LMFDB - Embedded newform 135.2.q.a.32.16

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			32.16
Character	$\chi$	$=$	135.32
Dual form			135.2.q.a.38.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.237511 - 2.71476i) q^{2} +(0.914466 - 1.47097i) q^{3} +(-5.34392 - 0.942278i) q^{4} +(0.428650 + 2.19460i) q^{5} +(-3.77614 - 2.83193i) q^{6} +(0.907744 - 1.29639i) q^{7} +(-2.41667 + 9.01913i) q^{8} +(-1.32750 - 2.69030i) q^{9} +(6.05963 - 0.642443i) q^{10} +(0.162954 - 0.447712i) q^{11} +(-6.27290 + 6.99907i) q^{12} +(2.76700 - 0.242081i) q^{13} +(-3.30380 - 2.77222i) q^{14} +(3.62017 + 1.37635i) q^{15} +(13.7126 + 4.99098i) q^{16} +(0.898665 + 3.35386i) q^{17} +(-7.61884 + 2.96488i) q^{18} +(1.97319 - 1.13922i) q^{19} +(-0.222753 - 12.1317i) q^{20} +(-1.07685 - 2.52077i) q^{21} +(-1.17673 - 0.548719i) q^{22} +(-0.329603 + 0.230790i) q^{23} +(11.0569 + 11.8025i) q^{24} +(-4.63252 + 1.88143i) q^{25} -7.56924i q^{26} +(-5.17131 - 0.507474i) q^{27} +(-6.07248 + 6.07248i) q^{28} +(-4.29568 + 3.60450i) q^{29} +(4.59631 - 9.50102i) q^{30} +(0.908475 - 5.15222i) q^{31} +(8.91403 - 19.1162i) q^{32} +(-0.509556 - 0.649118i) q^{33} +(9.31839 - 1.64308i) q^{34} +(3.23417 + 1.43643i) q^{35} +(4.55906 + 15.6276i) q^{36} +(1.44483 - 0.387140i) q^{37} +(-2.62407 - 5.62733i) q^{38} +(2.17423 - 4.29154i) q^{39} +(-20.8293 - 1.43756i) q^{40} +(-4.99389 + 5.95149i) q^{41} +(-7.09907 + 2.32469i) q^{42} +(-1.07467 + 0.501128i) q^{43} +(-1.29268 + 2.23899i) q^{44} +(5.33510 - 4.06654i) q^{45} +(0.548257 + 0.949609i) q^{46} +(9.92230 + 6.94767i) q^{47} +(19.8813 - 15.6068i) q^{48} +(1.53751 + 4.22426i) q^{49} +(4.00736 + 13.0231i) q^{50} +(5.75523 + 1.74508i) q^{51} +(-15.0147 - 1.31362i) 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} +(0.128655 - 3.94428i) q^{57} +(8.76510 + 12.5179i) q^{58} +(3.33385 - 1.21342i) q^{59} +(-18.0490 - 10.7663i) q^{60} +(-1.59716 - 9.05792i) q^{61} +(-13.7713 - 3.69001i) q^{62} +(-4.69272 - 0.721141i) q^{63} +(-24.5036 - 14.1471i) q^{64} +(1.71734 + 5.96868i) q^{65} +(-1.88323 + 1.22915i) q^{66} +(1.15101 + 13.1561i) q^{67} +(-1.64212 - 18.7696i) q^{68} +(0.0380751 + 0.695886i) q^{69} +(4.66773 - 8.43883i) q^{70} +(-13.8198 - 7.97886i) q^{71} +(27.4723 - 5.47136i) q^{72} +(-7.73957 - 2.07381i) q^{73} +(-0.707832 - 4.01431i) q^{74} +(-1.46875 + 8.53480i) q^{75} +(-11.6180 + 4.22862i) q^{76} +(-0.432491 - 0.617661i) q^{77} +(-11.1341 - 6.92182i) 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} +(-2.90211 - 0.253902i) q^{83} +(3.37935 + 14.4855i) q^{84} +(-6.97517 + 3.40984i) q^{85} +(1.10520 + 3.03651i) q^{86} +(1.37386 + 9.61501i) q^{87} +(3.64417 + 2.55168i) q^{88} +(-3.50126 - 6.06435i) q^{89} +(-9.77254 - 15.4494i) q^{90} +(2.19789 - 3.80686i) q^{91} +(1.97884 - 0.922748i) q^{92} +(-6.74799 - 6.04787i) q^{93} +(21.2179 - 25.2866i) q^{94} +(3.34594 + 3.84203i) q^{95} +(-19.9678 - 30.5934i) q^{96} +(-3.19969 - 6.86175i) q^{97} +(11.8331 - 3.17066i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.237511	−	2.71476i	0.167946	−	1.91963i	−0.182786	−	0.983153i	$-0.558512\pi$
$2$	0.237511	−	2.71476i	0.167946	−	1.91963i	0.350732	−	0.936476i	$-0.385933\pi$
$3$	0.914466	−	1.47097i	0.527967	−	0.849265i
$3$	0.914466	−	1.47097i	0.527967	−	0.849265i
$4$	−5.34392	−	0.942278i	−2.67196	−	0.471139i
$5$	0.428650	+	2.19460i	0.191698	+	0.981454i
$5$	0.428650	+	2.19460i	0.191698	+	0.981454i
$6$	−3.77614	−	2.83193i	−1.54160	−	1.15613i
$7$	0.907744	−	1.29639i	0.343095	−	0.489990i	−0.610109	−	0.792317i	$-0.708874\pi$
$7$	0.907744	−	1.29639i	0.343095	−	0.489990i	0.953204	+	0.302327i	$0.0977634\pi$
$8$	−2.41667	+	9.01913i	−0.854422	+	3.18874i
$9$	−1.32750	−	2.69030i	−0.442501	−	0.896768i
$10$	6.05963	−	0.642443i	1.91622	−	0.203158i
$11$	0.162954	−	0.447712i	0.0491325	−	0.134990i	−0.912699	−	0.408632i	$-0.866006\pi$
$11$	0.162954	−	0.447712i	0.0491325	−	0.134990i	0.961832	+	0.273642i	$0.0882282\pi$
$12$	−6.27290	+	6.99907i	−1.81083	+	2.02046i
$13$	2.76700	−	0.242081i	0.767427	−	0.0671411i	0.303282	−	0.952901i	$-0.401917\pi$
$13$	2.76700	−	0.242081i	0.767427	−	0.0671411i	0.464144	+	0.885760i	$0.346362\pi$
$14$	−3.30380	−	2.77222i	−0.882978	−	0.740907i
$15$	3.62017	+	1.37635i	0.934725	+	0.355373i
$16$	13.7126	+	4.99098i	3.42815	+	1.24775i
$17$	0.898665	+	3.35386i	0.217958	+	0.813431i	0.985104	+	0.171959i	$0.0550095\pi$
$17$	0.898665	+	3.35386i	0.217958	+	0.813431i	−0.767146	+	0.641473i	$0.778324\pi$
$18$	−7.61884	+	2.96488i	−1.79578	+	0.698830i
$19$	1.97319	−	1.13922i	0.452681	−	0.261356i	−0.256281	−	0.966602i	$-0.582497\pi$
$19$	1.97319	−	1.13922i	0.452681	−	0.261356i	0.708962	+	0.705247i	$0.249164\pi$
$20$	−0.222753	−	12.1317i	−0.0498090	−	2.71272i
$21$	−1.07685	−	2.52077i	−0.234989	−	0.550077i
$22$	−1.17673	−	0.548719i	−0.250880	−	0.116987i
$23$	−0.329603	+	0.230790i	−0.0687269	+	0.0481231i	−0.607435	−	0.794369i	$-0.707801\pi$
$23$	−0.329603	+	0.230790i	−0.0687269	+	0.0481231i	0.538708	+	0.842493i	$0.318913\pi$
$24$	11.0569	+	11.8025i	2.25698	+	2.40918i
$25$	−4.63252	+	1.88143i	−0.926504	+	0.376286i
$26$		−	7.56924i		−	1.48445i
$27$	−5.17131	−	0.507474i	−0.995220	−	0.0976633i
$28$	−6.07248	+	6.07248i	−1.14759	+	1.14759i
$29$	−4.29568	+	3.60450i	−0.797687	+	0.669339i	−0.947635	−	0.319355i	$-0.896534\pi$
$29$	−4.29568	+	3.60450i	−0.797687	+	0.669339i	0.149948	+	0.988694i	$0.452089\pi$
$30$	4.59631	−	9.50102i	0.839167	−	1.73464i
$31$	0.908475	−	5.15222i	0.163167	−	0.925366i	−0.787767	−	0.615973i	$-0.788763\pi$
$31$	0.908475	−	5.15222i	0.163167	−	0.925366i	0.950934	−	0.309393i	$-0.100126\pi$
$32$	8.91403	−	19.1162i	1.57579	−	3.37930i
$33$	−0.509556	−	0.649118i	−0.0887022	−	0.112997i
$34$	9.31839	−	1.64308i	1.59809	−	0.281787i
$35$	3.23417	+	1.43643i	0.546674	+	0.242802i
$36$	4.55906	+	15.6276i	0.759844	+	2.60461i
$37$	1.44483	−	0.387140i	0.237528	−	0.0636454i	−0.138091	−	0.990420i	$-0.544097\pi$
$37$	1.44483	−	0.387140i	0.237528	−	0.0636454i	0.375619	+	0.926774i	$0.377430\pi$
$38$	−2.62407	−	5.62733i	−0.425680	−	0.912873i
$39$	2.17423	−	4.29154i	0.348156	−	0.687197i
$40$	−20.8293	−	1.43756i	−3.29340	−	0.227299i
$41$	−4.99389	+	5.95149i	−0.779915	+	0.929467i	−0.998930	−	0.0462550i	$-0.985271\pi$
$41$	−4.99389	+	5.95149i	−0.779915	+	0.929467i	0.219015	+	0.975722i	$0.429716\pi$
$42$	−7.09907	+	2.32469i	−1.09541	+	0.358708i
$43$	−1.07467	+	0.501128i	−0.163886	+	0.0764213i	−0.502830	−	0.864385i	$-0.667708\pi$
$43$	−1.07467	+	0.501128i	−0.163886	+	0.0764213i	0.338944	+	0.940806i	$0.389930\pi$
$44$	−1.29268	+	2.23899i	−0.194879	+	0.337541i
$45$	5.33510	−	4.06654i	0.795310	−	0.606203i
$46$	0.548257	+	0.949609i	0.0808361	+	0.140012i
$47$	9.92230	+	6.94767i	1.44732	+	1.01342i	0.992422	+	0.122876i	$0.0392117\pi$
$47$	9.92230	+	6.94767i	1.44732	+	1.01342i	0.454894	+	0.890546i	$0.349677\pi$
$48$	19.8813	−	15.6068i	2.86962	−	2.25264i
$49$	1.53751	+	4.22426i	0.219644	+	0.603466i
$50$	4.00736	+	13.0231i	0.566727	+	1.84174i
$51$	5.75523	+	1.74508i	0.805893	+	0.244361i
$52$	−15.0147	−	1.31362i	−2.08217	−	0.182166i
$53$	0.274270	+	0.274270i	0.0376738	+	0.0376738i	0.725693	−	0.688019i	$-0.241519\pi$
$53$	0.274270	+	0.274270i	0.0376738	+	0.0376738i	−0.688019	+	0.725693i	$0.741519\pi$
$54$	−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
$57$	0.128655	−	3.94428i	0.0170407	−	0.522433i
$58$	8.76510	+	12.5179i	1.15091	+	1.64368i
$59$	3.33385	−	1.21342i	0.434031	−	0.157974i	−0.115759	−	0.993277i	$-0.536930\pi$
$59$	3.33385	−	1.21342i	0.434031	−	0.157974i	0.549790	+	0.835303i	$0.314708\pi$
$60$	−18.0490	−	10.7663i	−2.33012	−	1.38993i
$61$	−1.59716	−	9.05792i	−0.204495	−	1.15975i	−0.898233	−	0.439520i	$-0.855149\pi$
$61$	−1.59716	−	9.05792i	−0.204495	−	1.15975i	0.693738	−	0.720228i	$-0.255963\pi$
$62$	−13.7713	−	3.69001i	−1.74896	−	0.468631i
$63$	−4.69272	−	0.721141i	−0.591228	−	0.0908552i
$64$	−24.5036	−	14.1471i	−3.06294	−	1.76839i
$65$	1.71734	+	5.96868i	0.213010	+	0.740323i
$66$	−1.88323	+	1.22915i	−0.231809	+	0.151298i
$67$	1.15101	+	13.1561i	0.140618	+	1.60727i	0.659012	+	0.752132i	$0.270975\pi$
$67$	1.15101	+	13.1561i	0.140618	+	1.60727i	−0.518394	+	0.855142i	$0.673470\pi$
$68$	−1.64212	−	18.7696i	−0.199137	−	2.27614i
$69$	0.0380751	+	0.695886i	0.00458370	+	0.0837748i
$70$	4.66773	−	8.43883i	0.557901	−	1.00863i
$71$	−13.8198	−	7.97886i	−1.64011	−	0.946916i	−0.980794	−	0.195047i	$-0.937514\pi$
$71$	−13.8198	−	7.97886i	−1.64011	−	0.946916i	−0.659313	−	0.751869i	$-0.729153\pi$
$72$	27.4723	−	5.47136i	3.23765	−	0.644806i
$73$	−7.73957	−	2.07381i	−0.905849	−	0.242721i	−0.224322	−	0.974515i	$-0.572017\pi$
$73$	−7.73957	−	2.07381i	−0.905849	−	0.242721i	−0.681526	+	0.731794i	$0.738683\pi$
$74$	−0.707832	−	4.01431i	−0.0822838	−	0.466655i
$75$	−1.46875	+	8.53480i	−0.169597	+	0.985513i
$76$	−11.6180	+	4.22862i	−1.33268	+	0.485056i
$77$	−0.432491	−	0.617661i	−0.0492869	−	0.0703890i
$78$	−11.1341	−	6.92182i	−1.26069	−	0.783741i
$79$	2.85683	+	3.40464i	0.321418	+	0.383051i	0.902425	−	0.430848i	$-0.141785\pi$
$79$	2.85683	+	3.40464i	0.321418	+	0.383051i	−0.581006	+	0.813899i	$0.697341\pi$
$80$	−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
$83$	−2.90211	−	0.253902i	−0.318548	−	0.0278694i	−0.0732395	−	0.997314i	$-0.523334\pi$
$83$	−2.90211	−	0.253902i	−0.318548	−	0.0278694i	−0.245309	+	0.969445i	$0.578889\pi$
$84$	3.37935	+	14.4855i	0.368718	+	1.58050i
$85$	−6.97517	+	3.40984i	−0.756563	+	0.369849i
$86$	1.10520	+	3.03651i	0.119177	+	0.327435i
$87$	1.37386	+	9.61501i	0.147293	+	1.03084i
$88$	3.64417	+	2.55168i	0.388470	+	0.272010i
$89$	−3.50126	−	6.06435i	−0.371132	−	0.642820i	0.618608	−	0.785700i	$-0.287697\pi$
$89$	−3.50126	−	6.06435i	−0.371132	−	0.642820i	−0.989740	+	0.142880i	$0.954364\pi$
$90$	−9.77254	−	15.4494i	−1.03012	−	1.62851i
$91$	2.19789	−	3.80686i	0.230402	−	0.399068i
$92$	1.97884	−	0.922748i	0.206308	−	0.0962031i
$93$	−6.74799	−	6.04787i	−0.699734	−	0.627135i
$94$	21.2179	−	25.2866i	2.18846	−	2.60811i
$95$	3.34594	+	3.84203i	0.343287	+	0.394184i
$96$	−19.9678	−	30.5934i	−2.03795	−	3.12242i
$97$	−3.19969	−	6.86175i	−0.324879	−	0.696705i	0.674247	−	0.738506i	$-0.264468\pi$
$97$	−3.19969	−	6.86175i	−0.324879	−	0.696705i	−0.999126	+	0.0418007i	$0.986691\pi$
$98$	11.8331	−	3.17066i	1.19532	−	0.320285i
$99$	−1.42080	+	0.155944i	−0.142796	+	0.0156730i
$100$	26.5286	−	5.68909i	2.65286	−	0.568909i
$101$	5.72678	−	1.00979i	0.569836	−	0.100477i	0.118696	−	0.992931i	$-0.462129\pi$
$101$	5.72678	−	1.00979i	0.569836	−	0.100477i	0.451140	+	0.892453i	$0.351017\pi$
$102$	6.10443	−	15.2096i	0.604428	−	1.50598i
$103$	−1.89098	+	4.05522i	−0.186324	+	0.399573i	−0.977175	−	0.212436i	$-0.931860\pi$
$103$	−1.89098	+	4.05522i	−0.186324	+	0.399573i	0.790851	+	0.612009i	$0.209638\pi$
$104$	−4.50356	+	25.5409i	−0.441610	+	2.50450i
$105$	5.07049	−	3.44379i	0.494829	−	0.336079i
$106$	0.809720	−	0.679435i	0.0786469	−	0.0659926i
$107$	−0.577939	+	0.577939i	−0.0558714	+	0.0558714i	−0.734490	−	0.678619i	$-0.762579\pi$
$107$	−0.577939	+	0.577939i	−0.0558714	+	0.0558714i	0.678619	+	0.734490i	$0.262579\pi$
$108$	27.1569	+	7.58471i	2.61317	+	0.729839i
$109$		−	8.45996i		−	0.810317i	−0.914246	−	0.405159i	$-0.867216\pi$
$109$		−	8.45996i		−	0.810317i	0.914246	−	0.405159i	$-0.132784\pi$
$110$	0.699811	−	2.81766i	0.0667243	−	0.268653i
$111$	0.751773	−	2.47932i	0.0713552	−	0.235327i
$112$	18.9178	−	13.2464i	1.78757	−	1.25167i
$113$	1.97616	+	0.921497i	0.185901	+	0.0866871i	0.513340	−	0.858185i	$-0.328408\pi$
$113$	1.97616	+	0.921497i	0.185901	+	0.0866871i	−0.327439	+	0.944872i	$0.606186\pi$
$114$	−10.6772	−	1.28608i	−1.00002	−	0.120452i
$115$	−0.647776	−	0.624417i	−0.0604054	−	0.0582272i
$116$	26.3522	−	15.2145i	2.44674	−	1.41263i
$117$	−4.32447	−	7.12270i	−0.399797	−	0.658494i
$118$	−2.50233	−	9.33883i	−0.230358	−	0.859709i
$119$	5.16368	+	1.87943i	0.473354	+	0.172287i
$120$	−21.1623	+	29.3246i	−1.93184	+	2.67696i
$121$	8.25260	+	6.92475i	0.750236	+	0.629523i
$122$	−24.9695	+	2.18454i	−2.26063	+	0.197779i
$123$	4.18772	+	12.7883i	0.377594	+	1.15308i
$124$	−9.70964	+	26.6770i	−0.871952	+	2.39567i
$125$	−6.11471	−	9.36004i	−0.546916	−	0.837187i
$126$	−3.07230	+	12.5684i	−0.273702	+	1.11968i
$127$	0.923874	−	3.44795i	0.0819806	−	0.305956i	−0.912745	−	0.408530i	$-0.866041\pi$
$127$	0.923874	−	3.44795i	0.0819806	−	0.305956i	0.994725	+	0.102575i	$0.0327081\pi$
$128$	−20.0298	+	28.6056i	−1.77040	+	2.52840i
$129$	−0.245607	+	2.03908i	−0.0216245	+	0.179531i
$130$	16.6114	−	3.24456i	1.45692	−	0.284566i
$131$	−3.02885	−	0.534068i	−0.264632	−	0.0466617i	0.0397579	−	0.999209i	$-0.487341\pi$
$131$	−3.02885	−	0.534068i	−0.264632	−	0.0466617i	−0.304390	+	0.952548i	$0.598452\pi$
$132$	2.11138	+	3.94898i	0.183772	+	0.343715i
$133$	0.314273	−	3.59215i	0.0272509	−	0.311479i
$134$	35.9891			3.10899
$135$	−1.10298	−	11.5665i	−0.0949297	−	0.995484i
$136$	−32.4207			−2.78005
$137$	−0.181036	+	2.06926i	−0.0154670	+	0.176788i	0.984532	+	0.175206i	$0.0560592\pi$
$137$	−0.181036	+	2.06926i	−0.0154670	+	0.176788i	−0.999999	+	0.00158226i	$0.999496\pi$
$138$	1.89821	+	0.0619158i	0.161586	+	0.00527062i
$139$	−15.2015	−	2.68044i	−1.28938	−	0.227352i	−0.513420	−	0.858137i	$-0.671622\pi$
$139$	−15.2015	−	2.68044i	−1.28938	−	0.227352i	−0.775957	+	0.630785i	$0.782733\pi$
$140$	−15.9296	−	10.7237i	−1.34630	−	0.906316i
$141$	19.2934	−	8.24199i	1.62480	−	0.694101i
$142$	−24.9431	+	35.6224i	−2.09318	+	2.98937i
$143$	0.342511	−	1.27827i	0.0286422	−	0.106894i
$144$	−4.77629	−	43.5167i	−0.398024	−	3.62639i
$145$	−9.75177	−	7.88221i	−0.809841	−	0.654582i
$146$	−7.46815	+	20.5186i	−0.618068	+	1.69813i
$147$	7.61976	+	1.60132i	0.628467	+	0.132075i
$148$	−8.08583	+	0.707419i	−0.664651	+	0.0581495i
$149$	−12.0609	−	10.1203i	−0.988065	−	0.829085i	−0.00277827	−	0.999996i	$-0.500884\pi$
$149$	−12.0609	−	10.1203i	−0.988065	−	0.829085i	−0.985286	+	0.170911i	$0.945329\pi$
$150$	22.8211	+	6.01443i	1.86334	+	0.491076i
$151$	−1.00956	−	0.367451i	−0.0821571	−	0.0299027i	0.300615	−	0.953746i	$-0.402808\pi$
$151$	−1.00956	−	0.367451i	−0.0821571	−	0.0299027i	−0.382772	+	0.923843i	$0.625030\pi$
$152$	5.50625	+	20.5496i	0.446616	+	1.66679i
$153$	7.82993	−	6.86995i	0.633012	−	0.555402i
$154$	−1.77953	+	1.02741i	−0.143398	+	0.0827910i
$155$	11.6965	−	0.214762i	0.939483	−	0.0172501i
$156$	−15.6627	+	20.8849i	−1.25402	+	1.67213i
$157$	−15.6022	−	7.27543i	−1.24519	−	0.580643i	−0.315481	−	0.948932i	$-0.602166\pi$
$157$	−15.6022	−	7.27543i	−1.24519	−	0.580643i	−0.929711	+	0.368289i	$0.879944\pi$
$158$	9.92131	−	6.94698i	0.789297	−	0.552672i
$159$	0.654253	−	0.152632i	0.0518856	−	0.0121045i
$160$	45.7734	+	11.3685i	3.61870	+	0.898762i
$161$			0.636793i			0.0501863i
$162$	18.0905	+	16.5611i	1.42132	+	1.30116i
$163$	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
$165$	1.20613	−	1.39651i	0.0938973	−	0.108718i
$166$	−1.37857	+	7.81825i	−0.106998	+	0.606814i
$167$	2.78431	−	5.97097i	0.215456	−	0.462048i	−0.768640	−	0.639681i	$-0.779066\pi$
$167$	2.78431	−	5.97097i	0.215456	−	0.462048i	0.984097	+	0.177634i	$0.0568442\pi$
$168$	25.3376	−	3.62041i	1.95484	−	0.279321i
$169$	−5.20483	+	0.917752i	−0.400372	+	0.0705963i
$170$	7.60024	+	19.7458i	0.582912	+	1.51443i
$171$	−5.68427	−	3.79616i	−0.434687	−	0.290300i
$172$	6.21517	−	1.66535i	0.473902	−	0.126982i
$173$	4.51859	+	9.69016i	0.343542	+	0.736729i	0.999842	−	0.0177714i	$-0.00565711\pi$
$173$	4.51859	+	9.69016i	0.343542	+	0.736729i	−0.656300	+	0.754500i	$0.727879\pi$
$174$	26.4288	−	1.44604i	2.00356	−	0.109624i
$175$	−1.76607	+	7.71342i	−0.133502	+	0.583080i
$176$	4.46905	−	5.32601i	0.336867	−	0.401463i
$177$	1.26379	−	6.01363i	0.0949920	−	0.452012i
$178$	−17.2949	+	8.06473i	−1.29631	+	0.604477i
$179$	3.31311	−	5.73847i	0.247633	−	0.428913i	−0.715235	−	0.698884i	$-0.753681\pi$
$179$	3.31311	−	5.73847i	0.247633	−	0.428913i	0.962869	+	0.269970i	$0.0870139\pi$
$180$	−32.3422	+	16.7041i	−2.41064	+	1.24505i
$181$	−4.36897	−	7.56727i	−0.324743	−	0.562471i	0.656717	−	0.754137i	$-0.271944\pi$
$181$	−4.36897	−	7.56727i	−0.324743	−	0.562471i	−0.981460	+	0.191666i	$0.938611\pi$
$182$	−9.81271	−	6.87094i	−0.727367	−	0.509308i
$183$	−14.7845	−	5.93379i	−1.09290	−	0.438639i
$184$	−1.28499	−	3.53048i	−0.0947306	−	0.260270i
$185$	1.46894	+	3.00487i	0.107999	+	0.220922i
$186$	−18.0213	+	16.8828i	−1.32138	+	1.23790i
$187$	1.64801	+	0.144182i	0.120514	+	0.0105436i
$188$	−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	−0.992826	−	0.119569i	$-0.961849\pi$
$191$	−12.9658	−	15.4521i	−0.938176	−	1.11807i	0.0546500	−	0.998506i	$-0.482596\pi$
$192$	−43.2177	+	23.1069i	−3.11897	+	1.66760i
$193$	10.7709	+	15.3824i	0.775303	+	1.10725i	0.991399	+	0.130875i	$0.0417788\pi$
$193$	10.7709	+	15.3824i	0.775303	+	1.10725i	−0.216096	+	0.976372i	$0.569332\pi$
$194$	−19.3880	+	7.05665i	−1.39198	+	0.506638i
$195$	10.3502	+	2.93199i	0.741193	+	0.209964i
$196$	−4.23588	−	24.0229i	−0.302563	−	1.71592i
$197$	−4.84019	−	1.29693i	−0.344849	−	0.0924021i	0.0822373	−	0.996613i	$-0.473793\pi$
$197$	−4.84019	−	1.29693i	−0.344849	−	0.0924021i	−0.427087	+	0.904211i	$0.640460\pi$
$198$	0.0858949	+	3.89419i	0.00610428	+	0.276748i
$199$	14.4356	+	8.33443i	1.02332	+	0.590812i	0.915063	−	0.403312i	$-0.132141\pi$
$199$	14.4356	+	8.33443i	1.02332	+	0.590812i	0.108253	+	0.994123i	$0.465474\pi$
$200$	−5.77360	−	46.3281i	−0.408255	−	3.27589i
$201$	20.4048	+	10.3377i	1.43924	+	0.729166i
$202$	−1.38116	−	15.7867i	−0.0971779	−	1.11075i
$203$	0.773474	+	8.84085i	0.0542872	+	0.620506i
$204$	−29.1111	−	14.7486i	−2.03819	−	1.03261i
$205$	−15.2018	−	8.40848i	−1.06174	−	0.587274i
$206$	10.5599	+	6.09673i	0.735740	+	0.424779i
$207$	1.05845	+	0.580357i	0.0735670	+	0.0403376i
$208$	39.1510	+	10.4905i	2.71463	+	0.727384i
$209$	−0.188505	−	1.06906i	−0.0130391	−	0.0739486i
$210$	−8.14478	−	14.5831i	−0.562043	−	1.00633i
$211$	9.81899	−	3.57382i	0.675967	−	0.246032i	0.0188522	−	0.999822i	$-0.493999\pi$
$211$	9.81899	−	3.57382i	0.675967	−	0.246032i	0.657115	+	0.753790i	$0.271777\pi$
$212$	−1.20724	−	1.72411i	−0.0829134	−	0.118413i
$213$	−24.3744	+	13.0321i	−1.67010	+	0.892944i
$214$	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
$218$	−22.9668	−	2.00934i	−1.55551	−	0.136089i
$219$	−10.1281	+	9.48825i	−0.684393	+	0.641156i
$220$	−5.46780	−	1.87717i	−0.368639	−	0.126559i
$221$	3.29851	+	9.06258i	0.221882	+	0.609615i
$222$	−6.55222	−	2.62975i	−0.439756	−	0.176498i
$223$	19.2158	+	13.4550i	1.28678	+	0.901015i	0.998403	−	0.0565006i	$-0.0179943\pi$
$223$	19.2158	+	13.4550i	1.28678	+	0.901015i	0.288381	+	0.957516i	$0.406883\pi$
$224$	−16.6904	−	28.9087i	−1.11518	−	1.93154i
$225$	11.2113	+	9.96528i	0.747420	+	0.664352i
$226$	2.97101	−	5.14593i	0.197628	−	0.342302i
$227$	18.1424	−	8.45994i	1.20415	−	0.561506i	0.286191	−	0.958173i	$-0.407611\pi$
$227$	18.1424	−	8.45994i	1.20415	−	0.561506i	0.917963	+	0.396667i	$0.129833\pi$
$228$	−4.40413	+	20.9567i	−0.291671	+	1.38789i
$229$	−14.1827	+	16.9023i	−0.937218	+	1.11693i	0.0557370	+	0.998445i	$0.482249\pi$
$229$	−14.1827	+	16.9023i	−0.937218	+	1.11693i	−0.992955	+	0.118488i	$0.962195\pi$
$230$	−1.84900	+	1.61025i	−0.121919	+	0.106177i
$231$	−1.30406	+	0.0713510i	−0.0858007	+	0.00469455i
$232$	−22.1282	−	47.4542i	−1.45279	−	3.11552i
$233$	18.0369	−	4.83296i	1.18163	−	0.316618i	0.386059	−	0.922474i	$-0.373836\pi$
$233$	18.0369	−	4.83296i	1.18163	−	0.316618i	0.795574	+	0.605856i	$0.207169\pi$
$234$	−20.3636	+	10.0482i	−1.33121	+	0.656871i
$235$	−10.9941	+	24.7536i	−0.717179	+	1.61474i
$236$	−18.9592	+	3.34302i	−1.23414	+	0.217612i
$237$	7.62059	−	1.08888i	0.495010	−	0.0707306i
$238$	6.32863	−	13.5718i	0.410224	−	0.879729i
$239$	3.38846	−	19.2169i	0.219181	−	1.24304i	−0.654320	−	0.756218i	$-0.727045\pi$
$239$	3.38846	−	19.2169i	0.219181	−	1.24304i	0.873502	−	0.486821i	$-0.161844\pi$
$240$	42.7727	+	36.9416i	2.76096	+	2.38457i
$241$	−3.76991	+	3.16333i	−0.242841	+	0.203768i	−0.756082	−	0.654476i	$-0.772889\pi$
$241$	−3.76991	+	3.16333i	−0.242841	+	0.203768i	0.513241	+	0.858244i	$0.328445\pi$
$242$	20.7592	−	20.7592i	1.33445	−	1.33445i
$243$	5.49968	+	14.5861i	0.352805	+	0.935697i
$244$			49.9098i			3.19515i
$245$	−8.61150	+	5.18494i	−0.550169	+	0.331253i
$246$	35.7119	−	8.33130i	2.27690	−	0.531184i
$247$	5.18403	−	3.62990i	0.329852	−	0.230965i
$248$	44.2731	+	20.6449i	2.81134	+	1.31095i
$249$	−3.02737	+	4.03673i	−0.191851	+	0.255818i
$250$	−26.8626	+	14.3769i	−1.69894	+	0.909274i
$251$	−18.1080	+	10.4546i	−1.14297	+	0.659892i	−0.947163	−	0.320752i	$-0.896065\pi$
$251$	−18.1080	+	10.4546i	−1.14297	+	0.659892i	−0.195803	+	0.980643i	$0.562731\pi$
$252$	24.3980	+	8.27557i	1.53693	+	0.521312i
$253$	0.0496176	+	0.185175i	0.00311943	+	0.0116419i
$254$	−9.14093	−	3.32703i	−0.573553	−	0.208756i
$255$	−1.36278	+	13.3784i	−0.0853405	+	0.837791i
$256$	29.5507	+	24.7960i	1.84692	+	1.54975i
$257$	14.5430	−	1.27235i	0.907166	−	0.0793667i	0.375986	−	0.926626i	$-0.377304\pi$
$257$	14.5430	−	1.27235i	0.907166	−	0.0793667i	0.531180	+	0.847259i	$0.321749\pi$
$258$	5.47728	+	1.15107i	0.341000	+	0.0716625i
$259$	0.809647	−	2.22449i	0.0503090	−	0.138223i
$260$	−3.55320	−	33.5144i	−0.220360	−	2.07847i
$261$	15.3997	+	6.77169i	0.953219	+	0.419157i
$262$	−2.16925	+	8.09576i	−0.134017	+	0.500158i
$263$	17.5612	−	25.0799i	1.08287	−	1.54650i	0.271067	−	0.962561i	$-0.412624\pi$
$263$	17.5612	−	25.0799i	1.08287	−	1.54650i	0.811801	−	0.583935i	$-0.198488\pi$
$264$	7.08591	−	3.02704i	0.436108	−	0.186302i
$265$	−0.484346	+	0.719477i	−0.0297531	+	0.0441971i
$266$	−9.67721	−	1.70635i	−0.593348	−	0.104623i
$267$	−12.1223	−	0.395404i	−0.741870	−	0.0241983i
$268$	6.24580	−	71.3898i	0.381523	−	4.36083i
$269$	−23.6912			−1.44448			−0.722239	−	0.691643i	$-0.756887\pi$
$269$	−23.6912			−1.44448			−0.722239	+	0.691643i	$0.756887\pi$
$270$	−31.6622	+	0.247173i	−1.92690	+	0.0150425i
$271$	20.1164			1.22198			0.610991	−	0.791638i	$-0.290771\pi$
$271$	20.1164			1.22198			0.610991	+	0.791638i	$0.290771\pi$
$272$	−4.41603	+	50.4755i	−0.267761	+	3.06052i
$273$	−3.58988	−	6.71428i	−0.217269	−	0.406367i
$274$	5.57454	+	0.982943i	0.336771	+	0.0593817i
$275$	0.0874520	+	2.38062i	0.00527355	+	0.143557i
$276$	0.452247	−	3.75464i	0.0272221	−	0.226002i
$277$	8.72217	−	12.4565i	0.524064	−	0.748441i	−0.466644	−	0.884445i	$-0.654537\pi$
$277$	8.72217	−	12.4565i	0.524064	−	0.748441i	0.990708	+	0.136004i	$0.0434260\pi$
$278$	−10.8873	+	40.6320i	−0.652977	+	2.43694i
$279$	−15.0670	+	4.39552i	−0.902040	+	0.263153i
$280$	−20.7713	+	25.6980i	−1.24132	+	1.53575i
$281$	−8.16607	+	22.4361i	−0.487147	+	1.33842i	0.416106	+	0.909316i	$0.363394\pi$
$281$	−8.16607	+	22.4361i	−0.487147	+	1.33842i	−0.903253	+	0.429108i	$0.858828\pi$
$282$	−17.7927	−	54.3346i	−1.05954	−	3.23558i
$283$	−0.284217	+	0.0248657i	−0.0168949	+	0.00147811i	−0.0956001	−	0.995420i	$-0.530477\pi$
$283$	−0.284217	+	0.0248657i	−0.0168949	+	0.00147811i	0.0787051	+	0.996898i	$0.474921\pi$
$284$	66.3335	+	55.6605i	3.93617	+	3.30284i
$285$	8.71126	−	1.40837i	0.516011	−	0.0834248i
$286$	−3.38884	−	1.23344i	−0.200387	−	0.0729347i
$287$	3.18229	+	11.8765i	0.187845	+	0.701046i
$288$	−63.2618	+	1.39538i	−3.72774	+	0.0822234i
$289$	4.28164	−	2.47200i	0.251861	−	0.145412i
$290$	−23.7145	+	24.6017i	−1.39256	+	1.44466i
$291$	−13.0194	−	1.56820i	−0.763213	−	0.0919292i
$292$	39.4056	+	18.3751i	2.30604	+	1.07532i
$293$	−12.7347	+	8.91694i	−0.743969	+	0.520933i	−0.883010	−	0.469354i	$-0.844487\pi$
$293$	−12.7347	+	8.91694i	−0.743969	+	0.520933i	0.139041	+	0.990287i	$0.455598\pi$
$294$	6.15698	−	20.3055i	0.359083	−	1.18424i
$295$	4.09203	+	6.79633i	0.238247	+	0.395698i
$296$			13.9667i			0.811796i
$297$	−1.06989	+	2.23257i	−0.0620812	+	0.129547i
$298$	−30.3387	+	30.3387i	−1.75748	+	1.75748i
$299$	−0.856140	+	0.718387i	−0.0495119	+	0.0415454i
$300$	15.8911	−	44.2253i	0.917471	−	2.55335i
$301$	−0.325869	+	1.84809i	−0.0187828	+	0.106522i
$302$	−1.23733	+	2.65345i	−0.0712001	+	0.152689i
$303$	3.75158	−	9.34734i	0.215523	−	0.536990i
$304$	32.7435	−	5.77355i	1.87797	−	0.331136i
$305$	19.1939	−	7.38779i	1.09904	−	0.423024i
$306$	−16.7906	−	22.8881i	−0.959854	−	1.30843i
$307$	−10.1671	+	2.72426i	−0.580267	+	0.155482i	−0.537001	−	0.843582i	$-0.680443\pi$
$307$	−10.1671	+	2.72426i	−0.580267	+	0.155482i	−0.0432656	+	0.999064i	$0.513776\pi$
$308$	1.72919	+	3.70826i	0.0985297	+	0.211298i
$309$	4.23587	+	6.48994i	0.240970	+	0.369200i
$310$	2.19501	−	31.8042i	0.124668	−	1.80636i
$311$	2.06659	−	2.46287i	0.117186	−	0.139657i	−0.704262	−	0.709940i	$-0.748722\pi$
$311$	2.06659	−	2.46287i	0.117186	−	0.139657i	0.821448	+	0.570283i	$0.193167\pi$
$312$	33.4516	+	29.9809i	1.89382	+	1.69734i
$313$	22.0403	−	10.2775i	1.24579	−	0.580921i	0.315911	−	0.948789i	$-0.397690\pi$
$313$	22.0403	−	10.2775i	1.24579	−	0.580921i	0.929878	+	0.367868i	$0.119912\pi$
$314$	−23.4568	+	40.6283i	−1.32374	+	2.29279i
$315$	−0.428923	−	10.6078i	−0.0241671	−	0.597680i
$316$	−12.0586	−	20.8860i	−0.678347	−	1.17493i
$317$	17.0133	+	11.9128i	0.955562	+	0.669092i	0.943688	−	0.330838i	$-0.107331\pi$
$317$	17.0133	+	11.9128i	0.955562	+	0.669092i	0.0118742	+	0.999929i	$0.496220\pi$
$318$	−0.258968	−	1.81239i	−0.0145222	−	0.101634i
$319$	0.913782	+	2.51060i	0.0511620	+	0.140566i
$320$	20.5438	−	59.8396i	1.14843	−	3.34514i
$321$	0.321625	+	1.37864i	0.0179514	+	0.0769479i
$322$	1.72874	+	0.151246i	0.0963391	+	0.00842858i
$323$	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
$327$	−12.4443	−	7.73635i	−0.688174	−	0.427821i
$328$	−41.6087	−	59.4234i	−2.29746	−	3.28111i
$329$	18.0138	−	6.55649i	0.993134	−	0.361471i
$330$	−3.50474	−	3.60605i	−0.192929	−	0.198507i
$331$	1.03458	+	5.86738i	0.0568655	+	0.322500i	0.999949	−	0.0100545i	$-0.00320050\pi$
$331$	1.03458	+	5.86738i	0.0568655	+	0.322500i	−0.943084	+	0.332555i	$0.892089\pi$
$332$	15.2694	+	4.09143i	0.838018	+	0.224546i
$333$	−2.95954	−	3.37309i	−0.162182	−	0.184844i
$334$	−15.5485	−	8.97692i	−0.850775	−	0.491195i
$335$	−28.3790	+	8.16537i	−1.55051	+	0.446122i
$336$	−2.18535	−	39.9409i	−0.119221	−	2.17896i
$337$	−0.971978	−	11.1098i	−0.0529470	−	0.605187i	−0.975600	−	0.219556i	$-0.929539\pi$
$337$	−0.971978	−	11.1098i	−0.0529470	−	0.605187i	0.922653	−	0.385631i	$-0.126016\pi$
$338$	1.25528	+	14.3479i	0.0682780	+	0.780421i
$339$	3.16262	−	2.06419i	0.171770	−	0.112111i
$340$	40.4878	−	11.6494i	2.19576	−	0.631776i
$341$	−2.15867	−	1.24631i	−0.116899	−	0.0674915i
$342$	−11.6558	+	14.5298i	−0.630271	+	0.785683i
$343$	17.5727	+	4.70859i	0.948837	+	0.254240i
$344$	−1.92261	−	10.9037i	−0.103660	−	0.587887i
$345$	−1.51087	+	0.381851i	−0.0813424	+	0.0205582i
$346$	27.3797	−	9.96540i	1.47194	−	0.535743i
$347$	−13.6142	−	19.4431i	−0.730851	−	1.04376i	−0.996813	−	0.0797793i	$-0.974578\pi$
$347$	−13.6142	−	19.4431i	−0.730851	−	1.04376i	0.265962	−	0.963984i	$-0.414310\pi$
$348$	1.71820	−	52.6764i	0.0921051	−	2.82375i
$349$	4.82633	+	5.75179i	0.258347	+	0.307886i	0.879591	−	0.475731i	$-0.157817\pi$
$349$	4.82633	+	5.75179i	0.258347	+	0.307886i	−0.621243	+	0.783618i	$0.713372\pi$
$350$	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
$353$	−5.16281	−	0.451688i	−0.274789	−	0.0240409i	−0.0510716	−	0.998695i	$-0.516264\pi$
$353$	−5.16281	−	0.451688i	−0.274789	−	0.0240409i	−0.223717	+	0.974654i	$0.571819\pi$
$354$	−16.0254	−	4.85919i	−0.851742	−	0.258263i
$355$	11.5865	−	33.7490i	0.614949	−	1.79121i
$356$	12.9961	+	35.7066i	0.688793	+	1.89244i
$357$	7.48659	−	5.87695i	0.396232	−	0.311041i
$358$	−14.7917	−	10.3573i	−0.781765	−	0.547398i
$359$	−6.82697	−	11.8247i	−0.360314	−	0.624082i	0.627699	−	0.778457i	$-0.283997\pi$
$359$	−6.82697	−	11.8247i	−0.360314	−	0.624082i	−0.988012	+	0.154375i	$0.950664\pi$
$360$	23.7835	+	57.9454i	1.25350	+	3.05399i
$361$	−6.90435	+	11.9587i	−0.363387	+	0.629404i
$362$	−21.5810	+	10.0634i	−1.13427	+	0.528921i
$363$	17.7328	−	5.80687i	0.930732	−	0.304782i
$364$	−15.3325	+	18.2725i	−0.803641	+	0.957742i
$365$	1.23361	−	17.8742i	0.0645703	−	0.935578i
$366$	−19.6203	+	38.7270i	−1.02557	+	2.02429i
$367$	9.11448	+	19.5461i	0.475772	+	1.02030i	0.986981	+	0.160840i	$0.0514203\pi$
$367$	9.11448	+	19.5461i	0.475772	+	1.02030i	−0.511208	+	0.859457i	$0.670802\pi$
$368$	−5.67159	+	1.51970i	−0.295652	+	0.0792197i
$369$	22.6407	+	5.53446i	1.17863	+	0.288113i
$370$	8.50639	−	3.27414i	0.442226	−	0.170215i
$371$	0.604528	−	0.106595i	0.0313855	−	0.00553411i
$372$	30.3620	+	38.6778i	1.57419	+	2.00535i
$373$	−5.59299	+	11.9942i	−0.289594	+	0.621037i	−0.996250	−	0.0865206i	$-0.972425\pi$
$373$	−5.59299	+	11.9942i	−0.289594	+	0.621037i	0.706656	+	0.707557i	$0.250203\pi$
$374$	0.782840	−	4.43971i	0.0404797	−	0.229572i
$375$	−19.3600	+	0.435116i	−0.999748	+	0.0224693i
$376$	−86.6408	+	72.7003i	−4.46816	+	3.74923i
$377$	−11.0135	+	11.0135i	−0.567226	+	0.567226i
$378$	15.6782	+	16.0126i	0.806398	+	0.823600i
$379$		−	27.4089i		−	1.40790i	−0.710249	−	0.703951i	$-0.751417\pi$
$379$		−	27.4089i		−	1.40790i	0.710249	−	0.703951i	$-0.248583\pi$
$380$	−14.2602	−	23.6843i	−0.731533	−	1.21498i
$381$	−4.22697	−	4.51202i	−0.216554	−	0.231158i
$382$	−45.0283	+	31.5292i	−2.30385	+	1.61317i
$383$	−32.7469	−	15.2701i	−1.67329	−	0.780267i	−0.999131	−	0.0416793i	$-0.986729\pi$
$383$	−32.7469	−	15.2701i	−1.67329	−	0.780267i	−0.674157	−	0.738588i	$-0.735493\pi$
$384$	23.7613	+	55.6221i	1.21256	+	2.83845i
$385$	1.17013	−	1.21390i	0.0596353	−	0.0618663i
$386$	44.3177	−	25.5869i	2.25571	−	1.30234i
$387$	2.77482	+	2.22595i	0.141052	+	0.113151i
$388$	10.6332	+	39.6836i	0.539819	+	2.01463i
$389$	17.3733	+	6.32335i	0.880860	+	0.320607i	0.742557	−	0.669783i	$-0.233613\pi$
$389$	17.3733	+	6.32335i	0.880860	+	0.320607i	0.138303	+	0.990390i	$0.455835\pi$
$390$	10.4180	−	27.4020i	0.527534	−	1.38755i
$391$	−1.07024	−	0.898039i	−0.0541244	−	0.0454158i
$392$	−41.8148	+	3.65832i	−2.11197	+	0.184773i
$393$	−3.55538	+	3.96696i	−0.179345	+	0.200106i
$394$	−4.67045	+	12.8320i	−0.235294	+	0.646464i
$395$	−6.24723	+	7.72899i	−0.314332	+	0.388888i
$396$	7.73961	+	0.505439i	0.388930	+	0.0253992i
$397$	7.80671	−	29.1350i	0.391807	−	1.46224i	−0.435343	−	0.900265i	$-0.643373\pi$
$397$	7.80671	−	29.1350i	0.391807	−	1.46224i	0.827151	−	0.561980i	$-0.189960\pi$
$398$	26.0546	−	37.2099i	1.30600	−	1.86516i
$399$	−4.99656	−	3.74719i	−0.250141	−	0.187594i
$400$	−72.9141	+	2.67849i	−3.64571	+	0.133925i
$401$	34.2820	+	6.04485i	1.71196	+	0.301865i	0.941848	−	0.336040i	$-0.109088\pi$
$401$	34.2820	+	6.04485i	1.71196	+	0.301865i	0.770115	+	0.637905i	$0.220199\pi$
$402$	32.9108	−	52.9389i	1.64144	−	2.64035i
$403$	1.26649	−	14.4761i	0.0630886	−	0.721106i
$404$	−31.5550			−1.56992
$405$	−18.0226	−	8.95470i	−0.895549	−	0.444962i
$406$	24.1845			1.20026
$407$	0.0621128	−	0.709953i	0.00307882	−	0.0351911i
$408$	−29.6476	+	47.6899i	−1.46778	+	2.36100i
$409$	21.8207	+	3.84758i	1.07897	+	0.190251i	0.684758	−	0.728771i	$-0.259908\pi$
$409$	21.8207	+	3.84758i	1.07897	+	0.190251i	0.394208	+	0.919021i	$0.371019\pi$
$410$	−26.4376	+	39.2721i	−1.30566	+	1.93951i
$411$	2.87826	+	2.15856i	0.141974	+	0.106474i
$412$	13.9264	−	19.8890i	0.686105	−	0.979859i
$413$	1.45321	−	5.42346i	0.0715079	−	0.266871i
$414$	1.82692	−	2.73559i	0.0897884	−	0.134447i
$415$	−0.686778	−	6.47780i	−0.0337126	−	0.317983i
$416$	20.0374	−	55.0524i	0.982415	−	2.69916i
$417$	−17.8441	+	19.9098i	−0.873831	+	0.974989i
$418$	−2.94703	+	0.257831i	−0.144144	+	0.0126109i
$419$	3.82900	+	3.21291i	0.187059	+	0.156961i	0.731508	−	0.681833i	$-0.238817\pi$
$419$	3.82900	+	3.21291i	0.187059	+	0.156961i	−0.544449	+	0.838794i	$0.683261\pi$
$420$	−30.3413	+	13.6255i	−1.48050	+	0.664858i
$421$	12.3825	+	4.50685i	0.603485	+	0.219651i	0.625650	−	0.780104i	$-0.284834\pi$
$421$	12.3825	+	4.50685i	0.603485	+	0.219651i	−0.0221653	+	0.999754i	$0.507056\pi$
$422$	−7.36996	−	27.5051i	−0.358764	−	1.33893i
$423$	5.51945	−	35.9170i	0.268365	−	1.74635i
$424$	−3.13649	+	1.81086i	−0.152322	+	0.0879429i
$425$	−10.4731	−	13.8461i	−0.508022	−	0.671632i
$426$	29.5899	+	69.2660i	1.43363	+	3.35595i
$427$	−13.1924	−	6.15173i	−0.638426	−	0.297703i
$428$	3.63304	−	2.54388i	0.175609	−	0.122963i
$429$	−1.56708	−	1.67275i	−0.0756592	−	0.0807613i
$430$	−6.19017	+	3.72707i	−0.298516	+	0.179735i
$431$			14.5168i			0.699251i	0.936890	+	0.349625i	$0.113691\pi$
$431$			14.5168i			0.699251i	−0.936890	+	0.349625i	$0.886309\pi$
$432$	−68.3794	−	32.7687i	−3.28991	−	1.57659i
$433$	−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
$435$	−20.5122	+	7.13655i	−0.983483	+	0.342171i
$436$	−7.97163	+	45.2094i	−0.381772	+	2.16514i
$437$	−0.387448	+	0.830884i	−0.0185341	+	0.0397466i
$438$	23.3528	+	29.7490i	1.11584	+	1.42146i
$439$	21.2894	−	3.75390i	1.01609	−	0.179164i	0.359287	−	0.933227i	$-0.383020\pi$
$439$	21.2894	−	3.75390i	1.01609	−	0.179164i	0.656801	+	0.754064i	$0.271909\pi$
$440$	−4.03783	+	9.09127i	−0.192496	+	0.433409i
$441$	9.32350	−	9.74408i	0.443976	−	0.464004i
$442$	25.3862	−	6.80221i	1.20750	−	0.323548i
$443$	−5.07285	−	10.8788i	−0.241018	−	0.516866i	0.748172	−	0.663505i	$-0.230932\pi$
$443$	−5.07285	−	10.8788i	−0.241018	−	0.516866i	−0.989190	+	0.146640i	$0.953154\pi$
$444$	−6.35363	+	12.5409i	−0.301530	+	0.595166i
$445$	11.8080	−	10.2833i	0.559753	−	0.487477i
$446$	41.0912	−	48.9706i	1.94572	−	2.31882i
$447$	−25.9159	+	8.48653i	−1.22578	+	0.401399i
$448$	−40.5832	+	18.9243i	−1.91738	+	0.894087i
$449$	−15.1373	+	26.2186i	−0.714374	+	1.23733i	0.248826	+	0.968548i	$0.419955\pi$
$449$	−15.1373	+	26.2186i	−0.714374	+	1.23733i	−0.963200	+	0.268784i	$0.913378\pi$
$450$	29.7162	−	28.0692i	1.40083	−	1.32319i
$451$	1.85078	+	3.20565i	0.0871499	+	0.150948i
$452$	−9.69212	−	6.78649i	−0.455879	−	0.319210i
$453$	−1.46372	+	1.14902i	−0.0687716	+	0.0539855i
$454$	−18.6577	−	51.2617i	−0.875651	−	2.40583i
$455$	9.29666	+	3.19168i	0.435834	+	0.149628i
$456$	35.2631	+	10.6924i	1.65135	+	0.500717i
$457$	41.4537	+	3.62673i	1.93912	+	0.169651i	0.989579	−	0.143990i	$-0.0459935\pi$
$457$	41.4537	+	3.62673i	1.93912	+	0.169651i	0.949541	+	0.313642i	$0.101549\pi$
$458$	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	0.443184	−	0.896431i	$-0.353849\pi$
$461$	−11.0916	−	13.2184i	−0.516586	−	0.615643i	−0.959770	+	0.280788i	$0.909404\pi$
$462$	−0.116027	+	3.55716i	−0.00539808	+	0.165494i
$463$	9.45428	+	13.5021i	0.439378	+	0.627496i	0.976374	−	0.216088i	$-0.0693299\pi$
$463$	9.45428	+	13.5021i	0.439378	+	0.627496i	−0.536996	+	0.843585i	$0.680441\pi$
$464$	−76.8950	+	27.9875i	−3.56976	+	1.29929i
$465$	10.3801	−	17.4015i	0.481366	−	0.806977i
$466$	−8.83640	−	50.1137i	−0.409338	−	2.32147i
$467$	3.84448	+	1.03012i	0.177901	+	0.0476685i	0.346670	−	0.937987i	$-0.387312\pi$
$467$	3.84448	+	1.03012i	0.177901	+	0.0476685i	−0.168769	+	0.985656i	$0.553979\pi$
$468$	16.3981	+	42.1380i	0.758001	+	1.94783i
$469$	18.1003	+	10.4502i	0.835795	+	0.482546i
$470$	64.5889	+	35.7258i	2.97926	+	1.64791i
$471$	−24.9696	+	16.2972i	−1.15054	+	0.750937i
$472$	2.88720	+	33.0009i	0.132894	+	1.51899i
$473$	0.0492391	+	0.562805i	0.00226402	+	0.0258778i
$474$	−1.14609	−	20.9467i	−0.0526417	−	0.962115i
$475$	−6.99748	+	8.98989i	−0.321066	+	0.412484i
$476$	−25.8234	−	14.9091i	−1.18361	−	0.683359i
$477$	0.373775	−	1.10196i	0.0171140	−	0.0504554i
$478$	−51.3646	−	13.7631i	−2.34936	−	0.629510i
$479$	0.246236	+	1.39648i	0.0112508	+	0.0638066i	0.989916	−	0.141654i	$-0.0452420\pi$
$479$	0.246236	+	1.39648i	0.0112508	+	0.0638066i	−0.978665	+	0.205460i	$0.934131\pi$
$480$	58.5810	−	56.9351i	2.67384	−	2.59872i
$481$	3.90411	−	1.42098i	0.178012	−	0.0647911i
$482$	7.69230	+	10.9857i	0.350375	+	0.500387i
$483$	0.936704	+	0.582326i	0.0426215	+	0.0264967i
$484$	−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	$0.810852\pi$
$488$	85.5544	+	7.48504i	3.87286	+	0.338832i
$489$	−1.37629	−	5.89942i	−0.0622380	−	0.266781i
$490$	12.0306	+	24.6097i	0.543485	+	1.11175i
$491$	−9.16760	−	25.1878i	−0.413728	−	1.13671i	−0.955193	−	0.295985i	$-0.904352\pi$
$491$	−9.16760	−	25.1878i	−0.413728	−	1.13671i	0.541464	−	0.840724i	$-0.317870\pi$
$492$	−10.3287	−	72.2857i	−0.465654	−	3.25889i
$493$	−15.9494	−	11.1679i	−0.718324	−	0.502976i
$494$	−8.62305	−	14.9356i	−0.387969	−	0.671983i
$495$	−0.951263	−	3.05125i	−0.0427561	−	0.137143i
$496$	38.1722	−	66.1162i	1.71398	−	2.96871i
$497$	−22.8886	+	10.6731i	−1.02669	+	0.478754i
$498$	10.2398	+	9.17735i	0.458854	+	0.411247i
$499$	−7.19594	+	8.57579i	−0.322134	+	0.383905i	−0.902672	−	0.430328i	$-0.858398\pi$
$499$	−7.19594	+	8.57579i	−0.322134	+	0.383905i	0.580538	+	0.814233i	$0.302842\pi$
$500$	23.8568	+	55.7811i	1.06691	+	2.49460i
$501$	−6.23696	−	9.55588i	−0.278647	−	0.426925i
$502$	24.0811	+	51.6420i	1.07479	+	2.30490i
$503$	12.8521	−	3.44372i	0.573049	−	0.153548i	0.0393543	−	0.999225i	$-0.487470\pi$
$503$	12.8521	−	3.44372i	0.573049	−	0.153548i	0.533694	+	0.845677i	$0.320803\pi$
$504$	17.8448	−	40.5815i	0.794872	−	1.80765i
$505$	4.67086	+	12.1351i	0.207851	+	0.540006i
$506$	0.514493	−	0.0907189i	0.0228720	−	0.00403295i
$507$	−3.40966	+	8.49540i	−0.151428	+	0.377294i
$508$	−8.18603	+	17.5550i	−0.363197	+	0.778877i
$509$	1.12261	−	6.36664i	0.0497588	−	0.282196i	−0.949768	−	0.312955i	$-0.898681\pi$
$509$	1.12261	−	6.36664i	0.0497588	−	0.282196i	0.999527	+	0.0307584i	$0.00979226\pi$
$510$	35.9956	+	6.87715i	1.59391	+	0.304526i
$511$	−9.71403	+	8.15104i	−0.429723	+	0.360581i
$512$	24.9482	−	24.9482i	1.10257	−	1.10257i
$513$	−10.7821	+	4.88993i	−0.476042	+	0.215896i
$514$		−	39.7830i		−	1.75475i
$515$	−9.71015	−	2.41167i	−0.427881	−	0.106271i
$516$	3.23388	−	10.6652i	0.142364	−	0.469511i
$517$	4.72744	−	3.31019i	0.207912	−	0.145582i
$518$	−5.84666	−	2.72634i	−0.256887	−	0.119789i
$519$	18.3860	+	2.21460i	0.807057	+	0.0972103i
$520$	−57.9825	+	1.06463i	−2.54270	+	0.0466872i
$521$	−6.34977	+	3.66604i	−0.278188	+	0.160612i	−0.632603	−	0.774476i	$-0.718013\pi$
$521$	−6.34977	+	3.66604i	−0.278188	+	0.160612i	0.354415	+	0.935088i	$0.384680\pi$
$522$	22.0411	−	40.1983i	0.964715	−	1.75943i
$523$	−3.37240	−	12.5860i	−0.147465	−	0.550346i	−0.999633	−	0.0270787i	$-0.991380\pi$
$523$	−3.37240	−	12.5860i	−0.147465	−	0.550346i	0.852168	−	0.523268i	$-0.175287\pi$
$524$	15.6827	+	5.70803i	0.685101	+	0.249356i
$525$	9.73120	+	9.65150i	0.424704	+	0.421226i
$526$	−63.9152	−	53.6312i	−2.78683	−	2.33843i
$527$	18.0963	−	1.58322i	0.788285	−	0.0689660i
$528$	−3.74760	−	11.4443i	−0.163093	−	0.498049i
$529$	−7.81109	+	21.4608i	−0.339613	+	0.933078i
$530$	1.83817	+	1.48577i	0.0798452	+	0.0645377i
$531$	−7.69018	−	7.35825i	−0.333725	−	0.319321i
$532$	−5.06425	+	18.9001i	−0.219563	+	0.819421i
$533$	−12.3773	+	17.6767i	−0.536122	+	0.765662i
$534$	−3.95260	+	32.8152i	−0.171046	+	1.42005i
$535$	−1.51608	−	1.02061i	−0.0655457	−	0.0441248i
$536$	−121.438	−	21.4128i	−5.24534	−	0.924894i
$537$	−5.41139	−	10.1211i	−0.233519	−	0.436758i
$538$	−5.62693	+	64.3161i	−0.242594	+	2.77286i
$539$	2.14180			0.0922537
$540$	−5.00458	+	62.8497i	−0.215363	+	2.70462i
$541$	−19.4815			−0.837576			−0.418788	−	0.908084i	$-0.637545\pi$
$541$	−19.4815			−0.837576			−0.418788	+	0.908084i	$0.637545\pi$
$542$	4.77786	−	54.6112i	0.205227	−	2.34575i
$543$	−15.1265	−	0.493396i	−0.649140	−	0.0211737i
$544$	72.1238	+	12.7174i	3.09228	+	0.545253i
$545$	18.5662	−	3.62636i	0.795289	−	0.155336i
$546$	−19.0803	+	8.15097i	−0.816563	+	0.348829i
$547$	−8.23625	+	11.7626i	−0.352157	+	0.502932i	−0.955678	−	0.294415i	$-0.904875\pi$
$547$	−8.23625	+	11.7626i	−0.352157	+	0.502932i	0.603521	+	0.797347i	$0.293764\pi$
$548$	2.91726	−	10.8874i	0.124619	−	0.465085i
$549$	−22.2483	+	16.3213i	−0.949535	+	0.696574i
$550$	6.48360	+	0.328013i	0.276462	+	0.0139865i
$551$	−4.36986	+	12.0061i	−0.186162	+	0.511477i
$552$	−6.36830	−	1.33832i	−0.271053	−	0.0569627i
$553$	7.00702	−	0.613034i	0.297969	−	0.0260689i
$554$	−31.7450	−	26.6372i	−1.34871	−	1.13171i
$555$	5.76336	+	0.587078i	0.244641	+	0.0249201i
$556$	78.7101	+	28.6481i	3.33805	+	1.21495i
$557$	5.99902	+	22.3886i	0.254187	+	0.948637i	0.968541	+	0.248853i	$0.0800538\pi$
$557$	5.99902	+	22.3886i	0.254187	+	0.948637i	−0.714355	+	0.699784i	$0.753280\pi$
$558$	8.35420	+	41.9475i	0.353662	+	1.77578i
$559$	−2.85230	+	1.64678i	−0.120640	+	0.0696513i
$560$	37.1797	+	35.8389i	1.57113	+	1.51447i
$561$	1.71913	−	2.29232i	0.0725819	−	0.0967818i
$562$	58.9691	+	27.4978i	2.48746	+	1.15992i
$563$	−24.6767	+	17.2788i	−1.04000	+	0.728214i	−0.963187	−	0.268832i	$-0.913362\pi$
$563$	−24.6767	+	17.2788i	−1.04000	+	0.728214i	−0.0768099	+	0.997046i	$0.524473\pi$
$564$	−110.869	+	25.8648i	−4.66842	+	1.08911i
$565$	−1.17523	+	4.73187i	−0.0494425	+	0.199071i
$566$			0.777487i			0.0326802i
$567$	4.28952	+	13.5822i	0.180143	+	0.570398i
$568$	105.360	−	105.360i	4.42082	−	4.42082i
$569$	−14.2448	+	11.9528i	−0.597173	+	0.501088i	−0.890536	−	0.454913i	$-0.849670\pi$
$569$	−14.2448	+	11.9528i	−0.597173	+	0.501088i	0.293362	+	0.956001i	$0.405226\pi$
$570$	−1.75438	−	23.9835i	−0.0734829	−	1.00456i
$571$	6.82003	−	38.6783i	0.285409	−	1.61864i	−0.418410	−	0.908258i	$-0.637412\pi$
$571$	6.82003	−	38.6783i	0.285409	−	1.61864i	0.703819	−	0.710379i	$-0.251476\pi$
$572$	−3.03483	+	6.50822i	−0.126893	+	0.272122i
$573$	−34.5864	+	4.94195i	−1.44487	+	0.206453i
$574$	32.9977	−	5.81838i	1.37730	−	0.242854i
$575$	1.09268	−	1.68926i	0.0455677	−	0.0704472i
$576$	−5.53153	+	84.7024i	−0.230480	+	3.52927i
$577$	−42.2673	+	11.3255i	−1.75961	+	0.471486i	−0.986634	−	0.162950i	$-0.947899\pi$
$577$	−42.2673	+	11.3255i	−1.75961	+	0.471486i	−0.772975	+	0.634436i	$0.781232\pi$
$578$	−5.69397	−	12.2108i	−0.236838	−	0.507901i
$579$	32.4766	−	1.77694i	1.34968	−	0.0738472i
$580$	44.6855	+	51.3108i	1.85546	+	2.13057i
$581$	−2.96353	+	3.53180i	−0.122948	+	0.146524i
$582$	−7.34954	+	34.9722i	−0.304648	+	1.44965i
$583$	0.167487	−	0.0781006i	0.00693661	−	0.00323460i
$584$	37.4080	−	64.7925i	1.54795	−	2.68113i
$585$	13.7778	−	12.5436i	0.569641	−	0.518615i
$586$	21.1828	+	36.6896i	0.875051	+	1.51563i
$587$	−16.5731	−	11.6046i	−0.684046	−	0.478974i	0.179164	−	0.983819i	$-0.442661\pi$
$587$	−16.5731	−	11.6046i	−0.684046	−	0.478974i	−0.863210	+	0.504845i	$0.831550\pi$
$588$	−39.2105	−	15.7373i	−1.61701	−	0.648993i
$589$	−4.07693	−	11.2013i	−0.167987	−	0.461540i
$590$	19.4223	−	9.49470i	0.799605	−	0.390891i
$591$	−6.33393	+	5.93378i	−0.260543	+	0.244083i
$592$	21.7446	+	1.90240i	0.893696	+	0.0781883i
$593$	2.27116	+	2.27116i	0.0932652	+	0.0932652i	0.752200	−	0.658935i	$-0.228993\pi$
$593$	2.27116	+	2.27116i	0.0932652	+	0.0932652i	−0.658935	+	0.752200i	$0.728993\pi$
$594$	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
$597$	25.4606	−	13.6129i	1.04203	−	0.557137i
$598$	1.74691	+	2.49484i	0.0714364	+	0.102022i
$599$	−11.3910	+	4.14598i	−0.465423	+	0.169400i	−0.564078	−	0.825722i	$-0.690768\pi$
$599$	−11.3910	+	4.14598i	−0.465423	+	0.169400i	0.0986548	+	0.995122i	$0.468546\pi$
$600$	−73.4270	−	33.8727i	−2.99764	−	1.38285i
$601$	2.78962	+	15.8207i	0.113791	+	0.645340i	0.987342	+	0.158607i	$0.0507003\pi$
$601$	2.78962	+	15.8207i	0.113791	+	0.645340i	−0.873551	+	0.486733i	$0.838189\pi$
$602$	4.93974	+	1.32360i	0.201329	+	0.0539459i
$603$	33.8660	−	20.5614i	1.37913	−	0.837323i
$604$	5.04879	+	2.91492i	0.205432	+	0.118606i
$605$	−11.6596	+	21.0794i	−0.474029	+	0.857000i
$606$	−24.4848	−	12.4048i	−0.994626	−	0.503909i
$607$	−1.10665	−	12.6491i	−0.0449177	−	0.513412i	−0.985011	−	0.172494i	$-0.944818\pi$
$607$	−1.10665	−	12.6491i	−0.0449177	−	0.513412i	0.940093	−	0.340918i	$-0.110738\pi$
$608$	−4.18852	−	47.8750i	−0.169867	−	1.94159i
$609$	13.7119	+	6.94690i	0.555636	+	0.281503i
$610$	−15.4974	−	53.8615i	−0.627470	−	2.18079i
$611$	29.1369	+	16.8222i	1.17875	+	0.680552i
$612$	−48.3159	+	29.3345i	−1.95306	+	1.18578i
$613$	−11.7830	−	3.15725i	−0.475912	−	0.127520i	0.0128866	−	0.999917i	$-0.495898\pi$
$613$	−11.7830	−	3.15725i	−0.475912	−	0.127520i	−0.488798	+	0.872397i	$0.662565\pi$
$614$	4.98094	+	28.2483i	0.201014	+	1.14001i
$615$	−26.2701	+	14.6721i	−1.05931	+	0.591634i
$616$	6.61595	−	2.40801i	0.266564	−	0.0970215i
$617$	5.34672	+	7.63591i	0.215251	+	0.307410i	0.912228	−	0.409684i	$-0.134361\pi$
$617$	5.34672	+	7.63591i	0.215251	+	0.307410i	−0.696977	+	0.717094i	$0.745472\pi$
$618$	18.6247	−	9.95797i	0.749197	−	0.400568i
$619$	−10.1944	−	12.1492i	−0.409748	−	0.488319i	0.521218	−	0.853423i	$-0.325478\pi$
$619$	−10.1944	−	12.1492i	−0.409748	−	0.488319i	−0.930967	+	0.365104i	$0.881033\pi$
$620$	−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
$623$	−11.0400	−	0.965877i	−0.442309	−	0.0386971i
$624$	51.2334	−	47.9967i	2.05098	−	1.92141i
$625$	17.9204	−	17.4315i	0.716818	−	0.697260i
$626$	−22.6663	−	62.2751i	−0.905927	−	2.48901i
$627$	−1.74494	−	0.700337i	−0.0696862	−	0.0279688i
$628$	76.5215	+	53.5809i	3.05354	+	2.13811i
$629$	2.59683	+	4.49784i	0.103542	+	0.179341i
$630$	−28.8994	−	1.35504i	−1.15138	−	0.0539859i
$631$	−12.2239	+	21.1724i	−0.486626	+	0.842861i	−0.999882	−	0.0153745i	$-0.995106\pi$
$631$	−12.2239	+	21.1724i	−0.486626	+	0.842861i	0.513256	+	0.858236i	$0.328439\pi$
$632$	−37.6109	+	17.5382i	−1.49608	+	0.697634i
$633$	3.72215	−	17.7116i	0.147942	−	0.703972i
$634$	36.3814	−	43.3577i	1.44489	−	1.72195i
$635$	7.96287	+	0.549570i	0.315997	+	0.0218090i
$636$	−3.64010	+	0.199166i	−0.144339	+	0.00789745i
$637$	5.27689	+	11.3163i	0.209078	+	0.448369i
$638$	7.03271	−	1.88441i	0.278428	−	0.0746045i
$639$	−3.11973	+	47.7714i	−0.123415	+	1.88981i
$640$	−71.3635	−	31.6956i	−2.82089	−	1.25288i
$641$	−5.87001	+	1.03504i	−0.231852	+	0.0408817i	−0.288367	−	0.957520i	$-0.593112\pi$
$641$	−5.87001	+	1.03504i	−0.231852	+	0.0408817i	0.0565151	+	0.998402i	$0.482001\pi$
$642$	3.81906	−	0.545695i	0.150726	−	0.0215369i
$643$	−13.5999	+	29.1651i	−0.536328	+	1.15016i	0.432320	+	0.901720i	$0.357695\pi$
$643$	−13.5999	+	29.1651i	−0.536328	+	1.15016i	−0.968648	+	0.248438i	$0.920083\pi$
$644$	0.600036	−	3.40297i	0.0236447	−	0.134096i
$645$	−4.58023	+	0.335041i	−0.180346	+	0.0131922i
$646$	16.5151	−	13.8578i	0.649779	−	0.545229i
$647$	5.43613	−	5.43613i	0.213717	−	0.213717i	−0.592128	−	0.805844i	$-0.701712\pi$
$647$	5.43613	−	5.43613i	0.213717	−	0.213717i	0.805844	+	0.592128i	$0.201712\pi$
$648$	−51.1892	−	66.6457i	−2.01090	−	2.61809i
$649$		−	1.69034i		−	0.0663516i
$650$	14.2410	+	35.0647i	0.558578	+	1.37535i
$651$	−13.9659	+	3.25813i	−0.547365	+	0.127696i
$652$	−15.5464	+	10.8857i	−0.608844	+	0.426317i
$653$	14.5983	+	6.80729i	0.571275	+	0.266390i	0.686717	−	0.726924i	$-0.259051\pi$
$653$	14.5983	+	6.80729i	0.571275	+	0.266390i	−0.115443	+	0.993314i	$0.536829\pi$
$654$	−23.9580	+	31.9460i	−0.936833	+	1.24919i
$655$	−0.126253	−	6.87603i	−0.00493310	−	0.268669i
$656$	−98.1831	+	56.6861i	−3.83341	+	2.21322i
$657$	4.69513	+	23.5748i	0.183174	+	0.919740i
$658$	−13.5209	−	50.4605i	−0.527098	−	1.96716i
$659$	31.0994	+	11.3193i	1.21146	+	0.440936i	0.867210	−	0.497942i	$-0.165911\pi$
$659$	31.0994	+	11.3193i	1.21146	+	0.440936i	0.344250	+	0.938878i	$0.388133\pi$
$660$	−7.76138	+	6.32635i	−0.302111	+	0.246253i
$661$	22.7885	+	19.1218i	0.886369	+	0.743752i	0.967478	−	0.252954i	$-0.0814020\pi$
$661$	22.7885	+	19.1218i	0.886369	+	0.743752i	−0.0811098	+	0.996705i	$0.525846\pi$
$662$	16.1743	−	1.41507i	0.628631	−	0.0549981i
$663$	16.3472	+	3.43541i	0.634871	+	0.133420i
$664$	9.30342	−	25.5609i	0.361043	−	0.991957i
$665$	8.01804	−	0.850075i	0.310926	−	0.0329645i
$666$	−9.86008	+	7.23330i	−0.382070	+	0.280285i
$667$	0.583983	−	2.17945i	0.0226119	−	0.0843888i
$668$	−20.5054	+	29.2848i	−0.793379	+	1.13306i
$669$	37.3641	−	15.9617i	1.44458	−	0.617113i
$670$	15.4267	+	78.9816i	0.595987	+	3.05133i
$671$	−4.31561	−	0.760958i	−0.166602	−	0.0293764i
$672$	−57.7867	−	1.88488i	−2.22917	−	0.0727110i
$673$	3.02767	−	34.6064i	0.116708	−	1.33398i	−0.681598	−	0.731727i	$-0.738715\pi$
$673$	3.02767	−	34.6064i	0.116708	−	1.33398i	0.798306	−	0.602252i	$-0.205730\pi$
$674$	−30.3912			−1.17063
$675$	24.9110	−	7.37858i	0.958824	−	0.284002i
$676$	28.6790			1.10304
$677$	1.51507	−	17.3173i	0.0582289	−	0.665560i	−0.909854	−	0.414929i	$-0.863806\pi$
$677$	1.51507	−	17.3173i	0.0582289	−	0.665560i	0.968083	−	0.250631i	$-0.0806380\pi$
$678$	−4.85263	−	9.07604i	−0.186364	−	0.348563i
$679$	−11.8000	−	2.08066i	−0.452843	−	0.0798485i
$680$	−13.8971	−	71.1504i	−0.532931	−	2.72849i
$681$	4.14629	−	34.4233i	0.158886	−	1.31910i
$682$	−3.89615	+	5.56428i	−0.149191	+	0.213067i
$683$	−2.94108	+	10.9763i	−0.112537	+	0.419995i	−0.999091	−	0.0426308i	$-0.986426\pi$
$683$	−2.94108	+	10.9763i	−0.112537	+	0.419995i	0.886554	+	0.462626i	$0.153093\pi$
$684$	26.7993	+	25.6425i	1.02470	+	0.980467i
$685$	−4.61879	+	0.489685i	−0.176475	+	0.0187099i
$686$	16.9564	−	46.5874i	0.647400	−	1.77872i
$687$	11.8931	+	36.3189i	0.453752	+	1.38565i
$688$	−17.2377	+	1.50810i	−0.657181	+	0.0574959i
$689$	0.825299	+	0.692508i	0.0314414	+	0.0263824i
$690$	0.677788	+	4.19235i	0.0258029	+	0.159600i
$691$	−22.0909	−	8.04044i	−0.840378	−	0.305873i	−0.114267	−	0.993450i	$-0.536452\pi$
$691$	−22.0909	−	8.04044i	−0.840378	−	0.305873i	−0.726111	+	0.687577i	$0.758674\pi$
$692$	−15.0162	−	56.0412i	−0.570830	−	2.13037i
$693$	−1.08756	+	1.98348i	−0.0413131	+	0.0753461i
$694$	−56.0171	+	32.3415i	−2.12638	+	1.22767i
$695$	−0.633652	−	34.5102i	−0.0240358	−	1.30905i
$696$	−90.0392	−	10.8453i	−3.41293	−	0.411088i
$697$	−24.4483	−	11.4004i	−0.926046	−	0.431822i
$698$	16.7611	−	11.7362i	0.634416	−	0.444223i
$699$	9.38495	−	30.9512i	0.354971	−	1.17068i
$700$	16.7059	−	39.5558i	0.631424	−	1.49507i
$701$		−	44.6039i		−	1.68467i	−0.538956	−	0.842334i	$-0.681181\pi$
$701$		−	44.6039i		−	1.68467i	0.538956	−	0.842334i	$-0.318819\pi$
$702$	−3.84119	+	39.1429i	−0.144976	+	1.47735i
$703$	2.40988	−	2.40988i	0.0908903	−	0.0908903i
$704$	−10.3268	+	8.66522i	−0.389206	+	0.326583i
$705$	26.3580	+	38.8083i	0.992699	+	1.46161i
$706$	−2.45245	+	13.9085i	−0.0922992	+	0.523455i
$707$	3.88937	−	8.34079i	0.146275	−	0.313688i
$708$	−12.4201	+	30.9455i	−0.466775	+	1.16300i
$709$	−36.4781	+	6.43207i	−1.36996	+	0.241562i	−0.809744	−	0.586783i	$-0.800394\pi$
$709$	−36.4781	+	6.43207i	−1.36996	+	0.241562i	−0.560219	+	0.828344i	$0.689283\pi$
$710$	−88.8687	−	39.4705i	−3.33518	−	1.48130i
$711$	5.36705	−	12.2054i	0.201280	−	0.457738i
$712$	63.1566	−	16.9228i	2.36689	−	0.634207i
$713$	0.889647	+	1.90785i	0.0333175	+	0.0714497i
$714$	−14.1764	−	21.7202i	−0.530538	−	0.812857i
$715$	2.95210	+	0.203744i	0.110402	+	0.00761958i
$716$	−23.1122	+	27.5441i	−0.863744	+	1.02937i
$717$	−25.1689	−	22.5575i	−0.939949	−	0.842427i
$718$	−33.7227	+	15.7251i	−1.25852	+	0.586857i
$719$	19.2483	−	33.3390i	0.717839	−	1.24333i	−0.244016	−	0.969771i	$-0.578465\pi$
$719$	19.2483	−	33.3390i	0.717839	−	1.24333i	0.961854	−	0.273562i	$-0.0882018\pi$
$720$	93.4542	−	29.1354i	3.48283	−	1.08581i
$721$	3.54064	+	6.13256i	0.131860	+	0.228389i
$722$	30.8251	+	21.5840i	1.14719	+	0.803273i
$723$	1.20571	+	8.43818i	0.0448408	+	0.313819i
$724$	16.2169	+	44.5557i	0.602698	+	1.65590i
$725$	13.1182	−	24.7799i	0.487197	−	0.920304i
$726$	−11.5525	−	49.5196i	−0.428755	−	1.83785i
$727$	−25.9897	−	2.27381i	−0.963906	−	0.0843308i	−0.405676	−	0.914017i	$-0.632964\pi$
$727$	−25.9897	−	2.27381i	−0.963906	−	0.0843308i	−0.558230	+	0.829686i	$0.688519\pi$
$728$	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
$732$	73.4158	+	45.6408i	2.71352	+	1.68693i
$733$	−27.9576	−	39.9276i	−1.03264	−	1.47476i	−0.873083	−	0.487571i	$-0.837883\pi$
$733$	−27.9576	−	39.9276i	−1.03264	−	1.47476i	−0.159555	−	0.987189i	$-0.551006\pi$
$734$	55.2278	−	20.1013i	2.03849	−	0.741951i
$735$	−0.248042	+	17.4087i	−0.00914918	+	0.642130i
$736$	1.47374	+	8.35802i	0.0543230	+	0.308081i
$737$	6.07772	+	1.62852i	0.223876	+	0.0599873i
$738$	20.4022	−	60.1498i	0.751015	−	2.21414i
$739$	−11.7531	−	6.78566i	−0.432345	−	0.249614i	0.268000	−	0.963419i	$-0.413637\pi$
$739$	−11.7531	−	6.78566i	−0.432345	−	0.249614i	−0.700345	+	0.713804i	$0.746971\pi$
$740$	−5.01849	−	17.4419i	−0.184483	−	0.641178i
$741$	−0.598849	−	10.9450i	−0.0219993	−	0.402073i
$742$	−0.145797	−	1.66647i	−0.00535238	−	0.0611780i
$743$	0.108282	+	1.23767i	0.00397247	+	0.0454055i	0.997922	−	0.0644303i	$-0.0205230\pi$
$743$	0.108282	+	1.23767i	0.00397247	+	0.0454055i	−0.993950	+	0.109836i	$0.964967\pi$
$744$	70.8542	−	46.2453i	2.59764	−	1.69544i
$745$	17.0400	−	30.8068i	0.624298	−	1.12867i
$746$	31.2331	+	18.0324i	1.14352	+	0.660214i
$747$	3.16949	+	8.14462i	0.115966	+	0.297996i
$748$	−8.67096	−	2.32338i	−0.317042	−	0.0849511i
$749$	0.224615	+	1.27386i	0.00820726	+	0.0465457i
$750$	−3.41698	+	52.6613i	−0.124771	+	1.92292i
$751$	−8.15950	+	2.96982i	−0.297745	+	0.108370i	−0.486573	−	0.873640i	$-0.661753\pi$
$751$	−8.15950	+	2.96982i	−0.297745	+	0.108370i	0.188828	+	0.982010i	$0.439531\pi$
$752$	101.385	+	144.793i	3.69713	+	5.28005i
$753$	−1.18066	+	36.1967i	−0.0430258	+	1.31908i
$754$	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	$0.477025\pi$
$758$	−74.4088	−	6.50993i	−2.70265	−	0.236451i
$759$	0.317761	+	0.0963507i	0.0115340	+	0.00349731i
$760$	−42.7378	+	20.8926i	−1.55026	+	0.757854i
$761$	14.0169	+	38.5111i	0.508112	+	1.39603i	0.883183	+	0.469029i	$0.155396\pi$
$761$	14.0169	+	38.5111i	0.508112	+	1.39603i	−0.375071	+	0.926996i	$0.622382\pi$
$762$	−13.2530	+	10.4036i	−0.480107	+	0.376882i
$763$	−10.9674	−	7.67948i	−0.397048	−	0.278016i
$764$	54.7283	+	94.7922i	1.98000	+	3.42946i
$765$	18.4331	+	14.2387i	0.666449	+	0.514803i
$766$	−49.2326	+	85.2733i	−1.77884	+	3.08105i
$767$	8.93101	−	4.16460i	0.322480	−	0.150375i
$768$	63.4973	−	20.7931i	2.29126	−	0.750307i
$769$	3.94057	−	4.69619i	0.142100	−	0.169349i	−0.690300	−	0.723523i	$-0.742521\pi$
$769$	3.94057	−	4.69619i	0.142100	−	0.169349i	0.832401	+	0.554174i	$0.186966\pi$
$770$	−3.01754	−	3.46494i	−0.108745	−	0.124868i
$771$	11.4275	−	22.5558i	0.411550	−	0.812327i
$772$	−43.0641	−	92.3513i	−1.54991	−	3.32380i
$773$	−9.19044	+	2.46257i	−0.330557	+	0.0885726i	−0.420281	−	0.907394i	$-0.638068\pi$
$773$	−9.19044	+	2.46257i	−0.330557	+	0.0885726i	0.0897234	+	0.995967i	$0.471402\pi$
$774$	6.70197	−	7.00429i	0.240897	−	0.251764i
$775$	5.48501	+	25.5770i	0.197027	+	0.918752i
$776$	69.6196	−	12.2758i	2.49920	−	0.440676i
$777$	−2.53176	−	3.22518i	−0.0908263	−	0.115703i
$778$	21.2928	−	45.6625i	0.763382	−	1.63708i
$779$	−3.07383	+	17.4326i	−0.110132	+	0.624587i
$780$	−52.5479	−	25.4211i	−1.88152	−	0.910221i
$781$	−5.82422	+	4.88710i	−0.208407	+	0.174874i
$782$	−2.69216	+	2.69216i	−0.0962714	+	0.0962714i
$783$	24.0435	−	16.4601i	0.859244	−	0.588235i
$784$			65.5994i			2.34283i
$785$	9.27875	−	37.3592i	0.331173	−	1.33341i
$786$	9.92491	+	10.5942i	0.354010	+	0.377883i
$787$	−6.94038	+	4.85971i	−0.247398	+	0.173230i	−0.690698	−	0.723143i	$-0.742697\pi$
$787$	−6.94038	+	4.85971i	−0.247398	+	0.173230i	0.443300	+	0.896373i	$0.353808\pi$
$788$	24.6435	+	11.4915i	0.877890	+	0.409367i
$789$	−20.8327	−	48.7667i	−0.741665	−	1.73614i
$790$	19.4986	+	18.7955i	0.693729	+	0.668713i
$791$	2.98847	−	1.72539i	0.106258	−	0.0613479i
$792$	2.02713	−	13.1913i	0.0720310	−	0.468732i
$793$	−6.61207	−	24.6766i	−0.234802	−	0.876291i
$794$	−77.2406	−	28.1133i	−2.74116	−	0.997702i
$795$	0.615411	+	1.37040i	0.0218264	+	0.0486029i
$796$	−69.2896	−	58.1409i	−2.45591	−	2.06075i
$797$	−28.1786	+	2.46530i	−0.998136	+	0.0873256i	−0.574498	−	0.818506i	$-0.694803\pi$
$797$	−28.1786	+	2.46530i	−0.998136	+	0.0873256i	−0.423638	+	0.905832i	$0.639247\pi$
$798$	−11.3595	+	12.6745i	−0.402121	+	0.448672i
$799$	−14.3847	+	39.5216i	−0.508894	+	1.39818i
$800$	−5.32863	+	105.327i	−0.188395	+	3.72388i
$801$	−11.6670	+	17.4699i	−0.412234	+	0.617268i
$802$	24.5527	−	91.6319i	0.866986	−	3.23564i
$803$	−2.18967	+	3.12717i	−0.0772716	+	0.110355i
$804$	−99.3006	−	74.4709i	−3.50206	−	2.62639i
$805$	−1.39751	+	0.272962i	−0.0492556	+	0.00962063i
$806$	−38.9984	−	6.87647i	−1.37366	−	0.242213i
$807$	−21.6648	+	34.8490i	−0.762637	+	1.22674i
$808$	−4.73234	+	54.0909i	−0.166483	+	1.90291i
$809$	2.28591			0.0803683			0.0401841	−	0.999192i	$-0.487206\pi$
$809$	2.28591			0.0803683			0.0401841	+	0.999192i	$0.487206\pi$
$810$	−28.5905	+	46.8002i	−1.00457	+	1.64439i
$811$	21.6606			0.760605			0.380303	−	0.924862i	$-0.375820\pi$
$811$	21.6606			0.760605			0.380303	+	0.924862i	$0.375820\pi$
$812$	4.19715	−	47.9736i	0.147291	−	1.68354i
$813$	18.3957	−	29.5906i	0.645166	−	1.03779i
$814$	−1.91260	−	0.337243i	−0.0670367	−	0.0118204i
$815$	6.48756	+	4.36737i	0.227249	+	0.152982i
$816$	70.2096	+	52.6539i	2.45783	+	1.84326i
$817$	−1.54964	+	2.21311i	−0.0542150	+	0.0774270i
$818$	15.6279	−	58.3243i	0.546418	−	2.03926i
$819$	−13.1593	−	0.859376i	−0.459824	−	0.0300290i
$820$	73.3139	+	59.2585i	2.56023	+	2.06940i
$821$	7.91413	−	21.7439i	0.276205	−	0.758867i	−0.721579	−	0.692332i	$-0.756583\pi$
$821$	7.91413	−	21.7439i	0.276205	−	0.758867i	0.997784	−	0.0665351i	$-0.0211944\pi$
$822$	6.54361	−	7.30112i	0.228235	−	0.254656i
$823$	−6.50574	+	0.569178i	−0.226776	+	0.0198403i	−0.199977	−	0.979801i	$-0.564087\pi$
$823$	−6.50574	+	0.569178i	−0.226776	+	0.0198403i	−0.0267986	+	0.999641i	$0.508531\pi$
$824$	−32.0047	−	26.8552i	−1.11494	−	0.935544i
$825$	3.58180	+	2.04836i	0.124702	+	0.0713147i
$826$	−14.3783	−	5.23326i	−0.500284	−	0.182088i
$827$	2.39679	+	8.94494i	0.0833445	+	0.311046i	0.994996	−	0.0999193i	$-0.0318585\pi$
$827$	2.39679	+	8.94494i	0.0833445	+	0.311046i	−0.911651	+	0.410965i	$0.865192\pi$
$828$	−5.10939	−	4.09873i	−0.177564	−	0.142441i
$829$	−2.45210	+	1.41572i	−0.0851648	+	0.0491699i	−0.541978	−	0.840393i	$-0.682324\pi$
$829$	−2.45210	+	1.41572i	−0.0851648	+	0.0491699i	0.456813	+	0.889563i	$0.348991\pi$
$830$	−17.7488	+	0.325891i	−0.616071	+	0.0113118i
$831$	−10.3471	−	24.2211i	−0.358936	−	0.840222i
$832$	−71.2260	−	33.2132i	−2.46932	−	1.15146i
$833$	−12.7859	+	8.95278i	−0.443005	+	0.310195i
$834$	49.8123	+	53.1715i	1.72486	+	1.84118i
$835$	14.2974	+	3.55098i	0.494781	+	0.122887i
$836$			5.89061i			0.203731i
$837$	−7.31263	+	26.1827i	−0.252761	+	0.905007i
$838$	9.63173	−	9.63173i	0.332723	−	0.332723i
$839$	32.4518	−	27.2303i	1.12036	−	0.940095i	0.121739	−	0.992562i	$-0.461153\pi$
$839$	32.4518	−	27.2303i	1.12036	−	0.940095i	0.998623	+	0.0524668i	$0.0167084\pi$
$840$	18.8063	+	54.0539i	0.648879	+	1.86504i
$841$	0.424617	−	2.40812i	0.0146420	−	0.0830387i
$842$	15.1760	−	32.5451i	0.523000	−	1.12158i
$843$	25.5352	+	32.5291i	0.879479	+	1.12036i
$844$	−55.8394	+	9.84600i	−1.92207	+	0.338913i
$845$	−4.24515	−	11.0291i	−0.146038	−	0.379413i
$846$	−96.1954	−	23.5147i	−3.30727	−	0.808452i
$847$	16.4684	−	4.41271i	0.565862	−	0.151622i
$848$	2.39208	+	5.12983i	0.0821443	+	0.176159i
$849$	−0.223330	+	0.440813i	−0.00766466	+	0.0151287i
$850$	−40.0763	+	25.1435i	−1.37460	+	0.862415i
$851$	−0.386871	+	0.461054i	−0.0132618	+	0.0158047i
$852$	142.535	−	46.6750i	4.88316	−	1.59906i
$853$	30.1905	−	14.0780i	1.03370	−	0.482023i	0.169691	−	0.985497i	$-0.445723\pi$
$853$	30.1905	−	14.0780i	1.03370	−	0.482023i	0.864010	+	0.503474i	$0.167945\pi$
$854$	−19.8339	+	34.3532i	−0.678701	+	1.17554i
$855$	5.89448	−	14.1019i	0.201587	−	0.482275i
$856$	−3.81582	−	6.60919i	−0.130422	−	0.225897i
$857$	−25.1791	−	17.6306i	−0.860100	−	0.602249i	0.0581240	−	0.998309i	$-0.481488\pi$
$857$	−25.1791	−	17.6306i	−0.860100	−	0.602249i	−0.918224	+	0.396061i	$0.870377\pi$
$858$	−4.91333	+	3.85695i	−0.167738	+	0.131674i
$859$	−17.6716	−	48.5522i	−0.602946	−	1.65658i	−0.745272	−	0.666760i	$-0.767680\pi$
$859$	−17.6716	−	48.5522i	−0.602946	−	1.65658i	0.142326	−	0.989820i	$-0.454542\pi$
$860$	6.31891	+	12.9259i	0.215473	+	0.440771i
$861$	20.3800	+	6.17958i	0.694550	+	0.210600i
$862$	39.4098	+	3.44791i	1.34230	+	0.117436i
$863$	31.9076	+	31.9076i	1.08615	+	1.08615i	0.995921	+	0.0902264i	$0.0287591\pi$
$863$	31.9076	+	31.9076i	1.08615	+	1.08615i	0.0902264	+	0.995921i	$0.471241\pi$
$864$	−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
$867$	0.279168	−	8.55872i	0.00948105	−	0.290669i
$868$	25.7700	+	36.8034i	0.874692	+	1.24919i
$869$	1.98983	−	0.724239i	0.0675003	−	0.0245681i
$870$	14.5022	+	57.3807i	0.491670	+	1.94539i
$871$	6.36968	+	36.1243i	0.215829	+	1.22402i
$872$	76.3015	+	20.4449i	2.58390	+	0.692353i
$873$	−14.2126	+	17.7171i	−0.481023	+	0.599634i
$874$	2.16363	+	1.24917i	0.0731860	+	0.0422539i
$875$	−17.6849	−	0.569453i	−0.597858	−	0.0192510i
$876$	63.0643	−	41.1610i	2.13074	−	1.39070i
$877$	3.42618	+	39.1615i	0.115694	+	1.32239i	0.802982	+	0.596003i	$0.203245\pi$
$877$	3.42618	+	39.1615i	0.115694	+	1.32239i	−0.687288	+	0.726385i	$0.741199\pi$
$878$	−5.13448	−	58.6873i	−0.173280	−	1.98060i
$879$	1.47109	+	26.8866i	0.0496186	+	0.906863i
$880$	13.6041	+	7.52478i	0.458594	+	0.253660i
$881$	−34.0163	−	19.6393i	−1.14604	−	0.661666i	−0.198120	−	0.980178i	$-0.563484\pi$
$881$	−34.0163	−	19.6393i	−1.14604	−	0.661666i	−0.947919	+	0.318512i	$0.896817\pi$
$882$	−24.2385	−	27.6254i	−0.816151	−	0.930197i
$883$	17.3273	+	4.64284i	0.583111	+	0.156244i	0.538303	−	0.842752i	$-0.319066\pi$
$883$	17.3273	+	4.64284i	0.583111	+	0.156244i	0.0448081	+	0.998996i	$0.485732\pi$
$884$	−9.08751	−	51.5378i	−0.305646	−	1.73340i
$885$	13.7392	+	0.195759i	0.461839	+	0.00658036i
$886$	−30.7381	+	11.1878i	−1.03267	+	0.375860i
$887$	−9.98188	−	14.2556i	−0.335159	−	0.478656i	0.615831	−	0.787878i	$-0.288820\pi$
$887$	−9.98188	−	14.2556i	−0.335159	−	0.478656i	−0.950990	+	0.309222i	$0.899931\pi$
$888$	20.5446	+	12.7720i	0.689430	+	0.428602i
$889$	−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
$893$	27.4935	+	2.40537i	0.920036	+	0.0804927i
$894$	16.8836	+	72.3711i	0.564673	+	2.42045i
$895$	14.0138	+	4.81114i	0.468430	+	0.160819i
$896$	18.9021	+	51.9330i	0.631474	+	1.73496i
$897$	0.273814	+	1.91630i	0.00914239	+	0.0639833i
$898$	67.5821	+	47.3215i	2.25524	+	1.57914i
$899$	14.6687	+	25.4069i	0.489227	+	0.847367i
$900$	−50.5223	−	63.8178i	−1.68408	−	2.12726i
$901$	−0.673386	+	1.16634i	−0.0224337	+	0.0388564i
$902$	9.14216	−	4.26306i	0.304401	−	0.141944i
$903$	2.42050	+	2.16936i	0.0805490	+	0.0721919i
$904$	−13.0868	+	15.5963i	−0.435261	+	0.518724i
$905$	14.7344	−	12.8318i	0.489787	−	0.426545i
$906$	2.77166	+	4.24656i	0.0920821	+	0.141083i
$907$	−8.34207	−	17.8896i	−0.276994	−	0.594015i	0.717763	−	0.696288i	$-0.245166\pi$
$907$	−8.34207	−	17.8896i	−0.276994	−	0.594015i	−0.994756	+	0.102273i	$0.967389\pi$
$908$	−104.923	+	28.1141i	−3.48200	+	0.932999i
$909$	−10.3190	−	14.0663i	−0.342258	−	0.466549i
$910$	10.8727	−	24.4802i	0.360427	−	0.811510i
$911$	29.7171	−	5.23993i	0.984571	−	0.173606i	0.341890	−	0.939740i	$-0.388933\pi$
$911$	29.7171	−	5.23993i	0.984571	−	0.173606i	0.642681	+	0.766134i	$0.277822\pi$
$912$	21.4501	−	53.4443i	0.710282	−	1.76972i
$913$	−0.586586	+	1.25794i	−0.0194132	+	0.0416317i
$914$	19.6914	−	111.676i	0.651334	−	3.69390i
$915$	6.68492	−	34.9895i	0.220997	−	1.15672i
$916$	91.7178	−	76.9604i	3.03044	−	2.54284i
$917$	−3.44178	+	3.44178i	−0.113658	+	0.113658i
$918$	−49.0221	+	3.76806i	−1.61797	+	0.124365i
$919$		−	5.90514i		−	0.194793i	−0.995246	−	0.0973964i	$-0.968949\pi$
$919$		−	5.90514i		−	0.194793i	0.995246	−	0.0973964i	$-0.0310515\pi$
$920$	7.19716	−	4.33337i	0.237283	−	0.142867i
$921$	−5.29015	+	17.4467i	−0.174316	+	0.574889i
$922$	−38.5192	+	26.9715i	−1.26856	+	0.888258i
$923$	−40.1708	−	18.7320i	−1.32224	−	0.616570i
$924$	7.03602	+	0.847491i	0.231468	+	0.0278804i
$925$	−5.96481	+	4.51177i	−0.196122	+	0.148346i
$926$	38.9006	−	22.4592i	1.27835	−	0.738057i
$927$	13.4201	−	0.296009i	0.440773	−	0.00972221i
$928$	30.6126	+	114.248i	1.00491	+	3.75036i
$929$	6.36097	+	2.31520i	0.208697	+	0.0759593i	0.444253	−	0.895901i	$-0.353469\pi$
$929$	6.36097	+	2.31520i	0.208697	+	0.0759593i	−0.235557	+	0.971861i	$0.575691\pi$
$930$	−44.7757	−	32.3126i	−1.46825	−	1.05957i
$931$	7.84617	+	6.58371i	0.257148	+	0.215773i
$932$	−100.942	+	8.83124i	−3.30645	+	0.289277i
$933$	−1.73298	−	5.29211i	−0.0567352	−	0.173256i
$934$	3.70965	−	10.1922i	0.121383	−	0.333498i
$935$	0.389997	+	3.67852i	0.0127543	+	0.120300i
$936$	74.6914	−	21.7898i	2.44136	−	0.712220i
$937$	−1.63137	+	6.08835i	−0.0532945	+	0.198898i	−0.987440	−	0.157995i	$-0.949497\pi$
$937$	−1.63137	+	6.08835i	−0.0532945	+	0.198898i	0.934145	+	0.356892i	$0.116164\pi$
$938$	32.6689	−	46.6560i	1.06668	−	1.52337i
$939$	5.03711	−	41.8190i	0.164380	−	1.36471i
$940$	82.0766	−	121.922i	2.67704	−	3.97664i
$941$	26.7793	+	4.72192i	0.872981	+	0.153930i	0.592151	−	0.805827i	$-0.298279\pi$
$941$	26.7793	+	4.72192i	0.872981	+	0.153930i	0.280831	+	0.959757i	$0.409390\pi$
$942$	38.3126	+	71.6575i	1.24829	+	2.33473i
$943$	0.272455	−	3.11417i	0.00887234	−	0.101411i
$944$	51.7720			1.68504
$945$	−15.9959	−	9.06950i	−0.520348	−	0.295031i
$946$	1.53958			0.0500560
$947$	−4.20583	+	48.0728i	−0.136671	+	1.56216i	0.549985	+	0.835174i	$0.314633\pi$
$947$	−4.20583	+	48.0728i	−0.136671	+	1.56216i	−0.686656	+	0.726982i	$0.740922\pi$
$948$	−41.7499	−	1.36180i	−1.35597	−	0.0442291i
$949$	−21.9174	−	3.86463i	−0.711469	−	0.125451i
$950$	22.7435	+	21.1317i	0.737895	+	0.685603i
$951$	33.0815	−	14.1322i	1.07274	−	0.458267i
$952$	−29.4297	+	42.0300i	−0.953822	+	1.36220i
$953$	−5.07394	+	18.9362i	−0.164361	+	0.613404i	0.833760	+	0.552128i	$0.186184\pi$
$953$	−5.07394	+	18.9362i	−0.164361	+	0.613404i	−0.998121	+	0.0612767i	$0.980483\pi$
$954$	−2.90279	−	1.27644i	−0.0939814	−	0.0413262i
$955$	28.3533	−	35.0784i	0.917492	−	1.13511i
$956$	−36.2153	+	99.5008i	−1.17129	+	3.21809i
$957$	4.52863	+	0.951709i	0.146390	+	0.0307644i
$958$	3.84959	−	0.336795i	0.124375	−	0.0108814i
$959$	2.51823	+	2.11305i	0.0813180	+	0.0682339i
$960$	−69.2357	−	84.9406i	−2.23457	−	2.74145i
$961$	3.41043	+	1.24130i	0.110014	+	0.0400418i
$962$	−2.93036	−	10.9362i	−0.0944785	−	0.352599i
$963$	2.32205	+	0.787615i	0.0748269	+	0.0253805i
$964$	23.1268	−	13.3523i	0.744865	−	0.430048i
$965$	−29.1412	+	30.2314i	−0.938088	+	0.973182i
$966$	1.80336	−	2.40462i	0.0580220	−	0.0773674i
$967$	−3.93769	−	1.83617i	−0.126628	−	0.0590474i	0.358272	−	0.933617i	$-0.383366\pi$
$967$	−3.93769	−	1.83617i	−0.126628	−	0.0590474i	−0.484900	+	0.874570i	$0.661144\pi$
$968$	−82.3990	+	57.6964i	−2.64841	+	1.85443i
$969$	13.3442	−	3.11310i	0.428678	−	0.100007i
$970$	−23.7972	−	39.5240i	−0.764082	−	1.26904i
$971$			17.3753i			0.557601i	0.960349	+	0.278800i	$0.0899367\pi$
$971$			17.3753i			0.557601i	−0.960349	+	0.278800i	$0.910063\pi$
$972$	−15.6457	−	83.1291i	−0.501837	−	2.66637i
$973$	−17.2740	+	17.2740i	−0.553779	+	0.553779i
$974$	−17.5070	+	14.6901i	−0.560960	+	0.470701i
$975$	−1.99793	+	23.9713i	−0.0639849	+	0.767696i
$976$	23.3068	−	132.179i	0.746031	−	4.23095i
$977$	−10.2242	+	21.9259i	−0.327101	+	0.701470i	−0.999241	−	0.0389538i	$-0.987597\pi$
$977$	−10.2242	+	21.9259i	−0.327101	+	0.701470i	0.672140	+	0.740424i	$0.265375\pi$
$978$	−16.3424	+	2.33512i	−0.522573	+	0.0746690i
$979$	−3.28563	+	0.579345i	−0.105009	+	0.0185159i
$980$	50.9048	−	19.5935i	1.62610	−	0.625890i
$981$	−22.7599	+	11.2306i	−0.726667	+	0.358566i
$982$	−70.5563	+	18.9055i	−2.25154	+	0.603299i
$983$	−10.2662	−	22.0159i	−0.327441	−	0.702199i	0.671817	−	0.740717i	$-0.265514\pi$
$983$	−10.2662	−	22.0159i	−0.327441	−	0.702199i	−0.999258	+	0.0385180i	$0.987736\pi$
$984$	−125.460	+	6.86447i	−3.99951	+	0.218831i
$985$	0.771481	−	11.1782i	0.0245814	−	0.356167i
$986$	−34.1063	+	40.6463i	−1.08617	+	1.29444i
$987$	6.82862	−	32.4935i	0.217357	−	1.03428i
$988$	−31.1234	+	14.5131i	−0.990168	+	0.461723i
$989$	0.238560	−	0.413197i	0.00758575	−	0.0131389i
$990$	−8.50936	+	1.85775i	−0.270445	+	0.0590432i
$991$	−18.0498	−	31.2632i	−0.573372	−	0.993110i	−0.996216	−	0.0869073i	$-0.972302\pi$
$991$	−18.0498	−	31.2632i	−0.573372	−	0.993110i	0.422844	−	0.906202i	$-0.361032\pi$
$992$	−90.3927	−	63.2936i	−2.86997	−	2.00957i
$993$	9.57682	+	3.84369i	0.303911	+	0.121976i
$994$	23.5387	+	64.6720i	0.746602	+	2.05127i
$995$	−12.1029	+	35.2530i	−0.383687	+	1.11760i
$996$	19.9817	−	18.7194i	0.633145	−	0.593146i
$997$	19.8840	+	1.73962i	0.629732	+	0.0550944i	0.397554	−	0.917579i	$-0.369859\pi$
$997$	19.8840	+	1.73962i	0.629732	+	0.0550944i	0.232178	+	0.972673i	$0.425415\pi$
$998$	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.32.16	✓	192
3.2	odd	2		405.2.r.a.287.1		192
5.2	odd	4		675.2.ba.b.518.16		192
5.3	odd	4	inner	135.2.q.a.113.1	yes	192
5.4	even	2		675.2.ba.b.32.1		192
15.8	even	4		405.2.r.a.368.16		192
27.11	odd	18	inner	135.2.q.a.92.1	yes	192
27.16	even	9		405.2.r.a.197.16		192
135.38	even	36	inner	135.2.q.a.38.16	yes	192
135.43	odd	36		405.2.r.a.278.1		192
135.92	even	36		675.2.ba.b.443.1		192
135.119	odd	18		675.2.ba.b.632.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.16	✓	192	1.1	even	1	trivial
135.2.q.a.38.16	yes	192	135.38	even	36	inner
135.2.q.a.92.1	yes	192	27.11	odd	18	inner
135.2.q.a.113.1	yes	192	5.3	odd	4	inner
405.2.r.a.197.16		192	27.16	even	9
405.2.r.a.278.1		192	135.43	odd	36
405.2.r.a.287.1		192	3.2	odd	2
405.2.r.a.368.16		192	15.8	even	4
675.2.ba.b.32.1		192	5.4	even	2
675.2.ba.b.443.1		192	135.92	even	36
675.2.ba.b.518.16		192	5.2	odd	4
675.2.ba.b.632.16		192	135.119	odd	18

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+(0.237511 - 2.71476i) q^{2} +(0.914466 - 1.47097i) q^{3} +(-5.34392 - 0.942278i) q^{4} +(0.428650 + 2.19460i) q^{5} +(-3.77614 - 2.83193i) q^{6} +(0.907744 - 1.29639i) q^{7} +(-2.41667 + 9.01913i) q^{8} +(-1.32750 - 2.69030i) q^{9} +(6.05963 - 0.642443i) q^{10} +(0.162954 - 0.447712i) q^{11} +(-6.27290 + 6.99907i) q^{12} +(2.76700 - 0.242081i) q^{13} +(-3.30380 - 2.77222i) q^{14} +(3.62017 + 1.37635i) q^{15} +(13.7126 + 4.99098i) q^{16} +(0.898665 + 3.35386i) q^{17} +(-7.61884 + 2.96488i) q^{18} +(1.97319 - 1.13922i) q^{19} +(-0.222753 - 12.1317i) q^{20} +(-1.07685 - 2.52077i) q^{21} +(-1.17673 - 0.548719i) q^{22} +(-0.329603 + 0.230790i) q^{23} +(11.0569 + 11.8025i) q^{24} +(-4.63252 + 1.88143i) q^{25} -7.56924i q^{26} +(-5.17131 - 0.507474i) q^{27} +(-6.07248 + 6.07248i) q^{28} +(-4.29568 + 3.60450i) q^{29} +(4.59631 - 9.50102i) q^{30} +(0.908475 - 5.15222i) q^{31} +(8.91403 - 19.1162i) q^{32} +(-0.509556 - 0.649118i) q^{33} +(9.31839 - 1.64308i) q^{34} +(3.23417 + 1.43643i) q^{35} +(4.55906 + 15.6276i) q^{36} +(1.44483 - 0.387140i) q^{37} +(-2.62407 - 5.62733i) q^{38} +(2.17423 - 4.29154i) q^{39} +(-20.8293 - 1.43756i) q^{40} +(-4.99389 + 5.95149i) q^{41} +(-7.09907 + 2.32469i) q^{42} +(-1.07467 + 0.501128i) q^{43} +(-1.29268 + 2.23899i) q^{44} +(5.33510 - 4.06654i) q^{45} +(0.548257 + 0.949609i) q^{46} +(9.92230 + 6.94767i) q^{47} +(19.8813 - 15.6068i) q^{48} +(1.53751 + 4.22426i) q^{49} +(4.00736 + 13.0231i) q^{50} +(5.75523 + 1.74508i) q^{51} +(-15.0147 - 1.31362i) 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} +(0.128655 - 3.94428i) q^{57} +(8.76510 + 12.5179i) q^{58} +(3.33385 - 1.21342i) q^{59} +(-18.0490 - 10.7663i) q^{60} +(-1.59716 - 9.05792i) q^{61} +(-13.7713 - 3.69001i) q^{62} +(-4.69272 - 0.721141i) q^{63} +(-24.5036 - 14.1471i) q^{64} +(1.71734 + 5.96868i) q^{65} +(-1.88323 + 1.22915i) q^{66} +(1.15101 + 13.1561i) q^{67} +(-1.64212 - 18.7696i) q^{68} +(0.0380751 + 0.695886i) q^{69} +(4.66773 - 8.43883i) q^{70} +(-13.8198 - 7.97886i) q^{71} +(27.4723 - 5.47136i) q^{72} +(-7.73957 - 2.07381i) q^{73} +(-0.707832 - 4.01431i) q^{74} +(-1.46875 + 8.53480i) q^{75} +(-11.6180 + 4.22862i) q^{76} +(-0.432491 - 0.617661i) q^{77} +(-11.1341 - 6.92182i) 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} +(-2.90211 - 0.253902i) q^{83} +(3.37935 + 14.4855i) q^{84} +(-6.97517 + 3.40984i) q^{85} +(1.10520 + 3.03651i) q^{86} +(1.37386 + 9.61501i) q^{87} +(3.64417 + 2.55168i) q^{88} +(-3.50126 - 6.06435i) q^{89} +(-9.77254 - 15.4494i) q^{90} +(2.19789 - 3.80686i) q^{91} +(1.97884 - 0.922748i) q^{92} +(-6.74799 - 6.04787i) q^{93} +(21.2179 - 25.2866i) q^{94} +(3.34594 + 3.84203i) q^{95} +(-19.9678 - 30.5934i) q^{96} +(-3.19969 - 6.86175i) q^{97} +(11.8331 - 3.17066i) 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

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