LMFDB - Embedded newform 441.2.bb.d.424.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			424.4
Character	$\chi$	$=$	441.424
Dual form			441.2.bb.d.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.151065 + 2.01582i) q^{2} +(-2.06305 + 0.310954i) q^{4} +(1.66779 - 1.54748i) q^{5} +(-1.77774 + 1.95950i) q^{7} +(-0.0388416 - 0.170176i) q^{8} +(3.37138 + 3.12819i) q^{10} +(-1.57656 + 1.07488i) q^{11} +(4.29166 + 2.06676i) q^{13} +(-4.21856 - 3.28759i) q^{14} +(-3.65014 + 1.12592i) q^{16} +(1.47907 + 3.76862i) q^{17} +(0.218933 + 0.379203i) q^{19} +(-2.95953 + 3.71113i) q^{20} +(-2.40493 - 3.01568i) q^{22} +(-2.49370 + 6.35384i) q^{23} +(0.0131678 - 0.175712i) q^{25} +(-3.51789 + 8.96343i) q^{26} +(3.05824 - 4.59534i) q^{28} +(5.30231 - 6.64889i) q^{29} +(-0.409400 + 0.709102i) q^{31} +(-2.94860 - 7.51291i) q^{32} +(-7.37342 + 3.55085i) q^{34} +(0.0674026 + 6.01904i) q^{35} +(3.68347 + 0.555193i) q^{37} +(-0.731331 + 0.498613i) q^{38} +(-0.328124 - 0.223711i) q^{40} +(-2.40243 - 10.5257i) q^{41} +(1.79724 - 7.87423i) q^{43} +(2.91827 - 2.70776i) q^{44} +(-13.1849 - 4.06701i) q^{46} +(-0.114840 - 1.53244i) q^{47} +(-0.679297 - 6.96696i) q^{49} +0.356192 q^{50} +(-9.49656 - 2.92930i) q^{52} +(-0.818284 + 0.123336i) q^{53} +(-0.966009 + 4.23236i) q^{55} +(0.402511 + 0.226418i) q^{56} +(14.2040 + 9.68409i) q^{58} +(2.23892 + 2.07741i) q^{59} +(0.0576570 + 0.00869039i) q^{61} +(-1.49127 - 0.718157i) q^{62} +(7.81612 - 3.76404i) q^{64} +(10.3558 - 3.19435i) q^{65} +(6.06468 - 10.5043i) q^{67} +(-4.22327 - 7.31491i) q^{68} +(-12.1231 + 1.04514i) q^{70} +(-3.05705 - 3.83342i) q^{71} +(-0.809992 + 10.8086i) q^{73} +(-0.562728 + 7.50908i) q^{74} +(-0.569583 - 0.714235i) q^{76} +(0.696479 - 5.00012i) q^{77} +(-1.22996 - 2.13036i) q^{79} +(-4.34532 + 7.52631i) q^{80} +(20.8550 - 6.43292i) q^{82} +(4.16137 - 2.00401i) q^{83} +(8.29864 + 3.99642i) q^{85} +(16.1445 + 2.43340i) q^{86} +(0.244155 + 0.226543i) q^{88} +(3.36000 + 2.29081i) q^{89} +(-11.6793 + 4.73537i) q^{91} +(3.16886 - 13.8837i) q^{92} +(3.07177 - 0.462994i) q^{94} +(0.951941 + 0.293635i) q^{95} +4.05436 q^{97} +(13.9415 - 2.42180i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29}+ \cdots + 161 q^{98}+O(q^{100}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{21}\right)$	$1$

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 $

$2$	0.151065	+	2.01582i	0.106819	+	1.42540i	0.750887	+	0.660431i	$0.229626\pi$
$2$	0.151065	+	2.01582i	0.106819	+	1.42540i	−0.644068	+	0.764969i	$0.722754\pi$
$3$		0			0
$3$		0			0
$4$	−2.06305	+	0.310954i	−1.03152	+	0.155477i
$5$	1.66779	−	1.54748i	0.745857	−	0.692054i	−0.212649	−	0.977129i	$-0.568209\pi$
$5$	1.66779	−	1.54748i	0.745857	−	0.692054i	0.958505	+	0.285075i	$0.0920185\pi$
$6$		0			0
$7$	−1.77774	+	1.95950i	−0.671922	+	0.740622i
$7$	−1.77774	+	1.95950i	−0.671922	+	0.740622i
$8$	−0.0388416	−	0.170176i	−0.0137326	−	0.0601663i
$9$		0			0
$10$	3.37138	+	3.12819i	1.06613	+	0.989219i
$11$	−1.57656	+	1.07488i	−0.475350	+	0.324088i	−0.777185	−	0.629272i	$-0.783353\pi$
$11$	−1.57656	+	1.07488i	−0.475350	+	0.324088i	0.301835	+	0.953360i	$0.402401\pi$
$12$		0			0
$13$	4.29166	+	2.06676i	1.19029	+	0.573215i	0.920894	−	0.389814i	$-0.127461\pi$
$13$	4.29166	+	2.06676i	1.19029	+	0.573215i	0.269399	+	0.963029i	$0.413175\pi$
$14$	−4.21856	−	3.28759i	−1.12746	−	0.878645i
$15$		0			0
$16$	−3.65014	+	1.12592i	−0.912535	+	0.281480i
$17$	1.47907	+	3.76862i	0.358728	+	0.914025i	0.990330	+	0.138732i	$0.0443026\pi$
$17$	1.47907	+	3.76862i	0.358728	+	0.914025i	−0.631602	+	0.775293i	$0.717602\pi$
$18$		0			0
$19$	0.218933	+	0.379203i	0.0502266	+	0.0869951i	0.890046	−	0.455871i	$-0.150672\pi$
$19$	0.218933	+	0.379203i	0.0502266	+	0.0869951i	−0.839819	+	0.542866i	$0.817339\pi$
$20$	−2.95953	+	3.71113i	−0.661770	+	0.829833i
$21$		0			0
$22$	−2.40493	−	3.01568i	−0.512732	−	0.642945i
$23$	−2.49370	+	6.35384i	−0.519972	+	1.32487i	0.394007	+	0.919107i	$0.371088\pi$
$23$	−2.49370	+	6.35384i	−0.519972	+	1.32487i	−0.913980	+	0.405760i	$0.867007\pi$
$24$		0			0
$25$	0.0131678	−	0.175712i	0.00263355	−	0.0351423i
$26$	−3.51789	+	8.96343i	−0.689914	+	1.75787i
$27$		0			0
$28$	3.05824	−	4.59534i	0.577953	−	0.868437i
$29$	5.30231	−	6.64889i	0.984615	−	1.23467i	0.0125582	−	0.999921i	$-0.496003\pi$
$29$	5.30231	−	6.64889i	0.984615	−	1.23467i	0.972057	−	0.234747i	$-0.0754261\pi$
$30$		0			0
$31$	−0.409400	+	0.709102i	−0.0735305	+	0.127359i	−0.900446	−	0.434967i	$-0.856760\pi$
$31$	−0.409400	+	0.709102i	−0.0735305	+	0.127359i	0.826916	+	0.562326i	$0.190093\pi$
$32$	−2.94860	−	7.51291i	−0.521244	−	1.32811i
$33$		0			0
$34$	−7.37342	+	3.55085i	−1.26453	+	0.608966i
$35$	0.0674026	+	6.01904i	0.0113931	+	1.01740i
$36$		0			0
$37$	3.68347	+	0.555193i	0.605558	+	0.0912732i	0.444663	−	0.895698i	$-0.353324\pi$
$37$	3.68347	+	0.555193i	0.605558	+	0.0912732i	0.160896	+	0.986971i	$0.448562\pi$
$38$	−0.731331	+	0.498613i	−0.118638	+	0.0808857i
$39$		0			0
$40$	−0.328124	−	0.223711i	−0.0518809	−	0.0353718i
$41$	−2.40243	−	10.5257i	−0.375196	−	1.64384i	−0.711937	−	0.702243i	$-0.752182\pi$
$41$	−2.40243	−	10.5257i	−0.375196	−	1.64384i	0.336741	−	0.941597i	$-0.390675\pi$
$42$		0			0
$43$	1.79724	−	7.87423i	0.274077	−	1.20081i	−0.631075	−	0.775722i	$-0.717386\pi$
$43$	1.79724	−	7.87423i	0.274077	−	1.20081i	0.905152	−	0.425088i	$-0.139757\pi$
$44$	2.91827	−	2.70776i	0.439946	−	0.408211i
$45$		0			0
$46$	−13.1849	−	4.06701i	−1.94401	−	0.599647i
$47$	−0.114840	−	1.53244i	−0.0167512	−	0.223529i	−0.999296	−	0.0375051i	$-0.988059\pi$
$47$	−0.114840	−	1.53244i	−0.0167512	−	0.223529i	0.982545	−	0.186024i	$-0.0595601\pi$
$48$		0			0
$49$	−0.679297	−	6.96696i	−0.0970424	−	0.995280i
$50$	0.356192			0.0503732
$51$		0			0
$52$	−9.49656	−	2.92930i	−1.31694	−	0.406221i
$53$	−0.818284	+	0.123336i	−0.112400	+	0.0169416i	−0.205001	−	0.978762i	$-0.565720\pi$
$53$	−0.818284	+	0.123336i	−0.112400	+	0.0169416i	0.0926014	+	0.995703i	$0.470482\pi$
$54$		0			0
$55$	−0.966009	+	4.23236i	−0.130257	+	0.570691i
$56$	0.402511	+	0.226418i	0.0537877	+	0.0302564i
$57$		0			0
$58$	14.2040	+	9.68409i	1.86507	+	1.27158i
$59$	2.23892	+	2.07741i	0.291482	+	0.270456i	0.812336	−	0.583190i	$-0.198196\pi$
$59$	2.23892	+	2.07741i	0.291482	+	0.270456i	−0.520854	+	0.853646i	$0.674386\pi$
$60$		0			0
$61$	0.0576570	+	0.00869039i	0.00738222	+	0.00111269i	0.152732	−	0.988268i	$-0.451193\pi$
$61$	0.0576570	+	0.00869039i	0.00738222	+	0.00111269i	−0.145350	+	0.989380i	$0.546431\pi$
$62$	−1.49127	−	0.718157i	−0.189391	−	0.0912060i
$63$		0			0
$64$	7.81612	−	3.76404i	0.977015	−	0.470506i
$65$	10.3558	−	3.19435i	1.28448	−	0.396211i
$66$		0			0
$67$	6.06468	−	10.5043i	0.740918	−	1.28331i	−0.211159	−	0.977452i	$-0.567724\pi$
$67$	6.06468	−	10.5043i	0.740918	−	1.28331i	0.952078	−	0.305857i	$-0.0989429\pi$
$68$	−4.22327	−	7.31491i	−0.512146	−	0.887064i
$69$		0			0
$70$	−12.1231	+	1.04514i	−1.44899	+	0.124918i
$71$	−3.05705	−	3.83342i	−0.362805	−	0.454944i	0.566606	−	0.823989i	$-0.308256\pi$
$71$	−3.05705	−	3.83342i	−0.362805	−	0.454944i	−0.929411	+	0.369045i	$0.879685\pi$
$72$		0			0
$73$	−0.809992	+	10.8086i	−0.0948024	+	1.26505i	0.723525	+	0.690298i	$0.242521\pi$
$73$	−0.809992	+	10.8086i	−0.0948024	+	1.26505i	−0.818328	+	0.574752i	$0.805098\pi$
$74$	−0.562728	+	7.50908i	−0.0654157	+	0.872913i
$75$		0			0
$76$	−0.569583	−	0.714235i	−0.0653357	−	0.0819283i
$77$	0.696479	−	5.00012i	0.0793712	−	0.569817i
$78$		0			0
$79$	−1.22996	−	2.13036i	−0.138382	−	0.239684i	0.788502	−	0.615032i	$-0.210857\pi$
$79$	−1.22996	−	2.13036i	−0.138382	−	0.239684i	−0.926884	+	0.375347i	$0.877523\pi$
$80$	−4.34532	+	7.52631i	−0.485821	+	0.841467i
$81$		0			0
$82$	20.8550	−	6.43292i	2.30305	−	0.710398i
$83$	4.16137	−	2.00401i	0.456769	−	0.219968i	−0.191328	−	0.981526i	$-0.561279\pi$
$83$	4.16137	−	2.00401i	0.456769	−	0.219968i	0.648097	+	0.761558i	$0.275565\pi$
$84$		0			0
$85$	8.29864	+	3.99642i	0.900114	+	0.433472i
$86$	16.1445	+	2.43340i	1.74091	+	0.262400i
$87$		0			0
$88$	0.244155	+	0.226543i	0.0260270	+	0.0241495i
$89$	3.36000	+	2.29081i	0.356159	+	0.242825i	0.728160	−	0.685407i	$-0.240376\pi$
$89$	3.36000	+	2.29081i	0.356159	+	0.242825i	−0.372001	+	0.928232i	$0.621328\pi$
$90$		0			0
$91$	−11.6793	+	4.73537i	−1.22432	+	0.496402i
$92$	3.16886	−	13.8837i	0.330377	−	1.44748i
$93$		0			0
$94$	3.07177	−	0.462994i	0.316828	−	0.0477542i
$95$	0.951941	+	0.293635i	0.0976671	+	0.0301263i
$96$		0			0
$97$	4.05436			0.411658			0.205829	−	0.978588i	$-0.434011\pi$
$97$	4.05436			0.411658			0.205829	+	0.978588i	$0.434011\pi$
$98$	13.9415	−	2.42180i	1.40831	−	0.244639i
$99$		0			0
$100$	0.0274726	+	0.366596i	0.00274726	+	0.0366596i
$101$	3.43504	+	1.05957i	0.341799	+	0.105431i	0.460902	−	0.887451i	$-0.347526\pi$
$101$	3.43504	+	1.05957i	0.341799	+	0.105431i	−0.119104	+	0.992882i	$0.538002\pi$
$102$		0			0
$103$	−10.0573	+	9.33178i	−0.990972	+	0.919487i	−0.996755	−	0.0804960i	$-0.974350\pi$
$103$	−10.0573	+	9.33178i	−0.990972	+	0.919487i	0.00578335	+	0.999983i	$0.498159\pi$
$104$	0.185017	−	0.810614i	0.0181425	−	0.0794873i
$105$		0			0
$106$	−0.372238	−	1.63088i	−0.0361549	−	0.158405i
$107$	−2.51675	−	1.71589i	−0.243303	−	0.165881i	0.435529	−	0.900175i	$-0.356561\pi$
$107$	−2.51675	−	1.71589i	−0.243303	−	0.165881i	−0.678832	+	0.734293i	$0.737514\pi$
$108$		0			0
$109$	2.73299	−	1.86332i	0.261773	−	0.178473i	−0.425321	−	0.905043i	$-0.639839\pi$
$109$	2.73299	−	1.86332i	0.261773	−	0.178473i	0.687093	+	0.726569i	$0.258886\pi$
$110$	−8.67761	−	1.30794i	−0.827377	−	0.124707i
$111$		0			0
$112$	4.28275	−	9.15405i	0.404682	−	0.864976i
$113$	−2.55014	+	1.22808i	−0.239897	+	0.115528i	−0.549970	−	0.835185i	$-0.685361\pi$
$113$	−2.55014	+	1.22808i	−0.239897	+	0.115528i	0.310073	+	0.950713i	$0.399647\pi$
$114$		0			0
$115$	5.67348	+	14.4558i	0.529055	+	1.34801i
$116$	−8.87142	+	15.3657i	−0.823690	+	1.42667i
$117$		0			0
$118$	−3.84946	+	4.82707i	−0.354372	+	0.444368i
$119$	−10.0140	−	3.80137i	−0.917984	−	0.348471i
$120$		0			0
$121$	−2.68858	+	6.85039i	−0.244416	+	0.622763i
$122$	−0.00880832	+	0.117539i	−0.000797468	+	0.0106415i
$123$		0			0
$124$	0.624114	−	1.59022i	0.0560471	−	0.142806i
$125$	6.84264	+	8.58040i	0.612025	+	0.767455i
$126$		0			0
$127$	3.64167	−	4.56651i	0.323146	−	0.405212i	−0.593550	−	0.804797i	$-0.702274\pi$
$127$	3.64167	−	4.56651i	0.323146	−	0.405212i	0.916696	+	0.399585i	$0.130846\pi$
$128$	0.697559	+	1.20821i	0.0616561	+	0.106792i
$129$		0			0
$130$	8.00364	+	20.3929i	0.701966	+	1.78858i
$131$	4.26464	−	1.31547i	0.372603	−	0.114933i	−0.102797	−	0.994702i	$-0.532779\pi$
$131$	4.26464	−	1.31547i	0.372603	−	0.114933i	0.475401	+	0.879769i	$0.342303\pi$
$132$		0			0
$133$	−1.13225	−	0.245124i	−0.0981788	−	0.0212549i
$134$	22.0910	+	10.6385i	1.90837	+	0.919023i
$135$		0			0
$136$	0.583880	−	0.398082i	0.0500673	−	0.0341353i
$137$	3.19380	+	2.96341i	0.272865	+	0.253181i	0.804721	−	0.593653i	$-0.202315\pi$
$137$	3.19380	+	2.96341i	0.272865	+	0.253181i	−0.531856	+	0.846835i	$0.678505\pi$
$138$		0			0
$139$	−1.74312	−	7.63711i	−0.147849	−	0.647771i	−0.993480	−	0.114003i	$-0.963633\pi$
$139$	−1.74312	−	7.63711i	−0.147849	−	0.647771i	0.845631	−	0.533768i	$-0.179224\pi$
$140$	−2.01070	−	12.3966i	−0.169935	−	1.04770i
$141$		0			0
$142$	7.26567	−	6.74156i	0.609722	−	0.565739i
$143$	−8.98757	+	1.35466i	−0.751578	+	0.113282i
$144$		0			0
$145$	−1.44590	−	19.2941i	−0.120075	−	1.60229i
$146$	−21.9105			−1.81333
$147$		0			0
$148$	−7.77181			−0.638838
$149$	−0.502440	−	6.70459i	−0.0411615	−	0.549262i	−0.979222	−	0.202791i	$-0.934999\pi$
$149$	−0.502440	−	6.70459i	−0.0411615	−	0.549262i	0.938061	−	0.346471i	$-0.112620\pi$
$150$		0			0
$151$	−7.13195	+	1.07497i	−0.580390	+	0.0874796i	−0.432674	−	0.901550i	$-0.642430\pi$
$151$	−7.13195	+	1.07497i	−0.580390	+	0.0874796i	−0.147715	+	0.989030i	$0.547192\pi$
$152$	0.0560275	−	0.0519860i	0.00454443	−	0.00421662i
$153$		0			0
$154$	10.1846	+	0.648634i	0.820695	+	0.0522684i
$155$	0.414529	+	1.81617i	0.0332958	+	0.145878i
$156$		0			0
$157$	−17.9097	−	16.6178i	−1.42935	−	1.32624i	−0.866017	−	0.500015i	$-0.833328\pi$
$157$	−17.9097	−	16.6178i	−1.42935	−	1.32624i	−0.563334	−	0.826229i	$-0.690482\pi$
$158$	4.10862	−	2.80121i	0.326864	−	0.222852i
$159$		0			0
$160$	−16.5437	−	7.96703i	−1.30790	−	0.629849i
$161$	−8.01722	−	16.1819i	−0.631846	−	1.27531i
$162$		0			0
$163$	21.5436	−	6.64532i	1.68743	−	0.520502i	0.705329	−	0.708880i	$-0.250799\pi$
$163$	21.5436	−	6.64532i	1.68743	−	0.520502i	0.982097	+	0.188378i	$0.0603230\pi$
$164$	8.22933	+	20.9680i	0.642603	+	1.63733i
$165$		0			0
$166$	4.66835	+	8.08583i	0.362335	+	0.627582i
$167$	6.55741	−	8.22273i	0.507427	−	0.636294i	−0.460459	−	0.887681i	$-0.652315\pi$
$167$	6.55741	−	8.22273i	0.507427	−	0.636294i	0.967887	+	0.251387i	$0.0808867\pi$
$168$		0			0
$169$	6.04151	+	7.57582i	0.464732	+	0.582755i
$170$	−6.80242	+	17.3323i	−0.521722	+	1.32933i
$171$		0			0
$172$	−1.25927	+	16.8038i	−0.0960183	+	1.28128i
$173$	−1.71029	+	4.35774i	−0.130031	+	0.331313i	−0.981031	−	0.193853i	$-0.937901\pi$
$173$	−1.71029	+	4.35774i	−0.130031	+	0.331313i	0.851000	+	0.525166i	$0.175997\pi$
$174$		0			0
$175$	0.320899	+	0.338172i	0.0242576	+	0.0255634i
$176$	4.54443	−	5.69854i	0.342549	−	0.429543i
$177$		0			0
$178$	−4.11028	+	7.11921i	−0.308078	+	0.533607i
$179$	−1.81890	−	4.63449i	−0.135951	−	0.346398i	0.846643	−	0.532161i	$-0.178620\pi$
$179$	−1.81890	−	4.63449i	−0.135951	−	0.346398i	−0.982595	+	0.185763i	$0.940524\pi$
$180$		0			0
$181$	19.9703	−	9.61720i	1.48438	−	0.714841i	0.496212	−	0.868201i	$-0.334724\pi$
$181$	19.9703	−	9.61720i	1.48438	−	0.714841i	0.988170	+	0.153360i	$0.0490095\pi$
$182$	−11.3100	−	22.8279i	−0.838351	−	1.69212i
$183$		0			0
$184$	1.17813	+	0.177575i	0.0868530	+	0.0130910i
$185$	7.00239	−	4.77415i	0.514826	−	0.351002i
$186$		0			0
$187$	−6.38266	−	4.35162i	−0.466746	−	0.318222i
$188$	0.713438	+	3.12578i	0.0520328	+	0.227971i
$189$		0			0
$190$	−0.448110	+	1.96330i	−0.0325093	+	0.142433i
$191$	9.57738	−	8.88651i	0.692995	−	0.643005i	−0.252895	−	0.967494i	$-0.581383\pi$
$191$	9.57738	−	8.88651i	0.692995	−	0.643005i	0.945890	+	0.324488i	$0.105192\pi$
$192$		0			0
$193$	−10.2751	−	3.16945i	−0.739618	−	0.228142i	−0.0980217	−	0.995184i	$-0.531251\pi$
$193$	−10.2751	−	3.16945i	−0.739618	−	0.228142i	−0.641597	+	0.767042i	$0.721728\pi$
$194$	0.612471	+	8.17285i	0.0439728	+	0.586777i
$195$		0			0
$196$	3.56783	+	14.1619i	0.254845	+	1.01157i
$197$	5.67753			0.404507			0.202254	−	0.979333i	$-0.435173\pi$
$197$	5.67753			0.404507			0.202254	+	0.979333i	$0.435173\pi$
$198$		0			0
$199$	13.0167	+	4.01512i	0.922729	+	0.284624i	0.719488	−	0.694505i	$-0.244376\pi$
$199$	13.0167	+	4.01512i	0.922729	+	0.284624i	0.203241	+	0.979129i	$0.434853\pi$
$200$	−0.0304134	+	0.00458408i	−0.00215055	+	0.000324143i
$201$		0			0
$202$	−1.61699	+	7.08448i	−0.113771	+	0.498462i
$203$	3.60239	+	22.2099i	0.252838	+	1.55883i
$204$		0			0
$205$	−20.2951	−	13.8369i	−1.41747	−	0.966414i
$206$	−20.3305	−	18.8639i	−1.41649	−	1.31431i
$207$		0			0
$208$	−17.9922	−	2.71188i	−1.24753	−	0.188035i
$209$	−0.752757	−	0.362509i	−0.0520693	−	0.0250753i
$210$		0			0
$211$	−14.5359	+	7.00014i	−1.00069	+	0.481909i	−0.861174	−	0.508310i	$-0.830270\pi$
$211$	−14.5359	+	7.00014i	−1.00069	+	0.481909i	−0.139521	+	0.990219i	$0.544556\pi$
$212$	1.64981	−	0.508898i	0.113309	−	0.0349512i
$213$		0			0
$214$	3.07873	−	5.33252i	0.210458	−	0.364523i
$215$	−9.18780	−	15.9137i	−0.626603	−	1.08531i
$216$		0			0
$217$	−0.661681	−	2.06282i	−0.0449178	−	0.140033i
$218$	4.16897	+	5.22772i	0.282358	+	0.354066i
$219$		0			0
$220$	0.676850	−	9.03194i	0.0456332	−	0.608933i
$221$	−1.44113	+	19.2305i	−0.0969408	+	1.29359i
$222$		0			0
$223$	−4.65621	−	5.83871i	−0.311803	−	0.390989i	0.601094	−	0.799178i	$-0.294732\pi$
$223$	−4.65621	−	5.83871i	−0.311803	−	0.390989i	−0.912897	+	0.408190i	$0.866160\pi$
$224$	19.9634	+	7.57820i	1.33386	+	0.506340i
$225$		0			0
$226$	−2.86083	−	4.95510i	−0.190299	−	0.329608i
$227$	−4.81428	+	8.33857i	−0.319535	+	0.553450i	−0.980391	−	0.197062i	$-0.936860\pi$
$227$	−4.81428	+	8.33857i	−0.319535	+	0.553450i	0.660856	+	0.750512i	$0.270193\pi$
$228$		0			0
$229$	−13.3133	+	4.10660i	−0.879765	+	0.271372i	−0.701550	−	0.712620i	$-0.747508\pi$
$229$	−13.3133	+	4.10660i	−0.879765	+	0.271372i	−0.178215	+	0.983992i	$0.557032\pi$
$230$	−28.2832	+	13.6205i	−1.86494	+	0.898108i
$231$		0			0
$232$	−1.33743	−	0.644074i	−0.0878067	−	0.0422855i
$233$	−6.41172	−	0.966411i	−0.420046	−	0.0633117i	−0.0643811	−	0.997925i	$-0.520507\pi$
$233$	−6.41172	−	0.966411i	−0.420046	−	0.0633117i	−0.355665	+	0.934614i	$0.615745\pi$
$234$		0			0
$235$	−2.56294	−	2.37806i	−0.167188	−	0.155128i
$236$	−5.26497	−	3.58959i	−0.342720	−	0.233663i
$237$		0			0
$238$	6.15011	−	20.7607i	0.398652	−	1.34572i
$239$	−3.80981	+	16.6919i	−0.246436	+	1.07971i	0.688596	+	0.725145i	$0.258227\pi$
$239$	−3.80981	+	16.6919i	−0.246436	+	1.07971i	−0.935032	+	0.354563i	$0.884630\pi$
$240$		0			0
$241$	−1.56832	+	0.236387i	−0.101025	+	0.0152270i	−0.199360	−	0.979926i	$-0.563886\pi$
$241$	−1.56832	+	0.236387i	−0.101025	+	0.0152270i	0.0983354	+	0.995153i	$0.468648\pi$
$242$	−14.2153	−	4.38484i	−0.913794	−	0.281868i
$243$		0			0
$244$	−0.121651			−0.00778793
$245$	−11.9142	−	10.5682i	−0.761167	−	0.675178i
$246$		0			0
$247$	0.155866	+	2.07989i	0.00991753	+	0.132340i
$248$	0.136574	+	0.0421275i	0.00867246	+	0.00267510i
$249$		0			0
$250$	−16.2629	+	15.0897i	−1.02855	+	0.954359i
$251$	−3.72581	+	16.3239i	−0.235171	+	1.03035i	0.710109	+	0.704092i	$0.248646\pi$
$251$	−3.72581	+	16.3239i	−0.235171	+	1.03035i	−0.945280	+	0.326261i	$0.894211\pi$
$252$		0			0
$253$	−2.89815	−	12.6976i	−0.182205	−	0.798293i
$254$	9.75539	+	6.65111i	0.612108	+	0.417328i
$255$		0			0
$256$	12.0055	−	8.18520i	0.750343	−	0.511575i
$257$	−29.0195	−	4.37399i	−1.81019	−	0.272842i	−0.845069	−	0.534658i	$-0.820441\pi$
$257$	−29.0195	−	4.37399i	−1.81019	−	0.272842i	−0.965118	+	0.261816i	$0.915679\pi$
$258$		0			0
$259$	−7.63614	+	6.23077i	−0.474487	+	0.387162i
$260$	−20.3713	+	9.81029i	−1.26337	+	0.608408i
$261$		0			0
$262$	3.29598	+	8.39802i	0.203626	+	0.518831i
$263$	5.27309	−	9.13326i	0.325153	−	0.563181i	−0.656391	−	0.754421i	$-0.727918\pi$
$263$	5.27309	−	9.13326i	0.325153	−	0.563181i	0.981543	+	0.191240i	$0.0612510\pi$
$264$		0			0
$265$	−1.17386	+	1.47198i	−0.0721098	+	0.0904228i
$266$	0.323082	−	2.31945i	0.0198094	−	0.142214i
$267$		0			0
$268$	−9.24535	+	23.5568i	−0.564750	+	1.43896i
$269$	0.787107	−	10.5032i	0.0479907	−	0.640392i	−0.920404	−	0.390969i	$-0.872140\pi$
$269$	0.787107	−	10.5032i	0.0479907	−	0.640392i	0.968395	−	0.249423i	$-0.0802410\pi$
$270$		0			0
$271$	−9.07595	+	23.1251i	−0.551324	+	1.40475i	0.335234	+	0.942135i	$0.391185\pi$
$271$	−9.07595	+	23.1251i	−0.551324	+	1.40475i	−0.886558	+	0.462617i	$0.846911\pi$
$272$	−9.64199	−	12.0907i	−0.584632	−	0.733105i
$273$		0			0
$274$	−5.49123	+	6.88579i	−0.331737	+	0.415986i
$275$	0.168109	+	0.291173i	0.0101374	+	0.0175584i
$276$		0			0
$277$	4.81556	+	12.2698i	0.289339	+	0.737223i	0.999451	+	0.0331346i	$0.0105490\pi$
$277$	4.81556	+	12.2698i	0.289339	+	0.737223i	−0.710112	+	0.704089i	$0.751356\pi$
$278$	15.1317	−	4.66751i	0.907539	−	0.279939i
$279$		0			0
$280$	1.02168	−	0.245260i	0.0610570	−	0.0146571i
$281$	−18.3370	−	8.83064i	−1.09389	−	0.526792i	−0.202161	−	0.979352i	$-0.564796\pi$
$281$	−18.3370	−	8.83064i	−1.09389	−	0.526792i	−0.891734	+	0.452561i	$0.850511\pi$
$282$		0			0
$283$	19.0449	−	12.9846i	1.13210	−	0.771854i	0.155698	−	0.987805i	$-0.450237\pi$
$283$	19.0449	−	12.9846i	1.13210	−	0.771854i	0.976404	+	0.215950i	$0.0692849\pi$
$284$	7.49886	+	6.95792i	0.444975	+	0.412877i
$285$		0			0
$286$	−4.08845	−	17.9127i	−0.241755	−	1.05920i
$287$	24.8960	+	14.0044i	1.46957	+	0.826654i
$288$		0			0
$289$	0.447044	−	0.414796i	0.0262967	−	0.0243998i
$290$	38.6751	−	5.82933i	2.27108	−	0.342310i
$291$		0			0
$292$	−1.68993	−	22.5505i	−0.0988955	−	1.31967i
$293$	11.8715			0.693539			0.346769	−	0.937950i	$-0.387279\pi$
$293$	11.8715			0.693539			0.346769	+	0.937950i	$0.387279\pi$
$294$		0			0
$295$	6.94878			0.404574
$296$	−0.0485911	−	0.648403i	−0.00282430	−	0.0376877i
$297$		0			0
$298$	13.4393	−	2.02566i	0.778521	−	0.117343i
$299$	−23.8339	+	22.1147i	−1.37835	+	1.27892i
$300$		0			0
$301$	12.2345	+	17.5200i	0.705188	+	1.00984i
$302$	−3.24433	−	14.2143i	−0.186690	−	0.817943i
$303$		0			0
$304$	−1.22609	−	1.13764i	−0.0703209	−	0.0652483i
$305$	0.109608	−	0.0747293i	0.00627612	−	0.00427899i
$306$		0			0
$307$	13.2755	+	6.39317i	0.757676	+	0.364877i	0.772502	−	0.635013i	$-0.219005\pi$
$307$	13.2755	+	6.39317i	0.757676	+	0.364877i	−0.0148260	+	0.999890i	$0.504719\pi$
$308$	0.117940	+	10.5321i	0.00672027	+	0.600120i
$309$		0			0
$310$	−3.59845	+	1.10998i	−0.204378	+	0.0630423i
$311$	10.0956	+	25.7231i	0.572468	+	1.45862i	0.864706	+	0.502279i	$0.167505\pi$
$311$	10.0956	+	25.7231i	0.572468	+	1.45862i	−0.292238	+	0.956346i	$0.594400\pi$
$312$		0			0
$313$	12.5594	+	21.7536i	0.709901	+	1.22958i	0.964894	+	0.262641i	$0.0845936\pi$
$313$	12.5594	+	21.7536i	0.709901	+	1.22958i	−0.254993	+	0.966943i	$0.582073\pi$
$314$	30.7929	−	38.6131i	1.73775	−	2.17906i
$315$		0			0
$316$	3.19992	+	4.01257i	0.180009	+	0.225725i
$317$	8.00526	−	20.3971i	0.449620	−	1.14561i	−0.508959	−	0.860791i	$-0.669970\pi$
$317$	8.00526	−	20.3971i	0.449620	−	1.14561i	0.958580	−	0.284824i	$-0.0919351\pi$
$318$		0			0
$319$	−1.21265	+	16.1817i	−0.0678954	+	0.906002i
$320$	7.21083	−	18.3729i	0.403098	−	1.02708i
$321$		0			0
$322$	31.4086	−	18.6058i	1.75033	−	1.03686i
$323$	−1.10525	+	1.38594i	−0.0614979	+	0.0771160i
$324$		0			0
$325$	0.419665	−	0.726880i	0.0232788	−	0.0403201i
$326$	16.6503	+	42.4242i	0.922172	+	2.34966i
$327$		0			0
$328$	−1.69791	+	0.817671i	−0.0937515	+	0.0451483i
$329$	3.20697	+	2.49924i	0.176806	+	0.137788i
$330$		0			0
$331$	−12.5685	−	1.89440i	−0.690828	−	0.104126i	−0.205761	−	0.978602i	$-0.565967\pi$
$331$	−12.5685	−	1.89440i	−0.690828	−	0.104126i	−0.485067	+	0.874477i	$0.661205\pi$
$332$	−7.96193	+	5.42836i	−0.436968	+	0.297920i
$333$		0			0
$334$	17.5661	+	11.9764i	0.961176	+	0.655318i
$335$	−6.14065	−	26.9039i	−0.335500	−	1.46992i
$336$		0			0
$337$	−2.21226	+	9.69255i	−0.120509	+	0.527987i	0.878250	+	0.478201i	$0.158711\pi$
$337$	−2.21226	+	9.69255i	−0.120509	+	0.527987i	−0.998760	+	0.0497856i	$0.984146\pi$
$338$	−14.3588	+	13.3230i	−0.781017	+	0.724678i
$339$		0			0
$340$	−18.3632	−	5.66429i	−0.995884	−	0.307189i
$341$	−0.116756	−	1.55800i	−0.00632268	−	0.0843703i
$342$		0			0
$343$	14.8594	+	11.0543i	0.802331	+	0.596879i
$344$	−1.40981			−0.0760121
$345$		0			0
$346$	−9.04278	−	2.78933i	−0.486143	−	0.149955i
$347$	−16.4970	+	2.48652i	−0.885605	+	0.133483i	−0.576066	−	0.817403i	$-0.695413\pi$
$347$	−16.4970	+	2.48652i	−0.885605	+	0.133483i	−0.309539	+	0.950887i	$0.600175\pi$
$348$		0			0
$349$	0.185225	−	0.811522i	0.00991484	−	0.0434398i	−0.969729	−	0.244186i	$-0.921479\pi$
$349$	0.185225	−	0.811522i	0.00991484	−	0.0434398i	0.979643	+	0.200746i	$0.0643365\pi$
$350$	−0.633216	+	0.697959i	−0.0338468	+	0.0373075i
$351$		0			0
$352$	12.7241	+	8.67515i	0.678197	+	0.462387i
$353$	20.3502	+	18.8822i	1.08313	+	1.00500i	0.999964	+	0.00846270i	$0.00269379\pi$
$353$	20.3502	+	18.8822i	1.08313	+	1.00500i	0.0831665	+	0.996536i	$0.473497\pi$
$354$		0			0
$355$	−11.0307	−	1.66260i	−0.585446	−	0.0882418i
$356$	−7.64417	−	3.68124i	−0.405140	−	0.195105i
$357$		0			0
$358$	9.06752	−	4.36669i	0.479233	−	0.230787i
$359$	−24.3867	+	7.52231i	−1.28708	+	0.397012i	−0.861431	−	0.507875i	$-0.830431\pi$
$359$	−24.3867	+	7.52231i	−1.28708	+	0.397012i	−0.425652	+	0.904887i	$0.639955\pi$
$360$		0			0
$361$	9.40414	−	16.2884i	0.494955	−	0.857286i
$362$	22.4034	+	38.8038i	1.17749	+	2.03948i
$363$		0			0
$364$	22.6224	−	13.4010i	1.18573	−	0.702403i
$365$	15.3752	+	19.2799i	0.804774	+	1.00915i
$366$		0			0
$367$	1.63958	−	21.8787i	0.0855854	−	1.14206i	−0.774729	−	0.632293i	$-0.782114\pi$
$367$	1.63958	−	21.8787i	0.0855854	−	1.14206i	0.860314	−	0.509764i	$-0.170267\pi$
$368$	1.94844	−	26.0001i	0.101569	−	1.35535i
$369$		0			0
$370$	10.6816	+	13.3943i	0.555312	+	0.696339i
$371$	1.21302	−	1.82269i	0.0629767	−	0.0946293i
$372$		0			0
$373$	−14.8839	−	25.7796i	−0.770657	−	1.33482i	−0.937204	−	0.348783i	$-0.886595\pi$
$373$	−14.8839	−	25.7796i	−0.770657	−	1.33482i	0.166547	−	0.986034i	$-0.446738\pi$
$374$	7.80789	−	13.5237i	0.403737	−	0.699292i
$375$		0			0
$376$	−0.256323	+	0.0790653i	−0.0132189	+	0.00407748i
$377$	36.4974	−	17.5762i	1.87971	−	0.905220i
$378$		0			0
$379$	−6.35554	−	3.06067i	−0.326462	−	0.157216i	0.263473	−	0.964667i	$-0.415132\pi$
$379$	−6.35554	−	3.06067i	−0.326462	−	0.157216i	−0.589935	+	0.807451i	$0.700846\pi$
$380$	−2.05521	−	0.309773i	−0.105430	−	0.0158910i
$381$		0			0
$382$	19.3604	+	17.9638i	0.990565	+	0.919110i
$383$	11.1196	+	7.58121i	0.568184	+	0.387382i	0.813066	−	0.582171i	$-0.197797\pi$
$383$	11.1196	+	7.58121i	0.568184	+	0.387382i	−0.244882	+	0.969553i	$0.578749\pi$
$384$		0			0
$385$	−6.57601	−	9.41692i	−0.335144	−	0.479931i
$386$	4.83683	−	21.1916i	0.246188	−	1.07862i
$387$		0			0
$388$	−8.36433	+	1.26072i	−0.424634	+	0.0640033i
$389$	−11.4201	−	3.52262i	−0.579020	−	0.178604i	−0.00860837	−	0.999963i	$-0.502740\pi$
$389$	−11.4201	−	3.52262i	−0.579020	−	0.178604i	−0.570412	+	0.821359i	$0.693216\pi$
$390$		0			0
$391$	−27.6336			−1.39749
$392$	−1.15923	+	0.386208i	−0.0585497	+	0.0195064i
$393$		0			0
$394$	0.857674	+	11.4449i	0.0432090	+	0.576584i
$395$	−5.34801	−	1.64964i	−0.269087	−	0.0830025i
$396$		0			0
$397$	3.78525	−	3.51219i	0.189976	−	0.176272i	−0.579450	−	0.815008i	$-0.696733\pi$
$397$	3.78525	−	3.51219i	0.189976	−	0.176272i	0.769426	+	0.638736i	$0.220542\pi$
$398$	−6.12739	+	26.8459i	−0.307138	+	1.34566i
$399$		0			0
$400$	0.149773	+	0.656198i	0.00748865	+	0.0328099i
$401$	−14.1993	−	9.68089i	−0.709077	−	0.483441i	0.154284	−	0.988027i	$-0.450693\pi$
$401$	−14.1993	−	9.68089i	−0.709077	−	0.483441i	−0.863362	+	0.504586i	$0.831645\pi$
$402$		0			0
$403$	−3.22255	+	2.19710i	−0.160527	+	0.109445i
$404$	−7.41611	−	1.11780i	−0.368965	−	0.0556126i
$405$		0			0
$406$	−44.2269	+	10.6169i	−2.19494	+	0.526908i
$407$	−6.40397	+	3.08399i	−0.317433	+	0.152868i
$408$		0			0
$409$	7.93281	+	20.2125i	0.392252	+	0.999442i	0.981495	+	0.191486i	$0.0613308\pi$
$409$	7.93281	+	20.2125i	0.392252	+	0.999442i	−0.589243	+	0.807956i	$0.700574\pi$
$410$	24.8269	−	43.0015i	1.22611	−	2.12369i
$411$		0			0
$412$	17.8468	−	22.3792i	0.879251	−	1.10255i
$413$	−8.05089	+	0.694069i	−0.396159	+	0.0341529i
$414$		0			0
$415$	3.83911	−	9.78188i	0.188454	−	0.480174i
$416$	2.87295	−	38.3369i	0.140858	−	1.87962i
$417$		0			0
$418$	0.617037	−	1.57219i	0.0301803	−	0.0768981i
$419$	6.50497	+	8.15697i	0.317788	+	0.398494i	0.914911	−	0.403656i	$-0.132261\pi$
$419$	6.50497	+	8.15697i	0.317788	+	0.398494i	−0.597122	+	0.802150i	$0.703689\pi$
$420$		0			0
$421$	−6.92877	+	8.68841i	−0.337688	+	0.423447i	−0.921462	−	0.388469i	$-0.873004\pi$
$421$	−6.92877	+	8.68841i	−0.337688	+	0.423447i	0.583774	+	0.811916i	$0.301575\pi$
$422$	−16.3069	−	28.2443i	−0.793806	−	1.37491i
$423$		0			0
$424$	0.0527724	+	0.134462i	0.00256285	+	0.00653004i
$425$	0.681667	−	0.210266i	0.0330657	−	0.0101994i
$426$		0			0
$427$	−0.119528	+	0.0975298i	−0.00578436	+	0.00471980i
$428$	5.72573	+	2.75736i	0.276763	+	0.133282i
$429$		0			0
$430$	30.6913	−	20.9249i	1.48006	−	1.00909i
$431$	−16.7258	−	15.5193i	−0.805653	−	0.747537i	0.165445	−	0.986219i	$-0.447094\pi$
$431$	−16.7258	−	15.5193i	−0.805653	−	0.747537i	−0.971098	+	0.238682i	$0.923285\pi$
$432$		0			0
$433$	−3.39696	−	14.8831i	−0.163247	−	0.715234i	−0.988594	−	0.150607i	$-0.951877\pi$
$433$	−3.39696	−	14.8831i	−0.163247	−	0.715234i	0.825346	−	0.564627i	$-0.190980\pi$
$434$	4.05831	−	1.64545i	0.194805	−	0.0789841i
$435$		0			0
$436$	−5.05887	+	4.69394i	−0.242276	+	0.224799i
$437$	−2.95535	+	0.445447i	−0.141373	+	0.0213086i
$438$		0			0
$439$	−0.640084	−	8.54133i	−0.0305495	−	0.407655i	−0.991425	−	0.130675i	$-0.958285\pi$
$439$	−0.640084	−	8.54133i	−0.0305495	−	0.407655i	0.960876	−	0.276980i	$-0.0893336\pi$
$440$	0.757768			0.0361252
$441$		0			0
$442$	−38.9830			−1.85423
$443$	0.579640	+	7.73476i	0.0275395	+	0.367490i	0.993899	+	0.110294i	$0.0351793\pi$
$443$	0.579640	+	7.73476i	0.0275395	+	0.367490i	−0.966359	+	0.257195i	$0.917202\pi$
$444$		0			0
$445$	9.14874	−	1.37895i	0.433692	−	0.0653685i
$446$	11.0664	−	10.2681i	0.524009	−	0.486209i
$447$		0			0
$448$	−6.51936	+	22.0072i	−0.308011	+	1.03974i
$449$	0.364600	+	1.59742i	0.0172065	+	0.0753867i	0.982802	−	0.184661i	$-0.0591188\pi$
$449$	0.364600	+	1.59742i	0.0172065	+	0.0753867i	−0.965596	+	0.260048i	$0.916262\pi$
$450$		0			0
$451$	15.1014	+	14.0121i	0.711099	+	0.659804i
$452$	4.87918	−	3.32657i	0.229497	−	0.156468i
$453$		0			0
$454$	−17.5363	−	8.44505i	−0.823020	−	0.396346i
$455$	−12.1506	+	25.9710i	−0.569630	+	1.21754i
$456$		0			0
$457$	−17.3635	+	5.35593i	−0.812231	+	0.250540i	−0.672926	−	0.739710i	$-0.734963\pi$
$457$	−17.3635	+	5.35593i	−0.812231	+	0.250540i	−0.139304	+	0.990250i	$0.544487\pi$
$458$	−10.2893	−	26.2168i	−0.480788	−	1.22503i
$459$		0			0
$460$	−16.1997	−	28.0588i	−0.755317	−	1.30825i
$461$	−19.4601	+	24.4021i	−0.906345	+	1.13652i	0.0838006	+	0.996483i	$0.473294\pi$
$461$	−19.4601	+	24.4021i	−0.906345	+	1.13652i	−0.990146	+	0.140039i	$0.955277\pi$
$462$		0			0
$463$	20.1031	+	25.2085i	0.934272	+	1.17154i	0.984953	+	0.172825i	$0.0552895\pi$
$463$	20.1031	+	25.2085i	0.934272	+	1.17154i	−0.0506807	+	0.998715i	$0.516139\pi$
$464$	−11.8681	+	30.2394i	−0.550961	+	1.40383i
$465$		0			0
$466$	0.979525	−	13.0709i	0.0453756	−	0.605496i
$467$	7.58840	−	19.3349i	0.351149	−	0.894713i	−0.640757	−	0.767743i	$-0.721380\pi$
$467$	7.58840	−	19.3349i	0.351149	−	0.894713i	0.991907	−	0.126970i	$-0.0405252\pi$
$468$		0			0
$469$	9.80185	+	30.5577i	0.452607	+	1.41102i
$470$	4.40658	−	5.52567i	0.203260	−	0.254880i
$471$		0			0
$472$	0.266562	−	0.461700i	0.0122695	−	0.0212515i
$473$	5.63039	+	14.3460i	0.258886	+	0.659630i
$474$		0			0
$475$	0.0695132	−	0.0334758i	0.00318948	−	0.00153597i
$476$	21.8415	+	4.72850i	1.00110	+	0.216730i
$477$		0			0
$478$	−34.2233	−	5.15834i	−1.56534	−	0.235937i
$479$	19.5967	−	13.3608i	0.895395	−	0.610470i	−0.0257593	−	0.999668i	$-0.508200\pi$
$479$	19.5967	−	13.3608i	0.895395	−	0.610470i	0.921154	+	0.389198i	$0.127248\pi$
$480$		0			0
$481$	14.6607	+	9.99553i	0.668473	+	0.455757i
$482$	−0.713431	−	3.12575i	−0.0324959	−	0.142374i
$483$		0			0
$484$	3.41651	−	14.9687i	0.155296	−	0.680395i
$485$	6.76180	−	6.27404i	0.307038	−	0.284889i
$486$		0			0
$487$	−22.6372	−	6.98264i	−1.02579	−	0.316414i	−0.264195	−	0.964469i	$-0.585106\pi$
$487$	−22.6372	−	6.98264i	−1.02579	−	0.316414i	−0.761593	+	0.648056i	$0.775582\pi$
$488$	−0.000760592	−	0.0101494i	−3.44304e−5	−	0.000459441i
$489$		0			0
$490$	19.5038	−	25.6133i	0.881091	−	1.15709i
$491$	−2.93971			−0.132667			−0.0663337	−	0.997797i	$-0.521130\pi$
$491$	−2.93971			−0.132667			−0.0663337	+	0.997797i	$0.521130\pi$
$492$		0			0
$493$	32.8997	+	10.1482i	1.48173	+	0.457052i
$494$	−4.16914	+	0.628396i	−0.187578	+	0.0282729i
$495$		0			0
$496$	0.695977	−	3.04928i	0.0312503	−	0.136916i
$497$	12.9462	+	0.824520i	0.580718	+	0.0369848i
$498$		0			0
$499$	−1.68208	−	1.14682i	−0.0753004	−	0.0513389i	0.525085	−	0.851050i	$-0.324034\pi$
$499$	−1.68208	−	1.14682i	−0.0753004	−	0.0513389i	−0.600385	+	0.799711i	$0.704986\pi$
$500$	−16.7848	−	15.5740i	−0.750639	−	0.696492i
$501$		0			0
$502$	−33.4688	−	5.04461i	−1.49379	−	0.225152i
$503$	−7.22087	−	3.47739i	−0.321963	−	0.155049i	0.265920	−	0.963995i	$-0.414324\pi$
$503$	−7.22087	−	3.47739i	−0.321963	−	0.155049i	−0.587883	+	0.808946i	$0.700039\pi$
$504$		0			0
$505$	7.36857	−	3.54851i	0.327897	−	0.157907i
$506$	25.1583	−	7.76031i	1.11842	−	0.344988i
$507$		0			0
$508$	−6.09296	+	10.5533i	−0.270331	+	0.468228i
$509$	8.45276	+	14.6406i	0.374662	+	0.648934i	0.990276	−	0.139114i	$-0.0444254\pi$
$509$	8.45276	+	14.6406i	0.374662	+	0.648934i	−0.615614	+	0.788048i	$0.711092\pi$
$510$		0			0
$511$	−19.7395	−	20.8020i	−0.873224	−	0.920228i
$512$	20.0532	+	25.1459i	0.886233	+	1.11130i
$513$		0			0
$514$	4.43334	−	59.1588i	0.195546	−	2.60938i
$515$	−2.33263	+	31.1268i	−0.102788	+	1.37161i
$516$		0			0
$517$	1.82824	+	2.29254i	0.0804057	+	0.100826i
$518$	−13.7137	−	14.4518i	−0.602544	−	0.634977i
$519$		0			0
$520$	−0.945840	−	1.63824i	−0.0414778	−	0.0718417i
$521$	−4.75459	+	8.23520i	−0.208303	+	0.360791i	−0.951180	−	0.308637i	$-0.900127\pi$
$521$	−4.75459	+	8.23520i	−0.208303	+	0.360791i	0.742877	+	0.669427i	$0.233461\pi$
$522$		0			0
$523$	20.1529	−	6.21634i	0.881223	−	0.271821i	0.179061	−	0.983838i	$-0.442694\pi$
$523$	20.1529	−	6.21634i	0.881223	−	0.271821i	0.702163	+	0.712017i	$0.252218\pi$
$524$	−8.38909	+	4.03997i	−0.366479	+	0.176487i
$525$		0			0
$526$	19.2076	+	9.24989i	0.837490	+	0.403314i
$527$	−3.27787	−	0.494060i	−0.142786	−	0.0215216i
$528$		0			0
$529$	−17.2926	−	16.0452i	−0.751851	−	0.697616i
$530$	−3.14457	−	2.14393i	−0.136591	−	0.0931264i
$531$		0			0
$532$	2.41211	+	0.153623i	0.104578	+	0.00666039i
$533$	11.4437	−	50.1380i	0.495681	−	2.17172i
$534$		0			0
$535$	−6.85270	+	1.03288i	−0.296268	+	0.0446552i
$536$	−2.02315	−	0.624059i	−0.0873867	−	0.0269552i
$537$		0			0
$538$	21.2915			0.917941
$539$	8.55959	+	10.2537i	0.368688	+	0.441656i
$540$		0			0
$541$	−1.64081	−	21.8950i	−0.0705438	−	0.941341i	−0.914410	−	0.404788i	$-0.867345\pi$
$541$	−1.64081	−	21.8950i	−0.0705438	−	0.941341i	0.843867	−	0.536553i	$-0.180274\pi$
$542$	−47.9872	−	14.8021i	−2.06122	−	0.635804i
$543$		0			0
$544$	23.9521	−	22.2243i	1.02694	−	0.952859i
$545$	1.67459	−	7.33685i	0.0717315	−	0.314276i
$546$		0			0
$547$	7.11554	+	31.1752i	0.304238	+	1.33296i	0.863661	+	0.504073i	$0.168166\pi$
$547$	7.11554	+	31.1752i	0.304238	+	1.33296i	−0.559423	+	0.828883i	$0.688977\pi$
$548$	−7.51044	−	5.12053i	−0.320830	−	0.218738i
$549$		0			0
$550$	−0.561558	+	0.382864i	−0.0239449	+	0.0163254i
$551$	3.68213	+	0.554991i	0.156864	+	0.0236434i
$552$		0			0
$553$	6.36100	+	1.37710i	0.270497	+	0.0585605i
$554$	−24.0063	+	11.5608i	−1.01993	+	0.491173i
$555$		0			0
$556$	5.97093	+	15.2137i	0.253224	+	0.645204i
$557$	13.0047	−	22.5248i	0.551028	−	0.954408i	−0.447173	−	0.894447i	$-0.647569\pi$
$557$	13.0047	−	22.5248i	0.551028	−	0.954408i	0.998201	−	0.0599605i	$-0.0190975\pi$
$558$		0			0
$559$	23.9873	−	30.0791i	1.01455	−	1.27221i
$560$	−7.02299	−	21.8945i	−0.296775	−	0.925210i
$561$		0			0
$562$	15.0309	−	38.2981i	0.634040	−	1.61551i
$563$	−0.645745	+	8.61687i	−0.0272149	+	0.363158i	0.966925	+	0.255060i	$0.0820951\pi$
$563$	−0.645745	+	8.61687i	−0.0272149	+	0.363158i	−0.994140	+	0.108098i	$0.965524\pi$
$564$		0			0
$565$	−2.35265	+	5.99446i	−0.0989769	+	0.252189i
$566$	29.0516	+	36.4296i	1.22113	+	1.53125i
$567$		0			0
$568$	−0.533616	+	0.669133i	−0.0223900	+	0.0280762i
$569$	−4.45835	−	7.72209i	−0.186904	−	0.323727i	0.757313	−	0.653053i	$-0.226512\pi$
$569$	−4.45835	−	7.72209i	−0.186904	−	0.323727i	−0.944216	+	0.329326i	$0.893179\pi$
$570$		0			0
$571$	9.98494	+	25.4412i	0.417857	+	1.06468i	0.972564	+	0.232636i	$0.0747350\pi$
$571$	9.98494	+	25.4412i	0.417857	+	1.06468i	−0.554707	+	0.832046i	$0.687170\pi$
$572$	18.1205	−	5.58944i	0.757658	−	0.233706i
$573$		0			0
$574$	−24.4694	+	52.3015i	−1.02133	+	2.18302i
$575$	1.08361	+	0.521838i	0.0451896	+	0.0217621i
$576$		0			0
$577$	−36.8913	+	25.1520i	−1.53580	+	1.04709i	−0.559986	+	0.828502i	$0.689194\pi$
$577$	−36.8913	+	25.1520i	−1.53580	+	1.04709i	−0.975817	+	0.218591i	$0.929854\pi$
$578$	0.903687	+	0.838499i	0.0375884	+	0.0348770i
$579$		0			0
$580$	8.98255	+	39.3551i	0.372980	+	1.63413i
$581$	−3.47096	+	11.7168i	−0.144000	+	0.486095i
$582$		0			0
$583$	1.15750	−	1.07400i	0.0479388	−	0.0444807i
$584$	1.87083	−	0.281982i	0.0774153	−	0.0116685i
$585$		0			0
$586$	1.79336	+	23.9308i	0.0740831	+	0.988570i
$587$	2.64680			0.109245			0.0546226	−	0.998507i	$-0.482604\pi$
$587$	2.64680			0.109245			0.0546226	+	0.998507i	$0.482604\pi$
$588$		0			0
$589$	−0.358525			−0.0147728
$590$	1.04972	+	14.0075i	0.0432161	+	0.576679i
$591$		0			0
$592$	−14.0703	+	2.12075i	−0.578285	+	0.0871624i
$593$	21.0962	−	19.5744i	0.866317	−	0.803825i	−0.115569	−	0.993299i	$-0.536869\pi$
$593$	21.0962	−	19.5744i	0.866317	−	0.803825i	0.981886	+	0.189475i	$0.0606786\pi$
$594$		0			0
$595$	−22.5838	+	9.15663i	−0.925845	+	0.375385i
$596$	3.12138	+	13.6757i	0.127857	+	0.560177i
$597$		0			0
$598$	−48.1797	−	44.7042i	−1.97021	−	1.82809i
$599$	11.9464	−	8.14491i	0.488116	−	0.332792i	−0.294126	−	0.955767i	$-0.595028\pi$
$599$	11.9464	−	8.14491i	0.488116	−	0.332792i	0.782242	+	0.622975i	$0.214076\pi$
$600$		0			0
$601$	23.2856	+	11.2137i	0.949839	+	0.457418i	0.843630	−	0.536926i	$-0.180414\pi$
$601$	23.2856	+	11.2137i	0.949839	+	0.457418i	0.106209	+	0.994344i	$0.466129\pi$
$602$	−33.4690	+	27.3093i	−1.36409	+	1.11304i
$603$		0			0
$604$	14.3793	−	4.43542i	0.585084	−	0.180475i
$605$	6.11686	+	15.5855i	0.248686	+	0.633641i
$606$		0			0
$607$	−13.0197	−	22.5508i	−0.528454	−	0.915309i	−0.999450	−	0.0331736i	$-0.989439\pi$
$607$	−13.0197	−	22.5508i	−0.528454	−	0.915309i	0.470996	−	0.882136i	$-0.343895\pi$
$608$	2.20337	−	2.76294i	0.0893585	−	0.112052i
$609$		0			0
$610$	0.167199	+	0.209661i	0.00676968	+	0.00848891i
$611$	2.67431	−	6.81404i	0.108191	−	0.275667i
$612$		0			0
$613$	−1.59326	+	21.2605i	−0.0643510	+	0.858704i	0.867865	+	0.496801i	$0.165492\pi$
$613$	−1.59326	+	21.2605i	−0.0643510	+	0.858704i	−0.932216	+	0.361903i	$0.882127\pi$
$614$	−10.8820	+	27.7269i	−0.439162	+	1.11897i
$615$		0			0
$616$	−0.877954	+	0.0756886i	−0.0353738	+	0.00304958i
$617$	−29.9571	+	37.5650i	−1.20603	+	1.51231i	−0.404294	+	0.914629i	$0.632483\pi$
$617$	−29.9571	+	37.5650i	−1.20603	+	1.51231i	−0.801733	+	0.597682i	$0.796089\pi$
$618$		0			0
$619$	−18.6273	+	32.2635i	−0.748696	+	1.29678i	0.199751	+	0.979847i	$0.435987\pi$
$619$	−18.6273	+	32.2635i	−0.748696	+	1.29678i	−0.948448	+	0.316934i	$0.897347\pi$
$620$	−1.41994	−	3.61794i	−0.0570261	−	0.145300i
$621$		0			0
$622$	−50.3281	+	24.2367i	−2.01797	+	0.971804i
$623$	−10.4620	+	2.51147i	−0.419153	+	0.100620i
$624$		0			0
$625$	25.5613	+	3.85274i	1.02245	+	0.154110i
$626$	−41.9540	+	28.6037i	−1.67682	+	1.14324i
$627$		0			0
$628$	42.1160	+	28.7142i	1.68061	+	1.14582i
$629$	3.35581	+	14.7028i	0.133805	+	0.586238i
$630$		0			0
$631$	4.77509	−	20.9210i	0.190093	−	0.832854i	−0.786471	−	0.617627i	$-0.788094\pi$
$631$	4.77509	−	20.9210i	0.190093	−	0.832854i	0.976564	−	0.215226i	$-0.0690489\pi$
$632$	−0.314763	+	0.292057i	−0.0125206	+	0.0116174i
$633$		0			0
$634$	42.3262	+	13.0559i	1.68099	+	0.518516i
$635$	−0.993053	−	13.2514i	−0.0394081	−	0.525865i
$636$		0			0
$637$	11.4837	−	31.3038i	0.455001	−	1.24030i
$638$	−32.8026			−1.29867
$639$		0			0
$640$	3.03306	+	0.935574i	0.119892	+	0.0369818i
$641$	29.3549	−	4.42454i	1.15945	−	0.174759i	0.458983	−	0.888445i	$-0.348214\pi$
$641$	29.3549	−	4.42454i	1.15945	−	0.174759i	0.700465	+	0.713686i	$0.252976\pi$
$642$		0			0
$643$	−4.65518	+	20.3957i	−0.183582	+	0.804326i	0.796324	+	0.604870i	$0.206775\pi$
$643$	−4.65518	+	20.3957i	−0.183582	+	0.804326i	−0.979907	+	0.199457i	$0.936082\pi$
$644$	21.5717	+	30.8910i	0.850045	+	1.21727i
$645$		0			0
$646$	−2.96078	−	2.01862i	−0.116490	−	0.0794217i
$647$	−13.6118	−	12.6299i	−0.535135	−	0.496533i	0.365677	−	0.930742i	$-0.380838\pi$
$647$	−13.6118	−	12.6299i	−0.535135	−	0.496533i	−0.900812	+	0.434209i	$0.857028\pi$
$648$		0			0
$649$	−5.76275	−	0.868594i	−0.226208	−	0.0340953i
$650$	1.52866	+	0.736162i	0.0599588	+	0.0288747i
$651$		0			0
$652$	−42.3791	+	20.4087i	−1.65969	+	0.799266i
$653$	16.6348	−	5.13116i	0.650971	−	0.200798i	0.0483560	−	0.998830i	$-0.484602\pi$
$653$	16.6348	−	5.13116i	0.650971	−	0.200798i	0.602615	+	0.798032i	$0.294126\pi$
$654$		0			0
$655$	5.07685	−	8.79336i	0.198369	−	0.343585i
$656$	20.6203	+	35.7154i	0.805087	+	1.39445i
$657$		0			0
$658$	−4.55356	+	6.84221i	−0.177516	+	0.266737i
$659$	−12.6442	−	15.8554i	−0.492549	−	0.617637i	0.471981	−	0.881609i	$-0.343539\pi$
$659$	−12.6442	−	15.8554i	−0.492549	−	0.617637i	−0.964531	+	0.263971i	$0.914968\pi$
$660$		0			0
$661$	−0.580174	+	7.74188i	−0.0225661	+	0.301124i	0.974489	+	0.224435i	$0.0720538\pi$
$661$	−0.580174	+	7.74188i	−0.0225661	+	0.301124i	−0.997055	+	0.0766887i	$0.975565\pi$
$662$	1.92011	−	25.6220i	0.0746271	−	0.995829i
$663$		0			0
$664$	−0.502668	−	0.630326i	−0.0195073	−	0.0244614i
$665$	−2.26768	+	1.34333i	−0.0879369	+	0.0520919i
$666$		0			0
$667$	29.0236	+	50.2704i	1.12380	+	1.94648i
$668$	−10.9713	+	19.0029i	−0.424494	+	0.735245i
$669$		0			0
$670$	53.3059	−	16.4427i	2.05939	−	0.635236i
$671$	−0.100241	+	0.0482734i	−0.00386975	+	0.00186357i
$672$		0			0
$673$	−36.1235	−	17.3962i	−1.39246	−	0.670572i	−0.420841	−	0.907134i	$-0.638265\pi$
$673$	−36.1235	−	17.3962i	−1.39246	−	0.670572i	−0.971616	+	0.236562i	$0.923979\pi$
$674$	−19.8726	−	2.99532i	−0.765465	−	0.115375i
$675$		0			0
$676$	−14.8197	−	13.7506i	−0.569987	−	0.528870i
$677$	−25.4599	−	17.3583i	−0.978505	−	0.667133i	−0.0353108	−	0.999376i	$-0.511242\pi$
$677$	−25.4599	−	17.3583i	−0.978505	−	0.667133i	−0.943194	+	0.332243i	$0.892194\pi$
$678$		0			0
$679$	−7.20758	+	7.94452i	−0.276602	+	0.304883i
$680$	0.357762	−	1.56746i	0.0137195	−	0.0601093i
$681$		0			0
$682$	3.12300	−	0.470717i	0.119586	−	0.0180247i
$683$	−27.2475	−	8.40475i	−1.04260	−	0.321599i	−0.274268	−	0.961653i	$-0.588436\pi$
$683$	−27.2475	−	8.40475i	−1.04260	−	0.321599i	−0.768329	+	0.640055i	$0.778912\pi$
$684$		0			0
$685$	9.91239			0.378733
$686$	−20.0388	+	31.6238i	−0.765087	+	1.20740i
$687$		0			0
$688$	2.30556	+	30.7656i	0.0878988	+	1.17293i
$689$	−3.76670	−	1.16187i	−0.143500	−	0.0442639i
$690$		0			0
$691$	10.2920	−	9.54955i	0.391525	−	0.363282i	−0.459708	−	0.888070i	$-0.652046\pi$
$691$	10.2920	−	9.54955i	0.391525	−	0.363282i	0.851233	+	0.524788i	$0.175855\pi$
$692$	2.17334	−	9.52204i	0.0826181	−	0.361973i
$693$		0			0
$694$	−7.50449	−	32.8793i	−0.284867	−	1.24808i
$695$	−14.7254	−	10.0396i	−0.558567	−	0.380824i
$696$		0			0
$697$	36.1141	−	24.6222i	1.36792	−	0.932630i
$698$	1.66386	+	0.250787i	0.0629781	+	0.00949242i
$699$		0			0
$700$	−0.767184	−	0.597879i	−0.0289968	−	0.0225977i
$701$	−26.9527	+	12.9797i	−1.01799	+	0.490238i	−0.867005	−	0.498299i	$-0.833958\pi$
$701$	−26.9527	+	12.9797i	−1.01799	+	0.490238i	−0.150983	+	0.988536i	$0.548244\pi$
$702$		0			0
$703$	0.595901	+	1.51833i	0.0224748	+	0.0572649i
$704$	−8.27667	+	14.3356i	−0.311939	+	0.540294i
$705$		0			0
$706$	−34.9889	+	43.8747i	−1.31683	+	1.65125i
$707$	−8.18282	+	4.84732i	−0.307747	+	0.182302i
$708$		0			0
$709$	3.68198	−	9.38153i	0.138280	−	0.352331i	−0.844912	−	0.534905i	$-0.820348\pi$
$709$	3.68198	−	9.38153i	0.138280	−	0.352331i	0.983192	+	0.182574i	$0.0584428\pi$
$710$	1.68517	−	22.4870i	0.0632431	−	0.843921i
$711$		0			0
$712$	0.259333	−	0.660770i	0.00971892	−	0.0247634i
$713$	−3.48460	−	4.36955i	−0.130499	−	0.163641i
$714$		0			0
$715$	−12.8930	+	16.1674i	−0.482172	+	0.604625i
$716$	5.19360	+	8.99557i	0.194094	+	0.336180i
$717$		0			0
$718$	−18.8476	−	48.0229i	−0.703386	−	1.79220i
$719$	25.6265	−	7.90474i	0.955709	−	0.294797i	0.222601	−	0.974910i	$-0.428545\pi$
$719$	25.6265	−	7.90474i	0.955709	−	0.294797i	0.733108	+	0.680112i	$0.238069\pi$
$720$		0			0
$721$	−0.406458	−	36.2967i	−0.0151373	−	1.35176i
$722$	34.2552	+	16.4964i	1.27485	+	0.613934i
$723$		0			0
$724$	−38.2092	+	26.0506i	−1.42003	+	0.968163i
$725$	−1.09847	−	1.01923i	−0.0407961	−	0.0378532i
$726$		0			0
$727$	4.11406	+	18.0249i	0.152582	+	0.668506i	0.992129	+	0.125219i	$0.0399633\pi$
$727$	4.11406	+	18.0249i	0.152582	+	0.668506i	−0.839547	+	0.543287i	$0.817180\pi$
$728$	1.25949	+	1.80360i	0.0466797	+	0.0668459i
$729$		0			0
$730$	−36.5421	+	33.9061i	−1.35248	+	1.25492i
$731$	32.3332	−	4.87345i	1.19589	−	0.180251i
$732$		0			0
$733$	−3.89777	−	52.0121i	−0.143967	−	1.92111i	−0.339840	−	0.940483i	$-0.610373\pi$
$733$	−3.89777	−	52.0121i	−0.143967	−	1.92111i	0.195873	−	0.980629i	$-0.437246\pi$
$734$	44.3511			1.63703
$735$		0			0
$736$	55.0888			2.03060
$737$	1.72957	+	23.0795i	0.0637095	+	0.850144i
$738$		0			0
$739$	−28.6128	+	4.31269i	−1.05254	+	0.158645i	−0.652450	−	0.757832i	$-0.726259\pi$
$739$	−28.6128	+	4.31269i	−1.05254	+	0.158645i	−0.400089	+	0.916476i	$0.631021\pi$
$740$	−12.9617	+	12.0267i	−0.476482	+	0.442111i
$741$		0			0
$742$	3.85746	+	2.16988i	0.141612	+	0.0796587i
$743$	−2.89866	−	12.6998i	−0.106341	−	0.465912i	−0.999858	−	0.0168809i	$-0.994626\pi$
$743$	−2.89866	−	12.6998i	−0.106341	−	0.465912i	0.893516	−	0.449031i	$-0.148231\pi$
$744$		0			0
$745$	−11.2132	−	10.4043i	−0.410819	−	0.381185i
$746$	49.7186	−	33.8975i	1.82033	−	1.24108i
$747$		0			0
$748$	14.5209	+	6.99289i	0.530936	+	0.255685i
$749$	7.83640	−	1.88117i	0.286336	−	0.0687364i
$750$		0			0
$751$	−3.40673	+	1.05084i	−0.124313	+	0.0383456i	−0.356288	−	0.934376i	$-0.615958\pi$
$751$	−3.40673	+	1.05084i	−0.124313	+	0.0383456i	0.231974	+	0.972722i	$0.425482\pi$
$752$	2.14458	+	5.46431i	0.0782048	+	0.199263i
$753$		0			0
$754$	40.9439	+	70.9169i	1.49109	+	2.58264i
$755$	−10.2311	+	12.8294i	−0.372347	+	0.466908i
$756$		0			0
$757$	2.92962	+	3.67362i	0.106479	+	0.133520i	0.832215	−	0.554453i	$-0.187072\pi$
$757$	2.92962	+	3.67362i	0.106479	+	0.133520i	−0.725737	+	0.687973i	$0.758501\pi$
$758$	5.20965	−	13.2740i	0.189223	−	0.482132i
$759$		0			0
$760$	0.0129948	−	0.173403i	0.000471369	−	0.00628999i
$761$	−2.22850	+	5.67813i	−0.0807831	+	0.205832i	−0.965559	−	0.260185i	$-0.916216\pi$
$761$	−2.22850	+	5.67813i	−0.0807831	+	0.205832i	0.884776	+	0.466017i	$0.154312\pi$
$762$		0			0
$763$	−1.20736	+	8.66778i	−0.0437092	+	0.313795i
$764$	−16.9953	+	21.3114i	−0.614868	+	0.771020i
$765$		0			0
$766$	−13.6026	+	23.5603i	−0.491481	+	0.851270i
$767$	5.31517	+	13.5428i	0.191920	+	0.489003i
$768$		0			0
$769$	−7.74239	+	3.72854i	−0.279198	+	0.134455i	−0.568243	−	0.822861i	$-0.692377\pi$
$769$	−7.74239	+	3.72854i	−0.279198	+	0.134455i	0.289045	+	0.957316i	$0.406662\pi$
$770$	17.9894	−	14.6786i	0.648294	−	0.528981i
$771$		0			0
$772$	22.1836	+	3.34364i	0.798404	+	0.120340i
$773$	−37.6012	+	25.6361i	−1.35242	+	0.922066i	−0.999906	−	0.0137390i	$-0.995627\pi$
$773$	−37.6012	+	25.6361i	−1.35242	+	0.922066i	−0.352517	+	0.935805i	$0.614674\pi$
$774$		0			0
$775$	0.119207	+	0.0812737i	0.00428203	+	0.00291944i
$776$	−0.157478	−	0.689955i	−0.00565312	−	0.0247679i
$777$		0			0
$778$	5.37580	−	23.5529i	0.192732	−	0.844413i
$779$	3.46541	−	3.21543i	0.124161	−	0.115205i
$780$		0			0
$781$	8.94009	+	2.75765i	0.319901	+	0.0986765i
$782$	−4.17446	−	55.7043i	−0.149278	−	1.99198i
$783$		0			0
$784$	10.3238	+	24.6656i	0.368706	+	0.880913i
$785$	−55.5853			−1.98392
$786$		0			0
$787$	−43.9229	−	13.5484i	−1.56568	−	0.482949i	−0.613812	−	0.789452i	$-0.710365\pi$
$787$	−43.9229	−	13.5484i	−1.56568	−	0.482949i	−0.951869	+	0.306504i	$0.900841\pi$
$788$	−11.7130	+	1.76545i	−0.417258	+	0.0628916i
$789$		0			0
$790$	2.51748	−	11.0298i	0.0895681	−	0.392423i
$791$	2.12705	−	7.18021i	0.0756291	−	0.255299i
$792$		0			0
$793$	0.229483	+	0.156459i	0.00814919	+	0.00555603i
$794$	7.65177	+	7.09980i	0.271551	+	0.251963i
$795$		0			0
$796$	−28.1026	−	4.23578i	−0.996069	−	0.150133i
$797$	21.1004	+	10.1614i	0.747415	+	0.359936i	0.768507	−	0.639842i	$-0.221000\pi$
$797$	21.1004	+	10.1614i	0.747415	+	0.359936i	−0.0210922	+	0.999778i	$0.506714\pi$
$798$		0			0
$799$	5.60531	−	2.69938i	0.198302	−	0.0954971i
$800$	−1.35893	+	0.419175i	−0.0480455	+	0.0148201i
$801$		0			0
$802$	17.3699	−	30.0856i	0.613353	−	1.06236i
$803$	−10.3409	−	17.9110i	−0.364924	−	0.632066i
$804$		0			0
$805$	−38.4121	−	14.5814i	−1.35385	−	0.513927i
$806$	−4.91576	−	6.16417i	−0.173150	−	0.217124i
$807$		0			0
$808$	0.0468910	−	0.625716i	0.00164962	−	0.0220126i
$809$	0.372987	−	4.97717i	0.0131135	−	0.174988i	−0.986801	−	0.161936i	$-0.948226\pi$
$809$	0.372987	−	4.97717i	0.0131135	−	0.174988i	0.999915	−	0.0130520i	$-0.00415471\pi$
$810$		0			0
$811$	−0.433526	−	0.543624i	−0.0152231	−	0.0190892i	0.774162	−	0.632988i	$-0.218172\pi$
$811$	−0.433526	−	0.543624i	−0.0152231	−	0.0190892i	−0.789385	+	0.613899i	$0.789600\pi$
$812$	−14.3382	−	44.6998i	−0.503171	−	1.56866i
$813$		0			0
$814$	−7.18418	−	12.4434i	−0.251805	−	0.436140i
$815$	25.6466	−	44.4213i	0.898363	−	1.55601i
$816$		0			0
$817$	3.37940	−	1.04241i	0.118230	−	0.0364692i
$818$	−39.5463	+	19.0445i	−1.38270	+	0.665876i
$819$		0			0
$820$	46.1723	+	22.2354i	1.61241	+	0.776494i
$821$	11.8939	+	1.79272i	0.415101	+	0.0625664i	0.353273	−	0.935520i	$-0.385069\pi$
$821$	11.8939	+	1.79272i	0.415101	+	0.0625664i	0.0618282	+	0.998087i	$0.480307\pi$
$822$		0			0
$823$	−31.0979	−	28.8547i	−1.08401	−	1.00581i	−0.999956	−	0.00934933i	$-0.997024\pi$
$823$	−31.0979	−	28.8547i	−1.08401	−	1.00581i	−0.0840500	−	0.996462i	$-0.526786\pi$
$824$	1.97869	+	1.34904i	0.0689308	+	0.0469962i
$825$		0			0
$826$	−2.61532	−	16.1243i	−0.0909988	−	0.561036i
$827$	−1.01662	+	4.45411i	−0.0353514	+	0.154885i	−0.989523	−	0.144375i	$-0.953883\pi$
$827$	−1.01662	+	4.45411i	−0.0353514	+	0.154885i	0.954172	+	0.299260i	$0.0967398\pi$
$828$		0			0
$829$	1.30063	−	0.196038i	0.0451727	−	0.00680870i	−0.126417	−	0.991977i	$-0.540348\pi$
$829$	1.30063	−	0.196038i	0.0451727	−	0.00680870i	0.171590	+	0.985168i	$0.445110\pi$
$830$	20.2985	+	6.26125i	0.704570	+	0.217331i
$831$		0			0
$832$	41.3235			1.43263
$833$	25.2511	−	12.8647i	0.874899	−	0.445734i
$834$		0			0
$835$	−1.78815	−	23.8612i	−0.0618815	−	0.825751i
$836$	1.66570	+	0.513799i	0.0576093	+	0.0177701i
$837$		0			0
$838$	−15.4603	+	14.3451i	−0.534067	+	0.495542i
$839$	−1.84273	+	8.07355i	−0.0636183	+	0.278730i	−0.996725	−	0.0808707i	$-0.974230\pi$
$839$	−1.84273	+	8.07355i	−0.0636183	+	0.278730i	0.933106	+	0.359601i	$0.117087\pi$
$840$		0			0
$841$	−9.64011	−	42.2361i	−0.332418	−	1.45642i
$842$	−18.5610	−	12.6546i	−0.639653	−	0.436108i
$843$		0			0
$844$	27.8116	−	18.9616i	0.957314	−	0.652686i
$845$	21.7994	+	3.28573i	0.749921	+	0.113032i
$846$		0			0
$847$	−8.64376	−	17.4465i	−0.297003	−	0.599468i
$848$	2.84798	−	1.37152i	0.0978002	−	0.0470981i
$849$		0			0
$850$	0.526835	+	1.34235i	0.0180703	+	0.0460423i
$851$	−12.7131	+	22.0197i	−0.435798	+	0.754825i
$852$		0			0
$853$	4.03596	−	5.06093i	0.138189	−	0.173283i	−0.707922	−	0.706291i	$-0.750367\pi$
$853$	4.03596	−	5.06093i	0.138189	−	0.173283i	0.846110	+	0.533008i	$0.178938\pi$
$854$	−0.214659	−	0.226213i	−0.00734548	−	0.00774086i
$855$		0			0
$856$	−0.194249	+	0.494938i	−0.00663929	+	0.0169166i
$857$	2.66613	−	35.5770i	0.0910732	−	1.21529i	−0.745150	−	0.666897i	$-0.767622\pi$
$857$	2.66613	−	35.5770i	0.0910732	−	1.21529i	0.836223	−	0.548390i	$-0.184759\pi$
$858$		0			0
$859$	−10.2719	+	26.1724i	−0.350473	+	0.892991i	0.641567	+	0.767067i	$0.278285\pi$
$859$	−10.2719	+	26.1724i	−0.350473	+	0.892991i	−0.992040	+	0.125924i	$0.959811\pi$
$860$	23.9033	+	29.9738i	0.815096	+	1.02210i
$861$		0			0
$862$	28.7574	−	36.0606i	0.979480	−	1.22823i
$863$	23.2133	+	40.2067i	0.790191	+	1.36865i	0.925849	+	0.377895i	$0.123352\pi$
$863$	23.2133	+	40.2067i	0.790191	+	1.36865i	−0.135658	+	0.990756i	$0.543315\pi$
$864$		0			0
$865$	3.89112	+	9.91441i	0.132302	+	0.337100i
$866$	29.4884	−	9.09596i	1.00206	−	0.309093i
$867$		0			0
$868$	2.00652	+	4.04994i	0.0681058	+	0.137464i
$869$	4.22899	+	2.03657i	0.143459	+	0.0690861i
$870$		0			0
$871$	47.7374	−	32.5468i	1.61752	−	1.10281i
$872$	−0.423246	−	0.392715i	−0.0143329	−	0.0132990i
$873$		0			0
$874$	−1.34439	−	5.89015i	−0.0454746	−	0.199237i
$875$	−28.9777	−	1.84553i	−0.979627	−	0.0623904i
$876$		0			0
$877$	23.2616	−	21.5837i	0.785490	−	0.728828i	−0.181570	−	0.983378i	$-0.558118\pi$
$877$	23.2616	−	21.5837i	0.785490	−	0.728828i	0.967060	+	0.254550i	$0.0819273\pi$
$878$	17.1211	−	2.58059i	0.577808	−	0.0870906i
$879$		0			0
$880$	−1.23923	−	16.5364i	−0.0417744	−	0.557441i
$881$	39.5493			1.33245			0.666225	−	0.745750i	$-0.267909\pi$
$881$	39.5493			1.33245			0.666225	+	0.745750i	$0.267909\pi$
$882$		0			0
$883$	−8.59085			−0.289105			−0.144553	−	0.989497i	$-0.546174\pi$
$883$	−8.59085			−0.289105			−0.144553	+	0.989497i	$0.546174\pi$
$884$	−3.00670	−	40.1216i	−0.101126	−	1.34944i
$885$		0			0
$886$	−15.5043	+	2.33690i	−0.520878	+	0.0785097i
$887$	19.6661	−	18.2475i	0.660323	−	0.612691i	−0.277117	−	0.960836i	$-0.589379\pi$
$887$	19.6661	−	18.2475i	0.660323	−	0.612691i	0.937440	+	0.348146i	$0.113189\pi$
$888$		0			0
$889$	2.47415	+	15.2539i	0.0829804	+	0.511600i
$890$	4.16177	+	18.2339i	0.139503	+	0.611201i
$891$		0			0
$892$	11.4216	+	10.5977i	0.382422	+	0.354836i
$893$	0.555961	−	0.379048i	0.0186045	−	0.0126844i
$894$		0			0
$895$	−10.2053	−	4.91462i	−0.341126	−	0.164278i
$896$	−3.60756	−	0.781008i	−0.120520	−	0.0260917i
$897$		0			0
$898$	−3.16502	+	0.976280i	−0.105618	+	0.0325789i
$899$	2.54397	+	6.48194i	0.0848463	+	0.216185i
$900$		0			0
$901$	−1.67511	−	2.90138i	−0.0558060	−	0.0966589i
$902$	−25.9645	+	32.5585i	−0.864525	+	1.08408i
$903$		0			0
$904$	0.308042	+	0.386272i	0.0102453	+	0.0128472i
$905$	18.4238	−	46.9431i	0.612428	−	1.56044i
$906$		0			0
$907$	2.15166	−	28.7119i	0.0714447	−	0.953363i	−0.840172	−	0.542321i	$-0.817546\pi$
$907$	2.15166	−	28.7119i	0.0714447	−	0.953363i	0.911616	−	0.411042i	$-0.134835\pi$
$908$	7.33916	−	18.6999i	0.243559	−	0.620577i
$909$		0			0
$910$	−54.1884	−	20.5702i	−1.79633	−	0.681894i
$911$	31.1144	−	39.0162i	1.03087	−	1.29266i	0.0755295	−	0.997144i	$-0.475935\pi$
$911$	31.1144	−	39.0162i	1.03087	−	1.29266i	0.955336	−	0.295521i	$-0.0954933\pi$
$912$		0			0
$913$	−4.40657	+	7.63240i	−0.145836	+	0.252596i
$914$	−13.4196	−	34.1926i	−0.443881	−	1.13099i
$915$		0			0
$916$	26.1889	−	12.6119i	0.865306	−	0.416709i
$917$	−5.00375	+	10.6951i	−0.165238	+	0.353184i
$918$		0			0
$919$	−30.8314	−	4.64709i	−1.01704	−	0.153293i	−0.380694	−	0.924701i	$-0.624315\pi$
$919$	−30.8314	−	4.64709i	−1.01704	−	0.153293i	−0.636341	+	0.771408i	$0.719553\pi$
$920$	2.23966	−	1.52698i	0.0738395	−	0.0503430i
$921$		0			0
$922$	−52.1301	−	35.5417i	−1.71681	−	1.17050i
$923$	−5.19709	−	22.7699i	−0.171064	−	0.749481i
$924$		0			0
$925$	0.146057	−	0.639918i	0.00480233	−	0.0210404i
$926$	−47.7790	+	44.3324i	−1.57011	+	1.45685i
$927$		0			0
$928$	−65.5869	−	20.2309i	−2.15300	−	0.664111i
$929$	−0.307388	−	4.10181i	−0.0100851	−	0.134576i	0.989888	−	0.141848i	$-0.0453043\pi$
$929$	−0.307388	−	4.10181i	−0.0100851	−	0.134576i	−0.999974	+	0.00727180i	$0.997685\pi$
$930$		0			0
$931$	2.49317	−	1.78289i	0.0817103	−	0.0584318i
$932$	13.5282			0.443130
$933$		0			0
$934$	40.1221	+	12.3760i	1.31283	+	0.404956i
$935$	−17.3790	+	2.61946i	−0.568353	+	0.0856654i
$936$		0			0
$937$	−11.7963	+	51.6829i	−0.385367	+	1.68841i	0.294970	+	0.955506i	$0.404690\pi$
$937$	−11.7963	+	51.6829i	−0.385367	+	1.68841i	−0.680338	+	0.732899i	$0.738167\pi$
$938$	−60.1181	+	24.3750i	−1.96293	+	0.795871i
$939$		0			0
$940$	6.02694	+	4.10910i	0.196577	+	0.134024i
$941$	−42.0056	−	38.9755i	−1.36935	−	1.27057i	−0.927675	−	0.373389i	$-0.878196\pi$
$941$	−42.0056	−	38.9755i	−1.36935	−	1.27057i	−0.441670	−	0.897178i	$-0.645614\pi$
$942$		0			0
$943$	72.8697	+	10.9833i	2.37296	+	0.357667i
$944$	−10.5114	−	5.06200i	−0.342115	−	0.164754i
$945$		0			0
$946$	−28.0684	+	13.5170i	−0.912582	+	0.439477i
$947$	−34.2167	+	10.5544i	−1.11189	+	0.342973i	−0.795681	−	0.605716i	$-0.792887\pi$
$947$	−34.2167	+	10.5544i	−1.11189	+	0.342973i	−0.316211	+	0.948689i	$0.602411\pi$
$948$		0			0
$949$	−25.8149	+	44.7128i	−0.837988	+	1.45144i
$950$	0.0779821	+	0.135069i	0.00253007	+	0.00438222i
$951$		0			0
$952$	−0.257942	+	1.85180i	−0.00835994	+	0.0600172i
$953$	29.1457	+	36.5476i	0.944123	+	1.18389i	0.982806	+	0.184641i	$0.0591124\pi$
$953$	29.1457	+	36.5476i	0.944123	+	1.18389i	−0.0386828	+	0.999252i	$0.512316\pi$
$954$		0			0
$955$	2.22133	−	29.6416i	0.0718806	−	0.959180i
$956$	2.66941	−	35.6208i	0.0863349	−	1.15206i
$957$		0			0
$958$	29.8933	+	37.4850i	0.965808	+	1.21109i
$959$	−11.4845	+	0.990085i	−0.370855	+	0.0319715i
$960$		0			0
$961$	15.1648	+	26.2662i	0.489187	+	0.847296i
$962$	−17.9345	+	31.0634i	−0.578230	+	1.00152i
$963$		0			0
$964$	3.16202	−	0.975353i	0.101842	−	0.0314140i
$965$	−22.0413	+	10.6146i	−0.709536	+	0.341695i
$966$		0			0
$967$	−39.2046	−	18.8800i	−1.26074	−	0.607139i	−0.320367	−	0.947294i	$-0.603806\pi$
$967$	−39.2046	−	18.8800i	−1.26074	−	0.607139i	−0.940369	+	0.340155i	$0.889520\pi$
$968$	1.27020	+	0.191452i	0.0408258	+	0.00615350i
$969$		0			0
$970$	13.6688	+	12.6828i	0.438879	+	0.407220i
$971$	14.1610	+	9.65483i	0.454449	+	0.309838i	0.768824	−	0.639461i	$-0.220842\pi$
$971$	14.1610	+	9.65483i	0.454449	+	0.309838i	−0.314375	+	0.949299i	$0.601795\pi$
$972$		0			0
$973$	18.0637	+	10.1611i	0.579097	+	0.325751i
$974$	10.6561	−	46.6873i	0.341442	−	1.49596i
$975$		0			0
$976$	−0.220241	+	0.0331960i	−0.00704974	+	0.00106258i
$977$	−31.7054	−	9.77982i	−1.01435	−	0.312884i	−0.257360	−	0.966316i	$-0.582853\pi$
$977$	−31.7054	−	9.77982i	−1.01435	−	0.312884i	−0.756986	+	0.653431i	$0.773329\pi$
$978$		0			0
$979$	−7.75958			−0.247997
$980$	27.8657	+	18.0979i	0.890136	+	0.578118i
$981$		0			0
$982$	−0.444087	−	5.92593i	−0.0141714	−	0.189104i
$983$	57.6363	+	17.7784i	1.83831	+	0.567044i	0.999753	+	0.0222351i	$0.00707824\pi$
$983$	57.6363	+	17.7784i	1.83831	+	0.567044i	0.838560	+	0.544809i	$0.183398\pi$
$984$		0			0
$985$	9.46890	−	8.78586i	0.301704	−	0.279941i
$986$	−15.4870	+	67.8528i	−0.493205	+	2.16087i
$987$		0			0
$988$	−0.968310	−	4.24244i	−0.0308060	−	0.134970i
$989$	45.5498	+	31.0554i	1.44840	+	0.987503i
$990$		0			0
$991$	37.0562	−	25.2645i	1.17713	−	0.802553i	0.193208	−	0.981158i	$-0.438111\pi$
$991$	37.0562	−	25.2645i	1.17713	−	0.802553i	0.983921	+	0.178605i	$0.0571583\pi$
$992$	6.53458	+	0.984930i	0.207473	+	0.0312715i
$993$		0			0
$994$	0.293638	+	26.2218i	0.00931362	+	0.831706i
$995$	27.9224	−	13.4467i	0.885199	−	0.426289i
$996$		0			0
$997$	−0.421446	−	1.07383i	−0.0133473	−	0.0340084i	0.924045	−	0.382284i	$-0.124862\pi$
$997$	−0.421446	−	1.07383i	−0.0133473	−	0.0340084i	−0.937392	+	0.348276i	$0.886767\pi$
$998$	2.05769	−	3.56402i	0.0651350	−	0.112817i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.424.4		48
3.2	odd	2		49.2.g.a.32.1	yes	48
12.11	even	2		784.2.bg.c.81.1		48
21.2	odd	6		343.2.g.i.30.1		48
21.5	even	6		343.2.g.h.30.1		48
21.11	odd	6		343.2.e.d.197.7		48
21.17	even	6		343.2.e.c.197.7		48
21.20	even	2		343.2.g.g.116.1		48
49.23	even	21	inner	441.2.bb.d.415.4		48
147.11	odd	42		2401.2.a.h.1.5		24
147.23	odd	42		49.2.g.a.23.1	✓	48
147.26	even	42		343.2.g.g.275.1		48
147.38	even	42		2401.2.a.i.1.5		24
147.53	odd	42		343.2.e.d.148.7		48
147.71	odd	14		343.2.g.i.263.1		48
147.125	even	14		343.2.g.h.263.1		48
147.143	even	42		343.2.e.c.148.7		48
588.23	even	42		784.2.bg.c.513.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.1	✓	48	147.23	odd	42
49.2.g.a.32.1	yes	48	3.2	odd	2
343.2.e.c.148.7		48	147.143	even	42
343.2.e.c.197.7		48	21.17	even	6
343.2.e.d.148.7		48	147.53	odd	42
343.2.e.d.197.7		48	21.11	odd	6
343.2.g.g.116.1		48	21.20	even	2
343.2.g.g.275.1		48	147.26	even	42
343.2.g.h.30.1		48	21.5	even	6
343.2.g.h.263.1		48	147.125	even	14
343.2.g.i.30.1		48	21.2	odd	6
343.2.g.i.263.1		48	147.71	odd	14
441.2.bb.d.415.4		48	49.23	even	21	inner
441.2.bb.d.424.4		48	1.1	even	1	trivial
784.2.bg.c.81.1		48	12.11	even	2
784.2.bg.c.513.1		48	588.23	even	42
2401.2.a.h.1.5		24	147.11	odd	42
2401.2.a.i.1.5		24	147.38	even	42

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.151065 + 2.01582i) q^{2} +(-2.06305 + 0.310954i) q^{4} +(1.66779 - 1.54748i) q^{5} +(-1.77774 + 1.95950i) q^{7} +(-0.0388416 - 0.170176i) q^{8} +(3.37138 + 3.12819i) q^{10} +(-1.57656 + 1.07488i) q^{11} +(4.29166 + 2.06676i) q^{13} +(-4.21856 - 3.28759i) q^{14} +(-3.65014 + 1.12592i) q^{16} +(1.47907 + 3.76862i) q^{17} +(0.218933 + 0.379203i) q^{19} +(-2.95953 + 3.71113i) q^{20} +(-2.40493 - 3.01568i) q^{22} +(-2.49370 + 6.35384i) q^{23} +(0.0131678 - 0.175712i) q^{25} +(-3.51789 + 8.96343i) q^{26} +(3.05824 - 4.59534i) q^{28} +(5.30231 - 6.64889i) q^{29} +(-0.409400 + 0.709102i) q^{31} +(-2.94860 - 7.51291i) q^{32} +(-7.37342 + 3.55085i) q^{34} +(0.0674026 + 6.01904i) q^{35} +(3.68347 + 0.555193i) q^{37} +(-0.731331 + 0.498613i) q^{38} +(-0.328124 - 0.223711i) q^{40} +(-2.40243 - 10.5257i) q^{41} +(1.79724 - 7.87423i) q^{43} +(2.91827 - 2.70776i) q^{44} +(-13.1849 - 4.06701i) q^{46} +(-0.114840 - 1.53244i) q^{47} +(-0.679297 - 6.96696i) q^{49} +0.356192 q^{50} +(-9.49656 - 2.92930i) q^{52} +(-0.818284 + 0.123336i) q^{53} +(-0.966009 + 4.23236i) q^{55} +(0.402511 + 0.226418i) q^{56} +(14.2040 + 9.68409i) q^{58} +(2.23892 + 2.07741i) q^{59} +(0.0576570 + 0.00869039i) q^{61} +(-1.49127 - 0.718157i) q^{62} +(7.81612 - 3.76404i) q^{64} +(10.3558 - 3.19435i) q^{65} +(6.06468 - 10.5043i) q^{67} +(-4.22327 - 7.31491i) q^{68} +(-12.1231 + 1.04514i) q^{70} +(-3.05705 - 3.83342i) q^{71} +(-0.809992 + 10.8086i) q^{73} +(-0.562728 + 7.50908i) q^{74} +(-0.569583 - 0.714235i) q^{76} +(0.696479 - 5.00012i) q^{77} +(-1.22996 - 2.13036i) q^{79} +(-4.34532 + 7.52631i) q^{80} +(20.8550 - 6.43292i) q^{82} +(4.16137 - 2.00401i) q^{83} +(8.29864 + 3.99642i) q^{85} +(16.1445 + 2.43340i) q^{86} +(0.244155 + 0.226543i) q^{88} +(3.36000 + 2.29081i) q^{89} +(-11.6793 + 4.73537i) q^{91} +(3.16886 - 13.8837i) q^{92} +(3.07177 - 0.462994i) q^{94} +(0.951941 + 0.293635i) q^{95} +4.05436 q^{97} +(13.9415 - 2.42180i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29}+ \cdots + 161 q^{98}+O(q^{100}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more