LMFDB - Embedded newform 135.2.q.a.92.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,2,Mod(2,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			92.1
Character	$\chi$	$=$	135.92
Dual form			135.2.q.a.113.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.71476 + 0.237511i) q^{2} +(1.47097 - 0.914466i) q^{3} +(5.34392 - 0.942278i) q^{4} +(1.08230 - 1.95669i) q^{5} +(-3.77614 + 2.83193i) q^{6} +(-1.29639 + 0.907744i) q^{7} +(-9.01913 + 2.41667i) q^{8} +(1.32750 - 2.69030i) q^{9} +(-2.47344 + 5.56901i) q^{10} +(0.162954 + 0.447712i) q^{11} +(6.99907 - 6.27290i) q^{12} +(0.242081 - 2.76700i) q^{13} +(3.30380 - 2.77222i) q^{14} +(-0.197304 - 3.86795i) q^{15} +(13.7126 - 4.99098i) q^{16} +(3.35386 + 0.898665i) q^{17} +(-2.96488 + 7.61884i) q^{18} +(-1.97319 - 1.13922i) q^{19} +(3.93995 - 11.4762i) q^{20} +(-1.07685 + 2.52077i) q^{21} +(-0.548719 - 1.17673i) q^{22} +(-0.230790 + 0.329603i) q^{23} +(-11.0569 + 11.8025i) q^{24} +(-2.65727 - 4.23543i) q^{25} +7.56924i q^{26} +(-0.507474 - 5.17131i) q^{27} +(-6.07248 + 6.07248i) q^{28} +(4.29568 + 3.60450i) q^{29} +(1.45432 + 10.4537i) q^{30} +(0.908475 + 5.15222i) q^{31} +(-19.1162 + 8.91403i) q^{32} +(0.649118 + 0.509556i) q^{33} +(-9.31839 - 1.64308i) q^{34} +(0.373094 + 3.51909i) q^{35} +(4.55906 - 15.6276i) q^{36} +(-0.387140 + 1.44483i) q^{37} +(5.62733 + 2.62407i) q^{38} +(-2.17423 - 4.29154i) q^{39} +(-5.03269 + 20.2632i) q^{40} +(-4.99389 - 5.95149i) q^{41} +(2.32469 - 7.09907i) q^{42} +(-0.501128 + 1.07467i) q^{43} +(1.29268 + 2.23899i) q^{44} +(-3.82734 - 5.50922i) q^{45} +(0.548257 - 0.949609i) q^{46} +(6.94767 + 9.92230i) q^{47} +(15.6068 - 19.8813i) q^{48} +(-1.53751 + 4.22426i) q^{49} +(8.21984 + 10.8671i) q^{50} +(5.75523 - 1.74508i) q^{51} +(-1.31362 - 15.0147i) q^{52} +(-0.274270 - 0.274270i) q^{53} +(2.60592 + 13.9184i) q^{54} +(1.05240 + 0.165706i) q^{55} +(9.49862 - 11.3200i) q^{56} +(-3.94428 + 0.128655i) q^{57} +(-12.5179 - 8.76510i) q^{58} +(-3.33385 - 1.21342i) q^{59} +(-4.69906 - 20.4841i) q^{60} +(-1.59716 + 9.05792i) q^{61} +(-3.69001 - 13.7713i) q^{62} +(0.721141 + 4.69272i) q^{63} +(24.5036 - 14.1471i) q^{64} +(-5.15215 - 3.46838i) q^{65} +(-1.88323 - 1.22915i) q^{66} +(13.1561 + 1.15101i) q^{67} +(18.7696 + 1.64212i) q^{68} +(-0.0380751 + 0.695886i) q^{69} +(-1.84869 - 9.46488i) q^{70} +(-13.8198 + 7.97886i) q^{71} +(-5.47136 + 27.4723i) q^{72} +(2.07381 + 7.73957i) q^{73} +(0.707832 - 4.01431i) q^{74} +(-7.78193 - 3.80021i) q^{75} +(-11.6180 - 4.22862i) q^{76} +(-0.617661 - 0.432491i) q^{77} +(6.92182 + 11.1341i) q^{78} +(-2.85683 + 3.40464i) q^{79} +(5.07529 - 32.2331i) q^{80} +(-5.47547 - 7.14278i) q^{81} +(14.9708 + 14.9708i) q^{82} +(0.253902 + 2.90211i) q^{83} +(-3.37935 + 14.4855i) q^{84} +(5.38828 - 5.58985i) q^{85} +(1.10520 - 3.03651i) q^{86} +(9.61501 + 1.37386i) q^{87} +(-2.55168 - 3.64417i) q^{88} +(3.50126 - 6.06435i) q^{89} +(11.6988 + 14.0472i) q^{90} +(2.19789 + 3.80686i) q^{91} +(-0.922748 + 1.97884i) q^{92} +(6.04787 + 6.74799i) q^{93} +(-21.2179 - 25.2866i) q^{94} +(-4.36468 + 2.62795i) q^{95} +(-19.9678 + 30.5934i) q^{96} +(-6.86175 - 3.19969i) q^{97} +(3.17066 - 11.8331i) q^{98} +(1.42080 + 0.155944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.71476	+	0.237511i	−1.91963	+	0.167946i	−0.983153	−	0.182786i	$-0.941488\pi$
$2$	−2.71476	+	0.237511i	−1.91963	+	0.167946i	−0.936476	+	0.350732i	$0.885933\pi$
$3$	1.47097	−	0.914466i	0.849265	−	0.527967i
$3$	1.47097	−	0.914466i	0.849265	−	0.527967i
$4$	5.34392	−	0.942278i	2.67196	−	0.471139i
$5$	1.08230	−	1.95669i	0.484017	−	0.875059i
$5$	1.08230	−	1.95669i	0.484017	−	0.875059i
$6$	−3.77614	+	2.83193i	−1.54160	+	1.15613i
$7$	−1.29639	+	0.907744i	−0.489990	+	0.343095i	−0.792317	−	0.610109i	$-0.791126\pi$
$7$	−1.29639	+	0.907744i	−0.489990	+	0.343095i	0.302327	+	0.953204i	$0.402237\pi$
$8$	−9.01913	+	2.41667i	−3.18874	+	0.854422i
$9$	1.32750	−	2.69030i	0.442501	−	0.896768i
$10$	−2.47344	+	5.56901i	−0.782171	+	1.76108i
$11$	0.162954	+	0.447712i	0.0491325	+	0.134990i	0.961832	−	0.273642i	$-0.0882282\pi$
$11$	0.162954	+	0.447712i	0.0491325	+	0.134990i	−0.912699	+	0.408632i	$0.866006\pi$
$12$	6.99907	−	6.27290i	2.02046	−	1.81083i
$13$	0.242081	−	2.76700i	0.0671411	−	0.767427i	−0.885760	−	0.464144i	$-0.846362\pi$
$13$	0.242081	−	2.76700i	0.0671411	−	0.767427i	0.952901	−	0.303282i	$-0.0980826\pi$
$14$	3.30380	−	2.77222i	0.882978	−	0.740907i
$15$	−0.197304	−	3.86795i	−0.0509436	−	0.998702i
$16$	13.7126	−	4.99098i	3.42815	−	1.24775i
$17$	3.35386	+	0.898665i	0.813431	+	0.217958i	0.641473	−	0.767146i	$-0.278324\pi$
$17$	3.35386	+	0.898665i	0.813431	+	0.217958i	0.171959	+	0.985104i	$0.444990\pi$
$18$	−2.96488	+	7.61884i	−0.698830	+	1.79578i
$19$	−1.97319	−	1.13922i	−0.452681	−	0.261356i	0.256281	−	0.966602i	$-0.417503\pi$
$19$	−1.97319	−	1.13922i	−0.452681	−	0.261356i	−0.708962	+	0.705247i	$0.750836\pi$
$20$	3.93995	−	11.4762i	0.881001	−	2.56616i
$21$	−1.07685	+	2.52077i	−0.234989	+	0.550077i
$22$	−0.548719	−	1.17673i	−0.116987	−	0.250880i
$23$	−0.230790	+	0.329603i	−0.0481231	+	0.0687269i	−0.842493	−	0.538708i	$-0.818913\pi$
$23$	−0.230790	+	0.329603i	−0.0481231	+	0.0687269i	0.794369	+	0.607435i	$0.207801\pi$
$24$	−11.0569	+	11.8025i	−2.25698	+	2.40918i
$25$	−2.65727	−	4.23543i	−0.531455	−	0.847087i
$26$			7.56924i			1.48445i
$27$	−0.507474	−	5.17131i	−0.0976633	−	0.995220i
$28$	−6.07248	+	6.07248i	−1.14759	+	1.14759i
$29$	4.29568	+	3.60450i	0.797687	+	0.669339i	0.947635	−	0.319355i	$-0.103466\pi$
$29$	4.29568	+	3.60450i	0.797687	+	0.669339i	−0.149948	+	0.988694i	$0.547911\pi$
$30$	1.45432	+	10.4537i	0.265520	+	1.90858i
$31$	0.908475	+	5.15222i	0.163167	+	0.925366i	0.950934	+	0.309393i	$0.100126\pi$
$31$	0.908475	+	5.15222i	0.163167	+	0.925366i	−0.787767	+	0.615973i	$0.788763\pi$
$32$	−19.1162	+	8.91403i	−3.37930	+	1.57579i
$33$	0.649118	+	0.509556i	0.112997	+	0.0887022i
$34$	−9.31839	−	1.64308i	−1.59809	−	0.281787i
$35$	0.373094	+	3.51909i	0.0630645	+	0.594834i
$36$	4.55906	−	15.6276i	0.759844	−	2.60461i
$37$	−0.387140	+	1.44483i	−0.0636454	+	0.237528i	−0.990420	−	0.138091i	$-0.955903\pi$
$37$	−0.387140	+	1.44483i	−0.0636454	+	0.237528i	0.926774	+	0.375619i	$0.122570\pi$
$38$	5.62733	+	2.62407i	0.912873	+	0.425680i
$39$	−2.17423	−	4.29154i	−0.348156	−	0.687197i
$40$	−5.03269	+	20.2632i	−0.795738	+	3.20389i
$41$	−4.99389	−	5.95149i	−0.779915	−	0.929467i	0.219015	−	0.975722i	$-0.429716\pi$
$41$	−4.99389	−	5.95149i	−0.779915	−	0.929467i	−0.998930	+	0.0462550i	$0.985271\pi$
$42$	2.32469	−	7.09907i	0.358708	−	1.09541i
$43$	−0.501128	+	1.07467i	−0.0764213	+	0.163886i	−0.940806	−	0.338944i	$-0.889930\pi$
$43$	−0.501128	+	1.07467i	−0.0764213	+	0.163886i	0.864385	+	0.502830i	$0.167708\pi$
$44$	1.29268	+	2.23899i	0.194879	+	0.337541i
$45$	−3.82734	−	5.50922i	−0.570546	−	0.821265i
$46$	0.548257	−	0.949609i	0.0808361	−	0.140012i
$47$	6.94767	+	9.92230i	1.01342	+	1.44732i	0.890546	+	0.454894i	$0.150323\pi$
$47$	6.94767	+	9.92230i	1.01342	+	1.44732i	0.122876	+	0.992422i	$0.460788\pi$
$48$	15.6068	−	19.8813i	2.25264	−	2.86962i
$49$	−1.53751	+	4.22426i	−0.219644	+	0.603466i
$50$	8.21984	+	10.8671i	1.16246	+	1.53684i
$51$	5.75523	−	1.74508i	0.805893	−	0.244361i
$52$	−1.31362	−	15.0147i	−0.182166	−	2.08217i
$53$	−0.274270	−	0.274270i	−0.0376738	−	0.0376738i	0.688019	−	0.725693i	$-0.258481\pi$
$53$	−0.274270	−	0.274270i	−0.0376738	−	0.0376738i	−0.725693	+	0.688019i	$0.758481\pi$
$54$	2.60592	+	13.9184i	0.354620	+	1.89405i
$55$	1.05240	+	0.165706i	0.141905	+	0.0223439i
$56$	9.49862	−	11.3200i	1.26931	−	1.51270i
$57$	−3.94428	+	0.128655i	−0.522433	+	0.0170407i
$58$	−12.5179	−	8.76510i	−1.64368	−	1.15091i
$59$	−3.33385	−	1.21342i	−0.434031	−	0.157974i	0.115759	−	0.993277i	$-0.463070\pi$
$59$	−3.33385	−	1.21342i	−0.434031	−	0.157974i	−0.549790	+	0.835303i	$0.685292\pi$
$60$	−4.69906	−	20.4841i	−0.606646	−	2.64449i
$61$	−1.59716	+	9.05792i	−0.204495	+	1.15975i	0.693738	+	0.720228i	$0.255963\pi$
$61$	−1.59716	+	9.05792i	−0.204495	+	1.15975i	−0.898233	+	0.439520i	$0.855149\pi$
$62$	−3.69001	−	13.7713i	−0.468631	−	1.74896i
$63$	0.721141	+	4.69272i	0.0908552	+	0.591228i
$64$	24.5036	−	14.1471i	3.06294	−	1.76839i
$65$	−5.15215	−	3.46838i	−0.639046	−	0.430200i
$66$	−1.88323	−	1.22915i	−0.231809	−	0.151298i
$67$	13.1561	+	1.15101i	1.60727	+	0.140618i	0.855142	−	0.518394i	$-0.173470\pi$
$67$	13.1561	+	1.15101i	1.60727	+	0.140618i	0.752132	+	0.659012i	$0.229025\pi$
$68$	18.7696	+	1.64212i	2.27614	+	0.199137i
$69$	−0.0380751	+	0.695886i	−0.00458370	+	0.0837748i
$70$	−1.84869	−	9.46488i	−0.220960	−	1.13127i
$71$	−13.8198	+	7.97886i	−1.64011	+	0.946916i	−0.659313	+	0.751869i	$0.729153\pi$
$71$	−13.8198	+	7.97886i	−1.64011	+	0.946916i	−0.980794	+	0.195047i	$0.937514\pi$
$72$	−5.47136	+	27.4723i	−0.644806	+	3.23765i
$73$	2.07381	+	7.73957i	0.242721	+	0.905849i	0.974515	+	0.224322i	$0.0720168\pi$
$73$	2.07381	+	7.73957i	0.242721	+	0.905849i	−0.731794	+	0.681526i	$0.761317\pi$
$74$	0.707832	−	4.01431i	0.0822838	−	0.466655i
$75$	−7.78193	−	3.80021i	−0.898580	−	0.438810i
$76$	−11.6180	−	4.22862i	−1.33268	−	0.485056i
$77$	−0.617661	−	0.432491i	−0.0703890	−	0.0492869i
$78$	6.92182	+	11.1341i	0.783741	+	1.26069i
$79$	−2.85683	+	3.40464i	−0.321418	+	0.383051i	−0.902425	−	0.430848i	$-0.858215\pi$
$79$	−2.85683	+	3.40464i	−0.321418	+	0.383051i	0.581006	+	0.813899i	$0.302659\pi$
$80$	5.07529	−	32.2331i	0.567434	−	3.60377i
$81$	−5.47547	−	7.14278i	−0.608385	−	0.793642i
$82$	14.9708	+	14.9708i	1.65325	+	1.65325i
$83$	0.253902	+	2.90211i	0.0278694	+	0.318548i	0.997314	+	0.0732395i	$0.0233338\pi$
$83$	0.253902	+	2.90211i	0.0278694	+	0.318548i	−0.969445	+	0.245309i	$0.921111\pi$
$84$	−3.37935	+	14.4855i	−0.368718	+	1.58050i
$85$	5.38828	−	5.58985i	0.584441	−	0.606304i
$86$	1.10520	−	3.03651i	0.119177	−	0.327435i
$87$	9.61501	+	1.37386i	1.03084	+	0.147293i
$88$	−2.55168	−	3.64417i	−0.272010	−	0.388470i
$89$	3.50126	−	6.06435i	0.371132	−	0.642820i	−0.618608	−	0.785700i	$-0.712303\pi$
$89$	3.50126	−	6.06435i	0.371132	−	0.642820i	0.989740	+	0.142880i	$0.0456363\pi$
$90$	11.6988	+	14.0472i	1.23316	+	1.48070i
$91$	2.19789	+	3.80686i	0.230402	+	0.399068i
$92$	−0.922748	+	1.97884i	−0.0962031	+	0.206308i
$93$	6.04787	+	6.74799i	0.627135	+	0.699734i
$94$	−21.2179	−	25.2866i	−2.18846	−	2.60811i
$95$	−4.36468	+	2.62795i	−0.447807	+	0.269622i
$96$	−19.9678	+	30.5934i	−2.03795	+	3.12242i
$97$	−6.86175	−	3.19969i	−0.696705	−	0.324879i	0.0418007	−	0.999126i	$-0.486691\pi$
$97$	−6.86175	−	3.19969i	−0.696705	−	0.324879i	−0.738506	+	0.674247i	$0.764468\pi$
$98$	3.17066	−	11.8331i	0.320285	−	1.19532i
$99$	1.42080	+	0.155944i	0.142796	+	0.0156730i
$100$	−18.1912	−	20.1299i	−1.81912	−	2.01299i
$101$	5.72678	+	1.00979i	0.569836	+	0.100477i	0.451140	−	0.892453i	$-0.351017\pi$
$101$	5.72678	+	1.00979i	0.569836	+	0.100477i	0.118696	+	0.992931i	$0.462129\pi$
$102$	−15.2096	+	6.10443i	−1.50598	+	0.604428i
$103$	−4.05522	+	1.89098i	−0.399573	+	0.186324i	−0.612009	−	0.790851i	$-0.709638\pi$
$103$	−4.05522	+	1.89098i	−0.399573	+	0.186324i	0.212436	+	0.977175i	$0.431860\pi$
$104$	4.50356	+	25.5409i	0.441610	+	2.50450i
$105$	3.76690	+	4.83529i	0.367611	+	0.471876i
$106$	0.809720	+	0.679435i	0.0786469	+	0.0659926i
$107$	0.577939	−	0.577939i	0.0558714	−	0.0558714i	−0.678619	−	0.734490i	$-0.737421\pi$
$107$	0.577939	−	0.577939i	0.0558714	−	0.0558714i	0.734490	+	0.678619i	$0.237421\pi$
$108$	−7.58471	−	27.1569i	−0.729839	−	2.61317i
$109$		−	8.45996i		−	0.810317i	−0.914246	−	0.405159i	$-0.867216\pi$
$109$		−	8.45996i		−	0.810317i	0.914246	−	0.405159i	$-0.132784\pi$
$110$	−2.89637	−	0.199898i	−0.276158	−	0.0190595i
$111$	0.751773	+	2.47932i	0.0713552	+	0.235327i
$112$	−13.2464	+	18.9178i	−1.25167	+	1.78757i
$113$	−0.921497	−	1.97616i	−0.0866871	−	0.185901i	0.858185	−	0.513340i	$-0.171592\pi$
$113$	−0.921497	−	1.97616i	−0.0866871	−	0.185901i	−0.944872	+	0.327439i	$0.893814\pi$
$114$	10.6772	−	1.28608i	1.00002	−	0.120452i
$115$	0.395147	+	0.808313i	0.0368477	+	0.0753756i
$116$	26.3522	+	15.2145i	2.44674	+	1.41263i
$117$	−7.12270	−	4.32447i	−0.658494	−	0.399797i
$118$	9.33883	+	2.50233i	0.859709	+	0.230358i
$119$	−5.16368	+	1.87943i	−0.473354	+	0.172287i
$120$	11.1271	+	34.4088i	1.01576	+	3.14108i
$121$	8.25260	−	6.92475i	0.750236	−	0.629523i
$122$	2.18454	−	24.9695i	0.197779	−	2.26063i
$123$	−12.7883	−	4.18772i	−1.15308	−	0.377594i
$124$	9.70964	+	26.6770i	0.871952	+	2.39567i
$125$	−11.1634	+	0.615475i	−0.998484	+	0.0550498i
$126$	−3.07230	−	12.5684i	−0.273702	−	1.11968i
$127$	−3.44795	+	0.923874i	−0.305956	+	0.0819806i	−0.408530	−	0.912745i	$-0.633959\pi$
$127$	−3.44795	+	0.923874i	−0.305956	+	0.0819806i	0.102575	+	0.994725i	$0.467292\pi$
$128$	−28.6056	+	20.0298i	−2.52840	+	1.77040i
$129$	0.245607	+	2.03908i	0.0216245	+	0.179531i
$130$	14.8107	+	8.19215i	1.29898	+	0.718499i
$131$	−3.02885	+	0.534068i	−0.264632	+	0.0466617i	−0.304390	−	0.952548i	$-0.598452\pi$
$131$	−3.02885	+	0.534068i	−0.264632	+	0.0466617i	0.0397579	+	0.999209i	$0.487341\pi$
$132$	3.94898	+	2.11138i	0.343715	+	0.183772i
$133$	3.59215	−	0.314273i	0.311479	−	0.0272509i
$134$	−35.9891			−3.10899
$135$	−10.6679	−	4.60392i	−0.918146	−	0.396242i
$136$	−32.4207			−2.78005
$137$	2.06926	−	0.181036i	0.176788	−	0.0154670i	0.00158226	−	0.999999i	$-0.499496\pi$
$137$	2.06926	−	0.181036i	0.176788	−	0.0154670i	0.175206	+	0.984532i	$0.443941\pi$
$138$	−0.0619158	−	1.89821i	−0.00527062	−	0.161586i
$139$	15.2015	−	2.68044i	1.28938	−	0.227352i	0.513420	−	0.858137i	$-0.328378\pi$
$139$	15.2015	−	2.68044i	1.28938	−	0.227352i	0.775957	+	0.630785i	$0.217267\pi$
$140$	5.30974	+	18.4542i	0.448755	+	1.55966i
$141$	19.2934	+	8.24199i	1.62480	+	0.694101i
$142$	35.6224	−	24.9431i	2.98937	−	2.09318i
$143$	1.27827	−	0.342511i	0.106894	−	0.0286422i
$144$	4.77629	−	43.5167i	0.398024	−	3.62639i
$145$	11.7021	−	4.50418i	0.971805	−	0.374051i
$146$	−7.46815	−	20.5186i	−0.618068	−	1.69813i
$147$	1.60132	+	7.61976i	0.132075	+	0.628467i
$148$	−0.707419	+	8.08583i	−0.0581495	+	0.664651i
$149$	12.0609	−	10.1203i	0.988065	−	0.829085i	0.00277827	−	0.999996i	$-0.499116\pi$
$149$	12.0609	−	10.1203i	0.988065	−	0.829085i	0.985286	+	0.170911i	$0.0546712\pi$
$150$	22.0287	+	8.46837i	1.79864	+	0.691440i
$151$	−1.00956	+	0.367451i	−0.0821571	+	0.0299027i	−0.382772	−	0.923843i	$-0.625030\pi$
$151$	−1.00956	+	0.367451i	−0.0821571	+	0.0299027i	0.300615	+	0.953746i	$0.402808\pi$
$152$	20.5496	+	5.50625i	1.66679	+	0.446616i
$153$	6.86995	−	7.82993i	0.555402	−	0.633012i
$154$	1.77953	+	1.02741i	0.143398	+	0.0827910i
$155$	11.0645	+	3.79862i	0.888725	+	0.305112i
$156$	−15.6627	−	20.8849i	−1.25402	−	1.67213i
$157$	−7.27543	−	15.6022i	−0.580643	−	1.24519i	−0.948932	−	0.315481i	$-0.897834\pi$
$157$	−7.27543	−	15.6022i	−0.580643	−	1.24519i	0.368289	−	0.929711i	$-0.379944\pi$
$158$	6.94698	−	9.92131i	0.552672	−	0.789297i
$159$	−0.654253	−	0.152632i	−0.0518856	−	0.0121045i
$160$	−3.24737	+	47.0521i	−0.256727	+	3.71979i
$161$		−	0.636793i		−	0.0501863i
$162$	16.5611	+	18.0905i	1.30116	+	1.42132i
$163$	2.47310	−	2.47310i	0.193708	−	0.193708i	−0.603588	−	0.797296i	$-0.706263\pi$
$163$	2.47310	−	2.47310i	0.193708	−	0.193708i	0.797296	+	0.603588i	$0.206263\pi$
$164$	−32.2949	−	27.0987i	−2.52181	−	2.11605i
$165$	1.69958	−	0.718634i	0.132312	−	0.0559456i
$166$	−1.37857	−	7.81825i	−0.106998	−	0.606814i
$167$	−5.97097	+	2.78431i	−0.462048	+	0.215456i	−0.639681	−	0.768640i	$-0.720934\pi$
$167$	−5.97097	+	2.78431i	−0.462048	+	0.215456i	0.177634	+	0.984097i	$0.443156\pi$
$168$	3.62041	−	25.3376i	0.279321	−	1.95484i
$169$	5.20483	+	0.917752i	0.400372	+	0.0705963i
$170$	−13.3003	+	16.4549i	−1.02008	+	1.26203i
$171$	−5.68427	+	3.79616i	−0.434687	+	0.290300i
$172$	−1.66535	+	6.21517i	−0.126982	+	0.473902i
$173$	−9.69016	−	4.51859i	−0.736729	−	0.343542i	0.0177714	−	0.999842i	$-0.494343\pi$
$173$	−9.69016	−	4.51859i	−0.736729	−	0.343542i	−0.754500	+	0.656300i	$0.772121\pi$
$174$	−26.4288	−	1.44604i	−2.00356	−	0.109624i
$175$	7.28956	+	3.07866i	0.551039	+	0.232725i
$176$	4.46905	+	5.32601i	0.336867	+	0.401463i
$177$	−6.01363	+	1.26379i	−0.452012	+	0.0949920i
$178$	−8.06473	+	17.2949i	−0.604477	+	1.29631i
$179$	−3.31311	−	5.73847i	−0.247633	−	0.428913i	0.715235	−	0.698884i	$-0.246319\pi$
$179$	−3.31311	−	5.73847i	−0.247633	−	0.428913i	−0.962869	+	0.269970i	$0.912986\pi$
$180$	−25.6442	−	25.8344i	−1.91141	−	1.92558i
$181$	−4.36897	+	7.56727i	−0.324743	+	0.562471i	−0.981460	−	0.191666i	$-0.938611\pi$
$181$	−4.36897	+	7.56727i	−0.324743	+	0.562471i	0.656717	+	0.754137i	$0.271944\pi$
$182$	−6.87094	−	9.81271i	−0.509308	−	0.727367i
$183$	5.93379	+	14.7845i	0.438639	+	1.09290i
$184$	1.28499	−	3.53048i	0.0947306	−	0.260270i
$185$	2.40808	+	2.32124i	0.177045	+	0.170661i
$186$	−18.0213	−	16.8828i	−1.32138	−	1.23790i
$187$	0.144182	+	1.64801i	0.0105436	+	0.120514i
$188$	46.4773	+	46.4773i	3.38971	+	3.38971i
$189$	5.35211	+	6.24340i	0.389309	+	0.454140i
$190$	11.2249	−	8.17092i	0.814341	−	0.592781i
$191$	−12.9658	+	15.4521i	−0.938176	+	1.11807i	0.0546500	+	0.998506i	$0.482596\pi$
$191$	−12.9658	+	15.4521i	−0.938176	+	1.11807i	−0.992826	+	0.119569i	$0.961849\pi$
$192$	23.1069	−	43.2177i	1.66760	−	3.11897i
$193$	−15.3824	−	10.7709i	−1.10725	−	0.775303i	−0.130875	−	0.991399i	$-0.541779\pi$
$193$	−15.3824	−	10.7709i	−1.10725	−	0.775303i	−0.976372	+	0.216096i	$0.930668\pi$
$194$	19.3880	+	7.05665i	1.39198	+	0.506638i
$195$	−10.7504	−	0.390419i	−0.769851	−	0.0279585i
$196$	−4.23588	+	24.0229i	−0.302563	+	1.71592i
$197$	−1.29693	−	4.84019i	−0.0924021	−	0.344849i	0.904211	−	0.427087i	$-0.140460\pi$
$197$	−1.29693	−	4.84019i	−0.0924021	−	0.344849i	−0.996613	+	0.0822373i	$0.973793\pi$
$198$	−3.89419	−	0.0858949i	−0.276748	−	0.00610428i
$199$	−14.4356	+	8.33443i	−1.02332	+	0.590812i	−0.915063	−	0.403312i	$-0.867859\pi$
$199$	−14.4356	+	8.33443i	−1.02332	+	0.590812i	−0.108253	+	0.994123i	$0.534526\pi$
$200$	34.2020	+	31.7782i	2.41844	+	2.24706i
$201$	20.4048	−	10.3377i	1.43924	−	0.729166i
$202$	−15.7867	−	1.38116i	−1.11075	−	0.0971779i
$203$	−8.84085	−	0.773474i	−0.620506	−	0.0542872i
$204$	29.1111	−	14.7486i	2.03819	−	1.03261i
$205$	−17.0501	+	3.33023i	−1.19083	+	0.232594i
$206$	10.5599	−	6.09673i	0.735740	−	0.424779i
$207$	0.580357	+	1.05845i	0.0403376	+	0.0735670i
$208$	−10.4905	−	39.1510i	−0.727384	−	2.71463i
$209$	0.188505	−	1.06906i	0.0130391	−	0.0739486i
$210$	−11.3747	−	12.2320i	−0.784927	−	0.844087i
$211$	9.81899	+	3.57382i	0.675967	+	0.246032i	0.657115	−	0.753790i	$-0.271777\pi$
$211$	9.81899	+	3.57382i	0.675967	+	0.246032i	0.0188522	+	0.999822i	$0.493999\pi$
$212$	−1.72411	−	1.20724i	−0.118413	−	0.0829134i
$213$	−13.0321	+	24.3744i	−0.892944	+	1.67010i
$214$	−1.43170	+	1.70623i	−0.0978690	+	0.116636i
$215$	1.56043	+	2.14367i	0.106421	+	0.146197i
$216$	17.0743	+	45.4144i	1.16176	+	3.09006i
$217$	−5.85464	−	5.85464i	−0.397439	−	0.397439i
$218$	2.00934	+	22.9668i	0.136089	+	1.55551i
$219$	10.1281	+	9.48825i	0.684393	+	0.641156i
$220$	5.78008	−	0.106130i	0.389693	−	0.00715525i
$221$	3.29851	−	9.06258i	0.221882	−	0.609615i
$222$	−2.62975	−	6.55222i	−0.176498	−	0.439756i
$223$	−13.4550	−	19.2158i	−0.901015	−	1.28678i	−0.957516	−	0.288381i	$-0.906883\pi$
$223$	−13.4550	−	19.2158i	−0.901015	−	1.28678i	0.0565006	−	0.998403i	$-0.482006\pi$
$224$	16.6904	−	28.9087i	1.11518	−	1.93154i
$225$	−14.9221	+	1.52632i	−0.994810	+	0.101755i
$226$	2.97101	+	5.14593i	0.197628	+	0.342302i
$227$	−8.45994	+	18.1424i	−0.561506	+	1.20415i	0.396667	+	0.917963i	$0.370167\pi$
$227$	−8.45994	+	18.1424i	−0.561506	+	1.20415i	−0.958173	+	0.286191i	$0.907611\pi$
$228$	−20.9567	+	4.40413i	−1.38789	+	0.291671i
$229$	14.1827	+	16.9023i	0.937218	+	1.11693i	0.992955	+	0.118488i	$0.0378047\pi$
$229$	14.1827	+	16.9023i	0.937218	+	1.11693i	−0.0557370	+	0.998445i	$0.517751\pi$
$230$	−1.26472	−	2.10053i	−0.0833929	−	0.138505i
$231$	−1.30406	−	0.0713510i	−0.0858007	−	0.00469455i
$232$	−47.4542	−	22.1282i	−3.11552	−	1.45279i
$233$	4.83296	−	18.0369i	0.316618	−	1.18163i	−0.605856	−	0.795574i	$-0.707169\pi$
$233$	4.83296	−	18.0369i	0.316618	−	1.18163i	0.922474	−	0.386059i	$-0.126164\pi$
$234$	20.3636	+	10.0482i	1.33121	+	0.656871i
$235$	26.9343	−	2.85558i	1.75700	−	0.186277i
$236$	−18.9592	−	3.34302i	−1.23414	−	0.217612i
$237$	−1.08888	+	7.62059i	−0.0707306	+	0.495010i
$238$	13.5718	−	6.32863i	0.879729	−	0.410224i
$239$	−3.38846	−	19.2169i	−0.219181	−	1.24304i	−0.873502	−	0.486821i	$-0.838156\pi$
$239$	−3.38846	−	19.2169i	−0.219181	−	1.24304i	0.654320	−	0.756218i	$-0.272955\pi$
$240$	−22.0104	−	52.0550i	−1.42077	−	3.36014i
$241$	−3.76991	−	3.16333i	−0.242841	−	0.203768i	0.513241	−	0.858244i	$-0.328445\pi$
$241$	−3.76991	−	3.16333i	−0.242841	−	0.203768i	−0.756082	+	0.654476i	$0.772889\pi$
$242$	−20.7592	+	20.7592i	−1.33445	+	1.33445i
$243$	−14.5861	−	5.49968i	−0.935697	−	0.352805i
$244$			49.9098i			3.19515i
$245$	6.60154	+	7.58032i	0.421757	+	0.484289i
$246$	35.7119	+	8.33130i	2.27690	+	0.531184i
$247$	−3.62990	+	5.18403i	−0.230965	+	0.329852i
$248$	−20.6449	−	44.2731i	−1.31095	−	2.81134i
$249$	3.02737	+	4.03673i	0.191851	+	0.255818i
$250$	30.1598	−	4.32230i	1.90747	−	0.273366i
$251$	−18.1080	−	10.4546i	−1.14297	−	0.659892i	−0.195803	−	0.980643i	$-0.562731\pi$
$251$	−18.1080	−	10.4546i	−1.14297	−	0.659892i	−0.947163	+	0.320752i	$0.896065\pi$
$252$	8.27557	+	24.3980i	0.521312	+	1.53693i
$253$	−0.185175	−	0.0496176i	−0.0116419	−	0.00311943i
$254$	9.14093	−	3.32703i	0.573553	−	0.208756i
$255$	2.81427	−	13.1499i	0.176236	−	0.823478i
$256$	29.5507	−	24.7960i	1.84692	−	1.54975i
$257$	−1.27235	+	14.5430i	−0.0793667	+	0.907166i	0.847259	+	0.531180i	$0.178251\pi$
$257$	−1.27235	+	14.5430i	−0.0793667	+	0.907166i	−0.926626	+	0.375986i	$0.877304\pi$
$258$	−1.15107	−	5.47728i	−0.0716625	−	0.341000i
$259$	−0.809647	−	2.22449i	−0.0503090	−	0.138223i
$260$	−30.8009	−	13.6800i	−1.91019	−	0.848399i
$261$	15.3997	−	6.77169i	0.953219	−	0.419157i
$262$	8.09576	−	2.16925i	0.500158	−	0.134017i
$263$	25.0799	−	17.5612i	1.54650	−	1.08287i	0.583935	−	0.811801i	$-0.301512\pi$
$263$	25.0799	−	17.5612i	1.54650	−	1.08287i	0.962561	−	0.271067i	$-0.0873764\pi$
$264$	−7.08591	−	3.02704i	−0.436108	−	0.186302i
$265$	−0.833501	+	0.239820i	−0.0512016	+	0.0147320i
$266$	−9.67721	+	1.70635i	−0.593348	+	0.104623i
$267$	−0.395404	−	12.1223i	−0.0241983	−	0.741870i
$268$	71.3898	−	6.24580i	4.36083	−	0.381523i
$269$	23.6912			1.44448			0.722239	−	0.691643i	$-0.243113\pi$
$269$	23.6912			1.44448			0.722239	+	0.691643i	$0.243113\pi$
$270$	30.0543	+	9.96481i	1.82905	+	0.606439i
$271$	20.1164			1.22198			0.610991	−	0.791638i	$-0.290771\pi$
$271$	20.1164			1.22198			0.610991	+	0.791638i	$0.290771\pi$
$272$	50.4755	−	4.41603i	3.06052	−	0.267761i
$273$	6.71428	+	3.58988i	0.406367	+	0.217269i
$274$	−5.57454	+	0.982943i	−0.336771	+	0.0593817i
$275$	1.46324	−	1.87988i	0.0882368	−	0.113361i
$276$	0.452247	+	3.75464i	0.0272221	+	0.226002i
$277$	−12.4565	+	8.72217i	−0.748441	+	0.524064i	−0.884445	−	0.466644i	$-0.845463\pi$
$277$	−12.4565	+	8.72217i	−0.748441	+	0.524064i	0.136004	+	0.990708i	$0.456574\pi$
$278$	−40.6320	+	10.8873i	−2.43694	+	0.652977i
$279$	15.0670	+	4.39552i	0.902040	+	0.263153i
$280$	−11.8695	−	30.8375i	−0.709336	−	1.84289i
$281$	−8.16607	−	22.4361i	−0.487147	−	1.33842i	−0.903253	−	0.429108i	$-0.858828\pi$
$281$	−8.16607	−	22.4361i	−0.487147	−	1.33842i	0.416106	−	0.909316i	$-0.363394\pi$
$282$	−54.3346	−	17.7927i	−3.23558	−	1.05954i
$283$	−0.0248657	+	0.284217i	−0.00147811	+	0.0168949i	−0.996898	−	0.0787051i	$-0.974921\pi$
$283$	−0.0248657	+	0.284217i	−0.00147811	+	0.0168949i	0.995420	+	0.0956001i	$0.0304770\pi$
$284$	−66.3335	+	55.6605i	−3.93617	+	3.30284i
$285$	−4.01714	+	7.85699i	−0.237955	+	0.465408i
$286$	−3.38884	+	1.23344i	−0.200387	+	0.0729347i
$287$	11.8765	+	3.18229i	0.701046	+	0.187845i
$288$	−1.39538	+	63.2618i	−0.0822234	+	3.72774i
$289$	−4.28164	−	2.47200i	−0.251861	−	0.145412i
$290$	−30.6986	+	15.0072i	−1.80268	+	0.881250i
$291$	−13.0194	+	1.56820i	−0.763213	+	0.0919292i
$292$	18.3751	+	39.4056i	1.07532	+	2.30604i
$293$	−8.91694	+	12.7347i	−0.520933	+	0.743969i	−0.990287	−	0.139041i	$-0.955598\pi$
$293$	−8.91694	+	12.7347i	−0.520933	+	0.743969i	0.469354	+	0.883010i	$0.344487\pi$
$294$	−6.15698	−	20.3055i	−0.359083	−	1.18424i
$295$	−5.98250	+	5.21003i	−0.348315	+	0.303340i
$296$		−	13.9667i		−	0.811796i
$297$	2.23257	−	1.06989i	0.129547	−	0.0620812i
$298$	−30.3387	+	30.3387i	−1.75748	+	1.75748i
$299$	0.856140	+	0.718387i	0.0495119	+	0.0415454i
$300$	−45.1669	−	12.9753i	−2.60771	−	0.749127i
$301$	−0.325869	−	1.84809i	−0.0187828	−	0.106522i
$302$	2.65345	−	1.23733i	0.152689	−	0.0712001i
$303$	9.34734	−	3.75158i	0.536990	−	0.215523i
$304$	−32.7435	−	5.77355i	−1.87797	−	0.331136i
$305$	15.9949	+	12.9285i	0.915868	+	0.740283i
$306$	−16.7906	+	22.8881i	−0.959854	+	1.30843i
$307$	2.72426	−	10.1671i	0.155482	−	0.580267i	−0.843582	−	0.537001i	$-0.819557\pi$
$307$	2.72426	−	10.1671i	0.155482	−	0.580267i	0.999064	−	0.0432656i	$-0.0137762\pi$
$308$	−3.70826	−	1.72919i	−0.211298	−	0.0985297i
$309$	−4.23587	+	6.48994i	−0.240970	+	0.369200i
$310$	−30.9398	−	7.68440i	−1.75726	−	0.436445i
$311$	2.06659	+	2.46287i	0.117186	+	0.139657i	0.821448	−	0.570283i	$-0.193167\pi$
$311$	2.06659	+	2.46287i	0.117186	+	0.139657i	−0.704262	+	0.709940i	$0.748722\pi$
$312$	29.9809	+	33.4516i	1.69734	+	1.89382i
$313$	10.2775	−	22.0403i	0.580921	−	1.24579i	−0.367868	−	0.929878i	$-0.619912\pi$
$313$	10.2775	−	22.0403i	0.580921	−	1.24579i	0.948789	−	0.315911i	$-0.102310\pi$
$314$	23.4568	+	40.6283i	1.32374	+	2.29279i
$315$	9.96270	+	3.66786i	0.561334	+	0.206661i
$316$	−12.0586	+	20.8860i	−0.678347	+	1.17493i
$317$	11.9128	+	17.0133i	0.669092	+	0.955562i	0.999929	+	0.0118742i	$0.00377978\pi$
$317$	11.9128	+	17.0133i	0.669092	+	0.955562i	−0.330838	+	0.943688i	$0.607331\pi$
$318$	1.81239	+	0.258968i	0.101634	+	0.0145222i
$319$	−0.913782	+	2.51060i	−0.0511620	+	0.140566i
$320$	−1.16148	−	63.2573i	−0.0649289	−	3.53619i
$321$	0.321625	−	1.37864i	0.0179514	−	0.0769479i
$322$	0.151246	+	1.72874i	0.00842858	+	0.0963391i
$323$	−5.59403	−	5.59403i	−0.311260	−	0.311260i
$324$	−35.9909	−	33.0110i	−1.99950	−	1.83395i
$325$	−12.3627	+	6.32735i	−0.685759	+	0.350978i
$326$	−6.12650	+	7.30128i	−0.339315	+	0.404380i
$327$	−7.73635	−	12.4443i	−0.427821	−	0.688174i
$328$	59.4234	+	41.6087i	3.28111	+	2.29746i
$329$	−18.0138	−	6.55649i	−0.993134	−	0.361471i
$330$	−4.44328	+	2.35459i	−0.244594	+	0.129616i
$331$	1.03458	−	5.86738i	0.0568655	−	0.322500i	−0.943084	−	0.332555i	$-0.892089\pi$
$331$	1.03458	−	5.86738i	0.0568655	−	0.322500i	0.999949	+	0.0100545i	$0.00320050\pi$
$332$	4.09143	+	15.2694i	0.224546	+	0.838018i
$333$	3.37309	+	2.95954i	0.184844	+	0.162182i
$334$	15.5485	−	8.97692i	0.850775	−	0.491195i
$335$	16.4910	−	24.4967i	0.900998	−	1.33840i
$336$	−2.18535	+	39.9409i	−0.119221	+	2.17896i
$337$	−11.1098	−	0.971978i	−0.605187	−	0.0529470i	−0.219556	−	0.975600i	$-0.570461\pi$
$337$	−11.1098	−	0.971978i	−0.605187	−	0.0529470i	−0.385631	+	0.922653i	$0.626016\pi$
$338$	−14.3479	−	1.25528i	−0.780421	−	0.0682780i
$339$	−3.16262	−	2.06419i	−0.171770	−	0.112111i
$340$	23.5273	−	34.9490i	1.27595	−	1.89537i
$341$	−2.15867	+	1.24631i	−0.116899	+	0.0674915i
$342$	14.5298	−	11.6558i	0.785683	−	0.630271i
$343$	−4.70859	−	17.5727i	−0.254240	−	0.948837i
$344$	1.92261	−	10.9037i	0.103660	−	0.587887i
$345$	1.32042	+	0.827655i	0.0710893	+	0.0445594i
$346$	27.3797	+	9.96540i	1.47194	+	0.535743i
$347$	−19.4431	−	13.6142i	−1.04376	−	0.730851i	−0.0797793	−	0.996813i	$-0.525422\pi$
$347$	−19.4431	−	13.6142i	−1.04376	−	0.730851i	−0.963984	+	0.265962i	$0.914310\pi$
$348$	52.6764	−	1.71820i	2.82375	−	0.0921051i
$349$	−4.82633	+	5.75179i	−0.258347	+	0.307886i	−0.879591	−	0.475731i	$-0.842183\pi$
$349$	−4.82633	+	5.75179i	−0.258347	+	0.307886i	0.621243	+	0.783618i	$0.286628\pi$
$350$	−20.5207	−	6.62649i	−1.09688	−	0.354201i
$351$	−14.4319	+	0.152302i	−0.770315	+	0.00812929i
$352$	−7.10598	−	7.10598i	−0.378750	−	0.378750i
$353$	0.451688	+	5.16281i	0.0240409	+	0.274789i	0.998695	+	0.0510716i	$0.0162637\pi$
$353$	0.451688	+	5.16281i	0.0240409	+	0.274789i	−0.974654	+	0.223717i	$0.928181\pi$
$354$	16.0254	−	4.85919i	0.851742	−	0.258263i
$355$	0.655066	+	35.6765i	0.0347673	+	1.89351i
$356$	12.9961	−	35.7066i	0.688793	−	1.89244i
$357$	−5.87695	+	7.48659i	−0.311041	+	0.396232i
$358$	10.3573	+	14.7917i	0.547398	+	0.781765i
$359$	6.82697	−	11.8247i	0.360314	−	0.624082i	−0.627699	−	0.778457i	$-0.716003\pi$
$359$	6.82697	−	11.8247i	0.360314	−	0.624082i	0.988012	+	0.154375i	$0.0493363\pi$
$360$	47.8332	+	40.4389i	2.52103	+	2.13132i
$361$	−6.90435	−	11.9587i	−0.363387	−	0.629404i
$362$	10.0634	−	21.5810i	0.528921	−	1.13427i
$363$	5.80687	−	17.7328i	0.304782	−	0.930732i
$364$	15.3325	+	18.2725i	0.803641	+	0.957742i
$365$	17.3884	+	4.31869i	0.910152	+	0.226051i
$366$	−19.6203	−	38.7270i	−1.02557	−	2.02429i
$367$	19.5461	+	9.11448i	1.02030	+	0.475772i	0.859457	−	0.511208i	$-0.170802\pi$
$367$	19.5461	+	9.11448i	1.02030	+	0.475772i	0.160840	+	0.986981i	$0.448580\pi$
$368$	−1.51970	+	5.67159i	−0.0792197	+	0.295652i
$369$	−22.6407	+	5.53446i	−1.17863	+	0.288113i
$370$	−7.08869	−	5.72968i	−0.368523	−	0.297872i
$371$	0.604528	+	0.106595i	0.0313855	+	0.00553411i
$372$	38.6778	+	30.3620i	2.00535	+	1.57419i
$373$	−11.9942	+	5.59299i	−0.621037	+	0.289594i	−0.707557	−	0.706656i	$-0.750203\pi$
$373$	−11.9942	+	5.59299i	−0.621037	+	0.289594i	0.0865206	+	0.996250i	$0.472425\pi$
$374$	−0.782840	−	4.43971i	−0.0404797	−	0.229572i
$375$	−15.8582	+	11.1139i	−0.818912	+	0.573918i
$376$	−86.6408	−	72.7003i	−4.46816	−	3.74923i
$377$	11.0135	−	11.0135i	0.567226	−	0.567226i
$378$	−16.0126	−	15.6782i	−0.823600	−	0.806398i
$379$		−	27.4089i		−	1.40790i	−0.710249	−	0.703951i	$-0.751417\pi$
$379$		−	27.4089i		−	1.40790i	0.710249	−	0.703951i	$-0.248583\pi$
$380$	−20.8483	+	18.1563i	−1.06949	+	0.931398i
$381$	−4.22697	+	4.51202i	−0.216554	+	0.231158i
$382$	31.5292	−	45.0283i	1.61317	−	2.30385i
$383$	15.2701	+	32.7469i	0.780267	+	1.67329i	0.738588	+	0.674157i	$0.235493\pi$
$383$	15.2701	+	32.7469i	0.780267	+	1.67329i	0.0416793	+	0.999131i	$0.486729\pi$
$384$	−23.7613	+	55.6221i	−1.21256	+	2.83845i
$385$	−1.51474	+	0.740488i	−0.0771984	+	0.0377388i
$386$	44.3177	+	25.5869i	2.25571	+	1.30234i
$387$	2.22595	+	2.77482i	0.113151	+	0.141052i
$388$	−39.6836	−	10.6332i	−2.01463	−	0.539819i
$389$	−17.3733	+	6.32335i	−0.880860	+	0.320607i	−0.742557	−	0.669783i	$-0.766387\pi$
$389$	−17.3733	+	6.32335i	−0.880860	+	0.320607i	−0.138303	+	0.990390i	$0.544165\pi$
$390$	29.2775	−	1.49344i	1.48252	−	0.0756232i
$391$	−1.07024	+	0.898039i	−0.0541244	+	0.0454158i
$392$	3.65832	−	41.8148i	0.184773	−	2.11197i
$393$	−3.96696	+	3.55538i	−0.200106	+	0.179345i
$394$	4.67045	+	12.8320i	0.235294	+	0.646464i
$395$	3.56989	+	9.27475i	0.179620	+	0.466663i
$396$	7.73961	−	0.505439i	0.388930	−	0.0253992i
$397$	−29.1350	+	7.80671i	−1.46224	+	0.391807i	−0.900265	−	0.435343i	$-0.856627\pi$
$397$	−29.1350	+	7.80671i	−1.46224	+	0.391807i	−0.561980	+	0.827151i	$0.689960\pi$
$398$	37.2099	−	26.0546i	1.86516	−	1.30600i
$399$	4.99656	−	3.74719i	0.250141	−	0.187594i
$400$	−57.5772	−	44.8165i	−2.87886	−	2.24082i
$401$	34.2820	−	6.04485i	1.71196	−	0.301865i	0.770115	−	0.637905i	$-0.220199\pi$
$401$	34.2820	−	6.04485i	1.71196	−	0.301865i	0.941848	+	0.336040i	$0.109088\pi$
$402$	−52.9389	+	32.9108i	−2.64035	+	1.64144i
$403$	14.4761	−	1.26649i	0.721106	−	0.0630886i
$404$	31.5550			1.56992
$405$	−19.9023	+	2.98320i	−0.988952	+	0.148237i
$406$	24.1845			1.20026
$407$	−0.709953	+	0.0621128i	−0.0351911	+	0.00307882i
$408$	−47.6899	+	29.6476i	−2.36100	+	1.46778i
$409$	−21.8207	+	3.84758i	−1.07897	+	0.190251i	−0.684758	−	0.728771i	$-0.740092\pi$
$409$	−21.8207	+	3.84758i	−1.07897	+	0.190251i	−0.394208	+	0.919021i	$0.628981\pi$
$410$	45.4960	−	13.0904i	2.24689	−	0.646488i
$411$	2.87826	−	2.15856i	0.141974	−	0.106474i
$412$	−19.8890	+	13.9264i	−0.979859	+	0.686105i
$413$	5.42346	−	1.45321i	0.266871	−	0.0715079i
$414$	−1.82692	−	2.73559i	−0.0897884	−	0.134447i
$415$	5.95333	+	2.64413i	0.292238	+	0.129795i
$416$	20.0374	+	55.0524i	0.982415	+	2.69916i
$417$	19.9098	−	17.8441i	0.974989	−	0.873831i
$418$	−0.257831	+	2.94703i	−0.0126109	+	0.144144i
$419$	−3.82900	+	3.21291i	−0.187059	+	0.156961i	−0.731508	−	0.681833i	$-0.761183\pi$
$419$	−3.82900	+	3.21291i	−0.187059	+	0.156961i	0.544449	+	0.838794i	$0.316739\pi$
$420$	24.6862	+	22.2899i	1.20456	+	1.08764i
$421$	12.3825	−	4.50685i	0.603485	−	0.219651i	−0.0221653	−	0.999754i	$-0.507056\pi$
$421$	12.3825	−	4.50685i	0.603485	−	0.219651i	0.625650	+	0.780104i	$0.284834\pi$
$422$	−27.5051	−	7.36996i	−1.33893	−	0.358764i
$423$	35.9170	−	5.51945i	1.74635	−	0.268365i
$424$	3.13649	+	1.81086i	0.152322	+	0.0879429i
$425$	−5.10590	−	16.5931i	−0.247672	−	0.804882i
$426$	29.5899	−	69.2660i	1.43363	−	3.35595i
$427$	−6.15173	−	13.1924i	−0.297703	−	0.638426i
$428$	2.54388	−	3.63304i	0.122963	−	0.175609i
$429$	1.56708	−	1.67275i	0.0756592	−	0.0807613i
$430$	−4.74535	−	5.44893i	−0.228841	−	0.262771i
$431$		−	14.5168i		−	0.699251i	−0.936890	−	0.349625i	$-0.886309\pi$
$431$		−	14.5168i		−	0.699251i	0.936890	−	0.349625i	$-0.113691\pi$
$432$	−32.7687	−	68.3794i	−1.57659	−	3.28991i
$433$	−16.6348	+	16.6348i	−0.799416	+	0.799416i	−0.983003	−	0.183587i	$-0.941229\pi$
$433$	−16.6348	+	16.6348i	−0.799416	+	0.799416i	0.183587	+	0.983003i	$0.441229\pi$
$434$	17.2845	+	14.5034i	0.829683	+	0.696187i
$435$	13.0945	−	17.3267i	0.627833	−	0.830750i
$436$	−7.97163	−	45.2094i	−0.381772	−	2.16514i
$437$	0.830884	−	0.387448i	0.0397466	−	0.0185341i
$438$	−29.7490	−	23.3528i	−1.42146	−	1.11584i
$439$	−21.2894	−	3.75390i	−1.01609	−	0.179164i	−0.359287	−	0.933227i	$-0.616980\pi$
$439$	−21.2894	−	3.75390i	−1.01609	−	0.179164i	−0.656801	+	0.754064i	$0.728091\pi$
$440$	−9.89218	+	1.04877i	−0.471591	+	0.0499982i
$441$	9.32350	+	9.74408i	0.443976	+	0.464004i
$442$	−6.80221	+	25.3862i	−0.323548	+	1.20750i
$443$	10.8788	+	5.07285i	0.516866	+	0.241018i	0.663505	−	0.748172i	$-0.269068\pi$
$443$	10.8788	+	5.07285i	0.516866	+	0.241018i	−0.146640	+	0.989190i	$0.546846\pi$
$444$	6.35363	+	12.5409i	0.301530	+	0.595166i
$445$	−8.07667	−	13.4143i	−0.382871	−	0.635898i
$446$	41.0912	+	48.9706i	1.94572	+	2.31882i
$447$	8.48653	−	25.9159i	0.401399	−	1.22578i
$448$	−18.9243	+	40.5832i	−0.894087	+	1.91738i
$449$	15.1373	+	26.2186i	0.714374	+	1.23733i	0.963200	+	0.268784i	$0.0866218\pi$
$449$	15.1373	+	26.2186i	0.714374	+	1.23733i	−0.248826	+	0.968548i	$0.580045\pi$
$450$	40.1476	−	7.68778i	1.89258	−	0.362406i
$451$	1.85078	−	3.20565i	0.0871499	−	0.150948i
$452$	−6.78649	−	9.69212i	−0.319210	−	0.455879i
$453$	−1.14902	+	1.46372i	−0.0539855	+	0.0687716i
$454$	18.6577	−	51.2617i	0.875651	−	2.40583i
$455$	9.82762	−	0.180448i	0.460726	−	0.00845951i
$456$	35.2631	−	10.6924i	1.65135	−	0.500717i
$457$	3.62673	+	41.4537i	0.169651	+	1.93912i	0.313642	+	0.949541i	$0.398451\pi$
$457$	3.62673	+	41.4537i	0.169651	+	1.93912i	−0.143990	+	0.989579i	$0.545993\pi$
$458$	−42.5171	−	42.5171i	−1.98670	−	1.98670i
$459$	2.94528	−	17.7999i	0.137474	−	0.830829i
$460$	2.87329	+	3.94722i	0.133968	+	0.184040i
$461$	−11.0916	+	13.2184i	−0.516586	+	0.615643i	−0.959770	−	0.280788i	$-0.909404\pi$
$461$	−11.0916	+	13.2184i	−0.516586	+	0.615643i	0.443184	+	0.896431i	$0.353849\pi$
$462$	3.55716	−	0.116027i	0.165494	−	0.00539808i
$463$	−13.5021	−	9.45428i	−0.627496	−	0.439378i	0.216088	−	0.976374i	$-0.430670\pi$
$463$	−13.5021	−	9.45428i	−0.627496	−	0.439378i	−0.843585	+	0.536996i	$0.819559\pi$
$464$	76.8950	+	27.9875i	3.56976	+	1.29929i
$465$	19.7493	−	4.53049i	0.915852	−	0.210097i
$466$	−8.83640	+	50.1137i	−0.409338	+	2.32147i
$467$	1.03012	+	3.84448i	0.0476685	+	0.177901i	0.985656	−	0.168769i	$-0.0539791\pi$
$467$	1.03012	+	3.84448i	0.0476685	+	0.177901i	−0.937987	+	0.346670i	$0.887312\pi$
$468$	−42.1380	−	16.3981i	−1.94783	−	0.758001i
$469$	−18.1003	+	10.4502i	−0.835795	+	0.482546i
$470$	−72.4420	+	14.1494i	−3.34150	+	0.652664i
$471$	−24.9696	−	16.2972i	−1.15054	−	0.750937i
$472$	33.0009	+	2.88720i	1.51899	+	0.132894i
$473$	−0.562805	−	0.0492391i	−0.0258778	−	0.00226402i
$474$	1.14609	−	20.9467i	0.0526417	−	0.962115i
$475$	0.418210	+	11.3845i	0.0191888	+	0.522359i
$476$	−25.8234	+	14.9091i	−1.18361	+	0.683359i
$477$	−1.10196	+	0.373775i	−0.0504554	+	0.0171140i
$478$	13.7631	+	51.3646i	0.629510	+	2.34936i
$479$	−0.246236	+	1.39648i	−0.0112508	+	0.0638066i	−0.989916	−	0.141654i	$-0.954758\pi$
$479$	−0.246236	+	1.39648i	−0.0112508	+	0.0638066i	0.978665	+	0.205460i	$0.0658692\pi$
$480$	38.2507	+	72.1818i	1.74590	+	3.29463i
$481$	3.90411	+	1.42098i	0.178012	+	0.0647911i
$482$	10.9857	+	7.69230i	0.500387	+	0.350375i
$483$	−0.582326	−	0.936704i	−0.0264967	−	0.0426215i
$484$	37.5762	−	44.7816i	1.70801	−	2.03553i
$485$	−13.6872	+	9.96332i	−0.621505	+	0.452411i
$486$	40.9040	+	11.4660i	1.85544	+	0.520107i
$487$	−5.92999	−	5.92999i	−0.268714	−	0.268714i	0.559868	−	0.828582i	$-0.310852\pi$
$487$	−5.92999	−	5.92999i	−0.268714	−	0.268714i	−0.828582	+	0.559868i	$0.810852\pi$
$488$	−7.48504	−	85.5544i	−0.338832	−	3.87286i
$489$	1.37629	−	5.89942i	0.0622380	−	0.266781i
$490$	−19.7220	−	19.0109i	−0.890951	−	0.858823i
$491$	−9.16760	+	25.1878i	−0.413728	+	1.13671i	0.541464	+	0.840724i	$0.317870\pi$
$491$	−9.16760	+	25.1878i	−0.413728	+	1.13671i	−0.955193	+	0.295985i	$0.904352\pi$
$492$	−72.2857	−	10.3287i	−3.25889	−	0.465654i
$493$	11.1679	+	15.9494i	0.502976	+	0.718324i
$494$	8.62305	−	14.9356i	0.387969	−	0.671983i
$495$	1.84286	−	2.61130i	0.0828306	−	0.117369i
$496$	38.1722	+	66.1162i	1.71398	+	2.96871i
$497$	10.6731	−	22.8886i	0.478754	−	1.02669i
$498$	−9.17735	−	10.2398i	−0.411247	−	0.458854i
$499$	7.19594	+	8.57579i	0.322134	+	0.383905i	0.902672	−	0.430328i	$-0.141602\pi$
$499$	7.19594	+	8.57579i	0.322134	+	0.383905i	−0.580538	+	0.814233i	$0.697158\pi$
$500$	−59.0763	+	13.8081i	−2.64197	+	0.617515i
$501$	−6.23696	+	9.55588i	−0.278647	+	0.426925i
$502$	51.6420	+	24.0811i	2.30490	+	1.07479i
$503$	3.44372	−	12.8521i	0.153548	−	0.573049i	−0.845677	−	0.533694i	$-0.820803\pi$
$503$	3.44372	−	12.8521i	0.153548	−	0.573049i	0.999225	−	0.0393543i	$-0.0125301\pi$
$504$	−17.8448	−	40.5815i	−0.794872	−	1.80765i
$505$	8.17391	−	10.1127i	0.363734	−	0.450007i
$506$	0.514493	+	0.0907189i	0.0228720	+	0.00403295i
$507$	8.49540	−	3.40966i	0.377294	−	0.151428i
$508$	−17.5550	+	8.18603i	−0.778877	+	0.363197i
$509$	−1.12261	−	6.36664i	−0.0497588	−	0.282196i	0.949768	−	0.312955i	$-0.101319\pi$
$509$	−1.12261	−	6.36664i	−0.0497588	−	0.282196i	−0.999527	+	0.0307584i	$0.990208\pi$
$510$	−4.51682	+	36.3673i	−0.200008	+	1.61037i
$511$	−9.71403	−	8.15104i	−0.429723	−	0.360581i
$512$	−24.9482	+	24.9482i	−1.10257	+	1.10257i
$513$	−4.88993	+	10.7821i	−0.215896	+	0.476042i
$514$		−	39.7830i		−	1.75475i
$515$	−0.688883	+	9.98142i	−0.0303558	+	0.439834i
$516$	3.23388	+	10.6652i	0.142364	+	0.469511i
$517$	−3.31019	+	4.72744i	−0.145582	+	0.207912i
$518$	2.72634	+	5.84666i	0.119789	+	0.256887i
$519$	−18.3860	+	2.21460i	−0.807057	+	0.0972103i
$520$	54.8499	+	18.8308i	2.40533	+	0.825784i
$521$	−6.34977	−	3.66604i	−0.278188	−	0.160612i	0.354415	−	0.935088i	$-0.384680\pi$
$521$	−6.34977	−	3.66604i	−0.278188	−	0.160612i	−0.632603	+	0.774476i	$0.718013\pi$
$522$	−40.1983	+	22.0411i	−1.75943	+	0.964715i
$523$	12.5860	+	3.37240i	0.550346	+	0.147465i	0.523268	−	0.852168i	$-0.324713\pi$
$523$	12.5860	+	3.37240i	0.550346	+	0.147465i	0.0270787	+	0.999633i	$0.491380\pi$
$524$	−15.6827	+	5.70803i	−0.685101	+	0.249356i
$525$	13.5381	−	2.13744i	0.590849	−	0.0932856i
$526$	−63.9152	+	53.6312i	−2.78683	+	2.33843i
$527$	−1.58322	+	18.0963i	−0.0689660	+	0.788285i
$528$	11.4443	+	3.74760i	0.498049	+	0.163093i
$529$	7.81109	+	21.4608i	0.339613	+	0.933078i
$530$	2.20580	−	0.849021i	0.0958139	−	0.0368791i
$531$	−7.69018	+	7.35825i	−0.333725	+	0.319321i
$532$	18.9001	−	5.06425i	0.819421	−	0.219563i
$533$	−17.6767	+	12.3773i	−0.765662	+	0.536122i
$534$	3.95260	+	32.8152i	0.171046	+	1.42005i
$535$	−0.505347	−	1.75635i	−0.0218480	−	0.0759335i
$536$	−121.438	+	21.4128i	−5.24534	+	0.924894i
$537$	−10.1211	−	5.41139i	−0.436758	−	0.233519i
$538$	−64.3161	+	5.62693i	−2.77286	+	0.242594i
$539$	−2.14180			−0.0922537
$540$	−61.3465	−	14.5509i	−2.63994	−	0.626169i
$541$	−19.4815			−0.837576			−0.418788	−	0.908084i	$-0.637545\pi$
$541$	−19.4815			−0.837576			−0.418788	+	0.908084i	$0.637545\pi$
$542$	−54.6112	+	4.77786i	−2.34575	+	0.205227i
$543$	0.493396	+	15.1265i	0.0211737	+	0.649140i
$544$	−72.1238	+	12.7174i	−3.09228	+	0.545253i
$545$	−16.5535	−	9.15618i	−0.709075	−	0.392207i
$546$	−19.0803	−	8.15097i	−0.816563	−	0.348829i
$547$	11.7626	−	8.23625i	0.502932	−	0.352157i	−0.294415	−	0.955678i	$-0.595125\pi$
$547$	11.7626	−	8.23625i	0.502932	−	0.352157i	0.797347	+	0.603521i	$0.206236\pi$
$548$	10.8874	−	2.91726i	0.465085	−	0.124619i
$549$	22.2483	+	16.3213i	0.949535	+	0.696574i
$550$	−3.52587	+	5.45096i	−0.150344	+	0.232430i
$551$	−4.36986	−	12.0061i	−0.186162	−	0.511477i
$552$	−1.33832	−	6.36830i	−0.0569627	−	0.271053i
$553$	0.613034	−	7.00702i	0.0260689	−	0.297969i
$554$	31.7450	−	26.6372i	1.34871	−	1.13171i
$555$	5.66491	+	1.21237i	0.240462	+	0.0514623i
$556$	78.7101	−	28.6481i	3.33805	−	1.21495i
$557$	22.3886	+	5.99902i	0.948637	+	0.254187i	0.699784	−	0.714355i	$-0.253280\pi$
$557$	22.3886	+	5.99902i	0.948637	+	0.254187i	0.248853	+	0.968541i	$0.419946\pi$
$558$	−41.9475	−	8.35420i	−1.77578	−	0.353662i
$559$	2.85230	+	1.64678i	0.120640	+	0.0696513i
$560$	22.6798	+	46.3938i	0.958397	+	1.96049i
$561$	1.71913	+	2.29232i	0.0725819	+	0.0967818i
$562$	27.4978	+	58.9691i	1.15992	+	2.48746i
$563$	−17.2788	+	24.6767i	−0.728214	+	1.04000i	0.268832	+	0.963187i	$0.413362\pi$
$563$	−17.2788	+	24.6767i	−0.728214	+	1.04000i	−0.997046	+	0.0768099i	$0.975527\pi$
$564$	110.869	+	25.8648i	4.66842	+	1.08911i
$565$	−4.86406	−	0.335700i	−0.204632	−	0.0141230i
$566$		−	0.777487i		−	0.0326802i
$567$	13.5822	+	4.28952i	0.570398	+	0.180143i
$568$	105.360	−	105.360i	4.42082	−	4.42082i
$569$	14.2448	+	11.9528i	0.597173	+	0.501088i	0.890536	−	0.454913i	$-0.150330\pi$
$569$	14.2448	+	11.9528i	0.597173	+	0.501088i	−0.293362	+	0.956001i	$0.594774\pi$
$570$	9.03948	−	22.2840i	0.378622	−	0.933373i
$571$	6.82003	+	38.6783i	0.285409	+	1.61864i	0.703819	+	0.710379i	$0.251476\pi$
$571$	6.82003	+	38.6783i	0.285409	+	1.61864i	−0.418410	+	0.908258i	$0.637412\pi$
$572$	6.50822	−	3.03483i	0.272122	−	0.126893i
$573$	−4.94195	+	34.5864i	−0.206453	+	1.44487i
$574$	−32.9977	−	5.81838i	−1.37730	−	0.242854i
$575$	2.00928	+	0.101652i	0.0837929	+	0.00423918i
$576$	−5.53153	−	84.7024i	−0.230480	−	3.52927i
$577$	11.3255	−	42.2673i	0.471486	−	1.75961i	−0.162950	−	0.986634i	$-0.552101\pi$
$577$	11.3255	−	42.2673i	0.471486	−	1.75961i	0.634436	−	0.772975i	$-0.281232\pi$
$578$	12.2108	+	5.69397i	0.507901	+	0.236838i
$579$	−32.4766	−	1.77694i	−1.34968	−	0.0738472i
$580$	58.2908	−	35.0966i	2.42039	−	1.45731i
$581$	−2.96353	−	3.53180i	−0.122948	−	0.146524i
$582$	34.9722	−	7.34954i	1.44965	−	0.304648i
$583$	0.0781006	−	0.167487i	0.00323460	−	0.00693661i
$584$	−37.4080	−	64.7925i	−1.54795	−	2.68113i
$585$	−16.1705	+	9.25656i	−0.668568	+	0.382712i
$586$	21.1828	−	36.6896i	0.875051	−	1.51563i
$587$	−11.6046	−	16.5731i	−0.478974	−	0.684046i	0.504845	−	0.863210i	$-0.331550\pi$
$587$	−11.6046	−	16.5731i	−0.478974	−	0.684046i	−0.983819	+	0.179164i	$0.942661\pi$
$588$	15.7373	+	39.2105i	0.648993	+	1.61701i
$589$	4.07693	−	11.2013i	0.167987	−	0.461540i
$590$	15.0037	−	15.5649i	0.617691	−	0.640798i
$591$	−6.33393	−	5.93378i	−0.260543	−	0.244083i
$592$	1.90240	+	21.7446i	0.0781883	+	0.893696i
$593$	−2.27116	−	2.27116i	−0.0932652	−	0.0932652i	0.658935	−	0.752200i	$-0.271007\pi$
$593$	−2.27116	−	2.27116i	−0.0932652	−	0.0932652i	−0.752200	+	0.658935i	$0.771007\pi$
$594$	−5.80678	+	3.43475i	−0.238255	+	0.140930i
$595$	−1.91117	+	12.1378i	−0.0783504	+	0.497602i
$596$	54.9162	−	65.4466i	2.24946	−	2.68080i
$597$	−13.6129	+	25.4606i	−0.557137	+	1.04203i
$598$	−2.49484	−	1.74691i	−0.102022	−	0.0714364i
$599$	11.3910	+	4.14598i	0.465423	+	0.169400i	0.564078	−	0.825722i	$-0.309232\pi$
$599$	11.3910	+	4.14598i	0.465423	+	0.169400i	−0.0986548	+	0.995122i	$0.531454\pi$
$600$	79.3701	+	15.4682i	3.24027	+	0.631487i
$601$	2.78962	−	15.8207i	0.113791	−	0.645340i	−0.873551	−	0.486733i	$-0.838189\pi$
$601$	2.78962	−	15.8207i	0.113791	−	0.645340i	0.987342	−	0.158607i	$-0.0507003\pi$
$602$	1.32360	+	4.93974i	0.0539459	+	0.201329i
$603$	20.5614	−	33.8660i	0.837323	−	1.37913i
$604$	−5.04879	+	2.91492i	−0.205432	+	0.118606i
$605$	−4.61785	−	23.6424i	−0.187742	−	0.961200i
$606$	−24.4848	+	12.4048i	−0.994626	+	0.503909i
$607$	−12.6491	−	1.10665i	−0.513412	−	0.0449177i	−0.172494	−	0.985011i	$-0.555182\pi$
$607$	−12.6491	−	1.10665i	−0.513412	−	0.0449177i	−0.340918	+	0.940093i	$0.610738\pi$
$608$	47.8750	+	4.18852i	1.94159	+	0.169867i
$609$	−13.7119	+	6.94690i	−0.555636	+	0.281503i
$610$	−46.4932	−	31.2988i	−1.88245	−	1.26725i
$611$	29.1369	−	16.8222i	1.17875	−	0.680552i
$612$	29.3345	−	48.3159i	1.18578	−	1.95306i
$613$	3.15725	+	11.7830i	0.127520	+	0.475912i	0.999917	−	0.0128866i	$-0.00410204\pi$
$613$	3.15725	+	11.7830i	0.127520	+	0.475912i	−0.872397	+	0.488798i	$0.837435\pi$
$614$	−4.98094	+	28.2483i	−0.201014	+	1.14001i
$615$	−22.0348	+	20.4904i	−0.888528	+	0.826253i
$616$	6.61595	+	2.40801i	0.266564	+	0.0970215i
$617$	7.63591	+	5.34672i	0.307410	+	0.215251i	0.717094	−	0.696977i	$-0.245472\pi$
$617$	7.63591	+	5.34672i	0.307410	+	0.215251i	−0.409684	+	0.912228i	$0.634361\pi$
$618$	9.95797	−	18.6247i	0.400568	−	0.749197i
$619$	10.1944	−	12.1492i	0.409748	−	0.488319i	−0.521218	−	0.853423i	$-0.674522\pi$
$619$	10.1944	−	12.1492i	0.409748	−	0.488319i	0.930967	+	0.365104i	$0.118967\pi$
$620$	62.7074	+	9.87365i	2.51839	+	0.396535i
$621$	1.82160	+	1.02622i	0.0730982	+	0.0411810i
$622$	−6.19528	−	6.19528i	−0.248408	−	0.248408i
$623$	0.965877	+	11.0400i	0.0386971	+	0.442309i
$624$	−51.2334	−	47.9967i	−2.05098	−	1.92141i
$625$	−10.8778	+	22.5094i	−0.435111	+	0.900377i
$626$	−22.6663	+	62.2751i	−0.905927	+	2.48901i
$627$	−0.700337	−	1.74494i	−0.0279688	−	0.0696862i
$628$	−53.5809	−	76.5215i	−2.13811	−	3.05354i
$629$	−2.59683	+	4.49784i	−0.103542	+	0.179341i
$630$	−27.9175	−	7.59114i	−1.11226	−	0.302438i
$631$	−12.2239	−	21.1724i	−0.486626	−	0.842861i	0.513256	−	0.858236i	$-0.328439\pi$
$631$	−12.2239	−	21.1724i	−0.486626	−	0.842861i	−0.999882	+	0.0153745i	$0.995106\pi$
$632$	17.5382	−	37.6109i	0.697634	−	1.49608i
$633$	17.7116	−	3.72215i	0.703972	−	0.147942i
$634$	−36.3814	−	43.3577i	−1.44489	−	1.72195i
$635$	−1.92396	+	7.74647i	−0.0763500	+	0.307409i
$636$	−3.64010	−	0.199166i	−0.144339	−	0.00789745i
$637$	11.3163	+	5.27689i	0.448369	+	0.209078i
$638$	1.88441	−	7.03271i	0.0746045	−	0.278428i
$639$	3.11973	+	47.7714i	0.123415	+	1.88981i
$640$	8.23251	+	77.6504i	0.325419	+	3.06940i
$641$	−5.87001	−	1.03504i	−0.231852	−	0.0408817i	0.0565151	−	0.998402i	$-0.482001\pi$
$641$	−5.87001	−	1.03504i	−0.231852	−	0.0408817i	−0.288367	+	0.957520i	$0.593112\pi$
$642$	−0.545695	+	3.81906i	−0.0215369	+	0.150726i
$643$	−29.1651	+	13.5999i	−1.15016	+	0.536328i	−0.901720	−	0.432320i	$-0.857695\pi$
$643$	−29.1651	+	13.5999i	−1.15016	+	0.536328i	−0.248438	+	0.968648i	$0.579917\pi$
$644$	−0.600036	−	3.40297i	−0.0236447	−	0.134096i
$645$	4.25566	+	1.72630i	0.167566	+	0.0679732i
$646$	16.5151	+	13.8578i	0.649779	+	0.545229i
$647$	−5.43613	+	5.43613i	−0.213717	+	0.213717i	−0.805844	−	0.592128i	$-0.798288\pi$
$647$	−5.43613	+	5.43613i	−0.213717	+	0.213717i	0.592128	+	0.805844i	$0.298288\pi$
$648$	66.6457	+	51.1892i	2.61809	+	2.01090i
$649$		−	1.69034i		−	0.0663516i
$650$	32.0590	−	20.1136i	1.25746	−	0.788919i
$651$	−13.9659	−	3.25813i	−0.547365	−	0.127696i
$652$	10.8857	−	15.5464i	0.426317	−	0.608844i
$653$	−6.80729	−	14.5983i	−0.266390	−	0.571275i	0.726924	−	0.686717i	$-0.240949\pi$
$653$	−6.80729	−	14.5983i	−0.266390	−	0.571275i	−0.993314	+	0.115443i	$0.963171\pi$
$654$	23.9580	+	31.9460i	0.936833	+	1.24919i
$655$	−2.23310	+	6.50454i	−0.0872545	+	0.254153i
$656$	−98.1831	−	56.6861i	−3.83341	−	2.21322i
$657$	23.5748	+	4.69513i	0.919740	+	0.183174i
$658$	50.4605	+	13.5209i	1.96716	+	0.527098i
$659$	−31.0994	+	11.3193i	−1.21146	+	0.440936i	−0.867210	−	0.497942i	$-0.834089\pi$
$659$	−31.0994	+	11.3193i	−1.21146	+	0.440936i	−0.344250	+	0.938878i	$0.611867\pi$
$660$	8.40527	−	5.44180i	0.327175	−	0.211822i
$661$	22.7885	−	19.1218i	0.886369	−	0.743752i	−0.0811098	−	0.996705i	$-0.525846\pi$
$661$	22.7885	−	19.1218i	0.886369	−	0.743752i	0.967478	+	0.252954i	$0.0814020\pi$
$662$	−1.41507	+	16.1743i	−0.0549981	+	0.628631i
$663$	−3.43541	−	16.3472i	−0.133420	−	0.634871i
$664$	−9.30342	−	25.5609i	−0.361043	−	0.991957i
$665$	3.27284	−	7.36887i	0.126915	−	0.285752i
$666$	−9.86008	−	7.23330i	−0.382070	−	0.280285i
$667$	−2.17945	+	0.583983i	−0.0843888	+	0.0226119i
$668$	−29.2848	+	20.5054i	−1.13306	+	0.793379i
$669$	−37.3641	−	15.9617i	−1.44458	−	0.617113i
$670$	−38.9509	+	70.4196i	−1.50480	+	2.72055i
$671$	−4.31561	+	0.760958i	−0.166602	+	0.0293764i
$672$	−1.88488	−	57.7867i	−0.0727110	−	2.22917i
$673$	34.6064	−	3.02767i	1.33398	−	0.116708i	0.602252	−	0.798306i	$-0.294270\pi$
$673$	34.6064	−	3.02767i	1.33398	−	0.116708i	0.731727	+	0.681598i	$0.238715\pi$
$674$	30.3912			1.17063
$675$	−20.5542	+	15.8910i	−0.791133	+	0.611644i
$676$	28.6790			1.10304
$677$	−17.3173	+	1.51507i	−0.665560	+	0.0582289i	−0.414929	−	0.909854i	$-0.636194\pi$
$677$	−17.3173	+	1.51507i	−0.665560	+	0.0582289i	−0.250631	+	0.968083i	$0.580638\pi$
$678$	9.07604	+	4.85263i	0.348563	+	0.186364i
$679$	11.8000	−	2.08066i	0.452843	−	0.0798485i
$680$	−35.0888	+	63.4373i	−1.34559	+	2.43271i
$681$	4.14629	+	34.4233i	0.158886	+	1.31910i
$682$	5.56428	−	3.89615i	0.213067	−	0.149191i
$683$	−10.9763	+	2.94108i	−0.419995	+	0.112537i	−0.462626	−	0.886554i	$-0.653093\pi$
$683$	−10.9763	+	2.94108i	−0.419995	+	0.112537i	0.0426308	+	0.999091i	$0.486426\pi$
$684$	−26.7993	+	25.6425i	−1.02470	+	0.980467i
$685$	1.88531	−	4.24483i	0.0720341	−	0.162187i
$686$	16.9564	+	46.5874i	0.647400	+	1.77872i
$687$	36.3189	+	11.8931i	1.38565	+	0.453752i
$688$	−1.50810	+	17.2377i	−0.0574959	+	0.657181i
$689$	−0.825299	+	0.692508i	−0.0314414	+	0.0263824i
$690$	−3.78122	−	1.93327i	−0.143949	−	0.0735984i
$691$	−22.0909	+	8.04044i	−0.840378	+	0.305873i	−0.726111	−	0.687577i	$-0.758674\pi$
$691$	−22.0909	+	8.04044i	−0.840378	+	0.305873i	−0.114267	+	0.993450i	$0.536452\pi$
$692$	−56.0412	−	15.0162i	−2.13037	−	0.570830i
$693$	−1.98348	+	1.08756i	−0.0753461	+	0.0413131i
$694$	56.0171	+	32.3415i	2.12638	+	1.22767i
$695$	11.2078	−	32.6457i	0.425134	−	1.23832i
$696$	−90.0392	+	10.8453i	−3.41293	+	0.411088i
$697$	−11.4004	−	24.4483i	−0.431822	−	0.926046i
$698$	11.7362	−	16.7611i	0.444223	−	0.634416i
$699$	−9.38495	−	30.9512i	−0.354971	−	1.17068i
$700$	41.8558	+	9.58333i	1.58200	+	0.362216i
$701$			44.6039i			1.68467i	0.538956	+	0.842334i	$0.318819\pi$
$701$			44.6039i			1.68467i	−0.538956	+	0.842334i	$0.681181\pi$
$702$	39.1429	−	3.84119i	1.47735	−	0.144976i
$703$	2.40988	−	2.40988i	0.0908903	−	0.0908903i
$704$	10.3268	+	8.66522i	0.389206	+	0.326583i
$705$	37.0082	−	28.8310i	1.39381	−	1.08584i
$706$	−2.45245	−	13.9085i	−0.0922992	−	0.523455i
$707$	−8.34079	+	3.88937i	−0.313688	+	0.146275i
$708$	−30.9455	+	12.4201i	−1.16300	+	0.466775i
$709$	36.4781	+	6.43207i	1.36996	+	0.241562i	0.809744	−	0.586783i	$-0.199606\pi$
$709$	36.4781	+	6.43207i	1.36996	+	0.241562i	0.560219	+	0.828344i	$0.310717\pi$
$710$	−10.2519	−	96.6978i	−0.384748	−	3.62900i
$711$	5.36705	+	12.2054i	0.201280	+	0.457738i
$712$	−16.9228	+	63.1566i	−0.634207	+	2.36689i
$713$	−1.90785	−	0.889647i	−0.0714497	−	0.0333175i
$714$	14.1764	−	21.7202i	0.530538	−	0.812857i
$715$	0.713275	−	2.87187i	0.0266750	−	0.107402i
$716$	−23.1122	−	27.5441i	−0.863744	−	1.02937i
$717$	−22.5575	−	25.1689i	−0.842427	−	0.939949i
$718$	−15.7251	+	33.7227i	−0.586857	+	1.25852i
$719$	−19.2483	−	33.3390i	−0.717839	−	1.24333i	−0.961854	−	0.273562i	$-0.911798\pi$
$719$	−19.2483	−	33.3390i	−0.717839	−	1.24333i	0.244016	−	0.969771i	$-0.421535\pi$
$720$	−79.9793	−	56.4436i	−2.98065	−	2.10353i
$721$	3.54064	−	6.13256i	0.131860	−	0.228389i
$722$	21.5840	+	30.8251i	0.803273	+	1.14719i
$723$	−8.43818	−	1.20571i	−0.313819	−	0.0448408i
$724$	−16.2169	+	44.5557i	−0.602698	+	1.65590i
$725$	3.85183	−	27.7722i	0.143053	−	1.03143i
$726$	−11.5525	+	49.5196i	−0.428755	+	1.83785i
$727$	−2.27381	−	25.9897i	−0.0843308	−	0.963906i	−0.914017	−	0.405676i	$-0.867036\pi$
$727$	−2.27381	−	25.9897i	−0.0843308	−	0.963906i	0.829686	−	0.558230i	$-0.188519\pi$
$728$	−29.0230	−	29.0230i	−1.07566	−	1.07566i
$729$	−26.4849	+	5.24861i	−0.980924	+	0.194393i
$730$	−48.2312	−	7.59429i	−1.78512	−	0.281077i
$731$	−2.64649	+	3.15396i	−0.0978838	+	0.116653i
$732$	45.6408	+	73.4158i	1.68693	+	2.71352i
$733$	39.9276	+	27.9576i	1.47476	+	1.03264i	0.987189	+	0.159555i	$0.0510060\pi$
$733$	39.9276	+	27.9576i	1.47476	+	1.03264i	0.487571	+	0.873083i	$0.337883\pi$
$734$	−55.2278	−	20.1013i	−2.03849	−	0.741951i
$735$	16.6426	+	5.11354i	0.613872	+	0.188616i
$736$	1.47374	−	8.35802i	0.0543230	−	0.308081i
$737$	1.62852	+	6.07772i	0.0599873	+	0.223876i
$738$	60.1498	−	20.4022i	2.21414	−	0.751015i
$739$	11.7531	−	6.78566i	0.432345	−	0.249614i	−0.268000	−	0.963419i	$-0.586363\pi$
$739$	11.7531	−	6.78566i	0.432345	−	0.249614i	0.700345	+	0.713804i	$0.253029\pi$
$740$	15.0558	+	10.1355i	0.553464	+	0.372587i
$741$	−0.598849	+	10.9450i	−0.0219993	+	0.402073i
$742$	−1.66647	−	0.145797i	−0.0611780	−	0.00535238i
$743$	−1.23767	−	0.108282i	−0.0454055	−	0.00397247i	0.0644303	−	0.997922i	$-0.479477\pi$
$743$	−1.23767	−	0.108282i	−0.0454055	−	0.00397247i	−0.109836	+	0.993950i	$0.535033\pi$
$744$	−70.8542	−	46.2453i	−2.59764	−	1.69544i
$745$	−6.74882	−	34.5525i	−0.247257	−	1.26591i
$746$	31.2331	−	18.0324i	1.14352	−	0.660214i
$747$	8.14462	+	3.16949i	0.297996	+	0.115966i
$748$	2.32338	+	8.67096i	0.0849511	+	0.317042i
$749$	−0.224615	+	1.27386i	−0.00820726	+	0.0465457i
$750$	40.4115	−	33.9381i	1.47562	−	1.23924i
$751$	−8.15950	−	2.96982i	−0.297745	−	0.108370i	0.188828	−	0.982010i	$-0.439531\pi$
$751$	−8.15950	−	2.96982i	−0.297745	−	0.108370i	−0.486573	+	0.873640i	$0.661753\pi$
$752$	144.793	+	101.385i	5.28005	+	3.69713i
$753$	−36.1967	+	1.18066i	−1.31908	+	0.0430258i
$754$	−27.2833	+	32.5150i	−0.993601	+	1.18413i
$755$	−0.373658	+	2.37309i	−0.0135988	+	0.0863657i
$756$	34.4843	+	28.3210i	1.25418	+	1.03003i
$757$	29.4262	+	29.4262i	1.06951	+	1.06951i	0.997396	+	0.0721170i	$0.0229755\pi$
$757$	29.4262	+	29.4262i	1.06951	+	1.06951i	0.0721170	+	0.997396i	$0.477025\pi$
$758$	6.50993	+	74.4088i	0.236451	+	2.70265i
$759$	−0.317761	+	0.0963507i	−0.0115340	+	0.00349731i
$760$	33.0147	−	34.2498i	1.19757	−	1.24237i
$761$	14.0169	−	38.5111i	0.508112	−	1.39603i	−0.375071	−	0.926996i	$-0.622382\pi$
$761$	14.0169	−	38.5111i	0.508112	−	1.39603i	0.883183	−	0.469029i	$-0.155396\pi$
$762$	10.4036	−	13.2530i	0.376882	−	0.480107i
$763$	7.67948	+	10.9674i	0.278016	+	0.397048i
$764$	−54.7283	+	94.7922i	−1.98000	+	3.42946i
$765$	−7.88544	−	21.9166i	−0.285099	−	0.792398i
$766$	−49.2326	−	85.2733i	−1.77884	−	3.08105i
$767$	−4.16460	+	8.93101i	−0.150375	+	0.322480i
$768$	20.7931	−	63.4973i	0.750307	−	2.29126i
$769$	−3.94057	−	4.69619i	−0.142100	−	0.169349i	0.690300	−	0.723523i	$-0.257479\pi$
$769$	−3.94057	−	4.69619i	−0.142100	−	0.169349i	−0.832401	+	0.554174i	$0.813034\pi$
$770$	3.93629	−	2.37002i	0.141854	−	0.0854096i
$771$	11.4275	+	22.5558i	0.411550	+	0.812327i
$772$	−92.3513	−	43.0641i	−3.32380	−	1.54991i
$773$	−2.46257	+	9.19044i	−0.0885726	+	0.330557i	−0.995967	−	0.0897234i	$-0.971402\pi$
$773$	−2.46257	+	9.19044i	−0.0885726	+	0.330557i	0.907394	+	0.420281i	$0.138068\pi$
$774$	−6.70197	−	7.00429i	−0.240897	−	0.251764i
$775$	19.4078	−	17.5386i	0.697149	−	0.630007i
$776$	69.6196	+	12.2758i	2.49920	+	0.440676i
$777$	−3.22518	−	2.53176i	−0.115703	−	0.0908263i
$778$	45.6625	−	21.2928i	1.63708	−	0.763382i
$779$	3.07383	+	17.4326i	0.110132	+	0.624587i
$780$	−57.8171	+	8.04347i	−2.07018	+	0.288002i
$781$	−5.82422	−	4.88710i	−0.208407	−	0.174874i
$782$	2.69216	−	2.69216i	0.0962714	−	0.0962714i
$783$	16.4601	−	24.0435i	0.588235	−	0.859244i
$784$			65.5994i			2.34283i
$785$	−38.4029	−	2.65043i	−1.37066	−	0.0945980i
$786$	9.92491	−	10.5942i	0.354010	−	0.377883i
$787$	4.85971	−	6.94038i	0.173230	−	0.247398i	−0.723143	−	0.690698i	$-0.757303\pi$
$787$	4.85971	−	6.94038i	0.173230	−	0.247398i	0.896373	+	0.443300i	$0.146192\pi$
$788$	−11.4915	−	24.6435i	−0.409367	−	0.877890i
$789$	20.8327	−	48.7667i	0.741665	−	1.73614i
$790$	−11.8943	−	24.3309i	−0.423179	−	0.865654i
$791$	2.98847	+	1.72539i	0.106258	+	0.0613479i
$792$	−13.1913	+	2.02713i	−0.468732	+	0.0720310i
$793$	24.6766	+	6.61207i	0.876291	+	0.234802i
$794$	77.2406	−	28.1133i	2.74116	−	0.997702i
$795$	−1.00675	+	1.11498i	−0.0357057	+	0.0395442i
$796$	−69.2896	+	58.1409i	−2.45591	+	2.06075i
$797$	2.46530	−	28.1786i	0.0873256	−	0.998136i	−0.818506	−	0.574498i	$-0.805197\pi$
$797$	2.46530	−	28.1786i	0.0873256	−	0.998136i	0.905832	−	0.423638i	$-0.139247\pi$
$798$	−12.6745	+	11.3595i	−0.448672	+	0.402121i
$799$	14.3847	+	39.5216i	0.508894	+	1.39818i
$800$	88.5517	+	57.2783i	3.13078	+	2.02510i
$801$	−11.6670	−	17.4699i	−0.412234	−	0.617268i
$802$	−91.6319	+	24.5527i	−3.23564	+	0.866986i
$803$	−3.12717	+	2.18967i	−0.110355	+	0.0772716i
$804$	99.3006	−	74.4709i	3.50206	−	2.62639i
$805$	−1.24601	−	0.689198i	−0.0439160	−	0.0242910i
$806$	−38.9984	+	6.87647i	−1.37366	+	0.242213i
$807$	34.8490	−	21.6648i	1.22674	−	0.762637i
$808$	−54.0909	+	4.73234i	−1.90291	+	0.166483i
$809$	−2.28591			−0.0803683			−0.0401841	−	0.999192i	$-0.512794\pi$
$809$	−2.28591			−0.0803683			−0.0401841	+	0.999192i	$0.512794\pi$
$810$	53.3214	−	12.8257i	1.87352	−	0.450649i
$811$	21.6606			0.760605			0.380303	−	0.924862i	$-0.375820\pi$
$811$	21.6606			0.760605			0.380303	+	0.924862i	$0.375820\pi$
$812$	−47.9736	+	4.19715i	−1.68354	+	0.147291i
$813$	29.5906	−	18.3957i	1.03779	−	0.645166i
$814$	1.91260	−	0.337243i	0.0670367	−	0.0118204i
$815$	−2.16247	−	7.51572i	−0.0757480	−	0.263264i
$816$	70.2096	−	52.6539i	2.45783	−	1.84326i
$817$	2.21311	−	1.54964i	0.0774270	−	0.0542150i
$818$	58.3243	−	15.6279i	2.03926	−	0.546418i
$819$	13.1593	−	0.859376i	0.459824	−	0.0300290i
$820$	−87.9763	+	33.8624i	−3.07227	+	1.18253i
$821$	7.91413	+	21.7439i	0.276205	+	0.758867i	0.997784	+	0.0665351i	$0.0211944\pi$
$821$	7.91413	+	21.7439i	0.276205	+	0.758867i	−0.721579	+	0.692332i	$0.756583\pi$
$822$	−7.30112	+	6.54361i	−0.254656	+	0.228235i
$823$	−0.569178	+	6.50574i	−0.0198403	+	0.226776i	0.979801	+	0.199977i	$0.0640868\pi$
$823$	−0.569178	+	6.50574i	−0.0198403	+	0.226776i	−0.999641	+	0.0267986i	$0.991469\pi$
$824$	32.0047	−	26.8552i	1.11494	−	0.935544i
$825$	0.433303	−	4.10333i	0.0150857	−	0.142859i
$826$	−14.3783	+	5.23326i	−0.500284	+	0.182088i
$827$	8.94494	+	2.39679i	0.311046	+	0.0833445i	0.410965	−	0.911651i	$-0.365192\pi$
$827$	8.94494	+	2.39679i	0.311046	+	0.0833445i	−0.0999193	+	0.994996i	$0.531858\pi$
$828$	4.09873	+	5.10939i	0.142441	+	0.177564i
$829$	2.45210	+	1.41572i	0.0851648	+	0.0491699i	0.541978	−	0.840393i	$-0.317676\pi$
$829$	2.45210	+	1.41572i	0.0851648	+	0.0491699i	−0.456813	+	0.889563i	$0.651009\pi$
$830$	−16.7899	−	5.76422i	−0.582786	−	0.200079i
$831$	−10.3471	+	24.2211i	−0.358936	+	0.840222i
$832$	−33.2132	−	71.2260i	−1.15146	−	2.46932i
$833$	−8.95278	+	12.7859i	−0.310195	+	0.443005i
$834$	−49.8123	+	53.1715i	−1.72486	+	1.84118i
$835$	−1.01432	+	14.6968i	−0.0351020	+	0.508603i
$836$		−	5.89061i		−	0.203731i
$837$	26.1827	−	7.31263i	0.905007	−	0.252761i
$838$	9.63173	−	9.63173i	0.332723	−	0.332723i
$839$	−32.4518	−	27.2303i	−1.12036	−	0.940095i	−0.121739	−	0.992562i	$-0.538847\pi$
$839$	−32.4518	−	27.2303i	−1.12036	−	0.940095i	−0.998623	+	0.0524668i	$0.983292\pi$
$840$	−45.6594	−	34.5068i	−1.57540	−	1.19060i
$841$	0.424617	+	2.40812i	0.0146420	+	0.0830387i
$842$	−32.5451	+	15.1760i	−1.12158	+	0.523000i
$843$	−32.5291	−	25.5352i	−1.12036	−	0.879479i
$844$	55.8394	+	9.84600i	1.92207	+	0.338913i
$845$	7.42892	−	9.19097i	0.255563	−	0.316179i
$846$	−96.1954	+	23.5147i	−3.30727	+	0.808452i
$847$	−4.41271	+	16.4684i	−0.151622	+	0.565862i
$848$	−5.12983	−	2.39208i	−0.176159	−	0.0821443i
$849$	0.223330	+	0.440813i	0.00766466	+	0.0151287i
$850$	17.8024	+	43.8335i	0.610616	+	1.50348i
$851$	−0.386871	−	0.461054i	−0.0132618	−	0.0158047i
$852$	−46.6750	+	142.535i	−1.59906	+	4.88316i
$853$	14.0780	−	30.1905i	0.482023	−	1.03370i	−0.503474	−	0.864010i	$-0.667945\pi$
$853$	14.0780	−	30.1905i	0.482023	−	1.03370i	0.985497	−	0.169691i	$-0.0542771\pi$
$854$	19.8339	+	34.3532i	0.678701	+	1.17554i
$855$	1.27585	+	15.2309i	0.0436332	+	0.520887i
$856$	−3.81582	+	6.60919i	−0.130422	+	0.225897i
$857$	−17.6306	−	25.1791i	−0.602249	−	0.860100i	0.396061	−	0.918224i	$-0.370377\pi$
$857$	−17.6306	−	25.1791i	−0.602249	−	0.860100i	−0.998309	+	0.0581240i	$0.981488\pi$
$858$	−3.85695	+	4.91333i	−0.131674	+	0.167738i
$859$	17.6716	−	48.5522i	0.602946	−	1.65658i	−0.142326	−	0.989820i	$-0.545458\pi$
$859$	17.6716	−	48.5522i	0.602946	−	1.65658i	0.745272	−	0.666760i	$-0.232320\pi$
$860$	10.3588	+	9.98522i	0.353231	+	0.340493i
$861$	20.3800	−	6.17958i	0.694550	−	0.210600i
$862$	3.44791	+	39.4098i	0.117436	+	1.34230i
$863$	−31.9076	−	31.9076i	−1.08615	−	1.08615i	−0.995921	−	0.0902264i	$-0.971241\pi$
$863$	−31.9076	−	31.9076i	−1.08615	−	1.08615i	−0.0902264	−	0.995921i	$-0.528759\pi$
$864$	55.7982	+	94.3322i	1.89829	+	3.20925i
$865$	−19.3291	+	14.0702i	−0.657209	+	0.478401i
$866$	41.2086	−	49.1104i	1.40032	−	1.66884i
$867$	−8.55872	+	0.279168i	−0.290669	+	0.00948105i
$868$	−36.8034	−	25.7700i	−1.24919	−	0.874692i
$869$	−1.98983	−	0.724239i	−0.0675003	−	0.0245681i
$870$	−31.4332	+	50.1479i	−1.06569	+	1.70017i
$871$	6.36968	−	36.1243i	0.215829	−	1.22402i
$872$	20.4449	+	76.3015i	0.692353	+	2.58390i
$873$	−17.7171	+	14.2126i	−0.599634	+	0.481023i
$874$	−2.16363	+	1.24917i	−0.0731860	+	0.0422539i
$875$	13.9134	−	10.9314i	0.470360	−	0.369549i
$876$	63.0643	+	41.1610i	2.13074	+	1.39070i
$877$	39.1615	+	3.42618i	1.32239	+	0.115694i	0.726385	−	0.687288i	$-0.241199\pi$
$877$	39.1615	+	3.42618i	1.32239	+	0.115694i	0.596003	+	0.802982i	$0.296755\pi$
$878$	58.6873	+	5.13448i	1.98060	+	0.173280i
$879$	−1.47109	+	26.8866i	−0.0496186	+	0.906863i
$880$	15.2582	−	2.98024i	0.514353	−	0.100464i
$881$	−34.0163	+	19.6393i	−1.14604	+	0.661666i	−0.947919	−	0.318512i	$-0.896817\pi$
$881$	−34.0163	+	19.6393i	−1.14604	+	0.661666i	−0.198120	+	0.980178i	$0.563484\pi$
$882$	−27.6254	−	24.2385i	−0.930197	−	0.816151i
$883$	−4.64284	−	17.3273i	−0.156244	−	0.583111i	−0.998996	−	0.0448081i	$-0.985732\pi$
$883$	−4.64284	−	17.3273i	−0.156244	−	0.583111i	0.842752	−	0.538303i	$-0.180934\pi$
$884$	9.08751	−	51.5378i	0.305646	−	1.73340i
$885$	−4.03568	+	13.1346i	−0.135658	+	0.441515i
$886$	−30.7381	−	11.1878i	−1.03267	−	0.375860i
$887$	−14.2556	−	9.98188i	−0.478656	−	0.335159i	0.309222	−	0.950990i	$-0.399931\pi$
$887$	−14.2556	−	9.98188i	−0.478656	−	0.335159i	−0.787878	+	0.615831i	$0.788820\pi$
$888$	−12.7720	−	20.5446i	−0.428602	−	0.689430i
$889$	3.63125	−	4.32756i	0.121788	−	0.145142i
$890$	25.1123	+	34.4983i	0.841766	+	1.15639i
$891$	2.30566	−	3.61538i	0.0772425	−	0.121120i
$892$	−90.0092	−	90.0092i	−3.01373	−	3.01373i
$893$	−2.40537	−	27.4935i	−0.0804927	−	0.920036i
$894$	−16.8836	+	72.3711i	−0.564673	+	2.42045i
$895$	−14.8142	+	0.272007i	−0.495183	+	0.00909219i
$896$	18.9021	−	51.9330i	0.631474	−	1.73496i
$897$	1.91630	+	0.273814i	0.0639833	+	0.00914239i
$898$	−47.3215	−	67.5821i	−1.57914	−	2.25524i
$899$	−14.6687	+	25.4069i	−0.489227	+	0.847367i
$900$	−78.3045	+	22.2173i	−2.61015	+	0.740578i
$901$	−0.673386	−	1.16634i	−0.0224337	−	0.0388564i
$902$	−4.26306	+	9.14216i	−0.141944	+	0.304401i
$903$	−2.16936	−	2.42050i	−0.0721919	−	0.0805490i
$904$	13.0868	+	15.5963i	0.435261	+	0.518724i
$905$	10.0783	+	16.7387i	0.335014	+	0.556415i
$906$	2.77166	−	4.24656i	0.0920821	−	0.141083i
$907$	−17.8896	−	8.34207i	−0.594015	−	0.276994i	0.102273	−	0.994756i	$-0.467389\pi$
$907$	−17.8896	−	8.34207i	−0.594015	−	0.276994i	−0.696288	+	0.717763i	$0.745166\pi$
$908$	−28.1141	+	104.923i	−0.932999	+	3.48200i
$909$	10.3190	−	14.0663i	0.342258	−	0.466549i
$910$	−26.6368	+	2.82404i	−0.883002	+	0.0936161i
$911$	29.7171	+	5.23993i	0.984571	+	0.173606i	0.642681	−	0.766134i	$-0.277822\pi$
$911$	29.7171	+	5.23993i	0.984571	+	0.173606i	0.341890	+	0.939740i	$0.388933\pi$
$912$	−53.4443	+	21.4501i	−1.76972	+	0.710282i
$913$	−1.25794	+	0.586586i	−0.0416317	+	0.0194132i
$914$	−19.6914	−	111.676i	−0.651334	−	3.69390i
$915$	35.3507	+	4.39056i	1.16866	+	0.145148i
$916$	91.7178	+	76.9604i	3.03044	+	2.54284i
$917$	3.44178	−	3.44178i	0.113658	−	0.113658i
$918$	−3.76806	+	49.0221i	−0.124365	+	1.61797i
$919$		−	5.90514i		−	0.194793i	−0.995246	−	0.0973964i	$-0.968949\pi$
$919$		−	5.90514i		−	0.194793i	0.995246	−	0.0973964i	$-0.0310515\pi$
$920$	−5.51731	−	6.33534i	−0.181900	−	0.208870i
$921$	−5.29015	−	17.4467i	−0.174316	−	0.574889i
$922$	26.9715	−	38.5192i	0.888258	−	1.26856i
$923$	18.7320	+	40.1708i	0.616570	+	1.32224i
$924$	−7.03602	+	0.847491i	−0.231468	+	0.0278804i
$925$	7.14820	−	2.19959i	0.235031	−	0.0723222i
$926$	38.9006	+	22.4592i	1.27835	+	0.738057i
$927$	−0.296009	+	13.4201i	−0.00972221	+	0.440773i
$928$	−114.248	−	30.6126i	−3.75036	−	1.00491i
$929$	−6.36097	+	2.31520i	−0.208697	+	0.0759593i	−0.444253	−	0.895901i	$-0.646531\pi$
$929$	−6.36097	+	2.31520i	−0.208697	+	0.0759593i	0.235557	+	0.971861i	$0.424309\pi$
$930$	−52.5387	+	16.9899i	−1.72281	+	0.557121i
$931$	7.84617	−	6.58371i	0.257148	−	0.215773i
$932$	8.83124	−	100.942i	0.289277	−	3.30645i
$933$	5.29211	+	1.73298i	0.173256	+	0.0567352i
$934$	−3.70965	−	10.1922i	−0.121383	−	0.333498i
$935$	3.38069	+	1.50151i	0.110560	+	0.0491046i
$936$	74.6914	+	21.7898i	2.44136	+	0.712220i
$937$	6.08835	−	1.63137i	0.198898	−	0.0532945i	−0.157995	−	0.987440i	$-0.550503\pi$
$937$	6.08835	−	1.63137i	0.198898	−	0.0532945i	0.356892	+	0.934145i	$0.383836\pi$
$938$	46.6560	−	32.6689i	1.52337	−	1.06668i
$939$	−5.03711	−	41.8190i	−0.164380	−	1.36471i
$940$	141.244	−	40.6396i	4.60687	−	1.32552i
$941$	26.7793	−	4.72192i	0.872981	−	0.153930i	0.280831	−	0.959757i	$-0.409390\pi$
$941$	26.7793	−	4.72192i	0.872981	−	0.153930i	0.592151	+	0.805827i	$0.298279\pi$
$942$	71.6575	+	38.3126i	2.33473	+	1.24829i
$943$	3.11417	−	0.272455i	0.101411	−	0.00887234i
$944$	−51.7720			−1.68504
$945$	18.0090	−	3.71523i	0.585832	−	0.120856i
$946$	1.53958			0.0500560
$947$	48.0728	−	4.20583i	1.56216	−	0.136671i	0.726982	−	0.686656i	$-0.240922\pi$
$947$	48.0728	−	4.20583i	1.56216	−	0.136671i	0.835174	+	0.549985i	$0.185367\pi$
$948$	1.36180	+	41.7499i	0.0442291	+	1.35597i
$949$	21.9174	−	3.86463i	0.711469	−	0.125451i
$950$	−3.83930	−	30.8070i	−0.124563	−	0.999512i
$951$	33.0815	+	14.1322i	1.07274	+	0.458267i
$952$	42.0300	−	29.4297i	1.36220	−	0.953822i
$953$	−18.9362	+	5.07394i	−0.613404	+	0.164361i	−0.552128	−	0.833760i	$-0.686184\pi$
$953$	−18.9362	+	5.07394i	−0.613404	+	0.164361i	−0.0612767	+	0.998121i	$0.519517\pi$
$954$	2.90279	−	1.27644i	0.0939814	−	0.0413262i
$955$	16.2021	+	42.0939i	0.524287	+	1.36213i
$956$	−36.2153	−	99.5008i	−1.17129	−	3.21809i
$957$	0.951709	+	4.52863i	0.0307644	+	0.146390i
$958$	0.336795	−	3.84959i	0.0108814	−	0.124375i
$959$	−2.51823	+	2.11305i	−0.0813180	+	0.0682339i
$960$	−59.5551	−	91.9874i	−1.92213	−	2.96888i
$961$	3.41043	−	1.24130i	0.110014	−	0.0400418i
$962$	−10.9362	−	2.93036i	−0.352599	−	0.0944785i
$963$	−0.787615	−	2.32205i	−0.0253805	−	0.0748269i
$964$	−23.1268	−	13.3523i	−0.744865	−	0.430048i
$965$	−37.7235	+	18.4413i	−1.21436	+	0.593646i
$966$	1.80336	+	2.40462i	0.0580220	+	0.0773674i
$967$	−1.83617	−	3.93769i	−0.0590474	−	0.126628i	0.874570	−	0.484900i	$-0.161144\pi$
$967$	−1.83617	−	3.93769i	−0.0590474	−	0.126628i	−0.933617	+	0.358272i	$0.883366\pi$
$968$	−57.6964	+	82.3990i	−1.85443	+	2.64841i
$969$	−13.3442	−	3.11310i	−0.428678	−	0.100007i
$970$	34.7912	−	30.2989i	1.11708	−	0.972840i
$971$		−	17.3753i		−	0.557601i	−0.960349	−	0.278800i	$-0.910063\pi$
$971$		−	17.3753i		−	0.557601i	0.960349	−	0.278800i	$-0.0899367\pi$
$972$	−83.1291	−	15.6457i	−2.66637	−	0.501837i
$973$	−17.2740	+	17.2740i	−0.553779	+	0.553779i
$974$	17.5070	+	14.6901i	0.560960	+	0.470701i
$975$	−12.3990	+	20.6126i	−0.397086	+	0.660132i
$976$	23.3068	+	132.179i	0.746031	+	4.23095i
$977$	21.9259	−	10.2242i	0.701470	−	0.327101i	−0.0389538	−	0.999241i	$-0.512403\pi$
$977$	21.9259	−	10.2242i	0.701470	−	0.327101i	0.740424	+	0.672140i	$0.234625\pi$
$978$	−2.33512	+	16.3424i	−0.0746690	+	0.522573i
$979$	3.28563	+	0.579345i	0.105009	+	0.0185159i
$980$	42.4209	+	34.2882i	1.35508	+	1.09530i
$981$	−22.7599	−	11.2306i	−0.726667	−	0.358566i
$982$	18.9055	−	70.5563i	0.603299	−	2.25154i
$983$	22.0159	+	10.2662i	0.702199	+	0.327441i	0.740717	−	0.671817i	$-0.234486\pi$
$983$	22.0159	+	10.2662i	0.702199	+	0.327441i	−0.0385180	+	0.999258i	$0.512264\pi$
$984$	125.460	+	6.86447i	3.99951	+	0.218831i
$985$	−10.8744	−	2.70083i	−0.346488	−	0.0860557i
$986$	−34.1063	−	40.6463i	−1.08617	−	1.29444i
$987$	−32.4935	+	6.82862i	−1.03428	+	0.217357i
$988$	−14.5131	+	31.1234i	−0.461723	+	0.990168i
$989$	−0.238560	−	0.413197i	−0.00758575	−	0.0131389i
$990$	−4.38273	+	7.52676i	−0.139292	+	0.239216i
$991$	−18.0498	+	31.2632i	−0.573372	+	0.993110i	0.422844	+	0.906202i	$0.361032\pi$
$991$	−18.0498	+	31.2632i	−0.573372	+	0.993110i	−0.996216	+	0.0869073i	$0.972302\pi$
$992$	−63.2936	−	90.3927i	−2.00957	−	2.86997i
$993$	−3.84369	−	9.57682i	−0.121976	−	0.303911i
$994$	−23.5387	+	64.6720i	−0.746602	+	2.05127i
$995$	0.684258	+	37.2664i	0.0216924	+	1.18142i
$996$	19.9817	+	18.7194i	0.633145	+	0.593146i
$997$	1.73962	+	19.8840i	0.0550944	+	0.629732i	0.972673	+	0.232178i	$0.0745853\pi$
$997$	1.73962	+	19.8840i	0.0550944	+	0.629732i	−0.917579	+	0.397554i	$0.869859\pi$
$998$	−21.5721	−	21.5721i	−0.682854	−	0.682854i
$999$	7.66811	+	1.26881i	0.242608	+	0.0401434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.92.1	yes	192
3.2	odd	2		405.2.r.a.197.16		192
5.2	odd	4		675.2.ba.b.443.1		192
5.3	odd	4	inner	135.2.q.a.38.16	yes	192
5.4	even	2		675.2.ba.b.632.16		192
15.8	even	4		405.2.r.a.278.1		192
27.5	odd	18	inner	135.2.q.a.32.16	✓	192
27.22	even	9		405.2.r.a.287.1		192
135.32	even	36		675.2.ba.b.518.16		192
135.59	odd	18		675.2.ba.b.32.1		192
135.103	odd	36		405.2.r.a.368.16		192
135.113	even	36	inner	135.2.q.a.113.1	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.16	✓	192	27.5	odd	18	inner
135.2.q.a.38.16	yes	192	5.3	odd	4	inner
135.2.q.a.92.1	yes	192	1.1	even	1	trivial
135.2.q.a.113.1	yes	192	135.113	even	36	inner
405.2.r.a.197.16		192	3.2	odd	2
405.2.r.a.278.1		192	15.8	even	4
405.2.r.a.287.1		192	27.22	even	9
405.2.r.a.368.16		192	135.103	odd	36
675.2.ba.b.32.1		192	135.59	odd	18
675.2.ba.b.443.1		192	5.2	odd	4
675.2.ba.b.518.16		192	135.32	even	36
675.2.ba.b.632.16		192	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.71476 + 0.237511i) q^{2} +(1.47097 - 0.914466i) q^{3} +(5.34392 - 0.942278i) q^{4} +(1.08230 - 1.95669i) q^{5} +(-3.77614 + 2.83193i) q^{6} +(-1.29639 + 0.907744i) q^{7} +(-9.01913 + 2.41667i) q^{8} +(1.32750 - 2.69030i) q^{9} +(-2.47344 + 5.56901i) q^{10} +(0.162954 + 0.447712i) q^{11} +(6.99907 - 6.27290i) q^{12} +(0.242081 - 2.76700i) q^{13} +(3.30380 - 2.77222i) q^{14} +(-0.197304 - 3.86795i) q^{15} +(13.7126 - 4.99098i) q^{16} +(3.35386 + 0.898665i) q^{17} +(-2.96488 + 7.61884i) q^{18} +(-1.97319 - 1.13922i) q^{19} +(3.93995 - 11.4762i) q^{20} +(-1.07685 + 2.52077i) q^{21} +(-0.548719 - 1.17673i) q^{22} +(-0.230790 + 0.329603i) q^{23} +(-11.0569 + 11.8025i) q^{24} +(-2.65727 - 4.23543i) q^{25} +7.56924i q^{26} +(-0.507474 - 5.17131i) q^{27} +(-6.07248 + 6.07248i) q^{28} +(4.29568 + 3.60450i) q^{29} +(1.45432 + 10.4537i) q^{30} +(0.908475 + 5.15222i) q^{31} +(-19.1162 + 8.91403i) q^{32} +(0.649118 + 0.509556i) q^{33} +(-9.31839 - 1.64308i) q^{34} +(0.373094 + 3.51909i) q^{35} +(4.55906 - 15.6276i) q^{36} +(-0.387140 + 1.44483i) q^{37} +(5.62733 + 2.62407i) q^{38} +(-2.17423 - 4.29154i) q^{39} +(-5.03269 + 20.2632i) q^{40} +(-4.99389 - 5.95149i) q^{41} +(2.32469 - 7.09907i) q^{42} +(-0.501128 + 1.07467i) q^{43} +(1.29268 + 2.23899i) q^{44} +(-3.82734 - 5.50922i) q^{45} +(0.548257 - 0.949609i) q^{46} +(6.94767 + 9.92230i) q^{47} +(15.6068 - 19.8813i) q^{48} +(-1.53751 + 4.22426i) q^{49} +(8.21984 + 10.8671i) q^{50} +(5.75523 - 1.74508i) q^{51} +(-1.31362 - 15.0147i) q^{52} +(-0.274270 - 0.274270i) q^{53} +(2.60592 + 13.9184i) q^{54} +(1.05240 + 0.165706i) q^{55} +(9.49862 - 11.3200i) q^{56} +(-3.94428 + 0.128655i) q^{57} +(-12.5179 - 8.76510i) q^{58} +(-3.33385 - 1.21342i) q^{59} +(-4.69906 - 20.4841i) q^{60} +(-1.59716 + 9.05792i) q^{61} +(-3.69001 - 13.7713i) q^{62} +(0.721141 + 4.69272i) q^{63} +(24.5036 - 14.1471i) q^{64} +(-5.15215 - 3.46838i) q^{65} +(-1.88323 - 1.22915i) q^{66} +(13.1561 + 1.15101i) q^{67} +(18.7696 + 1.64212i) q^{68} +(-0.0380751 + 0.695886i) q^{69} +(-1.84869 - 9.46488i) q^{70} +(-13.8198 + 7.97886i) q^{71} +(-5.47136 + 27.4723i) q^{72} +(2.07381 + 7.73957i) q^{73} +(0.707832 - 4.01431i) q^{74} +(-7.78193 - 3.80021i) q^{75} +(-11.6180 - 4.22862i) q^{76} +(-0.617661 - 0.432491i) q^{77} +(6.92182 + 11.1341i) q^{78} +(-2.85683 + 3.40464i) q^{79} +(5.07529 - 32.2331i) q^{80} +(-5.47547 - 7.14278i) q^{81} +(14.9708 + 14.9708i) q^{82} +(0.253902 + 2.90211i) q^{83} +(-3.37935 + 14.4855i) q^{84} +(5.38828 - 5.58985i) q^{85} +(1.10520 - 3.03651i) q^{86} +(9.61501 + 1.37386i) q^{87} +(-2.55168 - 3.64417i) q^{88} +(3.50126 - 6.06435i) q^{89} +(11.6988 + 14.0472i) q^{90} +(2.19789 + 3.80686i) q^{91} +(-0.922748 + 1.97884i) q^{92} +(6.04787 + 6.74799i) q^{93} +(-21.2179 - 25.2866i) q^{94} +(-4.36468 + 2.62795i) q^{95} +(-19.9678 + 30.5934i) q^{96} +(-6.86175 - 3.19969i) q^{97} +(3.17066 - 11.8331i) q^{98} +(1.42080 + 0.155944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more