LMFDB - Embedded newform 117.2.bc.a.110.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(20,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 11]))

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

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

chi := DirichletCharacter("117.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			110.4
Character	$\chi$	$=$	117.110
Dual form			117.2.bc.a.50.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.411454 + 1.53557i) q^{2} +(-1.55144 + 0.770091i) q^{3} +(-0.456617 - 0.263628i) q^{4} +(-0.492404 + 1.83768i) q^{5} +(-0.544181 - 2.69919i) q^{6} +(-1.36095 - 1.36095i) q^{7} +(-1.65553 + 1.65553i) q^{8} +(1.81392 - 2.38950i) q^{9} +O(q^{10})$	\(q+(-0.411454 + 1.53557i) q^{2} +(-1.55144 + 0.770091i) q^{3} +(-0.456617 - 0.263628i) q^{4} +(-0.492404 + 1.83768i) q^{5} +(-0.544181 - 2.69919i) q^{6} +(-1.36095 - 1.36095i) q^{7} +(-1.65553 + 1.65553i) q^{8} +(1.81392 - 2.38950i) q^{9} +(-2.61927 - 1.51224i) q^{10} +(-1.67214 - 0.448047i) q^{11} +(0.911431 + 0.0573657i) q^{12} +(0.812525 + 3.51281i) q^{13} +(2.64980 - 1.52986i) q^{14} +(-0.651244 - 3.23023i) q^{15} +(-2.38826 - 4.13658i) q^{16} +(2.74894 + 4.76130i) q^{17} +(2.92289 + 3.76856i) q^{18} +(-0.121837 - 0.0326462i) q^{19} +(0.709302 - 0.709302i) q^{20} +(3.15949 + 1.06338i) q^{21} +(1.37601 - 2.38332i) q^{22} +5.98324 q^{23} +(1.29354 - 3.84336i) q^{24} +(1.19554 + 0.690245i) q^{25} +(-5.72846 - 0.197671i) q^{26} +(-0.974052 + 5.10404i) q^{27} +(0.262649 + 0.980220i) q^{28} +(-3.57718 + 2.06528i) q^{29} +(5.22819 + 0.329064i) q^{30} +(7.42505 + 1.98954i) q^{31} +(2.81166 - 0.753382i) q^{32} +(2.93925 - 0.592579i) q^{33} +(-8.44235 + 2.26212i) q^{34} +(3.17113 - 1.83085i) q^{35} +(-1.45820 + 0.612885i) q^{36} +(-3.76694 + 1.00935i) q^{37} +(0.100261 - 0.173657i) q^{38} +(-3.96576 - 4.82418i) q^{39} +(-2.22714 - 3.85751i) q^{40} +(-0.211390 - 0.211390i) q^{41} +(-2.93287 + 4.41408i) q^{42} +2.03274i q^{43} +(0.645408 + 0.645408i) q^{44} +(3.49794 + 4.50999i) q^{45} +(-2.46183 + 9.18767i) q^{46} +(-2.81142 - 10.4924i) q^{47} +(6.89078 + 4.57847i) q^{48} -3.29561i q^{49} +(-1.55182 + 1.55182i) q^{50} +(-7.93144 - 5.26993i) q^{51} +(0.555061 - 1.81821i) q^{52} -9.44984i q^{53} +(-7.43681 - 3.59580i) q^{54} +(1.64673 - 2.85222i) q^{55} +4.50620 q^{56} +(0.214164 - 0.0431773i) q^{57} +(-1.69954 - 6.34276i) q^{58} +(-2.05031 - 7.65187i) q^{59} +(-0.554211 + 1.64667i) q^{60} +12.7569 q^{61} +(-6.11013 + 10.5830i) q^{62} +(-5.72066 + 0.783335i) q^{63} -4.92556i q^{64} +(-6.85549 - 0.236561i) q^{65} +(-0.299422 + 4.75723i) q^{66} +(-8.66726 + 8.66726i) q^{67} -2.89879i q^{68} +(-9.28263 + 4.60764i) q^{69} +(1.50662 + 5.62279i) q^{70} +(-1.16407 + 4.34437i) q^{71} +(0.952886 + 6.95888i) q^{72} +(9.98266 + 9.98266i) q^{73} -6.19968i q^{74} +(-2.38636 - 0.150198i) q^{75} +(0.0470265 + 0.0470265i) q^{76} +(1.66593 + 2.88547i) q^{77} +(9.03957 - 4.10476i) q^{78} +(1.34539 - 2.33029i) q^{79} +(8.77768 - 2.35197i) q^{80} +(-2.41939 - 8.66871i) q^{81} +(0.411580 - 0.237626i) q^{82} +(-0.307307 + 0.0823426i) q^{83} +(-1.16234 - 1.31849i) q^{84} +(-10.1033 + 2.70717i) q^{85} +(-3.12140 - 0.836377i) q^{86} +(3.95931 - 5.95891i) q^{87} +(3.51003 - 2.02651i) q^{88} +(2.68454 + 10.0188i) q^{89} +(-8.36463 + 3.51566i) q^{90} +(3.67496 - 5.88658i) q^{91} +(-2.73205 - 1.57735i) q^{92} +(-13.0516 + 2.63132i) q^{93} +17.2685 q^{94} +(0.119986 - 0.207822i) q^{95} +(-3.78194 + 3.33406i) q^{96} +(2.81052 - 2.81052i) q^{97} +(5.06062 + 1.35599i) q^{98} +(-4.10373 + 3.18284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.411454	+	1.53557i	−0.290942	+	1.08581i	0.653446	+	0.756973i	$0.273323\pi$
$2$	−0.411454	+	1.53557i	−0.290942	+	1.08581i	−0.944387	+	0.328835i	$0.893344\pi$
$3$	−1.55144	+	0.770091i	−0.895723	+	0.444612i
$3$	−1.55144	+	0.770091i	−0.895723	+	0.444612i
$4$	−0.456617	−	0.263628i	−0.228309	−	0.131814i
$5$	−0.492404	+	1.83768i	−0.220210	+	0.821833i	0.764058	+	0.645148i	$0.223204\pi$
$5$	−0.492404	+	1.83768i	−0.220210	+	0.821833i	−0.984267	+	0.176685i	$0.943462\pi$
$6$	−0.544181	−	2.69919i	−0.222161	−	1.10194i
$7$	−1.36095	−	1.36095i	−0.514392	−	0.514392i	0.401477	−	0.915869i	$-0.368497\pi$
$7$	−1.36095	−	1.36095i	−0.514392	−	0.514392i	−0.915869	+	0.401477i	$0.868497\pi$
$8$	−1.65553	+	1.65553i	−0.585318	+	0.585318i
$9$	1.81392	−	2.38950i	0.604640	−	0.796499i
$10$	−2.61927	−	1.51224i	−0.828286	−	0.478211i
$11$	−1.67214	−	0.448047i	−0.504168	−	0.135091i	−0.00223421	−	0.999998i	$-0.500711\pi$
$11$	−1.67214	−	0.448047i	−0.504168	−	0.135091i	−0.501934	+	0.864906i	$0.667378\pi$
$12$	0.911431	+	0.0573657i	0.263107	+	0.0165600i
$13$	0.812525	+	3.51281i	0.225354	+	0.974277i
$13$	0.812525	+	3.51281i	0.225354	+	0.974277i
$14$	2.64980	−	1.52986i	0.708190	−	0.408874i
$15$	−0.651244	−	3.23023i	−0.168150	−	0.834043i
$16$	−2.38826	−	4.13658i	−0.597064	−	1.03415i
$17$	2.74894	+	4.76130i	0.666716	+	1.15479i	0.978817	+	0.204737i	$0.0656338\pi$
$17$	2.74894	+	4.76130i	0.666716	+	1.15479i	−0.312102	+	0.950049i	$0.601033\pi$
$18$	2.92289	+	3.76856i	0.688931	+	0.888258i
$19$	−0.121837	−	0.0326462i	−0.0279514	−	0.00748955i	0.244816	−	0.969569i	$-0.421272\pi$
$19$	−0.121837	−	0.0326462i	−0.0279514	−	0.00748955i	−0.272768	+	0.962080i	$0.587939\pi$
$20$	0.709302	−	0.709302i	0.158605	−	0.158605i
$21$	3.15949	+	1.06338i	0.689458	+	0.232048i
$22$	1.37601	−	2.38332i	0.293367	−	0.508126i
$23$	5.98324			1.24759			0.623796	−	0.781587i	$-0.285589\pi$
$23$	5.98324			1.24759			0.623796	+	0.781587i	$0.285589\pi$
$24$	1.29354	−	3.84336i	0.264043	−	0.784522i
$25$	1.19554	+	0.690245i	0.239108	+	0.138049i
$26$	−5.72846	−	0.197671i	−1.12344	−	0.0387665i
$27$	−0.974052	+	5.10404i	−0.187456	+	0.982273i
$28$	0.262649	+	0.980220i	0.0496360	+	0.185244i
$29$	−3.57718	+	2.06528i	−0.664265	+	0.383513i	−0.793900	−	0.608048i	$-0.791953\pi$
$29$	−3.57718	+	2.06528i	−0.664265	+	0.383513i	0.129635	+	0.991562i	$0.458619\pi$
$30$	5.22819	+	0.329064i	0.954533	+	0.0600786i
$31$	7.42505	+	1.98954i	1.33358	+	0.357331i	0.854048	−	0.520194i	$-0.174140\pi$
$31$	7.42505	+	1.98954i	1.33358	+	0.357331i	0.479530	+	0.877525i	$0.340807\pi$
$32$	2.81166	−	0.753382i	0.497036	−	0.133180i
$33$	2.93925	−	0.592579i	0.511658	−	0.103155i
$34$	−8.44235	+	2.26212i	−1.44785	+	0.387951i
$35$	3.17113	−	1.83085i	0.536019	−	0.309471i
$36$	−1.45820	+	0.612885i	−0.243034	+	0.102148i
$37$	−3.76694	+	1.00935i	−0.619281	+	0.165936i	−0.554801	−	0.831983i	$-0.687206\pi$
$37$	−3.76694	+	1.00935i	−0.619281	+	0.165936i	−0.0644801	+	0.997919i	$0.520539\pi$
$38$	0.100261	−	0.173657i	0.0162644	−	0.0281708i
$39$	−3.96576	−	4.82418i	−0.635030	−	0.772487i
$40$	−2.22714	−	3.85751i	−0.352141	−	0.609926i
$41$	−0.211390	−	0.211390i	−0.0330135	−	0.0330135i	0.690407	−	0.723421i	$-0.257431\pi$
$41$	−0.211390	−	0.211390i	−0.0330135	−	0.0330135i	−0.723421	+	0.690407i	$0.757431\pi$
$42$	−2.93287	+	4.41408i	−0.452552	+	0.681107i
$43$			2.03274i			0.309990i	0.987915	+	0.154995i	$0.0495361\pi$
$43$			2.03274i			0.309990i	−0.987915	+	0.154995i	$0.950464\pi$
$44$	0.645408	+	0.645408i	0.0972989	+	0.0972989i
$45$	3.49794	+	4.50999i	0.521442	+	0.672310i
$46$	−2.46183	+	9.18767i	−0.362977	+	1.35465i
$47$	−2.81142	−	10.4924i	−0.410088	−	1.53047i	−0.794475	−	0.607296i	$-0.792254\pi$
$47$	−2.81142	−	10.4924i	−0.410088	−	1.53047i	0.384388	−	0.923172i	$-0.374413\pi$
$48$	6.89078	+	4.57847i	0.994598	+	0.660846i
$49$		−	3.29561i		−	0.470801i
$50$	−1.55182	+	1.55182i	−0.219461	+	0.219461i
$51$	−7.93144	−	5.26993i	−1.11062	−	0.737938i
$52$	0.555061	−	1.81821i	0.0769731	−	0.252141i
$53$		−	9.44984i		−	1.29804i	−0.760773	−	0.649018i	$-0.775180\pi$
$53$		−	9.44984i		−	1.29804i	0.760773	−	0.649018i	$-0.224820\pi$
$54$	−7.43681	−	3.59580i	−1.01202	−	0.489326i
$55$	1.64673	−	2.85222i	0.222045	−	0.384594i
$56$	4.50620			0.602166
$57$	0.214164	−	0.0431773i	0.0283667	−	0.00571897i
$58$	−1.69954	−	6.34276i	−0.223160	−	0.832845i
$59$	−2.05031	−	7.65187i	−0.266928	−	0.996189i	−0.961060	−	0.276341i	$-0.910878\pi$
$59$	−2.05031	−	7.65187i	−0.266928	−	0.996189i	0.694132	−	0.719848i	$-0.255789\pi$
$60$	−0.554211	+	1.64667i	−0.0715483	+	0.212584i
$61$	12.7569			1.63335			0.816677	−	0.577095i	$-0.195814\pi$
$61$	12.7569			1.63335			0.816677	+	0.577095i	$0.195814\pi$
$62$	−6.11013	+	10.5830i	−0.775987	+	1.34405i
$63$	−5.72066	+	0.783335i	−0.720735	+	0.0986910i
$64$		−	4.92556i		−	0.615695i
$65$	−6.85549	−	0.236561i	−0.850318	−	0.0293418i
$66$	−0.299422	+	4.75723i	−0.0368562	+	0.585575i
$67$	−8.66726	+	8.66726i	−1.05887	+	1.05887i	−0.0607198	+	0.998155i	$0.519340\pi$
$67$	−8.66726	+	8.66726i	−1.05887	+	1.05887i	−0.998155	+	0.0607198i	$0.980660\pi$
$68$		−	2.89879i		−	0.351530i
$69$	−9.28263	+	4.60764i	−1.11750	+	0.554695i
$70$	1.50662	+	5.62279i	0.180076	+	0.672052i
$71$	−1.16407	+	4.34437i	−0.138150	+	0.515582i	0.861815	+	0.507222i	$0.169328\pi$
$71$	−1.16407	+	4.34437i	−0.138150	+	0.515582i	−0.999965	+	0.00835974i	$0.997339\pi$
$72$	0.952886	+	6.95888i	0.112299	+	0.820112i
$73$	9.98266	+	9.98266i	1.16838	+	1.16838i	0.982589	+	0.185793i	$0.0594855\pi$
$73$	9.98266	+	9.98266i	1.16838	+	1.16838i	0.185793	+	0.982589i	$0.440514\pi$
$74$		−	6.19968i		−	0.720699i
$75$	−2.38636	−	0.150198i	−0.275553	−	0.0173434i
$76$	0.0470265	+	0.0470265i	0.00539431	+	0.00539431i
$77$	1.66593	+	2.88547i	0.189850	+	0.328830i
$78$	9.03957	−	4.10476i	1.02353	−	0.464773i
$79$	1.34539	−	2.33029i	0.151369	−	0.262178i	−0.780362	−	0.625328i	$-0.784965\pi$
$79$	1.34539	−	2.33029i	0.151369	−	0.262178i	0.931731	+	0.363150i	$0.118299\pi$
$80$	8.77768	−	2.35197i	0.981374	−	0.262958i
$81$	−2.41939	−	8.66871i	−0.268822	−	0.963190i
$82$	0.411580	−	0.237626i	0.0454514	−	0.0262414i
$83$	−0.307307	+	0.0823426i	−0.0337313	+	0.00903827i	−0.275645	−	0.961259i	$-0.588891\pi$
$83$	−0.307307	+	0.0823426i	−0.0337313	+	0.00903827i	0.241914	+	0.970298i	$0.422225\pi$
$84$	−1.16234	−	1.31849i	−0.126822	−	0.143859i
$85$	−10.1033	+	2.70717i	−1.09586	+	0.293634i
$86$	−3.12140	−	0.836377i	−0.336589	−	0.0901889i
$87$	3.95931	−	5.95891i	0.424483	−	0.638862i
$88$	3.51003	−	2.02651i	0.374170	−	0.216027i
$89$	2.68454	+	10.0188i	0.284560	+	1.06199i	0.949160	+	0.314794i	$0.101935\pi$
$89$	2.68454	+	10.0188i	0.284560	+	1.06199i	−0.664600	+	0.747200i	$0.731398\pi$
$90$	−8.36463	+	3.51566i	−0.881709	+	0.370583i
$91$	3.67496	−	5.88658i	0.385240	−	0.617081i
$92$	−2.73205	−	1.57735i	−0.284836	−	0.164450i
$93$	−13.0516	+	2.63132i	−1.35339	+	0.272856i
$94$	17.2685			1.78111
$95$	0.119986	−	0.207822i	0.0123103	−	0.0213221i
$96$	−3.78194	+	3.33406i	−0.385993	+	0.340281i
$97$	2.81052	−	2.81052i	0.285365	−	0.285365i	−0.549879	−	0.835244i	$-0.685326\pi$
$97$	2.81052	−	2.81052i	0.285365	−	0.285365i	0.835244	+	0.549879i	$0.185326\pi$
$98$	5.06062	+	1.35599i	0.511200	+	0.136976i
$99$	−4.10373	+	3.18284i	−0.412440	+	0.319888i
$100$	−0.363936	−	0.630355i	−0.0363936	−	0.0630355i
$101$	1.41867	+	2.45721i	0.141163	+	0.244501i	0.927935	−	0.372743i	$-0.121583\pi$
$101$	1.41867	+	2.45721i	0.141163	+	0.244501i	−0.786772	+	0.617244i	$0.788249\pi$
$102$	11.3557	−	10.0109i	1.12439	−	0.991229i
$103$	2.44040	−	1.40896i	0.240460	−	0.138829i	−0.374928	−	0.927054i	$-0.622333\pi$
$103$	2.44040	−	1.40896i	0.240460	−	0.138829i	0.615388	+	0.788224i	$0.288999\pi$
$104$	−7.16071	−	4.47039i	−0.702166	−	0.438358i
$105$	−3.50989	+	5.28251i	−0.342530	+	0.515521i
$106$	14.5109	+	3.88817i	1.40942	+	0.377653i
$107$	2.20447	+	1.27275i	0.213114	+	0.123042i	0.602758	−	0.797924i	$-0.294069\pi$
$107$	2.20447	+	1.27275i	0.213114	+	0.123042i	−0.389644	+	0.920966i	$0.627402\pi$
$108$	1.79034	−	2.07380i	0.172275	−	0.199552i
$109$	7.73692	−	7.73692i	0.741062	−	0.741062i	−0.231720	−	0.972783i	$-0.574435\pi$
$109$	7.73692	−	7.73692i	0.741062	−	0.741062i	0.972783	+	0.231720i	$0.0744353\pi$
$110$	3.70222	+	3.70222i	0.352993	+	0.352993i
$111$	5.06688	−	4.46683i	0.480927	−	0.423973i
$112$	−2.37939	+	8.88001i	−0.224831	+	0.839082i
$113$	−3.02112	−	1.74424i	−0.284203	−	0.164085i	0.351122	−	0.936330i	$-0.385800\pi$
$113$	−3.02112	−	1.74424i	−0.284203	−	0.164085i	−0.635325	+	0.772245i	$0.719134\pi$
$114$	−0.0218168	+	0.346628i	−0.00204333	+	0.0324647i
$115$	−2.94617	+	10.9953i	−0.274732	+	1.02531i
$116$	2.17787			0.202210
$117$	9.86769	+	4.43042i	0.912269	+	0.409592i
$118$	12.5936			1.15933
$119$	2.73873	−	10.2211i	0.251059	−	0.936966i
$120$	6.42590	+	4.26959i	0.586602	+	0.389759i
$121$	−6.93099	−	4.00161i	−0.630090	−	0.363783i
$122$	−5.24887	+	19.5891i	−0.475211	+	1.77351i
$123$	0.490747	+	0.165169i	0.0442492	+	0.0148927i
$124$	−2.86591	−	2.86591i	−0.257366	−	0.257366i
$125$	−8.58349	+	8.58349i	−0.767731	+	0.767731i
$126$	1.15092	−	9.10675i	0.102532	−	0.811294i
$127$	−14.1044	−	8.14320i	−1.25157	−	0.722592i	−0.280146	−	0.959957i	$-0.590383\pi$
$127$	−14.1044	−	8.14320i	−1.25157	−	0.722592i	−0.971421	+	0.237365i	$0.923716\pi$
$128$	13.1868	+	3.53340i	1.16556	+	0.312312i
$129$	−1.56539	−	3.15367i	−0.137825	−	0.277665i
$130$	3.18397	−	10.4297i	0.279253	−	0.914746i
$131$	19.6906	−	11.3684i	1.72038	−	0.993259i	0.802230	−	0.597015i	$-0.203647\pi$
$131$	19.6906	−	11.3684i	1.72038	−	0.993259i	0.918145	−	0.396244i	$-0.129686\pi$
$132$	−1.49833	−	0.504287i	−0.130413	−	0.0438926i
$133$	0.121385	+	0.210245i	0.0105254	+	0.0182305i
$134$	−9.74297	−	16.8753i	−0.841665	−	1.45781i
$135$	−8.89994	−	4.30324i	−0.765985	−	0.370364i
$136$	−12.4334	−	3.33153i	−1.06616	−	0.285676i
$137$	10.0663	−	10.0663i	0.860025	−	0.860025i	−0.131316	−	0.991341i	$-0.541920\pi$
$137$	10.0663	−	10.0663i	0.860025	−	0.860025i	0.991341	+	0.131316i	$0.0419202\pi$
$138$	−3.25597	−	16.1499i	−0.277166	−	1.37477i
$139$	−9.68838	+	16.7808i	−0.821758	+	1.42333i	0.0826143	+	0.996582i	$0.473673\pi$
$139$	−9.68838	+	16.7808i	−0.821758	+	1.42333i	−0.904372	+	0.426745i	$0.859660\pi$
$140$	−1.93066			−0.163170
$141$	12.4418	+	14.1132i	1.04779	+	1.18855i
$142$	−6.19211	−	3.57501i	−0.519630	−	0.300009i
$143$	0.215251	−	6.23794i	0.0180002	−	0.521642i
$144$	−14.2165	−	1.79669i	−1.18470	−	0.149724i
$145$	−2.03391	−	7.59064i	−0.168907	−	0.630368i
$146$	−19.4364	+	11.2216i	−1.60857	+	0.928709i
$147$	2.53792	+	5.11293i	0.209324	+	0.421707i
$148$	1.98614	+	0.532185i	0.163260	+	0.0437453i
$149$	1.31404	−	0.352095i	0.107650	−	0.0288447i	−0.204592	−	0.978847i	$-0.565587\pi$
$149$	1.31404	−	0.352095i	0.107650	−	0.0288447i	0.312242	+	0.950003i	$0.398920\pi$
$150$	1.21251	−	3.60261i	0.0990013	−	0.294152i
$151$	−2.61755	+	0.701372i	−0.213014	+	0.0570768i	−0.363748	−	0.931498i	$-0.618503\pi$
$151$	−2.61755	+	0.701372i	−0.213014	+	0.0570768i	0.150734	+	0.988574i	$0.451836\pi$
$152$	0.255752	−	0.147658i	0.0207442	−	0.0119767i
$153$	16.3635	+	2.06803i	1.32291	+	0.167191i
$154$	−5.11628	+	1.37090i	−0.412282	+	0.110471i
$155$	−7.31224	+	12.6652i	−0.587333	+	1.01729i
$156$	0.539046	+	3.24829i	0.0431582	+	0.260071i
$157$	−7.07769	−	12.2589i	−0.564861	−	0.978368i	−0.997063	−	0.0765912i	$-0.975596\pi$
$157$	−7.07769	−	12.2589i	−0.564861	−	0.978368i	0.432201	−	0.901777i	$-0.357737\pi$
$158$	3.02474	+	3.02474i	0.240636	+	0.240636i
$159$	7.27724	+	14.6608i	0.577123	+	1.16268i
$160$			5.53788i			0.437808i
$161$	−8.14292	−	8.14292i	−0.641752	−	0.641752i
$162$	14.3068	−	0.148367i	1.12405	−	0.0116568i
$163$	−2.08852	+	7.79446i	−0.163585	+	0.610509i	0.834631	+	0.550810i	$0.185681\pi$
$163$	−2.08852	+	7.79446i	−0.163585	+	0.610509i	−0.998216	+	0.0596996i	$0.980986\pi$
$164$	0.0407959	+	0.152252i	0.00318562	+	0.0118889i
$165$	−0.358330	+	5.69318i	−0.0278960	+	0.443213i
$166$		−	0.505770i		−	0.0392554i
$167$	−5.46717	+	5.46717i	−0.423062	+	0.423062i	−0.886257	−	0.463194i	$-0.846703\pi$
$167$	−5.46717	+	5.46717i	−0.423062	+	0.423062i	0.463194	+	0.886257i	$0.346703\pi$
$168$	−6.99109	+	3.47018i	−0.539374	+	0.267731i
$169$	−11.6796	+	5.70848i	−0.898431	+	0.439114i
$170$		−	16.6282i		−	1.27532i
$171$	−0.299011	+	0.231912i	−0.0228659	+	0.0177348i
$172$	0.535886	−	0.928182i	0.0408610	−	0.0707733i
$173$	−1.06028			−0.0806114			−0.0403057	−	0.999187i	$-0.512833\pi$
$173$	−1.06028			−0.0806114			−0.0403057	+	0.999187i	$0.512833\pi$
$174$	7.52123	+	8.53159i	0.570183	+	0.646778i
$175$	−0.687682	−	2.56646i	−0.0519839	−	0.194006i
$176$	2.14010	+	7.98698i	0.161316	+	0.602041i
$177$	9.07358	+	10.2925i	0.682012	+	0.773630i
$178$	−16.4891			−1.23591
$179$	1.75852	−	3.04585i	0.131438	−	0.227658i	−0.792793	−	0.609491i	$-0.791374\pi$
$179$	1.75852	−	3.04585i	0.131438	−	0.227658i	0.924231	+	0.381833i	$0.124707\pi$
$180$	−0.408259	−	2.98149i	−0.0304298	−	0.222227i
$181$			11.1267i			0.827038i	0.910495	+	0.413519i	$0.135700\pi$
$181$			11.1267i			0.827038i	−0.910495	+	0.413519i	$0.864300\pi$
$182$	7.52715	+	8.06519i	0.557949	+	0.597832i
$183$	−19.7915	+	9.82398i	−1.46303	+	0.726209i
$184$	−9.90544	+	9.90544i	−0.730239	+	0.730239i
$185$		−	7.41942i		−	0.545486i
$186$	1.32957	−	21.1243i	0.0974887	−	1.54891i
$187$	−2.46331	−	9.19320i	−0.180135	−	0.672273i
$188$	−1.48234	+	5.53216i	−0.108111	+	0.403474i
$189$	8.27200	−	5.62072i	0.601700	−	0.408847i
$190$	0.269756	+	0.269756i	0.0195702	+	0.0195702i
$191$			22.6140i			1.63629i	0.575013	+	0.818144i	$0.304997\pi$
$191$			22.6140i			1.63629i	−0.575013	+	0.818144i	$0.695003\pi$
$192$	3.79313	+	7.64170i	0.273745	+	0.551492i
$193$	−5.45070	−	5.45070i	−0.392350	−	0.392350i	0.483174	−	0.875524i	$-0.339484\pi$
$193$	−5.45070	−	5.45070i	−0.392350	−	0.392350i	−0.875524	+	0.483174i	$0.839484\pi$
$194$	3.15934	+	5.47213i	0.226827	+	0.392876i
$195$	10.8180	−	4.91234i	0.774695	−	0.351780i
$196$	−0.868814	+	1.50483i	−0.0620582	+	0.107488i
$197$	11.5603	−	3.09758i	0.823638	−	0.220693i	0.177702	−	0.984084i	$-0.443134\pi$
$197$	11.5603	−	3.09758i	0.823638	−	0.220693i	0.645936	+	0.763391i	$0.276467\pi$
$198$	−3.19897	−	7.61113i	−0.227341	−	0.540900i
$199$	−11.5517	+	6.66937i	−0.818877	+	0.472779i	−0.850029	−	0.526736i	$-0.823416\pi$
$199$	−11.5517	+	6.66937i	−0.818877	+	0.472779i	0.0311521	+	0.999515i	$0.490082\pi$
$200$	−3.12197	+	0.836529i	−0.220757	+	0.0591515i
$201$	6.77214	−	20.1213i	0.477670	−	1.41925i
$202$	−4.35692	+	1.16743i	−0.306552	+	0.0821403i
$203$	7.67913	+	2.05762i	0.538969	+	0.144416i
$204$	2.23233	+	4.49729i	0.156294	+	0.314873i
$205$	0.492554	−	0.284376i	0.0344015	−	0.0198617i
$206$	1.15945	+	4.32712i	0.0807825	+	0.301484i
$207$	10.8531	−	14.2969i	0.754344	−	0.993706i
$208$	12.5905	−	11.7506i	0.872993	−	0.814755i
$209$	0.189101	+	0.109178i	0.0130804	+	0.00755198i
$210$	−6.66749	−	7.56317i	−0.460101	−	0.521908i
$211$	25.1235			1.72957			0.864786	−	0.502140i	$-0.167454\pi$
$211$	25.1235			1.72957			0.864786	+	0.502140i	$0.167454\pi$
$212$	−2.49124	+	4.31496i	−0.171099	+	0.296353i
$213$	−1.53958	−	7.63646i	−0.105490	−	0.523242i
$214$	−2.86143	+	2.86143i	−0.195603	+	0.195603i
$215$	−3.73551	−	1.00093i	−0.254760	−	0.0682627i
$216$	−6.83732	−	10.0625i	−0.465220	−	0.684664i
$217$	−7.39748	−	12.8128i	−0.502174	−	0.869791i
$218$	8.69716	+	15.0639i	0.589046	+	1.02026i
$219$	−23.1750	−	7.79992i	−1.56602	−	0.527070i
$220$	−1.50385	+	0.868249i	−0.101390	+	0.0585373i
$221$	−14.4919	+	13.5252i	−0.974834	+	0.909801i
$222$	4.77432	+	9.61842i	0.320431	+	0.645546i
$223$	−7.23808	−	1.93944i	−0.484697	−	0.129874i	0.00819164	−	0.999966i	$-0.497392\pi$
$223$	−7.23808	−	1.93944i	−0.484697	−	0.129874i	−0.492889	+	0.870092i	$0.664059\pi$
$224$	−4.85186	−	2.80122i	−0.324178	−	0.187164i
$225$	3.81795	−	1.60469i	0.254530	−	0.106979i
$226$	3.92145	−	3.92145i	0.260851	−	0.260851i
$227$	−5.28265	−	5.28265i	−0.350622	−	0.350622i	0.509719	−	0.860341i	$-0.329749\pi$
$227$	−5.28265	−	5.28265i	−0.350622	−	0.350622i	−0.860341	+	0.509719i	$0.829749\pi$
$228$	−0.109173	−	0.0367440i	−0.00723019	−	0.00243343i
$229$	7.03764	−	26.2648i	0.465061	−	1.73563i	−0.191627	−	0.981468i	$-0.561377\pi$
$229$	7.03764	−	26.2648i	0.465061	−	1.73563i	0.656688	−	0.754162i	$-0.271957\pi$
$230$	−15.6717	−	9.04808i	−1.03336	−	0.596613i
$231$	−4.80666	−	3.19371i	−0.316255	−	0.210131i
$232$	2.50298	−	9.34126i	0.164329	−	0.613284i
$233$	7.97223			0.522278			0.261139	−	0.965301i	$-0.415902\pi$
$233$	7.97223			0.522278			0.261139	+	0.965301i	$0.415902\pi$
$234$	−10.8633	+	13.3296i	−0.710156	+	0.871382i
$235$	20.6659			1.34809
$236$	−1.08104	+	4.03450i	−0.0703697	+	0.262623i
$237$	−0.292759	+	4.65137i	−0.0190167	+	0.302139i
$238$	14.5683	+	8.41101i	0.944322	+	0.545205i
$239$	5.42503	−	20.2465i	0.350916	−	1.30964i	−0.534631	−	0.845086i	$-0.679549\pi$
$239$	5.42503	−	20.2465i	0.350916	−	1.30964i	0.885547	−	0.464550i	$-0.153784\pi$
$240$	−11.8068	+	10.4086i	−0.762125	+	0.671869i
$241$	6.98986	+	6.98986i	0.450256	+	0.450256i	0.895440	−	0.445183i	$-0.146861\pi$
$241$	6.98986	+	6.98986i	0.450256	+	0.450256i	−0.445183	+	0.895440i	$0.646861\pi$
$242$	8.99651	−	8.99651i	0.578318	−	0.578318i
$243$	10.4292	+	11.5858i	0.669036	+	0.743230i
$244$	−5.82502	−	3.36308i	−0.372909	−	0.215299i
$245$	6.05626	+	1.62277i	0.386920	+	0.103675i
$246$	−0.455547	+	0.685615i	−0.0290446	+	0.0437132i
$247$	0.0156839	−	0.454517i	0.000997944	−	0.0289202i
$248$	−15.5861	+	8.99865i	−0.989720	+	0.571415i
$249$	0.413356	−	0.364404i	0.0261954	−	0.0230931i
$250$	−9.64881	−	16.7122i	−0.610244	−	1.05697i
$251$	12.2349	+	21.1915i	0.772261	+	1.33760i	0.936321	+	0.351146i	$0.114208\pi$
$251$	12.2349	+	21.1915i	0.772261	+	1.33760i	−0.164059	+	0.986450i	$0.552459\pi$
$252$	2.81866	+	1.15044i	0.177559	+	0.0724710i
$253$	−10.0048	−	2.68078i	−0.628996	−	0.168539i
$254$	18.3077	−	18.3077i	1.14873	−	1.14873i
$255$	13.5899	−	11.9805i	0.851032	−	0.750247i
$256$	−5.92598	+	10.2641i	−0.370374	+	0.641507i
$257$	−14.6654			−0.914804			−0.457402	−	0.889260i	$-0.651220\pi$
$257$	−14.6654			−0.914804			−0.457402	+	0.889260i	$0.651220\pi$
$258$	5.48675	−	1.10618i	0.341590	−	0.0688676i
$259$	6.50031	+	3.75296i	0.403910	+	0.233197i
$260$	3.06797	+	1.91532i	0.190267	+	0.118783i
$261$	−1.55372	+	12.2939i	−0.0961728	+	0.760974i
$262$	9.35511	+	34.9138i	0.577961	+	2.15698i
$263$	−3.90904	+	2.25689i	−0.241042	+	0.139166i	−0.615655	−	0.788015i	$-0.711109\pi$
$263$	−3.90904	+	2.25689i	−0.241042	+	0.139166i	0.374614	+	0.927181i	$0.377775\pi$
$264$	−3.88499	+	5.84705i	−0.239104	+	0.359861i
$265$	17.3657	+	4.65314i	1.06677	+	0.285840i
$266$	−0.372789	+	0.0998886i	−0.0228572	+	0.00612456i
$267$	−11.8803	−	13.4762i	−0.727063	−	0.824733i
$268$	6.24255	−	1.67269i	0.381325	−	0.102176i
$269$	−3.93827	+	2.27376i	−0.240120	+	0.138634i	−0.615232	−	0.788346i	$-0.710938\pi$
$269$	−3.93827	+	2.27376i	−0.240120	+	0.138634i	0.375112	+	0.926980i	$0.377604\pi$
$270$	10.2698	−	11.8959i	0.625001	−	0.723959i
$271$	10.2476	−	2.74584i	0.622498	−	0.166798i	0.0662348	−	0.997804i	$-0.478901\pi$
$271$	10.2476	−	2.74584i	0.622498	−	0.166798i	0.556263	+	0.831006i	$0.312235\pi$
$272$	13.1303	−	22.7424i	0.796144	−	1.37896i
$273$	−1.16827	+	11.9627i	−0.0707068	+	0.724016i
$274$	11.3157	+	19.5993i	0.683606	+	1.18404i
$275$	−1.68984	−	1.68984i	−0.101901	−	0.101901i
$276$	5.45331	+	0.343233i	0.328251	+	0.0206602i
$277$		−	30.6020i		−	1.83870i	−0.393445	−	0.919348i	$-0.628717\pi$
$277$		−	30.6020i		−	1.83870i	0.393445	−	0.919348i	$-0.371283\pi$
$278$	−21.7817	−	21.7817i	−1.30638	−	1.30638i
$279$	18.2224	−	14.1333i	1.09095	−	0.846137i
$280$	−2.21887	+	8.28093i	−0.132603	+	0.494880i
$281$	2.16271	+	8.07134i	0.129016	+	0.481496i	0.999951	−	0.00990333i	$-0.00315238\pi$
$281$	2.16271	+	8.07134i	0.129016	+	0.481496i	−0.870935	+	0.491399i	$0.836486\pi$
$282$	−26.7910	+	13.2983i	−1.59538	+	0.791902i
$283$			9.79879i			0.582478i	0.956650	+	0.291239i	$0.0940674\pi$
$283$			9.79879i			0.582478i	−0.956650	+	0.291239i	$0.905933\pi$
$284$	1.67683	−	1.67683i	0.0995017	−	0.0995017i
$285$	−0.0261091	+	0.414824i	−0.00154657	+	0.0245720i
$286$	9.49020	+	2.89715i	0.561167	+	0.171312i
$287$			0.575383i			0.0339638i
$288$	3.29992	−	8.08503i	0.194450	−	0.476415i
$289$	−6.61333	+	11.4546i	−0.389019	+	0.673801i
$290$	12.4928			0.733601
$291$	−2.19599	+	6.52470i	−0.128731	+	0.382485i
$292$	−1.92654	−	7.18996i	−0.112742	−	0.420761i
$293$	4.09522	+	15.2836i	0.239245	+	0.892875i	0.976189	+	0.216921i	$0.0696014\pi$
$293$	4.09522	+	15.2836i	0.239245	+	0.892875i	−0.736944	+	0.675954i	$0.763732\pi$
$294$	−8.89548	+	1.79341i	−0.518795	+	0.104594i
$295$	15.0712			0.877482
$296$	4.56527	−	7.90729i	0.265351	−	0.459602i
$297$	3.91560	−	8.09822i	0.227206	−	0.469907i
$298$			2.16266i			0.125280i
$299$	4.86154	+	21.0180i	0.281150	+	1.21550i
$300$	1.05005	+	0.697693i	0.0606249	+	0.0402813i
$301$	2.76646	−	2.76646i	0.159456	−	0.159456i
$302$		−	4.30801i		−	0.247898i
$303$	−4.09325	−	2.71970i	−0.235151	−	0.156243i
$304$	0.155935	+	0.581957i	0.00894349	+	0.0333775i
$305$	−6.28154	+	23.4430i	−0.359680	+	1.34234i
$306$	−9.90841	+	24.2763i	−0.566426	+	1.38778i
$307$	4.43600	+	4.43600i	0.253176	+	0.253176i	0.822271	−	0.569096i	$-0.192707\pi$
$307$	4.43600	+	4.43600i	0.253176	+	0.253176i	−0.569096	+	0.822271i	$0.692707\pi$
$308$		−	1.75674i		−	0.100100i
$309$	−2.70110	+	4.06525i	−0.153660	+	0.231264i
$310$	−16.4396	−	16.4396i	−0.933704	−	0.933704i
$311$	−4.71427	−	8.16536i	−0.267322	−	0.463015i	0.700847	−	0.713311i	$-0.252805\pi$
$311$	−4.71427	−	8.16536i	−0.267322	−	0.463015i	−0.968169	+	0.250296i	$0.919472\pi$
$312$	14.5520	+	1.42114i	0.823845	+	0.0804561i
$313$	−8.39997	+	14.5492i	−0.474794	+	0.822368i	−0.999583	−	0.0288644i	$-0.990811\pi$
$313$	−8.39997	+	14.5492i	−0.474794	+	0.822368i	0.524789	+	0.851232i	$0.324144\pi$
$314$	21.7365	−	5.82428i	1.22666	−	0.328683i
$315$	1.37736	−	10.8984i	0.0776052	−	0.614057i
$316$	−1.22866	+	0.709366i	−0.0691174	+	0.0399050i
$317$	−1.47287	+	0.394655i	−0.0827248	+	0.0221661i	−0.299944	−	0.953957i	$-0.596968\pi$
$317$	−1.47287	+	0.394655i	−0.0827248	+	0.0221661i	0.217219	+	0.976123i	$0.430301\pi$
$318$	−25.5069	+	5.14242i	−1.43036	+	0.288373i
$319$	6.90687	−	1.85069i	0.386710	−	0.103619i
$320$	9.05157	+	2.42536i	0.505998	+	0.135582i
$321$	−4.40023	−	0.276952i	−0.245597	−	0.0154579i
$322$	15.8544	−	9.15356i	0.883533	−	0.510108i
$323$	−0.179485	−	0.669846i	−0.00998680	−	0.0372713i
$324$	−1.18058	+	4.59610i	−0.0655877	+	0.255339i
$325$	−1.45329	+	4.76054i	−0.0806140	+	0.264067i
$326$	−11.1096	−	6.41412i	−0.615302	−	0.355245i
$327$	−6.04522	+	17.9615i	−0.334301	+	0.993272i
$328$	0.699923			0.0386468
$329$	−10.4534	+	18.1058i	−0.576315	+	0.998207i
$330$	−8.59481	−	2.89272i	−0.473129	−	0.159239i
$331$	−5.90998	+	5.90998i	−0.324842	+	0.324842i	−0.850621	−	0.525779i	$-0.823774\pi$
$331$	−5.90998	+	5.90998i	−0.324842	+	0.324842i	0.525779	+	0.850621i	$0.323774\pi$
$332$	0.162029	+	0.0434156i	0.00889251	+	0.00238274i
$333$	−4.42109	+	10.8320i	−0.242274	+	0.593588i
$334$	−6.14571	−	10.6447i	−0.336278	−	0.582451i
$335$	−11.6598	−	20.1954i	−0.637044	−	1.10339i
$336$	−3.14694	−	15.6091i	−0.171680	−	0.851548i
$337$	−2.69627	+	1.55669i	−0.146875	+	0.0847984i	−0.571637	−	0.820507i	$-0.693691\pi$
$337$	−2.69627	+	1.55669i	−0.146875	+	0.0847984i	0.424761	+	0.905305i	$0.360358\pi$
$338$	−3.96014	−	20.2836i	−0.215403	−	1.10328i
$339$	6.03030	+	0.379549i	0.327521	+	0.0206143i
$340$	5.32703	+	1.42737i	0.288899	+	0.0774102i
$341$	−11.5243	−	6.65355i	−0.624075	−	0.360310i
$342$	−0.233087	−	0.554572i	−0.0126039	−	0.0299878i
$343$	−14.0118	+	14.0118i	−0.756569	+	0.756569i
$344$	−3.36526	−	3.36526i	−0.181442	−	0.181442i
$345$	−3.89655	−	19.3273i	−0.209783	−	1.04055i
$346$	0.436255	−	1.62813i	0.0234532	−	0.0875286i
$347$	−7.54883	−	4.35832i	−0.405242	−	0.233967i	0.283501	−	0.958972i	$-0.408504\pi$
$347$	−7.54883	−	4.35832i	−0.405242	−	0.233967i	−0.688744	+	0.725005i	$0.741837\pi$
$348$	−3.37882	+	1.67716i	−0.181124	+	0.0899050i
$349$	−1.41612	+	5.28504i	−0.0758034	+	0.282902i	−0.993414	−	0.114578i	$-0.963448\pi$
$349$	−1.41612	+	5.28504i	−0.0758034	+	0.282902i	0.917611	+	0.397480i	$0.130115\pi$
$350$	4.22392			0.225778
$351$	−18.7209	+	0.725503i	−0.999250	+	0.0387245i
$352$	−5.03903			−0.268581
$353$	6.86875	−	25.6345i	0.365587	−	1.36439i	−0.501037	−	0.865426i	$-0.667048\pi$
$353$	6.86875	−	25.6345i	0.365587	−	1.36439i	0.866624	−	0.498962i	$-0.166285\pi$
$354$	−19.5381	+	9.69819i	−1.03844	+	0.515453i
$355$	−7.41035	−	4.27837i	−0.393301	−	0.227072i
$356$	1.41544	−	5.28249i	0.0750181	−	0.279971i
$357$	3.62220	+	17.9665i	0.191707	+	0.950886i
$358$	3.95355	+	3.95355i	0.208952	+	0.208952i
$359$	7.27304	−	7.27304i	0.383856	−	0.383856i	−0.488633	−	0.872489i	$-0.662504\pi$
$359$	7.27304	−	7.27304i	0.383856	−	0.383856i	0.872489	+	0.488633i	$0.162504\pi$
$360$	−13.2574	−	1.67548i	−0.698724	−	0.0883056i
$361$	−16.4407	−	9.49204i	−0.865300	−	0.499581i
$362$	−17.0857	−	4.57810i	−0.898005	−	0.240620i
$363$	13.8346	+	0.870754i	0.726128	+	0.0457027i
$364$	−3.22991	+	1.71909i	−0.169294	+	0.0901048i
$365$	−23.2604	+	13.4294i	−1.21750	+	0.702926i
$366$	−6.94206	−	34.4333i	−0.362867	−	1.79986i
$367$	−6.87509	−	11.9080i	−0.358877	−	0.621593i	0.628897	−	0.777489i	$-0.283507\pi$
$367$	−6.87509	−	11.9080i	−0.358877	−	0.621593i	−0.987773	+	0.155896i	$0.950173\pi$
$368$	−14.2895	−	24.7502i	−0.744893	−	1.29019i
$369$	−0.888558	+	0.121671i	−0.0462565	+	0.00633395i
$370$	11.3930	+	3.05275i	0.592294	+	0.158705i
$371$	−12.8608	+	12.8608i	−0.667699	+	0.667699i
$372$	6.65329	+	2.23927i	0.344957	+	0.116101i
$373$	13.1112	−	22.7092i	0.678870	−	1.17584i	−0.296452	−	0.955048i	$-0.595803\pi$
$373$	13.1112	−	22.7092i	0.678870	−	1.17584i	0.975322	−	0.220789i	$-0.0708632\pi$
$374$	15.1303			0.782369
$375$	6.70668	−	19.9268i	0.346332	−	1.02902i
$376$	22.0248	+	12.7160i	1.13584	+	0.655779i
$377$	−10.1615	−	10.8878i	−0.523343	−	0.560752i
$378$	5.22744	+	15.0149i	0.268871	+	0.772282i
$379$	1.90847	+	7.12251i	0.0980316	+	0.365859i	0.997462	−	0.0712058i	$-0.0226847\pi$
$379$	1.90847	+	7.12251i	0.0980316	+	0.365859i	−0.899430	+	0.437065i	$0.856018\pi$
$380$	−0.109576	+	0.0632635i	−0.00562111	+	0.00324535i
$381$	28.1532	+	1.77197i	1.44233	+	0.0907807i
$382$	−34.7252	−	9.30460i	−1.77670	−	0.476065i
$383$	27.3551	−	7.32978i	1.39778	−	0.374534i	0.520233	−	0.854024i	$-0.325845\pi$
$383$	27.3551	−	7.32978i	1.39778	−	0.374534i	0.877547	+	0.479490i	$0.159178\pi$
$384$	−23.1796	+	4.67321i	−1.18288	+	0.238479i
$385$	−6.12287	+	1.64062i	−0.312050	+	0.0836136i
$386$	10.6126	−	6.12720i	0.540168	−	0.311866i
$387$	4.85722	+	3.68722i	0.246906	+	0.187432i
$388$	−2.02426	+	0.542399i	−0.102766	+	0.0275361i
$389$	−1.14375	+	1.98103i	−0.0579904	+	0.100442i	−0.893563	−	0.448937i	$-0.851803\pi$
$389$	−1.14375	+	1.98103i	−0.0579904	+	0.100442i	0.835573	+	0.549380i	$0.185136\pi$
$390$	3.09210	+	18.6330i	0.156575	+	0.943519i
$391$	16.4476	+	28.4880i	0.831790	+	1.44070i
$392$	5.45598	+	5.45598i	0.275568	+	0.275568i
$393$	−21.7941	+	32.8009i	−1.09936	+	1.65459i
$394$			19.0261i			0.958522i
$395$	3.61984	+	3.61984i	0.182134	+	0.182134i
$396$	2.71292	−	0.371483i	0.136329	−	0.0186677i
$397$	7.79275	−	29.0830i	0.391107	−	1.45963i	−0.437204	−	0.899363i	$-0.644031\pi$
$397$	7.79275	−	29.0830i	0.391107	−	1.45963i	0.828311	−	0.560269i	$-0.189302\pi$
$398$	−5.48827	−	20.4825i	−0.275102	−	1.02669i
$399$	−0.350229	−	0.232704i	−0.0175334	−	0.0116498i
$400$		−	6.59392i		−	0.329696i
$401$	18.9591	−	18.9591i	0.946772	−	0.946772i	−0.0518817	−	0.998653i	$-0.516522\pi$
$401$	18.9591	−	18.9591i	0.946772	−	0.946772i	0.998653	+	0.0518817i	$0.0165219\pi$
$402$	28.1112	+	18.6780i	1.40206	+	0.931576i
$403$	−0.955815	+	27.6993i	−0.0476125	+	1.37980i
$404$		−	1.49600i		−	0.0744289i
$405$	17.1216	−	0.177557i	0.850779	−	0.00882287i
$406$	−6.31921	+	10.9452i	−0.313617	+	0.543201i
$407$	6.75107			0.334638
$408$	21.8553	−	4.40621i	1.08200	−	0.218140i
$409$	8.00309	+	29.8679i	0.395727	+	1.47687i	0.820538	+	0.571592i	$0.193674\pi$
$409$	8.00309	+	29.8679i	0.395727	+	1.47687i	−0.424811	+	0.905282i	$0.639659\pi$
$410$	0.234015	+	0.873357i	0.0115572	+	0.0431320i
$411$	−7.86530	+	23.3693i	−0.387966	+	1.15272i
$412$	−1.48577			−0.0731986
$413$	−7.62347	+	13.2042i	−0.375126	+	0.649738i
$414$	17.4883	+	22.5482i	0.859505	+	1.10818i
$415$		−	0.605276i		−	0.0297118i
$416$	4.93103	+	9.26467i	0.241763	+	0.454238i
$417$	2.10820	−	33.4953i	0.103239	−	1.64027i
$418$	−0.245456	+	0.245456i	−0.0120056	+	0.0120056i
$419$		−	15.1615i		−	0.740687i	−0.928895	−	0.370344i	$-0.879240\pi$
$419$		−	15.1615i		−	0.740687i	0.928895	−	0.370344i	$-0.120760\pi$
$420$	2.99529	−	1.48678i	0.146155	−	0.0725475i
$421$	−8.67607	−	32.3795i	−0.422846	−	1.57808i	−0.768583	−	0.639750i	$-0.779038\pi$
$421$	−8.67607	−	32.3795i	−0.422846	−	1.57808i	0.345737	−	0.938331i	$-0.387629\pi$
$422$	−10.3372	+	38.5788i	−0.503205	+	1.87799i
$423$	−30.1712	−	12.3144i	−1.46697	−	0.598747i
$424$	15.6445	+	15.6445i	0.759764	+	0.759764i
$425$			7.58976i			0.368157i
$426$	12.3598	+	0.777926i	0.598832	+	0.0376907i
$427$	−17.3616	−	17.3616i	−0.840185	−	0.840185i
$428$	−0.671066	−	1.16232i	−0.0324372	−	0.0561829i
$429$	4.46983	+	9.84354i	0.215805	+	0.475250i
$430$	3.07398	−	5.32429i	0.148240	−	0.256760i
$431$	8.80080	−	2.35817i	0.423920	−	0.113589i	−0.0405509	−	0.999177i	$-0.512911\pi$
$431$	8.80080	−	2.35817i	0.423920	−	0.113589i	0.464471	+	0.885589i	$0.346245\pi$
$432$	23.4396	−	8.16051i	1.12774	−	0.392623i
$433$	−2.45997	+	1.42027i	−0.118219	+	0.0682536i	−0.557943	−	0.829879i	$-0.688409\pi$
$433$	−2.45997	+	1.42027i	−0.118219	+	0.0682536i	0.439725	+	0.898133i	$0.355076\pi$
$434$	22.7186	−	6.08744i	1.09053	−	0.292207i
$435$	9.00096	+	10.2101i	0.431563	+	0.489537i
$436$	−5.57248	+	1.49314i	−0.266873	+	0.0715085i
$437$	−0.728982	−	0.195330i	−0.0348720	−	0.00934391i
$438$	21.5127	−	32.3775i	1.02792	−	1.54706i
$439$	−13.1914	+	7.61608i	−0.629593	+	0.363496i	−0.780594	−	0.625038i	$-0.785083\pi$
$439$	−13.1914	+	7.61608i	−0.629593	+	0.363496i	0.151002	+	0.988534i	$0.451750\pi$
$440$	1.99573	+	7.44815i	0.0951425	+	0.355077i
$441$	−7.87485	−	5.97797i	−0.374993	−	0.284665i
$442$	−14.8060	−	27.8183i	−0.704250	−	1.32318i
$443$	12.6896	+	7.32636i	0.602902	+	0.348086i	0.770183	−	0.637824i	$-0.220165\pi$
$443$	12.6896	+	7.32636i	0.602902	+	0.348086i	−0.167280	+	0.985909i	$0.553498\pi$
$444$	−3.49121	+	0.703858i	−0.165685	+	0.0334036i
$445$	−19.7332			−0.935444
$446$	5.95626	−	10.3166i	0.282037	−	0.488503i
$447$	−1.76750	+	1.55818i	−0.0835999	+	0.0736994i
$448$	−6.70346	+	6.70346i	−0.316709	+	0.316709i
$449$	−17.7641	−	4.75989i	−0.838342	−	0.224633i	−0.185992	−	0.982551i	$-0.559550\pi$
$449$	−17.7641	−	4.75989i	−0.838342	−	0.224633i	−0.652349	+	0.757918i	$0.726217\pi$
$450$	0.893196	+	6.52296i	0.0421057	+	0.307495i
$451$	0.258759	+	0.448185i	0.0121845	+	0.0211042i
$452$	0.919662	+	1.59290i	0.0432573	+	0.0749238i
$453$	3.52085	−	3.10389i	0.165424	−	0.145833i
$454$	10.2854	−	5.93830i	0.482719	−	0.278698i
$455$	9.00805	+	9.65195i	0.422304	+	0.452490i
$456$	−0.283073	+	0.426035i	−0.0132561	+	0.0199509i
$457$	19.3970	+	5.19741i	0.907354	+	0.243125i	0.682172	−	0.731192i	$-0.261036\pi$
$457$	19.3970	+	5.19741i	0.907354	+	0.243125i	0.225182	+	0.974317i	$0.427702\pi$
$458$	37.4357	+	21.6135i	1.74926	+	1.00993i
$459$	−26.9795	+	9.39294i	−1.25929	+	0.438425i
$460$	4.24393	−	4.24393i	0.197874	−	0.197874i
$461$	−17.5366	−	17.5366i	−0.816759	−	0.816759i	0.168878	−	0.985637i	$-0.445986\pi$
$461$	−17.5366	−	17.5366i	−0.816759	−	0.816759i	−0.985637	+	0.168878i	$0.945986\pi$
$462$	6.88187	−	6.06688i	0.320174	−	0.282257i
$463$	6.58529	−	24.5766i	0.306044	−	1.14217i	−0.625999	−	0.779824i	$-0.715308\pi$
$463$	6.58529	−	24.5766i	0.306044	−	1.14217i	0.932043	−	0.362348i	$-0.118025\pi$
$464$	17.0864	+	9.86485i	0.793217	+	0.457964i
$465$	1.59115	−	25.2803i	0.0737878	−	1.17235i
$466$	−3.28020	+	12.2419i	−0.151952	+	0.567094i
$467$	−6.28540			−0.290854			−0.145427	−	0.989369i	$-0.546456\pi$
$467$	−6.28540			−0.290854			−0.145427	+	0.989369i	$0.546456\pi$
$468$	−3.33777	−	4.62441i	−0.154289	−	0.213763i
$469$	23.5915			1.08935
$470$	−8.50306	+	31.7338i	−0.392217	+	1.46377i
$471$	20.4211	+	13.5685i	0.940954	+	0.625203i
$472$	16.0623	+	9.27355i	0.739325	+	0.426850i
$473$	0.910763	−	3.39901i	0.0418769	−	0.156287i
$474$	−7.02203	−	2.36337i	−0.322533	−	0.108553i
$475$	−0.123127	−	0.123127i	−0.00564947	−	0.00564947i
$476$	−3.94512	+	3.94512i	−0.180824	+	0.180824i
$477$	−22.5804	−	17.1412i	−1.03388	−	0.784844i
$478$	28.8576	+	16.6610i	1.31992	+	0.762055i
$479$	−19.1605	−	5.13405i	−0.875467	−	0.234581i	−0.207016	−	0.978337i	$-0.566375\pi$
$479$	−19.1605	−	5.13405i	−0.875467	−	0.234581i	−0.668450	+	0.743757i	$0.733042\pi$
$480$	−4.26468	−	8.59168i	−0.194655	−	0.392155i
$481$	−6.60638	−	12.4124i	−0.301225	−	0.565957i
$482$	−13.6094	+	7.85739i	−0.619891	+	0.357894i
$483$	18.9040	+	6.36245i	0.860163	+	0.289501i
$484$	2.10987	+	3.65440i	0.0959033	+	0.166109i
$485$	3.78091	+	6.54873i	0.171682	+	0.297362i
$486$	−22.0819	+	11.2478i	−1.00166	+	0.510209i
$487$	3.04184	+	0.815058i	0.137839	+	0.0369338i	0.327079	−	0.944997i	$-0.393936\pi$
$487$	3.04184	+	0.815058i	0.137839	+	0.0369338i	−0.189240	+	0.981931i	$0.560602\pi$
$488$	−21.1194	+	21.1194i	−0.956031	+	0.956031i
$489$	−2.76224	−	13.7010i	−0.124913	−	0.619579i
$490$	−4.98374	+	8.63209i	−0.225142	+	0.389958i
$491$	−6.77048			−0.305547			−0.152774	−	0.988261i	$-0.548821\pi$
$491$	−6.77048			−0.305547			−0.152774	+	0.988261i	$0.548821\pi$
$492$	−0.180540	−	0.204793i	−0.00813939	−	0.00923280i
$493$	−19.6669	−	11.3547i	−0.885751	−	0.511389i
$494$	0.691487	+	0.211096i	0.0311115	+	0.00949767i
$495$	−3.82834	−	9.10856i	−0.172071	−	0.409399i
$496$	−9.50304	−	35.4658i	−0.426699	−	1.59246i
$497$	7.49674	−	4.32824i	0.336275	−	0.194148i
$498$	0.389489	+	0.784670i	0.0174534	+	0.0351619i
$499$	10.4405	+	2.79751i	0.467380	+	0.125234i	0.484820	−	0.874614i	$-0.338885\pi$
$499$	10.4405	+	2.79751i	0.467380	+	0.125234i	−0.0174405	+	0.999848i	$0.505552\pi$
$500$	6.18222	−	1.65652i	0.276477	−	0.0740818i
$501$	4.27176	−	12.6922i	0.190848	−	0.567046i
$502$	−37.5751	+	10.0682i	−1.67706	+	0.449366i
$503$	−0.693828	+	0.400582i	−0.0309363	+	0.0178611i	−0.515388	−	0.856957i	$-0.672352\pi$
$503$	−0.693828	+	0.400582i	−0.0309363	+	0.0178611i	0.484452	+	0.874818i	$0.339019\pi$
$504$	8.17388	−	10.7676i	0.364094	−	0.479625i
$505$	−5.21410	+	1.39711i	−0.232025	+	0.0621708i
$506$	8.23302	−	14.2600i	0.366002	−	0.633935i
$507$	13.7241	−	17.8507i	0.609510	−	0.792778i
$508$	4.29355	+	7.43665i	0.190496	+	0.329948i
$509$	−13.2923	−	13.2923i	−0.589171	−	0.589171i	0.348236	−	0.937407i	$-0.386781\pi$
$509$	−13.2923	−	13.2923i	−0.589171	−	0.589171i	−0.937407	+	0.348236i	$0.886781\pi$
$510$	12.8052	+	25.7976i	0.567024	+	1.14234i
$511$		−	27.1719i		−	1.20201i
$512$	5.98393	+	5.98393i	0.264455	+	0.264455i
$513$	0.285303	−	0.590063i	0.0125965	−	0.0260519i
$514$	6.03414	−	22.5197i	0.266155	−	0.993303i
$515$	1.38756	+	5.17844i	0.0611431	+	0.228189i
$516$	−0.116609	+	1.85270i	−0.00513344	+	0.0815605i
$517$			18.8043i			0.827012i
$518$	−8.43748	+	8.43748i	−0.370722	+	0.370722i
$519$	1.64496	−	0.816511i	0.0722055	−	0.0358408i
$520$	11.7411	−	10.9578i	0.514881	−	0.480532i
$521$			8.77091i			0.384260i	0.981369	+	0.192130i	$0.0615396\pi$
$521$			8.77091i			0.384260i	−0.981369	+	0.192130i	$0.938460\pi$
$522$	−18.2388	−	7.44421i	−0.798291	−	0.325824i
$523$	11.9167	−	20.6403i	0.521079	−	0.902536i	−0.478620	−	0.878022i	$-0.658863\pi$
$523$	11.9167	−	20.6403i	0.521079	−	0.902536i	0.999699	−	0.0245139i	$-0.00780379\pi$
$524$	−11.9881			−0.523702
$525$	3.04331	+	3.45213i	0.132821	+	0.150663i
$526$	−1.85721	−	6.93119i	−0.0809781	−	0.302214i
$527$	10.9382	+	40.8220i	0.476477	+	1.77823i
$528$	−9.47094	−	10.7432i	−0.412170	−	0.467539i
$529$	12.7992			0.556488
$530$	−14.2904	+	24.7517i	−0.620735	+	1.07514i
$531$	−22.0032	−	8.98066i	−0.954859	−	0.389728i
$532$		−	0.128002i		−	0.00554959i
$533$	0.570811	−	0.914330i	0.0247246	−	0.0396040i
$534$	25.5819	−	12.6981i	1.10704	−	0.549502i
$535$	−3.42439	+	3.42439i	−0.148049	+	0.148049i
$536$		−	28.6978i		−	1.23956i
$537$	−0.382656	+	6.07967i	−0.0165128	+	0.262357i
$538$	−1.87109	−	6.98301i	−0.0806685	−	0.301059i
$539$	−1.47659	+	5.51070i	−0.0636012	+	0.237363i
$540$	2.92941	+	4.31121i	0.126062	+	0.185525i
$541$	−9.16297	−	9.16297i	−0.393947	−	0.393947i	0.482145	−	0.876092i	$-0.339858\pi$
$541$	−9.16297	−	9.16297i	−0.393947	−	0.393947i	−0.876092	+	0.482145i	$0.839858\pi$
$542$			16.8657i			0.724442i
$543$	−8.56854	−	17.2623i	−0.367711	−	0.740797i
$544$	11.3162	+	11.3162i	0.485176	+	0.485176i
$545$	10.4083	+	18.0276i	0.445841	+	0.772219i
$546$	−17.8888	−	6.71605i	−0.765572	−	0.287421i
$547$	−4.40705	+	7.63324i	−0.188432	+	0.326374i	−0.944728	−	0.327856i	$-0.893674\pi$
$547$	−4.40705	+	7.63324i	−0.188432	+	0.326374i	0.756296	+	0.654230i	$0.227007\pi$
$548$	−7.25023	+	1.94269i	−0.309714	+	0.0829877i
$549$	23.1400	−	30.4826i	0.987591	−	1.30096i
$550$	3.29015	−	1.89957i	0.140293	−	0.0809979i
$551$	0.503257	−	0.134847i	0.0214395	−	0.00574469i
$552$	7.73958	−	22.9958i	0.329418	−	0.978765i
$553$	−5.00243	+	1.34040i	−0.212725	+	0.0569995i
$554$	46.9914	+	12.5913i	1.99647	+	0.534953i
$555$	5.71363	+	11.5108i	0.242530	+	0.488605i
$556$	8.84776	−	5.10826i	0.375229	−	0.216638i
$557$	−2.92619	−	10.9207i	−0.123987	−	0.462724i	0.875815	−	0.482647i	$-0.160325\pi$
$557$	−2.92619	−	10.9207i	−0.123987	−	0.462724i	−0.999802	+	0.0199228i	$0.993658\pi$
$558$	14.2049	+	33.7969i	0.601341	+	1.43074i
$559$	−7.14061	+	1.65165i	−0.302016	+	0.0698573i
$560$	−15.1469	−	8.74509i	−0.640075	−	0.369548i
$561$	10.9013	+	12.3657i	0.460252	+	0.522080i
$562$	−13.2839			−0.560348
$563$	−3.43583	+	5.95102i	−0.144803	+	0.250806i	−0.929299	−	0.369327i	$-0.879588\pi$
$563$	−3.43583	+	5.95102i	−0.144803	+	0.250806i	0.784497	+	0.620133i	$0.212921\pi$
$564$	−1.96051	−	9.72434i	−0.0825525	−	0.409468i
$565$	4.69296	−	4.69296i	0.197434	−	0.197434i
$566$	−15.0467	−	4.03175i	−0.632459	−	0.169467i
$567$	−8.50503	+	15.0904i	−0.357178	+	0.633737i
$568$	−5.26508	−	9.11939i	−0.220918	−	0.382641i
$569$	4.44883	+	7.70561i	0.186505	+	0.323036i	0.944083	−	0.329709i	$-0.106951\pi$
$569$	4.44883	+	7.70561i	0.186505	+	0.323036i	−0.757578	+	0.652745i	$0.773617\pi$
$570$	−0.626246	−	0.210773i	−0.0262306	−	0.00882831i
$571$	−36.0860	+	20.8343i	−1.51015	+	0.871888i	−0.510224	+	0.860041i	$0.670438\pi$
$571$	−36.0860	+	20.8343i	−1.51015	+	0.871888i	−0.999930	+	0.0118466i	$0.996229\pi$
$572$	−1.74278	+	2.79160i	−0.0728694	+	0.116723i
$573$	−17.4148	−	35.0842i	−0.727514	−	1.46566i
$574$	−0.883538	−	0.236743i	−0.0368782	−	0.00988148i
$575$	7.15320	+	4.12990i	0.298309	+	0.172229i
$576$	−11.7696	−	8.93456i	−0.490400	−	0.372273i
$577$	−10.4946	+	10.4946i	−0.436896	+	0.436896i	−0.890966	−	0.454070i	$-0.849972\pi$
$577$	−10.4946	+	10.4946i	−0.436896	+	0.436896i	0.454070	+	0.890966i	$0.349972\pi$
$578$	−14.8682	−	14.8682i	−0.618437	−	0.618437i
$579$	12.6540	+	4.25889i	0.525881	+	0.176993i
$580$	−1.07239	+	4.00221i	−0.0445285	+	0.166183i
$581$	0.530295	+	0.306166i	0.0220003	+	0.0127019i
$582$	−9.11556	−	6.05670i	−0.377852	−	0.251058i
$583$	−4.23398	+	15.8014i	−0.175353	+	0.654428i
$584$	−33.0532			−1.36775
$585$	−13.0006	+	15.9521i	−0.537507	+	0.659537i
$586$	−25.1539			−1.03910
$587$	−6.67749	+	24.9207i	−0.275610	+	1.02859i	0.679822	+	0.733377i	$0.262057\pi$
$587$	−6.67749	+	24.9207i	−0.275610	+	1.02859i	−0.955432	+	0.295212i	$0.904610\pi$
$588$	0.189055	−	3.00372i	0.00779649	−	0.123871i
$589$	−0.839697	−	0.484799i	−0.0345991	−	0.0199758i
$590$	−6.20112	+	23.1429i	−0.255296	+	0.952777i
$591$	−15.5497	+	13.7082i	−0.639629	+	0.563880i
$592$	13.1717	+	13.1717i	0.541352	+	0.541352i
$593$	−17.9518	+	17.9518i	−0.737193	+	0.737193i	−0.972034	−	0.234841i	$-0.924543\pi$
$593$	−17.9518	+	17.9518i	−0.737193	+	0.737193i	0.234841	+	0.972034i	$0.424543\pi$
$594$	10.8243	+	9.34470i	0.444125	+	0.383418i
$595$	17.4345	+	10.0658i	0.714744	+	0.412658i
$596$	−0.692833	−	0.185644i	−0.0283796	−	0.00760428i
$597$	12.7857	−	19.2430i	0.523284	−	0.787562i
$598$	−34.2748	−	1.18271i	−1.40160	−	0.0483648i
$599$	11.0137	−	6.35875i	0.450007	−	0.259812i	−0.257826	−	0.966191i	$-0.583006\pi$
$599$	11.0137	−	6.35875i	0.450007	−	0.259812i	0.707833	+	0.706380i	$0.249673\pi$
$600$	4.19934	−	3.70202i	0.171437	−	0.151135i
$601$	0.128492	+	0.222555i	0.00524131	+	0.00907822i	0.868634	−	0.495454i	$-0.164998\pi$
$601$	0.128492	+	0.222555i	0.00524131	+	0.00907822i	−0.863393	+	0.504532i	$0.831665\pi$
$602$	3.10981	+	5.38636i	0.126747	+	0.219531i
$603$	4.98869	+	36.4321i	0.203155	+	1.48363i
$604$	1.38012	+	0.369802i	0.0561563	+	0.0150470i
$605$	10.7665	−	10.7665i	0.437720	−	0.437720i
$606$	5.86046	−	5.16642i	0.238065	−	0.209872i
$607$	8.63734	−	14.9603i	0.350579	−	0.607220i	−0.635772	−	0.771877i	$-0.719318\pi$
$607$	8.63734	−	14.9603i	0.350579	−	0.607220i	0.986351	+	0.164657i	$0.0526516\pi$
$608$	−0.367160			−0.0148903
$609$	−13.4982	+	2.72136i	−0.546976	+	0.110275i
$610$	−33.4138	−	19.2914i	−1.35288	−	0.781088i
$611$	34.5733	−	18.4013i	1.39868	−	0.744436i
$612$	−6.92665	−	5.25817i	−0.279993	−	0.212549i
$613$	1.54411	+	5.76269i	0.0623659	+	0.232753i	0.990073	−	0.140557i	$-0.0448894\pi$
$613$	1.54411	+	5.76269i	0.0623659	+	0.232753i	−0.927707	+	0.373310i	$0.878223\pi$
$614$	−8.63698	+	4.98656i	−0.348560	+	0.201241i
$615$	−0.545172	+	0.820504i	−0.0219834	+	0.0330859i
$616$	−7.53498	−	2.01899i	−0.303593	−	0.0813475i
$617$	8.29254	−	2.22198i	0.333845	−	0.0894535i	−0.0880025	−	0.996120i	$-0.528048\pi$
$617$	8.29254	−	2.22198i	0.333845	−	0.0894535i	0.421848	+	0.906667i	$0.361382\pi$
$618$	−5.13108	−	5.82037i	−0.206402	−	0.234130i
$619$	21.4022	−	5.73471i	0.860228	−	0.230497i	0.198370	−	0.980127i	$-0.436435\pi$
$619$	21.4022	−	5.73471i	0.860228	−	0.230497i	0.661857	+	0.749630i	$0.269768\pi$
$620$	6.67779	−	3.85542i	0.268186	−	0.154837i
$621$	−5.82799	+	30.5387i	−0.233869	+	1.22548i
$622$	14.4781	−	3.87941i	0.580521	−	0.155550i
$623$	9.98163	−	17.2887i	0.399906	−	0.692657i
$624$	−10.4844	+	27.9261i	−0.419710	+	1.11794i
$625$	−8.09590	−	14.0225i	−0.323836	−	0.560901i
$626$	−18.8850	−	18.8850i	−0.754797	−	0.754797i
$627$	−0.377456	−	0.0237572i	−0.0150741	−	0.000948770i
$628$			7.46351i			0.297826i
$629$	−15.1609	−	15.1609i	−0.604505	−	0.604505i
$630$	16.1685	+	6.59922i	0.644170	+	0.262919i
$631$	−0.0409626	+	0.152874i	−0.00163069	+	0.00608583i	−0.966736	−	0.255775i	$-0.917669\pi$
$631$	−0.0409626	+	0.152874i	−0.00163069	+	0.00608583i	0.965106	+	0.261861i	$0.0843361\pi$
$632$	1.63052	+	6.08520i	0.0648588	+	0.242056i
$633$	−38.9775	+	19.3474i	−1.54922	+	0.768989i
$634$		−	2.42408i		−	0.0962724i
$635$	21.9096	−	21.9096i	0.869457	−	0.869457i
$636$	0.542097	−	8.61287i	0.0214955	−	0.341523i
$637$	11.5768	−	2.67776i	0.458691	−	0.106097i
$638$			11.3674i			0.450041i
$639$	8.26933	+	10.6619i	0.327130	+	0.421778i
$640$	−12.9865	+	22.4933i	−0.513336	+	0.889124i
$641$	18.9474			0.748378			0.374189	−	0.927352i	$-0.377921\pi$
$641$	18.9474			0.748378			0.374189	+	0.927352i	$0.377921\pi$
$642$	2.23577	−	6.64289i	0.0882388	−	0.262174i
$643$	−2.67769	−	9.99329i	−0.105598	−	0.394097i	0.892814	−	0.450425i	$-0.148727\pi$
$643$	−2.67769	−	9.99329i	−0.105598	−	0.394097i	−0.998412	+	0.0563280i	$0.982061\pi$
$644$	1.57149	+	5.86490i	0.0619256	+	0.231109i
$645$	6.56622	−	1.32381i	0.258545	−	0.0521249i
$646$	1.10244			0.0433750
$647$	2.30295	−	3.98882i	0.0905382	−	0.156817i	−0.817200	−	0.576355i	$-0.804475\pi$
$647$	2.30295	−	3.98882i	0.0905382	−	0.156817i	0.907738	+	0.419538i	$0.137808\pi$
$648$	18.3567	+	10.3459i	0.721119	+	0.406426i
$649$			13.7136i			0.538306i
$650$	−6.71215	−	4.19036i	−0.263272	−	0.164359i
$651$	21.3438	+	14.1816i	0.836528	+	0.555819i
$652$	3.00849	−	3.00849i	0.117822	−	0.117822i
$653$		−	18.2172i		−	0.712894i	−0.934316	−	0.356447i	$-0.883988\pi$
$653$		−	18.2172i		−	0.712894i	0.934316	−	0.356447i	$-0.116012\pi$
$654$	−25.0937	−	16.6731i	−0.981242	−	0.651972i
$655$	11.1957	+	41.7827i	0.437450	+	1.63259i
$656$	−0.369578	+	1.37928i	−0.0144296	+	0.0538519i
$657$	41.9613	−	5.74580i	1.63707	−	0.224165i
$658$	−23.5016	−	23.5016i	−0.916188	−	0.916188i
$659$			3.98911i			0.155394i	0.996977	+	0.0776968i	$0.0247566\pi$
$659$			3.98911i			0.155394i	−0.996977	+	0.0776968i	$0.975243\pi$
$660$	1.66450	−	2.50514i	0.0647906	−	0.0975123i
$661$	20.4967	+	20.4967i	0.797229	+	0.797229i	0.982658	−	0.185429i	$-0.0593675\pi$
$661$	20.4967	+	20.4967i	0.797229	+	0.797229i	−0.185429	+	0.982658i	$0.559367\pi$
$662$	−6.64348	−	11.5068i	−0.258206	−	0.447226i
$663$	12.0677	−	32.1436i	0.468672	−	1.24835i
$664$	0.372435	−	0.645076i	0.0144533	−	0.0250338i
$665$	−0.446132	+	0.119541i	−0.0173003	+	0.00463559i
$666$	−14.8141	−	11.2457i	−0.574036	−	0.435763i
$667$	−21.4031	+	12.3571i	−0.828732	+	0.478469i
$668$	3.93770	−	1.05510i	0.152354	−	0.0408232i
$669$	12.7230	−	2.56506i	0.491898	−	0.0991711i
$670$	35.8088	−	9.59495i	1.38342	−	0.370685i
$671$	−21.3313	−	5.71570i	−0.823485	−	0.220652i
$672$	9.68455	+	0.609548i	0.373590	+	0.0235138i
$673$	−13.0317	+	7.52386i	−0.502336	+	0.290024i	−0.729678	−	0.683791i	$-0.760330\pi$
$673$	−13.0317	+	7.52386i	−0.502336	+	0.290024i	0.227342	+	0.973815i	$0.426997\pi$
$674$	−1.28101	−	4.78081i	−0.0493428	−	0.184150i
$675$	−4.68755	+	5.42974i	−0.180424	+	0.208991i
$676$	6.83802	+	0.472480i	0.263001	+	0.0181723i
$677$	−35.3403	−	20.4037i	−1.35824	−	0.784179i	−0.368852	−	0.929488i	$-0.620249\pi$
$677$	−35.3403	−	20.4037i	−1.35824	−	0.784179i	−0.989386	+	0.145309i	$0.953582\pi$
$678$	−3.06401	+	9.10376i	−0.117673	+	0.349628i
$679$	−7.64997			−0.293579
$680$	12.2445	−	21.2081i	0.469556	−	0.813295i
$681$	12.2638	+	4.12758i	0.469951	+	0.158169i
$682$	14.9587	−	14.9587i	0.572797	−	0.572797i
$683$	19.8985	+	5.33179i	0.761395	+	0.204015i	0.618567	−	0.785732i	$-0.287714\pi$
$683$	19.8985	+	5.33179i	0.761395	+	0.204015i	0.142828	+	0.989747i	$0.454380\pi$
$684$	0.197672	−	0.0270674i	0.00755818	−	0.00103495i
$685$	13.5420	+	23.4553i	0.517411	+	0.896183i
$686$	−15.7509	−	27.2813i	−0.601372	−	1.04161i
$687$	9.30786	+	46.1679i	0.355117	+	1.76142i
$688$	8.40858	−	4.85470i	0.320574	−	0.185084i
$689$	33.1955	−	7.67823i	1.26465	−	0.292517i
$690$	31.2816	+	1.96887i	1.19087	+	0.0749536i
$691$	−28.7160	−	7.69444i	−1.09241	−	0.292710i	−0.332739	−	0.943019i	$-0.607973\pi$
$691$	−28.7160	−	7.69444i	−1.09241	−	0.292710i	−0.759670	+	0.650309i	$0.774640\pi$
$692$	0.484141	+	0.279519i	0.0184043	+	0.0106257i
$693$	9.91669	+	1.25328i	0.376704	+	0.0476083i
$694$	9.79848	−	9.79848i	0.371945	−	0.371945i
$695$	−26.0670	−	26.0670i	−0.988778	−	0.988778i
$696$	3.31040	+	16.4199i	0.125480	+	0.622395i
$697$	0.425392	−	1.58759i	0.0161129	−	0.0601341i
$698$	−7.53286	−	4.34910i	−0.285123	−	0.164616i
$699$	−12.3684	+	6.13934i	−0.467817	+	0.232211i
$700$	−0.362584	+	1.35318i	−0.0137044	+	0.0511455i
$701$	8.68924			0.328188			0.164094	−	0.986445i	$-0.447530\pi$
$701$	8.68924			0.328188			0.164094	+	0.986445i	$0.447530\pi$
$702$	6.58874	−	29.0457i	0.248676	−	1.09626i
$703$	0.491905			0.0185526
$704$	−2.20688	+	8.23620i	−0.0831750	+	0.310413i
$705$	−32.0619	+	15.9146i	−1.20752	+	0.599380i
$706$	36.5373	+	21.0948i	1.37510	+	0.793914i
$707$	1.41340	−	5.27489i	0.0531564	−	0.198383i
$708$	−1.42976	−	7.09177i	−0.0537338	−	0.266525i
$709$	−1.57281	−	1.57281i	−0.0590680	−	0.0590680i	0.676956	−	0.736024i	$-0.263299\pi$
$709$	−1.57281	−	1.57281i	−0.0590680	−	0.0590680i	−0.736024	+	0.676956i	$0.763299\pi$
$710$	9.61873	−	9.61873i	0.360984	−	0.360984i
$711$	−3.12778	−	7.44177i	−0.117301	−	0.279088i
$712$	−21.0308	−	12.1421i	−0.788162	−	0.455046i
$713$	44.4259	+	11.9039i	1.66376	+	0.445804i
$714$	−29.0791	−	1.83024i	−1.08826	−	0.0684951i
$715$	11.3573	+	3.46714i	0.424739	+	0.129664i
$716$	−1.60594	+	0.927192i	−0.0600169	+	0.0346508i
$717$	7.17504	+	35.5889i	0.267957	+	1.32909i
$718$	8.17571	+	14.1607i	0.305115	+	0.528474i
$719$	−13.8404	−	23.9723i	−0.516160	−	0.894015i	−0.999824	−	0.0187613i	$-0.994028\pi$
$719$	−13.8404	−	23.9723i	−0.516160	−	0.894015i	0.483664	−	0.875254i	$-0.339306\pi$
$720$	10.3020	−	25.2405i	0.383932	−	0.940659i
$721$	−5.23881	−	1.40373i	−0.195103	−	0.0522778i
$722$	21.3402	−	21.3402i	0.794202	−	0.794202i
$723$	−16.2272	−	5.46150i	−0.603495	−	0.203116i
$724$	2.93330	−	5.08062i	0.109015	−	0.188820i
$725$	−5.70220			−0.211774
$726$	−7.02940	+	20.8857i	−0.260885	+	0.775140i
$727$	7.64034	+	4.41115i	0.283365	+	0.163601i	0.634946	−	0.772557i	$-0.281022\pi$
$727$	7.64034	+	4.41115i	0.283365	+	0.163601i	−0.351581	+	0.936157i	$0.614356\pi$
$728$	3.66140	+	15.8294i	0.135700	+	0.586677i
$729$	−25.1024	−	9.94320i	−0.929720	−	0.368267i
$730$	−11.0511	−	41.2434i	−0.409021	−	1.52649i
$731$	−9.67848	+	5.58787i	−0.357971	+	0.206675i
$732$	11.6270	+	0.731808i	0.429747	+	0.0270484i
$733$	10.7413	+	2.87813i	0.396739	+	0.106306i	0.451672	−	0.892184i	$-0.350828\pi$
$733$	10.7413	+	2.87813i	0.396739	+	0.106306i	−0.0549326	+	0.998490i	$0.517494\pi$
$734$	21.1143	−	5.65756i	0.779343	−	0.208824i
$735$	−10.6456	+	2.14624i	−0.392668	+	0.0791654i
$736$	16.8228	−	4.50767i	0.620098	−	0.166155i
$737$	18.3762	−	10.6095i	0.676895	−	0.390806i
$738$	0.178766	−	1.41450i	0.00658048	−	0.0520685i
$739$	34.2934	−	9.18890i	1.26150	−	0.338019i	0.434734	−	0.900559i	$-0.356842\pi$
$739$	34.2934	−	9.18890i	1.26150	−	0.338019i	0.826770	+	0.562540i	$0.190176\pi$
$740$	−1.95597	+	3.38783i	−0.0719027	+	0.124539i
$741$	0.325687	+	0.717232i	0.0119644	+	0.0263482i
$742$	−14.4570	−	25.0402i	−0.530732	−	0.919256i
$743$	−17.6137	−	17.6137i	−0.646183	−	0.646183i	0.305886	−	0.952068i	$-0.401048\pi$
$743$	−17.6137	−	17.6137i	−0.646183	−	0.646183i	−0.952068	+	0.305886i	$0.901048\pi$
$744$	17.2511	−	25.9636i	0.632457	−	0.951871i
$745$			2.58814i			0.0948223i
$746$	29.4768	+	29.4768i	1.07922	+	1.07922i
$747$	−0.360672	+	0.883671i	−0.0131963	+	0.0323318i
$748$	−1.29879	+	4.84717i	−0.0474886	+	0.177230i
$749$	−1.26803	−	4.73234i	−0.0463327	−	0.172916i
$750$	27.8395	+	18.4975i	1.01655	+	0.675434i
$751$			6.78197i			0.247478i	0.992315	+	0.123739i	$0.0394885\pi$
$751$			6.78197i			0.247478i	−0.992315	+	0.123739i	$0.960512\pi$
$752$	−36.6881	+	36.6881i	−1.33788	+	1.33788i
$753$	−35.3011	−	23.4553i	−1.28644	−	0.854759i
$754$	20.9000	−	11.1238i	0.761131	−	0.405104i
$755$		−	5.15557i		−	0.187630i
$756$	−5.25892	+	0.385786i	−0.191265	+	0.0140309i
$757$	−13.8632	+	24.0118i	−0.503868	+	0.872725i	0.496122	+	0.868253i	$0.334757\pi$
$757$	−13.8632	+	24.0118i	−0.503868	+	0.872725i	−0.999990	+	0.00447184i	$0.998577\pi$
$758$	−11.7223			−0.425774
$759$	17.5863	−	3.54555i	0.638341	−	0.128695i
$760$	0.145415	+	0.542697i	0.00527476	+	0.0196857i
$761$	3.79376	+	14.1585i	0.137524	+	0.513246i	0.999975	+	0.00710529i	$0.00226170\pi$
$761$	3.79376	+	14.1585i	0.137524	+	0.513246i	−0.862451	+	0.506141i	$0.831072\pi$
$762$	−14.3047	+	42.5020i	−0.518204	+	1.53968i
$763$	−21.0592			−0.762394
$764$	5.96167	−	10.3259i	0.215686	−	0.373579i
$765$	−11.8578	+	29.0524i	−0.428720	+	1.05039i
$766$			45.0214i			1.62669i
$767$	25.2136	−	13.4197i	0.910411	−	0.484557i
$768$	1.28950	−	20.4877i	0.0465308	−	0.739285i
$769$	9.57440	−	9.57440i	0.345262	−	0.345262i	−0.513080	−	0.858341i	$-0.671495\pi$
$769$	9.57440	−	9.57440i	0.345262	−	0.345262i	0.858341	+	0.513080i	$0.171495\pi$
$770$		−	10.0771i		−	0.363154i
$771$	22.7525	−	11.2937i	0.819411	−	0.406733i
$772$	1.05193	+	3.92584i	0.0378596	+	0.141294i
$773$	12.5962	−	47.0096i	0.453053	−	1.69082i	−0.240695	−	0.970601i	$-0.577375\pi$
$773$	12.5962	−	47.0096i	0.453053	−	1.69082i	0.693749	−	0.720217i	$-0.255958\pi$
$774$	−7.66049	+	5.94146i	−0.275351	+	0.213561i
$775$	7.50367	+	7.50367i	0.269540	+	0.269540i
$776$			9.30579i			0.334058i
$777$	−12.9749	−	0.816646i	−0.465473	−	0.0292970i
$778$	−2.57140	−	2.57140i	−0.0921893	−	0.0921893i
$779$	0.0188541	+	0.0326562i	0.000675517	+	0.00117003i
$780$	−6.23473	−	0.608879i	−0.223239	−	0.0218014i
$781$	3.89297	−	6.74282i	0.139301	−	0.241277i
$782$	−50.5127	+	13.5348i	−1.80633	+	0.484004i
$783$	−7.05693	−	20.2697i	−0.252194	−	0.724381i
$784$	−13.6326	+	7.87076i	−0.486877	+	0.281098i
$785$	26.0130	−	6.97016i	0.928443	−	0.248776i
$786$	−41.4007	−	46.9622i	−1.47671	−	1.67509i
$787$	22.1010	−	5.92193i	0.787814	−	0.211094i	0.157587	−	0.987505i	$-0.449629\pi$
$787$	22.1010	−	5.92193i	0.787814	−	0.211094i	0.630227	+	0.776411i	$0.282962\pi$
$788$	−6.09524	−	1.63322i	−0.217134	−	0.0581809i
$789$	4.32663	−	6.51174i	0.154032	−	0.231824i
$790$	−7.04789	+	4.06910i	−0.250753	+	0.144772i
$791$	1.73777	+	6.48543i	0.0617879	+	0.230596i
$792$	1.52455	−	12.0631i	0.0541726	−	0.428645i
$793$	10.3653	+	44.8125i	0.368083	+	1.59134i
$794$	41.4524	+	23.9326i	1.47109	+	0.849335i
$795$	−30.5252	+	6.15415i	−1.08262	+	0.218265i
$796$	7.03293			0.249275
$797$	−24.9011	+	43.1299i	−0.882041	+	1.52774i	−0.0329726	+	0.999456i	$0.510497\pi$
$797$	−24.9011	+	43.1299i	−0.882041	+	1.52774i	−0.849068	+	0.528283i	$0.822836\pi$
$798$	0.501436	−	0.442053i	0.0177506	−	0.0156485i
$799$	42.2289	−	42.2289i	1.49395	−	1.49395i
$800$	3.88146	+	1.04004i	0.137230	+	0.0367708i
$801$	28.8095	+	11.7586i	1.01793	+	0.415471i
$802$	21.3121	+	36.9137i	0.752558	+	1.30347i
$803$	−12.2197	−	21.1651i	−0.431222	−	0.746899i
$804$	−8.39681	+	7.40240i	−0.296133	+	0.261063i
$805$	18.9736	−	10.9544i	0.668733	−	0.386093i
$806$	−42.1408	−	12.8647i	−1.48435	−	0.453140i
$807$	4.35897	−	6.56042i	0.153443	−	0.230938i
$808$	−6.41662	−	1.71933i	−0.225736	−	0.0604858i
$809$	32.8923	+	18.9904i	1.15643	+	0.667667i	0.950447	−	0.310888i	$-0.100626\pi$
$809$	32.8923	+	18.9904i	1.15643	+	0.667667i	0.205986	+	0.978555i	$0.433960\pi$
$810$	−6.77209	+	26.3644i	−0.237947	+	0.926350i
$811$	−20.4953	+	20.4953i	−0.719687	+	0.719687i	−0.968541	−	0.248854i	$-0.919946\pi$
$811$	−20.4953	+	20.4953i	−0.719687	+	0.719687i	0.248854	+	0.968541i	$0.419946\pi$
$812$	−2.96398	−	2.96398i	−0.104015	−	0.104015i
$813$	−13.7840	+	12.1516i	−0.483425	+	0.426175i
$814$	−2.77775	+	10.3667i	−0.0973602	+	0.363353i
$815$	−13.2953	−	7.67604i	−0.465714	−	0.268880i
$816$	−2.85717	+	45.3950i	−0.100021	+	1.58914i
$817$	0.0663612	−	0.247663i	0.00232168	−	0.00866464i
$818$	−49.1571			−1.71874
$819$	−7.39988	−	19.4591i	−0.258573	−	0.679955i
$820$	−0.299878			−0.0104722
$821$	4.29990	−	16.0475i	0.150068	−	0.560060i	−0.849410	−	0.527734i	$-0.823042\pi$
$821$	4.29990	−	16.0475i	0.150068	−	0.560060i	0.999477	−	0.0323261i	$-0.0102915\pi$
$822$	−32.6489	−	21.6931i	−1.13876	−	0.756632i
$823$	−31.3003	−	18.0713i	−1.09106	−	0.629924i	−0.157202	−	0.987566i	$-0.550247\pi$
$823$	−31.3003	−	18.0713i	−1.09106	−	0.629924i	−0.933859	+	0.357642i	$0.883581\pi$
$824$	−1.70757	+	6.37273i	−0.0594860	+	0.222005i
$825$	3.92301	+	1.32035i	0.136582	+	0.0459687i
$826$	−17.1393	−	17.1393i	−0.596351	−	0.596351i
$827$	−31.5567	+	31.5567i	−1.09733	+	1.09733i	−0.102612	+	0.994721i	$0.532720\pi$
$827$	−31.5567	+	31.5567i	−1.09733	+	1.09733i	−0.994721	+	0.102612i	$0.967280\pi$
$828$	−8.72480	+	3.66704i	−0.303208	+	0.127439i
$829$	11.7204	+	6.76676i	0.407065	+	0.235019i	0.689528	−	0.724259i	$-0.257818\pi$
$829$	11.7204	+	6.76676i	0.407065	+	0.235019i	−0.282463	+	0.959278i	$0.591151\pi$
$830$	0.929441	+	0.249043i	0.0322614	+	0.00864440i
$831$	23.5663	+	47.4771i	0.817507	+	1.64696i
$832$	17.3025	−	4.00214i	0.599857	−	0.138749i
$833$	15.6914	−	9.05942i	0.543674	−	0.313890i
$834$	50.5667	+	17.0190i	1.75098	+	0.589321i
$835$	−7.35483	−	12.7389i	−0.254524	−	0.440849i
$836$	−0.0575646	−	0.0997048i	−0.00199091	−	0.00344836i
$837$	−17.3871	+	35.9598i	−0.600985	+	1.24295i
$838$	23.2815	+	6.23825i	0.804245	+	0.215497i
$839$	−1.21528	+	1.21528i	−0.0419563	+	0.0419563i	−0.727774	−	0.685817i	$-0.759445\pi$
$839$	−1.21528	+	1.21528i	−0.0419563	+	0.0419563i	0.685817	+	0.727774i	$0.259445\pi$
$840$	−2.93463	−	14.5561i	−0.101254	−	0.502232i
$841$	−5.96921	+	10.3390i	−0.205835	+	0.356516i
$842$	53.2907			1.83652
$843$	−9.57097	−	10.8567i	−0.329642	−	0.373924i
$844$	−11.4718	−	6.62326i	−0.394876	−	0.227982i
$845$	−4.73926	−	24.2742i	−0.163035	−	0.835058i
$846$	31.3236	−	41.2630i	1.07693	−	1.41865i
$847$	3.98675	+	14.8788i	0.136986	+	0.511240i
$848$	−39.0900	+	22.5686i	−1.34236	+	0.775010i
$849$	−7.54596	−	15.2022i	−0.258977	−	0.521739i
$850$	−11.6546	−	3.12283i	−0.399749	−	0.107112i
$851$	−22.5385	+	6.03918i	−0.772611	+	0.207020i
$852$	−1.31019	+	3.89281i	−0.0448863	+	0.133366i
$853$	6.80323	−	1.82292i	0.232938	−	0.0624156i	−0.140462	−	0.990086i	$-0.544859\pi$
$853$	6.80323	−	1.82292i	0.232938	−	0.0624156i	0.373400	+	0.927671i	$0.378192\pi$
$854$	33.8033	−	19.5163i	1.15672	−	0.667835i
$855$	−0.278945	−	0.663680i	−0.00953973	−	0.0226974i
$856$	−5.75664	+	1.54249i	−0.196758	+	0.0527211i
$857$	−13.5626	+	23.4910i	−0.463288	+	0.802439i	−0.999122	−	0.0418844i	$-0.986664\pi$
$857$	−13.5626	+	23.4910i	−0.463288	+	0.802439i	0.535834	+	0.844323i	$0.319997\pi$
$858$	−16.9545	+	2.81356i	−0.578818	+	0.0960534i
$859$	−8.05079	−	13.9444i	−0.274689	−	0.475776i	0.695367	−	0.718654i	$-0.255242\pi$
$859$	−8.05079	−	13.9444i	−0.274689	−	0.475776i	−0.970057	+	0.242879i	$0.921908\pi$
$860$	1.44183	+	1.44183i	0.0491658	+	0.0491658i
$861$	−0.443097	−	0.892671i	−0.0151007	−	0.0304221i
$862$			14.4845i			0.493344i
$863$	12.1282	+	12.1282i	0.412850	+	0.412850i	0.882730	−	0.469880i	$-0.155703\pi$
$863$	12.1282	+	12.1282i	0.412850	+	0.412850i	−0.469880	+	0.882730i	$0.655703\pi$
$864$	1.10659	+	15.0847i	0.0376469	+	0.513190i
$865$	0.522085	−	1.94845i	0.0177514	−	0.0662492i
$866$	−1.16875	−	4.36182i	−0.0397156	−	0.148221i
$867$	1.43907	−	22.8640i	0.0488733	−	0.776502i
$868$			7.80073i			0.264774i
$869$	−3.29376	+	3.29376i	−0.111733	+	0.111733i
$870$	−19.3818	+	9.62058i	−0.657104	+	0.326168i
$871$	−37.4888	−	23.4040i	−1.27026	−	0.793016i
$872$			25.6174i			0.867514i
$873$	−1.61767	−	11.8138i	−0.0547499	−	0.399836i
$874$	0.599885	−	1.03903i	0.0202914	−	0.0351457i
$875$	23.3635			0.789830
$876$	8.52584	+	9.67117i	0.288061	+	0.326758i
$877$	8.46869	+	31.6056i	0.285967	+	1.06725i	0.948129	+	0.317884i	$0.102972\pi$
$877$	8.46869	+	31.6056i	0.285967	+	1.06725i	−0.662162	+	0.749361i	$0.730361\pi$
$878$	−6.26732	−	23.3900i	−0.211512	−	0.789373i
$879$	−18.1232	−	20.5578i	−0.611280	−	0.693397i
$880$	−15.7313			−0.530301
$881$	23.5247	−	40.7460i	0.792567	−	1.37277i	−0.131805	−	0.991276i	$-0.542077\pi$
$881$	23.5247	−	40.7460i	0.792567	−	1.37277i	0.924372	−	0.381491i	$-0.124589\pi$
$882$	12.4197	−	9.63269i	0.418193	−	0.324349i
$883$		−	55.7691i		−	1.87678i	−0.345580	−	0.938389i	$-0.612318\pi$
$883$		−	55.7691i		−	1.87678i	0.345580	−	0.938389i	$-0.387682\pi$
$884$	10.1829	−	2.35534i	0.342487	−	0.0792186i
$885$	−23.3821	+	11.6062i	−0.785981	+	0.390139i
$886$	−16.4713	+	16.4713i	−0.553364	+	0.553364i
$887$			28.5905i			0.959975i	0.877275	+	0.479988i	$0.159359\pi$
$887$			28.5905i			0.959975i	−0.877275	+	0.479988i	$0.840641\pi$
$888$	−0.993408	+	15.7833i	−0.0333366	+	0.529654i
$889$	8.11297	+	30.2780i	0.272100	+	1.01549i
$890$	8.11931	−	30.3017i	0.272160	−	1.01571i
$891$	0.161562	+	15.5793i	0.00541255	+	0.521925i
$892$	2.79374	+	2.79374i	0.0935413	+	0.0935413i
$893$			1.37014i			0.0458501i
$894$	−1.66545	−	3.35523i	−0.0557008	−	0.112216i
$895$	4.73138	+	4.73138i	0.158153	+	0.158153i
$896$	−13.1379	−	22.7555i	−0.438906	−	0.760207i
$897$	−23.7281	−	28.8643i	−0.792259	−	0.963750i
$898$	14.6182	−	25.3195i	0.487817	−	0.844924i
$899$	−30.6697	+	8.21791i	−1.02289	+	0.274083i
$900$	−2.16638	−	0.273790i	−0.0722127	−	0.00912633i
$901$	44.9935	−	25.9770i	1.49895	−	0.865421i
$902$	−0.794684	+	0.212935i	−0.0264601	+	0.00708996i
$903$	−2.16157	+	6.42242i	−0.0719324	+	0.213725i
$904$	7.88919	−	2.11390i	0.262391	−	0.0703074i
$905$	−20.4472	−	5.47881i	−0.679687	−	0.182122i
$906$	3.31756	+	6.68361i	0.110219	+	0.222048i
$907$	22.6535	−	13.0790i	0.752198	−	0.434282i	−0.0742897	−	0.997237i	$-0.523669\pi$
$907$	22.6535	−	13.0790i	0.752198	−	0.434282i	0.826487	+	0.562955i	$0.190336\pi$
$908$	1.01949	+	3.80481i	0.0338331	+	0.126267i
$909$	8.44484	+	1.06727i	0.280098	+	0.0353991i
$910$	−18.5276	+	9.86113i	−0.614184	+	0.326893i
$911$	43.7522	+	25.2604i	1.44958	+	0.836913i	0.998456	−	0.0555505i	$-0.0176914\pi$
$911$	43.7522	+	25.2604i	1.44958	+	0.836913i	0.451120	+	0.892463i	$0.351025\pi$
$912$	−0.690084	−	0.782787i	−0.0228510	−	0.0259207i
$913$	0.550752			0.0182272
$914$	−15.9619	+	27.6469i	−0.527974	+	0.914478i
$915$	−8.30785	−	41.2078i	−0.274649	−	1.36229i
$916$	−10.1377	+	10.1377i	−0.334958	+	0.334958i
$917$	−42.2698	−	11.3262i	−1.39587	−	0.374023i
$918$	−3.32267	−	45.2935i	−0.109664	−	1.49491i
$919$	−4.94240	−	8.56050i	−0.163035	−	0.282385i	0.772921	−	0.634503i	$-0.218795\pi$
$919$	−4.94240	−	8.56050i	−0.163035	−	0.282385i	−0.935956	+	0.352118i	$0.885462\pi$
$920$	−13.3255	−	23.0804i	−0.439329	−	0.760940i
$921$	−10.2983	−	3.46605i	−0.339341	−	0.114210i
$922$	34.1440	−	19.7131i	1.12447	−	0.649215i
$923$	−16.2068	−	0.559244i	−0.533452	−	0.0184077i
$924$	1.35285	+	2.72547i	0.0445055	+	0.0896615i
$925$	−5.20022	−	1.39339i	−0.170982	−	0.0458145i
$926$	35.0295	+	20.2243i	1.15114	+	0.664611i
$927$	1.05997	−	8.38707i	0.0348139	−	0.275468i
$928$	−8.50185	+	8.50185i	−0.279087	+	0.279087i
$929$	17.4638	+	17.4638i	0.572970	+	0.572970i	0.932957	−	0.359987i	$-0.117219\pi$
$929$	17.4638	+	17.4638i	0.572970	+	0.572970i	−0.359987	+	0.932957i	$0.617219\pi$
$930$	38.1649	+	12.8450i	1.25148	+	0.421204i
$931$	−0.107589	+	0.401528i	−0.00352609	+	0.0131595i
$932$	−3.64026	−	2.10170i	−0.119241	−	0.0688436i
$933$	13.6020	+	9.03763i	0.445309	+	0.295879i
$934$	2.58615	−	9.65165i	0.0846215	−	0.315812i
$935$	18.1071			0.592164
$936$	−23.6709	+	9.00157i	−0.773709	+	0.294225i
$937$	−37.6354			−1.22950			−0.614748	−	0.788723i	$-0.710742\pi$
$937$	−37.6354			−1.22950			−0.614748	+	0.788723i	$0.710742\pi$
$938$	−9.70680	+	36.2263i	−0.316938	+	1.18283i
$939$	1.82784	−	29.0409i	0.0596493	−	0.947713i
$940$	−9.43640	−	5.44811i	−0.307782	−	0.177698i
$941$	−12.9529	+	48.3409i	−0.422253	+	1.57587i	0.347597	+	0.937644i	$0.386998\pi$
$941$	−12.9529	+	48.3409i	−0.422253	+	1.57587i	−0.769850	+	0.638225i	$0.779669\pi$
$942$	−29.2376	+	25.7751i	−0.952613	+	0.839798i
$943$	−1.26480	−	1.26480i	−0.0411874	−	0.0411874i
$944$	−26.7559	+	26.7559i	−0.870831	+	0.870831i
$945$	6.25590	+	17.9689i	0.203504	+	0.584529i
$946$	4.84467	+	2.79707i	0.157514	+	0.0909406i
$947$	−50.7805	−	13.6066i	−1.65014	−	0.442155i	−0.690490	−	0.723342i	$-0.742605\pi$
$947$	−50.7805	−	13.6066i	−1.65014	−	0.442155i	−0.959653	+	0.281187i	$0.909272\pi$
$948$	1.35991	−	2.04672i	0.0441678	−	0.0664743i
$949$	−26.9560	+	43.1783i	−0.875028	+	1.40163i
$950$	0.239731	−	0.138409i	0.00777791	−	0.00449058i
$951$	1.98115	−	1.74653i	0.0642433	−	0.0566351i
$952$	12.3873	+	21.4554i	0.401474	+	0.695373i
$953$	−23.1563	−	40.1079i	−0.750107	−	1.29922i	−0.947770	−	0.318953i	$-0.896669\pi$
$953$	−23.1563	−	40.1079i	−0.750107	−	1.29922i	0.197663	−	0.980270i	$-0.436665\pi$
$954$	35.6123	−	27.6208i	1.15299	−	0.894257i
$955$	−41.5571	−	11.1352i	−1.34476	−	0.360326i
$956$	−7.81470	+	7.81470i	−0.252745	+	0.252745i
$957$	−9.29038	+	8.19015i	−0.300315	+	0.264750i
$958$	15.7673	−	27.3098i	0.509419	−	0.882340i
$959$	−27.3996			−0.884780
$960$	−15.9107	+	3.20774i	−0.513516	+	0.103529i
$961$	24.3263	+	14.0448i	0.784720	+	0.453058i
$962$	21.7783	−	5.03740i	0.702160	−	0.162412i
$963$	7.03997	−	2.95891i	0.226860	−	0.0953494i
$964$	−1.34897	−	5.03441i	−0.0434473	−	0.162147i
$965$	12.7006	−	7.33267i	0.408845	−	0.236047i
$966$	−17.5481	+	26.4105i	−0.564600	+	0.849745i
$967$	7.57761	+	2.03041i	0.243679	+	0.0652937i	0.378592	−	0.925564i	$-0.376409\pi$
$967$	7.57761	+	2.03041i	0.243679	+	0.0652937i	−0.134912	+	0.990858i	$0.543075\pi$
$968$	18.0992	−	4.84968i	0.581731	−	0.155874i
$969$	0.794302	+	0.901006i	0.0255167	+	0.0289445i
$970$	−11.6117	+	3.11134i	−0.372828	+	0.0998990i
$971$	5.84118	−	3.37241i	0.187452	−	0.108226i	−0.403337	−	0.915052i	$-0.632150\pi$
$971$	5.84118	−	3.37241i	0.187452	−	0.108226i	0.590789	+	0.806826i	$0.298816\pi$
$972$	−1.70782	−	8.03972i	−0.0547785	−	0.257874i
$973$	36.0233	−	9.65241i	1.15485	−	0.309442i
$974$	−2.50315	+	4.33559i	−0.0802061	+	0.138921i
$975$	−1.41136	−	8.50484i	−0.0451996	−	0.272373i
$976$	−30.4668	−	52.7700i	−0.975217	−	1.68913i
$977$	15.2342	+	15.2342i	0.487387	+	0.487387i	0.907481	−	0.420094i	$-0.138003\pi$
$977$	15.2342	+	15.2342i	0.487387	+	0.487387i	−0.420094	+	0.907481i	$0.638003\pi$
$978$	22.1753	+	1.39572i	0.709087	+	0.0446301i
$979$		−	17.9556i		−	0.573865i
$980$	−2.33758	−	2.33758i	−0.0746713	−	0.0746713i
$981$	−4.45320	−	32.5215i	−0.142180	−	1.03833i
$982$	2.78574	−	10.3965i	0.0888965	−	0.331766i
$983$	−0.410820	−	1.53320i	−0.0131031	−	0.0489015i	0.959065	−	0.283187i	$-0.0913917\pi$
$983$	−0.410820	−	1.53320i	−0.0131031	−	0.0489015i	−0.972168	+	0.234285i	$0.924725\pi$
$984$	−1.08589	+	0.539005i	−0.0346168	+	0.0171828i
$985$			22.7694i			0.725492i
$986$	25.5279	−	25.5279i	0.812972	−	0.812972i
$987$	2.27467	−	36.1402i	0.0724036	−	1.15035i
$988$	−0.126985	+	0.203405i	−0.00403993	+	0.00647118i
$989$			12.1624i			0.386741i
$990$	15.5620	−	2.13092i	0.494592	−	0.0677250i
$991$	16.2299	−	28.1110i	0.515560	−	0.892976i	−0.484277	−	0.874915i	$-0.660917\pi$
$991$	16.2299	−	28.1110i	0.515560	−	0.892976i	0.999837	−	0.0180614i	$-0.00574943\pi$
$992$	22.3756			0.710426
$993$	4.61774	−	13.7202i	0.146540	−	0.435397i
$994$	3.56174	+	13.2926i	0.112972	+	0.421616i
$995$	−6.56804	−	24.5123i	−0.208221	−	0.777091i
$996$	−0.284812	+	0.0574207i	−0.00902463	+	0.00181944i
$997$	2.75343			0.0872019			0.0436009	−	0.999049i	$-0.486117\pi$
$997$	2.75343			0.0872019			0.0436009	+	0.999049i	$0.486117\pi$
$998$	−8.59154	+	14.8810i	−0.271960	+	0.471049i
$999$	−1.48256	−	20.2098i	−0.0469061	−	0.639409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.bc.a.110.4	yes	48
3.2	odd	2		351.2.bf.a.305.9		48
9.4	even	3		351.2.ba.a.71.4		48
9.5	odd	6		117.2.x.a.32.9	yes	48
13.11	odd	12		117.2.x.a.11.9	✓	48
39.11	even	12		351.2.ba.a.89.4		48
117.50	even	12	inner	117.2.bc.a.50.4	yes	48
117.76	odd	12		351.2.bf.a.206.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.9	✓	48	13.11	odd	12
117.2.x.a.32.9	yes	48	9.5	odd	6
117.2.bc.a.50.4	yes	48	117.50	even	12	inner
117.2.bc.a.110.4	yes	48	1.1	even	1	trivial
351.2.ba.a.71.4		48	9.4	even	3
351.2.ba.a.89.4		48	39.11	even	12
351.2.bf.a.206.9		48	117.76	odd	12
351.2.bf.a.305.9		48	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.411454 + 1.53557i) q^{2} +(-1.55144 + 0.770091i) q^{3} +(-0.456617 - 0.263628i) q^{4} +(-0.492404 + 1.83768i) q^{5} +(-0.544181 - 2.69919i) q^{6} +(-1.36095 - 1.36095i) q^{7} +(-1.65553 + 1.65553i) q^{8} +(1.81392 - 2.38950i) q^{9} +O(q^{10})\)	\(q+(-0.411454 + 1.53557i) q^{2} +(-1.55144 + 0.770091i) q^{3} +(-0.456617 - 0.263628i) q^{4} +(-0.492404 + 1.83768i) q^{5} +(-0.544181 - 2.69919i) q^{6} +(-1.36095 - 1.36095i) q^{7} +(-1.65553 + 1.65553i) q^{8} +(1.81392 - 2.38950i) q^{9} +(-2.61927 - 1.51224i) q^{10} +(-1.67214 - 0.448047i) q^{11} +(0.911431 + 0.0573657i) q^{12} +(0.812525 + 3.51281i) q^{13} +(2.64980 - 1.52986i) q^{14} +(-0.651244 - 3.23023i) q^{15} +(-2.38826 - 4.13658i) q^{16} +(2.74894 + 4.76130i) q^{17} +(2.92289 + 3.76856i) q^{18} +(-0.121837 - 0.0326462i) q^{19} +(0.709302 - 0.709302i) q^{20} +(3.15949 + 1.06338i) q^{21} +(1.37601 - 2.38332i) q^{22} +5.98324 q^{23} +(1.29354 - 3.84336i) q^{24} +(1.19554 + 0.690245i) q^{25} +(-5.72846 - 0.197671i) q^{26} +(-0.974052 + 5.10404i) q^{27} +(0.262649 + 0.980220i) q^{28} +(-3.57718 + 2.06528i) q^{29} +(5.22819 + 0.329064i) q^{30} +(7.42505 + 1.98954i) q^{31} +(2.81166 - 0.753382i) q^{32} +(2.93925 - 0.592579i) q^{33} +(-8.44235 + 2.26212i) q^{34} +(3.17113 - 1.83085i) q^{35} +(-1.45820 + 0.612885i) q^{36} +(-3.76694 + 1.00935i) q^{37} +(0.100261 - 0.173657i) q^{38} +(-3.96576 - 4.82418i) q^{39} +(-2.22714 - 3.85751i) q^{40} +(-0.211390 - 0.211390i) q^{41} +(-2.93287 + 4.41408i) q^{42} +2.03274i q^{43} +(0.645408 + 0.645408i) q^{44} +(3.49794 + 4.50999i) q^{45} +(-2.46183 + 9.18767i) q^{46} +(-2.81142 - 10.4924i) q^{47} +(6.89078 + 4.57847i) q^{48} -3.29561i q^{49} +(-1.55182 + 1.55182i) q^{50} +(-7.93144 - 5.26993i) q^{51} +(0.555061 - 1.81821i) q^{52} -9.44984i q^{53} +(-7.43681 - 3.59580i) q^{54} +(1.64673 - 2.85222i) q^{55} +4.50620 q^{56} +(0.214164 - 0.0431773i) q^{57} +(-1.69954 - 6.34276i) q^{58} +(-2.05031 - 7.65187i) q^{59} +(-0.554211 + 1.64667i) q^{60} +12.7569 q^{61} +(-6.11013 + 10.5830i) q^{62} +(-5.72066 + 0.783335i) q^{63} -4.92556i q^{64} +(-6.85549 - 0.236561i) q^{65} +(-0.299422 + 4.75723i) q^{66} +(-8.66726 + 8.66726i) q^{67} -2.89879i q^{68} +(-9.28263 + 4.60764i) q^{69} +(1.50662 + 5.62279i) q^{70} +(-1.16407 + 4.34437i) q^{71} +(0.952886 + 6.95888i) q^{72} +(9.98266 + 9.98266i) q^{73} -6.19968i q^{74} +(-2.38636 - 0.150198i) q^{75} +(0.0470265 + 0.0470265i) q^{76} +(1.66593 + 2.88547i) q^{77} +(9.03957 - 4.10476i) q^{78} +(1.34539 - 2.33029i) q^{79} +(8.77768 - 2.35197i) q^{80} +(-2.41939 - 8.66871i) q^{81} +(0.411580 - 0.237626i) q^{82} +(-0.307307 + 0.0823426i) q^{83} +(-1.16234 - 1.31849i) q^{84} +(-10.1033 + 2.70717i) q^{85} +(-3.12140 - 0.836377i) q^{86} +(3.95931 - 5.95891i) q^{87} +(3.51003 - 2.02651i) q^{88} +(2.68454 + 10.0188i) q^{89} +(-8.36463 + 3.51566i) q^{90} +(3.67496 - 5.88658i) q^{91} +(-2.73205 - 1.57735i) q^{92} +(-13.0516 + 2.63132i) q^{93} +17.2685 q^{94} +(0.119986 - 0.207822i) q^{95} +(-3.78194 + 3.33406i) q^{96} +(2.81052 - 2.81052i) q^{97} +(5.06062 + 1.35599i) q^{98} +(-4.10373 + 3.18284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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