LMFDB - Embedded newform 650.2.m.c.251.1

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			251.1
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	650.251
Dual form			650.2.m.c.101.1

$q$-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 $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

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

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	−0.939558	−	0.342389i	$-0.888764\pi$
$3$	−0.300098	+	0.519785i	−0.173262	+	0.300098i	0.766297	+	0.642487i	$0.222097\pi$
$4$	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	−0.716719	−	0.697362i	$-0.754357\pi$
$7$	−1.24653	+	0.719687i	−0.471146	+	0.272016i	0.245574	+	0.969378i	$0.421024\pi$
$8$		−	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	0.0924030	−	0.995722i	$-0.470545\pi$
$11$	−2.40029	−	1.38581i	−0.723716	−	0.417837i	−0.816119	+	0.577884i	$0.803879\pi$
$12$	−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	0.998534	+	0.0541365i	$0.0172406\pi$
$17$	2.25184	+	3.90029i	0.546150	+	0.945960i	−0.452383	+	0.891824i	$0.649426\pi$
$18$		−	2.63977i		−	0.622199i
$19$	−3.75184	+	2.16612i	−0.860730	+	0.496943i	−0.864257	−	0.503051i	$-0.832211\pi$
$19$	−3.75184	+	2.16612i	−0.860730	+	0.496943i	0.00352661	+	0.999994i	$0.498877\pi$
$20$		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	−0.999101	−	0.0423934i	$-0.986502\pi$
$23$	−2.21969	+	3.84461i	−0.462837	+	0.801657i	0.536264	+	0.844050i	$0.319835\pi$
$24$	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	0.226546	+	0.974000i	$0.427257\pi$
$29$	−3.93244	+	6.81119i	−0.730236	+	1.26481i	−0.956782	+	0.290806i	$0.906077\pi$
$30$		0			0
$31$		−	4.16082i		−	0.747306i	−0.927569	−	0.373653i	$-0.878105\pi$
$31$		−	4.16082i		−	0.747306i	0.927569	−	0.373653i	$-0.121895\pi$
$32$	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	0.458475	−	0.888708i	$-0.348396\pi$
$37$	−0.498370	−	0.287734i	−0.0819315	−	0.0473032i	−0.540406	+	0.841404i	$0.681729\pi$
$38$	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	0.757728	−	0.652571i	$-0.226309\pi$
$41$	3.65906	+	2.11256i	0.571449	+	0.329926i	−0.186279	+	0.982497i	$0.559643\pi$
$42$	−0.431953	+	0.748164i	−0.0666518	+	0.115444i
$43$	−1.30752	−	2.26469i	−0.199395	−	0.345362i	0.748938	−	0.662641i	$-0.230564\pi$
$43$	−1.30752	−	2.26469i	−0.199395	−	0.345362i	−0.948332	+	0.317279i	$0.897231\pi$
$44$		−	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	$0.381262\pi$
$47$			12.7684i			1.86246i	−0.364436	+	0.931228i	$0.618738\pi$
$48$	−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	−0.682406	−	0.730974i	$-0.739066\pi$
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	0.291839	+	0.956467i	$0.405733\pi$
$60$		0			0
$61$	6.25184	+	10.8285i	0.800466	+	1.38645i	0.919310	+	0.393534i	$0.128748\pi$
$61$	6.25184	+	10.8285i	0.800466	+	1.38645i	−0.118845	+	0.992913i	$0.537919\pi$
$62$	−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	0.190859	−	0.981617i	$-0.438873\pi$
$67$	−4.61504	−	2.66449i	−0.563817	−	0.325520i	−0.754676	+	0.656098i	$0.772206\pi$
$68$	−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	−0.158901	−	0.987294i	$-0.550795\pi$
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	0.775571	+	0.631260i	$0.217462\pi$
$72$	2.28610	−	1.31988i	0.269420	−	0.155550i
$73$			1.66351i			0.194700i	0.995250	+	0.0973498i	$0.0310366\pi$
$73$			1.66351i			0.194700i	−0.995250	+	0.0973498i	$0.968963\pi$
$74$	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	$0.185905\pi$
$83$			10.0469i			1.10279i	−0.834244	+	0.551396i	$0.814095\pi$
$84$	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	0.200995	−	0.979592i	$-0.435583\pi$
$89$	−5.15906	−	2.97859i	−0.546859	−	0.315729i	−0.747854	+	0.663863i	$0.768916\pi$
$90$		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	−0.568120	−	0.822946i	$-0.692329\pi$
$97$	−1.37380	+	0.793166i	−0.139489	+	0.0805338i	0.428632	+	0.903479i	$0.358996\pi$
$98$	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	−0.289405	−	0.957207i	$-0.593457\pi$
$101$	6.87676	−	11.9109i	0.684263	−	1.18518i	0.973668	−	0.227972i	$-0.0732093\pi$
$102$	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	−0.730490	−	0.682924i	$-0.760708\pi$
$107$	2.33967	−	4.05242i	0.226184	−	0.391762i	0.956674	+	0.291161i	$0.0940415\pi$
$108$	−1.69248	−	2.93146i	−0.162859	−	0.282080i
$109$		−	2.32164i		−	0.222373i	−0.993800	−	0.111187i	$-0.964535\pi$
$109$		−	2.32164i		−	0.222373i	0.993800	−	0.111187i	$-0.0354651\pi$
$110$		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	0.988596	−	0.150589i	$-0.0481170\pi$
$113$	3.86814	+	6.69982i	0.363884	+	0.630266i	−0.624712	+	0.780855i	$0.714784\pi$
$114$	−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	−0.247401	−	0.968913i	$-0.579577\pi$
$127$	8.06218	−	13.9641i	0.715403	−	1.23911i	0.962804	−	0.270201i	$-0.0870900\pi$
$128$	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	0.301036	−	0.953613i	$-0.402668\pi$
$137$	14.9517	−	8.63234i	1.27741	−	0.737511i	0.976371	+	0.216102i	$0.0693344\pi$
$138$			2.66449i			0.226817i
$139$	−1.47328	−	2.55180i	−0.124962	−	0.216441i	0.796756	−	0.604301i	$-0.206548\pi$
$139$	−1.47328	−	2.55180i	−0.124962	−	0.216441i	−0.921718	+	0.387860i	$0.873214\pi$
$140$		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	−0.729235	−	0.684263i	$-0.760124\pi$
$149$	−6.11871	+	3.53264i	−0.501264	+	0.289405i	0.227971	+	0.973668i	$0.426791\pi$
$150$		0			0
$151$		−	15.8327i		−	1.28844i	−0.764839	−	0.644222i	$-0.777181\pi$
$151$		−	15.8327i		−	1.28844i	0.764839	−	0.644222i	$-0.222819\pi$
$152$	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	0.275677	−	0.961250i	$-0.411098\pi$
$163$	15.9076	−	9.18428i	1.24598	−	0.719368i	0.970306	+	0.241882i	$0.0777648\pi$
$164$			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	−0.449728	−	0.893166i	$-0.648479\pi$
$167$	−18.7135	−	10.8043i	−1.44810	−	0.836059i	−0.998368	+	0.0571070i	$0.981812\pi$
$168$	−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	0.780182	−	0.625553i	$-0.215127\pi$
$173$	−1.99470	−	3.45492i	−0.151654	−	0.262673i	−0.931836	+	0.362880i	$0.881793\pi$
$174$			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	−0.532867	−	0.846199i	$-0.678885\pi$
$179$	6.23996	−	10.8079i	0.466397	−	0.807823i	0.999263	+	0.0383766i	$0.0122186\pi$
$180$		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	0.979864	+	0.199666i	$0.0639858\pi$
$191$	9.16074	+	15.8669i	0.662848	+	1.14809i	−0.317016	+	0.948420i	$0.602681\pi$
$192$	0.300098	−	0.519785i	0.0216577	−	0.0375122i
$193$	−4.10811	−	2.37182i	−0.295708	−	0.170727i	0.344805	−	0.938674i	$-0.387945\pi$
$193$	−4.10811	−	2.37182i	−0.295708	−	0.170727i	−0.640513	+	0.767947i	$0.721278\pi$
$194$	1.58633			0.113892
$195$		0			0
$196$	−4.92820			−0.352015
$197$	9.35358	+	5.40029i	0.666415	+	0.384755i	0.794717	−	0.606980i	$-0.207619\pi$
$197$	9.35358	+	5.40029i	0.666415	+	0.384755i	−0.128302	+	0.991735i	$0.540953\pi$
$198$	−3.65821	+	6.33621i	−0.259978	+	0.450295i
$199$	5.50367	+	9.53264i	0.390145	+	0.675751i	0.992468	−	0.122501i	$-0.0390916\pi$
$199$	5.50367	+	9.53264i	0.390145	+	0.675751i	−0.602323	+	0.798252i	$0.705758\pi$
$200$		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	−0.0813811	+	0.996683i	$0.525933\pi$
$211$	−13.1291	+	22.7402i	−0.903843	+	1.56550i	−0.822462	+	0.568820i	$0.807400\pi$
$212$	−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	0.978243	−	0.207463i	$-0.0665205\pi$
$223$	19.2294	+	11.1021i	1.28770	+	0.743452i	0.309454	+	0.950915i	$0.399854\pi$
$224$	−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	−0.558563	−	0.829462i	$-0.688647\pi$
$227$	−1.80059	+	1.03957i	−0.119509	+	0.0689986i	0.439054	+	0.898461i	$0.355314\pi$
$228$	2.25184	−	1.30010i	0.149131	−	0.0861011i
$229$		−	4.67933i		−	0.309219i	−0.987976	−	0.154610i	$-0.950588\pi$
$229$		−	4.67933i		−	0.309219i	0.987976	−	0.154610i	$-0.0494120\pi$
$230$		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	$0.311385\pi$
$239$			25.6481i			1.65904i	−0.558479	+	0.829518i	$0.688615\pi$
$240$		0			0
$241$	23.4633	−	13.5466i	1.51141	−	0.872610i	0.511494	−	0.859287i	$-0.329092\pi$
$241$	23.4633	−	13.5466i	1.51141	−	0.872610i	0.999911	−	0.0133234i	$-0.00424108\pi$
$242$			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	0.888777	−	0.458339i	$-0.151555\pi$
$251$	0.751836	+	1.30222i	0.0474554	+	0.0821952i	−0.841322	+	0.540534i	$0.818222\pi$
$252$		−	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	−0.352076	−	0.935971i	$-0.614524\pi$
$257$	10.1724	−	17.6191i	0.634537	−	1.09905i	0.986613	−	0.163079i	$-0.0521425\pi$
$258$	−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	0.471343	+	0.881950i	$0.343769\pi$
$263$	−8.56466	+	14.8344i	−0.528119	+	0.914729i	−0.999463	+	0.0327796i	$0.989564\pi$
$264$	−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	−0.994114	−	0.108342i	$-0.965446\pi$
$269$	−9.69121	−	16.7857i	−0.590883	−	1.02344i	0.403230	−	0.915099i	$-0.367887\pi$
$270$		0			0
$271$	−15.9098	−	9.18555i	−0.966454	−	0.557982i	−0.0683006	−	0.997665i	$-0.521758\pi$
$271$	−15.9098	−	9.18555i	−0.966454	−	0.557982i	−0.898153	+	0.439682i	$0.855091\pi$
$272$	−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	0.907028	+	0.421069i	$0.138345\pi$
$277$	13.6171	+	23.5855i	0.818171	+	1.41711i	−0.0888576	+	0.996044i	$0.528322\pi$
$278$			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	$0.354443\pi$
$281$			30.0815i			1.79451i	−0.441509	+	0.897257i	$0.645557\pi$
$282$	3.83176	+	6.63680i	0.228178	+	0.395216i
$283$	12.7394	−	22.0653i	0.757278	−	1.31164i	−0.186955	−	0.982368i	$-0.559862\pi$
$283$	12.7394	−	22.0653i	0.757278	−	1.31164i	0.944234	−	0.329276i	$-0.106805\pi$
$284$	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	−0.0180985	−	0.999836i	$-0.505761\pi$
$293$	14.3568	−	8.28893i	0.838736	−	0.484244i	0.856834	+	0.515592i	$0.172428\pi$
$294$			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	$0.153713\pi$
$307$			16.2722i			0.928703i	−0.885651	+	0.464351i	$0.846287\pi$
$308$	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	$-0.998173\pi$
$317$		−	0.204368i		−	0.0114785i	0.999984	−	0.00573923i	$-0.00182686\pi$
$318$	−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	0.0278926	−	0.999611i	$-0.491120\pi$
$331$	16.5110	−	9.53264i	0.907527	−	0.523961i	0.879635	+	0.475650i	$0.157787\pi$
$332$	−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	0.998837	−	0.0482211i	$-0.0153552\pi$
$347$	8.52522	+	14.7661i	0.457658	+	0.792686i	−0.541179	+	0.840907i	$0.682022\pi$
$348$	2.36023	−	4.08805i	0.126522	−	0.219142i
$349$	18.3917	+	10.6185i	0.984488	+	0.568394i	0.903622	−	0.428331i	$-0.140898\pi$
$349$	18.3917	+	10.6185i	0.984488	+	0.568394i	0.0808657	+	0.996725i	$0.474232\pi$
$350$		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	0.0831659	−	0.996536i	$-0.473497\pi$
$353$	−13.8710	−	8.00840i	−0.738276	−	0.426244i	−0.821442	+	0.570292i	$0.806830\pi$
$354$	−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	$0.221024\pi$
$359$			24.2487i			1.27980i	−0.768459	+	0.639899i	$0.778976\pi$
$360$		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	0.156648	+	0.987655i	$0.449931\pi$
$367$	−14.8854	+	25.7822i	−0.777010	+	1.34582i	−0.933658	+	0.358167i	$0.883402\pi$
$368$	−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	0.954776	+	0.297326i	$0.0960949\pi$
$373$	14.1929	+	24.5828i	0.734880	+	1.27285i	−0.219896	+	0.975523i	$0.570572\pi$
$374$	−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	−0.290137	−	0.956985i	$-0.593701\pi$
$379$	−24.6070	−	14.2069i	−1.26398	−	0.729759i	−0.973842	+	0.227226i	$0.927034\pi$
$380$		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	−0.277452	−	0.960739i	$-0.589490\pi$
$383$	8.13827	−	4.69863i	0.415846	−	0.240089i	0.693298	+	0.720651i	$0.256157\pi$
$384$	−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	−0.491286	−	0.870998i	$-0.663473\pi$
$397$	0.346241	−	0.199902i	0.0173773	−	0.0100328i	0.508663	+	0.860965i	$0.330140\pi$
$398$		−	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	0.672557	−	0.740046i	$-0.265196\pi$
$401$	7.36793	+	4.25388i	0.367937	+	0.212428i	−0.304620	+	0.952474i	$0.598529\pi$
$402$	−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	−0.769071	−	0.639164i	$-0.779281\pi$
$409$	−12.1357	+	7.00657i	−0.600074	+	0.346453i	0.168997	+	0.985617i	$0.445947\pi$
$410$		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	−0.403084	−	0.915163i	$-0.632062\pi$
$419$	12.0977	−	20.9539i	0.591012	−	1.02366i	0.994096	−	0.108500i	$-0.0346048\pi$
$420$		0			0
$421$		−	35.6392i		−	1.73695i	−0.495735	−	0.868474i	$-0.665101\pi$
$421$		−	35.6392i		−	1.73695i	0.495735	−	0.868474i	$-0.334899\pi$
$422$	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	0.599881	−	0.800089i	$-0.295215\pi$
$431$	4.29586	+	2.48022i	0.206924	+	0.119468i	−0.392957	+	0.919557i	$0.628548\pi$
$432$	1.69248	−	2.93146i	0.0814295	−	0.141040i
$433$	−2.10811	−	3.65135i	−0.101309	−	0.175472i	0.810915	−	0.585164i	$-0.198970\pi$
$433$	−2.10811	−	3.65135i	−0.101309	−	0.175472i	−0.912224	+	0.409691i	$0.865636\pi$
$434$		−	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	−0.986598	−	0.163170i	$-0.947828\pi$
$439$	−7.37500	+	12.7739i	−0.351989	+	0.609664i	0.634608	+	0.772834i	$0.281161\pi$
$440$		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	−0.836236	−	0.548370i	$-0.815249\pi$
$449$	−16.5163	+	9.53569i	−0.779452	+	0.450017i	0.0567839	+	0.998386i	$0.481915\pi$
$450$		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	0.136738	−	0.990607i	$-0.456338\pi$
$457$	−13.9549	−	8.05688i	−0.652784	−	0.376885i	−0.789522	+	0.613722i	$0.789671\pi$
$458$	−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	−0.399104	−	0.916906i	$-0.630679\pi$
$461$	4.19560	−	2.42233i	0.195408	−	0.112819i	0.594512	+	0.804087i	$0.297345\pi$
$462$	2.07363	−	1.19721i	0.0964739	−	0.0556992i
$463$			8.23164i			0.382557i	0.981536	+	0.191278i	$0.0612633\pi$
$463$			8.23164i			0.382557i	−0.981536	+	0.191278i	$0.938737\pi$
$464$	−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	0.650800	−	0.759249i	$-0.274433\pi$
$479$	6.97448	+	4.02672i	0.318672	+	0.183985i	−0.332128	+	0.943234i	$0.607767\pi$
$480$		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	−0.467806	−	0.883831i	$-0.654955\pi$
$487$	1.40601	−	0.811758i	0.0637122	−	0.0367842i	0.531518	+	0.847047i	$0.321622\pi$
$488$	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	−0.725773	−	0.687935i	$-0.758518\pi$
$491$	5.16033	−	8.93796i	0.232883	−	0.403364i	0.958655	+	0.284570i	$0.0918509\pi$
$492$	−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	$0.101311\pi$
$499$			13.9807i			0.625860i	−0.949776	+	0.312930i	$0.898689\pi$
$500$		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	0.999377	+	0.0352988i	$0.0112383\pi$
$503$	11.8924	+	20.5983i	0.530258	+	0.918434i	−0.469119	+	0.883135i	$0.655428\pi$
$504$	−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	−0.0805958	−	0.996747i	$-0.525682\pi$
$509$	−22.2023	−	12.8185i	−0.984102	−	0.568171i	−0.903506	+	0.428575i	$0.859016\pi$
$510$		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	−0.970737	−	0.240146i	$-0.922805\pi$
$523$	−6.34383	+	10.9878i	−0.277396	+	0.480464i	0.693341	+	0.720610i	$0.256138\pi$
$524$	−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	$0.359347\pi$
$541$			42.0507i			1.80790i	−0.427636	+	0.903951i	$0.640653\pi$
$542$	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	0.347905	−	0.937530i	$-0.386893\pi$
$557$	−6.84583	−	3.95244i	−0.290067	−	0.167470i	−0.637972	+	0.770059i	$0.720227\pi$
$558$	−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	0.691645	−	0.722238i	$-0.256886\pi$
$563$	−6.63553	−	11.4931i	−0.279654	−	0.484375i	−0.971299	+	0.237863i	$0.923553\pi$
$564$		−	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	0.0412443	−	0.999149i	$-0.486868\pi$
$569$	21.1323	−	36.6022i	0.885911	−	1.53444i	0.844666	−	0.535293i	$-0.179799\pi$
$570$		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	$-0.798138\pi$
$577$		−	28.4651i		−	1.18502i	0.805564	−	0.592508i	$-0.201862\pi$
$578$	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	0.0483779	−	0.998829i	$-0.484595\pi$
$587$	−19.1994	−	11.0848i	−0.792445	−	0.457518i	−0.840822	+	0.541311i	$0.817928\pi$
$588$	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	$-0.936265\pi$
$593$		−	9.68683i		−	0.397791i	0.980021	−	0.198895i	$-0.0637354\pi$
$594$	−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	−0.714341	−	0.699798i	$-0.753273\pi$
$601$	6.10117	−	10.5675i	0.248872	−	0.431059i	0.963213	+	0.268739i	$0.0866068\pi$
$602$	−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	0.748748	−	0.662854i	$-0.230655\pi$
$607$	−4.91946	−	8.52075i	−0.199675	−	0.345847i	−0.948423	+	0.317008i	$0.897322\pi$
$608$	−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	0.209782	−	0.977748i	$-0.432725\pi$
$613$	−13.1737	−	7.60586i	−0.532082	−	0.307198i	−0.741864	+	0.670551i	$0.766058\pi$
$614$	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	−0.00853345	−	0.999964i	$-0.502716\pi$
$617$	21.1929	−	12.2357i	0.853194	−	0.492592i	0.861727	+	0.507372i	$0.169383\pi$
$618$	2.97943	−	1.72018i	0.119850	−	0.0691956i
$619$		−	42.4157i		−	1.70483i	−0.522864	−	0.852416i	$-0.675136\pi$
$619$		−	42.4157i		−	1.70483i	0.522864	−	0.852416i	$-0.324864\pi$
$620$		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	−0.500487	−	0.865744i	$-0.666846\pi$
$631$	−0.0244657	+	0.0141253i	−0.000973964	+	0.000562318i	0.499513	+	0.866306i	$0.333512\pi$
$632$		−	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	0.980511	−	0.196462i	$-0.0629453\pi$
$641$	8.10465	+	14.0377i	0.320114	+	0.554454i	−0.660397	+	0.750917i	$0.729612\pi$
$642$		−	2.80852i		−	0.110843i
$643$	−15.7718	+	9.10586i	−0.621979	+	0.359100i	−0.777639	−	0.628711i	$-0.783583\pi$
$643$	−15.7718	+	9.10586i	−0.621979	+	0.359100i	0.155660	+	0.987811i	$0.450250\pi$
$644$	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	−0.787488	−	0.616330i	$-0.788619\pi$
$647$	3.56139	−	6.16852i	0.140013	−	0.242509i	0.927501	+	0.373820i	$0.121952\pi$
$648$	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	−0.979321	−	0.202313i	$-0.935154\pi$
$653$	−8.03546	+	13.9178i	−0.314452	+	0.544647i	0.664869	+	0.746960i	$0.268487\pi$
$654$	−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	−0.850979	−	0.525200i	$-0.823990\pi$
$659$	−22.5988	−	39.1423i	−0.880326	−	1.52477i	−0.0293473	−	0.999569i	$-0.509343\pi$
$660$		0			0
$661$	−7.63354	−	4.40723i	−0.296910	−	0.171421i	0.344144	−	0.938917i	$-0.388169\pi$
$661$	−7.63354	−	4.40723i	−0.296910	−	0.171421i	−0.641054	+	0.767496i	$0.721503\pi$
$662$	−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	0.121775	+	0.992558i	$0.461141\pi$
$673$	−20.7199	+	35.8879i	−0.798693	+	1.38338i	−0.920468	+	0.390819i	$0.872192\pi$
$674$	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	−0.826095	−	0.563531i	$-0.809443\pi$
$683$	−19.6297	+	11.3332i	−0.751110	+	0.433654i	0.0749846	+	0.997185i	$0.476109\pi$
$684$		−	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	0.922355	−	0.386343i	$-0.126262\pi$
$691$	27.5736	+	15.9196i	1.04895	+	0.605612i	0.126595	+	0.991954i	$0.459595\pi$
$692$	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	−0.274131	−	0.961692i	$-0.588390\pi$
$709$	11.2274	−	6.48212i	0.421653	−	0.243441i	0.695784	+	0.718251i	$0.255057\pi$
$710$		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	0.978979	+	0.203963i	$0.0653821\pi$
$719$	17.8616	+	30.9372i	0.666126	+	1.15376i	−0.312853	+	0.949802i	$0.601285\pi$
$720$		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	$-0.837675\pi$
$733$		−	26.4319i		−	0.976284i	0.872764	−	0.488142i	$-0.162325\pi$
$734$	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	−0.00480000	−	0.999988i	$-0.501528\pi$
$739$	−23.7380	−	13.7051i	−0.873215	−	0.504151i	−0.868415	+	0.495837i	$0.834861\pi$
$740$		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	0.986833	−	0.161742i	$-0.0517113\pi$
$743$	36.5306	+	21.0909i	1.34018	+	0.773751i	0.353344	+	0.935494i	$0.385045\pi$
$744$	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	−0.634082	−	0.773266i	$-0.718622\pi$
$751$	9.66351	−	16.7377i	0.352627	−	0.610767i	0.986709	+	0.162498i	$0.0519552\pi$
$752$	−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	−0.989402	−	0.145200i	$-0.953618\pi$
$757$	−10.1513	+	17.5825i	−0.368955	+	0.639048i	0.620448	+	0.784248i	$0.286951\pi$
$758$	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	−0.993289	−	0.115656i	$-0.963103\pi$
$761$	−38.3386	+	22.1348i	−1.38977	+	0.802386i	−0.396484	+	0.918042i	$0.629770\pi$
$762$		−	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	0.557263	−	0.830336i	$-0.311852\pi$
$769$	3.23903	+	1.87005i	0.116802	+	0.0674359i	−0.440461	+	0.897772i	$0.645185\pi$
$770$		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	−0.568161	−	0.822917i	$-0.692345\pi$
$773$	−3.88057	+	2.24045i	−0.139575	+	0.0805834i	0.428587	+	0.903501i	$0.359012\pi$
$774$	−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	0.0853077	−	0.996355i	$-0.472813\pi$
$787$	27.7963	−	16.0482i	0.990830	−	0.572056i	0.905522	+	0.424299i	$0.139479\pi$
$788$			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	0.599429	−	0.800428i	$-0.295395\pi$
$797$	−11.1083	−	19.2402i	−0.393477	−	0.681522i	−0.992905	+	0.118906i	$0.962061\pi$
$798$		−	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	−0.758293	−	0.651914i	$-0.773966\pi$
$809$	5.27410	−	9.13501i	0.185427	−	0.321170i	0.943720	+	0.330744i	$0.107300\pi$
$810$		0			0
$811$			41.6434i			1.46230i	0.682218	+	0.731149i	$0.261016\pi$
$811$			41.6434i			1.46230i	−0.682218	+	0.731149i	$0.738984\pi$
$812$	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	0.808112	−	0.589029i	$-0.200490\pi$
$821$	20.1160	+	11.6140i	0.702053	+	0.405331i	−0.106058	+	0.994360i	$0.533823\pi$
$822$	5.18110	−	8.97392i	0.180711	−	0.313001i
$823$	0.499427	+	0.865033i	0.0174089	+	0.0301531i	0.874599	−	0.484848i	$-0.161125\pi$
$823$	0.499427	+	0.865033i	0.0174089	+	0.0301531i	−0.857190	+	0.515001i	$0.827792\pi$
$824$		−	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	$0.173389\pi$
$827$			29.8030i			1.03635i	−0.855274	+	0.518175i	$0.826611\pi$
$828$	−5.85945	−	10.1489i	−0.203630	−	0.352698i
$829$	11.8508	−	20.5261i	0.411594	−	0.712902i	−0.583470	−	0.812134i	$-0.698306\pi$
$829$	11.8508	−	20.5261i	0.411594	−	0.712902i	0.995064	+	0.0992329i	$0.0316389\pi$
$830$		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	−0.820368	−	0.571836i	$-0.806231\pi$
$839$	−21.2991	+	12.2971i	−0.735327	+	0.424541i	0.0850406	+	0.996377i	$0.472898\pi$
$840$		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	$0.253418\pi$
$853$			41.7449i			1.42932i	−0.699473	+	0.714659i	$0.746582\pi$
$854$	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	$0.0435253\pi$
$863$			8.00891i			0.272626i	−0.990666	+	0.136313i	$0.956475\pi$
$864$	−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	−0.935579	−	0.353117i	$-0.885122\pi$
$877$	−32.5033	+	18.7658i	−1.09756	+	0.633677i	−0.161981	+	0.986794i	$0.551788\pi$
$878$	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	−0.745744	−	0.666232i	$-0.767906\pi$
$881$	6.05808	−	10.4929i	0.204102	−	0.353515i	0.949846	+	0.312717i	$0.101239\pi$
$882$	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	−0.915513	−	0.402289i	$-0.868215\pi$
$887$	−3.25714	+	5.64153i	−0.109364	+	0.189424i	0.806149	+	0.591713i	$0.201548\pi$
$888$	−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	−0.812518	−	0.582936i	$-0.801904\pi$
$907$	2.96883	−	5.14216i	0.0985784	−	0.170743i	0.911096	+	0.412193i	$0.135237\pi$
$908$	−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	0.999935	−	0.0114312i	$-0.00363874\pi$
$919$	14.8564	+	25.7321i	0.490068	+	0.848822i	−0.509867	+	0.860253i	$0.670305\pi$
$920$		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	−0.221739	−	0.975106i	$-0.571173\pi$
$929$	15.6012	−	9.00734i	0.511858	−	0.295521i	0.733597	+	0.679585i	$0.237840\pi$
$930$		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	$0.0239669\pi$
$941$			4.61504i			0.150446i	−0.997167	+	0.0752230i	$0.976033\pi$
$942$	−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	0.343366	−	0.939202i	$-0.388433\pi$
$947$	−9.18041	−	5.30031i	−0.298323	−	0.172237i	−0.641689	+	0.766965i	$0.721766\pi$
$948$	−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	0.533717	−	0.845663i	$-0.320795\pi$
$953$	−14.3705	−	24.8905i	−0.465508	−	0.806283i	−0.999224	+	0.0393806i	$0.987462\pi$
$954$			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	$0.0415047\pi$
$967$			8.08648i			0.260044i	−0.991511	+	0.130022i	$0.958495\pi$
$968$	−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	0.861126	−	0.508392i	$-0.169760\pi$
$971$	−0.302790	−	0.524448i	−0.00971701	−	0.0168304i	−0.870843	+	0.491561i	$0.836426\pi$
$972$	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	−0.369356	−	0.929288i	$-0.620422\pi$
$977$	−42.4727	−	24.5216i	−1.35882	−	0.784516i	−0.989465	+	0.144772i	$0.953755\pi$
$978$	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	$-0.836749\pi$
$983$		−	30.7684i		−	0.981358i	0.871340	−	0.490679i	$-0.163251\pi$
$984$	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	−0.962414	−	0.271585i	$-0.912452\pi$
$991$	−7.74435	+	13.4136i	−0.246007	+	0.426097i	0.716407	+	0.697683i	$0.245785\pi$
$992$	−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	0.797423	−	0.603421i	$-0.206196\pi$
$997$	−3.91111	−	6.77423i	−0.123866	−	0.214542i	−0.921289	+	0.388878i	$0.872863\pi$
$998$	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.251.1		8
5.2	odd	4		650.2.n.e.199.3		8
5.3	odd	4		650.2.n.d.199.2		8
5.4	even	2		130.2.l.b.121.4	yes	8
13.6	odd	12		8450.2.a.cm.1.3		4
13.7	odd	12		8450.2.a.ci.1.3		4
13.10	even	6	inner	650.2.m.c.101.1		8
15.14	odd	2		1170.2.bs.g.901.2		8
20.19	odd	2		1040.2.da.d.641.2		8
65.4	even	6		1690.2.d.k.1351.6		8
65.9	even	6		1690.2.d.k.1351.2		8
65.19	odd	12		1690.2.a.t.1.2		4
65.23	odd	12		650.2.n.e.49.3		8
65.24	odd	12		1690.2.e.s.991.3		8
65.29	even	6		1690.2.l.j.361.2		8
65.34	odd	4		1690.2.e.s.191.3		8
65.44	odd	4		1690.2.e.t.191.3		8
65.49	even	6		130.2.l.b.101.4	✓	8
65.54	odd	12		1690.2.e.t.991.3		8
65.59	odd	12		1690.2.a.u.1.2		4
65.62	odd	12		650.2.n.d.49.2		8
65.64	even	2		1690.2.l.j.1161.2		8
195.179	odd	6		1170.2.bs.g.361.2		8
260.179	odd	6		1040.2.da.d.881.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.4	✓	8	65.49	even	6
130.2.l.b.121.4	yes	8	5.4	even	2
650.2.m.c.101.1		8	13.10	even	6	inner
650.2.m.c.251.1		8	1.1	even	1	trivial
650.2.n.d.49.2		8	65.62	odd	12
650.2.n.d.199.2		8	5.3	odd	4
650.2.n.e.49.3		8	65.23	odd	12
650.2.n.e.199.3		8	5.2	odd	4
1040.2.da.d.641.2		8	20.19	odd	2
1040.2.da.d.881.2		8	260.179	odd	6
1170.2.bs.g.361.2		8	195.179	odd	6
1170.2.bs.g.901.2		8	15.14	odd	2
1690.2.a.t.1.2		4	65.19	odd	12
1690.2.a.u.1.2		4	65.59	odd	12
1690.2.d.k.1351.2		8	65.9	even	6
1690.2.d.k.1351.6		8	65.4	even	6
1690.2.e.s.191.3		8	65.34	odd	4
1690.2.e.s.991.3		8	65.24	odd	12
1690.2.e.t.191.3		8	65.44	odd	4
1690.2.e.t.991.3		8	65.54	odd	12
1690.2.l.j.361.2		8	65.29	even	6
1690.2.l.j.1161.2		8	65.64	even	2
8450.2.a.ci.1.3		4	13.7	odd	12
8450.2.a.cm.1.3		4	13.6	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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