LMFDB - Embedded newform 117.2.x.a.11.8

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			11.8
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.375702 - 0.375702i) q^{2} +(-0.0440912 + 1.73149i) q^{3} +1.71770i q^{4} +(-2.85246 - 0.764314i) q^{5} +(0.633958 + 0.667088i) q^{6} +(3.85210 + 1.03217i) q^{7} +(1.39674 + 1.39674i) q^{8} +(-2.99611 - 0.152687i) q^{9} +O(q^{10})$	\(q+(0.375702 - 0.375702i) q^{2} +(-0.0440912 + 1.73149i) q^{3} +1.71770i q^{4} +(-2.85246 - 0.764314i) q^{5} +(0.633958 + 0.667088i) q^{6} +(3.85210 + 1.03217i) q^{7} +(1.39674 + 1.39674i) q^{8} +(-2.99611 - 0.152687i) q^{9} +(-1.35883 + 0.784520i) q^{10} +(1.41956 + 1.41956i) q^{11} +(-2.97417 - 0.0757353i) q^{12} +(-0.867991 - 3.49951i) q^{13} +(1.83503 - 1.05945i) q^{14} +(1.44917 - 4.90531i) q^{15} -2.38588 q^{16} +(2.38198 - 4.12571i) q^{17} +(-1.18301 + 1.06828i) q^{18} +(3.57782 - 0.958675i) q^{19} +(1.31286 - 4.89966i) q^{20} +(-1.95703 + 6.62436i) q^{21} +1.06666 q^{22} +(-0.469242 + 0.812751i) q^{23} +(-2.48003 + 2.35686i) q^{24} +(3.22223 + 1.86035i) q^{25} +(-1.64088 - 0.988667i) q^{26} +(0.396478 - 5.18100i) q^{27} +(-1.77295 + 6.61674i) q^{28} -4.41168i q^{29} +(-1.29848 - 2.38739i) q^{30} +(0.0175135 - 0.0653613i) q^{31} +(-3.68987 + 3.68987i) q^{32} +(-2.52054 + 2.39536i) q^{33} +(-0.655122 - 2.44495i) q^{34} +(-10.1991 - 5.88843i) q^{35} +(0.262270 - 5.14641i) q^{36} +(-0.00215078 - 0.000576301i) q^{37} +(0.984018 - 1.70437i) q^{38} +(6.09764 - 1.34862i) q^{39} +(-2.91661 - 5.05171i) q^{40} +(2.08295 + 7.77367i) q^{41} +(1.75352 + 3.22404i) q^{42} +(-8.64818 + 4.99303i) q^{43} +(-2.43837 + 2.43837i) q^{44} +(8.42959 + 2.72550i) q^{45} +(0.129057 + 0.481647i) q^{46} +(5.69908 - 1.52706i) q^{47} +(0.105196 - 4.13112i) q^{48} +(7.71112 + 4.45202i) q^{49} +(1.90953 - 0.511658i) q^{50} +(7.03860 + 4.30628i) q^{51} +(6.01110 - 1.49094i) q^{52} +7.99684i q^{53} +(-1.79755 - 2.09547i) q^{54} +(-2.96424 - 5.13421i) q^{55} +(3.93872 + 6.82207i) q^{56} +(1.50218 + 6.23723i) q^{57} +(-1.65747 - 1.65747i) q^{58} +(-3.08306 - 3.08306i) q^{59} +(8.42583 + 2.48924i) q^{60} +(-6.15531 - 10.6613i) q^{61} +(-0.0179765 - 0.0311362i) q^{62} +(-11.3837 - 3.68065i) q^{63} -1.99917i q^{64} +(-0.198820 + 10.6456i) q^{65} +(-0.0470303 + 1.84691i) q^{66} +(1.05601 - 0.282958i) q^{67} +(7.08672 + 4.09152i) q^{68} +(-1.38658 - 0.848323i) q^{69} +(-6.04409 + 1.61951i) q^{70} +(-4.06655 - 15.1766i) q^{71} +(-3.97154 - 4.39807i) q^{72} +(0.854579 - 0.854579i) q^{73} +(-0.00102457 + 0.000591536i) q^{74} +(-3.36325 + 5.49722i) q^{75} +(1.64671 + 6.14561i) q^{76} +(4.00305 + 6.93349i) q^{77} +(1.78421 - 2.79757i) q^{78} +(-0.501428 + 0.868498i) q^{79} +(6.80561 + 1.82356i) q^{80} +(8.95337 + 0.914934i) q^{81} +(3.70315 + 2.13801i) q^{82} +(2.06478 + 7.70588i) q^{83} +(-11.3786 - 3.36158i) q^{84} +(-9.94785 + 9.94785i) q^{85} +(-1.37325 + 5.12502i) q^{86} +(7.63878 + 0.194516i) q^{87} +3.96551i q^{88} +(0.189782 - 0.708276i) q^{89} +(4.19099 - 2.14303i) q^{90} +(0.268496 - 14.3764i) q^{91} +(-1.39606 - 0.806016i) q^{92} +(0.112400 + 0.0332063i) q^{93} +(1.56743 - 2.71488i) q^{94} -10.9383 q^{95} +(-6.22627 - 6.55165i) q^{96} +(1.36963 - 5.11155i) q^{97} +(4.56971 - 1.22445i) q^{98} +(-4.03640 - 4.46990i) 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 $

$2$	0.375702	−	0.375702i	0.265661	−	0.265661i	−0.561688	−	0.827349i	$-0.689848\pi$
$2$	0.375702	−	0.375702i	0.265661	−	0.265661i	0.827349	+	0.561688i	$0.189848\pi$
$3$	−0.0440912	+	1.73149i	−0.0254561	+	0.999676i
$3$	−0.0440912	+	1.73149i	−0.0254561	+	0.999676i
$4$			1.71770i			0.858848i
$5$	−2.85246	−	0.764314i	−1.27566	−	0.341812i	−0.443463	−	0.896293i	$-0.646250\pi$
$5$	−2.85246	−	0.764314i	−1.27566	−	0.341812i	−0.832196	+	0.554481i	$0.812917\pi$
$6$	0.633958	+	0.667088i	0.258812	+	0.272338i
$7$	3.85210	+	1.03217i	1.45596	+	0.390122i	0.898091	−	0.439809i	$-0.144954\pi$
$7$	3.85210	+	1.03217i	1.45596	+	0.390122i	0.557865	+	0.829931i	$0.311621\pi$
$8$	1.39674	+	1.39674i	0.493824	+	0.493824i
$9$	−2.99611	−	0.152687i	−0.998704	−	0.0508956i
$10$	−1.35883	+	0.784520i	−0.429699	+	0.248087i
$11$	1.41956	+	1.41956i	0.428012	+	0.428012i	0.887951	−	0.459938i	$-0.152129\pi$
$11$	1.41956	+	1.41956i	0.428012	+	0.428012i	−0.459938	+	0.887951i	$0.652129\pi$
$12$	−2.97417	−	0.0757353i	−0.858570	−	0.0218629i
$13$	−0.867991	−	3.49951i	−0.240737	−	0.970590i
$13$	−0.867991	−	3.49951i	−0.240737	−	0.970590i
$14$	1.83503	−	1.05945i	0.490431	−	0.283151i
$15$	1.44917	−	4.90531i	0.374174	−	1.26654i
$16$	−2.38588			−0.596469
$17$	2.38198	−	4.12571i	0.577715	−	1.00063i	−0.418026	−	0.908435i	$-0.637278\pi$
$17$	2.38198	−	4.12571i	0.577715	−	1.00063i	0.995741	−	0.0921968i	$-0.0293889\pi$
$18$	−1.18301	+	1.06828i	−0.278838	+	0.251796i
$19$	3.57782	−	0.958675i	0.820809	−	0.219935i	0.176109	−	0.984371i	$-0.443649\pi$
$19$	3.57782	−	0.958675i	0.820809	−	0.219935i	0.644700	+	0.764436i	$0.276982\pi$
$20$	1.31286	−	4.89966i	0.293565	−	1.09560i
$21$	−1.95703	+	6.62436i	−0.427059	+	1.44555i
$22$	1.06666			0.227412
$23$	−0.469242	+	0.812751i	−0.0978437	+	0.169470i	−0.910792	−	0.412866i	$-0.864528\pi$
$23$	−0.469242	+	0.812751i	−0.0978437	+	0.169470i	0.812948	+	0.582336i	$0.197861\pi$
$24$	−2.48003	+	2.35686i	−0.506234	+	0.481093i
$25$	3.22223	+	1.86035i	0.644445	+	0.372071i
$26$	−1.64088	−	0.988667i	−0.321803	−	0.193894i
$27$	0.396478	−	5.18100i	0.0763022	−	0.997085i
$28$	−1.77295	+	6.61674i	−0.335056	+	1.25045i
$29$		−	4.41168i		−	0.819228i	−0.912259	−	0.409614i	$-0.865663\pi$
$29$		−	4.41168i		−	0.819228i	0.912259	−	0.409614i	$-0.134337\pi$
$30$	−1.29848	−	2.38739i	−0.237068	−	0.435875i
$31$	0.0175135	−	0.0653613i	0.00314552	−	0.0117392i	−0.964335	−	0.264684i	$-0.914732\pi$
$31$	0.0175135	−	0.0653613i	0.00314552	−	0.0117392i	0.967481	+	0.252945i	$0.0813991\pi$
$32$	−3.68987	+	3.68987i	−0.652282	+	0.652282i
$33$	−2.52054	+	2.39536i	−0.438769	+	0.416978i
$34$	−0.655122	−	2.44495i	−0.112353	−	0.419305i
$35$	−10.1991	−	5.88843i	−1.72396	−	0.995326i
$36$	0.262270	−	5.14641i	0.0437116	−	0.857735i
$37$	−0.00215078		0.000576301i	−0.000353587		9.47433e-5i	0.258642	−	0.965973i	$-0.416725\pi$
$37$	−0.00215078		0.000576301i	−0.000353587		9.47433e-5i	−0.258996	+	0.965878i	$0.583392\pi$
$38$	0.984018	−	1.70437i	0.159629	−	0.276485i
$39$	6.09764	−	1.34862i	0.976404	−	0.215952i
$40$	−2.91661	−	5.05171i	−0.461156	−	0.798745i
$41$	2.08295	+	7.77367i	0.325302	+	1.21404i	0.914008	+	0.405696i	$0.132971\pi$
$41$	2.08295	+	7.77367i	0.325302	+	1.21404i	−0.588706	+	0.808347i	$0.700363\pi$
$42$	1.75352	+	3.22404i	0.270574	+	0.497480i
$43$	−8.64818	+	4.99303i	−1.31883	+	0.761430i	−0.983541	−	0.180684i	$-0.942169\pi$
$43$	−8.64818	+	4.99303i	−1.31883	+	0.761430i	−0.335293	+	0.942114i	$0.608835\pi$
$44$	−2.43837	+	2.43837i	−0.367598	+	0.367598i
$45$	8.42959	+	2.72550i	1.25661	+	0.406294i
$46$	0.129057	+	0.481647i	0.0190284	+	0.0710150i
$47$	5.69908	−	1.52706i	0.831297	−	0.222745i	0.182017	−	0.983295i	$-0.441737\pi$
$47$	5.69908	−	1.52706i	0.831297	−	0.222745i	0.649279	+	0.760550i	$0.275071\pi$
$48$	0.105196	−	4.13112i	0.0151837	−	0.596276i
$49$	7.71112	+	4.45202i	1.10159	+	0.636003i
$50$	1.90953	−	0.511658i	0.270049	−	0.0723593i
$51$	7.03860	+	4.30628i	0.985601	+	0.603000i
$52$	6.01110	−	1.49094i	0.833590	−	0.206757i
$53$			7.99684i			1.09845i	0.835674	+	0.549225i	$0.185077\pi$
$53$			7.99684i			1.09845i	−0.835674	+	0.549225i	$0.814923\pi$
$54$	−1.79755	−	2.09547i	−0.244616	−	0.285157i
$55$	−2.96424	−	5.13421i	−0.399698	−	0.692297i
$56$	3.93872	+	6.82207i	0.526334	+	0.911638i
$57$	1.50218	+	6.23723i	0.198969	+	0.826142i
$58$	−1.65747	−	1.65747i	−0.217637	−	0.217637i
$59$	−3.08306	−	3.08306i	−0.401380	−	0.401380i	0.477339	−	0.878719i	$-0.341601\pi$
$59$	−3.08306	−	3.08306i	−0.401380	−	0.401380i	−0.878719	+	0.477339i	$0.841601\pi$
$60$	8.42583	+	2.48924i	1.08777	+	0.321359i
$61$	−6.15531	−	10.6613i	−0.788107	−	1.36504i	−0.927125	−	0.374751i	$-0.877728\pi$
$61$	−6.15531	−	10.6613i	−0.788107	−	1.36504i	0.139018	−	0.990290i	$-0.455605\pi$
$62$	−0.0179765	−	0.0311362i	−0.00228302	−	0.00395430i
$63$	−11.3837	−	3.68065i	−1.43421	−	0.463719i
$64$		−	1.99917i		−	0.249897i
$65$	−0.198820	+	10.6456i	−0.0246605	+	1.32043i
$66$	−0.0470303	+	1.84691i	−0.00578902	+	0.227339i
$67$	1.05601	−	0.282958i	0.129012	−	0.0345688i	−0.193735	−	0.981054i	$-0.562060\pi$
$67$	1.05601	−	0.282958i	0.129012	−	0.0345688i	0.322747	+	0.946485i	$0.395394\pi$
$68$	7.08672	+	4.09152i	0.859391	+	0.496170i
$69$	−1.38658	−	0.848323i	−0.166925	−	0.102126i
$70$	−6.04409	+	1.61951i	−0.722407	+	0.193568i
$71$	−4.06655	−	15.1766i	−0.482611	−	1.80113i	−0.590585	−	0.806976i	$-0.701103\pi$
$71$	−4.06655	−	15.1766i	−0.482611	−	1.80113i	0.107974	−	0.994154i	$-0.465564\pi$
$72$	−3.97154	−	4.39807i	−0.468050	−	0.518317i
$73$	0.854579	−	0.854579i	0.100021	−	0.100021i	−0.655326	−	0.755347i	$-0.727469\pi$
$73$	0.854579	−	0.854579i	0.100021	−	0.100021i	0.755347	+	0.655326i	$0.227469\pi$
$74$	−0.00102457		0.000591536i	−0.000119104		6.87646e-5i
$75$	−3.36325	+	5.49722i	−0.388355	+	0.634765i
$76$	1.64671	+	6.14561i	0.188891	+	0.704950i
$77$	4.00305	+	6.93349i	0.456190	+	0.790144i
$78$	1.78421	−	2.79757i	0.202023	−	0.316763i
$79$	−0.501428	+	0.868498i	−0.0564150	+	0.0977137i	−0.892854	−	0.450347i	$-0.851300\pi$
$79$	−0.501428	+	0.868498i	−0.0564150	+	0.0977137i	0.836439	+	0.548061i	$0.184634\pi$
$80$	6.80561	+	1.82356i	0.760891	+	0.203880i
$81$	8.95337	+	0.914934i	0.994819	+	0.101659i
$82$	3.70315	+	2.13801i	0.408944	+	0.236104i
$83$	2.06478	+	7.70588i	0.226640	+	0.845830i	0.981741	+	0.190222i	$0.0609209\pi$
$83$	2.06478	+	7.70588i	0.226640	+	0.845830i	−0.755101	+	0.655608i	$0.772412\pi$
$84$	−11.3786	−	3.36158i	−1.24151	−	0.366779i
$85$	−9.94785	+	9.94785i	−1.07900	+	1.07900i
$86$	−1.37325	+	5.12502i	−0.148081	+	0.552645i
$87$	7.63878	+	0.194516i	0.818963	+	0.0208543i
$88$			3.96551i			0.422725i
$89$	0.189782	−	0.708276i	0.0201168	−	0.0750771i	−0.955138	−	0.296162i	$-0.904293\pi$
$89$	0.189782	−	0.708276i	0.0201168	−	0.0750771i	0.975255	+	0.221085i	$0.0709598\pi$
$90$	4.19099	−	2.14303i	0.441769	−	0.225896i
$91$	0.268496	−	14.3764i	0.0281460	−	1.50705i
$92$	−1.39606	−	0.806016i	−0.145549	−	0.0840329i
$93$	0.112400	+	0.0332063i	0.0116554	+	0.00344334i
$94$	1.56743	−	2.71488i	0.161668	−	0.280018i
$95$	−10.9383			−1.12225
$96$	−6.22627	−	6.55165i	−0.635466	−	0.668675i
$97$	1.36963	−	5.11155i	0.139065	−	0.518999i	−0.860883	−	0.508803i	$-0.830088\pi$
$97$	1.36963	−	5.11155i	0.139065	−	0.518999i	0.999948	−	0.0101954i	$-0.00324535\pi$
$98$	4.56971	−	1.22445i	0.461610	−	0.123688i
$99$	−4.03640	−	4.46990i	−0.405674	−	0.449242i
$100$	−3.19552	+	5.53481i	−0.319552	+	0.553481i
$101$	−10.4297			−1.03780			−0.518899	−	0.854835i	$-0.673658\pi$
$101$	−10.4297			−1.03780			−0.518899	+	0.854835i	$0.673658\pi$
$102$	4.26229	−	1.02654i	0.422030	−	0.101642i
$103$	1.51292	−	0.873482i	0.149072	−	0.0860668i	−0.423609	−	0.905845i	$-0.639237\pi$
$103$	1.51292	−	0.873482i	0.149072	−	0.0860668i	0.572681	+	0.819779i	$0.305903\pi$
$104$	3.67556	−	6.10029i	0.360419	−	0.598182i
$105$	10.6454	−	17.3999i	1.03889	−	1.69806i
$106$	3.00443	+	3.00443i	0.291816	+	0.291816i
$107$	−15.7290	+	9.08114i	−1.52058	+	0.877907i	−0.520875	+	0.853633i	$0.674394\pi$
$107$	−15.7290	+	9.08114i	−1.52058	+	0.877907i	−0.999705	+	0.0242741i	$0.992273\pi$
$108$	8.89939	+	0.681029i	0.856345	+	0.0655320i
$109$	−9.07306	−	9.07306i	−0.869042	−	0.869042i	0.123325	−	0.992366i	$-0.460644\pi$
$109$	−9.07306	−	9.07306i	−0.869042	−	0.869042i	−0.992366	+	0.123325i	$0.960644\pi$
$110$	−3.04260	−	0.815263i	−0.290101	−	0.0777323i
$111$	0.00109269	−	0.00369865i	0.000103713	−	0.000351060i
$112$	−9.19063	−	2.46262i	−0.868433	−	0.232696i
$113$			3.50743i			0.329951i	0.986298	+	0.164976i	$0.0527546\pi$
$113$			3.50743i			0.329951i	−0.986298	+	0.164976i	$0.947245\pi$
$114$	2.90771	+	1.77896i	0.272332	+	0.166615i
$115$	1.95969	−	1.95969i	0.182742	−	0.182742i
$116$	7.57793			0.703593
$117$	2.06627	+	10.6175i	0.191026	+	0.981585i
$118$	−2.31662			−0.213262
$119$	13.4340	−	13.4340i	1.23150	−	1.23150i
$120$	8.87558	−	4.82734i	0.810226	−	0.440674i
$121$		−	6.96972i		−	0.633611i
$122$	−6.31803	−	1.69291i	−0.572008	−	0.153269i
$123$	−13.5519	+	3.26385i	−1.22193	+	0.294292i
$124$	0.112271	+	0.0300829i	0.0100822	+	0.00270152i
$125$	2.67135	+	2.67135i	0.238933	+	0.238933i
$126$	−5.65971	+	2.89405i	−0.504207	+	0.257823i
$127$	2.34115	−	1.35166i	0.207744	−	0.119941i	−0.392519	−	0.919744i	$-0.628396\pi$
$127$	2.34115	−	1.35166i	0.207744	−	0.119941i	0.600262	+	0.799803i	$0.295063\pi$
$128$	−8.13082	−	8.13082i	−0.718670	−	0.718670i
$129$	−8.26407	−	15.1944i	−0.727610	−	1.33779i
$130$	3.92489	+	4.07428i	0.344235	+	0.357338i
$131$	−6.39301	+	3.69101i	−0.558560	+	0.322485i	−0.752567	−	0.658515i	$-0.771185\pi$
$131$	−6.39301	+	3.69101i	−0.558560	+	0.322485i	0.194007	+	0.981000i	$0.437851\pi$
$132$	−4.11450	−	4.32952i	−0.358121	−	0.376836i
$133$	14.7716			1.28086
$134$	0.290438	−	0.503053i	0.0250900	−	0.0434571i
$135$	−5.09085	+	14.4756i	−0.438151	+	1.24586i
$136$	9.08958	−	2.43555i	0.779425	−	0.208846i
$137$	−1.94499	+	7.25879i	−0.166171	+	0.620160i	0.831717	+	0.555200i	$0.187358\pi$
$137$	−1.94499	+	7.25879i	−0.166171	+	0.620160i	−0.997888	+	0.0649594i	$0.979308\pi$
$138$	−0.839657	+	0.202224i	−0.0714763	+	0.0172145i
$139$	4.09380			0.347231			0.173616	−	0.984813i	$-0.444455\pi$
$139$	4.09380			0.347231			0.173616	+	0.984813i	$0.444455\pi$
$140$	10.1145	−	17.5189i	0.854834	−	1.48062i
$141$	2.39282	+	9.93523i	0.201512	+	0.836698i
$142$	−7.22968	−	4.17406i	−0.606701	−	0.350279i
$143$	3.73559	−	6.19992i	0.312386	−	0.518463i
$144$	7.14835	+	0.364292i	0.595696	+	0.0303577i
$145$	−3.37191	+	12.5841i	−0.280022	+	1.04506i
$146$		−	0.642133i		−	0.0531433i
$147$	−8.04861	+	13.1554i	−0.663839	+	1.08504i
$148$	0.000989910	−	0.00369439i	8.13701e−5	−	0.000303677i
$149$	11.5534	−	11.5534i	0.946489	−	0.946489i	−0.0521503	−	0.998639i	$-0.516607\pi$
$149$	11.5534	−	11.5534i	0.946489	−	0.946489i	0.998639	+	0.0521503i	$0.0166075\pi$
$150$	0.801736	+	3.32890i	0.0654615	+	0.271803i
$151$	4.75855	+	17.7591i	0.387245	+	1.44522i	0.834597	+	0.550861i	$0.185700\pi$
$151$	4.75855	+	17.7591i	0.387245	+	1.44522i	−0.447352	+	0.894358i	$0.647633\pi$
$152$	6.33633	+	3.65828i	0.513944	+	0.296726i
$153$	−7.76662	+	11.9974i	−0.627894	+	0.969932i
$154$	4.10888	+	1.10097i	0.331103	+	0.0887187i
$155$	−0.0999132	+	0.173055i	−0.00802522	+	0.0139001i
$156$	2.31652	+	10.4739i	0.185470	+	0.838583i
$157$	−8.36429	−	14.4874i	−0.667543	−	1.15622i	−0.978589	−	0.205824i	$-0.934013\pi$
$157$	−8.36429	−	14.4874i	−0.667543	−	1.15622i	0.311046	−	0.950395i	$-0.399321\pi$
$158$	0.137909	+	0.514683i	0.0109714	+	0.0409460i
$159$	−13.8464	−	0.352590i	−1.09809	−	0.0279622i
$160$	13.3454	−	7.70498i	1.05505	−	0.609132i
$161$	−2.64646	+	2.64646i	−0.208570	+	0.208570i
$162$	3.70754	−	3.02005i	0.291292	−	0.237278i
$163$	3.36060	+	12.5419i	0.263222	+	0.982359i	0.963329	+	0.268321i	$0.0864689\pi$
$163$	3.36060	+	12.5419i	0.263222	+	0.982359i	−0.700107	+	0.714038i	$0.746864\pi$
$164$	−13.3528	+	3.57787i	−1.04268	+	0.279385i
$165$	9.02054	−	4.90618i	0.702248	−	0.381945i
$166$	3.67085	+	2.11937i	0.284914	+	0.164495i
$167$	2.18187	−	0.584630i	0.168838	−	0.0452400i	−0.173410	−	0.984850i	$-0.555478\pi$
$167$	2.18187	−	0.584630i	0.168838	−	0.0452400i	0.342248	+	0.939610i	$0.388812\pi$
$168$	−11.9860	+	6.51907i	−0.924741	+	0.502957i
$169$	−11.4932	+	6.07509i	−0.884091	+	0.467315i
$170$			7.47484i			0.573294i
$171$	−10.8659	+	2.32601i	−0.830939	+	0.177874i
$172$	−8.57651	−	14.8549i	−0.653953	−	1.13268i
$173$	−0.199026	−	0.344724i	−0.0151317	−	0.0262089i	0.858360	−	0.513047i	$-0.171483\pi$
$173$	−0.199026	−	0.344724i	−0.0151317	−	0.0262089i	−0.873492	+	0.486838i	$0.838150\pi$
$174$	2.94298	−	2.79682i	0.223107	−	0.212026i
$175$	10.4921	+	10.4921i	0.793131	+	0.793131i
$176$	−3.38688	−	3.38688i	−0.255296	−	0.255296i
$177$	5.47422	−	5.20235i	0.411468	−	0.391033i
$178$	−0.194799	−	0.337402i	−0.0146008	−	0.0252893i
$179$	−1.13164	−	1.96005i	−0.0845824	−	0.146501i	0.820631	−	0.571459i	$-0.193622\pi$
$179$	−1.13164	−	1.96005i	−0.0845824	−	0.146501i	−0.905213	+	0.424958i	$0.860289\pi$
$180$	−4.68159	+	14.4795i	−0.348945	+	1.07924i
$181$			20.5643i			1.52853i	0.644903	+	0.764265i	$0.276898\pi$
$181$			20.5643i			1.52853i	−0.644903	+	0.764265i	$0.723102\pi$
$182$	−5.30035	−	5.50210i	−0.392888	−	0.407843i
$183$	18.7313	−	10.1878i	1.38466	−	0.753103i
$184$	−1.79062	+	0.479794i	−0.132006	+	0.0353709i
$185$	0.00569455	+	0.00328775i	0.000418672	+	0.000241720i
$186$	0.0547046	−	0.0297533i	0.00401114	−	0.00218162i
$187$	9.23804	−	2.47532i	0.675552	−	0.181014i
$188$	2.62303	+	9.78930i	0.191304	+	0.713958i
$189$	6.87493	−	19.5485i	0.500078	−	1.42194i
$190$	−4.10955	+	4.10955i	−0.298138	+	0.298138i
$191$	16.3392	−	9.43345i	1.18226	−	0.682581i	0.225727	−	0.974191i	$-0.427524\pi$
$191$	16.3392	−	9.43345i	1.18226	−	0.682581i	0.956537	+	0.291610i	$0.0941909\pi$
$192$	3.46155	+	0.0881460i	0.249816	+	0.00636139i
$193$	4.48792	+	16.7491i	0.323047	+	1.20563i	0.916260	+	0.400584i	$0.131193\pi$
$193$	4.48792	+	16.7491i	0.323047	+	1.20563i	−0.593213	+	0.805046i	$0.702141\pi$
$194$	−1.40584	−	2.43499i	−0.100934	−	0.174822i
$195$	−18.4240	−	0.813633i	−1.31937	−	0.0582655i
$196$	−7.64722	+	13.2454i	−0.546230	+	0.946098i
$197$	10.4644	+	2.80393i	0.745558	+	0.199772i	0.611547	−	0.791208i	$-0.290548\pi$
$197$	10.4644	+	2.80393i	0.745558	+	0.199772i	0.134011	+	0.990980i	$0.457214\pi$
$198$	−3.19583	−	0.162865i	−0.227118	−	0.0115743i
$199$	10.0108	+	5.77971i	0.709643	+	0.409713i	0.810929	−	0.585145i	$-0.198962\pi$
$199$	10.0108	+	5.77971i	0.709643	+	0.409713i	−0.101286	+	0.994857i	$0.532296\pi$
$200$	1.90219	+	7.09906i	0.134505	+	0.501980i
$201$	0.443377	+	1.84095i	0.0312734	+	0.129851i
$202$	−3.91847	+	3.91847i	−0.275703	+	0.275703i
$203$	4.55359	−	16.9942i	0.319599	−	1.19276i
$204$	−7.39689	+	12.0902i	−0.517886	+	0.846482i
$205$		−	23.7661i		−	1.65990i
$206$	0.240236	−	0.896573i	0.0167380	−	0.0624672i
$207$	1.53000	−	2.36345i	0.106342	−	0.164271i
$208$	2.07092	+	8.34940i	0.143592	+	0.578927i
$209$	6.43981	+	3.71803i	0.445451	+	0.257181i
$210$	−2.53767	−	10.5367i	−0.175116	−	0.727101i
$211$	3.93135	−	6.80930i	0.270645	−	0.468771i	−0.698382	−	0.715725i	$-0.746096\pi$
$211$	3.93135	−	6.80930i	0.270645	−	0.468771i	0.969027	+	0.246954i	$0.0794296\pi$
$212$	−13.7361			−0.943402
$213$	26.4574	−	6.37204i	1.81283	−	0.436605i
$214$	−2.49761	+	9.32121i	−0.170733	+	0.637185i
$215$	28.4848	−	7.63249i	1.94265	−	0.520531i
$216$	7.79032	−	6.68276i	0.530064	−	0.454704i
$217$	0.134928	−	0.233701i	0.00915948	−	0.0158647i
$218$	−6.81752			−0.461741
$219$	1.44201	+	1.51737i	0.0974423	+	0.102535i
$220$	8.81902	−	5.09167i	0.594578	−	0.343280i
$221$	−16.5055	−	4.75469i	−1.11028	−	0.319835i
$222$	−0.000979063	−	0.00180011i	−6.57104e−5	−	0.000120816i
$223$	−3.43229	−	3.43229i	−0.229843	−	0.229843i	0.582784	−	0.812627i	$-0.301963\pi$
$223$	−3.43229	−	3.43229i	−0.229843	−	0.229843i	−0.812627	+	0.582784i	$0.801963\pi$
$224$	−18.0223	+	10.4052i	−1.20416	+	0.695225i
$225$	−9.37010	−	6.06582i	−0.624673	−	0.404388i
$226$	1.31775	+	1.31775i	0.0876553	+	0.0876553i
$227$	−14.3638	−	3.84876i	−0.953357	−	0.255451i	−0.251571	−	0.967839i	$-0.580947\pi$
$227$	−14.3638	−	3.84876i	−0.953357	−	0.255451i	−0.701786	+	0.712388i	$0.747614\pi$
$228$	−10.7137	+	2.58030i	−0.709530	+	0.170884i
$229$	1.80010	+	0.482337i	0.118954	+	0.0318737i	0.317805	−	0.948156i	$-0.397054\pi$
$229$	1.80010	+	0.482337i	0.118954	+	0.0318737i	−0.198851	+	0.980030i	$0.563721\pi$
$230$		−	1.47252i		−	0.0970950i
$231$	−12.1818	+	6.62554i	−0.801501	+	0.435928i
$232$	6.16199	−	6.16199i	0.404554	−	0.404554i
$233$	2.34929			0.153907			0.0769534	−	0.997035i	$-0.475481\pi$
$233$	2.34929			0.153907			0.0769534	+	0.997035i	$0.475481\pi$
$234$	4.76530	+	3.21270i	0.311517	+	0.210021i
$235$	−17.4236			−1.13659
$236$	5.29577	−	5.29577i	0.344725	−	0.344725i
$237$	−1.48169	−	0.906510i	−0.0962459	−	0.0588841i
$238$		−	10.0944i		−	0.654322i
$239$	9.94862	+	2.66572i	0.643523	+	0.172431i	0.565799	−	0.824543i	$-0.308568\pi$
$239$	9.94862	+	2.66572i	0.643523	+	0.172431i	0.0777242	+	0.996975i	$0.475235\pi$
$240$	−3.45754	+	11.7034i	−0.223183	+	0.755454i
$241$	−5.30721	−	1.42206i	−0.341867	−	0.0916031i	0.0838005	−	0.996483i	$-0.473294\pi$
$241$	−5.30721	−	1.42206i	−0.341867	−	0.0916031i	−0.425668	+	0.904879i	$0.639961\pi$
$242$	−2.61853	−	2.61853i	−0.168326	−	0.168326i
$243$	−1.97896	+	15.4623i	−0.126951	+	0.991909i
$244$	18.3129	−	10.5730i	1.17236	−	0.676864i
$245$	−18.5929	−	18.5929i	−1.18786	−	1.18786i
$246$	−3.86522	+	6.31769i	−0.246437	+	0.402801i
$247$	−6.46041	−	11.6885i	−0.411066	−	0.743723i
$248$	0.115755	−	0.0668312i	0.00735045	−	0.00424378i
$249$	−13.4337	+	3.23539i	−0.851326	+	0.205035i
$250$	2.00726			0.126950
$251$	13.5910	−	23.5402i	0.857853	−	1.48585i	−0.0161194	−	0.999870i	$-0.505131\pi$
$251$	13.5910	−	23.5402i	0.857853	−	1.48585i	0.873973	−	0.485975i	$-0.161535\pi$
$252$	6.32224	−	19.5538i	0.398264	−	1.23177i
$253$	−1.81986	+	0.487630i	−0.114414	+	0.0306571i
$254$	0.371752	−	1.38740i	0.0233258	−	0.0870530i
$255$	−16.7860	−	17.6632i	−1.05118	−	1.10611i
$256$	−2.11118			−0.131949
$257$	−11.3425	+	19.6458i	−0.707525	+	1.22547i	0.258248	+	0.966079i	$0.416855\pi$
$257$	−11.3425	+	19.6458i	−0.707525	+	1.22547i	−0.965773	+	0.259390i	$0.916478\pi$
$258$	−8.81337	−	2.60373i	−0.548697	−	0.162101i
$259$	−0.00769019	−	0.00443994i	−0.000477845	−	0.000275884i
$260$	−18.2860	−	0.341512i	−1.13405	−	0.0211797i
$261$	−0.673605	+	13.2179i	−0.0416951	+	0.818167i
$262$	−1.01515	+	3.78858i	−0.0627160	+	0.234059i
$263$			23.1742i			1.42898i	0.699645	+	0.714491i	$0.253342\pi$
$263$			23.1742i			1.42898i	−0.699645	+	0.714491i	$0.746658\pi$
$264$	−6.86625	−	0.174844i	−0.422588	−	0.0107609i
$265$	6.11210	−	22.8107i	0.375463	−	1.40125i
$266$	5.54973	−	5.54973i	0.340276	−	0.340276i
$267$	1.21800	+	0.359834i	0.0745406	+	0.0220215i
$268$	0.486035	+	1.81391i	0.0296893	+	0.110802i
$269$	−4.69487	−	2.71058i	−0.286251	−	0.165267i	0.349999	−	0.936750i	$-0.386182\pi$
$269$	−4.69487	−	2.71058i	−0.286251	−	0.165267i	−0.636250	+	0.771483i	$0.719515\pi$
$270$	3.52585	+	7.35114i	0.214577	+	0.447376i
$271$	5.09582	+	1.36542i	0.309549	+	0.0829433i	0.410249	−	0.911973i	$-0.365442\pi$
$271$	5.09582	+	1.36542i	0.309549	+	0.0829433i	−0.100700	+	0.994917i	$0.532108\pi$
$272$	−5.68311	+	9.84343i	−0.344589	+	0.596846i
$273$	24.8807	+	1.09877i	1.50585	+	0.0665005i
$274$	1.99640	+	3.45787i	0.120607	+	0.208898i
$275$	1.93326	+	7.21501i	0.116580	+	0.435081i
$276$	1.45716	−	2.38173i	0.0877108	−	0.143363i
$277$	−2.35062	+	1.35713i	−0.141235	+	0.0815422i	−0.568953	−	0.822370i	$-0.692651\pi$
$277$	−2.35062	+	1.35713i	−0.141235	+	0.0815422i	0.427717	+	0.903913i	$0.359318\pi$
$278$	1.53805	−	1.53805i	0.0922458	−	0.0922458i
$279$	−0.0624523	+	0.193156i	−0.00373892	+	0.0115639i
$280$	−6.02085	−	22.4701i	−0.359814	−	1.34285i
$281$	7.44158	−	1.99396i	0.443927	−	0.118950i	−0.0299292	−	0.999552i	$-0.509528\pi$
$281$	7.44158	−	1.99396i	0.443927	−	0.118950i	0.473857	+	0.880602i	$0.342862\pi$
$282$	4.63167	+	2.83370i	0.275812	+	0.168744i
$283$	−1.36389	−	0.787444i	−0.0810750	−	0.0468087i	0.458914	−	0.888480i	$-0.348238\pi$
$283$	−1.36389	−	0.787444i	−0.0810750	−	0.0468087i	−0.539989	+	0.841672i	$0.681572\pi$
$284$	26.0688	−	6.98511i	1.54690	−	0.414490i
$285$	0.482284	−	18.9396i	0.0285680	−	1.12188i
$286$	−0.925850	−	3.73279i	−0.0547467	−	0.220724i
$287$			32.0949i			1.89450i
$288$	11.6186	−	10.4919i	0.684635	−	0.618239i
$289$	−2.84767	−	4.93230i	−0.167510	−	0.290135i
$290$	3.46105	+	5.99471i	0.203240	+	0.352022i
$291$	8.79020	+	2.59688i	0.515291	+	0.152232i
$292$	1.46791	+	1.46791i	0.0859028	+	0.0859028i
$293$	2.05393	+	2.05393i	0.119992	+	0.119992i	0.764553	−	0.644561i	$-0.222960\pi$
$293$	2.05393	+	2.05393i	0.119992	+	0.119992i	−0.644561	+	0.764553i	$0.722960\pi$
$294$	1.91864	+	7.96639i	0.111897	+	0.464609i
$295$	6.43788	+	11.1507i	0.374828	+	0.649221i
$296$	−0.00219915	−	0.00380904i	−0.000127823	−	0.000221396i
$297$	7.91755	−	6.79190i	0.459423	−	0.394106i
$298$		−	8.68124i		−	0.502891i
$299$	3.25153	+	0.936659i	0.188041	+	0.0541684i
$300$	−9.44257	−	5.77705i	−0.545167	−	0.333538i
$301$	−38.4673	+	10.3073i	−2.21722	+	0.594101i
$302$	8.45993	+	4.88434i	0.486814	+	0.281062i
$303$	0.459860	−	18.0590i	0.0264183	−	1.03746i
$304$	−8.53624	+	2.28728i	−0.489587	+	0.131184i
$305$	9.40919	+	35.1156i	0.538768	+	2.01071i
$306$	1.58951	+	7.42537i	0.0908661	+	0.424480i
$307$	10.9083	−	10.9083i	0.622567	−	0.622567i	−0.323620	−	0.946187i	$-0.604900\pi$
$307$	10.9083	−	10.9083i	0.622567	−	0.622567i	0.946187	+	0.323620i	$0.104900\pi$
$308$	−11.9096	+	6.87603i	−0.678614	+	0.391798i
$309$	1.44572	+	2.65811i	0.0822441	+	0.151215i
$310$	0.0274794	+	0.102554i	0.00156072	+	0.00582470i
$311$	−11.1819	−	19.3675i	−0.634065	−	1.09823i	−0.986713	−	0.162476i	$-0.948052\pi$
$311$	−11.1819	−	19.3675i	−0.634065	−	1.09823i	0.352648	−	0.935756i	$-0.385281\pi$
$312$	10.4005	+	6.63317i	0.588814	+	0.375529i
$313$	−5.75339	+	9.96517i	−0.325201	+	0.563264i	−0.981553	−	0.191190i	$-0.938765\pi$
$313$	−5.75339	+	9.96517i	−0.325201	+	0.563264i	0.656352	+	0.754455i	$0.272099\pi$
$314$	−8.58541	−	2.30045i	−0.484503	−	0.129822i
$315$	29.6584	+	19.1997i	1.67106	+	1.08178i
$316$	−1.49182	−	0.861301i	−0.0839212	−	0.0484519i
$317$	0.379738	+	1.41720i	0.0213282	+	0.0795979i	0.975770	−	0.218800i	$-0.0702143\pi$
$317$	0.379738	+	1.41720i	0.0213282	+	0.0795979i	−0.954441	+	0.298398i	$0.903548\pi$
$318$	−5.33460	+	5.06966i	−0.299149	+	0.284293i
$319$	6.26263	−	6.26263i	0.350640	−	0.350640i
$320$	−1.52800	+	5.70257i	−0.0854177	+	0.318783i
$321$	−15.0304	−	27.6350i	−0.838915	−	1.54244i
$322$			1.98856i			0.110818i
$323$	4.56709	−	17.0446i	0.254120	−	0.948388i
$324$	−1.57158	+	15.3792i	−0.0873099	+	0.854399i
$325$	3.71347	−	12.8910i	0.205986	−	0.715063i
$326$	5.97460	+	3.44944i	0.330903	+	0.191047i
$327$	16.1099	−	15.3099i	0.890882	−	0.846638i
$328$	−7.94848	+	13.7672i	−0.438881	+	0.760165i
$329$	23.5296			1.29723
$330$	1.54577	−	5.23229i	0.0850919	−	0.288028i
$331$	−1.46579	+	5.47041i	−0.0805673	+	0.300681i	−0.994438	−	0.105324i	$-0.966412\pi$
$331$	−1.46579	+	5.47041i	−0.0805673	+	0.300681i	0.913871	+	0.406005i	$0.133079\pi$
$332$	−13.2364	+	3.54667i	−0.726440	+	0.194649i
$333$	0.00635600	+	0.00205506i	0.000348306	+	0.000112616i
$334$	0.600085	−	1.03938i	0.0328352	−	0.0568722i
$335$	−3.22850			−0.176392
$336$	4.66923	−	15.8049i	0.254727	−	0.862228i
$337$	−20.4710	+	11.8189i	−1.11512	+	0.643818i	−0.940152	−	0.340756i	$-0.889317\pi$
$337$	−20.4710	+	11.8189i	−1.11512	+	0.643818i	−0.174973	+	0.984573i	$0.555984\pi$
$338$	−2.03559	+	6.60043i	−0.110721	+	0.359016i
$339$	−6.07308	−	0.154647i	−0.329845	−	0.00839926i
$340$	−17.0874	−	17.0874i	−0.926693	−	0.926693i
$341$	0.117645	−	0.0679226i	0.00637086	−	0.00367822i
$342$	−3.20846	+	4.95623i	−0.173494	+	0.268002i
$343$	5.36925	+	5.36925i	0.289912	+	0.289912i
$344$	−19.0533	−	5.10531i	−1.02728	−	0.275260i
$345$	3.30678	+	3.47959i	0.178031	+	0.187335i
$346$	−0.204288	−	0.0547387i	−0.0109826	−	0.00294277i
$347$			14.5722i			0.782275i	0.920332	+	0.391138i	$0.127918\pi$
$347$			14.5722i			0.782275i	−0.920332	+	0.391138i	$0.872082\pi$
$348$	−0.334120	+	13.1211i	−0.0179107	+	0.703365i
$349$	−2.90053	+	2.90053i	−0.155262	+	0.155262i	−0.780463	−	0.625201i	$-0.785017\pi$
$349$	−2.90053	+	2.90053i	−0.155262	+	0.155262i	0.625201	+	0.780463i	$0.285017\pi$
$350$	7.88382			0.421408
$351$	−18.4751	+	3.10958i	−0.986130	+	0.165977i
$352$	−10.4759			−0.558370
$353$	−0.632037	+	0.632037i	−0.0336399	+	0.0336399i	−0.723727	−	0.690087i	$-0.757572\pi$
$353$	−0.632037	+	0.632037i	−0.0336399	+	0.0336399i	0.690087	+	0.723727i	$0.257572\pi$
$354$	0.102143	−	4.01121i	0.00542882	−	0.213193i
$355$			46.3987i			2.46259i
$356$	1.21660	+	0.325988i	0.0644798	+	0.0172773i
$357$	22.6686	+	23.8532i	1.19975	+	1.26245i
$358$	−1.16155	−	0.311237i	−0.0613899	−	0.0164494i
$359$	−6.27393	−	6.27393i	−0.331126	−	0.331126i	0.521888	−	0.853014i	$-0.325228\pi$
$359$	−6.27393	−	6.27393i	−0.331126	−	0.331126i	−0.853014	+	0.521888i	$0.825228\pi$
$360$	7.96715	+	15.5808i	0.419906	+	0.821181i
$361$	−4.57272	+	2.64006i	−0.240670	+	0.138951i
$362$	7.72602	+	7.72602i	0.406071	+	0.406071i
$363$	12.0680	+	0.307303i	0.633406	+	0.0161292i
$364$	24.6943	+	0.461194i	1.29433	+	0.0241731i
$365$	−3.09082	+	1.78449i	−0.161781	+	0.0934042i
$366$	3.20983	−	10.8650i	0.167780	−	0.567921i
$367$	−22.4448			−1.17161			−0.585805	−	0.810452i	$-0.699221\pi$
$367$	−22.4448			−1.17161			−0.585805	+	0.810452i	$0.699221\pi$
$368$	1.11955	−	1.93912i	0.0583607	−	0.101084i
$369$	−5.05381	−	23.6088i	−0.263091	−	1.22903i
$370$	0.00337466		0.000904238i	0.000175440		4.70091e-5i
$371$	−8.25407	+	30.8046i	−0.428530	+	1.59930i
$372$	−0.0570384	+	0.193070i	−0.00295730	+	0.0100102i
$373$	36.2063			1.87469			0.937346	−	0.348400i	$-0.113275\pi$
$373$	36.2063			1.87469			0.937346	+	0.348400i	$0.113275\pi$
$374$	2.54076	−	4.40073i	0.131380	−	0.227556i
$375$	−4.74320	+	4.50764i	−0.244938	+	0.232773i
$376$	10.0931	+	5.82724i	0.520511	+	0.300517i
$377$	−15.4387	+	3.82930i	−0.795135	+	0.197219i
$378$	−4.76148	−	9.92733i	−0.244904	−	0.510607i
$379$	−3.01779	+	11.2625i	−0.155013	+	0.578518i	0.844091	+	0.536200i	$0.180141\pi$
$379$	−3.01779	+	11.2625i	−0.155013	+	0.578518i	−0.999104	+	0.0423177i	$0.986526\pi$
$380$		−	18.7887i		−	0.963841i
$381$	2.23717	+	4.11328i	0.114614	+	0.210730i
$382$	2.59451	−	9.68283i	0.132747	−	0.495417i
$383$	17.8850	−	17.8850i	0.913881	−	0.913881i	−0.0826943	−	0.996575i	$-0.526353\pi$
$383$	17.8850	−	17.8850i	0.913881	−	0.913881i	0.996575	+	0.0826943i	$0.0263525\pi$
$384$	14.4369	−	13.7199i	0.736732	−	0.700143i
$385$	−6.11918	−	22.8371i	−0.311862	−	1.16389i
$386$	7.97880	+	4.60656i	0.406110	+	0.234468i
$387$	26.6733	−	13.6392i	1.35588	−	0.693320i
$388$	8.78009	+	2.35262i	0.445741	+	0.119436i
$389$	−0.974393	+	1.68770i	−0.0494037	+	0.0855697i	−0.889670	−	0.456605i	$-0.849065\pi$
$389$	−0.974393	+	1.68770i	−0.0494037	+	0.0855697i	0.840266	+	0.542174i	$0.182399\pi$
$390$	−7.22763	+	6.61626i	−0.365985	+	0.335027i
$391$	2.23545	+	3.87192i	0.113052	+	0.195811i
$392$	4.55213	+	16.9888i	0.229917	+	0.858064i
$393$	−6.10906	−	11.2322i	−0.308162	−	0.566588i
$394$	4.98493	−	2.87805i	0.251137	−	0.144994i
$395$	2.09411	−	2.09411i	0.105366	−	0.105366i
$396$	7.67793	−	6.93331i	0.385830	−	0.348412i
$397$	7.70119	+	28.7412i	0.386511	+	1.44248i	0.835771	+	0.549079i	$0.185021\pi$
$397$	7.70119	+	28.7412i	0.386511	+	1.44248i	−0.449259	+	0.893401i	$0.648312\pi$
$398$	5.93250	−	1.58961i	0.297369	−	0.0796799i
$399$	−0.651299	+	25.5769i	−0.0326057	+	1.28045i
$400$	−7.68783	−	4.43857i	−0.384391	−	0.221929i
$401$	−20.8260	+	5.58031i	−1.04000	+	0.278668i	−0.738114	−	0.674676i	$-0.764283\pi$
$401$	−20.8260	+	5.58031i	−1.04000	+	0.278668i	−0.301888	+	0.953344i	$0.597617\pi$
$402$	0.858225	+	0.525070i	0.0428044	+	0.0261881i
$403$	−0.243934	−	0.00455576i	−0.0121512	−	0.000226938i
$404$		−	17.9151i		−	0.891312i
$405$	−24.8398	−	9.45300i	−1.23430	−	0.469724i
$406$	−4.67397	−	8.09555i	−0.231965	−	0.401775i
$407$	−0.00223507	−	0.00387125i	−0.000110788	−	0.000191891i
$408$	3.81635	+	15.8459i	0.188938	+	0.784489i
$409$	−11.8153	−	11.8153i	−0.584227	−	0.584227i	0.351835	−	0.936062i	$-0.385558\pi$
$409$	−11.8153	−	11.8153i	−0.584227	−	0.584227i	−0.936062	+	0.351835i	$0.885558\pi$
$410$	−8.92896	−	8.92896i	−0.440970	−	0.440970i
$411$	−12.4828	−	3.68777i	−0.615729	−	0.181904i
$412$	1.50038	+	2.59873i	0.0739183	+	0.128030i
$413$	−8.69403	−	15.0585i	−0.427805	−	0.740980i
$414$	−0.313128	−	1.46277i	−0.0153894	−	0.0718914i
$415$		−	23.5589i		−	1.15646i
$416$	16.1155	+	9.70996i	0.790128	+	0.476070i
$417$	−0.180500	+	7.08836i	−0.00883914	+	0.347119i
$418$	3.81632	−	1.02258i	0.186662	−	0.0500160i
$419$	−4.32648	−	2.49790i	−0.211363	−	0.122030i	0.390582	−	0.920568i	$-0.372274\pi$
$419$	−4.32648	−	2.49790i	−0.211363	−	0.122030i	−0.601944	+	0.798538i	$0.705607\pi$
$420$	29.8878	+	18.2856i	1.45838	+	0.892248i
$421$	11.4441	−	3.06643i	0.557751	−	0.149449i	0.0310779	−	0.999517i	$-0.490106\pi$
$421$	11.4441	−	3.06643i	0.557751	−	0.149449i	0.526673	+	0.850068i	$0.323439\pi$
$422$	−1.08125	−	4.03528i	−0.0526344	−	0.196434i
$423$	−17.3083	+	3.70508i	−0.841556	+	0.180147i
$424$	−11.1695	+	11.1695i	−0.542441	+	0.542441i
$425$	15.3506	−	8.86265i	0.744612	−	0.429902i
$426$	7.54610	−	12.3341i	0.365610	−	0.597588i
$427$	−12.7066	−	47.4217i	−0.614916	−	2.29490i
$428$	−15.5987	−	27.0177i	−0.753989	−	1.30595i
$429$	10.5704	+	6.74150i	0.510343	+	0.325483i
$430$	7.83426	−	13.5693i	0.377801	−	0.654371i
$431$	1.37787	+	0.369200i	0.0663698	+	0.0177837i	0.291851	−	0.956464i	$-0.405729\pi$
$431$	1.37787	+	0.369200i	0.0663698	+	0.0177837i	−0.225481	+	0.974247i	$0.572395\pi$
$432$	−0.945947	+	12.3612i	−0.0455119	+	0.594730i
$433$	−32.8919	−	18.9901i	−1.58068	−	0.912608i	−0.994760	−	0.102242i	$-0.967398\pi$
$433$	−32.8919	−	18.9901i	−1.58068	−	0.912608i	−0.585924	−	0.810366i	$-0.699268\pi$
$434$	−0.0371095	−	0.138494i	−0.00178131	−	0.00664795i
$435$	−21.6406	−	6.39328i	−1.03759	−	0.306534i
$436$	15.5848	−	15.5848i	0.746375	−	0.746375i
$437$	−0.899701	+	3.35773i	−0.0430385	+	0.160622i
$438$	1.11185	+	0.0283124i	0.0531261	+	0.00135282i
$439$			14.7837i			0.705589i	0.935701	+	0.352794i	$0.114768\pi$
$439$			14.7837i			0.705589i	−0.935701	+	0.352794i	$0.885232\pi$
$440$	3.03090	−	11.3115i	0.144492	−	0.539253i
$441$	−22.4236	−	14.5161i	−1.06779	−	0.691244i
$442$	−7.98749	+	4.41480i	−0.379926	+	0.209991i
$443$	20.7433	+	11.9761i	0.985543	+	0.569003i	0.903939	−	0.427662i	$-0.140662\pi$
$443$	20.7433	+	11.9761i	0.985543	+	0.569003i	0.0816037	+	0.996665i	$0.473996\pi$
$444$	0.00635316	+	0.00187691i	0.000301508	+	8.90742e-5i
$445$	−1.08269	+	1.87527i	−0.0513244	+	0.0888965i
$446$	−2.57903			−0.122121
$447$	19.4951	+	20.5139i	0.922088	+	0.970276i
$448$	2.06348	−	7.70102i	0.0974904	−	0.363839i
$449$	24.5951	−	6.59023i	1.16071	−	0.311012i	0.373463	−	0.927645i	$-0.378170\pi$
$449$	24.5951	−	6.59023i	1.16071	−	0.311012i	0.787251	+	0.616633i	$0.211504\pi$
$450$	−5.79930	+	1.24142i	−0.273381	+	0.0585213i
$451$	−8.07830	+	13.9920i	−0.380392	+	0.658858i
$452$	−6.02470			−0.283378
$453$	−30.9596	+	7.45636i	−1.45461	+	0.350330i
$454$	−6.84247	+	3.95050i	−0.321133	+	0.185406i
$455$	−11.7539	+	40.8028i	−0.551034	+	1.91287i
$456$	−6.61365	+	10.8100i	−0.309713	+	0.506224i
$457$	20.4989	+	20.4989i	0.958897	+	0.958897i	0.999188	−	0.0402908i	$-0.0128284\pi$
$457$	20.4989	+	20.4989i	0.958897	+	0.958897i	−0.0402908	+	0.999188i	$0.512828\pi$
$458$	0.857517	−	0.495088i	0.0400691	−	0.0231339i
$459$	−20.4309	−	13.9768i	−0.953634	−	0.652381i
$460$	3.36616	+	3.36616i	0.156948	+	0.156948i
$461$	−20.6632	−	5.53669i	−0.962382	−	0.257870i	−0.256774	−	0.966471i	$-0.582660\pi$
$461$	−20.6632	−	5.53669i	−0.962382	−	0.257870i	−0.705608	+	0.708602i	$0.749326\pi$
$462$	−2.08748	+	7.06593i	−0.0971185	+	0.328737i
$463$	−3.29295	−	0.882343i	−0.153036	−	0.0410060i	0.181487	−	0.983393i	$-0.441909\pi$
$463$	−3.29295	−	0.882343i	−0.153036	−	0.0410060i	−0.334524	+	0.942387i	$0.608575\pi$
$464$			10.5257i			0.488644i
$465$	−0.295237	−	0.180629i	−0.0136913	−	0.00837646i
$466$	0.882631	−	0.882631i	0.0408871	−	0.0408871i
$467$	−4.17553			−0.193221			−0.0966103	−	0.995322i	$-0.530800\pi$
$467$	−4.17553			−0.193221			−0.0966103	+	0.995322i	$0.530800\pi$
$468$	−18.2376	+	3.54922i	−0.843033	+	0.164063i
$469$	4.35992			0.201322
$470$	−6.54606	+	6.54606i	−0.301947	+	0.301947i
$471$	25.4535	−	13.8439i	1.17284	−	0.637894i
$472$		−	8.61250i		−	0.396422i
$473$	−19.3645	−	5.18869i	−0.890379	−	0.238576i
$474$	−0.897249	+	0.216095i	−0.0412120	+	0.00992557i
$475$	13.3120	+	3.56695i	0.610798	+	0.163663i
$476$	23.0756	+	23.0756i	1.05767	+	1.05767i
$477$	1.22101	−	23.9594i	0.0559063	−	1.09703i
$478$	4.73923	−	2.73620i	0.216767	−	0.125151i
$479$	9.81892	+	9.81892i	0.448638	+	0.448638i	0.894902	−	0.446264i	$-0.147246\pi$
$479$	9.81892	+	9.81892i	0.448638	+	0.448638i	−0.446264	+	0.894902i	$0.647246\pi$
$480$	12.7527	+	23.4472i	0.582077	+	1.07021i
$481$	−0.000149912		0.00802692i	−6.83540e−6		0.000365996i
$482$	−2.52820	+	1.45966i	−0.115156	+	0.0664855i
$483$	−4.46564	−	4.69901i	−0.203193	−	0.213812i
$484$	11.9719			0.544176
$485$	−7.81366	+	13.5337i	−0.354800	+	0.614531i
$486$	5.06572	+	6.55272i	0.229786	+	0.297237i
$487$	9.96873	−	2.67111i	0.451726	−	0.121040i	−0.0257807	−	0.999668i	$-0.508207\pi$
$487$	9.96873	−	2.67111i	0.451726	−	0.121040i	0.477507	+	0.878628i	$0.341540\pi$
$488$	6.29373	−	23.4885i	0.284904	−	1.06328i
$489$	−21.8644	+	5.26585i	−0.988741	+	0.238130i
$490$	−13.9708			−0.631136
$491$	10.8153	−	18.7326i	0.488086	−	0.845389i	−0.511820	−	0.859093i	$-0.671029\pi$
$491$	10.8153	−	18.7326i	0.488086	−	0.845389i	0.999906	+	0.0137031i	$0.00436197\pi$
$492$	−5.60631	−	23.2780i	−0.252752	−	1.04945i
$493$	−18.2013	−	10.5085i	−0.819746	−	0.473281i
$494$	−6.81858	−	1.96421i	−0.306782	−	0.0883739i
$495$	8.09727	+	15.8353i	0.363945	+	0.711743i
$496$	−0.0417851	+	0.155944i	−0.00187620	+	0.00700209i
$497$		−	62.6591i		−	2.81064i
$498$	−3.83152	+	6.26260i	−0.171694	+	0.280634i
$499$	−9.65684	+	36.0398i	−0.432299	+	1.61336i	0.315148	+	0.949042i	$0.397946\pi$
$499$	−9.65684	+	36.0398i	−0.432299	+	1.61336i	−0.747448	+	0.664321i	$0.768721\pi$
$500$	−4.58857	+	4.58857i	−0.205207	+	0.205207i
$501$	0.916079	+	3.80366i	0.0409274	+	0.169935i
$502$	−3.73795	−	13.9502i	−0.166833	−	0.622630i
$503$	−33.8792	−	19.5602i	−1.51060	−	0.872146i	−0.999923	−	0.0123736i	$-0.996061\pi$
$503$	−33.8792	−	19.5602i	−1.51060	−	0.872146i	−0.510678	−	0.859772i	$-0.670605\pi$
$504$	−10.7592	−	21.0411i	−0.479254	−	0.937244i
$505$	29.7504	+	7.97161i	1.32388	+	0.354732i
$506$	−0.500521	+	0.866928i	−0.0222509	+	0.0385397i
$507$	−10.0122	−	20.1682i	−0.444658	−	0.895701i
$508$	2.32175	+	4.02139i	0.103011	+	0.178420i
$509$	−4.48749	−	16.7475i	−0.198904	−	0.742321i	−0.991221	−	0.132212i	$-0.957792\pi$
$509$	−4.48749	−	16.7475i	−0.198904	−	0.742321i	0.792317	−	0.610110i	$-0.208875\pi$
$510$	−12.9426	−	0.329575i	−0.573108	−	0.0145938i
$511$	4.17399	−	2.40985i	0.184646	−	0.106606i
$512$	15.4685	−	15.4685i	0.683617	−	0.683617i
$513$	−3.54837	−	18.9168i	−0.156664	−	0.835198i
$514$	3.11955	+	11.6423i	0.137598	+	0.513521i
$515$	−4.98315	+	1.33523i	−0.219584	+	0.0588373i
$516$	26.0993	−	14.1952i	1.14896	−	0.624907i
$517$	10.2579	+	5.92242i	0.451143	+	0.260468i
$518$	−0.00455731	+	0.00122113i	−0.000200237	+	5.36532e-5i
$519$	0.605661	−	0.329413i	0.0265856	−	0.0144596i
$520$	−15.1469	+	14.5915i	−0.664237	+	0.639881i
$521$		−	23.5604i		−	1.03220i	−0.856528	−	0.516100i	$-0.827383\pi$
$521$		−	23.5604i		−	1.03220i	0.856528	−	0.516100i	$-0.172617\pi$
$522$	4.71290	+	5.21905i	0.206278	+	0.228432i
$523$	7.50109	+	12.9923i	0.328000	+	0.568112i	0.982115	−	0.188283i	$-0.0602921\pi$
$523$	7.50109	+	12.9923i	0.328000	+	0.568112i	−0.654115	+	0.756395i	$0.726959\pi$
$524$	−6.34003	−	10.9813i	−0.276966	−	0.479718i
$525$	−18.6296	+	17.7044i	−0.813064	+	0.772684i
$526$	8.70658	+	8.70658i	0.379625	+	0.379625i
$527$	−0.227945	−	0.227945i	−0.00992944	−	0.00992944i
$528$	6.01369	−	5.71502i	0.261712	−	0.248714i
$529$	11.0596	+	19.1558i	0.480853	+	0.832862i
$530$	−6.27368	−	10.8663i	−0.272511	−	0.472003i
$531$	8.76645	+	9.70794i	0.380432	+	0.421289i
$532$			25.3732i			1.10007i
$533$	25.3961	−	14.0368i	1.10003	−	0.608000i
$534$	0.592796	−	0.322416i	0.0256528	−	0.0139523i
$535$	51.8072	−	13.8817i	2.23982	−	0.600158i
$536$	1.87020	+	1.07976i	0.0807802	+	0.0466385i
$537$	3.44370	−	1.87299i	0.148607	−	0.0808257i
$538$	−2.78224	+	0.745499i	−0.119951	+	0.0321407i
$539$	4.62648	+	17.2663i	0.199277	+	0.743710i
$540$	−24.8646	−	8.74454i	−1.07000	−	0.376305i
$541$	10.2478	−	10.2478i	0.440589	−	0.440589i	−0.451621	−	0.892210i	$-0.649154\pi$
$541$	10.2478	−	10.2478i	0.440589	−	0.440589i	0.892210	+	0.451621i	$0.149154\pi$
$542$	2.42750	−	1.40152i	0.104270	−	0.0602002i
$543$	−35.6068	−	0.906703i	−1.52803	−	0.0389103i
$544$	6.43413	+	24.0125i	0.275861	+	1.02953i
$545$	18.9459	+	32.8152i	0.811552	+	1.40565i
$546$	9.76053	−	8.93491i	0.417712	−	0.382379i
$547$	14.6364	−	25.3509i	0.625805	−	1.08393i	−0.362579	−	0.931953i	$-0.618104\pi$
$547$	14.6364	−	25.3509i	0.625805	−	1.08393i	0.988385	−	0.151974i	$-0.0485629\pi$
$548$	−12.4684	−	3.34090i	−0.532623	−	0.142716i
$549$	16.8142	+	32.8823i	0.717611	+	1.40338i
$550$	3.43702	+	1.98436i	0.146555	+	0.0846135i
$551$	−4.22937	−	15.7842i	−0.180177	−	0.672430i
$552$	−0.751808	−	3.12159i	−0.0319991	−	0.132864i
$553$	−2.82798	+	2.82798i	−0.120258	+	0.120258i
$554$	−0.373256	+	1.39301i	−0.0158581	+	0.0591833i
$555$	−0.00594378	+	0.00971509i	−0.000252300	+	0.000412383i
$556$			7.03190i			0.298219i
$557$	−7.97968	+	29.7806i	−0.338110	+	1.26184i	0.562348	+	0.826900i	$0.309898\pi$
$557$	−7.97968	+	29.7806i	−0.338110	+	1.26184i	−0.900458	+	0.434943i	$0.856769\pi$
$558$	0.0491055	+	0.0960323i	0.00207880	+	0.00406537i
$559$	24.9797	+	25.9305i	1.05653	+	1.09674i
$560$	24.3337	+	14.0491i	1.02829	+	0.593681i
$561$	3.87868	+	16.1047i	0.163758	+	0.679941i
$562$	2.04668	−	3.54495i	0.0863338	−	0.149535i
$563$	−14.1071			−0.594545			−0.297272	−	0.954793i	$-0.596077\pi$
$563$	−14.1071			−0.594545			−0.297272	+	0.954793i	$0.596077\pi$
$564$	−17.0657	+	4.11014i	−0.718596	+	0.173068i
$565$	2.68078	−	10.0048i	0.112781	−	0.420906i
$566$	−0.808261	+	0.216573i	−0.0339737	+	0.00910323i
$567$	33.5449	+	12.7658i	1.40875	+	0.536113i
$568$	15.5179	−	26.8777i	0.651116	−	1.12777i
$569$	35.6960			1.49645			0.748227	−	0.663443i	$-0.230906\pi$
$569$	35.6960			1.49645			0.748227	+	0.663443i	$0.230906\pi$
$570$	−6.93444	−	7.29683i	−0.290452	−	0.305631i
$571$	−9.63955	+	5.56540i	−0.403403	+	0.232905i	−0.687951	−	0.725757i	$-0.741490\pi$
$571$	−9.63955	+	5.56540i	−0.403403	+	0.232905i	0.284548	+	0.958662i	$0.408156\pi$
$572$	10.6496	+	6.41662i	0.445281	+	0.268292i
$573$	15.6135	+	28.7071i	0.652264	+	1.19926i
$574$	12.0581	+	12.0581i	0.503295	+	0.503295i
$575$	−3.02401	+	1.74591i	−0.126110	+	0.0728096i
$576$	−0.305248	+	5.98975i	−0.0127187	+	0.249573i
$577$	−18.9592	−	18.9592i	−0.789280	−	0.789280i	0.192096	−	0.981376i	$-0.438472\pi$
$577$	−18.9592	−	18.9592i	−0.789280	−	0.789280i	−0.981376	+	0.192096i	$0.938472\pi$
$578$	−2.92295	−	0.783201i	−0.121578	−	0.0325769i
$579$	−29.1988	+	7.03229i	−1.21346	+	0.292252i
$580$	−21.6157	−	5.79192i	−0.897545	−	0.240496i
$581$			31.8150i			1.31991i
$582$	4.27814	−	2.32684i	0.177335	−	0.0964506i
$583$	−11.3520	+	11.3520i	−0.470150	+	0.470150i
$584$	2.38726			0.0987854
$585$	2.22114	−	31.8652i	0.0918326	−	1.31746i
$586$	1.54333			0.0637542
$587$	23.4259	−	23.4259i	0.966890	−	0.966890i	−0.0325791	−	0.999469i	$-0.510372\pi$
$587$	23.4259	−	23.4259i	0.966890	−	0.966890i	0.999469	+	0.0325791i	$0.0103721\pi$
$588$	−22.5970	−	13.8251i	−0.931886	−	0.570137i
$589$		−	0.250641i		−	0.0103275i
$590$	6.60807	+	1.77063i	0.272050	+	0.0728956i
$591$	−5.31636	+	17.9954i	−0.218686	+	0.740231i
$592$	0.00513150	+	0.00137498i	0.000210903	+	5.65114e-5i
$593$	−17.3464	−	17.3464i	−0.712332	−	0.712332i	0.254690	−	0.967023i	$-0.418026\pi$
$593$	−17.3464	−	17.3464i	−0.712332	−	0.712332i	−0.967023	+	0.254690i	$0.918026\pi$
$594$	0.422907	−	5.52636i	0.0173521	−	0.226749i
$595$	−48.5879	+	28.0523i	−1.99191	+	1.15003i
$596$	19.8452	+	19.8452i	0.812891	+	0.812891i
$597$	−10.4489	+	17.0787i	−0.427645	+	0.698984i
$598$	1.57351	−	0.869701i	0.0643456	−	0.0355647i
$599$	−21.4691	+	12.3952i	−0.877204	+	0.506454i	−0.869735	−	0.493518i	$-0.835711\pi$
$599$	−21.4691	+	12.3952i	−0.877204	+	0.506454i	−0.00746823	+	0.999972i	$0.502377\pi$
$600$	−12.3758	+	2.98061i	−0.505241	+	0.121683i
$601$	−11.1172			−0.453479			−0.226739	−	0.973955i	$-0.572807\pi$
$601$	−11.1172			−0.453479			−0.226739	+	0.973955i	$0.572807\pi$
$602$	−10.5798	+	18.3247i	−0.431199	+	0.746858i
$603$	−3.20713	+	0.686533i	−0.130605	+	0.0279578i
$604$	−30.5048	+	8.17374i	−1.24122	+	0.332585i
$605$	−5.32706	+	19.8809i	−0.216576	+	0.808272i
$606$	−6.61202	−	6.95756i	−0.268595	−	0.282632i
$607$	−29.6350			−1.20285			−0.601424	−	0.798930i	$-0.705400\pi$
$607$	−29.6350			−1.20285			−0.601424	+	0.798930i	$0.705400\pi$
$608$	−9.66431	+	16.7391i	−0.391939	+	0.678859i
$609$	29.2245	+	8.63379i	1.18424	+	0.349859i
$610$	16.7280	+	9.65793i	0.677298	+	0.391038i
$611$	−10.2907	−	18.6185i	−0.416319	−	0.753226i
$612$	−20.6079	−	13.3407i	−0.833025	−	0.539266i
$613$	9.99926	−	37.3178i	0.403866	−	1.50725i	−0.402270	−	0.915521i	$-0.631779\pi$
$613$	9.99926	−	37.3178i	0.403866	−	1.50725i	0.806137	−	0.591729i	$-0.201555\pi$
$614$		−	8.19650i		−	0.330784i
$615$	41.1508	+	1.04788i	1.65936	+	0.0422544i
$616$	−4.09307	+	15.2756i	−0.164915	+	0.615470i
$617$	24.2646	−	24.2646i	0.976857	−	0.976857i	−0.0228808	−	0.999738i	$-0.507284\pi$
$617$	24.2646	−	24.2646i	0.976857	−	0.976857i	0.999738	+	0.0228808i	$0.00728381\pi$
$618$	1.54182	+	0.455497i	0.0620209	+	0.0183228i
$619$	5.54966	+	20.7116i	0.223060	+	0.832470i	0.983173	+	0.182679i	$0.0584770\pi$
$619$	5.54966	+	20.7116i	0.223060	+	0.832470i	−0.760113	+	0.649791i	$0.774856\pi$
$620$	−0.297256	−	0.171621i	−0.0119381	−	0.00689245i
$621$	4.02482	+	2.75338i	0.161511	+	0.110489i
$622$	−11.4774	−	3.07537i	−0.460204	−	0.123311i
$623$	1.46212	−	2.53246i	0.0585785	−	0.101461i
$624$	−14.5482	+	3.21764i	−0.582395	+	0.128809i
$625$	−14.8799	−	25.7728i	−0.595198	−	1.03091i
$626$	1.58237	+	5.90549i	0.0632442	+	0.236031i
$627$	−6.72167	+	10.9865i	−0.268437	+	0.438760i
$628$	24.8849	−	14.3673i	0.993017	−	0.573318i
$629$	−0.00750078	+	0.00750078i	−0.000299076	+	0.000299076i
$630$	18.3561	−	3.92938i	0.731323	−	0.156550i
$631$	−8.09616	−	30.2153i	−0.322303	−	1.20285i	−0.916996	−	0.398897i	$-0.869393\pi$
$631$	−8.09616	−	30.2153i	−0.322303	−	1.20285i	0.594693	−	0.803953i	$-0.297274\pi$
$632$	−1.91344	+	0.512704i	−0.0761124	+	0.0203943i
$633$	11.6169	+	7.10732i	0.461730	+	0.282491i
$634$	0.675113	+	0.389776i	0.0268121	+	0.0154800i
$635$	−7.71114	+	2.06619i	−0.306007	+	0.0819944i
$636$	0.605643	−	23.7840i	0.0240153	−	0.943097i
$637$	8.88671	−	30.8495i	0.352104	−	1.22230i
$638$		−	4.70576i		−	0.186303i
$639$	9.86659	+	46.0917i	0.390316	+	1.82336i
$640$	16.9783	+	29.4074i	0.671128	+	1.16243i
$641$	8.80502	+	15.2507i	0.347778	+	0.602368i	0.985854	−	0.167604i	$-0.0536031\pi$
$641$	8.80502	+	15.2507i	0.347778	+	0.602368i	−0.638077	+	0.769973i	$0.720270\pi$
$642$	−16.0295	−	4.73557i	−0.632632	−	0.186898i
$643$	16.3953	+	16.3953i	0.646567	+	0.646567i	0.952162	−	0.305595i	$-0.0988553\pi$
$643$	16.3953	+	16.3953i	0.646567	+	0.646567i	−0.305595	+	0.952162i	$0.598855\pi$
$644$	−4.54582	−	4.54582i	−0.179130	−	0.179130i
$645$	11.9596	+	49.6577i	0.470910	+	1.95527i
$646$	−4.68782	−	8.11955i	−0.184440	−	0.319459i
$647$	7.72825	+	13.3857i	0.303829	+	0.526247i	0.977000	−	0.213240i	$-0.0684015\pi$
$647$	7.72825	+	13.3857i	0.303829	+	0.526247i	−0.673171	+	0.739487i	$0.735068\pi$
$648$	11.2276	+	13.7835i	0.441064	+	0.541467i
$649$		−	8.75316i		−	0.343592i
$650$	−3.44801	−	6.23832i	−0.135242	−	0.244687i
$651$	0.398702	+	0.243930i	0.0156264	+	0.00956036i
$652$	−21.5432	+	5.77249i	−0.843698	+	0.226068i
$653$	30.3329	+	17.5127i	1.18702	+	0.685325i	0.957627	−	0.288010i	$-0.0929937\pi$
$653$	30.3329	+	17.5127i	1.18702	+	0.685325i	0.229390	+	0.973335i	$0.426327\pi$
$654$	0.300593	−	11.8045i	0.0117541	−	0.461591i
$655$	21.0569	−	5.64218i	0.822761	−	0.220458i
$656$	−4.96965	−	18.5470i	−0.194032	−	0.724139i
$657$	−2.69090	+	2.42993i	−0.104982	+	0.0948006i
$658$	8.84012	−	8.84012i	0.344624	−	0.344624i
$659$	−9.72722	+	5.61601i	−0.378919	+	0.218769i	−0.677348	−	0.735663i	$-0.736871\pi$
$659$	−9.72722	+	5.61601i	−0.378919	+	0.218769i	0.298429	+	0.954432i	$0.403537\pi$
$660$	8.42732	+	15.4945i	0.328033	+	0.603124i
$661$	−7.08485	−	26.4410i	−0.275569	−	1.02844i	−0.955459	−	0.295123i	$-0.904639\pi$
$661$	−7.08485	−	26.4410i	−0.275569	−	1.02844i	0.679890	−	0.733314i	$-0.262027\pi$
$662$	1.50454	+	2.60594i	0.0584757	+	0.101283i
$663$	8.96045	−	28.3695i	0.347995	−	1.10178i
$664$	−7.87917	+	13.6471i	−0.305771	+	0.529611i
$665$	−42.1355	−	11.2902i	−1.63395	−	0.437814i
$666$	0.00316005	−	0.00161587i	0.000122449	−	6.26136e-5i
$667$	3.58560	+	2.07015i	0.138835	+	0.0801564i
$668$	1.00422	+	3.74779i	0.0388543	+	0.145006i
$669$	6.09430	−	5.79164i	0.235619	−	0.223918i
$670$	−1.21295	+	1.21295i	−0.0468604	+	0.0468604i
$671$	6.39652	−	23.8721i	0.246935	−	0.921574i
$672$	−17.2218	−	31.6642i	−0.664346	−	1.22147i
$673$			19.0851i			0.735676i	0.929890	+	0.367838i	$0.119902\pi$
$673$			19.0851i			0.735676i	−0.929890	+	0.367838i	$0.880098\pi$
$674$	−3.25059	+	12.1314i	−0.125208	+	0.467283i
$675$	10.9160	−	15.9568i	0.420158	−	0.614177i
$676$	−10.4352	−	19.7418i	−0.401352	−	0.759300i
$677$	−44.6358	−	25.7705i	−1.71549	−	0.990440i	−0.926718	−	0.375758i	$-0.877382\pi$
$677$	−44.6358	−	25.7705i	−1.71549	−	0.990440i	−0.788775	−	0.614682i	$-0.789284\pi$
$678$	−2.33977	+	2.22357i	−0.0898582	+	0.0853955i
$679$	10.5519	−	18.2765i	0.404946	−	0.701387i
$680$	−27.7892			−1.06567
$681$	7.29740	−	24.7010i	0.279637	−	0.946545i
$682$	0.0186809	−	0.0697182i	0.000715330	−	0.00266965i
$683$	−0.321997	+	0.0862789i	−0.0123209	+	0.00330137i	−0.264974	−	0.964255i	$-0.585363\pi$
$683$	−0.321997	+	0.0862789i	−0.0123209	+	0.00330137i	0.252653	+	0.967557i	$0.418697\pi$
$684$	−3.99538	−	18.6644i	−0.152767	−	0.713650i
$685$	11.0960	−	19.2188i	0.423956	−	0.734313i
$686$	4.03447			0.154037
$687$	−0.914530	+	3.09560i	−0.0348915	+	0.118104i
$688$	20.6335	−	11.9127i	0.786644	−	0.454169i
$689$	27.9850	−	6.94118i	1.06615	−	0.264438i
$690$	2.54965	+	0.0649251i	0.0970635	+	0.00247166i
$691$	−0.661397	−	0.661397i	−0.0251607	−	0.0251607i	0.694414	−	0.719575i	$-0.255663\pi$
$691$	−0.661397	−	0.661397i	−0.0251607	−	0.0251607i	−0.719575	+	0.694414i	$0.755663\pi$
$692$	0.592131	−	0.341867i	0.0225094	−	0.0129958i
$693$	−10.9349	−	21.3847i	−0.415384	−	0.812339i
$694$	5.47479	+	5.47479i	0.207820	+	0.207820i
$695$	−11.6774	−	3.12895i	−0.442949	−	0.118688i
$696$	10.3977	+	10.9411i	0.394125	+	0.414722i
$697$	37.0334	+	9.92308i	1.40274	+	0.375864i
$698$			2.17947i			0.0824942i
$699$	−0.103583	+	4.06777i	−0.00391786	+	0.153857i
$700$	−18.0223	+	18.0223i	−0.681179	+	0.681179i
$701$	14.5438			0.549312			0.274656	−	0.961543i	$-0.411436\pi$
$701$	14.5438			0.549312			0.274656	+	0.961543i	$0.411436\pi$
$702$	−5.77286	+	8.10941i	−0.217883	+	0.306070i
$703$	−0.00824761			−0.000311064
$704$	2.83794	−	2.83794i	0.106959	−	0.106959i
$705$	0.768226	−	30.1687i	0.0289331	−	1.13622i
$706$			0.474914i			0.0178736i
$707$	−40.1764	−	10.7652i	−1.51099	−	0.404868i
$708$	8.93607	+	9.40306i	0.335838	+	0.353389i
$709$	−26.8319	−	7.18959i	−1.00769	−	0.270011i	−0.283028	−	0.959112i	$-0.591339\pi$
$709$	−26.8319	−	7.18959i	−1.00769	−	0.270011i	−0.724666	+	0.689101i	$0.758006\pi$
$710$	17.4321	+	17.4321i	0.654214	+	0.654214i
$711$	1.63494	−	2.52556i	0.0613151	−	0.0947158i
$712$	1.25436	−	0.724203i	0.0470090	−	0.0271407i
$713$	0.0449044	+	0.0449044i	0.00168168	+	0.00168168i
$714$	17.4783	+	0.445073i	0.654110	+	0.0166565i
$715$	−15.3943	+	14.8298i	−0.575715	+	0.554605i
$716$	3.36677	−	1.94381i	0.125822	−	0.0726435i
$717$	−5.05432	+	17.1084i	−0.188757	+	0.638925i
$718$	−4.71425			−0.175934
$719$	17.0187	−	29.4773i	0.634691	−	1.09932i	−0.351890	−	0.936041i	$-0.614461\pi$
$719$	17.0187	−	29.4773i	0.634691	−	1.09932i	0.986581	−	0.163275i	$-0.0522058\pi$
$720$	−20.1120	−	6.50272i	−0.749528	−	0.242342i
$721$	6.72948	−	1.80316i	0.250619	−	0.0671531i
$722$	−0.726103	+	2.70985i	−0.0270228	+	0.100850i
$723$	2.69629	−	9.12668i	0.100276	−	0.339425i
$724$	−35.3232			−1.31278
$725$	8.20728	−	14.2154i	0.304811	−	0.527948i
$726$	4.64942	−	4.41851i	0.172556	−	0.163986i
$727$	−4.19076	−	2.41953i	−0.155427	−	0.0897355i	0.420270	−	0.907399i	$-0.361936\pi$
$727$	−4.19076	−	2.41953i	−0.155427	−	0.0897355i	−0.575696	+	0.817664i	$0.695269\pi$
$728$	20.4552	−	19.7051i	0.758118	−	0.730320i
$729$	−26.6856	−	4.10831i	−0.988356	−	0.152160i
$730$	−0.490792	+	1.83166i	−0.0181650	+	0.0677928i
$731$			47.5732i			1.75956i
$732$	17.4995	+	32.1748i	0.646801	+	1.18921i
$733$	−3.22240	+	12.0262i	−0.119022	+	0.444196i	−0.999556	−	0.0297863i	$-0.990517\pi$
$733$	−3.22240	+	12.0262i	−0.119022	+	0.444196i	0.880534	+	0.473982i	$0.157184\pi$
$734$	−8.43255	+	8.43255i	−0.311251	+	0.311251i
$735$	33.0132	−	31.3737i	1.21771	−	1.15724i
$736$	−1.26750	−	4.73038i	−0.0467208	−	0.174364i
$737$	1.90074	+	1.09739i	0.0700147	+	0.0404230i
$738$	−10.7686	−	6.97114i	−0.396397	−	0.256611i
$739$	−22.8438	−	6.12098i	−0.840323	−	0.225164i	−0.187111	−	0.982339i	$-0.559912\pi$
$739$	−22.8438	−	6.12098i	−0.840323	−	0.225164i	−0.653212	+	0.757175i	$0.726579\pi$
$740$	−0.00564736	+	0.00978151i	−0.000207601	+	0.000359575i
$741$	20.5234	−	10.6708i	0.753946	−	0.392001i
$742$	8.47228	+	14.6744i	0.311027	+	0.538715i
$743$	−3.36460	−	12.5569i	−0.123435	−	0.460667i	0.876344	−	0.481686i	$-0.159976\pi$
$743$	−3.36460	−	12.5569i	−0.123435	−	0.460667i	−0.999779	+	0.0210193i	$0.993309\pi$
$744$	0.110614	+	0.203375i	0.00405529	+	0.00745609i
$745$	−41.7859	+	24.1251i	−1.53092	+	0.883876i
$746$	13.6028	−	13.6028i	0.498033	−	0.498033i
$747$	−5.00974	−	23.4029i	−0.183297	−	0.856269i
$748$	4.25186	+	15.8681i	0.155463	+	0.580197i
$749$	−69.9629	+	18.7465i	−2.55639	+	0.684983i
$750$	−0.0885026	+	3.47555i	−0.00323166	+	0.126909i
$751$	−9.25978	−	5.34613i	−0.337894	−	0.195083i	0.321446	−	0.946928i	$-0.395831\pi$
$751$	−9.25978	−	5.34613i	−0.337894	−	0.195083i	−0.659340	+	0.751845i	$0.729164\pi$
$752$	−13.5973	+	3.64339i	−0.495843	+	0.132861i
$753$	40.1604	+	24.5705i	1.46353	+	0.895399i
$754$	−4.36168	+	7.23903i	−0.158843	+	0.263630i
$755$		−	54.2943i		−	1.97597i
$756$	33.5784	+	11.8090i	1.22124	+	0.429491i
$757$	9.51134	+	16.4741i	0.345696	+	0.598762i	0.985480	−	0.169792i	$-0.0543097\pi$
$757$	9.51134	+	16.4741i	0.345696	+	0.598762i	−0.639784	+	0.768554i	$0.720976\pi$
$758$	3.09757	+	5.36514i	0.112509	+	0.194871i
$759$	−0.764087	−	3.17257i	−0.0277346	−	0.115157i
$760$	−15.2780	−	15.2780i	−0.554193	−	0.554193i
$761$	−1.88870	−	1.88870i	−0.0684654	−	0.0684654i	0.672045	−	0.740510i	$-0.265416\pi$
$761$	−1.88870	−	1.88870i	−0.0684654	−	0.0684654i	−0.740510	+	0.672045i	$0.765416\pi$
$762$	2.38587	+	0.704856i	0.0864310	+	0.0255343i
$763$	−25.5854	−	44.3152i	−0.926254	−	1.60432i
$764$	16.2038	+	28.0658i	0.586233	+	1.01539i
$765$	31.3238	−	28.2860i	1.13251	−	1.02268i
$766$		−	13.4388i		−	0.485565i
$767$	−8.11315	+	13.4653i	−0.292949	+	0.486203i
$768$	0.0930843	−	3.65548i	0.00335889	−	0.131906i
$769$	10.9935	−	2.94569i	0.396435	−	0.106224i	−0.0550934	−	0.998481i	$-0.517546\pi$
$769$	10.9935	−	2.94569i	0.396435	−	0.106224i	0.451528	+	0.892257i	$0.350879\pi$
$770$	−10.8789	−	6.28095i	−0.392049	−	0.226350i
$771$	−33.5163	−	20.5056i	−1.20706	−	0.738491i
$772$	−28.7699	+	7.70888i	−1.03545	+	0.277449i
$773$	11.3980	+	42.5378i	0.409956	+	1.52998i	0.794728	+	0.606966i	$0.207613\pi$
$773$	11.3980	+	42.5378i	0.409956	+	1.52998i	−0.384772	+	0.923012i	$0.625720\pi$
$774$	4.89692	−	15.1455i	0.176016	−	0.544392i
$775$	0.178028	−	0.178028i	0.00639494	−	0.00639494i
$776$	9.05255	−	5.22649i	0.324968	−	0.187620i
$777$	0.00802677	−	0.0131197i	0.000287959	−	0.000470668i
$778$	0.267990	+	1.00015i	0.00960790	+	0.0358572i
$779$	14.9048	+	25.8159i	0.534021	+	0.924952i
$780$	1.39757	−	31.6469i	0.0500412	−	1.13314i
$781$	15.7713	−	27.3167i	0.564342	−	0.977469i
$782$	2.29455	+	0.614822i	0.0820528	+	0.0219860i
$783$	−22.8569	−	1.74913i	−0.816840	−	0.0625089i
$784$	−18.3978	−	10.6220i	−0.657063	−	0.379356i
$785$	12.7859	+	47.7176i	0.456348	+	1.70312i
$786$	−6.51513	−	1.92476i	−0.232387	−	0.0686539i
$787$	22.8022	−	22.8022i	0.812812	−	0.812812i	−0.172242	−	0.985055i	$-0.555101\pi$
$787$	22.8022	−	22.8022i	0.812812	−	0.812812i	0.985055	+	0.172242i	$0.0551013\pi$
$788$	−4.81630	+	17.9747i	−0.171574	+	0.640321i
$789$	−40.1259	−	1.02178i	−1.42852	−	0.0363762i
$790$		−	1.57352i		−	0.0559833i
$791$	−3.62026	+	13.5110i	−0.128721	+	0.480395i
$792$	0.605482	−	11.8811i	0.0215149	−	0.422177i
$793$	−31.9667	+	30.7945i	−1.13517	+	1.09355i
$794$	13.6915	+	7.90477i	0.485892	+	0.280530i
$795$	39.2269	+	11.5888i	1.39124	+	0.411012i
$796$	−9.92779	+	17.1954i	−0.351881	+	0.609476i
$797$	32.7755			1.16097			0.580483	−	0.814272i	$-0.302864\pi$
$797$	32.7755			1.16097			0.580483	+	0.814272i	$0.302864\pi$
$798$	9.36460	+	9.85399i	0.331503	+	0.348827i
$799$	7.27488	−	27.1502i	0.257367	−	0.960506i
$800$	−18.7540	+	5.02513i	−0.663055	+	0.177665i
$801$	−0.676752	+	2.09310i	−0.0239119	+	0.0739559i
$802$	−5.72783	+	9.92090i	−0.202257	+	0.350319i
$803$	2.42625			0.0856203
$804$	−3.16219	+	0.761587i	−0.111522	+	0.0268591i
$805$	9.57166	−	5.52620i	0.337357	−	0.194773i
$806$	−0.0933581	+	0.0899349i	−0.00328840	+	0.00316782i
$807$	4.90035	−	8.00961i	0.172501	−	0.281951i
$808$	−14.5677	−	14.5677i	−0.512489	−	0.512489i
$809$	−31.0324	+	17.9166i	−1.09104	+	0.629912i	−0.933853	−	0.357656i	$-0.883576\pi$
$809$	−31.0324	+	17.9166i	−1.09104	+	0.629912i	−0.157187	+	0.987569i	$0.550243\pi$
$810$	−12.8839	+	5.78086i	−0.452693	+	0.203119i
$811$	12.8808	+	12.8808i	0.452304	+	0.452304i	0.896119	−	0.443814i	$-0.146375\pi$
$811$	12.8808	+	12.8808i	0.452304	+	0.452304i	−0.443814	+	0.896119i	$0.646375\pi$
$812$	29.1909	+	7.82168i	1.02440	+	0.274487i
$813$	−2.58889	+	8.76315i	−0.0907963	+	0.307337i
$814$	−0.00229415		0.000614716i	−8.04100e−5		2.15458e-5i
$815$		−	38.3439i		−	1.34313i
$816$	−16.7932	−	10.2743i	−0.587881	−	0.359671i
$817$	−26.1550	+	26.1550i	−0.915046	+	0.915046i
$818$	−8.87803			−0.310413
$819$	−2.99953	+	43.0323i	−0.104812	+	1.50367i
$820$	40.8230			1.42560
$821$	−32.5258	+	32.5258i	−1.13516	+	1.13516i	−0.145852	+	0.989306i	$0.546592\pi$
$821$	−32.5258	+	32.5258i	−1.13516	+	1.13516i	−0.989306	+	0.145852i	$0.953408\pi$
$822$	−6.07529	+	3.30429i	−0.211900	+	0.115250i
$823$		−	39.1887i		−	1.36603i	−0.730403	−	0.683016i	$-0.760668\pi$
$823$		−	39.1887i		−	1.36603i	0.730403	−	0.683016i	$-0.239332\pi$
$824$	3.33319	+	0.893125i	0.116117	+	0.0311135i
$825$	−12.5779	+	3.02929i	−0.437908	+	0.105466i
$826$	−8.92386	−	2.39114i	−0.310501	−	0.0831984i
$827$	40.0423	+	40.0423i	1.39241	+	1.39241i	0.819902	+	0.572503i	$0.194028\pi$
$827$	40.0423	+	40.0423i	1.39241	+	1.39241i	0.572503	+	0.819902i	$0.305972\pi$
$828$	4.05968	+	2.62807i	0.141084	+	0.0913319i
$829$	30.1978	−	17.4347i	1.04881	−	0.605532i	0.126496	−	0.991967i	$-0.459627\pi$
$829$	30.1978	−	17.4347i	1.04881	−	0.605532i	0.922317	+	0.386435i	$0.126294\pi$
$830$	−8.85110	−	8.85110i	−0.307226	−	0.307226i
$831$	−2.24622	−	4.12991i	−0.0779205	−	0.143265i
$832$	−6.99614	+	1.73526i	−0.242547	+	0.0601595i
$833$	36.7355	−	21.2092i	1.27281	−	0.734857i
$834$	2.59529	+	2.73092i	0.0898677	+	0.0945641i
$835$	−6.67053			−0.230843
$836$	−6.38644	+	11.0616i	−0.220880	+	0.382575i
$837$	−0.331694	−	0.116652i	−0.0114650	−	0.00403208i
$838$	−2.56393	+	0.687003i	−0.0885695	+	0.0237321i
$839$	0.814322	−	3.03909i	0.0281135	−	0.104921i	−0.950443	−	0.310898i	$-0.899370\pi$
$839$	0.814322	−	3.03909i	0.0281135	−	0.104921i	0.978557	+	0.205977i	$0.0660370\pi$
$840$	39.1722	−	9.43430i	1.35157	−	0.325514i
$841$	9.53709			0.328865
$842$	3.14750	−	5.45163i	0.108470	−	0.187875i
$843$	3.12442	+	12.9729i	0.107611	+	0.446811i
$844$	11.6963	+	6.75287i	0.402604	+	0.232443i
$845$	37.4271	−	8.54454i	1.28753	−	0.293941i
$846$	−5.11073	+	7.89474i	−0.175711	+	0.271427i
$847$	7.19391	−	26.8481i	0.247186	−	0.922510i
$848$		−	19.0795i		−	0.655192i
$849$	1.42359	−	2.32685i	0.0488574	−	0.0798572i
$850$	2.43752	−	9.09694i	0.0836062	−	0.312022i
$851$	0.00147763	−	0.00147763i	5.06524e−5	−	5.06524e-5i
$852$	10.9452	+	45.4458i	0.374978	+	1.55695i
$853$	13.2618	+	49.4936i	0.454074	+	1.69463i	0.690795	+	0.723051i	$0.257261\pi$
$853$	13.2618	+	49.4936i	0.454074	+	1.69463i	−0.236720	+	0.971578i	$0.576072\pi$
$854$	−22.5903	−	13.0425i	−0.773025	−	0.446306i
$855$	32.7725	+	1.67014i	1.12079	+	0.0571175i
$856$	−34.6534	−	9.28536i	−1.18443	−	0.317367i
$857$	2.28955	−	3.96562i	0.0782096	−	0.135463i	−0.824268	−	0.566200i	$-0.808413\pi$
$857$	2.28955	−	3.96562i	0.0782096	−	0.135463i	0.902478	+	0.430737i	$0.141746\pi$
$858$	6.50410	−	1.43852i	0.222046	−	0.0491101i
$859$	24.3962	+	42.2555i	0.832388	+	1.44174i	0.896139	+	0.443773i	$0.146360\pi$
$859$	24.3962	+	42.2555i	0.832388	+	1.44174i	−0.0637513	+	0.997966i	$0.520306\pi$
$860$	13.1103	+	48.9283i	0.447057	+	1.66844i
$861$	−55.5720	−	1.41510i	−1.89389	−	0.0482265i
$862$	0.656378	−	0.378960i	0.0223563	−	0.0129074i
$863$	−17.8688	+	17.8688i	−0.608261	+	0.608261i	−0.942491	−	0.334230i	$-0.891524\pi$
$863$	−17.8688	+	17.8688i	−0.608261	+	0.608261i	0.334230	+	0.942491i	$0.391524\pi$
$864$	17.6543	+	20.5802i	0.600610	+	0.700151i
$865$	0.304237	+	1.13543i	0.0103444	+	0.0386058i
$866$	−19.4922	+	5.22291i	−0.662371	+	0.177482i
$867$	8.66578	−	4.71323i	0.294305	−	0.160070i
$868$	0.401428	+	0.231765i	0.0136254	+	0.00786660i
$869$	−1.94469	+	0.521077i	−0.0659690	+	0.0176763i
$870$	−10.5324	+	5.72846i	−0.357081	+	0.194213i
$871$	−1.90682	−	3.44992i	−0.0646102	−	0.116896i
$872$		−	25.3455i		−	0.858307i
$873$	−4.88404	+	15.1056i	−0.165300	+	0.511248i
$874$	0.923485	+	1.59952i	0.0312374	+	0.0541047i
$875$	7.53303	+	13.0476i	0.254663	+	0.441089i
$876$	−2.60639	+	2.47694i	−0.0880617	+	0.0836882i
$877$	−7.74361	−	7.74361i	−0.261483	−	0.261483i	0.564173	−	0.825656i	$-0.309195\pi$
$877$	−7.74361	−	7.74361i	−0.261483	−	0.261483i	−0.825656	+	0.564173i	$0.809195\pi$
$878$	5.55427	+	5.55427i	0.187447	+	0.187447i
$879$	−3.64691	+	3.46579i	−0.123007	+	0.116898i
$880$	7.07231	+	12.2496i	0.238407	+	0.412934i
$881$	24.9112	+	43.1474i	0.839279	+	1.45367i	0.890498	+	0.454987i	$0.150356\pi$
$881$	24.9112	+	43.1474i	0.839279	+	1.45367i	−0.0512192	+	0.998687i	$0.516311\pi$
$882$	−13.8783	+	2.97085i	−0.467307	+	0.100034i
$883$		−	10.5403i		−	0.354711i	−0.984147	−	0.177355i	$-0.943246\pi$
$883$		−	10.5403i		−	0.354711i	0.984147	−	0.177355i	$-0.0567542\pi$
$884$	8.16712	−	28.3515i	0.274690	−	0.953563i
$885$	−19.5912	+	10.6555i	−0.658552	+	0.358180i
$886$	12.2927	−	3.29383i	0.412982	−	0.110658i
$887$	29.5392	+	17.0545i	0.991831	+	0.572634i	0.905821	−	0.423661i	$-0.139255\pi$
$887$	29.5392	+	17.0545i	0.991831	+	0.572634i	0.0860096	+	0.996294i	$0.472588\pi$
$888$	0.00669228	−	0.00363986i	0.000224578	−	0.000122146i
$889$	10.4135	−	2.79029i	0.349257	−	0.0935832i
$890$	0.297775	+	1.11131i	0.00998145	+	0.0372513i
$891$	11.4110	+	14.0086i	0.382283	+	0.469306i
$892$	5.89563	−	5.89563i	0.197400	−	0.197400i
$893$	18.9264	−	10.9271i	0.633346	−	0.365663i
$894$	15.0315	+	0.382766i	0.502728	+	0.0128016i
$895$	1.72985	+	6.45589i	0.0578225	+	0.215797i
$896$	−22.9284	−	39.7131i	−0.765983	−	1.32672i
$897$	−1.76518	+	5.58869i	−0.0589376	+	0.186601i
$898$	6.76445	−	11.7164i	0.225733	−	0.390980i
$899$	−0.288353	−	0.0772640i	−0.00961712	−	0.00257690i
$900$	10.4192	−	16.0950i	0.347308	−	0.536500i
$901$	32.9927	+	19.0483i	1.09914	+	0.634592i
$902$	2.22179	+	8.29185i	0.0739777	+	0.276088i
$903$	−16.1509	−	67.0601i	−0.537467	−	2.23162i
$904$	−4.89899	+	4.89899i	−0.162938	+	0.162938i
$905$	15.7176	−	58.6587i	0.522469	−	1.94988i
$906$	−8.83020	+	14.4329i	−0.293364	+	0.479502i
$907$		−	54.8784i		−	1.82221i	−0.412177	−	0.911104i	$-0.635231\pi$
$907$		−	54.8784i		−	1.82221i	0.412177	−	0.911104i	$-0.364769\pi$
$908$	6.61100	−	24.6726i	0.219394	−	0.818789i
$909$	31.2487	+	1.59249i	1.03645	+	0.0528194i
$910$	10.9137	+	19.7457i	0.361786	+	0.654563i
$911$	−36.5277	−	21.0893i	−1.21022	−	0.698719i	−0.247410	−	0.968911i	$-0.579579\pi$
$911$	−36.5277	−	21.0893i	−1.21022	−	0.698719i	−0.962806	+	0.270192i	$0.912913\pi$
$912$	−3.58403	−	14.8813i	−0.118679	−	0.492768i
$913$	−8.00785	+	13.8700i	−0.265021	+	0.459030i
$914$	15.4029			0.509483
$915$	−61.2171	+	14.7436i	−2.02377	+	0.487409i
$916$	−0.828508	+	3.09203i	−0.0273747	+	0.102164i
$917$	−28.4363	+	7.61947i	−0.939048	+	0.251617i
$918$	−12.9270	+	2.42482i	−0.426656	+	0.0800311i
$919$	6.26475	−	10.8509i	0.206655	−	0.357937i	−0.744004	−	0.668175i	$-0.767076\pi$
$919$	6.26475	−	10.8509i	0.206655	−	0.357937i	0.950659	+	0.310239i	$0.100409\pi$
$920$	5.47438			0.180485
$921$	18.4066	+	19.3685i	0.606517	+	0.638214i
$922$	−9.84335	+	5.68306i	−0.324173	+	0.187162i
$923$	−49.5809	+	27.4041i	−1.63198	+	0.902017i
$924$	−11.3807	−	20.9246i	−0.374396	−	0.688368i
$925$	−0.00585819	−	0.00585819i	−0.000192616	−	0.000192616i
$926$	−1.56866	+	0.905669i	−0.0515495	+	0.0297621i
$927$	−4.66623	+	2.38605i	−0.153259	+	0.0783681i
$928$	16.2785	+	16.2785i	0.534368	+	0.534368i
$929$	−14.3907	−	3.85598i	−0.472144	−	0.126511i	0.0148982	−	0.999889i	$-0.495258\pi$
$929$	−14.3907	−	3.85598i	−0.472144	−	0.126511i	−0.487042	+	0.873378i	$0.661924\pi$
$930$	−0.178784	+	0.0430585i	−0.00586254	+	0.00141194i
$931$	31.8571	+	8.53607i	1.04407	+	0.279759i
$932$			4.03536i			0.132183i
$933$	34.0277	−	18.5073i	1.11402	−	0.605902i
$934$	−1.56875	+	1.56875i	−0.0513312	+	0.0513312i
$935$	−28.2431			−0.923647
$936$	−11.9438	+	17.7159i	−0.390396	+	0.579063i
$937$	15.7594			0.514837			0.257418	−	0.966300i	$-0.417128\pi$
$937$	15.7594			0.514837			0.257418	+	0.966300i	$0.417128\pi$
$938$	1.63803	−	1.63803i	0.0534835	−	0.0534835i
$939$	−17.0009	−	10.4013i	−0.554804	−	0.339434i
$940$		−	29.9284i		−	0.976157i
$941$	−44.2231	−	11.8495i	−1.44163	−	0.386284i	−0.548526	−	0.836133i	$-0.684811\pi$
$941$	−44.2231	−	11.8495i	−1.44163	−	0.386284i	−0.893104	+	0.449850i	$0.851478\pi$
$942$	4.36175	−	14.7641i	0.142114	−	0.481041i
$943$	−7.29546	−	1.95481i	−0.237573	−	0.0636575i
$944$	7.35580	+	7.35580i	0.239411	+	0.239411i
$945$	−34.5517	+	50.5067i	−1.12397	+	1.64298i
$946$	−9.22465	+	5.32586i	−0.299919	+	0.173159i
$947$	−12.6619	−	12.6619i	−0.411455	−	0.411455i	0.470790	−	0.882245i	$-0.343969\pi$
$947$	−12.6619	−	12.6619i	−0.411455	−	0.411455i	−0.882245	+	0.470790i	$0.843969\pi$
$948$	1.55711	−	2.54509i	0.0505725	−	0.0826606i
$949$	−3.73238	−	2.24884i	−0.121158	−	0.0730005i
$950$	6.34146	−	3.66124i	0.205744	−	0.118786i
$951$	−2.47061	+	0.595026i	−0.0801151	+	0.0192950i
$952$	37.5279			1.21629
$953$	−14.3666	+	24.8836i	−0.465379	+	0.806060i	−0.999219	−	0.0395258i	$-0.987415\pi$
$953$	−14.3666	+	24.8836i	−0.465379	+	0.806060i	0.533840	+	0.845586i	$0.320749\pi$
$954$	−8.54286	−	9.46033i	−0.276585	−	0.306290i
$955$	−53.8171	+	14.4202i	−1.74148	+	0.466628i
$956$	−4.57891	+	17.0887i	−0.148092	+	0.552689i
$957$	10.5675	+	11.1198i	0.341600	+	0.359452i
$958$	7.37797			0.238371
$959$	−14.9846	+	25.9540i	−0.483877	+	0.838099i
$960$	−9.80656	−	2.89715i	−0.316505	−	0.0935050i
$961$	26.8428	+	15.4977i	0.865897	+	0.499926i
$962$	0.00295940	+	0.00307205i	9.54150e−5	+	9.90468e-5i
$963$	48.5124	−	24.8065i	1.56329	−	0.799379i
$964$	2.44267	−	9.11618i	0.0786732	−	0.293612i
$965$		−	51.2064i		−	1.64839i
$966$	−3.44317	−	0.0876780i	−0.110782	−	0.00282099i
$967$	−0.630263	+	2.35217i	−0.0202679	+	0.0756408i	−0.975319	−	0.220800i	$-0.929133\pi$
$967$	−0.630263	+	2.35217i	−0.0202679	+	0.0756408i	0.955051	+	0.296441i	$0.0957998\pi$
$968$	9.73492	−	9.73492i	0.312892	−	0.312892i
$969$	29.3112	+	8.65939i	0.941611	+	0.278180i
$970$	2.14901	+	8.02022i	0.0690006	+	0.257514i
$971$	23.6877	+	13.6761i	0.760174	+	0.438887i	0.829358	−	0.558717i	$-0.188706\pi$
$971$	23.6877	+	13.6761i	0.760174	+	0.438887i	−0.0691841	+	0.997604i	$0.522040\pi$
$972$	−26.5596	−	3.39926i	−0.851899	−	0.109031i
$973$	15.7697	+	4.22548i	0.505554	+	0.135463i
$974$	2.74173	−	4.74881i	0.0878506	−	0.152162i
$975$	22.1569	+	6.99821i	0.709588	+	0.224122i
$976$	14.6858	+	25.4366i	0.470081	+	0.814205i
$977$	−10.1779	−	37.9843i	−0.325619	−	1.21523i	−0.913688	−	0.406416i	$-0.866778\pi$
$977$	−10.1779	−	37.9843i	−0.325619	−	1.21523i	0.588069	−	0.808811i	$-0.299888\pi$
$978$	−6.23609	+	10.1929i	−0.199408	+	0.325932i
$979$	1.27484	−	0.736031i	0.0407442	−	0.0235236i
$980$	31.9370	−	31.9370i	1.02019	−	1.02019i
$981$	25.7986	+	28.5692i	0.823685	+	0.912146i
$982$	−2.97455	−	11.1012i	−0.0949217	−	0.354253i
$983$	15.3385	−	4.10993i	0.489221	−	0.131086i	−0.00577180	−	0.999983i	$-0.501837\pi$
$983$	15.3385	−	4.10993i	0.489221	−	0.131086i	0.494993	+	0.868897i	$0.335171\pi$
$984$	−23.4873	−	14.3697i	−0.748746	−	0.458090i
$985$	−27.7062	−	15.9962i	−0.882793	−	0.509681i
$986$	−10.7863	+	2.89019i	−0.343507	+	0.0920424i
$987$	−1.03745	+	40.7413i	−0.0330224	+	1.29681i
$988$	20.0773	−	11.0970i	0.638745	−	0.353043i
$989$		−	9.37175i		−	0.298004i
$990$	8.99150	+	2.90718i	0.285769	+	0.0923964i
$991$	−5.19253	−	8.99373i	−0.164946	−	0.285695i	0.771690	−	0.635999i	$-0.219412\pi$
$991$	−5.19253	−	8.99373i	−0.164946	−	0.285695i	−0.936636	+	0.350304i	$0.886078\pi$
$992$	0.176552	+	0.305797i	0.00560553	+	0.00970906i
$993$	−9.40734	−	2.77920i	−0.298533	−	0.0881953i
$994$	−23.5411	−	23.5411i	−0.746679	−	0.746679i
$995$	−24.1378	−	24.1378i	−0.765218	−	0.765218i
$996$	−5.55742	−	23.0750i	−0.176094	−	0.731160i
$997$	16.2642	+	28.1704i	0.515092	+	0.892165i	0.999847	+	0.0175151i	$0.00557551\pi$
$997$	16.2642	+	28.1704i	0.515092	+	0.892165i	−0.484755	+	0.874650i	$0.661091\pi$
$998$	9.91212	+	17.1683i	0.313763	+	0.543453i
$999$	−0.00383855	+	0.0109147i	−0.000121446	+	0.000345327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.8	✓	48
3.2	odd	2		351.2.ba.a.89.5		48
9.4	even	3		351.2.bf.a.206.8		48
9.5	odd	6		117.2.bc.a.50.5	yes	48
13.6	odd	12		117.2.bc.a.110.5	yes	48
39.32	even	12		351.2.bf.a.305.8		48
117.32	even	12	inner	117.2.x.a.32.8	yes	48
117.58	odd	12		351.2.ba.a.71.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.8	✓	48	1.1	even	1	trivial
117.2.x.a.32.8	yes	48	117.32	even	12	inner
117.2.bc.a.50.5	yes	48	9.5	odd	6
117.2.bc.a.110.5	yes	48	13.6	odd	12
351.2.ba.a.71.5		48	117.58	odd	12
351.2.ba.a.89.5		48	3.2	odd	2
351.2.bf.a.206.8		48	9.4	even	3
351.2.bf.a.305.8		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)

\(f(q)\)	\(=\)	\(q+(0.375702 - 0.375702i) q^{2} +(-0.0440912 + 1.73149i) q^{3} +1.71770i q^{4} +(-2.85246 - 0.764314i) q^{5} +(0.633958 + 0.667088i) q^{6} +(3.85210 + 1.03217i) q^{7} +(1.39674 + 1.39674i) q^{8} +(-2.99611 - 0.152687i) q^{9} +O(q^{10})\)	\(q+(0.375702 - 0.375702i) q^{2} +(-0.0440912 + 1.73149i) q^{3} +1.71770i q^{4} +(-2.85246 - 0.764314i) q^{5} +(0.633958 + 0.667088i) q^{6} +(3.85210 + 1.03217i) q^{7} +(1.39674 + 1.39674i) q^{8} +(-2.99611 - 0.152687i) q^{9} +(-1.35883 + 0.784520i) q^{10} +(1.41956 + 1.41956i) q^{11} +(-2.97417 - 0.0757353i) q^{12} +(-0.867991 - 3.49951i) q^{13} +(1.83503 - 1.05945i) q^{14} +(1.44917 - 4.90531i) q^{15} -2.38588 q^{16} +(2.38198 - 4.12571i) q^{17} +(-1.18301 + 1.06828i) q^{18} +(3.57782 - 0.958675i) q^{19} +(1.31286 - 4.89966i) q^{20} +(-1.95703 + 6.62436i) q^{21} +1.06666 q^{22} +(-0.469242 + 0.812751i) q^{23} +(-2.48003 + 2.35686i) q^{24} +(3.22223 + 1.86035i) q^{25} +(-1.64088 - 0.988667i) q^{26} +(0.396478 - 5.18100i) q^{27} +(-1.77295 + 6.61674i) q^{28} -4.41168i q^{29} +(-1.29848 - 2.38739i) q^{30} +(0.0175135 - 0.0653613i) q^{31} +(-3.68987 + 3.68987i) q^{32} +(-2.52054 + 2.39536i) q^{33} +(-0.655122 - 2.44495i) q^{34} +(-10.1991 - 5.88843i) q^{35} +(0.262270 - 5.14641i) q^{36} +(-0.00215078 - 0.000576301i) q^{37} +(0.984018 - 1.70437i) q^{38} +(6.09764 - 1.34862i) q^{39} +(-2.91661 - 5.05171i) q^{40} +(2.08295 + 7.77367i) q^{41} +(1.75352 + 3.22404i) q^{42} +(-8.64818 + 4.99303i) q^{43} +(-2.43837 + 2.43837i) q^{44} +(8.42959 + 2.72550i) q^{45} +(0.129057 + 0.481647i) q^{46} +(5.69908 - 1.52706i) q^{47} +(0.105196 - 4.13112i) q^{48} +(7.71112 + 4.45202i) q^{49} +(1.90953 - 0.511658i) q^{50} +(7.03860 + 4.30628i) q^{51} +(6.01110 - 1.49094i) q^{52} +7.99684i q^{53} +(-1.79755 - 2.09547i) q^{54} +(-2.96424 - 5.13421i) q^{55} +(3.93872 + 6.82207i) q^{56} +(1.50218 + 6.23723i) q^{57} +(-1.65747 - 1.65747i) q^{58} +(-3.08306 - 3.08306i) q^{59} +(8.42583 + 2.48924i) q^{60} +(-6.15531 - 10.6613i) q^{61} +(-0.0179765 - 0.0311362i) q^{62} +(-11.3837 - 3.68065i) q^{63} -1.99917i q^{64} +(-0.198820 + 10.6456i) q^{65} +(-0.0470303 + 1.84691i) q^{66} +(1.05601 - 0.282958i) q^{67} +(7.08672 + 4.09152i) q^{68} +(-1.38658 - 0.848323i) q^{69} +(-6.04409 + 1.61951i) q^{70} +(-4.06655 - 15.1766i) q^{71} +(-3.97154 - 4.39807i) q^{72} +(0.854579 - 0.854579i) q^{73} +(-0.00102457 + 0.000591536i) q^{74} +(-3.36325 + 5.49722i) q^{75} +(1.64671 + 6.14561i) q^{76} +(4.00305 + 6.93349i) q^{77} +(1.78421 - 2.79757i) q^{78} +(-0.501428 + 0.868498i) q^{79} +(6.80561 + 1.82356i) q^{80} +(8.95337 + 0.914934i) q^{81} +(3.70315 + 2.13801i) q^{82} +(2.06478 + 7.70588i) q^{83} +(-11.3786 - 3.36158i) q^{84} +(-9.94785 + 9.94785i) q^{85} +(-1.37325 + 5.12502i) q^{86} +(7.63878 + 0.194516i) q^{87} +3.96551i q^{88} +(0.189782 - 0.708276i) q^{89} +(4.19099 - 2.14303i) q^{90} +(0.268496 - 14.3764i) q^{91} +(-1.39606 - 0.806016i) q^{92} +(0.112400 + 0.0332063i) q^{93} +(1.56743 - 2.71488i) q^{94} -10.9383 q^{95} +(-6.22627 - 6.55165i) q^{96} +(1.36963 - 5.11155i) q^{97} +(4.56971 - 1.22445i) q^{98} +(-4.03640 - 4.46990i) 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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