LMFDB - Embedded newform 392.2.e.c.195.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(195,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.195"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,0,0,0,-8] 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:	$8$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.3
Root			$-1.60021 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	392.195
Dual form			392.2.e.c.195.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 1.22474i) q^{2} -1.08239i q^{3} +(-1.00000 - 1.73205i) q^{4} -1.32565 q^{5} +(1.32565 + 0.765367i) q^{6} +2.82843 q^{8} +1.82843 q^{9} +(0.937379 - 1.62359i) q^{10} -2.00000 q^{11} +(-1.87476 + 1.08239i) q^{12} -5.85172 q^{13} +1.43488i q^{15} +(-2.00000 + 3.46410i) q^{16} -4.46088i q^{17} +(-1.29289 + 2.23936i) q^{18} -4.14386i q^{19} +(1.32565 + 2.29610i) q^{20} +(1.41421 - 2.44949i) q^{22} -8.36308i q^{23} -3.06147i q^{24} -3.24264 q^{25} +(4.13779 - 7.16687i) q^{26} -5.22625i q^{27} +4.47871i q^{29} +(-1.75736 - 1.01461i) q^{30} -6.40083 q^{31} +(-2.82843 - 4.89898i) q^{32} +2.16478i q^{33} +(5.46345 + 3.15432i) q^{34} +(-1.82843 - 3.16693i) q^{36} +2.44949i q^{37} +(5.07517 + 2.93015i) q^{38} +6.33386i q^{39} -3.74952 q^{40} -0.317025i q^{41} -3.17157 q^{43} +(2.00000 + 3.46410i) q^{44} -2.42386 q^{45} +(10.2426 + 5.91359i) q^{46} +12.8017 q^{47} +(3.74952 + 2.16478i) q^{48} +(2.29289 - 3.97141i) q^{50} -4.82843 q^{51} +(5.85172 + 10.1355i) q^{52} -3.46410i q^{53} +(6.40083 + 3.69552i) q^{54} +2.65131 q^{55} -4.48528 q^{57} +(-5.48528 - 3.16693i) q^{58} -1.08239i q^{59} +(2.48528 - 1.43488i) q^{60} -9.60124 q^{61} +(4.52607 - 7.83938i) q^{62} +8.00000 q^{64} +7.75736 q^{65} +(-2.65131 - 1.53073i) q^{66} +12.0000 q^{67} +(-7.72648 + 4.46088i) q^{68} -9.05213 q^{69} +5.17157 q^{72} +7.07401i q^{73} +(-3.00000 - 1.73205i) q^{74} +3.50981i q^{75} +(-7.17738 + 4.14386i) q^{76} +(-7.75736 - 4.47871i) q^{78} -2.02922i q^{79} +(2.65131 - 4.59220i) q^{80} -0.171573 q^{81} +(0.388275 + 0.224171i) q^{82} -5.67459i q^{83} +5.91359i q^{85} +(2.24264 - 3.88437i) q^{86} +4.84772 q^{87} -5.65685 q^{88} +12.7486i q^{89} +(1.71393 - 2.96861i) q^{90} +(-14.4853 + 8.36308i) q^{92} +6.92820i q^{93} +(-9.05213 + 15.6788i) q^{94} +5.49333i q^{95} +(-5.30262 + 3.06147i) q^{96} +9.23880i q^{97} -3.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{18} + 8 q^{25} - 48 q^{30} + 8 q^{36} - 48 q^{43} + 16 q^{44} + 48 q^{46} + 24 q^{50} - 16 q^{51} + 32 q^{57} + 24 q^{58} - 48 q^{60} + 64 q^{64}+ \cdots + 16 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^18 + 8 * q^25 - 48 * q^30 + 8 * q^36 - 48 * q^43 + 16 * q^44 + 48 * q^46 + 24 * q^50 - 16 * q^51 + 32 * q^57 + 24 * q^58 - 48 * q^60 + 64 * q^64 + 96 * q^65 + 96 * q^67 + 64 * q^72 - 24 * q^74 - 96 * q^78 - 24 * q^81 - 16 * q^86 - 48 * q^92 + 16 * q^99

Character values

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

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$-1$

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
$3$		−	1.08239i		−	0.624919i	−0.949931	−	0.312460i	$-0.898847\pi$
$3$		−	1.08239i		−	0.624919i	0.949931	−	0.312460i	$-0.101153\pi$
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	−1.32565			−0.592851			−0.296425	−	0.955056i	$-0.595795\pi$
$5$	−1.32565			−0.592851			−0.296425	+	0.955056i	$0.595795\pi$
$6$	1.32565	+	0.765367i	0.541196	+	0.312460i
$7$		0			0
$7$		0			0
$8$	2.82843			1.00000
$9$	1.82843			0.609476
$10$	0.937379	−	1.62359i	0.296425	−	0.513424i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	−1.87476	+	1.08239i	−0.541196	+	0.312460i
$13$	−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
$17$		−	4.46088i		−	1.08192i	−0.841047	−	0.540962i	$-0.818060\pi$
$17$		−	4.46088i		−	1.08192i	0.841047	−	0.540962i	$-0.181940\pi$
$18$	−1.29289	+	2.23936i	−0.304738	+	0.527821i
$19$		−	4.14386i		−	0.950667i	−0.879806	−	0.475333i	$-0.842327\pi$
$19$		−	4.14386i		−	0.950667i	0.879806	−	0.475333i	$-0.157673\pi$
$20$	1.32565	+	2.29610i	0.296425	+	0.513424i
$21$		0			0
$22$	1.41421	−	2.44949i	0.301511	−	0.522233i
$23$		−	8.36308i		−	1.74382i	−0.489664	−	0.871911i	$-0.662880\pi$
$23$		−	8.36308i		−	1.74382i	0.489664	−	0.871911i	$-0.337120\pi$
$24$		−	3.06147i		−	0.624919i
$25$	−3.24264			−0.648528
$26$	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
$31$	−6.40083			−1.14962			−0.574811	−	0.818286i	$-0.694924\pi$
$31$	−6.40083			−1.14962			−0.574811	+	0.818286i	$0.694924\pi$
$32$	−2.82843	−	4.89898i	−0.500000	−	0.866025i
$33$			2.16478i			0.376841i
$34$	5.46345	+	3.15432i	0.936973	+	0.540962i
$35$		0			0
$36$	−1.82843	−	3.16693i	−0.304738	−	0.527821i
$37$			2.44949i			0.402694i	0.979520	+	0.201347i	$0.0645318\pi$
$37$			2.44949i			0.402694i	−0.979520	+	0.201347i	$0.935468\pi$
$38$	5.07517	+	2.93015i	0.823301	+	0.475333i
$39$			6.33386i			1.01423i
$40$	−3.74952			−0.592851
$41$		−	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	$0.577748\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$	−2.42386			−0.361328
$46$	10.2426	+	5.91359i	1.51019	+	0.871911i
$47$	12.8017			1.86731			0.933656	−	0.358170i	$-0.116599\pi$
$47$	12.8017			1.86731			0.933656	+	0.358170i	$0.116599\pi$
$48$	3.74952	+	2.16478i	0.541196	+	0.312460i
$49$		0			0
$50$	2.29289	−	3.97141i	0.324264	−	0.561642i
$51$	−4.82843			−0.676115
$52$	5.85172	+	10.1355i	0.811488	+	1.40554i
$53$		−	3.46410i		−	0.475831i	−0.971286	−	0.237915i	$-0.923536\pi$
$53$		−	3.46410i		−	0.475831i	0.971286	−	0.237915i	$-0.0764641\pi$
$54$	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
$59$		−	1.08239i		−	0.140915i	−0.997515	−	0.0704577i	$-0.977554\pi$
$59$		−	1.08239i		−	0.140915i	0.997515	−	0.0704577i	$-0.0224460\pi$
$60$	2.48528	−	1.43488i	0.320848	−	0.185242i
$61$	−9.60124			−1.22931			−0.614656	−	0.788795i	$-0.710705\pi$
$61$	−9.60124			−1.22931			−0.614656	+	0.788795i	$0.710705\pi$
$62$	4.52607	−	7.83938i	0.574811	−	0.995602i
$63$		0			0
$64$	8.00000			1.00000
$65$	7.75736			0.962182
$66$	−2.65131	−	1.53073i	−0.326354	−	0.188420i
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$	−7.72648	+	4.46088i	−0.936973	+	0.540962i
$69$	−9.05213			−1.08975
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	5.17157			0.609476
$73$			7.07401i			0.827950i	0.910288	+	0.413975i	$0.135860\pi$
$73$			7.07401i			0.827950i	−0.910288	+	0.413975i	$0.864140\pi$
$74$	−3.00000	−	1.73205i	−0.348743	−	0.201347i
$75$			3.50981i			0.405278i
$76$	−7.17738	+	4.14386i	−0.823301	+	0.475333i
$77$		0			0
$78$	−7.75736	−	4.47871i	−0.878348	−	0.507114i
$79$		−	2.02922i		−	0.228306i	−0.993463	−	0.114153i	$-0.963585\pi$
$79$		−	2.02922i		−	0.228306i	0.993463	−	0.114153i	$-0.0364153\pi$
$80$	2.65131	−	4.59220i	0.296425	−	0.513424i
$81$	−0.171573			−0.0190637
$82$	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
$87$	4.84772			0.519731
$88$	−5.65685			−0.603023
$89$			12.7486i			1.35135i	0.737200	+	0.675675i	$0.236148\pi$
$89$			12.7486i			1.35135i	−0.737200	+	0.675675i	$0.763852\pi$
$90$	1.71393	−	2.96861i	0.180664	−	0.312919i
$91$		0			0
$92$	−14.4853	+	8.36308i	−1.51019	+	0.871911i
$93$			6.92820i			0.718421i
$94$	−9.05213	+	15.6788i	−0.933656	+	1.61714i
$95$			5.49333i			0.563603i
$96$	−5.30262	+	3.06147i	−0.541196	+	0.312460i
$97$			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
$100$	3.24264	+	5.61642i	0.324264	+	0.561642i
$101$	−0.549104			−0.0546379			−0.0273189	−	0.999627i	$-0.508697\pi$
$101$	−0.549104			−0.0546379			−0.0273189	+	0.999627i	$0.508697\pi$
$102$	3.41421	−	5.91359i	0.338058	−	0.585533i
$103$	1.09821			0.108210			0.0541048	−	0.998535i	$-0.482769\pi$
$103$	1.09821			0.108210			0.0541048	+	0.998535i	$0.482769\pi$
$104$	−16.5512			−1.62298
$105$		0			0
$106$	4.24264	+	2.44949i	0.412082	+	0.237915i
$107$	8.48528			0.820303			0.410152	−	0.912017i	$-0.365476\pi$
$107$	8.48528			0.820303			0.410152	+	0.912017i	$0.365476\pi$
$108$	−9.05213	+	5.22625i	−0.871042	+	0.502896i
$109$		−	14.2767i		−	1.36746i	−0.729736	−	0.683729i	$-0.760357\pi$
$109$		−	14.2767i		−	1.36746i	0.729736	−	0.683729i	$-0.239643\pi$
$110$	−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
$115$			11.0866i			1.03383i
$116$	7.75736	−	4.47871i	0.720253	−	0.415838i
$117$	−10.6994			−0.989164
$118$	1.32565	+	0.765367i	0.122036	+	0.0704577i
$119$		0			0
$120$			4.05845i			0.370484i
$121$	−7.00000			−0.636364
$122$	6.78910	−	11.7591i	0.614656	−	1.06462i
$123$	−0.343146			−0.0309404
$124$	6.40083	+	11.0866i	0.574811	+	0.995602i
$125$	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
$129$			3.43289i			0.302249i
$130$	−5.48528	+	9.50079i	−0.481091	+	0.833274i
$131$		−	13.6997i		−	1.19695i	−0.801143	−	0.598473i	$-0.795774\pi$
$131$		−	13.6997i		−	1.19695i	0.801143	−	0.598473i	$-0.204226\pi$
$132$	3.74952	−	2.16478i	0.326354	−	0.188420i
$133$		0			0
$134$	−8.48528	+	14.6969i	−0.733017	+	1.26962i
$135$			6.92820i			0.596285i
$136$		−	12.6173i		−	1.08192i
$137$	−8.24264			−0.704216			−0.352108	−	0.935959i	$-0.614535\pi$
$137$	−8.24264			−0.704216			−0.352108	+	0.935959i	$0.614535\pi$
$138$	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
$143$	11.7034			0.978691
$144$	−3.65685	+	6.33386i	−0.304738	+	0.527821i
$145$		−	5.93723i		−	0.493060i
$146$	−8.66386	−	5.00208i	−0.717026	−	0.413975i
$147$		0			0
$148$	4.24264	−	2.44949i	0.348743	−	0.201347i
$149$			0.594346i			0.0486907i	0.999704	+	0.0243454i	$0.00775013\pi$
$149$			0.594346i			0.0486907i	−0.999704	+	0.0243454i	$0.992250\pi$
$150$	−4.29862	−	2.48181i	−0.350981	−	0.202639i
$151$			5.49333i			0.447040i	0.974699	+	0.223520i	$0.0717549\pi$
$151$			5.49333i			0.447040i	−0.974699	+	0.223520i	$0.928245\pi$
$152$		−	11.7206i		−	0.950667i
$153$		−	8.15640i		−	0.659406i
$154$		0			0
$155$	8.48528			0.681554
$156$	10.9706	−	6.33386i	0.878348	−	0.507114i
$157$	12.5742			1.00353			0.501765	−	0.865004i	$-0.332684\pi$
$157$	12.5742			1.00353			0.501765	+	0.865004i	$0.332684\pi$
$158$	2.48528	+	1.43488i	0.197718	+	0.114153i
$159$	−3.74952			−0.297356
$160$	3.74952	+	6.49435i	0.296425	+	0.513424i
$161$		0			0
$162$	0.121320	−	0.210133i	0.00953183	−	0.0165096i
$163$	−20.1421			−1.57765			−0.788827	−	0.614615i	$-0.789311\pi$
$163$	−20.1421			−1.57765			−0.788827	+	0.614615i	$0.789311\pi$
$164$	−0.549104	+	0.317025i	−0.0428778	+	0.0247555i
$165$		−	2.86976i		−	0.223410i
$166$	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
$171$		−	7.57675i		−	0.579408i
$172$	3.17157	+	5.49333i	0.241830	+	0.418862i
$173$	10.3778			0.789009			0.394504	−	0.918894i	$-0.370916\pi$
$173$	10.3778			0.789009			0.394504	+	0.918894i	$0.370916\pi$
$174$	−3.42786	+	5.93723i	−0.259865	+	0.450100i
$175$		0			0
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	−1.17157			−0.0880608
$178$	−15.6138	−	9.01462i	−1.17030	−	0.675675i
$179$	−3.51472			−0.262702			−0.131351	−	0.991336i	$-0.541932\pi$
$179$	−3.51472			−0.262702			−0.131351	+	0.991336i	$0.541932\pi$
$180$	2.42386	+	4.19825i	0.180664	+	0.312919i
$181$	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
$184$		−	23.6544i		−	1.74382i
$185$		−	3.24718i		−	0.238737i
$186$	−8.48528	−	4.89898i	−0.622171	−	0.359211i
$187$			8.92177i			0.652424i
$188$	−12.8017	−	22.1731i	−0.933656	−	1.61714i
$189$		0			0
$190$	−6.72792	−	3.88437i	−0.488095	−	0.281802i
$191$		−	2.02922i		−	0.146829i	−0.997301	−	0.0734147i	$-0.976610\pi$
$191$		−	2.02922i		−	0.146829i	0.997301	−	0.0734147i	$-0.0233897\pi$
$192$		−	8.65914i		−	0.624919i
$193$	14.1421			1.01797			0.508987	−	0.860774i	$-0.330020\pi$
$193$	14.1421			1.01797			0.508987	+	0.860774i	$0.330020\pi$
$194$	−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
$199$	−6.40083			−0.453742			−0.226871	−	0.973925i	$-0.572850\pi$
$199$	−6.40083			−0.453742			−0.226871	+	0.973925i	$0.572850\pi$
$200$	−9.17157			−0.648528
$201$		−	12.9887i		−	0.916153i
$202$	0.388275	−	0.672512i	0.0273189	−	0.0473178i
$203$		0			0
$204$	4.82843	+	8.36308i	0.338058	+	0.585533i
$205$			0.420266i			0.0293527i
$206$	−0.776550	+	1.34502i	−0.0541048	+	0.0937123i
$207$		−	15.2913i		−	1.06282i
$208$	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	$0.461396\pi$
$212$	−6.00000	+	3.46410i	−0.412082	+	0.237915i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	4.20441			0.286738
$216$		−	14.7821i		−	1.00579i
$217$		0			0
$218$	17.4853	+	10.0951i	1.18425	+	0.683729i
$219$	7.65685			0.517402
$220$	−2.65131	−	4.59220i	−0.178751	−	0.309606i
$221$			26.1039i			1.75594i
$222$	−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
$227$		−	11.7975i		−	0.783029i	−0.920172	−	0.391515i	$-0.871951\pi$
$227$		−	11.7975i		−	0.783029i	0.920172	−	0.391515i	$-0.128049\pi$
$228$	4.48528	+	7.76874i	0.297045	+	0.514497i
$229$	15.2255			1.00613			0.503065	−	0.864249i	$-0.332206\pi$
$229$	15.2255			1.00613			0.503065	+	0.864249i	$0.332206\pi$
$230$	−13.5782	−	7.83938i	−0.895320	−	0.516913i
$231$		0			0
$232$			12.6677i			0.831676i
$233$	−11.7574			−0.770250			−0.385125	−	0.922864i	$-0.625842\pi$
$233$	−11.7574			−0.770250			−0.385125	+	0.922864i	$0.625842\pi$
$234$	7.56565	−	13.1041i	0.494582	−	0.856641i
$235$	−16.9706			−1.10704
$236$	−1.87476	+	1.08239i	−0.122036	+	0.0704577i
$237$	−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
$241$		−	16.8155i		−	1.08318i	−0.840641	−	0.541592i	$-0.817822\pi$
$241$		−	16.8155i		−	1.08318i	0.840641	−	0.541592i	$-0.182178\pi$
$242$	4.94975	−	8.57321i	0.318182	−	0.551107i
$243$		−	15.4930i		−	0.993879i
$244$	9.60124	+	16.6298i	0.614656	+	1.06462i
$245$		0			0
$246$	0.242641	−	0.420266i	0.0154702	−	0.0267952i
$247$			24.2487i			1.54291i
$248$	−18.1043			−1.14962
$249$	−6.14214			−0.389242
$250$	−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
$255$	6.40083			0.400835
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$			1.21371i			0.0757090i	0.999283	+	0.0378545i	$0.0120523\pi$
$257$			1.21371i			0.0757090i	−0.999283	+	0.0378545i	$0.987948\pi$
$258$	−4.20441	−	2.42742i	−0.261755	−	0.151124i
$259$		0			0
$260$	−7.75736	−	13.4361i	−0.481091	−	0.833274i
$261$			8.18900i			0.506886i
$262$	16.7786	+	9.68714i	1.03659	+	0.598473i
$263$		−	18.7554i		−	1.15651i	−0.815857	−	0.578253i	$-0.803735\pi$
$263$		−	18.7554i		−	1.15651i	0.815857	−	0.578253i	$-0.196265\pi$
$264$			6.12293i			0.376841i
$265$			4.59220i			0.282097i
$266$		0			0
$267$	13.7990			0.844484
$268$	−12.0000	−	20.7846i	−0.733017	−	1.26962i
$269$	−12.2525			−0.747051			−0.373525	−	0.927620i	$-0.621851\pi$
$269$	−12.2525			−0.747051			−0.373525	+	0.927620i	$0.621851\pi$
$270$	−8.48528	−	4.89898i	−0.516398	−	0.298142i
$271$	−32.0041			−1.94411			−0.972056	−	0.234749i	$-0.924573\pi$
$271$	−32.0041			−1.94411			−0.972056	+	0.234749i	$0.924573\pi$
$272$	15.4530	+	8.92177i	0.936973	+	0.540962i
$273$		0			0
$274$	5.82843	−	10.0951i	0.352108	−	0.609869i
$275$	6.48528			0.391077
$276$	9.05213	+	15.6788i	0.544874	+	0.943750i
$277$			2.86976i			0.172427i	0.996277	+	0.0862135i	$0.0274767\pi$
$277$			2.86976i			0.172427i	−0.996277	+	0.0862135i	$0.972523\pi$
$278$	−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
$283$			15.2304i			0.905354i	0.891675	+	0.452677i	$0.149531\pi$
$283$			15.2304i			0.905354i	−0.891675	+	0.452677i	$0.850469\pi$
$284$		0			0
$285$	5.94593			0.352207
$286$	−8.27558	+	14.3337i	−0.489346	+	0.847571i
$287$		0			0
$288$	−5.17157	−	8.95743i	−0.304738	−	0.527821i
$289$	−2.89949			−0.170559
$290$	7.27159	+	4.19825i	0.427002	+	0.246530i
$291$	10.0000			0.586210
$292$	12.2525	−	7.07401i	0.717026	−	0.413975i
$293$	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
$296$			6.92820i			0.402694i
$297$			10.4525i			0.606516i
$298$	−0.727922	−	0.420266i	−0.0421674	−	0.0243454i
$299$			48.9384i			2.83018i
$300$	6.07917	−	3.50981i	0.350981	−	0.202639i
$301$		0			0
$302$	−6.72792	−	3.88437i	−0.387148	−	0.223520i
$303$			0.594346i			0.0341443i
$304$	14.3548	+	8.28772i	0.823301	+	0.475333i
$305$	12.7279			0.728799
$306$	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
$311$	−11.2485			−0.637847			−0.318923	−	0.947781i	$-0.603321\pi$
$311$	−11.2485			−0.637847			−0.318923	+	0.947781i	$0.603321\pi$
$312$			17.9149i			1.01423i
$313$		−	15.0991i		−	0.853451i	−0.904381	−	0.426726i	$-0.859667\pi$
$313$		−	15.0991i		−	0.853451i	0.904381	−	0.426726i	$-0.140333\pi$
$314$	−8.89130	+	15.4002i	−0.501765	+	0.869083i
$315$		0			0
$316$	−3.51472	+	2.02922i	−0.197718	+	0.114153i
$317$		−	23.6544i		−	1.32856i	−0.747483	−	0.664281i	$-0.768738\pi$
$317$		−	23.6544i		−	1.32856i	0.747483	−	0.664281i	$-0.231262\pi$
$318$	2.65131	−	4.59220i	0.148678	−	0.257518i
$319$		−	8.95743i		−	0.501520i
$320$	−10.6052			−0.592851
$321$		−	9.18440i		−	0.512623i
$322$		0			0
$323$	−18.4853			−1.02855
$324$	0.171573	+	0.297173i	0.00953183	+	0.0165096i
$325$	18.9750			1.05255
$326$	14.2426	−	24.6690i	0.788827	−	1.36629i
$327$	−15.4530			−0.854551
$328$		−	0.896683i		−	0.0495110i
$329$		0			0
$330$	3.51472	+	2.02922i	0.193479	+	0.111705i
$331$	15.1716			0.833905			0.416953	−	0.908928i	$-0.363098\pi$
$331$	15.1716			0.833905			0.416953	+	0.908928i	$0.363098\pi$
$332$	−9.82868	+	5.67459i	−0.539419	+	0.311434i
$333$			4.47871i			0.245432i
$334$	−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
$339$		−	0.525265i		−	0.0285285i
$340$	10.2426	−	5.91359i	0.555485	−	0.320710i
$341$	12.8017			0.693248
$342$	9.27958	+	5.35757i	0.501782	+	0.289704i
$343$		0			0
$344$	−8.97056			−0.483660
$345$	12.0000			0.646058
$346$	−7.33820	+	12.7101i	−0.394504	+	0.683302i
$347$	−26.9706			−1.44786			−0.723928	−	0.689876i	$-0.757665\pi$
$347$	−26.9706			−1.44786			−0.723928	+	0.689876i	$0.757665\pi$
$348$	−4.84772	−	8.39651i	−0.259865	−	0.450100i
$349$	−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
$352$	5.65685	+	9.79796i	0.301511	+	0.522233i
$353$			20.5880i			1.09579i	0.836548	+	0.547894i	$0.184570\pi$
$353$			20.5880i			1.09579i	−0.836548	+	0.547894i	$0.815430\pi$
$354$	0.828427	−	1.43488i	0.0440304	−	0.0762629i
$355$		0			0
$356$	22.0812	−	12.7486i	1.17030	−	0.675675i
$357$		0			0
$358$	2.48528	−	4.30463i	0.131351	−	0.227507i
$359$		−	17.3205i		−	0.914141i	−0.889430	−	0.457071i	$-0.848899\pi$
$359$		−	17.3205i		−	0.914141i	0.889430	−	0.457071i	$-0.151101\pi$
$360$	−6.85572			−0.361328
$361$	1.82843			0.0962330
$362$	−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
$367$	−22.9520			−1.19808			−0.599042	−	0.800718i	$-0.704452\pi$
$367$	−22.9520			−1.19808			−0.599042	+	0.800718i	$0.704452\pi$
$368$	28.9706	+	16.7262i	1.51019	+	0.871911i
$369$		−	0.579658i		−	0.0301758i
$370$	3.97696	+	2.29610i	0.206752	+	0.119369i
$371$		0			0
$372$	12.0000	−	6.92820i	0.622171	−	0.359211i
$373$		−	29.9882i		−	1.55273i	−0.630283	−	0.776366i	$-0.717061\pi$
$373$		−	29.9882i		−	1.55273i	0.630283	−	0.776366i	$-0.282939\pi$
$374$	−10.9269	−	6.30864i	−0.565016	−	0.326212i
$375$		−	11.8272i		−	0.610753i
$376$	36.2085			1.86731
$377$		−	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	$0.543577\pi$
$380$	9.51472	−	5.49333i	0.488095	−	0.281802i
$381$	−16.5512			−0.847942
$382$	2.48528	+	1.43488i	0.127158	+	0.0734147i
$383$	12.8017			0.654134			0.327067	−	0.945001i	$-0.393940\pi$
$383$	12.8017			0.654134			0.327067	+	0.945001i	$0.393940\pi$
$384$	10.6052	+	6.12293i	0.541196	+	0.312460i
$385$		0			0
$386$	−10.0000	+	17.3205i	−0.508987	+	0.881591i
$387$	−5.79899			−0.294779
$388$	16.0021	−	9.23880i	0.812382	−	0.469029i
$389$			37.9310i			1.92318i	0.274490	+	0.961590i	$0.411491\pi$
$389$			37.9310i			1.92318i	−0.274490	+	0.961590i	$0.588509\pi$
$390$	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
$395$			2.69005i			0.135351i
$396$	3.65685	+	6.33386i	0.183764	+	0.318288i
$397$	13.8056			0.692886			0.346443	−	0.938071i	$-0.387389\pi$
$397$	13.8056			0.692886			0.346443	+	0.938071i	$0.387389\pi$
$398$	4.52607	−	7.83938i	0.226871	−	0.392953i
$399$		0			0
$400$	6.48528	−	11.2328i	0.324264	−	0.561642i
$401$	16.2426			0.811119			0.405559	−	0.914069i	$-0.367077\pi$
$401$	16.2426			0.811119			0.405559	+	0.914069i	$0.367077\pi$
$402$	15.9079	+	9.18440i	0.793412	+	0.458076i
$403$	37.4558			1.86581
$404$	0.549104	+	0.951076i	0.0273189	+	0.0473178i
$405$	0.227446			0.0113019
$406$		0			0
$407$		−	4.89898i		−	0.242833i
$408$	−13.6569			−0.676115
$409$		−	9.23880i		−	0.456829i	−0.973564	−	0.228415i	$-0.926646\pi$
$409$		−	9.23880i		−	0.456829i	0.973564	−	0.228415i	$-0.0733541\pi$
$410$	−0.514719	−	0.297173i	−0.0254201	−	0.0146763i
$411$			8.92177i			0.440078i
$412$	−1.09821	−	1.90215i	−0.0541048	−	0.0937123i
$413$		0			0
$414$	18.7279	+	10.8126i	0.920427	+	0.531409i
$415$			7.52255i			0.369267i
$416$	16.5512	+	28.6675i	0.811488	+	1.40554i
$417$	18.8284			0.922032
$418$	−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
$423$	23.4069			1.13808
$424$		−	9.79796i		−	0.475831i
$425$			14.4650i			0.701658i
$426$		0			0
$427$		0			0
$428$	−8.48528	−	14.6969i	−0.410152	−	0.710403i
$429$		−	12.6677i		−	0.611603i
$430$	−2.97297	+	5.14933i	−0.143369	+	0.248323i
$431$			27.1185i			1.30625i	0.757250	+	0.653125i	$0.226543\pi$
$431$			27.1185i			1.30625i	−0.757250	+	0.653125i	$0.773457\pi$
$432$	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
$436$	−24.7279	+	14.2767i	−1.18425	+	0.683729i
$437$	−34.6554			−1.65779
$438$	−5.41421	+	9.37769i	−0.258701	+	0.448084i
$439$	−22.3087			−1.06474			−0.532368	−	0.846513i	$-0.678698\pi$
$439$	−22.3087			−1.06474			−0.532368	+	0.846513i	$0.678698\pi$
$440$	7.49903			0.357502
$441$		0			0
$442$	−31.9706	−	18.4582i	−1.52068	−	0.877968i
$443$	28.2843			1.34383			0.671913	−	0.740630i	$-0.265473\pi$
$443$	28.2843			1.34383			0.671913	+	0.740630i	$0.265473\pi$
$444$	−2.65131	−	4.59220i	−0.125826	−	0.217936i
$445$		−	16.9002i		−	0.801148i
$446$	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
$451$			0.634051i			0.0298563i
$452$	−0.485281	−	0.840532i	−0.0228257	−	0.0395353i
$453$	5.94593			0.279364
$454$	14.4490	+	8.34211i	0.678123	+	0.391515i
$455$		0			0
$456$	−12.6863			−0.594090
$457$	−26.8284			−1.25498			−0.627490	−	0.778624i	$-0.715918\pi$
$457$	−26.8284			−1.25498			−0.627490	+	0.778624i	$0.715918\pi$
$458$	−10.7661	+	18.6474i	−0.503065	+	0.871334i
$459$	−23.3137			−1.08819
$460$	19.2025	−	11.0866i	0.895320	−	0.516913i
$461$	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
$465$		−	9.18440i		−	0.425916i
$466$	8.31371	−	14.3998i	0.385125	−	0.667056i
$467$		−	36.7695i		−	1.70149i	−0.525580	−	0.850744i	$-0.676152\pi$
$467$		−	36.7695i		−	1.70149i	0.525580	−	0.850744i	$-0.323848\pi$
$468$	10.6994	+	18.5320i	0.494582	+	0.856641i
$469$		0			0
$470$	12.0000	−	20.7846i	0.553519	−	0.958723i
$471$		−	13.6102i		−	0.627126i
$472$		−	3.06147i		−	0.140915i
$473$	6.34315			0.291658
$474$	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
$479$	10.1503			0.463781			0.231890	−	0.972742i	$-0.425509\pi$
$479$	10.1503			0.463781			0.231890	+	0.972742i	$0.425509\pi$
$480$	7.02944	−	4.05845i	0.320848	−	0.185242i
$481$		−	14.3337i		−	0.653562i
$482$	20.5947	+	11.8904i	0.938065	+	0.541592i
$483$		0			0
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$		−	12.2474i		−	0.556128i
$486$	18.9750	+	10.9552i	0.860725	+	0.496940i
$487$			14.4508i			0.654826i	0.944881	+	0.327413i	$0.106177\pi$
$487$			14.4508i			0.654826i	−0.944881	+	0.327413i	$0.893823\pi$
$488$	−27.1564			−1.22931
$489$			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	$0.443690\pi$
$492$	0.343146	+	0.594346i	0.0154702	+	0.0267952i
$493$	19.9790			0.899810
$494$	−29.6985	−	17.1464i	−1.33620	−	0.771454i
$495$	4.84772			0.217889
$496$	12.8017	−	22.1731i	0.574811	−	0.995602i
$497$		0			0
$498$	4.34315	−	7.52255i	0.194621	−	0.337093i
$499$	8.48528			0.379853			0.189927	−	0.981798i	$-0.439175\pi$
$499$	8.48528			0.379853			0.189927	+	0.981798i	$0.439175\pi$
$500$	−10.9269	−	18.9259i	−0.488665	−	0.846393i
$501$		−	17.9149i		−	0.800377i
$502$	−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
$507$		−	22.9929i		−	1.02115i
$508$	−26.4853	+	15.2913i	−1.17509	+	0.678441i
$509$	2.10220			0.0931786			0.0465893	−	0.998914i	$-0.485165\pi$
$509$	2.10220			0.0931786			0.0465893	+	0.998914i	$0.485165\pi$
$510$	−4.52607	+	7.83938i	−0.200418	+	0.347133i
$511$		0			0
$512$	22.6274			1.00000
$513$	−21.6569			−0.956173
$514$	−1.48648	−	0.858221i	−0.0655660	−	0.0378545i
$515$	−1.45584			−0.0641522
$516$	5.94593	−	3.43289i	0.261755	−	0.151124i
$517$	−25.6033			−1.12603
$518$		0			0
$519$		−	11.2328i		−	0.493067i
$520$	21.9411			0.962182
$521$			3.11586i			0.136508i	0.997668	+	0.0682542i	$0.0217429\pi$
$521$			3.11586i			0.136508i	−0.997668	+	0.0682542i	$0.978257\pi$
$522$	−10.0294	−	5.79050i	−0.438977	−	0.253443i
$523$			20.0852i			0.878267i	0.898422	+	0.439133i	$0.144714\pi$
$523$			20.0852i			0.878267i	−0.898422	+	0.439133i	$0.855286\pi$
$524$	−23.7285	+	13.6997i	−1.03659	+	0.598473i
$525$		0			0
$526$	22.9706	+	13.2621i	1.00156	+	0.578253i
$527$			28.5533i			1.24380i
$528$	−7.49903	−	4.32957i	−0.326354	−	0.188420i
$529$	−46.9411			−2.04092
$530$	−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
$535$	−11.2485			−0.486317
$536$	33.9411			1.46603
$537$			3.80430i			0.164168i
$538$	8.66386	−	15.0062i	0.373525	−	0.646965i
$539$		0			0
$540$	12.0000	−	6.92820i	0.516398	−	0.298142i
$541$			25.9298i			1.11481i	0.830241	+	0.557404i	$0.188203\pi$
$541$			25.9298i			1.11481i	−0.830241	+	0.557404i	$0.811797\pi$
$542$	22.6303	−	39.1969i	0.972056	−	1.68365i
$543$		−	15.2913i		−	0.656212i
$544$	−21.8538	+	12.6173i	−0.936973	+	0.540962i
$545$			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	$0.646896\pi$
$548$	8.24264	+	14.2767i	0.352108	+	0.609869i
$549$	−17.5552			−0.749236
$550$	−4.58579	+	7.94282i	−0.195539	+	0.338683i
$551$	18.5592			0.790647
$552$	−25.6033			−1.08975
$553$		0			0
$554$	−3.51472	−	2.02922i	−0.149326	−	0.0862135i
$555$	−3.51472			−0.149191
$556$	30.1294	−	17.3952i	1.27777	−	0.737721i
$557$			2.86976i			0.121595i	0.998150	+	0.0607977i	$0.0193645\pi$
$557$			2.86976i			0.121595i	−0.998150	+	0.0607977i	$0.980636\pi$
$558$	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
$563$		−	3.88123i		−	0.163574i	−0.996650	−	0.0817871i	$-0.973937\pi$
$563$		−	3.88123i		−	0.163574i	0.996650	−	0.0817871i	$-0.0260628\pi$
$564$	−24.0000	+	13.8564i	−1.01058	+	0.583460i
$565$	−0.643315			−0.0270645
$566$	−18.6534	−	10.7695i	−0.784060	−	0.452677i
$567$		0			0
$568$		0			0
$569$	33.8995			1.42114			0.710570	−	0.703626i	$-0.248437\pi$
$569$	33.8995			1.42114			0.710570	+	0.703626i	$0.248437\pi$
$570$	−4.20441	+	7.28225i	−0.176103	+	0.305020i
$571$	−12.3431			−0.516545			−0.258272	−	0.966072i	$-0.583153\pi$
$571$	−12.3431			−0.516545			−0.258272	+	0.966072i	$0.583153\pi$
$572$	−11.7034	−	20.2710i	−0.489346	−	0.847571i
$573$	−2.19642			−0.0917566
$574$		0			0
$575$			27.1185i			1.13092i
$576$	14.6274			0.609476
$577$		−	20.7737i		−	0.864820i	−0.901677	−	0.432410i	$-0.857663\pi$
$577$		−	20.7737i		−	0.864820i	0.901677	−	0.432410i	$-0.142337\pi$
$578$	2.05025	−	3.55114i	0.0852793	−	0.147708i
$579$		−	15.3073i		−	0.636151i
$580$	−10.2836	+	5.93723i	−0.427002	+	0.246530i
$581$		0			0
$582$	−7.07107	+	12.2474i	−0.293105	+	0.507673i
$583$			6.92820i			0.286937i
$584$			20.0083i			0.827950i
$585$	14.1838			0.586427
$586$	−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
$591$	−13.7114			−0.564013
$592$	−8.48528	−	4.89898i	−0.348743	−	0.201347i
$593$		−	3.56420i		−	0.146364i	−0.997319	−	0.0731821i	$-0.976685\pi$
$593$		−	3.56420i		−	0.146364i	0.997319	−	0.0731821i	$-0.0233154\pi$
$594$	−12.8017	−	7.39104i	−0.525258	−	0.303258i
$595$		0			0
$596$	1.02944	−	0.594346i	0.0421674	−	0.0243454i
$597$			6.92820i			0.283552i
$598$	−59.9371	−	34.6047i	−2.45101	−	1.41509i
$599$		−	6.08767i		−	0.248736i	−0.992236	−	0.124368i	$-0.960310\pi$
$599$		−	6.08767i		−	0.248736i	0.992236	−	0.124368i	$-0.0396903\pi$
$600$			9.92724i			0.405278i
$601$		−	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
$604$	9.51472	−	5.49333i	0.387148	−	0.223520i
$605$	9.27958			0.377269
$606$	−0.727922	−	0.420266i	−0.0295698	−	0.0170721i
$607$	−10.6052			−0.430453			−0.215227	−	0.976564i	$-0.569049\pi$
$607$	−10.6052			−0.430453			−0.215227	+	0.976564i	$0.569049\pi$
$608$	−20.3007	+	11.7206i	−0.823301	+	0.475333i
$609$		0			0
$610$	−9.00000	+	15.5885i	−0.364399	+	0.631158i
$611$	−74.9117			−3.03060
$612$	−14.1273	+	8.15640i	−0.571062	+	0.329703i
$613$		−	26.9444i		−	1.08827i	−0.838997	−	0.544137i	$-0.816857\pi$
$613$		−	26.9444i		−	1.08827i	0.838997	−	0.544137i	$-0.183143\pi$
$614$	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
$619$		−	18.5545i		−	0.745769i	−0.927878	−	0.372884i	$-0.878369\pi$
$619$		−	18.5545i		−	0.745769i	0.927878	−	0.372884i	$-0.121631\pi$
$620$	−8.48528	−	14.6969i	−0.340777	−	0.590243i
$621$	−43.7076			−1.75392
$622$	7.95393	−	13.7766i	0.318923	−	0.552391i
$623$		0			0
$624$	−21.9411	−	12.6677i	−0.878348	−	0.507114i
$625$	1.72792			0.0691169
$626$	18.4925	+	10.6767i	0.739111	+	0.426726i
$627$	8.97056			0.358250
$628$	−12.5742	−	21.7792i	−0.501765	−	0.869083i
$629$	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	$-0.288383\pi$
$632$		−	5.73951i		−	0.228306i
$633$		−	3.80430i		−	0.151208i
$634$	28.9706	+	16.7262i	1.15057	+	0.664281i
$635$			20.2710i			0.804428i
$636$	3.74952	+	6.49435i	0.148678	+	0.257518i
$637$		0			0
$638$	10.9706	+	6.33386i	0.434329	+	0.250760i
$639$		0			0
$640$	7.49903	−	12.9887i	0.296425	−	0.513424i
$641$	−31.0711			−1.22723			−0.613617	−	0.789604i	$-0.710286\pi$
$641$	−31.0711			−1.22723			−0.613617	+	0.789604i	$0.710286\pi$
$642$	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
$647$	10.1503			0.399051			0.199526	−	0.979893i	$-0.436060\pi$
$647$	10.1503			0.399051			0.199526	+	0.979893i	$0.436060\pi$
$648$	−0.485281			−0.0190637
$649$			2.16478i			0.0849752i
$650$	−13.4174	+	23.2396i	−0.526273	+	0.911531i
$651$		0			0
$652$	20.1421	+	34.8872i	0.788827	+	1.36629i
$653$			20.3643i			0.796918i	0.917186	+	0.398459i	$0.130455\pi$
$653$			20.3643i			0.796918i	−0.917186	+	0.398459i	$0.869545\pi$
$654$	10.9269	−	18.9259i	0.427275	−	0.740063i
$655$			18.1610i			0.709611i
$656$	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	$0.189765\pi$
$660$	−4.97056	+	2.86976i	−0.193479	+	0.111705i
$661$	31.1334			1.21095			0.605474	−	0.795865i	$-0.292984\pi$
$661$	31.1334			1.21095			0.605474	+	0.795865i	$0.292984\pi$
$662$	−10.7279	+	18.5813i	−0.416953	+	0.722183i
$663$	28.2546			1.09732
$664$		−	16.0502i		−	0.622868i
$665$		0			0
$666$	−5.48528	−	3.16693i	−0.212550	−	0.122716i
$667$	37.4558			1.45030
$668$	−16.5512	−	28.6675i	−0.640384	−	1.10918i
$669$			5.24714i			0.202866i
$670$	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
$675$			16.9469i			0.652285i
$676$	−21.2426	−	36.7933i	−0.817025	−	1.41513i
$677$	−29.5803			−1.13686			−0.568431	−	0.822731i	$-0.692449\pi$
$677$	−29.5803			−1.13686			−0.568431	+	0.822731i	$0.692449\pi$
$678$	0.643315	+	0.371418i	0.0247064	+	0.0142642i
$679$		0			0
$680$			16.7262i			0.641419i
$681$	−12.7696			−0.489330
$682$	−9.05213	+	15.6788i	−0.346624	+	0.600371i
$683$	14.1421			0.541134			0.270567	−	0.962701i	$-0.412789\pi$
$683$	14.1421			0.541134			0.270567	+	0.962701i	$0.412789\pi$
$684$	−13.1233	+	7.57675i	−0.501782	+	0.289704i
$685$	10.9269			0.417495
$686$		0			0
$687$		−	16.4800i		−	0.628750i
$688$	6.34315	−	10.9867i	0.241830	−	0.418862i
$689$			20.2710i			0.772262i
$690$	−8.48528	+	14.6969i	−0.323029	+	0.559503i
$691$		−	40.7276i		−	1.54935i	−0.632358	−	0.774676i	$-0.717913\pi$
$691$		−	40.7276i		−	1.54935i	0.632358	−	0.774676i	$-0.282087\pi$
$692$	−10.3778	−	17.9749i	−0.394504	−	0.683302i
$693$		0			0
$694$	19.0711	−	33.0321i	0.723928	−	1.25388i
$695$		−	23.0600i		−	0.874716i
$696$	13.7114			0.519731
$697$	−1.41421			−0.0535672
$698$	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
$703$	10.1503			0.382827
$704$	−16.0000			−0.603023
$705$			18.3688i			0.691809i
$706$	−25.2150	−	14.5579i	−0.948980	−	0.547894i
$707$		0			0
$708$	1.17157	+	2.02922i	0.0440304	+	0.0762629i
$709$			36.7423i			1.37989i	0.723863	+	0.689944i	$0.242365\pi$
$709$			36.7423i			1.37989i	−0.723863	+	0.689944i	$0.757635\pi$
$710$		0			0
$711$		−	3.71029i		−	0.139147i
$712$			36.0585i			1.35135i
$713$			53.5306i			2.00474i
$714$		0			0
$715$	−15.5147			−0.580218
$716$	3.51472	+	6.08767i	0.131351	+	0.227507i
$717$	−6.85572			−0.256031
$718$	21.2132	+	12.2474i	0.791670	+	0.457071i
$719$	19.6574			0.733096			0.366548	−	0.930399i	$-0.380540\pi$
$719$	19.6574			0.733096			0.366548	+	0.930399i	$0.380540\pi$
$720$	4.84772	−	8.39651i	0.180664	−	0.312919i
$721$		0			0
$722$	−1.29289	+	2.23936i	−0.0481165	+	0.0833402i
$723$	−18.2010			−0.676903
$724$	−14.1273	−	24.4692i	−0.525037	−	0.909391i
$725$		−	14.5229i		−	0.539365i
$726$	−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
$731$			14.1480i			0.523283i
$732$	18.0000	−	10.3923i	0.665299	−	0.384111i
$733$	26.9290			0.994644			0.497322	−	0.867566i	$-0.334317\pi$
$733$	26.9290			0.994644			0.497322	+	0.867566i	$0.334317\pi$
$734$	16.2295	−	28.1103i	0.599042	−	1.03757i
$735$		0			0
$736$	−40.9706	+	23.6544i	−1.51019	+	0.871911i
$737$	−24.0000			−0.884051
$738$	0.709933	+	0.409880i	0.0261330	+	0.0150879i
$739$	20.8284			0.766186			0.383093	−	0.923710i	$-0.374859\pi$
$739$	20.8284			0.766186			0.383093	+	0.923710i	$0.374859\pi$
$740$	−5.62427	+	3.24718i	−0.206752	+	0.119369i
$741$	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	$0.962934\pi$
$744$			19.5959i			0.718421i
$745$		−	0.787897i		−	0.0288663i
$746$	36.7279	+	21.2049i	1.34470	+	0.776366i
$747$		−	10.3756i		−	0.379623i
$748$	15.4530	−	8.92177i	0.565016	−	0.326212i
$749$		0			0
$750$	14.4853	+	8.36308i	0.528928	+	0.305377i
$751$		−	42.6559i		−	1.55654i	−0.627931	−	0.778269i	$-0.716098\pi$
$751$		−	42.6559i		−	1.55654i	0.627931	−	0.778269i	$-0.283902\pi$
$752$	−25.6033	+	44.3462i	−0.933656	+	1.61714i
$753$	21.8579			0.796545
$754$	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
$759$	18.1043			0.657143
$760$			15.5375i			0.563603i
$761$		−	4.72352i		−	0.171227i	−0.996328	−	0.0856137i	$-0.972715\pi$
$761$		−	4.72352i		−	0.171227i	0.996328	−	0.0856137i	$-0.0272851\pi$
$762$	11.7034	−	20.2710i	0.423971	−	0.734339i
$763$		0			0
$764$	−3.51472	+	2.02922i	−0.127158	+	0.0734147i
$765$			10.8126i			0.390929i
$766$	−9.05213	+	15.6788i	−0.327067	+	0.566496i
$767$			6.33386i			0.228702i
$768$	−14.9981	+	8.65914i	−0.541196	+	0.312460i
$769$			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
$772$	−14.1421	−	24.4949i	−0.508987	−	0.881591i
$773$	42.8368			1.54073			0.770366	−	0.637601i	$-0.220073\pi$
$773$	42.8368			1.54073			0.770366	+	0.637601i	$0.220073\pi$
$774$	4.10051	−	7.10228i	0.147390	−	0.255286i
$775$	20.7556			0.745562
$776$			26.1313i			0.938058i
$777$		0			0
$778$	−46.4558	−	26.8213i	−1.66552	−	0.961590i
$779$	−1.31371			−0.0470685
$780$	−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
$787$			46.6967i			1.66456i	0.554357	+	0.832279i	$0.312964\pi$
$787$			46.6967i			1.66456i	−0.554357	+	0.832279i	$0.687036\pi$
$788$	−21.9411	+	12.6677i	−0.781620	+	0.451269i
$789$	−20.3007			−0.722723
$790$	−3.29462	−	1.90215i	−0.117217	−	0.0676755i
$791$		0			0
$792$	−10.3431			−0.367528
$793$	56.1838			1.99514
$794$	−9.76207	+	16.9084i	−0.346443	+	0.600056i
$795$	4.97056			0.176288
$796$	6.40083	+	11.0866i	0.226871	+	0.392953i
$797$	−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
$800$	9.17157	+	15.8856i	0.324264	+	0.561642i
$801$			23.3099i			0.823615i
$802$	−11.4853	+	19.8931i	−0.405559	+	0.702449i
$803$		−	14.1480i		−	0.499273i
$804$	−22.4971	+	12.9887i	−0.793412	+	0.458076i
$805$		0			0
$806$	−26.4853	+	45.8739i	−0.932904	+	1.61584i
$807$			13.2621i			0.466847i
$808$	−1.55310			−0.0546379
$809$	35.4558			1.24656			0.623281	−	0.781998i	$-0.285799\pi$
$809$	35.4558			1.24656			0.623281	+	0.781998i	$0.285799\pi$
$810$	−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
$815$	26.7015			0.935313
$816$	9.65685	−	16.7262i	0.338058	−	0.585533i
$817$			13.1426i			0.459800i
$818$	11.3152	+	6.53281i	0.395626	+	0.228415i
$819$		0			0
$820$	0.727922	−	0.420266i	0.0254201	−	0.0146763i
$821$			37.5108i			1.30913i	0.756004	+	0.654567i	$0.227149\pi$
$821$			37.5108i			1.30913i	−0.756004	+	0.654567i	$0.772851\pi$
$822$	−10.9269	−	6.30864i	−0.381119	−	0.220039i
$823$			20.7846i			0.724506i	0.932080	+	0.362253i	$0.117992\pi$
$823$			20.7846i			0.724506i	−0.932080	+	0.362253i	$0.882008\pi$
$824$	3.10620			0.108210
$825$		−	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	$0.566904\pi$
$828$	−26.4853	+	15.2913i	−0.920427	+	0.531409i
$829$	4.29862			0.149297			0.0746486	−	0.997210i	$-0.476216\pi$
$829$	4.29862			0.149297			0.0746486	+	0.997210i	$0.476216\pi$
$830$	−9.21320	−	5.31925i	−0.319795	−	0.184634i
$831$	3.10620			0.107753
$832$	−46.8138			−1.62298
$833$		0			0
$834$	−13.3137	+	23.0600i	−0.461016	+	0.798503i
$835$	−21.9411			−0.759304
$836$	14.3548	−	8.28772i	0.496469	−	0.286637i
$837$			33.4523i			1.15628i
$838$	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
$843$			18.1062i			0.623610i
$844$	−3.51472	−	6.08767i	−0.120982	−	0.209546i
$845$	−28.1604			−0.968747
$846$	−16.5512	+	28.6675i	−0.569041	+	0.985608i
$847$		0			0
$848$	12.0000	+	6.92820i	0.412082	+	0.237915i
$849$	16.4853			0.565773
$850$	−17.7160	−	10.2283i	−0.607654	−	0.350829i
$851$	20.4853			0.702226
$852$		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
$856$	24.0000			0.820303
$857$		−	5.62020i		−	0.191982i	−0.995382	−	0.0959912i	$-0.969398\pi$
$857$		−	5.62020i		−	0.191982i	0.995382	−	0.0959912i	$-0.0306021\pi$
$858$	15.5147	+	8.95743i	0.529664	+	0.305802i
$859$			33.5992i			1.14639i	0.819419	+	0.573195i	$0.194296\pi$
$859$			33.5992i			1.14639i	−0.819419	+	0.573195i	$0.805704\pi$
$860$	−4.20441	−	7.28225i	−0.143369	−	0.248323i
$861$		0			0
$862$	−33.2132	−	19.1757i	−1.13125	−	0.653125i
$863$		−	23.6544i		−	0.805204i	−0.915375	−	0.402602i	$-0.868106\pi$
$863$		−	23.6544i		−	0.805204i	0.915375	−	0.402602i	$-0.131894\pi$
$864$	−25.6033	+	14.7821i	−0.871042	+	0.502896i
$865$	−13.7574			−0.467764
$866$	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
$871$	−70.2207			−2.37934
$872$		−	40.3805i		−	1.36746i
$873$			16.8925i			0.571723i
$874$	24.5051	−	42.4441i	0.828897	−	1.43569i
$875$		0			0
$876$	−7.65685	−	13.2621i	−0.258701	−	0.448084i
$877$		−	37.0905i		−	1.25246i	−0.779639	−	0.626229i	$-0.784598\pi$
$877$		−	37.0905i		−	1.25246i	0.779639	−	0.626229i	$-0.215402\pi$
$878$	15.7746	−	27.3224i	0.532368	−	0.922088i
$879$		−	6.33386i		−	0.213636i
$880$	−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	$0.785385\pi$
$884$	45.2132	−	26.1039i	1.52068	−	0.877968i
$885$	1.55310			0.0522069
$886$	−20.0000	+	34.6410i	−0.671913	+	1.16379i
$887$	5.94593			0.199645			0.0998224	−	0.995005i	$-0.468173\pi$
$887$	5.94593			0.199645			0.0998224	+	0.995005i	$0.468173\pi$
$888$	7.49903			0.251651
$889$		0			0
$890$	20.6985	+	11.9503i	0.693815	+	0.400574i
$891$	0.343146			0.0114958
$892$	4.84772	+	8.39651i	0.162314	+	0.281136i
$893$		−	53.0482i		−	1.77519i
$894$	−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
$899$		−	28.6675i		−	0.956113i
$900$	5.92893	+	10.2692i	0.197631	+	0.342307i
$901$	−15.4530			−0.514813
$902$	−0.776550	−	0.448342i	−0.0258563	−	0.0149281i
$903$		0			0
$904$	1.37258			0.0456514
$905$	−18.7279			−0.622537
$906$	−4.20441	+	7.28225i	−0.139682	+	0.241937i
$907$	−16.0000			−0.531271			−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000			−0.531271			−0.265636	+	0.964073i	$0.585582\pi$
$908$	−20.4339	+	11.7975i	−0.678123	+	0.391515i
$909$	−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
$913$			11.3492i			0.375603i
$914$	18.9706	−	32.8580i	0.627490	−	1.08685i
$915$		−	13.7766i		−	0.455440i
$916$	−15.2255	−	26.3714i	−0.503065	−	0.871334i
$917$		0			0
$918$	16.4853	−	28.5533i	0.544095	−	0.942401i
$919$			37.5108i			1.23737i	0.785641	+	0.618683i	$0.212334\pi$
$919$			37.5108i			1.23737i	−0.785641	+	0.618683i	$0.787666\pi$
$920$			31.3575i			1.03383i
$921$	−23.7990			−0.784203
$922$	−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
$927$	2.00799			0.0659512
$928$	21.9411	−	12.6677i	0.720253	−	0.415838i
$929$			22.3044i			0.731784i	0.930657	+	0.365892i	$0.119236\pi$
$929$			22.3044i			0.731784i	−0.930657	+	0.365892i	$0.880764\pi$
$930$	11.2485	+	6.49435i	0.368854	+	0.212958i
$931$		0			0
$932$	11.7574	+	20.3643i	0.385125	+	0.667056i
$933$			12.1753i			0.398603i
$934$	45.0332	+	25.9999i	1.47353	+	0.850744i
$935$		−	11.8272i		−	0.386790i
$936$	−30.2626			−0.989164
$937$			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
$940$	16.9706	+	29.3939i	0.553519	+	0.958723i
$941$	−12.2525			−0.399422			−0.199711	−	0.979855i	$-0.564000\pi$
$941$	−12.2525			−0.399422			−0.199711	+	0.979855i	$0.564000\pi$
$942$	16.6690	+	9.62388i	0.543107	+	0.313563i
$943$	−2.65131			−0.0863385
$944$	3.74952	+	2.16478i	0.122036	+	0.0704577i
$945$		0			0
$946$	−4.48528	+	7.76874i	−0.145829	+	0.252583i
$947$	0.544156			0.0176827			0.00884135	−	0.999961i	$-0.497186\pi$
$947$	0.544156			0.0176827			0.00884135	+	0.999961i	$0.497186\pi$
$948$	2.19642	+	3.80430i	0.0713363	+	0.123558i
$949$		−	41.3951i		−	1.34374i
$950$	−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
$955$			2.69005i			0.0870479i
$956$	−10.9706	+	6.33386i	−0.354813	+	0.204852i
$957$	−9.69545			−0.313409
$958$	−7.17738	+	12.4316i	−0.231890	+	0.401646i
$959$		0			0
$960$			11.4790i			0.370484i
$961$	9.97056			0.321631
$962$	17.5552	+	10.1355i	0.566001	+	0.326781i
$963$	15.5147			0.499955
$964$	−29.1254	+	16.8155i	−0.938065	+	0.541592i
$965$	−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	$0.851584\pi$
$968$	−19.7990			−0.636364
$969$			20.0083i			0.642760i
$970$	15.0000	+	8.66025i	0.481621	+	0.278064i
$971$		−	8.10201i		−	0.260006i	−0.991514	−	0.130003i	$-0.958501\pi$
$971$		−	8.10201i		−	0.260006i	0.991514	−	0.130003i	$-0.0414987\pi$
$972$	−26.8347	+	15.4930i	−0.860725	+	0.496940i
$973$		0			0
$974$	−17.6985	−	10.2182i	−0.567096	−	0.327413i
$975$		−	20.5384i		−	0.657756i
$976$	19.2025	−	33.2597i	0.614656	−	1.06462i
$977$	−5.21320			−0.166785			−0.0833926	−	0.996517i	$-0.526576\pi$
$977$	−5.21320			−0.166785			−0.0833926	+	0.996517i	$0.526576\pi$
$978$	−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
$983$	26.7015			0.851646			0.425823	−	0.904807i	$-0.359985\pi$
$983$	26.7015			0.851646			0.425823	+	0.904807i	$0.359985\pi$
$984$	−0.970563			−0.0309404
$985$			16.7930i			0.535070i
$986$	−14.1273	+	24.4692i	−0.449905	+	0.779258i
$987$		0			0
$988$	42.0000	−	24.2487i	1.33620	−	0.771454i
$989$			26.5241i			0.843418i
$990$	−3.42786	+	5.93723i	−0.108945	+	0.188697i
$991$			46.1200i			1.46505i	0.680739	+	0.732526i	$0.261659\pi$
$991$			46.1200i			1.46505i	−0.680739	+	0.732526i	$0.738341\pi$
$992$	18.1043	+	31.3575i	0.574811	+	0.995602i
$993$		−	16.4216i		−	0.521123i
$994$		0			0
$995$	8.48528			0.269002
$996$	6.14214	+	10.6385i	0.194621	+	0.337093i
$997$	−32.2316			−1.02078			−0.510392	−	0.859942i	$-0.670500\pi$
$997$	−32.2316			−1.02078			−0.510392	+	0.859942i	$0.670500\pi$
$998$	−6.00000	+	10.3923i	−0.189927	+	0.328963i
$999$	12.8017			0.405026

Twists

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

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

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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} -1.08239i q^{3} +(-1.00000 - 1.73205i) q^{4} -1.32565 q^{5} +(1.32565 + 0.765367i) q^{6} +2.82843 q^{8} +1.82843 q^{9} +(0.937379 - 1.62359i) q^{10} -2.00000 q^{11} +(-1.87476 + 1.08239i) q^{12} -5.85172 q^{13} +1.43488i q^{15} +(-2.00000 + 3.46410i) q^{16} -4.46088i q^{17} +(-1.29289 + 2.23936i) q^{18} -4.14386i q^{19} +(1.32565 + 2.29610i) q^{20} +(1.41421 - 2.44949i) q^{22} -8.36308i q^{23} -3.06147i q^{24} -3.24264 q^{25} +(4.13779 - 7.16687i) q^{26} -5.22625i q^{27} +4.47871i q^{29} +(-1.75736 - 1.01461i) q^{30} -6.40083 q^{31} +(-2.82843 - 4.89898i) q^{32} +2.16478i q^{33} +(5.46345 + 3.15432i) q^{34} +(-1.82843 - 3.16693i) q^{36} +2.44949i q^{37} +(5.07517 + 2.93015i) q^{38} +6.33386i q^{39} -3.74952 q^{40} -0.317025i q^{41} -3.17157 q^{43} +(2.00000 + 3.46410i) q^{44} -2.42386 q^{45} +(10.2426 + 5.91359i) q^{46} +12.8017 q^{47} +(3.74952 + 2.16478i) q^{48} +(2.29289 - 3.97141i) q^{50} -4.82843 q^{51} +(5.85172 + 10.1355i) q^{52} -3.46410i q^{53} +(6.40083 + 3.69552i) q^{54} +2.65131 q^{55} -4.48528 q^{57} +(-5.48528 - 3.16693i) q^{58} -1.08239i q^{59} +(2.48528 - 1.43488i) q^{60} -9.60124 q^{61} +(4.52607 - 7.83938i) q^{62} +8.00000 q^{64} +7.75736 q^{65} +(-2.65131 - 1.53073i) q^{66} +12.0000 q^{67} +(-7.72648 + 4.46088i) q^{68} -9.05213 q^{69} +5.17157 q^{72} +7.07401i q^{73} +(-3.00000 - 1.73205i) q^{74} +3.50981i q^{75} +(-7.17738 + 4.14386i) q^{76} +(-7.75736 - 4.47871i) q^{78} -2.02922i q^{79} +(2.65131 - 4.59220i) q^{80} -0.171573 q^{81} +(0.388275 + 0.224171i) q^{82} -5.67459i q^{83} +5.91359i q^{85} +(2.24264 - 3.88437i) q^{86} +4.84772 q^{87} -5.65685 q^{88} +12.7486i q^{89} +(1.71393 - 2.96861i) q^{90} +(-14.4853 + 8.36308i) q^{92} +6.92820i q^{93} +(-9.05213 + 15.6788i) q^{94} +5.49333i q^{95} +(-5.30262 + 3.06147i) q^{96} +9.23880i q^{97} -3.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{18} + 8 q^{25} - 48 q^{30} + 8 q^{36} - 48 q^{43} + 16 q^{44} + 48 q^{46} + 24 q^{50} - 16 q^{51} + 32 q^{57} + 24 q^{58} - 48 q^{60} + 64 q^{64}+ \cdots + 16 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^18 + 8 * q^25 - 48 * q^30 + 8 * q^36 - 48 * q^43 + 16 * q^44 + 48 * q^46 + 24 * q^50 - 16 * q^51 + 32 * q^57 + 24 * q^58 - 48 * q^60 + 64 * q^64 + 96 * q^65 + 96 * q^67 + 64 * q^72 - 24 * q^74 - 96 * q^78 - 24 * q^81 - 16 * q^86 - 48 * q^92 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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