LMFDB - Embedded newform 171.2.x.a.14.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.17
Character	$\chi$	$=$	171.14
Dual form			171.2.x.a.110.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98542 + 1.66596i) q^{2} +(0.915994 - 1.47002i) q^{3} +(0.819153 + 4.64565i) q^{4} +(-1.06492 - 2.92585i) q^{5} +(4.26763 - 1.39259i) q^{6} +(-1.52472 + 2.64090i) q^{7} +(-3.52134 + 6.09914i) q^{8} +(-1.32191 - 2.69306i) q^{9} +O(q^{10})$	\(q+(1.98542 + 1.66596i) q^{2} +(0.915994 - 1.47002i) q^{3} +(0.819153 + 4.64565i) q^{4} +(-1.06492 - 2.92585i) q^{5} +(4.26763 - 1.39259i) q^{6} +(-1.52472 + 2.64090i) q^{7} +(-3.52134 + 6.09914i) q^{8} +(-1.32191 - 2.69306i) q^{9} +(2.76004 - 7.58315i) q^{10} +3.42745i q^{11} +(7.57953 + 3.05122i) q^{12} +(0.864317 - 2.37469i) q^{13} +(-7.42686 + 2.70316i) q^{14} +(-5.27651 - 1.11461i) q^{15} +(-8.28661 + 3.01608i) q^{16} +(-1.79294 - 4.92607i) q^{17} +(1.86199 - 7.54909i) q^{18} +(-3.57649 + 2.49173i) q^{19} +(12.7201 - 7.34397i) q^{20} +(2.48553 + 4.66042i) q^{21} +(-5.71001 + 6.80493i) q^{22} +(2.96343 - 0.522533i) q^{23} +(5.74032 + 10.7632i) q^{24} +(-3.59631 + 3.01766i) q^{25} +(5.67218 - 3.27483i) q^{26} +(-5.16970 - 0.523595i) q^{27} +(-13.5177 - 4.92003i) q^{28} +(-0.536153 - 3.04067i) q^{29} +(-8.61919 - 11.0034i) q^{30} +0.794029i q^{31} +(-8.24116 - 2.99954i) q^{32} +(5.03842 + 3.13953i) q^{33} +(4.64691 - 12.7673i) q^{34} +(9.35059 + 1.64876i) q^{35} +(11.4282 - 8.34715i) q^{36} +7.02028i q^{37} +(-11.2520 - 1.01117i) q^{38} +(-2.69913 - 3.44577i) q^{39} +(21.5951 + 3.80780i) q^{40} +(4.12573 + 3.46190i) q^{41} +(-2.82927 + 13.3937i) q^{42} +(-0.331522 + 1.88015i) q^{43} +(-15.9227 + 2.80761i) q^{44} +(-6.47175 + 6.73560i) q^{45} +(6.75417 + 3.89952i) q^{46} +(12.8465 - 2.26518i) q^{47} +(-3.15680 + 14.9442i) q^{48} +(-1.14957 - 1.99111i) q^{49} -12.1675 q^{50} +(-8.88374 - 1.87659i) q^{51} +(11.7400 + 2.07008i) q^{52} +(3.01965 - 2.53379i) q^{53} +(-9.39173 - 9.65209i) q^{54} +(10.0282 - 3.64997i) q^{55} +(-10.7381 - 18.5990i) q^{56} +(0.386850 + 7.53992i) q^{57} +(4.00116 - 6.93022i) q^{58} +(-0.194589 + 1.10357i) q^{59} +(0.855795 - 25.4259i) q^{60} +(-1.80227 - 0.655973i) q^{61} +(-1.32282 + 1.57648i) q^{62} +(9.12764 + 0.615141i) q^{63} +(-2.54660 - 4.41084i) q^{64} -7.86842 q^{65} +(4.77303 + 14.6271i) q^{66} +(-0.412278 - 0.491334i) q^{67} +(21.4161 - 12.3646i) q^{68} +(1.94635 - 4.83494i) q^{69} +(15.8180 + 18.8512i) q^{70} +(-5.62967 - 4.72386i) q^{71} +(21.0802 + 1.42066i) q^{72} +(0.808108 - 4.58301i) q^{73} +(-11.6955 + 13.9382i) q^{74} +(1.14182 + 8.05081i) q^{75} +(-14.5054 - 14.5740i) q^{76} +(-9.05156 - 5.22592i) q^{77} +(0.381617 - 11.3379i) q^{78} +(-2.33565 - 6.41714i) q^{79} +(17.6492 + 21.0335i) q^{80} +(-5.50511 + 7.11995i) q^{81} +(2.42390 + 13.7466i) q^{82} +(-1.59043 - 0.918238i) q^{83} +(-19.6147 + 15.3645i) q^{84} +(-12.5036 + 10.4918i) q^{85} +(-3.79048 + 3.18059i) q^{86} +(-4.96096 - 1.99709i) q^{87} +(-20.9045 - 12.0692i) q^{88} +(2.03020 + 11.5138i) q^{89} +(-24.0704 + 2.59129i) q^{90} +(4.95348 + 5.90333i) q^{91} +(4.85501 + 13.3390i) q^{92} +(1.16724 + 0.727326i) q^{93} +(29.2793 + 16.9044i) q^{94} +(11.0991 + 7.81076i) q^{95} +(-11.9582 + 9.36710i) q^{96} +(-9.52510 + 11.3516i) q^{97} +(1.03475 - 5.86834i) q^{98} +(9.23033 - 4.53078i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	1.98542	+	1.66596i	1.40390	+	1.17801i	0.959336	+	0.282268i	$0.0910867\pi$
$2$	1.98542	+	1.66596i	1.40390	+	1.17801i	0.444566	+	0.895746i	$0.353358\pi$
$3$	0.915994	−	1.47002i	0.528850	−	0.848716i
$3$	0.915994	−	1.47002i	0.528850	−	0.848716i
$4$	0.819153	+	4.64565i	0.409577	+	2.32282i
$5$	−1.06492	−	2.92585i	−0.476248	−	1.30848i	−0.912655	−	0.408730i	$-0.865972\pi$
$5$	−1.06492	−	2.92585i	−0.476248	−	1.30848i	0.436408	−	0.899749i	$-0.356251\pi$
$6$	4.26763	−	1.39259i	1.74225	−	0.568522i
$7$	−1.52472	+	2.64090i	−0.576292	+	0.998167i	0.419608	+	0.907705i	$0.362167\pi$
$7$	−1.52472	+	2.64090i	−0.576292	+	0.998167i	−0.995900	+	0.0904613i	$0.971166\pi$
$8$	−3.52134	+	6.09914i	−1.24498	+	2.15637i
$9$	−1.32191	−	2.69306i	−0.440636	−	0.897686i
$10$	2.76004	−	7.58315i	0.872802	−	2.39800i
$11$			3.42745i			1.03342i	0.856162	+	0.516708i	$0.172843\pi$
$11$			3.42745i			1.03342i	−0.856162	+	0.516708i	$0.827157\pi$
$12$	7.57953	+	3.05122i	2.18802	+	0.880811i
$13$	0.864317	−	2.37469i	0.239718	−	0.658621i	−0.760241	−	0.649641i	$-0.774919\pi$
$13$	0.864317	−	2.37469i	0.239718	−	0.658621i	0.999960	−	0.00898021i	$-0.00285853\pi$
$14$	−7.42686	+	2.70316i	−1.98491	+	0.722449i
$15$	−5.27651	−	1.11461i	−1.36239	−	0.287790i
$16$	−8.28661	+	3.01608i	−2.07165	+	0.754020i
$17$	−1.79294	−	4.92607i	−0.434853	−	1.19475i	−0.942800	−	0.333359i	$-0.891818\pi$
$17$	−1.79294	−	4.92607i	−0.434853	−	1.19475i	0.507947	−	0.861388i	$-0.330404\pi$
$18$	1.86199	−	7.54909i	0.438876	−	1.77934i
$19$	−3.57649	+	2.49173i	−0.820503	+	0.571643i
$19$	−3.57649	+	2.49173i	−0.820503	+	0.571643i
$20$	12.7201	−	7.34397i	2.84431	−	1.64216i
$21$	2.48553	+	4.66042i	0.542388	+	1.01699i
$22$	−5.71001	+	6.80493i	−1.21738	+	1.45082i
$23$	2.96343	−	0.522533i	0.617918	−	0.108956i	0.144078	−	0.989566i	$-0.453978\pi$
$23$	2.96343	−	0.522533i	0.617918	−	0.108956i	0.473840	+	0.880611i	$0.342867\pi$
$24$	5.74032	+	10.7632i	1.17174	+	2.19703i
$25$	−3.59631	+	3.01766i	−0.719262	+	0.603533i
$26$	5.67218	−	3.27483i	1.11241	−	0.642248i
$27$	−5.16970	−	0.523595i	−0.994910	−	0.100766i
$28$	−13.5177	−	4.92003i	−2.55460	−	0.929799i
$29$	−0.536153	−	3.04067i	−0.0995611	−	0.564639i	−0.993254	−	0.115960i	$-0.963006\pi$
$29$	−0.536153	−	3.04067i	−0.0995611	−	0.564639i	0.893693	−	0.448679i	$-0.148105\pi$
$30$	−8.61919	−	11.0034i	−1.57364	−	2.00894i
$31$			0.794029i			0.142612i	0.997454	+	0.0713059i	$0.0227167\pi$
$31$			0.794029i			0.142612i	−0.997454	+	0.0713059i	$0.977283\pi$
$32$	−8.24116	−	2.99954i	−1.45685	−	0.530248i
$33$	5.03842	+	3.13953i	0.877076	+	0.546522i
$34$	4.64691	−	12.7673i	0.796939	−	2.18957i
$35$	9.35059	+	1.64876i	1.58054	+	0.278691i
$36$	11.4282	−	8.34715i	1.90469	−	1.39119i
$37$			7.02028i			1.15413i	0.816699	+	0.577064i	$0.195802\pi$
$37$			7.02028i			1.15413i	−0.816699	+	0.577064i	$0.804198\pi$
$38$	−11.2520	−	1.01117i	−1.82531	−	0.164033i
$39$	−2.69913	−	3.44577i	−0.432207	−	0.551764i
$40$	21.5951	+	3.80780i	3.41449	+	0.602066i
$41$	4.12573	+	3.46190i	0.644330	+	0.540657i	0.905345	−	0.424678i	$-0.139613\pi$
$41$	4.12573	+	3.46190i	0.644330	+	0.540657i	−0.261014	+	0.965335i	$0.584057\pi$
$42$	−2.82927	+	13.3937i	−0.436566	+	2.06669i
$43$	−0.331522	+	1.88015i	−0.0505566	+	0.286721i	−0.999596	−	0.0284381i	$-0.990947\pi$
$43$	−0.331522	+	1.88015i	−0.0505566	+	0.286721i	0.949039	+	0.315159i	$0.102058\pi$
$44$	−15.9227	+	2.80761i	−2.40044	+	0.423263i
$45$	−6.47175	+	6.73560i	−0.964751	+	1.00408i
$46$	6.75417	+	3.89952i	0.995848	+	0.574953i
$47$	12.8465	−	2.26518i	1.87385	−	0.330410i	0.883435	−	0.468553i	$-0.155225\pi$
$47$	12.8465	−	2.26518i	1.87385	−	0.330410i	0.990412	+	0.138143i	$0.0441135\pi$
$48$	−3.15680	+	14.9442i	−0.455644	+	2.15701i
$49$	−1.14957	−	1.99111i	−0.164224	−	0.284445i
$50$	−12.1675			−1.72074
$51$	−8.88374	−	1.87659i	−1.24397	−	0.262776i
$52$	11.7400	+	2.07008i	1.62804	+	0.287068i
$53$	3.01965	−	2.53379i	0.414781	−	0.348043i	−0.411392	−	0.911458i	$-0.634957\pi$
$53$	3.01965	−	2.53379i	0.414781	−	0.348043i	0.826174	+	0.563416i	$0.190513\pi$
$54$	−9.39173	−	9.65209i	−1.27805	−	1.31348i
$55$	10.0282	−	3.64997i	1.35220	−	0.492162i
$56$	−10.7381	−	18.5990i	−1.43494	−	2.48540i
$57$	0.386850	+	7.53992i	0.0512395	+	0.998686i
$58$	4.00116	−	6.93022i	0.525379	−	0.909982i
$59$	−0.194589	+	1.10357i	−0.0253333	+	0.143672i	−0.994851	−	0.101349i	$-0.967684\pi$
$59$	−0.194589	+	1.10357i	−0.0253333	+	0.143672i	0.969518	+	0.245022i	$0.0787951\pi$
$60$	0.855795	−	25.4259i	0.110483	−	3.28246i
$61$	−1.80227	−	0.655973i	−0.230757	−	0.0839888i	0.224054	−	0.974577i	$-0.428071\pi$
$61$	−1.80227	−	0.655973i	−0.230757	−	0.0839888i	−0.454811	+	0.890588i	$0.650293\pi$
$62$	−1.32282	+	1.57648i	−0.167999	+	0.200213i
$63$	9.12764	+	0.615141i	1.14997	+	0.0775005i
$64$	−2.54660	−	4.41084i	−0.318325	−	0.551354i
$65$	−7.86842			−0.975958
$66$	4.77303	+	14.6271i	0.587519	+	1.80047i
$67$	−0.412278	−	0.491334i	−0.0503678	−	0.0600260i	0.740272	−	0.672307i	$-0.234697\pi$
$67$	−0.412278	−	0.491334i	−0.0503678	−	0.0600260i	−0.790640	+	0.612281i	$0.790252\pi$
$68$	21.4161	−	12.3646i	2.59708	−	1.49943i
$69$	1.94635	−	4.83494i	0.234313	−	0.582058i
$70$	15.8180	+	18.8512i	1.89062	+	2.25315i
$71$	−5.62967	−	4.72386i	−0.668119	−	0.560619i	0.244389	−	0.969677i	$-0.421413\pi$
$71$	−5.62967	−	4.72386i	−0.668119	−	0.560619i	−0.912508	+	0.409059i	$0.865857\pi$
$72$	21.0802	+	1.42066i	2.48433	+	0.167427i
$73$	0.808108	−	4.58301i	0.0945819	−	0.536401i	−0.900293	−	0.435285i	$-0.856648\pi$
$73$	0.808108	−	4.58301i	0.0945819	−	0.536401i	0.994875	−	0.101116i	$-0.0322413\pi$
$74$	−11.6955	+	13.9382i	−1.35958	+	1.62028i
$75$	1.14182	+	8.05081i	0.131846	+	0.929627i
$76$	−14.5054	−	14.5740i	−1.66388	−	1.67175i
$77$	−9.05156	−	5.22592i	−1.03152	−	0.595549i
$78$	0.381617	−	11.3379i	0.0432096	−	1.28377i
$79$	−2.33565	−	6.41714i	−0.262781	−	0.721985i	−0.998977	−	0.0452165i	$-0.985602\pi$
$79$	−2.33565	−	6.41714i	−0.262781	−	0.721985i	0.736196	−	0.676768i	$-0.236620\pi$
$80$	17.6492	+	21.0335i	1.97324	+	2.35162i
$81$	−5.50511	+	7.11995i	−0.611679	+	0.791106i
$82$	2.42390	+	13.7466i	0.267675	+	1.51806i
$83$	−1.59043	−	0.918238i	−0.174573	−	0.100790i	0.410167	−	0.912010i	$-0.365470\pi$
$83$	−1.59043	−	0.918238i	−0.174573	−	0.100790i	−0.584740	+	0.811221i	$0.698804\pi$
$84$	−19.6147	+	15.3645i	−2.14013	+	1.67641i
$85$	−12.5036	+	10.4918i	−1.35621	+	1.13799i
$86$	−3.79048	+	3.18059i	−0.408737	+	0.342971i
$87$	−4.96096	−	1.99709i	−0.531871	−	0.214110i
$88$	−20.9045	−	12.0692i	−2.22843	−	1.28658i
$89$	2.03020	+	11.5138i	0.215201	+	1.22046i	0.880558	+	0.473938i	$0.157168\pi$
$89$	2.03020	+	11.5138i	0.215201	+	1.22046i	−0.665358	+	0.746525i	$0.731721\pi$
$90$	−24.0704	+	2.59129i	−2.53724	+	0.273145i
$91$	4.95348	+	5.90333i	0.519266	+	0.618837i
$92$	4.85501	+	13.3390i	0.506170	+	1.39069i
$93$	1.16724	+	0.727326i	0.121037	+	0.0754202i
$94$	29.2793	+	16.9044i	3.01993	+	1.74355i
$95$	11.0991	+	7.81076i	1.13874	+	0.801368i
$96$	−11.9582	+	9.36710i	−1.22048	+	0.956026i
$97$	−9.52510	+	11.3516i	−0.967127	+	1.15258i	0.0211298	+	0.999777i	$0.493274\pi$
$97$	−9.52510	+	11.3516i	−0.967127	+	1.15258i	−0.988257	+	0.152801i	$0.951171\pi$
$98$	1.03475	−	5.86834i	0.104525	−	0.592791i
$99$	9.23033	−	4.53078i	0.927683	−	0.455361i
$100$	−16.9649	−	14.2353i	−1.69649	−	1.42353i
$101$	−8.87600	−	10.5780i	−0.883195	−	1.05255i	−0.998247	−	0.0591910i	$-0.981148\pi$
$101$	−8.87600	−	10.5780i	−0.883195	−	1.05255i	0.115052	−	0.993359i	$-0.463297\pi$
$102$	−14.5116	−	18.5258i	−1.43686	−	1.83433i
$103$	−8.42013	+	4.86136i	−0.829660	+	0.479004i	−0.853736	−	0.520706i	$-0.825669\pi$
$103$	−8.42013	+	4.86136i	−0.829660	+	0.479004i	0.0240764	+	0.999710i	$0.492336\pi$
$104$	11.4400	+	13.6337i	1.12179	+	1.33689i
$105$	10.9888	−	12.2353i	1.07240	−	1.19404i
$106$	10.2165			0.992311
$107$	0.465034	+	0.805463i	0.0449565	+	0.0778670i	0.887628	−	0.460561i	$-0.152352\pi$
$107$	0.465034	+	0.805463i	0.0449565	+	0.0778670i	−0.842672	+	0.538428i	$0.819018\pi$
$108$	−1.80234	−	24.4455i	−0.173431	−	2.35227i
$109$	7.80746	−	9.30457i	0.747819	−	0.891216i	−0.249194	−	0.968454i	$-0.580166\pi$
$109$	7.80746	−	9.30457i	0.747819	−	0.891216i	0.997013	+	0.0772376i	$0.0246100\pi$
$110$	25.9909	+	9.45991i	2.47814	+	0.901967i
$111$	10.3199	+	6.43054i	0.979526	+	0.610360i
$112$	4.66964	−	26.4828i	0.441239	−	2.50239i
$113$	1.89033	−	3.27415i	0.177827	−	0.308006i	−0.763309	−	0.646034i	$-0.776426\pi$
$113$	1.89033	−	3.27415i	0.177827	−	0.308006i	0.941136	+	0.338028i	$0.109760\pi$
$114$	−11.7932	+	15.6144i	−1.10453	+	1.46242i
$115$	−4.68468	−	8.11410i	−0.436848	−	0.756643i
$116$	13.6867	−	4.98156i	1.27078	−	0.462526i
$117$	−7.53773	+	0.811471i	−0.696863	+	0.0750205i
$118$	−2.22485	+	1.86687i	−0.204814	+	0.171859i
$119$	15.7430	+	2.77592i	1.44316	+	0.254468i
$120$	25.3785	−	28.2573i	2.31673	−	2.57953i
$121$	−0.747440			−0.0679491
$122$	−2.48544	−	4.30490i	−0.225021	−	0.389747i
$123$	8.86820	−	2.89382i	0.799618	−	0.260927i
$124$	−3.68878	+	0.650431i	−0.331262	+	0.0584105i
$125$	−0.823369	−	0.475372i	−0.0736443	−	0.0425186i
$126$	17.0974	+	16.4276i	1.52316	+	1.46349i
$127$	−0.789992	+	0.139297i	−0.0701005	+	0.0123606i	−0.208588	−	0.978004i	$-0.566887\pi$
$127$	−0.789992	+	0.139297i	−0.0701005	+	0.0123606i	0.138488	+	0.990364i	$0.455776\pi$
$128$	−0.753580	+	4.27376i	−0.0666077	+	0.377751i
$129$	2.46019	+	2.20955i	0.216607	+	0.194540i
$130$	−15.6221	−	13.1085i	−1.37015	−	1.14969i
$131$	−16.9135	−	2.98231i	−1.47774	−	0.260566i	−0.624066	−	0.781371i	$-0.714520\pi$
$131$	−16.9135	−	2.98231i	−1.47774	−	0.260566i	−0.853675	+	0.520806i	$0.825632\pi$
$132$	−10.4579	+	25.9785i	−0.910244	+	2.26114i
$133$	−1.12726	−	13.2444i	−0.0977456	−	1.14843i
$134$		−	1.66234i		−	0.143604i
$135$	3.97337	+	15.6834i	0.341973	+	1.34981i
$136$	36.3583	+	6.41096i	3.11770	+	0.549735i
$137$	1.11713	−	3.06929i	0.0954428	−	0.262227i	−0.882779	−	0.469788i	$-0.844330\pi$
$137$	1.11713	−	3.06929i	0.0954428	−	0.262227i	0.978222	+	0.207561i	$0.0665526\pi$
$138$	11.9191	−	6.35681i	1.01463	−	0.541128i
$139$	−15.7878	−	5.74629i	−1.33910	−	0.487394i	−0.429574	−	0.903032i	$-0.641336\pi$
$139$	−15.7878	−	5.74629i	−1.33910	−	0.487394i	−0.909530	+	0.415638i	$0.863559\pi$
$140$			44.7901i			3.78546i
$141$	8.43743	−	20.9594i	0.710559	−	1.76510i
$142$	−3.30748	−	18.7576i	−0.277558	−	1.57411i
$143$	8.13915	+	2.96241i	0.680630	+	0.247729i
$144$	19.0766	+	18.3293i	1.58972	+	1.52745i
$145$	−8.32559	+	4.80678i	−0.691403	+	0.399182i
$146$	9.23956	−	7.75291i	0.764671	−	0.641635i
$147$	−3.97998	−	0.133960i	−0.328263	−	0.0110488i
$148$	−32.6138	+	5.75069i	−2.68083	+	0.472704i
$149$	−1.77882	+	2.11991i	−0.145727	+	0.173670i	−0.833970	−	0.551809i	$-0.813938\pi$
$149$	−1.77882	+	2.11991i	−0.145727	+	0.173670i	0.688244	+	0.725480i	$0.258382\pi$
$150$	−11.1454	+	17.8864i	−0.910014	+	1.46042i
$151$	18.1509	−	10.4794i	1.47710	−	0.852802i	0.477431	−	0.878669i	$-0.341568\pi$
$151$	18.1509	−	10.4794i	1.47710	−	0.852802i	0.999665	+	0.0258672i	$0.00823469\pi$
$152$	−2.60339	−	30.5877i	−0.211163	−	2.48099i
$153$	−10.8961	+	11.3403i	−0.880896	+	0.916810i
$154$	−9.26494	−	25.4552i	−0.746590	−	2.05124i
$155$	2.32321	−	0.845579i	0.186605	−	0.0679185i
$156$	13.7968	−	15.3618i	1.10463	−	1.22993i
$157$	11.4026	−	4.15020i	0.910026	−	0.331222i	0.155763	−	0.987795i	$-0.450217\pi$
$157$	11.4026	−	4.15020i	0.910026	−	0.331222i	0.754263	+	0.656572i	$0.227994\pi$
$158$	6.05348	−	16.6318i	0.481589	−	1.32316i
$159$	−0.958733	−	6.75988i	−0.0760325	−	0.536094i
$160$			27.3067i			2.15878i
$161$	−3.13846	+	8.62285i	−0.247345	+	0.679576i
$162$	−22.7915	+	4.96476i	−1.79067	+	0.390068i
$163$	−9.42180	+	16.3190i	−0.737972	+	1.27821i	0.215435	+	0.976518i	$0.430883\pi$
$163$	−9.42180	+	16.3190i	−0.737972	+	1.27821i	−0.953407	+	0.301687i	$0.902450\pi$
$164$	−12.7032	+	22.0025i	−0.991949	+	1.71811i
$165$	3.82026	−	18.0850i	0.297407	−	1.40792i
$166$	−1.62793	−	4.47269i	−0.126352	−	0.347148i
$167$	−2.22563	−	12.6222i	−0.172224	−	0.976733i	−0.941299	−	0.337574i	$-0.890394\pi$
$167$	−2.22563	−	12.6222i	−0.172224	−	0.976733i	0.769075	−	0.639159i	$-0.220717\pi$
$168$	−37.1770	−	1.25132i	−2.86827	−	0.0965413i
$169$	5.06646	+	4.25126i	0.389728	+	0.327020i
$170$	−42.3037			−3.24455
$171$	11.4382	+	6.33785i	0.874699	+	0.484667i
$172$	−9.00610			−0.686709
$173$	−19.0859	−	16.0149i	−1.45107	−	1.21759i	−0.931794	−	0.362989i	$-0.881756\pi$
$173$	−19.0859	−	16.0149i	−1.45107	−	1.21759i	−0.519278	−	0.854605i	$-0.673799\pi$
$174$	−6.52251	−	12.2298i	−0.494470	−	0.927141i
$175$	−2.48596	−	14.0986i	−0.187921	−	1.06575i
$176$	−10.3375	−	28.4020i	−0.779217	−	2.14088i
$177$	1.44402	+	1.29691i	0.108540	+	0.0974819i
$178$	−15.1508	+	26.2420i	−1.13560	+	1.96692i
$179$	−1.94730	+	3.37283i	−0.145548	+	0.252097i	−0.929577	−	0.368627i	$-0.879828\pi$
$179$	−1.94730	+	3.37283i	−0.145548	+	0.252097i	0.784029	+	0.620724i	$0.213161\pi$
$180$	−36.5926	−	24.5480i	−2.72745	−	1.82970i
$181$	−3.86632	+	10.6226i	−0.287382	+	0.789575i	0.709049	+	0.705159i	$0.249124\pi$
$181$	−3.86632	+	10.6226i	−0.287382	+	0.789575i	−0.996431	+	0.0844154i	$0.973098\pi$
$182$			19.9729i			1.48049i
$183$	−2.61516	+	2.04851i	−0.193318	+	0.151430i
$184$	−7.24825	+	19.9144i	−0.534348	+	1.46811i
$185$	20.5403	−	7.47605i	1.51015	−	0.549650i
$186$	1.10575	+	3.38862i	0.0810779	+	0.248466i
$187$	16.8839	−	6.14523i	1.23467	−	0.449384i
$188$	21.0464	+	57.8246i	1.53497	+	4.21729i
$189$	9.26514	−	12.8543i	0.673940	−	0.935016i
$190$	9.02393	+	33.9983i	0.654665	+	2.46650i
$191$	2.71951	−	1.57011i	0.196777	−	0.113609i	−0.398375	−	0.917223i	$-0.630426\pi$
$191$	2.71951	−	1.57011i	0.196777	−	0.113609i	0.595151	+	0.803614i	$0.297092\pi$
$192$	−8.81668	−	0.296756i	−0.636289	−	0.0214165i
$193$	9.45903	−	11.2728i	0.680876	−	0.811436i	−0.309344	−	0.950950i	$-0.600110\pi$
$193$	9.45903	−	11.2728i	0.680876	−	0.811436i	0.990220	+	0.139514i	$0.0445540\pi$
$194$	−37.8226	+	6.66914i	−2.71550	+	0.478817i
$195$	−7.20743	+	11.5667i	−0.516135	+	0.828310i
$196$	8.30834	−	6.97153i	0.593453	−	0.497966i
$197$	7.47294	−	4.31450i	0.532425	−	0.307396i	−0.209579	−	0.977792i	$-0.567209\pi$
$197$	7.47294	−	4.31450i	0.532425	−	0.307396i	0.742003	+	0.670396i	$0.233876\pi$
$198$	25.8742	+	6.38190i	1.83880	+	0.453542i
$199$	16.7532	+	6.09765i	1.18760	+	0.432251i	0.858880	−	0.512177i	$-0.171161\pi$
$199$	16.7532	+	6.09765i	1.18760	+	0.432251i	0.328720	+	0.944428i	$0.393383\pi$
$200$	−5.74131	−	32.5606i	−0.405972	−	2.30238i
$201$	−1.09991	+	0.155997i	−0.0775819	+	0.0110032i
$202$		−	35.7888i		−	2.51809i
$203$	8.84760	+	3.22026i	0.620980	+	0.226018i
$204$	1.44085	−	42.8079i	0.100880	−	2.99716i
$205$	5.73541	−	15.7579i	0.400578	−	1.10058i
$206$	−24.8163	−	4.37579i	−1.72903	−	0.304875i
$207$	−5.32460	−	7.28995i	−0.370085	−	0.506687i
$208$			22.2850i			1.54519i
$209$	−8.54030	−	12.2582i	−0.590745	−	0.847921i
$210$	42.2009	−	5.98522i	2.91214	−	0.413019i
$211$	1.03505	+	0.182508i	0.0712559	+	0.0125643i	0.209162	−	0.977881i	$-0.432926\pi$
$211$	1.03505	+	0.182508i	0.0712559	+	0.0125643i	−0.137907	+	0.990445i	$0.544037\pi$
$212$	14.2447	+	11.9527i	0.978327	+	0.820914i
$213$	−12.1009	+	3.94870i	−0.829140	+	0.270560i
$214$	−0.418584	+	2.37391i	−0.0286138	+	0.162277i
$215$	5.85409	−	1.03223i	0.399246	−	0.0703978i
$216$	21.3978	−	29.6870i	1.45593	−	2.01994i
$217$	−2.09695	−	1.21068i	−0.142350	−	0.0821860i
$218$	31.0021	−	5.46651i	2.09973	−	0.370239i
$219$	−5.99689	−	5.38595i	−0.405232	−	0.363948i
$220$	25.1711	+	43.5977i	1.69704	+	2.93935i
$221$	−13.2476			−0.891128
$222$	9.77636	+	29.9599i	0.656146	+	2.01078i
$223$	8.86131	+	1.56249i	0.593397	+	0.104632i	0.462279	−	0.886735i	$-0.347032\pi$
$223$	8.86131	+	1.56249i	0.593397	+	0.104632i	0.131119	+	0.991367i	$0.458143\pi$
$224$	20.4870	−	17.1906i	1.36884	−	1.14860i
$225$	12.8807	+	5.69600i	0.858716	+	0.379733i
$226$	9.20770	−	3.35133i	0.612487	−	0.222927i
$227$	−1.16058	−	2.01018i	−0.0770303	−	0.133420i	0.824937	−	0.565225i	$-0.191210\pi$
$227$	−1.16058	−	2.01018i	−0.0770303	−	0.133420i	−0.901967	+	0.431804i	$0.857877\pi$
$228$	−34.7109	+	7.97351i	−2.29879	+	0.528059i
$229$	0.134472	−	0.232913i	0.00888618	−	0.0153913i	−0.861548	−	0.507676i	$-0.830505\pi$
$229$	0.134472	−	0.232913i	0.00888618	−	0.0153913i	0.870434	+	0.492285i	$0.163838\pi$
$230$	4.21675	−	23.9144i	0.278044	−	1.57687i
$231$	−15.9734	+	8.51905i	−1.05097	+	0.560512i
$232$	20.4335	+	7.43717i	1.34152	+	0.488274i
$233$	−10.8217	+	12.8968i	−0.708955	+	0.844899i	−0.993508	−	0.113761i	$-0.963710\pi$
$233$	−10.8217	+	12.8968i	−0.708955	+	0.844899i	0.284554	+	0.958660i	$0.408155\pi$
$234$	−16.3174	−	10.9465i	−1.06670	−	0.715593i
$235$	−20.3080	−	35.1745i	−1.32475	−	2.29453i
$236$	−5.28619			−0.344102
$237$	−11.5728	−	2.44462i	−0.751731	−	0.158795i
$238$	26.6319	+	31.7386i	1.72629	+	2.05731i
$239$	−20.4969	+	11.8339i	−1.32583	+	0.765471i	−0.984653	−	0.174526i	$-0.944161\pi$
$239$	−20.4969	+	11.8339i	−1.32583	+	0.765471i	−0.341182	+	0.939997i	$0.610827\pi$
$240$	47.0862	−	6.67808i	3.03940	−	0.431068i
$241$	−10.6959	−	12.7468i	−0.688981	−	0.821095i	0.302251	−	0.953228i	$-0.402262\pi$
$241$	−10.6959	−	12.7468i	−0.688981	−	0.821095i	−0.991232	+	0.132133i	$0.957817\pi$
$242$	−1.48398	−	1.24521i	−0.0953938	−	0.0800449i
$243$	5.42381	+	14.6145i	0.347937	+	0.937518i
$244$	1.57108	−	8.91007i	0.100578	−	0.570408i
$245$	−4.60150	+	5.48385i	−0.293979	+	0.350350i
$246$	22.4281	+	9.02865i	1.42996	+	0.575646i
$247$	2.82588	+	10.6467i	0.179806	+	0.677434i
$248$	−4.84289	−	2.79605i	−0.307524	−	0.177549i
$249$	−2.80666	+	1.49687i	−0.177865	+	0.0948601i
$250$	−0.842778	−	2.31551i	−0.0533020	−	0.146446i
$251$	12.3791	+	14.7528i	0.781362	+	0.931191i	0.998994	−	0.0448395i	$-0.0142776\pi$
$251$	12.3791	+	14.7528i	0.781362	+	0.931191i	−0.217632	+	0.976031i	$0.569833\pi$
$252$	4.61921	+	42.9077i	0.290983	+	2.70293i
$253$	1.79096	+	10.1570i	0.112597	+	0.638567i
$254$	−1.80053	−	1.03954i	−0.112975	−	0.0652262i
$255$	3.96986	+	27.9909i	0.248602	+	1.75286i
$256$	−16.4193	+	13.7775i	−1.02621	+	0.861091i
$257$	4.11404	−	3.45209i	0.256627	−	0.215336i	−0.505393	−	0.862889i	$-0.668652\pi$
$257$	4.11404	−	3.45209i	0.256627	−	0.215336i	0.762020	+	0.647554i	$0.224208\pi$
$258$	1.20347	+	8.48547i	0.0749246	+	0.528282i
$259$	−18.5399	−	10.7040i	−1.15201	−	0.665114i
$260$	−6.44544	−	36.5539i	−0.399729	−	2.26698i
$261$	−7.47996	+	5.46338i	−0.462998	+	0.338175i
$262$	−28.6120	−	34.0984i	−1.76765	−	2.10661i
$263$	6.84717	+	18.8124i	0.422215	+	1.16003i	0.950436	+	0.310919i	$0.100637\pi$
$263$	6.84717	+	18.8124i	0.422215	+	1.16003i	−0.528222	+	0.849106i	$0.677141\pi$
$264$	−36.8904	+	19.6747i	−2.27045	+	1.21089i
$265$	−10.6292	−	6.13676i	−0.652945	−	0.376978i
$266$	19.8265	−	28.1735i	1.21564	−	1.72743i
$267$	18.7852	+	7.56217i	1.14963	+	0.462797i
$268$	1.94484	−	2.31778i	0.118800	−	0.141581i
$269$	3.88108	−	22.0107i	0.236633	−	1.34202i	−0.602513	−	0.798109i	$-0.705834\pi$
$269$	3.88108	−	22.0107i	0.236633	−	1.34202i	0.839146	−	0.543906i	$-0.183055\pi$
$270$	−18.2391	+	37.7575i	−1.11000	+	2.29785i
$271$	11.7304	+	9.84300i	0.712573	+	0.597920i	0.925320	−	0.379188i	$-0.123797\pi$
$271$	11.7304	+	9.84300i	0.712573	+	0.597920i	−0.212747	+	0.977107i	$0.568241\pi$
$272$	29.7149	+	35.4128i	1.80173	+	2.14722i
$273$	13.2154	−	1.87429i	0.799830	−	0.113437i
$274$	7.33129	−	4.23272i	0.442899	−	0.255708i
$275$	−10.3429	−	12.3262i	−0.623700	−	0.743297i
$276$	24.0558	+	5.08152i	1.44799	+	0.305872i
$277$	14.4462			0.867990			0.433995	−	0.900915i	$-0.357104\pi$
$277$	14.4462			0.867990			0.433995	+	0.900915i	$0.357104\pi$
$278$	−21.7723	−	37.7107i	−1.30581	−	2.26174i
$279$	2.13837	−	1.04963i	0.128021	−	0.0628399i
$280$	−42.9826	+	51.2247i	−2.56870	+	3.06126i
$281$	−9.69609	−	3.52909i	−0.578420	−	0.210528i	0.0362087	−	0.999344i	$-0.488472\pi$
$281$	−9.69609	−	3.52909i	−0.578420	−	0.210528i	−0.614629	+	0.788817i	$0.710694\pi$
$282$	51.6694	−	27.5567i	3.07687	−	1.64098i
$283$	−1.73085	+	9.81613i	−0.102888	+	0.583508i	0.889155	+	0.457607i	$0.151293\pi$
$283$	−1.73085	+	9.81613i	−0.102888	+	0.583508i	−0.992043	+	0.125901i	$0.959818\pi$
$284$	17.3338	−	30.0230i	1.02857	−	1.78154i
$285$	21.6487	−	9.16129i	1.28236	−	0.542668i
$286$	11.2243	+	19.4411i	0.663709	+	1.14958i
$287$	−15.4331	+	5.61720i	−0.910988	+	0.331573i
$288$	2.81614	+	26.1590i	0.165943	+	1.54144i
$289$	−8.02877	+	6.73694i	−0.472280	+	0.396290i
$290$	−24.5377	−	4.32666i	−1.44090	−	0.254070i
$291$	7.96208	+	24.4000i	0.466746	+	1.43036i
$292$	21.9530			1.28470
$293$	15.0205	+	26.0162i	0.877506	+	1.51989i	0.854069	+	0.520160i	$0.174128\pi$
$293$	15.0205	+	26.0162i	0.877506	+	1.51989i	0.0234370	+	0.999725i	$0.492539\pi$
$294$	−7.67874	−	6.89646i	−0.447833	−	0.402210i
$295$	3.43610	−	0.605877i	0.200057	−	0.0352755i
$296$	−42.8177	−	24.7208i	−2.48873	−	1.43687i
$297$	1.79460	−	17.7189i	0.104133	−	1.02816i
$298$	−7.06340	+	1.24547i	−0.409172	+	0.0721480i
$299$	1.32049	−	7.48887i	0.0763659	−	0.433093i
$300$	−36.4659	+	11.8993i	−2.10536	+	0.687009i
$301$	−4.45982	−	3.74223i	−0.257060	−	0.215699i
$302$	53.4953	+	9.43267i	3.07831	+	0.542789i
$303$	−23.6802	+	3.35849i	−1.36039	+	0.192940i
$304$	22.1217	−	31.4350i	1.26877	−	1.80292i
$305$			5.97174i			0.341941i
$306$	−40.5258	+	4.36279i	−2.31671	+	0.249404i
$307$	5.31850	+	0.937796i	0.303543	+	0.0535228i	0.323345	−	0.946281i	$-0.395193\pi$
$307$	5.31850	+	0.937796i	0.303543	+	0.0535228i	−0.0198021	+	0.999804i	$0.506304\pi$
$308$	16.8632	−	46.3312i	0.960869	−	2.63997i
$309$	−0.566496	+	16.8307i	−0.0322268	+	0.957466i
$310$	6.02124	+	2.19155i	0.341984	+	0.124472i
$311$			11.4051i			0.646725i	0.946275	+	0.323363i	$0.104813\pi$
$311$			11.4051i			0.646725i	−0.946275	+	0.323363i	$0.895187\pi$
$312$	30.5208	−	4.32866i	1.72790	−	0.245062i
$313$	5.20232	+	29.5038i	0.294053	+	1.66766i	0.671028	+	0.741432i	$0.265853\pi$
$313$	5.20232	+	29.5038i	0.294053	+	1.66766i	−0.376975	+	0.926223i	$0.623036\pi$
$314$	29.5530	+	10.7564i	1.66777	+	0.607019i
$315$	−7.92042	−	27.3612i	−0.446265	−	1.54163i
$316$	27.8985	−	16.1072i	1.56941	−	0.906102i
$317$	−2.32211	+	1.94848i	−0.130422	+	0.109437i	−0.705666	−	0.708545i	$-0.749352\pi$
$317$	−2.32211	+	1.94848i	−0.130422	+	0.109437i	0.575243	+	0.817982i	$0.304907\pi$
$318$	9.35823	−	15.0184i	0.524784	−	0.842190i
$319$	10.4218	−	1.83764i	0.583507	−	0.102888i
$320$	−10.1935	+	12.1482i	−0.569835	+	0.679102i
$321$	1.61001	+	0.0541905i	0.0898622	+	0.00302462i
$322$	−20.5965	+	11.8914i	−1.14780	+	0.662681i
$323$	18.6869	+	13.1505i	1.03977	+	0.731713i
$324$	−37.5863	−	19.7425i	−2.08813	−	1.09681i
$325$	4.05767	+	11.1483i	0.225079	+	0.618399i
$326$	−45.8931	+	16.7037i	−2.54178	+	0.925134i
$327$	−6.52630	−	20.0000i	−0.360905	−	1.10601i
$328$	−35.6427	+	12.9729i	−1.96804	+	0.716307i
$329$	−13.6052	+	37.3800i	−0.750079	+	2.06082i
$330$	37.7138	−	29.5419i	2.07607	−	1.62623i
$331$		−	21.4843i		−	1.18088i	−0.807080	−	0.590442i	$-0.798954\pi$
$331$		−	21.4843i		−	1.18088i	0.807080	−	0.590442i	$-0.201046\pi$
$332$	2.96300	−	8.14078i	0.162616	−	0.446783i
$333$	18.9060	−	9.28017i	1.03604	−	0.508550i
$334$	16.6093	−	28.7681i	0.908818	−	1.57412i
$335$	−0.998524	+	1.72949i	−0.0545552	+	0.0944924i
$336$	−34.6529	−	31.1226i	−1.89047	−	1.69787i
$337$	7.31787	+	20.1057i	0.398630	+	1.09523i	0.962952	+	0.269671i	$0.0869151\pi$
$337$	7.31787	+	20.1057i	0.398630	+	1.09523i	−0.564323	+	0.825554i	$0.690863\pi$
$338$	2.97659	+	16.8811i	0.161905	+	0.918209i
$339$	−3.08153	−	5.77792i	−0.167366	−	0.313814i
$340$	−58.9834	−	49.4929i	−3.19882	−	2.68413i
$341$	−2.72150			−0.147377
$342$	12.1509	+	31.6388i	0.657047	+	1.71083i
$343$	−14.3350			−0.774019
$344$	−10.2999	−	8.64265i	−0.555334	−	0.465981i
$345$	−16.2190	−	0.545906i	−0.873202	−	0.0293906i
$346$	−11.2131	−	63.5927i	−0.602821	−	3.41877i
$347$	2.72226	+	7.47935i	0.146139	+	0.401513i	0.991067	−	0.133367i	$-0.0425790\pi$
$347$	2.72226	+	7.47935i	0.146139	+	0.401513i	−0.844928	+	0.534880i	$0.820357\pi$
$348$	5.21397	−	24.6828i	0.279498	−	1.32314i
$349$	−13.7505	+	23.8165i	−0.736047	+	1.27487i	0.218216	+	0.975900i	$0.429976\pi$
$349$	−13.7505	+	23.8165i	−0.736047	+	1.27487i	−0.954263	+	0.298970i	$0.903357\pi$
$350$	18.5521	−	32.1331i	0.991650	−	1.71759i
$351$	−5.71164	+	11.8239i	−0.304865	+	0.631113i
$352$	10.2808	−	28.2462i	0.547967	−	1.50553i
$353$		−	8.49237i		−	0.452003i	−0.974127	−	0.226002i	$-0.927435\pi$
$353$		−	8.49237i		−	0.452003i	0.974127	−	0.226002i	$-0.0725654\pi$
$354$	0.706383	+	4.98060i	0.0375438	+	0.264716i
$355$	−7.82613	+	21.5021i	−0.415368	+	1.14121i
$356$	−51.8261	+	18.8632i	−2.74678	+	0.999746i
$357$	18.5012	−	20.5998i	0.979185	−	1.09026i
$358$	−9.48521	+	3.45233i	−0.501309	+	0.182462i
$359$	−10.3379	−	28.4032i	−0.545615	−	1.49907i	−0.839573	−	0.543247i	$-0.817195\pi$
$359$	−10.3379	−	28.4032i	−0.545615	−	1.49907i	0.293958	−	0.955818i	$-0.405027\pi$
$360$	−18.2921	−	63.1904i	−0.964080	−	3.33043i
$361$	6.58254	−	17.8233i	0.346449	−	0.938069i
$362$	−25.3732	+	14.6492i	−1.33359	+	0.769946i
$363$	−0.684651	+	1.09875i	−0.0359348	+	0.0576694i
$364$	−23.3671	+	27.8479i	−1.22477	+	1.45962i
$365$	−14.2698	+	2.51615i	−0.746914	+	0.131701i
$366$	−8.60493	−	0.289628i	−0.449787	−	0.0151391i
$367$	5.50400	−	4.61841i	0.287307	−	0.241079i	−0.487731	−	0.872994i	$-0.662175\pi$
$367$	5.50400	−	4.61841i	0.287307	−	0.241079i	0.775038	+	0.631915i	$0.217731\pi$
$368$	−22.9808	+	13.2680i	−1.19796	+	0.691641i
$369$	3.86925	−	15.6871i	0.201425	−	0.816639i
$370$	53.2359	+	19.3763i	2.76760	+	1.00732i
$371$	2.08735	+	11.8379i	0.108370	+	0.614595i
$372$	−2.42275	+	6.01837i	−0.125614	+	0.312038i
$373$			11.1335i			0.576472i	0.957559	+	0.288236i	$0.0930688\pi$
$373$			11.1335i			0.576472i	−0.957559	+	0.288236i	$0.906931\pi$
$374$	43.7593	+	15.9271i	2.26274	+	0.823569i
$375$	−1.45301	+	0.774929i	−0.0750330	+	0.0400172i
$376$	−31.4211	+	86.3287i	−1.62042	+	4.45206i
$377$	−7.68407	−	1.35491i	−0.395750	−	0.0697814i
$378$	39.8100	−	10.0859i	2.04761	−	0.518760i
$379$		−	17.2308i		−	0.885085i	−0.896747	−	0.442543i	$-0.854077\pi$
$379$		−	17.2308i		−	0.885085i	0.896747	−	0.442543i	$-0.145923\pi$
$380$	−27.1942	+	57.9608i	−1.39503	+	2.97333i
$381$	−0.518859	+	1.28890i	−0.0265820	+	0.0660323i
$382$	8.01509	+	1.41328i	0.410088	+	0.0723096i
$383$	−1.14387	−	0.959818i	−0.0584488	−	0.0490444i	0.613095	−	0.790009i	$-0.289924\pi$
$383$	−1.14387	−	0.959818i	−0.0584488	−	0.0490444i	−0.671544	+	0.740965i	$0.734369\pi$
$384$	5.59224	+	5.02252i	0.285378	+	0.256304i
$385$	−5.65105	+	32.0487i	−0.288004	+	1.63335i
$386$	37.5602	−	6.62288i	1.91177	−	0.337096i
$387$	5.50160	−	1.59258i	0.279662	−	0.0809556i
$388$	−60.5379	−	34.9516i	−3.07335	−	1.77440i
$389$	−0.561528	+	0.0990126i	−0.0284706	+	0.00502014i	−0.187865	−	0.982195i	$-0.560157\pi$
$389$	−0.561528	+	0.0990126i	−0.0284706	+	0.00502014i	0.159395	+	0.987215i	$0.449046\pi$
$390$	−33.5795	+	10.9575i	−1.70036	+	0.554853i
$391$	−7.88730	−	13.6612i	−0.398878	−	0.690877i
$392$	16.1921			0.817825
$393$	−19.8767	+	22.1314i	−1.00265	+	1.11638i
$394$	22.0247	+	3.88355i	1.10959	+	0.195650i
$395$	−16.2883	+	13.6675i	−0.819553	+	0.687687i
$396$	28.6095	+	39.1695i	1.43768	+	1.96834i
$397$	21.8120	−	7.93890i	1.09471	−	0.398442i	0.269347	−	0.963043i	$-0.413192\pi$
$397$	21.8120	−	7.93890i	1.09471	−	0.398442i	0.825364	+	0.564601i	$0.190970\pi$
$398$	23.1036	+	40.0165i	1.15808	+	2.00585i
$399$	−20.5020	−	10.4747i	−1.02638	−	0.524389i
$400$	20.6997	−	35.8530i	1.03499	−	1.79265i
$401$	−0.833566	+	4.72739i	−0.0416263	+	0.236074i	−0.998521	−	0.0543591i	$-0.982688\pi$
$401$	−0.833566	+	4.72739i	−0.0416263	+	0.236074i	0.956895	+	0.290434i	$0.0937995\pi$
$402$	−2.44367	−	1.52270i	−0.121879	−	0.0759452i
$403$	1.88557	+	0.686293i	0.0939272	+	0.0341867i
$404$	41.8709	−	49.8998i	2.08315	−	2.48261i
$405$	26.6944	+	8.52494i	1.32646	+	0.423608i
$406$	12.2013	+	21.1333i	0.605543	+	1.04883i
$407$	−24.0617			−1.19269
$408$	42.7283	−	47.5750i	2.11536	−	2.35532i
$409$	−15.6632	−	18.6667i	−0.774497	−	0.923010i	0.224174	−	0.974549i	$-0.428032\pi$
$409$	−15.6632	−	18.6667i	−0.774497	−	0.923010i	−0.998671	+	0.0515396i	$0.983587\pi$
$410$	37.6393	−	21.7310i	1.85887	−	1.07322i
$411$	−3.48863	−	4.45365i	−0.172081	−	0.219682i
$412$	−29.4816	−	35.1348i	−1.45245	−	1.73096i
$413$	−2.61772	−	2.19653i	−0.128810	−	0.108084i
$414$	1.57324	−	23.3442i	0.0773205	−	1.14730i
$415$	−0.992937	+	5.63122i	−0.0487413	+	0.276426i
$416$	−14.2460	+	16.9777i	−0.698466	+	0.832399i
$417$	−22.9087	+	17.9448i	−1.12184	+	0.878761i
$418$	3.46573	−	38.5656i	0.169515	−	1.88630i
$419$	−15.4069	−	8.89520i	−0.752678	−	0.434559i	0.0739825	−	0.997260i	$-0.476429\pi$
$419$	−15.4069	−	8.89520i	−0.752678	−	0.434559i	−0.826661	+	0.562700i	$0.809762\pi$
$420$	65.8423	+	41.0275i	3.21278	+	2.00194i
$421$	1.21029	+	3.32523i	0.0589857	+	0.162062i	0.965685	−	0.259715i	$-0.0836287\pi$
$421$	1.21029	+	3.32523i	0.0589857	+	0.162062i	−0.906700	+	0.421777i	$0.861406\pi$
$422$	1.75096	+	2.08671i	0.0852353	+	0.101580i
$423$	−23.0821	−	31.6019i	−1.12229	−	1.53654i
$424$	4.82071	+	27.3396i	0.234114	+	1.32773i
$425$	21.3132	+	12.3052i	1.03384	+	0.596889i
$426$	−30.6037	−	12.3198i	−1.48276	−	0.596898i
$427$	4.48033	−	3.75944i	0.216818	−	0.181932i
$428$	−3.36096	+	2.82018i	−0.162458	+	0.136319i
$429$	11.8102	−	9.25115i	0.570202	−	0.446650i
$430$	13.3425	+	7.70328i	0.643431	+	0.371485i
$431$	−3.46228	−	19.6356i	−0.166772	−	0.945813i	−0.947218	−	0.320590i	$-0.896119\pi$
$431$	−3.46228	−	19.6356i	−0.166772	−	0.945813i	0.780446	−	0.625223i	$-0.214992\pi$
$432$	44.4186	−	11.2534i	2.13709	−	0.541430i
$433$	−5.66492	−	6.75119i	−0.272239	−	0.324442i	0.612552	−	0.790431i	$-0.290143\pi$
$433$	−5.66492	−	6.75119i	−0.272239	−	0.324442i	−0.884791	+	0.465989i	$0.845699\pi$
$434$	−2.14638	−	5.89714i	−0.103030	−	0.283072i
$435$	−0.560135	+	16.6418i	−0.0268564	+	0.797911i
$436$	49.6213	+	28.6489i	2.37643	+	1.37203i
$437$	−9.29667	+	9.25291i	−0.444720	+	0.442627i
$438$	−2.93354	−	20.6839i	−0.140170	−	0.988317i
$439$	2.76157	−	3.29111i	0.131803	−	0.157076i	−0.696106	−	0.717939i	$-0.745086\pi$
$439$	2.76157	−	3.29111i	0.131803	−	0.157076i	0.827909	+	0.560862i	$0.189530\pi$
$440$	−13.0511	+	74.0162i	−0.622185	+	3.52859i
$441$	−3.84256	+	5.72793i	−0.182979	+	0.272759i
$442$	−26.3020	−	22.0700i	−1.25106	−	1.04976i
$443$	14.8477	+	17.6948i	0.705434	+	0.840704i	0.993130	−	0.117018i	$-0.0373335\pi$
$443$	14.8477	+	17.6948i	0.705434	+	0.840704i	−0.287695	+	0.957722i	$0.592889\pi$
$444$	−21.4204	+	53.2104i	−1.01657	+	2.52526i
$445$	31.5257	−	18.2014i	1.49446	−	0.862828i
$446$	14.9904	+	17.8648i	0.709814	+	0.845923i
$447$	1.48692	+	4.55673i	0.0703291	+	0.215526i
$448$	15.5314			0.733791
$449$	2.64334	+	4.57841i	0.124747	+	0.216068i	0.921634	−	0.388060i	$-0.126855\pi$
$449$	2.64334	+	4.57841i	0.124747	+	0.216068i	−0.796887	+	0.604128i	$0.793521\pi$
$450$	16.0843	+	32.7678i	0.758222	+	1.54469i
$451$	−11.8655	+	14.1407i	−0.558724	+	0.665861i
$452$	16.7590	+	6.09978i	0.788278	+	0.286910i
$453$	1.22117	−	36.2812i	0.0573755	−	1.70464i
$454$	1.04465	−	5.92453i	0.0490281	−	0.278052i
$455$	11.9972	−	20.7797i	0.562436	−	0.974168i
$456$	−47.3492	−	24.1912i	−2.21733	−	1.13285i
$457$	−2.11635	−	3.66563i	−0.0989988	−	0.171471i	0.812272	−	0.583279i	$-0.198231\pi$
$457$	−2.11635	−	3.66563i	−0.0989988	−	0.171471i	−0.911271	+	0.411808i	$0.864897\pi$
$458$	0.655008	−	0.238403i	0.0306065	−	0.0111399i
$459$	6.68972	+	26.4051i	0.312249	+	1.23248i
$460$	33.8578	−	28.4100i	1.57863	−	1.32463i
$461$	8.15109	+	1.43726i	0.379634	+	0.0669397i	0.360209	−	0.932872i	$-0.382705\pi$
$461$	8.15109	+	1.43726i	0.379634	+	0.0669397i	0.0194249	+	0.999811i	$0.493816\pi$
$462$	−45.9063	−	9.69720i	−2.13575	−	0.451154i
$463$	22.6191			1.05120			0.525600	−	0.850732i	$-0.323841\pi$
$463$	22.6191			1.05120			0.525600	+	0.850732i	$0.323841\pi$
$464$	13.6138	+	23.5798i	0.632005	+	1.09467i
$465$	0.885029	−	4.18971i	0.0410423	−	0.194293i
$466$	−42.9713	+	7.57699i	−1.99061	+	0.350997i
$467$	−4.72757	−	2.72946i	−0.218766	−	0.126304i	0.386613	−	0.922242i	$-0.373645\pi$
$467$	−4.72757	−	2.72946i	−0.218766	−	0.126304i	−0.605379	+	0.795938i	$0.706978\pi$
$468$	−9.94436	−	34.3529i	−0.459678	−	1.58796i
$469$	1.92617	−	0.339636i	0.0889424	−	0.0156829i
$470$	18.2796	−	103.669i	0.843173	−	4.78187i
$471$	4.34383	−	20.5636i	0.200153	−	0.947520i
$472$	−6.04561	−	5.07287i	−0.278272	−	0.233498i
$473$	−6.44414	−	1.13628i	−0.296302	−	0.0522460i
$474$	−18.9041	−	24.1334i	−0.868294	−	1.10848i
$475$	5.34296	−	19.7537i	0.245152	−	0.906361i
$476$			75.4104i			3.45643i
$477$	−10.8153	−	4.78266i	−0.495201	−	0.218983i
$478$	−60.4097	−	10.6519i	−2.76308	−	0.487205i
$479$	4.03299	−	11.0805i	0.184272	−	0.506283i	−0.812818	−	0.582518i	$-0.802068\pi$
$479$	4.03299	−	11.0805i	0.184272	−	0.506283i	0.997090	+	0.0762349i	$0.0242899\pi$
$480$	40.1413	+	25.0128i	1.83219	+	1.14167i
$481$	16.6710	+	6.06775i	0.760133	+	0.276666i
$482$		−	43.1267i		−	1.96437i
$483$	9.80093	+	12.5121i	0.445958	+	0.569319i
$484$	−0.612268	−	3.47234i	−0.0278303	−	0.157834i
$485$	43.3565	+	15.7805i	1.96872	+	0.716554i
$486$	−13.5786	+	38.0517i	−0.615939	+	1.72606i
$487$	21.0568	−	12.1571i	0.954173	−	0.550892i	0.0597985	−	0.998210i	$-0.480954\pi$
$487$	21.0568	−	12.1571i	0.954173	−	0.550892i	0.894375	+	0.447318i	$0.147621\pi$
$488$	10.3473	−	8.68240i	0.468400	−	0.393034i
$489$	15.3590	+	28.7984i	0.694557	+	1.30231i
$490$	−18.2718	+	3.22181i	−0.825435	+	0.145546i
$491$	13.1022	−	15.6145i	0.591292	−	0.704674i	−0.384562	−	0.923099i	$-0.625647\pi$
$491$	13.1022	−	15.6145i	0.591292	−	0.704674i	0.975854	+	0.218425i	$0.0700918\pi$
$492$	20.7081	+	38.8280i	0.933592	+	1.75050i
$493$	−14.0173	+	8.09288i	−0.631307	+	0.364485i
$494$	−12.1265	+	25.8460i	−0.545596	+	1.16286i
$495$	−23.0860	−	22.1816i	−1.03764	−	0.996990i
$496$	−2.39486	−	6.57981i	−0.107532	−	0.295442i
$497$	21.0589	−	7.66482i	0.944622	−	0.343814i
$498$	−8.06611	−	1.70388i	−0.361451	−	0.0763526i
$499$	−34.7935	+	12.6638i	−1.55757	+	0.566910i	−0.970179	−	0.242391i	$-0.922068\pi$
$499$	−34.7935	+	12.6638i	−1.55757	+	0.566910i	−0.587394	+	0.809301i	$0.699846\pi$
$500$	1.53395	−	4.21448i	0.0686002	−	0.188477i
$501$	−20.5935	−	8.29012i	−0.920049	−	0.370375i
$502$			49.9137i			2.22776i
$503$	1.56626	−	4.30327i	0.0698361	−	0.191873i	−0.899864	−	0.436170i	$-0.856335\pi$
$503$	1.56626	−	4.30327i	0.0698361	−	0.191873i	0.969701	+	0.244296i	$0.0785570\pi$
$504$	−35.8934	+	53.5046i	−1.59882	+	2.38329i
$505$	−21.4974	+	37.2346i	−0.956621	+	1.65692i
$506$	−13.3654	+	23.1496i	−0.594166	+	1.02913i
$507$	10.8903	−	3.55365i	0.483654	−	0.157823i
$508$	−1.29425	−	3.55592i	−0.0574230	−	0.157768i
$509$	−0.670492	−	3.80255i	−0.0297190	−	0.168545i	0.966336	−	0.257284i	$-0.0828275\pi$
$509$	−0.670492	−	3.80255i	−0.0297190	−	0.168545i	−0.996055	+	0.0887387i	$0.971716\pi$
$510$	−38.7500	+	62.1873i	−1.71588	+	2.75370i
$511$	10.8711	+	9.12196i	0.480911	+	0.403532i
$512$	−46.8726			−2.07149
$513$	19.7940	−	11.0089i	0.873929	−	0.486054i
$514$	13.9191			0.613947
$515$	23.1904	+	19.4590i	1.02189	+	0.857468i
$516$	−8.24954	+	13.2391i	−0.363166	+	0.582820i
$517$	7.76379	+	44.0306i	0.341451	+	1.93646i
$518$	−18.9769	−	52.1386i	−0.833798	−	2.29084i
$519$	−41.0248	+	13.3870i	−1.80079	+	0.587623i
$520$	27.7074	−	47.9906i	1.21505	−	2.10453i
$521$	15.8717	−	27.4906i	0.695352	−	1.20438i	−0.274711	−	0.961527i	$-0.588582\pi$
$521$	15.8717	−	27.4906i	0.695352	−	1.20438i	0.970062	−	0.242857i	$-0.0780846\pi$
$522$	−23.9526	−	1.61425i	−1.04838	−	0.0706536i
$523$	11.3436	−	31.1662i	0.496019	−	1.36280i	−0.399073	−	0.916919i	$-0.630668\pi$
$523$	11.3436	−	31.1662i	0.496019	−	1.36280i	0.895092	−	0.445882i	$-0.147110\pi$
$524$		−	81.0173i		−	3.53926i
$525$	−23.0023	−	9.25983i	−1.00390	−	0.404132i
$526$	−17.7464	+	48.7577i	−0.773778	+	2.12594i
$527$	3.91144	−	1.42365i	0.170385	−	0.0620151i
$528$	−51.2205	−	10.8198i	−2.22909	−	0.470870i
$529$	−13.1040	+	4.76948i	−0.569741	+	0.207369i
$530$	−10.8797	−	29.8919i	−0.472586	−	1.29842i
$531$	3.22920	−	0.934778i	0.140135	−	0.0405659i
$532$	60.6052	−	16.0860i	2.62757	−	0.697416i
$533$	11.7869	−	6.80516i	0.510546	−	0.294764i
$534$	24.6981	+	46.3095i	1.06879	+	2.00401i
$535$	1.86144	−	2.21837i	0.0804770	−	0.0959087i
$536$	4.44848	−	0.784387i	0.192145	−	0.0338804i
$537$	3.17440	+	5.95206i	0.136985	+	0.256850i
$538$	44.3745	−	37.2347i	1.91312	−	1.60530i
$539$	6.82445	−	3.94010i	0.293950	−	0.169712i
$540$	−69.6046	+	31.3060i	−2.99530	+	1.34719i
$541$	−18.7285	−	6.81663i	−0.805203	−	0.293070i	−0.0935619	−	0.995613i	$-0.529825\pi$
$541$	−18.7285	−	6.81663i	−0.805203	−	0.293070i	−0.711641	+	0.702544i	$0.752048\pi$
$542$	6.89173	+	39.0849i	0.296025	+	1.67884i
$543$	12.0739	+	15.4138i	0.518143	+	0.661471i
$544$			45.9745i			1.97114i
$545$	−35.5381	−	12.9348i	−1.52228	−	0.554066i
$546$	29.3605	+	18.2950i	1.25651	+	0.782956i
$547$	1.48706	−	4.08566i	0.0635820	−	0.174690i	−0.903833	−	0.427885i	$-0.859259\pi$
$547$	1.48706	−	4.08566i	0.0635820	−	0.174690i	0.967415	+	0.253194i	$0.0814812\pi$
$548$	15.1739	+	2.67557i	0.648198	+	0.114295i
$549$	0.615865	+	5.72076i	0.0262845	+	0.244156i
$550$		−	41.7035i		−	1.77824i
$551$	9.49409	+	9.53899i	0.404462	+	0.406374i
$552$	22.6352	+	28.8965i	0.963417	+	1.22992i
$553$	20.5082	+	3.61616i	0.872099	+	0.153775i
$554$	28.6818	+	24.0669i	1.21857	+	1.02250i
$555$	7.82485	−	37.0426i	0.332146	−	1.57237i
$556$	13.7626	−	78.0517i	0.583665	−	3.31013i
$557$	−31.1769	+	5.49732i	−1.32101	+	0.232929i	−0.789304	−	0.614002i	$-0.789559\pi$
$557$	−31.1769	+	5.49732i	−1.32101	+	0.232929i	−0.531702	+	0.846931i	$0.678447\pi$
$558$	5.99420	+	1.47848i	0.253755	+	0.0625889i
$559$	4.17825	+	2.41231i	0.176721	+	0.102030i
$560$	−82.4575	+	14.5395i	−3.48447	+	0.614405i
$561$	6.43194	−	30.4486i	0.271557	−	1.28554i
$562$	−13.3714	−	23.1600i	−0.564041	−	0.976947i
$563$	−29.3082			−1.23519			−0.617597	−	0.786494i	$-0.711894\pi$
$563$	−29.3082			−1.23519			−0.617597	+	0.786494i	$0.711894\pi$
$564$	104.282	+	22.0283i	4.39105	+	0.927561i
$565$	−11.5927	−	2.04411i	−0.487709	−	0.0859963i
$566$	−19.7898	+	16.6056i	−0.831826	+	0.697985i
$567$	−10.4093	−	25.3944i	−0.437150	−	1.06647i
$568$	48.6354	−	17.7018i	2.04070	−	0.742753i
$569$	−16.0751	−	27.8429i	−0.673903	−	1.16723i	−0.976788	−	0.214207i	$-0.931283\pi$
$569$	−16.0751	−	27.8429i	−0.673903	−	1.16723i	0.302885	−	0.953027i	$-0.402050\pi$
$570$	58.2441	+	17.8769i	2.43958	+	0.748783i
$571$	11.4607	−	19.8505i	0.479615	−	0.830717i	−0.520112	−	0.854098i	$-0.674110\pi$
$571$	11.4607	−	19.8505i	0.479615	−	0.830717i	0.999727	+	0.0233811i	$0.00744312\pi$
$572$	−7.09510	+	40.2383i	−0.296661	+	1.68245i
$573$	0.182965	−	5.43593i	0.00764347	−	0.227089i
$574$	−39.9992	−	14.5585i	−1.66954	−	0.607661i
$575$	−9.08059	+	10.8218i	−0.378687	+	0.451301i
$576$	−8.51226	+	12.6889i	−0.354678	+	0.528702i
$577$	6.14875	+	10.6500i	0.255976	+	0.443363i	0.965160	−	0.261660i	$-0.0842699\pi$
$577$	6.14875	+	10.6500i	0.255976	+	0.443363i	−0.709184	+	0.705023i	$0.750937\pi$
$578$	−27.1639			−1.12987
$579$	−7.90685	−	24.2308i	−0.328598	−	1.00700i
$580$	−29.1506	−	34.7403i	−1.21041	−	1.44251i
$581$	4.84995	−	2.80012i	0.201210	−	0.116169i
$582$	−24.8415	+	61.7088i	−1.02971	+	2.55791i
$583$	8.68445	+	10.3497i	0.359673	+	0.428642i
$584$	25.1068	+	21.0671i	1.03893	+	0.871763i
$585$	10.4013	+	21.1901i	0.430042	+	0.876103i
$586$	−13.5202	+	76.6767i	−0.558513	+	3.16748i
$587$	12.3452	−	14.7125i	0.509543	−	0.607250i	−0.448532	−	0.893767i	$-0.648053\pi$
$587$	12.3452	−	14.7125i	0.509543	−	0.607250i	0.958075	+	0.286517i	$0.0924975\pi$
$588$	−2.63788	−	18.5993i	−0.108784	−	0.767022i
$589$	−1.97851	−	2.83984i	−0.0815230	−	0.117013i
$590$	7.83146	+	4.52149i	0.322416	+	0.186147i
$591$	0.502770	−	14.9374i	0.0206812	−	0.614443i
$592$	−21.1737	−	58.1744i	−0.870235	−	2.39095i
$593$	18.0028	+	21.4549i	0.739287	+	0.881048i	0.996351	−	0.0853460i	$-0.0271996\pi$
$593$	18.0028	+	21.4549i	0.739287	+	0.881048i	−0.257064	+	0.966394i	$0.582755\pi$
$594$	33.0821	−	32.1897i	1.35737	−	1.32076i
$595$	−8.64316	−	49.0178i	−0.354335	−	2.00953i
$596$	−11.3055	−	6.52723i	−0.463091	−	0.267366i
$597$	24.3095	−	19.0420i	0.994920	−	0.779339i
$598$	15.0979	−	12.6687i	0.617399	−	0.518060i
$599$	19.2546	−	16.1565i	0.786721	−	0.660138i	−0.158210	−	0.987405i	$-0.550572\pi$
$599$	19.2546	−	16.1565i	0.786721	−	0.660138i	0.944932	+	0.327268i	$0.106128\pi$
$600$	−53.1237	−	21.3855i	−2.16877	−	0.873059i
$601$	40.2954	+	23.2645i	1.64368	+	0.948980i	0.979509	+	0.201401i	$0.0645494\pi$
$601$	40.2954	+	23.2645i	1.64368	+	0.948980i	0.664173	+	0.747579i	$0.268784\pi$
$602$	−2.62018	−	14.8598i	−0.106791	−	0.605640i
$603$	−0.778196	+	1.75979i	−0.0316906	+	0.0716640i
$604$	63.5520	+	75.7383i	2.58589	+	3.08175i
$605$	0.795965	+	2.18690i	0.0323606	+	0.0889100i
$606$	−52.6102	−	32.7824i	−2.13714	−	1.33169i
$607$	25.8987	+	14.9526i	1.05120	+	0.606909i	0.922984	−	0.384838i	$-0.125743\pi$
$607$	25.8987	+	14.9526i	1.05120	+	0.606909i	0.128213	+	0.991747i	$0.459076\pi$
$608$	36.9485	−	9.80696i	1.49846	−	0.397725i
$609$	12.8382	−	10.0564i	0.520230	−	0.407506i
$610$	−9.94869	+	11.8564i	−0.402811	+	0.480051i
$611$	5.72431	−	32.4642i	0.231581	−	1.31336i
$612$	−61.6087	−	41.3299i	−2.49038	−	1.67066i
$613$	31.4292	+	26.3722i	1.26941	+	1.06516i	0.994612	+	0.103664i	$0.0330565\pi$
$613$	31.4292	+	26.3722i	1.26941	+	1.06516i	0.274801	+	0.961501i	$0.411388\pi$
$614$	8.99712	+	10.7223i	0.363094	+	0.432719i
$615$	−17.9108	−	22.8653i	−0.722234	−	0.922018i
$616$	63.7473	−	36.8045i	2.56845	−	1.48290i
$617$	−21.9918	−	26.2088i	−0.885356	−	1.05513i	−0.998107	−	0.0615034i	$-0.980411\pi$
$617$	−21.9918	−	26.2088i	−0.885356	−	1.05513i	0.112750	−	0.993623i	$-0.464034\pi$
$618$	−29.1641	+	32.4723i	−1.17315	+	1.30623i
$619$	−19.2560			−0.773964			−0.386982	−	0.922087i	$-0.626482\pi$
$619$	−19.2560			−0.773964			−0.386982	+	0.922087i	$0.626482\pi$
$620$	5.83133	+	10.1002i	0.234192	+	0.405632i
$621$	−15.5937	+	1.14970i	−0.625752	+	0.0461360i
$622$	−19.0005	+	22.6439i	−0.761851	+	0.907939i
$623$	−33.5024	−	12.1939i	−1.34224	−	0.488537i
$624$	32.7594	+	20.4129i	1.31142	+	0.817172i
$625$	−4.59013	+	26.0319i	−0.183605	+	1.04128i
$626$	−38.8235	+	67.2443i	−1.55170	+	2.68762i
$627$	−25.8427	+	1.32591i	−1.03206	+	0.0529517i
$628$	28.6209	+	49.5728i	1.14210	+	1.97817i
$629$	34.5824	−	12.5870i	1.37889	−	0.501875i
$630$	29.8574	−	67.5185i	1.18955	−	2.69000i
$631$	−14.4502	+	12.1251i	−0.575253	+	0.482694i	−0.883384	−	0.468650i	$-0.844741\pi$
$631$	−14.4502	+	12.1251i	−0.575253	+	0.482694i	0.308132	+	0.951344i	$0.400296\pi$
$632$	47.3636	+	8.35148i	1.88402	+	0.332204i
$633$	1.21639	−	1.35437i	0.0483472	−	0.0538313i
$634$	−7.85644			−0.312019
$635$	1.24884	+	2.16306i	0.0495588	+	0.0858383i
$636$	30.6187	−	9.99131i	1.21411	−	0.396181i
$637$	−5.72188	+	1.00892i	−0.226709	+	0.0399749i
$638$	23.7530	+	13.7138i	0.940390	+	0.542935i
$639$	−5.27970	+	21.4055i	−0.208862	+	0.846790i
$640$	13.3069	−	2.34636i	0.526001	−	0.0927482i
$641$	−3.63113	+	20.5932i	−0.143421	+	0.813381i	0.825200	+	0.564840i	$0.191062\pi$
$641$	−3.63113	+	20.5932i	−0.143421	+	0.813381i	−0.968621	+	0.248541i	$0.920049\pi$
$642$	3.10627	+	2.78981i	0.122595	+	0.110105i
$643$	29.7629	+	24.9741i	1.17373	+	0.984881i	1.00000		8.81556e-5i	$2.80608e-5\pi$
$643$	29.7629	+	24.9741i	1.17373	+	0.984881i	0.173735	+	0.984792i	$0.444416\pi$
$644$	−42.6296	−	7.51675i	−1.67984	−	0.296201i
$645$	3.84491	−	9.55114i	0.151393	−	0.376076i
$646$	15.1930	+	57.2409i	0.597762	+	2.25211i
$647$			46.7535i			1.83807i	0.394177	+	0.919034i	$0.371030\pi$
$647$			46.7535i			1.83807i	−0.394177	+	0.919034i	$0.628970\pi$
$648$	−24.0402	−	58.6482i	−0.944388	−	2.30392i
$649$	−3.78243	−	0.666945i	−0.148473	−	0.0261799i
$650$	−10.5166	+	28.8941i	−0.412494	+	1.13332i
$651$	−3.70051	+	1.97359i	−0.145034	+	0.0773509i
$652$	−83.5304	−	30.4026i	−3.27130	−	1.19066i
$653$			5.22968i			0.204653i	0.994751	+	0.102327i	$0.0326287\pi$
$653$			5.22968i			0.204653i	−0.994751	+	0.102327i	$0.967371\pi$
$654$	20.3619	−	50.5810i	0.796214	−	1.97787i
$655$	9.28579	+	52.6623i	0.362826	+	2.05769i
$656$	−44.6297	−	16.2439i	−1.74250	−	0.634217i
$657$	−13.4106	+	3.88204i	−0.523196	+	0.151453i
$658$	−89.2856	+	51.5491i	−3.48072	+	2.00959i
$659$	−3.87066	+	3.24787i	−0.150780	+	0.126519i	−0.715057	−	0.699066i	$-0.753599\pi$
$659$	−3.87066	+	3.24787i	−0.150780	+	0.126519i	0.564277	+	0.825585i	$0.309155\pi$
$660$	87.1460	+	2.93320i	3.39215	+	0.114175i
$661$	−18.0773	+	3.18751i	−0.703125	+	0.123980i	−0.513769	−	0.857929i	$-0.671751\pi$
$661$	−18.0773	+	3.18751i	−0.703125	+	0.123980i	−0.189356	+	0.981908i	$0.560640\pi$
$662$	35.7920	−	42.6553i	1.39110	−	1.65784i
$663$	−12.1347	+	19.4742i	−0.471273	+	0.756314i
$664$	11.2009	−	6.46685i	0.434680	−	0.250963i
$665$	−37.5505	+	17.4024i	−1.45615	+	0.674836i
$666$	52.9968	+	13.0717i	2.05358	+	0.506519i
$667$	−3.17771	−	8.73067i	−0.123041	−	0.338053i
$668$	56.8150	−	20.6790i	2.19824	−	0.800094i
$669$	10.4138	−	11.5951i	0.402621	−	0.448291i
$670$	−4.86376	+	1.77026i	−0.187903	+	0.0683913i
$671$	2.24832	−	6.17720i	0.0867954	−	0.238468i
$672$	−6.50457	−	45.8628i	−0.250919	−	1.76919i
$673$		−	1.89398i		−	0.0730077i	−0.999334	−	0.0365039i	$-0.988378\pi$
$673$		−	1.89398i		−	0.0730077i	0.999334	−	0.0365039i	$-0.0116221\pi$
$674$	−18.9663	+	52.1094i	−0.730554	+	2.00718i
$675$	20.1719	−	13.7174i	0.776417	−	0.527984i
$676$	−15.5997	+	27.0194i	−0.599987	+	1.03921i
$677$	24.4372	−	42.3265i	0.939198	−	1.62674i	0.172226	−	0.985057i	$-0.444904\pi$
$677$	24.4372	−	42.3265i	0.939198	−	1.62674i	0.766972	−	0.641681i	$-0.221763\pi$
$678$	3.50769	−	16.6053i	0.134712	−	0.637723i
$679$	−15.4552	−	42.4629i	−0.593117	−	1.62957i
$680$	−19.9613	−	113.206i	−0.765481	−	4.34126i
$681$	−4.01809	−	0.135242i	−0.153973	−	0.00518250i
$682$	−5.40331	−	4.53391i	−0.206903	−	0.173613i
$683$	48.2589			1.84657			0.923287	−	0.384111i	$-0.125492\pi$
$683$	48.2589			1.84657			0.923287	+	0.384111i	$0.125492\pi$
$684$	−20.0738	+	58.3294i	−0.767540	+	2.23028i
$685$	−10.1699			−0.388573
$686$	−28.4610	−	23.8816i	−1.08665	−	0.911805i
$687$	−0.219210	−	0.411024i	−0.00836340	−	0.0156815i
$688$	−2.92350	−	16.5800i	−0.111457	−	0.632107i
$689$	−3.40703	−	9.36075i	−0.129798	−	0.356616i
$690$	−31.2920	−	28.1041i	−1.19127	−	1.06991i
$691$	−24.2403	+	41.9854i	−0.922144	+	1.59720i	−0.126053	+	0.992023i	$0.540231\pi$
$691$	−24.2403	+	41.9854i	−0.922144	+	1.59720i	−0.796091	+	0.605177i	$0.793102\pi$
$692$	58.7656	−	101.785i	2.23393	−	3.86928i
$693$	−2.10837	+	31.2846i	−0.0800903	+	1.18840i
$694$	−7.05550	+	19.3848i	−0.267823	+	0.735838i
$695$			52.3121i			1.98431i
$696$	29.6497	−	23.2252i	1.12387	−	0.880348i
$697$	9.65635	−	26.5306i	0.365760	−	1.00492i
$698$	−66.9779	+	24.3780i	−2.53515	+	0.922720i
$699$	9.04594	+	27.7216i	0.342149	+	1.04853i
$700$	63.4608	−	23.0978i	2.39859	−	0.873016i
$701$	−6.42122	−	17.6422i	−0.242526	−	0.666335i	−0.999911	−	0.0133661i	$-0.995745\pi$
$701$	−6.42122	−	17.6422i	−0.242526	−	0.666335i	0.757384	−	0.652969i	$-0.226477\pi$
$702$	−31.0382	+	13.9600i	−1.17146	+	0.526886i
$703$	−17.4927	−	25.1080i	−0.659748	−	0.946965i
$704$	15.1179	−	8.72834i	0.569779	−	0.328962i
$705$	−70.3093	−	2.36650i	−2.64800	−	0.0891275i
$706$	14.1480	−	16.8609i	0.532466	−	0.634568i
$707$	41.4689	−	7.31209i	1.55960	−	0.274999i
$708$	−4.84212	+	7.77080i	−0.181978	+	0.292045i
$709$	13.1075	−	10.9985i	0.492264	−	0.413059i	−0.362573	−	0.931955i	$-0.618102\pi$
$709$	13.1075	−	10.9985i	0.492264	−	0.413059i	0.854837	+	0.518897i	$0.173657\pi$
$710$	−51.3598	+	29.6526i	−1.92750	+	1.11284i
$711$	−14.1942	+	14.7729i	−0.532324	+	0.554027i
$712$	−77.3734	−	28.1616i	−2.89969	−	1.05540i
$713$	0.414906	+	2.35305i	0.0155384	+	0.0881224i
$714$	71.0510	−	10.0769i	2.65902	−	0.377120i
$715$		−	26.9687i		−	1.00857i
$716$	−17.2641	−	6.28362i	−0.645190	−	0.234830i
$717$	−1.37901	+	40.9706i	−0.0514999	+	1.53008i
$718$	26.7936	−	73.6149i	0.999929	−	2.74728i
$719$	−15.3670	−	2.70961i	−0.573091	−	0.101051i	−0.120411	−	0.992724i	$-0.538421\pi$
$719$	−15.3670	−	2.70961i	−0.573091	−	0.101051i	−0.452681	+	0.891673i	$0.649532\pi$
$720$	33.3138	−	75.3346i	1.24153	−	2.80756i
$721$		−	29.6490i		−	1.10418i
$722$	42.7621	−	24.4204i	1.59144	−	0.908834i
$723$	−28.5354	+	4.04709i	−1.06124	+	0.150513i
$724$	−52.5162	−	9.26002i	−1.95175	−	0.344146i
$725$	11.1039	+	9.31728i	0.412389	+	0.346035i
$726$	−3.18979	+	1.04088i	−0.118384	+	0.0386305i
$727$	−1.10141	+	6.24641i	−0.0408490	+	0.231666i	−0.998396	−	0.0566096i	$-0.981971\pi$
$727$	−1.10141	+	6.24641i	−0.0408490	+	0.231666i	0.957547	+	0.288276i	$0.0930821\pi$
$728$	−53.4481	+	9.42434i	−1.98092	+	0.349289i
$729$	26.4517	+	5.41366i	0.979692	+	0.200506i
$730$	−32.5233	−	18.7773i	−1.20374	−	0.694979i
$731$	9.85617	−	1.73791i	0.364544	−	0.0642789i
$732$	−11.6589	−	10.4711i	−0.430924	−	0.387023i
$733$	−14.5143	−	25.1395i	−0.536097	−	0.928548i	−0.999109	−	0.0421960i	$-0.986565\pi$
$733$	−14.5143	−	25.1395i	−0.536097	−	0.928548i	0.463012	−	0.886352i	$-0.346769\pi$
$734$	18.6218			0.687345
$735$	3.84642	+	11.7875i	0.141877	+	0.434787i
$736$	−25.9895	−	4.58265i	−0.957985	−	0.168919i
$737$	1.68402	−	1.41306i	0.0620318	−	0.0520509i
$738$	33.8163	−	24.6995i	1.24479	−	0.909200i
$739$	0.118940	−	0.0432906i	0.00437528	−	0.00159247i	−0.339832	−	0.940486i	$-0.610370\pi$
$739$	0.118940	−	0.0432906i	0.00437528	−	0.00159247i	0.344207	+	0.938894i	$0.388148\pi$
$740$	51.5567	+	89.2989i	1.89526	+	3.28269i
$741$	18.2393	+	5.59823i	0.670039	+	0.205656i
$742$	−15.5773	+	26.9807i	−0.571861	+	0.990492i
$743$	−9.01776	+	51.1422i	−0.330829	+	1.87623i	0.134234	+	0.990950i	$0.457143\pi$
$743$	−9.01776	+	51.1422i	−0.330829	+	1.87623i	−0.465064	+	0.885277i	$0.653969\pi$
$744$	−8.54630	+	4.55798i	−0.313323	+	0.167104i
$745$	8.09685	+	2.94701i	0.296646	+	0.107970i
$746$	−18.5480	+	22.1047i	−0.679092	+	0.809311i
$747$	−0.370458	+	5.49696i	−0.0135543	+	0.201123i
$748$	42.3791	+	73.4027i	1.54953	+	2.68387i
$749$	−2.83620			−0.103632
$750$	−4.17583	−	0.882098i	−0.152480	−	0.0322097i
$751$	−4.42954	−	5.27892i	−0.161636	−	0.192630i	0.679147	−	0.734002i	$-0.262350\pi$
$751$	−4.42954	−	5.27892i	−0.161636	−	0.192630i	−0.840783	+	0.541372i	$0.817905\pi$
$752$	−99.6216	+	57.5166i	−3.63283	+	2.09741i
$753$	33.0262	−	4.68399i	1.20354	−	0.170694i
$754$	−12.9989	−	15.4914i	−0.473391	−	0.564165i
$755$	−49.9904	−	41.9469i	−1.81934	−	1.52661i
$756$	67.3063	+	32.5129i	2.44791	+	1.18248i
$757$	1.12341	−	6.37117i	0.0408310	−	0.231564i	−0.957562	−	0.288226i	$-0.906935\pi$
$757$	1.12341	−	6.37117i	0.0408310	−	0.231564i	0.998393	+	0.0566619i	$0.0180457\pi$
$758$	28.7058	−	34.2103i	1.04264	−	1.24257i
$759$	16.5715	+	6.67104i	0.601508	+	0.242143i
$760$	−86.7227	+	40.1907i	−3.14576	+	1.45787i
$761$	22.4632	+	12.9692i	0.814292	+	0.470132i	0.848444	−	0.529285i	$-0.177540\pi$
$761$	22.4632	+	12.9692i	0.814292	+	0.470132i	−0.0341523	+	0.999417i	$0.510873\pi$
$762$	−3.17741	+	1.69460i	−0.115105	+	0.0613889i
$763$	12.6682	+	34.8056i	0.458620	+	1.26005i
$764$	9.52186	+	11.3477i	0.344489	+	0.410546i
$765$	44.7835	+	19.8037i	1.61915	+	0.716006i
$766$	−0.672031	−	3.81128i	−0.0242815	−	0.137707i
$767$	2.45245	+	1.41592i	0.0885528	+	0.0511260i
$768$	5.21310	+	36.7568i	0.188111	+	1.32635i
$769$	12.1577	−	10.2015i	0.438416	−	0.367875i

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.98542 + 1.66596i) q^{2} +(0.915994 - 1.47002i) q^{3} +(0.819153 + 4.64565i) q^{4} +(-1.06492 - 2.92585i) q^{5} +(4.26763 - 1.39259i) q^{6} +(-1.52472 + 2.64090i) q^{7} +(-3.52134 + 6.09914i) q^{8} +(-1.32191 - 2.69306i) q^{9} +O(q^{10})\)	\(q+(1.98542 + 1.66596i) q^{2} +(0.915994 - 1.47002i) q^{3} +(0.819153 + 4.64565i) q^{4} +(-1.06492 - 2.92585i) q^{5} +(4.26763 - 1.39259i) q^{6} +(-1.52472 + 2.64090i) q^{7} +(-3.52134 + 6.09914i) q^{8} +(-1.32191 - 2.69306i) q^{9} +(2.76004 - 7.58315i) q^{10} +3.42745i q^{11} +(7.57953 + 3.05122i) q^{12} +(0.864317 - 2.37469i) q^{13} +(-7.42686 + 2.70316i) q^{14} +(-5.27651 - 1.11461i) q^{15} +(-8.28661 + 3.01608i) q^{16} +(-1.79294 - 4.92607i) q^{17} +(1.86199 - 7.54909i) q^{18} +(-3.57649 + 2.49173i) q^{19} +(12.7201 - 7.34397i) q^{20} +(2.48553 + 4.66042i) q^{21} +(-5.71001 + 6.80493i) q^{22} +(2.96343 - 0.522533i) q^{23} +(5.74032 + 10.7632i) q^{24} +(-3.59631 + 3.01766i) q^{25} +(5.67218 - 3.27483i) q^{26} +(-5.16970 - 0.523595i) q^{27} +(-13.5177 - 4.92003i) q^{28} +(-0.536153 - 3.04067i) q^{29} +(-8.61919 - 11.0034i) q^{30} +0.794029i q^{31} +(-8.24116 - 2.99954i) q^{32} +(5.03842 + 3.13953i) q^{33} +(4.64691 - 12.7673i) q^{34} +(9.35059 + 1.64876i) q^{35} +(11.4282 - 8.34715i) q^{36} +7.02028i q^{37} +(-11.2520 - 1.01117i) q^{38} +(-2.69913 - 3.44577i) q^{39} +(21.5951 + 3.80780i) q^{40} +(4.12573 + 3.46190i) q^{41} +(-2.82927 + 13.3937i) q^{42} +(-0.331522 + 1.88015i) q^{43} +(-15.9227 + 2.80761i) q^{44} +(-6.47175 + 6.73560i) q^{45} +(6.75417 + 3.89952i) q^{46} +(12.8465 - 2.26518i) q^{47} +(-3.15680 + 14.9442i) q^{48} +(-1.14957 - 1.99111i) q^{49} -12.1675 q^{50} +(-8.88374 - 1.87659i) q^{51} +(11.7400 + 2.07008i) q^{52} +(3.01965 - 2.53379i) q^{53} +(-9.39173 - 9.65209i) q^{54} +(10.0282 - 3.64997i) q^{55} +(-10.7381 - 18.5990i) q^{56} +(0.386850 + 7.53992i) q^{57} +(4.00116 - 6.93022i) q^{58} +(-0.194589 + 1.10357i) q^{59} +(0.855795 - 25.4259i) q^{60} +(-1.80227 - 0.655973i) q^{61} +(-1.32282 + 1.57648i) q^{62} +(9.12764 + 0.615141i) q^{63} +(-2.54660 - 4.41084i) q^{64} -7.86842 q^{65} +(4.77303 + 14.6271i) q^{66} +(-0.412278 - 0.491334i) q^{67} +(21.4161 - 12.3646i) q^{68} +(1.94635 - 4.83494i) q^{69} +(15.8180 + 18.8512i) q^{70} +(-5.62967 - 4.72386i) q^{71} +(21.0802 + 1.42066i) q^{72} +(0.808108 - 4.58301i) q^{73} +(-11.6955 + 13.9382i) q^{74} +(1.14182 + 8.05081i) q^{75} +(-14.5054 - 14.5740i) q^{76} +(-9.05156 - 5.22592i) q^{77} +(0.381617 - 11.3379i) q^{78} +(-2.33565 - 6.41714i) q^{79} +(17.6492 + 21.0335i) q^{80} +(-5.50511 + 7.11995i) q^{81} +(2.42390 + 13.7466i) q^{82} +(-1.59043 - 0.918238i) q^{83} +(-19.6147 + 15.3645i) q^{84} +(-12.5036 + 10.4918i) q^{85} +(-3.79048 + 3.18059i) q^{86} +(-4.96096 - 1.99709i) q^{87} +(-20.9045 - 12.0692i) q^{88} +(2.03020 + 11.5138i) q^{89} +(-24.0704 + 2.59129i) q^{90} +(4.95348 + 5.90333i) q^{91} +(4.85501 + 13.3390i) q^{92} +(1.16724 + 0.727326i) q^{93} +(29.2793 + 16.9044i) q^{94} +(11.0991 + 7.81076i) q^{95} +(-11.9582 + 9.36710i) q^{96} +(-9.52510 + 11.3516i) q^{97} +(1.03475 - 5.86834i) q^{98} +(9.23033 - 4.53078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

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