LMFDB - Embedded newform 650.2.m.c.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(101,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2,4,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$1.40994 - 0.109843i$ of defining polynomial
Character	$\chi$	$=$	650.101
Dual form			650.2.m.c.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.300098 - 0.519785i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.519785 + 0.300098i) q^{6} +(-1.24653 - 0.719687i) q^{7} +1.00000i q^{8} +(1.31988 - 2.28610i) q^{9} +(-2.40029 + 1.38581i) q^{11} -0.600196 q^{12} +(2.76632 + 2.31246i) q^{13} +1.43937 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.25184 - 3.90029i) q^{17} +2.63977i q^{18} +(-3.75184 - 2.16612i) q^{19} +0.863906i q^{21} +(1.38581 - 2.40029i) q^{22} +(-2.21969 - 3.84461i) q^{23} +(0.519785 - 0.300098i) q^{24} +(-3.55193 - 0.619491i) q^{26} -3.38496 q^{27} +(-1.24653 + 0.719687i) q^{28} +(-3.93244 - 6.81119i) q^{29} +4.16082i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.44065 + 0.831757i) q^{33} +4.50367i q^{34} +(-1.31988 - 2.28610i) q^{36} +(-0.498370 + 0.287734i) q^{37} +4.33225 q^{38} +(0.371816 - 2.13186i) q^{39} +(3.65906 - 2.11256i) q^{41} +(-0.431953 - 0.748164i) q^{42} +(-1.30752 + 2.26469i) q^{43} +2.77162i q^{44} +(3.84461 + 2.21969i) q^{46} -12.7684i q^{47} +(-0.300098 + 0.519785i) q^{48} +(-2.46410 - 4.26795i) q^{49} -2.70308 q^{51} +(3.38581 - 1.23947i) q^{52} -9.57123 q^{53} +(2.93146 - 1.69248i) q^{54} +(0.719687 - 1.24653i) q^{56} +2.60020i q^{57} +(6.81119 + 3.93244i) q^{58} +(-3.00000 - 1.73205i) q^{59} +(6.25184 - 10.8285i) q^{61} +(-2.08041 - 3.60338i) q^{62} +(-3.29056 + 1.89980i) q^{63} -1.00000 q^{64} -1.66351 q^{66} +(-4.61504 + 2.66449i) q^{67} +(-2.25184 - 3.90029i) q^{68} +(-1.33225 + 2.30752i) q^{69} +(5.19615 + 3.00000i) q^{71} +(2.28610 + 1.31988i) q^{72} -1.66351i q^{73} +(0.287734 - 0.498370i) q^{74} +(-3.75184 + 2.16612i) q^{76} +3.98940 q^{77} +(0.743926 + 2.03215i) q^{78} +12.7288 q^{79} +(-2.94383 - 5.09886i) q^{81} +(-2.11256 + 3.65906i) q^{82} -10.0469i q^{83} +(0.748164 + 0.431953i) q^{84} -2.61504i q^{86} +(-2.36023 + 4.08805i) q^{87} +(-1.38581 - 2.40029i) q^{88} +(-5.15906 + 2.97859i) q^{89} +(-1.78406 - 4.87345i) q^{91} -4.43937 q^{92} +(2.16273 - 1.24865i) q^{93} +(6.38418 + 11.0577i) q^{94} -0.600196i q^{96} +(-1.37380 - 0.793166i) q^{97} +(4.26795 + 2.46410i) q^{98} +7.31643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} - 6 q^{11} + 4 q^{12} + 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} - 6 q^{22} - 12 q^{23} - 6 q^{24} - 40 q^{27} + 42 q^{33} + 4 q^{36} + 30 q^{37} + 12 q^{38}+ \cdots + 48 q^{98}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 - 6 * q^11 + 4 * q^12 + 2 * q^13 - 4 * q^16 - 6 * q^17 - 6 * q^19 - 6 * q^22 - 12 * q^23 - 6 * q^24 - 40 * q^27 + 42 * q^33 + 4 * q^36 + 30 * q^37 + 12 * q^38 - 40 * q^39 + 12 * q^41 + 6 * q^42 - 4 * q^43 + 2 * q^48 + 8 * q^49 + 10 * q^52 - 60 * q^53 + 36 * q^54 - 24 * q^59 + 26 * q^61 - 18 * q^62 - 12 * q^63 - 8 * q^64 - 12 * q^66 - 24 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^72 + 6 * q^74 - 6 * q^76 + 60 * q^77 + 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 48 * q^87 + 6 * q^88 - 24 * q^89 - 66 * q^91 - 24 * q^92 - 48 * q^93 + 6 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.300098	−	0.519785i	−0.173262	−	0.300098i	0.766297	−	0.642487i	$-0.222097\pi$
$3$	−0.300098	−	0.519785i	−0.173262	−	0.300098i	−0.939558	+	0.342389i	$0.888764\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.519785	+	0.300098i	0.212201	+	0.122514i
$7$	−1.24653	−	0.719687i	−0.471146	−	0.272016i	0.245574	−	0.969378i	$-0.421024\pi$
$7$	−1.24653	−	0.719687i	−0.471146	−	0.272016i	−0.716719	+	0.697362i	$0.754357\pi$
$8$			1.00000i			0.353553i
$9$	1.31988	−	2.28610i	0.439961	−	0.762035i
$10$		0			0
$11$	−2.40029	+	1.38581i	−0.723716	+	0.417837i	−0.816119	−	0.577884i	$-0.803879\pi$
$11$	−2.40029	+	1.38581i	−0.723716	+	0.417837i	0.0924030	+	0.995722i	$0.470545\pi$
$12$	−0.600196			−0.173262
$13$	2.76632	+	2.31246i	0.767239	+	0.641362i
$13$	2.76632	+	2.31246i	0.767239	+	0.641362i
$14$	1.43937			0.384689
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.25184	−	3.90029i	0.546150	−	0.945960i	−0.452383	−	0.891824i	$-0.649426\pi$
$17$	2.25184	−	3.90029i	0.546150	−	0.945960i	0.998534	−	0.0541365i	$-0.0172406\pi$
$18$			2.63977i			0.622199i
$19$	−3.75184	−	2.16612i	−0.860730	−	0.496943i	0.00352661	−	0.999994i	$-0.498877\pi$
$19$	−3.75184	−	2.16612i	−0.860730	−	0.496943i	−0.864257	+	0.503051i	$0.832211\pi$
$20$		0			0
$21$			0.863906i			0.188520i
$22$	1.38581	−	2.40029i	0.295456	−	0.511744i
$23$	−2.21969	−	3.84461i	−0.462837	−	0.801657i	0.536264	−	0.844050i	$-0.319835\pi$
$23$	−2.21969	−	3.84461i	−0.462837	−	0.801657i	−0.999101	+	0.0423934i	$0.986502\pi$
$24$	0.519785	−	0.300098i	0.106101	−	0.0612572i
$25$		0			0
$26$	−3.55193	−	0.619491i	−0.696591	−	0.121492i
$27$	−3.38496			−0.651436
$28$	−1.24653	+	0.719687i	−0.235573	+	0.136008i
$29$	−3.93244	−	6.81119i	−0.730236	−	1.26481i	−0.956782	−	0.290806i	$-0.906077\pi$
$29$	−3.93244	−	6.81119i	−0.730236	−	1.26481i	0.226546	−	0.974000i	$-0.427257\pi$
$30$		0			0
$31$			4.16082i			0.747306i	0.927569	+	0.373653i	$0.121895\pi$
$31$			4.16082i			0.747306i	−0.927569	+	0.373653i	$0.878105\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.44065	+	0.831757i	0.250784	+	0.144790i
$34$			4.50367i			0.772373i
$35$		0			0
$36$	−1.31988	−	2.28610i	−0.219980	−	0.381017i
$37$	−0.498370	+	0.287734i	−0.0819315	+	0.0473032i	−0.540406	−	0.841404i	$-0.681729\pi$
$37$	−0.498370	+	0.287734i	−0.0819315	+	0.0473032i	0.458475	+	0.888708i	$0.348396\pi$
$38$	4.33225			0.702783
$39$	0.371816	−	2.13186i	0.0595382	−	0.341370i
$40$		0			0
$41$	3.65906	−	2.11256i	0.571449	−	0.329926i	−0.186279	−	0.982497i	$-0.559643\pi$
$41$	3.65906	−	2.11256i	0.571449	−	0.329926i	0.757728	+	0.652571i	$0.226309\pi$
$42$	−0.431953	−	0.748164i	−0.0666518	−	0.115444i
$43$	−1.30752	+	2.26469i	−0.199395	+	0.345362i	−0.948332	−	0.317279i	$-0.897231\pi$
$43$	−1.30752	+	2.26469i	−0.199395	+	0.345362i	0.748938	+	0.662641i	$0.230564\pi$
$44$			2.77162i			0.417837i
$45$		0			0
$46$	3.84461	+	2.21969i	0.566857	+	0.327275i
$47$		−	12.7684i		−	1.86246i	−0.364436	−	0.931228i	$-0.618738\pi$
$47$		−	12.7684i		−	1.86246i	0.364436	−	0.931228i	$-0.381262\pi$
$48$	−0.300098	+	0.519785i	−0.0433154	+	0.0750245i
$49$	−2.46410	−	4.26795i	−0.352015	−	0.609707i
$50$		0			0
$51$	−2.70308			−0.378507
$52$	3.38581	−	1.23947i	0.469527	−	0.171884i
$53$	−9.57123			−1.31471			−0.657355	−	0.753581i	$-0.728325\pi$
$53$	−9.57123			−1.31471			−0.657355	+	0.753581i	$0.728325\pi$
$54$	2.93146	−	1.69248i	0.398922	−	0.230318i
$55$		0			0
$56$	0.719687	−	1.24653i	0.0961722	−	0.166575i
$57$			2.60020i			0.344404i
$58$	6.81119	+	3.93244i	0.894353	+	0.516355i
$59$	−3.00000	−	1.73205i	−0.390567	−	0.225494i	0.291839	−	0.956467i	$-0.405733\pi$
$59$	−3.00000	−	1.73205i	−0.390567	−	0.225494i	−0.682406	+	0.730974i	$0.739066\pi$
$60$		0			0
$61$	6.25184	−	10.8285i	0.800466	−	1.38645i	−0.118845	−	0.992913i	$-0.537919\pi$
$61$	6.25184	−	10.8285i	0.800466	−	1.38645i	0.919310	−	0.393534i	$-0.128748\pi$
$62$	−2.08041	−	3.60338i	−0.264212	−	0.457629i
$63$	−3.29056	+	1.89980i	−0.414571	+	0.239353i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.66351			−0.204764
$67$	−4.61504	+	2.66449i	−0.563817	+	0.325520i	−0.754676	−	0.656098i	$-0.772206\pi$
$67$	−4.61504	+	2.66449i	−0.563817	+	0.325520i	0.190859	+	0.981617i	$0.438873\pi$
$68$	−2.25184	−	3.90029i	−0.273075	−	0.472980i
$69$	−1.33225	+	2.30752i	−0.160384	+	0.277793i
$70$		0			0
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$	2.28610	+	1.31988i	0.269420	+	0.155550i
$73$		−	1.66351i		−	0.194700i	−0.995250	−	0.0973498i	$-0.968963\pi$
$73$		−	1.66351i		−	0.194700i	0.995250	−	0.0973498i	$-0.0310366\pi$
$74$	0.287734	−	0.498370i	0.0334484	−	0.0579343i
$75$		0			0
$76$	−3.75184	+	2.16612i	−0.430365	+	0.248471i
$77$	3.98940			0.454634
$78$	0.743926	+	2.03215i	0.0842330	+	0.230096i
$79$	12.7288			1.43210			0.716050	−	0.698049i	$-0.245948\pi$
$79$	12.7288			1.43210			0.716050	+	0.698049i	$0.245948\pi$
$80$		0			0
$81$	−2.94383	−	5.09886i	−0.327092	−	0.566540i
$82$	−2.11256	+	3.65906i	−0.233293	+	0.404076i
$83$		−	10.0469i		−	1.10279i	−0.834244	−	0.551396i	$-0.814095\pi$
$83$		−	10.0469i		−	1.10279i	0.834244	−	0.551396i	$-0.185905\pi$
$84$	0.748164	+	0.431953i	0.0816314	+	0.0471299i
$85$		0			0
$86$		−	2.61504i		−	0.281987i
$87$	−2.36023	+	4.08805i	−0.253044	+	0.438285i
$88$	−1.38581	−	2.40029i	−0.147728	−	0.255872i
$89$	−5.15906	+	2.97859i	−0.546859	+	0.315729i	−0.747854	−	0.663863i	$-0.768916\pi$
$89$	−5.15906	+	2.97859i	−0.546859	+	0.315729i	0.200995	+	0.979592i	$0.435583\pi$
$90$		0			0
$91$	−1.78406	−	4.87345i	−0.187021	−	0.510876i
$92$	−4.43937			−0.462837
$93$	2.16273	−	1.24865i	0.224265	−	0.129479i
$94$	6.38418	+	11.0577i	0.658478	+	1.14052i
$95$		0			0
$96$		−	0.600196i		−	0.0612572i
$97$	−1.37380	−	0.793166i	−0.139489	−	0.0805338i	0.428632	−	0.903479i	$-0.358996\pi$
$97$	−1.37380	−	0.793166i	−0.139489	−	0.0805338i	−0.568120	+	0.822946i	$0.692329\pi$
$98$	4.26795	+	2.46410i	0.431128	+	0.248912i
$99$			7.31643i			0.735329i
$100$		0			0
$101$	6.87676	+	11.9109i	0.684263	+	1.18518i	0.973668	+	0.227972i	$0.0732093\pi$
$101$	6.87676	+	11.9109i	0.684263	+	1.18518i	−0.289405	+	0.957207i	$0.593457\pi$
$102$	2.34094	−	1.35154i	0.231788	−	0.133823i
$103$	5.73205			0.564796			0.282398	−	0.959297i	$-0.408870\pi$
$103$	5.73205			0.564796			0.282398	+	0.959297i	$0.408870\pi$
$104$	−2.31246	+	2.76632i	−0.226756	+	0.271260i
$105$		0			0
$106$	8.28893	−	4.78561i	0.805092	−	0.464820i
$107$	2.33967	+	4.05242i	0.226184	+	0.391762i	0.956674	−	0.291161i	$-0.0940415\pi$
$107$	2.33967	+	4.05242i	0.226184	+	0.391762i	−0.730490	+	0.682924i	$0.760708\pi$
$108$	−1.69248	+	2.93146i	−0.162859	+	0.282080i
$109$			2.32164i			0.222373i	0.993800	+	0.111187i	$0.0354651\pi$
$109$			2.32164i			0.222373i	−0.993800	+	0.111187i	$0.964535\pi$
$110$		0			0
$111$	0.299119	+	0.172697i	0.0283912	+	0.0163916i
$112$			1.43937i			0.136008i
$113$	3.86814	−	6.69982i	0.363884	−	0.630266i	−0.624712	−	0.780855i	$-0.714784\pi$
$113$	3.86814	−	6.69982i	0.363884	−	0.630266i	0.988596	+	0.150589i	$0.0481170\pi$
$114$	−1.30010	−	2.25184i	−0.121765	−	0.210904i
$115$		0			0
$116$	−7.86488			−0.730236
$117$	8.93774	−	3.27191i	0.826295	−	0.302489i
$118$	3.46410			0.318896
$119$	−5.61398	+	3.24123i	−0.514633	+	0.297123i
$120$		0			0
$121$	−1.65906	+	2.87358i	−0.150824	+	0.261234i
$122$			12.5037i			1.13203i
$123$	−2.19615	−	1.26795i	−0.198020	−	0.114327i
$124$	3.60338	+	2.08041i	0.323593	+	0.186826i
$125$		0			0
$126$	1.89980	−	3.29056i	0.169248	−	0.293146i
$127$	8.06218	+	13.9641i	0.715403	+	1.23911i	0.962804	+	0.270201i	$0.0870900\pi$
$127$	8.06218	+	13.9641i	0.715403	+	1.23911i	−0.247401	+	0.968913i	$0.579577\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.56953			0.138190
$130$		0			0
$131$	−19.7609			−1.72651			−0.863257	−	0.504764i	$-0.831579\pi$
$131$	−19.7609			−1.72651			−0.863257	+	0.504764i	$0.831579\pi$
$132$	1.44065	−	0.831757i	0.125392	−	0.0723952i
$133$	3.11786	+	5.40029i	0.270353	+	0.468265i
$134$	2.66449	−	4.61504i	0.230177	−	0.398678i
$135$		0			0
$136$	3.90029	+	2.25184i	0.334447	+	0.193093i
$137$	14.9517	+	8.63234i	1.27741	+	0.737511i	0.976371	−	0.216102i	$-0.0693344\pi$
$137$	14.9517	+	8.63234i	1.27741	+	0.737511i	0.301036	+	0.953613i	$0.402668\pi$
$138$		−	2.66449i		−	0.226817i
$139$	−1.47328	+	2.55180i	−0.124962	+	0.216441i	−0.921718	−	0.387860i	$-0.873214\pi$
$139$	−1.47328	+	2.55180i	−0.124962	+	0.216441i	0.796756	+	0.604301i	$0.206548\pi$
$140$		0			0
$141$	−6.63680	+	3.83176i	−0.558919	+	0.322692i
$142$	−6.00000			−0.503509
$143$	−9.84461	−	1.71699i	−0.823248	−	0.143582i
$144$	−2.63977			−0.219980
$145$		0			0
$146$	0.831757	+	1.44065i	0.0688367	+	0.119229i
$147$	−1.47894	+	2.56160i	−0.121981	+	0.211278i
$148$			0.575468i			0.0473032i
$149$	−6.11871	−	3.53264i	−0.501264	−	0.289405i	0.227971	−	0.973668i	$-0.426791\pi$
$149$	−6.11871	−	3.53264i	−0.501264	−	0.289405i	−0.729235	+	0.684263i	$0.760124\pi$
$150$		0			0
$151$			15.8327i			1.28844i	0.764839	+	0.644222i	$0.222819\pi$
$151$			15.8327i			1.28844i	−0.764839	+	0.644222i	$0.777181\pi$
$152$	2.16612	−	3.75184i	0.175696	−	0.304314i
$153$	−5.94432	−	10.2959i	−0.480570	−	0.832371i
$154$	−3.45492	+	1.99470i	−0.278405	+	0.160737i
$155$		0			0
$156$	−1.66033	−	1.38793i	−0.132933	−	0.111123i
$157$	−12.6280			−1.00783			−0.503913	−	0.863754i	$-0.668107\pi$
$157$	−12.6280			−1.00783			−0.503913	+	0.863754i	$0.668107\pi$
$158$	−11.0235	+	6.36440i	−0.876979	+	0.506324i
$159$	2.87231	+	4.97498i	0.227789	+	0.394541i
$160$		0			0
$161$			6.38992i			0.503596i
$162$	5.09886	+	2.94383i	0.400604	+	0.231289i
$163$	15.9076	+	9.18428i	1.24598	+	0.719368i	0.970306	−	0.241882i	$-0.0777648\pi$
$163$	15.9076	+	9.18428i	1.24598	+	0.719368i	0.275677	+	0.961250i	$0.411098\pi$
$164$		−	4.22512i		−	0.329926i
$165$		0			0
$166$	5.02346	+	8.70088i	0.389896	+	0.675319i
$167$	−18.7135	+	10.8043i	−1.44810	+	0.836059i	−0.998368	−	0.0571070i	$-0.981812\pi$
$167$	−18.7135	+	10.8043i	−1.44810	+	0.836059i	−0.449728	+	0.893166i	$0.648479\pi$
$168$	−0.863906			−0.0666518
$169$	2.30504	+	12.7940i	0.177311	+	0.984155i
$170$		0			0
$171$	−9.90396	+	5.71806i	−0.757375	+	0.437271i
$172$	1.30752	+	2.26469i	0.0996974	+	0.172681i
$173$	−1.99470	+	3.45492i	−0.151654	+	0.262673i	−0.931836	−	0.362880i	$-0.881793\pi$
$173$	−1.99470	+	3.45492i	−0.151654	+	0.262673i	0.780182	+	0.625553i	$0.215127\pi$
$174$		−	4.72047i		−	0.357858i
$175$		0			0
$176$	2.40029	+	1.38581i	0.180929	+	0.104459i
$177$			2.07914i			0.156278i
$178$	2.97859	−	5.15906i	0.223254	−	0.386688i
$179$	6.23996	+	10.8079i	0.466397	+	0.807823i	0.999263	−	0.0383766i	$-0.0122186\pi$
$179$	6.23996	+	10.8079i	0.466397	+	0.807823i	−0.532867	+	0.846199i	$0.678885\pi$
$180$		0			0
$181$	19.4319			1.44436			0.722180	−	0.691705i	$-0.243140\pi$
$181$	19.4319			1.44436			0.722180	+	0.691705i	$0.243140\pi$
$182$	3.98177	+	3.32850i	0.295148	+	0.246725i
$183$	−7.50465			−0.554760
$184$	3.84461	−	2.21969i	0.283428	−	0.163637i
$185$		0			0
$186$	−1.24865	+	2.16273i	−0.0915557	+	0.158579i
$187$			12.4825i			0.912808i
$188$	−11.0577	−	6.38418i	−0.806467	−	0.465614i
$189$	4.21947	+	2.43611i	0.306921	+	0.177201i
$190$		0			0
$191$	9.16074	−	15.8669i	0.662848	−	1.14809i	−0.317016	−	0.948420i	$-0.602681\pi$
$191$	9.16074	−	15.8669i	0.662848	−	1.14809i	0.979864	−	0.199666i	$-0.0639858\pi$
$192$	0.300098	+	0.519785i	0.0216577	+	0.0375122i
$193$	−4.10811	+	2.37182i	−0.295708	+	0.170727i	−0.640513	−	0.767947i	$-0.721278\pi$
$193$	−4.10811	+	2.37182i	−0.295708	+	0.170727i	0.344805	+	0.938674i	$0.387945\pi$
$194$	1.58633			0.113892
$195$		0			0
$196$	−4.92820			−0.352015
$197$	9.35358	−	5.40029i	0.666415	−	0.384755i	−0.128302	−	0.991735i	$-0.540953\pi$
$197$	9.35358	−	5.40029i	0.666415	−	0.384755i	0.794717	+	0.606980i	$0.207619\pi$
$198$	−3.65821	−	6.33621i	−0.259978	−	0.450295i
$199$	5.50367	−	9.53264i	0.390145	−	0.675751i	−0.602323	−	0.798252i	$-0.705758\pi$
$199$	5.50367	−	9.53264i	0.390145	−	0.675751i	0.992468	+	0.122501i	$0.0390916\pi$
$200$		0			0
$201$	2.76993	+	1.59922i	0.195375	+	0.112800i
$202$	−11.9109	−	6.87676i	−0.838048	−	0.483847i
$203$			11.3205i			0.794544i
$204$	−1.35154	+	2.34094i	−0.0946269	+	0.163899i
$205$		0			0
$206$	−4.96410	+	2.86603i	−0.345865	+	0.199685i
$207$	−11.7189			−0.814520
$208$	0.619491	−	3.55193i	0.0429540	−	0.246282i
$209$	12.0073			0.830565
$210$		0			0
$211$	−13.1291	−	22.7402i	−0.903843	−	1.56550i	−0.822462	−	0.568820i	$-0.807400\pi$
$211$	−13.1291	−	22.7402i	−0.903843	−	1.56550i	−0.0813811	−	0.996683i	$-0.525933\pi$
$212$	−4.78561	+	8.28893i	−0.328677	+	0.569286i
$213$		−	3.60117i		−	0.246748i
$214$	−4.05242	−	2.33967i	−0.277018	−	0.159936i
$215$		0			0
$216$		−	3.38496i		−	0.230318i
$217$	2.99449	−	5.18661i	0.203279	−	0.352090i
$218$	−1.16082	−	2.01060i	−0.0786208	−	0.136175i
$219$	−0.864669	+	0.499217i	−0.0584289	+	0.0337340i
$220$		0			0
$221$	15.2486	−	5.58217i	1.02573	−	0.375498i
$222$	−0.345393			−0.0231813
$223$	19.2294	−	11.1021i	1.28770	−	0.743452i	0.309454	−	0.950915i	$-0.399854\pi$
$223$	19.2294	−	11.1021i	1.28770	−	0.743452i	0.978243	+	0.207463i	$0.0665205\pi$
$224$	−0.719687	−	1.24653i	−0.0480861	−	0.0832876i
$225$		0			0
$226$			7.73629i			0.514610i
$227$	−1.80059	−	1.03957i	−0.119509	−	0.0689986i	0.439054	−	0.898461i	$-0.355314\pi$
$227$	−1.80059	−	1.03957i	−0.119509	−	0.0689986i	−0.558563	+	0.829462i	$0.688647\pi$
$228$	2.25184	+	1.30010i	0.149131	+	0.0861011i
$229$			4.67933i			0.309219i	0.987976	+	0.154610i	$0.0494120\pi$
$229$			4.67933i			0.309219i	−0.987976	+	0.154610i	$0.950588\pi$
$230$		0			0
$231$	−1.19721	−	2.07363i	−0.0787706	−	0.136435i
$232$	6.81119	−	3.93244i	0.447177	−	0.258177i
$233$	−0.611060			−0.0400319			−0.0200160	−	0.999800i	$-0.506372\pi$
$233$	−0.611060			−0.0400319			−0.0200160	+	0.999800i	$0.506372\pi$
$234$	−6.10436	+	7.30243i	−0.399054	+	0.477375i
$235$		0			0
$236$	−3.00000	+	1.73205i	−0.195283	+	0.112747i
$237$	−3.81988	−	6.61623i	−0.248128	−	0.429770i
$238$	3.24123	−	5.61398i	0.210098	−	0.363900i
$239$		−	25.6481i		−	1.65904i	−0.558479	−	0.829518i	$-0.688615\pi$
$239$		−	25.6481i		−	1.65904i	0.558479	−	0.829518i	$-0.311385\pi$
$240$		0			0
$241$	23.4633	+	13.5466i	1.51141	+	0.872610i	0.999911	+	0.0133234i	$0.00424108\pi$
$241$	23.4633	+	13.5466i	1.51141	+	0.872610i	0.511494	+	0.859287i	$0.329092\pi$
$242$		−	3.31812i		−	0.213297i
$243$	−6.84432	+	11.8547i	−0.439063	+	0.760480i
$244$	−6.25184	−	10.8285i	−0.400233	−	0.693223i
$245$		0			0
$246$	2.53590			0.161683
$247$	−5.36970	−	14.6682i	−0.341666	−	0.933313i
$248$	−4.16082			−0.264212
$249$	−5.22223	+	3.01506i	−0.330945	+	0.191071i
$250$		0			0
$251$	0.751836	−	1.30222i	0.0474554	−	0.0821952i	−0.841322	−	0.540534i	$-0.818222\pi$
$251$	0.751836	−	1.30222i	0.0474554	−	0.0821952i	0.888777	+	0.458339i	$0.151555\pi$
$252$			3.79961i			0.239353i
$253$	10.6558	+	6.15213i	0.669924	+	0.386781i
$254$	−13.9641	−	8.06218i	−0.876186	−	0.505866i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.1724	+	17.6191i	0.634537	+	1.09905i	0.986613	+	0.163079i	$0.0521425\pi$
$257$	10.1724	+	17.6191i	0.634537	+	1.09905i	−0.352076	+	0.935971i	$0.614524\pi$
$258$	−1.35926	+	0.784767i	−0.0846236	+	0.0488575i
$259$	0.828313			0.0514689
$260$		0			0
$261$	−20.7614			−1.28510
$262$	17.1134	−	9.88043i	1.05727	−	0.610415i
$263$	−8.56466	−	14.8344i	−0.528119	−	0.914729i	−0.999463	−	0.0327796i	$-0.989564\pi$
$263$	−8.56466	−	14.8344i	−0.528119	−	0.914729i	0.471343	−	0.881950i	$-0.343769\pi$
$264$	−0.831757	+	1.44065i	−0.0511911	+	0.0886656i
$265$		0			0
$266$	−5.40029	−	3.11786i	−0.331113	−	0.191168i
$267$	3.09645	+	1.78773i	0.189499	+	0.109408i
$268$			5.32899i			0.325520i
$269$	−9.69121	+	16.7857i	−0.590883	+	1.02344i	0.403230	+	0.915099i	$0.367887\pi$
$269$	−9.69121	+	16.7857i	−0.590883	+	1.02344i	−0.994114	+	0.108342i	$0.965446\pi$
$270$		0			0
$271$	−15.9098	+	9.18555i	−0.966454	+	0.557982i	−0.898153	−	0.439682i	$-0.855091\pi$
$271$	−15.9098	+	9.18555i	−0.966454	+	0.557982i	−0.0683006	+	0.997665i	$0.521758\pi$
$272$	−4.50367			−0.273075
$273$	−1.99775	+	2.38984i	−0.120909	+	0.144640i
$274$	−17.2647			−1.04300
$275$		0			0
$276$	1.33225	+	2.30752i	0.0801918	+	0.138896i
$277$	13.6171	−	23.5855i	0.818171	−	1.41711i	−0.0888576	−	0.996044i	$-0.528322\pi$
$277$	13.6171	−	23.5855i	0.818171	−	1.41711i	0.907028	−	0.421069i	$-0.138345\pi$
$278$		−	2.94657i		−	0.176723i
$279$	9.51207	+	5.49180i	0.569473	+	0.328785i
$280$		0			0
$281$		−	30.0815i		−	1.79451i	−0.441509	−	0.897257i	$-0.645557\pi$
$281$		−	30.0815i		−	1.79451i	0.441509	−	0.897257i	$-0.354443\pi$
$282$	3.83176	−	6.63680i	0.228178	−	0.395216i
$283$	12.7394	+	22.0653i	0.757278	+	1.31164i	0.944234	+	0.329276i	$0.106805\pi$
$283$	12.7394	+	22.0653i	0.757278	+	1.31164i	−0.186955	+	0.982368i	$0.559862\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$		0			0
$286$	9.38418	−	3.43534i	0.554898	−	0.203136i
$287$	−6.08153			−0.358981
$288$	2.28610	−	1.31988i	0.134710	−	0.0777748i
$289$	−1.64153	−	2.84321i	−0.0965604	−	0.167247i
$290$		0			0
$291$			0.952110i			0.0558137i
$292$	−1.44065	−	0.831757i	−0.0843074	−	0.0486749i
$293$	14.3568	+	8.28893i	0.838736	+	0.484244i	0.856834	−	0.515592i	$-0.172428\pi$
$293$	14.3568	+	8.28893i	0.838736	+	0.484244i	−0.0180985	+	0.999836i	$0.505761\pi$
$294$		−	2.95789i		−	0.172507i
$295$		0			0
$296$	−0.287734	−	0.498370i	−0.0167242	−	0.0289672i
$297$	8.12490	−	4.69092i	0.471455	−	0.272195i
$298$	7.06528			0.409280
$299$	2.75015	−	15.7684i	0.159045	−	0.911908i
$300$		0			0
$301$	3.25973	−	1.88201i	0.187888	−	0.108477i
$302$	−7.91633	−	13.7115i	−0.455534	−	0.789007i
$303$	4.12740	−	7.14887i	0.237113	−	0.410692i
$304$			4.33225i			0.248471i
$305$		0			0
$306$	10.2959	+	5.94432i	0.588575	+	0.339814i
$307$		−	16.2722i		−	0.928703i	−0.885651	−	0.464351i	$-0.846287\pi$
$307$		−	16.2722i		−	0.928703i	0.885651	−	0.464351i	$-0.153713\pi$
$308$	1.99470	−	3.45492i	0.113659	−	0.196862i
$309$	−1.72018	−	2.97943i	−0.0978574	−	0.169494i
$310$		0			0
$311$	−16.1053			−0.913246			−0.456623	−	0.889660i	$-0.650941\pi$
$311$	−16.1053			−0.913246			−0.456623	+	0.889660i	$0.650941\pi$
$312$	2.13186	+	0.371816i	0.120693	+	0.0210499i
$313$	10.2162			0.577454			0.288727	−	0.957411i	$-0.406768\pi$
$313$	10.2162			0.577454			0.288727	+	0.957411i	$0.406768\pi$
$314$	10.9362	−	6.31401i	0.617165	−	0.356320i
$315$		0			0
$316$	6.36440	−	11.0235i	0.358025	−	0.620118i
$317$			0.204368i			0.0114785i	0.999984	+	0.00573923i	$0.00182686\pi$
$317$			0.204368i			0.0114785i	−0.999984	+	0.00573923i	$0.998173\pi$
$318$	−4.97498	−	2.87231i	−0.278983	−	0.161071i
$319$	18.8780	+	10.8992i	1.05697	+	0.610240i
$320$		0			0
$321$	1.40426	−	2.43225i	0.0783781	−	0.135755i
$322$	−3.19496	−	5.53383i	−0.178048	−	0.308388i
$323$	−16.8970	+	9.75551i	−0.940176	+	0.542811i
$324$	−5.88766			−0.327092
$325$		0			0
$326$	−18.3686			−1.01734
$327$	1.20676	−	0.696720i	0.0667337	−	0.0385287i
$328$	2.11256	+	3.65906i	0.116647	+	0.202038i
$329$	−9.18922	+	15.9162i	−0.506618	+	0.877488i
$330$		0			0
$331$	16.5110	+	9.53264i	0.907527	+	0.523961i	0.879635	−	0.475650i	$-0.157787\pi$
$331$	16.5110	+	9.53264i	0.907527	+	0.523961i	0.0278926	+	0.999611i	$0.491120\pi$
$332$	−8.70088	−	5.02346i	−0.477523	−	0.275698i
$333$			1.51910i			0.0832462i
$334$	10.8043	−	18.7135i	0.591183	−	1.02396i
$335$		0			0
$336$	0.748164	−	0.431953i	0.0408157	−	0.0235650i
$337$	−19.8609			−1.08189			−0.540946	−	0.841057i	$-0.681934\pi$
$337$	−19.8609			−1.08189			−0.540946	+	0.841057i	$0.681934\pi$
$338$	−8.39323	−	9.92742i	−0.456532	−	0.539980i
$339$	−4.64329			−0.252189
$340$		0			0
$341$	−5.76611	−	9.98719i	−0.312252	−	0.540837i
$342$	5.71806	−	9.90396i	0.309197	−	0.535545i
$343$			17.1691i			0.927047i
$344$	−2.26469	−	1.30752i	−0.122104	−	0.0704967i
$345$		0			0
$346$		−	3.98940i		−	0.214471i
$347$	8.52522	−	14.7661i	0.457658	−	0.792686i	−0.541179	−	0.840907i	$-0.682022\pi$
$347$	8.52522	−	14.7661i	0.457658	−	0.792686i	0.998837	+	0.0482211i	$0.0153552\pi$
$348$	2.36023	+	4.08805i	0.126522	+	0.219142i
$349$	18.3917	−	10.6185i	0.984488	−	0.568394i	0.0808657	−	0.996725i	$-0.474232\pi$
$349$	18.3917	−	10.6185i	0.984488	−	0.568394i	0.903622	+	0.428331i	$0.140898\pi$
$350$		0			0
$351$	−9.36389	−	7.82760i	−0.499807	−	0.417806i
$352$	−2.77162			−0.147728
$353$	−13.8710	+	8.00840i	−0.738276	+	0.426244i	−0.821442	−	0.570292i	$-0.806830\pi$
$353$	−13.8710	+	8.00840i	−0.738276	+	0.426244i	0.0831659	+	0.996536i	$0.473497\pi$
$354$	−1.03957	−	1.80059i	−0.0552525	−	0.0957001i
$355$		0			0
$356$			5.95717i			0.315729i
$357$	3.36949	+	1.94537i	0.178332	+	0.102960i
$358$	−10.8079	−	6.23996i	−0.571217	−	0.329792i
$359$		−	24.2487i		−	1.27980i	−0.768459	−	0.639899i	$-0.778976\pi$
$359$		−	24.2487i		−	1.27980i	0.768459	−	0.639899i	$-0.221024\pi$
$360$		0			0
$361$	−0.115820	−	0.200606i	−0.00609580	−	0.0105582i
$362$	−16.8285	+	9.71594i	−0.884486	+	0.510658i
$363$	1.99152			0.104528
$364$	−5.11256	−	0.891679i	−0.267971	−	0.0467367i
$365$		0			0
$366$	6.49922	−	3.75232i	0.339720	−	0.196137i
$367$	−14.8854	−	25.7822i	−0.777010	−	1.34582i	−0.933658	−	0.358167i	$-0.883402\pi$
$367$	−14.8854	−	25.7822i	−0.777010	−	1.34582i	0.156648	−	0.987655i	$-0.449931\pi$
$368$	−2.21969	+	3.84461i	−0.115709	+	0.200414i
$369$		−	11.1533i		−	0.580619i
$370$		0			0
$371$	11.9309	+	6.88829i	0.619420	+	0.357622i
$372$		−	2.49731i		−	0.129479i
$373$	14.1929	−	24.5828i	0.734880	−	1.27285i	−0.219896	−	0.975523i	$-0.570572\pi$
$373$	14.1929	−	24.5828i	0.734880	−	1.27285i	0.954776	−	0.297326i	$-0.0960949\pi$
$374$	−6.24123	−	10.8101i	−0.322726	−	0.558979i
$375$		0			0
$376$	12.7684			0.658478
$377$	4.87223	−	27.9355i	0.250932	−	1.43875i
$378$	−4.87223			−0.250600
$379$	−24.6070	+	14.2069i	−1.26398	+	0.729759i	−0.973842	−	0.227226i	$-0.927034\pi$
$379$	−24.6070	+	14.2069i	−1.26398	+	0.729759i	−0.290137	+	0.956985i	$0.593701\pi$
$380$		0			0
$381$	4.83888	−	8.38119i	0.247904	−	0.429382i
$382$			18.3215i			0.937409i
$383$	8.13827	+	4.69863i	0.415846	+	0.240089i	0.693298	−	0.720651i	$-0.256157\pi$
$383$	8.13827	+	4.69863i	0.415846	+	0.240089i	−0.277452	+	0.960739i	$0.589490\pi$
$384$	−0.519785	−	0.300098i	−0.0265252	−	0.0153143i
$385$		0			0
$386$	2.37182	−	4.10811i	0.120722	−	0.209097i
$387$	3.45154	+	5.97825i	0.175452	+	0.303891i
$388$	−1.37380	+	0.793166i	−0.0697443	+	0.0402669i
$389$	11.6461			0.590482			0.295241	−	0.955423i	$-0.404600\pi$
$389$	11.6461			0.590482			0.295241	+	0.955423i	$0.404600\pi$
$390$		0			0
$391$	−19.9935			−1.01111
$392$	4.26795	−	2.46410i	0.215564	−	0.124456i
$393$	5.93019	+	10.2714i	0.299139	+	0.518123i
$394$	−5.40029	+	9.35358i	−0.272063	+	0.471227i
$395$		0			0
$396$	6.33621	+	3.65821i	0.318407	+	0.183832i
$397$	0.346241	+	0.199902i	0.0173773	+	0.0100328i	0.508663	−	0.860965i	$-0.330140\pi$
$397$	0.346241	+	0.199902i	0.0173773	+	0.0100328i	−0.491286	+	0.870998i	$0.663473\pi$
$398$			11.0073i			0.551748i
$399$	1.87133	−	3.24123i	0.0936835	−	0.162265i
$400$		0			0
$401$	7.36793	−	4.25388i	0.367937	−	0.212428i	−0.304620	−	0.952474i	$-0.598529\pi$
$401$	7.36793	−	4.25388i	0.367937	−	0.212428i	0.672557	+	0.740046i	$0.265196\pi$
$402$	−3.19843			−0.159523
$403$	−9.62174	+	11.5102i	−0.479293	+	0.573362i
$404$	13.7535			0.684263
$405$		0			0
$406$	−5.66025	−	9.80385i	−0.280914	−	0.486557i
$407$	0.797489	−	1.38129i	0.0395301	−	0.0684681i
$408$		−	2.70308i		−	0.133823i
$409$	−12.1357	−	7.00657i	−0.600074	−	0.346453i	0.168997	−	0.985617i	$-0.445947\pi$
$409$	−12.1357	−	7.00657i	−0.600074	−	0.346453i	−0.769071	+	0.639164i	$0.779281\pi$
$410$		0			0
$411$		−	10.3622i		−	0.511129i
$412$	2.86603	−	4.96410i	0.141199	−	0.244564i
$413$	2.49307	+	4.31812i	0.122676	+	0.212481i
$414$	10.1489	−	5.85945i	0.498790	−	0.287976i
$415$		0			0
$416$	1.23947	+	3.38581i	0.0607701	+	0.166003i
$417$	1.76852			0.0866047
$418$	−10.3987	+	6.00367i	−0.508615	+	0.293649i
$419$	12.0977	+	20.9539i	0.591012	+	1.02366i	0.994096	+	0.108500i	$0.0346048\pi$
$419$	12.0977	+	20.9539i	0.591012	+	1.02366i	−0.403084	+	0.915163i	$0.632062\pi$
$420$		0			0
$421$			35.6392i			1.73695i	0.495735	+	0.868474i	$0.334899\pi$
$421$			35.6392i			1.73695i	−0.495735	+	0.868474i	$0.665101\pi$
$422$	22.7402	+	13.1291i	1.10698	+	0.639114i
$423$	−29.1898	−	16.8527i	−1.41926	−	0.819408i
$424$		−	9.57123i		−	0.464820i
$425$		0			0
$426$	1.80059	+	3.11871i	0.0872387	+	0.151102i
$427$	−15.5863	+	8.99873i	−0.754272	+	0.435479i
$428$	4.67933			0.226184
$429$	2.06188	+	5.63234i	0.0995485	+	0.271932i
$430$		0			0
$431$	4.29586	−	2.48022i	0.206924	−	0.119468i	−0.392957	−	0.919557i	$-0.628548\pi$
$431$	4.29586	−	2.48022i	0.206924	−	0.119468i	0.599881	+	0.800089i	$0.295215\pi$
$432$	1.69248	+	2.93146i	0.0814295	+	0.141040i
$433$	−2.10811	+	3.65135i	−0.101309	+	0.175472i	−0.912224	−	0.409691i	$-0.865636\pi$
$433$	−2.10811	+	3.65135i	−0.101309	+	0.175472i	0.810915	+	0.585164i	$0.198970\pi$
$434$			5.98898i			0.287480i
$435$		0			0
$436$	2.01060	+	1.16082i	0.0962904	+	0.0555933i
$437$			19.2325i			0.920013i
$438$	0.499217	−	0.864669i	0.0238535	−	0.0413155i
$439$	−7.37500	−	12.7739i	−0.351989	−	0.609664i	0.634608	−	0.772834i	$-0.281161\pi$
$439$	−7.37500	−	12.7739i	−0.351989	−	0.609664i	−0.986598	+	0.163170i	$0.947828\pi$
$440$		0			0
$441$	−13.0093			−0.619490
$442$	−10.4146	+	12.4586i	−0.495370	+	0.592595i
$443$	12.2374			0.581417			0.290709	−	0.956812i	$-0.406109\pi$
$443$	12.2374			0.581417			0.290709	+	0.956812i	$0.406109\pi$
$444$	0.299119	−	0.172697i	0.0141956	−	0.00819582i
$445$		0			0
$446$	−11.1021	+	19.2294i	−0.525700	+	0.910539i
$447$			4.24055i			0.200571i
$448$	1.24653	+	0.719687i	0.0588932	+	0.0340020i
$449$	−16.5163	−	9.53569i	−0.779452	−	0.450017i	0.0567839	−	0.998386i	$-0.481915\pi$
$449$	−16.5163	−	9.53569i	−0.779452	−	0.450017i	−0.836236	+	0.548370i	$0.815249\pi$
$450$		0			0
$451$	−5.85521	+	10.1415i	−0.275711	+	0.477546i
$452$	−3.86814	−	6.69982i	−0.181942	−	0.315133i
$453$	8.22957	−	4.75135i	0.386659	−	0.223238i
$454$	2.07914			0.0975788
$455$		0			0
$456$	−2.60020			−0.121765
$457$	−13.9549	+	8.05688i	−0.652784	+	0.376885i	−0.789522	−	0.613722i	$-0.789671\pi$
$457$	−13.9549	+	8.05688i	−0.652784	+	0.376885i	0.136738	+	0.990607i	$0.456338\pi$
$458$	−2.33967	−	4.05242i	−0.109325	−	0.189357i
$459$	−7.62238	+	13.2023i	−0.355782	+	0.616233i
$460$		0			0
$461$	4.19560	+	2.42233i	0.195408	+	0.112819i	0.594512	−	0.804087i	$-0.297345\pi$
$461$	4.19560	+	2.42233i	0.195408	+	0.112819i	−0.399104	+	0.916906i	$0.630679\pi$
$462$	2.07363	+	1.19721i	0.0964739	+	0.0556992i
$463$		−	8.23164i		−	0.382557i	−0.981536	−	0.191278i	$-0.938737\pi$
$463$		−	8.23164i		−	0.382557i	0.981536	−	0.191278i	$-0.0612633\pi$
$464$	−3.93244	+	6.81119i	−0.182559	+	0.316202i
$465$		0			0
$466$	0.529194	−	0.305530i	0.0245144	−	0.0141534i
$467$	33.4873			1.54961			0.774803	−	0.632203i	$-0.217849\pi$
$467$	33.4873			1.54961			0.774803	+	0.632203i	$0.217849\pi$
$468$	1.63531	−	9.37627i	0.0755923	−	0.433418i
$469$	7.67040			0.354186
$470$		0			0
$471$	3.78964	+	6.56386i	0.174618	+	0.302446i
$472$	1.73205	−	3.00000i	0.0797241	−	0.138086i
$473$		−	7.24789i		−	0.333258i
$474$	6.61623	+	3.81988i	0.303894	+	0.175453i
$475$		0			0
$476$			6.48247i			0.297123i
$477$	−12.6329	+	21.8808i	−0.578421	+	1.00185i
$478$	12.8240	+	22.2119i	0.586558	+	1.01595i
$479$	6.97448	−	4.02672i	0.318672	−	0.183985i	−0.332128	−	0.943234i	$-0.607767\pi$
$479$	6.97448	−	4.02672i	0.318672	−	0.183985i	0.650800	+	0.759249i	$0.274433\pi$
$480$		0			0
$481$	−2.04402	−	0.356497i	−0.0931994	−	0.0162549i
$482$	−27.0931			−1.23406
$483$	3.32138	−	1.91760i	0.151128	−	0.0872538i
$484$	1.65906	+	2.87358i	0.0754118	+	0.130617i
$485$		0			0
$486$		−	13.6886i		−	0.620929i
$487$	1.40601	+	0.811758i	0.0637122	+	0.0367842i	0.531518	−	0.847047i	$-0.321622\pi$
$487$	1.40601	+	0.811758i	0.0637122	+	0.0367842i	−0.467806	+	0.883831i	$0.654955\pi$
$488$	10.8285	+	6.25184i	0.490183	+	0.283007i
$489$		−	11.0247i		−	0.498555i
$490$		0			0
$491$	5.16033	+	8.93796i	0.232883	+	0.403364i	0.958655	−	0.284570i	$-0.0918509\pi$
$491$	5.16033	+	8.93796i	0.232883	+	0.403364i	−0.725773	+	0.687935i	$0.758518\pi$
$492$	−2.19615	+	1.26795i	−0.0990102	+	0.0571636i
$493$	−35.4209			−1.59527
$494$	11.9844	+	10.0182i	0.539203	+	0.450738i
$495$		0			0
$496$	3.60338	−	2.08041i	0.161796	−	0.0934132i
$497$	−4.31812	−	7.47921i	−0.193694	−	0.335488i
$498$	3.01506	−	5.22223i	0.135108	−	0.234014i
$499$		−	13.9807i		−	0.625860i	−0.949776	−	0.312930i	$-0.898689\pi$
$499$		−	13.9807i		−	0.625860i	0.949776	−	0.312930i	$-0.101311\pi$
$500$		0			0
$501$	11.2318	+	6.48467i	0.501799	+	0.289714i
$502$			1.50367i			0.0671121i
$503$	11.8924	−	20.5983i	0.530258	−	0.918434i	−0.469119	−	0.883135i	$-0.655428\pi$
$503$	11.8924	−	20.5983i	0.530258	−	0.918434i	0.999377	−	0.0352988i	$-0.0112383\pi$
$504$	−1.89980	−	3.29056i	−0.0846240	−	0.146573i
$505$		0			0
$506$	−12.3043			−0.546991
$507$	5.95839	−	5.03758i	0.264622	−	0.223727i
$508$	16.1244			0.715403
$509$	−22.2023	+	12.8185i	−0.984102	+	0.568171i	−0.903506	−	0.428575i	$-0.859016\pi$
$509$	−22.2023	+	12.8185i	−0.984102	+	0.568171i	−0.0805958	+	0.996747i	$0.525682\pi$
$510$		0			0
$511$	−1.19721	+	2.07363i	−0.0529614	+	0.0917319i
$512$		−	1.00000i		−	0.0441942i
$513$	12.6998	+	7.33225i	0.560711	+	0.323727i
$514$	−17.6191	−	10.1724i	−0.777146	−	0.448685i
$515$		0			0
$516$	0.784767	−	1.35926i	0.0345474	−	0.0598379i
$517$	17.6945	+	30.6478i	0.778204	+	1.34789i
$518$	−0.717340	+	0.414157i	−0.0315181	+	0.0181970i
$519$	2.39442			0.105103
$520$		0			0
$521$	−8.53476			−0.373915			−0.186957	−	0.982368i	$-0.559863\pi$
$521$	−8.53476			−0.373915			−0.186957	+	0.982368i	$0.559863\pi$
$522$	17.9799	−	10.3807i	0.786961	−	0.454352i
$523$	−6.34383	−	10.9878i	−0.277396	−	0.480464i	0.693341	−	0.720610i	$-0.256138\pi$
$523$	−6.34383	−	10.9878i	−0.277396	−	0.480464i	−0.970737	+	0.240146i	$0.922805\pi$
$524$	−9.88043	+	17.1134i	−0.431629	+	0.747603i
$525$		0			0
$526$	14.8344	+	8.56466i	0.646811	+	0.373437i
$527$	16.2284	+	9.36949i	0.706921	+	0.408141i
$528$		−	1.66351i		−	0.0723952i
$529$	1.64598	−	2.85092i	0.0715644	−	0.123953i
$530$		0			0
$531$	−7.91930	+	4.57221i	−0.343668	+	0.198417i
$532$	6.23572			0.270353
$533$	15.0073	+	2.61742i	0.650040	+	0.113373i
$534$	−3.57547			−0.154726
$535$		0			0
$536$	−2.66449	−	4.61504i	−0.115089	−	0.199339i
$537$	3.74520	−	6.48687i	0.161617	−	0.279929i
$538$		−	19.3824i		−	0.835635i
$539$	11.8291	+	6.82955i	0.509517	+	0.294170i
$540$		0			0
$541$		−	42.0507i		−	1.80790i	−0.427636	−	0.903951i	$-0.640653\pi$
$541$		−	42.0507i		−	1.80790i	0.427636	−	0.903951i	$-0.359347\pi$
$542$	9.18555	−	15.9098i	0.394553	−	0.683386i
$543$	−5.83146	−	10.1004i	−0.250252	−	0.433449i
$544$	3.90029	−	2.25184i	0.167224	−	0.0965467i
$545$		0			0
$546$	0.535182	−	3.06854i	0.0229037	−	0.131321i
$547$	−24.6297			−1.05309			−0.526545	−	0.850147i	$-0.676513\pi$
$547$	−24.6297			−1.05309			−0.526545	+	0.850147i	$0.676513\pi$
$548$	14.9517	−	8.63234i	0.638703	−	0.368755i
$549$	−16.5034	−	28.5847i	−0.704347	−	1.21996i
$550$		0			0
$551$			34.0726i			1.45154i
$552$	−2.30752	−	1.33225i	−0.0982145	−	0.0567042i
$553$	−15.8669	−	9.16074i	−0.674728	−	0.389554i
$554$			27.2342i			1.15707i
$555$		0			0
$556$	1.47328	+	2.55180i	0.0624811	+	0.108221i
$557$	−6.84583	+	3.95244i	−0.290067	+	0.167470i	−0.637972	−	0.770059i	$-0.720227\pi$
$557$	−6.84583	+	3.95244i	−0.290067	+	0.167470i	0.347905	+	0.937530i	$0.386893\pi$
$558$	−10.9836			−0.464973
$559$	−8.85402	+	3.24126i	−0.374485	+	0.137091i
$560$		0			0
$561$	6.48819	−	3.74596i	0.273932	−	0.158155i
$562$	15.0408	+	26.0514i	0.634456	+	1.09891i
$563$	−6.63553	+	11.4931i	−0.279654	+	0.484375i	−0.971299	−	0.237863i	$-0.923553\pi$
$563$	−6.63553	+	11.4931i	−0.279654	+	0.484375i	0.691645	+	0.722238i	$0.256886\pi$
$564$			7.66351i			0.322692i
$565$		0			0
$566$	−22.0653	−	12.7394i	−0.927473	−	0.535477i
$567$			8.47454i			0.355897i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	21.1323	+	36.6022i	0.885911	+	1.53444i	0.844666	+	0.535293i	$0.179799\pi$
$569$	21.1323	+	36.6022i	0.885911	+	1.53444i	0.0412443	+	0.999149i	$0.486868\pi$
$570$		0			0
$571$	1.64965			0.0690358			0.0345179	−	0.999404i	$-0.489010\pi$
$571$	1.64965			0.0690358			0.0345179	+	0.999404i	$0.489010\pi$
$572$	−6.40927	+	7.66719i	−0.267985	+	0.320581i
$573$	−10.9965			−0.459384
$574$	5.26676	−	3.04076i	0.219830	−	0.126919i
$575$		0			0
$576$	−1.31988	+	2.28610i	−0.0549951	+	0.0952543i
$577$			28.4651i			1.18502i	0.805564	+	0.592508i	$0.201862\pi$
$577$			28.4651i			1.18502i	−0.805564	+	0.592508i	$0.798138\pi$
$578$	2.84321	+	1.64153i	0.118262	+	0.0682785i
$579$	2.46567	+	1.42355i	0.102470	+	0.0591609i
$580$		0			0
$581$	−7.23063	+	12.5238i	−0.299977	+	0.519576i
$582$	−0.476055	−	0.824551i	−0.0197331	−	0.0341788i
$583$	22.9738	−	13.2639i	0.951476	−	0.549335i
$584$	1.66351			0.0688367
$585$		0			0
$586$	−16.5779			−0.684825
$587$	−19.1994	+	11.0848i	−0.792445	+	0.457518i	−0.840822	−	0.541311i	$-0.817928\pi$
$587$	−19.1994	+	11.0848i	−0.792445	+	0.457518i	0.0483779	+	0.998829i	$0.484595\pi$
$588$	1.47894	+	2.56160i	0.0609906	+	0.105639i
$589$	9.01285	−	15.6107i	0.371368	−	0.643228i
$590$		0			0
$591$	−5.61398	−	3.24123i	−0.230928	−	0.133327i
$592$	0.498370	+	0.287734i	0.0204829	+	0.0118258i
$593$			9.68683i			0.397791i	0.980021	+	0.198895i	$0.0637354\pi$
$593$			9.68683i			0.397791i	−0.980021	+	0.198895i	$0.936265\pi$
$594$	−4.69092	+	8.12490i	−0.192471	+	0.333369i
$595$		0			0
$596$	−6.11871	+	3.53264i	−0.250632	+	0.144702i
$597$	−6.60656			−0.270388
$598$	5.50248	+	15.0309i	0.225013	+	0.614658i
$599$	8.33012			0.340360			0.170180	−	0.985413i	$-0.445565\pi$
$599$	8.33012			0.340360			0.170180	+	0.985413i	$0.445565\pi$
$600$		0			0
$601$	6.10117	+	10.5675i	0.248872	+	0.431059i	0.963213	−	0.268739i	$-0.0866068\pi$
$601$	6.10117	+	10.5675i	0.248872	+	0.431059i	−0.714341	+	0.699798i	$0.753273\pi$
$602$	−1.88201	+	3.25973i	−0.0767049	+	0.132857i
$603$			14.0673i			0.572864i
$604$	13.7115	+	7.91633i	0.557912	+	0.322111i
$605$		0			0
$606$			8.25480i			0.335328i
$607$	−4.91946	+	8.52075i	−0.199675	+	0.345847i	−0.948423	−	0.317008i	$-0.897322\pi$
$607$	−4.91946	+	8.52075i	−0.199675	+	0.345847i	0.748748	+	0.662854i	$0.230655\pi$
$608$	−2.16612	−	3.75184i	−0.0878479	−	0.152157i
$609$	5.88423	−	3.39726i	0.238441	−	0.137664i
$610$		0			0
$611$	29.5263	−	35.3214i	1.19451	−	1.42895i
$612$	−11.8886			−0.480570
$613$	−13.1737	+	7.60586i	−0.532082	+	0.307198i	−0.741864	−	0.670551i	$-0.766058\pi$
$613$	−13.1737	+	7.60586i	−0.532082	+	0.307198i	0.209782	+	0.977748i	$0.432725\pi$
$614$	8.13609	+	14.0921i	0.328346	+	0.568712i
$615$		0			0
$616$			3.98940i			0.160737i
$617$	21.1929	+	12.2357i	0.853194	+	0.492592i	0.861727	−	0.507372i	$-0.169383\pi$
$617$	21.1929	+	12.2357i	0.853194	+	0.492592i	−0.00853345	+	0.999964i	$0.502716\pi$
$618$	2.97943	+	1.72018i	0.119850	+	0.0691956i
$619$			42.4157i			1.70483i	0.522864	+	0.852416i	$0.324864\pi$
$619$			42.4157i			1.70483i	−0.522864	+	0.852416i	$0.675136\pi$
$620$		0			0
$621$	7.51356	+	13.0139i	0.301509	+	0.522228i
$622$	13.9476	−	8.05264i	0.559247	−	0.322881i
$623$	8.57459			0.343534
$624$	−2.03215	+	0.743926i	−0.0813511	+	0.0297809i
$625$		0			0
$626$	−8.84750	+	5.10811i	−0.353617	+	0.204161i
$627$	−3.60338	−	6.24123i	−0.143905	−	0.249251i
$628$	−6.31401	+	10.9362i	−0.251957	+	0.436402i
$629$			2.59172i			0.103339i
$630$		0			0
$631$	−0.0244657	−	0.0141253i	−0.000973964	−	0.000562318i	0.499513	−	0.866306i	$-0.333512\pi$
$631$	−0.0244657	−	0.0141253i	−0.000973964	−	0.000562318i	−0.500487	+	0.865744i	$0.666846\pi$
$632$			12.7288i			0.506324i
$633$	−7.88002	+	13.6486i	−0.313203	+	0.542483i
$634$	−0.102184	−	0.176988i	−0.00405825	−	0.00702909i
$635$		0			0
$636$	5.74461			0.227789
$637$	3.05298	−	17.5046i	0.120963	−	0.693559i
$638$	−21.7985			−0.863010
$639$	13.7166	−	7.91930i	0.542621	−	0.313282i
$640$		0			0
$641$	8.10465	−	14.0377i	0.320114	−	0.554454i	−0.660397	−	0.750917i	$-0.729612\pi$
$641$	8.10465	−	14.0377i	0.320114	−	0.554454i	0.980511	+	0.196462i	$0.0629453\pi$
$642$			2.80852i			0.110843i
$643$	−15.7718	−	9.10586i	−0.621979	−	0.359100i	0.155660	−	0.987811i	$-0.450250\pi$
$643$	−15.7718	−	9.10586i	−0.621979	−	0.359100i	−0.777639	+	0.628711i	$0.783583\pi$
$644$	5.53383	+	3.19496i	0.218064	+	0.125899i
$645$		0			0
$646$	9.75551	−	16.8970i	0.383825	−	0.664805i
$647$	3.56139	+	6.16852i	0.140013	+	0.242509i	0.927501	−	0.373820i	$-0.121952\pi$
$647$	3.56139	+	6.16852i	0.140013	+	0.242509i	−0.787488	+	0.616330i	$0.788619\pi$
$648$	5.09886	−	2.94383i	0.200302	−	0.115644i
$649$	9.60117			0.376879
$650$		0			0
$651$	−3.59456			−0.140882
$652$	15.9076	−	9.18428i	0.622991	−	0.359684i
$653$	−8.03546	−	13.9178i	−0.314452	−	0.544647i	0.664869	−	0.746960i	$-0.268487\pi$
$653$	−8.03546	−	13.9178i	−0.314452	−	0.544647i	−0.979321	+	0.202313i	$0.935154\pi$
$654$	−0.696720	+	1.20676i	−0.0272439	+	0.0471879i
$655$		0			0
$656$	−3.65906	−	2.11256i	−0.142862	−	0.0824816i
$657$	−3.80297	−	2.19564i	−0.148368	−	0.0856602i
$658$		−	18.3784i		−	0.716466i
$659$	−22.5988	+	39.1423i	−0.880326	+	1.52477i	−0.0293473	+	0.999569i	$0.509343\pi$
$659$	−22.5988	+	39.1423i	−0.880326	+	1.52477i	−0.850979	+	0.525200i	$0.823990\pi$
$660$		0			0
$661$	−7.63354	+	4.40723i	−0.296910	+	0.171421i	−0.641054	−	0.767496i	$-0.721503\pi$
$661$	−7.63354	+	4.40723i	−0.296910	+	0.171421i	0.344144	+	0.938917i	$0.388169\pi$
$662$	−19.0653			−0.740993
$663$	−7.47759	−	6.25078i	−0.290406	−	0.242760i
$664$	10.0469			0.389896
$665$		0			0
$666$	−0.759550	−	1.31558i	−0.0294320	−	0.0509777i
$667$	−17.4576	+	30.2374i	−0.675960	+	1.17080i
$668$			21.6085i			0.836059i
$669$	−11.5414	−	6.66344i	−0.446217	−	0.257623i
$670$		0			0
$671$			34.6554i			1.33786i
$672$	−0.431953	+	0.748164i	−0.0166629	+	0.0288611i
$673$	−20.7199	−	35.8879i	−0.798693	−	1.38338i	−0.920468	−	0.390819i	$-0.872192\pi$
$673$	−20.7199	−	35.8879i	−0.798693	−	1.38338i	0.121775	−	0.992558i	$-0.461141\pi$
$674$	17.2001	−	9.93045i	0.662521	−	0.382507i
$675$		0			0
$676$	12.2325	+	4.40078i	0.470479	+	0.169261i
$677$	18.8510			0.724504			0.362252	−	0.932080i	$-0.382008\pi$
$677$	18.8510			0.724504			0.362252	+	0.932080i	$0.382008\pi$
$678$	4.02121	−	2.32164i	0.154433	−	0.0891622i
$679$	1.14166	+	1.97742i	0.0438130	+	0.0758863i
$680$		0			0
$681$			1.24789i			0.0478193i
$682$	9.98719	+	5.76611i	0.382429	+	0.220796i
$683$	−19.6297	−	11.3332i	−0.751110	−	0.433654i	0.0749846	−	0.997185i	$-0.476109\pi$
$683$	−19.6297	−	11.3332i	−0.751110	−	0.433654i	−0.826095	+	0.563531i	$0.809443\pi$
$684$			11.4361i			0.437271i
$685$		0			0
$686$	−8.58457	−	14.8689i	−0.327760	−	0.567698i
$687$	2.43225	−	1.40426i	0.0927960	−	0.0535758i
$688$	2.61504			0.0996974
$689$	−26.4771	−	22.1331i	−1.00870	−	0.843204i
$690$		0			0
$691$	27.5736	−	15.9196i	1.04895	−	0.605612i	0.126595	−	0.991954i	$-0.459595\pi$
$691$	27.5736	−	15.9196i	1.04895	−	0.605612i	0.922355	+	0.386343i	$0.126262\pi$
$692$	1.99470	+	3.45492i	0.0758271	+	0.131336i
$693$	5.26554	−	9.12018i	0.200021	−	0.346447i
$694$			17.0504i			0.647226i
$695$		0			0
$696$	−4.08805	−	2.36023i	−0.154957	−	0.0894645i
$697$		−	19.0285i		−	0.720758i
$698$	−10.6185	+	18.3917i	−0.401915	+	0.696138i
$699$	0.183378	+	0.317620i	0.00693599	+	0.0120135i
$700$		0			0
$701$	0.611060			0.0230794			0.0115397	−	0.999933i	$-0.496327\pi$
$701$	0.611060			0.0230794			0.0115397	+	0.999933i	$0.496327\pi$
$702$	12.0232	+	2.09695i	0.453785	+	0.0791444i
$703$	2.49307			0.0940279
$704$	2.40029	−	1.38581i	0.0904645	−	0.0522297i
$705$		0			0
$706$	8.00840	−	13.8710i	0.301400	−	0.522040i
$707$		−	19.7965i		−	0.744522i
$708$	1.80059	+	1.03957i	0.0676702	+	0.0390694i
$709$	11.2274	+	6.48212i	0.421653	+	0.243441i	0.695784	−	0.718251i	$-0.255057\pi$
$709$	11.2274	+	6.48212i	0.421653	+	0.243441i	−0.274131	+	0.961692i	$0.588390\pi$
$710$		0			0
$711$	16.8005	−	29.0993i	0.630068	−	1.09131i
$712$	−2.97859	−	5.15906i	−0.111627	−	0.193344i
$713$	15.9967	−	9.23572i	0.599083	−	0.345881i
$714$	−3.89075			−0.145608
$715$		0			0
$716$	12.4799			0.466397
$717$	−13.3315	+	7.69694i	−0.497873	+	0.287447i
$718$	12.1244	+	21.0000i	0.452477	+	0.783713i
$719$	17.8616	−	30.9372i	0.666126	−	1.15376i	−0.312853	−	0.949802i	$-0.601285\pi$
$719$	17.8616	−	30.9372i	0.666126	−	1.15376i	0.978979	−	0.203963i	$-0.0653821\pi$
$720$		0			0
$721$	−7.14520	−	4.12528i	−0.266101	−	0.153634i
$722$	0.200606	+	0.115820i	0.00746580	+	0.00431038i
$723$		−	16.2612i		−	0.604759i
$724$	9.71594	−	16.8285i	0.361090	−	0.625426i
$725$		0			0
$726$	−1.72471	+	0.995761i	−0.0640099	+	0.0369562i
$727$	51.7313			1.91861			0.959304	−	0.282375i	$-0.0911224\pi$
$727$	51.7313			1.91861			0.959304	+	0.282375i	$0.0911224\pi$
$728$	4.87345	−	1.78406i	0.180622	−	0.0661218i
$729$	−9.44711			−0.349893
$730$		0			0
$731$	5.88863	+	10.1994i	0.217799	+	0.377239i
$732$	−3.75232	+	6.49922i	−0.138690	+	0.240218i
$733$			26.4319i			0.976284i	0.872764	+	0.488142i	$0.162325\pi$
$733$			26.4319i			0.976284i	−0.872764	+	0.488142i	$0.837675\pi$
$734$	25.7822	+	14.8854i	0.951639	+	0.549429i
$735$		0			0
$736$		−	4.43937i		−	0.163637i
$737$	7.38496	−	12.7911i	0.272029	−	0.471167i
$738$	5.57666	+	9.65906i	0.205280	+	0.355555i
$739$	−23.7380	+	13.7051i	−0.873215	+	0.504151i	−0.868415	−	0.495837i	$-0.834861\pi$
$739$	−23.7380	+	13.7051i	−0.873215	+	0.504151i	−0.00480000	+	0.999988i	$0.501528\pi$
$740$		0			0
$741$	−6.01285	+	7.19297i	−0.220888	+	0.264240i
$742$	−13.7766			−0.505754
$743$	36.5306	−	21.0909i	1.34018	−	0.773751i	0.353344	−	0.935494i	$-0.385045\pi$
$743$	36.5306	−	21.0909i	1.34018	−	0.773751i	0.986833	+	0.161742i	$0.0517113\pi$
$744$	1.24865	+	2.16273i	0.0457779	+	0.0792896i
$745$		0			0
$746$			28.3858i			1.03928i
$747$	−22.9683	−	13.2607i	−0.840365	−	0.485185i
$748$	10.8101	+	6.24123i	0.395258	+	0.228202i
$749$		−	6.73531i		−	0.246103i
$750$		0			0
$751$	9.66351	+	16.7377i	0.352627	+	0.610767i	0.986709	−	0.162498i	$-0.0519552\pi$
$751$	9.66351	+	16.7377i	0.352627	+	0.610767i	−0.634082	+	0.773266i	$0.718622\pi$
$752$	−11.0577	+	6.38418i	−0.403234	+	0.232807i
$753$	−0.902497			−0.0328888
$754$	9.74830	+	26.6290i	0.355012	+	0.969771i
$755$		0			0
$756$	4.21947	−	2.43611i	0.153461	−	0.0886006i
$757$	−10.1513	−	17.5825i	−0.368955	−	0.639048i	0.620448	−	0.784248i	$-0.286951\pi$
$757$	−10.1513	−	17.5825i	−0.368955	−	0.639048i	−0.989402	+	0.145200i	$0.953618\pi$
$758$	14.2069	−	24.6070i	0.516017	−	0.893768i
$759$		−	7.38496i		−	0.268057i
$760$		0			0
$761$	−38.3386	−	22.1348i	−1.38977	−	0.802386i	−0.396484	−	0.918042i	$-0.629770\pi$
$761$	−38.3386	−	22.1348i	−1.38977	−	0.802386i	−0.993289	+	0.115656i	$0.963103\pi$
$762$			9.67777i			0.350589i
$763$	1.67086	−	2.89401i	0.0604891	−	0.104770i
$764$	−9.16074	−	15.8669i	−0.331424	−	0.574043i
$765$		0			0
$766$	−9.39726			−0.339537
$767$	−4.29366	−	11.7288i	−0.155035	−	0.423502i
$768$	0.600196			0.0216577
$769$	3.23903	−	1.87005i	0.116802	−	0.0674359i	−0.440461	−	0.897772i	$-0.645185\pi$
$769$	3.23903	−	1.87005i	0.116802	−	0.0674359i	0.557263	+	0.830336i	$0.311852\pi$
$770$		0			0
$771$	6.10543	−	10.5749i	0.219882	−	0.380846i
$772$			4.74363i			0.170727i
$773$	−3.88057	−	2.24045i	−0.139575	−	0.0805834i	0.428587	−	0.903501i	$-0.359012\pi$
$773$	−3.88057	−	2.24045i	−0.139575	−	0.0805834i	−0.568161	+	0.822917i	$0.692345\pi$
$774$	−5.97825	−	3.45154i	−0.214884	−	0.124063i
$775$		0			0
$776$	0.793166	−	1.37380i	0.0284730	−	0.0493167i
$777$	−0.248575	−	0.430545i	−0.00891758	−	0.0154457i
$778$	−10.0858	+	5.82306i	−0.361595	+	0.208767i
$779$	−18.3043			−0.655818
$780$		0			0
$781$	−16.6297			−0.595058
$782$	17.3149	−	9.99674i	0.619178	−	0.357483i
$783$	13.3112	+	23.0556i	0.475702	+	0.823941i
$784$	−2.46410	+	4.26795i	−0.0880036	+	0.152427i
$785$		0			0
$786$	−10.2714	−	5.93019i	−0.366368	−	0.211523i
$787$	27.7963	+	16.0482i	0.990830	+	0.572056i	0.905522	−	0.424299i	$-0.139479\pi$
$787$	27.7963	+	16.0482i	0.990830	+	0.572056i	0.0853077	+	0.996355i	$0.472813\pi$
$788$		−	10.8006i		−	0.384755i
$789$	−5.14047	+	8.90355i	−0.183006	+	0.316975i
$790$		0			0
$791$	−9.64355	+	5.56771i	−0.342885	+	0.197965i
$792$	−7.31643			−0.259978
$793$	42.3351	−	15.4979i	1.50336	−	0.550348i
$794$	−0.399804			−0.0141885
$795$		0			0
$796$	−5.50367	−	9.53264i	−0.195072	−	0.337875i
$797$	−11.1083	+	19.2402i	−0.393477	+	0.681522i	−0.992905	−	0.118906i	$-0.962061\pi$
$797$	−11.1083	+	19.2402i	−0.393477	+	0.681522i	0.599429	+	0.800428i	$0.295395\pi$
$798$			3.74265i			0.132488i
$799$	−49.8004	−	28.7522i	−1.76181	−	1.01718i
$800$		0			0
$801$			15.7255i			0.555634i
$802$	−4.25388	+	7.36793i	−0.150210	+	0.260171i
$803$	2.30532	+	3.99292i	0.0813528	+	0.140907i
$804$	2.76993	−	1.59922i	0.0976877	−	0.0564000i
$805$		0			0
$806$	2.57759	−	14.7790i	0.0907918	−	0.520567i
$807$	11.6332			0.409510
$808$	−11.9109	+	6.87676i	−0.419024	+	0.241924i
$809$	5.27410	+	9.13501i	0.185427	+	0.321170i	0.943720	−	0.330744i	$-0.107300\pi$
$809$	5.27410	+	9.13501i	0.185427	+	0.321170i	−0.758293	+	0.651914i	$0.773966\pi$
$810$		0			0
$811$		−	41.6434i		−	1.46230i	−0.682218	−	0.731149i	$-0.738984\pi$
$811$		−	41.6434i		−	1.46230i	0.682218	−	0.731149i	$-0.261016\pi$
$812$	9.80385	+	5.66025i	0.344048	+	0.198636i
$813$	9.54902	+	5.51313i	0.334899	+	0.193354i
$814$			1.59498i			0.0559040i
$815$		0			0
$816$	1.35154	+	2.34094i	0.0473134	+	0.0819493i
$817$	9.81119	−	5.66449i	0.343250	−	0.198176i
$818$	14.0131			0.489958
$819$	−13.4960	−	2.35382i	−0.471587	−	0.0822493i
$820$		0			0
$821$	20.1160	−	11.6140i	0.702053	−	0.405331i	−0.106058	−	0.994360i	$-0.533823\pi$
$821$	20.1160	−	11.6140i	0.702053	−	0.405331i	0.808112	+	0.589029i	$0.200490\pi$
$822$	5.18110	+	8.97392i	0.180711	+	0.313001i
$823$	0.499427	−	0.865033i	0.0174089	−	0.0301531i	−0.857190	−	0.515001i	$-0.827792\pi$
$823$	0.499427	−	0.865033i	0.0174089	−	0.0301531i	0.874599	+	0.484848i	$0.161125\pi$
$824$			5.73205i			0.199685i
$825$		0			0
$826$	−4.31812	−	2.49307i	−0.150247	−	0.0867449i
$827$		−	29.8030i		−	1.03635i	−0.855274	−	0.518175i	$-0.826611\pi$
$827$		−	29.8030i		−	1.03635i	0.855274	−	0.518175i	$-0.173389\pi$
$828$	−5.85945	+	10.1489i	−0.203630	+	0.352698i
$829$	11.8508	+	20.5261i	0.411594	+	0.712902i	0.995064	−	0.0992329i	$-0.0316389\pi$
$829$	11.8508	+	20.5261i	0.411594	+	0.712902i	−0.583470	+	0.812134i	$0.698306\pi$
$830$		0			0
$831$	−16.3458			−0.567030
$832$	−2.76632	−	2.31246i	−0.0959049	−	0.0801702i
$833$	−22.1950			−0.769011
$834$	−1.53158	+	0.884259i	−0.0530343	+	0.0306194i
$835$		0			0
$836$	6.00367	−	10.3987i	0.207641	−	0.359645i
$837$		−	14.0842i		−	0.486822i
$838$	−20.9539	−	12.0977i	−0.723839	−	0.417909i
$839$	−21.2991	−	12.2971i	−0.735327	−	0.424541i	0.0850406	−	0.996377i	$-0.472898\pi$
$839$	−21.2991	−	12.2971i	−0.735327	−	0.424541i	−0.820368	+	0.571836i	$0.806231\pi$
$840$		0			0
$841$	−16.4282	+	28.4545i	−0.566490	+	0.981189i
$842$	−17.8196	−	30.8644i	−0.614104	−	1.06366i
$843$	−15.6359	+	9.02740i	−0.538530	+	0.310920i
$844$	−26.2582			−0.903843
$845$		0			0
$846$	33.7055			1.15882
$847$	4.13615	−	2.38801i	0.142120	−	0.0820529i
$848$	4.78561	+	8.28893i	0.164339	+	0.284643i
$849$	7.64613	−	13.2435i	0.262414	−	0.454515i
$850$		0			0
$851$	2.21245	+	1.27736i	0.0758418	+	0.0437873i
$852$	−3.11871	−	1.80059i	−0.106845	−	0.0616871i
$853$		−	41.7449i		−	1.42932i	−0.699473	−	0.714659i	$-0.746582\pi$
$853$		−	41.7449i		−	1.42932i	0.699473	−	0.714659i	$-0.253418\pi$
$854$	8.99873	−	15.5863i	0.307930	−	0.533351i
$855$		0			0
$856$	−4.05242	+	2.33967i	−0.138509	+	0.0799682i
$857$	−18.7543			−0.640636			−0.320318	−	0.947310i	$-0.603790\pi$
$857$	−18.7543			−0.640636			−0.320318	+	0.947310i	$0.603790\pi$
$858$	−4.60181	−	3.84681i	−0.157103	−	0.131328i
$859$	13.8357			0.472066			0.236033	−	0.971745i	$-0.424153\pi$
$859$	13.8357			0.472066			0.236033	+	0.971745i	$0.424153\pi$
$860$		0			0
$861$	1.82505	+	3.16108i	0.0621976	+	0.107729i
$862$	−2.48022	+	4.29586i	−0.0844765	+	0.146318i
$863$		−	8.00891i		−	0.272626i	−0.990666	−	0.136313i	$-0.956475\pi$
$863$		−	8.00891i		−	0.272626i	0.990666	−	0.136313i	$-0.0435253\pi$
$864$	−2.93146	−	1.69248i	−0.0997304	−	0.0575794i
$865$		0			0
$866$		−	4.21621i		−	0.143273i
$867$	−0.985237	+	1.70648i	−0.0334604	+	0.0579551i
$868$	−2.99449	−	5.18661i	−0.101640	−	0.176045i
$869$	−30.5528	+	17.6397i	−1.03643	+	0.598385i
$870$		0			0
$871$	−18.9282	−	3.30126i	−0.641358	−	0.111859i
$872$	−2.32164			−0.0786208
$873$	−3.62652	+	2.09377i	−0.122739	+	0.0708635i
$874$	−9.61623	−	16.6558i	−0.325274	−	0.563391i
$875$		0			0
$876$			0.998434i			0.0337340i
$877$	−32.5033	−	18.7658i	−1.09756	−	0.633677i	−0.161981	−	0.986794i	$-0.551788\pi$
$877$	−32.5033	−	18.7658i	−1.09756	−	0.633677i	−0.935579	+	0.353117i	$0.885122\pi$
$878$	12.7739	+	7.37500i	0.431097	+	0.248894i
$879$		−	9.94996i		−	0.335604i
$880$		0			0
$881$	6.05808	+	10.4929i	0.204102	+	0.353515i	0.949846	−	0.312717i	$-0.101239\pi$
$881$	6.05808	+	10.4929i	0.204102	+	0.353515i	−0.745744	+	0.666232i	$0.767906\pi$
$882$	11.2664	−	6.50465i	0.379359	−	0.219023i
$883$	−44.4026			−1.49427			−0.747133	−	0.664675i	$-0.768570\pi$
$883$	−44.4026			−1.49427			−0.747133	+	0.664675i	$0.768570\pi$
$884$	2.78998	−	15.9967i	0.0938373	−	0.538029i
$885$		0			0
$886$	−10.5979	+	6.11871i	−0.356044	+	0.205562i
$887$	−3.25714	−	5.64153i	−0.109364	−	0.189424i	0.806149	−	0.591713i	$-0.201548\pi$
$887$	−3.25714	−	5.64153i	−0.109364	−	0.189424i	−0.915513	+	0.402289i	$0.868215\pi$
$888$	−0.172697	+	0.299119i	−0.00579532	+	0.0100378i
$889$		−	23.2090i		−	0.778404i
$890$		0			0
$891$	14.1321	+	8.15917i	0.473443	+	0.273343i
$892$		−	22.2042i		−	0.743452i
$893$	−27.6578	+	47.9048i	−0.925534	+	1.60307i
$894$	−2.12027	−	3.67242i	−0.0709126	−	0.122824i
$895$		0			0
$896$	−1.43937			−0.0480861
$897$	−9.02147	+	3.30256i	−0.301218	+	0.110269i
$898$	19.0714			0.636420
$899$	28.3401	−	16.3622i	0.945197	−	0.545710i
$900$		0			0
$901$	−21.5528	+	37.3306i	−0.718029	+	1.24366i
$902$		−	11.7104i		−	0.389915i
$903$	−1.95648	−	1.12957i	−0.0651075	−	0.0375898i
$904$	6.69982	+	3.86814i	0.222833	+	0.128653i
$905$		0			0
$906$	−4.75135	+	8.22957i	−0.157853	+	0.273409i
$907$	2.96883	+	5.14216i	0.0985784	+	0.170743i	0.911096	−	0.412193i	$-0.135237\pi$
$907$	2.96883	+	5.14216i	0.0985784	+	0.170743i	−0.812518	+	0.582936i	$0.801904\pi$
$908$	−1.80059	+	1.03957i	−0.0597546	+	0.0344993i
$909$	36.3061			1.20420
$910$		0			0
$911$	48.7860			1.61635			0.808177	−	0.588940i	$-0.200455\pi$
$911$	48.7860			1.61635			0.808177	+	0.588940i	$0.200455\pi$
$912$	2.25184	−	1.30010i	0.0745657	−	0.0430505i
$913$	13.9231	+	24.1155i	0.460788	+	0.798108i
$914$	8.05688	−	13.9549i	0.266498	−	0.461588i
$915$		0			0
$916$	4.05242	+	2.33967i	0.133896	+	0.0773048i
$917$	24.6326	+	14.2216i	0.813440	+	0.469640i
$918$		−	15.2448i		−	0.503152i
$919$	14.8564	−	25.7321i	0.490068	−	0.848822i	−0.509867	−	0.860253i	$-0.670305\pi$
$919$	14.8564	−	25.7321i	0.490068	−	0.848822i	0.999935	+	0.0114312i	$0.00363874\pi$
$920$		0			0
$921$	−8.45803	+	4.88325i	−0.278702	+	0.160909i
$922$	−4.84466			−0.159550
$923$	7.43683	+	20.3149i	0.244786	+	0.668672i
$924$	−2.39442			−0.0787706
$925$		0			0
$926$	4.11582	+	7.12881i	0.135254	+	0.234267i
$927$	7.56563	−	13.1041i	0.248488	−	0.430394i
$928$		−	7.86488i		−	0.258177i
$929$	15.6012	+	9.00734i	0.511858	+	0.295521i	0.733597	−	0.679585i	$-0.237840\pi$
$929$	15.6012	+	9.00734i	0.511858	+	0.295521i	−0.221739	+	0.975106i	$0.571173\pi$
$930$		0			0
$931$			21.3502i			0.699724i
$932$	−0.305530	+	0.529194i	−0.0100080	+	0.0173343i
$933$	4.83316	+	8.37128i	0.158231	+	0.274063i
$934$	−29.0008	+	16.7436i	−0.948936	+	0.547868i
$935$		0			0
$936$	3.27191	+	8.93774i	0.106946	+	0.292139i
$937$	−28.9796			−0.946723			−0.473361	−	0.880868i	$-0.656960\pi$
$937$	−28.9796			−0.946723			−0.473361	+	0.880868i	$0.656960\pi$
$938$	−6.64276	+	3.83520i	−0.216894	+	0.125224i
$939$	−3.06586	−	5.31023i	−0.100051	−	0.173293i
$940$		0			0
$941$		−	4.61504i		−	0.150446i	−0.997167	−	0.0752230i	$-0.976033\pi$
$941$		−	4.61504i		−	0.150446i	0.997167	−	0.0752230i	$-0.0239669\pi$
$942$	−6.56386	−	3.78964i	−0.213862	−	0.123473i
$943$	−16.2439	−	9.37844i	−0.528975	−	0.305404i
$944$			3.46410i			0.112747i
$945$		0			0
$946$	3.62395	+	6.27686i	0.117825	+	0.204078i
$947$	−9.18041	+	5.30031i	−0.298323	+	0.172237i	−0.641689	−	0.766965i	$-0.721766\pi$
$947$	−9.18041	+	5.30031i	−0.298323	+	0.172237i	0.343366	+	0.939202i	$0.388433\pi$
$948$	−7.63977			−0.248128
$949$	3.84681	−	4.60181i	0.124873	−	0.149381i
$950$		0			0
$951$	0.106227	−	0.0613304i	0.00344466	−	0.00198878i
$952$	−3.24123	−	5.61398i	−0.105049	−	0.181950i
$953$	−14.3705	+	24.8905i	−0.465508	+	0.806283i	−0.999224	−	0.0393806i	$-0.987462\pi$
$953$	−14.3705	+	24.8905i	−0.465508	+	0.806283i	0.533717	+	0.845663i	$0.320795\pi$
$954$		−	25.2658i		−	0.818010i
$955$		0			0
$956$	−22.2119	−	12.8240i	−0.718384	−	0.414759i
$957$		−	13.0833i		−	0.422925i
$958$	−4.02672	+	6.97448i	−0.130097	+	0.225335i
$959$	−12.4252	−	21.5210i	−0.401230	−	0.694950i
$960$		0			0
$961$	13.6876			0.441534
$962$	1.94842	−	0.713276i	0.0628197	−	0.0229969i
$963$	12.3523			0.398049
$964$	23.4633	−	13.5466i	0.755703	−	0.436305i
$965$		0			0
$966$	−1.91760	+	3.32138i	−0.0616978	+	0.106864i
$967$		−	8.08648i		−	0.260044i	−0.991511	−	0.130022i	$-0.958495\pi$
$967$		−	8.08648i		−	0.260044i	0.991511	−	0.130022i	$-0.0415047\pi$
$968$	−2.87358	−	1.65906i	−0.0923603	−	0.0533242i
$969$	10.1415	+	5.85521i	0.325793	+	0.188097i
$970$		0			0
$971$	−0.302790	+	0.524448i	−0.00971701	+	0.0168304i	−0.870843	−	0.491561i	$-0.836426\pi$
$971$	−0.302790	+	0.524448i	−0.00971701	+	0.0168304i	0.861126	+	0.508392i	$0.169760\pi$
$972$	6.84432	+	11.8547i	0.219532	+	0.380240i
$973$	3.67300	−	2.12061i	0.117751	−	0.0679835i
$974$	−1.62352			−0.0520208
$975$		0			0
$976$	−12.5037			−0.400233
$977$	−42.4727	+	24.5216i	−1.35882	+	0.784516i	−0.989465	−	0.144772i	$-0.953755\pi$
$977$	−42.4727	+	24.5216i	−1.35882	+	0.784516i	−0.369356	+	0.929288i	$0.620422\pi$
$978$	5.51236	+	9.54769i	0.176266	+	0.305302i
$979$	8.25551	−	14.2990i	0.263847	−	0.456997i
$980$		0			0
$981$	5.30752	+	3.06430i	0.169456	+	0.0978355i
$982$	−8.93796	−	5.16033i	−0.285222	−	0.164673i
$983$			30.7684i			0.981358i	0.871340	+	0.490679i	$0.163251\pi$
$983$			30.7684i			0.981358i	−0.871340	+	0.490679i	$0.836749\pi$
$984$	1.26795	−	2.19615i	0.0404207	−	0.0700108i
$985$		0			0
$986$	30.6754	−	17.7104i	0.976902	−	0.564015i
$987$	11.0307			0.351110
$988$	−15.3879	−	2.68379i	−0.489553	−	0.0853827i
$989$	11.6091			0.369149
$990$		0			0
$991$	−7.74435	−	13.4136i	−0.246007	−	0.426097i	0.716407	−	0.697683i	$-0.245785\pi$
$991$	−7.74435	−	13.4136i	−0.246007	−	0.426097i	−0.962414	+	0.271585i	$0.912452\pi$
$992$	−2.08041	+	3.60338i	−0.0660531	+	0.114407i
$993$		−	11.4429i		−	0.363129i
$994$	7.47921	+	4.31812i	0.237226	+	0.136962i
$995$		0			0
$996$			6.03011i			0.191071i
$997$	−3.91111	+	6.77423i	−0.123866	+	0.214542i	−0.921289	−	0.388878i	$-0.872863\pi$
$997$	−3.91111	+	6.77423i	−0.123866	+	0.214542i	0.797423	+	0.603421i	$0.206196\pi$
$998$	6.99033	+	12.1076i	0.221275	+	0.383260i
$999$	1.68696	−	0.973969i	0.0533731	−	0.0308150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.m.c.101.1		8
5.2	odd	4		650.2.n.d.49.2		8
5.3	odd	4		650.2.n.e.49.3		8
5.4	even	2		130.2.l.b.101.4	✓	8
13.2	odd	12		8450.2.a.ci.1.3		4
13.4	even	6	inner	650.2.m.c.251.1		8
13.11	odd	12		8450.2.a.cm.1.3		4
15.14	odd	2		1170.2.bs.g.361.2		8
20.19	odd	2		1040.2.da.d.881.2		8
65.4	even	6		130.2.l.b.121.4	yes	8
65.9	even	6		1690.2.l.j.1161.2		8
65.17	odd	12		650.2.n.e.199.3		8
65.19	odd	12		1690.2.e.s.191.3		8
65.24	odd	12		1690.2.a.t.1.2		4
65.29	even	6		1690.2.d.k.1351.6		8
65.34	odd	4		1690.2.e.t.991.3		8
65.43	odd	12		650.2.n.d.199.2		8
65.44	odd	4		1690.2.e.s.991.3		8
65.49	even	6		1690.2.d.k.1351.2		8
65.54	odd	12		1690.2.a.u.1.2		4
65.59	odd	12		1690.2.e.t.191.3		8
65.64	even	2		1690.2.l.j.361.2		8
195.134	odd	6		1170.2.bs.g.901.2		8
260.199	odd	6		1040.2.da.d.641.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.4	✓	8	5.4	even	2
130.2.l.b.121.4	yes	8	65.4	even	6
650.2.m.c.101.1		8	1.1	even	1	trivial
650.2.m.c.251.1		8	13.4	even	6	inner
650.2.n.d.49.2		8	5.2	odd	4
650.2.n.d.199.2		8	65.43	odd	12
650.2.n.e.49.3		8	5.3	odd	4
650.2.n.e.199.3		8	65.17	odd	12
1040.2.da.d.641.2		8	260.199	odd	6
1040.2.da.d.881.2		8	20.19	odd	2
1170.2.bs.g.361.2		8	15.14	odd	2
1170.2.bs.g.901.2		8	195.134	odd	6
1690.2.a.t.1.2		4	65.24	odd	12
1690.2.a.u.1.2		4	65.54	odd	12
1690.2.d.k.1351.2		8	65.49	even	6
1690.2.d.k.1351.6		8	65.29	even	6
1690.2.e.s.191.3		8	65.19	odd	12
1690.2.e.s.991.3		8	65.44	odd	4
1690.2.e.t.191.3		8	65.59	odd	12
1690.2.e.t.991.3		8	65.34	odd	4
1690.2.l.j.361.2		8	65.64	even	2
1690.2.l.j.1161.2		8	65.9	even	6
8450.2.a.ci.1.3		4	13.2	odd	12
8450.2.a.cm.1.3		4	13.11	odd	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.300098 - 0.519785i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.519785 + 0.300098i) q^{6} +(-1.24653 - 0.719687i) q^{7} +1.00000i q^{8} +(1.31988 - 2.28610i) q^{9} +(-2.40029 + 1.38581i) q^{11} -0.600196 q^{12} +(2.76632 + 2.31246i) q^{13} +1.43937 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.25184 - 3.90029i) q^{17} +2.63977i q^{18} +(-3.75184 - 2.16612i) q^{19} +0.863906i q^{21} +(1.38581 - 2.40029i) q^{22} +(-2.21969 - 3.84461i) q^{23} +(0.519785 - 0.300098i) q^{24} +(-3.55193 - 0.619491i) q^{26} -3.38496 q^{27} +(-1.24653 + 0.719687i) q^{28} +(-3.93244 - 6.81119i) q^{29} +4.16082i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.44065 + 0.831757i) q^{33} +4.50367i q^{34} +(-1.31988 - 2.28610i) q^{36} +(-0.498370 + 0.287734i) q^{37} +4.33225 q^{38} +(0.371816 - 2.13186i) q^{39} +(3.65906 - 2.11256i) q^{41} +(-0.431953 - 0.748164i) q^{42} +(-1.30752 + 2.26469i) q^{43} +2.77162i q^{44} +(3.84461 + 2.21969i) q^{46} -12.7684i q^{47} +(-0.300098 + 0.519785i) q^{48} +(-2.46410 - 4.26795i) q^{49} -2.70308 q^{51} +(3.38581 - 1.23947i) q^{52} -9.57123 q^{53} +(2.93146 - 1.69248i) q^{54} +(0.719687 - 1.24653i) q^{56} +2.60020i q^{57} +(6.81119 + 3.93244i) q^{58} +(-3.00000 - 1.73205i) q^{59} +(6.25184 - 10.8285i) q^{61} +(-2.08041 - 3.60338i) q^{62} +(-3.29056 + 1.89980i) q^{63} -1.00000 q^{64} -1.66351 q^{66} +(-4.61504 + 2.66449i) q^{67} +(-2.25184 - 3.90029i) q^{68} +(-1.33225 + 2.30752i) q^{69} +(5.19615 + 3.00000i) q^{71} +(2.28610 + 1.31988i) q^{72} -1.66351i q^{73} +(0.287734 - 0.498370i) q^{74} +(-3.75184 + 2.16612i) q^{76} +3.98940 q^{77} +(0.743926 + 2.03215i) q^{78} +12.7288 q^{79} +(-2.94383 - 5.09886i) q^{81} +(-2.11256 + 3.65906i) q^{82} -10.0469i q^{83} +(0.748164 + 0.431953i) q^{84} -2.61504i q^{86} +(-2.36023 + 4.08805i) q^{87} +(-1.38581 - 2.40029i) q^{88} +(-5.15906 + 2.97859i) q^{89} +(-1.78406 - 4.87345i) q^{91} -4.43937 q^{92} +(2.16273 - 1.24865i) q^{93} +(6.38418 + 11.0577i) q^{94} -0.600196i q^{96} +(-1.37380 - 0.793166i) q^{97} +(4.26795 + 2.46410i) q^{98} +7.31643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} - 6 q^{11} + 4 q^{12} + 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} - 6 q^{22} - 12 q^{23} - 6 q^{24} - 40 q^{27} + 42 q^{33} + 4 q^{36} + 30 q^{37} + 12 q^{38}+ \cdots + 48 q^{98}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 - 6 * q^11 + 4 * q^12 + 2 * q^13 - 4 * q^16 - 6 * q^17 - 6 * q^19 - 6 * q^22 - 12 * q^23 - 6 * q^24 - 40 * q^27 + 42 * q^33 + 4 * q^36 + 30 * q^37 + 12 * q^38 - 40 * q^39 + 12 * q^41 + 6 * q^42 - 4 * q^43 + 2 * q^48 + 8 * q^49 + 10 * q^52 - 60 * q^53 + 36 * q^54 - 24 * q^59 + 26 * q^61 - 18 * q^62 - 12 * q^63 - 8 * q^64 - 12 * q^66 - 24 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^72 + 6 * q^74 - 6 * q^76 + 60 * q^77 + 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 48 * q^87 + 6 * q^88 - 24 * q^89 - 66 * q^91 - 24 * q^92 - 48 * q^93 + 6 * q^97 + 48 * q^98

Introduction

L-functions

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