LMFDB - Embedded newform 117.2.x.a.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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, 1]))

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

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

chi := DirichletCharacter("117.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (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			11.10
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23549 - 1.23549i) q^{2} +(1.69049 + 0.377148i) q^{3} -1.05286i q^{4} +(-1.93883 - 0.519509i) q^{5} +(2.55454 - 1.62262i) q^{6} +(-4.02297 - 1.07795i) q^{7} +(1.17018 + 1.17018i) q^{8} +(2.71552 + 1.27513i) q^{9} +O(q^{10})$	\(q+(1.23549 - 1.23549i) q^{2} +(1.69049 + 0.377148i) q^{3} -1.05286i q^{4} +(-1.93883 - 0.519509i) q^{5} +(2.55454 - 1.62262i) q^{6} +(-4.02297 - 1.07795i) q^{7} +(1.17018 + 1.17018i) q^{8} +(2.71552 + 1.27513i) q^{9} +(-3.03725 + 1.75356i) q^{10} +(1.90315 + 1.90315i) q^{11} +(0.397082 - 1.77984i) q^{12} +(-3.45103 + 1.04423i) q^{13} +(-6.30212 + 3.63853i) q^{14} +(-3.08165 - 1.60945i) q^{15} +4.99721 q^{16} +(2.33837 - 4.05018i) q^{17} +(4.93039 - 1.77958i) q^{18} +(-5.11006 + 1.36924i) q^{19} +(-0.546967 + 2.04131i) q^{20} +(-6.39425 - 3.33952i) q^{21} +4.70262 q^{22} +(1.57986 - 2.73639i) q^{23} +(1.53685 + 2.41952i) q^{24} +(-0.840946 - 0.485520i) q^{25} +(-2.97356 + 5.55383i) q^{26} +(4.10965 + 3.17975i) q^{27} +(-1.13493 + 4.23560i) q^{28} +3.96412i q^{29} +(-5.79579 + 1.81888i) q^{30} +(1.68342 - 6.28262i) q^{31} +(3.83361 - 3.83361i) q^{32} +(2.49948 + 3.93502i) q^{33} +(-2.11492 - 7.89298i) q^{34} +(7.23986 + 4.17993i) q^{35} +(1.34253 - 2.85905i) q^{36} +(5.70017 + 1.52736i) q^{37} +(-4.62174 + 8.00509i) q^{38} +(-6.22776 + 0.463719i) q^{39} +(-1.66087 - 2.87671i) q^{40} +(0.784740 + 2.92869i) q^{41} +(-12.0259 + 3.77407i) q^{42} +(-1.54773 + 0.893580i) q^{43} +(2.00374 - 2.00374i) q^{44} +(-4.60249 - 3.88300i) q^{45} +(-1.42889 - 5.33267i) q^{46} +(-0.921304 + 0.246863i) q^{47} +(8.44773 + 1.88469i) q^{48} +(8.96013 + 5.17313i) q^{49} +(-1.63883 + 0.439123i) q^{50} +(5.48052 - 5.96488i) q^{51} +(1.09943 + 3.63343i) q^{52} -11.3261i q^{53} +(9.00595 - 1.14887i) q^{54} +(-2.70118 - 4.67858i) q^{55} +(-3.44622 - 5.96902i) q^{56} +(-9.15491 + 0.387432i) q^{57} +(4.89762 + 4.89762i) q^{58} +(0.106474 + 0.106474i) q^{59} +(-1.69452 + 3.24453i) q^{60} +(-0.0799975 - 0.138560i) q^{61} +(-5.68225 - 9.84194i) q^{62} +(-9.54992 - 8.05701i) q^{63} +0.521656i q^{64} +(7.23345 - 0.231756i) q^{65} +(7.94974 + 1.77359i) q^{66} +(-6.65084 + 1.78209i) q^{67} +(-4.26426 - 2.46197i) q^{68} +(3.70276 - 4.03001i) q^{69} +(14.1090 - 3.78050i) q^{70} +(1.98176 + 7.39602i) q^{71} +(1.68552 + 4.66980i) q^{72} +(5.30711 - 5.30711i) q^{73} +(8.92951 - 5.15545i) q^{74} +(-1.23850 - 1.13793i) q^{75} +(1.44161 + 5.38015i) q^{76} +(-5.60480 - 9.70780i) q^{77} +(-7.12139 + 8.26723i) q^{78} +(-6.90128 + 11.9534i) q^{79} +(-9.68874 - 2.59609i) q^{80} +(5.74808 + 6.92528i) q^{81} +(4.58789 + 2.64882i) q^{82} +(0.436532 + 1.62916i) q^{83} +(-3.51603 + 6.73221i) q^{84} +(-6.63782 + 6.63782i) q^{85} +(-0.808188 + 3.01620i) q^{86} +(-1.49506 + 6.70131i) q^{87} +4.45407i q^{88} +(3.29592 - 12.3005i) q^{89} +(-10.4837 + 0.888924i) q^{90} +(15.0090 - 0.480881i) q^{91} +(-2.88103 - 1.66336i) q^{92} +(5.21529 - 9.98581i) q^{93} +(-0.833264 + 1.44325i) q^{94} +10.6189 q^{95} +(7.92653 - 5.03485i) q^{96} +(-2.22397 + 8.29997i) q^{97} +(17.4615 - 4.67878i) q^{98} +(2.74127 + 7.59479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.23549	−	1.23549i	0.873621	−	0.873621i	−0.119244	−	0.992865i	$-0.538047\pi$
$2$	1.23549	−	1.23549i	0.873621	−	0.873621i	0.992865	+	0.119244i	$0.0380470\pi$
$3$	1.69049	+	0.377148i	0.976005	+	0.217747i
$3$	1.69049	+	0.377148i	0.976005	+	0.217747i
$4$		−	1.05286i		−	0.526428i
$5$	−1.93883	−	0.519509i	−0.867072	−	0.232331i	−0.202251	−	0.979334i	$-0.564826\pi$
$5$	−1.93883	−	0.519509i	−0.867072	−	0.232331i	−0.664821	+	0.747002i	$0.731492\pi$
$6$	2.55454	−	1.62262i	1.04289	−	0.662431i
$7$	−4.02297	−	1.07795i	−1.52054	−	0.407427i	−0.600620	−	0.799535i	$-0.705080\pi$
$7$	−4.02297	−	1.07795i	−1.52054	−	0.407427i	−0.919919	+	0.392107i	$0.871746\pi$
$8$	1.17018	+	1.17018i	0.413723	+	0.413723i
$9$	2.71552	+	1.27513i	0.905173	+	0.425044i
$10$	−3.03725	+	1.75356i	−0.960462	+	0.554523i
$11$	1.90315	+	1.90315i	0.573820	+	0.573820i	0.933194	−	0.359374i	$-0.117010\pi$
$11$	1.90315	+	1.90315i	0.573820	+	0.573820i	−0.359374	+	0.933194i	$0.617010\pi$
$12$	0.397082	−	1.77984i	0.114628	−	0.513796i
$13$	−3.45103	+	1.04423i	−0.957142	+	0.289618i
$13$	−3.45103	+	1.04423i	−0.957142	+	0.289618i
$14$	−6.30212	+	3.63853i	−1.68431	+	0.972438i
$15$	−3.08165	−	1.60945i	−0.795678	−	0.415559i
$16$	4.99721			1.24930
$17$	2.33837	−	4.05018i	0.567139	−	0.982313i	−0.429708	−	0.902968i	$-0.641384\pi$
$17$	2.33837	−	4.05018i	0.567139	−	0.982313i	0.996847	−	0.0793457i	$-0.0252831\pi$
$18$	4.93039	−	1.77958i	1.16211	−	0.419451i
$19$	−5.11006	+	1.36924i	−1.17233	+	0.314124i	−0.791879	−	0.610678i	$-0.790897\pi$
$19$	−5.11006	+	1.36924i	−1.17233	+	0.314124i	−0.380449	+	0.924802i	$0.624230\pi$
$20$	−0.546967	+	2.04131i	−0.122306	+	0.456451i
$21$	−6.39425	−	3.33952i	−1.39534	−	0.728744i
$22$	4.70262			1.00260
$23$	1.57986	−	2.73639i	0.329423	−	0.570578i	−0.652974	−	0.757380i	$-0.726479\pi$
$23$	1.57986	−	2.73639i	0.329423	−	0.570578i	0.982398	+	0.186802i	$0.0598124\pi$
$24$	1.53685	+	2.41952i	0.313709	+	0.493882i
$25$	−0.840946	−	0.485520i	−0.168189	−	0.0971040i
$26$	−2.97356	+	5.55383i	−0.583163	+	1.08920i
$27$	4.10965	+	3.17975i	0.790902	+	0.611943i
$28$	−1.13493	+	4.23560i	−0.214481	+	0.800454i
$29$			3.96412i			0.736119i	0.929802	+	0.368059i	$0.119978\pi$
$29$			3.96412i			0.736119i	−0.929802	+	0.368059i	$0.880022\pi$
$30$	−5.79579	+	1.81888i	−1.05816	+	0.332080i
$31$	1.68342	−	6.28262i	0.302352	−	1.12839i	−0.632849	−	0.774275i	$-0.718115\pi$
$31$	1.68342	−	6.28262i	0.302352	−	1.12839i	0.935201	−	0.354117i	$-0.115219\pi$
$32$	3.83361	−	3.83361i	0.677693	−	0.677693i
$33$	2.49948	+	3.93502i	0.435104	+	0.684999i
$34$	−2.11492	−	7.89298i	−0.362705	−	1.35363i
$35$	7.23986	+	4.17993i	1.22376	+	0.706538i
$36$	1.34253	−	2.85905i	0.223755	−	0.476508i
$37$	5.70017	+	1.52736i	0.937102	+	0.251096i	0.694880	−	0.719125i	$-0.255457\pi$
$37$	5.70017	+	1.52736i	0.937102	+	0.251096i	0.242221	+	0.970221i	$0.422124\pi$
$38$	−4.62174	+	8.00509i	−0.749745	+	1.29860i
$39$	−6.22776	+	0.463719i	−0.997239	+	0.0742544i
$40$	−1.66087	−	2.87671i	−0.262607	−	0.454848i
$41$	0.784740	+	2.92869i	0.122556	+	0.457384i	0.999741	−	0.0227682i	$-0.00724795\pi$
$41$	0.784740	+	2.92869i	0.122556	+	0.457384i	−0.877185	+	0.480153i	$0.840581\pi$
$42$	−12.0259	+	3.77407i	−1.85564	+	0.582352i
$43$	−1.54773	+	0.893580i	−0.236026	+	0.136270i	−0.613349	−	0.789812i	$-0.710178\pi$
$43$	−1.54773	+	0.893580i	−0.236026	+	0.136270i	0.377323	+	0.926082i	$0.376845\pi$
$44$	2.00374	−	2.00374i	0.302075	−	0.302075i
$45$	−4.60249	−	3.88300i	−0.686099	−	0.578844i
$46$	−1.42889	−	5.33267i	−0.210678	−	0.786260i
$47$	−0.921304	+	0.246863i	−0.134386	+	0.0360086i	−0.325385	−	0.945582i	$-0.605494\pi$
$47$	−0.921304	+	0.246863i	−0.134386	+	0.0360086i	0.190999	+	0.981590i	$0.438827\pi$
$48$	8.44773	+	1.88469i	1.21933	+	0.272031i
$49$	8.96013	+	5.17313i	1.28002	+	0.739019i
$50$	−1.63883	+	0.439123i	−0.231766	+	0.0621014i
$51$	5.48052	−	5.96488i	0.767426	−	0.835251i
$52$	1.09943	+	3.63343i	0.152463	+	0.503866i
$53$		−	11.3261i		−	1.55576i	−0.628410	−	0.777882i	$-0.716294\pi$
$53$		−	11.3261i		−	1.55576i	0.628410	−	0.777882i	$-0.283706\pi$
$54$	9.00595	−	1.14887i	1.22555	−	0.156342i
$55$	−2.70118	−	4.67858i	−0.364227	−	0.630860i
$56$	−3.44622	−	5.96902i	−0.460520	−	0.797644i
$57$	−9.15491	+	0.387432i	−1.21260	+	0.0513166i
$58$	4.89762	+	4.89762i	0.643089	+	0.643089i
$59$	0.106474	+	0.106474i	0.0138618	+	0.0138618i	0.714004	−	0.700142i	$-0.246880\pi$
$59$	0.106474	+	0.106474i	0.0138618	+	0.0138618i	−0.700142	+	0.714004i	$0.746880\pi$
$60$	−1.69452	+	3.24453i	−0.218762	+	0.418867i
$61$	−0.0799975	−	0.138560i	−0.0102426	−	0.0177407i	0.860859	−	0.508844i	$-0.169927\pi$
$61$	−0.0799975	−	0.138560i	−0.0102426	−	0.0177407i	−0.871101	+	0.491103i	$0.836594\pi$
$62$	−5.68225	−	9.84194i	−0.721646	−	1.24993i
$63$	−9.54992	−	8.05701i	−1.20318	−	1.01509i
$64$			0.521656i			0.0652071i
$65$	7.23345	−	0.231756i	0.897199	−	0.0287458i
$66$	7.94974	+	1.77359i	0.978546	+	0.218313i
$67$	−6.65084	+	1.78209i	−0.812530	+	0.217717i	−0.641078	−	0.767476i	$-0.721512\pi$
$67$	−6.65084	+	1.78209i	−0.812530	+	0.217717i	−0.171452	+	0.985193i	$0.554846\pi$
$68$	−4.26426	−	2.46197i	−0.517117	−	0.298558i
$69$	3.70276	−	4.03001i	0.445760	−	0.485156i
$70$	14.1090	−	3.78050i	1.68635	−	0.451856i
$71$	1.98176	+	7.39602i	0.235191	+	0.877746i	0.978063	+	0.208312i	$0.0667968\pi$
$71$	1.98176	+	7.39602i	0.235191	+	0.877746i	−0.742871	+	0.669434i	$0.766537\pi$
$72$	1.68552	+	4.66980i	0.198640	+	0.550341i
$73$	5.30711	−	5.30711i	0.621151	−	0.621151i	−0.324675	−	0.945826i	$-0.605255\pi$
$73$	5.30711	−	5.30711i	0.621151	−	0.621151i	0.945826	+	0.324675i	$0.105255\pi$
$74$	8.92951	−	5.15545i	1.03803	−	0.599309i
$75$	−1.23850	−	1.13793i	−0.143009	−	0.131397i
$76$	1.44161	+	5.38015i	0.165364	+	0.617146i
$77$	−5.60480	−	9.70780i	−0.638726	−	1.10631i
$78$	−7.12139	+	8.26723i	−0.806339	+	0.936080i
$79$	−6.90128	+	11.9534i	−0.776454	+	1.34486i	0.157519	+	0.987516i	$0.449650\pi$
$79$	−6.90128	+	11.9534i	−0.776454	+	1.34486i	−0.933973	+	0.357342i	$0.883683\pi$
$80$	−9.68874	−	2.59609i	−1.08323	−	0.290252i
$81$	5.74808	+	6.92528i	0.638676	+	0.769476i
$82$	4.58789	+	2.64882i	0.506648	+	0.292513i
$83$	0.436532	+	1.62916i	0.0479156	+	0.178823i	0.985736	−	0.168296i	$-0.0538265\pi$
$83$	0.436532	+	1.62916i	0.0479156	+	0.178823i	−0.937821	+	0.347120i	$0.887160\pi$
$84$	−3.51603	+	6.73221i	−0.383631	+	0.734545i
$85$	−6.63782	+	6.63782i	−0.719973	+	0.719973i
$86$	−0.808188	+	3.01620i	−0.0871492	+	0.325245i
$87$	−1.49506	+	6.70131i	−0.160287	+	0.718456i
$88$			4.45407i			0.474805i
$89$	3.29592	−	12.3005i	0.349367	−	1.30386i	−0.538060	−	0.842907i	$-0.680843\pi$
$89$	3.29592	−	12.3005i	0.349367	−	1.30386i	0.887427	−	0.460949i	$-0.152491\pi$
$90$	−10.4837	+	0.888924i	−1.10508	+	0.0937008i
$91$	15.0090	−	0.480881i	1.57337	−	0.0504100i
$92$	−2.88103	−	1.66336i	−0.300368	−	0.173417i
$93$	5.21529	−	9.98581i	0.540801	−	1.03548i
$94$	−0.833264	+	1.44325i	−0.0859446	+	0.148860i
$95$	10.6189			1.08947
$96$	7.92653	−	5.03485i	0.808998	−	0.513867i
$97$	−2.22397	+	8.29997i	−0.225810	+	0.842735i	0.756268	+	0.654262i	$0.227020\pi$
$97$	−2.22397	+	8.29997i	−0.225810	+	0.842735i	−0.982078	+	0.188473i	$0.939646\pi$
$98$	17.4615	−	4.67878i	1.76387	−	0.472628i
$99$	2.74127	+	7.59479i	0.275508	+	0.763305i
$100$	−0.511182	+	0.885394i	−0.0511182	+	0.0885394i
$101$	−1.62520			−0.161713			−0.0808566	−	0.996726i	$-0.525766\pi$
$101$	−1.62520			−0.161713			−0.0808566	+	0.996726i	$0.525766\pi$
$102$	−0.598425	−	14.1406i	−0.0592529	−	1.40013i
$103$	−2.80861	+	1.62155i	−0.276741	+	0.159776i	−0.631947	−	0.775012i	$-0.717744\pi$
$103$	−2.80861	+	1.62155i	−0.276741	+	0.159776i	0.355206	+	0.934788i	$0.384411\pi$
$104$	−5.26028	−	2.81639i	−0.515813	−	0.276170i
$105$	10.6625	+	9.79664i	1.04055	+	0.956054i
$106$	−13.9933	−	13.9933i	−1.35915	−	1.35915i
$107$	−9.61500	+	5.55123i	−0.929518	+	0.536657i	−0.886659	−	0.462424i	$-0.846980\pi$
$107$	−9.61500	+	5.55123i	−0.929518	+	0.536657i	−0.0428586	+	0.999081i	$0.513646\pi$
$108$	3.34782	−	4.32686i	0.322144	−	0.416353i
$109$	1.26435	+	1.26435i	0.121103	+	0.121103i	0.765061	−	0.643958i	$-0.222709\pi$
$109$	1.26435	+	1.26435i	0.121103	+	0.121103i	−0.643958	+	0.765061i	$0.722709\pi$
$110$	−9.11760	−	2.44305i	−0.869329	−	0.232936i
$111$	9.06004	+	4.73179i	0.859941	+	0.449121i
$112$	−20.1036	−	5.38675i	−1.89961	−	0.509000i
$113$			2.48923i			0.234167i	0.993122	+	0.117084i	$0.0373545\pi$
$113$			2.48923i			0.234167i	−0.993122	+	0.117084i	$0.962645\pi$
$114$	−10.8321	+	11.7894i	−1.01452	+	1.10418i
$115$	−4.48466	+	4.48466i	−0.418197	+	0.418197i
$116$	4.17365			0.387513
$117$	−10.7029	−	1.56488i	−0.989480	−	0.144673i
$118$	0.263096			0.0242199
$119$	−13.7731	+	13.7731i	−1.26258	+	1.26258i
$120$	−1.72274	−	5.48945i	−0.157264	−	0.501116i
$121$		−	3.75607i		−	0.341461i
$122$	−0.270024	−	0.0723528i	−0.0244469	−	0.00655052i
$123$	0.222046	+	5.24689i	0.0200212	+	0.473096i
$124$	−6.61469	−	1.77240i	−0.594017	−	0.159166i
$125$	8.47484	+	8.47484i	0.758013	+	0.758013i
$126$	−21.7531	+	1.84447i	−1.93792	+	0.164318i
$127$	−8.29530	+	4.78929i	−0.736089	+	0.424981i	−0.820645	−	0.571438i	$-0.806386\pi$
$127$	−8.29530	+	4.78929i	−0.736089	+	0.424981i	0.0845569	+	0.996419i	$0.473053\pi$
$128$	8.31173	+	8.31173i	0.734660	+	0.734660i
$129$	−2.95343	+	0.926866i	−0.260035	+	0.0816060i
$130$	8.65050	−	9.22316i	0.758699	−	0.808925i
$131$	−13.4536	+	7.76742i	−1.17544	+	0.678643i	−0.954956	−	0.296747i	$-0.904098\pi$
$131$	−13.4536	+	7.76742i	−1.17544	+	0.678643i	−0.220488	+	0.975390i	$0.570765\pi$
$132$	4.14301	−	2.63159i	0.360602	−	0.229051i
$133$	22.0336			1.91055
$134$	−6.01528	+	10.4188i	−0.519641	+	0.900045i
$135$	−6.31601	−	8.30000i	−0.543595	−	0.714350i
$136$	7.47579	−	2.00313i	0.641044	−	0.171767i
$137$	3.83532	−	14.3136i	0.327674	−	1.22289i	−0.583923	−	0.811809i	$-0.698483\pi$
$137$	3.83532	−	14.3136i	0.327674	−	1.22289i	0.911597	−	0.411085i	$-0.134850\pi$
$138$	−0.404310	−	9.55374i	−0.0344171	−	0.813268i
$139$	1.25946			0.106826			0.0534132	−	0.998572i	$-0.482990\pi$
$139$	1.25946			0.106826			0.0534132	+	0.998572i	$0.482990\pi$
$140$	4.40087	−	7.62252i	0.371941	−	0.644221i
$141$	−1.65056	+	0.0698509i	−0.139002	+	0.00588251i
$142$	11.5861	+	6.68925i	0.972285	+	0.561349i
$143$	−8.55514	−	4.58048i	−0.715416	−	0.383039i
$144$	13.5700	+	6.37209i	1.13083	+	0.531008i
$145$	2.05939	−	7.68576i	0.171023	−	0.638268i
$146$		−	13.1137i		−	1.08530i
$147$	13.1960	+	12.1244i	1.08839	+	1.00001i
$148$	1.60808	−	6.00145i	0.132184	−	0.493316i
$149$	7.41653	−	7.41653i	0.607586	−	0.607586i	−0.334729	−	0.942315i	$-0.608645\pi$
$149$	7.41653	−	7.41653i	0.607586	−	0.607586i	0.942315	+	0.334729i	$0.108645\pi$
$150$	−2.93604	+	0.124252i	−0.239727	+	0.0101451i
$151$	4.27675	+	15.9610i	0.348037	+	1.29889i	0.889024	+	0.457861i	$0.151384\pi$
$151$	4.27675	+	15.9610i	0.348037	+	1.29889i	−0.540987	+	0.841031i	$0.681949\pi$
$152$	−7.58197	−	4.37745i	−0.614979	−	0.355058i
$153$	11.5144	−	8.01661i	0.930885	−	0.648105i
$154$	−18.9185	−	5.06920i	−1.52450	−	0.408488i
$155$	−6.52775	+	11.3064i	−0.524322	+	0.908152i
$156$	0.488229	+	6.55693i	0.0390896	+	0.524974i
$157$	−4.04664	−	7.00899i	−0.322957	−	0.559379i	0.658139	−	0.752896i	$-0.271344\pi$
$157$	−4.04664	−	7.00899i	−0.322957	−	0.559379i	−0.981097	+	0.193517i	$0.938010\pi$
$158$	6.24178	+	23.2947i	0.496570	+	1.85322i
$159$	4.27163	−	19.1467i	0.338762	−	1.51843i
$160$	−9.42433	+	5.44114i	−0.745058	+	0.430160i
$161$	−9.30542	+	9.30542i	−0.733370	+	0.733370i
$162$	15.6578	+	1.45442i	1.23019	+	0.114270i
$163$	−2.62126	−	9.78266i	−0.205313	−	0.766237i	−0.989354	−	0.145529i	$-0.953512\pi$
$163$	−2.62126	−	9.78266i	−0.205313	−	0.766237i	0.784041	−	0.620709i	$-0.213155\pi$
$164$	3.08349	−	0.826218i	0.240780	−	0.0645168i
$165$	−2.80180	−	8.92785i	−0.218120	−	0.695032i
$166$	2.55213	+	1.47348i	0.198084	+	0.114364i
$167$	14.3111	−	3.83465i	1.10743	−	0.296734i	0.341641	−	0.939831i	$-0.389017\pi$
$167$	14.3111	−	3.83465i	1.10743	−	0.296734i	0.765785	+	0.643097i	$0.222351\pi$
$168$	−3.57459	−	11.3903i	−0.275786	−	0.878781i
$169$	10.8192	−	7.20735i	0.832243	−	0.554412i
$170$			16.4019i			1.25797i
$171$	−15.6224	−	2.79781i	−1.19468	−	0.213954i
$172$	0.940810	+	1.62953i	0.0717361	+	0.124251i
$173$	9.36737	+	16.2248i	0.712188	+	1.23355i	0.964034	+	0.265778i	$0.0856288\pi$
$173$	9.36737	+	16.2248i	0.712188	+	1.23355i	−0.251847	+	0.967767i	$0.581038\pi$
$174$	6.43225	+	10.1265i	0.487628	+	0.767689i
$175$	2.85973	+	2.85973i	0.216175	+	0.216175i
$176$	9.51041	+	9.51041i	0.716874	+	0.716874i
$177$	0.139837	+	0.220151i	0.0105108	+	0.0165475i
$178$	−11.1251	−	19.2692i	−0.833861	−	1.44429i
$179$	2.11432	+	3.66210i	0.158031	+	0.273718i	0.934159	−	0.356858i	$-0.116152\pi$
$179$	2.11432	+	3.66210i	0.158031	+	0.273718i	−0.776127	+	0.630576i	$0.782819\pi$
$180$	−4.08824	+	4.84576i	−0.304719	+	0.361182i
$181$			13.1355i			0.976354i	0.872745	+	0.488177i	$0.162338\pi$
$181$			13.1355i			0.976354i	−0.872745	+	0.488177i	$0.837662\pi$
$182$	17.9493	−	19.1375i	1.33049	−	1.41857i
$183$	−0.0829774	−	0.264405i	−0.00613387	−	0.0195454i
$184$	5.05081	−	1.35336i	0.372351	−	0.0997711i
$185$	−10.2582	−	5.92257i	−0.754198	−	0.435436i
$186$	−5.89392	−	18.7808i	−0.432163	−	1.37707i
$187$	12.1584	−	3.25782i	0.889107	−	0.238236i
$188$	0.259911	+	0.970000i	0.0189559	+	0.0707445i
$189$	−13.1054	−	17.2220i	−0.953275	−	1.25272i
$190$	13.1195	−	13.1195i	0.951787	−	0.951787i
$191$	3.62575	−	2.09333i	0.262350	−	0.151468i	−0.363056	−	0.931767i	$-0.618267\pi$
$191$	3.62575	−	2.09333i	0.262350	−	0.151468i	0.625406	+	0.780299i	$0.284933\pi$
$192$	−0.196742	+	0.881855i	−0.0141986	+	0.0636424i
$193$	−3.81394	−	14.2338i	−0.274534	−	1.02457i	−0.956153	−	0.292867i	$-0.905391\pi$
$193$	−3.81394	−	14.2338i	−0.274534	−	1.02457i	0.681620	−	0.731707i	$-0.261276\pi$
$194$	7.50682	+	13.0022i	0.538958	+	0.933503i
$195$	12.3155	+	2.33630i	0.881930	+	0.167306i
$196$	5.44656	−	9.43372i	0.389040	−	0.673837i
$197$	25.1379	+	6.73568i	1.79100	+	0.479898i	0.992516	−	0.122116i	$-0.0389679\pi$
$197$	25.1379	+	6.73568i	1.79100	+	0.479898i	0.798486	+	0.602013i	$0.205635\pi$
$198$	12.7701	+	5.99646i	0.907529	+	0.426150i
$199$	−18.0224	−	10.4052i	−1.27758	−	0.737608i	−0.301173	−	0.953569i	$-0.597378\pi$
$199$	−18.0224	−	10.4052i	−1.27758	−	0.737608i	−0.976402	+	0.215961i	$0.930712\pi$
$200$	−0.415913	−	1.55221i	−0.0294095	−	0.109758i
$201$	−11.9153	+	0.504250i	−0.840440	+	0.0355670i
$202$	−2.00791	+	2.00791i	−0.141276	+	0.141276i
$203$	4.27313	−	15.9475i	0.299915	−	1.11930i
$204$	−6.28016	−	5.77019i	−0.439699	−	0.403994i
$205$		−	6.08592i		−	0.425059i
$206$	−1.46660	+	5.47341i	−0.102183	+	0.381350i
$207$	7.77940	−	5.41620i	0.540705	−	0.376452i
$208$	−17.2455	+	5.21825i	−1.19576	+	0.361820i
$209$	−12.3310	−	7.11933i	−0.852957	−	0.492455i
$210$	25.2769	−	1.06971i	1.74427	−	0.0738169i
$211$	0.686227	−	1.18858i	0.0472418	−	0.0818253i	−0.841438	−	0.540354i	$-0.818290\pi$
$211$	0.686227	−	1.18858i	0.0472418	−	0.0818253i	0.888679	+	0.458529i	$0.151624\pi$
$212$	−11.9248			−0.818997
$213$	0.560747	+	13.2503i	0.0384218	+	0.907897i
$214$	−5.02075	+	18.7377i	−0.343211	+	1.28088i
$215$	3.46500	−	0.928445i	0.236311	−	0.0633194i
$216$	1.08815	+	8.52994i	0.0740392	+	0.580389i
$217$	−13.5447	+	23.4601i	−0.919476	+	1.59258i
$218$	3.12419			0.211597
$219$	10.9732	−	6.97006i	0.741500	−	0.470993i
$220$	−4.92587	+	2.84395i	−0.332102	+	0.191739i
$221$	−3.84045	+	16.4191i	−0.258337	+	1.10447i
$222$	17.0396	−	5.34750i	1.14362	−	0.358901i
$223$	−14.4095	−	14.4095i	−0.964930	−	0.964930i	0.0344752	−	0.999406i	$-0.489024\pi$
$223$	−14.4095	−	14.4095i	−0.964930	−	0.964930i	−0.999406	+	0.0344752i	$0.989024\pi$
$224$	−19.5550	+	11.2901i	−1.30657	+	0.754349i
$225$	−1.66450	−	2.39076i	−0.110967	−	0.159384i
$226$	3.07541	+	3.07541i	0.204573	+	0.204573i
$227$	−1.88834	−	0.505980i	−0.125334	−	0.0335831i	0.195607	−	0.980682i	$-0.437332\pi$
$227$	−1.88834	−	0.505980i	−0.125334	−	0.0335831i	−0.320941	+	0.947099i	$0.603999\pi$
$228$	0.407910	+	9.63880i	0.0270145	+	0.638345i
$229$	−12.2602	−	3.28511i	−0.810176	−	0.217086i	−0.170129	−	0.985422i	$-0.554418\pi$
$229$	−12.2602	−	3.28511i	−0.810176	−	0.217086i	−0.640047	+	0.768336i	$0.721085\pi$
$230$			11.0815i			0.730691i
$231$	−5.81358	−	18.5248i	−0.382506	−	1.21884i
$232$	−4.63875	+	4.63875i	−0.304549	+	0.304549i
$233$	−16.9583			−1.11097			−0.555486	−	0.831526i	$-0.687468\pi$
$233$	−16.9583			−1.11097			−0.555486	+	0.831526i	$0.687468\pi$
$234$	−15.1566	+	11.2899i	−0.990819	+	0.738041i
$235$	1.91450			0.124888
$236$	0.112102	−	0.112102i	0.00729723	−	0.00729723i
$237$	−16.1747	+	17.6042i	−1.05066	+	1.14352i
$238$			34.0330i			2.20603i
$239$	−21.9145	−	5.87196i	−1.41753	−	0.379826i	−0.532922	−	0.846164i	$-0.678906\pi$
$239$	−21.9145	−	5.87196i	−1.41753	−	0.379826i	−0.884606	+	0.466339i	$0.845573\pi$
$240$	−15.3996	−	8.04276i	−0.994041	−	0.519158i
$241$	−11.0585	−	2.96311i	−0.712340	−	0.190871i	−0.115589	−	0.993297i	$-0.536875\pi$
$241$	−11.0585	−	2.96311i	−0.712340	−	0.190871i	−0.596751	+	0.802426i	$0.703542\pi$
$242$	−4.64057	−	4.64057i	−0.298307	−	0.298307i
$243$	7.10522	+	13.8750i	0.455800	+	0.890082i
$244$	−0.145883	+	0.0842257i	−0.00933922	+	0.00539200i
$245$	−14.6847	−	14.6847i	−0.938171	−	0.938171i
$246$	6.75679	+	6.20812i	0.430797	+	0.395815i
$247$	16.2051	−	10.0614i	1.03111	−	0.640189i
$248$	9.32175	−	5.38191i	0.591931	−	0.341752i
$249$	0.123519	+	2.91872i	0.00782768	+	0.184966i
$250$	20.9411			1.32443
$251$	3.36922	−	5.83566i	0.212663	−	0.368344i	−0.739884	−	0.672735i	$-0.765120\pi$
$251$	3.36922	−	5.83566i	0.212663	−	0.368344i	0.952547	+	0.304391i	$0.0984529\pi$
$252$	−8.48287	+	10.0547i	−0.534370	+	0.633385i
$253$	8.21446	−	2.20106i	0.516439	−	0.138379i
$254$	−4.33162	+	16.1658i	−0.271790	+	1.01433i
$255$	−13.7246	+	8.71773i	−0.859469	+	0.545925i
$256$	19.4947			1.21842
$257$	−6.34823	+	10.9954i	−0.395991	+	0.685877i	−0.993227	−	0.116188i	$-0.962932\pi$
$257$	−6.34823	+	10.9954i	−0.395991	+	0.685877i	0.597236	+	0.802066i	$0.296266\pi$
$258$	−2.50379	+	4.79405i	−0.155879	+	0.298465i
$259$	−21.2852	−	12.2890i	−1.32260	−	0.763602i
$260$	−0.244006	−	7.61577i	−0.0151326	−	0.472310i
$261$	−5.05477	+	10.7646i	−0.312883	+	0.666315i
$262$	−7.02516	+	26.2183i	−0.434016	+	1.61977i
$263$		−	17.8703i		−	1.10193i	−0.834528	−	0.550966i	$-0.814259\pi$
$263$		−	17.8703i		−	1.10193i	0.834528	−	0.550966i	$-0.185741\pi$
$264$	−1.67984	+	7.52956i	−0.103387	+	0.463412i
$265$	−5.88402	+	21.9595i	−0.361453	+	1.34896i
$266$	27.2222	−	27.2222i	1.66910	−	1.66910i
$267$	10.2109	−	19.5509i	0.624894	−	1.19650i
$268$	1.87628	+	7.00237i	0.114612	+	0.427738i
$269$	−10.3151	−	5.95544i	−0.628924	−	0.363110i	0.151411	−	0.988471i	$-0.451618\pi$
$269$	−10.3151	−	5.95544i	−0.628924	−	0.363110i	−0.780335	+	0.625361i	$0.784952\pi$
$270$	−18.0579	−	2.45120i	−1.09897	−	0.149175i
$271$	23.8167	+	6.38168i	1.44676	+	0.387659i	0.894897	−	0.446273i	$-0.147249\pi$
$271$	23.8167	+	6.38168i	1.44676	+	0.387659i	0.551867	+	0.833932i	$0.313916\pi$
$272$	11.6853	−	20.2396i	0.708528	−	1.22721i
$273$	25.5539	+	4.84769i	1.54660	+	0.293396i
$274$	−12.9458	−	22.4228i	−0.782084	−	1.35461i
$275$	−0.676427	−	2.52446i	−0.0407901	−	0.152231i
$276$	−4.24302	−	3.89847i	−0.255400	−	0.234660i
$277$	12.3305	−	7.11900i	0.740866	−	0.427739i	−0.0815180	−	0.996672i	$-0.525977\pi$
$277$	12.3305	−	7.11900i	0.740866	−	0.427739i	0.822384	+	0.568933i	$0.192643\pi$
$278$	1.55605	−	1.55605i	0.0933257	−	0.0933257i
$279$	12.5825	−	14.9140i	0.753297	−	0.892877i
$280$	3.58068	+	13.3633i	0.213986	+	0.798608i
$281$	−6.54222	+	1.75298i	−0.390276	+	0.104574i	−0.448620	−	0.893722i	$-0.648084\pi$
$281$	−6.54222	+	1.75298i	−0.390276	+	0.104574i	0.0583446	+	0.998297i	$0.481418\pi$
$282$	−1.95295	+	2.12555i	−0.116296	+	0.126574i
$283$	14.1493	+	8.16909i	0.841087	+	0.485602i	0.857634	−	0.514261i	$-0.171934\pi$
$283$	14.1493	+	8.16909i	0.841087	+	0.485602i	−0.0165465	+	0.999863i	$0.505267\pi$
$284$	7.78694	−	2.08650i	0.462070	−	0.123811i
$285$	17.9511	+	4.00489i	1.06333	+	0.237229i
$286$	−16.2289	+	4.91064i	−0.959634	+	0.290372i
$287$		−	12.6279i		−	0.745404i
$288$	15.2986	−	5.52189i	0.901479	−	0.325380i
$289$	−2.43598	−	4.21925i	−0.143293	−	0.248191i
$290$	−6.95131	−	12.0400i	−0.408195	−	0.707014i
$291$	−6.88992	+	13.1923i	−0.403894	+	0.773344i
$292$	−5.58762	−	5.58762i	−0.326991	−	0.326991i
$293$	−4.83972	−	4.83972i	−0.282740	−	0.282740i	0.551461	−	0.834201i	$-0.314071\pi$
$293$	−4.83972	−	4.83972i	−0.282740	−	0.282740i	−0.834201	+	0.551461i	$0.814071\pi$
$294$	31.2830	−	1.32388i	1.82446	−	0.0772104i
$295$	−0.151122	−	0.261750i	−0.00879865	−	0.0152397i
$296$	4.88296	+	8.45754i	0.283816	+	0.491584i
$297$	1.76973	+	13.8728i	0.102690	+	0.804981i
$298$		−	18.3261i		−	1.06160i
$299$	−2.59470	+	11.0931i	−0.150055	+	0.641531i
$300$	−1.19807	+	1.30396i	−0.0691708	+	0.0752841i
$301$	7.18969	−	1.92647i	0.414407	−	0.111040i
$302$	25.0035	+	14.4358i	1.43879	+	0.830687i
$303$	−2.74738	−	0.612940i	−0.157833	−	0.0352125i
$304$	−25.5360	+	6.84236i	−1.46459	+	0.392436i
$305$	0.0831187	+	0.310203i	0.00475936	+	0.0177622i
$306$	4.32148	−	24.1303i	0.247043	−	1.37944i
$307$	−4.90134	+	4.90134i	−0.279734	+	0.279734i	−0.833003	−	0.553269i	$-0.813380\pi$
$307$	−4.90134	+	4.90134i	−0.279734	+	0.279734i	0.553269	+	0.833003i	$0.313380\pi$
$308$	−10.2209	+	5.90104i	−0.582390	+	0.336243i
$309$	−5.35950	+	1.68196i	−0.304891	+	0.0956832i
$310$	5.90395	+	22.0339i	0.335322	+	1.25144i
$311$	7.37487	+	12.7737i	0.418191	+	0.724327i	0.995758	−	0.0920160i	$-0.0293311\pi$
$311$	7.37487	+	12.7737i	0.418191	+	0.724327i	−0.577567	+	0.816343i	$0.695998\pi$
$312$	−7.83026	−	6.74499i	−0.443301	−	0.381860i
$313$	13.7442	−	23.8057i	0.776868	−	1.34558i	−0.156870	−	0.987619i	$-0.550141\pi$
$313$	13.7442	−	23.8057i	0.776868	−	1.34558i	0.933739	−	0.357956i	$-0.116526\pi$
$314$	−13.6591	−	3.65994i	−0.770827	−	0.206543i
$315$	14.3300	+	20.5825i	0.807404	+	1.15969i
$316$	12.5852	+	7.26605i	0.707971	+	0.408747i
$317$	−0.827111	−	3.08682i	−0.0464552	−	0.173373i	0.938801	−	0.344461i	$-0.111938\pi$
$317$	−0.827111	−	3.08682i	−0.0464552	−	0.173373i	−0.985256	+	0.171088i	$0.945272\pi$
$318$	−18.3780	−	28.9331i	−1.03059	−	1.62249i
$319$	−7.54430	+	7.54430i	−0.422400	+	0.422400i
$320$	0.271005	−	1.01140i	0.0151496	−	0.0565392i
$321$	−18.3477	+	5.75801i	−1.02407	+	0.321381i
$322$			22.9935i			1.28137i
$323$	−6.40357	+	23.8985i	−0.356304	+	1.32975i
$324$	7.29132	−	6.05190i	0.405073	−	0.336217i
$325$	3.40912	+	0.797399i	0.189104	+	0.0442317i
$326$	−15.3249	−	8.84782i	−0.848767	−	0.490036i
$327$	1.66053	+	2.61423i	0.0918276	+	0.144567i
$328$	−2.50882	+	4.34540i	−0.138526	+	0.239934i
$329$	3.97248			0.219010
$330$	−14.4918	−	7.56865i	−0.797749	−	0.416640i
$331$	7.16660	−	26.7461i	0.393912	−	1.47010i	−0.429713	−	0.902965i	$-0.641385\pi$
$331$	7.16660	−	26.7461i	0.393912	−	1.47010i	0.823625	−	0.567134i	$-0.191948\pi$
$332$	1.71527	−	0.459605i	0.0941376	−	0.0252241i
$333$	13.5313	+	11.4160i	0.741512	+	0.625594i
$334$	12.9435	−	22.4188i	0.708237	−	1.22670i
$335$	13.8207			0.755104
$336$	−31.9534	−	16.6883i	−1.74320	−	0.910420i
$337$	18.5718	−	10.7224i	1.01167	−	0.584087i	0.0999890	−	0.994989i	$-0.468119\pi$
$337$	18.5718	−	10.7224i	1.01167	−	0.584087i	0.911680	+	0.410901i	$0.134786\pi$
$338$	4.46233	−	22.2715i	0.242719	−	1.21141i
$339$	−0.938809	+	4.20802i	−0.0509891	+	0.228548i
$340$	6.98866	+	6.98866i	0.379013	+	0.379013i
$341$	15.1605	−	8.75295i	0.820990	−	0.473999i
$342$	−22.7579	+	15.8446i	−1.23061	+	0.856780i
$343$	−9.85480	−	9.85480i	−0.532109	−	0.532109i
$344$	−2.85678	−	0.765471i	−0.154027	−	0.0412714i
$345$	−9.27266	+	5.88990i	−0.499223	+	0.317101i
$346$	31.6187	+	8.47221i	1.69983	+	0.455469i
$347$		−	18.3146i		−	0.983177i	−0.870828	−	0.491588i	$-0.836416\pi$
$347$		−	18.3146i		−	0.983177i	0.870828	−	0.491588i	$-0.163584\pi$
$348$	7.05551	+	1.57408i	0.378215	+	0.0843797i
$349$	−16.9418	+	16.9418i	−0.906873	+	0.906873i	−0.996019	−	0.0891454i	$-0.971586\pi$
$349$	−16.9418	+	16.9418i	−0.906873	+	0.906873i	0.0891454	+	0.996019i	$0.471586\pi$
$350$	7.06632			0.377711
$351$	−17.5029	−	6.68197i	−0.934235	−	0.356657i
$352$	14.5919			0.777748
$353$	21.9788	−	21.9788i	1.16981	−	1.16981i	0.187562	−	0.982253i	$-0.439941\pi$
$353$	21.9788	−	21.9788i	1.16981	−	1.16981i	0.982253	−	0.187562i	$-0.0600586\pi$
$354$	0.444761	+	0.0992260i	0.0236388	+	0.00527380i
$355$		−	15.3692i		−	0.815711i
$356$	−12.9507	−	3.47013i	−0.686385	−	0.183916i
$357$	−28.4778	+	18.0888i	−1.50721	+	0.957361i
$358$	7.13669	+	1.91227i	0.377186	+	0.101067i
$359$	8.04945	+	8.04945i	0.424834	+	0.424834i	0.886864	−	0.462030i	$-0.152879\pi$
$359$	8.04945	+	8.04945i	0.424834	+	0.424834i	−0.462030	+	0.886864i	$0.652879\pi$
$360$	−0.841940	−	9.92960i	−0.0443741	−	0.523336i
$361$	7.78342	−	4.49376i	0.409654	−	0.236514i
$362$	16.2287	+	16.2287i	0.852964	+	0.852964i
$363$	1.41659	−	6.34960i	0.0743519	−	0.333268i
$364$	−0.506298	−	15.8023i	−0.0265372	−	0.828266i
$365$	−13.0467	+	7.53251i	−0.682895	+	0.394270i
$366$	−0.429186	−	0.224151i	−0.0224339	−	0.0117166i
$367$	−5.39348			−0.281538			−0.140769	−	0.990042i	$-0.544957\pi$
$367$	−5.39348			−0.281538			−0.140769	+	0.990042i	$0.544957\pi$
$368$	7.89488	−	13.6743i	0.411549	−	0.712824i
$369$	−1.60349	+	8.95356i	−0.0834742	+	0.466104i
$370$	−19.9911	+	5.35661i	−1.03929	+	0.278477i
$371$	−12.2090	+	45.5647i	−0.633861	+	2.36560i
$372$	−10.5136	−	5.49095i	−0.545106	−	0.284692i
$373$	2.93452			0.151944			0.0759719	−	0.997110i	$-0.475794\pi$
$373$	2.93452			0.151944			0.0759719	+	0.997110i	$0.475794\pi$
$374$	10.9965	−	19.0465i	0.568615	−	0.984870i
$375$	11.1304	+	17.5229i	0.574770	+	0.904879i
$376$	−1.36697	−	0.789221i	−0.0704962	−	0.0407010i
$377$	−4.13947	−	13.6803i	−0.213193	−	0.704570i
$378$	−37.4691	−	5.08610i	−1.92720	−	0.261601i
$379$	−0.480953	+	1.79494i	−0.0247049	+	0.0922000i	−0.977178	−	0.212424i	$-0.931864\pi$
$379$	−0.480953	+	1.79494i	−0.0247049	+	0.0922000i	0.952473	+	0.304624i	$0.0985308\pi$
$380$		−	11.1801i		−	0.573529i
$381$	−15.8294	+	4.96770i	−0.810964	+	0.254503i
$382$	1.89329	−	7.06584i	0.0968689	−	0.361520i
$383$	−16.1161	+	16.1161i	−0.823497	+	0.823497i	−0.986608	−	0.163111i	$-0.947847\pi$
$383$	−16.1161	+	16.1161i	−0.823497	+	0.823497i	0.163111	+	0.986608i	$0.447847\pi$
$384$	10.9161	+	17.1856i	0.557062	+	0.877001i
$385$	5.82348	+	21.7335i	0.296792	+	1.10764i
$386$	−22.2978	−	12.8736i	−1.13493	−	0.655250i
$387$	−5.34231	+	0.452979i	−0.271565	+	0.0230262i
$388$	8.73867	+	2.34152i	0.443639	+	0.118873i
$389$	12.1401	−	21.0272i	0.615526	−	1.06612i	−0.374766	−	0.927119i	$-0.622277\pi$
$389$	12.1401	−	21.0272i	0.615526	−	1.06612i	0.990292	−	0.139003i	$-0.0443897\pi$
$390$	18.1021	−	12.3291i	0.916635	−	0.624311i
$391$	−7.38860	−	12.7974i	−0.373657	−	0.647194i
$392$	4.43148	+	16.5385i	0.223824	+	0.835321i
$393$	−25.6726	+	8.05677i	−1.29501	+	0.406410i
$394$	39.3794	−	22.7357i	1.98391	−	1.14541i
$395$	19.5903	−	19.5903i	0.985694	−	0.985694i
$396$	7.99621	−	2.88616i	0.401825	−	0.145035i
$397$	1.40504	+	5.24368i	0.0705170	+	0.263173i	0.992179	−	0.124820i	$-0.0398352\pi$
$397$	1.40504	+	5.24368i	0.0705170	+	0.263173i	−0.921662	+	0.387993i	$0.873169\pi$
$398$	−35.1220	+	9.41091i	−1.76051	+	0.471726i
$399$	37.2476	+	8.30993i	1.86471	+	0.416017i
$400$	−4.20238	−	2.42624i	−0.210119	−	0.121312i
$401$	19.5025	−	5.22567i	0.973907	−	0.260958i	0.263431	−	0.964678i	$-0.415146\pi$
$401$	19.5025	−	5.22567i	0.973907	−	0.260958i	0.710477	+	0.703721i	$0.248479\pi$
$402$	−14.0982	+	15.3442i	−0.703154	+	0.765298i
$403$	0.750986	+	23.4394i	0.0374093	+	1.16760i
$404$			1.71110i			0.0851303i
$405$	−7.54682	−	16.4131i	−0.375005	−	0.815576i
$406$	−14.4236	−	24.9824i	−0.715830	−	1.23985i
$407$	7.94147	+	13.7550i	0.393644	+	0.681812i
$408$	13.3932	−	0.566795i	0.663064	−	0.0280606i
$409$	14.1216	+	14.1216i	0.698269	+	0.698269i	0.964037	−	0.265768i	$-0.0856256\pi$
$409$	14.1216	+	14.1216i	0.698269	+	0.698269i	−0.265768	+	0.964037i	$0.585626\pi$
$410$	−7.51907	−	7.51907i	−0.371340	−	0.371340i
$411$	11.8819	−	22.7505i	0.586092	−	1.12220i
$412$	1.70726	+	2.95706i	0.0841107	+	0.145684i
$413$	−0.313569	−	0.543118i	−0.0154297	−	0.0267251i
$414$	2.91969	−	16.3030i	0.143495	−	0.801248i
$415$		−	3.38545i		−	0.166185i
$416$	−9.22671	+	17.2331i	−0.452377	+	0.844921i
$417$	2.12911	+	0.475005i	0.104263	+	0.0232611i
$418$	−24.0307	+	6.43900i	−1.17538	+	0.314942i
$419$	10.3709	+	5.98766i	0.506653	+	0.292516i	0.731457	−	0.681888i	$-0.238841\pi$
$419$	10.3709	+	5.98766i	0.506653	+	0.292516i	−0.224804	+	0.974404i	$0.572174\pi$
$420$	10.3144	−	11.2260i	0.503293	−	0.547774i
$421$	1.64704	−	0.441323i	0.0802719	−	0.0215088i	−0.218460	−	0.975846i	$-0.570103\pi$
$421$	1.64704	−	0.441323i	0.0802719	−	0.0215088i	0.298731	+	0.954337i	$0.403437\pi$
$422$	−0.620651	−	2.31630i	−0.0302128	−	0.112756i
$423$	−2.81660	−	0.504423i	−0.136948	−	0.0245259i
$424$	13.2537	−	13.2537i	0.643655	−	0.643655i
$425$	−3.93289	+	2.27066i	−0.190773	+	0.110143i
$426$	17.0634	+	15.6778i	0.826724	+	0.759592i
$427$	0.172467	+	0.643655i	0.00834625	+	0.0311486i
$428$	5.84464	+	10.1232i	0.282511	+	0.489324i
$429$	−12.7349	−	10.9698i	−0.614845	−	0.529627i
$430$	3.13388	−	5.42805i	0.151129	−	0.261764i
$431$	16.0139	+	4.29090i	0.771361	+	0.206686i	0.622973	−	0.782244i	$-0.285925\pi$
$431$	16.0139	+	4.29090i	0.771361	+	0.206686i	0.148388	+	0.988929i	$0.452591\pi$
$432$	20.5367	+	15.8899i	0.988075	+	0.764502i
$433$	−26.2463	−	15.1533i	−1.26131	−	0.728220i	−0.287986	−	0.957635i	$-0.592986\pi$
$433$	−26.2463	−	15.1533i	−1.26131	−	0.728220i	−0.973329	+	0.229414i	$0.926319\pi$
$434$	12.2504	+	45.7190i	0.588037	+	2.19458i
$435$	6.38006	−	12.2160i	0.305900	−	0.585713i
$436$	1.33118	−	1.33118i	0.0637521	−	0.0637521i
$437$	−4.32640	+	16.1463i	−0.206960	+	0.772384i
$438$	4.94582	−	22.1686i	0.236320	−	1.05926i
$439$		−	33.5620i		−	1.60183i	−0.598781	−	0.800913i	$-0.704348\pi$
$439$		−	33.5620i		−	1.60183i	0.598781	−	0.800913i	$-0.295652\pi$
$440$	2.31393	−	8.63569i	0.110312	−	0.411690i
$441$	17.7350	+	25.4731i	0.844522	+	1.21300i
$442$	15.5407	+	25.0304i	0.739198	+	1.19057i
$443$	17.3233	+	10.0016i	0.823056	+	0.475192i	0.851469	−	0.524404i	$-0.175712\pi$
$443$	17.3233	+	10.0016i	0.823056	+	0.475192i	−0.0284130	+	0.999596i	$0.509045\pi$
$444$	4.98189	−	9.53891i	0.236430	−	0.452697i
$445$	−12.7805	+	22.1364i	−0.605853	+	1.04937i
$446$	−35.6055			−1.68597
$447$	15.3347	−	9.74045i	0.725307	−	0.460707i
$448$	0.562320	−	2.09861i	0.0265671	−	0.0991499i
$449$	−33.6003	+	9.00319i	−1.58570	+	0.424887i	−0.940684	−	0.339284i	$-0.889815\pi$
$449$	−33.6003	+	9.00319i	−1.58570	+	0.424887i	−0.645014	+	0.764170i	$0.723149\pi$
$450$	−5.01022	−	0.897277i	−0.236184	−	0.0422980i
$451$	−4.08025	+	7.06720i	−0.192131	+	0.332781i
$452$	2.62080			0.123272
$453$	1.21013	+	28.5950i	0.0568567	+	1.34351i
$454$	−2.95816	+	1.70789i	−0.138833	+	0.0801553i
$455$	−29.3498	−	6.86496i	−1.37594	−	0.321834i
$456$	−11.1663	−	10.2596i	−0.522910	−	0.480449i
$457$	4.68069	+	4.68069i	0.218954	+	0.218954i	0.808057	−	0.589104i	$-0.200519\pi$
$457$	4.68069	+	4.68069i	0.218954	+	0.218954i	−0.589104	+	0.808057i	$0.700519\pi$
$458$	−19.2060	+	11.0886i	−0.897437	+	0.518136i
$459$	22.4885	−	9.20937i	1.04967	−	0.429857i
$460$	4.72170	+	4.72170i	0.220150	+	0.220150i
$461$	−2.00506	−	0.537253i	−0.0933848	−	0.0250224i	0.211824	−	0.977308i	$-0.432060\pi$
$461$	−2.00506	−	0.537253i	−0.0933848	−	0.0250224i	−0.305209	+	0.952285i	$0.598726\pi$
$462$	−30.0697	−	15.7045i	−1.39897	−	0.730640i
$463$	−22.5684	−	6.04718i	−1.04884	−	0.281037i	−0.307069	−	0.951687i	$-0.599348\pi$
$463$	−22.5684	−	6.04718i	−1.04884	−	0.281037i	−0.741773	+	0.670651i	$0.766015\pi$
$464$			19.8095i			0.919634i
$465$	−15.2993	+	16.6514i	−0.709488	+	0.772192i
$466$	−20.9517	+	20.9517i	−0.970569	+	0.970569i
$467$	23.3698			1.08143			0.540713	−	0.841207i	$-0.318155\pi$
$467$	23.3698			1.08143			0.540713	+	0.841207i	$0.318155\pi$
$468$	−1.64759	+	11.2686i	−0.0761597	+	0.520889i
$469$	28.6771			1.32419
$470$	2.36534	−	2.36534i	0.109105	−	0.109105i
$471$	−4.19739	−	13.3748i	−0.193405	−	0.616279i
$472$			0.249190i			0.0114699i
$473$	−4.64616	−	1.24493i	−0.213631	−	0.0572422i
$474$	1.76614	+	41.7335i	0.0811216	+	1.91688i
$475$	4.96207	+	1.32958i	0.227676	+	0.0610055i
$476$	14.5011	+	14.5011i	0.664656	+	0.664656i
$477$	14.4423	−	30.7563i	0.661268	−	1.40824i
$478$	−34.3298	+	19.8203i	−1.57021	+	0.906559i
$479$	−6.83639	−	6.83639i	−0.312362	−	0.312362i	0.533462	−	0.845824i	$-0.320891\pi$
$479$	−6.83639	−	6.83639i	−0.312362	−	0.312362i	−0.845824	+	0.533462i	$0.820891\pi$
$480$	−17.9839	+	5.64383i	−0.820847	+	0.257604i
$481$	−21.2663	+	0.681363i	−0.969662	+	0.0310675i
$482$	−17.3235	+	10.0017i	−0.789064	+	0.455566i
$483$	−19.2403	+	12.2212i	−0.875462	+	0.556084i
$484$	−3.95460			−0.179754
$485$	8.62381	−	14.9369i	0.391587	−	0.678249i
$486$	25.9208	+	8.36398i	1.17579	+	0.379398i
$487$	−22.2757	+	5.96876i	−1.00941	+	0.270470i	−0.725383	−	0.688346i	$-0.758337\pi$
$487$	−22.2757	+	5.96876i	−1.00941	+	0.270470i	−0.284027	+	0.958816i	$0.591671\pi$
$488$	0.0685286	−	0.255752i	0.00310214	−	0.0115774i
$489$	−0.741697	−	17.5261i	−0.0335407	−	0.792558i
$490$	−36.2855			−1.63921
$491$	14.9504	−	25.8948i	0.674701	−	1.16862i	−0.301856	−	0.953354i	$-0.597606\pi$
$491$	14.9504	−	25.8948i	0.674701	−	1.16862i	0.976556	−	0.215262i	$-0.0690606\pi$
$492$	5.52421	−	0.233782i	0.249051	−	0.0105397i
$493$	16.0554	+	9.26960i	0.723099	+	0.417482i
$494$	7.59056	−	32.4519i	0.341515	−	1.46008i
$495$	−1.36930	−	16.1491i	−0.0615455	−	0.725850i
$496$	8.41241	−	31.3956i	0.377729	−	1.40970i
$497$		−	31.8902i		−	1.43047i
$498$	3.75864	+	3.45343i	0.168429	+	0.154752i
$499$	−0.725325	+	2.70695i	−0.0324700	+	0.121180i	−0.980259	−	0.197719i	$-0.936646\pi$
$499$	−0.725325	+	2.70695i	−0.0324700	+	0.121180i	0.947789	+	0.318899i	$0.103313\pi$
$500$	8.92278	−	8.92278i	0.399039	−	0.399039i
$501$	25.6390	−	1.08503i	1.14547	−	0.0484756i
$502$	−3.04725	−	11.3725i	−0.136006	−	0.507580i
$503$	−10.5400	−	6.08525i	−0.469954	−	0.271328i	0.246267	−	0.969202i	$-0.420796\pi$
$503$	−10.5400	−	6.08525i	−0.469954	−	0.271328i	−0.716220	+	0.697874i	$0.754129\pi$
$504$	−1.74698	−	20.6034i	−0.0778166	−	0.917747i
$505$	3.15098	+	0.844304i	0.140217	+	0.0375710i
$506$	7.42948	−	12.8682i	0.330281	−	0.572063i
$507$	21.0079	−	8.10354i	0.932994	−	0.359891i
$508$	5.04243	+	8.73375i	0.223722	+	0.387497i
$509$	5.20813	+	19.4370i	0.230847	+	0.861531i	0.979977	+	0.199109i	$0.0638047\pi$
$509$	5.20813	+	19.4370i	0.230847	+	0.861531i	−0.749131	+	0.662422i	$0.769529\pi$
$510$	−6.18594	+	27.7272i	−0.273918	+	1.22778i
$511$	−27.0712	+	15.6295i	−1.19756	+	0.691410i
$512$	7.46204	−	7.46204i	0.329779	−	0.329779i
$513$	−25.3544	−	10.6216i	−1.11942	−	0.468957i
$514$	5.74158	+	21.4279i	0.253250	+	0.945143i
$515$	6.28784	−	1.68482i	0.277075	−	0.0742421i
$516$	0.975856	+	3.10953i	0.0429597	+	0.136889i
$517$	−2.22319	−	1.28356i	−0.0977759	−	0.0564509i
$518$	−41.4805	+	11.1147i	−1.82255	+	0.488350i
$519$	9.71631	+	30.9607i	0.426499	+	1.35902i
$520$	8.73567	+	8.19327i	0.383084	+	0.359299i
$521$			39.5352i			1.73207i	0.499986	+	0.866034i	$0.333339\pi$
$521$			39.5352i			1.73207i	−0.499986	+	0.866034i	$0.666661\pi$
$522$	7.05447	+	19.5447i	0.308766	+	0.855447i
$523$	−6.80411	−	11.7851i	−0.297523	−	0.515325i	0.678046	−	0.735020i	$-0.262827\pi$
$523$	−6.80411	−	11.7851i	−0.297523	−	0.515325i	−0.975569	+	0.219695i	$0.929494\pi$
$524$	8.17797	+	14.1647i	0.357256	+	0.618786i
$525$	3.75581	+	5.91289i	0.163917	+	0.258060i
$526$	−22.0786	−	22.0786i	−0.962671	−	0.962671i
$527$	−21.5093	−	21.5093i	−0.936959	−	0.936959i
$528$	12.4904	+	19.6641i	0.543576	+	0.855770i
$529$	6.50810	+	11.2724i	0.282961	+	0.490102i
$530$	19.8610	+	34.4003i	0.862707	+	1.49425i
$531$	0.153364	+	0.424902i	0.00665545	+	0.0184392i
$532$		−	23.1982i		−	1.00577i
$533$	−5.76639	−	9.28753i	−0.249770	−	0.402288i
$534$	−11.5395	−	36.7703i	−0.499364	−	1.59120i
$535$	21.5258	−	5.76782i	0.930641	−	0.249365i
$536$	−9.86808	−	5.69734i	−0.426236	−	0.246088i
$537$	2.19308	+	6.98816i	0.0946382	+	0.301561i
$538$	−20.1021	+	5.38633i	−0.866662	+	0.232221i
$539$	7.20720	+	26.8977i	0.310436	+	1.15856i
$540$	−8.73870	+	6.64984i	−0.376054	+	0.286164i
$541$	−19.4805	+	19.4805i	−0.837531	+	0.837531i	−0.988533	−	0.151002i	$-0.951750\pi$
$541$	−19.4805	+	19.4805i	−0.837531	+	0.837531i	0.151002	+	0.988533i	$0.451750\pi$
$542$	37.3098	−	21.5408i	1.60259	−	0.925256i
$543$	−4.95403	+	22.2054i	−0.212598	+	0.952927i
$544$	−6.56241	−	24.4913i	−0.281361	−	1.05005i
$545$	−1.79453	−	3.10822i	−0.0768692	−	0.133141i
$546$	37.5608	−	25.5823i	1.60745	−	1.09482i
$547$	2.57937	−	4.46760i	0.110286	−	0.191021i	−0.805600	−	0.592460i	$-0.798157\pi$
$547$	2.57937	−	4.46760i	0.110286	−	0.191021i	0.915885	+	0.401440i	$0.131490\pi$
$548$	−15.0702	−	4.03804i	−0.643765	−	0.172496i
$549$	−0.0405528	−	0.478269i	−0.00173075	−	0.0204120i
$550$	−3.95465	−	2.28322i	−0.168627	−	0.0973568i
$551$	−5.42782	−	20.2569i	−0.231233	−	0.862973i
$552$	9.04877	−	0.382940i	0.385141	−	0.0162990i
$553$	40.6488	−	40.6488i	1.72856	−	1.72856i
$554$	6.43870	−	24.0296i	0.273554	−	1.02092i
$555$	−15.1077	−	13.8809i	−0.641286	−	0.589212i
$556$		−	1.32603i		−	0.0562363i
$557$	−3.94692	+	14.7301i	−0.167236	+	0.624135i	0.830508	+	0.557007i	$0.188050\pi$
$557$	−3.94692	+	14.7301i	−0.167236	+	0.624135i	−0.997744	+	0.0671280i	$0.978616\pi$
$558$	−2.88048	−	33.9716i	−0.121941	−	1.43813i
$559$	4.40813	−	4.69995i	0.186444	−	0.198787i
$560$	36.1791	+	20.8880i	1.52884	+	0.882679i
$561$	21.7823	−	0.921816i	0.919648	−	0.0389191i
$562$	−5.91704	+	10.2486i	−0.249595	+	0.432311i
$563$	10.6746			0.449879			0.224940	−	0.974373i	$-0.427782\pi$
$563$	10.6746			0.449879			0.224940	+	0.974373i	$0.427782\pi$
$564$	0.0735429	+	1.73780i	0.00309672	+	0.0731746i
$565$	1.29318	−	4.82620i	0.0544043	−	0.203040i
$566$	27.5740	−	7.38844i	1.15902	−	0.310559i
$567$	−15.6592	−	34.0564i	−0.657626	−	1.43023i
$568$	−6.33569	+	10.9737i	−0.265839	+	0.460447i
$569$	−30.4337			−1.27585			−0.637923	−	0.770100i	$-0.720206\pi$
$569$	−30.4337			−1.27585			−0.637923	+	0.770100i	$0.720206\pi$
$570$	27.1264	−	17.2304i	1.13620	−	0.721701i
$571$	−38.3594	+	22.1468i	−1.60529	+	0.926815i	−0.614885	+	0.788616i	$0.710798\pi$
$571$	−38.3594	+	22.1468i	−1.60529	+	0.926815i	−0.990405	+	0.138198i	$0.955869\pi$
$572$	−4.82258	+	9.00732i	−0.201642	+	0.376615i
$573$	6.91879	−	2.17130i	0.289036	−	0.0907076i
$574$	−15.6017	−	15.6017i	−0.651200	−	0.651200i
$575$	−2.65715	+	1.53411i	−0.110811	+	0.0639766i
$576$	−0.665180	+	1.41657i	−0.0277158	+	0.0590237i
$577$	−4.82724	−	4.82724i	−0.200961	−	0.200961i	0.599451	−	0.800412i	$-0.295386\pi$
$577$	−4.82724	−	4.82724i	−0.200961	−	0.200961i	−0.800412	+	0.599451i	$0.795386\pi$
$578$	−8.22245	−	2.20320i	−0.342009	−	0.0916410i
$579$	−1.07917	−	25.5006i	−0.0448489	−	1.05977i
$580$	−8.09200	−	2.16824i	−0.336002	−	0.0900314i
$581$		−	7.02462i		−	0.291430i
$582$	7.78646	+	24.8113i	0.322759	+	1.02846i
$583$	21.5553	−	21.5553i	0.892729	−	0.892729i
$584$	12.4206			0.513968
$585$	19.9381	+	8.59426i	0.824338	+	0.355329i
$586$	−11.9588			−0.494014
$587$	−11.6695	+	11.6695i	−0.481653	+	0.481653i	−0.905659	−	0.424006i	$-0.860623\pi$
$587$	−11.6695	+	11.6695i	−0.481653	+	0.481653i	0.424006	+	0.905659i	$0.360623\pi$
$588$	12.7653	−	13.8934i	0.526431	−	0.572956i
$589$			34.4096i			1.41782i
$590$	−0.510098	−	0.136680i	−0.0210004	−	0.00562704i
$591$	39.9551	+	20.8673i	1.64353	+	0.858367i
$592$	28.4849	+	7.63251i	1.17072	+	0.313694i
$593$	−5.63735	−	5.63735i	−0.231498	−	0.231498i	0.581820	−	0.813318i	$-0.302341\pi$
$593$	−5.63735	−	5.63735i	−0.231498	−	0.231498i	−0.813318	+	0.581820i	$0.802341\pi$
$594$	19.3261	+	14.9532i	0.792960	+	0.613536i
$595$	33.8590	−	19.5485i	1.38808	−	0.801410i
$596$	−7.80854	−	7.80854i	−0.319850	−	0.319850i
$597$	−26.5424	−	24.3871i	−1.08631	−	0.998097i
$598$	10.4997	+	16.9111i	0.429364	+	0.691546i
$599$	25.6339	−	14.7997i	1.04737	−	0.604700i	0.125459	−	0.992099i	$-0.459960\pi$
$599$	25.6339	−	14.7997i	1.04737	−	0.604700i	0.921912	+	0.387399i	$0.126626\pi$
$600$	−0.117685	−	2.78086i	−0.00480445	−	0.113528i
$601$	−29.9806			−1.22293			−0.611467	−	0.791270i	$-0.709420\pi$
$601$	−29.9806			−1.22293			−0.611467	+	0.791270i	$0.709420\pi$
$602$	6.50263	−	11.2629i	0.265028	−	0.459041i
$603$	−20.3329	−	3.64140i	−0.828019	−	0.148289i
$604$	16.8047	−	4.50280i	0.683772	−	0.183216i
$605$	−1.95131	+	7.28239i	−0.0793320	+	0.296071i
$606$	−4.15163	+	2.63707i	−0.168648	+	0.107124i
$607$	5.96986			0.242309			0.121155	−	0.992634i	$-0.461340\pi$
$607$	5.96986			0.242309			0.121155	+	0.992634i	$0.461340\pi$
$608$	−14.3409	+	24.8391i	−0.581599	+	1.00736i
$609$	13.2383	−	25.3476i	0.536442	−	1.02713i
$610$	0.485944	+	0.280560i	0.0196753	+	0.0113595i
$611$	2.92166	−	1.81399i	0.118198	−	0.0733860i
$612$	−8.44033	−	12.1230i	−0.341180	−	0.490044i
$613$	3.38242	−	12.6234i	0.136615	−	0.509853i	−0.863371	−	0.504569i	$-0.831651\pi$
$613$	3.38242	−	12.6234i	0.136615	−	0.509853i	0.999986	−	0.00528392i	$-0.00168193\pi$
$614$			12.1111i			0.488763i
$615$	2.29529	−	10.2882i	0.0925551	−	0.414860i
$616$	4.80127	−	17.9186i	0.193449	−	0.721960i
$617$	−7.81306	+	7.81306i	−0.314542	+	0.314542i	−0.846666	−	0.532124i	$-0.821394\pi$
$617$	−7.81306	+	7.81306i	−0.314542	+	0.314542i	0.532124	+	0.846666i	$0.321394\pi$
$618$	−4.54355	+	8.69962i	−0.182768	+	0.349950i
$619$	8.38710	+	31.3011i	0.337106	+	1.25810i	0.901568	+	0.432637i	$0.142417\pi$
$619$	8.38710	+	31.3011i	0.337106	+	1.25810i	−0.564462	+	0.825459i	$0.690916\pi$
$620$	11.9040	+	6.87278i	0.478076	+	0.276017i
$621$	15.1937	−	6.22206i	0.609703	−	0.249683i
$622$	24.8932	+	6.67012i	0.998128	+	0.267448i
$623$	−26.5188	+	45.9319i	−1.06245	+	1.84022i
$624$	−31.1214	+	2.31730i	−1.24585	+	0.0927662i
$625$	−9.60094	−	16.6293i	−0.384038	−	0.665173i
$626$	−12.4308	−	46.3923i	−0.496834	−	1.85421i
$627$	−18.1605	−	16.6858i	−0.725260	−	0.666367i
$628$	−7.37946	+	4.26053i	−0.294472	+	0.170014i
$629$	19.5152	−	19.5152i	0.778122	−	0.778122i
$630$	43.1339	+	7.72482i	1.71850	+	0.307764i
$631$	7.83516	+	29.2412i	0.311913	+	1.16407i	0.926829	+	0.375482i	$0.122523\pi$
$631$	7.83516	+	29.2412i	0.311913	+	1.16407i	−0.614917	+	0.788592i	$0.710810\pi$
$632$	−22.0634	+	5.91187i	−0.877635	+	0.235162i
$633$	1.60833	−	1.75048i	0.0639255	−	0.0695751i
$634$	−4.83561	−	2.79184i	−0.192047	−	0.110878i
$635$	18.5713	−	4.97616i	0.736978	−	0.197473i
$636$	−20.1587	−	4.49741i	−0.799346	−	0.178334i
$637$	−36.3236	−	8.49614i	−1.43919	−	0.336630i
$638$			18.6418i			0.738035i
$639$	−4.04940	+	22.6110i	−0.160192	+	0.894478i
$640$	−11.7970	−	20.4331i	−0.466319	−	0.807687i
$641$	24.0437	+	41.6450i	0.949670	+	1.64488i	0.746119	+	0.665813i	$0.231915\pi$
$641$	24.0437	+	41.6450i	0.949670	+	1.64488i	0.203552	+	0.979064i	$0.434751\pi$
$642$	−15.5544	+	29.7823i	−0.613883	+	1.17541i
$643$	22.9426	+	22.9426i	0.904767	+	0.904767i	0.995844	−	0.0910768i	$-0.0290309\pi$
$643$	22.9426	+	22.9426i	0.904767	+	0.904767i	−0.0910768	+	0.995844i	$0.529031\pi$
$644$	9.79726	+	9.79726i	0.386066	+	0.386066i
$645$	6.20772	−	0.262708i	0.244429	−	0.0103441i
$646$	21.6147	+	37.4378i	0.850419	+	1.47297i
$647$	−8.80655	−	15.2534i	−0.346221	−	0.599673i	0.639354	−	0.768913i	$-0.279202\pi$
$647$	−8.80655	−	15.2534i	−0.346221	−	0.599673i	−0.985575	+	0.169240i	$0.945869\pi$
$648$	−1.37755	+	14.8302i	−0.0541151	+	0.582584i
$649$			0.405273i			0.0159084i
$650$	5.19710	−	3.22675i	0.203847	−	0.126563i
$651$	−31.7452	+	34.5508i	−1.24419	+	1.35415i
$652$	−10.2997	+	2.75980i	−0.403369	+	0.108082i
$653$	33.2721	+	19.2097i	1.30204	+	0.751733i	0.980754	−	0.195250i	$-0.0625517\pi$
$653$	33.2721	+	19.2097i	1.30204	+	0.751733i	0.321286	+	0.946982i	$0.395885\pi$
$654$	5.28141	+	1.17828i	0.206519	+	0.0460745i
$655$	30.1195	−	8.07048i	1.17686	−	0.315340i
$656$	3.92151	+	14.6353i	0.153109	+	0.571411i
$657$	21.1788	−	7.64430i	0.826265	−	0.298232i
$658$	4.90795	−	4.90795i	0.191332	−	0.191332i
$659$	2.95377	−	1.70536i	0.115063	−	0.0664314i	−0.441364	−	0.897328i	$-0.645505\pi$
$659$	2.95377	−	1.70536i	0.115063	−	0.0664314i	0.556427	+	0.830897i	$0.312172\pi$
$660$	−9.39973	+	2.94989i	−0.365884	+	0.114824i
$661$	−2.73775	−	10.2174i	−0.106486	−	0.397411i	0.892023	−	0.451989i	$-0.149285\pi$
$661$	−2.73775	−	10.2174i	−0.106486	−	0.397411i	−0.998510	+	0.0545778i	$0.982619\pi$
$662$	−24.1902	−	41.8987i	−0.940180	−	1.62844i
$663$	−12.6847	+	26.3079i	−0.492632	+	1.02171i
$664$	−1.39559	+	2.41724i	−0.0541596	+	0.0938071i
$665$	−42.7194	−	11.4466i	−1.65659	−	0.443881i
$666$	30.8221	−	2.61344i	1.19433	−	0.101269i
$667$	10.8474	+	6.26275i	0.420013	+	0.242495i
$668$	−4.03733	−	15.0675i	−0.156209	−	0.582979i
$669$	−18.9246	−	29.7936i	−0.731667	−	1.15189i
$670$	17.0753	−	17.0753i	0.659675	−	0.659675i
$671$	0.111452	−	0.415946i	0.00430257	−	0.0160574i
$672$	−37.3155	+	11.7106i	−1.43948	+	0.451747i
$673$		−	25.1066i		−	0.967788i	−0.875127	−	0.483894i	$-0.839222\pi$
$673$		−	25.1066i		−	0.967788i	0.875127	−	0.483894i	$-0.160778\pi$
$674$	9.69777	−	36.1926i	0.373544	−	1.39409i
$675$	−1.91216	−	4.66931i	−0.0735989	−	0.179722i
$676$	−7.58830	−	11.3910i	−0.291858	−	0.438115i
$677$	14.9587	+	8.63644i	0.574911	+	0.331925i	0.759109	−	0.650964i	$-0.225635\pi$
$677$	14.9587	+	8.63644i	0.574911	+	0.331925i	−0.184197	+	0.982889i	$0.558968\pi$
$678$	4.03907	+	6.35884i	0.155119	+	0.244210i
$679$	17.8939	−	30.9932i	0.686706	−	1.18941i
$680$	−15.5349			−0.595738
$681$	−3.00140	−	1.56754i	−0.115014	−	0.0600683i
$682$	7.91651	−	29.5448i	0.303139	−	1.13133i
$683$	−16.4590	+	4.41018i	−0.629787	+	0.168751i	−0.559573	−	0.828781i	$-0.689035\pi$
$683$	−16.4590	+	4.41018i	−0.629787	+	0.168751i	−0.0702141	+	0.997532i	$0.522368\pi$
$684$	−2.94569	+	16.4481i	−0.112631	+	0.628911i
$685$	−14.8721	+	25.7592i	−0.568233	+	0.984209i
$686$	−24.3510			−0.929724
$687$	−19.4868	−	10.1773i	−0.743466	−	0.388290i
$688$	−7.73430	+	4.46540i	−0.294868	+	0.170242i
$689$	11.8271	+	39.0868i	0.450578	+	1.48909i
$690$	−4.17936	+	18.7331i	−0.159105	+	0.713158i
$691$	26.2382	+	26.2382i	0.998149	+	0.998149i	0.999998	−	0.00184907i	$-0.000588576\pi$
$691$	26.2382	+	26.2382i	0.998149	+	0.998149i	−0.00184907	+	0.999998i	$0.500589\pi$
$692$	17.0823	−	9.86248i	0.649372	−	0.374915i
$693$	−2.84122	−	33.5086i	−0.107929	−	1.27288i
$694$	−22.6274	−	22.6274i	−0.858924	−	0.858924i
$695$	−2.44189	−	0.654302i	−0.0926261	−	0.0248191i
$696$	−9.59127	+	6.09227i	−0.363556	+	0.230927i
$697$	13.6967	+	3.67003i	0.518801	+	0.139012i
$698$			41.8627i			1.58453i
$699$	−28.6678	−	6.39578i	−1.08431	−	0.241910i
$700$	3.01088	−	3.01088i	0.113801	−	0.113801i
$701$	−10.1414			−0.383035			−0.191517	−	0.981489i	$-0.561341\pi$
$701$	−10.1414			−0.383035			−0.191517	+	0.981489i	$0.561341\pi$
$702$	−29.8801	+	13.3691i	−1.12775	+	0.504584i
$703$	−31.2195			−1.17747
$704$	−0.992789	+	0.992789i	−0.0374171	+	0.0374171i
$705$	3.23645	+	0.722051i	0.121892	+	0.0271940i
$706$		−	54.3091i		−	2.04395i
$707$	6.53812	+	1.75188i	0.245891	+	0.0658863i
$708$	0.231787	−	0.147229i	0.00871108	−	0.00553319i
$709$	−9.57384	−	2.56530i	−0.359553	−	0.0963420i	0.0745202	−	0.997220i	$-0.476257\pi$
$709$	−9.57384	−	2.56530i	−0.359553	−	0.0963420i	−0.434073	+	0.900878i	$0.642924\pi$
$710$	−18.9884	−	18.9884i	−0.712623	−	0.712623i
$711$	−33.9826	+	23.6595i	−1.27445	+	0.887302i
$712$	18.2507	−	10.5371i	0.683976	−	0.394894i
$713$	−14.5322	−	14.5322i	−0.544234	−	0.544234i
$714$	−12.8355	+	57.5324i	−0.480356	+	2.15310i
$715$	14.2074	+	13.3252i	0.531326	+	0.498336i
$716$	3.85566	−	2.22607i	0.144093	−	0.0831921i
$717$	−34.8316	−	18.1915i	−1.30081	−	0.679374i
$718$	19.8900			0.742287
$719$	3.21191	−	5.56319i	0.119784	−	0.207472i	−0.799898	−	0.600136i	$-0.795113\pi$
$719$	3.21191	−	5.56319i	0.119784	−	0.207472i	0.919682	+	0.392664i	$0.128446\pi$
$720$	−22.9996	−	19.4042i	−0.857145	−	0.723150i
$721$	13.0469	−	3.49591i	0.485892	−	0.130194i
$722$	4.06433	−	15.1683i	0.151259	−	0.564506i
$723$	−17.5767	−	9.17981i	−0.653686	−	0.341401i
$724$	13.8298			0.513980
$725$	1.92466	−	3.33361i	0.0714801	−	0.123807i
$726$	−6.09466	−	9.59503i	−0.226194	−	0.356105i
$727$	−15.8150	−	9.13081i	−0.586547	−	0.338643i	0.177184	−	0.984178i	$-0.443301\pi$
$727$	−15.8150	−	9.13081i	−0.586547	−	0.338643i	−0.763731	+	0.645535i	$0.776635\pi$
$728$	18.1260	+	17.0006i	0.671795	+	0.630084i
$729$	6.77838	+	26.1353i	0.251051	+	0.967974i
$730$	−6.81270	+	25.4253i	−0.252149	+	0.941034i
$731$			8.35809i			0.309135i
$732$	−0.278380	+	0.0873632i	−0.0102892	+	0.00322904i
$733$	−8.64939	+	32.2800i	−0.319473	+	1.19229i	0.600280	+	0.799790i	$0.295056\pi$
$733$	−8.64939	+	32.2800i	−0.319473	+	1.19229i	−0.919753	+	0.392498i	$0.871611\pi$
$734$	−6.66358	+	6.66358i	−0.245957	+	0.245957i
$735$	−19.2860	−	30.3626i	−0.711376	−	1.11994i
$736$	−4.43371	−	16.5468i	−0.163429	−	0.609925i
$737$	−16.0491	−	9.26595i	−0.591176	−	0.341316i
$738$	9.08091	+	13.0431i	0.334273	+	0.480123i
$739$	−18.6190	−	4.98896i	−0.684912	−	0.183522i	−0.100450	−	0.994942i	$-0.532028\pi$
$739$	−18.6190	−	4.98896i	−0.684912	−	0.183522i	−0.584463	+	0.811420i	$0.698695\pi$
$740$	−6.23561	+	10.8004i	−0.229226	+	0.397030i
$741$	31.1893	−	10.8969i	1.14577	−	0.400308i
$742$	41.2105	+	71.3787i	1.51288	+	2.62039i
$743$	0.667921	+	2.49272i	0.0245037	+	0.0914489i	0.977095	−	0.212804i	$-0.0682597\pi$
$743$	0.667921	+	2.49272i	0.0245037	+	0.0914489i	−0.952591	+	0.304253i	$0.901593\pi$
$744$	17.7881	−	5.58239i	0.652144	−	0.204660i
$745$	−18.2324	+	10.5265i	−0.667982	+	0.385660i
$746$	3.62556	−	3.62556i	0.132741	−	0.132741i
$747$	−0.891981	+	4.98065i	−0.0326359	+	0.182232i
$748$	−3.43001	−	12.8010i	−0.125414	−	0.468051i
$749$	44.6648	−	11.9679i	1.63202	−	0.437298i
$750$	35.4007	+	7.89790i	1.29265	+	0.288391i
$751$	−2.07972	−	1.20072i	−0.0758899	−	0.0438151i	0.461575	−	0.887101i	$-0.347285\pi$
$751$	−2.07972	−	1.20072i	−0.0758899	−	0.0438151i	−0.537465	+	0.843286i	$0.680618\pi$
$752$	−4.60395	+	1.23362i	−0.167889	+	0.0449856i
$753$	7.89654	−	8.59443i	0.287766	−	0.313199i
$754$	−22.0161	−	11.7876i	−0.801778	−	0.429277i
$755$		−	33.1676i		−	1.20709i
$756$	−18.1323	+	13.7980i	−0.659466	+	0.501830i
$757$	23.9269	+	41.4425i	0.869637	+	1.50625i	0.862368	+	0.506281i	$0.168980\pi$
$757$	23.9269	+	41.4425i	0.869637	+	1.50625i	0.00726836	+	0.999974i	$0.497686\pi$
$758$	1.62342	+	2.81184i	0.0589651	+	0.102131i
$759$	14.7166	−	0.622800i	0.534179	−	0.0226062i
$760$	12.4261	+	12.4261i	0.450740	+	0.450740i
$761$	−13.2737	−	13.2737i	−0.481170	−	0.481170i	0.424335	−	0.905505i	$-0.360508\pi$
$761$	−13.2737	−	13.2737i	−0.481170	−	0.481170i	−0.905505	+	0.424335i	$0.860508\pi$
$762$	−13.4195	+	25.6945i	−0.486137	+	0.930815i
$763$	−3.72355	−	6.44937i	−0.134801	−	0.233483i
$764$	−2.20397	−	3.81739i	−0.0797368	−	0.138108i
$765$	−26.4892	+	9.56103i	−0.957719	+	0.345680i
$766$			39.8226i			1.43885i
$767$	−0.478630	−	0.256262i	−0.0172823	−	0.00925308i
$768$	32.9557	+	7.35241i	1.18919	+	0.265307i
$769$	7.28576	−	1.95221i	0.262731	−	0.0703986i	−0.125049	−	0.992151i	$-0.539909\pi$
$769$	7.28576	−	1.95221i	0.262731	−	0.0703986i	0.387780	+	0.921752i	$0.373242\pi$
$770$	34.0463	+	19.6567i	1.22694	+	0.708377i
$771$	−14.8785	+	16.1935i	−0.535837	+	0.583194i
$772$	−14.9862	+	4.01553i	−0.539364	+	0.144522i
$773$	−3.03666	−	11.3330i	−0.109221	−	0.407619i	0.889569	−	0.456801i	$-0.151005\pi$
$773$	−3.03666	−	11.3330i	−0.109221	−	0.407619i	−0.998790	+	0.0491827i	$0.984338\pi$
$774$	−6.04070	+	7.16000i	−0.217129	+	0.257361i
$775$	−4.46601	+	4.46601i	−0.160424	+	0.160424i
$776$	−12.3150	+	7.11005i	−0.442081	+	0.255236i
$777$	−31.3476	−	28.8021i	−1.12459	−	1.03327i
$778$	−10.9800	−	40.9777i	−0.393650	−	1.46912i
$779$	−8.02014	−	13.8913i	−0.287351	−	0.497707i
$780$	2.45979	−	12.9664i	0.0880745	−	0.464272i
$781$	−10.3041	+	17.8473i	−0.368711	+	0.638626i
$782$	−24.9396	−	6.68254i	−0.891837	−	0.238967i
$783$	−12.6049	+	16.2911i	−0.450463	+	0.582198i
$784$	44.7756	+	25.8512i	1.59913	+	0.923257i
$785$	4.20453	+	15.6915i	0.150066	+	0.560055i
$786$	−21.7641	+	41.6722i	−0.776301	+	1.48640i
$787$	−22.8170	+	22.8170i	−0.813340	+	0.813340i	−0.985133	−	0.171793i	$-0.945044\pi$
$787$	−22.8170	+	22.8170i	−0.813340	+	0.813340i	0.171793	+	0.985133i	$0.445044\pi$
$788$	7.09170	−	26.4666i	0.252631	−	0.942833i
$789$	6.73976	−	30.2096i	0.239942	−	1.07549i
$790$		−	48.4071i		−	1.72225i
$791$	2.68327	−	10.0141i	0.0954060	−	0.356060i
$792$	−5.67952	+	12.0951i	−0.201813	+	0.429781i
$793$	0.420762	+	0.394637i	0.0149417	+	0.0140140i
$794$	8.21441	+	4.74259i	0.291519	+	0.168308i
$795$	−18.2289	+	34.9031i	−0.646511	+	1.23789i
$796$	−10.9552	+	18.9750i	−0.388297	+	0.672551i
$797$	−14.0936			−0.499223			−0.249611	−	0.968346i	$-0.580303\pi$
$797$	−14.0936			−0.499223			−0.249611	+	0.968346i	$0.580303\pi$
$798$	56.2857	−	35.7521i	1.99249	−	1.26561i
$799$	−1.15451	+	4.30871i	−0.0408438	+	0.152431i
$800$	−5.08516	+	1.36256i	−0.179787	+	0.0481739i
$801$	24.6349	−	29.1996i	0.870433	−	1.03172i
$802$	17.6388	−	30.5513i	0.622848	−	1.07880i
$803$	20.2004			0.712857
$804$	0.530902	+	12.5451i	0.0187235	+	0.442431i
$805$	22.8759	−	13.2074i	0.806269	−	0.465500i
$806$	29.8869	+	28.0312i	1.05272	+	0.987357i
$807$	−15.1915	−	13.9579i	−0.534768	−	0.491343i
$808$	−1.90178	−	1.90178i	−0.0669044	−	0.0669044i
$809$	−15.1596	+	8.75238i	−0.532982	+	0.307717i	−0.742230	−	0.670145i	$-0.766232\pi$
$809$	−15.1596	+	8.75238i	−0.532982	+	0.307717i	0.209248	+	0.977863i	$0.432898\pi$
$810$	−29.6022	−	10.9542i	−1.04012	−	0.384892i
$811$	−1.05231	−	1.05231i	−0.0369516	−	0.0369516i	0.688390	−	0.725341i	$-0.258318\pi$
$811$	−1.05231	−	1.05231i	−0.0369516	−	0.0369516i	−0.725341	+	0.688390i	$0.758318\pi$
$812$	−16.7904	−	4.49899i	−0.589229	−	0.157883i
$813$	37.8551	+	19.7706i	1.32764	+	0.693386i
$814$	26.8057	+	7.18258i	0.939541	+	0.251749i
$815$			20.3287i			0.712084i
$816$	27.3873	−	29.8077i	0.958747	−	1.04348i
$817$	6.68545	−	6.68545i	0.233894	−	0.233894i
$818$	34.8941			1.22004
$819$	41.3704	+	17.8326i	1.44560	+	0.623122i
$820$	−6.40759			−0.223763
$821$	31.4709	−	31.4709i	1.09834	−	1.09834i	0.103739	−	0.994605i	$-0.466919\pi$
$821$	31.4709	−	31.4709i	1.09834	−	1.09834i	0.994605	−	0.103739i	$-0.0330807\pi$
$822$	−13.4280	−	42.7880i	−0.468356	−	1.49240i
$823$			33.2662i			1.15959i	0.814764	+	0.579793i	$0.196866\pi$
$823$			33.2662i			1.15959i	−0.814764	+	0.579793i	$0.803134\pi$
$824$	−5.18411	−	1.38908i	−0.180597	−	0.0483908i
$825$	−0.191398	−	4.52269i	−0.00666362	−	0.157460i
$826$	−1.05843	−	0.283604i	−0.0368273	−	0.00986785i
$827$	−8.99580	−	8.99580i	−0.312814	−	0.312814i	0.533185	−	0.845999i	$-0.320995\pi$
$827$	−8.99580	−	8.99580i	−0.312814	−	0.312814i	−0.845999	+	0.533185i	$0.820995\pi$
$828$	−5.70248	−	8.19058i	−0.198175	−	0.284642i
$829$	−22.4023	+	12.9340i	−0.778064	+	0.449216i	−0.835744	−	0.549120i	$-0.814963\pi$
$829$	−22.4023	+	12.9340i	−0.778064	+	0.449216i	0.0576796	+	0.998335i	$0.481630\pi$
$830$	−4.18268	−	4.18268i	−0.145183	−	0.145183i
$831$	23.5295	−	7.38419i	0.816228	−	0.256155i
$832$	−0.544731	−	1.80025i	−0.0188852	−	0.0624124i
$833$	41.9042	−	24.1934i	1.45190	−	0.838253i
$834$	3.21735	−	2.04363i	0.111408	−	0.0707651i
$835$	−29.7389			−1.02916
$836$	−7.49563	+	12.9828i	−0.259242	+	0.449020i
$837$	26.8954	−	20.4665i	0.929643	−	0.707425i
$838$	20.2108	−	5.41548i	0.698172	−	0.187075i
$839$	5.01733	−	18.7249i	0.173217	−	0.646456i	−0.823631	−	0.567126i	$-0.808055\pi$
$839$	5.01733	−	18.7249i	0.173217	−	0.646456i	0.996848	−	0.0793300i	$-0.0252781\pi$
$840$	1.01317	+	23.9409i	0.0349576	+	0.826040i
$841$	13.2857			0.458129
$842$	1.48965	−	2.58015i	0.0513367	−	0.0889177i
$843$	−11.7207	+	0.496014i	−0.403682	+	0.0170836i
$844$	−1.25140	−	0.722498i	−0.0430751	−	0.0248694i
$845$	−24.7208	+	8.35320i	−0.850422	+	0.287359i
$846$	−4.10308	+	2.85667i	−0.141067	+	0.0982142i
$847$	−4.04886	+	15.1105i	−0.139120	+	0.519205i
$848$		−	56.5990i		−	1.94362i
$849$	20.8383	+	19.1461i	0.715167	+	0.657094i
$850$	−2.05367	+	7.66440i	−0.0704403	+	0.262887i
$851$	13.1849	−	13.1849i	0.451973	−	0.451973i
$852$	13.9507	−	0.590386i	0.477942	−	0.0202263i
$853$	−2.55893	−	9.55006i	−0.0876161	−	0.326988i	0.908181	−	0.418578i	$-0.137472\pi$
$853$	−2.55893	−	9.55006i	−0.0876161	−	0.326988i	−0.995797	+	0.0915907i	$0.970805\pi$
$854$	1.00831	+	0.582146i	0.0345036	+	0.0199206i
$855$	28.8358	+	13.5405i	0.986162	+	0.463074i
$856$	−17.7473	−	4.75537i	−0.606590	−	0.162535i
$857$	0.920083	−	1.59363i	0.0314294	−	0.0544374i	−0.849883	−	0.526972i	$-0.823327\pi$
$857$	0.920083	−	1.59363i	0.0314294	−	0.0544374i	0.881312	+	0.472534i	$0.156661\pi$
$858$	−29.2868	+	2.18070i	−0.999835	+	0.0744477i
$859$	15.1557	+	26.2505i	0.517106	+	0.895655i	0.999803	+	0.0198668i	$0.00632421\pi$
$859$	15.1557	+	26.2505i	0.517106	+	0.895655i	−0.482696	+	0.875788i	$0.660342\pi$
$860$	−0.977518	−	3.64815i	−0.0333331	−	0.124401i
$861$	4.76260	−	21.3474i	0.162309	−	0.727518i
$862$	25.0863	−	14.4836i	0.854442	−	0.493312i
$863$	5.15592	−	5.15592i	0.175509	−	0.175509i	−0.613886	−	0.789395i	$-0.710394\pi$
$863$	5.15592	−	5.15592i	0.175509	−	0.175509i	0.789395	+	0.613886i	$0.210394\pi$
$864$	27.9447	−	3.56486i	0.950699	−	0.121279i
$865$	−9.73285	−	36.3235i	−0.330927	−	1.23504i
$866$	−51.1486	+	13.7052i	−1.73810	+	0.465723i
$867$	−2.52673	−	8.05133i	−0.0858122	−	0.273437i
$868$	24.7001	+	14.2606i	0.838377	+	0.484037i
$869$	−35.8831	+	9.61486i	−1.21725	+	0.326162i
$870$	−7.21025	−	22.9752i	−0.244450	−	0.778933i
$871$	21.0913	−	13.0951i	0.714652	−	0.443709i
$872$			2.95906i			0.100206i
$873$	−16.6228	+	19.7029i	−0.562596	+	0.666841i
$874$	14.6034	+	25.2938i	0.493967	+	0.855576i
$875$	−24.9586	−	43.2295i	−0.843753	−	1.46142i
$876$	−7.33846	−	11.5532i	−0.247944	−	0.390346i
$877$	−17.2465	−	17.2465i	−0.582371	−	0.582371i	0.353183	−	0.935554i	$-0.385099\pi$
$877$	−17.2465	−	17.2465i	−0.582371	−	0.582371i	−0.935554	+	0.353183i	$0.885099\pi$
$878$	−41.4654	−	41.4654i	−1.39939	−	1.39939i
$879$	−6.35621	−	10.0068i	−0.214390	−	0.337521i
$880$	−13.4984	−	23.3798i	−0.455030	−	0.788134i
$881$	−0.849065	−	1.47062i	−0.0286057	−	0.0495466i	0.851368	−	0.524569i	$-0.175773\pi$
$881$	−0.849065	−	1.47062i	−0.0286057	−	0.0495466i	−0.879974	+	0.475022i	$0.842440\pi$
$882$	53.3830	+	9.56032i	1.79750	+	0.321913i
$883$		−	23.3870i		−	0.787034i	−0.919317	−	0.393517i	$-0.871258\pi$
$883$		−	23.3870i		−	0.787034i	0.919317	−	0.393517i	$-0.128742\pi$
$884$	17.2869	+	4.04344i	0.581422	+	0.135996i
$885$	−0.156751	−	0.499482i	−0.00526913	−	0.0167899i
$886$	33.7596	−	9.04587i	1.13418	−	0.303902i
$887$	6.04763	+	3.49160i	0.203060	+	0.117237i	0.598082	−	0.801435i	$-0.295930\pi$
$887$	6.04763	+	3.49160i	0.203060	+	0.117237i	−0.395022	+	0.918672i	$0.629263\pi$
$888$	5.06486	+	16.1390i	0.169965	+	0.541589i
$889$	38.5343	−	10.3252i	1.29240	−	0.346298i
$890$	11.5592	+	43.1394i	0.387464	+	1.44604i
$891$	−2.24039	+	24.1193i	−0.0750559	+	0.808026i
$892$	−15.1711	+	15.1711i	−0.507966	+	0.507966i
$893$	4.36991	−	2.52297i	0.146233	−	0.0844279i
$894$	6.91164	−	30.9800i	0.231160	−	1.03613i
$895$	−2.19681	−	8.19861i	−0.0734313	−	0.274049i
$896$	−24.4782	−	42.3975i	−0.817759	−	1.41640i
$897$	−8.57006	+	17.7742i	−0.286146	+	0.593464i
$898$	−30.3895	+	52.6361i	−1.01411	+	1.75649i
$899$	24.9051	+	6.67329i	0.830631	+	0.222567i
$900$	−2.51712	+	1.75248i	−0.0839040	+	0.0584160i
$901$	−45.8729	−	26.4847i	−1.52825	−	0.882334i
$902$	3.69034	+	13.7725i	0.122875	+	0.458575i
$903$	12.8807	−	0.545104i	0.428642	−	0.0181399i
$904$	−2.91286	+	2.91286i	−0.0968802	+	0.0968802i
$905$	6.82401	−	25.4675i	0.226838	−	0.846570i
$906$	36.8238	+	33.8336i	1.22339	+	1.12405i
$907$			53.5987i			1.77972i	0.456237	+	0.889858i	$0.349197\pi$
$907$			53.5987i			1.77972i	−0.456237	+	0.889858i	$0.650803\pi$
$908$	−0.532724	+	1.98815i	−0.0176791	+	0.0659792i
$909$	−4.41325	−	2.07234i	−0.146378	−	0.0687351i
$910$	−44.7428	+	27.7797i	−1.48321	+	0.920887i
$911$	−46.3679	−	26.7705i	−1.53624	−	0.886946i	−0.999054	−	0.0434800i	$-0.986156\pi$
$911$	−46.3679	−	26.7705i	−1.53624	−	0.886946i	−0.537182	−	0.843466i	$-0.680511\pi$
$912$	−45.7490	+	1.93608i	−1.51490	+	0.0641099i
$913$	−2.26974	+	3.93131i	−0.0751176	+	0.130107i
$914$	11.5659			0.382565
$915$	0.0235188	+	0.555744i	0.000777508	+	0.0183723i
$916$	−3.45874	+	12.9082i	−0.114280	+	0.426499i
$917$	62.4962	−	16.7458i	2.06381	−	0.552995i
$918$	16.4061	−	39.1622i	0.541483	−	1.29255i
$919$	27.1663	−	47.0535i	0.896135	−	1.55215i	0.0637409	−	0.997966i	$-0.479697\pi$
$919$	27.1663	−	47.0535i	0.896135	−	1.55215i	0.832394	−	0.554184i	$-0.186970\pi$
$920$	−10.4958			−0.346035
$921$	−10.1342	+	6.43714i	−0.333933	+	0.212111i
$922$	−3.14099	+	1.81345i	−0.103443	+	0.0597229i
$923$	−14.5623	−	23.4544i	−0.479323	−	0.772012i
$924$	−19.5039	+	6.12086i	−0.641632	+	0.201362i
$925$	−4.05197	−	4.05197i	−0.133228	−	0.133228i
$926$	−35.3542	+	20.4117i	−1.16181	+	0.670772i
$927$	−9.69453	+	0.822008i	−0.318410	+	0.0269983i
$928$	15.1969	+	15.1969i	0.498863	+	0.498863i
$929$	−15.1804	−	4.06757i	−0.498052	−	0.133453i	0.00104363	−	0.999999i	$-0.499668\pi$
$929$	−15.1804	−	4.06757i	−0.498052	−	0.133453i	−0.499096	+	0.866547i	$0.666334\pi$
$930$	1.67055	+	39.4747i	0.0547795	+	1.29443i
$931$	−52.8700	−	14.1665i	−1.73274	−	0.464288i
$932$			17.8546i			0.584847i
$933$	7.64959	+	24.3752i	0.250436	+	0.798007i
$934$	28.8731	−	28.8731i	0.944756	−	0.944756i
$935$	−25.2655			−0.826270
$936$	−10.6931	−	14.3555i	−0.349516	−	0.469225i
$937$	33.8155			1.10471			0.552353	−	0.833610i	$-0.313730\pi$
$937$	33.8155			1.10471			0.552353	+	0.833610i	$0.313730\pi$
$938$	35.4302	−	35.4302i	1.15684	−	1.15684i
$939$	32.2127	−	35.0596i	1.05122	−	1.14413i
$940$		−	2.01569i		−	0.0657447i
$941$	52.8843	+	14.1703i	1.72398	+	0.461939i	0.978782	−	0.204906i	$-0.0656890\pi$
$941$	52.8843	+	14.1703i	1.72398	+	0.461939i	0.745196	+	0.666845i	$0.232356\pi$
$942$	−21.7102	−	11.3386i	−0.707358	−	0.369432i
$943$	9.25383	+	2.47956i	0.301346	+	0.0807454i
$944$	0.532075	+	0.532075i	0.0173176	+	0.0173176i
$945$	16.4621	+	40.1990i	0.535512	+	1.30767i
$946$	−7.27837	+	4.20217i	−0.236640	+	0.136624i
$947$	−6.63107	−	6.63107i	−0.215481	−	0.215481i	0.591110	−	0.806591i	$-0.298690\pi$
$947$	−6.63107	−	6.63107i	−0.215481	−	0.215481i	−0.806591	+	0.591110i	$0.798690\pi$
$948$	18.5347	+	17.0297i	0.601980	+	0.553097i
$949$	−12.7731	+	23.8568i	−0.414633	+	0.774426i
$950$	7.77326	−	4.48789i	0.252198	−	0.145607i
$951$	−0.234035	−	5.53018i	−0.00758910	−	0.179328i
$952$	−32.2342			−1.04472
$953$	−15.1514	+	26.2429i	−0.490801	+	0.850092i	−0.999944	−	0.0105897i	$-0.996629\pi$
$953$	−15.1514	+	26.2429i	−0.490801	+	0.850092i	0.509143	+	0.860682i	$0.329962\pi$
$954$	−20.1558	−	55.8423i	−0.652567	−	1.80796i
$955$	−8.11722	+	2.17500i	−0.262667	+	0.0703814i
$956$	−6.18233	+	23.0728i	−0.199951	+	0.746226i
$957$	−15.5989	+	9.90825i	−0.504241	+	0.320288i
$958$	−16.8925			−0.545773
$959$	−30.8588	+	53.4489i	−0.996481	+	1.72596i
$960$	0.839581	−	1.60756i	0.0270974	−	0.0518838i
$961$	−9.79064	−	5.65263i	−0.315827	−	0.182343i
$962$	−25.4325	+	27.1161i	−0.819976	+	0.874258i
$963$	−33.1883	+	2.81406i	−1.06948	+	0.0906819i
$964$	−3.11973	+	11.6430i	−0.100480	+	0.374995i
$965$			29.5784i			0.952162i
$966$	−8.67194	+	38.8702i	−0.279015	+	1.25063i
$967$	−2.18902	+	8.16953i	−0.0703941	+	0.262715i	−0.992150	−	0.125057i	$-0.960089\pi$
$967$	−2.18902	+	8.16953i	−0.0703941	+	0.262715i	0.921755	+	0.387772i	$0.126755\pi$
$968$	4.39529	−	4.39529i	0.141270	−	0.141270i
$969$	−19.8384	+	37.9850i	−0.637303	+	1.22026i
$970$	−7.79971	−	29.1089i	−0.250434	−	0.934631i
$971$	28.8326	+	16.6465i	0.925282	+	0.534212i	0.885316	−	0.464989i	$-0.153942\pi$
$971$	28.8326	+	16.6465i	0.925282	+	0.534212i	0.0399654	+	0.999201i	$0.487275\pi$
$972$	14.6084	−	7.48077i	0.468564	−	0.239946i
$973$	−5.06679	−	1.35764i	−0.162434	−	0.0435240i
$974$	−20.1470	+	34.8957i	−0.645553	+	1.11813i
$975$	5.46235	+	2.63374i	0.174935	+	0.0843472i
$976$	−0.399764	−	0.692411i	−0.0127961	−	0.0221635i
$977$	3.88364	+	14.4939i	0.124249	+	0.463702i	0.999812	−	0.0194016i	$-0.00617612\pi$
$977$	3.88364	+	14.4939i	0.124249	+	0.463702i	−0.875563	+	0.483104i	$0.839509\pi$
$978$	−22.5696	−	20.7369i	−0.721697	−	0.663093i
$979$	29.6824	−	17.1371i	0.948652	−	0.547705i
$980$	−15.4609	+	15.4609i	−0.493879	+	0.493879i
$981$	1.82116	+	5.04560i	0.0581452	+	0.161094i
$982$	−13.5217	−	50.4637i	−0.431495	−	1.61036i
$983$	44.9970	−	12.0569i	1.43518	−	0.384556i	0.544338	−	0.838866i	$-0.316781\pi$
$983$	44.9970	−	12.0569i	1.43518	−	0.384556i	0.890844	+	0.454310i	$0.150114\pi$
$984$	−5.87999	+	6.39966i	−0.187447	+	0.204014i
$985$	−45.2389	−	26.1187i	−1.44143	−	0.832212i
$986$	31.2887	−	8.38378i	0.996436	−	0.266994i
$987$	6.71545	+	1.49822i	0.213755	+	0.0476887i
$988$	−10.5932	−	17.0617i	−0.337013	−	0.542804i
$989$			5.64692i			0.179561i
$990$	−21.6438	−	18.2603i	−0.687885	−	0.580350i
$991$	22.3695	+	38.7452i	0.710592	+	1.23078i	0.964635	+	0.263589i	$0.0849062\pi$
$991$	22.3695	+	38.7452i	0.710592	+	1.23078i	−0.254043	+	0.967193i	$0.581760\pi$
$992$	−17.6315	−	30.5387i	−0.559802	−	0.969606i
$993$	22.2023	−	42.5112i	0.704569	−	1.34905i
$994$	−39.3999	−	39.3999i	−1.24969	−	1.24969i
$995$	29.5368	+	29.5368i	0.936380	+	0.936380i
$996$	3.07299	−	0.130047i	0.0973713	−	0.00412071i
$997$	−11.2979	−	19.5685i	−0.357808	−	0.619741i	0.629787	−	0.776768i	$-0.283142\pi$
$997$	−11.2979	−	19.5685i	−0.357808	−	0.619741i	−0.987594	+	0.157027i	$0.949809\pi$
$998$	2.44827	+	4.24053i	0.0774987	+	0.134232i
$999$	18.5691	+	24.4020i	0.587499	+	0.772045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.10	✓	48
3.2	odd	2		351.2.ba.a.89.3		48
9.4	even	3		351.2.bf.a.206.10		48
9.5	odd	6		117.2.bc.a.50.3	yes	48
13.6	odd	12		117.2.bc.a.110.3	yes	48
39.32	even	12		351.2.bf.a.305.10		48
117.32	even	12	inner	117.2.x.a.32.10	yes	48
117.58	odd	12		351.2.ba.a.71.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.10	✓	48	1.1	even	1	trivial
117.2.x.a.32.10	yes	48	117.32	even	12	inner
117.2.bc.a.50.3	yes	48	9.5	odd	6
117.2.bc.a.110.3	yes	48	13.6	odd	12
351.2.ba.a.71.3		48	117.58	odd	12
351.2.ba.a.89.3		48	3.2	odd	2
351.2.bf.a.206.10		48	9.4	even	3
351.2.bf.a.305.10		48	39.32	even	12

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.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23549 - 1.23549i) q^{2} +(1.69049 + 0.377148i) q^{3} -1.05286i q^{4} +(-1.93883 - 0.519509i) q^{5} +(2.55454 - 1.62262i) q^{6} +(-4.02297 - 1.07795i) q^{7} +(1.17018 + 1.17018i) q^{8} +(2.71552 + 1.27513i) q^{9} +O(q^{10})\)	\(q+(1.23549 - 1.23549i) q^{2} +(1.69049 + 0.377148i) q^{3} -1.05286i q^{4} +(-1.93883 - 0.519509i) q^{5} +(2.55454 - 1.62262i) q^{6} +(-4.02297 - 1.07795i) q^{7} +(1.17018 + 1.17018i) q^{8} +(2.71552 + 1.27513i) q^{9} +(-3.03725 + 1.75356i) q^{10} +(1.90315 + 1.90315i) q^{11} +(0.397082 - 1.77984i) q^{12} +(-3.45103 + 1.04423i) q^{13} +(-6.30212 + 3.63853i) q^{14} +(-3.08165 - 1.60945i) q^{15} +4.99721 q^{16} +(2.33837 - 4.05018i) q^{17} +(4.93039 - 1.77958i) q^{18} +(-5.11006 + 1.36924i) q^{19} +(-0.546967 + 2.04131i) q^{20} +(-6.39425 - 3.33952i) q^{21} +4.70262 q^{22} +(1.57986 - 2.73639i) q^{23} +(1.53685 + 2.41952i) q^{24} +(-0.840946 - 0.485520i) q^{25} +(-2.97356 + 5.55383i) q^{26} +(4.10965 + 3.17975i) q^{27} +(-1.13493 + 4.23560i) q^{28} +3.96412i q^{29} +(-5.79579 + 1.81888i) q^{30} +(1.68342 - 6.28262i) q^{31} +(3.83361 - 3.83361i) q^{32} +(2.49948 + 3.93502i) q^{33} +(-2.11492 - 7.89298i) q^{34} +(7.23986 + 4.17993i) q^{35} +(1.34253 - 2.85905i) q^{36} +(5.70017 + 1.52736i) q^{37} +(-4.62174 + 8.00509i) q^{38} +(-6.22776 + 0.463719i) q^{39} +(-1.66087 - 2.87671i) q^{40} +(0.784740 + 2.92869i) q^{41} +(-12.0259 + 3.77407i) q^{42} +(-1.54773 + 0.893580i) q^{43} +(2.00374 - 2.00374i) q^{44} +(-4.60249 - 3.88300i) q^{45} +(-1.42889 - 5.33267i) q^{46} +(-0.921304 + 0.246863i) q^{47} +(8.44773 + 1.88469i) q^{48} +(8.96013 + 5.17313i) q^{49} +(-1.63883 + 0.439123i) q^{50} +(5.48052 - 5.96488i) q^{51} +(1.09943 + 3.63343i) q^{52} -11.3261i q^{53} +(9.00595 - 1.14887i) q^{54} +(-2.70118 - 4.67858i) q^{55} +(-3.44622 - 5.96902i) q^{56} +(-9.15491 + 0.387432i) q^{57} +(4.89762 + 4.89762i) q^{58} +(0.106474 + 0.106474i) q^{59} +(-1.69452 + 3.24453i) q^{60} +(-0.0799975 - 0.138560i) q^{61} +(-5.68225 - 9.84194i) q^{62} +(-9.54992 - 8.05701i) q^{63} +0.521656i q^{64} +(7.23345 - 0.231756i) q^{65} +(7.94974 + 1.77359i) q^{66} +(-6.65084 + 1.78209i) q^{67} +(-4.26426 - 2.46197i) q^{68} +(3.70276 - 4.03001i) q^{69} +(14.1090 - 3.78050i) q^{70} +(1.98176 + 7.39602i) q^{71} +(1.68552 + 4.66980i) q^{72} +(5.30711 - 5.30711i) q^{73} +(8.92951 - 5.15545i) q^{74} +(-1.23850 - 1.13793i) q^{75} +(1.44161 + 5.38015i) q^{76} +(-5.60480 - 9.70780i) q^{77} +(-7.12139 + 8.26723i) q^{78} +(-6.90128 + 11.9534i) q^{79} +(-9.68874 - 2.59609i) q^{80} +(5.74808 + 6.92528i) q^{81} +(4.58789 + 2.64882i) q^{82} +(0.436532 + 1.62916i) q^{83} +(-3.51603 + 6.73221i) q^{84} +(-6.63782 + 6.63782i) q^{85} +(-0.808188 + 3.01620i) q^{86} +(-1.49506 + 6.70131i) q^{87} +4.45407i q^{88} +(3.29592 - 12.3005i) q^{89} +(-10.4837 + 0.888924i) q^{90} +(15.0090 - 0.480881i) q^{91} +(-2.88103 - 1.66336i) q^{92} +(5.21529 - 9.98581i) q^{93} +(-0.833264 + 1.44325i) q^{94} +10.6189 q^{95} +(7.92653 - 5.03485i) q^{96} +(-2.22397 + 8.29997i) q^{97} +(17.4615 - 4.67878i) q^{98} +(2.74127 + 7.59479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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