455i	0.341128	+	1.27311i
$932$	−6.31835	−	11.3909i	−0.206965	−	0.373121i
$933$		0			0
$934$	−19.2535	+	4.98223i	−0.629993	+	0.163024i
$935$		−	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	$-0.235076\pi$
$938$	0.386515	+	1.49366i	0.0126202	+	0.0487697i
$939$		0			0
$940$	−7.54176	+	26.3298i	−0.245985	+	0.858782i
$941$	−3.22526	−	12.0368i	−0.105141	−	0.392390i	0.893221	−	0.449619i	$-0.148440\pi$
$941$	−3.22526	−	12.0368i	−0.105141	−	0.392390i	−0.998361	+	0.0572290i	$0.981773\pi$
$942$		0			0
$943$	−8.40987	+	4.85544i	−0.273863	+	0.158115i
$944$	21.3305	+	6.50799i	0.694247	+	0.211817i
$945$		0			0
$946$	−15.8260	−	27.9630i	−0.514547	−	0.909154i
$947$	−3.96886	+	14.8120i	−0.128971	+	0.481325i	−0.999950	−	0.00999447i	$-0.996819\pi$
$947$	−3.96886	+	14.8120i	−0.128971	+	0.481325i	0.870979	+	0.491320i	$0.163485\pi$
$948$		0			0
$949$	−6.89426	−	25.7297i	−0.223797	−	0.835222i
$950$	19.8246	+	20.1679i	0.643196	+	0.654333i
$951$		0			0
$952$	−2.59360	+	1.40966i	−0.0840592	+	0.0456873i
$953$	−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
$956$	−9.47490	−	0.162665i	−0.306440	−	0.00526097i
$957$		0			0
$958$	40.6903	+	0.349260i	1.31464	+	0.0112841i
$959$	2.91935	−	5.05646i	0.0942707	−	0.163282i
$960$		0			0
$961$	36.2559	+	62.7971i	1.16955	+	2.02571i
$962$	4.99088	+	8.81841i	0.160913	+	0.284317i
$963$		0			0
$964$	15.3162	−	25.5070i	0.493302	−	0.821526i
$965$	4.18105	−	15.6039i	0.134593	−	0.502307i
$966$		0			0
$967$	−16.3485	+	28.3164i	−0.525732	+	0.910594i	0.473819	+	0.880622i	$0.342875\pi$
$967$	−16.3485	+	28.3164i	−0.525732	+	0.910594i	−0.999551	+	0.0299719i	$0.990458\pi$
$968$	−2.09666	−	1.28359i	−0.0673892	−	0.0412562i
$969$		0			0
$970$	31.4169	−	8.12977i	1.00874	−	0.261031i
$971$	12.2406	−	12.2406i	0.392820	−	0.392820i	−0.482871	−	0.875691i	$-0.660406\pi$
$971$	12.2406	−	12.2406i	0.392820	−	0.392820i	0.875691	+	0.482871i	$0.160406\pi$
$972$		0			0
$973$	0.164710	+	0.164710i	0.00528037	+	0.00528037i
$974$	−30.8704	+	52.4247i	−0.989151	+	1.67980i
$975$		0			0
$976$	17.6105	+	18.8632i	0.563698	+	0.603797i
$977$	−34.1771	−	19.7322i	−1.09342	−	0.631288i	−0.158938	−	0.987289i	$-0.550807\pi$
$977$	−34.1771	−	19.7322i	−1.09342	−	0.631288i	−0.934486	+	0.356000i	$0.884140\pi$
$978$		0			0
$979$	5.76880	+	1.54575i	0.184372	+	0.0494022i
$980$	16.7662	−	4.18539i	0.535577	−	0.133698i
$981$		0			0
$982$	7.42246	+	2.05728i	0.236860	+	0.0656506i
$983$	−3.78032	+	2.18257i	−0.120574	+	0.0696132i	−0.559074	−	0.829118i	$-0.688843\pi$
$983$	−3.78032	+	2.18257i	−0.120574	+	0.0696132i	0.438500	+	0.898731i	$0.355510\pi$
$984$		0			0
$985$	−12.2666	−	7.08211i	−0.390845	−	0.225655i
$986$	−14.6245	−	14.8777i	−0.465739	−	0.473804i
$987$		0			0
$988$	33.2650	+	0.571094i	1.05830	+	0.0181689i
$989$	−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	$-0.109108\pi$
$992$	2.46919	−	57.5003i	0.0783968	−	1.82564i
$993$		0			0
$994$	0.0363700	−	4.23726i	0.00115359	−	0.134398i
$995$	−13.1676	+	3.52825i	−0.417441	+	0.111853i
$996$		0			0
$997$	12.7473	+	3.41563i	0.403712	+	0.108174i	0.454960	−	0.890512i	$-0.349653\pi$
$997$	12.7473	+	3.41563i	0.403712	+	0.108174i	−0.0512486	+	0.998686i	$0.516320\pi$
$998$	24.2983	+	6.73475i	0.769148	+	0.213185i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.179.7		88
3.2	odd	2		144.2.u.a.131.16	yes	88
4.3	odd	2		1728.2.z.a.1583.7		88
9.2	odd	6	inner	432.2.v.a.35.1		88
9.7	even	3		144.2.u.a.83.22	yes	88
12.11	even	2		576.2.y.a.239.6		88
16.5	even	4		1728.2.z.a.719.7		88
16.11	odd	4	inner	432.2.v.a.395.1		88
36.7	odd	6		576.2.y.a.47.17		88
36.11	even	6		1728.2.z.a.1007.7		88
48.5	odd	4		576.2.y.a.527.17		88
48.11	even	4		144.2.u.a.59.22	yes	88
144.11	even	12	inner	432.2.v.a.251.7		88
144.43	odd	12		144.2.u.a.11.16	✓	88
144.101	odd	12		1728.2.z.a.143.7		88
144.133	even	12		576.2.y.a.335.6		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.16	✓	88	144.43	odd	12
144.2.u.a.59.22	yes	88	48.11	even	4
144.2.u.a.83.22	yes	88	9.7	even	3
144.2.u.a.131.16	yes	88	3.2	odd	2
432.2.v.a.35.1		88	9.2	odd	6	inner
432.2.v.a.179.7		88	1.1	even	1	trivial
432.2.v.a.251.7		88	144.11	even	12	inner
432.2.v.a.395.1		88	16.11	odd	4	inner
576.2.y.a.47.17		88	36.7	odd	6
576.2.y.a.239.6		88	12.11	even	2
576.2.y.a.335.6		88	144.133	even	12
576.2.y.a.527.17		88	48.5	odd	4
1728.2.z.a.143.7		88	144.101	odd	12
1728.2.z.a.719.7		88	16.5	even	4
1728.2.z.a.1007.7		88	36.11	even	6
1728.2.z.a.1583.7		88	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.717593 + 1.21863i) q^{2} +(-0.970121 - 1.74896i) q^{4} +(-1.20583 + 0.323102i) q^{5} +(0.140266 + 0.242948i) q^{7} +(2.82749 + 0.0728225i) q^{8} +(0.471556 - 1.70132i) q^{10} +(3.07444 + 0.823794i) q^{11} +(2.76539 - 0.740984i) q^{13} +(-0.396717 - 0.00340517i) q^{14} +(-2.11773 + 3.39341i) q^{16} +3.72031i q^{17} +(-4.10860 + 4.10860i) q^{19} +(1.73490 + 1.79551i) q^{20} +(-3.21010 + 3.15546i) q^{22} +(1.57595 + 0.909876i) q^{23} +(-2.98049 + 1.72078i) q^{25} +(-1.08144 + 3.90172i) q^{26} +(0.288831 - 0.481009i) q^{28} +(3.83006 + 1.02626i) q^{29} +(8.81101 + 5.08704i) q^{31} +(-2.61564 - 5.01582i) q^{32} +(-4.53369 - 2.66967i) q^{34} +(-0.247635 - 0.247635i) q^{35} +(1.76964 - 1.76964i) q^{37} +(-2.05856 - 7.95516i) q^{38} +(-3.43301 + 0.825757i) q^{40} +(-2.66819 + 4.62144i) q^{41} +(-1.84748 + 6.89490i) q^{43} +(-1.54180 - 6.17626i) q^{44} +(-2.23969 + 1.26758i) q^{46} +(5.48486 + 9.50006i) q^{47} +(3.46065 - 5.99402i) q^{49} +(0.0417747 - 4.86693i) q^{50} +(-3.97872 - 4.11772i) q^{52} +(-8.58403 - 8.58403i) q^{53} -3.97344 q^{55} +(0.378909 + 0.697147i) q^{56} +(-3.99906 + 3.93099i) q^{58} +(-1.44299 - 5.38532i) q^{59} +(1.66977 - 6.23168i) q^{61} +(-12.5219 + 7.08695i) q^{62} +(7.98939 + 0.411810i) q^{64} +(-3.09519 + 1.78701i) q^{65} +(-1.00652 - 3.75640i) q^{67} +(6.50668 - 3.60915i) q^{68} +(0.479476 - 0.124074i) q^{70} +10.6808i q^{71} -9.30419i q^{73} +(0.886658 + 3.42643i) q^{74} +(11.1716 + 3.19994i) q^{76} +(0.231101 + 0.862479i) q^{77} +(8.70990 - 5.02866i) q^{79} +(1.45721 - 4.77613i) q^{80} +(-3.71715 - 6.56784i) q^{82} +(-0.588691 + 2.19703i) q^{83} +(-1.20204 - 4.48608i) q^{85} +(-7.07659 - 7.19913i) q^{86} +(8.63296 + 2.55316i) q^{88} +1.87637 q^{89} +(0.567911 + 0.567911i) q^{91} +(0.0624738 - 3.63897i) q^{92} +(-15.5130 - 0.133153i) q^{94} +(3.62679 - 6.28179i) q^{95} +(9.19070 + 15.9188i) q^{97} +(4.82116 + 8.51852i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Introduction

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