LMFDB - Embedded newform 117.2.x.a.59.10

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			59.10
Character	$\chi$	$=$	117.59
Dual form			117.2.x.a.2.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.954676 - 0.954676i) q^{2} +(-0.157210 - 1.72490i) q^{3} +0.177187i q^{4} +(-0.0632653 - 0.236109i) q^{5} +(-1.79681 - 1.49664i) q^{6} +(-0.804746 - 3.00335i) q^{7} +(2.07851 + 2.07851i) q^{8} +(-2.95057 + 0.542344i) q^{9} +O(q^{10})$	\(q+(0.954676 - 0.954676i) q^{2} +(-0.157210 - 1.72490i) q^{3} +0.177187i q^{4} +(-0.0632653 - 0.236109i) q^{5} +(-1.79681 - 1.49664i) q^{6} +(-0.804746 - 3.00335i) q^{7} +(2.07851 + 2.07851i) q^{8} +(-2.95057 + 0.542344i) q^{9} +(-0.285806 - 0.165010i) q^{10} +(4.14014 + 4.14014i) q^{11} +(0.305630 - 0.0278556i) q^{12} +(-3.46171 + 1.00824i) q^{13} +(-3.63550 - 2.09896i) q^{14} +(-0.397319 + 0.146245i) q^{15} +3.61423 q^{16} +(-0.931829 - 1.61398i) q^{17} +(-2.29908 + 3.33460i) q^{18} +(-0.337244 + 1.25861i) q^{19} +(0.0418355 - 0.0112098i) q^{20} +(-5.05397 + 1.86026i) q^{21} +7.90498 q^{22} +(2.65154 + 4.59261i) q^{23} +(3.25846 - 3.91198i) q^{24} +(4.27838 - 2.47012i) q^{25} +(-2.34227 + 4.26736i) q^{26} +(1.39935 + 5.00418i) q^{27} +(0.532155 - 0.142591i) q^{28} +0.159233i q^{29} +(-0.239694 + 0.518928i) q^{30} +(-7.81438 + 2.09386i) q^{31} +(-0.706597 + 0.706597i) q^{32} +(6.49046 - 7.79220i) q^{33} +(-2.43042 - 0.651229i) q^{34} +(-0.658207 + 0.380016i) q^{35} +(-0.0960963 - 0.522803i) q^{36} +(-1.98445 - 7.40608i) q^{37} +(0.879607 + 1.52352i) q^{38} +(2.28333 + 5.81261i) q^{39} +(0.359258 - 0.622252i) q^{40} +(-8.02934 - 2.15146i) q^{41} +(-3.04896 + 6.60086i) q^{42} +(-3.08916 - 1.78352i) q^{43} +(-0.733579 + 0.733579i) q^{44} +(0.314721 + 0.662345i) q^{45} +(6.91582 + 1.85309i) q^{46} +(1.23983 - 4.62713i) q^{47} +(-0.568194 - 6.23419i) q^{48} +(-2.31033 + 1.33387i) q^{49} +(1.72630 - 6.44264i) q^{50} +(-2.63746 + 1.86105i) q^{51} +(-0.178647 - 0.613371i) q^{52} -2.20599i q^{53} +(6.11330 + 3.44145i) q^{54} +(0.715598 - 1.23945i) q^{55} +(4.56982 - 7.91516i) q^{56} +(2.22400 + 0.383846i) q^{57} +(0.152016 + 0.152016i) q^{58} +(-0.222958 - 0.222958i) q^{59} +(-0.0259127 - 0.0703998i) q^{60} +(-4.08824 + 7.08105i) q^{61} +(-5.46125 + 9.45915i) q^{62} +(4.00331 + 8.42515i) q^{63} +8.57760i q^{64} +(0.457061 + 0.753556i) q^{65} +(-1.24274 - 13.6353i) q^{66} +(2.14635 - 8.01031i) q^{67} +(0.285976 - 0.165108i) q^{68} +(7.50495 - 5.29566i) q^{69} +(-0.265582 + 0.991166i) q^{70} +(-4.12800 - 1.10609i) q^{71} +(-7.26005 - 5.00552i) q^{72} +(-0.634876 + 0.634876i) q^{73} +(-8.96492 - 5.17590i) q^{74} +(-4.93333 - 6.99146i) q^{75} +(-0.223010 - 0.0597552i) q^{76} +(9.10254 - 15.7661i) q^{77} +(7.72900 + 3.36932i) q^{78} +(-1.01186 - 1.75259i) q^{79} +(-0.228655 - 0.853353i) q^{80} +(8.41173 - 3.20045i) q^{81} +(-9.71937 + 5.61148i) q^{82} +(3.46192 + 0.927619i) q^{83} +(-0.329615 - 0.895499i) q^{84} +(-0.322122 + 0.322122i) q^{85} +(-4.65183 + 1.24645i) q^{86} +(0.274662 - 0.0250331i) q^{87} +17.2106i q^{88} +(8.08378 - 2.16604i) q^{89} +(0.932782 + 0.331868i) q^{90} +(5.81390 + 9.58537i) q^{91} +(-0.813751 + 0.469819i) q^{92} +(4.84020 + 13.1499i) q^{93} +(-3.23377 - 5.60105i) q^{94} +0.318505 q^{95} +(1.32989 + 1.10773i) q^{96} +(-6.34792 + 1.70092i) q^{97} +(-0.932205 + 3.47904i) q^{98} +(-14.4612 - 9.97039i) 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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.954676	−	0.954676i	0.675058	−	0.675058i	−0.283820	−	0.958878i	$-0.591602\pi$
$2$	0.954676	−	0.954676i	0.675058	−	0.675058i	0.958878	+	0.283820i	$0.0916017\pi$
$3$	−0.157210	−	1.72490i	−0.0907653	−	0.995872i
$3$	−0.157210	−	1.72490i	−0.0907653	−	0.995872i
$4$			0.177187i			0.0885935i
$5$	−0.0632653	−	0.236109i	−0.0282931	−	0.105591i	0.950335	−	0.311228i	$-0.100740\pi$
$5$	−0.0632653	−	0.236109i	−0.0282931	−	0.105591i	−0.978628	+	0.205637i	$0.934074\pi$
$6$	−1.79681	−	1.49664i	−0.733543	−	0.611000i
$7$	−0.804746	−	3.00335i	−0.304165	−	1.13516i	−0.933661	−	0.358157i	$-0.883405\pi$
$7$	−0.804746	−	3.00335i	−0.304165	−	1.13516i	0.629496	−	0.777004i	$-0.283261\pi$
$8$	2.07851	+	2.07851i	0.734864	+	0.734864i
$9$	−2.95057	+	0.542344i	−0.983523	+	0.180781i
$10$	−0.285806	−	0.165010i	−0.0903797	−	0.0521807i
$11$	4.14014	+	4.14014i	1.24830	+	1.24830i	0.956471	+	0.291828i	$0.0942636\pi$
$11$	4.14014	+	4.14014i	1.24830	+	1.24830i	0.291828	+	0.956471i	$0.405736\pi$
$12$	0.305630	−	0.0278556i	0.0882278	−	0.00804122i
$13$	−3.46171	+	1.00824i	−0.960106	+	0.279635i
$13$	−3.46171	+	1.00824i	−0.960106	+	0.279635i
$14$	−3.63550	−	2.09896i	−0.971628	−	0.560970i
$15$	−0.397319	+	0.146245i	−0.102587	+	0.0377603i
$16$	3.61423			0.903558
$17$	−0.931829	−	1.61398i	−0.226002	−	0.391447i	0.730618	−	0.682787i	$-0.239232\pi$
$17$	−0.931829	−	1.61398i	−0.226002	−	0.391447i	−0.956620	+	0.291340i	$0.905899\pi$
$18$	−2.29908	+	3.33460i	−0.541897	+	0.785973i
$19$	−0.337244	+	1.25861i	−0.0773690	+	0.288745i	−0.993760	−	0.111539i	$-0.964422\pi$
$19$	−0.337244	+	1.25861i	−0.0773690	+	0.288745i	0.916391	+	0.400284i	$0.131089\pi$
$20$	0.0418355	−	0.0112098i	0.00935470	−	0.00250658i
$21$	−5.05397	+	1.86026i	−1.10287	+	0.405943i
$22$	7.90498			1.68535
$23$	2.65154	+	4.59261i	0.552885	+	0.957625i	0.998065	+	0.0621838i	$0.0198065\pi$
$23$	2.65154	+	4.59261i	0.552885	+	0.957625i	−0.445180	+	0.895441i	$0.646860\pi$
$24$	3.25846	−	3.91198i	0.665130	−	0.798531i
$25$	4.27838	−	2.47012i	0.855676	−	0.494025i
$26$	−2.34227	+	4.26736i	−0.459358	+	0.836897i
$27$	1.39935	+	5.00418i	0.269305	+	0.963055i
$28$	0.532155	−	0.142591i	0.100568	−	0.0269471i
$29$			0.159233i			0.0295689i	0.999891	+	0.0147844i	$0.00470621\pi$
$29$			0.159233i			0.0295689i	−0.999891	+	0.0147844i	$0.995294\pi$
$30$	−0.239694	+	0.518928i	−0.0437620	+	0.0947428i
$31$	−7.81438	+	2.09386i	−1.40350	+	0.376068i	−0.879602	−	0.475711i	$-0.842191\pi$
$31$	−7.81438	+	2.09386i	−1.40350	+	0.376068i	−0.523902	+	0.851779i	$0.675524\pi$
$32$	−0.706597	+	0.706597i	−0.124910	+	0.124910i
$33$	6.49046	−	7.79220i	1.12984	−	1.35645i
$34$	−2.43042	−	0.651229i	−0.416813	−	0.111685i
$35$	−0.658207	+	0.380016i	−0.111257	+	0.0642344i
$36$	−0.0960963	−	0.522803i	−0.0160161	−	0.0871338i
$37$	−1.98445	−	7.40608i	−0.326242	−	1.21755i	−0.913057	−	0.407832i	$-0.866285\pi$
$37$	−1.98445	−	7.40608i	−0.326242	−	1.21755i	0.586815	−	0.809721i	$-0.300382\pi$
$38$	0.879607	+	1.52352i	0.142691	+	0.247148i
$39$	2.28333	+	5.81261i	0.365625	+	0.930762i
$40$	0.359258	−	0.622252i	0.0568036	−	0.0983867i
$41$	−8.02934	−	2.15146i	−1.25397	−	0.336001i	−0.430103	−	0.902780i	$-0.641523\pi$
$41$	−8.02934	−	2.15146i	−1.25397	−	0.336001i	−0.823870	+	0.566779i	$0.808189\pi$
$42$	−3.04896	+	6.60086i	−0.470464	+	1.01853i
$43$	−3.08916	−	1.78352i	−0.471092	−	0.271985i	0.245605	−	0.969370i	$-0.421013\pi$
$43$	−3.08916	−	1.78352i	−0.471092	−	0.271985i	−0.716697	+	0.697385i	$0.754347\pi$
$44$	−0.733579	+	0.733579i	−0.110591	+	0.110591i
$45$	0.314721	+	0.662345i	0.0469158	+	0.0987366i
$46$	6.91582	+	1.85309i	1.01968	+	0.273223i
$47$	1.23983	−	4.62713i	0.180848	−	0.674936i	−0.814633	−	0.579977i	$-0.803061\pi$
$47$	1.23983	−	4.62713i	0.180848	−	0.674936i	0.995481	−	0.0949586i	$-0.0302719\pi$
$48$	−0.568194	−	6.23419i	−0.0820117	−	0.899828i
$49$	−2.31033	+	1.33387i	−0.330048	+	0.190553i
$50$	1.72630	−	6.44264i	0.244136	−	0.911127i
$51$	−2.63746	+	1.86105i	−0.369318	+	0.260599i
$52$	−0.178647	−	0.613371i	−0.0247739	−	0.0850592i
$53$		−	2.20599i		−	0.303016i	−0.988456	−	0.151508i	$-0.951587\pi$
$53$		−	2.20599i		−	0.303016i	0.988456	−	0.151508i	$-0.0484129\pi$
$54$	6.11330	+	3.44145i	0.831914	+	0.468321i
$55$	0.715598	−	1.23945i	0.0964912	−	0.167128i
$56$	4.56982	−	7.91516i	0.610668	−	1.05771i
$57$	2.22400	+	0.383846i	0.294576	+	0.0508416i
$58$	0.152016	+	0.152016i	0.0199607	+	0.0199607i
$59$	−0.222958	−	0.222958i	−0.0290266	−	0.0290266i	0.692445	−	0.721471i	$-0.256534\pi$
$59$	−0.222958	−	0.222958i	−0.0290266	−	0.0290266i	−0.721471	+	0.692445i	$0.756534\pi$
$60$	−0.0259127	−	0.0703998i	−0.00334532	−	0.00908858i
$61$	−4.08824	+	7.08105i	−0.523446	+	0.906635i	0.476182	+	0.879347i	$0.342021\pi$
$61$	−4.08824	+	7.08105i	−0.523446	+	0.906635i	−0.999628	+	0.0272882i	$0.991313\pi$
$62$	−5.46125	+	9.45915i	−0.693579	+	1.20131i
$63$	4.00331	+	8.42515i	0.504370	+	1.06147i
$64$			8.57760i			1.07220i
$65$	0.457061	+	0.753556i	0.0566914	+	0.0934671i
$66$	−1.24274	−	13.6353i	−0.152971	−	1.67839i
$67$	2.14635	−	8.01031i	0.262219	−	0.978615i	−0.701712	−	0.712461i	$-0.747581\pi$
$67$	2.14635	−	8.01031i	0.262219	−	0.978615i	0.963931	−	0.266154i	$-0.0857528\pi$
$68$	0.285976	−	0.165108i	0.0346796	−	0.0200223i
$69$	7.50495	−	5.29566i	0.903489	−	0.637522i
$70$	−0.265582	+	0.991166i	−0.0317431	+	0.118467i
$71$	−4.12800	−	1.10609i	−0.489903	−	0.131269i	0.00540700	−	0.999985i	$-0.498279\pi$
$71$	−4.12800	−	1.10609i	−0.489903	−	0.131269i	−0.495310	+	0.868716i	$0.664946\pi$
$72$	−7.26005	−	5.00552i	−0.855605	−	0.589906i
$73$	−0.634876	+	0.634876i	−0.0743066	+	0.0743066i	−0.743283	−	0.668977i	$-0.766733\pi$
$73$	−0.634876	+	0.634876i	−0.0743066	+	0.0743066i	0.668977	+	0.743283i	$0.266733\pi$
$74$	−8.96492	−	5.17590i	−1.04215	−	0.601686i
$75$	−4.93333	−	6.99146i	−0.569652	−	0.807304i
$76$	−0.223010	−	0.0597552i	−0.0255809	−	0.00685439i
$77$	9.10254	−	15.7661i	1.03733	−	1.79671i
$78$	7.72900	+	3.36932i	0.875137	+	0.381500i
$79$	−1.01186	−	1.75259i	−0.113843	−	0.197182i	0.803474	−	0.595340i	$-0.202983\pi$
$79$	−1.01186	−	1.75259i	−0.113843	−	0.197182i	−0.917317	+	0.398158i	$0.869649\pi$
$80$	−0.228655	−	0.853353i	−0.0255644	−	0.0954078i
$81$	8.41173	−	3.20045i	0.934636	−	0.355605i
$82$	−9.71937	+	5.61148i	−1.07332	+	0.619684i
$83$	3.46192	+	0.927619i	0.379995	+	0.101819i	0.443760	−	0.896146i	$-0.353644\pi$
$83$	3.46192	+	0.927619i	0.379995	+	0.101819i	−0.0637651	+	0.997965i	$0.520311\pi$
$84$	−0.329615	−	0.895499i	−0.0359639	−	0.0977069i
$85$	−0.322122	+	0.322122i	−0.0349390	+	0.0349390i
$86$	−4.65183	+	1.24645i	−0.501620	+	0.134409i
$87$	0.274662	−	0.0250331i	0.0294468	−	0.00268383i
$88$			17.2106i			1.83466i
$89$	8.08378	−	2.16604i	0.856879	−	0.229600i	0.196474	−	0.980509i	$-0.437051\pi$
$89$	8.08378	−	2.16604i	0.856879	−	0.229600i	0.660406	+	0.750909i	$0.270384\pi$
$90$	0.932782	+	0.331868i	0.0983238	+	0.0349820i
$91$	5.81390	+	9.58537i	0.609462	+	1.00482i
$92$	−0.813751	+	0.469819i	−0.0848394	+	0.0489820i
$93$	4.84020	+	13.1499i	0.501905	+	1.36358i
$94$	−3.23377	−	5.60105i	−0.333538	−	0.577704i
$95$	0.318505			0.0326780
$96$	1.32989	+	1.10773i	0.135732	+	0.113057i
$97$	−6.34792	+	1.70092i	−0.644534	+	0.172702i	−0.566256	−	0.824229i	$-0.691609\pi$
$97$	−6.34792	+	1.70092i	−0.644534	+	0.172702i	−0.0782776	+	0.996932i	$0.524942\pi$
$98$	−0.932205	+	3.47904i	−0.0941669	+	0.351436i
$99$	−14.4612	−	9.97039i	−1.45340	−	1.00206i
$100$	0.437674	+	0.758074i	0.0437674	+	0.0758074i
$101$	4.66687			0.464371			0.232185	−	0.972672i	$-0.425412\pi$
$101$	4.66687			0.464371			0.232185	+	0.972672i	$0.425412\pi$
$102$	−0.741219	+	4.29461i	−0.0733916	+	0.425230i
$103$	12.2023	+	7.04502i	1.20233	+	0.694167i	0.961073	−	0.276294i	$-0.0891063\pi$
$103$	12.2023	+	7.04502i	1.20233	+	0.694167i	0.241259	+	0.970461i	$0.422440\pi$
$104$	−9.29083	−	5.09957i	−0.911041	−	0.500054i
$105$	0.758967	+	1.07560i	0.0740676	+	0.104968i
$106$	−2.10600	−	2.10600i	−0.204553	−	0.204553i
$107$	16.8176	+	9.70962i	1.62581	+	0.938665i	0.985323	+	0.170700i	$0.0546028\pi$
$107$	16.8176	+	9.70962i	1.62581	+	0.938665i	0.640492	+	0.767965i	$0.278731\pi$
$108$	−0.886676	+	0.247947i	−0.0853204	+	0.0238587i
$109$	−7.32490	−	7.32490i	−0.701599	−	0.701599i	0.263155	−	0.964754i	$-0.415237\pi$
$109$	−7.32490	−	7.32490i	−0.701599	−	0.701599i	−0.964754	+	0.263155i	$0.915237\pi$
$110$	−0.500111	−	1.86644i	−0.0476837	−	0.177958i
$111$	−12.4628	+	4.58730i	−1.18292	+	0.435407i
$112$	−2.90854	−	10.8548i	−0.274831	−	1.02568i
$113$			1.72068i			0.161868i	0.996719	+	0.0809339i	$0.0257903\pi$
$113$			1.72068i			0.161868i	−0.996719	+	0.0809339i	$0.974210\pi$
$114$	2.48965	−	1.75675i	0.233177	−	0.164535i
$115$	0.916606	−	0.916606i	0.0854740	−	0.0854740i
$116$	−0.0282141			−0.00261961
$117$	9.66721	−	4.85232i	0.893734	−	0.448597i
$118$	−0.425705			−0.0391893
$119$	−4.09745	+	4.09745i	−0.375613	+	0.375613i
$120$	−1.12980	−	0.521859i	−0.103136	−	0.0476390i
$121$			23.2815i			2.11650i
$122$	2.85716	+	10.6631i	0.258675	+	0.965388i
$123$	−2.44876	+	14.1881i	−0.220797	+	1.27929i
$124$	−0.371004	−	1.38461i	−0.0333172	−	0.124341i
$125$	−1.71811	−	1.71811i	−0.153673	−	0.153673i
$126$	11.8652	+	4.22143i	1.05703	+	0.376075i
$127$	−8.41321	−	4.85737i	−0.746552	−	0.431022i	0.0778950	−	0.996962i	$-0.475180\pi$
$127$	−8.41321	−	4.85737i	−0.746552	−	0.431022i	−0.824447	+	0.565940i	$0.808513\pi$
$128$	6.77564	+	6.77564i	0.598888	+	0.598888i
$129$	−2.59076	+	5.60888i	−0.228104	+	0.493834i
$130$	1.15575	+	0.283057i	0.101366	+	0.0248257i
$131$	8.50194	+	4.90860i	0.742818	+	0.428866i	0.823093	−	0.567907i	$-0.192247\pi$
$131$	8.50194	+	4.90860i	0.742818	+	0.428866i	−0.0802751	+	0.996773i	$0.525580\pi$
$132$	1.38068	+	1.15003i	0.120173	+	0.100097i
$133$	4.05145			0.351305
$134$	−5.59817	−	9.69632i	−0.483609	−	0.837635i
$135$	1.09300	−	0.646990i	0.0940707	−	0.0556840i
$136$	1.41785	−	5.29148i	0.121579	−	0.453740i
$137$	−17.7541	+	4.75720i	−1.51684	+	0.406435i	−0.918699	−	0.394959i	$-0.870759\pi$
$137$	−17.7541	+	4.75720i	−1.51684	+	0.406435i	−0.598137	+	0.801394i	$0.704092\pi$
$138$	2.10916	−	12.2204i	0.179543	−	1.04027i
$139$	7.70279			0.653342			0.326671	−	0.945138i	$-0.394073\pi$
$139$	7.70279			0.653342			0.326671	+	0.945138i	$0.394073\pi$
$140$	−0.0673339	−	0.116626i	−0.00569075	−	0.00985667i
$141$	−8.17625	−	1.41116i	−0.688565	−	0.118841i
$142$	−4.99686	+	2.88494i	−0.419327	+	0.242099i
$143$	−18.5062	−	10.1577i	−1.54757	−	0.849432i
$144$	−10.6640	+	1.96016i	−0.888670	+	0.163346i
$145$	0.0375965	−	0.0100739i	0.00312222	−	0.000836595i
$146$			1.21220i			0.100322i
$147$	2.66400	+	3.77540i	0.219723	+	0.311390i
$148$	1.31226	−	0.351620i	0.107867	−	0.0289030i
$149$	1.88621	−	1.88621i	0.154524	−	0.154524i	−0.625611	−	0.780135i	$-0.715150\pi$
$149$	1.88621	−	1.88621i	0.154524	−	0.154524i	0.780135	+	0.625611i	$0.215150\pi$
$150$	−11.3843	−	1.96485i	−0.929525	−	0.160429i
$151$	8.05217	+	2.15757i	0.655277	+	0.175581i	0.571113	−	0.820871i	$-0.306512\pi$
$151$	8.05217	+	2.15757i	0.655277	+	0.175581i	0.0841631	+	0.996452i	$0.473178\pi$
$152$	−3.31700	+	1.91507i	−0.269044	+	0.155333i
$153$	3.62476	+	4.25678i	0.293044	+	0.344140i
$154$	−6.36150	−	23.7415i	−0.512625	−	1.91314i
$155$	0.988757	+	1.71258i	0.0794189	+	0.137558i
$156$	−1.02992	+	0.404576i	−0.0824595	+	0.0323920i
$157$	10.7341	−	18.5920i	0.856673	−	1.48380i	−0.0184121	−	0.999830i	$-0.505861\pi$
$157$	10.7341	−	18.5920i	0.856673	−	1.48380i	0.875085	−	0.483970i	$-0.160806\pi$
$158$	−2.63915	−	0.707159i	−0.209960	−	0.0562585i
$159$	−3.80511	+	0.346804i	−0.301765	+	0.0275033i
$160$	0.211537	+	0.122131i	0.0167235	+	0.00965531i
$161$	11.6594	−	11.6594i	0.918890	−	0.918890i
$162$	4.97508	−	11.0859i	0.390879	−	0.870988i
$163$	17.6970	+	4.74191i	1.38614	+	0.371415i	0.873347	−	0.487098i	$-0.161945\pi$
$163$	17.6970	+	4.74191i	1.38614	+	0.371415i	0.512792	+	0.858513i	$0.328611\pi$
$164$	0.381210	−	1.42270i	0.0297675	−	0.111094i
$165$	−2.25043	−	1.03948i	−0.175196	−	0.0809235i
$166$	4.19059	−	2.41944i	0.325253	−	0.187785i
$167$	−4.68978	+	17.5025i	−0.362906	+	1.35438i	0.507332	+	0.861751i	$0.330632\pi$
$167$	−4.68978	+	17.5025i	−0.362906	+	1.35438i	−0.870238	+	0.492632i	$0.836035\pi$
$168$	−14.3713	−	6.63815i	−1.10877	−	0.512144i
$169$	10.9669	−	6.98047i	0.843608	−	0.536959i
$170$			0.615044i			0.0471718i
$171$	0.312461	−	3.89652i	0.0238945	−	0.297974i
$172$	0.316017	−	0.547358i	0.0240961	−	0.0417357i
$173$	1.66922	−	2.89117i	0.126908	−	0.219812i	−0.795569	−	0.605863i	$-0.792828\pi$
$173$	1.66922	−	2.89117i	0.126908	−	0.219812i	0.922477	+	0.386051i	$0.126161\pi$
$174$	0.238315	−	0.286112i	0.0180666	−	0.0216901i
$175$	−10.8617	−	10.8617i	−0.821065	−	0.821065i
$176$	14.9634	+	14.9634i	1.12791	+	1.12791i
$177$	−0.349529	+	0.419631i	−0.0262722	+	0.0315414i
$178$	5.64953	−	9.78526i	0.423450	−	0.733437i
$179$	−2.15203	+	3.72743i	−0.160851	+	0.278601i	−0.935174	−	0.354189i	$-0.884757\pi$
$179$	−2.15203	+	3.72743i	−0.160851	+	0.278601i	0.774323	+	0.632790i	$0.218090\pi$
$180$	−0.117359	+	0.0557645i	−0.00874742	+	0.00415644i
$181$		−	18.6572i		−	1.38678i	−0.720563	−	0.693390i	$-0.756116\pi$
$181$		−	18.6572i		−	1.38678i	0.720563	−	0.693390i	$-0.243884\pi$
$182$	14.7013	+	3.60053i	1.08973	+	0.266889i
$183$	12.8568	+	5.93861i	0.950404	+	0.438994i
$184$	−4.03452	+	15.0570i	−0.297429	+	1.11002i
$185$	−1.62310	+	0.937096i	−0.119332	+	0.0688966i
$186$	17.1747	+	7.93304i	1.25931	+	0.581678i
$187$	2.82418	−	10.5400i	0.206525	−	0.770760i
$188$	0.819867	+	0.219683i	0.0597949	+	0.0160220i
$189$	13.9032	−	8.22983i	1.01131	−	0.598632i
$190$	0.304069	−	0.304069i	0.0220595	−	0.0220595i
$191$	−11.3569	−	6.55691i	−0.821756	−	0.474441i	0.0292655	−	0.999572i	$-0.490683\pi$
$191$	−11.3569	−	6.55691i	−0.821756	−	0.474441i	−0.851022	+	0.525130i	$0.824017\pi$
$192$	14.7955	−	1.34849i	1.06777	−	0.0973186i
$193$	−23.1963	−	6.21542i	−1.66970	−	0.447396i	−0.704673	−	0.709532i	$-0.748906\pi$
$193$	−23.1963	−	6.21542i	−1.66970	−	0.447396i	−0.965031	+	0.262136i	$0.915573\pi$
$194$	−4.43638	+	7.68404i	−0.318514	+	0.551682i
$195$	1.22795	−	0.906851i	0.0879357	−	0.0649410i
$196$	−0.236345	−	0.409361i	−0.0168818	−	0.0292401i
$197$	−3.54728	−	13.2386i	−0.252734	−	0.943214i	−0.969337	−	0.245734i	$-0.920971\pi$
$197$	−3.54728	−	13.2386i	−0.252734	−	0.943214i	0.716604	−	0.697480i	$-0.245696\pi$
$198$	−23.3242	+	4.28722i	−1.65758	+	0.304680i
$199$	−2.98016	+	1.72060i	−0.211258	+	0.121970i	−0.601896	−	0.798575i	$-0.705588\pi$
$199$	−2.98016	+	1.72060i	−0.211258	+	0.121970i	0.390638	+	0.920544i	$0.372254\pi$
$200$	14.0268	+	3.75848i	0.991847	+	0.265764i
$201$	−14.1544	−	2.44295i	−0.998376	−	0.172312i
$202$	4.45535	−	4.45535i	0.313477	−	0.313477i
$203$	0.478234	−	0.128142i	0.0335654	−	0.00899383i
$204$	−0.329753	−	0.467323i	−0.0230874	−	0.0327192i
$205$			2.03191i			0.141915i
$206$	18.3750	−	4.92357i	1.28025	−	0.343041i
$207$	−10.3143	−	12.1128i	−0.716896	−	0.841895i
$208$	−12.5114	+	3.64401i	−0.867511	+	0.252666i
$209$	−6.60706	+	3.81459i	−0.457020	+	0.263861i
$210$	1.75142	+	0.302282i	0.120859	+	0.0208594i
$211$	2.59160	+	4.48878i	0.178413	+	0.309021i	0.941337	−	0.337468i	$-0.109570\pi$
$211$	2.59160	+	4.48878i	0.178413	+	0.309021i	−0.762924	+	0.646488i	$0.776237\pi$
$212$	0.390873			0.0268452
$213$	−1.25894	+	7.29428i	−0.0862611	+	0.499796i
$214$	25.3249	−	6.78578i	1.73117	−	0.463866i
$215$	−0.225670	+	0.842213i	−0.0153906	+	0.0574385i
$216$	−7.49267	+	13.3098i	−0.509812	+	0.905617i
$217$	12.5772	+	21.7843i	0.853794	+	1.47882i
$218$	−13.9858			−0.947239
$219$	1.19491	+	0.995289i	0.0807443	+	0.0672554i
$220$	0.219615	+	0.126795i	0.0148064	+	0.00854850i
$221$	4.85300	+	4.64761i	0.326448	+	0.312632i
$222$	−7.51854	+	16.2773i	−0.504611	+	1.09246i
$223$	−9.78019	−	9.78019i	−0.654930	−	0.654930i	0.299246	−	0.954176i	$-0.403265\pi$
$223$	−9.78019	−	9.78019i	−0.654930	−	0.654930i	−0.954176	+	0.299246i	$0.903265\pi$
$224$	2.69079	+	1.55353i	0.179786	+	0.103800i
$225$	−11.2840	+	9.60863i	−0.752267	+	0.640575i
$226$	1.64269	+	1.64269i	0.109270	+	0.109270i
$227$	3.20548	+	11.9630i	0.212755	+	0.794013i	0.986945	+	0.161060i	$0.0514911\pi$
$227$	3.20548	+	11.9630i	0.212755	+	0.794013i	−0.774189	+	0.632954i	$0.781842\pi$
$228$	−0.0680125	+	0.394064i	−0.00450424	+	0.0260975i
$229$	4.13178	+	15.4200i	0.273036	+	1.01898i	0.957146	+	0.289605i	$0.0935238\pi$
$229$	4.13178	+	15.4200i	0.273036	+	1.01898i	−0.684111	+	0.729378i	$0.739810\pi$
$230$		−	1.75012i		−	0.115400i
$231$	−28.6259	−	13.2224i	−1.88345	−	0.869970i
$232$	−0.330968	+	0.330968i	−0.0217291	+	0.0217291i
$233$	−13.8449			−0.907012			−0.453506	−	0.891253i	$-0.649827\pi$
$233$	−13.8449			−0.907012			−0.453506	+	0.891253i	$0.649827\pi$
$234$	4.59667	−	13.8614i	0.300493	−	0.906151i
$235$	−1.17095			−0.0763841
$236$	0.0395052	−	0.0395052i	0.00257157	−	0.00257157i
$237$	−2.86397	+	2.02088i	−0.186035	+	0.131270i
$238$			7.82348i			0.507121i
$239$	−3.47760	−	12.9786i	−0.224947	−	0.839514i	−0.982426	−	0.186654i	$-0.940236\pi$
$239$	−3.47760	−	12.9786i	−0.224947	−	0.839514i	0.757479	−	0.652860i	$-0.226431\pi$
$240$	−1.43600	+	0.528564i	−0.0926936	+	0.0341186i
$241$	0.719865	+	2.68657i	0.0463706	+	0.173057i	0.985228	−	0.171250i	$-0.0547805\pi$
$241$	0.719865	+	2.68657i	0.0463706	+	0.173057i	−0.938857	+	0.344307i	$0.888114\pi$
$242$	22.2263	+	22.2263i	1.42876	+	1.42876i
$243$	−6.84287	−	14.0063i	−0.438970	−	0.898502i
$244$	−1.25467	−	0.724384i	−0.0803220	−	0.0463739i
$245$	0.461103	+	0.461103i	0.0294588	+	0.0294588i
$246$	11.2072	+	15.8828i	0.714547	+	1.01265i
$247$	−0.101539	−	4.69697i	−0.00646078	−	0.298861i
$248$	−20.5943	−	11.8902i	−1.30774	−	0.755025i
$249$	1.05580	−	6.11730i	0.0669088	−	0.387668i
$250$	−3.28048			−0.207476
$251$	−7.07571	−	12.2555i	−0.446615	−	0.773560i	0.551548	−	0.834143i	$-0.314037\pi$
$251$	−7.07571	−	12.2555i	−0.446615	−	0.773560i	−0.998163	+	0.0605830i	$0.980704\pi$
$252$	−1.49283	+	0.709335i	−0.0940393	+	0.0446839i
$253$	−8.03628	+	29.9918i	−0.505237	+	1.88557i
$254$	−12.6691	+	3.39468i	−0.794930	+	0.213001i
$255$	0.606270	+	0.504988i	0.0379661	+	0.0316236i
$256$	−4.21813			−0.263633
$257$	5.65874	+	9.80122i	0.352982	+	0.611384i	0.986771	−	0.162123i	$-0.0518342\pi$
$257$	5.65874	+	9.80122i	0.352982	+	0.611384i	−0.633788	+	0.773507i	$0.718501\pi$
$258$	2.88133	+	7.82800i	0.179384	+	0.487350i
$259$	−20.6461	+	11.9200i	−1.28289	+	0.740675i
$260$	−0.133520	+	0.0809852i	−0.00828058	+	0.00502249i
$261$	−0.0863593	−	0.469829i	−0.00534550	−	0.0290817i
$262$	12.8027	−	3.43048i	0.790955	−	0.211936i
$263$			7.38073i			0.455115i	0.973765	+	0.227558i	$0.0730740\pi$
$263$			7.38073i			0.455115i	−0.973765	+	0.227558i	$0.926926\pi$
$264$	29.6866	−	2.70569i	1.82709	−	0.166523i
$265$	−0.520854	+	0.139562i	−0.0319958	+	0.00857325i
$266$	3.86782	−	3.86782i	0.237151	−	0.237151i
$267$	−5.00706	−	13.6032i	−0.306427	−	0.832503i
$268$	1.41932	+	0.380306i	0.0866989	+	0.0232309i
$269$	7.84189	−	4.52752i	0.478128	−	0.276048i	−0.241508	−	0.970399i	$-0.577642\pi$
$269$	7.84189	−	4.52752i	0.478128	−	0.276048i	0.719636	+	0.694351i	$0.244309\pi$
$270$	0.425798	−	1.66113i	0.0259132	−	0.101093i
$271$	2.37500	+	8.86360i	0.144271	+	0.538426i	0.999787	+	0.0206493i	$0.00657336\pi$
$271$	2.37500	+	8.86360i	0.144271	+	0.538426i	−0.855516	+	0.517776i	$0.826760\pi$
$272$	−3.36785	−	5.83328i	−0.204206	−	0.353695i
$273$	15.6198	−	11.5353i	0.945354	−	0.698149i
$274$	−12.4078	+	21.4910i	−0.749585	+	1.29832i
$275$	27.9398	+	7.48644i	1.68483	+	0.451449i
$276$	0.938322	+	1.32978i	0.0564803	+	0.0800433i
$277$	−13.4627	−	7.77268i	−0.808894	−	0.467015i	0.0376779	−	0.999290i	$-0.488004\pi$
$277$	−13.4627	−	7.77268i	−0.808894	−	0.467015i	−0.846572	+	0.532275i	$0.821337\pi$
$278$	7.35367	−	7.35367i	0.441044	−	0.441044i
$279$	21.9213	−	10.4162i	1.31239	−	0.623599i
$280$	−2.15795	−	0.578222i	−0.128962	−	0.0345554i
$281$	−0.0511831	+	0.191018i	−0.00305333	+	0.0113952i	−0.967436	−	0.253117i	$-0.918544\pi$
$281$	−0.0511831	+	0.191018i	−0.00305333	+	0.0113952i	0.964382	+	0.264512i	$0.0852109\pi$
$282$	−9.15287	+	6.45847i	−0.545046	+	0.384596i
$283$	21.8971	−	12.6423i	1.30165	−	0.751506i	0.320960	−	0.947093i	$-0.395995\pi$
$283$	21.8971	−	12.6423i	1.30165	−	0.751506i	0.980686	+	0.195587i	$0.0626612\pi$
$284$	0.195985	−	0.731428i	0.0116296	−	0.0434022i
$285$	−0.0500723	−	0.549390i	−0.00296603	−	0.0325431i
$286$	−27.3648	+	7.97011i	−1.61811	+	0.471283i
$287$			25.8463i			1.52566i
$288$	1.70165	−	2.46808i	0.100270	−	0.145433i
$289$	6.76339	−	11.7145i	0.397846	−	0.689090i
$290$	0.0262751	−	0.0455098i	0.00154293	−	0.00267243i
$291$	3.93188	+	10.6821i	0.230491	+	0.626198i
$292$	−0.112492	−	0.112492i	−0.00658308	−	0.00658308i
$293$	5.16075	+	5.16075i	0.301494	+	0.301494i	0.841598	−	0.540104i	$-0.181615\pi$
$293$	5.16075	+	5.16075i	0.301494	+	0.301494i	−0.540104	+	0.841598i	$0.681615\pi$
$294$	6.14754	+	1.06102i	0.358532	+	0.0618800i
$295$	−0.0385369	+	0.0667478i	−0.00224370	+	0.00388621i
$296$	11.2689	−	19.5183i	0.654992	−	1.13448i
$297$	−14.9245	+	26.5115i	−0.866008	+	1.53835i
$298$		−	3.60143i		−	0.208625i
$299$	−13.8093	−	13.2249i	−0.798614	−	0.764816i
$300$	1.23880	−	0.874122i	0.0715219	−	0.0504674i
$301$	−2.87057	+	10.7131i	−0.165457	+	0.617493i
$302$	9.74700	−	5.62743i	0.560877	−	0.323822i
$303$	−0.733679	−	8.04989i	−0.0421488	−	0.462454i
$304$	−1.21888	+	4.54891i	−0.0699074	+	0.260898i
$305$	1.93054	+	0.517288i	0.110543	+	0.0296198i
$306$	7.52431	+	0.603373i	0.430136	+	0.0344925i
$307$	17.1711	−	17.1711i	0.980009	−	0.980009i	−0.0197955	−	0.999804i	$-0.506302\pi$
$307$	17.1711	−	17.1711i	0.980009	−	0.980009i	0.999804	+	0.0197955i	$0.00630152\pi$
$308$	2.79354	+	1.61285i	0.159177	+	0.0919008i
$309$	10.2336	−	22.1554i	0.582171	−	1.26038i
$310$	2.57890	+	0.691014i	0.146472	+	0.0392470i
$311$	6.83702	−	11.8421i	0.387692	−	0.671502i	−0.604447	−	0.796645i	$-0.706606\pi$
$311$	6.83702	−	11.8421i	0.387692	−	0.671502i	0.992139	+	0.125144i	$0.0399392\pi$
$312$	−7.33564	+	16.8275i	−0.415299	+	0.952668i
$313$	15.2838	+	26.4724i	0.863893	+	1.49631i	0.868143	+	0.496315i	$0.165314\pi$
$313$	15.2838	+	26.4724i	0.863893	+	1.49631i	−0.00425012	+	0.999991i	$0.501353\pi$
$314$	−7.50174	−	27.9969i	−0.423348	−	1.57995i
$315$	1.73599	−	1.47824i	0.0978117	−	0.0832893i
$316$	0.310536	−	0.179288i	0.0174690	−	0.0100857i
$317$	−31.2309	−	8.36829i	−1.75410	−	0.470010i	−0.768608	−	0.639720i	$-0.779050\pi$
$317$	−31.2309	−	8.36829i	−1.75410	−	0.470010i	−0.985494	+	0.169710i	$0.945717\pi$
$318$	−3.30156	+	3.96374i	−0.185143	+	0.222275i
$319$	−0.659248	+	0.659248i	−0.0369108	+	0.0369108i
$320$	2.02525	−	0.542664i	0.113215	−	0.0303359i
$321$	14.1043	−	30.5351i	0.787223	−	1.70430i
$322$		−	22.2619i		−	1.24061i
$323$	2.34562	−	0.628507i	0.130514	−	0.0349711i
$324$	0.567078	+	1.49045i	0.0315043	+	0.0828027i
$325$	−12.3201	+	12.8645i	−0.683394	+	0.713594i
$326$	21.4219	−	12.3680i	1.18645	−	0.684998i
$327$	−11.4832	+	13.7863i	−0.635022	+	0.762383i
$328$	−12.2172	−	21.1609i	−0.674584	−	1.16841i
$329$	−14.8946			−0.821168
$330$	−3.14080	+	1.15607i	−0.172895	+	0.0636393i
$331$	4.95642	−	1.32807i	0.272429	−	0.0729973i	−0.120018	−	0.992772i	$-0.538295\pi$
$331$	4.95642	−	1.32807i	0.272429	−	0.0729973i	0.392447	+	0.919774i	$0.371629\pi$
$332$	−0.164362	+	0.613408i	−0.00902054	+	0.0336651i
$333$	9.87192	+	20.7759i	0.540978	+	1.13851i
$334$	12.2320	+	21.1864i	0.669304	+	1.15927i
$335$	−2.02710			−0.110752
$336$	−18.2662	+	6.72343i	−0.996504	+	0.366793i
$337$	−10.4841	−	6.05298i	−0.571103	−	0.329727i	0.186487	−	0.982458i	$-0.440290\pi$
$337$	−10.4841	−	6.05298i	−0.571103	−	0.329727i	−0.757590	+	0.652731i	$0.773623\pi$
$338$	3.80576	−	17.1339i	0.207006	−	0.931963i
$339$	2.96800	−	0.270508i	0.161200	−	0.0146920i
$340$	−0.0570759	−	0.0570759i	−0.00309537	−	0.00309537i
$341$	−41.0215	−	23.6838i	−2.22144	−	1.28255i
$342$	−3.42162	−	4.01821i	−0.185020	−	0.217280i
$343$	−9.52493	−	9.52493i	−0.514298	−	0.514298i
$344$	−2.71376	−	10.1279i	−0.146316	−	0.546060i
$345$	−1.72516	−	1.43696i	−0.0928793	−	0.0773631i
$346$	−1.16657	−	4.35370i	−0.0627152	−	0.234056i
$347$			31.5325i			1.69275i	0.532585	+	0.846376i	$0.321221\pi$
$347$			31.5325i			1.69275i	−0.532585	+	0.846376i	$0.678779\pi$
$348$	0.00443554	+	0.0486665i	0.000237770	+	0.00260880i
$349$	−3.30225	+	3.30225i	−0.176765	+	0.176765i	−0.789944	−	0.613179i	$-0.789890\pi$
$349$	−3.30225	+	3.30225i	−0.176765	+	0.176765i	0.613179	+	0.789944i	$0.289890\pi$
$350$	−20.7387			−1.10853
$351$	−9.88955	−	15.9122i	−0.527865	−	0.849328i
$352$	−5.85082			−0.311850
$353$	−7.37755	+	7.37755i	−0.392667	+	0.392667i	−0.875637	−	0.482970i	$-0.839558\pi$
$353$	−7.37755	+	7.37755i	−0.392667	+	0.392667i	0.482970	+	0.875637i	$0.339558\pi$
$354$	0.0669251	+	0.734298i	0.00355703	+	0.0390275i
$355$			1.04464i			0.0554435i
$356$	0.383795	+	1.43234i	0.0203411	+	0.0759140i
$357$	7.71186	+	6.42354i	0.408155	+	0.339970i
$358$	1.50399	+	5.61299i	0.0794886	+	0.296655i
$359$	14.7889	+	14.7889i	0.780529	+	0.780529i	0.979920	−	0.199391i	$-0.0638963\pi$
$359$	14.7889	+	14.7889i	0.780529	+	0.780529i	−0.199391	+	0.979920i	$0.563896\pi$
$360$	−0.722540	+	2.03084i	−0.0380812	+	0.107035i
$361$	14.9841	+	8.65108i	0.788638	+	0.455320i
$362$	−17.8116	−	17.8116i	−0.936156	−	0.936156i
$363$	40.1583	−	3.66009i	2.10776	−	0.192105i
$364$	−1.69840	+	1.03015i	−0.0890205	+	0.0539944i
$365$	0.190066	+	0.109734i	0.00994849	+	0.00574376i
$366$	17.9435	−	6.60466i	0.937924	−	0.345231i
$367$	−3.00820			−0.157027			−0.0785134	−	0.996913i	$-0.525017\pi$
$367$	−3.00820			−0.157027			−0.0785134	+	0.996913i	$0.525017\pi$
$368$	9.58329	+	16.5987i	0.499564	+	0.865269i
$369$	24.8580	+	1.99336i	1.29405	+	0.103770i
$370$	−0.654909	+	2.44416i	−0.0340471	+	0.127066i
$371$	−6.62536	+	1.77526i	−0.343972	+	0.0921669i
$372$	−2.32998	+	0.857620i	−0.120804	+	0.0444655i
$373$	−13.4086			−0.694270			−0.347135	−	0.937815i	$-0.612845\pi$
$373$	−13.4086			−0.694270			−0.347135	+	0.937815i	$0.612845\pi$
$374$	−7.36610	−	12.7585i	−0.380892	−	0.659724i
$375$	−2.69347	+	3.23368i	−0.139090	+	0.166986i
$376$	12.1945	−	7.04051i	0.628885	−	0.363087i
$377$	−0.160545	−	0.551220i	−0.00826850	−	0.0283893i
$378$	5.41623	−	21.1299i	0.278581	−	1.08680i
$379$	−8.77045	+	2.35004i	−0.450508	+	0.120713i	−0.476937	−	0.878937i	$-0.658253\pi$
$379$	−8.77045	+	2.35004i	−0.450508	+	0.120713i	0.0264291	+	0.999651i	$0.491586\pi$
$380$			0.0564350i			0.00289506i
$381$	−7.05584	+	15.2756i	−0.361482	+	0.782592i
$382$	−17.1019	+	4.58244i	−0.875008	+	0.234458i
$383$	5.48477	−	5.48477i	0.280258	−	0.280258i	−0.552954	−	0.833212i	$-0.686499\pi$
$383$	5.48477	−	5.48477i	0.280258	−	0.280258i	0.833212	+	0.552954i	$0.186499\pi$
$384$	10.6221	−	12.7525i	0.542057	−	0.650774i
$385$	−4.29839	−	1.15175i	−0.219066	−	0.0586986i
$386$	−28.0786	+	16.2112i	−1.42916	+	0.825129i
$387$	10.0821	+	3.58703i	0.512500	+	0.182339i
$388$	−0.301381	−	1.12477i	−0.0153003	−	0.0571015i
$389$	18.8121	+	32.5834i	0.953809	+	1.65205i	0.737069	+	0.675817i	$0.236209\pi$
$389$	18.8121	+	32.5834i	0.953809	+	1.65205i	0.216740	+	0.976229i	$0.430458\pi$
$390$	0.306550	−	2.03805i	0.0155228	−	0.103201i
$391$	4.94157	−	8.55905i	0.249906	−	0.432850i
$392$	−7.57451	−	2.02958i	−0.382571	−	0.102509i
$393$	7.13025	−	15.4367i	0.359674	−	0.778678i
$394$	−16.0251	−	9.25211i	−0.807334	−	0.466115i
$395$	−0.349787	+	0.349787i	−0.0175997	+	0.0175997i
$396$	1.76662	−	2.56233i	0.0887762	−	0.128762i
$397$	3.33356	+	0.893224i	0.167306	+	0.0448296i	0.341500	−	0.939882i	$-0.389065\pi$
$397$	3.33356	+	0.893224i	0.167306	+	0.0448296i	−0.174193	+	0.984711i	$0.555732\pi$
$398$	−1.20248	+	4.48770i	−0.0602747	+	0.224948i
$399$	−0.636929	−	6.98835i	−0.0318863	−	0.349855i
$400$	15.4631	−	8.92760i	0.773153	−	0.446380i
$401$	4.33040	−	16.1613i	0.216250	−	0.807056i	−0.769473	−	0.638679i	$-0.779481\pi$
$401$	4.33040	−	16.1613i	0.216250	−	0.807056i	0.985723	−	0.168376i	$-0.0538523\pi$
$402$	−15.8451	+	11.1807i	−0.790282	+	0.557641i
$403$	24.9400	−	15.1271i	1.24235	−	0.753534i
$404$			0.826909i			0.0411403i
$405$	−1.28783	−	1.78361i	−0.0639925	−	0.0886282i
$406$	0.334224	−	0.578893i	0.0165873	−	0.0287300i
$407$	22.4463	−	38.8781i	1.11262	−	1.92712i
$408$	−9.35018	−	1.61377i	−0.462903	−	0.0798936i
$409$	−8.80041	−	8.80041i	−0.435152	−	0.435152i	0.455224	−	0.890377i	$-0.349559\pi$
$409$	−8.80041	−	8.80041i	−0.435152	−	0.435152i	−0.890377	+	0.455224i	$0.849559\pi$
$410$	1.93982	+	1.93982i	0.0958009	+	0.0958009i
$411$	10.9968	+	29.8762i	0.542433	+	1.47368i
$412$	−1.24829	+	2.16210i	−0.0614987	+	0.106519i
$413$	−0.490196	+	0.849044i	−0.0241210	+	0.0417787i
$414$	−21.4106	−	1.71691i	−1.05227	−	0.0843817i
$415$		−	0.876078i		−	0.0430050i
$416$	1.73362	−	3.15846i	0.0849976	−	0.154856i
$417$	−1.21096	−	13.2866i	−0.0593008	−	0.650646i
$418$	−2.66591	+	9.94930i	−0.130394	+	0.486636i
$419$	−24.6012	+	14.2035i	−1.20185	+	0.693887i	−0.960966	−	0.276668i	$-0.910770\pi$
$419$	−24.6012	+	14.2035i	−1.20185	+	0.693887i	−0.240881	+	0.970555i	$0.577436\pi$
$420$	−0.190582	+	0.134479i	−0.00929946	+	0.00656191i
$421$	−3.71710	+	13.8724i	−0.181161	+	0.676100i	0.814259	+	0.580501i	$0.197143\pi$
$421$	−3.71710	+	13.8724i	−0.181161	+	0.676100i	−0.995420	+	0.0955991i	$0.969523\pi$
$422$	6.75947	+	1.81120i	0.329046	+	0.0881676i
$423$	−1.14873	+	14.3251i	−0.0558529	+	0.696509i
$424$	4.58517	−	4.58517i	0.222675	−	0.222675i
$425$	−7.97344	−	4.60347i	−0.386769	−	0.223301i
$426$	5.76179	+	8.16555i	0.279160	+	0.395622i
$427$	24.5569	+	6.58000i	1.18839	+	0.318428i
$428$	−1.72042	+	2.97985i	−0.0831596	+	0.144037i
$429$	−14.6117	+	33.5183i	−0.705460	+	1.61828i
$430$	0.588599	+	1.01948i	0.0283847	+	0.0491638i
$431$	6.59038	+	24.5956i	0.317447	+	1.18473i	0.921689	+	0.387928i	$0.126809\pi$
$431$	6.59038	+	24.5956i	0.317447	+	1.18473i	−0.604242	+	0.796801i	$0.706524\pi$
$432$	5.05757	+	18.0863i	0.243333	+	0.870176i
$433$	6.57149	−	3.79405i	0.315806	−	0.182330i	−0.333716	−	0.942674i	$-0.608303\pi$
$433$	6.57149	−	3.79405i	0.315806	−	0.182330i	0.649521	+	0.760343i	$0.274969\pi$
$434$	32.8041	+	8.78983i	1.57465	+	0.421925i
$435$	−0.0232871	−	0.0632665i	−0.00111653	−	0.00303340i
$436$	1.29788	−	1.29788i	0.0621571	−	0.0621571i
$437$	−6.67452	+	1.78843i	−0.319286	+	0.0855523i
$438$	2.09093	−	0.190570i	0.0999084	−	0.00910580i
$439$			16.4351i			0.784405i	0.919879	+	0.392203i	$0.128287\pi$
$439$			16.4351i			0.784405i	−0.919879	+	0.392203i	$0.871713\pi$
$440$	4.06359	−	1.08884i	0.193724	−	0.0519082i
$441$	6.09338	−	5.18868i	0.290161	−	0.247080i
$442$	9.07001	−	0.196076i	0.431416	−	0.00932636i
$443$	22.1394	−	12.7822i	1.05188	−	0.607301i	0.128702	−	0.991683i	$-0.458919\pi$
$443$	22.1394	−	12.7822i	1.05188	−	0.607301i	0.923174	+	0.384383i	$0.125586\pi$
$444$	−0.812810	−	2.20824i	−0.0385743	−	0.104799i
$445$	−1.02285	−	1.77162i	−0.0484875	−	0.0839829i
$446$	−18.6738			−0.884231
$447$	−3.55005	−	2.95699i	−0.167912	−	0.139861i
$448$	25.7616	−	6.90279i	1.21712	−	0.326126i
$449$	0.689276	−	2.57241i	0.0325289	−	0.121400i	−0.947752	−	0.319007i	$-0.896651\pi$
$449$	0.689276	−	2.57241i	0.0325289	−	0.121400i	0.980281	+	0.197608i	$0.0633172\pi$
$450$	−1.59944	+	19.9457i	−0.0753984	+	0.940249i
$451$	−24.3353	−	42.1499i	−1.14590	−	1.98476i
$452$	−0.304882			−0.0143404
$453$	2.45572	−	14.2284i	0.115380	−	0.668508i
$454$	14.4810	+	8.36061i	0.679627	+	0.392383i
$455$	1.89538	−	1.97913i	0.0888566	−	0.0927833i
$456$	3.82477	+	5.42042i	0.179111	+	0.253835i
$457$	3.98731	+	3.98731i	0.186519	+	0.186519i	0.794189	−	0.607671i	$-0.207896\pi$
$457$	3.98731	+	3.98731i	0.186519	+	0.186519i	−0.607671	+	0.794189i	$0.707896\pi$
$458$	18.6656	+	10.7766i	0.872187	+	0.503558i
$459$	6.77267	−	6.92156i	0.316121	−	0.323071i
$460$	0.162411	+	0.162411i	0.00757244	+	0.00757244i
$461$	8.89319	+	33.1898i	0.414197	+	1.54581i	0.786438	+	0.617669i	$0.211923\pi$
$461$	8.89319	+	33.1898i	0.414197	+	1.54581i	−0.372241	+	0.928136i	$0.621411\pi$
$462$	−39.9516	+	14.7054i	−1.85872	+	0.684156i
$463$	0.595260	+	2.22154i	0.0276641	+	0.103244i	0.978377	−	0.206827i	$-0.0663138\pi$
$463$	0.595260	+	2.22154i	0.0276641	+	0.103244i	−0.950713	+	0.310071i	$0.899647\pi$
$464$			0.575506i			0.0267172i
$465$	2.79859	−	1.97474i	0.129781	−	0.0915765i
$466$	−13.2174	+	13.2174i	−0.612285	+	0.612285i
$467$	5.55724			0.257159			0.128579	−	0.991699i	$-0.458958\pi$
$467$	5.55724			0.257159			0.128579	+	0.991699i	$0.458958\pi$
$468$	0.859768	+	1.71290i	0.0397428	+	0.0791791i
$469$	−25.7850			−1.19064
$470$	−1.11787	+	1.11787i	−0.0515637	+	0.0515637i
$471$	−33.7568	−	15.5924i	−1.55543	−	0.718459i
$472$		−	0.926838i		−	0.0426612i
$473$	−5.40549	−	20.1736i	−0.248545	−	0.927582i
$474$	−0.804878	+	4.66345i	−0.0369693	+	0.214199i
$475$	1.66607	+	6.21785i	0.0764445	+	0.285295i
$476$	−0.726015	−	0.726015i	−0.0332769	−	0.0332769i
$477$	1.19640	+	6.50892i	0.0547796	+	0.298023i
$478$	−15.7103	−	9.07035i	−0.718573	−	0.414868i
$479$	−5.73194	−	5.73194i	−0.261899	−	0.261899i	0.563926	−	0.825825i	$-0.309290\pi$
$479$	−5.73194	−	5.73194i	−0.261899	−	0.261899i	−0.825825	+	0.563926i	$0.809290\pi$
$480$	0.177408	−	0.384081i	0.00809754	−	0.0175308i
$481$	14.3367	+	23.6369i	0.653698	+	1.07775i
$482$	3.25204	+	1.87757i	0.148126	+	0.0855209i
$483$	−21.9443	−	18.2783i	−0.998500	−	0.831693i
$484$	−4.12518			−0.187508
$485$	0.803206	+	1.39119i	0.0364717	+	0.0631708i
$486$	−19.9042	−	6.83872i	−0.902871	−	0.310211i
$487$	0.576775	−	2.15255i	0.0261362	−	0.0975415i	−0.951626	−	0.307260i	$-0.900588\pi$
$487$	0.576775	−	2.15255i	0.0261362	−	0.0975415i	0.977762	+	0.209718i	$0.0672546\pi$
$488$	−23.2155	+	6.22057i	−1.05091	+	0.281592i
$489$	5.39717	−	31.2711i	0.244068	−	1.41413i
$490$	0.880408			0.0397728
$491$	−15.2266	−	26.3732i	−0.687166	−	1.19021i	−0.972751	−	0.231854i	$-0.925521\pi$
$491$	−15.2266	−	26.3732i	−0.687166	−	1.19021i	0.285584	−	0.958354i	$-0.407812\pi$
$492$	−2.51394	−	0.433888i	−0.113337	−	0.0195612i
$493$	0.256999	−	0.148378i	0.0115746	−	0.00668262i
$494$	−4.58102	−	4.38715i	−0.206110	−	0.197387i
$495$	−1.43921	+	4.04519i	−0.0646878	+	0.181818i
$496$	−28.2430	+	7.56768i	−1.26815	+	0.339799i
$497$			13.2880i			0.596046i
$498$	−4.83210	−	6.84799i	−0.216531	−	0.306866i
$499$	19.1902	−	5.14200i	0.859072	−	0.230188i	0.197716	−	0.980259i	$-0.436648\pi$
$499$	19.1902	−	5.14200i	0.859072	−	0.230188i	0.661356	+	0.750072i	$0.269981\pi$
$500$	0.304427	−	0.304427i	0.0136144	−	0.0136144i
$501$	30.9273	+	5.33783i	1.38173	+	0.238477i
$502$	−18.4550	−	4.94501i	−0.823689	−	0.220707i
$503$	17.8334	−	10.2961i	0.795150	−	0.459080i	−0.0466226	−	0.998913i	$-0.514846\pi$
$503$	17.8334	−	10.2961i	0.795150	−	0.459080i	0.841772	+	0.539833i	$0.181512\pi$
$504$	−9.19084	+	25.8327i	−0.409393	+	1.15068i
$505$	−0.295251	−	1.10189i	−0.0131385	−	0.0490335i
$506$	20.9604	+	36.3045i	0.931804	+	1.61393i
$507$	−13.7647	−	17.8194i	−0.611313	−	0.791389i
$508$	0.860663	−	1.49071i	0.0381857	−	0.0661396i
$509$	26.0020	+	6.96723i	1.15252	+	0.308817i	0.783975	−	0.620793i	$-0.213189\pi$
$509$	26.0020	+	6.96723i	1.15252	+	0.308817i	0.368546	+	0.929610i	$0.379856\pi$
$510$	1.06089	−	0.0966912i	0.0469770	−	0.00428156i
$511$	2.41767	+	1.39584i	0.106951	+	0.0617484i
$512$	−17.5782	+	17.5782i	−0.776855	+	0.776855i
$513$	−6.77024	+	0.0736078i	−0.298913	+	0.00324986i
$514$	14.7593	+	3.95473i	0.651003	+	0.174436i
$515$	0.891411	−	3.32679i	0.0392802	−	0.146596i
$516$	−0.993820	−	0.459049i	−0.0437505	−	0.0202085i
$517$	24.2900	−	14.0239i	1.06827	−	0.616769i
$518$	−8.33057	+	31.0901i	−0.366024	+	1.36602i
$519$	−5.24941	−	2.42472i	−0.230423	−	0.106433i
$520$	−0.616268	+	2.51628i	−0.0270251	+	0.110346i
$521$			31.3448i			1.37324i	0.727017	+	0.686620i	$0.240906\pi$
$521$			31.3448i			1.37324i	−0.727017	+	0.686620i	$0.759094\pi$
$522$	−0.530980	−	0.366090i	−0.0232404	−	0.0160233i
$523$	−14.9743	+	25.9363i	−0.654781	+	1.13411i	0.327167	+	0.944966i	$0.393906\pi$
$523$	−14.9743	+	25.9363i	−0.654781	+	1.13411i	−0.981949	+	0.189148i	$0.939427\pi$
$524$	−0.869740	+	1.50643i	−0.0379948	+	0.0658089i
$525$	−17.0277	+	20.4429i	−0.743152	+	0.892200i
$526$	7.04621	+	7.04621i	0.307229	+	0.307229i
$527$	10.6611	+	10.6611i	0.464405	+	0.464405i
$528$	23.4580	−	28.1628i	1.02088	−	1.22563i
$529$	−2.56137	+	4.43642i	−0.111364	+	0.192888i
$530$	−0.364010	+	0.630484i	−0.0158116	+	0.0273865i
$531$	0.778772	+	0.536932i	0.0337958	+	0.0233009i
$532$			0.717864i			0.0311234i
$533$	29.9645	−	0.647772i	1.29790	−	0.0280581i
$534$	−17.7668	−	8.20653i	−0.768844	−	0.355131i
$535$	1.22856	−	4.58506i	0.0531154	−	0.198230i
$536$	21.1107	−	12.1883i	0.911844	−	0.526453i
$537$	6.76777	+	3.12606i	0.292051	+	0.134899i
$538$	3.16415	−	11.8088i	0.136416	−	0.509113i
$539$	−15.0875	−	4.04269i	−0.649865	−	0.174131i
$540$	0.114638	+	0.193666i	0.00493325	+	0.00833405i
$541$	5.20236	−	5.20236i	0.223667	−	0.223667i	−0.586374	−	0.810041i	$-0.699445\pi$
$541$	5.20236	−	5.20236i	0.223667	−	0.223667i	0.810041	+	0.586374i	$0.199445\pi$
$542$	10.7292	+	6.19452i	0.460860	+	0.266077i
$543$	−32.1818	+	2.93310i	−1.38106	+	0.125871i
$544$	1.79886	+	0.482003i	0.0771254	+	0.0206657i
$545$	−1.26607	+	2.19289i	−0.0542323	+	0.0939331i
$546$	3.89937	−	25.9243i	0.166878	−	1.10946i
$547$	−7.35686	−	12.7425i	−0.314556	−	0.544828i	0.664787	−	0.747033i	$-0.268522\pi$
$547$	−7.35686	−	12.7425i	−0.314556	−	0.544828i	−0.979343	+	0.202205i	$0.935189\pi$
$548$	−0.842914	−	3.14580i	−0.0360075	−	0.134382i
$549$	8.22229	−	23.1104i	0.350919	−	0.986326i
$550$	33.8205	−	19.5263i	1.44211	−	0.832604i
$551$	−0.200413	−	0.0537005i	−0.00853787	−	0.00228772i
$552$	26.6062	+	4.59203i	1.13243	+	0.195450i
$553$	−4.44936	+	4.44936i	−0.189206	+	0.189206i
$554$	−20.2729	+	5.43210i	−0.861312	+	0.230788i
$555$	1.87157	+	2.65236i	0.0794435	+	0.112586i
$556$			1.36484i			0.0578819i
$557$	16.6138	−	4.45166i	0.703950	−	0.188623i	0.110951	−	0.993826i	$-0.464610\pi$
$557$	16.6138	−	4.45166i	0.703950	−	0.188623i	0.592999	+	0.805203i	$0.297944\pi$
$558$	10.9837	−	30.8718i	0.464976	−	1.30691i
$559$	12.4920	+	3.05944i	0.528355	+	0.129401i
$560$	−2.37891	+	1.37346i	−0.100527	+	0.0580395i
$561$	−18.6244	−	3.21444i	−0.786324	−	0.135714i
$562$	0.133497	+	0.231224i	0.00563123	+	0.00975358i
$563$	−25.1526			−1.06006			−0.530028	−	0.847980i	$-0.677819\pi$
$563$	−25.1526			−1.06006			−0.530028	+	0.847980i	$0.677819\pi$
$564$	0.250040	−	1.44873i	0.0105286	−	0.0610024i
$565$	0.406268	−	0.108859i	0.0170918	−	0.00457974i
$566$	8.83533	−	32.9739i	0.371377	−	1.38600i
$567$	−16.3814	−	22.6878i	−0.687953	−	0.952799i
$568$	−6.28105	−	10.8791i	−0.263547	−	0.456477i
$569$	15.7663			0.660959			0.330480	−	0.943813i	$-0.392789\pi$
$569$	15.7663			0.660959			0.330480	+	0.943813i	$0.392789\pi$
$570$	−0.572293	−	0.476687i	−0.0239707	−	0.0199662i
$571$	−35.4431	−	20.4631i	−1.48325	−	0.856352i	−0.483427	−	0.875385i	$-0.660608\pi$
$571$	−35.4431	−	20.4631i	−1.48325	−	0.856352i	−0.999819	+	0.0190322i	$0.993942\pi$
$572$	1.79982	−	3.27906i	0.0752541	−	0.137105i
$573$	−9.52460	+	20.6203i	−0.397896	+	0.861427i
$574$	24.6749	+	24.6749i	1.02991	+	1.02991i
$575$	22.6886	+	13.0993i	0.946181	+	0.546278i
$576$	−4.65201	−	25.3088i	−0.193834	−	1.05453i
$577$	−3.78823	−	3.78823i	−0.157706	−	0.157706i	0.623843	−	0.781549i	$-0.285570\pi$
$577$	−3.78823	−	3.78823i	−0.157706	−	0.157706i	−0.781549	+	0.623843i	$0.785570\pi$
$578$	−4.72674	−	17.6404i	−0.196606	−	0.733745i
$579$	−7.07430	+	40.9884i	−0.293998	+	1.70342i
$580$	0.00178497	+	0.00666161i	7.41169e−5	+	0.000276608i
$581$		−	11.1439i		−	0.462326i
$582$	13.9517	+	6.44431i	0.578315	+	0.267125i
$583$	9.13310	−	9.13310i	0.378254	−	0.378254i
$584$	−2.63919			−0.109210
$585$	−1.75728	−	1.97553i	−0.0726544	−	0.0816783i
$586$	9.85368			0.407052
$587$	24.5518	−	24.5518i	1.01336	−	1.01336i	0.0134534	−	0.999909i	$-0.495718\pi$
$587$	24.5518	−	24.5518i	1.01336	−	1.01336i	0.999909	−	0.0134534i	$-0.00428249\pi$
$588$	−0.668952	+	0.472027i	−0.0275871	+	0.0194661i
$589$		−	10.5414i		−	0.434351i
$590$	0.0269323	+	0.100513i	0.00110879	+	0.00413804i
$591$	−22.2777	+	8.19996i	−0.916382	+	0.337301i
$592$	−7.17227	−	26.7673i	−0.294779	−	1.10013i
$593$	−21.1124	−	21.1124i	−0.866984	−	0.866984i	0.125153	−	0.992137i	$-0.460058\pi$
$593$	−21.1124	−	21.1124i	−0.866984	−	0.866984i	−0.992137	+	0.125153i	$0.960058\pi$
$594$	11.0618	+	39.5580i	0.453873	+	1.62308i
$595$	1.22667	+	0.708220i	0.0502887	+	0.0290342i
$596$	0.334211	+	0.334211i	0.0136898	+	0.0136898i
$597$	3.43637	+	4.86999i	0.140641	+	0.199315i
$598$	−25.8089	+	0.557938i	−1.05541	+	0.0228158i
$599$	−26.7053	−	15.4183i	−1.09115	−	0.629976i	−0.157268	−	0.987556i	$-0.550269\pi$
$599$	−26.7053	−	15.4183i	−1.09115	−	0.629976i	−0.933882	+	0.357580i	$0.883602\pi$
$600$	4.27784	−	24.7858i	0.174642	−	1.01187i
$601$	10.2029			0.416183			0.208092	−	0.978109i	$-0.433275\pi$
$601$	10.2029			0.416183			0.208092	+	0.978109i	$0.433275\pi$
$602$	7.48708	+	12.9680i	0.305151	+	0.528537i
$603$	−1.98863	+	24.7990i	−0.0809832	+	1.00989i
$604$	−0.382294	+	1.42674i	−0.0155553	+	0.0580533i
$605$	5.49698	−	1.47291i	0.223484	−	0.0598824i
$606$	−8.38546	−	6.98461i	−0.340636	−	0.283730i
$607$	−12.4728			−0.506256			−0.253128	−	0.967433i	$-0.581459\pi$
$607$	−12.4728			−0.506256			−0.253128	+	0.967433i	$0.581459\pi$
$608$	−0.651035	−	1.12763i	−0.0264030	−	0.0457313i
$609$	−0.296216	−	0.804761i	−0.0120033	−	0.0326106i
$610$	2.33689	−	1.34920i	0.0946178	−	0.0546276i
$611$	0.373296	+	17.2678i	0.0151019	+	0.698582i
$612$	−0.754246	+	0.642260i	−0.0304886	+	0.0259618i
$613$	−8.66051	+	2.32058i	−0.349795	+	0.0937272i	−0.429438	−	0.903096i	$-0.641288\pi$
$613$	−8.66051	+	2.32058i	−0.349795	+	0.0937272i	0.0796437	+	0.996823i	$0.474622\pi$
$614$		−	32.7857i		−	1.32313i
$615$	3.50485	−	0.319438i	0.141329	−	0.0128810i
$616$	51.6896	−	13.8502i	2.08263	−	0.558040i
$617$	4.18144	−	4.18144i	0.168338	−	0.168338i	−0.617910	−	0.786249i	$-0.712021\pi$
$617$	4.18144	−	4.18144i	0.168338	−	0.168338i	0.786249	+	0.617910i	$0.212021\pi$
$618$	−11.3814	−	30.9210i	−0.457827	−	1.24383i
$619$	22.7101	+	6.08517i	0.912798	+	0.244583i	0.684504	−	0.729009i	$-0.260019\pi$
$619$	22.7101	+	6.08517i	0.912798	+	0.244583i	0.228294	+	0.973592i	$0.426685\pi$
$620$	−0.303447	+	0.175195i	−0.0121867	+	0.00703600i
$621$	−19.2718	+	19.6955i	−0.773351	+	0.790352i
$622$	−4.77820	−	17.8325i	−0.191588	−	0.715017i
$623$	−13.0108	−	22.5353i	−0.521266	−	0.902859i
$624$	8.25248	+	21.0081i	0.330363	+	0.840997i
$625$	12.0537	−	20.8776i	0.482146	−	0.835102i
$626$	39.8636	+	10.6814i	1.59327	+	0.426916i
$627$	7.61849	+	10.7968i	0.304253	+	0.431184i
$628$	3.29426	+	1.90194i	0.131455	+	0.0758956i
$629$	−10.1041	+	10.1041i	−0.402876	+	0.402876i
$630$	0.246066	−	3.06854i	0.00980350	−	0.122254i
$631$	−16.0334	−	4.29614i	−0.638281	−	0.171027i	−0.0748561	−	0.997194i	$-0.523850\pi$
$631$	−16.0334	−	4.29614i	−0.638281	−	0.171027i	−0.563424	+	0.826168i	$0.690516\pi$
$632$	1.53962	−	5.74593i	0.0612427	−	0.228561i
$633$	7.33528	−	5.17594i	0.291551	−	0.205725i
$634$	−37.8044	+	21.8264i	−1.50140	+	0.866836i
$635$	−0.614605	+	2.29374i	−0.0243899	+	0.0910242i
$636$	−0.0614491	−	0.674217i	−0.00243662	−	0.0267344i
$637$	6.65285	−	6.94685i	0.263595	−	0.275244i
$638$			1.25874i			0.0498339i
$639$	12.7798	+	1.02481i	0.505562	+	0.0405409i
$640$	1.17113	−	2.02845i	0.0462929	−	0.0801817i
$641$	−23.3131	+	40.3794i	−0.920810	+	1.59489i	−0.122646	+	0.992451i	$0.539138\pi$
$641$	−23.3131	+	40.3794i	−0.920810	+	1.59489i	−0.798165	+	0.602439i	$0.794196\pi$
$642$	−15.6861	−	42.6161i	−0.619082	−	1.68192i
$643$	−6.58925	−	6.58925i	−0.259855	−	0.259855i	0.565140	−	0.824995i	$-0.308822\pi$
$643$	−6.58925	−	6.58925i	−0.259855	−	0.259855i	−0.824995	+	0.565140i	$0.808822\pi$
$644$	2.06590	+	2.06590i	0.0814077	+	0.0814077i
$645$	1.48821	+	0.256855i	0.0585983	+	0.0101136i
$646$	1.63929	−	2.83933i	0.0644969	−	0.111712i
$647$	−8.16482	+	14.1419i	−0.320992	+	0.555975i	−0.980693	−	0.195553i	$-0.937350\pi$
$647$	−8.16482	+	14.1419i	−0.320992	+	0.555975i	0.659701	+	0.751528i	$0.270683\pi$
$648$	24.1360	+	10.8317i	0.948152	+	0.425509i
$649$		−	1.84615i		−	0.0724678i
$650$	0.519764	+	24.0431i	0.0203868	+	0.943047i
$651$	35.5985	−	25.1191i	1.39522	−	0.984495i
$652$	−0.840205	+	3.13569i	−0.0329049	+	0.122803i
$653$	15.0285	−	8.67671i	0.588111	−	0.339546i	−0.176239	−	0.984347i	$-0.556393\pi$
$653$	15.0285	−	8.67671i	0.588111	−	0.339546i	0.764350	+	0.644801i	$0.223060\pi$
$654$	2.19871	+	24.1242i	0.0859765	+	0.943330i
$655$	0.621087	−	2.31793i	0.0242679	−	0.0905690i
$656$	−29.0199	−	7.77586i	−1.13304	−	0.303596i
$657$	1.52892	−	2.21757i	0.0596490	−	0.0865155i
$658$	−14.2196	+	14.2196i	−0.554336	+	0.554336i
$659$	15.1982	+	8.77471i	0.592040	+	0.341814i	0.765904	−	0.642955i	$-0.222292\pi$
$659$	15.1982	+	8.77471i	0.592040	+	0.341814i	−0.173864	+	0.984770i	$0.555625\pi$
$660$	0.184183	−	0.398747i	0.00716930	−	0.0155212i
$661$	5.02043	+	1.34522i	0.195272	+	0.0523230i	0.355129	−	0.934817i	$-0.384437\pi$
$661$	5.02043	+	1.34522i	0.195272	+	0.0523230i	−0.159857	+	0.987140i	$0.551103\pi$
$662$	3.46390	−	5.99965i	0.134628	−	0.233183i
$663$	7.25374	−	9.10160i	0.281712	−	0.353477i
$664$	5.26757	+	9.12370i	0.204421	+	0.354068i
$665$	−0.256316	−	0.956584i	−0.00993950	−	0.0370947i
$666$	29.2587	+	10.4098i	1.13375	+	0.403371i
$667$	−0.731297	+	0.422214i	−0.0283159	+	0.0163482i
$668$	−3.10121	−	0.830967i	−0.119990	−	0.0321511i
$669$	−15.3323	+	18.4074i	−0.592782	+	0.711671i
$670$	−1.93522	+	1.93522i	−0.0747641	+	0.0747641i
$671$	−46.2424	+	12.3906i	−1.78517	+	0.478335i
$672$	2.25667	−	4.88558i	0.0870528	−	0.188465i
$673$			10.2016i			0.393241i	0.980480	+	0.196620i	$0.0629967\pi$
$673$			10.2016i			0.393241i	−0.980480	+	0.196620i	$0.937003\pi$
$674$	−15.7875	+	4.23025i	−0.608112	+	0.162943i
$675$	18.3479	+	17.9532i	0.706211	+	0.691020i
$676$	1.23685	+	1.94319i	0.0475711	+	0.0747382i
$677$	14.0535	−	8.11378i	0.540119	−	0.311838i	−0.205008	−	0.978760i	$-0.565722\pi$
$677$	14.0535	−	8.11378i	0.540119	−	0.311838i	0.745127	+	0.666923i	$0.232389\pi$
$678$	2.57523	−	3.09173i	0.0989012	−	0.118737i
$679$	10.2169	+	17.6962i	0.392090	+	0.679119i
$680$	−1.33907			−0.0513509
$681$	20.1311	−	7.40985i	0.771425	−	0.283946i
$682$	−61.7725	+	16.5519i	−2.36539	+	0.633805i
$683$	6.66463	−	24.8727i	0.255015	−	0.951728i	−0.713067	−	0.701095i	$-0.752695\pi$
$683$	6.66463	−	24.8727i	0.255015	−	0.951728i	0.968082	−	0.250633i	$-0.0806387\pi$
$684$	0.690413	+	0.0553641i	0.0263986	+	0.00211690i
$685$	2.24644	+	3.89094i	0.0858319	+	0.148665i
$686$	−18.1864			−0.694362
$687$	25.9484	−	9.55109i	0.989995	−	0.364397i
$688$	−11.1649	−	6.44607i	−0.425659	−	0.245754i
$689$	2.22416	+	7.63650i	0.0847339	+	0.290927i
$690$	−3.01879	+	0.275137i	−0.114923	+	0.0104743i
$691$	−22.7148	−	22.7148i	−0.864113	−	0.864113i	0.127700	−	0.991813i	$-0.459240\pi$
$691$	−22.7148	−	22.7148i	−0.864113	−	0.864113i	−0.991813	+	0.127700i	$0.959240\pi$
$692$	0.512278	+	0.295764i	0.0194739	+	0.0112433i
$693$	−18.3070	+	51.4556i	−0.695427	+	1.95464i
$694$	30.1033	+	30.1033i	1.14271	+	1.14271i
$695$	−0.487319	−	1.81870i	−0.0184851	−	0.0689872i
$696$	0.622919	+	0.518856i	0.0236117	+	0.0196672i
$697$	4.00958	+	14.9640i	0.151874	+	0.566800i
$698$			6.30515i			0.238654i
$699$	2.17656	+	23.8811i	0.0823252	+	0.903268i
$700$	1.92455	−	1.92455i	0.0727410	−	0.0727410i
$701$	−32.1444			−1.21408			−0.607038	−	0.794673i	$-0.707642\pi$
$701$	−32.1444			−1.21408			−0.607038	+	0.794673i	$0.707642\pi$
$702$	−24.6323	−	5.74963i	−0.929685	−	0.217006i
$703$	9.99062			0.376803
$704$	−35.5125	+	35.5125i	−1.33843	+	1.33843i
$705$	0.184085	+	2.01977i	0.00693302	+	0.0760688i
$706$			14.0863i			0.530146i
$707$	−3.75564	−	14.0163i	−0.141246	−	0.527135i
$708$	−0.0743532	−	0.0619319i	−0.00279436	−	0.00232755i
$709$	−3.59586	−	13.4199i	−0.135045	−	0.503996i	−0.999998	−	0.00214195i	$-0.999318\pi$
$709$	−3.59586	−	13.4199i	−0.135045	−	0.503996i	0.864952	−	0.501854i	$-0.167348\pi$
$710$	0.997288	+	0.997288i	0.0374276	+	0.0374276i
$711$	3.93607	+	4.62236i	0.147614	+	0.173352i
$712$	21.3044	+	12.3001i	0.798414	+	0.460965i
$713$	−30.3364	−	30.3364i	−1.13611	−	1.13611i
$714$	13.4947	−	1.22993i	0.505028	−	0.0460290i
$715$	−1.22753	+	5.01212i	−0.0459071	+	0.187443i
$716$	−0.660453	−	0.381313i	−0.0246823	−	0.0142503i
$717$	−21.8400	+	8.03887i	−0.815631	+	0.300217i
$718$	28.2373			1.05381
$719$	17.4721	+	30.2626i	0.651600	+	1.12860i	0.982735	+	0.185021i	$0.0592352\pi$
$719$	17.4721	+	30.2626i	0.651600	+	1.12860i	−0.331135	+	0.943583i	$0.607431\pi$
$720$	1.13747	+	2.39387i	0.0423912	+	0.0892142i
$721$	11.3389	−	42.3174i	0.422283	−	1.57598i
$722$	22.5640	−	6.04599i	0.839744	−	0.225009i
$723$	4.52090	−	1.66405i	0.168134	−	0.0618867i
$724$	3.30582			0.122860
$725$	0.393326	+	0.681261i	0.0146078	+	0.0253014i
$726$	34.8440	−	41.8324i	1.29318	−	1.55255i
$727$	−3.14945	+	1.81834i	−0.116807	+	0.0674383i	−0.557265	−	0.830335i	$-0.688149\pi$
$727$	−3.14945	+	1.81834i	−0.116807	+	0.0674383i	0.440458	+	0.897773i	$0.354816\pi$
$728$	−7.83904	+	32.0075i	−0.290534	+	1.18628i
$729$	−23.0836	+	14.0052i	−0.854950	+	0.518711i
$730$	0.286212	−	0.0766902i	0.0105932	−	0.00283843i
$731$			6.64776i			0.245876i
$732$	−1.05224	+	2.27806i	−0.0388921	+	0.0841996i
$733$	−23.0962	+	6.18860i	−0.853077	+	0.228581i	−0.658756	−	0.752357i	$-0.728917\pi$
$733$	−23.0962	+	6.18860i	−0.853077	+	0.228581i	−0.194321	+	0.980938i	$0.562250\pi$
$734$	−2.87186	+	2.87186i	−0.106002	+	0.106002i
$735$	0.722867	−	0.867848i	0.0266634	−	0.0320110i
$736$	−5.11870	−	1.37155i	−0.188678	−	0.0505560i
$737$	42.0500	−	24.2776i	1.54893	−	0.894276i
$738$	25.6343	−	21.8283i	0.943612	−	0.803511i
$739$	10.7240	+	40.0224i	0.394488	+	1.47225i	0.822651	+	0.568547i	$0.192494\pi$
$739$	10.7240	+	40.0224i	0.394488	+	1.47225i	−0.428163	+	0.903702i	$0.640839\pi$
$740$	−0.166041	−	0.287592i	−0.00610380	−	0.0105721i
$741$	−8.08585	+	0.913556i	−0.297041	+	0.0335603i
$742$	−4.63028	+	8.01987i	−0.169983	+	0.294419i
$743$	−25.9599	−	6.95593i	−0.952376	−	0.255188i	−0.251006	−	0.967986i	$-0.580761\pi$
$743$	−25.9599	−	6.95593i	−0.952376	−	0.255188i	−0.701370	+	0.712797i	$0.747428\pi$
$744$	−17.2717	+	37.3925i	−0.633211	+	1.37087i
$745$	−0.564682	−	0.326019i	−0.0206883	−	0.0119444i
$746$	−12.8009	+	12.8009i	−0.468672	+	0.468672i
$747$	−10.7177	−	0.859453i	−0.392141	−	0.0314457i
$748$	1.86755	+	0.500408i	0.0682844	+	0.0182967i
$749$	15.6276	−	58.3228i	0.571019	−	2.13107i
$750$	0.515725	+	5.65851i	0.0188316	+	0.206619i
$751$	−31.1394	+	17.9784i	−1.13629	+	0.656040i	−0.945510	−	0.325592i	$-0.894436\pi$
$751$	−31.1394	+	17.9784i	−1.13629	+	0.656040i	−0.190784	+	0.981632i	$0.561103\pi$
$752$	4.48105	−	16.7235i	0.163407	−	0.609843i
$753$	−20.0272	+	14.1316i	−0.729830	+	0.514984i
$754$	−0.679506	−	0.372968i	−0.0247461	−	0.0135827i
$755$		−	2.03769i		−	0.0741592i
$756$	1.45822	+	2.46347i	0.0530349	+	0.0895954i
$757$	−9.51324	+	16.4774i	−0.345764	+	0.598882i	−0.985492	−	0.169720i	$-0.945714\pi$
$757$	−9.51324	+	16.4774i	−0.345764	+	0.598882i	0.639728	+	0.768601i	$0.279047\pi$
$758$	−6.12942	+	10.6165i	−0.222631	+	0.385607i
$759$	52.9963	+	9.14677i	1.92364	+	0.332007i
$760$	0.662016	+	0.662016i	0.0240138	+	0.0240138i
$761$	−14.4793	−	14.4793i	−0.524874	−	0.524874i	0.394165	−	0.919039i	$-0.371034\pi$
$761$	−14.4793	−	14.4793i	−0.524874	−	0.524874i	−0.919039	+	0.394165i	$0.871034\pi$
$762$	7.84719	+	21.3193i	0.284274	+	0.772316i
$763$	−16.1046	+	27.8940i	−0.583025	+	1.00983i
$764$	1.16180	−	2.01230i	0.0420324	−	0.0728023i
$765$	0.775743	−	1.12514i	0.0280470	−	0.0406797i
$766$		−	10.4724i		−	0.378381i
$767$	0.996610	+	0.547021i	0.0359855	+	0.0197518i
$768$	0.663132	+	7.27585i	0.0239287	+	0.262545i
$769$	−0.356627	+	1.33095i	−0.0128603	+	0.0479952i	−0.972058	−	0.234742i	$-0.924576\pi$
$769$	−0.356627	+	1.33095i	−0.0128603	+	0.0479952i	0.959198	+	0.282737i	$0.0912423\pi$
$770$	−5.20311	+	3.00402i	−0.187507	+	0.108257i
$771$	16.0165	−	11.3016i	0.576821	−	0.407018i
$772$	1.10129	−	4.11008i	0.0396364	−	0.147925i
$773$	5.25558	+	1.40823i	0.189030	+	0.0506504i	0.352092	−	0.935965i	$-0.385470\pi$
$773$	5.25558	+	1.40823i	0.189030	+	0.0506504i	−0.163062	+	0.986616i	$0.552137\pi$
$774$	13.0495	−	6.20064i	0.469056	−	0.222878i
$775$	−28.2608	+	28.2608i	−1.01516	+	1.01516i
$776$	−16.7296	−	9.65883i	−0.600557	−	0.346732i
$777$	23.8067	+	33.7385i	0.854059	+	1.21036i
$778$	49.0661	+	13.1472i	1.75910	+	0.471350i
$779$	5.41569	−	9.38025i	0.194037	−	0.336082i
$780$	0.160682	+	0.217578i	0.00575335	+	0.00779053i
$781$	−12.5111	−	21.6699i	−0.447682	−	0.775409i
$782$	−3.45352	−	12.8887i	−0.123498	−	0.460900i
$783$	−0.796833	+	0.222823i	−0.0284765	+	0.00796305i
$784$	−8.35008	+	4.82092i	−0.298217	+	0.172176i
$785$	−5.06883	−	1.35819i	−0.180914	−	0.0484758i
$786$	−7.92995	−	21.5441i	−0.282852	−	0.768453i
$787$	−31.1958	+	31.1958i	−1.11201	+	1.11201i	−0.119131	+	0.992879i	$0.538011\pi$
$787$	−31.1958	+	31.1958i	−1.11201	+	1.11201i	−0.992879	+	0.119131i	$0.961989\pi$
$788$	2.34572	−	0.628533i	0.0835627	−	0.0223906i
$789$	12.7310	−	1.16033i	0.453237	−	0.0413087i
$790$			0.667867i			0.0237616i
$791$	5.16780	−	1.38471i	0.183746	−	0.0492346i
$792$	−9.33408	−	50.7812i	−0.331672	−	1.80443i
$793$	7.01294	−	28.6345i	0.249037	−	1.01684i
$794$	4.03521	−	2.32973i	0.143204	−	0.0826790i
$795$	0.322615	+	0.876481i	0.0114420	+	0.0310856i
$796$	−0.304867	−	0.528046i	−0.0108057	−	0.0187161i
$797$	49.6265			1.75786			0.878930	−	0.476951i	$-0.158258\pi$
$797$	49.6265			1.75786			0.878930	+	0.476951i	$0.158258\pi$
$798$	−7.27967	−	6.06355i	−0.257697	−	0.214647i
$799$	−8.62338	+	2.31063i	−0.305073	+	0.0817442i
$800$	−1.27771	+	4.76848i	−0.0451739	+	0.168591i
$801$	−22.6770	+	10.7753i	−0.801253	+	0.380725i
$802$	−11.2947	−	19.5629i	−0.398828	−	0.690790i
$803$	−5.25695			−0.185514
$804$	0.432859	−	2.50798i	0.0152658	−	0.0884496i
$805$	−3.49053	−	2.01526i	−0.123025	−	0.0710285i
$806$	9.36818	−	38.2511i	0.329980	−	1.34734i
$807$	−9.04234	−	12.8147i	−0.318306	−	0.451099i
$808$	9.70013	+	9.70013i	0.341249	+	0.341249i
$809$	−16.8749	−	9.74272i	−0.593290	−	0.342536i	0.173108	−	0.984903i	$-0.444619\pi$
$809$	−16.8749	−	9.74272i	−0.593290	−	0.342536i	−0.766397	+	0.642367i	$0.777952\pi$
$810$	−2.93222	−	0.473313i	−0.103028	−	0.0166305i
$811$	9.84811	+	9.84811i	0.345814	+	0.345814i	0.858548	−	0.512734i	$-0.171367\pi$
$811$	9.84811	+	9.84811i	0.345814	+	0.345814i	−0.512734	+	0.858548i	$0.671367\pi$
$812$	0.0227052	+	0.0847369i	0.000796796	+	0.00297368i
$813$	14.9155	−	5.49008i	0.523108	−	0.192546i
$814$	−15.6871	−	58.5450i	−0.549832	−	2.05200i
$815$		−	4.47843i		−	0.156873i
$816$	−9.53237	+	6.72625i	−0.333700	+	0.235466i
$817$	3.28656	−	3.28656i	0.114982	−	0.114982i
$818$	−16.8031			−0.587506
$819$	−22.3529	−	25.1292i	−0.781073	−	0.878084i
$820$	−0.360029			−0.0125728
$821$	3.96886	−	3.96886i	0.138514	−	0.138514i	−0.634450	−	0.772964i	$-0.718773\pi$
$821$	3.96886	−	3.96886i	0.138514	−	0.138514i	0.772964	+	0.634450i	$0.218773\pi$
$822$	39.0205	+	18.0237i	1.36100	+	0.628648i
$823$		−	42.9803i		−	1.49820i	−0.662458	−	0.749099i	$-0.730487\pi$
$823$		−	42.9803i		−	1.49820i	0.662458	−	0.749099i	$-0.269513\pi$
$824$	10.7195	+	40.0058i	0.373432	+	1.39367i
$825$	8.52095	−	49.3703i	0.296661	−	1.71885i
$826$	0.342584	+	1.27854i	0.0119200	+	0.0444861i
$827$	5.85020	+	5.85020i	0.203431	+	0.203431i	0.801468	−	0.598037i	$-0.204052\pi$
$827$	5.85020	+	5.85020i	0.203431	+	0.203431i	−0.598037	+	0.801468i	$0.704052\pi$
$828$	2.14622	−	1.82757i	0.0745865	−	0.0635123i
$829$	−10.4831	−	6.05242i	−0.364093	−	0.210209i	0.306782	−	0.951780i	$-0.400748\pi$
$829$	−10.4831	−	6.05242i	−0.364093	−	0.210209i	−0.670875	+	0.741571i	$0.734081\pi$
$830$	−0.836370	−	0.836370i	−0.0290308	−	0.0290308i
$831$	−11.2906	+	24.4437i	−0.391668	+	0.847944i
$832$	−8.64827	−	29.6932i	−0.299825	−	1.02943i
$833$	4.30567	+	2.48588i	0.149183	+	0.0861307i
$834$	−13.8404	−	11.5283i	−0.479255	−	0.399192i
$835$	4.42920			0.153279
$836$	−0.675896	−	1.17069i	−0.0233763	−	0.0404890i
$837$	−21.4131	−	36.1745i	−0.740144	−	1.25037i
$838$	−9.92642	+	37.0459i	−0.342903	+	1.27973i
$839$	−7.84284	+	2.10148i	−0.270765	+	0.0725512i	−0.391647	−	0.920116i	$-0.628094\pi$
$839$	−7.84284	+	2.10148i	−0.270765	+	0.0725512i	0.120882	+	0.992667i	$0.461428\pi$
$840$	−0.658124	+	3.81316i	−0.0227074	+	0.131567i
$841$	28.9746			0.999126
$842$	9.69504	+	16.7923i	0.334113	+	0.578701i
$843$	0.337534	+	0.0582559i	0.0116253	+	0.00200644i
$844$	−0.795354	+	0.459198i	−0.0273772	+	0.0158062i
$845$	−2.34198	−	2.14777i	−0.0805664	−	0.0738854i
$846$	12.5791	+	14.7725i	0.432480	+	0.507888i
$847$	69.9226	−	18.7357i	2.40257	−	0.643766i
$848$		−	7.97295i		−	0.273792i
$849$	−25.2491	−	35.7828i	−0.866548	−	1.22806i
$850$	−12.0069	+	3.21723i	−0.411833	+	0.110350i
$851$	28.7514	−	28.7514i	0.985584	−	0.985584i
$852$	−1.29245	−	0.223068i	−0.0442787	−	0.00764217i
$853$	−37.3639	−	10.0116i	−1.27932	−	0.342792i	−0.445723	−	0.895171i	$-0.647054\pi$
$853$	−37.3639	−	10.0116i	−1.27932	−	0.342792i	−0.833593	+	0.552379i	$0.813720\pi$
$854$	29.7256	−	17.1621i	1.01719	−	0.587275i
$855$	−0.939772	+	0.172739i	−0.0321395	+	0.00590757i
$856$	14.7739	+	55.1370i	0.504962	+	1.88454i
$857$	11.7539	+	20.3584i	0.401507	+	0.695431i	0.993908	−	0.110213i	$-0.0351532\pi$
$857$	11.7539	+	20.3584i	0.401507	+	0.695431i	−0.592401	+	0.805643i	$0.701820\pi$
$858$	18.0497	+	45.9486i	0.616206	+	1.56866i
$859$	−14.2284	+	24.6442i	−0.485465	+	0.840850i	−0.999860	−	0.0167028i	$-0.994683\pi$
$859$	−14.2284	+	24.6442i	−0.485465	+	0.840850i	0.514395	+	0.857553i	$0.328016\pi$
$860$	−0.149229	−	0.0399859i	−0.00508868	−	0.00136351i
$861$	44.5824	−	4.06330i	1.51936	−	0.138477i
$862$	29.7725	+	17.1892i	1.01406	+	0.585466i
$863$	34.0374	−	34.0374i	1.15865	−	1.15865i	0.173878	−	0.984767i	$-0.444370\pi$
$863$	34.0374	−	34.0374i	1.15865	−	1.15865i	0.984767	−	0.173878i	$-0.0556300\pi$
$864$	−4.52472	−	2.54716i	−0.153934	−	0.0866563i
$865$	−0.788236	−	0.211207i	−0.0268008	−	0.00718126i
$866$	2.65155	−	9.89574i	0.0901035	−	0.336271i
$867$	−21.2697	−	9.82453i	−0.722356	−	0.333659i
$868$	−3.85990	+	2.22851i	−0.131013	+	0.0756407i
$869$	3.06673	−	11.4452i	0.104032	−	0.388252i
$870$	−0.0826306	−	0.0381673i	−0.00280144	−	0.00129399i
$871$	0.646236	+	29.8934i	0.0218969	+	1.01290i
$872$		−	30.4498i		−	1.03116i
$873$	17.8075	−	8.46144i	0.602693	−	0.286376i
$874$	−4.66463	+	8.07938i	−0.157784	+	0.273289i
$875$	−3.77745	+	6.54274i	−0.127701	+	0.221185i
$876$	−0.176352	+	0.211722i	−0.00595839	+	0.00715342i
$877$	0.563479	+	0.563479i	0.0190273	+	0.0190273i	0.716556	−	0.697529i	$-0.245717\pi$
$877$	0.563479	+	0.563479i	0.0190273	+	0.0190273i	−0.697529	+	0.716556i	$0.745717\pi$
$878$	15.6902	+	15.6902i	0.529519	+	0.529519i
$879$	8.09046	−	9.71310i	0.272884	−	0.327615i
$880$	2.58634	−	4.47967i	0.0871854	−	0.151009i
$881$	−6.01833	+	10.4241i	−0.202763	+	0.351196i	−0.949418	−	0.314016i	$-0.898325\pi$
$881$	−6.01833	+	10.4241i	−0.202763	+	0.351196i	0.746655	+	0.665212i	$0.231659\pi$
$882$	0.863701	−	10.7707i	0.0290823	−	0.362669i
$883$			19.0018i			0.639461i	0.947509	+	0.319731i	$0.103592\pi$
$883$			19.0018i			0.639461i	−0.947509	+	0.319731i	$0.896408\pi$
$884$	−0.823497	+	0.859888i	−0.0276972	+	0.0289212i
$885$	0.121192	+	0.0559789i	0.00407382	+	0.00188171i
$886$	8.93311	−	33.3388i	0.300114	−	1.12004i
$887$	−48.9543	+	28.2638i	−1.64373	+	0.949005i	−0.664232	+	0.747526i	$0.731241\pi$
$887$	−48.9543	+	28.2638i	−1.64373	+	0.949005i	−0.979493	+	0.201479i	$0.935425\pi$
$888$	−35.4388	−	16.3693i	−1.18925	−	0.549317i
$889$	−7.81789	+	29.1768i	−0.262204	+	0.978558i
$890$	−2.66781	−	0.714837i	−0.0894252	−	0.0239614i
$891$	48.0760	+	21.5754i	1.61061	+	0.722804i
$892$	1.73292	−	1.73292i	0.0580225	−	0.0580225i
$893$	5.40562	+	3.12094i	0.180892	+	0.104438i
$894$	−6.21211	+	0.566181i	−0.207764	+	0.0189359i
$895$	1.01623	+	0.272298i	0.0339688	+	0.00910192i
$896$	14.8970	−	25.8023i	0.497673	−	0.861994i
$897$	−20.6407	+	25.8988i	−0.689172	+	0.864736i
$898$	−1.79778	−	3.11385i	−0.0599929	−	0.103911i
$899$	−0.333412	−	1.24431i	−0.0111199	−	0.0415001i
$900$	−1.70253	−	1.99938i	−0.0567508	−	0.0666460i
$901$	−3.56041	+	2.05560i	−0.118615	+	0.0684821i
$902$	−63.4718	−	17.0072i	−2.11338	−	0.566279i
$903$	18.9303	+	3.26724i	0.629962	+	0.108727i
$904$	−3.57644	+	3.57644i	−0.118951	+	0.118951i
$905$	−4.40514	+	1.18035i	−0.146432	+	0.0392363i
$906$	−11.2391	−	15.9279i	−0.373394	−	0.529170i
$907$		−	9.24845i		−	0.307090i	−0.988142	−	0.153545i	$-0.950931\pi$
$907$		−	9.24845i		−	0.307090i	0.988142	−	0.153545i	$-0.0490690\pi$
$908$	−2.11969	+	0.567970i	−0.0703445	+	0.0188487i
$909$	−13.7699	+	2.53105i	−0.456720	+	0.0839496i
$910$	−0.0799629	−	3.69890i	−0.00265075	−	0.122617i
$911$	−14.7274	+	8.50286i	−0.487940	+	0.281712i	−0.723719	−	0.690094i	$-0.757569\pi$
$911$	−14.7274	+	8.50286i	−0.487940	+	0.281712i	0.235779	+	0.971807i	$0.424236\pi$
$912$	8.03804	+	1.38731i	0.266166	+	0.0459383i
$913$	10.4924	+	18.1733i	0.347247	+	0.601449i
$914$	7.61319			0.251822
$915$	0.588769	−	3.41132i	0.0194641	−	0.112775i
$916$	−2.73223	+	0.732098i	−0.0902753	+	0.0241892i
$917$	7.90035	−	29.4845i	0.260892	−	0.973664i
$918$	−0.142139	−	13.0736i	−0.00469129	−	0.431492i
$919$	−7.27854	−	12.6068i	−0.240097	−	0.415860i	0.720645	−	0.693304i	$-0.243846\pi$
$919$	−7.27854	−	12.6068i	−0.240097	−	0.415860i	−0.960742	+	0.277445i	$0.910513\pi$
$920$	3.81035			0.125623
$921$	−32.3180	−	26.9190i	−1.06491	−	0.887013i
$922$	40.1757	+	23.1954i	1.32312	+	0.763901i
$923$	15.4051	−	0.333029i	0.507067	−	0.0109618i
$924$	2.34284	−	5.07214i	0.0770737	−	0.166861i
$925$	−26.7842	−	26.7842i	−0.880659	−	0.880659i
$926$	2.68913	+	1.55257i	0.0883704	+	0.0510207i
$927$	−39.8247	−	14.1690i	−1.30801	−	0.465370i
$928$	−0.112514	−	0.112514i	−0.00369345	−	0.00369345i
$929$	−1.25468	−	4.68252i	−0.0411647	−	0.153629i	0.942284	−	0.334814i	$-0.108673\pi$
$929$	−1.25468	−	4.68252i	−0.0411647	−	0.153629i	−0.983449	+	0.181185i	$0.942007\pi$
$930$	0.786502	−	4.55698i	0.0257904	−	0.149429i
$931$	−0.899680	−	3.35765i	−0.0294858	−	0.110043i
$932$		−	2.45314i		−	0.0803553i
$933$	−21.5012	−	9.93149i	−0.703919	−	0.325142i
$934$	5.30537	−	5.30537i	0.173597	−	0.173597i
$935$	−2.66726			−0.0872288
$936$	30.1790	+	10.0078i	0.986430	+	0.327115i
$937$	−11.3405			−0.370479			−0.185239	−	0.982693i	$-0.559306\pi$
$937$	−11.3405			−0.370479			−0.185239	+	0.982693i	$0.559306\pi$
$938$	−24.6164	+	24.6164i	−0.803753	+	0.803753i
$939$	43.2594	−	30.5248i	1.41172	−	0.996139i
$940$		−	0.207476i		−	0.00676713i
$941$	10.3541	+	38.6421i	0.337535	+	1.25970i	0.901095	+	0.433622i	$0.142765\pi$
$941$	10.3541	+	38.6421i	0.337535	+	1.25970i	−0.563560	+	0.826075i	$0.690569\pi$
$942$	−47.1125	+	17.3412i	−1.53501	+	0.565005i
$943$	−11.4094	−	42.5803i	−0.371540	−	1.38661i
$944$	−0.805820	−	0.805820i	−0.0262272	−	0.0262272i
$945$	−2.82273	−	2.76201i	−0.0918234	−	0.0898482i
$946$	−24.4197	−	14.0987i	−0.793954	−	0.458389i
$947$	16.1922	+	16.1922i	0.526176	+	0.526176i	0.919430	−	0.393254i	$-0.128651\pi$
$947$	16.1922	+	16.1922i	0.526176	+	0.526176i	−0.393254	+	0.919430i	$0.628651\pi$
$948$	−0.358074	−	0.507458i	−0.0116297	−	0.0164815i
$949$	1.55765	−	2.83786i	0.0505635	−	0.0921209i
$950$	7.52659	+	4.34548i	0.244195	+	0.140986i
$951$	−9.52467	+	55.1858i	−0.308859	+	1.78952i
$952$	−17.0332			−0.552049
$953$	11.0672	+	19.1690i	0.358502	+	0.620944i	0.987711	−	0.156292i	$-0.0499542\pi$
$953$	11.0672	+	19.1690i	0.358502	+	0.620944i	−0.629209	+	0.777237i	$0.716621\pi$
$954$	7.35609	+	5.07173i	0.238162	+	0.164203i
$955$	−0.829649	+	3.09629i	−0.0268468	+	0.100194i
$956$	2.29963	−	0.616185i	0.0743755	−	0.0199289i
$957$	1.24078	+	1.03350i	0.0401087	+	0.0334082i
$958$	−10.9443			−0.353594
$959$	28.5751	+	49.4935i	0.922738	+	1.59823i
$960$	−1.25443	−	3.40805i	−0.0404866	−	0.109994i
$961$	29.8335	−	17.2244i	0.962370	−	0.555625i
$962$	36.2525	+	8.87870i	1.16883	+	0.286261i
$963$	−54.8873	−	19.5280i	−1.76872	−	0.629282i
$964$	−0.476026	+	0.127551i	−0.0153318	+	0.00410813i
$965$			5.87007i			0.188964i
$966$	−38.3996	+	3.49980i	−1.23549	+	0.112604i
$967$	−33.3431	+	8.93425i	−1.07224	+	0.287306i	−0.751414	−	0.659831i	$-0.770628\pi$
$967$	−33.3431	+	8.93425i	−1.07224	+	0.287306i	−0.320828	+	0.947138i	$0.603961\pi$
$968$	−48.3908	+	48.3908i	−1.55534	+	1.55534i
$969$	−1.45287	−	3.94716i	−0.0466729	−	0.126801i
$970$	2.09494	+	0.561338i	0.0672645	+	0.0180235i
$971$	−8.83985	+	5.10369i	−0.283684	+	0.163785i	−0.635090	−	0.772438i	$-0.719037\pi$
$971$	−8.83985	+	5.10369i	−0.283684	+	0.163785i	0.351406	+	0.936223i	$0.385704\pi$
$972$	2.48173	−	1.21247i	0.0796014	−	0.0388899i
$973$	−6.19879	−	23.1342i	−0.198724	−	0.741648i
$974$	−1.50436	−	2.60563i	−0.0482028	−	0.0834896i
$975$	24.1268	+	19.2284i	0.772677	+	0.615803i
$976$	−14.7759	+	25.5925i	−0.472964	+	0.819197i
$977$	−10.0767	−	2.70003i	−0.322381	−	0.0863817i	0.0939994	−	0.995572i	$-0.470035\pi$
$977$	−10.0767	−	2.70003i	−0.322381	−	0.0863817i	−0.416380	+	0.909191i	$0.636701\pi$
$978$	−24.7012	−	35.0063i	−0.789859	−	1.11938i
$979$	42.4357	+	24.5003i	1.35625	+	0.783032i
$980$	−0.0817015	+	0.0817015i	−0.00260986	+	0.00260986i
$981$	25.5853	+	17.6400i	0.816875	+	0.563203i
$982$	−39.7144	−	10.6414i	−1.26734	−	0.339582i
$983$	1.42486	−	5.31765i	0.0454460	−	0.169607i	−0.939473	−	0.342623i	$-0.888685\pi$
$983$	1.42486	−	5.31765i	0.0454460	−	0.169607i	0.984919	+	0.173016i	$0.0553513\pi$
$984$	−34.5798	+	24.4002i	−1.10236	+	0.777851i
$985$	−2.90135	+	1.67509i	−0.0924446	+	0.0533729i
$986$	0.103697	−	0.387004i	0.00330240	−	0.0123247i
$987$	2.34159	+	25.6918i	0.0745336	+	0.817779i
$988$	0.832242	−	0.0179914i	0.0264772	−	0.000572383i
$989$		−	18.9164i		−	0.601506i
$990$	2.48786	+	5.23583i	0.0790695	+	0.166406i
$991$	23.6874	−	41.0278i	0.752456	−	1.30329i	−0.194173	−	0.980967i	$-0.562202\pi$
$991$	23.6874	−	41.0278i	0.752456	−	1.30329i	0.946629	−	0.322325i	$-0.104464\pi$
$992$	4.04210	−	7.00113i	0.128337	−	0.222286i
$993$	−3.06999	−	8.34055i	−0.0974231	−	0.264679i
$994$	12.6857	+	12.6857i	0.402366	+	0.402366i
$995$	0.594789	+	0.594789i	0.0188561	+	0.0188561i
$996$	1.08391	+	0.187074i	0.0343449	+	0.00592768i
$997$	22.7093	−	39.3336i	0.719210	−	1.24571i	−0.242103	−	0.970250i	$-0.577837\pi$
$997$	22.7093	−	39.3336i	0.719210	−	1.24571i	0.961313	−	0.275457i	$-0.0888293\pi$
$998$	13.4115	−	23.2294i	0.424533	−	0.735313i
$999$	34.2844	−	20.2943i	1.08471	−	0.642082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.59.10	yes	48
3.2	odd	2		351.2.ba.a.98.3		48
9.2	odd	6		117.2.bc.a.20.10	yes	48
9.7	even	3		351.2.bf.a.332.3		48
13.2	odd	12		117.2.bc.a.41.10	yes	48
39.2	even	12		351.2.bf.a.314.3		48
117.2	even	12	inner	117.2.x.a.2.10	✓	48
117.106	odd	12		351.2.ba.a.197.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.2.10	✓	48	117.2	even	12	inner
117.2.x.a.59.10	yes	48	1.1	even	1	trivial
117.2.bc.a.20.10	yes	48	9.2	odd	6
117.2.bc.a.41.10	yes	48	13.2	odd	12
351.2.ba.a.98.3		48	3.2	odd	2
351.2.ba.a.197.3		48	117.106	odd	12
351.2.bf.a.314.3		48	39.2	even	12
351.2.bf.a.332.3		48	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.954676 - 0.954676i) q^{2} +(-0.157210 - 1.72490i) q^{3} +0.177187i q^{4} +(-0.0632653 - 0.236109i) q^{5} +(-1.79681 - 1.49664i) q^{6} +(-0.804746 - 3.00335i) q^{7} +(2.07851 + 2.07851i) q^{8} +(-2.95057 + 0.542344i) q^{9} +O(q^{10})\)	\(q+(0.954676 - 0.954676i) q^{2} +(-0.157210 - 1.72490i) q^{3} +0.177187i q^{4} +(-0.0632653 - 0.236109i) q^{5} +(-1.79681 - 1.49664i) q^{6} +(-0.804746 - 3.00335i) q^{7} +(2.07851 + 2.07851i) q^{8} +(-2.95057 + 0.542344i) q^{9} +(-0.285806 - 0.165010i) q^{10} +(4.14014 + 4.14014i) q^{11} +(0.305630 - 0.0278556i) q^{12} +(-3.46171 + 1.00824i) q^{13} +(-3.63550 - 2.09896i) q^{14} +(-0.397319 + 0.146245i) q^{15} +3.61423 q^{16} +(-0.931829 - 1.61398i) q^{17} +(-2.29908 + 3.33460i) q^{18} +(-0.337244 + 1.25861i) q^{19} +(0.0418355 - 0.0112098i) q^{20} +(-5.05397 + 1.86026i) q^{21} +7.90498 q^{22} +(2.65154 + 4.59261i) q^{23} +(3.25846 - 3.91198i) q^{24} +(4.27838 - 2.47012i) q^{25} +(-2.34227 + 4.26736i) q^{26} +(1.39935 + 5.00418i) q^{27} +(0.532155 - 0.142591i) q^{28} +0.159233i q^{29} +(-0.239694 + 0.518928i) q^{30} +(-7.81438 + 2.09386i) q^{31} +(-0.706597 + 0.706597i) q^{32} +(6.49046 - 7.79220i) q^{33} +(-2.43042 - 0.651229i) q^{34} +(-0.658207 + 0.380016i) q^{35} +(-0.0960963 - 0.522803i) q^{36} +(-1.98445 - 7.40608i) q^{37} +(0.879607 + 1.52352i) q^{38} +(2.28333 + 5.81261i) q^{39} +(0.359258 - 0.622252i) q^{40} +(-8.02934 - 2.15146i) q^{41} +(-3.04896 + 6.60086i) q^{42} +(-3.08916 - 1.78352i) q^{43} +(-0.733579 + 0.733579i) q^{44} +(0.314721 + 0.662345i) q^{45} +(6.91582 + 1.85309i) q^{46} +(1.23983 - 4.62713i) q^{47} +(-0.568194 - 6.23419i) q^{48} +(-2.31033 + 1.33387i) q^{49} +(1.72630 - 6.44264i) q^{50} +(-2.63746 + 1.86105i) q^{51} +(-0.178647 - 0.613371i) q^{52} -2.20599i q^{53} +(6.11330 + 3.44145i) q^{54} +(0.715598 - 1.23945i) q^{55} +(4.56982 - 7.91516i) q^{56} +(2.22400 + 0.383846i) q^{57} +(0.152016 + 0.152016i) q^{58} +(-0.222958 - 0.222958i) q^{59} +(-0.0259127 - 0.0703998i) q^{60} +(-4.08824 + 7.08105i) q^{61} +(-5.46125 + 9.45915i) q^{62} +(4.00331 + 8.42515i) q^{63} +8.57760i q^{64} +(0.457061 + 0.753556i) q^{65} +(-1.24274 - 13.6353i) q^{66} +(2.14635 - 8.01031i) q^{67} +(0.285976 - 0.165108i) q^{68} +(7.50495 - 5.29566i) q^{69} +(-0.265582 + 0.991166i) q^{70} +(-4.12800 - 1.10609i) q^{71} +(-7.26005 - 5.00552i) q^{72} +(-0.634876 + 0.634876i) q^{73} +(-8.96492 - 5.17590i) q^{74} +(-4.93333 - 6.99146i) q^{75} +(-0.223010 - 0.0597552i) q^{76} +(9.10254 - 15.7661i) q^{77} +(7.72900 + 3.36932i) q^{78} +(-1.01186 - 1.75259i) q^{79} +(-0.228655 - 0.853353i) q^{80} +(8.41173 - 3.20045i) q^{81} +(-9.71937 + 5.61148i) q^{82} +(3.46192 + 0.927619i) q^{83} +(-0.329615 - 0.895499i) q^{84} +(-0.322122 + 0.322122i) q^{85} +(-4.65183 + 1.24645i) q^{86} +(0.274662 - 0.0250331i) q^{87} +17.2106i q^{88} +(8.08378 - 2.16604i) q^{89} +(0.932782 + 0.331868i) q^{90} +(5.81390 + 9.58537i) q^{91} +(-0.813751 + 0.469819i) q^{92} +(4.84020 + 13.1499i) q^{93} +(-3.23377 - 5.60105i) q^{94} +0.318505 q^{95} +(1.32989 + 1.10773i) q^{96} +(-6.34792 + 1.70092i) q^{97} +(-0.932205 + 3.47904i) q^{98} +(-14.4612 - 9.97039i) 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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