LMFDB - Embedded newform 588.2.e.c.491.5

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			491.5
Root			$-1.37027 + 0.349801i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.c.491.6

$q$-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} +(0.323018 + 2.42810i) q^{6} +(1.92760 + 2.06987i) q^{8} +(2.91729 + 0.699602i) q^{9} +(3.12065 - 0.796636i) q^{10} -4.31834 q^{11} +(3.21416 - 1.29197i) q^{12} +0.406728 q^{13} +(0.463141 - 3.91729i) q^{15} +(2.16201 - 3.36537i) q^{16} -4.31834i q^{17} +(-0.0618260 - 4.24219i) q^{18} -5.42784i q^{19} +(-2.18321 - 3.99747i) q^{20} +(1.51056 + 5.91729i) q^{22} -1.16274 q^{23} +(-2.89467 - 3.95233i) q^{24} -0.186543 q^{25} +(-0.142274 - 0.557328i) q^{26} +(-4.87566 - 1.79664i) q^{27} -3.72469i q^{29} +(-5.52975 + 0.735641i) q^{30} +5.83457i q^{31} +(-5.36774 - 1.78532i) q^{32} +(7.42784 + 0.878195i) q^{33} +(-5.91729 + 1.51056i) q^{34} +(-5.79132 + 1.56864i) 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} +(-4.40320 + 5.34900i) q^{48} +(0.0652529 + 0.255614i) q^{50} +(-0.878195 + 7.42784i) q^{51} +(-0.713922 + 0.389907i) q^{52} -5.48108i q^{53} +(-0.756365 + 7.30944i) q^{54} -9.83457i q^{55} +(-1.10383 + 9.33627i) q^{57} +(-5.10383 + 1.30290i) q^{58} +3.91306 q^{59} +(2.94234 + 7.31992i) q^{60} -10.4490 q^{61} +(7.99494 - 2.04094i) q^{62} +(-0.568736 + 7.97976i) q^{64} +0.926283i q^{65} +(-1.39490 - 10.4853i) q^{66} -7.83457i q^{67} +(4.13974 + 7.57988i) q^{68} +(2.00000 + 0.236460i) q^{69} +4.88743 q^{71} +(4.17527 + 7.38696i) q^{72} -2.81346 q^{73} +(2.74054 + 10.7355i) q^{74} +(0.320867 + 0.0379362i) q^{75} +(5.20336 + 9.52738i) q^{76} +(0.131381 + 0.987576i) 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} +(9.66116 - 0.140802i) q^{90} +(2.04094 - 1.11466i) q^{92} +(1.18654 - 10.0359i) q^{93} +(-0.813457 - 3.18654i) q^{94} +12.3614 q^{95} +(8.86982 + 4.16249i) 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	$0.170074\pi$
$5$			2.27740i			1.01848i	−0.860624	+	0.509242i	$0.829926\pi$
$6$	0.323018	+	2.42810i	0.131872	+	0.991267i
$7$		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	$-0.725656\pi$
$11$	−4.31834			−1.30203			−0.651014	+	0.759066i	$0.725656\pi$
$12$	3.21416	−	1.29197i	0.927847	−	0.372960i
$13$	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	$-0.824561\pi$
$17$		−	4.31834i		−	1.04735i	0.851918	−	0.523675i	$-0.175439\pi$
$18$	−0.0618260	−	4.24219i	−0.0145725	−	0.999894i
$19$		−	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	$-0.538682\pi$
$23$	−1.16274			−0.242449			−0.121224	+	0.992625i	$0.538682\pi$
$24$	−2.89467	−	3.95233i	−0.590871	−	0.806766i
$25$	−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	$-0.887598\pi$
$29$		−	3.72469i		−	0.691657i	0.938298	−	0.345829i	$-0.112402\pi$
$30$	−5.52975	+	0.735641i	−1.00959	+	0.134309i
$31$			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
$36$	−5.79132	+	1.56864i	−0.965220	+	0.261440i
$37$	−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	$-0.935888\pi$
$41$		−	2.56195i		−	0.400109i	0.979785	−	0.200054i	$-0.0641119\pi$
$42$		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	$-0.445751\pi$
$47$	2.32549			0.339207			0.169603	+	0.985512i	$0.445751\pi$
$48$	−4.40320	+	5.34900i	−0.635547	+	0.772062i
$49$		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	$-0.877147\pi$
$53$		−	5.48108i		−	0.752884i	0.926440	−	0.376442i	$-0.122853\pi$
$54$	−0.756365	+	7.30944i	−0.102928	+	0.994689i
$55$		−	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	$-0.418017\pi$
$59$	3.91306			0.509437			0.254719	+	0.967015i	$0.418017\pi$
$60$	2.94234	+	7.31992i	0.379854	+	0.944997i
$61$	−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
$66$	−1.39490	−	10.4853i	−0.171701	−	1.29066i
$67$		−	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	$-0.406339\pi$
$71$	4.88743			0.580031			0.290016	+	0.957022i	$0.406339\pi$
$72$	4.17527	+	7.38696i	0.492060	+	0.870561i
$73$	−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
$78$	0.131381	+	0.987576i	0.0148759	+	0.111821i
$79$			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	$-0.488787\pi$
$83$	0.641735			0.0704395			0.0352198	+	0.999380i	$0.488787\pi$
$84$		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	$-0.733953\pi$
$89$		−	13.9970i		−	1.48368i	0.670576	−	0.741841i	$-0.266047\pi$
$90$	9.66116	−	0.140802i	1.01838	−	0.0148419i
$91$		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
$96$	8.86982	+	4.16249i	0.905272	+	0.424832i
$97$	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	$-0.857779\pi$
$101$		−	8.68476i		−	0.864166i	0.901834	−	0.432083i	$-0.142221\pi$
$102$	10.4853	−	1.39490i	1.03820	−	0.138116i
$103$		−	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	$-0.366910\pi$
$107$	8.40021			0.812079			0.406040	+	0.913855i	$0.366910\pi$
$108$	10.2805	−	1.52042i	0.989240	−	0.146303i
$109$	−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	$-0.851494\pi$
$113$		−	9.56296i		−	0.899607i	0.893128	−	0.449804i	$-0.148506\pi$
$114$	13.1793	−	1.75329i	1.23436	−	0.164211i
$115$		−	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
$120$	9.00103	−	6.59231i	0.821678	−	0.601793i
$121$	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	$-0.716604\pi$
$131$	−14.4023			−1.25833			−0.629167	+	0.777270i	$0.716604\pi$
$132$	−13.8798	+	5.57917i	−1.20808	+	0.485605i
$133$		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	$-0.968327\pi$
$137$		−	2.32549i		−	0.198680i	0.995054	−	0.0993398i	$-0.0316731\pi$
$138$	−0.375587	−	2.82325i	−0.0319721	−	0.240331i
$139$			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
$144$	8.66161	−	8.30521i	0.721801	−	0.692101i
$145$	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	$0.252339\pi$
$149$			17.3891i			1.42457i	−0.701891	+	0.712284i	$0.747661\pi$
$150$	−0.0602568	−	0.452945i	−0.00491995	−	0.0369828i
$151$			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
$156$	1.30729	−	0.525482i	0.104667	−	0.0420722i
$157$	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
$162$	2.78748	−	12.4189i	0.219005	−	0.975724i
$163$		−	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	$-0.521648\pi$
$167$	−1.75639			−0.135914			−0.0679568	+	0.997688i	$0.521648\pi$
$168$		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	$0.0967640\pi$
$173$			7.87421i			0.598665i	−0.954149	+	0.299333i	$0.903236\pi$
$174$	9.04391	−	1.20314i	0.685617	−	0.0912100i
$175$		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	$-0.386427\pi$
$179$	9.34605			0.698557			0.349278	+	0.937019i	$0.386427\pi$
$180$	−3.57242	−	13.1891i	−0.266272	−	0.983060i
$181$	−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
$186$	−14.1669	+	1.88467i	−1.03877	+	0.138191i
$187$			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	$-0.762689\pi$
$191$	−20.3082			−1.46945			−0.734725	+	0.678365i	$0.762689\pi$
$192$	2.60106	−	13.6101i	0.187716	−	0.982223i
$193$	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	$0.0223375\pi$
$197$			1.96830i			0.140235i	−0.997539	+	0.0701177i	$0.977662\pi$
$198$	0.266986	+	18.3192i	0.0189738	+	1.30189i
$199$		−	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
$204$	−5.57917	−	13.8798i	−0.390620	−	0.971781i
$205$	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
$216$	−5.67951	−	13.5552i	−0.386442	−	0.922314i
$217$		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
$222$	−2.53071	−	19.0231i	−0.169850	−	1.27675i
$223$			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	$-0.275606\pi$
$227$	19.5262			1.29600			0.647999	+	0.761641i	$0.275606\pi$
$228$	−7.01263	−	17.4459i	−0.464423	−	1.15539i
$229$	−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	$-0.965826\pi$
$233$		−	3.27133i		−	0.214312i	0.994242	−	0.107156i	$-0.0341744\pi$
$234$	−0.0251464	−	1.72542i	−0.00164387	−	0.112794i
$235$			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	$-0.208740\pi$
$239$	24.5058			1.58515			0.792575	+	0.609775i	$0.208740\pi$
$240$	−12.1818	−	10.0278i	−0.786332	−	0.647294i
$241$	−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
$246$	6.22066	−	0.827555i	0.396615	−	0.0527630i
$247$		−	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	$-0.662061\pi$
$251$	−15.4443			−0.974837			−0.487418	+	0.873169i	$0.662061\pi$
$252$		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	$0.0902499\pi$
$257$			8.96931i			0.559490i	−0.960074	+	0.279745i	$0.909750\pi$
$258$	26.7603	−	3.56002i	1.66603	−	0.221637i
$259$		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	$-0.703628\pi$
$263$	−19.3624			−1.19393			−0.596967	+	0.802265i	$0.703628\pi$
$264$	12.5001	+	17.0675i	0.769331	+	1.05043i
$265$	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	$-0.999533\pi$
$269$		−	0.0480876i		−	0.00293195i	0.999999	−	0.00146598i	$-0.000466635\pi$
$270$	−16.6465	−	1.72254i	−1.01307	−	0.104831i
$271$			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
$276$	−3.73724	+	1.50223i	−0.224955	+	0.0904238i
$277$	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	$-0.935141\pi$
$281$		−	6.78411i		−	0.404706i	0.979313	−	0.202353i	$-0.0648588\pi$
$282$	0.751174	+	5.64651i	0.0447318	+	0.336245i
$283$			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
$288$	−14.4102	−	8.96358i	−0.849130	−	0.528184i
$289$	−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	$-0.692095\pi$
$293$		−	28.1874i		−	1.64673i	0.567515	−	0.823363i	$-0.307905\pi$
$294$		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
$300$	−0.599579	+	0.241009i	−0.0346167	+	0.0139146i
$301$		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
$306$	−18.3192	+	0.266986i	−1.04724	+	0.0152625i
$307$			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	$-0.770306\pi$
$311$	−26.4791			−1.50149			−0.750746	+	0.660591i	$0.770306\pi$
$312$	−1.17734	−	1.60752i	−0.0666539	−	0.0910082i
$313$	−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	$0.107440\pi$
$317$			11.7923i			0.662320i	−0.943575	+	0.331160i	$0.892560\pi$
$318$	13.3086	−	1.77049i	0.746309	−	0.0992841i
$319$			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
$324$	−17.9924	+	0.524555i	−0.999575	+	0.0291420i
$325$	−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
$330$	23.8793	−	3.17675i	1.31451	−	0.174874i
$331$		−	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
$342$	−23.0259	+	0.335582i	−1.24510	+	0.0181462i
$343$		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	$-0.766346\pi$
$347$	−27.6614			−1.48494			−0.742471	+	0.669878i	$0.766346\pi$
$348$	−4.81220	−	11.9717i	−0.257961	−	0.641752i
$349$	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	$-0.983111\pi$
$353$		−	1.99285i		−	0.106069i	0.998593	−	0.0530344i	$-0.0168893\pi$
$354$	1.26399	+	9.50130i	0.0671803	+	0.504988i
$355$			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	$-0.480247\pi$
$359$	2.35004			0.124030			0.0620151	+	0.998075i	$0.480247\pi$
$360$	−16.8230	+	9.50875i	−0.886652	+	0.501155i
$361$	−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
$366$	−3.37520	−	25.3711i	−0.176425	−	1.32617i
$367$		−	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
$372$	7.53811	+	18.7532i	0.390833	+	0.972310i
$373$	−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	$-0.484928\pi$
$383$	1.85257			0.0946617			0.0473308	+	0.998879i	$0.484928\pi$
$384$	−19.5593	+	1.19666i	−0.998134	+	0.0610669i
$385$		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	$-0.956411\pi$
$389$		−	5.38490i		−	0.273025i	0.990638	−	0.136513i	$-0.0435895\pi$
$390$	−2.24910	+	0.299206i	−0.113888	+	0.0151509i
$391$			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
$396$	25.0089	−	6.77391i	1.25674	−	0.340402i
$397$	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	$-0.595219\pi$
$401$		−	38.2714i		−	1.91118i	0.294697	−	0.955591i	$-0.404781\pi$
$402$	19.0231	−	2.53071i	0.948786	−	0.126220i
$403$			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
$408$	−17.0675	+	12.5001i	−0.844967	+	0.618849i
$409$	−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
$414$	0.0718878	+	4.93258i	0.00353309	+	0.242423i
$415$			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	$-0.565243\pi$
$419$	−8.33257			−0.407072			−0.203536	+	0.979067i	$0.565243\pi$
$420$		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
$426$	1.57873	+	11.8672i	0.0764897	+	0.574966i
$427$		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	$-0.180890\pi$
$431$	34.9951			1.68565			0.842826	+	0.538186i	$0.180890\pi$
$432$	−16.5876	+	12.5241i	−0.798070	+	0.602565i
$433$	−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
$438$	−0.908798	−	6.83135i	−0.0434240	−	0.326414i
$439$		−	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	$-0.432397\pi$
$443$	8.87313			0.421575			0.210788	+	0.977532i	$0.432397\pi$
$444$	−25.1815	+	10.1221i	−1.19506	+	0.480371i
$445$	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	$0.213901\pi$
$449$			26.3829i			1.24509i	−0.782585	+	0.622544i	$0.786099\pi$
$450$	0.0115332	+	0.791351i	0.000543681	+	0.0373047i
$451$			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
$456$	−21.4526	+	15.7118i	−1.00461	+	0.735772i
$457$	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	$-0.988411\pi$
$461$		−	1.56302i		−	0.0727973i	0.999337	−	0.0363987i	$-0.0115886\pi$
$462$		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	$-0.631060\pi$
$467$	−17.2969			−0.800404			−0.400202	+	0.916427i	$0.631060\pi$
$468$	−2.35549	+	0.638010i	−0.108883	+	0.0294920i
$469$		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
$474$	−9.71239	+	1.29207i	−0.446105	+	0.0593469i
$475$			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	$-0.376123\pi$
$479$	16.6081			0.758842			0.379421	+	0.925224i	$0.376123\pi$
$480$	−9.47964	+	20.2001i	−0.432685	+	0.922005i
$481$	−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
$486$	−7.32023	+	20.7946i	−0.332052	+	0.943261i
$487$		−	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	$-0.651523\pi$
$491$	−20.3082			−0.916497			−0.458248	+	0.888824i	$0.651523\pi$
$492$	−3.30996	−	8.23450i	−0.149225	−	0.371240i
$493$	−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
$498$	0.207292	+	1.55819i	0.00928898	+	0.0698244i
$499$			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	$-0.288432\pi$
$503$	27.6664			1.23358			0.616792	+	0.787126i	$0.288432\pi$
$504$		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	$0.214776\pi$
$509$			28.1874i			1.24939i	−0.780871	+	0.624693i	$0.785224\pi$
$510$	3.17675	+	23.8793i	0.140669	+	1.05739i
$511$		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
$516$	−14.2390	−	35.4236i	−0.626836	−	1.55944i
$517$	−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	$0.176317\pi$
$521$			24.0133i			1.05204i	−0.850471	+	0.526022i	$0.823683\pi$
$522$	−15.8008	+	0.230283i	−0.691584	+	0.0100792i
$523$		−	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
$528$	19.0145	−	23.0988i	0.827500	−	1.00525i
$529$	−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
$534$	33.9861	−	4.52129i	1.47072	−	0.195656i
$535$			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
$540$	3.46261	+	23.4128i	0.149007	+	1.00752i
$541$	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
$552$	3.36575	+	4.59554i	0.143256	+	0.195599i
$553$		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	$0.0919936\pi$
$557$			13.4525i			0.570000i	−0.958528	+	0.285000i	$0.908006\pi$
$558$	24.7514	−	0.360728i	1.04781	−	0.0152708i
$559$		−	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	$-0.245748\pi$
$563$	34.0011			1.43298			0.716488	+	0.697599i	$0.245748\pi$
$564$	7.47448	−	3.00446i	0.314732	−	0.126511i
$565$	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	$0.188223\pi$
$569$			26.5948i			1.11491i	−0.830206	+	0.557457i	$0.811777\pi$
$570$	3.99295	+	30.0146i	0.167246	+	1.25717i
$571$			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
$576$	−7.24182	+	22.8813i	−0.301742	+	0.953390i
$577$	−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
$582$	0.646037	+	4.85620i	0.0267791	+	0.201296i
$583$			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	$-0.719812\pi$
$587$	−30.8651			−1.27394			−0.636969	+	0.770889i	$0.719812\pi$
$588$		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	$0.0422892\pi$
$593$			6.45147i			0.264930i	−0.991188	+	0.132465i	$0.957711\pi$
$594$	3.26624	−	31.5646i	0.134015	−	1.29511i
$595$		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	$-0.584282\pi$
$599$	−12.8097			−0.523391			−0.261696	+	0.965150i	$0.584282\pi$
$600$	0.539980	+	0.737280i	0.0220446	+	0.0300993i
$601$	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
$606$	21.0874	−	2.80534i	0.856619	−	0.113959i
$607$			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
$612$	6.77391	+	25.0089i	0.273819	+	1.01092i
$613$	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	$-0.798471\pi$
$617$		−	29.3933i		−	1.18333i	0.806185	−	0.591664i	$-0.201529\pi$
$618$	25.8545	−	3.43951i	1.04002	−	0.138357i
$619$			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
$624$	−1.79091	+	2.17559i	−0.0716937	+	0.0870933i
$625$	−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
$636$	−7.08141	−	17.6171i	−0.280796	−	0.698561i
$637$		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	$0.142674\pi$
$641$			21.9439i			0.866731i	−0.901218	+	0.433365i	$0.857326\pi$
$642$	2.71342	+	20.3965i	0.107090	+	0.804987i
$643$		−	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	$-0.655761\pi$
$647$	−23.9122			−0.940085			−0.470042	+	0.882644i	$0.655761\pi$
$648$	7.01252	+	24.4709i	0.275478	+	0.961307i
$649$	−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	$-0.633680\pi$
$653$		−	46.6666i		−	1.82621i	0.407730	−	0.913103i	$-0.366320\pi$
$654$	−3.38607	−	25.4528i	−0.132406	−	0.995282i
$655$		−	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	$-0.702165\pi$
$659$	−30.4598			−1.18655			−0.593273	+	0.805001i	$0.702165\pi$
$660$	−12.7060	−	31.6099i	−0.494580	−	1.23041i
$661$	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
$666$	0.484380	+	33.2357i	0.0187694	+	1.28786i
$667$			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	$0.0613531\pi$
$677$			9.96823i			0.383110i	−0.981482	+	0.191555i	$0.938647\pi$
$678$	23.2198	−	3.08901i	0.891751	−	0.118633i
$679$		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	$-0.691703\pi$
$683$	−29.6102			−1.13300			−0.566501	+	0.824061i	$0.691703\pi$
$684$	8.51433	+	31.4344i	0.325554	+	1.20192i
$685$	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
$690$	6.42967	−	0.855362i	0.244773	−	0.0325631i
$691$		−	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
$696$	−14.7212	+	10.7817i	−0.558006	+	0.408680i
$697$	−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	$0.257120\pi$
$701$			38.2714i			1.44549i	−0.691115	+	0.722745i	$0.742880\pi$
$702$	−0.307635	+	2.97296i	−0.0116109	+	0.112207i
$703$			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
$708$	12.5772	−	5.05557i	0.472680	−	0.190000i
$709$	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	$-0.323503\pi$
$719$	28.2355			1.05301			0.526503	+	0.850173i	$0.323503\pi$
$720$	18.9143	+	19.7259i	0.704893	+	0.735142i
$721$		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
$726$	2.47045	+	18.5702i	0.0916871	+	0.689203i
$727$		−	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
$732$	−33.5846	+	13.4998i	−1.24132	+	0.498966i
$733$	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
$738$	−10.8683	+	0.158395i	−0.400066	+	0.00583060i
$739$			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	$-0.486561\pi$
$743$	2.30093			0.0844131			0.0422065	+	0.999109i	$0.486561\pi$
$744$	23.0602	−	16.8891i	0.845426	−	0.619186i
$745$	−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
$750$	−26.6172	+	3.54098i	−0.971922	+	0.129298i
$751$		−	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	$-0.927927\pi$
$761$		−	12.3859i		−	0.448989i	0.974475	−	0.224495i	$-0.0720731\pi$
$762$	−15.0728	+	2.00519i	−0.546030	+	0.0726403i
$763$		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
$768$	8.48162	+	26.3830i	0.306054	+	0.952014i
$769$	−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	$0.376631\pi$
$773$			51.4814i			1.85166i	−0.377944	+	0.925828i	$0.623369\pi$
$774$	−46.7537	+	0.681392i	−1.68053	+	0.0244921i
$775$		−	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
$780$	1.19673	+	2.97722i	0.0428499	+	0.106602i
$781$	−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
$786$	−4.65221	−	34.9702i	−0.165939	−	1.24735i
$787$		−	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
$792$	−18.0302	−	31.8994i	−0.640676	−	1.13349i
$793$	−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	$-0.772418\pi$
$797$		−	37.0164i		−	1.31119i	0.755113	−	0.655595i	$-0.227582\pi$
$798$		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
$804$	−10.1221	−	25.1815i	−0.356977	−	0.888085i
$805$		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	$-0.628509\pi$
$809$		−	52.3125i		−	1.83921i	0.392844	−	0.919605i	$-0.371491\pi$
$810$	28.2829	+	6.34820i	0.993759	+	0.223053i
$811$			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
$816$	23.0988	+	19.0145i	0.808619	+	0.665641i
$817$	−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	$-0.830681\pi$
$821$		−	29.0656i		−	1.01440i	0.861829	−	0.507198i	$-0.169319\pi$
$822$	5.64651	−	0.751174i	0.196945	−	0.0262002i
$823$			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	$-0.527081\pi$
$827$	−4.88743			−0.169953			−0.0849763	+	0.996383i	$0.527081\pi$
$828$	6.73381	−	1.82392i	0.234016	−	0.0633858i
$829$	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
$834$	−22.3875	+	2.97829i	−0.775216	+	0.103130i
$835$		−	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	$-0.824527\pi$
$839$	−49.3493			−1.70373			−0.851863	+	0.523765i	$0.824527\pi$
$840$		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
$846$	−0.143776	−	9.86515i	−0.00494310	−	0.339171i
$847$		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
$852$	15.7090	−	6.31443i	0.538181	−	0.216329i
$853$	−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	$0.213859\pi$
$857$			36.4434i			1.24488i	−0.782667	+	0.622441i	$0.786141\pi$
$858$	−0.567346	−	4.26469i	−0.0193689	−	0.145594i
$859$		−	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	$-0.589609\pi$
$863$	−16.3225			−0.555625			−0.277812	+	0.960635i	$0.589609\pi$
$864$	22.9637	+	18.3485i	0.781241	+	0.624229i
$865$	−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
$870$	2.74003	+	20.5966i	0.0928959	+	0.698290i
$871$		−	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
$876$	−9.04289	+	3.63491i	−0.305531	+	0.122812i
$877$	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	$0.0544624\pi$
$881$			10.1075i			0.340530i	−0.985398	+	0.170265i	$0.945538\pi$
$882$		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	$-0.231721\pi$
$887$	44.4668			1.49305			0.746525	+	0.665357i	$0.231721\pi$
$888$	22.6785	+	30.9648i	0.761040	+	1.03911i
$889$		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
$894$	−42.2224	+	5.61699i	−1.41213	+	0.187860i
$895$			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
$900$	1.08033	−	0.292619i	0.0360110	−	0.00975397i
$901$	−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
$906$	−10.1141	+	1.34551i	−0.336017	+	0.0447016i
$907$		−	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	$-0.459205\pi$
$911$	7.71538			0.255622			0.127811	+	0.991799i	$0.459205\pi$
$912$	29.0335	+	23.8999i	0.961397	+	0.791404i
$913$	−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
$918$	31.5646	+	3.26624i	1.04179	+	0.107802i
$919$		−	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	$-0.983643\pi$
$929$		−	3.13104i		−	0.102726i	0.998680	−	0.0513631i	$-0.0163566\pi$
$930$	−4.29215	−	32.2637i	−0.140745	−	1.05797i
$931$		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
$936$	1.69820	+	3.00449i	0.0555074	+	0.0982047i
$937$	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	$-0.881850\pi$
$941$		−	22.2530i		−	0.725426i	0.931901	−	0.362713i	$-0.118150\pi$
$942$	6.22211	+	46.7710i	0.202727	+	1.52388i
$943$			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	$-0.314115\pi$
$947$	33.9335			1.10269			0.551345	+	0.834277i	$0.314115\pi$
$948$	5.16789	+	12.8566i	0.167845	+	0.417564i
$949$	−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	$0.106445\pi$
$953$			20.2641i			0.656419i	−0.944605	+	0.328209i	$0.893555\pi$
$954$	−23.2518	+	0.338873i	−0.752804	+	0.0109714i
$955$		−	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
$960$	30.9956	+	5.92366i	1.00038	+	0.191185i
$961$	−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	$-0.481236\pi$
$971$	3.67161			0.117828			0.0589138	+	0.998263i	$0.481236\pi$
$972$	31.0548	+	2.75673i	0.996083	+	0.0884221i
$973$		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	$0.183492\pi$
$977$			34.0738i			1.09012i	−0.838398	+	0.545058i	$0.816508\pi$
$978$	20.9983	−	2.79347i	0.671450	−	0.0893254i
$979$			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	$-0.833091\pi$
$983$	−54.2808			−1.73129			−0.865645	+	0.500659i	$0.833091\pi$
$984$	−10.1257	+	7.41598i	−0.322794	+	0.236413i
$985$	−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
$990$	−41.7201	+	0.608032i	−1.32595	+	0.0193245i
$991$		−	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
$996$	2.06264	−	0.829104i	0.0653571	−	0.0262712i
$997$	−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.491.5		12
3.2	odd	2	inner	588.2.e.c.491.8		12
4.3	odd	2	inner	588.2.e.c.491.7		12
7.2	even	3		588.2.n.g.263.4		24
7.3	odd	6		588.2.n.f.275.11		24
7.4	even	3		588.2.n.g.275.11		24
7.5	odd	6		588.2.n.f.263.4		24
7.6	odd	2		84.2.e.a.71.5	✓	12
12.11	even	2	inner	588.2.e.c.491.6		12
21.2	odd	6		588.2.n.g.263.9		24
21.5	even	6		588.2.n.f.263.9		24
21.11	odd	6		588.2.n.g.275.2		24
21.17	even	6		588.2.n.f.275.2		24
21.20	even	2		84.2.e.a.71.8	yes	12
28.3	even	6		588.2.n.f.275.9		24
28.11	odd	6		588.2.n.g.275.9		24
28.19	even	6		588.2.n.f.263.2		24
28.23	odd	6		588.2.n.g.263.2		24
28.27	even	2		84.2.e.a.71.7	yes	12
56.13	odd	2		1344.2.h.h.575.1		12
56.27	even	2		1344.2.h.h.575.12		12
84.11	even	6		588.2.n.g.275.4		24
84.23	even	6		588.2.n.g.263.11		24
84.47	odd	6		588.2.n.f.263.11		24
84.59	odd	6		588.2.n.f.275.4		24
84.83	odd	2		84.2.e.a.71.6	yes	12
168.83	odd	2		1344.2.h.h.575.2		12
168.125	even	2		1344.2.h.h.575.11		12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
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} +(0.323018 + 2.42810i) q^{6} +(1.92760 + 2.06987i) q^{8} +(2.91729 + 0.699602i) q^{9} +(3.12065 - 0.796636i) q^{10} -4.31834 q^{11} +(3.21416 - 1.29197i) q^{12} +0.406728 q^{13} +(0.463141 - 3.91729i) q^{15} +(2.16201 - 3.36537i) q^{16} -4.31834i q^{17} +(-0.0618260 - 4.24219i) q^{18} -5.42784i q^{19} +(-2.18321 - 3.99747i) q^{20} +(1.51056 + 5.91729i) q^{22} -1.16274 q^{23} +(-2.89467 - 3.95233i) q^{24} -0.186543 q^{25} +(-0.142274 - 0.557328i) q^{26} +(-4.87566 - 1.79664i) q^{27} -3.72469i q^{29} +(-5.52975 + 0.735641i) q^{30} +5.83457i q^{31} +(-5.36774 - 1.78532i) q^{32} +(7.42784 + 0.878195i) q^{33} +(-5.91729 + 1.51056i) q^{34} +(-5.79132 + 1.56864i) 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} +(-4.40320 + 5.34900i) q^{48} +(0.0652529 + 0.255614i) q^{50} +(-0.878195 + 7.42784i) q^{51} +(-0.713922 + 0.389907i) q^{52} -5.48108i q^{53} +(-0.756365 + 7.30944i) q^{54} -9.83457i q^{55} +(-1.10383 + 9.33627i) q^{57} +(-5.10383 + 1.30290i) q^{58} +3.91306 q^{59} +(2.94234 + 7.31992i) q^{60} -10.4490 q^{61} +(7.99494 - 2.04094i) q^{62} +(-0.568736 + 7.97976i) q^{64} +0.926283i q^{65} +(-1.39490 - 10.4853i) q^{66} -7.83457i q^{67} +(4.13974 + 7.57988i) q^{68} +(2.00000 + 0.236460i) q^{69} +4.88743 q^{71} +(4.17527 + 7.38696i) q^{72} -2.81346 q^{73} +(2.74054 + 10.7355i) q^{74} +(0.320867 + 0.0379362i) q^{75} +(5.20336 + 9.52738i) q^{76} +(0.131381 + 0.987576i) 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} +(9.66116 - 0.140802i) q^{90} +(2.04094 - 1.11466i) q^{92} +(1.18654 - 10.0359i) q^{93} +(-0.813457 - 3.18654i) q^{94} +12.3614 q^{95} +(8.86982 + 4.16249i) 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

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