LMFDB - Embedded newform 588.2.e.c.491.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(491,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-4,0,6,0,0,-4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.2593100598870016.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 + x^8 + 4x^6 + 4x^4 - 32x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.8
Root			$1.37027 - 0.349801i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.c.491.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.349801 + 1.37027i) q^{2} +(1.72007 - 0.203364i) q^{3} +(-1.75528 + 0.958643i) q^{4} -2.27740i q^{5} +(0.880346 + 2.28582i) q^{6} +(-1.92760 - 2.06987i) q^{8} +(2.91729 - 0.699602i) q^{9} +(3.12065 - 0.796636i) q^{10} +4.31834 q^{11} +(-2.82425 + 2.00589i) q^{12} +0.406728 q^{13} +(-0.463141 - 3.91729i) q^{15} +(2.16201 - 3.36537i) q^{16} +4.31834i q^{17} +(1.97911 + 3.75275i) q^{18} -5.42784i q^{19} +(2.18321 + 3.99747i) q^{20} +(1.51056 + 5.91729i) q^{22} +1.16274 q^{23} +(-3.73654 - 3.16832i) q^{24} -0.186543 q^{25} +(0.142274 + 0.557328i) q^{26} +(4.87566 - 1.79664i) q^{27} +3.72469i q^{29} +(5.20573 - 2.00490i) q^{30} +5.83457i q^{31} +(5.36774 + 1.78532i) q^{32} +(7.42784 - 0.878195i) q^{33} +(-5.91729 + 1.51056i) q^{34} +(-4.44998 + 4.02463i) q^{36} -7.83457 q^{37} +(7.43761 - 1.89866i) q^{38} +(0.699602 - 0.0827140i) q^{39} +(-4.71392 + 4.38991i) q^{40} +2.56195i q^{41} -11.0211i q^{43} +(-7.57988 + 4.13974i) q^{44} +(-1.59327 - 6.64382i) q^{45} +(0.406728 + 1.59327i) q^{46} -2.32549 q^{47} +(3.03441 - 6.22835i) q^{48} +(-0.0652529 - 0.255614i) q^{50} +(0.878195 + 7.42784i) q^{51} +(-0.713922 + 0.389907i) q^{52} +5.48108i q^{53} +(4.16739 + 6.05251i) q^{54} -9.83457i q^{55} +(-1.10383 - 9.33627i) q^{57} +(-5.10383 + 1.30290i) q^{58} -3.91306 q^{59} +(4.56822 + 6.43194i) q^{60} -10.4490 q^{61} +(-7.99494 + 2.04094i) q^{62} +(-0.568736 + 7.97976i) q^{64} -0.926283i q^{65} +(3.80163 + 9.87096i) q^{66} -7.83457i q^{67} +(-4.13974 - 7.57988i) q^{68} +(2.00000 - 0.236460i) q^{69} -4.88743 q^{71} +(-7.07144 - 4.68986i) q^{72} -2.81346 q^{73} +(-2.74054 - 10.7355i) q^{74} +(-0.320867 + 0.0379362i) q^{75} +(5.20336 + 9.52738i) q^{76} +(0.358062 + 0.929710i) q^{78} +4.00000i q^{79} +(-7.66429 - 4.92375i) q^{80} +(8.02112 - 4.08188i) q^{81} +(-3.51056 + 0.896171i) q^{82} -0.641735 q^{83} +9.83457 q^{85} +(15.1019 - 3.85520i) q^{86} +(0.757468 + 6.40673i) q^{87} +(-8.32401 - 8.93840i) q^{88} +13.9970i q^{89} +(8.54650 - 4.50723i) q^{90} +(-2.04094 + 1.11466i) q^{92} +(1.18654 + 10.0359i) q^{93} +(-0.813457 - 3.18654i) q^{94} -12.3614 q^{95} +(9.59596 + 1.97928i) q^{96} +2.00000 q^{97} +(12.5978 - 3.02112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} - 2 q^{24} - 12 q^{25} + 20 q^{30} + 16 q^{33} - 32 q^{34} - 20 q^{36} - 16 q^{37} - 20 q^{40} - 24 q^{45} - 46 q^{48}+ \cdots + 24 q^{97}+O(q^{100}) $ 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 - 2 * q^24 - 12 * q^25 + 20 * q^30 + 16 * q^33 - 32 * q^34 - 20 * q^36 - 16 * q^37 - 20 * q^40 - 24 * q^45 - 46 * q^48 + 28 * q^52 - 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 + 16 * q^61 + 20 * q^64 + 12 * q^66 + 24 * q^69 - 32 * q^72 - 24 * q^73 + 60 * q^76 + 20 * q^78 + 28 * q^81 - 8 * q^82 + 40 * q^85 - 56 * q^88 + 80 * q^90 + 24 * q^93 + 34 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.349801	+	1.37027i	0.247347	+	0.968927i
$2$	0.349801	+	1.37027i	0.247347	+	0.968927i
$3$	1.72007	−	0.203364i	0.993083	−	0.117412i
$3$	1.72007	−	0.203364i	0.993083	−	0.117412i
$4$	−1.75528	+	0.958643i	−0.877639	+	0.479321i
$5$		−	2.27740i		−	1.01848i	−0.860624	−	0.509242i	$-0.829926\pi$
$5$		−	2.27740i		−	1.01848i	0.860624	−	0.509242i	$-0.170074\pi$
$6$	0.880346	+	2.28582i	0.359400	+	0.933184i
$7$		0			0
$7$		0			0
$8$	−1.92760	−	2.06987i	−0.681509	−	0.731810i
$9$	2.91729	−	0.699602i	0.972429	−	0.233201i
$10$	3.12065	−	0.796636i	0.986836	−	0.251918i
$11$	4.31834			1.30203			0.651014	−	0.759066i	$-0.274344\pi$
$11$	4.31834			1.30203			0.651014	+	0.759066i	$0.274344\pi$
$12$	−2.82425	+	2.00589i	−0.815291	+	0.579052i
$13$	0.406728			0.112806			0.0564031	−	0.998408i	$-0.482037\pi$
$13$	0.406728			0.112806			0.0564031	+	0.998408i	$0.482037\pi$
$14$		0			0
$15$	−0.463141	−	3.91729i	−0.119583	−	1.01144i
$16$	2.16201	−	3.36537i	0.540502	−	0.841343i
$17$			4.31834i			1.04735i	0.851918	+	0.523675i	$0.175439\pi$
$17$			4.31834i			1.04735i	−0.851918	+	0.523675i	$0.824561\pi$
$18$	1.97911	+	3.75275i	0.466481	+	0.884531i
$19$		−	5.42784i		−	1.24523i	−0.782527	−	0.622616i	$-0.786070\pi$
$19$		−	5.42784i		−	1.24523i	0.782527	−	0.622616i	$-0.213930\pi$
$20$	2.18321	+	3.99747i	0.488181	+	0.893861i
$21$		0			0
$22$	1.51056	+	5.91729i	0.322052	+	1.26157i
$23$	1.16274			0.242449			0.121224	−	0.992625i	$-0.461318\pi$
$23$	1.16274			0.242449			0.121224	+	0.992625i	$0.461318\pi$
$24$	−3.73654	−	3.16832i	−0.762718	−	0.646731i
$25$	−0.186543			−0.0373086
$26$	0.142274	+	0.557328i	0.0279022	+	0.109301i
$27$	4.87566	−	1.79664i	0.938322	−	0.345763i
$28$		0			0
$29$			3.72469i			0.691657i	0.938298	+	0.345829i	$0.112402\pi$
$29$			3.72469i			0.691657i	−0.938298	+	0.345829i	$0.887598\pi$
$30$	5.20573	−	2.00490i	0.950432	−	0.366043i
$31$			5.83457i			1.04792i	0.851743	+	0.523960i	$0.175546\pi$
$31$			5.83457i			1.04792i	−0.851743	+	0.523960i	$0.824454\pi$
$32$	5.36774	+	1.78532i	0.948891	+	0.315604i
$33$	7.42784	−	0.878195i	1.29302	−	0.152874i
$34$	−5.91729	+	1.51056i	−1.01481	+	0.259058i
$35$		0			0
$36$	−4.44998	+	4.02463i	−0.741664	+	0.670772i
$37$	−7.83457			−1.28800			−0.643998	−	0.765027i	$-0.722725\pi$
$37$	−7.83457			−1.28800			−0.643998	+	0.765027i	$0.722725\pi$
$38$	7.43761	−	1.89866i	1.20654	−	0.308004i
$39$	0.699602	−	0.0827140i	0.112026	−	0.0132448i
$40$	−4.71392	+	4.38991i	−0.745336	+	0.694105i
$41$			2.56195i			0.400109i	0.979785	+	0.200054i	$0.0641119\pi$
$41$			2.56195i			0.400109i	−0.979785	+	0.200054i	$0.935888\pi$
$42$		0			0
$43$		−	11.0211i		−	1.68070i	−0.542041	−	0.840352i	$-0.682348\pi$
$43$		−	11.0211i		−	1.68070i	0.542041	−	0.840352i	$-0.317652\pi$
$44$	−7.57988	+	4.13974i	−1.14271	+	0.624090i
$45$	−1.59327	−	6.64382i	−0.237511	−	0.990403i
$46$	0.406728	+	1.59327i	0.0599688	+	0.234915i
$47$	−2.32549			−0.339207			−0.169603	−	0.985512i	$-0.554249\pi$
$47$	−2.32549			−0.339207			−0.169603	+	0.985512i	$0.554249\pi$
$48$	3.03441	−	6.22835i	0.437979	−	0.898985i
$49$		0			0
$50$	−0.0652529	−	0.255614i	−0.00922816	−	0.0361493i
$51$	0.878195	+	7.42784i	0.122972	+	1.04011i
$52$	−0.713922	+	0.389907i	−0.0990031	+	0.0540704i
$53$			5.48108i			0.752884i	0.926440	+	0.376442i	$0.122853\pi$
$53$			5.48108i			0.752884i	−0.926440	+	0.376442i	$0.877147\pi$
$54$	4.16739	+	6.05251i	0.567110	+	0.823642i
$55$		−	9.83457i		−	1.32609i
$56$		0			0
$57$	−1.10383	−	9.33627i	−0.146206	−	1.23662i
$58$	−5.10383	+	1.30290i	−0.670166	+	0.171079i
$59$	−3.91306			−0.509437			−0.254719	−	0.967015i	$-0.581983\pi$
$59$	−3.91306			−0.509437			−0.254719	+	0.967015i	$0.581983\pi$
$60$	4.56822	+	6.43194i	0.589755	+	0.830360i
$61$	−10.4490			−1.33785			−0.668926	−	0.743329i	$-0.733246\pi$
$61$	−10.4490			−1.33785			−0.668926	+	0.743329i	$0.733246\pi$
$62$	−7.99494	+	2.04094i	−1.01536	+	0.259199i
$63$		0			0
$64$	−0.568736	+	7.97976i	−0.0710920	+	0.997470i
$65$		−	0.926283i		−	0.114891i
$66$	3.80163	+	9.87096i	0.467948	+	1.21503i
$67$		−	7.83457i		−	0.957145i	−0.878048	−	0.478573i	$-0.841154\pi$
$67$		−	7.83457i		−	0.957145i	0.878048	−	0.478573i	$-0.158846\pi$
$68$	−4.13974	−	7.57988i	−0.502018	−	0.919196i
$69$	2.00000	−	0.236460i	0.240772	−	0.0284665i
$70$		0			0
$71$	−4.88743			−0.580031			−0.290016	−	0.957022i	$-0.593661\pi$
$71$	−4.88743			−0.580031			−0.290016	+	0.957022i	$0.593661\pi$
$72$	−7.07144	−	4.68986i	−0.833377	−	0.552705i
$73$	−2.81346			−0.329290			−0.164645	−	0.986353i	$-0.552648\pi$
$73$	−2.81346			−0.329290			−0.164645	+	0.986353i	$0.552648\pi$
$74$	−2.74054	−	10.7355i	−0.318581	−	1.24797i
$75$	−0.320867	+	0.0379362i	−0.0370506	+	0.00438050i
$76$	5.20336	+	9.52738i	0.596867	+	1.09287i
$77$		0			0
$78$	0.358062	+	0.929710i	0.0405425	+	0.105269i
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	−7.66429	−	4.92375i	−0.856894	−	0.550492i
$81$	8.02112	−	4.08188i	0.891235	−	0.453542i
$82$	−3.51056	+	0.896171i	−0.387676	+	0.0989655i
$83$	−0.641735			−0.0704395			−0.0352198	−	0.999380i	$-0.511213\pi$
$83$	−0.641735			−0.0704395			−0.0352198	+	0.999380i	$0.511213\pi$
$84$		0			0
$85$	9.83457			1.06671
$86$	15.1019	−	3.85520i	1.62848	−	0.415716i
$87$	0.757468	+	6.40673i	0.0812091	+	0.686873i
$88$	−8.32401	−	8.93840i	−0.887343	−	0.952837i
$89$			13.9970i			1.48368i	0.670576	+	0.741841i	$0.266047\pi$
$89$			13.9970i			1.48368i	−0.670576	+	0.741841i	$0.733953\pi$
$90$	8.54650	−	4.50723i	0.900880	−	0.475103i
$91$		0			0
$92$	−2.04094	+	1.11466i	−0.212782	+	0.116211i
$93$	1.18654	+	10.0359i	0.123039	+	1.04067i
$94$	−0.813457	−	3.18654i	−0.0839017	−	0.328667i
$95$	−12.3614			−1.26825
$96$	9.59596	+	1.97928i	0.979384	+	0.202009i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	12.5978	−	3.02112i	1.26613	−	0.303633i
$100$	0.327435	−	0.178828i	0.0327435	−	0.0178828i
$101$			8.68476i			0.864166i	0.901834	+	0.432083i	$0.142221\pi$
$101$			8.68476i			0.864166i	−0.901834	+	0.432083i	$0.857779\pi$
$102$	−9.87096	+	3.80163i	−0.977370	+	0.376417i
$103$		−	10.6480i		−	1.04918i	−0.851355	−	0.524591i	$-0.824218\pi$
$103$		−	10.6480i		−	1.04918i	0.851355	−	0.524591i	$-0.175782\pi$
$104$	−0.784009	−	0.841876i	−0.0768784	−	0.0825527i
$105$		0			0
$106$	−7.51056	+	1.91729i	−0.729490	+	0.186223i
$107$	−8.40021			−0.812079			−0.406040	−	0.913855i	$-0.633090\pi$
$107$	−8.40021			−0.812079			−0.406040	+	0.913855i	$0.633090\pi$
$108$	−6.83582	+	7.82762i	−0.657777	+	0.753213i
$109$	−10.4826			−1.00405			−0.502026	−	0.864853i	$-0.667412\pi$
$109$	−10.4826			−1.00405			−0.502026	+	0.864853i	$0.667412\pi$
$110$	13.4760	−	3.44014i	1.28489	−	0.328005i
$111$	−13.4760	+	1.59327i	−1.27909	+	0.151227i
$112$		0			0
$113$			9.56296i			0.899607i	0.893128	+	0.449804i	$0.148506\pi$
$113$			9.56296i			0.899607i	−0.893128	+	0.449804i	$0.851494\pi$
$114$	12.4071	−	4.77838i	1.16203	−	0.447536i
$115$		−	2.64803i		−	0.246930i
$116$	−3.57065	−	6.53787i	−0.331526	−	0.607026i
$117$	1.18654	−	0.284548i	0.109696	−	0.0263065i
$118$	−1.36879	−	5.36195i	−0.126008	−	0.493608i
$119$		0			0
$120$	−7.21553	+	8.50959i	−0.658685	+	0.776816i
$121$	7.64803			0.695275
$122$	−3.65505	−	14.3179i	−0.330913	−	1.29628i
$123$	0.521008	+	4.40673i	0.0469777	+	0.397341i
$124$	−5.59327	−	10.2413i	−0.502291	−	0.919696i
$125$		−	10.9622i		−	0.980485i
$126$		0			0
$127$			6.20766i			0.550841i	0.961324	+	0.275420i	$0.0888170\pi$
$127$			6.20766i			0.550841i	−0.961324	+	0.275420i	$0.911183\pi$
$128$	−11.1334	+	2.01200i	−0.984060	+	0.177838i
$129$	−2.24130	−	18.9571i	−0.197335	−	1.66908i
$130$	1.26926	−	0.324014i	0.111321	−	0.0284179i
$131$	14.4023			1.25833			0.629167	−	0.777270i	$-0.283396\pi$
$131$	14.4023			1.25833			0.629167	+	0.777270i	$0.283396\pi$
$132$	−12.1961	+	8.66213i	−1.06153	+	0.753941i
$133$		0			0
$134$	10.7355	−	2.74054i	0.927404	−	0.236747i
$135$	−4.09166	−	11.1038i	−0.352154	−	0.955665i
$136$	8.93840	−	8.32401i	0.766462	−	0.713778i
$137$			2.32549i			0.198680i	0.995054	+	0.0993398i	$0.0316731\pi$
$137$			2.32549i			0.198680i	−0.995054	+	0.0993398i	$0.968327\pi$
$138$	1.02362	+	2.65783i	0.0871360	+	0.226249i
$139$			9.22019i			0.782046i	0.920381	+	0.391023i	$0.127879\pi$
$139$			9.22019i			0.782046i	−0.920381	+	0.391023i	$0.872121\pi$
$140$		0			0
$141$	−4.00000	+	0.472921i	−0.336861	+	0.0398271i
$142$	−1.70963	−	6.69710i	−0.143469	−	0.562008i
$143$	1.75639			0.146877
$144$	3.95277	−	11.3303i	0.329398	−	0.944191i
$145$	8.48260			0.704442
$146$	−0.984149	−	3.85520i	−0.0814488	−	0.319058i
$147$		0			0
$148$	13.7519	−	7.51056i	1.13040	−	0.617364i
$149$		−	17.3891i		−	1.42457i	−0.701891	−	0.712284i	$-0.747661\pi$
$149$		−	17.3891i		−	1.42457i	0.701891	−	0.712284i	$-0.252339\pi$
$150$	−0.164223	−	0.426405i	−0.0134087	−	0.0348158i
$151$			4.16543i			0.338978i	0.985532	+	0.169489i	$0.0542117\pi$
$151$			4.16543i			0.338978i	−0.985532	+	0.169489i	$0.945788\pi$
$152$	−11.2349	+	10.4627i	−0.911274	+	0.848637i
$153$	3.02112	+	12.5978i	0.244243	+	1.01847i
$154$		0			0
$155$	13.2876			1.06729
$156$	−1.14870	+	0.815854i	−0.0919698	+	0.0653206i
$157$	19.2624			1.53731			0.768654	−	0.639665i	$-0.220927\pi$
$157$	19.2624			1.53731			0.768654	+	0.639665i	$0.220927\pi$
$158$	−5.48108	+	1.39920i	−0.436051	+	0.111315i
$159$	1.11466	+	9.42784i	0.0883979	+	0.747677i
$160$	4.06589	−	12.2245i	0.321437	−	0.966430i
$161$		0			0
$162$	8.39906	+	9.56325i	0.659893	+	0.751360i
$163$		−	8.64803i		−	0.677366i	−0.940901	−	0.338683i	$-0.890019\pi$
$163$		−	8.64803i		−	0.677366i	0.940901	−	0.338683i	$-0.109981\pi$
$164$	−2.45599	−	4.49693i	−0.191781	−	0.351151i
$165$	−2.00000	−	16.9162i	−0.155700	−	1.31692i
$166$	−0.224479	−	0.879350i	−0.0174230	−	0.0682508i
$167$	1.75639			0.135914			0.0679568	−	0.997688i	$-0.478352\pi$
$167$	1.75639			0.135914			0.0679568	+	0.997688i	$0.478352\pi$
$168$		0			0
$169$	−12.8346			−0.987275
$170$	3.44014	+	13.4760i	0.263847	+	1.03356i
$171$	−3.79733	−	15.8346i	−0.290389	−	1.21090i
$172$	10.5653	+	19.3451i	0.805598	+	1.47505i
$173$		−	7.87421i		−	0.598665i	−0.954149	−	0.299333i	$-0.903236\pi$
$173$		−	7.87421i		−	0.598665i	0.954149	−	0.299333i	$-0.0967640\pi$
$174$	−8.51398	+	3.27902i	−0.645443	+	0.248581i
$175$		0			0
$176$	9.33627	−	14.5328i	0.703748	−	1.09545i
$177$	−6.73074	+	0.795777i	−0.505914	+	0.0598142i
$178$	−19.1797	+	4.89617i	−1.43758	+	0.366984i
$179$	−9.34605			−0.698557			−0.349278	−	0.937019i	$-0.613573\pi$
$179$	−9.34605			−0.698557			−0.349278	+	0.937019i	$0.613573\pi$
$180$	9.16569	+	10.1344i	0.683170	+	0.755372i
$181$	−16.8893			−1.25537			−0.627687	−	0.778466i	$-0.715998\pi$
$181$	−16.8893			−1.25537			−0.627687	+	0.778466i	$0.715998\pi$
$182$		0			0
$183$	−17.9729	+	2.12494i	−1.32860	+	0.157080i
$184$	−2.24130	−	2.40673i	−0.165231	−	0.177426i
$185$			17.8424i			1.31180i
$186$	−13.3368	+	5.13644i	−0.977902	+	0.376622i
$187$			18.6480i			1.36368i
$188$	4.08188	−	2.22931i	0.297701	−	0.162589i
$189$		0			0
$190$	−4.32401	−	16.9384i	−0.313697	−	1.22884i
$191$	20.3082			1.46945			0.734725	−	0.678365i	$-0.237311\pi$
$191$	20.3082			1.46945			0.734725	+	0.678365i	$0.237311\pi$
$192$	0.644532	+	13.8414i	0.0465151	+	0.998918i
$193$	6.85569			0.493483			0.246742	−	0.969081i	$-0.420640\pi$
$193$	6.85569			0.493483			0.246742	+	0.969081i	$0.420640\pi$
$194$	0.699602	+	2.74054i	0.0502285	+	0.196759i
$195$	−0.188373	−	1.59327i	−0.0134897	−	0.114097i
$196$		0			0
$197$		−	1.96830i		−	0.140235i	−0.997539	−	0.0701177i	$-0.977662\pi$
$197$		−	1.96830i		−	0.140235i	0.997539	−	0.0701177i	$-0.0223375\pi$
$198$	8.54647	+	16.2056i	0.607371	+	1.15168i
$199$		−	6.37309i		−	0.451776i	−0.974153	−	0.225888i	$-0.927472\pi$
$199$		−	6.37309i		−	0.451776i	0.974153	−	0.225888i	$-0.0725284\pi$
$200$	0.359580	+	0.386120i	0.0254262	+	0.0273028i
$201$	−1.59327	−	13.4760i	−0.112381	−	0.950525i
$202$	−11.9005	+	3.03794i	−0.837314	+	0.213748i
$203$		0			0
$204$	−8.66213	−	12.1961i	−0.606470	−	0.853895i
$205$	5.83457			0.407504
$206$	14.5907	−	3.72469i	1.01658	−	0.259511i
$207$	3.39205	−	0.813457i	0.235764	−	0.0565392i
$208$	0.879350	−	1.36879i	0.0609719	−	0.0949087i
$209$		−	23.4393i		−	1.62133i
$210$		0			0
$211$			25.1306i			1.73006i	0.501717	+	0.865032i	$0.332702\pi$
$211$			25.1306i			1.73006i	−0.501717	+	0.865032i	$0.667298\pi$
$212$	−5.25440	−	9.62082i	−0.360874	−	0.660761i
$213$	−8.40673	+	0.993929i	−0.576020	+	0.0681029i
$214$	−2.93840	−	11.5106i	−0.200865	−	0.786846i
$215$	−25.0995			−1.71177
$216$	−13.1171	−	6.62881i	−0.892507	−	0.451033i
$217$		0			0
$218$	−3.66682	−	14.3640i	−0.248349	−	0.972852i
$219$	−4.83934	+	0.572156i	−0.327013	+	0.0386627i
$220$	9.42784	+	17.2624i	0.635625	+	1.16383i
$221$			1.75639i			0.118148i
$222$	−6.89713	−	17.9085i	−0.462905	−	1.20194i
$223$			9.22877i			0.618004i	0.951061	+	0.309002i	$0.0999950\pi$
$223$			9.22877i			0.618004i	−0.951061	+	0.309002i	$0.900005\pi$
$224$		0			0
$225$	−0.544200	+	0.130506i	−0.0362800	+	0.00870039i
$226$	−13.1038	+	3.34513i	−0.871654	+	0.222515i
$227$	−19.5262			−1.29600			−0.647999	−	0.761641i	$-0.724394\pi$
$227$	−19.5262			−1.29600			−0.647999	+	0.761641i	$0.724394\pi$
$228$	10.8877	+	15.3296i	0.721054	+	1.01523i
$229$	−2.03364			−0.134387			−0.0671934	−	0.997740i	$-0.521404\pi$
$229$	−2.03364			−0.134387			−0.0671934	+	0.997740i	$0.521404\pi$
$230$	3.62851	−	0.926283i	0.239257	−	0.0610773i
$231$		0			0
$232$	7.70963	−	7.17970i	0.506162	−	0.471370i
$233$			3.27133i			0.214312i	0.994242	+	0.107156i	$0.0341744\pi$
$233$			3.27133i			0.214312i	−0.994242	+	0.107156i	$0.965826\pi$
$234$	0.804961	+	1.52635i	0.0526220	+	0.0997806i
$235$			5.29606i			0.345477i
$236$	6.86851	−	3.75123i	0.447102	−	0.244184i
$237$	0.813457	+	6.88028i	0.0528397	+	0.446922i
$238$		0			0
$239$	−24.5058			−1.58515			−0.792575	−	0.609775i	$-0.791260\pi$
$239$	−24.5058			−1.58515			−0.792575	+	0.609775i	$0.791260\pi$
$240$	−14.1844	−	6.91056i	−0.915601	−	0.446075i
$241$	−18.4153			−1.18623			−0.593117	−	0.805116i	$-0.702103\pi$
$241$	−18.4153			−1.18623			−0.593117	+	0.805116i	$0.702103\pi$
$242$	2.67529	+	10.4799i	0.171974	+	0.673671i
$243$	12.9668	−	8.65232i	0.831819	−	0.555047i
$244$	18.3408	−	10.0168i	1.17415	−	0.641261i
$245$		0			0
$246$	−5.85616	+	2.25540i	−0.373375	+	0.143799i
$247$		−	2.20766i		−	0.140470i
$248$	12.0768	−	11.2467i	0.766878	−	0.714167i
$249$	−1.10383	+	0.130506i	−0.0699523	+	0.00827047i
$250$	15.0211	−	3.83457i	0.950019	−	0.242520i
$251$	15.4443			0.974837			0.487418	−	0.873169i	$-0.337939\pi$
$251$	15.4443			0.974837			0.487418	+	0.873169i	$0.337939\pi$
$252$		0			0
$253$	5.02112			0.315675
$254$	−8.50617	+	2.17144i	−0.533724	+	0.136249i
$255$	16.9162	−	2.00000i	1.05933	−	0.125245i
$256$	−6.65145	−	14.5519i	−0.415716	−	0.909495i
$257$		−	8.96931i		−	0.559490i	−0.960074	−	0.279745i	$-0.909750\pi$
$257$		−	8.96931i		−	0.559490i	0.960074	−	0.279745i	$-0.0902499\pi$
$258$	25.1923	−	9.70239i	1.56841	−	0.604045i
$259$		0			0
$260$	0.887974	+	1.62588i	0.0550698	+	0.100833i
$261$	2.60580	+	10.8660i	0.161295	+	0.672587i
$262$	5.03794	+	19.7350i	0.311245	+	1.21923i
$263$	19.3624			1.19393			0.596967	−	0.802265i	$-0.296372\pi$
$263$	19.3624			1.19393			0.596967	+	0.802265i	$0.296372\pi$
$264$	−16.1356	−	13.6819i	−0.993080	−	0.842061i
$265$	12.4826			0.766800
$266$		0			0
$267$	2.84649	+	24.0759i	0.174203	+	1.47342i
$268$	7.51056	+	13.7519i	0.458780	+	0.840028i
$269$			0.0480876i			0.00293195i	0.999999	+	0.00146598i	$0.000466635\pi$
$269$			0.0480876i			0.00293195i	−0.999999	+	0.00146598i	$0.999533\pi$
$270$	13.7840	−	9.49080i	0.838866	−	0.577592i
$271$			19.8768i			1.20743i	0.797200	+	0.603715i	$0.206313\pi$
$271$			19.8768i			1.20743i	−0.797200	+	0.603715i	$0.793687\pi$
$272$	14.5328	+	9.33627i	0.881181	+	0.566095i
$273$		0			0
$274$	−3.18654	+	0.813457i	−0.192506	+	0.0491427i
$275$	−0.805556			−0.0485769
$276$	−3.28388	+	2.33234i	−0.197666	+	0.140390i
$277$	10.2749			0.617361			0.308681	−	0.951166i	$-0.400113\pi$
$277$	10.2749			0.617361			0.308681	+	0.951166i	$0.400113\pi$
$278$	−12.6341	+	3.22523i	−0.757745	+	0.193436i
$279$	4.08188	+	17.0211i	0.244376	+	1.01903i
$280$		0			0
$281$			6.78411i			0.404706i	0.979313	+	0.202353i	$0.0648588\pi$
$281$			6.78411i			0.404706i	−0.979313	+	0.202353i	$0.935141\pi$
$282$	−2.04723	−	5.31565i	−0.121911	−	0.316542i
$283$			5.42784i			0.322652i	0.986901	+	0.161326i	$0.0515770\pi$
$283$			5.42784i			0.322652i	−0.986901	+	0.161326i	$0.948423\pi$
$284$	8.57881	−	4.68530i	0.509058	−	0.278022i
$285$	−21.2624	+	2.51386i	−1.25948	+	0.148908i
$286$	0.614387	+	2.40673i	0.0363294	+	0.142313i
$287$		0			0
$288$	16.9082	+	1.45302i	0.996328	+	0.0856201i
$289$	−1.64803			−0.0969429
$290$	2.96722	+	11.6235i	0.174241	+	0.682553i
$291$	3.44014	−	0.406728i	0.201665	−	0.0238428i
$292$	4.93840	−	2.69710i	0.288998	−	0.157836i
$293$			28.1874i			1.64673i	0.567515	+	0.823363i	$0.307905\pi$
$293$			28.1874i			1.64673i	−0.567515	+	0.823363i	$0.692095\pi$
$294$		0			0
$295$			8.91160i			0.518853i
$296$	15.1019	+	16.2166i	0.877780	+	0.942568i
$297$	21.0548	−	7.75848i	1.22172	−	0.450193i
$298$	23.8277	−	6.08271i	1.38030	−	0.352362i
$299$	0.472921			0.0273497
$300$	0.526844	−	0.374186i	0.0304174	−	0.0216036i
$301$		0			0
$302$	−5.70776	+	1.45707i	−0.328445	+	0.0838450i
$303$	1.76617	+	14.9384i	0.101464	+	0.858189i
$304$	−18.2667	−	11.7350i	−1.04767	−	0.673051i
$305$			23.7964i			1.36258i
$306$	−16.2056	+	8.54647i	−0.926414	+	0.488569i
$307$			2.24130i			0.127918i	0.997953	+	0.0639589i	$0.0203727\pi$
$307$			2.24130i			0.127918i	−0.997953	+	0.0639589i	$0.979627\pi$
$308$		0			0
$309$	−2.16543	−	18.3154i	−0.123187	−	1.04192i
$310$	4.64803	+	18.2077i	0.263990	+	1.03413i
$311$	26.4791			1.50149			0.750746	−	0.660591i	$-0.229694\pi$
$311$	26.4791			1.50149			0.750746	+	0.660591i	$0.229694\pi$
$312$	−1.51976	−	1.28865i	−0.0860393	−	0.0729552i
$313$	−0.440371			−0.0248912			−0.0124456	−	0.999923i	$-0.503962\pi$
$313$	−0.440371			−0.0248912			−0.0124456	+	0.999923i	$0.503962\pi$
$314$	6.73801	+	26.3947i	0.380248	+	1.48954i
$315$		0			0
$316$	−3.83457	−	7.02112i	−0.215712	−	0.394969i
$317$		−	11.7923i		−	0.662320i	−0.943575	−	0.331160i	$-0.892560\pi$
$317$		−	11.7923i		−	0.662320i	0.943575	−	0.331160i	$-0.107440\pi$
$318$	−12.5288	+	4.82525i	−0.702579	+	0.270586i
$319$			16.0845i			0.900557i
$320$	18.1731	+	1.29524i	1.01591	+	0.0724060i
$321$	−14.4490	+	1.70830i	−0.806462	+	0.0953482i
$322$		0			0
$323$	23.4393			1.30419
$324$	−10.1662	+	14.8542i	−0.564791	+	0.825234i
$325$	−0.0758724			−0.00420864
$326$	11.8501	−	3.02509i	0.656318	−	0.167544i
$327$	−18.0308	+	2.13179i	−0.997106	+	0.117888i
$328$	5.30290	−	4.93840i	0.292804	−	0.272678i
$329$		0			0
$330$	22.4801	−	8.65783i	1.23749	−	0.476598i
$331$		−	1.30974i		−	0.0719899i	−0.999352	−	0.0359949i	$-0.988540\pi$
$331$		−	1.30974i		−	0.0719899i	0.999352	−	0.0359949i	$-0.0114600\pi$
$332$	1.12642	−	0.615195i	0.0618205	−	0.0337632i
$333$	−22.8557	+	5.48108i	−1.25248	+	0.300361i
$334$	0.614387	+	2.40673i	0.0336177	+	0.131690i
$335$	−17.8424			−0.974837
$336$		0			0
$337$	−15.4615			−0.842241			−0.421120	−	0.907005i	$-0.638363\pi$
$337$	−15.4615			−0.842241			−0.421120	+	0.907005i	$0.638363\pi$
$338$	−4.48954	−	17.5868i	−0.244199	−	0.956597i
$339$	1.94476	+	16.4490i	0.105625	+	0.893385i
$340$	−17.2624	+	9.42784i	−0.936186	+	0.511297i
$341$			25.1956i			1.36442i
$342$	20.3693	−	10.7423i	1.10145	−	0.580878i
$343$		0			0
$344$	−22.8123	+	21.2443i	−1.22996	+	1.14541i
$345$	−0.538514	−	4.55480i	−0.0289926	−	0.245222i
$346$	10.7898	−	2.75441i	0.580063	−	0.148078i
$347$	27.6614			1.48494			0.742471	−	0.669878i	$-0.233654\pi$
$347$	27.6614			1.48494			0.742471	+	0.669878i	$0.233654\pi$
$348$	−7.47133	−	10.5195i	−0.400506	−	0.563902i
$349$	18.9316			1.01338			0.506692	−	0.862127i	$-0.330868\pi$
$349$	18.9316			1.01338			0.506692	+	0.862127i	$0.330868\pi$
$350$		0			0
$351$	1.98307	−	0.730743i	0.105849	−	0.0390042i
$352$	23.1797	+	7.70963i	1.23548	+	0.410925i
$353$			1.99285i			0.106069i	0.998593	+	0.0530344i	$0.0168893\pi$
$353$			1.99285i			0.106069i	−0.998593	+	0.0530344i	$0.983111\pi$
$354$	−3.44485	−	8.94457i	−0.183092	−	0.475399i
$355$			11.1306i			0.590752i
$356$	−13.4182	−	24.5687i	−0.711161	−	1.30214i
$357$		0			0
$358$	−3.26926	−	12.8066i	−0.172786	−	0.676851i
$359$	−2.35004			−0.124030			−0.0620151	−	0.998075i	$-0.519753\pi$
$359$	−2.35004			−0.124030			−0.0620151	+	0.998075i	$0.519753\pi$
$360$	−10.6807	+	16.1045i	−0.562921	+	0.848781i
$361$	−10.4615			−0.550605
$362$	−5.90790	−	23.1429i	−0.310512	−	1.21637i
$363$	13.1551	−	1.55534i	0.690466	−	0.0816339i
$364$		0			0
$365$			6.40736i			0.335377i
$366$	−9.19870	−	23.8845i	−0.480824	−	1.24846i
$367$		−	34.1940i		−	1.78491i	−0.451135	−	0.892455i	$-0.648981\pi$
$367$		−	34.1940i		−	1.78491i	0.451135	−	0.892455i	$-0.351019\pi$
$368$	2.51386	−	3.91306i	0.131044	−	0.203982i
$369$	1.79234	+	7.47393i	0.0933056	+	0.389077i
$370$	−24.4490	+	6.24130i	−1.27104	+	0.324470i
$371$		0			0
$372$	−11.7035	−	16.4783i	−0.606800	−	0.854359i
$373$	−17.6691			−0.914874			−0.457437	−	0.889242i	$-0.651232\pi$
$373$	−17.6691			−0.914874			−0.457437	+	0.889242i	$0.651232\pi$
$374$	−25.5528	+	6.52310i	−1.32131	+	0.337301i
$375$	−2.22931	−	18.8557i	−0.115121	−	0.973703i
$376$	4.48260	+	4.81346i	0.231172	+	0.248235i
$377$			1.51494i			0.0780232i
$378$		0			0
$379$		−	5.39420i		−	0.277082i	−0.990357	−	0.138541i	$-0.955759\pi$
$379$		−	5.39420i		−	0.277082i	0.990357	−	0.138541i	$-0.0442412\pi$
$380$	21.6976	−	11.8501i	1.11307	−	0.607899i
$381$	1.26242	+	10.6776i	0.0646755	+	0.547031i
$382$	7.10383	+	27.8277i	0.363464	+	1.42379i
$383$	−1.85257			−0.0946617			−0.0473308	−	0.998879i	$-0.515072\pi$
$383$	−1.85257			−0.0946617			−0.0473308	+	0.998879i	$0.515072\pi$
$384$	−18.7410	+	5.72492i	−0.956373	+	0.292149i
$385$		0			0
$386$	2.39812	+	9.39414i	0.122061	+	0.478149i
$387$	−7.71039	−	32.1517i	−0.391941	−	1.63437i
$388$	−3.51056	+	1.91729i	−0.178222	+	0.0973354i
$389$			5.38490i			0.273025i	0.990638	+	0.136513i	$0.0435895\pi$
$389$			5.38490i			0.273025i	−0.990638	+	0.136513i	$0.956411\pi$
$390$	2.11732	−	0.815449i	0.107215	−	0.0412919i
$391$			5.02112i			0.253929i
$392$		0			0
$393$	24.7730	−	2.92891i	1.24963	−	0.147744i
$394$	2.69710	−	0.688513i	0.135878	−	0.0346868i
$395$	9.10959			0.458353
$396$	−19.2165	+	17.3797i	−0.965666	+	0.873363i
$397$	21.6355			1.08585			0.542927	−	0.839780i	$-0.317316\pi$
$397$	21.6355			1.08585			0.542927	+	0.839780i	$0.317316\pi$
$398$	8.73285	−	2.22931i	0.437738	−	0.111745i
$399$		0			0
$400$	−0.403308	+	0.627787i	−0.0201654	+	0.0313893i
$401$			38.2714i			1.91118i	0.294697	+	0.955591i	$0.404781\pi$
$401$			38.2714i			1.91118i	−0.294697	+	0.955591i	$0.595219\pi$
$402$	17.9085	−	6.89713i	0.893192	−	0.343998i
$403$			2.37309i			0.118212i
$404$	−8.32558	−	15.2442i	−0.414213	−	0.758426i
$405$	−9.29606	−	18.2673i	−0.461925	−	0.907708i
$406$		0			0
$407$	−33.8323			−1.67701
$408$	13.6819	−	16.1356i	0.677354	−	0.798833i
$409$	−4.77123			−0.235922			−0.117961	−	0.993018i	$-0.537636\pi$
$409$	−4.77123			−0.235922			−0.117961	+	0.993018i	$0.537636\pi$
$410$	2.04094	+	7.99494i	0.100795	+	0.394842i
$411$	0.472921	+	4.00000i	0.0233275	+	0.197305i
$412$	10.2077	+	18.6903i	0.502895	+	0.920803i
$413$		0			0
$414$	2.30120	+	4.36348i	0.113098	+	0.214453i
$415$			1.46149i			0.0717415i
$416$	2.18321	+	0.726142i	0.107041	+	0.0356020i
$417$	1.87506	+	15.8594i	0.0918219	+	0.776637i
$418$	32.1181	−	8.19907i	1.57095	−	0.401030i
$419$	8.33257			0.407072			0.203536	−	0.979067i	$-0.434757\pi$
$419$	8.33257			0.407072			0.203536	+	0.979067i	$0.434757\pi$
$420$		0			0
$421$	−20.7325			−1.01044			−0.505220	−	0.862991i	$-0.668589\pi$
$421$	−20.7325			−1.01044			−0.505220	+	0.862991i	$0.668589\pi$
$422$	−34.4357	+	8.79071i	−1.67631	+	0.427925i
$423$	−6.78411	+	1.62691i	−0.329855	+	0.0791033i
$424$	11.3451	−	10.5653i	0.550968	−	0.513097i
$425$		−	0.805556i		−	0.0390752i
$426$	−4.30263	−	11.1718i	−0.208463	−	0.541276i
$427$		0			0
$428$	14.7447	−	8.05280i	0.712713	−	0.389247i
$429$	3.02112	−	0.357187i	0.145861	−	0.0172451i
$430$	−8.77981	−	34.3930i	−0.423400	−	1.65858i
$431$	−34.9951			−1.68565			−0.842826	−	0.538186i	$-0.819110\pi$
$431$	−34.9951			−1.68565			−0.842826	+	0.538186i	$0.819110\pi$
$432$	4.49487	−	20.2928i	0.216260	−	0.976336i
$433$	−17.3383			−0.833225			−0.416612	−	0.909084i	$-0.636783\pi$
$433$	−17.3383			−0.833225			−0.416612	+	0.909084i	$0.636783\pi$
$434$		0			0
$435$	14.5907	−	1.72506i	0.699569	−	0.0827102i
$436$	18.3999	−	10.0491i	0.881195	−	0.481263i
$437$		−	6.31119i		−	0.301905i
$438$	−2.47682	−	6.43107i	−0.118347	−	0.307288i
$439$		−	33.2961i		−	1.58913i	−0.607176	−	0.794567i	$-0.707698\pi$
$439$		−	33.2961i		−	1.58913i	0.607176	−	0.794567i	$-0.292302\pi$
$440$	−20.3563	+	18.9571i	−0.970449	+	0.903744i
$441$		0			0
$442$	−2.40673	+	0.614387i	−0.114476	+	0.0292234i
$443$	−8.87313			−0.421575			−0.210788	−	0.977532i	$-0.567603\pi$
$443$	−8.87313			−0.421575			−0.210788	+	0.977532i	$0.567603\pi$
$444$	22.1268	−	15.7153i	1.05009	−	0.745816i
$445$	31.8768			1.51111
$446$	−12.6459	+	3.22823i	−0.598801	+	0.152861i
$447$	−3.53632	−	29.9104i	−0.167262	−	1.41472i
$448$		0			0
$449$		−	26.3829i		−	1.24509i	−0.782585	−	0.622544i	$-0.786099\pi$
$449$		−	26.3829i		−	1.24509i	0.782585	−	0.622544i	$-0.213901\pi$
$450$	−0.369190	−	0.700049i	−0.0174038	−	0.0330006i
$451$			11.0633i			0.520953i
$452$	−9.16746	−	16.7857i	−0.431201	−	0.789531i
$453$	0.847099	+	7.16483i	0.0398002	+	0.336633i
$454$	−6.83028	−	26.7562i	−0.320561	−	1.25573i
$455$		0			0
$456$	−17.1971	+	20.2814i	−0.805330	+	0.949762i
$457$	30.2499			1.41503			0.707515	−	0.706698i	$-0.249816\pi$
$457$	30.2499			1.41503			0.707515	+	0.706698i	$0.249816\pi$
$458$	−0.711370	−	2.78664i	−0.0332401	−	0.130211i
$459$	7.75848	+	21.0548i	0.362135	+	0.982752i
$460$	2.53851	+	4.64803i	0.118359	+	0.216715i
$461$			1.56302i			0.0727973i	0.999337	+	0.0363987i	$0.0115886\pi$
$461$			1.56302i			0.0727973i	−0.999337	+	0.0363987i	$0.988411\pi$
$462$		0			0
$463$		−	33.2961i		−	1.54740i	−0.633553	−	0.773700i	$-0.718404\pi$
$463$		−	33.2961i		−	1.54740i	0.633553	−	0.773700i	$-0.281596\pi$
$464$	12.5350	+	8.05280i	0.581921	+	0.373842i
$465$	22.8557	−	2.70223i	1.05991	−	0.125313i
$466$	−4.48260	+	1.14431i	−0.207652	+	0.0530093i
$467$	17.2969			0.800404			0.400202	−	0.916427i	$-0.368940\pi$
$467$	17.2969			0.800404			0.400202	+	0.916427i	$0.368940\pi$
$468$	−1.80993	+	1.63693i	−0.0836642	+	0.0756672i
$469$		0			0
$470$	−7.25703	+	1.85257i	−0.334742	+	0.0854525i
$471$	33.1327	−	3.91729i	1.52667	−	0.180499i
$472$	7.54281	+	8.09954i	0.347186	+	0.372811i
$473$		−	47.5929i		−	2.18832i
$474$	−9.14330	+	3.52138i	−0.419965	+	0.161743i
$475$			1.01253i			0.0464579i
$476$		0			0
$477$	3.83457	+	15.9899i	0.175573	+	0.732126i
$478$	−8.57216	−	33.5796i	−0.392081	−	1.53589i
$479$	−16.6081			−0.758842			−0.379421	−	0.925224i	$-0.623877\pi$
$479$	−16.6081			−0.758842			−0.379421	+	0.925224i	$0.623877\pi$
$480$	4.50760	−	21.8538i	0.205743	−	0.997486i
$481$	−3.18654			−0.145294
$482$	−6.44169	−	25.2340i	−0.293411	−	1.14938i
$483$		0			0
$484$	−13.4244	+	7.33173i	−0.610201	+	0.333260i
$485$		−	4.55480i		−	0.206823i
$486$	16.3918	+	14.7414i	0.743547	+	0.668683i
$487$		−	24.2499i		−	1.09887i	−0.835537	−	0.549434i	$-0.814844\pi$
$487$		−	24.2499i		−	1.09887i	0.835537	−	0.549434i	$-0.185156\pi$
$488$	20.1414	+	21.6280i	0.911758	+	0.979054i
$489$	−1.75870	−	14.8752i	−0.0795311	−	0.672681i
$490$		0			0
$491$	20.3082			0.916497			0.458248	−	0.888824i	$-0.348477\pi$
$491$	20.3082			0.916497			0.458248	+	0.888824i	$0.348477\pi$
$492$	−5.13899	−	7.23558i	−0.231684	−	0.326205i
$493$	−16.0845			−0.724408
$494$	3.02509	−	0.772241i	0.136105	−	0.0347447i
$495$	−6.88028	−	28.6903i	−0.309246	−	1.28953i
$496$	19.6355	+	12.6144i	0.881660	+	0.566403i
$497$		0			0
$498$	−0.564949	−	1.46689i	−0.0253160	−	0.0657330i
$499$			10.5385i			0.471769i	0.971781	+	0.235884i	$0.0757987\pi$
$499$			10.5385i			0.471769i	−0.971781	+	0.235884i	$0.924201\pi$
$500$	10.5088	+	19.2416i	0.469968	+	0.860512i
$501$	3.02112	−	0.357187i	0.134973	−	0.0159579i
$502$	5.40243	+	21.1629i	0.241122	+	0.944546i
$503$	−27.6664			−1.23358			−0.616792	−	0.787126i	$-0.711568\pi$
$503$	−27.6664			−1.23358			−0.616792	+	0.787126i	$0.711568\pi$
$504$		0			0
$505$	19.7787			0.880139
$506$	1.75639	+	6.88028i	0.0780811	+	0.305866i
$507$	−22.0764	+	2.61009i	−0.980446	+	0.115918i
$508$	−5.95093	−	10.8962i	−0.264030	−	0.483439i
$509$		−	28.1874i		−	1.24939i	−0.780871	−	0.624693i	$-0.785224\pi$
$509$		−	28.1874i		−	1.24939i	0.780871	−	0.624693i	$-0.214776\pi$
$510$	8.65783	+	22.4801i	0.383375	+	0.995436i
$511$		0			0
$512$	17.6134	−	14.2046i	0.778408	−	0.627758i
$513$	−9.75186	−	26.4643i	−0.430555	−	1.16843i
$514$	12.2904	−	3.13747i	0.542105	−	0.138388i
$515$	−24.2498			−1.06857
$516$	22.1072	+	31.1264i	0.973215	+	1.37026i
$517$	−10.0422			−0.441657
$518$		0			0
$519$	−1.60133	−	13.5442i	−0.0702907	−	0.594524i
$520$	−1.91729	+	1.78550i	−0.0840786	+	0.0782994i
$521$		−	24.0133i		−	1.05204i	−0.850471	−	0.526022i	$-0.823683\pi$
$521$		−	24.0133i		−	1.05204i	0.850471	−	0.526022i	$-0.176317\pi$
$522$	−13.9778	+	7.37158i	−0.611793	+	0.322645i
$523$		−	2.77981i		−	0.121553i	−0.998151	−	0.0607764i	$-0.980642\pi$
$523$		−	2.77981i		−	0.121553i	0.998151	−	0.0607764i	$-0.0193577\pi$
$524$	−25.2801	+	13.8067i	−1.10436	+	0.603147i
$525$		0			0
$526$	6.77297	+	26.5317i	0.295316	+	1.15684i
$527$	−25.1956			−1.09754
$528$	13.1036	−	26.8961i	0.570261	−	1.17050i
$529$	−21.6480			−0.941219
$530$	4.36642	+	17.1045i	0.189665	+	0.742973i
$531$	−11.4155	+	2.73758i	−0.495391	+	0.118801i
$532$		0			0
$533$			1.04202i			0.0451347i
$534$	−31.9947	+	12.3222i	−1.38455	+	0.533235i
$535$			19.1306i			0.827089i
$536$	−16.2166	+	15.1019i	−0.700449	+	0.652303i
$537$	−16.0759	+	1.90065i	−0.693725	+	0.0820192i
$538$	−0.0658929	+	0.0168211i	−0.00284085	+	0.000725208i
$539$		0			0
$540$	17.8266	+	15.5679i	0.767135	+	0.669935i
$541$	8.31717			0.357583			0.178792	−	0.983887i	$-0.442781\pi$
$541$	8.31717			0.357583			0.178792	+	0.983887i	$0.442781\pi$
$542$	−27.2366	+	6.95292i	−1.16991	+	0.298654i
$543$	−29.0508	+	3.43469i	−1.24669	+	0.147396i
$544$	−7.70963	+	23.1797i	−0.330548	+	0.993822i
$545$			23.8731i			1.02261i
$546$		0			0
$547$		−	15.4364i		−	0.660014i	−0.943978	−	0.330007i	$-0.892949\pi$
$547$		−	15.4364i		−	0.660014i	0.943978	−	0.330007i	$-0.107051\pi$
$548$	−2.22931	−	4.08188i	−0.0952314	−	0.174369i
$549$	−30.4826	+	7.31011i	−1.30097	+	0.311988i
$550$	−0.281784	−	1.10383i	−0.0120153	−	0.0470674i
$551$	20.2170			0.861274
$552$	−4.34464	−	3.68394i	−0.184920	−	0.156799i
$553$		0			0
$554$	3.59418	+	14.0794i	0.152702	+	0.598178i
$555$	3.62851	+	30.6903i	0.154022	+	1.30273i
$556$	−8.83887	−	16.1840i	−0.374851	−	0.686354i
$557$		−	13.4525i		−	0.570000i	−0.958528	−	0.285000i	$-0.908006\pi$
$557$		−	13.4525i		−	0.570000i	0.958528	−	0.285000i	$-0.0919936\pi$
$558$	−21.8957	+	11.5473i	−0.926918	+	0.488835i
$559$		−	4.48260i		−	0.189594i
$560$		0			0
$561$	3.79234	+	32.0759i	0.160113	+	1.35425i
$562$	−9.29606	+	2.37309i	−0.392131	+	0.100103i
$563$	−34.0011			−1.43298			−0.716488	−	0.697599i	$-0.754252\pi$
$563$	−34.0011			−1.43298			−0.716488	+	0.697599i	$0.754252\pi$
$564$	6.56775	−	4.66468i	0.276552	−	0.196418i
$565$	21.7787			0.916235
$566$	−7.43761	+	1.89866i	−0.312626	+	0.0798068i
$567$		0			0
$568$	9.42100	+	10.1164i	0.395296	+	0.424473i
$569$		−	26.5948i		−	1.11491i	−0.830206	−	0.557457i	$-0.811777\pi$
$569$		−	26.5948i		−	1.11491i	0.830206	−	0.557457i	$-0.188223\pi$
$570$	−10.8823	−	28.2559i	−0.455808	−	1.18351i
$571$			8.23271i			0.344528i	0.985051	+	0.172264i	$0.0551083\pi$
$571$			8.23271i			0.344528i	−0.985051	+	0.172264i	$0.944892\pi$
$572$	−3.08295	+	1.68375i	−0.128905	+	0.0704012i
$573$	34.9316	−	4.12996i	1.45929	−	0.172532i
$574$		0			0
$575$	−0.216902			−0.00904543
$576$	3.92349	+	23.6771i	0.163479	+	0.986547i
$577$	−1.58468			−0.0659712			−0.0329856	−	0.999456i	$-0.510502\pi$
$577$	−1.58468			−0.0659712			−0.0329856	+	0.999456i	$0.510502\pi$
$578$	−0.576482	−	2.25824i	−0.0239785	−	0.0939306i
$579$	11.7923	−	1.39420i	0.490070	−	0.0579410i
$580$	−14.8893	+	8.13179i	−0.618246	+	0.337654i
$581$		0			0
$582$	1.76069	+	4.57165i	0.0729830	+	0.189501i
$583$			23.6691i			0.980276i
$584$	5.42321	+	5.82349i	0.224414	+	0.240978i
$585$	−0.648029	−	2.70223i	−0.0267927	−	0.111724i
$586$	−38.6244	+	9.85998i	−1.59556	+	0.407312i
$587$	30.8651			1.27394			0.636969	−	0.770889i	$-0.280188\pi$
$587$	30.8651			1.27394			0.636969	+	0.770889i	$0.280188\pi$
$588$		0			0
$589$	31.6691			1.30490
$590$	−12.2113	+	3.11729i	−0.502731	+	0.128337i
$591$	−0.400282	−	3.38561i	−0.0164654	−	0.139266i
$592$	−16.9384	+	26.3662i	−0.696164	+	1.08365i
$593$		−	6.45147i		−	0.264930i	−0.991188	−	0.132465i	$-0.957711\pi$
$593$		−	6.45147i		−	0.264930i	0.991188	−	0.132465i	$-0.0422892\pi$
$594$	17.9962	+	26.1368i	0.738392	+	1.07240i
$595$		0			0
$596$	16.6699	+	30.5227i	0.682826	+	1.25026i
$597$	−1.29606	−	10.9622i	−0.0530441	−	0.448651i
$598$	0.165428	+	0.648029i	0.00676485	+	0.0264999i
$599$	12.8097			0.523391			0.261696	−	0.965150i	$-0.415718\pi$
$599$	12.8097			0.523391			0.261696	+	0.965150i	$0.415718\pi$
$600$	0.697026	+	0.591029i	0.0284560	+	0.0241286i
$601$	37.2710			1.52032			0.760158	−	0.649738i	$-0.225122\pi$
$601$	37.2710			1.52032			0.760158	+	0.649738i	$0.225122\pi$
$602$		0			0
$603$	−5.48108	−	22.8557i	−0.223207	−	0.930756i
$604$	−3.99316	−	7.31149i	−0.162479	−	0.297500i
$605$		−	17.4176i		−	0.708126i
$606$	−19.8518	+	7.64559i	−0.806426	+	0.310581i
$607$			20.8135i			0.844792i	0.906411	+	0.422396i	$0.138811\pi$
$607$			20.8135i			0.844792i	−0.906411	+	0.422396i	$0.861189\pi$
$608$	9.69046	−	29.1352i	0.393000	−	1.18159i
$609$		0			0
$610$	−32.6075	+	8.32401i	−1.32024	+	0.337029i
$611$	−0.945841			−0.0382646
$612$	−17.3797	−	19.2165i	−0.702533	−	0.776782i
$613$	19.2288			0.776643			0.388321	−	0.921524i	$-0.373055\pi$
$613$	19.2288			0.776643			0.388321	+	0.921524i	$0.373055\pi$
$614$	−3.07119	+	0.784009i	−0.123943	+	0.0316400i
$615$	10.0359	−	1.18654i	0.404686	−	0.0478460i
$616$		0			0
$617$			29.3933i			1.18333i	0.806185	+	0.591664i	$0.201529\pi$
$617$			29.3933i			1.18333i	−0.806185	+	0.591664i	$0.798471\pi$
$618$	24.3395	−	9.37395i	0.979079	−	0.377076i
$619$			19.9241i			0.800818i	0.916336	+	0.400409i	$0.131132\pi$
$619$			19.9241i			0.800818i	−0.916336	+	0.400409i	$0.868868\pi$
$620$	−23.3235	+	12.7381i	−0.936695	+	0.511575i
$621$	5.66914	−	2.08903i	0.227495	−	0.0838297i
$622$	9.26242	+	36.2835i	0.371389	+	1.45484i
$623$		0			0
$624$	1.23418	−	2.53325i	0.0494068	−	0.101411i
$625$	−25.8979			−1.03592
$626$	−0.154042	−	0.603426i	−0.00615676	−	0.0241178i
$627$	−4.76671	−	40.3172i	−0.190364	−	1.61011i
$628$	−33.8109	+	18.4658i	−1.34920	+	0.736865i
$629$		−	33.8323i		−	1.34898i
$630$		0			0
$631$		−	17.6269i		−	0.701716i	−0.936429	−	0.350858i	$-0.885890\pi$
$631$		−	17.6269i		−	0.701716i	0.936429	−	0.350858i	$-0.114110\pi$
$632$	8.27949	−	7.71039i	0.329340	−	0.306703i
$633$	5.11067	+	43.2265i	0.203131	+	1.71810i
$634$	16.1586	−	4.12494i	0.641739	−	0.163822i
$635$	14.1373			0.561022
$636$	−10.9945	−	15.4799i	−0.435959	−	0.613819i
$637$		0			0
$638$	−22.0401	+	5.62636i	−0.872574	+	0.222750i
$639$	−14.2580	+	3.41926i	−0.564039	+	0.135264i
$640$	4.58214	+	25.3551i	0.181125	+	1.00225i
$641$		−	21.9439i		−	0.866731i	−0.901218	−	0.433365i	$-0.857326\pi$
$641$		−	21.9439i		−	0.866731i	0.901218	−	0.433365i	$-0.142674\pi$
$642$	−7.39509	−	19.2014i	−0.291861	−	0.757819i
$643$		−	49.5796i		−	1.95523i	−0.210406	−	0.977614i	$-0.567479\pi$
$643$		−	49.5796i		−	1.95523i	0.210406	−	0.977614i	$-0.432521\pi$
$644$		0			0
$645$	−43.1729	+	5.10433i	−1.69993	+	0.200983i
$646$	8.19907	+	32.1181i	0.322588	+	1.26367i
$647$	23.9122			0.940085			0.470042	−	0.882644i	$-0.344239\pi$
$647$	23.9122			0.940085			0.470042	+	0.882644i	$0.344239\pi$
$648$	−23.9104	−	8.73446i	−0.939291	−	0.343122i
$649$	−16.8979			−0.663301
$650$	−0.0265402	−	0.103966i	−0.00104099	−	0.00407787i
$651$		0			0
$652$	8.29037	+	15.1797i	0.324676	+	0.594483i
$653$			46.6666i			1.82621i	0.407730	+	0.913103i	$0.366320\pi$
$653$			46.6666i			1.82621i	−0.407730	+	0.913103i	$0.633680\pi$
$654$	−9.22832	−	23.9614i	−0.360856	−	0.936964i
$655$		−	32.7998i		−	1.28159i
$656$	8.62190	+	5.53895i	0.336629	+	0.216260i
$657$	−8.20766	+	1.96830i	−0.320211	+	0.0767907i
$658$		0			0
$659$	30.4598			1.18655			0.593273	−	0.805001i	$-0.297835\pi$
$659$	30.4598			1.18655			0.593273	+	0.805001i	$0.297835\pi$
$660$	19.7271	+	27.7753i	0.767877	+	1.08115i
$661$	49.3046			1.91773			0.958864	−	0.283865i	$-0.0916168\pi$
$661$	49.3046			1.91773			0.958864	+	0.283865i	$0.0916168\pi$
$662$	1.79470	−	0.458148i	0.0697529	−	0.0178064i
$663$	0.357187	+	3.02112i	0.0138720	+	0.117330i
$664$	1.23701	+	1.32831i	0.0480052	+	0.0515484i
$665$		0			0
$666$	−15.5055	−	29.4012i	−0.600826	−	1.13927i
$667$			4.33086i			0.167691i
$668$	−3.08295	+	1.68375i	−0.119283	+	0.0651463i
$669$	1.87680	+	15.8741i	0.0725614	+	0.613730i
$670$	−6.24130	−	24.4490i	−0.241122	−	0.944546i
$671$	−45.1221			−1.74192
$672$		0			0
$673$	−19.4364			−0.749219			−0.374610	−	0.927183i	$-0.622223\pi$
$673$	−19.4364			−0.749219			−0.374610	+	0.927183i	$0.622223\pi$
$674$	−5.40844	−	21.1864i	−0.208325	−	0.816070i
$675$	−0.909522	+	0.335150i	−0.0350075	+	0.0128999i
$676$	22.5283	−	12.3038i	0.866471	−	0.473222i
$677$		−	9.96823i		−	0.383110i	−0.981482	−	0.191555i	$-0.938647\pi$
$677$		−	9.96823i		−	0.383110i	0.981482	−	0.191555i	$-0.0613531\pi$
$678$	−21.8592	+	8.41871i	−0.839499	+	0.323319i
$679$		0			0
$680$	−18.9571	−	20.3563i	−0.726971	−	0.780628i
$681$	−33.5864	+	3.97093i	−1.28703	+	0.152166i
$682$	−34.5248	+	8.81346i	−1.32202	+	0.337485i
$683$	29.6102			1.13300			0.566501	−	0.824061i	$-0.308297\pi$
$683$	29.6102			1.13300			0.566501	+	0.824061i	$0.308297\pi$
$684$	21.8451	+	24.1538i	0.835267	+	0.923544i
$685$	5.29606			0.202352
$686$		0			0
$687$	−3.49801	+	0.413570i	−0.133457	+	0.0157787i
$688$	−37.0901	−	23.8277i	−1.41405	−	0.908424i
$689$			2.22931i			0.0849300i
$690$	6.05293	−	2.33118i	0.230431	−	0.0887466i
$691$		−	44.1603i		−	1.67994i	−0.542634	−	0.839969i	$-0.682573\pi$
$691$		−	44.1603i		−	1.67994i	0.542634	−	0.839969i	$-0.317427\pi$
$692$	7.54856	+	13.8214i	0.286953	+	0.525412i
$693$		0			0
$694$	9.67599	+	37.9036i	0.367295	+	1.43880i
$695$	20.9980			0.796501
$696$	11.8010	−	13.9175i	0.447316	−	0.527540i
$697$	−11.0633			−0.419054
$698$	6.62227	+	25.9413i	0.250657	+	0.981894i
$699$	0.665271	+	5.62691i	0.0251629	+	0.212829i
$700$		0			0
$701$		−	38.2714i		−	1.44549i	−0.691115	−	0.722745i	$-0.742880\pi$
$701$		−	38.2714i		−	1.44549i	0.691115	−	0.722745i	$-0.257120\pi$
$702$	1.69499	+	2.46173i	0.0639735	+	0.0929119i
$703$			42.5248i			1.60385i
$704$	−2.45599	+	34.4593i	−0.0925637	+	1.29873i
$705$	1.07703	+	9.10959i	0.0405632	+	0.343087i
$706$	−2.73074	+	0.697101i	−0.102773	+	0.0262357i
$707$		0			0
$708$	11.0515	−	7.84919i	0.415339	−	0.294991i
$709$	6.89792			0.259057			0.129528	−	0.991576i	$-0.458654\pi$
$709$	6.89792			0.259057			0.129528	+	0.991576i	$0.458654\pi$
$710$	−15.2520	+	3.89350i	−0.572396	+	0.146121i
$711$	2.79841	+	11.6691i	0.104948	+	0.437627i
$712$	28.9720	−	26.9806i	1.08577	−	1.01114i
$713$			6.78411i			0.254067i
$714$		0			0
$715$		−	4.00000i		−	0.149592i
$716$	16.4049	−	8.95953i	0.613081	−	0.334833i
$717$	−42.1517	+	4.98361i	−1.57419	+	0.186116i
$718$	−0.822045	−	3.22019i	−0.0306784	−	0.120176i
$719$	−28.2355			−1.05301			−0.526503	−	0.850173i	$-0.676497\pi$
$719$	−28.2355			−1.05301			−0.526503	+	0.850173i	$0.676497\pi$
$720$	−25.8036	−	9.00204i	−0.961643	−	0.335486i
$721$		0			0
$722$	−3.65944	−	14.3351i	−0.136190	−	0.533496i
$723$	−31.6756	+	3.74502i	−1.17803	+	0.139279i
$724$	29.6455	−	16.1908i	1.10177	−	0.601728i
$725$		−	0.694815i		−	0.0258048i
$726$	6.73291	+	17.4820i	0.249882	+	0.648820i
$727$		−	27.3942i		−	1.01599i	−0.861359	−	0.507997i	$-0.830386\pi$
$727$		−	27.3942i		−	1.01599i	0.861359	−	0.507997i	$-0.169614\pi$
$728$		0			0
$729$	20.5442	−	17.5196i	0.760896	−	0.648874i
$730$	−8.77981	+	2.24130i	−0.324956	+	0.0829543i
$731$	47.5929			1.76029
$732$	29.5105	−	20.9595i	1.09074	−	0.774686i
$733$	29.7028			1.09710			0.548549	−	0.836119i	$-0.315181\pi$
$733$	29.7028			1.09710			0.548549	+	0.836119i	$0.315181\pi$
$734$	46.8550	−	11.9611i	1.72945	−	0.441492i
$735$		0			0
$736$	6.24130	+	2.07587i	0.230057	+	0.0765177i
$737$		−	33.8323i		−	1.24623i
$738$	−9.61434	+	5.07038i	−0.353909	+	0.186643i
$739$			27.4364i			1.00927i	0.863334	+	0.504633i	$0.168372\pi$
$739$			27.4364i			1.00927i	−0.863334	+	0.504633i	$0.831628\pi$
$740$	−17.1045	−	31.3185i	−0.628775	−	1.15129i
$741$	−0.448959	−	3.79733i	−0.0164929	−	0.139498i
$742$		0			0
$743$	−2.30093			−0.0844131			−0.0422065	−	0.999109i	$-0.513439\pi$
$743$	−2.30093			−0.0844131			−0.0422065	+	0.999109i	$0.513439\pi$
$744$	18.4858	−	21.8011i	0.677722	−	0.799268i
$745$	−39.6019			−1.45090
$746$	−6.18068	−	24.2115i	−0.226291	−	0.886446i
$747$	−1.87212	+	0.448959i	−0.0684974	+	0.0164265i
$748$	−17.8768	−	32.7325i	−0.653641	−	1.19682i
$749$		0			0
$750$	25.0576	−	9.65049i	0.914973	−	0.352386i
$751$		−	19.4193i		−	0.708619i	−0.935128	−	0.354309i	$-0.884716\pi$
$751$		−	19.4193i		−	0.708619i	0.935128	−	0.354309i	$-0.115284\pi$
$752$	−5.02772	+	7.82612i	−0.183342	+	0.285389i
$753$	26.5653	−	3.14082i	0.968094	−	0.114458i
$754$	−2.07587	+	0.529926i	−0.0755988	+	0.0192988i
$755$	9.48634			0.345243
$756$		0			0
$757$	13.9327			0.506393			0.253197	−	0.967415i	$-0.418518\pi$
$757$	13.9327			0.506393			0.253197	+	0.967415i	$0.418518\pi$
$758$	7.39151	−	1.88690i	0.268472	−	0.0685352i
$759$	8.63667	−	1.02112i	0.313491	−	0.0370641i
$760$	23.8277	+	25.5864i	0.864323	+	0.928117i
$761$			12.3859i			0.448989i	0.974475	+	0.224495i	$0.0720731\pi$
$761$			12.3859i			0.448989i	−0.974475	+	0.224495i	$0.927927\pi$
$762$	−14.1896	+	5.46489i	−0.514035	+	0.197972i
$763$		0			0
$764$	−35.6466	+	19.4683i	−1.28965	+	0.704339i
$765$	28.6903	−	6.88028i	1.03730	−	0.248757i
$766$	−0.648029	−	2.53851i	−0.0234142	−	0.0917203i
$767$	−1.59155			−0.0574677
$768$	−14.4003	−	23.6777i	−0.519626	−	0.854394i
$769$	−45.0074			−1.62301			−0.811505	−	0.584346i	$-0.801351\pi$
$769$	−45.0074			−1.62301			−0.811505	+	0.584346i	$0.801351\pi$
$770$		0			0
$771$	−1.82404	−	15.4278i	−0.0656911	−	0.555620i
$772$	−12.0336	+	6.57216i	−0.433100	+	0.236537i
$773$		−	51.4814i		−	1.85166i	−0.377944	−	0.925828i	$-0.623369\pi$
$773$		−	51.4814i		−	1.85166i	0.377944	−	0.925828i	$-0.376631\pi$
$774$	41.3595	−	21.8120i	1.48664	−	0.784017i
$775$		−	1.08840i		−	0.0390965i
$776$	−3.85520	−	4.13974i	−0.138393	−	0.148608i
$777$		0			0
$778$	−7.37877	+	1.88364i	−0.264542	+	0.0675319i
$779$	13.9058			0.498229
$780$	1.85803	+	2.61605i	0.0665280	+	0.0936697i
$781$	−21.1056			−0.755217
$782$	−6.88028	+	1.75639i	−0.246038	+	0.0628084i
$783$	6.69191	+	18.1603i	0.239149	+	0.648997i
$784$		0			0
$785$		−	43.8682i		−	1.56572i
$786$	12.6790	+	32.9211i	0.452245	+	1.17426i
$787$		−	41.2202i		−	1.46934i	−0.678424	−	0.734670i	$-0.737337\pi$
$787$		−	41.2202i		−	1.46934i	0.678424	−	0.734670i	$-0.262663\pi$
$788$	1.88690	+	3.45491i	0.0672179	+	0.123076i
$789$	33.3046	−	3.93761i	1.18568	−	0.140183i
$790$	3.18654	+	12.4826i	0.113372	+	0.444111i
$791$		0			0
$792$	−30.5369	−	20.2524i	−1.08508	−	0.719637i
$793$	−4.24989			−0.150918
$794$	7.56812	+	29.6465i	0.268582	+	1.05211i
$795$	21.4710	−	2.53851i	0.761496	−	0.0900318i
$796$	6.10951	+	11.1865i	0.216546	+	0.396497i
$797$			37.0164i			1.31119i	0.755113	+	0.655595i	$0.227582\pi$
$797$			37.0164i			1.31119i	−0.755113	+	0.655595i	$0.772418\pi$
$798$		0			0
$799$		−	10.0422i		−	0.355269i
$800$	−1.00131	−	0.333040i	−0.0354018	−	0.0117747i
$801$	9.79234	+	40.8333i	0.345995	+	1.44277i
$802$	−52.4421	+	13.3874i	−1.85180	+	0.472724i
$803$	−12.1495			−0.428745
$804$	15.7153	+	22.1268i	0.554237	+	0.780352i
$805$		0			0
$806$	−3.25177	+	0.830108i	−0.114539	+	0.0292393i
$807$	0.00977929	+	0.0827140i	0.000344247	+	0.00291167i
$808$	17.9763	−	16.7407i	0.632405	−	0.588937i
$809$			52.3125i			1.83921i	0.392844	+	0.919605i	$0.371491\pi$
$809$			52.3125i			1.83921i	−0.392844	+	0.919605i	$0.628509\pi$
$810$	21.7793	−	19.1280i	0.765248	−	0.672090i
$811$			25.3719i			0.890929i	0.895300	+	0.445464i	$0.146961\pi$
$811$			25.3719i			0.890929i	−0.895300	+	0.445464i	$0.853039\pi$
$812$		0			0
$813$	4.04223	+	34.1895i	0.141767	+	1.19908i
$814$	−11.8346	−	46.3594i	−0.414802	−	1.62490i
$815$	−19.6950			−0.689886
$816$	26.8961	+	13.1036i	0.941552	+	0.458718i
$817$	−59.8209			−2.09287
$818$	−1.66898	−	6.53787i	−0.0583545	−	0.228591i
$819$		0			0
$820$	−10.2413	+	5.59327i	−0.357642	+	0.195326i
$821$			29.0656i			1.01440i	0.861829	+	0.507198i	$0.169319\pi$
$821$			29.0656i			1.01440i	−0.861829	+	0.507198i	$0.830681\pi$
$822$	−5.31565	+	2.04723i	−0.185405	+	0.0714054i
$823$			28.6343i			0.998131i	0.866564	+	0.499065i	$0.166323\pi$
$823$			28.6343i			0.998131i	−0.866564	+	0.499065i	$0.833677\pi$
$824$	−22.0401	+	20.5251i	−0.767802	+	0.715026i
$825$	−1.38561	+	0.163821i	−0.0482409	+	0.00570352i
$826$		0			0
$827$	4.88743			0.169953			0.0849763	−	0.996383i	$-0.472919\pi$
$827$	4.88743			0.169953			0.0849763	+	0.996383i	$0.472919\pi$
$828$	−5.17419	+	4.67961i	−0.179815	+	0.162628i
$829$	38.9316			1.35215			0.676074	−	0.736833i	$-0.263680\pi$
$829$	38.9316			1.35215			0.676074	+	0.736833i	$0.263680\pi$
$830$	−2.00263	+	0.511229i	−0.0695123	+	0.0177450i
$831$	17.6736	−	2.08956i	0.613091	−	0.0724859i
$832$	−0.231321	+	3.24559i	−0.00801961	+	0.112521i
$833$		0			0
$834$	−21.0757	+	8.11695i	−0.729793	+	0.281067i
$835$		−	4.00000i		−	0.138426i
$836$	22.4699	+	41.1424i	0.777137	+	1.42294i
$837$	10.4826	+	28.4474i	0.362332	+	0.983286i
$838$	2.91474	+	11.4179i	0.100688	+	0.394424i
$839$	49.3493			1.70373			0.851863	−	0.523765i	$-0.175473\pi$
$839$	49.3493			1.70373			0.851863	+	0.523765i	$0.175473\pi$
$840$		0			0
$841$	15.1267			0.521610
$842$	−7.25224	−	28.4091i	−0.249929	−	0.979042i
$843$	1.37964	+	11.6691i	0.0475175	+	0.401907i
$844$	−24.0913	−	44.1113i	−0.829257	−	1.51837i
$845$			29.2294i			1.00552i
$846$	−4.60240	−	8.72696i	−0.158234	−	0.300039i
$847$		0			0
$848$	18.4459	+	11.8501i	0.633434	+	0.406935i
$849$	1.10383	+	9.33627i	0.0378833	+	0.320420i
$850$	1.10383	−	0.281784i	0.0378610	−	0.00966512i
$851$	−9.10959			−0.312273
$852$	13.8033	−	9.80367i	0.472894	−	0.335868i
$853$	−36.4912			−1.24943			−0.624717	−	0.780851i	$-0.714786\pi$
$853$	−36.4912			−1.24943			−0.624717	+	0.780851i	$0.714786\pi$
$854$		0			0
$855$	−36.0616	+	8.64803i	−1.23328	+	0.295756i
$856$	16.1922	+	17.3874i	0.553439	+	0.594288i
$857$		−	36.4434i		−	1.24488i	−0.782667	−	0.622441i	$-0.786141\pi$
$857$		−	36.4434i		−	1.24488i	0.782667	−	0.622441i	$-0.213859\pi$
$858$	1.54623	+	4.01480i	0.0527875	+	0.137063i
$859$		−	11.8682i		−	0.404938i	−0.979289	−	0.202469i	$-0.935103\pi$
$859$		−	11.8682i		−	0.404938i	0.979289	−	0.202469i	$-0.0648966\pi$
$860$	44.0566	−	24.0614i	1.50232	−	0.820488i
$861$		0			0
$862$	−12.2413	−	47.9527i	−0.416940	−	1.63327i
$863$	16.3225			0.555625			0.277812	−	0.960635i	$-0.410391\pi$
$863$	16.3225			0.555625			0.277812	+	0.960635i	$0.410391\pi$
$864$	29.3789	−	0.939234i	0.999489	−	0.0319534i
$865$	−17.9327			−0.609731
$866$	−6.06495	−	23.7581i	−0.206095	−	0.807334i
$867$	−2.83473	+	0.335150i	−0.0962723	+	0.0113823i
$868$		0			0
$869$			17.2733i			0.585958i
$870$	7.46762	+	19.3897i	0.253176	+	0.657373i
$871$		−	3.18654i		−	0.107972i
$872$	20.2062	+	21.6976i	0.684269	+	0.734775i
$873$	5.83457	−	1.39920i	0.197470	−	0.0473559i
$874$	8.64803	−	2.20766i	0.292524	−	0.0746752i
$875$		0			0
$876$	7.94591	−	5.64350i	0.268467	−	0.190676i
$877$	6.81346			0.230074			0.115037	−	0.993361i	$-0.463301\pi$
$877$	6.81346			0.230074			0.115037	+	0.993361i	$0.463301\pi$
$878$	45.6246	−	11.6470i	1.53976	−	0.393067i
$879$	5.73231	+	48.4843i	0.193346	+	1.63534i
$880$	−33.0970	−	21.2624i	−1.11570	−	0.716756i
$881$		−	10.1075i		−	0.340530i	−0.985398	−	0.170265i	$-0.945538\pi$
$881$		−	10.1075i		−	0.340530i	0.985398	−	0.170265i	$-0.0544624\pi$
$882$		0			0
$883$			29.4615i			0.991458i	0.868477	+	0.495729i	$0.165099\pi$
$883$			29.4615i			0.991458i	−0.868477	+	0.495729i	$0.834901\pi$
$884$	−1.68375	−	3.08295i	−0.0566307	−	0.103691i
$885$	1.81230	+	15.3286i	0.0609198	+	0.515265i
$886$	−3.10383	−	12.1586i	−0.104275	−	0.408476i
$887$	−44.4668			−1.49305			−0.746525	−	0.665357i	$-0.768279\pi$
$887$	−44.4668			−1.49305			−0.746525	+	0.665357i	$0.768279\pi$
$888$	29.2742	+	24.8224i	0.982378	+	0.832986i
$889$		0			0
$890$	11.1505	+	43.6798i	0.373767	+	1.46415i
$891$	34.6379	−	17.6269i	1.16041	−	0.590524i
$892$	−8.84710	−	16.1991i	−0.296223	−	0.542385i
$893$			12.6224i			0.422392i
$894$	39.7484	−	15.3084i	1.32938	−	0.511990i
$895$			21.2847i			0.711469i
$896$		0			0
$897$	0.813457	−	0.0961751i	0.0271605	−	0.00321119i
$898$	36.1517	−	9.22877i	1.20640	−	0.307968i
$899$	−21.7320			−0.724802
$900$	0.830114	−	0.750767i	0.0276705	−	0.0250256i
$901$	−23.6691			−0.788534
$902$	−15.1598	+	3.86997i	−0.504765	+	0.128856i
$903$		0			0
$904$	19.7941	−	18.4335i	0.658342	−	0.613090i
$905$			38.4637i			1.27858i
$906$	−9.52144	+	3.66702i	−0.316328	+	0.121829i
$907$		−	55.9190i		−	1.85676i	−0.371631	−	0.928380i	$-0.621201\pi$
$907$		−	55.9190i		−	1.85676i	0.371631	−	0.928380i	$-0.378799\pi$
$908$	34.2739	−	18.7186i	1.13742	−	0.621200i
$909$	6.07587	+	25.3359i	0.201524	+	0.840340i
$910$		0			0
$911$	−7.71538			−0.255622			−0.127811	−	0.991799i	$-0.540795\pi$
$911$	−7.71538			−0.255622			−0.127811	+	0.991799i	$0.540795\pi$
$912$	−33.8065	−	16.4703i	−1.11945	−	0.545386i
$913$	−2.77123			−0.0917142
$914$	10.5814	+	41.4505i	0.350003	+	1.37106i
$915$	4.83934	+	40.9316i	0.159984	+	1.35316i
$916$	3.56961	−	1.94954i	0.117943	−	0.0644145i
$917$		0			0
$918$	−26.1368	+	17.9962i	−0.862642	+	0.593962i
$919$		−	10.0422i		−	0.331263i	−0.986188	−	0.165631i	$-0.947034\pi$
$919$		−	10.0422i		−	0.331263i	0.986188	−	0.165631i	$-0.0529662\pi$
$920$	−5.48108	+	5.10433i	−0.180706	+	0.168285i
$921$	0.455800	+	3.85520i	0.0150191	+	0.127033i
$922$	−2.14177	+	0.546747i	−0.0705353	+	0.0180062i
$923$	−1.98786			−0.0654311
$924$		0			0
$925$	1.46149			0.0480534
$926$	45.6246	−	11.6470i	1.49932	−	0.382744i
$927$	−7.44938	−	31.0633i	−0.244670	−	1.02025i
$928$	−6.64978	+	19.9932i	−0.218290	+	0.656308i
$929$			3.13104i			0.102726i	0.998680	+	0.0513631i	$0.0163566\pi$
$929$			3.13104i			0.102726i	−0.998680	+	0.0513631i	$0.983643\pi$
$930$	11.6977	+	30.3732i	0.383583	+	0.995977i
$931$		0			0
$932$	−3.13603	−	5.74209i	−0.102724	−	0.188088i
$933$	45.5459	−	5.38490i	1.49111	−	0.176294i
$934$	6.05046	+	23.7014i	0.197977	+	0.775533i
$935$	42.4690			1.38888
$936$	−2.87616	−	1.90750i	−0.0940101	−	0.0623485i
$937$	47.0325			1.53648			0.768242	−	0.640159i	$-0.221132\pi$
$937$	47.0325			1.53648			0.768242	+	0.640159i	$0.221132\pi$
$938$		0			0
$939$	−0.757468	+	0.0895556i	−0.0247190	+	0.00292254i
$940$	−5.07703	−	9.29606i	−0.165594	−	0.303204i
$941$			22.2530i			0.725426i	0.931901	+	0.362713i	$0.118150\pi$
$941$			22.2530i			0.725426i	−0.931901	+	0.362713i	$0.881850\pi$
$942$	16.9576	+	44.0305i	0.552508	+	1.43459i
$943$			2.97888i			0.0970058i
$944$	−8.46007	+	13.1689i	−0.275352	+	0.428611i
$945$		0			0
$946$	65.2151	−	16.6480i	2.12033	−	0.541274i
$947$	−33.9335			−1.10269			−0.551345	−	0.834277i	$-0.685885\pi$
$947$	−33.9335			−1.10269			−0.551345	+	0.834277i	$0.685885\pi$
$948$	−8.02358	−	11.2970i	−0.260594	−	0.366909i
$949$	−1.14431			−0.0371460
$950$	−1.38744	+	0.354183i	−0.0450143	+	0.0114912i
$951$	−2.39812	−	20.2835i	−0.0777645	−	0.657739i
$952$		0			0
$953$		−	20.2641i		−	0.656419i	−0.944605	−	0.328209i	$-0.893555\pi$
$953$		−	20.2641i		−	0.656419i	0.944605	−	0.328209i	$-0.106445\pi$
$954$	−20.5691	+	10.8477i	−0.665949	+	0.351206i
$955$		−	46.2499i		−	1.49661i
$956$	43.0145	−	23.4923i	1.39119	−	0.759796i
$957$	3.27100	+	27.6664i	0.105737	+	0.894328i
$958$	−5.80952	−	22.7575i	−0.187697	−	0.735263i
$959$		0			0
$960$	31.5224	−	1.46786i	1.01738	−	0.0473748i
$961$	−3.04223			−0.0981365
$962$	−1.11466	−	4.36642i	−0.0359379	−	0.140779i
$963$	−24.5058	+	5.87680i	−0.789689	+	0.189377i
$964$	32.3240	−	17.6537i	1.04109	−	0.568588i
$965$		−	15.6131i		−	0.502604i
$966$		0			0
$967$			43.5882i			1.40170i	0.713308	+	0.700851i	$0.247196\pi$
$967$			43.5882i			1.40170i	−0.713308	+	0.700851i	$0.752804\pi$
$968$	−14.7423	−	15.8304i	−0.473836	−	0.508810i
$969$	40.3172	−	4.76671i	1.29517	−	0.153129i
$970$	6.24130	−	1.59327i	0.200396	−	0.0511569i
$971$	−3.67161			−0.117828			−0.0589138	−	0.998263i	$-0.518764\pi$
$971$	−3.67161			−0.117828			−0.0589138	+	0.998263i	$0.518764\pi$
$972$	−14.4658	+	27.6177i	−0.463991	+	0.885840i
$973$		0			0
$974$	33.2289	−	8.48263i	1.06472	−	0.271801i
$975$	−0.130506	+	0.0154297i	−0.00417953	+	0.000494147i
$976$	−22.5907	+	35.1646i	−0.723111	+	1.12559i
$977$		−	34.0738i		−	1.09012i	−0.838398	−	0.545058i	$-0.816508\pi$
$977$		−	34.0738i		−	1.09012i	0.838398	−	0.545058i	$-0.183492\pi$
$978$	19.7679	−	7.61326i	0.632107	−	0.243445i
$979$			60.4439i			1.93179i
$980$		0			0
$981$	−30.5807	+	7.33364i	−0.976368	+	0.234145i
$982$	7.10383	+	27.8277i	0.226692	+	0.888019i
$983$	54.2808			1.73129			0.865645	−	0.500659i	$-0.166909\pi$
$983$	54.2808			1.73129			0.865645	+	0.500659i	$0.166909\pi$
$984$	8.11707	−	9.57282i	0.258763	−	0.305170i
$985$	−4.48260			−0.142828
$986$	−5.62636	−	22.0401i	−0.179180	−	0.701898i
$987$		0			0
$988$	2.11636	+	3.87506i	0.0673303	+	0.123282i
$989$		−	12.8147i		−	0.407485i
$990$	36.9067	−	19.4637i	1.17297	−	0.618598i
$991$		−	10.5077i		−	0.333787i	−0.985975	−	0.166893i	$-0.946626\pi$
$991$		−	10.5077i		−	0.333787i	0.985975	−	0.166893i	$-0.0533736\pi$
$992$	−10.4166	+	31.3185i	−0.330727	+	0.994362i
$993$	−0.266354	−	2.25285i	−0.00845250	−	0.0714919i
$994$		0			0
$995$	−14.5141			−0.460127
$996$	1.81242	−	1.28725i	0.0574287	−	0.0407881i
$997$	−21.4564			−0.679531			−0.339765	−	0.940510i	$-0.610348\pi$
$997$	−21.4564			−0.679531			−0.339765	+	0.940510i	$0.610348\pi$
$998$	−14.4406	+	3.68638i	−0.457109	+	0.116690i
$999$	−38.1987	+	14.0759i	−1.20855	+	0.445341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.c.491.8		12
3.2	odd	2	inner	588.2.e.c.491.5		12
4.3	odd	2	inner	588.2.e.c.491.6		12
7.2	even	3		588.2.n.g.263.9		24
7.3	odd	6		588.2.n.f.275.2		24
7.4	even	3		588.2.n.g.275.2		24
7.5	odd	6		588.2.n.f.263.9		24
7.6	odd	2		84.2.e.a.71.8	yes	12
12.11	even	2	inner	588.2.e.c.491.7		12
21.2	odd	6		588.2.n.g.263.4		24
21.5	even	6		588.2.n.f.263.4		24
21.11	odd	6		588.2.n.g.275.11		24
21.17	even	6		588.2.n.f.275.11		24
21.20	even	2		84.2.e.a.71.5	✓	12
28.3	even	6		588.2.n.f.275.4		24
28.11	odd	6		588.2.n.g.275.4		24
28.19	even	6		588.2.n.f.263.11		24
28.23	odd	6		588.2.n.g.263.11		24
28.27	even	2		84.2.e.a.71.6	yes	12
56.13	odd	2		1344.2.h.h.575.11		12
56.27	even	2		1344.2.h.h.575.2		12
84.11	even	6		588.2.n.g.275.9		24
84.23	even	6		588.2.n.g.263.2		24
84.47	odd	6		588.2.n.f.263.2		24
84.59	odd	6		588.2.n.f.275.9		24
84.83	odd	2		84.2.e.a.71.7	yes	12
168.83	odd	2		1344.2.h.h.575.12		12
168.125	even	2		1344.2.h.h.575.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.5	✓	12	21.20	even	2
84.2.e.a.71.6	yes	12	28.27	even	2
84.2.e.a.71.7	yes	12	84.83	odd	2
84.2.e.a.71.8	yes	12	7.6	odd	2
588.2.e.c.491.5		12	3.2	odd	2	inner
588.2.e.c.491.6		12	4.3	odd	2	inner
588.2.e.c.491.7		12	12.11	even	2	inner
588.2.e.c.491.8		12	1.1	even	1	trivial
588.2.n.f.263.2		24	84.47	odd	6
588.2.n.f.263.4		24	21.5	even	6
588.2.n.f.263.9		24	7.5	odd	6
588.2.n.f.263.11		24	28.19	even	6
588.2.n.f.275.2		24	7.3	odd	6
588.2.n.f.275.4		24	28.3	even	6
588.2.n.f.275.9		24	84.59	odd	6
588.2.n.f.275.11		24	21.17	even	6
588.2.n.g.263.2		24	84.23	even	6
588.2.n.g.263.4		24	21.2	odd	6
588.2.n.g.263.9		24	7.2	even	3
588.2.n.g.263.11		24	28.23	odd	6
588.2.n.g.275.2		24	7.4	even	3
588.2.n.g.275.4		24	28.11	odd	6
588.2.n.g.275.9		24	84.11	even	6
588.2.n.g.275.11		24	21.11	odd	6
1344.2.h.h.575.1		12	168.125	even	2
1344.2.h.h.575.2		12	56.27	even	2
1344.2.h.h.575.11		12	56.13	odd	2
1344.2.h.h.575.12		12	168.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.349801 + 1.37027i) q^{2} +(1.72007 - 0.203364i) q^{3} +(-1.75528 + 0.958643i) q^{4} -2.27740i q^{5} +(0.880346 + 2.28582i) q^{6} +(-1.92760 - 2.06987i) q^{8} +(2.91729 - 0.699602i) q^{9} +(3.12065 - 0.796636i) q^{10} +4.31834 q^{11} +(-2.82425 + 2.00589i) q^{12} +0.406728 q^{13} +(-0.463141 - 3.91729i) q^{15} +(2.16201 - 3.36537i) q^{16} +4.31834i q^{17} +(1.97911 + 3.75275i) q^{18} -5.42784i q^{19} +(2.18321 + 3.99747i) q^{20} +(1.51056 + 5.91729i) q^{22} +1.16274 q^{23} +(-3.73654 - 3.16832i) q^{24} -0.186543 q^{25} +(0.142274 + 0.557328i) q^{26} +(4.87566 - 1.79664i) q^{27} +3.72469i q^{29} +(5.20573 - 2.00490i) q^{30} +5.83457i q^{31} +(5.36774 + 1.78532i) q^{32} +(7.42784 - 0.878195i) q^{33} +(-5.91729 + 1.51056i) q^{34} +(-4.44998 + 4.02463i) q^{36} -7.83457 q^{37} +(7.43761 - 1.89866i) q^{38} +(0.699602 - 0.0827140i) q^{39} +(-4.71392 + 4.38991i) q^{40} +2.56195i q^{41} -11.0211i q^{43} +(-7.57988 + 4.13974i) q^{44} +(-1.59327 - 6.64382i) q^{45} +(0.406728 + 1.59327i) q^{46} -2.32549 q^{47} +(3.03441 - 6.22835i) q^{48} +(-0.0652529 - 0.255614i) q^{50} +(0.878195 + 7.42784i) q^{51} +(-0.713922 + 0.389907i) q^{52} +5.48108i q^{53} +(4.16739 + 6.05251i) q^{54} -9.83457i q^{55} +(-1.10383 - 9.33627i) q^{57} +(-5.10383 + 1.30290i) q^{58} -3.91306 q^{59} +(4.56822 + 6.43194i) q^{60} -10.4490 q^{61} +(-7.99494 + 2.04094i) q^{62} +(-0.568736 + 7.97976i) q^{64} -0.926283i q^{65} +(3.80163 + 9.87096i) q^{66} -7.83457i q^{67} +(-4.13974 - 7.57988i) q^{68} +(2.00000 - 0.236460i) q^{69} -4.88743 q^{71} +(-7.07144 - 4.68986i) q^{72} -2.81346 q^{73} +(-2.74054 - 10.7355i) q^{74} +(-0.320867 + 0.0379362i) q^{75} +(5.20336 + 9.52738i) q^{76} +(0.358062 + 0.929710i) q^{78} +4.00000i q^{79} +(-7.66429 - 4.92375i) q^{80} +(8.02112 - 4.08188i) q^{81} +(-3.51056 + 0.896171i) q^{82} -0.641735 q^{83} +9.83457 q^{85} +(15.1019 - 3.85520i) q^{86} +(0.757468 + 6.40673i) q^{87} +(-8.32401 - 8.93840i) q^{88} +13.9970i q^{89} +(8.54650 - 4.50723i) q^{90} +(-2.04094 + 1.11466i) q^{92} +(1.18654 + 10.0359i) q^{93} +(-0.813457 - 3.18654i) q^{94} -12.3614 q^{95} +(9.59596 + 1.97928i) q^{96} +2.00000 q^{97} +(12.5978 - 3.02112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} - 2 q^{24} - 12 q^{25} + 20 q^{30} + 16 q^{33} - 32 q^{34} - 20 q^{36} - 16 q^{37} - 20 q^{40} - 24 q^{45} - 46 q^{48}+ \cdots + 24 q^{97}+O(q^{100}) \) 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 - 2 * q^24 - 12 * q^25 + 20 * q^30 + 16 * q^33 - 32 * q^34 - 20 * q^36 - 16 * q^37 - 20 * q^40 - 24 * q^45 - 46 * q^48 + 28 * q^52 - 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 + 16 * q^61 + 20 * q^64 + 12 * q^66 + 24 * q^69 - 32 * q^72 - 24 * q^73 + 60 * q^76 + 20 * q^78 + 28 * q^81 - 8 * q^82 + 40 * q^85 - 56 * q^88 + 80 * q^90 + 24 * q^93 + 34 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more