LMFDB - Embedded newform 392.2.m.c.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(19,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$0.662827 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	392.19
Dual form			392.2.m.c.227.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 1.22474i) q^{2} +(-0.937379 + 0.541196i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.662827 - 1.14805i) q^{5} +(1.32565 + 0.765367i) q^{6} +2.82843 q^{8} +(-0.914214 + 1.58346i) q^{9} -1.87476 q^{10} +(1.00000 + 1.73205i) q^{11} -2.16478i q^{12} -5.85172 q^{13} +1.43488i q^{15} +(-2.00000 - 3.46410i) q^{16} +(-3.86324 + 2.23044i) q^{17} +2.58579 q^{18} +(3.58869 + 2.07193i) q^{19} +(1.32565 + 2.29610i) q^{20} +(1.41421 - 2.44949i) q^{22} +(7.24264 + 4.18154i) q^{23} +(-2.65131 + 1.53073i) q^{24} +(1.62132 + 2.80821i) q^{25} +(4.13779 + 7.16687i) q^{26} -5.22625i q^{27} +4.47871i q^{29} +(1.75736 - 1.01461i) q^{30} +(3.20041 + 5.54328i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-1.87476 - 1.08239i) q^{33} +(5.46345 + 3.15432i) q^{34} +(-1.82843 - 3.16693i) q^{36} +(-2.12132 - 1.22474i) q^{37} -5.86030i q^{38} +(5.48528 - 3.16693i) q^{39} +(1.87476 - 3.24718i) q^{40} -0.317025i q^{41} -3.17157 q^{43} -4.00000 q^{44} +(1.21193 + 2.09913i) q^{45} -11.8272i q^{46} +(-6.40083 + 11.0866i) q^{47} +(3.74952 + 2.16478i) q^{48} +(2.29289 - 3.97141i) q^{50} +(2.41421 - 4.18154i) q^{51} +(5.85172 - 10.1355i) q^{52} +(-3.00000 + 1.73205i) q^{53} +(-6.40083 + 3.69552i) q^{54} +2.65131 q^{55} -4.48528 q^{57} +(5.48528 - 3.16693i) q^{58} +(-0.937379 + 0.541196i) q^{59} +(-2.48528 - 1.43488i) q^{60} +(4.80062 - 8.31492i) q^{61} +(4.52607 - 7.83938i) q^{62} +8.00000 q^{64} +(-3.87868 + 6.71807i) q^{65} +3.06147i q^{66} +(-6.00000 - 10.3923i) q^{67} -8.92177i q^{68} -9.05213 q^{69} +(-2.58579 + 4.47871i) q^{72} +(6.12627 - 3.53701i) q^{73} +3.46410i q^{74} +(-3.03958 - 1.75490i) q^{75} +(-7.17738 + 4.14386i) q^{76} +(-7.75736 - 4.47871i) q^{78} +(1.75736 + 1.01461i) q^{79} -5.30262 q^{80} +(0.0857864 + 0.148586i) q^{81} +(-0.388275 + 0.224171i) q^{82} -5.67459i q^{83} +5.91359i q^{85} +(2.24264 + 3.88437i) q^{86} +(-2.42386 - 4.19825i) q^{87} +(2.82843 + 4.89898i) q^{88} +(-11.0406 - 6.37430i) q^{89} +(1.71393 - 2.96861i) q^{90} +(-14.4853 + 8.36308i) q^{92} +(-6.00000 - 3.46410i) q^{93} +18.1043 q^{94} +(4.75736 - 2.74666i) q^{95} -6.12293i q^{96} +9.23880i q^{97} -3.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{9} + 8 q^{11} - 16 q^{16} + 32 q^{18} + 24 q^{23} - 4 q^{25} + 48 q^{30} + 8 q^{36} - 24 q^{39} - 48 q^{43} - 32 q^{44} + 24 q^{50} + 8 q^{51} - 24 q^{53} + 32 q^{57} - 24 q^{58} + 48 q^{60}+ \cdots + 16 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^9 + 8 * q^11 - 16 * q^16 + 32 * q^18 + 24 * q^23 - 4 * q^25 + 48 * q^30 + 8 * q^36 - 24 * q^39 - 48 * q^43 - 32 * q^44 + 24 * q^50 + 8 * q^51 - 24 * q^53 + 32 * q^57 - 24 * q^58 + 48 * q^60 + 64 * q^64 - 48 * q^65 - 48 * q^67 - 32 * q^72 - 96 * q^78 + 48 * q^79 + 12 * q^81 - 16 * q^86 - 48 * q^92 - 48 * q^93 + 72 * q^95 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$3$	−0.937379	+	0.541196i	−0.541196	+	0.312460i	−0.745564	−	0.666435i	$-0.767820\pi$
$3$	−0.937379	+	0.541196i	−0.541196	+	0.312460i	0.204367	+	0.978894i	$0.434486\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	0.662827	−	1.14805i	0.296425	−	0.513424i	−0.678890	−	0.734240i	$-0.737539\pi$
$5$	0.662827	−	1.14805i	0.296425	−	0.513424i	0.975315	+	0.220816i	$0.0708721\pi$
$6$	1.32565	+	0.765367i	0.541196	+	0.312460i
$7$		0			0
$7$		0			0
$8$	2.82843			1.00000
$9$	−0.914214	+	1.58346i	−0.304738	+	0.527821i
$10$	−1.87476			−0.592851
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		−	2.16478i		−	0.624919i
$13$	−5.85172			−1.62298			−0.811488	−	0.584369i	$-0.801342\pi$
$13$	−5.85172			−1.62298			−0.811488	+	0.584369i	$0.801342\pi$
$14$		0			0
$15$			1.43488i			0.370484i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−3.86324	+	2.23044i	−0.936973	+	0.540962i	−0.889010	−	0.457887i	$-0.848606\pi$
$17$	−3.86324	+	2.23044i	−0.936973	+	0.540962i	−0.0479630	+	0.998849i	$0.515273\pi$
$18$	2.58579			0.609476
$19$	3.58869	+	2.07193i	0.823301	+	0.475333i	0.851554	−	0.524268i	$-0.175661\pi$
$19$	3.58869	+	2.07193i	0.823301	+	0.475333i	−0.0282522	+	0.999601i	$0.508994\pi$
$20$	1.32565	+	2.29610i	0.296425	+	0.513424i
$21$		0			0
$22$	1.41421	−	2.44949i	0.301511	−	0.522233i
$23$	7.24264	+	4.18154i	1.51019	+	0.871911i	0.999929	+	0.0118947i	$0.00378628\pi$
$23$	7.24264	+	4.18154i	1.51019	+	0.871911i	0.510266	+	0.860017i	$0.329547\pi$
$24$	−2.65131	+	1.53073i	−0.541196	+	0.312460i
$25$	1.62132	+	2.80821i	0.324264	+	0.561642i
$26$	4.13779	+	7.16687i	0.811488	+	1.40554i
$27$		−	5.22625i		−	1.00579i
$28$		0			0
$29$			4.47871i			0.831676i	0.909439	+	0.415838i	$0.136512\pi$
$29$			4.47871i			0.831676i	−0.909439	+	0.415838i	$0.863488\pi$
$30$	1.75736	−	1.01461i	0.320848	−	0.185242i
$31$	3.20041	+	5.54328i	0.574811	+	0.995602i	0.996062	+	0.0886579i	$0.0282578\pi$
$31$	3.20041	+	5.54328i	0.574811	+	0.995602i	−0.421251	+	0.906944i	$0.638409\pi$
$32$	−2.82843	+	4.89898i	−0.500000	+	0.866025i
$33$	−1.87476	−	1.08239i	−0.326354	−	0.188420i
$34$	5.46345	+	3.15432i	0.936973	+	0.540962i
$35$		0			0
$36$	−1.82843	−	3.16693i	−0.304738	−	0.527821i
$37$	−2.12132	−	1.22474i	−0.348743	−	0.201347i	0.315389	−	0.948963i	$-0.397865\pi$
$37$	−2.12132	−	1.22474i	−0.348743	−	0.201347i	−0.664131	+	0.747616i	$0.731198\pi$
$38$		−	5.86030i		−	0.950667i
$39$	5.48528	−	3.16693i	0.878348	−	0.507114i
$40$	1.87476	−	3.24718i	0.296425	−	0.513424i
$41$		−	0.317025i		−	0.0495110i	−0.999694	−	0.0247555i	$-0.992119\pi$
$41$		−	0.317025i		−	0.0495110i	0.999694	−	0.0247555i	$-0.00788073\pi$
$42$		0			0
$43$	−3.17157			−0.483660			−0.241830	−	0.970319i	$-0.577748\pi$
$43$	−3.17157			−0.483660			−0.241830	+	0.970319i	$0.577748\pi$
$44$	−4.00000			−0.603023
$45$	1.21193	+	2.09913i	0.180664	+	0.312919i
$46$		−	11.8272i		−	1.74382i
$47$	−6.40083	+	11.0866i	−0.933656	+	1.61714i	−0.156644	+	0.987655i	$0.550067\pi$
$47$	−6.40083	+	11.0866i	−0.933656	+	1.61714i	−0.777013	+	0.629485i	$0.783266\pi$
$48$	3.74952	+	2.16478i	0.541196	+	0.312460i
$49$		0			0
$50$	2.29289	−	3.97141i	0.324264	−	0.561642i
$51$	2.41421	−	4.18154i	0.338058	−	0.585533i
$52$	5.85172	−	10.1355i	0.811488	−	1.40554i
$53$	−3.00000	+	1.73205i	−0.412082	+	0.237915i	−0.691684	−	0.722200i	$-0.743131\pi$
$53$	−3.00000	+	1.73205i	−0.412082	+	0.237915i	0.279602	+	0.960116i	$0.409797\pi$
$54$	−6.40083	+	3.69552i	−0.871042	+	0.502896i
$55$	2.65131			0.357502
$56$		0			0
$57$	−4.48528			−0.594090
$58$	5.48528	−	3.16693i	0.720253	−	0.415838i
$59$	−0.937379	+	0.541196i	−0.122036	+	0.0704577i	−0.559776	−	0.828644i	$-0.689113\pi$
$59$	−0.937379	+	0.541196i	−0.122036	+	0.0704577i	0.437739	+	0.899102i	$0.355779\pi$
$60$	−2.48528	−	1.43488i	−0.320848	−	0.185242i
$61$	4.80062	−	8.31492i	0.614656	−	1.06462i	−0.375788	−	0.926705i	$-0.622628\pi$
$61$	4.80062	−	8.31492i	0.614656	−	1.06462i	0.990445	−	0.137910i	$-0.0440386\pi$
$62$	4.52607	−	7.83938i	0.574811	−	0.995602i
$63$		0			0
$64$	8.00000			1.00000
$65$	−3.87868	+	6.71807i	−0.481091	+	0.833274i
$66$			3.06147i			0.376841i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		−	8.92177i		−	1.08192i
$69$	−9.05213			−1.08975
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−2.58579	+	4.47871i	−0.304738	+	0.527821i
$73$	6.12627	−	3.53701i	0.717026	−	0.413975i	−0.0966311	−	0.995320i	$-0.530807\pi$
$73$	6.12627	−	3.53701i	0.717026	−	0.413975i	0.813657	+	0.581345i	$0.197473\pi$
$74$			3.46410i			0.402694i
$75$	−3.03958	−	1.75490i	−0.350981	−	0.202639i
$76$	−7.17738	+	4.14386i	−0.823301	+	0.475333i
$77$		0			0
$78$	−7.75736	−	4.47871i	−0.878348	−	0.507114i
$79$	1.75736	+	1.01461i	0.197718	+	0.114153i	0.595591	−	0.803288i	$-0.296918\pi$
$79$	1.75736	+	1.01461i	0.197718	+	0.114153i	−0.397872	+	0.917441i	$0.630251\pi$
$80$	−5.30262			−0.592851
$81$	0.0857864	+	0.148586i	0.00953183	+	0.0165096i
$82$	−0.388275	+	0.224171i	−0.0428778	+	0.0247555i
$83$		−	5.67459i		−	0.622868i	−0.950268	−	0.311434i	$-0.899191\pi$
$83$		−	5.67459i		−	0.622868i	0.950268	−	0.311434i	$-0.100809\pi$
$84$		0			0
$85$			5.91359i			0.641419i
$86$	2.24264	+	3.88437i	0.241830	+	0.418862i
$87$	−2.42386	−	4.19825i	−0.259865	−	0.450100i
$88$	2.82843	+	4.89898i	0.301511	+	0.522233i
$89$	−11.0406	−	6.37430i	−1.17030	−	0.675675i	−0.216551	−	0.976271i	$-0.569481\pi$
$89$	−11.0406	−	6.37430i	−1.17030	−	0.675675i	−0.953751	+	0.300597i	$0.902814\pi$
$90$	1.71393	−	2.96861i	0.180664	−	0.312919i
$91$		0			0
$92$	−14.4853	+	8.36308i	−1.51019	+	0.871911i
$93$	−6.00000	−	3.46410i	−0.622171	−	0.359211i
$94$	18.1043			1.86731
$95$	4.75736	−	2.74666i	0.488095	−	0.281802i
$96$		−	6.12293i		−	0.624919i
$97$			9.23880i			0.938058i	0.883183	+	0.469029i	$0.155396\pi$
$97$			9.23880i			0.938058i	−0.883183	+	0.469029i	$0.844604\pi$
$98$		0			0
$99$	−3.65685			−0.367528
$100$	−6.48528			−0.648528
$101$	0.274552	+	0.475538i	0.0273189	+	0.0473178i	0.879362	−	0.476154i	$-0.157970\pi$
$101$	0.274552	+	0.475538i	0.0273189	+	0.0473178i	−0.852043	+	0.523472i	$0.824636\pi$
$102$	−6.82843			−0.676115
$103$	−0.549104	+	0.951076i	−0.0541048	+	0.0937123i	−0.891809	−	0.452411i	$-0.850564\pi$
$103$	−0.549104	+	0.951076i	−0.0541048	+	0.0937123i	0.837704	+	0.546124i	$0.183897\pi$
$104$	−16.5512			−1.62298
$105$		0			0
$106$	4.24264	+	2.44949i	0.412082	+	0.237915i
$107$	−4.24264	+	7.34847i	−0.410152	+	0.710403i	−0.994906	−	0.100807i	$-0.967858\pi$
$107$	−4.24264	+	7.34847i	−0.410152	+	0.710403i	0.584754	+	0.811210i	$0.301191\pi$
$108$	9.05213	+	5.22625i	0.871042	+	0.502896i
$109$	−12.3640	+	7.13834i	−1.18425	+	0.683729i	−0.956995	−	0.290106i	$-0.906309\pi$
$109$	−12.3640	+	7.13834i	−1.18425	+	0.683729i	−0.227258	+	0.973835i	$0.572976\pi$
$110$	−1.87476	−	3.24718i	−0.178751	−	0.309606i
$111$	2.65131			0.251651
$112$		0			0
$113$	0.485281			0.0456514			0.0228257	−	0.999739i	$-0.492734\pi$
$113$	0.485281			0.0456514			0.0228257	+	0.999739i	$0.492734\pi$
$114$	3.17157	+	5.49333i	0.297045	+	0.514497i
$115$	9.60124	−	5.54328i	0.895320	−	0.516913i
$116$	−7.75736	−	4.47871i	−0.720253	−	0.415838i
$117$	5.34972	−	9.26599i	0.494582	−	0.856641i
$118$	1.32565	+	0.765367i	0.122036	+	0.0704577i
$119$		0			0
$120$			4.05845i			0.370484i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−13.5782			−1.22931
$123$	0.171573	+	0.297173i	0.0154702	+	0.0267952i
$124$	−12.8017			−1.14962
$125$	10.9269			0.977331
$126$		0			0
$127$		−	15.2913i		−	1.35688i	−0.734655	−	0.678441i	$-0.762656\pi$
$127$		−	15.2913i		−	1.35688i	0.734655	−	0.678441i	$-0.237344\pi$
$128$	−5.65685	−	9.79796i	−0.500000	−	0.866025i
$129$	2.97297	−	1.71644i	0.261755	−	0.151124i
$130$	10.9706			0.962182
$131$	11.8643	+	6.84984i	1.03659	+	0.598473i	0.918864	−	0.394573i	$-0.129108\pi$
$131$	11.8643	+	6.84984i	1.03659	+	0.598473i	0.117722	+	0.993047i	$0.462441\pi$
$132$	3.74952	−	2.16478i	0.326354	−	0.188420i
$133$		0			0
$134$	−8.48528	+	14.6969i	−0.733017	+	1.26962i
$135$	−6.00000	−	3.46410i	−0.516398	−	0.298142i
$136$	−10.9269	+	6.30864i	−0.936973	+	0.540962i
$137$	4.12132	+	7.13834i	0.352108	+	0.609869i	0.986619	−	0.163045i	$-0.0521316\pi$
$137$	4.12132	+	7.13834i	0.352108	+	0.609869i	−0.634510	+	0.772914i	$0.718798\pi$
$138$	6.40083	+	11.0866i	0.544874	+	0.943750i
$139$			17.3952i			1.47544i	0.675106	+	0.737721i	$0.264098\pi$
$139$			17.3952i			1.47544i	−0.675106	+	0.737721i	$0.735902\pi$
$140$		0			0
$141$		−	13.8564i		−	1.16692i
$142$		0			0
$143$	−5.85172	−	10.1355i	−0.489346	−	0.847571i
$144$	7.31371			0.609476
$145$	5.14179	+	2.96861i	0.427002	+	0.246530i
$146$	−8.66386	−	5.00208i	−0.717026	−	0.413975i
$147$		0			0
$148$	4.24264	−	2.44949i	0.348743	−	0.201347i
$149$	−0.514719	−	0.297173i	−0.0421674	−	0.0243454i	0.478768	−	0.877941i	$-0.341083\pi$
$149$	−0.514719	−	0.297173i	−0.0421674	−	0.0243454i	−0.520936	+	0.853596i	$0.674417\pi$
$150$			4.96362i			0.405278i
$151$	4.75736	−	2.74666i	0.387148	−	0.223520i	−0.293775	−	0.955874i	$-0.594912\pi$
$151$	4.75736	−	2.74666i	0.387148	−	0.223520i	0.680924	+	0.732354i	$0.261578\pi$
$152$	10.1503	+	5.86030i	0.823301	+	0.475333i
$153$		−	8.15640i		−	0.659406i
$154$		0			0
$155$	8.48528			0.681554
$156$			12.6677i			1.01423i
$157$	−6.28710	−	10.8896i	−0.501765	−	0.869083i	−0.999998	−	0.00203967i	$-0.999351\pi$
$157$	−6.28710	−	10.8896i	−0.501765	−	0.869083i	0.498233	−	0.867043i	$-0.333983\pi$
$158$		−	2.86976i		−	0.228306i
$159$	1.87476	−	3.24718i	0.148678	−	0.257518i
$160$	3.74952	+	6.49435i	0.296425	+	0.513424i
$161$		0			0
$162$	0.121320	−	0.210133i	0.00953183	−	0.0165096i
$163$	10.0711	−	17.4436i	0.788827	−	1.36629i	−0.137859	−	0.990452i	$-0.544022\pi$
$163$	10.0711	−	17.4436i	0.788827	−	1.36629i	0.926686	−	0.375836i	$-0.122645\pi$
$164$	0.549104	+	0.317025i	0.0428778	+	0.0247555i
$165$	−2.48528	+	1.43488i	−0.193479	+	0.111705i
$166$	−6.94993	+	4.01254i	−0.539419	+	0.311434i
$167$	16.5512			1.28077			0.640384	−	0.768055i	$-0.278775\pi$
$167$	16.5512			1.28077			0.640384	+	0.768055i	$0.278775\pi$
$168$		0			0
$169$	21.2426			1.63405
$170$	7.24264	−	4.18154i	0.555485	−	0.320710i
$171$	−6.56165	+	3.78837i	−0.501782	+	0.289704i
$172$	3.17157	−	5.49333i	0.241830	−	0.418862i
$173$	−5.18889	+	8.98743i	−0.394504	+	0.683302i	−0.993038	−	0.117796i	$-0.962417\pi$
$173$	−5.18889	+	8.98743i	−0.394504	+	0.683302i	0.598533	+	0.801098i	$0.295750\pi$
$174$	−3.42786	+	5.93723i	−0.259865	+	0.450100i
$175$		0			0
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	0.585786	−	1.01461i	0.0440304	−	0.0762629i
$178$			18.0292i			1.35135i
$179$	1.75736	+	3.04384i	0.131351	+	0.227507i	0.924198	−	0.381914i	$-0.124735\pi$
$179$	1.75736	+	3.04384i	0.131351	+	0.227507i	−0.792846	+	0.609421i	$0.791402\pi$
$180$	−4.84772			−0.361328
$181$	14.1273			1.05007			0.525037	−	0.851079i	$-0.324051\pi$
$181$	14.1273			1.05007			0.525037	+	0.851079i	$0.324051\pi$
$182$		0			0
$183$			10.3923i			0.768221i
$184$	20.4853	+	11.8272i	1.51019	+	0.871911i
$185$	−2.81214	+	1.62359i	−0.206752	+	0.119369i
$186$			9.79796i			0.718421i
$187$	−7.72648	−	4.46088i	−0.565016	−	0.326212i
$188$	−12.8017	−	22.1731i	−0.933656	−	1.61714i
$189$		0			0
$190$	−6.72792	−	3.88437i	−0.488095	−	0.281802i
$191$	1.75736	+	1.01461i	0.127158	+	0.0734147i	0.562230	−	0.826981i	$-0.309944\pi$
$191$	1.75736	+	1.01461i	0.127158	+	0.0734147i	−0.435072	+	0.900396i	$0.643277\pi$
$192$	−7.49903	+	4.32957i	−0.541196	+	0.312460i
$193$	−7.07107	−	12.2474i	−0.508987	−	0.881591i	−0.999946	−	0.0104081i	$-0.996687\pi$
$193$	−7.07107	−	12.2474i	−0.508987	−	0.881591i	0.490959	−	0.871183i	$-0.336646\pi$
$194$	11.3152	−	6.53281i	0.812382	−	0.469029i
$195$		−	8.39651i		−	0.601286i
$196$		0			0
$197$		−	12.6677i		−	0.902537i	−0.892388	−	0.451269i	$-0.850972\pi$
$197$		−	12.6677i		−	0.902537i	0.892388	−	0.451269i	$-0.149028\pi$
$198$	2.58579	+	4.47871i	0.183764	+	0.318288i
$199$	3.20041	+	5.54328i	0.226871	+	0.392953i	0.956879	−	0.290486i	$-0.0938170\pi$
$199$	3.20041	+	5.54328i	0.226871	+	0.392953i	−0.730008	+	0.683439i	$0.760484\pi$
$200$	4.58579	+	7.94282i	0.324264	+	0.561642i
$201$	11.2485	+	6.49435i	0.793412	+	0.458076i
$202$	0.388275	−	0.672512i	0.0273189	−	0.0473178i
$203$		0			0
$204$	4.82843	+	8.36308i	0.338058	+	0.585533i
$205$	−0.363961	−	0.210133i	−0.0254201	−	0.0146763i
$206$	1.55310			0.108210
$207$	−13.2426	+	7.64564i	−0.920427	+	0.531409i
$208$	11.7034	+	20.2710i	0.811488	+	1.40554i
$209$			8.28772i			0.573274i
$210$		0			0
$211$	3.51472			0.241963			0.120982	−	0.992655i	$-0.461396\pi$
$211$	3.51472			0.241963			0.120982	+	0.992655i	$0.461396\pi$
$212$		−	6.92820i		−	0.475831i
$213$		0			0
$214$	12.0000			0.820303
$215$	−2.10220	+	3.64113i	−0.143369	+	0.248323i
$216$		−	14.7821i		−	1.00579i
$217$		0			0
$218$	17.4853	+	10.0951i	1.18425	+	0.683729i
$219$	−3.82843	+	6.63103i	−0.258701	+	0.448084i
$220$	−2.65131	+	4.59220i	−0.178751	+	0.309606i
$221$	22.6066	−	13.0519i	1.52068	−	0.877968i
$222$	−1.87476	−	3.24718i	−0.125826	−	0.217936i
$223$	−4.84772			−0.324628			−0.162314	−	0.986739i	$-0.551896\pi$
$223$	−4.84772			−0.324628			−0.162314	+	0.986739i	$0.551896\pi$
$224$		0			0
$225$	−5.92893			−0.395262
$226$	−0.343146	−	0.594346i	−0.0228257	−	0.0395353i
$227$	−10.2170	+	5.89876i	−0.678123	+	0.391515i	−0.799148	−	0.601135i	$-0.794715\pi$
$227$	−10.2170	+	5.89876i	−0.678123	+	0.391515i	0.121024	+	0.992650i	$0.461382\pi$
$228$	4.48528	−	7.76874i	0.297045	−	0.514497i
$229$	−7.61276	+	13.1857i	−0.503065	+	0.871334i	0.496929	+	0.867791i	$0.334461\pi$
$229$	−7.61276	+	13.1857i	−0.503065	+	0.871334i	−0.999994	+	0.00354289i	$0.998872\pi$
$230$	−13.5782	−	7.83938i	−0.895320	−	0.516913i
$231$		0			0
$232$			12.6677i			0.831676i
$233$	5.87868	−	10.1822i	0.385125	−	0.667056i	−0.606661	−	0.794960i	$-0.707492\pi$
$233$	5.87868	−	10.1822i	0.385125	−	0.667056i	0.991787	+	0.127904i	$0.0408250\pi$
$234$	−15.1313			−0.989164
$235$	8.48528	+	14.6969i	0.553519	+	0.958723i
$236$		−	2.16478i		−	0.140915i
$237$	−2.19642			−0.142673
$238$		0			0
$239$		−	6.33386i		−	0.409703i	−0.978793	−	0.204852i	$-0.934329\pi$
$239$		−	6.33386i		−	0.409703i	0.978793	−	0.204852i	$-0.0656712\pi$
$240$	4.97056	−	2.86976i	0.320848	−	0.185242i
$241$	−14.5627	+	8.40777i	−0.938065	+	0.541592i	−0.889353	−	0.457221i	$-0.848845\pi$
$241$	−14.5627	+	8.40777i	−0.938065	+	0.541592i	−0.0487118	+	0.998813i	$0.515512\pi$
$242$	−9.89949			−0.636364
$243$	13.4174	+	7.74652i	0.860725	+	0.496940i
$244$	9.60124	+	16.6298i	0.614656	+	1.06462i
$245$		0			0
$246$	0.242641	−	0.420266i	0.0154702	−	0.0267952i
$247$	−21.0000	−	12.1244i	−1.33620	−	0.771454i
$248$	9.05213	+	15.6788i	0.574811	+	0.995602i
$249$	3.07107	+	5.31925i	0.194621	+	0.337093i
$250$	−7.72648	−	13.3827i	−0.488665	−	0.846393i
$251$			20.1940i			1.27464i	0.770601	+	0.637318i	$0.219956\pi$
$251$			20.1940i			1.27464i	−0.770601	+	0.637318i	$0.780044\pi$
$252$		0			0
$253$			16.7262i			1.05156i
$254$	−18.7279	+	10.8126i	−1.17509	+	0.678441i
$255$	−3.20041	−	5.54328i	−0.200418	−	0.347133i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−1.05110	−	0.606854i	−0.0655660	−	0.0378545i	0.466859	−	0.884332i	$-0.345386\pi$
$257$	−1.05110	−	0.606854i	−0.0655660	−	0.0378545i	−0.532425	+	0.846477i	$0.678719\pi$
$258$	−4.20441	−	2.42742i	−0.261755	−	0.151124i
$259$		0			0
$260$	−7.75736	−	13.4361i	−0.481091	−	0.833274i
$261$	−7.09188	−	4.09450i	−0.438977	−	0.253443i
$262$		−	19.3743i		−	1.19695i
$263$	−16.2426	+	9.37769i	−1.00156	+	0.578253i	−0.908711	−	0.417426i	$-0.862932\pi$
$263$	−16.2426	+	9.37769i	−1.00156	+	0.578253i	−0.0928534	+	0.995680i	$0.529599\pi$
$264$	−5.30262	−	3.06147i	−0.326354	−	0.188420i
$265$			4.59220i			0.282097i
$266$		0			0
$267$	13.7990			0.844484
$268$	24.0000			1.46603
$269$	6.12627	+	10.6110i	0.373525	+	0.646965i	0.990105	−	0.140327i	$-0.0448155\pi$
$269$	6.12627	+	10.6110i	0.373525	+	0.646965i	−0.616580	+	0.787293i	$0.711482\pi$
$270$			9.79796i			0.596285i
$271$	16.0021	−	27.7164i	0.972056	−	1.68365i	0.282730	−	0.959200i	$-0.408760\pi$
$271$	16.0021	−	27.7164i	0.972056	−	1.68365i	0.689326	−	0.724451i	$-0.257907\pi$
$272$	15.4530	+	8.92177i	0.936973	+	0.540962i
$273$		0			0
$274$	5.82843	−	10.0951i	0.352108	−	0.609869i
$275$	−3.24264	+	5.61642i	−0.195539	+	0.338683i
$276$	9.05213	−	15.6788i	0.544874	−	0.943750i
$277$	2.48528	−	1.43488i	0.149326	−	0.0862135i	−0.423475	−	0.905908i	$-0.639190\pi$
$277$	2.48528	−	1.43488i	0.149326	−	0.0862135i	0.572801	+	0.819694i	$0.305857\pi$
$278$	21.3047	−	12.3003i	1.27777	−	0.737721i
$279$	−11.7034			−0.700667
$280$		0			0
$281$	−16.7279			−0.997904			−0.498952	−	0.866630i	$-0.666282\pi$
$281$	−16.7279			−0.997904			−0.498952	+	0.866630i	$0.666282\pi$
$282$	−16.9706	+	9.79796i	−1.01058	+	0.583460i
$283$	13.1899	−	7.61521i	0.784060	−	0.452677i	−0.0538074	−	0.998551i	$-0.517136\pi$
$283$	13.1899	−	7.61521i	0.784060	−	0.452677i	0.837867	+	0.545874i	$0.183802\pi$
$284$		0			0
$285$	−2.97297	+	5.14933i	−0.176103	+	0.305020i
$286$	−8.27558	+	14.3337i	−0.489346	+	0.847571i
$287$		0			0
$288$	−5.17157	−	8.95743i	−0.304738	−	0.527821i
$289$	1.44975	−	2.51104i	0.0852793	−	0.147708i
$290$		−	8.39651i		−	0.493060i
$291$	−5.00000	−	8.66025i	−0.293105	−	0.507673i
$292$			14.1480i			0.827950i
$293$	5.85172			0.341861			0.170931	−	0.985283i	$-0.445323\pi$
$293$	5.85172			0.341861			0.170931	+	0.985283i	$0.445323\pi$
$294$		0			0
$295$			1.43488i			0.0835418i
$296$	−6.00000	−	3.46410i	−0.348743	−	0.201347i
$297$	9.05213	−	5.22625i	0.525258	−	0.303258i
$298$			0.840532i			0.0486907i
$299$	−42.3819	−	24.4692i	−2.45101	−	1.41509i
$300$	6.07917	−	3.50981i	0.350981	−	0.202639i
$301$		0			0
$302$	−6.72792	−	3.88437i	−0.387148	−	0.223520i
$303$	−0.514719	−	0.297173i	−0.0295698	−	0.0170721i
$304$		−	16.5754i		−	0.950667i
$305$	−6.36396	−	11.0227i	−0.364399	−	0.631158i
$306$	−9.98951	+	5.76745i	−0.571062	+	0.329703i
$307$		−	21.9874i		−	1.25489i	−0.778662	−	0.627444i	$-0.784101\pi$
$307$		−	21.9874i		−	1.25489i	0.778662	−	0.627444i	$-0.215899\pi$
$308$		0			0
$309$		−	1.18869i		−	0.0676223i
$310$	−6.00000	−	10.3923i	−0.340777	−	0.590243i
$311$	5.62427	+	9.74153i	0.318923	+	0.552391i	0.980264	−	0.197695i	$-0.0633454\pi$
$311$	5.62427	+	9.74153i	0.318923	+	0.552391i	−0.661340	+	0.750086i	$0.730012\pi$
$312$	15.5147	−	8.95743i	0.878348	−	0.507114i
$313$	13.0762	+	7.54955i	0.739111	+	0.426726i	0.821746	−	0.569854i	$-0.193000\pi$
$313$	13.0762	+	7.54955i	0.739111	+	0.426726i	−0.0826352	+	0.996580i	$0.526334\pi$
$314$	−8.89130	+	15.4002i	−0.501765	+	0.869083i
$315$		0			0
$316$	−3.51472	+	2.02922i	−0.197718	+	0.114153i
$317$	20.4853	+	11.8272i	1.15057	+	0.664281i	0.949026	−	0.315199i	$-0.102071\pi$
$317$	20.4853	+	11.8272i	1.15057	+	0.664281i	0.201542	+	0.979480i	$0.435405\pi$
$318$	−5.30262			−0.297356
$319$	−7.75736	+	4.47871i	−0.434329	+	0.250760i
$320$	5.30262	−	9.18440i	0.296425	−	0.513424i
$321$		−	9.18440i		−	0.512623i
$322$		0			0
$323$	−18.4853			−1.02855
$324$	−0.343146			−0.0190637
$325$	−9.48751	−	16.4329i	−0.526273	−	0.911531i
$326$	−28.4853			−1.57765
$327$	7.72648	−	13.3827i	0.427275	−	0.740063i
$328$		−	0.896683i		−	0.0495110i
$329$		0			0
$330$	3.51472	+	2.02922i	0.193479	+	0.111705i
$331$	−7.58579	+	13.1390i	−0.416953	+	0.722183i	−0.995631	−	0.0933726i	$-0.970235\pi$
$331$	−7.58579	+	13.1390i	−0.416953	+	0.722183i	0.578679	+	0.815556i	$0.303569\pi$
$332$	9.82868	+	5.67459i	0.539419	+	0.311434i
$333$	3.87868	−	2.23936i	0.212550	−	0.122716i
$334$	−11.7034	−	20.2710i	−0.640384	−	1.10918i
$335$	−15.9079			−0.869139
$336$		0			0
$337$	−4.24264			−0.231111			−0.115556	−	0.993301i	$-0.536865\pi$
$337$	−4.24264			−0.231111			−0.115556	+	0.993301i	$0.536865\pi$
$338$	−15.0208	−	26.0168i	−0.817025	−	1.41513i
$339$	−0.454893	+	0.262632i	−0.0247064	+	0.0142642i
$340$	−10.2426	−	5.91359i	−0.555485	−	0.320710i
$341$	−6.40083	+	11.0866i	−0.346624	+	0.600371i
$342$	9.27958	+	5.35757i	0.501782	+	0.289704i
$343$		0			0
$344$	−8.97056			−0.483660
$345$	−6.00000	+	10.3923i	−0.323029	+	0.559503i
$346$	14.6764			0.789009
$347$	13.4853	+	23.3572i	0.723928	+	1.25388i	0.959414	+	0.282002i	$0.0909985\pi$
$347$	13.4853	+	23.3572i	0.723928	+	1.25388i	−0.235486	+	0.971878i	$0.575668\pi$
$348$	9.69545			0.519731
$349$	−9.27958			−0.496725			−0.248362	−	0.968667i	$-0.579892\pi$
$349$	−9.27958			−0.496725			−0.248362	+	0.968667i	$0.579892\pi$
$350$		0			0
$351$			30.5826i			1.63238i
$352$	−11.3137			−0.603023
$353$	17.8297	−	10.2940i	0.948980	−	0.547894i	0.0562161	−	0.998419i	$-0.482096\pi$
$353$	17.8297	−	10.2940i	0.948980	−	0.547894i	0.892764	+	0.450525i	$0.148763\pi$
$354$	−1.65685			−0.0880608
$355$		0			0
$356$	22.0812	−	12.7486i	1.17030	−	0.675675i
$357$		0			0
$358$	2.48528	−	4.30463i	0.131351	−	0.227507i
$359$	15.0000	+	8.66025i	0.791670	+	0.457071i	0.840550	−	0.541734i	$-0.182232\pi$
$359$	15.0000	+	8.66025i	0.791670	+	0.457071i	−0.0488803	+	0.998805i	$0.515565\pi$
$360$	3.42786	+	5.93723i	0.180664	+	0.312919i
$361$	−0.914214	−	1.58346i	−0.0481165	−	0.0833402i
$362$	−9.98951	−	17.3023i	−0.525037	−	0.909391i
$363$			7.57675i			0.397676i
$364$		0			0
$365$		−	9.37769i		−	0.490851i
$366$	12.7279	−	7.34847i	0.665299	−	0.384111i
$367$	11.4760	+	19.8770i	0.599042	+	1.03757i	0.992963	+	0.118427i	$0.0377851\pi$
$367$	11.4760	+	19.8770i	0.599042	+	1.03757i	−0.393921	+	0.919144i	$0.628882\pi$
$368$		−	33.4523i		−	1.74382i
$369$	0.501998	+	0.289829i	0.0261330	+	0.0150879i
$370$	3.97696	+	2.29610i	0.206752	+	0.119369i
$371$		0			0
$372$	12.0000	−	6.92820i	0.622171	−	0.359211i
$373$	25.9706	+	14.9941i	1.34470	+	0.776366i	0.987494	−	0.157658i	$-0.0503944\pi$
$373$	25.9706	+	14.9941i	1.34470	+	0.776366i	0.357211	+	0.934024i	$0.383728\pi$
$374$			12.6173i			0.652424i
$375$	−10.2426	+	5.91359i	−0.528928	+	0.305377i
$376$	−18.1043	+	31.3575i	−0.933656	+	1.61714i
$377$		−	26.2082i		−	1.34979i
$378$		0			0
$379$	−5.31371			−0.272947			−0.136473	−	0.990644i	$-0.543577\pi$
$379$	−5.31371			−0.272947			−0.136473	+	0.990644i	$0.543577\pi$
$380$			10.9867i			0.563603i
$381$	8.27558	+	14.3337i	0.423971	+	0.734339i
$382$		−	2.86976i		−	0.146829i
$383$	−6.40083	+	11.0866i	−0.327067	+	0.566496i	−0.981928	−	0.189252i	$-0.939394\pi$
$383$	−6.40083	+	11.0866i	−0.327067	+	0.566496i	0.654862	+	0.755749i	$0.272727\pi$
$384$	10.6052	+	6.12293i	0.541196	+	0.312460i
$385$		0			0
$386$	−10.0000	+	17.3205i	−0.508987	+	0.881591i
$387$	2.89949	−	5.02207i	0.147390	−	0.255286i
$388$	−16.0021	−	9.23880i	−0.812382	−	0.469029i
$389$	32.8492	−	18.9655i	1.66552	−	0.961590i	0.695516	−	0.718510i	$-0.255176\pi$
$389$	32.8492	−	18.9655i	1.66552	−	0.961590i	0.970006	−	0.243080i	$-0.0781577\pi$
$390$	−10.2836	+	5.93723i	−0.520729	+	0.300643i
$391$	−37.3067			−1.88668
$392$		0			0
$393$	−14.8284			−0.747995
$394$	−15.5147	+	8.95743i	−0.781620	+	0.451269i
$395$	2.32965	−	1.34502i	0.117217	−	0.0676755i
$396$	3.65685	−	6.33386i	0.183764	−	0.318288i
$397$	−6.90282	+	11.9560i	−0.346443	+	0.600056i	−0.985615	−	0.169007i	$-0.945944\pi$
$397$	−6.90282	+	11.9560i	−0.346443	+	0.600056i	0.639172	+	0.769064i	$0.279277\pi$
$398$	4.52607	−	7.83938i	0.226871	−	0.392953i
$399$		0			0
$400$	6.48528	−	11.2328i	0.324264	−	0.561642i
$401$	−8.12132	+	14.0665i	−0.405559	+	0.702449i	−0.994386	−	0.105810i	$-0.966257\pi$
$401$	−8.12132	+	14.0665i	−0.405559	+	0.702449i	0.588827	+	0.808259i	$0.299590\pi$
$402$		−	18.3688i		−	0.916153i
$403$	−18.7279	−	32.4377i	−0.932904	−	1.61584i
$404$	−1.09821			−0.0546379
$405$	0.227446			0.0113019
$406$		0			0
$407$		−	4.89898i		−	0.242833i
$408$	6.82843	−	11.8272i	0.338058	−	0.585533i
$409$	−8.00103	+	4.61940i	−0.395626	+	0.228415i	−0.684595	−	0.728924i	$-0.740021\pi$
$409$	−8.00103	+	4.61940i	−0.395626	+	0.228415i	0.288969	+	0.957338i	$0.406687\pi$
$410$			0.594346i			0.0293527i
$411$	−7.72648	−	4.46088i	−0.381119	−	0.220039i
$412$	−1.09821	−	1.90215i	−0.0541048	−	0.0937123i
$413$		0			0
$414$	18.7279	+	10.8126i	0.920427	+	0.531409i
$415$	−6.51472	−	3.76127i	−0.319795	−	0.184634i
$416$	16.5512	−	28.6675i	0.811488	−	1.40554i
$417$	−9.41421	−	16.3059i	−0.461016	−	0.798503i
$418$	10.1503	−	5.86030i	0.496469	−	0.286637i
$419$		−	7.31411i		−	0.357318i	−0.983911	−	0.178659i	$-0.942824\pi$
$419$		−	7.31411i		−	0.357318i	0.983911	−	0.178659i	$-0.0571759\pi$
$420$		0			0
$421$			12.6677i			0.617387i	0.951162	+	0.308693i	$0.0998917\pi$
$421$			12.6677i			0.617387i	−0.951162	+	0.308693i	$0.900108\pi$
$422$	−2.48528	−	4.30463i	−0.120982	−	0.209546i
$423$	−11.7034	−	20.2710i	−0.569041	−	0.985608i
$424$	−8.48528	+	4.89898i	−0.412082	+	0.237915i
$425$	−12.5271	−	7.23252i	−0.607654	−	0.350829i
$426$		0			0
$427$		0			0
$428$	−8.48528	−	14.6969i	−0.410152	−	0.710403i
$429$	10.9706	+	6.33386i	0.529664	+	0.305802i
$430$	5.94593			0.286738
$431$	23.4853	−	13.5592i	1.13125	−	0.653125i	0.186998	−	0.982360i	$-0.440124\pi$
$431$	23.4853	−	13.5592i	1.13125	−	0.653125i	0.944248	+	0.329235i	$0.106791\pi$
$432$	−18.1043	+	10.4525i	−0.871042	+	0.502896i
$433$		−	28.1647i		−	1.35351i	−0.736208	−	0.676755i	$-0.763386\pi$
$433$		−	28.1647i		−	1.35351i	0.736208	−	0.676755i	$-0.236614\pi$
$434$		0			0
$435$	−6.42641			−0.308123
$436$		−	28.5533i		−	1.36746i
$437$	17.3277	+	30.0125i	0.828897	+	1.43569i
$438$	10.8284			0.517402
$439$	11.1543	−	19.3199i	0.532368	−	0.922088i	−0.466918	−	0.884300i	$-0.654636\pi$
$439$	11.1543	−	19.3199i	0.532368	−	0.922088i	0.999286	−	0.0377871i	$-0.0120309\pi$
$440$	7.49903			0.357502
$441$		0			0
$442$	−31.9706	−	18.4582i	−1.52068	−	0.877968i
$443$	−14.1421	+	24.4949i	−0.671913	+	1.16379i	0.305448	+	0.952209i	$0.401194\pi$
$443$	−14.1421	+	24.4949i	−0.671913	+	1.16379i	−0.977361	+	0.211579i	$0.932139\pi$
$444$	−2.65131	+	4.59220i	−0.125826	+	0.217936i
$445$	−14.6360	+	8.45012i	−0.693815	+	0.400574i
$446$	3.42786	+	5.93723i	0.162314	+	0.281136i
$447$	0.643315			0.0304278
$448$		0			0
$449$	5.65685			0.266963			0.133482	−	0.991051i	$-0.457384\pi$
$449$	5.65685			0.266963			0.133482	+	0.991051i	$0.457384\pi$
$450$	4.19239	+	7.26143i	0.197631	+	0.342307i
$451$	0.549104	−	0.317025i	0.0258563	−	0.0149281i
$452$	−0.485281	+	0.840532i	−0.0228257	+	0.0395353i
$453$	−2.97297	+	5.14933i	−0.139682	+	0.241937i
$454$	14.4490	+	8.34211i	0.678123	+	0.391515i
$455$		0			0
$456$	−12.6863			−0.594090
$457$	13.4142	−	23.2341i	0.627490	−	1.08685i	−0.360563	−	0.932735i	$-0.617415\pi$
$457$	13.4142	−	23.2341i	0.627490	−	1.08685i	0.988054	−	0.154111i	$-0.0492512\pi$
$458$	21.5321			1.00613
$459$	11.6569	+	20.1903i	0.544095	+	0.942401i
$460$			22.1731i			1.03383i
$461$	18.9750			0.883755			0.441878	−	0.897075i	$-0.354313\pi$
$461$	18.9750			0.883755			0.441878	+	0.897075i	$0.354313\pi$
$462$		0			0
$463$			8.95743i			0.416287i	0.978098	+	0.208143i	$0.0667421\pi$
$463$			8.95743i			0.416287i	−0.978098	+	0.208143i	$0.933258\pi$
$464$	15.5147	−	8.95743i	0.720253	−	0.415838i
$465$	−7.95393	+	4.59220i	−0.368854	+	0.212958i
$466$	−16.6274			−0.770250
$467$	31.8433	+	18.3847i	1.47353	+	0.850744i	0.999556	−	0.0297936i	$-0.00948502\pi$
$467$	31.8433	+	18.3847i	1.47353	+	0.850744i	0.473976	+	0.880538i	$0.342818\pi$
$468$	10.6994	+	18.5320i	0.494582	+	0.856641i
$469$		0			0
$470$	12.0000	−	20.7846i	0.553519	−	0.958723i
$471$	11.7868	+	6.80511i	0.543107	+	0.313563i
$472$	−2.65131	+	1.53073i	−0.122036	+	0.0704577i
$473$	−3.17157	−	5.49333i	−0.145829	−	0.252583i
$474$	1.55310	+	2.69005i	0.0713363	+	0.123558i
$475$			13.4370i			0.616534i
$476$		0			0
$477$		−	6.33386i		−	0.290007i
$478$	−7.75736	+	4.47871i	−0.354813	+	0.204852i
$479$	−5.07517	−	8.79045i	−0.231890	−	0.401646i	0.726474	−	0.687194i	$-0.241158\pi$
$479$	−5.07517	−	8.79045i	−0.231890	−	0.401646i	−0.958364	+	0.285548i	$0.907824\pi$
$480$	−7.02944	−	4.05845i	−0.320848	−	0.185242i
$481$	12.4134	+	7.16687i	0.566001	+	0.326781i
$482$	20.5947	+	11.8904i	0.938065	+	0.541592i
$483$		0			0
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	10.6066	+	6.12372i	0.481621	+	0.278064i
$486$		−	21.9105i		−	0.993879i
$487$	12.5147	−	7.22538i	0.567096	−	0.327413i	−0.188893	−	0.981998i	$-0.560490\pi$
$487$	12.5147	−	7.22538i	0.567096	−	0.327413i	0.755989	+	0.654585i	$0.227156\pi$
$488$	13.5782	−	23.5181i	0.614656	−	1.06462i
$489$			21.8017i			0.985907i
$490$		0			0
$491$	7.79899			0.351963			0.175982	−	0.984393i	$-0.443690\pi$
$491$	7.79899			0.351963			0.175982	+	0.984393i	$0.443690\pi$
$492$	−0.686292			−0.0309404
$493$	−9.98951	−	17.3023i	−0.449905	−	0.779258i
$494$			34.2929i			1.54291i
$495$	−2.42386	+	4.19825i	−0.108945	+	0.188697i
$496$	12.8017	−	22.1731i	0.574811	−	0.995602i
$497$		0			0
$498$	4.34315	−	7.52255i	0.194621	−	0.337093i
$499$	−4.24264	+	7.34847i	−0.189927	+	0.328963i	−0.945226	−	0.326418i	$-0.894158\pi$
$499$	−4.24264	+	7.34847i	−0.189927	+	0.328963i	0.755299	+	0.655380i	$0.227492\pi$
$500$	−10.9269	+	18.9259i	−0.488665	+	0.846393i
$501$	−15.5147	+	8.95743i	−0.693147	+	0.400188i
$502$	24.7325	−	14.2793i	1.10387	−	0.637318i
$503$	−4.84772			−0.216149			−0.108075	−	0.994143i	$-0.534469\pi$
$503$	−4.84772			−0.216149			−0.108075	+	0.994143i	$0.534469\pi$
$504$		0			0
$505$	0.727922			0.0323921
$506$	20.4853	−	11.8272i	0.910682	−	0.525782i
$507$	−19.9124	+	11.4964i	−0.884341	+	0.510575i
$508$	26.4853	+	15.2913i	1.17509	+	0.678441i
$509$	−1.05110	+	1.82056i	−0.0465893	+	0.0806950i	−0.888380	−	0.459110i	$-0.848169\pi$
$509$	−1.05110	+	1.82056i	−0.0465893	+	0.0806950i	0.841790	+	0.539805i	$0.181502\pi$
$510$	−4.52607	+	7.83938i	−0.200418	+	0.347133i
$511$		0			0
$512$	22.6274			1.00000
$513$	10.8284	−	18.7554i	0.478087	−	0.828071i
$514$			1.71644i			0.0757090i
$515$	0.727922	+	1.26080i	0.0320761	+	0.0555574i
$516$			6.86577i			0.302249i
$517$	−25.6033			−1.12603
$518$		0			0
$519$		−	11.2328i		−	0.493067i
$520$	−10.9706	+	19.0016i	−0.481091	+	0.833274i
$521$	2.69841	−	1.55793i	0.118220	−	0.0682542i	−0.439724	−	0.898133i	$-0.644924\pi$
$521$	2.69841	−	1.55793i	0.118220	−	0.0682542i	0.557944	+	0.829879i	$0.311590\pi$
$522$			11.5810i			0.506886i
$523$	−17.3943	−	10.0426i	−0.760601	−	0.439133i	0.0689104	−	0.997623i	$-0.478048\pi$
$523$	−17.3943	−	10.0426i	−0.760601	−	0.439133i	−0.829512	+	0.558490i	$0.811381\pi$
$524$	−23.7285	+	13.6997i	−1.03659	+	0.598473i
$525$		0			0
$526$	22.9706	+	13.2621i	1.00156	+	0.578253i
$527$	−24.7279	−	14.2767i	−1.07717	−	0.621902i
$528$			8.65914i			0.376841i
$529$	23.4706	+	40.6522i	1.02046	+	1.76749i
$530$	5.62427	−	3.24718i	0.244303	−	0.141048i
$531$		−	1.97908i		−	0.0858846i
$532$		0			0
$533$			1.85514i			0.0803552i
$534$	−9.75736	−	16.9002i	−0.422242	−	0.731345i
$535$	5.62427	+	9.74153i	0.243159	+	0.421163i
$536$	−16.9706	−	29.3939i	−0.733017	−	1.26962i
$537$	−3.29462	−	1.90215i	−0.142174	−	0.0820839i
$538$	8.66386	−	15.0062i	0.373525	−	0.646965i
$539$		0			0
$540$	12.0000	−	6.92820i	0.516398	−	0.298142i
$541$	−22.4558	−	12.9649i	−0.965452	−	0.557404i	−0.0676054	−	0.997712i	$-0.521536\pi$
$541$	−22.4558	−	12.9649i	−0.965452	−	0.557404i	−0.897847	+	0.440308i	$0.854869\pi$
$542$	−45.2607			−1.94411
$543$	−13.2426	+	7.64564i	−0.568296	+	0.328106i
$544$		−	25.2346i		−	1.08192i
$545$			18.9259i			0.810698i
$546$		0			0
$547$	−20.8284			−0.890559			−0.445280	−	0.895392i	$-0.646896\pi$
$547$	−20.8284			−0.890559			−0.445280	+	0.895392i	$0.646896\pi$
$548$	−16.4853			−0.704216
$549$	8.77758	+	15.2032i	0.374618	+	0.648858i
$550$	9.17157			0.391077
$551$	−9.27958	+	16.0727i	−0.395323	+	0.684720i
$552$	−25.6033			−1.08975
$553$		0			0
$554$	−3.51472	−	2.02922i	−0.149326	−	0.0862135i
$555$	1.75736	−	3.04384i	0.0745957	−	0.129204i
$556$	−30.1294	−	17.3952i	−1.27777	−	0.737721i
$557$	2.48528	−	1.43488i	0.105305	−	0.0607977i	−0.446423	−	0.894822i	$-0.647302\pi$
$557$	2.48528	−	1.43488i	0.105305	−	0.0607977i	0.551727	+	0.834024i	$0.313969\pi$
$558$	8.27558	+	14.3337i	0.350333	+	0.606795i
$559$	18.5592			0.784969
$560$		0			0
$561$	9.65685			0.407713
$562$	11.8284	+	20.4874i	0.498952	+	0.864210i
$563$	−3.36124	+	1.94061i	−0.141659	+	0.0817871i	−0.569155	−	0.822231i	$-0.692729\pi$
$563$	−3.36124	+	1.94061i	−0.141659	+	0.0817871i	0.427495	+	0.904018i	$0.359396\pi$
$564$	24.0000	+	13.8564i	1.01058	+	0.583460i
$565$	0.321658	−	0.557127i	0.0135322	−	0.0234385i
$566$	−18.6534	−	10.7695i	−0.784060	−	0.452677i
$567$		0			0
$568$		0			0
$569$	−16.9497	+	29.3578i	−0.710570	+	1.23074i	0.254073	+	0.967185i	$0.418230\pi$
$569$	−16.9497	+	29.3578i	−0.710570	+	1.23074i	−0.964643	+	0.263559i	$0.915104\pi$
$570$	8.40882			0.352207
$571$	6.17157	+	10.6895i	0.258272	+	0.447341i	0.965779	−	0.259366i	$-0.0835135\pi$
$571$	6.17157	+	10.6895i	0.258272	+	0.447341i	−0.707507	+	0.706706i	$0.750180\pi$
$572$	23.4069			0.978691
$573$	−2.19642			−0.0917566
$574$		0			0
$575$			27.1185i			1.13092i
$576$	−7.31371	+	12.6677i	−0.304738	+	0.527821i
$577$	−17.9905	+	10.3868i	−0.748956	+	0.432410i	−0.825317	−	0.564670i	$-0.809003\pi$
$577$	−17.9905	+	10.3868i	−0.748956	+	0.432410i	0.0763605	+	0.997080i	$0.475670\pi$
$578$	−4.10051			−0.170559
$579$	13.2565	+	7.65367i	0.550923	+	0.318076i
$580$	−10.2836	+	5.93723i	−0.427002	+	0.246530i
$581$		0			0
$582$	−7.07107	+	12.2474i	−0.293105	+	0.507673i
$583$	−6.00000	−	3.46410i	−0.248495	−	0.143468i
$584$	17.3277	−	10.0042i	0.717026	−	0.413975i
$585$	−7.09188	−	12.2835i	−0.293213	−	0.507860i
$586$	−4.13779	−	7.16687i	−0.170931	−	0.296060i
$587$			15.7557i			0.650306i	0.945661	+	0.325153i	$0.105416\pi$
$587$			15.7557i			0.650306i	−0.945661	+	0.325153i	$0.894584\pi$
$588$		0			0
$589$			26.5241i			1.09291i
$590$	1.75736	−	1.01461i	0.0723493	−	0.0417709i
$591$	6.85572	+	11.8745i	0.282007	+	0.488450i
$592$			9.79796i			0.402694i
$593$	3.08669	+	1.78210i	0.126755	+	0.0731821i	0.562037	−	0.827112i	$-0.310018\pi$
$593$	3.08669	+	1.78210i	0.126755	+	0.0731821i	−0.435282	+	0.900294i	$0.643351\pi$
$594$	−12.8017	−	7.39104i	−0.525258	−	0.303258i
$595$		0			0
$596$	1.02944	−	0.594346i	0.0421674	−	0.0243454i
$597$	−6.00000	−	3.46410i	−0.245564	−	0.141776i
$598$			69.2094i			2.83018i
$599$	−5.27208	+	3.04384i	−0.215411	+	0.124368i	−0.603824	−	0.797118i	$-0.706357\pi$
$599$	−5.27208	+	3.04384i	−0.215411	+	0.124368i	0.388412	+	0.921486i	$0.373024\pi$
$600$	−8.59724	−	4.96362i	−0.350981	−	0.202639i
$601$		−	22.2275i		−	0.906679i	−0.891338	−	0.453339i	$-0.850233\pi$
$601$		−	22.2275i		−	0.906679i	0.891338	−	0.453339i	$-0.149767\pi$
$602$		0			0
$603$	21.9411			0.893512
$604$			10.9867i			0.447040i
$605$	−4.63979	−	8.03635i	−0.188634	−	0.326724i
$606$			0.840532i			0.0341443i
$607$	5.30262	−	9.18440i	0.215227	−	0.372783i	−0.738116	−	0.674674i	$-0.764284\pi$
$607$	5.30262	−	9.18440i	0.215227	−	0.372783i	0.953343	+	0.301890i	$0.0976177\pi$
$608$	−20.3007	+	11.7206i	−0.823301	+	0.475333i
$609$		0			0
$610$	−9.00000	+	15.5885i	−0.364399	+	0.631158i
$611$	37.4558	−	64.8754i	1.51530	−	2.62458i
$612$	14.1273	+	8.15640i	0.571062	+	0.329703i
$613$	−23.3345	+	13.4722i	−0.942473	+	0.544137i	−0.890735	−	0.454524i	$-0.849809\pi$
$613$	−23.3345	+	13.4722i	−0.942473	+	0.544137i	−0.0517380	+	0.998661i	$0.516476\pi$
$614$	−26.9290	+	15.5474i	−1.08676	+	0.627444i
$615$	0.454893			0.0183430
$616$		0			0
$617$	33.2132			1.33711			0.668557	−	0.743661i	$-0.266912\pi$
$617$	33.2132			1.33711			0.668557	+	0.743661i	$0.266912\pi$
$618$	−1.45584	+	0.840532i	−0.0585626	+	0.0338112i
$619$	−16.0687	+	9.27726i	−0.645855	+	0.372884i	−0.786866	−	0.617124i	$-0.788298\pi$
$619$	−16.0687	+	9.27726i	−0.645855	+	0.372884i	0.141011	+	0.990008i	$0.454965\pi$
$620$	−8.48528	+	14.6969i	−0.340777	+	0.590243i
$621$	21.8538	−	37.8519i	0.876962	−	1.51894i
$622$	7.95393	−	13.7766i	0.318923	−	0.552391i
$623$		0			0
$624$	−21.9411	−	12.6677i	−0.878348	−	0.507114i
$625$	−0.863961	+	1.49642i	−0.0345584	+	0.0598570i
$626$		−	21.3533i		−	0.853451i
$627$	−4.48528	−	7.76874i	−0.179125	−	0.310253i
$628$	25.1484			1.00353
$629$	10.9269			0.435684
$630$		0			0
$631$		−	39.5400i		−	1.57406i	−0.616913	−	0.787031i	$-0.711617\pi$
$631$		−	39.5400i		−	1.57406i	0.616913	−	0.787031i	$-0.288383\pi$
$632$	4.97056	+	2.86976i	0.197718	+	0.114153i
$633$	−3.29462	+	1.90215i	−0.130950	+	0.0756038i
$634$		−	33.4523i		−	1.32856i
$635$	−17.5552	−	10.1355i	−0.696655	−	0.402214i
$636$	3.74952	+	6.49435i	0.148678	+	0.257518i
$637$		0			0
$638$	10.9706	+	6.33386i	0.434329	+	0.250760i
$639$		0			0
$640$	−14.9981			−0.592851
$641$	15.5355	+	26.9083i	0.613617	+	1.06282i	0.990626	+	0.136606i	$0.0436193\pi$
$641$	15.5355	+	26.9083i	0.613617	+	1.06282i	−0.377009	+	0.926210i	$0.623047\pi$
$642$	−11.2485	+	6.49435i	−0.443945	+	0.256312i
$643$		−	30.3839i		−	1.19822i	−0.800665	−	0.599112i	$-0.795520\pi$
$643$		−	30.3839i		−	1.19822i	0.800665	−	0.599112i	$-0.204480\pi$
$644$		0			0
$645$		−	4.55082i		−	0.179188i
$646$	13.0711	+	22.6398i	0.514274	+	0.890749i
$647$	−5.07517	−	8.79045i	−0.199526	−	0.345588i	0.748849	−	0.662741i	$-0.230607\pi$
$647$	−5.07517	−	8.79045i	−0.199526	−	0.345588i	−0.948375	+	0.317152i	$0.897273\pi$
$648$	0.242641	+	0.420266i	0.00953183	+	0.0165096i
$649$	−1.87476	−	1.08239i	−0.0735907	−	0.0424876i
$650$	−13.4174	+	23.2396i	−0.526273	+	0.911531i
$651$		0			0
$652$	20.1421	+	34.8872i	0.788827	+	1.36629i
$653$	−17.6360	−	10.1822i	−0.690152	−	0.398459i	0.113517	−	0.993536i	$-0.463788\pi$
$653$	−17.6360	−	10.1822i	−0.690152	−	0.398459i	−0.803669	+	0.595077i	$0.797122\pi$
$654$	−21.8538			−0.854551
$655$	15.7279	−	9.08052i	0.614541	−	0.354805i
$656$	−1.09821	+	0.634051i	−0.0428778	+	0.0247555i
$657$			12.9343i			0.504616i
$658$		0			0
$659$	42.4853			1.65499			0.827496	−	0.561472i	$-0.189765\pi$
$659$	42.4853			1.65499			0.827496	+	0.561472i	$0.189765\pi$
$660$		−	5.73951i		−	0.223410i
$661$	−15.5667	−	26.9623i	−0.605474	−	1.04871i	−0.991976	−	0.126423i	$-0.959650\pi$
$661$	−15.5667	−	26.9623i	−0.605474	−	1.04871i	0.386503	−	0.922288i	$-0.373683\pi$
$662$	21.4558			0.833905
$663$	−14.1273	+	24.4692i	−0.548659	+	0.950305i
$664$		−	16.0502i		−	0.622868i
$665$		0			0
$666$	−5.48528	−	3.16693i	−0.212550	−	0.122716i
$667$	−18.7279	+	32.4377i	−0.725148	+	1.25599i
$668$	−16.5512	+	28.6675i	−0.640384	+	1.10918i
$669$	4.54416	−	2.62357i	0.175687	−	0.101433i
$670$	11.2485	+	19.4831i	0.434569	+	0.752696i
$671$	19.2025			0.741303
$672$		0			0
$673$	−6.38478			−0.246115			−0.123058	−	0.992400i	$-0.539270\pi$
$673$	−6.38478			−0.246115			−0.123058	+	0.992400i	$0.539270\pi$
$674$	3.00000	+	5.19615i	0.115556	+	0.200148i
$675$	14.6764	−	8.47343i	0.564895	−	0.326142i
$676$	−21.2426	+	36.7933i	−0.817025	+	1.41513i
$677$	14.7901	−	25.6173i	0.568431	−	0.984551i	−0.428290	−	0.903641i	$-0.640884\pi$
$677$	14.7901	−	25.6173i	0.568431	−	0.984551i	0.996721	−	0.0809101i	$-0.0257827\pi$
$678$	0.643315	+	0.371418i	0.0247064	+	0.0142642i
$679$		0			0
$680$			16.7262i			0.641419i
$681$	6.38478	−	11.0588i	0.244665	−	0.423772i
$682$	18.1043			0.693248
$683$	−7.07107	−	12.2474i	−0.270567	−	0.468636i	0.698440	−	0.715668i	$-0.253878\pi$
$683$	−7.07107	−	12.2474i	−0.270567	−	0.468636i	−0.969007	+	0.247033i	$0.920544\pi$
$684$		−	15.1535i		−	0.579408i
$685$	10.9269			0.417495
$686$		0			0
$687$		−	16.4800i		−	0.628750i
$688$	6.34315	+	10.9867i	0.241830	+	0.418862i
$689$	17.5552	−	10.1355i	0.668798	−	0.386131i
$690$	16.9706			0.646058
$691$	35.2712	+	20.3638i	1.34178	+	0.774676i	0.987068	−	0.160301i	$-0.0512463\pi$
$691$	35.2712	+	20.3638i	1.34178	+	0.774676i	0.354710	+	0.934976i	$0.384580\pi$
$692$	−10.3778	−	17.9749i	−0.394504	−	0.683302i
$693$		0			0
$694$	19.0711	−	33.0321i	0.723928	−	1.25388i
$695$	19.9706	+	11.5300i	0.757527	+	0.437358i
$696$	−6.85572	−	11.8745i	−0.259865	−	0.450100i
$697$	0.707107	+	1.22474i	0.0267836	+	0.0463905i
$698$	6.56165	+	11.3651i	0.248362	+	0.430176i
$699$			12.7261i			0.481344i
$700$		0			0
$701$		−	47.7290i		−	1.80270i	−0.433092	−	0.901350i	$-0.642578\pi$
$701$		−	47.7290i		−	1.80270i	0.433092	−	0.901350i	$-0.357422\pi$
$702$	37.4558	−	21.6251i	1.41368	−	0.816188i
$703$	−5.07517	−	8.79045i	−0.191414	−	0.331538i
$704$	8.00000	+	13.8564i	0.301511	+	0.522233i
$705$	−15.9079	−	9.18440i	−0.599124	−	0.345905i
$706$	−25.2150	−	14.5579i	−0.948980	−	0.547894i
$707$		0			0
$708$	1.17157	+	2.02922i	0.0440304	+	0.0762629i
$709$	−31.8198	−	18.3712i	−1.19502	−	0.689944i	−0.235578	−	0.971856i	$-0.575698\pi$
$709$	−31.8198	−	18.3712i	−1.19502	−	0.689944i	−0.959440	+	0.281912i	$0.909031\pi$
$710$		0			0
$711$	−3.21320	+	1.85514i	−0.120505	+	0.0695733i
$712$	−31.2276	−	18.0292i	−1.17030	−	0.675675i
$713$			53.5306i			2.00474i
$714$		0			0
$715$	−15.5147			−0.580218
$716$	−7.02944			−0.262702
$717$	3.42786	+	5.93723i	0.128016	+	0.221730i
$718$		−	24.4949i		−	0.914141i
$719$	−9.82868	+	17.0238i	−0.366548	+	0.634880i	−0.989023	−	0.147760i	$-0.952794\pi$
$719$	−9.82868	+	17.0238i	−0.366548	+	0.634880i	0.622475	+	0.782639i	$0.286127\pi$
$720$	4.84772	−	8.39651i	0.180664	−	0.312919i
$721$		0			0
$722$	−1.29289	+	2.23936i	−0.0481165	+	0.0833402i
$723$	9.10051	−	15.7625i	0.338451	−	0.586215i
$724$	−14.1273	+	24.4692i	−0.525037	+	0.909391i
$725$	−12.5772	+	7.26143i	−0.467104	+	0.269683i
$726$	9.27958	−	5.35757i	0.344398	−	0.198838i
$727$	49.6535			1.84155			0.920773	−	0.390098i	$-0.127559\pi$
$727$	49.6535			1.84155			0.920773	+	0.390098i	$0.127559\pi$
$728$		0			0
$729$	−17.2843			−0.640158
$730$	−11.4853	+	6.63103i	−0.425089	+	0.245425i
$731$	12.2525	−	7.07401i	0.453177	−	0.261642i
$732$	−18.0000	−	10.3923i	−0.665299	−	0.384111i
$733$	−13.4645	+	23.3212i	−0.497322	+	0.861387i	−0.999995	−	0.00308974i	$-0.999017\pi$
$733$	−13.4645	+	23.3212i	−0.497322	+	0.861387i	0.502673	+	0.864476i	$0.332350\pi$
$734$	16.2295	−	28.1103i	0.599042	−	1.03757i
$735$		0			0
$736$	−40.9706	+	23.6544i	−1.51019	+	0.871911i
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$		−	0.819760i		−	0.0301758i
$739$	−10.4142	−	18.0379i	−0.383093	−	0.663537i	0.608410	−	0.793623i	$-0.291808\pi$
$739$	−10.4142	−	18.0379i	−0.383093	−	0.663537i	−0.991503	+	0.130087i	$0.958474\pi$
$740$		−	6.49435i		−	0.238737i
$741$	26.2466			0.964194
$742$		0			0
$743$			6.33386i			0.232367i	0.993228	+	0.116183i	$0.0370660\pi$
$743$			6.33386i			0.232367i	−0.993228	+	0.116183i	$0.962934\pi$
$744$	−16.9706	−	9.79796i	−0.622171	−	0.359211i
$745$	−0.682339	+	0.393949i	−0.0249990	+	0.0144332i
$746$		−	42.4098i		−	1.55273i
$747$	8.98552	+	5.18779i	0.328763	+	0.189811i
$748$	15.4530	−	8.92177i	0.565016	−	0.326212i
$749$		0			0
$750$	14.4853	+	8.36308i	0.528928	+	0.305377i
$751$	36.9411	+	21.3280i	1.34800	+	0.778269i	0.987966	−	0.154670i	$-0.0494315\pi$
$751$	36.9411	+	21.3280i	1.34800	+	0.778269i	0.360035	+	0.932939i	$0.382765\pi$
$752$	51.2066			1.86731
$753$	−10.9289	−	18.9295i	−0.398272	−	0.689828i
$754$	−32.0983	+	18.5320i	−1.16895	+	0.674895i
$755$		−	7.28225i		−	0.265028i
$756$		0			0
$757$		−	8.18900i		−	0.297634i	−0.988865	−	0.148817i	$-0.952453\pi$
$757$		−	8.18900i		−	0.297634i	0.988865	−	0.148817i	$-0.0475466\pi$
$758$	3.75736	+	6.50794i	0.136473	+	0.236379i
$759$	−9.05213	−	15.6788i	−0.328572	−	0.569103i
$760$	13.4558	−	7.76874i	0.488095	−	0.281802i
$761$	4.09069	+	2.36176i	0.148287	+	0.0856137i	0.572308	−	0.820039i	$-0.306048\pi$
$761$	4.09069	+	2.36176i	0.148287	+	0.0856137i	−0.424021	+	0.905653i	$0.639382\pi$
$762$	11.7034	−	20.2710i	0.423971	−	0.734339i
$763$		0			0
$764$	−3.51472	+	2.02922i	−0.127158	+	0.0734147i
$765$	−9.36396	−	5.40629i	−0.338555	−	0.195465i
$766$	18.1043			0.654134
$767$	5.48528	−	3.16693i	0.198062	−	0.114351i
$768$		−	17.3183i		−	0.624919i
$769$			19.1342i			0.689996i	0.938603	+	0.344998i	$0.112120\pi$
$769$			19.1342i			0.689996i	−0.938603	+	0.344998i	$0.887880\pi$
$770$		0			0
$771$	1.31371			0.0473121
$772$	28.2843			1.01797
$773$	−21.4184	−	37.0978i	−0.770366	−	1.33431i	−0.937362	−	0.348356i	$-0.886740\pi$
$773$	−21.4184	−	37.0978i	−0.770366	−	1.33431i	0.166996	−	0.985958i	$-0.446593\pi$
$774$	−8.20101			−0.294779
$775$	−10.3778	+	17.9749i	−0.372781	+	0.645676i
$776$			26.1313i			0.938058i
$777$		0			0
$778$	−46.4558	−	26.8213i	−1.66552	−	0.961590i
$779$	0.656854	−	1.13770i	0.0235342	−	0.0407625i
$780$	14.5432	+	8.39651i	0.520729	+	0.300643i
$781$		0			0
$782$	26.3799	+	45.6912i	0.943342	+	1.63392i
$783$	23.4069			0.836494
$784$		0			0
$785$	−16.6690			−0.594944
$786$	10.4853	+	18.1610i	0.373998	+	0.647783i
$787$	40.4405	−	23.3484i	1.44155	−	0.832279i	0.443596	−	0.896227i	$-0.353702\pi$
$787$	40.4405	−	23.3484i	1.44155	−	0.832279i	0.997953	+	0.0639477i	$0.0203691\pi$
$788$	21.9411	+	12.6677i	0.781620	+	0.451269i
$789$	10.1503	−	17.5809i	0.361362	−	0.625897i
$790$	−3.29462	−	1.90215i	−0.117217	−	0.0676755i
$791$		0			0
$792$	−10.3431			−0.367528
$793$	−28.0919	+	48.6566i	−0.997572	+	1.72785i
$794$	19.5241			0.692886
$795$	−2.48528	−	4.30463i	−0.0881438	−	0.152670i
$796$	−12.8017			−0.453742
$797$	−50.6575			−1.79438			−0.897190	−	0.441644i	$-0.854395\pi$
$797$	−50.6575			−1.79438			−0.897190	+	0.441644i	$0.854395\pi$
$798$		0			0
$799$		−	57.1067i		−	2.02029i
$800$	−18.3431			−0.648528
$801$	20.1870	−	11.6549i	0.713271	−	0.411807i
$802$	22.9706			0.811119
$803$	12.2525	+	7.07401i	0.432383	+	0.249636i
$804$	−22.4971	+	12.9887i	−0.793412	+	0.458076i
$805$		0			0
$806$	−26.4853	+	45.8739i	−0.932904	+	1.61584i
$807$	−11.4853	−	6.63103i	−0.404301	−	0.233423i
$808$	0.776550	+	1.34502i	0.0273189	+	0.0473178i
$809$	−17.7279	−	30.7057i	−0.623281	−	1.07955i	−0.988871	−	0.148778i	$-0.952466\pi$
$809$	−17.7279	−	30.7057i	−0.623281	−	1.07955i	0.365590	−	0.930776i	$-0.380867\pi$
$810$	−0.160829	−	0.278564i	−0.00565095	−	0.00978773i
$811$		−	9.63274i		−	0.338251i	−0.985594	−	0.169126i	$-0.945906\pi$
$811$		−	9.63274i		−	0.338251i	0.985594	−	0.169126i	$-0.0540944\pi$
$812$		0			0
$813$			34.6410i			1.21491i
$814$	−6.00000	+	3.46410i	−0.210300	+	0.121417i
$815$	−13.3508	−	23.1242i	−0.467657	−	0.810005i
$816$	−19.3137			−0.676115
$817$	−11.3818	−	6.57128i	−0.398198	−	0.229900i
$818$	11.3152	+	6.53281i	0.395626	+	0.228415i
$819$		0			0
$820$	0.727922	−	0.420266i	0.0254201	−	0.0146763i
$821$	−32.4853	−	18.7554i	−1.13374	−	0.654567i	−0.188870	−	0.982002i	$-0.560483\pi$
$821$	−32.4853	−	18.7554i	−1.13374	−	0.654567i	−0.944874	+	0.327435i	$0.893816\pi$
$822$			12.6173i			0.440078i
$823$	18.0000	−	10.3923i	0.627441	−	0.362253i	−0.152320	−	0.988331i	$-0.548674\pi$
$823$	18.0000	−	10.3923i	0.627441	−	0.362253i	0.779760	+	0.626078i	$0.215341\pi$
$824$	−1.55310	+	2.69005i	−0.0541048	+	0.0937123i
$825$		−	7.01962i		−	0.244392i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		−	30.5826i		−	1.06282i
$829$	−2.14931	−	3.72271i	−0.0746486	−	0.129295i	0.826285	−	0.563253i	$-0.190450\pi$
$829$	−2.14931	−	3.72271i	−0.0746486	−	0.129295i	−0.900933	+	0.433957i	$0.857117\pi$
$830$			10.6385i			0.369267i
$831$	−1.55310	+	2.69005i	−0.0538765	+	0.0933168i
$832$	−46.8138			−1.62298
$833$		0			0
$834$	−13.3137	+	23.0600i	−0.461016	+	0.798503i
$835$	10.9706	−	19.0016i	0.379652	−	0.657577i
$836$	−14.3548	−	8.28772i	−0.496469	−	0.286637i
$837$	28.9706	−	16.7262i	1.00137	−	0.578141i
$838$	−8.95792	+	5.17186i	−0.309446	+	0.178659i
$839$	35.1103			1.21214			0.606072	−	0.795410i	$-0.292745\pi$
$839$	35.1103			1.21214			0.606072	+	0.795410i	$0.292745\pi$
$840$		0			0
$841$	8.94113			0.308315
$842$	15.5147	−	8.95743i	0.534673	−	0.308693i
$843$	15.6804	−	9.05309i	0.540062	−	0.311805i
$844$	−3.51472	+	6.08767i	−0.120982	+	0.209546i
$845$	14.0802	−	24.3876i	0.484374	−	0.838960i
$846$	−16.5512	+	28.6675i	−0.569041	+	0.985608i
$847$		0			0
$848$	12.0000	+	6.92820i	0.412082	+	0.237915i
$849$	−8.24264	+	14.2767i	−0.282887	+	0.489974i
$850$			20.4567i			0.701658i
$851$	−10.2426	−	17.7408i	−0.351113	−	0.608146i
$852$		0			0
$853$	−20.9830			−0.718445			−0.359223	−	0.933252i	$-0.616958\pi$
$853$	−20.9830			−0.718445			−0.359223	+	0.933252i	$0.616958\pi$
$854$		0			0
$855$			10.0441i			0.343503i
$856$	−12.0000	+	20.7846i	−0.410152	+	0.710403i
$857$	−4.86724	+	2.81010i	−0.166262	+	0.0959912i	−0.580822	−	0.814031i	$-0.697269\pi$
$857$	−4.86724	+	2.81010i	−0.166262	+	0.0959912i	0.414560	+	0.910022i	$0.363935\pi$
$858$		−	17.9149i		−	0.611603i
$859$	−29.0978	−	16.7996i	−0.992803	−	0.573195i	−0.0866923	−	0.996235i	$-0.527630\pi$
$859$	−29.0978	−	16.7996i	−0.992803	−	0.573195i	−0.906111	+	0.423040i	$0.860963\pi$
$860$	−4.20441	−	7.28225i	−0.143369	−	0.248323i
$861$		0			0
$862$	−33.2132	−	19.1757i	−1.13125	−	0.653125i
$863$	20.4853	+	11.8272i	0.697327	+	0.402602i	0.806351	−	0.591437i	$-0.201439\pi$
$863$	20.4853	+	11.8272i	0.697327	+	0.402602i	−0.109024	+	0.994039i	$0.534773\pi$
$864$	25.6033	+	14.7821i	0.871042	+	0.502896i
$865$	6.87868	+	11.9142i	0.233882	+	0.405096i
$866$	−34.4946	+	19.9155i	−1.17217	+	0.676755i
$867$			3.13839i			0.106585i
$868$		0			0
$869$			4.05845i			0.137673i
$870$	4.54416	+	7.87071i	0.154061	+	0.266842i
$871$	35.1103	+	60.8129i	1.18967	+	2.06057i
$872$	−34.9706	+	20.1903i	−1.18425	+	0.683729i
$873$	−14.6293	−	8.44623i	−0.495127	−	0.285862i
$874$	24.5051	−	42.4441i	0.828897	−	1.43569i
$875$		0			0
$876$	−7.65685	−	13.2621i	−0.258701	−	0.448084i
$877$	32.1213	+	18.5453i	1.08466	+	0.626229i	0.932150	−	0.362073i	$-0.117931\pi$
$877$	32.1213	+	18.5453i	1.08466	+	0.626229i	0.152510	+	0.988302i	$0.451264\pi$
$878$	−31.5492			−1.06474
$879$	−5.48528	+	3.16693i	−0.185014	+	0.106818i
$880$	−5.30262	−	9.18440i	−0.178751	−	0.309606i
$881$		−	36.0810i		−	1.21560i	−0.794090	−	0.607800i	$-0.792052\pi$
$881$		−	36.0810i		−	1.21560i	0.794090	−	0.607800i	$-0.207948\pi$
$882$		0			0
$883$	−46.4264			−1.56237			−0.781186	−	0.624298i	$-0.785385\pi$
$883$	−46.4264			−1.56237			−0.781186	+	0.624298i	$0.785385\pi$
$884$			52.2077i			1.75594i
$885$	−0.776550	−	1.34502i	−0.0261035	−	0.0452125i
$886$	40.0000			1.34383
$887$	−2.97297	+	5.14933i	−0.0998224	+	0.172898i	−0.911611	−	0.411054i	$-0.865161\pi$
$887$	−2.97297	+	5.14933i	−0.0998224	+	0.172898i	0.811789	+	0.583951i	$0.198494\pi$
$888$	7.49903			0.251651
$889$		0			0
$890$	20.6985	+	11.9503i	0.693815	+	0.400574i
$891$	−0.171573	+	0.297173i	−0.00574791	+	0.00995567i
$892$	4.84772	−	8.39651i	0.162314	−	0.281136i
$893$	−45.9411	+	26.5241i	−1.53736	+	0.887596i
$894$	−0.454893	−	0.787897i	−0.0152139	−	0.0263512i
$895$	4.65930			0.155743
$896$		0			0
$897$	52.9706			1.76864
$898$	−4.00000	−	6.92820i	−0.133482	−	0.231197i
$899$	−24.8268	+	14.3337i	−0.828018	+	0.478057i
$900$	5.92893	−	10.2692i	0.197631	−	0.342307i
$901$	7.72648	−	13.3827i	0.257406	−	0.445841i
$902$	−0.776550	−	0.448342i	−0.0258563	−	0.0149281i
$903$		0			0
$904$	1.37258			0.0456514
$905$	9.36396	−	16.2189i	0.311269	−	0.539133i
$906$	8.40882			0.279364
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	0.967730	−	0.251990i	$-0.0810849\pi$
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	−0.702094	+	0.712084i	$0.747752\pi$
$908$		−	23.5951i		−	0.783029i
$909$	−1.00400			−0.0333005
$910$		0			0
$911$			15.2913i			0.506623i	0.967385	+	0.253311i	$0.0815197\pi$
$911$			15.2913i			0.506623i	−0.967385	+	0.253311i	$0.918480\pi$
$912$	8.97056	+	15.5375i	0.297045	+	0.514497i
$913$	9.82868	−	5.67459i	0.325282	−	0.187802i
$914$	−37.9411			−1.25498
$915$	11.9309	+	6.88830i	0.394423	+	0.227720i
$916$	−15.2255	−	26.3714i	−0.503065	−	0.871334i
$917$		0			0
$918$	16.4853	−	28.5533i	0.544095	−	0.942401i
$919$	−32.4853	−	18.7554i	−1.07159	−	0.618683i	−0.142975	−	0.989726i	$-0.545667\pi$
$919$	−32.4853	−	18.7554i	−1.07159	−	0.618683i	−0.928616	+	0.371043i	$0.879000\pi$
$920$	27.1564	−	15.6788i	0.895320	−	0.516913i
$921$	11.8995	+	20.6105i	0.392102	+	0.679140i
$922$	−13.4174	−	23.2396i	−0.441878	−	0.765354i
$923$		0			0
$924$		0			0
$925$		−	7.94282i		−	0.261158i
$926$	10.9706	−	6.33386i	0.360515	−	0.208143i
$927$	−1.00400	−	1.73897i	−0.0329756	−	0.0571154i
$928$	−21.9411	−	12.6677i	−0.720253	−	0.415838i
$929$	−19.3162	−	11.1522i	−0.633744	−	0.365892i	0.148457	−	0.988919i	$-0.452569\pi$
$929$	−19.3162	−	11.1522i	−0.633744	−	0.365892i	−0.782201	+	0.623027i	$0.785903\pi$
$930$	11.2485	+	6.49435i	0.368854	+	0.212958i
$931$		0			0
$932$	11.7574	+	20.3643i	0.385125	+	0.667056i
$933$	−10.5442	−	6.08767i	−0.345200	−	0.199301i
$934$		−	51.9999i		−	1.70149i
$935$	−10.2426	+	5.91359i	−0.334970	+	0.193395i
$936$	15.1313	−	26.2082i	0.494582	−	0.856641i
$937$			51.4202i			1.67983i	0.542721	+	0.839913i	$0.317394\pi$
$937$			51.4202i			1.67983i	−0.542721	+	0.839913i	$0.682606\pi$
$938$		0			0
$939$	−16.3431			−0.533338
$940$	−33.9411			−1.10704
$941$	6.12627	+	10.6110i	0.199711	+	0.345909i	0.948435	−	0.316973i	$-0.102666\pi$
$941$	6.12627	+	10.6110i	0.199711	+	0.345909i	−0.748724	+	0.662882i	$0.769333\pi$
$942$		−	19.2478i		−	0.627126i
$943$	1.32565	−	2.29610i	0.0431692	−	0.0747713i
$944$	3.74952	+	2.16478i	0.122036	+	0.0704577i
$945$		0			0
$946$	−4.48528	+	7.76874i	−0.145829	+	0.252583i
$947$	−0.272078	+	0.471253i	−0.00884135	+	0.0153137i	−0.870412	−	0.492324i	$-0.836148\pi$
$947$	−0.272078	+	0.471253i	−0.00884135	+	0.0153137i	0.861571	+	0.507637i	$0.169481\pi$
$948$	2.19642	−	3.80430i	0.0713363	−	0.123558i
$949$	−35.8492	+	20.6976i	−1.16372	+	0.671872i
$950$	16.4570	−	9.50143i	0.533934	−	0.308267i
$951$	−25.6033			−0.830244
$952$		0			0
$953$	−18.6863			−0.605308			−0.302654	−	0.953100i	$-0.597873\pi$
$953$	−18.6863			−0.605308			−0.302654	+	0.953100i	$0.597873\pi$
$954$	−7.75736	+	4.47871i	−0.251154	+	0.145004i
$955$	2.32965	−	1.34502i	0.0753857	−	0.0435240i
$956$	10.9706	+	6.33386i	0.354813	+	0.204852i
$957$	4.84772	−	8.39651i	0.156705	−	0.271420i
$958$	−7.17738	+	12.4316i	−0.231890	+	0.401646i
$959$		0			0
$960$			11.4790i			0.370484i
$961$	−4.98528	+	8.63476i	−0.160816	+	0.278541i
$962$		−	20.2710i		−	0.653562i
$963$	−7.75736	−	13.4361i	−0.249977	−	0.432974i
$964$		−	33.6311i		−	1.08318i
$965$	−18.7476			−0.603506
$966$		0			0
$967$			27.9590i			0.899101i	0.893255	+	0.449550i	$0.148416\pi$
$967$			27.9590i			0.899101i	−0.893255	+	0.449550i	$0.851584\pi$
$968$	9.89949	−	17.1464i	0.318182	−	0.551107i
$969$	17.3277	−	10.0042i	0.556646	−	0.321380i
$970$		−	17.3205i		−	0.556128i
$971$	7.01655	+	4.05101i	0.225172	+	0.130003i	0.608343	−	0.793675i	$-0.291835\pi$
$971$	7.01655	+	4.05101i	0.225172	+	0.130003i	−0.383171	+	0.923677i	$0.625168\pi$
$972$	−26.8347	+	15.4930i	−0.860725	+	0.496940i
$973$		0			0
$974$	−17.6985	−	10.2182i	−0.567096	−	0.327413i
$975$	17.7868	+	10.2692i	0.569633	+	0.328878i
$976$	−38.4050			−1.22931
$977$	2.60660	+	4.51477i	0.0833926	+	0.144440i	0.904705	−	0.426038i	$-0.140091\pi$
$977$	2.60660	+	4.51477i	0.0833926	+	0.144440i	−0.821313	+	0.570478i	$0.806758\pi$
$978$	26.7015	−	15.4161i	0.853820	−	0.492953i
$979$		−	25.4972i		−	0.814894i
$980$		0			0
$981$		−	26.1039i		−	0.833432i
$982$	−5.51472	−	9.55177i	−0.175982	−	0.304809i
$983$	−13.3508	−	23.1242i	−0.425823	−	0.737547i	0.570674	−	0.821177i	$-0.306682\pi$
$983$	−13.3508	−	23.1242i	−0.425823	−	0.737547i	−0.996497	+	0.0836298i	$0.973349\pi$
$984$	0.485281	+	0.840532i	0.0154702	+	0.0267952i
$985$	−14.5432	−	8.39651i	−0.463384	−	0.267535i
$986$	−14.1273	+	24.4692i	−0.449905	+	0.779258i
$987$		0			0
$988$	42.0000	−	24.2487i	1.33620	−	0.771454i
$989$	−22.9706	−	13.2621i	−0.730421	−	0.421709i
$990$	6.85572			0.217889
$991$	39.9411	−	23.0600i	1.26877	−	0.732526i	0.294016	−	0.955800i	$-0.405008\pi$
$991$	39.9411	−	23.0600i	1.26877	−	0.732526i	0.974756	+	0.223275i	$0.0716747\pi$
$992$	−36.2085			−1.14962
$993$		−	16.4216i		−	0.521123i
$994$		0			0
$995$	8.48528			0.269002
$996$	−12.2843			−0.389242
$997$	16.1158	+	27.9134i	0.510392	+	0.884025i	0.999927	+	0.0120416i	$0.00383305\pi$
$997$	16.1158	+	27.9134i	0.510392	+	0.884025i	−0.489535	+	0.871983i	$0.662834\pi$
$998$	12.0000			0.379853
$999$	−6.40083	+	11.0866i	−0.202513	+	0.350763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.m.c.19.1		8
4.3	odd	2		1568.2.q.c.1391.3		8
7.2	even	3		392.2.e.c.195.3	yes	8
7.3	odd	6		392.2.m.e.227.3		8
7.4	even	3		392.2.m.e.227.4		8
7.5	odd	6		392.2.e.c.195.4	yes	8
7.6	odd	2	inner	392.2.m.c.19.2		8
8.3	odd	2		392.2.m.e.19.3		8
8.5	even	2		1568.2.q.d.1391.3		8
28.3	even	6		1568.2.q.d.815.3		8
28.11	odd	6		1568.2.q.d.815.2		8
28.19	even	6		1568.2.e.c.783.4		8
28.23	odd	6		1568.2.e.c.783.5		8
28.27	even	2		1568.2.q.c.1391.2		8
56.3	even	6	inner	392.2.m.c.227.1		8
56.5	odd	6		1568.2.e.c.783.3		8
56.11	odd	6	inner	392.2.m.c.227.2		8
56.13	odd	2		1568.2.q.d.1391.2		8
56.19	even	6		392.2.e.c.195.2	yes	8
56.27	even	2		392.2.m.e.19.4		8
56.37	even	6		1568.2.e.c.783.6		8
56.45	odd	6		1568.2.q.c.815.3		8
56.51	odd	6		392.2.e.c.195.1	✓	8
56.53	even	6		1568.2.q.c.815.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.c.195.1	✓	8	56.51	odd	6
392.2.e.c.195.2	yes	8	56.19	even	6
392.2.e.c.195.3	yes	8	7.2	even	3
392.2.e.c.195.4	yes	8	7.5	odd	6
392.2.m.c.19.1		8	1.1	even	1	trivial
392.2.m.c.19.2		8	7.6	odd	2	inner
392.2.m.c.227.1		8	56.3	even	6	inner
392.2.m.c.227.2		8	56.11	odd	6	inner
392.2.m.e.19.3		8	8.3	odd	2
392.2.m.e.19.4		8	56.27	even	2
392.2.m.e.227.3		8	7.3	odd	6
392.2.m.e.227.4		8	7.4	even	3
1568.2.e.c.783.3		8	56.5	odd	6
1568.2.e.c.783.4		8	28.19	even	6
1568.2.e.c.783.5		8	28.23	odd	6
1568.2.e.c.783.6		8	56.37	even	6
1568.2.q.c.815.2		8	56.53	even	6
1568.2.q.c.815.3		8	56.45	odd	6
1568.2.q.c.1391.2		8	28.27	even	2
1568.2.q.c.1391.3		8	4.3	odd	2
1568.2.q.d.815.2		8	28.11	odd	6
1568.2.q.d.815.3		8	28.3	even	6
1568.2.q.d.1391.2		8	56.13	odd	2
1568.2.q.d.1391.3		8	8.5	even	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-0.937379 + 0.541196i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.662827 - 1.14805i) q^{5} +(1.32565 + 0.765367i) q^{6} +2.82843 q^{8} +(-0.914214 + 1.58346i) q^{9} -1.87476 q^{10} +(1.00000 + 1.73205i) q^{11} -2.16478i q^{12} -5.85172 q^{13} +1.43488i q^{15} +(-2.00000 - 3.46410i) q^{16} +(-3.86324 + 2.23044i) q^{17} +2.58579 q^{18} +(3.58869 + 2.07193i) q^{19} +(1.32565 + 2.29610i) q^{20} +(1.41421 - 2.44949i) q^{22} +(7.24264 + 4.18154i) q^{23} +(-2.65131 + 1.53073i) q^{24} +(1.62132 + 2.80821i) q^{25} +(4.13779 + 7.16687i) q^{26} -5.22625i q^{27} +4.47871i q^{29} +(1.75736 - 1.01461i) q^{30} +(3.20041 + 5.54328i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-1.87476 - 1.08239i) q^{33} +(5.46345 + 3.15432i) q^{34} +(-1.82843 - 3.16693i) q^{36} +(-2.12132 - 1.22474i) q^{37} -5.86030i q^{38} +(5.48528 - 3.16693i) q^{39} +(1.87476 - 3.24718i) q^{40} -0.317025i q^{41} -3.17157 q^{43} -4.00000 q^{44} +(1.21193 + 2.09913i) q^{45} -11.8272i q^{46} +(-6.40083 + 11.0866i) q^{47} +(3.74952 + 2.16478i) q^{48} +(2.29289 - 3.97141i) q^{50} +(2.41421 - 4.18154i) q^{51} +(5.85172 - 10.1355i) q^{52} +(-3.00000 + 1.73205i) q^{53} +(-6.40083 + 3.69552i) q^{54} +2.65131 q^{55} -4.48528 q^{57} +(5.48528 - 3.16693i) q^{58} +(-0.937379 + 0.541196i) q^{59} +(-2.48528 - 1.43488i) q^{60} +(4.80062 - 8.31492i) q^{61} +(4.52607 - 7.83938i) q^{62} +8.00000 q^{64} +(-3.87868 + 6.71807i) q^{65} +3.06147i q^{66} +(-6.00000 - 10.3923i) q^{67} -8.92177i q^{68} -9.05213 q^{69} +(-2.58579 + 4.47871i) q^{72} +(6.12627 - 3.53701i) q^{73} +3.46410i q^{74} +(-3.03958 - 1.75490i) q^{75} +(-7.17738 + 4.14386i) q^{76} +(-7.75736 - 4.47871i) q^{78} +(1.75736 + 1.01461i) q^{79} -5.30262 q^{80} +(0.0857864 + 0.148586i) q^{81} +(-0.388275 + 0.224171i) q^{82} -5.67459i q^{83} +5.91359i q^{85} +(2.24264 + 3.88437i) q^{86} +(-2.42386 - 4.19825i) q^{87} +(2.82843 + 4.89898i) q^{88} +(-11.0406 - 6.37430i) q^{89} +(1.71393 - 2.96861i) q^{90} +(-14.4853 + 8.36308i) q^{92} +(-6.00000 - 3.46410i) q^{93} +18.1043 q^{94} +(4.75736 - 2.74666i) q^{95} -6.12293i q^{96} +9.23880i q^{97} -3.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{9} + 8 q^{11} - 16 q^{16} + 32 q^{18} + 24 q^{23} - 4 q^{25} + 48 q^{30} + 8 q^{36} - 24 q^{39} - 48 q^{43} - 32 q^{44} + 24 q^{50} + 8 q^{51} - 24 q^{53} + 32 q^{57} - 24 q^{58} + 48 q^{60}+ \cdots + 16 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^9 + 8 * q^11 - 16 * q^16 + 32 * q^18 + 24 * q^23 - 4 * q^25 + 48 * q^30 + 8 * q^36 - 24 * q^39 - 48 * q^43 - 32 * q^44 + 24 * q^50 + 8 * q^51 - 24 * q^53 + 32 * q^57 - 24 * q^58 + 48 * q^60 + 64 * q^64 - 48 * q^65 - 48 * q^67 - 32 * q^72 - 96 * q^78 + 48 * q^79 + 12 * q^81 - 16 * q^86 - 48 * q^92 - 48 * q^93 + 72 * q^95 + 16 * q^99

Introduction

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