LMFDB - Embedded newform 175.2.x.a.117.10

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			117.10
Character	$\chi$	$=$	175.117
Dual form			175.2.x.a.3.10

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{20}\right)$

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	0.845812	−	0.533481i	$-0.179117\pi$
$2$	0.0204066	+	0.0314234i	0.0144296	+	0.0222197i	−0.831382	+	0.555701i	$0.812450\pi$
$3$	−0.0391619	−	0.102020i	−0.0226101	−	0.0589014i	0.921811	−	0.387640i	$-0.126710\pi$
$3$	−0.0391619	−	0.102020i	−0.0226101	−	0.0589014i	−0.944421	+	0.328739i	$0.893376\pi$
$4$	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	−0.588177	−	0.808733i	$-0.700154\pi$
$11$	0.920718	−	1.02256i	0.277607	−	0.308314i	0.865783	+	0.500419i	$0.166821\pi$
$12$	−0.218104	−	0.0114304i	−0.0629612	−	0.00329966i
$13$	−1.43400	+	0.730661i	−0.397721	+	0.202649i	−0.641399	−	0.767207i	$-0.721646\pi$
$13$	−1.43400	+	0.730661i	−0.397721	+	0.202649i	0.243679	+	0.969856i	$0.421646\pi$
$14$	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	0.992490	−	0.122324i	$-0.0390346\pi$
$17$	2.74801	+	3.39351i	0.666489	+	0.823046i	−0.326001	+	0.945369i	$0.605701\pi$
$18$	0.108142	+	0.0289766i	0.0254893	+	0.00682984i
$19$	−0.0625826	+	0.0278636i	−0.0143574	+	0.00639234i	−0.413903	−	0.910321i	$-0.635835\pi$
$19$	−0.0625826	+	0.0278636i	−0.0143574	+	0.00639234i	0.399545	+	0.916713i	$0.369168\pi$
$20$	−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	−0.934010	−	0.357246i	$-0.883716\pi$
$23$	−4.73611	+	3.07566i	−0.987547	+	0.641320i	−0.0535361	+	0.998566i	$0.517049\pi$
$24$	−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	0.999453	+	0.0330712i	$0.0105288\pi$
$29$	3.88840	+	5.35192i	0.722058	+	0.993827i	−0.277395	+	0.960756i	$0.589471\pi$
$30$	−0.00349804	+	0.00846088i	−0.000638651	+	0.00154474i
$31$	3.48857	+	0.366663i	0.626565	+	0.0658546i	0.412489	−	0.910962i	$-0.364659\pi$
$31$	3.48857	+	0.366663i	0.626565	+	0.0658546i	0.214076	+	0.976817i	$0.431326\pi$
$32$	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	0.737086	+	0.675799i	$0.236201\pi$
$37$	−0.405127	+	7.73028i	−0.0666024	+	1.27085i	−0.803688	+	0.595050i	$0.797132\pi$
$38$	−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	−0.507618	−	0.861582i	$-0.669474\pi$
$41$	−9.12263	−	2.96412i	−1.42472	−	0.462918i	−0.917097	+	0.398664i	$0.869474\pi$
$42$	−0.00377404	−	0.0101542i	−0.000582347	−	0.00156683i
$43$	−3.38639	+	3.38639i	−0.516420	+	0.516420i	−0.916486	−	0.400067i	$-0.868987\pi$
$43$	−3.38639	+	3.38639i	−0.516420	+	0.516420i	0.400067	+	0.916486i	$0.368987\pi$
$44$	−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	0.941626	−	0.336661i	$-0.109298\pi$
$47$	5.54003	+	4.48623i	0.808096	+	0.654384i	−0.133529	+	0.991045i	$0.542631\pi$
$48$	−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	−0.541020	−	0.841010i	$-0.681962\pi$
$53$	−2.76885	+	1.06286i	−0.380331	+	0.145996i	0.160689	+	0.987005i	$0.448628\pi$
$54$	−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	0.501007	−	0.865443i	$-0.332963\pi$
$59$	10.0677	−	2.13996i	1.31071	−	0.278599i	0.809700	+	0.586844i	$0.199630\pi$
$60$	0.480128	−	0.0893160i	0.0619843	−	0.0115306i
$61$	−1.57245	+	7.39781i	−0.201332	+	0.947192i	0.755184	+	0.655513i	$0.227547\pi$
$61$	−1.57245	+	7.39781i	−0.201332	+	0.947192i	−0.956516	+	0.291679i	$0.905786\pi$
$62$	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	−0.107380	−	0.994218i	$-0.534246\pi$
$67$	6.89851	−	5.58630i	0.842787	−	0.682475i	0.950166	+	0.311743i	$0.100913\pi$
$68$	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	−0.209189	−	0.977875i	$-0.567082\pi$
$71$	5.52909	−	4.01712i	0.656182	−	0.476744i	0.865372	+	0.501131i	$0.167082\pi$
$72$	0.281728	−	0.347905i	0.0332020	−	0.0410010i
$73$	−0.428243	+	0.0224433i	−0.0501221	+	0.00262679i	−0.0773805	−	0.997002i	$-0.524656\pi$
$73$	−0.428243	+	0.0224433i	−0.0501221	+	0.00262679i	0.0272584	+	0.999628i	$0.491322\pi$
$74$	−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	0.419559	−	0.907728i	$-0.362185\pi$
$79$	9.05420	−	0.951635i	1.01868	−	0.107067i	0.599118	+	0.800661i	$0.295518\pi$
$80$	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	−0.996964	−	0.0778662i	$-0.975189\pi$
$83$	−0.663758	−	4.19080i	−0.0728569	−	0.460000i	0.924107	−	0.382134i	$-0.124811\pi$
$84$	−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	−0.229335	−	0.973348i	$-0.573655\pi$
$89$	−7.87491	−	1.67386i	−0.834739	−	0.177429i	−0.605404	+	0.795918i	$0.706988\pi$
$90$	−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	−0.400814	−	0.916159i	$-0.631273\pi$
$97$	2.59509	−	16.3848i	0.263492	−	1.66362i	0.664306	−	0.747461i	$-0.268727\pi$
$98$	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	−0.660197	−	0.751092i	$-0.729527\pi$
$101$	−3.41526	+	1.97180i	−0.339831	+	0.196202i	0.320366	+	0.947294i	$0.396194\pi$
$102$	0.0178544		0.000935712i	0.00176785		9.26493e-5i
$103$	−4.83309	+	5.96836i	−0.476218	+	0.588080i	−0.957481	−	0.288496i	$-0.906845\pi$
$103$	−4.83309	+	5.96836i	−0.476218	+	0.588080i	0.481263	+	0.876576i	$0.340178\pi$
$104$	−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	−0.724659	−	0.689108i	$-0.758003\pi$
$107$	−10.4235	+	2.79297i	−1.00768	+	0.270006i	−0.283019	+	0.959114i	$0.591336\pi$
$108$	−1.01636	+	0.823033i	−0.0977994	+	0.0791964i
$109$	0.599063	+	2.81837i	0.0573798	+	0.269951i	0.997480	−	0.0709472i	$-0.0226022\pi$
$109$	0.599063	+	2.81837i	0.0573798	+	0.269951i	−0.940100	+	0.340898i	$0.889269\pi$
$110$	−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	0.999639	+	0.0268803i	$0.00855729\pi$
$113$	4.61149	+	9.05056i	0.433812	+	0.851405i	−0.565826	+	0.824524i	$0.691443\pi$
$114$	−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	0.119588	−	0.992824i	$-0.461843\pi$
$127$	9.60727	−	18.8553i	0.852507	−	1.67314i	0.732919	−	0.680316i	$-0.238157\pi$
$128$	−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	0.879958	−	0.475052i	$-0.157571\pi$
$131$	−0.708263	−	1.59079i	−0.0618813	−	0.138988i	−0.941839	+	0.336064i	$0.890904\pi$
$132$	−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	0.295897	−	0.955220i	$-0.404382\pi$
$137$	−5.34189	−	3.46906i	−0.456388	−	0.296382i	−0.752285	+	0.658838i	$0.771048\pi$
$138$	−0.00121011	+	0.0230904i	−0.000103012	+	0.00196558i
$139$	6.65731	+	20.4891i	0.564665	+	1.73786i	0.668944	+	0.743313i	$0.266747\pi$
$139$	6.65731	+	20.4891i	0.564665	+	1.73786i	−0.104278	+	0.994548i	$0.533253\pi$
$140$	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	−0.399055	−	0.916927i	$-0.630662\pi$
$149$	−16.9996	−	9.81475i	−1.39266	−	0.804055i	−0.993610	+	0.112871i	$0.963995\pi$
$150$	0.00317573	−	0.0202245i	0.000259298	−	0.00165132i
$151$	4.56259	+	7.90264i	0.371299	+	0.643108i	0.989766	−	0.142703i	$-0.0455793\pi$
$151$	4.56259	+	7.90264i	0.371299	+	0.643108i	−0.618467	+	0.785811i	$0.712246\pi$
$152$	−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	−0.536601	−	0.843836i	$-0.680292\pi$
$157$	−17.8330	−	4.77834i	−1.42323	−	0.381353i	−0.886628	+	0.462483i	$0.846959\pi$
$158$	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	−0.0833374	−	0.996521i	$-0.526558\pi$
$163$	−3.45202	−	0.180913i	−0.270383	−	0.0141702i	−0.187046	+	0.982351i	$0.559891\pi$
$164$	−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	−0.640595	−	0.767879i	$-0.721312\pi$
$167$	−13.0850	+	2.07246i	−1.01255	+	0.160372i	−0.371954	+	0.928251i	$0.621312\pi$
$168$	−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	0.563618	−	0.826035i	$-0.309409\pi$
$173$	−5.52749	−	8.51158i	−0.420247	−	0.647123i	−0.983865	+	0.178912i	$0.942742\pi$
$174$	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	−0.997198	−	0.0748069i	$-0.976166\pi$
$179$	−3.67055	+	8.24419i	−0.274350	+	0.616200i	0.722848	+	0.691007i	$0.242833\pi$
$180$	6.98480	+	11.3812i	0.520616	+	0.848305i
$181$	−9.31589	+	12.8222i	−0.692445	+	0.953069i	0.307554	+	0.951531i	$0.400490\pi$
$181$	−9.31589	+	12.8222i	−0.692445	+	0.953069i	−0.999999	+	0.00153805i	$0.999510\pi$
$182$	−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	0.977833	+	0.209387i	$0.0671468\pi$
$191$	14.9793	+	16.6362i	1.08386	+	1.20375i	0.106028	+	0.994363i	$0.466187\pi$
$192$	0.547853	+	0.676542i	0.0395379	+	0.0488252i
$193$	−11.7643	−	3.15224i	−0.846814	−	0.226903i	−0.190779	−	0.981633i	$-0.561101\pi$
$193$	−11.7643	−	3.15224i	−0.846814	−	0.226903i	−0.656036	+	0.754730i	$0.727768\pi$
$194$	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	0.607161	−	0.794579i	$-0.292308\pi$
$197$	13.1804	+	2.08757i	0.939067	+	0.148734i	0.331906	+	0.943313i	$0.392308\pi$
$198$	0.129199	−	0.0839025i	0.00918174	−	0.00596269i
$199$	−9.16969	−	15.8824i	−0.650022	−	1.12587i	−0.983117	−	0.182978i	$-0.941426\pi$
$199$	−9.16969	−	15.8824i	−0.650022	−	1.12587i	0.333095	−	0.942893i	$-0.391907\pi$
$200$	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	−0.999796	−	0.0202178i	$-0.993564\pi$
$211$	−2.94624	−	9.06760i	−0.202828	−	0.624239i	0.796968	−	0.604022i	$-0.206436\pi$
$212$	−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	−0.0994426	−	0.995043i	$-0.531706\pi$
$223$	11.4092	−	22.3918i	0.764015	−	1.49946i	0.863458	−	0.504421i	$-0.168294\pi$
$224$	−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	−0.932040	−	0.362357i	$-0.881972\pi$
$227$	−0.647595	−	12.3568i	−0.0429824	−	0.820153i	0.889057	−	0.457796i	$-0.151361\pi$
$228$	0.0139680	−	0.00536182i	0.000925054	−	0.000355095i
$229$	1.54378	+	14.6881i	0.102016	+	0.970617i	0.919080	+	0.394070i	$0.128933\pi$
$229$	1.54378	+	14.6881i	0.102016	+	0.970617i	−0.817064	+	0.576547i	$0.804400\pi$
$230$	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	−0.947088	−	0.320973i	$-0.895990\pi$
$233$	−0.434909	+	1.13298i	−0.0284918	+	0.0742237i	0.918597	+	0.395197i	$0.129324\pi$
$234$	−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	−0.962864	−	0.269986i	$-0.912981\pi$
$239$	−24.4748	+	7.95235i	−1.58314	+	0.514395i	−0.620280	+	0.784380i	$0.712981\pi$
$240$	0.227064	−	0.948560i	0.0146569	−	0.0612293i
$241$	2.84821	+	13.3998i	0.183470	+	0.863156i	0.969524	+	0.244998i	$0.0787874\pi$
$241$	2.84821	+	13.3998i	0.183470	+	0.863156i	−0.786054	+	0.618158i	$0.787879\pi$
$242$	−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	$-0.717352\pi$
$251$		−	24.5816i		−	1.55158i	0.630992	−	0.775789i	$-0.282648\pi$
$252$	−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	−0.908381	−	0.418143i	$-0.862681\pi$
$257$	−5.30267	−	19.7898i	−0.330772	−	1.23446i	0.577610	−	0.816313i	$-0.303986\pi$
$258$	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	−0.985186	−	0.171488i	$-0.945143\pi$
$263$	−6.93796	+	10.6835i	−0.427813	+	0.658774i	0.557373	+	0.830262i	$0.311809\pi$
$264$	−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	−0.727882	−	0.685703i	$-0.759495\pi$
$269$	2.07737	−	19.7649i	0.126660	−	1.20509i	0.854542	−	0.519383i	$-0.173838\pi$
$270$	0.0183348	+	0.0516668i	0.00111582	+	0.00314434i
$271$	8.02915	−	0.843898i	0.487736	−	0.0512631i	0.142531	−	0.989790i	$-0.454476\pi$
$271$	8.02915	−	0.843898i	0.487736	−	0.0512631i	0.345205	+	0.938527i	$0.387809\pi$
$272$	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	−0.173415	−	0.984849i	$-0.555480\pi$
$277$	−4.04324	+	0.211897i	−0.242935	+	0.0127317i	−0.0695201	+	0.997581i	$0.522147\pi$
$278$	−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	0.618330	−	0.785919i	$-0.287810\pi$
$281$	1.03849	+	0.754506i	0.0619510	+	0.0450100i	−0.556379	+	0.830929i	$0.687810\pi$
$282$	0.0281935	−	0.00755443i	0.00167890	−	0.000449860i
$283$	−0.243356	+	0.197066i	−0.0144660	+	0.0117143i	−0.636526	−	0.771255i	$-0.719629\pi$
$283$	−0.243356	+	0.197066i	−0.0144660	+	0.0117143i	0.622060	+	0.782969i	$0.286296\pi$
$284$	−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	0.985317	−	0.170733i	$-0.0546137\pi$
$293$	13.9434	+	13.9434i	0.814584	+	0.814584i	−0.170733	+	0.985317i	$0.554614\pi$
$294$	−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	−0.147555	−	0.989054i	$-0.547140\pi$
$307$	14.7442	−	14.7442i	0.841499	−	0.841499i	0.989054	+	0.147555i	$0.0471404\pi$
$308$	−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	0.468309	−	0.883565i	$-0.344863\pi$
$311$	−6.37447	−	5.73960i	−0.361463	−	0.325463i	−0.829773	+	0.558102i	$0.811530\pi$
$312$	0.0220986	+	0.0143510i	0.00125108	+	0.000812464i
$313$	−1.27272	+	24.2850i	−0.0719386	+	1.37267i	0.689430	+	0.724352i	$0.257861\pi$
$313$	−1.27272	+	24.2850i	−0.0719386	+	1.37267i	−0.761369	+	0.648319i	$0.775472\pi$
$314$	−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	0.475364	−	0.879789i	$-0.342316\pi$
$317$	4.27191	+	1.63983i	0.239934	+	0.0921021i	−0.235430	+	0.971891i	$0.575650\pi$
$318$	−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	−0.346207	−	0.938158i	$-0.612531\pi$
$331$	2.17087	−	0.966535i	0.119322	−	0.0531256i	0.465529	+	0.885032i	$0.345864\pi$
$332$	−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	0.149117	−	0.988820i	$-0.452357\pi$
$337$	19.0320	−	9.69727i	1.03674	−	0.528244i	0.887621	+	0.460575i	$0.152357\pi$
$338$	−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	0.915076	+	0.403282i	$0.132130\pi$
$347$	9.40506	+	24.5010i	0.504890	+	1.31528i	−0.410186	+	0.912002i	$0.634536\pi$
$348$	−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	−0.874270	−	0.485440i	$-0.838660\pi$
$353$	−10.3220	−	26.8897i	−0.549383	−	1.43119i	0.324887	−	0.945753i	$-0.394674\pi$
$354$	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	−0.576399	−	0.817168i	$-0.695543\pi$
$359$	3.33552	−	3.00332i	0.176042	−	0.158509i	0.752441	+	0.658659i	$0.228876\pi$
$360$	−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	0.940279	+	0.340406i	$0.110564\pi$
$367$	20.6467	+	25.4966i	1.07775	+	1.33091i	0.137472	+	0.990506i	$0.456102\pi$
$368$	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	−0.702539	+	0.711645i	$0.747950\pi$
$373$	−31.6429	+	20.5491i	−1.63841	+	1.06399i	−0.935869	+	0.352349i	$0.885383\pi$
$374$	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	0.747428	−	0.664343i	$-0.231288\pi$
$379$	−2.24596	−	3.09129i	−0.115367	−	0.158789i	−0.862795	+	0.505553i	$0.831288\pi$
$380$	−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	−0.0570442	−	0.998372i	$-0.518168\pi$
$383$	−15.0198	−	5.76557i	−0.767477	−	0.294607i	−0.710433	+	0.703765i	$0.751501\pi$
$384$	−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	0.325867	−	0.945415i	$-0.394344\pi$
$389$	−11.4454	−	10.3055i	−0.580306	−	0.522510i	−0.906174	+	0.422905i	$0.861010\pi$
$390$	−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	0.373102	−	0.927791i	$-0.378294\pi$
$397$	−9.10252	−	7.37108i	−0.456842	−	0.369944i	−0.829944	+	0.557847i	$0.811628\pi$
$398$	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	−0.661852	−	0.749635i	$-0.730229\pi$
$401$	6.37349	−	11.0392i	0.318277	−	0.551271i	0.980129	+	0.198363i	$0.0635626\pi$
$402$	−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	0.0434702	−	0.999055i	$-0.486159\pi$
$409$	9.90022	−	2.10436i	0.489534	−	0.104054i	0.446064	+	0.895001i	$0.352825\pi$
$410$	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	0.640333	−	0.768098i	$-0.278797\pi$
$419$	2.20460	+	1.60174i	0.107702	+	0.0782499i	−0.532631	+	0.846348i	$0.678797\pi$
$420$	0.506382	−	1.18873i	0.0247089	−	0.0580041i
$421$	27.0480	−	19.6515i	1.31824	−	0.957756i	0.318286	−	0.947995i	$-0.396893\pi$
$421$	27.0480	−	19.6515i	1.31824	−	0.957756i	0.999952	−	0.00976112i	$-0.00310711\pi$
$422$	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	−0.579283	−	0.815126i	$-0.696668\pi$
$431$	3.25558	−	30.9747i	0.156816	−	1.49200i	0.736099	−	0.676874i	$-0.236666\pi$
$432$	0.676023	+	2.52295i	0.0325252	+	0.121386i
$433$	0.835932	+	5.27787i	0.0401723	+	0.253638i	0.999599	−	0.0283205i	$-0.00901590\pi$
$433$	0.835932	+	5.27787i	0.0401723	+	0.253638i	−0.959427	+	0.281959i	$0.909016\pi$
$434$	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	0.784129	−	0.620598i	$-0.213110\pi$
$439$	26.1495	+	5.55824i	1.24805	+	0.265280i	0.463917	+	0.885878i	$0.346443\pi$
$440$	−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	−0.870092	−	0.492889i	$-0.835941\pi$
$443$	−7.64058	−	28.5150i	−0.363015	−	1.35479i	0.507077	−	0.861901i	$-0.330726\pi$
$444$	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	$0.128814\pi$
$449$			16.6858i			0.787450i	−0.919228	+	0.393725i	$0.871186\pi$
$450$	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	−0.0110724	−	0.999939i	$-0.503525\pi$
$457$	10.2464	−	2.74552i	0.479308	−	0.128430i	0.490380	+	0.871509i	$0.336858\pi$
$458$	−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	−0.726290	−	0.687389i	$-0.758757\pi$
$461$	−19.5350	+	6.34729i	−0.909833	+	0.295623i	−0.183544	+	0.983012i	$0.558757\pi$
$462$	−0.0138581	−	0.00549000i	−0.000644739	−	0.000255418i
$463$	−1.32037	−	2.59137i	−0.0613628	−	0.120431i	0.858288	−	0.513168i	$-0.171528\pi$
$463$	−1.32037	−	2.59137i	−0.0613628	−	0.120431i	−0.919651	+	0.392737i	$0.871528\pi$
$464$	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	−0.980853	−	0.194749i	$-0.937611\pi$
$467$	−2.62833	+	6.84704i	−0.121625	+	0.316843i	0.859228	+	0.511592i	$0.170944\pi$
$468$	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	0.526219	−	0.850349i	$-0.323609\pi$
$479$	5.39262	+	2.40095i	0.246395	+	0.109702i	−0.279824	+	0.960051i	$0.590276\pi$
$480$	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	0.170109	−	0.985425i	$-0.445588\pi$
$487$	−14.5855	−	9.47193i	−0.660932	−	0.429214i	−0.831041	+	0.556211i	$0.812255\pi$
$488$	−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	−0.981655	−	0.190665i	$-0.938936\pi$
$491$	−1.67096	+	5.14268i	−0.0754092	+	0.232086i	0.906246	+	0.422751i	$0.138936\pi$
$492$	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	0.545954	−	0.837815i	$-0.316167\pi$
$499$	2.08554	+	1.20409i	0.0933616	+	0.0539023i	−0.452592	+	0.891718i	$0.649501\pi$
$500$	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	−0.403946	−	0.914783i	$-0.632362\pi$
$503$	−24.0156	−	3.80370i	−1.07080	−	0.169599i	−0.666859	+	0.745184i	$0.732362\pi$
$504$	−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	0.411652	−	0.911341i	$-0.364952\pi$
$509$	−12.1317	−	13.4736i	−0.537726	−	0.597205i	−0.949378	+	0.314136i	$0.898285\pi$
$510$	−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	−0.721411	−	0.692507i	$-0.756506\pi$
$521$	6.29845	−	14.1465i	0.275940	−	0.619772i	0.997351	+	0.0727354i	$0.0231729\pi$
$522$	0.265419	+	0.691440i	0.0116171	+	0.0302635i
$523$	−10.7494	−	16.5526i	−0.470037	−	0.723794i	0.521552	−	0.853220i	$-0.325353\pi$
$523$	−10.7494	−	16.5526i	−0.470037	−	0.723794i	−0.991589	+	0.129426i	$0.958687\pi$
$524$	−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	0.208596	−	0.978002i	$-0.433111\pi$
$541$	−18.2785	−	20.3003i	−0.785853	−	0.872778i	−0.994449	+	0.105224i	$0.966444\pi$
$542$	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	0.366787	−	0.930305i	$-0.380458\pi$
$547$	10.0134	+	1.58597i	0.428143	+	0.0678111i	0.0613554	+	0.998116i	$0.480458\pi$
$548$	−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	−0.963997	−	0.265913i	$-0.914327\pi$
$557$	0.0898136	−	0.335189i	0.00380552	−	0.0142024i	0.967802	+	0.251711i	$0.0809932\pi$
$558$	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	0.783657	−	0.621194i	$-0.213352\pi$
$563$	12.6921	+	8.24238i	0.534910	+	0.347375i	−0.248747	+	0.968569i	$0.580019\pi$
$564$	−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	0.974073	−	0.226232i	$-0.0726407\pi$
$569$	3.67748	+	8.25975i	0.154168	+	0.346267i	−0.819905	+	0.572499i	$0.805974\pi$
$570$	−1.68341e−5	0	0.000626972i	−7.05104e−7	0	2.62610e-5i
$571$	16.8896	+	7.51972i	0.706806	+	0.314690i	0.728473	−	0.685075i	$-0.240231\pi$
$571$	16.8896	+	7.51972i	0.706806	+	0.314690i	−0.0216664	+	0.999765i	$0.506897\pi$
$572$	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	0.862523	+	0.506018i	$0.168883\pi$
$577$	1.38404	+	26.4090i	0.0576183	+	1.09942i	−0.804905	+	0.593404i	$0.797784\pi$
$578$	−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	0.635215	−	0.772336i	$-0.280912\pi$
$587$	−8.79450	−	17.2602i	−0.362988	−	0.712404i	−0.998202	+	0.0599321i	$0.980912\pi$
$588$	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	0.682118	−	0.731242i	$-0.261059\pi$
$593$	39.8994	−	10.6910i	1.63847	−	0.439027i	0.956353	+	0.292215i	$0.0943924\pi$
$594$	−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	−0.449285	−	0.893389i	$-0.648321\pi$
$599$	2.44181	−	1.40978i	0.0997698	−	0.0576021i	0.549055	+	0.835786i	$0.314988\pi$
$600$	−0.0687130	−	0.0444932i	−0.00280520	−	0.00181643i
$601$			33.6982i			1.37458i	0.726384	+	0.687289i	$0.241199\pi$
$601$			33.6982i			1.37458i	−0.726384	+	0.687289i	$0.758801\pi$
$602$	−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	0.880385	+	0.474259i	$0.157284\pi$
$607$	8.74821	+	32.6488i	0.355079	+	1.32517i	−0.525306	+	0.850913i	$0.676049\pi$
$608$	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	−0.897690	−	0.440627i	$-0.854756\pi$
$613$	−3.21949	+	4.95757i	−0.130034	+	0.200235i	0.767656	+	0.640862i	$0.221423\pi$
$614$	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	0.968300	−	0.249790i	$-0.0803615\pi$
$617$	−0.740149	−	4.67312i	−0.0297973	−	0.188133i	−0.998097	+	0.0616571i	$0.980361\pi$
$618$	0.00813851	+	0.0303733i	0.000327379	+	0.00122180i
$619$	−0.113041	+	1.07551i	−0.00454350	+	0.0432285i	−0.996559	−	0.0828895i	$-0.973585\pi$
$619$	−0.113041	+	1.07551i	−0.00454350	+	0.0432285i	0.992015	+	0.126118i	$0.0402518\pi$
$620$	−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	0.177244	−	0.984167i	$-0.443282\pi$
$631$	−17.6839	−	12.8481i	−0.703983	−	0.511474i	−0.881227	+	0.472693i	$0.843282\pi$
$632$	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	0.238297	−	0.971192i	$-0.423411\pi$
$641$	21.5459	−	4.57972i	0.851011	−	0.180888i	0.612715	+	0.790304i	$0.290078\pi$
$642$	−0.0158342	+	0.0412494i	−0.000624924	+	0.00162798i
$643$	−7.57933	−	7.57933i	−0.298899	−	0.298899i	0.541683	−	0.840583i	$-0.317787\pi$
$643$	−7.57933	−	7.57933i	−0.298899	−	0.298899i	−0.840583	+	0.541683i	$0.817787\pi$
$644$	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	−0.899279	−	0.437376i	$-0.855908\pi$
$647$	−32.4289	+	12.4483i	−1.27491	+	0.489393i	−0.375633	+	0.926769i	$0.622575\pi$
$648$	−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	0.847611	−	0.530618i	$-0.178040\pi$
$653$	12.9000	+	10.4462i	0.504817	+	0.408792i	−0.342794	+	0.939410i	$0.611373\pi$
$654$	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	−0.192235	−	0.981349i	$-0.561574\pi$
$659$	−23.7349	−	7.71192i	−0.924579	−	0.300414i	−0.732344	+	0.680935i	$0.761574\pi$
$660$	0.350731	−	0.573195i	0.0136522	−	0.0223116i
$661$	2.27939	+	2.05237i	0.0886581	+	0.0798281i	0.712268	−	0.701907i	$-0.247668\pi$
$661$	2.27939	+	2.05237i	0.0886581	+	0.0798281i	−0.623610	+	0.781736i	$0.714335\pi$
$662$	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	0.609779	−	0.792572i	$-0.291258\pi$
$673$	8.48294	+	4.32228i	0.326993	+	0.166611i	−0.282785	+	0.959183i	$0.591258\pi$
$674$	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	−0.365513	−	0.930806i	$-0.619107\pi$
$677$	8.74643	−	5.68000i	0.336153	−	0.218300i	0.701666	+	0.712506i	$0.252440\pi$
$678$	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	0.879067	−	0.476698i	$-0.158166\pi$
$683$	6.01135	+	7.42340i	0.230018	+	0.284048i	−0.649049	+	0.760746i	$0.724833\pi$
$684$	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	−0.929997	−	0.367567i	$-0.880191\pi$
$691$	−17.3929	+	15.6606i	−0.661655	+	0.595757i	0.268342	+	0.963324i	$0.413524\pi$
$692$	−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	−0.403233	+	0.915097i	$0.632114\pi$
$709$	−36.0921	+	32.4975i	−1.35547	+	1.22047i	−0.952234	+	0.305371i	$0.901220\pi$
$710$	−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	−0.505607	−	0.862764i	$-0.668731\pi$
$719$	−5.43700	+	2.42071i	−0.202766	+	0.0902773i	0.302841	+	0.953041i	$0.402065\pi$
$720$	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	0.273567	−	0.961853i	$-0.411796\pi$
$727$	−9.26956	−	4.72308i	−0.343789	−	0.175169i	−0.617356	+	0.786684i	$0.711796\pi$
$728$	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	0.914097	−	0.405494i	$-0.132901\pi$
$733$	35.7938	+	13.7400i	1.32208	+	0.507497i	0.407978	+	0.912992i	$0.366234\pi$
$734$	−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	0.962389	−	0.271677i	$-0.0875782\pi$
$739$	21.5518	+	19.4054i	0.792797	+	0.713838i	−0.169592	+	0.985514i	$0.554245\pi$
$740$	−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	−0.999028	−	0.0440723i	$-0.985967\pi$
$743$	−26.0302	+	26.0302i	−0.954956	+	0.954956i	0.0440723	+	0.999028i	$0.485967\pi$
$744$	−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	−0.792126	−	0.610358i	$-0.791026\pi$
$751$	3.63171	−	6.29030i	0.132523	−	0.229536i	0.924648	+	0.380822i	$0.124359\pi$
$752$	−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	0.269495	−	0.963002i	$-0.413143\pi$
$757$	−19.0809	−	19.0809i	−0.693507	−	0.693507i	−0.963002	+	0.269495i	$0.913143\pi$
$758$	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	−0.994101	−	0.108459i	$-0.965408\pi$
$761$	−1.15394	+	5.42884i	−0.0418302	+	0.196795i	0.952271	+	0.305255i	$0.0987416\pi$
$762$	−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
$765$	−29.0841	+	2.30839i	−1.05154	+	0.0834600i
$766$	−0.125330	−	0.589630i	−0.00452834	−	0.0213042i
$767$	−12.8736	+	10.4248i	−0.464837	+	0.376418i
$768$	1.67704	−	0.449360i	0.0605148	−	0.0162149i
$769$	−19.1561	−	13.9177i	−0.690787	−	0.501886i	0.186131	−	0.982525i	$-0.440405\pi$
$769$	−19.1561	−	13.9177i	−0.690787	−	0.501886i	−0.876919	+	0.480638i	$0.840405\pi$
$770$	−0.148212	+	0.266577i	−0.00534119	+	0.00960675i
$771$	−1.81130	+	1.31599i	−0.0652324	+	0.0473941i
$772$	−15.3186	+	18.9169i	−0.551330	+	0.680835i
$773$	44.3620	−	2.32491i	1.59559	−	0.0836213i	0.766316	−	0.642464i	$-0.222088\pi$
$773$	44.3620	−	2.32491i	1.59559	−	0.0836213i	0.829274	+	0.558843i	$0.188754\pi$
$774$	−0.464337	+	0.268085i	−0.0166902	+	0.00963612i
$775$	16.3656	−	6.30711i	0.587871	−	0.226558i
$776$		−	2.48536i		−	0.0892193i
$777$	0.602288	−	2.15551i	0.0216070	−	0.0773284i
$778$	0.0902720	−	0.569955i	0.00323641	−	0.0204339i
$779$	0.653509	−	0.0686866i	0.0234144	−	0.00246095i
$780$	−0.623245	+	0.478890i	−0.0223157	+	0.0171470i
$781$	0.982984	−	9.35246i	0.0351739	−	0.334658i
$782$	−0.239130	−	0.892445i	−0.00855127	−	0.0319138i
$783$	−0.677181	−	4.27555i	−0.0242005	−	0.152796i
$784$	−11.9067	+	25.2771i	−0.425240	+	0.902754i
$785$	41.2691	+	1.05327i	1.47296	+	0.0375928i
$786$	−0.00697400	−	0.00148237i	−0.000248754	−	5.28744e-5i
$787$	2.46325	−	3.79307i	0.0878053	−	0.135208i	−0.792039	−	0.610471i	$-0.790980\pi$
$787$	2.46325	−	3.79307i	0.0878053	−	0.135208i	0.879844	+	0.475263i	$0.157647\pi$
$788$	14.5259	−	22.3679i	0.517464	−	0.796825i
$789$	1.36164	+	0.289425i	0.0484756	+	0.0103038i
$790$	−0.605439	−	0.463931i	−0.0215405	−	0.0165059i
$791$	26.6960	+	3.09418i	0.949199	+	0.110016i
$792$	−0.0963621	−	0.608406i	−0.00342408	−	0.0216188i
$793$	−3.15038	−	11.7574i	−0.111873	−	0.417517i
$794$	0.0458728	−	0.436451i	0.00162797	−	0.0154891i
$795$	−0.597529	−	0.410087i	−0.0211922	−	0.0145443i
$796$	−36.4522	+	3.83128i	−1.29202	+	0.135796i
$797$	−6.87517	+	43.4081i	−0.243531	+	1.53759i	0.498299	+	0.867005i	$0.333958\pi$
$797$	−6.87517	+	43.4081i	−0.243531	+	1.53759i	−0.741830	+	0.670588i	$0.766042\pi$
$798$	0.000519123	0	0.000530320i	1.83767e−5	0	1.87731e-5i
$799$			31.1283i			1.10124i
$800$	−0.469881	−	2.19628i	−0.0166128	−	0.0776503i
$801$	−20.8334	+	12.0282i	−0.736113	+	0.424995i
$802$	0.476950	−	0.0249959i	0.0168417	−	0.000882636i
$803$	−0.371342	+	0.458569i	−0.0131044	+	0.0161825i
$804$	−1.56845	+	1.13954i	−0.0553148	+	0.0401886i
$805$	−7.47374	−	32.5624i	−0.263415	−	1.14767i
$806$	−0.171128	−	0.124332i	−0.00602772	−	0.00437940i
$807$	−2.09777	+	0.562096i	−0.0738450	+	0.0197867i
$808$	−0.459161	+	0.371821i	−0.0161532	+	0.0130806i
$809$	3.82574	+	17.9987i	0.134506	+	0.632800i	0.992814	+	0.119666i	$0.0381823\pi$
$809$	3.82574	+	17.9987i	0.134506	+	0.632800i	−0.858309	+	0.513134i	$0.828484\pi$
$810$	−0.566211	+	0.484240i	−0.0198946	+	0.0170144i
$811$	29.0804	−	9.44881i	1.02115	−	0.331793i	0.249866	−	0.968280i	$-0.419613\pi$
$811$	29.0804	−	9.44881i	1.02115	−	0.331793i	0.771287	+	0.636488i	$0.219613\pi$
$812$	12.8836	−	32.5215i	0.452127	−	1.14128i
$813$	−0.400531	−	0.786087i	−0.0140472	−	0.0275693i
$814$	−0.0829749	+	0.390366i	−0.00290827	+	0.0136823i
$815$	7.59918	−	1.41364i	0.266187	−	0.0495176i
$816$	−1.86307	+	0.396008i	−0.0652205	+	0.0138631i
$817$	0.117572	−	0.306286i	0.00411333	−	0.0107156i
$818$	0.268156	+	0.268156i	0.00937585	+	0.00937585i
$819$	7.36844	+	10.3727i	0.257474	+	0.362453i
$820$	20.4294	−	37.6859i	0.713425	−	1.31605i
$821$	−0.660433	−	6.28360i	−0.0230493	−	0.219299i	−0.999983	−	0.00575837i	$-0.998167\pi$
$821$	−0.660433	−	6.28360i	−0.0230493	−	0.219299i	0.976934	−	0.213541i	$-0.0684996\pi$
$822$	−0.0243473	+	0.00934606i	−0.000849210	+	0.000325981i
$823$	−1.84356	−	35.1772i	−0.0642623	−	1.22620i	−0.820402	−	0.571788i	$-0.806250\pi$
$823$	−1.84356	−	35.1772i	−0.0642623	−	1.22620i	0.756139	−	0.654411i	$-0.227083\pi$
$824$	−0.575297	+	0.996444i	−0.0200414	+	0.0347128i
$825$	−0.747607	+	0.0795798i	−0.0260283	+	0.00277061i
$826$	1.00023	−	0.201477i	0.0348026	−	0.00701026i
$827$	−13.9609	+	27.3997i	−0.485466	+	0.952782i	0.510224	+	0.860042i	$0.329563\pi$
$827$	−13.9609	+	27.3997i	−0.485466	+	0.952782i	−0.995690	+	0.0927399i	$0.970437\pi$
$828$	26.2088	+	21.2235i	0.910818	+	0.737566i
$829$	−43.7547	−	19.4808i	−1.51966	−	0.676598i	−0.534025	−	0.845469i	$-0.679321\pi$
$829$	−43.7547	−	19.4808i	−1.51966	−	0.676598i	−0.985638	+	0.168871i	$0.945988\pi$
$830$	−0.201156	+	0.293100i	−0.00698222	+	0.0101736i
$831$	0.179959	+	0.404194i	0.00624270	+	0.0140213i
$832$	9.06592	−	9.06592i	0.314304	−	0.314304i
$833$	14.4548	−	26.9325i	0.500830	−	0.933157i
$834$	0.0838916	+	0.0272580i	0.00290493	+	0.000943869i
$835$	27.3612	−	11.3547i	0.946873	−	0.392944i
$836$	0.140003	+	0.126059i	0.00484211	+	0.00435985i
$837$	−1.92506	−	1.25015i	−0.0665398	−	0.0432115i
$838$	−0.00534360	+	0.101962i	−0.000184592	+	0.00352222i
$839$	4.53318	+	13.9517i	0.156503	+	0.481666i	0.998310	−	0.0581120i	$-0.0185080\pi$
$839$	4.53318	+	13.9517i	0.156503	+	0.481666i	−0.841807	+	0.539778i	$0.818508\pi$
$840$	0.0954084	−	0.0166972i	0.00329190	−	0.000576109i
$841$	−4.56193	+	14.0402i	−0.157308	+	0.484144i
$842$	1.16947	+	0.448919i	0.0403027	+	0.0154708i
$843$	0.0363057	−	0.135495i	0.00125043	−	0.00466668i
$844$	−18.9507	−	1.99180i	−0.652310	−	0.0685606i
$845$	8.89344	−	21.5110i	0.305944	−	0.740001i
$846$	0.469115	+	0.645681i	0.0161285	+	0.0221990i
$847$	21.3499	+	11.1668i	0.733592	+	0.383697i
$848$	10.5481	+	5.37452i	0.362223	+	0.184562i
$849$	0.0296350	+	0.0171098i	0.00101707	+	0.000587205i
$850$	0.129043	+	0.807804i	0.00442613	+	0.0277074i
$851$	−21.8570	−	37.8574i	−0.749249	−	1.29774i
$852$	−1.25183	+	0.812951i	−0.0428871	+	0.0278512i
$853$	23.1114	+	3.66049i	0.791320	+	0.125333i	0.538994	−	0.842310i	$-0.318805\pi$
$853$	23.1114	+	3.66049i	0.791320	+	0.125333i	0.252326	+	0.967642i	$0.418805\pi$
$854$	−0.163695	+	0.731649i	−0.00560153	+	0.0250365i
$855$	0.0831138	−	0.450108i	0.00284243	−	0.0153934i
$856$	−1.47696	+	0.657586i	−0.0504815	+	0.0224758i
$857$	40.5488	+	10.8650i	1.38512	+	0.371142i	0.872979	−	0.487758i	$-0.162185\pi$
$857$	40.5488	+	10.8650i	1.38512	+	0.371142i	0.512143	+	0.858900i	$0.328852\pi$
$858$	0.00570627	+	0.00704666i	0.000194809	+	0.000240569i
$859$	−31.3524	−	34.8204i	−1.06973	−	1.18806i	−0.981402	−	0.191964i	$-0.938514\pi$
$859$	−31.3524	−	34.8204i	−1.06973	−	1.18806i	−0.0883284	−	0.996091i	$-0.528152\pi$
$860$	−12.1341	−	17.6302i	−0.413771	−	0.601185i
$861$	2.38682	+	1.41220i	0.0813425	+	0.0481276i
$862$	1.03977	−	0.529787i	0.0354146	−	0.0180446i
$863$	43.4268	+	2.27590i	1.47827	+	0.0774726i	0.774326	−	0.632787i	$-0.218089\pi$
$863$	43.4268	+	2.27590i	1.47827	+	0.0774726i	0.703940	+	0.710260i	$0.251423\pi$
$864$	−0.196683	+	0.218439i	−0.00669130	+	0.00743145i
$865$	16.4717	+	15.6103i	0.560056	+	0.530767i
$866$	−0.148790	+	0.133971i	−0.00505609	+	0.00455252i
$867$	0.223142	−	0.0353423i	0.00757832	−	0.00120029i
$868$	−8.24399	−	16.6157i	−0.279819	−	0.563972i
$869$	7.36326	−	10.1347i	0.249781	−	0.343795i
$870$	−0.0588838	+	0.0141781i	−0.00199635	+	0.000480681i
$871$	−5.81078	+	13.0512i	−0.196891	+	0.442224i
$872$	0.154701	+	0.403009i	0.00523883	+	0.0136476i
$873$	−26.9972	−	41.5720i	−0.913715	−	1.40700i
$874$	0.0144949			0.000490297
$875$	3.60633	+	29.3597i	0.121916	+	0.992540i
$876$	0.0936581			0.00316442
$877$	−15.8350	−	24.3838i	−0.534712	−	0.823384i	0.463314	−	0.886194i	$-0.346660\pi$
$877$	−15.8350	−	24.3838i	−0.534712	−	0.823384i	−0.998025	+	0.0628106i	$0.979994\pi$
$878$	0.358963	+	0.935130i	0.0121144	+	0.0315591i
$879$	0.876460	−	1.96856i	0.0295623	−	0.0663980i
$880$	11.9401	−	2.87494i	0.402500	−	0.0969143i
$881$	−3.61462	+	4.97510i	−0.121780	+	0.167616i	−0.865554	−	0.500815i	$-0.833034\pi$
$881$	−3.61462	+	4.97510i	−0.121780	+	0.167616i	0.743774	+	0.668431i	$0.233034\pi$
$882$	−0.106053	−	0.776489i	−0.00357098	−	0.0261458i
$883$	−25.5292	+	4.04343i	−0.859126	+	0.136072i	−0.570428	−	0.821348i	$-0.693223\pi$
$883$	−25.5292	+	4.04343i	−0.859126	+	0.136072i	−0.288698	+	0.957420i	$0.593223\pi$
$884$	−10.4379	+	9.39833i	−0.351065	+	0.316100i
$885$	1.82550	+	1.73003i	0.0613635	+	0.0581545i
$886$	0.740121	−	0.821988i	0.0248648	−	0.0276152i
$887$	35.6368	+	1.86765i	1.19657	+	0.0627094i	0.640187	−	0.768219i	$-0.278857\pi$
$887$	35.6368	+	1.86765i	1.19657	+	0.0627094i	0.556379	+	0.830928i	$0.312190\pi$
$888$	0.112921	−	0.0575362i	0.00378938	−	0.00193079i
$889$	−27.4755	−	48.7838i	−0.921499	−	1.63615i
$890$	0.382415	+	0.555627i	0.0128186	+	0.0186247i
$891$	−8.18764	−	9.09329i	−0.274296	−	0.304637i
$892$	−31.6085	−	39.0333i	−1.05833	−	1.30693i
$893$	−0.471712	−	0.126395i	−0.0157852	−	0.00422964i
$894$	−0.0734235	+	0.0326903i	−0.00245565	+	0.00109333i
$895$	3.66419	−	19.8437i	0.122481	−	0.663301i
$896$	−3.02192	+	0.946356i	−0.100955	+	0.0316155i
$897$	−0.980964	−	0.155370i	−0.0327534	−	0.00518764i
$898$	−0.524324	+	0.340500i	−0.0174969	+	0.0113626i
$899$	11.6026	+	20.0963i	0.386968	+	0.670248i
$900$	−21.1419	−	21.0859i	−0.704731	−	0.702863i
$901$	−11.2157	−	6.47536i	−0.373648	−	0.215726i
$902$	−0.440628	−	0.224511i	−0.0146713	−	0.00747540i
$903$	1.16923	−	0.741693i	0.0389096	−	0.0246820i
$904$	0.894504	+	1.23118i	0.0297508	+	0.0409484i
$905$	13.5405	−	32.7511i	0.450101	−	1.08868i
$906$	0.0371580	+	0.00390546i	0.00123449	+	0.000129750i
$907$	0.544417	−	2.03179i	0.0180771	−	0.0674645i	−0.956298	−	0.292393i	$-0.905548\pi$
$907$	0.544417	−	2.03179i	0.0180771	−	0.0674645i	0.974375	+	0.224929i	$0.0722150\pi$
$908$	−23.0877	−	8.86253i	−0.766191	−	0.294113i
$909$	−3.64137	+	11.2070i	−0.120777	+	0.371712i
$910$	0.273580	−	0.228965i	0.00906909	−	0.00759011i
$911$	7.06918	+	21.7567i	0.234212	+	0.720831i	0.997225	+	0.0744476i	$0.0237194\pi$
$911$	7.06918	+	21.7567i	0.234212	+	0.720831i	−0.763013	+	0.646383i	$0.776281\pi$
$912$	0.00156388	−	0.0298406i	5.17852e−5	−	0.000988120i
$913$	−4.89648	−	3.17981i	−0.162050	−	0.105236i
$914$	0.295369	+	0.265951i	0.00976992	+	0.00879688i
$915$	−1.70692	+	0.708358i	−0.0564291	+	0.0234176i
$916$	28.0726	+	9.12134i	0.927545	+	0.301378i
$917$	−4.54246	−	0.769224i	−0.150005	−	0.0254020i
$918$	0.0757030	−	0.0757030i	0.00249857	−	0.00249857i
$919$	22.2654	+	50.0090i	0.734468	+	1.64964i	0.759961	+	0.649968i	$0.225218\pi$
$919$	22.2654	+	50.0090i	0.734468	+	1.64964i	−0.0254929	+	0.999675i	$0.508116\pi$
$920$	1.07052	−	1.55983i	0.0352938	−	0.0514259i
$921$	−2.08162	−	0.926798i	−0.0685918	−	0.0305390i
$922$	−0.598095	−	0.484328i	−0.0196972	−	0.0159505i
$923$	−4.99358	+	9.80045i	−0.164366	+	0.322586i
$924$	0.157004	+	0.779449i	0.00516505	+	0.0256420i
$925$	15.7894	+	35.3373i	0.519153	+	1.16188i
$926$	0.0544855	−	0.0943716i	0.00179050	−	0.00310124i
$927$	1.20100	+	22.9164i	0.0394459	+	0.752673i
$928$	2.77422	−	1.06492i	0.0910681	−	0.0349578i
$929$	0.805098	+	7.66000i	0.0264144	+	0.251316i	0.999759	+	0.0219675i	$0.00699302\pi$
$929$	0.805098	+	7.66000i	0.0264144	+	0.251316i	−0.973344	+	0.229349i	$0.926340\pi$
$930$	−0.0153054	+	0.0282338i	−0.000501885	+	0.000925821i
$931$	0.349437	+	0.328404i	0.0114523	+	0.0107630i
$932$	1.71506	+	1.71506i	0.0561786	+	0.0561786i
$933$	−0.335919	+	0.875098i	−0.0109975	+	0.0286494i
$934$	−0.268793	+	0.0571336i	−0.00879516	+	0.00186947i
$935$	−13.2087	+	2.45715i	−0.431970	+	0.0803573i
$936$	−0.149798	+	0.704744i	−0.00489630	+	0.0230353i
$937$	5.96599	+	11.7089i	0.194901	+	0.382514i	0.967688	−	0.252151i	$-0.0811380\pi$
$937$	5.96599	+	11.7089i	0.194901	+	0.382514i	−0.772787	+	0.634665i	$0.781138\pi$
$938$	0.689727	−	0.546449i	0.0225204	−	0.0178422i
$939$	2.52741	−	0.821204i	0.0824788	−	0.0267990i
$940$	−24.2113	+	20.7062i	−0.789687	+	0.675363i
$941$	3.94190	+	18.5452i	0.128502	+	0.604556i	0.994520	+	0.104543i	$0.0333380\pi$
$941$	3.94190	+	18.5452i	0.128502	+	0.604556i	−0.866018	+	0.500013i	$0.833329\pi$
$942$	−0.0587462	+	0.0475717i	−0.00191405	+	0.00154997i
$943$	52.3224	−	14.0197i	1.70385	−	0.456546i
$944$	−33.2376	−	24.1485i	−1.08179	−	0.785967i
$945$	2.83465	−	2.63658i	0.0922112	−	0.0857680i
$946$	−0.199750	+	0.145127i	−0.00649443	+	0.00471848i
$947$	1.70869	−	2.11006i	0.0555251	−	0.0685678i	−0.748627	−	0.662992i	$-0.769286\pi$
$947$	1.70869	−	2.11006i	0.0555251	−	0.0685678i	0.804152	+	0.594424i	$0.202620\pi$
$948$	−1.98564	+	0.104063i	−0.0644904	+	0.00337980i
$949$	0.597703	−	0.345084i	0.0194023	−	0.0112019i
$950$	−0.0127653	−	0.00132456i	−0.000414160	−	4.29744e-5i
$951$		−	0.500039i		−	0.0162149i
$952$	1.67658	−	0.430118i	0.0543381	−	0.0139402i
$953$	4.71919	−	29.7958i	0.152870	−	0.965180i	−0.785328	−	0.619080i	$-0.787506\pi$
$953$	4.71919	−	29.7958i	0.152870	−	0.965180i	0.938197	−	0.346100i	$-0.112494\pi$
$954$	−0.330228	+	0.0347083i	−0.0106915	+	0.00112372i
$955$	−41.2721	−	28.3252i	−1.33553	−	0.916582i
$956$	−5.37617	+	51.1508i	−0.173878	+	1.65434i
$957$	−0.257453	−	0.960828i	−0.00832228	−	0.0310592i
$958$	0.0345990	+	0.218450i	0.00111784	+	0.00705779i
$959$	−15.4674	+	6.68969i	−0.499467	+	0.216021i
$960$	−1.54513	−	1.18399i	−0.0498689	−	0.0382132i
$961$	−18.2869	−	3.88701i	−0.589901	−	0.125387i
$962$	0.254232	−	0.391483i	0.00819676	−	0.0126219i
$963$	−17.5617	+	27.0427i	−0.565919	+	0.871439i
$964$	26.7808	+	5.69243i	0.862550	+	0.183341i
$965$	27.2249	+	0.694834i	0.876401	+	0.0223675i
$966$	0.0491053	+	0.0364839i	0.00157994	+	0.00117385i
$967$	−7.46599	−	47.1384i	−0.240090	−	1.51587i	−0.753341	−	0.657631i	$-0.771559\pi$
$967$	−7.46599	−	47.1384i	−0.240090	−	1.51587i	0.513250	−	0.858239i	$-0.328441\pi$
$968$	0.353121	+	1.31787i	0.0113498	+	0.0423579i
$969$	−0.00341695	+	0.0325101i	−0.000109768	+	0.00104437i
$970$	−1.10208	+	0.846817i	−0.0353856	+	0.0271896i
$971$	52.3848	−	5.50587i	1.68111	−	0.176692i	0.784687	−	0.619892i	$-0.212824\pi$
$971$	52.3848	−	5.50587i	1.68111	−	0.176692i	0.896422	+	0.443201i	$0.146157\pi$
$972$	−0.917586	+	5.79341i	−0.0294316	+	0.185824i
$973$	54.8960	+	15.3390i	1.75989	+	0.491744i
$974$		−	0.651616i		−	0.0208791i
$975$	0.849711	+	0.226471i	0.0272125	+	0.00725288i
$976$	26.1441	−	15.0943i	0.836853	−	0.483157i
$977$	−42.4430	+	2.22434i	−1.35787	+	0.0711631i	−0.717316	−	0.696748i	$-0.754630\pi$
$977$	−42.4430	+	2.22434i	−1.35787	+	0.0711631i	−0.640556	+	0.767911i	$0.721296\pi$
$978$	−0.00890711	+	0.0109994i	−0.000284818	+	0.000351721i
$979$	−8.96219	+	6.51142i	−0.286433	+	0.208106i
$980$	30.5631	−	6.67241i	0.976303	−	0.213142i
$981$	6.96531	+	5.06059i	0.222385	+	0.161572i
$982$	−0.195699	+	0.0524374i	−0.00624500	+	0.00167334i
$983$	14.5581	−	11.7889i	0.464332	−	0.376008i	−0.368416	−	0.929661i	$-0.620100\pi$
$983$	14.5581	−	11.7889i	0.464332	−	0.376008i	0.832748	+	0.553653i	$0.186766\pi$
$984$	0.0326510	+	0.153611i	0.00104088	+	0.00489693i
$985$	−29.7462	+	2.36093i	−0.947792	+	0.0752256i
$986$	−1.02936	+	0.334458i	−0.0327814	+	0.0106513i
$987$	−1.27991	−	1.61550i	−0.0407400	−	0.0514220i
$988$	−0.100038	−	0.196335i	−0.00318263	−	0.00624626i
$989$	5.62291	−	26.4537i	0.178798	−	0.841179i
$990$	−0.236952	+	0.250027i	−0.00753082	+	0.00794638i
$991$	−21.5296	+	4.57626i	−0.683911	+	0.145370i	−0.536748	−	0.843743i	$-0.680347\pi$
$991$	−21.5296	+	4.57626i	−0.683911	+	0.145370i	−0.147163	+	0.989112i	$0.547014\pi$
$992$	0.564675	−	1.47103i	0.0179284	−	0.0467052i
$993$	−0.183622	−	0.183622i	−0.00582705	−	0.00582705i
$994$	0.552324	−	0.392352i	0.0175186	−	0.0124446i
$995$	28.2479	+	29.7275i	0.895517	+	0.942425i
$996$	0.0968659	+	0.921618i	0.00306931	+	0.0292026i
$997$	−15.5050	+	5.95182i	−0.491049	+	0.188496i	−0.591277	−	0.806469i	$-0.701376\pi$
$997$	−15.5050	+	5.95182i	−0.491049	+	0.188496i	0.100228	+	0.994964i	$0.468043\pi$
$998$	0.00472226	+	0.0901061i	0.000149481	+	0.00285226i
$999$	2.53268	−	4.38674i	0.0801306	−	0.138790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.117.10	yes	288
5.2	odd	4		875.2.bb.a.768.9		288
5.3	odd	4		875.2.bb.b.768.10		288
5.4	even	2		875.2.bb.c.607.9		288
7.3	odd	6	inner	175.2.x.a.17.9	yes	288
25.3	odd	20	inner	175.2.x.a.103.9	yes	288
25.4	even	10		875.2.bb.a.257.9		288
25.21	even	5		875.2.bb.b.257.10		288
25.22	odd	20		875.2.bb.c.243.10		288
35.3	even	12		875.2.bb.b.143.10		288
35.17	even	12		875.2.bb.a.143.9		288
35.24	odd	6		875.2.bb.c.857.10		288
175.3	even	60	inner	175.2.x.a.3.10	✓	288
175.122	even	60		875.2.bb.c.493.9		288
175.129	odd	30		875.2.bb.a.507.9		288
175.171	odd	30		875.2.bb.b.507.10		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.10	✓	288	175.3	even	60	inner
175.2.x.a.17.9	yes	288	7.3	odd	6	inner
175.2.x.a.103.9	yes	288	25.3	odd	20	inner
175.2.x.a.117.10	yes	288	1.1	even	1	trivial
875.2.bb.a.143.9		288	35.17	even	12
875.2.bb.a.257.9		288	25.4	even	10
875.2.bb.a.507.9		288	175.129	odd	30
875.2.bb.a.768.9		288	5.2	odd	4
875.2.bb.b.143.10		288	35.3	even	12
875.2.bb.b.257.10		288	25.21	even	5
875.2.bb.b.507.10		288	175.171	odd	30
875.2.bb.b.768.10		288	5.3	odd	4
875.2.bb.c.243.10		288	25.22	odd	20
875.2.bb.c.493.9		288	175.122	even	60
875.2.bb.c.607.9		288	5.4	even	2
875.2.bb.c.857.10		288	35.24	odd	6

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more