LMFDB - Embedded newform 175.2.x.a.3.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.10
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0204066 - 0.0314234i) q^{2} +(-0.0391619 + 0.102020i) q^{3} +(0.812902 + 1.82581i) q^{4} +(-2.17394 - 0.523442i) q^{5} +(0.00240666 + 0.00331248i) q^{6} +(1.46457 + 2.20341i) q^{7} +(0.147975 + 0.0234370i) q^{8} +(2.22056 + 1.99940i) q^{9} +O(q^{10})$	\(q+(0.0204066 - 0.0314234i) q^{2} +(-0.0391619 + 0.102020i) q^{3} +(0.812902 + 1.82581i) q^{4} +(-2.17394 - 0.523442i) q^{5} +(0.00240666 + 0.00331248i) q^{6} +(1.46457 + 2.20341i) q^{7} +(0.147975 + 0.0234370i) q^{8} +(2.22056 + 1.99940i) q^{9} +(-0.0608110 + 0.0576309i) q^{10} +(0.920718 + 1.02256i) q^{11} +(-0.218104 + 0.0114304i) q^{12} +(-1.43400 - 0.730661i) q^{13} +(0.0991256 - 0.00105770i) q^{14} +(0.138537 - 0.201287i) q^{15} +(-2.67089 + 2.96632i) q^{16} +(2.74801 - 3.39351i) q^{17} +(0.108142 - 0.0289766i) q^{18} +(-0.0625826 - 0.0278636i) q^{19} +(-0.811494 - 4.39470i) q^{20} +(-0.282148 + 0.0631262i) q^{21} +(0.0509210 - 0.00806510i) q^{22} +(-4.73611 - 3.07566i) q^{23} +(-0.00818604 + 0.0141786i) q^{24} +(4.45202 + 2.27586i) q^{25} +(-0.0522229 + 0.0301509i) q^{26} +(-0.583044 + 0.297076i) q^{27} +(-2.83246 + 4.46519i) q^{28} +(3.88840 - 5.35192i) q^{29} +(-0.00349804 - 0.00846088i) q^{30} +(3.48857 - 0.366663i) q^{31} +(0.116261 + 0.433891i) q^{32} +(-0.140379 + 0.0538864i) q^{33} +(-0.0505580 - 0.155602i) q^{34} +(-2.03053 - 5.55670i) q^{35} +(-1.84543 + 5.67963i) q^{36} +(-0.405127 - 7.73028i) q^{37} +(-0.00215267 + 0.00139796i) q^{38} +(0.130700 - 0.117683i) q^{39} +(-0.309421 - 0.128407i) q^{40} +(-9.12263 + 2.96412i) q^{41} +(-0.00377404 + 0.0101542i) q^{42} +(-3.38639 - 3.38639i) q^{43} +(-1.11855 + 2.51230i) q^{44} +(-3.78079 - 5.50891i) q^{45} +(-0.193296 + 0.0860608i) q^{46} +(5.54003 - 4.48623i) q^{47} +(-0.198028 - 0.388651i) q^{48} +(-2.71005 + 6.45412i) q^{49} +(0.162366 - 0.0934549i) q^{50} +(0.238589 + 0.413248i) q^{51} +(0.168343 - 3.21217i) q^{52} +(-2.76885 - 1.06286i) q^{53} +(-0.00256281 + 0.0243835i) q^{54} +(-1.46633 - 2.70493i) q^{55} +(0.165079 + 0.360376i) q^{56} +(0.00529350 - 0.00529350i) q^{57} +(-0.0888266 - 0.231401i) q^{58} +(10.0677 + 2.13996i) q^{59} +(0.480128 + 0.0893160i) q^{60} +(-1.57245 - 7.39781i) q^{61} +(0.0596680 - 0.117105i) q^{62} +(-1.15333 + 7.82108i) q^{63} +(-7.57643 - 2.46173i) q^{64} +(2.73497 + 2.33903i) q^{65} +(-0.00117136 + 0.00551082i) q^{66} +(6.89851 + 5.58630i) q^{67} +(8.42975 + 2.25874i) q^{68} +(0.499255 - 0.362730i) q^{69} +(-0.216047 - 0.0495872i) q^{70} +(5.52909 + 4.01712i) q^{71} +(0.281728 + 0.347905i) q^{72} +(-0.428243 - 0.0224433i) q^{73} +(-0.251179 - 0.145018i) q^{74} +(-0.406533 + 0.365068i) q^{75} -0.136914i q^{76} +(-0.904665 + 3.52633i) q^{77} +(-0.00103085 - 0.00650856i) q^{78} +(9.05420 + 0.951635i) q^{79} +(7.35904 - 5.05054i) q^{80} +(0.929537 + 8.84395i) q^{81} +(-0.0930190 + 0.347152i) q^{82} +(-0.663758 + 4.19080i) q^{83} +(-0.344615 - 0.463833i) q^{84} +(-7.75030 + 5.93885i) q^{85} +(-0.175517 + 0.0373072i) q^{86} +(0.393727 + 0.606287i) q^{87} +(0.112278 + 0.172893i) q^{88} +(-7.87491 + 1.67386i) q^{89} +(-0.250262 + 0.00638718i) q^{90} +(-0.490253 - 4.22980i) q^{91} +(1.76558 - 11.1474i) q^{92} +(-0.0992118 + 0.370263i) q^{93} +(-0.0279194 - 0.265635i) q^{94} +(0.121466 + 0.0933321i) q^{95} +(-0.0488186 - 0.00513104i) q^{96} +(2.59509 + 16.3848i) q^{97} +(0.147507 + 0.216866i) q^{98} +4.11154i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.0204066	−	0.0314234i	0.0144296	−	0.0222197i	−0.831382	−	0.555701i	$-0.812450\pi$
$2$	0.0204066	−	0.0314234i	0.0144296	−	0.0222197i	0.845812	+	0.533481i	$0.179117\pi$
$3$	−0.0391619	+	0.102020i	−0.0226101	+	0.0589014i	−0.944421	−	0.328739i	$-0.893376\pi$
$3$	−0.0391619	+	0.102020i	−0.0226101	+	0.0589014i	0.921811	+	0.387640i	$0.126710\pi$
$4$	0.812902	+	1.82581i	0.406451	+	0.912904i
$5$	−2.17394	−	0.523442i	−0.972215	−	0.234090i
$5$	−2.17394	−	0.523442i	−0.972215	−	0.234090i
$6$	0.00240666	+	0.00331248i	0.000982515	+	0.00135232i
$7$	1.46457	+	2.20341i	0.553556	+	0.832812i
$7$	1.46457	+	2.20341i	0.553556	+	0.832812i
$8$	0.147975	+	0.0234370i	0.0523172	+	0.00828623i
$9$	2.22056	+	1.99940i	0.740187	+	0.666467i
$10$	−0.0608110	+	0.0576309i	−0.0192301	+	0.0182245i
$11$	0.920718	+	1.02256i	0.277607	+	0.308314i	0.865783	−	0.500419i	$-0.166821\pi$
$11$	0.920718	+	1.02256i	0.277607	+	0.308314i	−0.588177	+	0.808733i	$0.700154\pi$
$12$	−0.218104	+	0.0114304i	−0.0629612	+	0.00329966i
$13$	−1.43400	−	0.730661i	−0.397721	−	0.202649i	0.243679	−	0.969856i	$-0.421646\pi$
$13$	−1.43400	−	0.730661i	−0.397721	−	0.202649i	−0.641399	+	0.767207i	$0.721646\pi$
$14$	0.0991256	−	0.00105770i	0.0264924	−	0.000282682i
$15$	0.138537	−	0.201287i	0.0357701	−	0.0519720i
$16$	−2.67089	+	2.96632i	−0.667722	+	0.741580i
$17$	2.74801	−	3.39351i	0.666489	−	0.823046i	−0.326001	−	0.945369i	$-0.605701\pi$
$17$	2.74801	−	3.39351i	0.666489	−	0.823046i	0.992490	+	0.122324i	$0.0390346\pi$
$18$	0.108142	−	0.0289766i	0.0254893	−	0.00682984i
$19$	−0.0625826	−	0.0278636i	−0.0143574	−	0.00639234i	0.399545	−	0.916713i	$-0.369168\pi$
$19$	−0.0625826	−	0.0278636i	−0.0143574	−	0.00639234i	−0.413903	+	0.910321i	$0.635835\pi$
$20$	−0.811494	−	4.39470i	−0.181456	−	0.982685i
$21$	−0.282148	+	0.0631262i	−0.0615697	+	0.0137753i
$22$	0.0509210	−	0.00806510i	0.0108564	−	0.00171949i
$23$	−4.73611	−	3.07566i	−0.987547	−	0.641320i	−0.0535361	−	0.998566i	$-0.517049\pi$
$23$	−4.73611	−	3.07566i	−0.987547	−	0.641320i	−0.934010	+	0.357246i	$0.883716\pi$
$24$	−0.00818604	+	0.0141786i	−0.00167097	+	0.00289420i
$25$	4.45202	+	2.27586i	0.890403	+	0.455172i
$26$	−0.0522229	+	0.0301509i	−0.0102418	+	0.00591308i
$27$	−0.583044	+	0.297076i	−0.112207	+	0.0571722i
$28$	−2.83246	+	4.46519i	−0.535284	+	0.843841i
$29$	3.88840	−	5.35192i	0.722058	−	0.993827i	−0.277395	−	0.960756i	$-0.589471\pi$
$29$	3.88840	−	5.35192i	0.722058	−	0.993827i	0.999453	−	0.0330712i	$-0.0105288\pi$
$30$	−0.00349804	−	0.00846088i	−0.000638651	−	0.00154474i
$31$	3.48857	−	0.366663i	0.626565	−	0.0658546i	0.214076	−	0.976817i	$-0.431326\pi$
$31$	3.48857	−	0.366663i	0.626565	−	0.0658546i	0.412489	+	0.910962i	$0.364659\pi$
$32$	0.116261	+	0.433891i	0.0205522	+	0.0767017i
$33$	−0.140379	+	0.0538864i	−0.0244368	+	0.00938042i
$34$	−0.0505580	−	0.155602i	−0.00867063	−	0.0266855i
$35$	−2.03053	−	5.55670i	−0.343222	−	0.939254i
$36$	−1.84543	+	5.67963i	−0.307571	+	0.946606i
$37$	−0.405127	−	7.73028i	−0.0666024	−	1.27085i	−0.803688	−	0.595050i	$-0.797132\pi$
$37$	−0.405127	−	7.73028i	−0.0666024	−	1.27085i	0.737086	−	0.675799i	$-0.236201\pi$
$38$	−0.00215267	+	0.00139796i	−0.000349209	+	0.000226779i
$39$	0.130700	−	0.117683i	0.0209288	−	0.0188444i
$40$	−0.309421	−	0.128407i	−0.0489238	−	0.0203029i
$41$	−9.12263	+	2.96412i	−1.42472	+	0.462918i	−0.917097	−	0.398664i	$-0.869474\pi$
$41$	−9.12263	+	2.96412i	−1.42472	+	0.462918i	−0.507618	+	0.861582i	$0.669474\pi$
$42$	−0.00377404	+	0.0101542i	−0.000582347	+	0.00156683i
$43$	−3.38639	−	3.38639i	−0.516420	−	0.516420i	0.400067	−	0.916486i	$-0.368987\pi$
$43$	−3.38639	−	3.38639i	−0.516420	−	0.516420i	−0.916486	+	0.400067i	$0.868987\pi$
$44$	−1.11855	+	2.51230i	−0.168627	+	0.378743i
$45$	−3.78079	−	5.50891i	−0.563607	−	0.821220i
$46$	−0.193296	+	0.0860608i	−0.0284999	+	0.0126890i
$47$	5.54003	−	4.48623i	0.808096	−	0.654384i	−0.133529	−	0.991045i	$-0.542631\pi$
$47$	5.54003	−	4.48623i	0.808096	−	0.654384i	0.941626	+	0.336661i	$0.109298\pi$
$48$	−0.198028	−	0.388651i	−0.0285828	−	0.0560970i
$49$	−2.71005	+	6.45412i	−0.387151	+	0.922016i
$50$	0.162366	−	0.0934549i	0.0229620	−	0.0132165i
$51$	0.238589	+	0.413248i	0.0334091	+	0.0578663i
$52$	0.168343	−	3.21217i	0.0233449	−	0.445448i
$53$	−2.76885	−	1.06286i	−0.380331	−	0.145996i	0.160689	−	0.987005i	$-0.448628\pi$
$53$	−2.76885	−	1.06286i	−0.380331	−	0.145996i	−0.541020	+	0.841010i	$0.681962\pi$
$54$	−0.00256281	+	0.0243835i	−0.000348754	+	0.00331818i
$55$	−1.46633	−	2.70493i	−0.197720	−	0.364732i
$56$	0.165079	+	0.360376i	0.0220596	+	0.0481572i
$57$	0.00529350	−	0.00529350i	0.000701141	−	0.000701141i
$58$	−0.0888266	−	0.231401i	−0.0116635	−	0.0303845i
$59$	10.0677	+	2.13996i	1.31071	+	0.278599i	0.809700	−	0.586844i	$-0.199630\pi$
$59$	10.0677	+	2.13996i	1.31071	+	0.278599i	0.501007	+	0.865443i	$0.332963\pi$
$60$	0.480128	+	0.0893160i	0.0619843	+	0.0115306i
$61$	−1.57245	−	7.39781i	−0.201332	−	0.947192i	−0.956516	−	0.291679i	$-0.905786\pi$
$61$	−1.57245	−	7.39781i	−0.201332	−	0.947192i	0.755184	−	0.655513i	$-0.227547\pi$
$62$	0.0596680	−	0.117105i	0.00757784	−	0.0148723i
$63$	−1.15333	+	7.82108i	−0.145307	+	0.985363i
$64$	−7.57643	−	2.46173i	−0.947053	−	0.307716i
$65$	2.73497	+	2.33903i	0.339232	+	0.290121i
$66$	−0.00117136	+	0.00551082i	−0.000144185	+	0.000678335i
$67$	6.89851	+	5.58630i	0.842787	+	0.682475i	0.950166	−	0.311743i	$-0.100913\pi$
$67$	6.89851	+	5.58630i	0.842787	+	0.682475i	−0.107380	+	0.994218i	$0.534246\pi$
$68$	8.42975	+	2.25874i	1.02226	+	0.273913i
$69$	0.499255	−	0.362730i	0.0601032	−	0.0436675i
$70$	−0.216047	−	0.0495872i	−0.0258225	−	0.00592680i
$71$	5.52909	+	4.01712i	0.656182	+	0.476744i	0.865372	−	0.501131i	$-0.167082\pi$
$71$	5.52909	+	4.01712i	0.656182	+	0.476744i	−0.209189	+	0.977875i	$0.567082\pi$
$72$	0.281728	+	0.347905i	0.0332020	+	0.0410010i
$73$	−0.428243	−	0.0224433i	−0.0501221	−	0.00262679i	0.0272584	−	0.999628i	$-0.491322\pi$
$73$	−0.428243	−	0.0224433i	−0.0501221	−	0.00262679i	−0.0773805	+	0.997002i	$0.524656\pi$
$74$	−0.251179	−	0.145018i	−0.0291989	−	0.0168580i
$75$	−0.406533	+	0.365068i	−0.0469424	+	0.0421545i
$76$		−	0.136914i		−	0.0157051i
$77$	−0.904665	+	3.52633i	−0.103096	+	0.401863i
$78$	−0.00103085	−	0.00650856i	−0.000116721	−	0.000736949i
$79$	9.05420	+	0.951635i	1.01868	+	0.107067i	0.599118	−	0.800661i	$-0.295518\pi$
$79$	9.05420	+	0.951635i	1.01868	+	0.107067i	0.419559	+	0.907728i	$0.362185\pi$
$80$	7.35904	−	5.05054i	0.822766	−	0.564668i
$81$	0.929537	+	8.84395i	0.103282	+	0.982661i
$82$	−0.0930190	+	0.347152i	−0.0102722	+	0.0383365i
$83$	−0.663758	+	4.19080i	−0.0728569	+	0.460000i	0.924107	+	0.382134i	$0.124811\pi$
$83$	−0.663758	+	4.19080i	−0.0728569	+	0.460000i	−0.996964	+	0.0778662i	$0.975189\pi$
$84$	−0.344615	−	0.463833i	−0.0376006	−	0.0506083i
$85$	−7.75030	+	5.93885i	−0.840638	+	0.644159i
$86$	−0.175517	+	0.0373072i	−0.0189264	+	0.00402294i
$87$	0.393727	+	0.606287i	0.0422120	+	0.0650007i
$88$	0.112278	+	0.172893i	0.0119688	+	0.0184304i
$89$	−7.87491	+	1.67386i	−0.834739	+	0.177429i	−0.605404	−	0.795918i	$-0.706988\pi$
$89$	−7.87491	+	1.67386i	−0.834739	+	0.177429i	−0.229335	+	0.973348i	$0.573655\pi$
$90$	−0.250262	+	0.00638718i	−0.0263799	+	0.000673268i
$91$	−0.490253	−	4.22980i	−0.0513925	−	0.443404i
$92$	1.76558	−	11.1474i	0.184075	−	1.16220i
$93$	−0.0992118	+	0.370263i	−0.0102878	+	0.0383945i
$94$	−0.0279194	−	0.265635i	−0.00287966	−	0.0273982i
$95$	0.121466	+	0.0933321i	0.0124621	+	0.00957567i
$96$	−0.0488186	−	0.00513104i	−0.00498253	−	0.000523684i
$97$	2.59509	+	16.3848i	0.263492	+	1.66362i	0.664306	+	0.747461i	$0.268727\pi$
$97$	2.59509	+	16.3848i	0.263492	+	1.66362i	−0.400814	+	0.916159i	$0.631273\pi$
$98$	0.147507	+	0.216866i	0.0149005	+	0.0219067i
$99$			4.11154i			0.413225i
$100$	−0.536234	+	9.97858i	−0.0536234	+	0.997858i
$101$	−3.41526	−	1.97180i	−0.339831	−	0.196202i	0.320366	−	0.947294i	$-0.396194\pi$
$101$	−3.41526	−	1.97180i	−0.339831	−	0.196202i	−0.660197	+	0.751092i	$0.729527\pi$
$102$	0.0178544		0.000935712i	0.00176785		9.26493e-5i
$103$	−4.83309	−	5.96836i	−0.476218	−	0.588080i	0.481263	−	0.876576i	$-0.340178\pi$
$103$	−4.83309	−	5.96836i	−0.476218	−	0.588080i	−0.957481	+	0.288496i	$0.906845\pi$
$104$	−0.195072	−	0.141728i	−0.0191284	−	0.0138976i
$105$	0.646415	+	0.0104557i	0.0630837	+	0.00102038i
$106$	−0.0899016	+	0.0653174i	−0.00873202	+	0.00634418i
$107$	−10.4235	−	2.79297i	−1.00768	−	0.270006i	−0.283019	−	0.959114i	$-0.591336\pi$
$107$	−10.4235	−	2.79297i	−1.00768	−	0.270006i	−0.724659	+	0.689108i	$0.758003\pi$
$108$	−1.01636	−	0.823033i	−0.0977994	−	0.0791964i
$109$	0.599063	−	2.81837i	0.0573798	−	0.269951i	−0.940100	−	0.340898i	$-0.889269\pi$
$109$	0.599063	−	2.81837i	0.0573798	−	0.269951i	0.997480	+	0.0709472i	$0.0226022\pi$
$110$	−0.114921	−	0.00912119i	−0.0109573	−	0.000869671i
$111$	0.804510	+	0.261401i	0.0763607	+	0.0248111i
$112$	−10.4477	−	1.54068i	−0.987218	−	0.145580i
$113$	4.61149	−	9.05056i	0.433812	−	0.851405i	−0.565826	−	0.824524i	$-0.691443\pi$
$113$	4.61149	−	9.05056i	0.433812	−	0.851405i	0.999639	−	0.0268803i	$-0.00855729\pi$
$114$	−5.83174e−5	0	0.000274362i	−5.46193e−6	0	2.56964e-5i
$115$	8.68607	+	9.16538i	0.809980	+	0.854676i
$116$	12.9325	+	2.74888i	1.20075	+	0.255227i
$117$	−1.72340	−	4.48962i	−0.159329	−	0.415066i
$118$	0.272693	−	0.272693i	0.0251034	−	0.0251034i
$119$	11.5019	+	1.08496i	1.05438	+	0.0994579i
$120$	0.0252176	−	0.0265386i	0.00230204	−	0.00242263i
$121$	0.951904	−	9.05676i	0.0865367	−	0.823342i
$122$	−0.264553	−	0.101552i	−0.0239515	−	0.00919411i
$123$	0.0548590	−	1.04677i	0.00494647	−	0.0943843i
$124$	3.50532	+	6.07139i	0.314787	+	0.545227i
$125$	−8.48713	−	7.27796i	−0.759112	−	0.650960i
$126$	0.222229	+	0.195843i	0.0197978	+	0.0174471i
$127$	9.60727	+	18.8553i	0.852507	+	1.67314i	0.732919	+	0.680316i	$0.238157\pi$
$127$	9.60727	+	18.8553i	0.852507	+	1.67314i	0.119588	+	0.992824i	$0.461843\pi$
$128$	−0.930148	+	0.753219i	−0.0822142	+	0.0665758i
$129$	0.478097	−	0.212863i	0.0420941	−	0.0187415i
$130$	0.129312	−	0.0382106i	0.0113414	−	0.00335129i
$131$	−0.708263	+	1.59079i	−0.0618813	+	0.138988i	−0.941839	−	0.336064i	$-0.890904\pi$
$131$	−0.708263	+	1.59079i	−0.0618813	+	0.138988i	0.879958	+	0.475052i	$0.157571\pi$
$132$	−0.212501	−	0.212501i	−0.0184958	−	0.0184958i
$133$	−0.0302618	−	0.178704i	−0.00262403	−	0.0154956i
$134$	0.316315	−	0.102777i	0.0273255	−	0.00887859i
$135$	1.42300	−	0.340635i	0.122473	−	0.0293172i
$136$	0.486171	−	0.437750i	0.0416888	−	0.0375367i
$137$	−5.34189	+	3.46906i	−0.456388	+	0.296382i	−0.752285	−	0.658838i	$-0.771048\pi$
$137$	−5.34189	+	3.46906i	−0.456388	+	0.296382i	0.295897	+	0.955220i	$0.404382\pi$
$138$	−0.00121011	−	0.0230904i	−0.000103012	−	0.00196558i
$139$	6.65731	−	20.4891i	0.564665	−	1.73786i	−0.104278	−	0.994548i	$-0.533253\pi$
$139$	6.65731	−	20.4891i	0.564665	−	1.73786i	0.668944	−	0.743313i	$-0.266747\pi$
$140$	8.49485	−	8.22442i	0.717946	−	0.695090i
$141$	0.240728	+	0.740884i	0.0202729	+	0.0623937i
$142$	0.239062	−	0.0917671i	0.0200616	−	0.00770093i
$143$	−0.573166	−	2.13909i	−0.0479306	−	0.178879i
$144$	−11.8617	+	1.24672i	−0.988478	+	0.103893i
$145$	−11.2546	+	9.59940i	−0.934641	+	0.797187i
$146$	−0.00944423	+	0.0129989i	−0.000781610	+	0.00107579i
$147$	−0.552319	−	0.529236i	−0.0455545	−	0.0436506i
$148$	13.7847	−	7.02364i	1.13309	−	0.577340i
$149$	−16.9996	+	9.81475i	−1.39266	+	0.804055i	−0.993610	−	0.112871i	$-0.963995\pi$
$149$	−16.9996	+	9.81475i	−1.39266	+	0.804055i	−0.399055	+	0.916927i	$0.630662\pi$
$150$	0.00317573	+	0.0202245i	0.000259298	+	0.00165132i
$151$	4.56259	−	7.90264i	0.371299	−	0.643108i	−0.618467	−	0.785811i	$-0.712246\pi$
$151$	4.56259	−	7.90264i	0.371299	−	0.643108i	0.989766	+	0.142703i	$0.0455793\pi$
$152$	−0.00860764	−	0.00558987i	−0.000698172	−	0.000453398i
$153$	12.8871	−	2.04111i	1.04186	−	0.165014i
$154$	0.0923483	+	0.100388i	0.00744164	+	0.00808951i
$155$	−7.77586	−	1.02896i	−0.624572	−	0.0826480i
$156$	0.321113	+	0.142969i	0.0257096	+	0.0114467i
$157$	−17.8330	+	4.77834i	−1.42323	+	0.381353i	−0.886628	−	0.462483i	$-0.846959\pi$
$157$	−17.8330	+	4.77834i	−1.42323	+	0.381353i	−0.536601	+	0.843836i	$0.680292\pi$
$158$	0.214669	−	0.265094i	0.0170781	−	0.0210898i
$159$	0.216867	−	0.240855i	0.0171987	−	0.0191011i
$160$	−0.0256268	−	1.00411i	−0.00202598	−	0.0793816i
$161$	−0.159415	−	14.9401i	−0.0125637	−	1.17745i
$162$	0.296876	+	0.151266i	0.0233248	+	0.0118846i
$163$	−3.45202	+	0.180913i	−0.270383	+	0.0141702i	−0.187046	−	0.982351i	$-0.559891\pi$
$163$	−3.45202	+	0.180913i	−0.270383	+	0.0141702i	−0.0833374	+	0.996521i	$0.526558\pi$
$164$	−12.8277	−	14.2466i	−1.00168	−	1.11248i
$165$	0.333381	−	0.0436655i	0.0259537	−	0.00339935i
$166$	0.118144	+	0.106377i	0.00916977	+	0.00825649i
$167$	−13.0850	−	2.07246i	−1.01255	−	0.160372i	−0.371954	−	0.928251i	$-0.621312\pi$
$167$	−13.0850	−	2.07246i	−1.01255	−	0.160372i	−0.640595	+	0.767879i	$0.721312\pi$
$168$	−0.0432304	+	0.00272842i	−0.00333530	+	0.000210502i
$169$	−6.11871	−	8.42168i	−0.470670	−	0.647822i
$170$	0.0284616	+	0.364732i	0.00218290	+	0.0279737i
$171$	−0.0832580	−	0.187000i	−0.00636690	−	0.0143003i
$172$	3.43009	−	8.93570i	0.261542	−	0.681341i
$173$	−5.52749	+	8.51158i	−0.420247	+	0.647123i	−0.983865	−	0.178912i	$-0.942742\pi$
$173$	−5.52749	+	8.51158i	−0.420247	+	0.647123i	0.563618	+	0.826035i	$0.309409\pi$
$174$	0.0270862			0.00205340
$175$	1.50564	+	13.1428i	0.113815	+	0.993502i
$176$	−5.49238			−0.414003
$177$	−0.612591	+	0.943307i	−0.0460451	+	0.0709033i
$178$	−0.108102	+	0.281614i	−0.00810256	+	0.0211079i
$179$	−3.67055	−	8.24419i	−0.274350	−	0.616200i	0.722848	−	0.691007i	$-0.242833\pi$
$179$	−3.67055	−	8.24419i	−0.274350	−	0.616200i	−0.997198	+	0.0748069i	$0.976166\pi$
$180$	6.98480	−	11.3812i	0.520616	−	0.848305i
$181$	−9.31589	−	12.8222i	−0.692445	−	0.953069i	−0.999999	−	0.00153805i	$-0.999510\pi$
$181$	−9.31589	−	12.8222i	−0.692445	−	0.953069i	0.307554	−	0.951531i	$-0.400490\pi$
$182$	−0.142919	−	0.0709105i	−0.0105939	−	0.00525623i
$183$	0.816306	+	0.129290i	0.0603430	+	0.00955740i
$184$	−0.628743	−	0.566122i	−0.0463515	−	0.0417351i
$185$	−3.16563	+	17.0172i	−0.232742	+	1.25113i
$186$	0.00961036	+	0.0106734i	0.000704666	+	0.000782611i
$187$	6.00020	−	0.314457i	0.438778	−	0.0229954i
$188$	12.6945	+	6.46817i	0.925841	+	0.471740i
$189$	−1.50849	−	0.849597i	−0.109727	−	0.0617991i
$190$	0.00541151	−	0.00191228i	0.000392592	−	0.000138731i
$191$	14.9793	−	16.6362i	1.08386	−	1.20375i	0.106028	−	0.994363i	$-0.466187\pi$
$191$	14.9793	−	16.6362i	1.08386	−	1.20375i	0.977833	−	0.209387i	$-0.0671468\pi$
$192$	0.547853	−	0.676542i	0.0395379	−	0.0488252i
$193$	−11.7643	+	3.15224i	−0.846814	+	0.226903i	−0.656036	−	0.754730i	$-0.727768\pi$
$193$	−11.7643	+	3.15224i	−0.846814	+	0.226903i	−0.190779	+	0.981633i	$0.561101\pi$
$194$	0.567822	+	0.252811i	0.0407672	+	0.0181507i
$195$	−0.345735	+	0.187422i	−0.0247586	+	0.0134216i
$196$	−13.9870	+	0.298524i	−0.999071	+	0.0213231i
$197$	13.1804	−	2.08757i	0.939067	−	0.148734i	0.331906	−	0.943313i	$-0.392308\pi$
$197$	13.1804	−	2.08757i	0.939067	−	0.148734i	0.607161	+	0.794579i	$0.292308\pi$
$198$	0.129199	+	0.0839025i	0.00918174	+	0.00596269i
$199$	−9.16969	+	15.8824i	−0.650022	+	1.12587i	0.333095	+	0.942893i	$0.391907\pi$
$199$	−9.16969	+	15.8824i	−0.650022	+	1.12587i	−0.983117	+	0.182978i	$0.941426\pi$
$200$	0.605449	+	0.441113i	0.0428117	+	0.0311914i
$201$	−0.840074	+	0.485017i	−0.0592542	+	0.0342104i
$202$	−0.131654	+	0.0670813i	−0.00926318	+	0.00471982i
$203$	17.4873	+	0.729470i	1.22737	+	0.0511987i
$204$	−0.560562	+	0.771548i	−0.0392472	+	0.0540192i
$205$	21.3836	−	1.66865i	1.49349	−	0.116544i
$206$	−0.286173	+	0.0300780i	−0.0199386	+	0.00209563i
$207$	−4.36732	−	16.2991i	−0.303550	−	1.13286i
$208$	5.99743	−	2.30220i	0.415847	−	0.159629i
$209$	−0.0291287	−	0.0896490i	−0.00201488	−	0.00620115i
$210$	0.0135197	−	0.0200992i	0.000932947	−	0.00138698i
$211$	−2.94624	+	9.06760i	−0.202828	+	0.624239i	0.796968	+	0.604022i	$0.206436\pi$
$211$	−2.94624	+	9.06760i	−0.202828	+	0.624239i	−0.999796	+	0.0202178i	$0.993564\pi$
$212$	−0.310223	−	5.91940i	−0.0213062	−	0.406546i
$213$	−0.626357	+	0.406761i	−0.0429173	+	0.0278708i
$214$	−0.300473	+	0.270547i	−0.0205399	+	0.0184942i
$215$	5.58922	+	9.13438i	0.381182	+	0.622960i
$216$	−0.0932387	+	0.0302951i	−0.00634409	+	0.00206132i
$217$	5.91717	+	7.14975i	0.401684	+	0.485356i
$218$	−0.0763379	−	0.0763379i	−0.00517026	−	0.00517026i
$219$	0.0190605	−	0.0428105i	0.00128799	−	0.00289287i
$220$	3.74669	−	4.87608i	0.252602	−	0.328745i
$221$	−6.42015	+	2.85843i	−0.431866	+	0.192279i
$222$	0.0246314	−	0.0199461i	0.00165315	−	0.00133870i
$223$	11.4092	+	22.3918i	0.764015	+	1.49946i	0.863458	+	0.504421i	$0.168294\pi$
$223$	11.4092	+	22.3918i	0.764015	+	1.49946i	−0.0994426	+	0.995043i	$0.531706\pi$
$224$	−0.785768	+	0.891634i	−0.0525013	+	0.0595748i
$225$	5.33561	+	13.9551i	0.355707	+	0.930337i
$226$	−0.190294	−	0.329600i	−0.0126582	−	0.0219246i
$227$	−0.647595	+	12.3568i	−0.0429824	+	0.820153i	0.889057	+	0.457796i	$0.151361\pi$
$227$	−0.647595	+	12.3568i	−0.0429824	+	0.820153i	−0.932040	+	0.362357i	$0.881972\pi$
$228$	0.0139680	+	0.00536182i	0.000925054	+	0.000355095i
$229$	1.54378	−	14.6881i	0.102016	−	0.970617i	−0.817064	−	0.576547i	$-0.804400\pi$
$229$	1.54378	−	14.6881i	0.102016	−	0.970617i	0.919080	−	0.394070i	$-0.128933\pi$
$230$	0.465261	−	0.0859117i	0.0306784	−	0.00566485i
$231$	−0.324329	−	0.230392i	−0.0213393	−	0.0151587i
$232$	0.700820	−	0.700820i	0.0460111	−	0.0460111i
$233$	−0.434909	−	1.13298i	−0.0284918	−	0.0742237i	0.918597	−	0.395197i	$-0.129324\pi$
$233$	−0.434909	−	1.13298i	−0.0284918	−	0.0742237i	−0.947088	+	0.320973i	$0.895990\pi$
$234$	−0.176248	−	0.0374627i	−0.0115217	−	0.00244901i
$235$	−14.3920	+	6.85290i	−0.938828	+	0.447034i
$236$	4.27692	+	20.1213i	0.278404	+	1.30979i
$237$	−0.451665	+	0.886443i	−0.0293388	+	0.0575807i
$238$	0.268809	−	0.339290i	0.0174243	−	0.0219929i
$239$	−24.4748	−	7.95235i	−1.58314	−	0.514395i	−0.620280	−	0.784380i	$-0.712981\pi$
$239$	−24.4748	−	7.95235i	−1.58314	−	0.514395i	−0.962864	+	0.269986i	$0.912981\pi$
$240$	0.227064	+	0.948560i	0.0146569	+	0.0612293i
$241$	2.84821	−	13.3998i	0.183470	−	0.863156i	−0.786054	−	0.618158i	$-0.787879\pi$
$241$	2.84821	−	13.3998i	0.183470	−	0.863156i	0.969524	−	0.244998i	$-0.0787874\pi$
$242$	−0.265169	−	0.214730i	−0.0170457	−	0.0138033i
$243$	−2.83487	−	0.759601i	−0.181857	−	0.0487284i
$244$	12.2287	−	8.88469i	0.782864	−	0.568784i
$245$	9.26985	−	12.6123i	0.592229	−	0.805770i
$246$	−0.0317737	−	0.0230849i	−0.00202582	−	0.00147184i
$247$	0.0693848	+	0.0856831i	0.00441485	+	0.00545188i
$248$	0.524815	+	0.0275044i	0.0333258	+	0.00174653i
$249$	−0.401552	−	0.231836i	−0.0254473	−	0.0146920i
$250$	−0.401892	+	0.118176i	−0.0254179	+	0.00747411i
$251$			24.5816i			1.55158i	0.630992	+	0.775789i	$0.282648\pi$
$251$			24.5816i			1.55158i	−0.630992	+	0.775789i	$0.717352\pi$
$252$	−15.2173	+	4.25200i	−0.958602	+	0.267851i
$253$	−1.21556	−	7.67477i	−0.0764219	−	0.482509i
$254$	0.788550	+	0.0828799i	0.0494780	+	0.00520035i
$255$	−0.302366	−	1.02326i	−0.0189349	−	0.0640792i
$256$	−1.66073	−	15.8008i	−0.103796	−	0.987548i
$257$	−5.30267	+	19.7898i	−0.330772	+	1.23446i	0.577610	+	0.816313i	$0.303986\pi$
$257$	−5.30267	+	19.7898i	−0.330772	+	1.23446i	−0.908381	+	0.418143i	$0.862681\pi$
$258$	0.00306747	−	0.0193672i	0.000190972	−	0.00120575i
$259$	16.4397	−	12.2142i	1.02151	−	0.758954i
$260$	−2.04735	+	6.89494i	−0.126971	+	0.427606i
$261$	19.3351	−	4.10979i	1.19681	−	0.254390i
$262$	0.0355346	+	0.0547186i	0.00219534	+	0.00338052i
$263$	−6.93796	−	10.6835i	−0.427813	−	0.658774i	0.557373	−	0.830262i	$-0.311809\pi$
$263$	−6.93796	−	10.6835i	−0.427813	−	0.658774i	−0.985186	+	0.171488i	$0.945143\pi$
$264$	−0.0220355	+	0.00468380i	−0.00135619	+	0.000288268i
$265$	5.46297	+	3.75993i	0.335588	+	0.230971i
$266$	−0.00623301	−	0.00269580i	−0.000382171	−	0.000165290i
$267$	0.137628	−	0.868951i	0.00842272	−	0.0531790i
$268$	−4.59170	+	17.1365i	−0.280483	+	1.04678i
$269$	2.07737	+	19.7649i	0.126660	+	1.20509i	0.854542	+	0.519383i	$0.173838\pi$
$269$	2.07737	+	19.7649i	0.126660	+	1.20509i	−0.727882	+	0.685703i	$0.759495\pi$
$270$	0.0183348	−	0.0516668i	0.00111582	−	0.00314434i
$271$	8.02915	+	0.843898i	0.487736	+	0.0512631i	0.345205	−	0.938527i	$-0.387809\pi$
$271$	8.02915	+	0.843898i	0.487736	+	0.0512631i	0.142531	+	0.989790i	$0.454476\pi$
$272$	2.72661	+	17.2151i	0.165325	+	1.04382i
$273$	0.450725	+	0.115631i	0.0272791	+	0.00699833i
$274$			0.238652i			0.0144175i
$275$	1.77184	+	6.64788i	0.106846	+	0.400882i
$276$	1.06812	+	0.616679i	0.0642933	+	0.0371197i
$277$	−4.04324	−	0.211897i	−0.242935	−	0.0127317i	−0.0695201	−	0.997581i	$-0.522147\pi$
$277$	−4.04324	−	0.211897i	−0.242935	−	0.0127317i	−0.173415	+	0.984849i	$0.555480\pi$
$278$	−0.507984	−	0.627307i	−0.0304668	−	0.0376234i
$279$	8.47968	+	6.16085i	0.507665	+	0.368840i
$280$	−0.170236	−	0.869844i	−0.0101736	−	0.0519831i
$281$	1.03849	−	0.754506i	0.0619510	−	0.0450100i	−0.556379	−	0.830929i	$-0.687810\pi$
$281$	1.03849	−	0.754506i	0.0619510	−	0.0450100i	0.618330	+	0.785919i	$0.287810\pi$
$282$	0.0281935	+	0.00755443i	0.00167890	+	0.000449860i
$283$	−0.243356	−	0.197066i	−0.0144660	−	0.0117143i	0.622060	−	0.782969i	$-0.286296\pi$
$283$	−0.243356	−	0.197066i	−0.0144660	−	0.0117143i	−0.636526	+	0.771255i	$0.719629\pi$
$284$	−2.83988	+	13.3606i	−0.168516	+	0.792805i
$285$	−0.0142786	+	0.00873690i	−0.000845790	+	0.000517529i
$286$	−0.0789137	−	0.0256406i	−0.00466627	−	0.00151616i
$287$	−19.8919	−	15.7597i	−1.17418	−	0.930268i
$288$	−0.609358	+	1.19593i	−0.0359067	+	0.0704709i
$289$	−0.429840	−	2.02224i	−0.0252847	−	0.118955i
$290$	0.0719784	+	0.549548i	0.00422672	+	0.0322705i
$291$	−1.77320	−	0.376906i	−0.103947	−	0.0220946i
$292$	−0.307143	−	0.800134i	−0.0179742	−	0.0468243i
$293$	13.9434	−	13.9434i	0.814584	−	0.814584i	−0.170733	−	0.985317i	$-0.554614\pi$
$293$	13.9434	−	13.9434i	0.814584	−	0.814584i	0.985317	+	0.170733i	$0.0546137\pi$
$294$	−0.0279013	+	0.00655585i	−0.00162724	+	0.000382345i
$295$	−20.7665	−	9.92202i	−1.20907	−	0.577682i
$296$	0.121226	−	1.15338i	0.00704610	−	0.0670391i
$297$	−0.840597	−	0.322675i	−0.0487764	−	0.0187235i
$298$	−0.0384920	+	0.734472i	−0.00222978	+	0.0425468i
$299$	4.54432	+	7.87099i	0.262805	+	0.455191i
$300$	−0.997017	−	0.445487i	−0.0575628	−	0.0257202i
$301$	2.50200	−	12.4212i	0.144213	−	0.715948i
$302$	−0.155221	−	0.304638i	−0.00893196	−	0.0175300i
$303$	0.334911	−	0.271206i	0.0192402	−	0.0155804i
$304$	0.249803	−	0.111220i	0.0143272	−	0.00637888i
$305$	−0.453910	+	16.9055i	−0.0259908	+	0.968004i
$306$	0.198843	−	0.446608i	0.0113671	−	0.0255309i
$307$	14.7442	+	14.7442i	0.841499	+	0.841499i	0.989054	−	0.147555i	$-0.0471404\pi$
$307$	14.7442	+	14.7442i	0.841499	+	0.841499i	−0.147555	+	0.989054i	$0.547140\pi$
$308$	−7.17382	+	1.21482i	−0.408766	+	0.0692208i
$309$	0.798166	−	0.259340i	0.0454061	−	0.0147533i
$310$	−0.191012	+	0.223346i	−0.0108488	+	0.0126852i
$311$	−6.37447	+	5.73960i	−0.361463	+	0.325463i	−0.829773	−	0.558102i	$-0.811530\pi$
$311$	−6.37447	+	5.73960i	−0.361463	+	0.325463i	0.468309	+	0.883565i	$0.344863\pi$
$312$	0.0220986	−	0.0143510i	0.00125108	−	0.000812464i
$313$	−1.27272	−	24.2850i	−0.0719386	−	1.37267i	−0.761369	−	0.648319i	$-0.775472\pi$
$313$	−1.27272	−	24.2850i	−0.0719386	−	1.37267i	0.689430	−	0.724352i	$-0.257861\pi$
$314$	−0.213759	+	0.657884i	−0.0120631	+	0.0371265i
$315$	6.60116	−	16.3988i	0.371933	−	0.923970i
$316$	5.62268	+	17.3048i	0.316300	+	0.973472i
$317$	4.27191	−	1.63983i	0.239934	−	0.0921021i	−0.235430	−	0.971891i	$-0.575650\pi$
$317$	4.27191	−	1.63983i	0.239934	−	0.0921021i	0.475364	+	0.879789i	$0.342316\pi$
$318$	−0.00314297	−	0.0117297i	−0.000176249	−	0.000657771i
$319$	9.05278	−	0.951486i	0.506858	−	0.0532730i
$320$	15.1821	+	9.31747i	0.848706	+	0.520863i
$321$	0.693143	−	0.954029i	0.0386875	−	0.0532487i
$322$	−0.472723	−	0.299868i	−0.0263438	−	0.0167110i
$323$	−0.266533	+	0.135805i	−0.0148303	+	0.00755640i
$324$	−15.3917	+	8.88642i	−0.855097	+	0.493690i
$325$	−4.72132	−	6.51650i	−0.261892	−	0.361471i
$326$	−0.0647591	+	0.112166i	−0.00358667	+	0.00621230i
$327$	0.264070	+	0.171489i	0.0146031	+	0.00948338i
$328$	−1.41939	+	0.224810i	−0.0783729	+	0.0124130i
$329$	17.9988	+	5.63657i	0.992305	+	0.310754i
$330$	0.00543106	−	0.0113670i	0.000298970	−	0.000625735i
$331$	2.17087	+	0.966535i	0.119322	+	0.0531256i	0.465529	−	0.885032i	$-0.345864\pi$
$331$	2.17087	+	0.966535i	0.119322	+	0.0531256i	−0.346207	+	0.938158i	$0.612531\pi$
$332$	−8.19117	+	2.19482i	−0.449549	+	0.120456i
$333$	14.5563	−	17.9756i	0.797681	−	0.985054i
$334$	−0.332144	+	0.368884i	−0.0181741	+	0.0201844i
$335$	−12.0728	−	15.7552i	−0.659609	−	0.860801i
$336$	0.566333	−	1.00554i	0.0308960	−	0.0548569i
$337$	19.0320	+	9.69727i	1.03674	+	0.528244i	0.887621	−	0.460575i	$-0.152357\pi$
$337$	19.0320	+	9.69727i	1.03674	+	0.528244i	0.149117	+	0.988820i	$0.452357\pi$
$338$	−0.389500	+	0.0204128i	−0.0211860	+	0.00111031i
$339$	0.742745	+	0.824902i	0.0403404	+	0.0448025i
$340$	−17.1434	−	9.32286i	−0.929733	−	0.505603i
$341$	3.58692	+	3.22968i	0.194243	+	0.174897i
$342$	−0.00757520	−	0.00119979i	−0.000409620	−	6.48774e-5i
$343$	−18.1902	+	3.48115i	−0.982176	+	0.187964i
$344$	−0.421735	−	0.580469i	−0.0227384	−	0.0312968i
$345$	−1.27522	+	0.527221i	−0.0686554	+	0.0283846i
$346$	0.154666	+	0.347385i	0.00831488	+	0.0186755i
$347$	9.40506	−	24.5010i	0.504890	−	1.31528i	−0.410186	−	0.912002i	$-0.634536\pi$
$347$	9.40506	−	24.5010i	0.504890	−	1.31528i	0.915076	−	0.403282i	$-0.132130\pi$
$348$	−0.786901	+	1.21172i	−0.0421823	+	0.0649551i
$349$	16.7152			0.894745			0.447373	−	0.894348i	$-0.352360\pi$
$349$	16.7152			0.894745			0.447373	+	0.894348i	$0.352360\pi$
$350$	0.443716	+	0.220887i	0.0237176	+	0.0118069i
$351$	1.05315			0.0562129
$352$	−0.336636	+	0.518374i	−0.0179428	+	0.0276294i
$353$	−10.3220	+	26.8897i	−0.549383	+	1.43119i	0.324887	+	0.945753i	$0.394674\pi$
$353$	−10.3220	+	26.8897i	−0.549383	+	1.43119i	−0.874270	+	0.485440i	$0.838660\pi$
$354$	0.0171410	+	0.0384994i	0.000911035	+	0.00204622i
$355$	−9.91717	−	11.6271i	−0.526349	−	0.617104i
$356$	−9.45769	−	13.0174i	−0.501256	−	0.689920i
$357$	−0.561125	+	1.13094i	−0.0296979	+	0.0598558i
$358$	−0.333964	−	0.0528947i	−0.0176505	−	0.00279557i
$359$	3.33552	+	3.00332i	0.176042	+	0.158509i	0.752441	−	0.658659i	$-0.228876\pi$
$359$	3.33552	+	3.00332i	0.176042	+	0.158509i	−0.576399	+	0.817168i	$0.695543\pi$
$360$	−0.430351	−	0.903793i	−0.0226815	−	0.0476341i
$361$	−12.7103	−	14.1163i	−0.668965	−	0.742961i
$362$	−0.593024	+	0.0310791i	−0.0311686	+	0.00163348i
$363$	0.886694	+	0.451793i	0.0465394	+	0.0237130i
$364$	7.32428	−	4.33353i	0.383897	−	0.227138i
$365$	0.919227	+	0.272951i	0.0481145	+	0.0142869i
$366$	0.0207208	−	0.0230127i	0.00108309	−	0.00120289i
$367$	20.6467	−	25.4966i	1.07775	−	1.33091i	0.137472	−	0.990506i	$-0.456102\pi$
$367$	20.6467	−	25.4966i	1.07775	−	1.33091i	0.940279	−	0.340406i	$-0.110564\pi$
$368$	21.7730	−	5.83406i	1.13500	−	0.304121i
$369$	−26.1838	−	11.6578i	−1.36307	−	0.606880i
$370$	0.470139	+	0.446738i	0.0244413	+	0.0232248i
$371$	−1.71326	−	7.65757i	−0.0889480	−	0.397561i
$372$	−0.756679	+	0.119846i	−0.0392320	+	0.00621374i
$373$	−31.6429	−	20.5491i	−1.63841	−	1.06399i	−0.935869	−	0.352349i	$-0.885383\pi$
$373$	−31.6429	−	20.5491i	−1.63841	−	1.06399i	−0.702539	−	0.711645i	$-0.747950\pi$
$374$	0.112562	−	0.194964i	0.00582046	−	0.0100813i
$375$	1.07487	−	0.580840i	0.0555061	−	0.0299944i
$376$	0.924931	−	0.534009i	0.0476997	−	0.0275394i
$377$	−9.48641	+	4.83357i	−0.488575	+	0.248941i
$378$	−0.0574804	+	0.0300645i	−0.00295647	+	0.00154635i
$379$	−2.24596	+	3.09129i	−0.115367	+	0.158789i	−0.862795	−	0.505553i	$-0.831288\pi$
$379$	−2.24596	+	3.09129i	−0.115367	+	0.158789i	0.747428	+	0.664343i	$0.231288\pi$
$380$	−0.0716667	+	0.297643i	−0.00367642	+	0.0152688i
$381$	−2.29986	+	0.241725i	−0.117825	+	0.0123840i
$382$	−0.217089	−	0.810186i	−0.0111072	−	0.0414527i
$383$	−15.0198	+	5.76557i	−0.767477	+	0.294607i	−0.710433	−	0.703765i	$-0.751501\pi$
$383$	−15.0198	+	5.76557i	−0.767477	+	0.294607i	−0.0570442	+	0.998372i	$0.518168\pi$
$384$	−0.0404172	−	0.124391i	−0.00206253	−	0.00634782i
$385$	3.81252	−	7.19250i	0.194304	−	0.366563i
$386$	−0.141016	+	0.434001i	−0.00717751	+	0.0220901i
$387$	−0.748930	−	14.2904i	−0.0380702	−	0.726423i
$388$	−27.8059	+	18.0573i	−1.41163	+	0.916723i
$389$	−11.4454	+	10.3055i	−0.580306	+	0.522510i	−0.906174	−	0.422905i	$-0.861010\pi$
$389$	−11.4454	+	10.3055i	−0.580306	+	0.522510i	0.325867	+	0.945415i	$0.394344\pi$
$390$	−0.00116584	+	0.0146888i	−5.90346e−5	+	0.000743796i
$391$	−23.4521	+	7.62006i	−1.18603	+	0.385363i
$392$	−0.552286	+	0.891534i	−0.0278947	+	0.0450293i
$393$	−0.134555	−	0.134555i	−0.00678742	−	0.00678742i
$394$	0.203369	−	0.456774i	0.0102456	−	0.0230119i
$395$	−19.1851	−	6.80814i	−0.965309	−	0.342555i
$396$	−7.50689	+	3.34228i	−0.377235	+	0.167956i
$397$	−9.10252	+	7.37108i	−0.456842	+	0.369944i	−0.829944	−	0.557847i	$-0.811628\pi$
$397$	−9.10252	+	7.37108i	−0.456842	+	0.369944i	0.373102	+	0.927791i	$0.378294\pi$
$398$	0.311956	+	0.612248i	0.0156369	+	0.0306892i
$399$	0.0194165	+	0.00391105i	0.000972040	+	0.000195797i
$400$	−18.6418	+	7.12754i	−0.932089	+	0.356377i
$401$	6.37349	+	11.0392i	0.318277	+	0.551271i	0.980129	−	0.198363i	$-0.0635626\pi$
$401$	6.37349	+	11.0392i	0.318277	+	0.551271i	−0.661852	+	0.749635i	$0.730229\pi$
$402$	−0.00190217	+	0.0362955i	−9.48715e−5	+	0.00181026i
$403$	−5.27052	−	2.02316i	−0.262543	−	0.100781i
$404$	0.823859	−	7.83849i	0.0409885	−	0.389979i
$405$	2.60854	−	19.7128i	0.129619	−	0.979535i
$406$	0.379779	−	0.534626i	0.0188481	−	0.0265330i
$407$	7.53167	−	7.53167i	0.373331	−	0.373331i
$408$	0.0256200	+	0.0667423i	0.00126838	+	0.00330424i
$409$	9.90022	+	2.10436i	0.489534	+	0.104054i	0.446064	−	0.895001i	$-0.352825\pi$
$409$	9.90022	+	2.10436i	0.489534	+	0.104054i	0.0434702	+	0.999055i	$0.486159\pi$
$410$	0.383931	−	0.705996i	0.0189610	−	0.0348667i
$411$	−0.144716	−	0.680835i	−0.00713831	−	0.0335831i
$412$	6.96826	−	13.6760i	0.343302	−	0.673768i
$413$	10.0297	+	25.3175i	0.493529	+	1.24579i
$414$	−0.601294	−	0.195372i	−0.0295520	−	0.00960203i
$415$	3.63661	−	8.76310i	0.178514	−	0.430164i
$416$	0.150309	−	0.707147i	0.00736949	−	0.0346707i
$417$	1.82959	+	1.48157i	0.0895953	+	0.0725528i
$418$	−0.00341149		0.000914107i	−0.000166862		4.47104e-5i
$419$	2.20460	−	1.60174i	0.107702	−	0.0782499i	−0.532631	−	0.846348i	$-0.678797\pi$
$419$	2.20460	−	1.60174i	0.107702	−	0.0782499i	0.640333	+	0.768098i	$0.278797\pi$
$420$	0.506382	+	1.18873i	0.0247089	+	0.0580041i
$421$	27.0480	+	19.6515i	1.31824	+	0.957756i	0.999952	+	0.00976112i	$0.00310711\pi$
$421$	27.0480	+	19.6515i	1.31824	+	0.957756i	0.318286	+	0.947995i	$0.396893\pi$
$422$	0.224812	+	0.277620i	0.0109437	+	0.0135143i
$423$	21.2717	+	1.11480i	1.03427	+	0.0542037i
$424$	−0.384812	−	0.222171i	−0.0186881	−	0.0107896i
$425$	19.9573	−	8.85386i	0.968072	−	0.429475i
$426$			0.0279829i			0.00135577i
$427$	13.9974	−	14.2994i	0.677384	−	0.691996i
$428$	−3.37386	−	21.3017i	−0.163082	−	1.02966i
$429$	0.240676	+	0.0252961i	0.0116200	+	0.00122131i
$430$	0.401090	+	0.0107692i	0.0193423	+	0.000519338i
$431$	3.25558	+	30.9747i	0.156816	+	1.49200i	0.736099	+	0.676874i	$0.236666\pi$
$431$	3.25558	+	30.9747i	0.156816	+	1.49200i	−0.579283	+	0.815126i	$0.696668\pi$
$432$	0.676023	−	2.52295i	0.0325252	−	0.121386i
$433$	0.835932	−	5.27787i	0.0401723	−	0.253638i	−0.959427	−	0.281959i	$-0.909016\pi$
$433$	0.835932	−	5.27787i	0.0401723	−	0.253638i	0.999599	+	0.0283205i	$0.00901590\pi$
$434$	0.345419	−	0.0400356i	0.0165806	−	0.00192177i
$435$	−0.538582	−	1.52412i	−0.0258231	−	0.0730761i
$436$	5.63278	−	1.19729i	0.269761	−	0.0573396i
$437$	0.210699	+	0.324448i	0.0100791	+	0.0155204i
$438$	−0.000956293	−	0.00147256i	−4.56935e−5	−	7.03617e-5i
$439$	26.1495	−	5.55824i	1.24805	−	0.265280i	0.463917	−	0.885878i	$-0.346443\pi$
$439$	26.1495	−	5.55824i	1.24805	−	0.265280i	0.784129	+	0.620598i	$0.213110\pi$
$440$	−0.153586	−	0.434629i	−0.00732191	−	0.0207201i
$441$	−18.9222	+	8.91326i	−0.901057	+	0.424441i
$442$	−0.0411916	+	0.260074i	−0.00195929	+	0.0123704i
$443$	−7.64058	+	28.5150i	−0.363015	+	1.35479i	0.507077	+	0.861901i	$0.330726\pi$
$443$	−7.64058	+	28.5150i	−0.363015	+	1.35479i	−0.870092	+	0.492889i	$0.835941\pi$
$444$	0.176720	+	1.68137i	0.00838674	+	0.0797945i
$445$	17.9957	+	0.483183i	0.853080	+	0.0229051i
$446$	0.936448	+	0.0984247i	0.0443421	+	0.00466054i
$447$	−0.335564	−	2.11867i	−0.0158717	−	0.100210i
$448$	−5.67202	−	20.2994i	−0.267978	−	0.959055i
$449$		−	16.6858i		−	0.787450i	−0.919228	−	0.393725i	$-0.871186\pi$
$449$		−	16.6858i		−	0.787450i	0.919228	−	0.393725i	$-0.128814\pi$
$450$	0.547397	+	0.117112i	0.0258045	+	0.00552072i
$451$	−11.4304	−	6.59932i	−0.538235	−	0.310750i
$452$	20.2733	+	1.06248i	0.953575	+	0.0499747i
$453$	0.627549	+	0.774959i	0.0294848	+	0.0364107i
$454$	0.375079	+	0.272511i	0.0176033	+	0.0127896i
$455$	−1.14828	+	9.45195i	−0.0538321	+	0.443114i
$456$	0.000907371	0	0.000659243i	4.24915e−5	0	3.08719e-5i
$457$	10.2464	+	2.74552i	0.479308	+	0.128430i	0.490380	−	0.871509i	$-0.336858\pi$
$457$	10.2464	+	2.74552i	0.479308	+	0.128430i	−0.0110724	+	0.999939i	$0.503525\pi$
$458$	−0.430047	−	0.348245i	−0.0200948	−	0.0162724i
$459$	−0.594080	+	2.79493i	−0.0277293	+	0.130456i
$460$	−9.67330	+	23.3097i	−0.451020	+	1.08682i
$461$	−19.5350	−	6.34729i	−0.909833	−	0.295623i	−0.183544	−	0.983012i	$-0.558757\pi$
$461$	−19.5350	−	6.34729i	−0.909833	−	0.295623i	−0.726290	+	0.687389i	$0.758757\pi$
$462$	−0.0138581	+	0.00549000i	−0.000644739	+	0.000255418i
$463$	−1.32037	+	2.59137i	−0.0613628	+	0.120431i	−0.919651	−	0.392737i	$-0.871528\pi$
$463$	−1.32037	+	2.59137i	−0.0613628	+	0.120431i	0.858288	+	0.513168i	$0.171528\pi$
$464$	5.49004	+	25.8286i	0.254869	+	1.19906i
$465$	0.409492	−	0.752998i	0.0189897	−	0.0349195i
$466$	−0.0444770	−	0.00945387i	−0.00206036	−	0.000437942i
$467$	−2.62833	−	6.84704i	−0.121625	−	0.316843i	0.859228	−	0.511592i	$-0.170944\pi$
$467$	−2.62833	−	6.84704i	−0.121625	−	0.316843i	−0.980853	+	0.194749i	$0.937611\pi$
$468$	6.79623	−	6.79623i	0.314156	−	0.314156i
$469$	−2.20556	+	23.3818i	−0.101843	+	1.07967i
$470$	−0.0783497	+	0.592089i	−0.00361400	+	0.0273110i
$471$	0.210887	−	2.00646i	0.00971716	−	0.0924526i
$472$	1.43962	+	0.552619i	0.0662639	+	0.0254363i
$473$	0.344880	−	6.58070i	0.0158576	−	0.302581i
$474$	0.0186381	+	0.0322821i	0.000856077	+	0.00148277i
$475$	−0.215205	−	0.266478i	−0.00987429	−	0.0122269i
$476$	7.36903	+	21.8823i	0.337759	+	1.00297i
$477$	−4.02332	−	7.89620i	−0.184215	−	0.361542i
$478$	−0.749338	+	0.606802i	−0.0342739	+	0.0277545i
$479$	5.39262	−	2.40095i	0.246395	−	0.109702i	−0.279824	−	0.960051i	$-0.590276\pi$
$479$	5.39262	−	2.40095i	0.246395	−	0.109702i	0.526219	+	0.850349i	$0.323609\pi$
$480$	0.103443	+	0.0367083i	0.00472150	+	0.00167550i
$481$	−5.06726	+	11.3812i	−0.231047	+	0.518940i
$482$	−0.362945	−	0.362945i	−0.0165317	−	0.0165317i
$483$	1.53044	+	0.568820i	0.0696373	+	0.0258822i
$484$	17.3097	−	5.62427i	0.786805	−	0.255649i
$485$	2.93491	−	36.9778i	0.133267	−	1.67908i
$486$	−0.0817193	+	0.0735804i	−0.00370686	+	0.00333767i
$487$	−14.5855	+	9.47193i	−0.660932	+	0.429214i	−0.831041	−	0.556211i	$-0.812255\pi$
$487$	−14.5855	+	9.47193i	−0.660932	+	0.429214i	0.170109	+	0.985425i	$0.445588\pi$
$488$	−0.0593018	−	1.13155i	−0.00268447	−	0.0512227i
$489$	0.116731	−	0.359261i	0.00527875	−	0.0162463i
$490$	−0.207155	−	0.548664i	−0.00935831	−	0.0247861i
$491$	−1.67096	−	5.14268i	−0.0754092	−	0.232086i	0.906246	−	0.422751i	$-0.138936\pi$
$491$	−1.67096	−	5.14268i	−0.0754092	−	0.232086i	−0.981655	+	0.190665i	$0.938936\pi$
$492$	1.95580	−	0.750762i	0.0881743	−	0.0338470i
$493$	−7.47643	−	27.9024i	−0.336721	−	1.25666i
$494$	0.00410836		0.000431806i	0.000184844		1.94279e-5i
$495$	2.15215	−	8.93824i	0.0967321	−	0.401744i
$496$	−8.22993	+	11.3275i	−0.369535	+	0.508621i
$497$	−0.753618	+	18.0662i	−0.0338044	+	0.810381i
$498$	−0.0154794	+	0.00788715i	−0.000693648	+	0.000353432i
$499$	2.08554	−	1.20409i	0.0933616	−	0.0539023i	−0.452592	−	0.891718i	$-0.649501\pi$
$499$	2.08554	−	1.20409i	0.0933616	−	0.0539023i	0.545954	+	0.837815i	$0.316167\pi$
$500$	6.38895	−	21.4121i	0.285723	−	0.957580i
$501$	0.723867	−	1.25377i	0.0323400	−	0.0560145i
$502$	0.772438	+	0.501627i	0.0344756	+	0.0223887i
$503$	−24.0156	+	3.80370i	−1.07080	+	0.169599i	−0.666859	−	0.745184i	$-0.732362\pi$
$503$	−24.0156	+	3.80370i	−1.07080	+	0.169599i	−0.403946	+	0.914783i	$0.632362\pi$
$504$	−0.353968	+	1.13030i	−0.0157670	+	0.0503474i
$505$	6.39244	+	6.07426i	0.284460	+	0.270301i
$506$	−0.265973	−	0.118419i	−0.0118239	−	0.00526436i
$507$	1.09880	−	0.294423i	0.0487995	−	0.0130758i
$508$	−26.6164	+	32.8686i	−1.18091	+	1.45831i
$509$	−12.1317	+	13.4736i	−0.537726	+	0.597205i	−0.949378	−	0.314136i	$-0.898285\pi$
$509$	−12.1317	+	13.4736i	−0.537726	+	0.597205i	0.411652	+	0.911341i	$0.364952\pi$
$510$	−0.0383247	−	0.0113800i	−0.00169705	−	0.000503913i
$511$	−0.577742	−	0.976467i	−0.0255578	−	0.0431963i
$512$	−2.66325	−	1.35700i	−0.117700	−	0.0599713i
$513$	0.0447660	−	0.00234609i	0.00197647	−	0.000103582i
$514$	0.513655	+	0.570471i	0.0226563	+	0.0251624i
$515$	7.38274	+	15.5047i	0.325322	+	0.683219i
$516$	0.777293	+	0.699878i	0.0342184	+	0.0308104i
$517$	9.68824	+	1.53447i	0.426088	+	0.0674858i
$518$	−0.0483347	−	0.765840i	−0.00212371	−	0.0336491i
$519$	−0.651886	−	0.897245i	−0.0286146	−	0.0393847i
$520$	0.349889	+	0.410218i	0.0153436	+	0.0179892i
$521$	6.29845	+	14.1465i	0.275940	+	0.619772i	0.997351	−	0.0727354i	$-0.0231729\pi$
$521$	6.29845	+	14.1465i	0.275940	+	0.619772i	−0.721411	+	0.692507i	$0.756506\pi$
$522$	0.265419	−	0.691440i	0.0116171	−	0.0302635i
$523$	−10.7494	+	16.5526i	−0.470037	+	0.723794i	−0.991589	−	0.129426i	$-0.958687\pi$
$523$	−10.7494	+	16.5526i	−0.470037	+	0.723794i	0.521552	+	0.853220i	$0.325353\pi$
$524$	−3.48022			−0.152034
$525$	−1.39979	−	0.361091i	−0.0610920	−	0.0157593i
$526$	−0.477293			−0.0208110
$527$	8.34233	−	12.8461i	0.363398	−	0.559583i
$528$	0.215092	−	0.560333i	0.00936067	−	0.0243854i
$529$	3.61606	+	8.12180i	0.157220	+	0.353122i
$530$	0.229631	−	0.0949376i	0.00997451	−	0.00412383i
$531$	18.0774	+	24.8813i	0.784490	+	1.07976i
$532$	0.301679	−	0.200521i	0.0130794	−	0.00869368i
$533$	15.2476	+	2.41499i	0.660448	+	0.104605i
$534$	−0.0244969	−	0.0220571i	−0.00106008	−	0.000954503i
$535$	21.1981	+	11.5278i	0.916473	+	0.498392i
$536$	0.889882	+	0.988314i	0.0384371	+	0.0426887i
$537$	0.984820	−	0.0516122i	0.0424981	−	0.00222723i
$538$	0.663472	+	0.338056i	0.0286043	+	0.0145746i
$539$	−9.09492	+	3.17122i	−0.391746	+	0.136594i
$540$	1.77870	+	2.32123i	0.0765429	+	0.0998898i
$541$	−18.2785	+	20.3003i	−0.785853	+	0.872778i	−0.994449	−	0.105224i	$-0.966444\pi$
$541$	−18.2785	+	20.3003i	−0.785853	+	0.872778i	0.208596	+	0.978002i	$0.433111\pi$
$542$	0.190366	−	0.235082i	0.00817691	−	0.0100976i
$543$	1.67295	−	0.448267i	0.0717933	−	0.0192370i
$544$	1.79189	+	0.797803i	0.0768269	+	0.0342055i
$545$	−2.77758	+	5.81339i	−0.118978	+	0.249018i
$546$	0.0128313	−	0.0118037i	0.000549128	−	0.000505150i
$547$	10.0134	−	1.58597i	0.428143	−	0.0678111i	0.0613554	−	0.998116i	$-0.480458\pi$
$547$	10.0134	−	1.58597i	0.428143	−	0.0678111i	0.366787	+	0.930305i	$0.380458\pi$
$548$	−10.6763	−	6.93325i	−0.456068	−	0.296174i
$549$	11.2995	−	19.5712i	0.482249	−	0.835280i
$550$	0.245056	+	0.0799833i	0.0104492	+	0.00341050i
$551$	−0.392470	+	0.226593i	−0.0167198	+	0.00965317i
$552$	0.0823786	−	0.0419740i	0.00350627	−	0.00178653i
$553$	11.1637	+	21.3439i	0.474728	+	0.907634i
$554$	−0.0891673	+	0.122728i	−0.00378836	+	0.00521423i
$555$	−1.61213	−	0.989384i	−0.0684309	−	0.0419970i
$556$	42.8209	−	4.50066i	1.81601	−	0.190870i
$557$	0.0898136	+	0.335189i	0.00380552	+	0.0142024i	0.967802	−	0.251711i	$-0.0809932\pi$
$557$	0.0898136	+	0.335189i	0.00380552	+	0.0142024i	−0.963997	+	0.265913i	$0.914327\pi$
$558$	0.366636	−	0.140738i	0.0155209	−	0.00595793i
$559$	2.38179	+	7.33039i	0.100739	+	0.310042i
$560$	21.9063	+	8.81812i	0.925709	+	0.372634i
$561$	−0.202898	+	0.624456i	−0.00856637	+	0.0263646i
$562$	−0.00251713	−	0.0480297i	−0.000106179	−	0.00202601i
$563$	12.6921	−	8.24238i	0.534910	−	0.347375i	−0.248747	−	0.968569i	$-0.580019\pi$
$563$	12.6921	−	8.24238i	0.534910	−	0.347375i	0.783657	+	0.621194i	$0.213352\pi$
$564$	−1.15702	+	1.04179i	−0.0487195	+	0.0438672i
$565$	−14.7625	+	17.2615i	−0.621065	+	0.726197i
$566$	−0.0111585	+	0.00362563i	−0.000469029	+	0.000152397i
$567$	−18.1255	+	15.0008i	−0.761200	+	0.629973i
$568$	0.724020	+	0.724020i	0.0303792	+	0.0303792i
$569$	3.67748	−	8.25975i	0.154168	−	0.346267i	−0.819905	−	0.572499i	$-0.805974\pi$
$569$	3.67748	−	8.25975i	0.154168	−	0.346267i	0.974073	+	0.226232i	$0.0726407\pi$
$570$	−1.68341e−5	0	0.000626972i	−7.05104e−7	0	2.62610e-5i
$571$	16.8896	−	7.51972i	0.706806	−	0.314690i	−0.0216664	−	0.999765i	$-0.506897\pi$
$571$	16.8896	−	7.51972i	0.706806	−	0.314690i	0.728473	+	0.685075i	$0.240231\pi$
$572$	3.43963	−	2.78536i	0.143818	−	0.116462i
$573$	1.11061	+	2.17969i	0.0463963	+	0.0910579i
$574$	−0.901151	+	0.303469i	−0.0376133	+	0.0126666i
$575$	−14.0854	−	24.4716i	−0.587403	−	1.02054i
$576$	−11.9019	−	20.6147i	−0.495914	−	0.858947i
$577$	1.38404	−	26.4090i	0.0576183	−	1.09942i	−0.804905	−	0.593404i	$-0.797784\pi$
$577$	1.38404	−	26.4090i	0.0576183	−	1.09942i	0.862523	−	0.506018i	$-0.168883\pi$
$578$	−0.0723172	−	0.0277600i	−0.00300800	−	0.00115466i
$579$	0.139121	−	1.32365i	0.00578166	−	0.0550088i
$580$	−26.6755	−	12.7453i	−1.10764	−	0.529220i
$581$	−10.2062	+	4.67520i	−0.423424	+	0.193960i
$582$	−0.0480288	+	0.0480288i	−0.00199086	+	0.00199086i
$583$	−1.46249	−	3.80992i	−0.0605702	−	0.157791i
$584$	−0.0628434	−	0.0133578i	−0.00260048	−	0.000552749i
$585$	1.39652	+	10.6623i	0.0577389	+	0.440830i
$586$	−0.153612	−	0.722688i	−0.00634566	−	0.0298540i
$587$	−8.79450	+	17.2602i	−0.362988	+	0.712404i	−0.998202	−	0.0599321i	$-0.980912\pi$
$587$	−8.79450	+	17.2602i	−0.362988	+	0.712404i	0.635215	+	0.772336i	$0.280912\pi$
$588$	0.517301	−	1.43865i	0.0213331	−	0.0593288i
$589$	−0.228540	−	0.0742572i	−0.00941683	−	0.00305971i
$590$	−0.735557	+	0.450079i	−0.0302824	+	0.0185294i
$591$	−0.303196	+	1.42642i	−0.0124718	+	0.0586752i
$592$	24.0125	+	19.4450i	0.986909	+	0.799183i
$593$	39.8994	+	10.6910i	1.63847	+	0.439027i	0.956353	−	0.292215i	$-0.0943924\pi$
$593$	39.8994	+	10.6910i	1.63847	+	0.439027i	0.682118	+	0.731242i	$0.261059\pi$
$594$	−0.0272933	+	0.0198297i	−0.00111986	+	0.000813623i
$595$	−24.4366	−	8.37924i	−1.00180	−	0.343515i
$596$	−31.7389	−	23.0597i	−1.30008	−	0.944560i
$597$	−1.26122	−	1.55748i	−0.0516183	−	0.0637433i
$598$	0.340068	+	0.0178222i	0.0139064	+	0.000728803i
$599$	2.44181	+	1.40978i	0.0997698	+	0.0576021i	0.549055	−	0.835786i	$-0.314988\pi$
$599$	2.44181	+	1.40978i	0.0997698	+	0.0576021i	−0.449285	+	0.893389i	$0.648321\pi$
$600$	−0.0687130	+	0.0444932i	−0.00280520	+	0.00181643i
$601$		−	33.6982i		−	1.37458i	−0.726384	−	0.687289i	$-0.758801\pi$
$601$		−	33.6982i		−	1.37458i	0.726384	−	0.687289i	$-0.241199\pi$
$602$	−0.339260	−	0.332096i	−0.0138272	−	0.0135352i
$603$	4.14929	+	26.1976i	0.168972	+	1.06685i
$604$	18.1377	+	1.90634i	0.738011	+	0.0775680i
$605$	−6.81007	+	19.1906i	−0.276869	+	0.780208i
$606$	−0.00168781	−	0.0160584i	−6.85626e−5	−	0.000652330i
$607$	8.74821	−	32.6488i	0.355079	−	1.32517i	−0.525306	−	0.850913i	$-0.676049\pi$
$607$	8.74821	−	32.6488i	0.355079	−	1.32517i	0.880385	−	0.474259i	$-0.157284\pi$
$608$	0.00481385	−	0.0303934i	0.000195227	−	0.00123262i
$609$	−0.759258	+	1.75549i	−0.0307667	+	0.0711362i
$610$	0.521964	+	0.359246i	0.0211337	+	0.0145455i
$611$	−11.2223	+	2.38538i	−0.454007	+	0.0965021i
$612$	14.2026	+	21.8701i	0.574107	+	0.884048i
$613$	−3.21949	−	4.95757i	−0.130034	−	0.200235i	0.767656	−	0.640862i	$-0.221423\pi$
$613$	−3.21949	−	4.95757i	−0.130034	−	0.200235i	−0.897690	+	0.440627i	$0.854756\pi$
$614$	0.764194	−	0.162434i	0.0308404	−	0.00655532i
$615$	−0.667185	+	2.24690i	−0.0269035	+	0.0906039i
$616$	−0.216515	+	0.500608i	−0.00872363	+	0.0201701i
$617$	−0.740149	+	4.67312i	−0.0297973	+	0.188133i	−0.998097	−	0.0616571i	$-0.980361\pi$
$617$	−0.740149	+	4.67312i	−0.0297973	+	0.188133i	0.968300	+	0.249790i	$0.0803615\pi$
$618$	0.00813851	−	0.0303733i	0.000327379	−	0.00122180i
$619$	−0.113041	−	1.07551i	−0.00454350	−	0.0432285i	0.992015	−	0.126118i	$-0.0402518\pi$
$619$	−0.113041	−	1.07551i	−0.00454350	−	0.0432285i	−0.996559	+	0.0828895i	$0.973585\pi$
$620$	−4.44233	−	15.0337i	−0.178408	−	0.603767i
$621$	3.67506	+	0.386265i	0.147475	+	0.0155003i
$622$	0.0502765	+	0.317433i	0.00201590	+	0.0127279i
$623$	−15.2216	−	14.9002i	−0.609840	−	0.596963i
$624$			0.702018i			0.0281032i
$625$	14.6409	+	20.2644i	0.585636	+	0.810574i
$626$	−0.789090	−	0.455581i	−0.0315384	−	0.0182087i
$627$	0.0102867		0.000539105i	0.000410813		2.15298e-5i
$628$	−23.2208	−	28.6753i	−0.926612	−	1.14427i
$629$	−27.3460	−	19.8680i	−1.09036	−	0.792191i
$630$	−0.380600	−	0.542075i	−0.0151635	−	0.0215968i
$631$	−17.6839	+	12.8481i	−0.703983	+	0.511474i	−0.881227	−	0.472693i	$-0.843282\pi$
$631$	−17.6839	+	12.8481i	−0.703983	+	0.511474i	0.177244	+	0.984167i	$0.443282\pi$
$632$	1.31749	+	0.353022i	0.0524071	+	0.0140424i
$633$	−0.809698	−	0.655680i	−0.0321826	−	0.0260610i
$634$	0.0356460	−	0.167701i	0.00141568	−	0.00666026i
$635$	−11.0159	−	46.0192i	−0.437154	−	1.82621i
$636$	0.616047	+	0.200166i	0.0244279	+	0.00793709i
$637$	8.60199	−	7.27508i	0.340823	−	0.288249i
$638$	0.154838	−	0.303886i	0.00613008	−	0.0120310i
$639$	4.24584	+	19.9751i	0.167963	+	0.790204i
$640$	2.41635	−	1.15057i	0.0955146	−	0.0454804i
$641$	21.5459	+	4.57972i	0.851011	+	0.180888i	0.612715	−	0.790304i	$-0.290078\pi$
$641$	21.5459	+	4.57972i	0.851011	+	0.180888i	0.238297	+	0.971192i	$0.423411\pi$
$642$	−0.0158342	−	0.0412494i	−0.000624924	−	0.00162798i
$643$	−7.57933	+	7.57933i	−0.298899	+	0.298899i	−0.840583	−	0.541683i	$-0.817787\pi$
$643$	−7.57933	+	7.57933i	−0.298899	+	0.298899i	0.541683	+	0.840583i	$0.317787\pi$
$644$	27.1482	−	12.4359i	1.06979	−	0.490044i
$645$	−1.15078	+	0.212494i	−0.0453117	+	0.00836694i
$646$	−0.00117156	+	0.0111467i	−4.60945e−5	+	0.000438560i
$647$	−32.4289	−	12.4483i	−1.27491	−	0.489393i	−0.375633	−	0.926769i	$-0.622575\pi$
$647$	−32.4289	−	12.4483i	−1.27491	−	0.489393i	−0.899279	+	0.437376i	$0.855908\pi$
$648$	−0.0697271	+	1.33047i	−0.00273914	+	0.0522659i
$649$	7.08130	+	12.2652i	0.277965	+	0.481450i
$650$	−0.301117	+	0.0153802i	−0.0118108	+	0.000603262i
$651$	−0.961146	+	0.323673i	−0.0376703	+	0.0126857i
$652$	−3.13647	−	6.15566i	−0.122834	−	0.241074i
$653$	12.9000	−	10.4462i	0.504817	−	0.408792i	−0.342794	−	0.939410i	$-0.611373\pi$
$653$	12.9000	−	10.4462i	0.504817	−	0.408792i	0.847611	+	0.530618i	$0.178040\pi$
$654$	0.0107775	−	0.00479847i	0.000421435	−	0.000187635i
$655$	2.37241	−	3.08753i	0.0926975	−	0.120640i
$656$	15.5730	−	34.9775i	0.608023	−	1.36564i
$657$	−0.906067	−	0.906067i	−0.0353490	−	0.0353490i
$658$	0.544414	−	0.450560i	0.0212235	−	0.0175647i
$659$	−23.7349	+	7.71192i	−0.924579	+	0.300414i	−0.732344	−	0.680935i	$-0.761574\pi$
$659$	−23.7349	+	7.71192i	−0.924579	+	0.300414i	−0.192235	+	0.981349i	$0.561574\pi$
$660$	0.350731	+	0.573195i	0.0136522	+	0.0223116i
$661$	2.27939	−	2.05237i	0.0886581	−	0.0798281i	−0.623610	−	0.781736i	$-0.714335\pi$
$661$	2.27939	−	2.05237i	0.0886581	−	0.0798281i	0.712268	+	0.701907i	$0.247668\pi$
$662$	0.0746719	−	0.0484925i	0.00290221	−	0.00188472i
$663$	−0.0401929	−	0.766926i	−0.00156096	−	0.0297849i
$664$	−0.196439	+	0.604578i	−0.00762333	+	0.0234622i
$665$	−0.0277536	+	0.404331i	−0.00107624	+	0.0156793i
$666$	−0.267808	−	0.824229i	−0.0103774	−	0.0319382i
$667$	−34.8766	+	13.3879i	−1.35043	+	0.518380i
$668$	−6.85292	−	25.5754i	−0.265147	−	0.989543i
$669$	−2.73122	+	0.287063i	−0.105595	+	0.0110985i
$670$	−0.741448	+	0.0578583i	−0.0286446	+	0.00223526i
$671$	6.11692	−	8.41922i	0.236141	−	0.325020i
$672$	−0.0601925	−	0.115082i	−0.00232198	−	0.00443939i
$673$	8.48294	−	4.32228i	0.326993	−	0.166611i	−0.282785	−	0.959183i	$-0.591258\pi$
$673$	8.48294	−	4.32228i	0.326993	−	0.166611i	0.609779	+	0.792572i	$0.291258\pi$
$674$	0.693099	−	0.400161i	0.0266972	−	0.0154136i
$675$	−3.27182	−	0.00434165i	−0.125933	−	0.000167110i
$676$	10.4025	−	18.0176i	0.400095	−	0.692985i
$677$	8.74643	+	5.68000i	0.336153	+	0.218300i	0.701666	−	0.712506i	$-0.252440\pi$
$677$	8.74643	+	5.68000i	0.336153	+	0.218300i	−0.365513	+	0.930806i	$0.619107\pi$
$678$	0.0410781	−	0.00650613i	0.00157760	−	0.000249867i
$679$	−32.3017	+	29.7147i	−1.23963	+	1.14035i
$680$	−1.28604	+	0.697159i	−0.0493174	+	0.0267348i
$681$	−1.23529	−	0.549985i	−0.0473363	−	0.0210755i
$682$	0.174684	−	0.0468065i	0.00668901	−	0.00179231i
$683$	6.01135	−	7.42340i	0.230018	−	0.284048i	−0.649049	−	0.760746i	$-0.724833\pi$
$683$	6.01135	−	7.42340i	0.230018	−	0.284048i	0.879067	+	0.476698i	$0.158166\pi$
$684$	0.273746	−	0.304026i	0.0104670	−	0.0116247i
$685$	13.4288	−	4.74536i	0.513087	−	0.181311i
$686$	−0.261809	+	0.642635i	−0.00999593	+	0.0245359i
$687$	1.43803	+	0.732711i	0.0548641	+	0.0279546i
$688$	19.0898	−	1.00045i	0.727791	−	0.0381419i
$689$	3.19395	+	3.54724i	0.121680	+	0.135139i
$690$	−0.00945575	+	0.0508304i	−0.000359974	+	0.00193508i
$691$	−17.3929	−	15.6606i	−0.661655	−	0.595757i	0.268342	−	0.963324i	$-0.413524\pi$
$691$	−17.3929	−	15.6606i	−0.661655	−	0.595757i	−0.929997	+	0.367567i	$0.880191\pi$
$692$	−20.0338	−	3.17305i	−0.761572	−	0.120621i
$693$	−9.05942	+	6.02165i	−0.344139	+	0.228744i
$694$	−0.577980	−	0.795521i	−0.0219398	−	0.0301976i
$695$	−25.1974	+	41.0573i	−0.955793	+	1.55739i
$696$	0.0440524	+	0.0989432i	0.00166980	+	0.00375043i
$697$	−15.0103	+	39.1031i	−0.568555	+	1.48114i
$698$	0.341101	−	0.525249i	0.0129108	−	0.0198810i
$699$	0.132618			0.00501608
$700$	−22.7723	+	13.4328i	−0.860712	+	0.507713i
$701$	24.9909			0.943892			0.471946	−	0.881628i	$-0.343552\pi$
$701$	24.9909			0.943892			0.471946	+	0.881628i	$0.343552\pi$
$702$	0.0214912	−	0.0330935i	0.000811131	−	0.00124903i
$703$	−0.190039	+	0.495069i	−0.00716746	+	0.0186719i
$704$	−4.45848	−	10.0139i	−0.168035	−	0.377414i
$705$	−0.135517	−	1.73664i	−0.00510388	−	0.0654058i
$706$	0.634328	+	0.873078i	0.0238733	+	0.0328587i
$707$	−0.657204	−	10.4131i	−0.0247167	−	0.391624i
$708$	−2.22027	−	0.351657i	−0.0834430	−	0.0132161i
$709$	−36.0921	−	32.4975i	−1.35547	−	1.22047i	−0.952234	−	0.305371i	$-0.901220\pi$
$709$	−36.0921	−	32.4975i	−1.35547	−	1.22047i	−0.403233	−	0.915097i	$-0.632114\pi$
$710$	−0.567740	+	0.0743612i	−0.0213069	+	0.00279073i
$711$	18.2027	+	20.2161i	0.682654	+	0.758164i
$712$	−1.20452	+	0.0631263i	−0.0451414	+	0.00236576i
$713$	−17.6500	−	8.99310i	−0.660996	−	0.336794i
$714$	0.0240874	+	0.0407111i	0.000901447	+	0.00152358i
$715$	0.126340	+	4.95026i	0.00472487	+	0.185129i
$716$	12.0685	−	13.4034i	0.451022	−	0.500910i
$717$	1.76978	−	2.18550i	0.0660937	−	0.0816189i
$718$	0.162441	−	0.0435259i	0.00606224	−	0.00162437i
$719$	−5.43700	−	2.42071i	−0.202766	−	0.0902773i	0.302841	−	0.953041i	$-0.402065\pi$
$719$	−5.43700	−	2.42071i	−0.202766	−	0.0902773i	−0.505607	+	0.862764i	$0.668731\pi$
$720$	26.4393	+	3.49864i	0.985333	+	0.130387i
$721$	6.07237	−	19.3904i	0.226147	−	0.722136i
$722$	−0.702956	+	0.111337i	−0.0261613	+	0.00414354i
$723$	1.25551	+	0.815336i	0.0466928	+	0.0303227i
$724$	15.8380	−	27.4323i	0.588615	−	1.01951i
$725$	29.4915	−	14.9774i	1.09529	−	0.556246i
$726$	0.0322913	−	0.0186434i	0.00119844	−	0.000691921i
$727$	−9.26956	+	4.72308i	−0.343789	+	0.175169i	−0.617356	−	0.786684i	$-0.711796\pi$
$727$	−9.26956	+	4.72308i	−0.343789	+	0.175169i	0.273567	+	0.961853i	$0.411796\pi$
$728$	0.0265885	−	0.637396i	0.000985434	−	0.0236235i
$729$	−15.4924	+	21.3235i	−0.573793	+	0.789759i
$730$	0.0273353	−	0.0233152i	0.00101173	−	0.000862935i
$731$	−20.7975	+	2.18591i	−0.769225	+	0.0808488i
$732$	0.427518	+	1.59552i	0.0158015	+	0.0589720i
$733$	35.7938	−	13.7400i	1.32208	−	0.507497i	0.407978	−	0.912992i	$-0.366234\pi$
$733$	35.7938	−	13.7400i	1.32208	−	0.507497i	0.914097	+	0.405494i	$0.132901\pi$
$734$	−0.379860	−	1.16909i	−0.0140209	−	0.0431519i
$735$	0.923684	+	1.43963i	0.0340706	+	0.0531017i
$736$	0.783879	−	2.41253i	0.0288942	−	0.0889271i
$737$	0.639246	+	12.1975i	0.0235469	+	0.449302i
$738$	−0.900650	+	0.584889i	−0.0331534	+	0.0215301i
$739$	21.5518	−	19.4054i	0.792797	−	0.713838i	−0.169592	−	0.985514i	$-0.554245\pi$
$739$	21.5518	−	19.4054i	0.792797	−	0.713838i	0.962389	+	0.271677i	$0.0875782\pi$
$740$	−33.6435	+	8.05349i	−1.23676	+	0.296052i
$741$	−0.0114586	+	0.00372314i	−0.000420944	+	0.000136773i
$742$	−0.275589	−	0.102428i	−0.0101172	−	0.00376027i
$743$	−26.0302	−	26.0302i	−0.954956	−	0.954956i	0.0440723	−	0.999028i	$-0.485967\pi$
$743$	−26.0302	−	26.0302i	−0.954956	−	0.954956i	−0.999028	+	0.0440723i	$0.985967\pi$
$744$	−0.0233587	+	0.0524646i	−0.000856373	+	0.00192345i
$745$	42.0936	−	12.4383i	1.54219	−	0.455705i
$746$	−1.29145	+	0.574990i	−0.0472833	+	0.0210519i
$747$	−9.85301	+	7.97881i	−0.360503	+	0.291929i
$748$	5.45172	+	10.6996i	0.199335	+	0.391216i
$749$	−9.11191	−	27.0578i	−0.332942	−	0.988669i
$750$	0.00368248	−	0.0456290i	0.000134465	−	0.00166614i
$751$	3.63171	+	6.29030i	0.132523	+	0.229536i	0.924648	−	0.380822i	$-0.124359\pi$
$751$	3.63171	+	6.29030i	0.132523	+	0.229536i	−0.792126	+	0.610358i	$0.791026\pi$
$752$	−1.48920	+	28.4157i	−0.0543057	+	1.03621i
$753$	−2.50782	−	0.962662i	−0.0913901	−	0.0350814i
$754$	−0.0416982	+	0.396732i	−0.00151856	+	0.0144481i
$755$	−14.0554	+	14.7916i	−0.511527	+	0.538322i
$756$	0.324947	−	3.44485i	0.0118182	−	0.125288i
$757$	−19.0809	+	19.0809i	−0.693507	+	0.693507i	−0.963002	−	0.269495i	$-0.913143\pi$
$757$	−19.0809	+	19.0809i	−0.693507	+	0.693507i	0.269495	+	0.963002i	$0.413143\pi$
$758$	0.0513066	+	0.133658i	0.00186354	+	0.00485469i
$759$	0.830586	+	0.176546i	0.0301483	+	0.00640823i
$760$	0.0157865	+	0.0166576i	0.000572637	+	0.000604236i
$761$	−1.15394	−	5.42884i	−0.0418302	−	0.196795i	0.952271	−	0.305255i	$-0.0987416\pi$
$761$	−1.15394	−	5.42884i	−0.0418302	−	0.196795i	−0.994101	+	0.108459i	$0.965408\pi$
$762$	−0.0393365	+	0.0772023i	−0.00142501	+	0.00279674i
$763$	7.08741	−	2.80772i	0.256581	−	0.101646i
$764$	42.5511	+	13.8257i	1.53944	+	0.500196i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0204066 - 0.0314234i) q^{2} +(-0.0391619 + 0.102020i) q^{3} +(0.812902 + 1.82581i) q^{4} +(-2.17394 - 0.523442i) q^{5} +(0.00240666 + 0.00331248i) q^{6} +(1.46457 + 2.20341i) q^{7} +(0.147975 + 0.0234370i) q^{8} +(2.22056 + 1.99940i) q^{9} +O(q^{10})\)	\(q+(0.0204066 - 0.0314234i) q^{2} +(-0.0391619 + 0.102020i) q^{3} +(0.812902 + 1.82581i) q^{4} +(-2.17394 - 0.523442i) q^{5} +(0.00240666 + 0.00331248i) q^{6} +(1.46457 + 2.20341i) q^{7} +(0.147975 + 0.0234370i) q^{8} +(2.22056 + 1.99940i) q^{9} +(-0.0608110 + 0.0576309i) q^{10} +(0.920718 + 1.02256i) q^{11} +(-0.218104 + 0.0114304i) q^{12} +(-1.43400 - 0.730661i) q^{13} +(0.0991256 - 0.00105770i) q^{14} +(0.138537 - 0.201287i) q^{15} +(-2.67089 + 2.96632i) q^{16} +(2.74801 - 3.39351i) q^{17} +(0.108142 - 0.0289766i) q^{18} +(-0.0625826 - 0.0278636i) q^{19} +(-0.811494 - 4.39470i) q^{20} +(-0.282148 + 0.0631262i) q^{21} +(0.0509210 - 0.00806510i) q^{22} +(-4.73611 - 3.07566i) q^{23} +(-0.00818604 + 0.0141786i) q^{24} +(4.45202 + 2.27586i) q^{25} +(-0.0522229 + 0.0301509i) q^{26} +(-0.583044 + 0.297076i) q^{27} +(-2.83246 + 4.46519i) q^{28} +(3.88840 - 5.35192i) q^{29} +(-0.00349804 - 0.00846088i) q^{30} +(3.48857 - 0.366663i) q^{31} +(0.116261 + 0.433891i) q^{32} +(-0.140379 + 0.0538864i) q^{33} +(-0.0505580 - 0.155602i) q^{34} +(-2.03053 - 5.55670i) q^{35} +(-1.84543 + 5.67963i) q^{36} +(-0.405127 - 7.73028i) q^{37} +(-0.00215267 + 0.00139796i) q^{38} +(0.130700 - 0.117683i) q^{39} +(-0.309421 - 0.128407i) q^{40} +(-9.12263 + 2.96412i) q^{41} +(-0.00377404 + 0.0101542i) q^{42} +(-3.38639 - 3.38639i) q^{43} +(-1.11855 + 2.51230i) q^{44} +(-3.78079 - 5.50891i) q^{45} +(-0.193296 + 0.0860608i) q^{46} +(5.54003 - 4.48623i) q^{47} +(-0.198028 - 0.388651i) q^{48} +(-2.71005 + 6.45412i) q^{49} +(0.162366 - 0.0934549i) q^{50} +(0.238589 + 0.413248i) q^{51} +(0.168343 - 3.21217i) q^{52} +(-2.76885 - 1.06286i) q^{53} +(-0.00256281 + 0.0243835i) q^{54} +(-1.46633 - 2.70493i) q^{55} +(0.165079 + 0.360376i) q^{56} +(0.00529350 - 0.00529350i) q^{57} +(-0.0888266 - 0.231401i) q^{58} +(10.0677 + 2.13996i) q^{59} +(0.480128 + 0.0893160i) q^{60} +(-1.57245 - 7.39781i) q^{61} +(0.0596680 - 0.117105i) q^{62} +(-1.15333 + 7.82108i) q^{63} +(-7.57643 - 2.46173i) q^{64} +(2.73497 + 2.33903i) q^{65} +(-0.00117136 + 0.00551082i) q^{66} +(6.89851 + 5.58630i) q^{67} +(8.42975 + 2.25874i) q^{68} +(0.499255 - 0.362730i) q^{69} +(-0.216047 - 0.0495872i) q^{70} +(5.52909 + 4.01712i) q^{71} +(0.281728 + 0.347905i) q^{72} +(-0.428243 - 0.0224433i) q^{73} +(-0.251179 - 0.145018i) q^{74} +(-0.406533 + 0.365068i) q^{75} -0.136914i q^{76} +(-0.904665 + 3.52633i) q^{77} +(-0.00103085 - 0.00650856i) q^{78} +(9.05420 + 0.951635i) q^{79} +(7.35904 - 5.05054i) q^{80} +(0.929537 + 8.84395i) q^{81} +(-0.0930190 + 0.347152i) q^{82} +(-0.663758 + 4.19080i) q^{83} +(-0.344615 - 0.463833i) q^{84} +(-7.75030 + 5.93885i) q^{85} +(-0.175517 + 0.0373072i) q^{86} +(0.393727 + 0.606287i) q^{87} +(0.112278 + 0.172893i) q^{88} +(-7.87491 + 1.67386i) q^{89} +(-0.250262 + 0.00638718i) q^{90} +(-0.490253 - 4.22980i) q^{91} +(1.76558 - 11.1474i) q^{92} +(-0.0992118 + 0.370263i) q^{93} +(-0.0279194 - 0.265635i) q^{94} +(0.121466 + 0.0933321i) q^{95} +(-0.0488186 - 0.00513104i) q^{96} +(2.59509 + 16.3848i) q^{97} +(0.147507 + 0.216866i) q^{98} +4.11154i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

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