LMFDB - Embedded newform 360.2.bo.a.67.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 8, 9]))

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

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

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.17
Character	$\chi$	$=$	360.67
Dual form			360.2.bo.a.43.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07322 - 0.920972i) q^{2} +(0.380005 - 1.68985i) q^{3} +(0.303622 + 1.97682i) q^{4} +(0.0281379 - 2.23589i) q^{5} +(-1.96414 + 1.46362i) q^{6} +(-1.94379 - 0.520837i) q^{7} +(1.49474 - 2.40120i) q^{8} +(-2.71119 - 1.28430i) q^{9} +O(q^{10})$	\(q+(-1.07322 - 0.920972i) q^{2} +(0.380005 - 1.68985i) q^{3} +(0.303622 + 1.97682i) q^{4} +(0.0281379 - 2.23589i) q^{5} +(-1.96414 + 1.46362i) q^{6} +(-1.94379 - 0.520837i) q^{7} +(1.49474 - 2.40120i) q^{8} +(-2.71119 - 1.28430i) q^{9} +(-2.08939 + 2.37370i) q^{10} +(0.660500 + 1.14402i) q^{11} +(3.45591 + 0.238125i) q^{12} +(-0.243400 + 0.0652188i) q^{13} +(1.60645 + 2.34915i) q^{14} +(-3.76763 - 0.897199i) q^{15} +(-3.81563 + 1.20041i) q^{16} +(-4.73524 - 4.73524i) q^{17} +(1.72691 + 3.87528i) q^{18} +1.98509i q^{19} +(4.42850 - 0.623243i) q^{20} +(-1.61879 + 3.08679i) q^{21} +(0.344745 - 1.83609i) q^{22} +(6.95463 - 1.86349i) q^{23} +(-3.48966 - 3.43835i) q^{24} +(-4.99842 - 0.125827i) q^{25} +(0.321287 + 0.154170i) q^{26} +(-3.20055 + 4.09347i) q^{27} +(0.439422 - 4.00066i) q^{28} +(-0.0551733 - 0.0955630i) q^{29} +(3.21722 + 4.43278i) q^{30} +(-2.75811 - 1.59240i) q^{31} +(5.20057 + 2.22577i) q^{32} +(2.18422 - 0.681413i) q^{33} +(0.720954 + 9.44299i) q^{34} +(-1.21923 + 4.33145i) q^{35} +(1.71566 - 5.74948i) q^{36} +(-2.56353 + 2.56353i) q^{37} +(1.82821 - 2.13045i) q^{38} +(0.0177168 + 0.436093i) q^{39} +(-5.32676 - 3.40964i) q^{40} +(-1.89848 + 3.28826i) q^{41} +(4.58017 - 1.82197i) q^{42} +(1.65871 + 0.444450i) q^{43} +(-2.06098 + 1.65304i) q^{44} +(-2.94785 + 6.02579i) q^{45} +(-9.18009 - 4.40507i) q^{46} +(3.58815 + 0.961442i) q^{47} +(0.578560 + 6.90400i) q^{48} +(-2.55513 - 1.47521i) q^{49} +(5.24854 + 4.73844i) q^{50} +(-9.80126 + 6.20243i) q^{51} +(-0.202827 - 0.461355i) q^{52} +(-8.40903 - 8.40903i) q^{53} +(7.20488 - 1.44559i) q^{54} +(2.57649 - 1.44462i) q^{55} +(-4.15609 + 3.88891i) q^{56} +(3.35450 + 0.754344i) q^{57} +(-0.0287974 + 0.153374i) q^{58} +(5.18353 + 2.99271i) q^{59} +(0.629664 - 7.72033i) q^{60} +(7.90390 - 4.56332i) q^{61} +(1.49352 + 4.24914i) q^{62} +(4.60107 + 3.90851i) q^{63} +(-3.53151 - 7.17833i) q^{64} +(0.138973 + 0.546050i) q^{65} +(-2.97172 - 1.28029i) q^{66} +(10.9852 - 2.94347i) q^{67} +(7.92299 - 10.7984i) q^{68} +(-0.506220 - 12.4604i) q^{69} +(5.29764 - 3.52574i) q^{70} -13.2069i q^{71} +(-7.13640 + 4.59041i) q^{72} +(9.45101 - 9.45101i) q^{73} +(5.11219 - 0.390305i) q^{74} +(-2.11205 + 8.39876i) q^{75} +(-3.92416 + 0.602717i) q^{76} +(-0.688025 - 2.56775i) q^{77} +(0.382615 - 0.484342i) q^{78} +(1.34585 + 2.33107i) q^{79} +(2.57663 + 8.56510i) q^{80} +(5.70112 + 6.96399i) q^{81} +(5.06589 - 1.78060i) q^{82} +(-10.7685 - 2.88542i) q^{83} +(-6.59353 - 2.26283i) q^{84} +(-10.7207 + 10.4542i) q^{85} +(-1.37084 - 2.00462i) q^{86} +(-0.182453 + 0.0569202i) q^{87} +(3.73429 + 0.124020i) q^{88} -16.2645i q^{89} +(8.71329 - 3.75214i) q^{90} +0.507086 q^{91} +(5.79535 + 13.1822i) q^{92} +(-3.73901 + 4.05568i) q^{93} +(-2.96543 - 4.33643i) q^{94} +(4.43844 + 0.0558563i) q^{95} +(5.73747 - 7.94238i) q^{96} +(-2.00757 + 7.49237i) q^{97} +(1.38361 + 3.93643i) q^{98} +(-0.321473 - 3.94994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.07322	−	0.920972i	−0.758884	−	0.651225i
$2$	−1.07322	−	0.920972i	−0.758884	−	0.651225i
$3$	0.380005	−	1.68985i	0.219396	−	0.975636i
$3$	0.380005	−	1.68985i	0.219396	−	0.975636i
$4$	0.303622	+	1.97682i	0.151811	+	0.988410i
$5$	0.0281379	−	2.23589i	0.0125837	−	0.999921i
$5$	0.0281379	−	2.23589i	0.0125837	−	0.999921i
$6$	−1.96414	+	1.46362i	−0.801855	+	0.597519i
$7$	−1.94379	−	0.520837i	−0.734683	−	0.196858i	−0.127969	−	0.991778i	$-0.540846\pi$
$7$	−1.94379	−	0.520837i	−0.734683	−	0.196858i	−0.606714	+	0.794920i	$0.707513\pi$
$8$	1.49474	−	2.40120i	0.528470	−	0.848952i
$9$	−2.71119	−	1.28430i	−0.903731	−	0.428101i
$10$	−2.08939	+	2.37370i	−0.660723	+	0.750630i
$11$	0.660500	+	1.14402i	0.199148	+	0.344935i	0.948252	−	0.317517i	$-0.102849\pi$
$11$	0.660500	+	1.14402i	0.199148	+	0.344935i	−0.749104	+	0.662452i	$0.769516\pi$
$12$	3.45591	+	0.238125i	0.997635	+	0.0687408i
$13$	−0.243400	+	0.0652188i	−0.0675069	+	0.0180884i	−0.292414	−	0.956292i	$-0.594459\pi$
$13$	−0.243400	+	0.0652188i	−0.0675069	+	0.0180884i	0.224908	+	0.974380i	$0.427792\pi$
$14$	1.60645	+	2.34915i	0.429341	+	0.627837i
$15$	−3.76763	−	0.897199i	−0.972798	−	0.231656i
$16$	−3.81563	+	1.20041i	−0.953907	+	0.300103i
$17$	−4.73524	−	4.73524i	−1.14846	−	1.14846i	−0.986855	−	0.161609i	$-0.948332\pi$
$17$	−4.73524	−	4.73524i	−1.14846	−	1.14846i	−0.161609	−	0.986855i	$-0.551668\pi$
$18$	1.72691	+	3.87528i	0.407037	+	0.913412i
$19$			1.98509i			0.455411i	0.973730	+	0.227705i	$0.0731223\pi$
$19$			1.98509i			0.455411i	−0.973730	+	0.227705i	$0.926878\pi$
$20$	4.42850	−	0.623243i	0.990242	−	0.139361i
$21$	−1.61879	+	3.08679i	−0.353248	+	0.673593i
$22$	0.344745	−	1.83609i	0.0734998	−	0.391456i
$23$	6.95463	−	1.86349i	1.45014	−	0.388564i	0.554067	−	0.832472i	$-0.313075\pi$
$23$	6.95463	−	1.86349i	1.45014	−	0.388564i	0.896072	+	0.443908i	$0.146408\pi$
$24$	−3.48966	−	3.43835i	−0.712324	−	0.701851i
$25$	−4.99842	−	0.125827i	−0.999683	−	0.0251653i
$26$	0.321287	+	0.154170i	0.0630096	+	0.0302352i
$27$	−3.20055	+	4.09347i	−0.615946	+	0.787788i
$28$	0.439422	−	4.00066i	0.0830430	−	0.756053i
$29$	−0.0551733	−	0.0955630i	−0.0102454	−	0.0177456i	0.860857	−	0.508847i	$-0.169928\pi$
$29$	−0.0551733	−	0.0955630i	−0.0102454	−	0.0177456i	−0.871103	+	0.491101i	$0.836595\pi$
$30$	3.21722	+	4.43278i	0.587381	+	0.809311i
$31$	−2.75811	−	1.59240i	−0.495371	−	0.286003i	0.231429	−	0.972852i	$-0.425660\pi$
$31$	−2.75811	−	1.59240i	−0.495371	−	0.286003i	−0.726800	+	0.686849i	$0.758993\pi$
$32$	5.20057	+	2.22577i	0.919340	+	0.393465i
$33$	2.18422	−	0.681413i	0.380223	−	0.118619i
$34$	0.720954	+	9.44299i	0.123643	+	1.61946i
$35$	−1.21923	+	4.33145i	−0.206087	+	0.732148i
$36$	1.71566	−	5.74948i	0.285943	−	0.958247i
$37$	−2.56353	+	2.56353i	−0.421442	+	0.421442i	−0.885700	−	0.464258i	$-0.846321\pi$
$37$	−2.56353	+	2.56353i	−0.421442	+	0.421442i	0.464258	+	0.885700i	$0.346321\pi$
$38$	1.82821	−	2.13045i	0.296575	−	0.345604i
$39$	0.0177168	+	0.436093i	0.00283696	+	0.0698307i
$40$	−5.32676	−	3.40964i	−0.842235	−	0.539111i
$41$	−1.89848	+	3.28826i	−0.296493	+	0.513540i	−0.975331	−	0.220747i	$-0.929150\pi$
$41$	−1.89848	+	3.28826i	−0.296493	+	0.513540i	0.678838	+	0.734288i	$0.262484\pi$
$42$	4.58017	−	1.82197i	0.706736	−	0.281135i
$43$	1.65871	+	0.444450i	0.252951	+	0.0677780i	0.383066	−	0.923721i	$-0.374868\pi$
$43$	1.65871	+	0.444450i	0.252951	+	0.0677780i	−0.130115	+	0.991499i	$0.541535\pi$
$44$	−2.06098	+	1.65304i	−0.310704	+	0.249205i
$45$	−2.94785	+	6.02579i	−0.439440	+	0.898272i
$46$	−9.18009	−	4.40507i	−1.35353	−	0.649493i
$47$	3.58815	+	0.961442i	0.523385	+	0.140241i	0.510832	−	0.859681i	$-0.329337\pi$
$47$	3.58815	+	0.961442i	0.523385	+	0.140241i	0.0125533	+	0.999921i	$0.496004\pi$
$48$	0.578560	+	6.90400i	0.0835079	+	0.996507i
$49$	−2.55513	−	1.47521i	−0.365019	−	0.210744i
$50$	5.24854	+	4.73844i	0.742256	+	0.670117i
$51$	−9.80126	+	6.20243i	−1.37245	+	0.868514i
$52$	−0.202827	−	0.461355i	−0.0281271	−	0.0639785i
$53$	−8.40903	−	8.40903i	−1.15507	−	1.15507i	−0.985522	−	0.169548i	$-0.945769\pi$
$53$	−8.40903	−	8.40903i	−1.15507	−	1.15507i	−0.169548	−	0.985522i	$-0.554231\pi$
$54$	7.20488	−	1.44559i	0.980460	−	0.196721i
$55$	2.57649	−	1.44462i	0.347414	−	0.194792i
$56$	−4.15609	+	3.88891i	−0.555381	+	0.519677i
$57$	3.35450	+	0.754344i	0.444315	+	0.0999153i
$58$	−0.0287974	+	0.153374i	−0.00378129	+	0.0201389i
$59$	5.18353	+	2.99271i	0.674838	+	0.389618i	0.797907	−	0.602780i	$-0.205940\pi$
$59$	5.18353	+	2.99271i	0.674838	+	0.389618i	−0.123069	+	0.992398i	$0.539274\pi$
$60$	0.629664	−	7.72033i	0.0812893	−	0.996691i
$61$	7.90390	−	4.56332i	1.01199	−	0.584273i	0.100216	−	0.994966i	$-0.468046\pi$
$61$	7.90390	−	4.56332i	1.01199	−	0.584273i	0.911774	+	0.410693i	$0.134713\pi$
$62$	1.49352	+	4.24914i	0.189677	+	0.539641i
$63$	4.60107	+	3.90851i	0.579681	+	0.492425i
$64$	−3.53151	−	7.17833i	−0.441438	−	0.897292i
$65$	0.138973	+	0.546050i	0.0172375	+	0.0677292i
$66$	−2.97172	−	1.28029i	−0.365793	−	0.157593i
$67$	10.9852	−	2.94347i	1.34205	−	0.359602i	0.484857	−	0.874593i	$-0.338871\pi$
$67$	10.9852	−	2.94347i	1.34205	−	0.359602i	0.857195	+	0.514991i	$0.172205\pi$
$68$	7.92299	−	10.7984i	0.960803	−	1.30950i
$69$	−0.506220	−	12.4604i	−0.0609417	−	1.50006i
$70$	5.29764	−	3.52574i	0.633190	−	0.421406i
$71$		−	13.2069i		−	1.56737i	−0.621161	−	0.783683i	$-0.713339\pi$
$71$		−	13.2069i		−	1.56737i	0.621161	−	0.783683i	$-0.286661\pi$
$72$	−7.13640	+	4.59041i	−0.841032	+	0.540985i
$73$	9.45101	−	9.45101i	1.10616	−	1.10616i	0.112506	−	0.993651i	$-0.464112\pi$
$73$	9.45101	−	9.45101i	1.10616	−	1.10616i	0.993651	−	0.112506i	$-0.0358877\pi$
$74$	5.11219	−	0.390305i	0.594280	−	0.0453721i
$75$	−2.11205	+	8.39876i	−0.243879	+	0.969806i
$76$	−3.92416	+	0.602717i	−0.450132	+	0.0691364i
$77$	−0.688025	−	2.56775i	−0.0784078	−	0.292622i
$78$	0.382615	−	0.484342i	0.0433226	−	0.0548409i
$79$	1.34585	+	2.33107i	0.151419	+	0.262266i	0.931750	−	0.363102i	$-0.118282\pi$
$79$	1.34585	+	2.33107i	0.151419	+	0.262266i	−0.780330	+	0.625368i	$0.784949\pi$
$80$	2.57663	+	8.56510i	0.288076	+	0.957608i
$81$	5.70112	+	6.96399i	0.633458	+	0.773777i
$82$	5.06589	−	1.78060i	0.559434	−	0.196634i
$83$	−10.7685	−	2.88542i	−1.18200	−	0.316716i	−0.386282	−	0.922381i	$-0.626241\pi$
$83$	−10.7685	−	2.88542i	−1.18200	−	0.316716i	−0.795720	+	0.605664i	$0.792907\pi$
$84$	−6.59353	−	2.26283i	−0.719413	−	0.246895i
$85$	−10.7207	+	10.4542i	−1.16282	+	1.13392i
$86$	−1.37084	−	2.00462i	−0.147822	−	0.216164i
$87$	−0.182453	+	0.0569202i	−0.0195611	+	0.00610249i
$88$	3.73429	+	0.124020i	0.398077	+	0.0132206i
$89$		−	16.2645i		−	1.72404i	−0.506877	−	0.862019i	$-0.669200\pi$
$89$		−	16.2645i		−	1.72404i	0.506877	−	0.862019i	$-0.330800\pi$
$90$	8.71329	−	3.75214i	0.918462	−	0.395510i
$91$	0.507086			0.0531571
$92$	5.79535	+	13.1822i	0.604207	+	1.37434i
$93$	−3.73901	+	4.05568i	−0.387717	+	0.420554i
$94$	−2.96543	−	4.33643i	−0.305861	−	0.447268i
$95$	4.43844	+	0.0558563i	0.455375	+	0.00573074i
$96$	5.73747	−	7.94238i	0.585578	−	0.810616i
$97$	−2.00757	+	7.49237i	−0.203838	+	0.760735i	0.785962	+	0.618274i	$0.212168\pi$
$97$	−2.00757	+	7.49237i	−0.203838	+	0.760735i	−0.989801	+	0.142460i	$0.954499\pi$
$98$	1.38361	+	3.93643i	0.139765	+	0.397640i
$99$	−0.321473	−	3.94994i	−0.0323093	−	0.396984i
$100$	−1.26889	−	9.91917i	−0.126889	−	0.991917i
$101$	12.7342	−	7.35210i	1.26710	−	0.731561i	0.292662	−	0.956216i	$-0.405459\pi$
$101$	12.7342	−	7.35210i	1.26710	−	0.731561i	0.974438	+	0.224655i	$0.0721255\pi$
$102$	16.2312	+	2.37008i	1.60713	+	0.234673i
$103$	5.97851	−	1.60194i	0.589080	−	0.157843i	0.0480473	−	0.998845i	$-0.484700\pi$
$103$	5.97851	−	1.60194i	0.589080	−	0.157843i	0.541033	+	0.841002i	$0.318034\pi$
$104$	−0.207216	+	0.681936i	−0.0203192	+	0.0668693i
$105$	6.85618	+	3.70629i	0.669095	+	0.361696i
$106$	1.28030	+	16.7693i	0.124354	+	1.62878i
$107$	1.39450	+	1.39450i	0.134811	+	0.134811i	0.771292	−	0.636481i	$-0.219611\pi$
$107$	1.39450	+	1.39450i	0.134811	+	0.134811i	−0.636481	+	0.771292i	$0.719611\pi$
$108$	−9.06380	−	5.08404i	−0.872165	−	0.489212i
$109$	8.71503			0.834749			0.417374	−	0.908735i	$-0.362950\pi$
$109$	8.71503			0.834749			0.417374	+	0.908735i	$0.362950\pi$
$110$	−4.09560	−	0.822476i	−0.390500	−	0.0784200i
$111$	3.35783	+	5.30614i	0.318711	+	0.503637i
$112$	8.04199	−	0.346030i	0.759897	−	0.0326967i
$113$	−2.90868	−	10.8553i	−0.273626	−	1.02119i	−0.956757	−	0.290889i	$-0.906049\pi$
$113$	−2.90868	−	10.8553i	−0.273626	−	1.02119i	0.683131	−	0.730296i	$-0.260618\pi$
$114$	−2.90541	−	3.89898i	−0.272116	−	0.365173i
$115$	−3.97086	−	15.6022i	−0.370285	−	1.45491i
$116$	0.172159	−	0.138083i	0.0159846	−	0.0128207i
$117$	0.743664	+	0.135779i	0.0687518	+	0.0125527i
$118$	−2.80689	−	7.98574i	−0.258395	−	0.735147i
$119$	6.73802	+	11.6706i	0.617673	+	1.06984i
$120$	−7.78598	+	7.70575i	−0.710759	+	0.703435i
$121$	4.62748	−	8.01503i	0.420680	−	0.728639i
$122$	−12.6853	−	2.38180i	−1.14848	−	0.215638i
$123$	4.83524	+	4.45770i	0.435979	+	0.401938i
$124$	2.31045	−	5.93577i	0.207485	−	0.533048i
$125$	−0.421980	+	11.1724i	−0.0377430	+	0.999287i
$126$	−1.33836	−	8.43216i	−0.119231	−	0.751197i
$127$	−14.0814	+	14.0814i	−1.24952	+	1.24952i	−0.293586	+	0.955933i	$0.594849\pi$
$127$	−14.0814	+	14.0814i	−1.24952	+	1.24952i	−0.955933	+	0.293586i	$0.905151\pi$
$128$	−2.82094	+	10.9564i	−0.249338	+	0.968416i
$129$	1.38137	−	2.63408i	0.121623	−	0.231918i
$130$	0.353747	−	0.714025i	0.0310257	−	0.0626241i
$131$	−5.44918	+	9.43825i	−0.476097	+	0.824624i	−0.999625	−	0.0273844i	$-0.991282\pi$
$131$	−5.44918	+	9.43825i	−0.476097	+	0.824624i	0.523528	+	0.852008i	$0.324616\pi$
$132$	2.01021	+	4.11091i	0.174966	+	0.357809i
$133$	1.03391	−	3.85859i	0.0896511	−	0.334583i
$134$	−14.5004	−	6.95803i	−1.25264	−	0.601082i
$135$	9.06249	+	7.27126i	0.779975	+	0.625811i
$136$	−18.4482	+	4.29230i	−1.58192	+	0.368062i
$137$	4.37984	−	16.3458i	0.374195	−	1.39652i	−0.480321	−	0.877093i	$-0.659480\pi$
$137$	4.37984	−	16.3458i	0.374195	−	1.39652i	0.854517	−	0.519424i	$-0.173853\pi$
$138$	−10.9324	+	13.8390i	−0.930628	+	1.17806i
$139$	11.6637	+	6.73403i	0.989301	+	0.571173i	0.905065	−	0.425272i	$-0.139822\pi$
$139$	11.6637	+	6.73403i	0.989301	+	0.571173i	0.0842359	+	0.996446i	$0.473155\pi$
$140$	−8.93267	−	1.09507i	−0.754948	−	0.0925504i
$141$	2.98821	−	5.69808i	0.251653	−	0.479865i
$142$	−12.1632	+	14.1739i	−1.02071	+	1.18945i
$143$	−0.235377	−	0.235377i	−0.0196832	−	0.0196832i
$144$	11.8866	+	1.64588i	0.990549	+	0.137156i
$145$	−0.215221	+	0.120673i	−0.0178731	+	0.0100213i
$146$	−18.8472	+	1.43894i	−1.55980	+	0.119088i
$147$	−3.46384	+	3.75721i	−0.285693	+	0.309889i
$148$	−5.84599	−	4.28929i	−0.480537	−	0.352578i
$149$	−1.31331	+	2.27472i	−0.107590	+	0.186352i	−0.914794	−	0.403922i	$-0.867647\pi$
$149$	−1.31331	+	2.27472i	−0.107590	+	0.186352i	0.807203	+	0.590274i	$0.200980\pi$
$150$	10.0017	−	7.06862i	0.816638	−	0.577150i
$151$	−2.81469	+	1.62506i	−0.229056	+	0.132246i	−0.610137	−	0.792296i	$-0.708885\pi$
$151$	−2.81469	+	1.62506i	−0.229056	+	0.132246i	0.381080	+	0.924542i	$0.375552\pi$
$152$	4.76659	+	2.96719i	0.386622	+	0.240671i
$153$	6.75665	+	18.9196i	0.546243	+	1.52956i
$154$	−1.62642	+	3.38942i	−0.131060	+	0.273127i
$155$	−3.63803	+	6.12203i	−0.292214	+	0.491733i
$156$	−0.856697	+	0.167430i	−0.0685907	+	0.0134052i
$157$	1.46475	+	5.46651i	0.116900	+	0.436275i	0.999422	−	0.0339952i	$-0.0108231\pi$
$157$	1.46475	+	5.46651i	0.116900	+	0.436275i	−0.882522	+	0.470270i	$0.844156\pi$
$158$	0.702457	−	3.74125i	0.0558845	−	0.297638i
$159$	−17.4055	+	11.0145i	−1.38035	+	0.873510i
$160$	5.12292	−	11.5653i	0.405002	−	0.914316i
$161$	−14.4889			−1.14189
$162$	0.295051	−	12.7245i	0.0231814	−	0.999731i
$163$	9.35371	−	9.35371i	0.732639	−	0.732639i	−0.238502	−	0.971142i	$-0.576657\pi$
$163$	9.35371	−	9.35371i	0.732639	−	0.732639i	0.971142	+	0.238502i	$0.0766565\pi$
$164$	−7.07672	−	2.75456i	−0.552599	−	0.215095i
$165$	−1.46211	−	4.90284i	−0.113825	−	0.381686i
$166$	8.89968	+	13.0142i	0.690749	+	1.01010i
$167$	−6.09975	−	22.7646i	−0.472013	−	1.76158i	−0.632522	−	0.774542i	$-0.717980\pi$
$167$	−6.09975	−	22.7646i	−0.472013	−	1.76158i	0.160509	−	0.987034i	$-0.448686\pi$
$168$	4.99234	+	8.50098i	0.385167	+	0.655865i
$169$	−11.2033	+	6.46825i	−0.861795	+	0.497558i
$170$	21.1338	−	1.34627i	1.62089	−	0.103254i
$171$	2.54946	−	5.38196i	0.194962	−	0.411569i
$172$	−0.374976	+	3.41392i	−0.0285917	+	0.260309i
$173$	−3.51086	+	13.1027i	−0.266926	+	0.996180i	0.694135	+	0.719844i	$0.255787\pi$
$173$	−3.51086	+	13.1027i	−0.266926	+	0.996180i	−0.961061	+	0.276336i	$0.910880\pi$
$174$	0.248235	+	0.106946i	0.0188187	+	0.00810757i
$175$	9.65033	+	2.84794i	0.729497	+	0.215284i
$176$	−3.89352	−	3.57228i	−0.293485	−	0.269271i
$177$	7.02701	−	7.62215i	0.528182	−	0.572916i
$178$	−14.9792	+	17.4555i	−1.12274	+	1.30835i
$179$			17.6631i			1.32020i	0.751176	+	0.660102i	$0.229487\pi$
$179$			17.6631i			1.32020i	−0.751176	+	0.660102i	$0.770513\pi$
$180$	−12.8069	−	3.99781i	−0.954572	−	0.297979i
$181$			15.0184i			1.11631i	0.829738	+	0.558154i	$0.188490\pi$
$181$			15.0184i			1.11631i	−0.829738	+	0.558154i	$0.811510\pi$
$182$	−0.544217	−	0.467012i	−0.0403401	−	0.0346172i
$183$	−4.70780	−	15.0905i	−0.348011	−	1.11552i
$184$	5.92075	−	19.4849i	0.436484	−	1.43644i
$185$	5.65965	+	5.80391i	0.416105	+	0.426712i
$186$	7.74796	−	0.909132i	0.568108	−	0.0666608i
$187$	2.28958	−	8.54483i	0.167431	−	0.624860i
$188$	−0.811154	+	7.38504i	−0.0591595	+	0.538609i
$189$	8.35322	−	6.28987i	0.607608	−	0.457521i
$190$	−4.71200	−	4.14763i	−0.341845	−	0.300900i
$191$	−6.66926	+	3.85050i	−0.482571	+	0.278612i	−0.721487	−	0.692428i	$-0.756541\pi$
$191$	−6.66926	+	3.85050i	−0.482571	+	0.278612i	0.238916	+	0.971040i	$0.423208\pi$
$192$	−13.4723	+	3.23992i	−0.972280	+	0.233821i
$193$	4.60552	+	17.1880i	0.331513	+	1.23722i	0.907601	+	0.419834i	$0.137912\pi$
$193$	4.60552	+	17.1880i	0.331513	+	1.23722i	−0.576088	+	0.817388i	$0.695422\pi$
$194$	9.05484	−	6.19208i	0.650099	−	0.444565i
$195$	0.975554	−	0.0273421i	0.0698609	−	0.00195801i
$196$	2.14042	−	5.49894i	0.152887	−	0.392781i
$197$	−12.8991	+	12.8991i	−0.919020	+	0.919020i	−0.996958	−	0.0779380i	$-0.975166\pi$
$197$	−12.8991	+	12.8991i	−0.919020	+	0.919020i	0.0779380	+	0.996958i	$0.475166\pi$
$198$	−3.29277	+	4.53524i	−0.234007	+	0.322305i
$199$	6.60482			0.468203			0.234102	−	0.972212i	$-0.424785\pi$
$199$	6.60482			0.468203			0.234102	+	0.972212i	$0.424785\pi$
$200$	−7.77347	+	11.8141i	−0.549667	+	0.835384i
$201$	−0.799600	−	19.6818i	−0.0563994	−	1.38825i
$202$	−20.4377	−	3.83739i	−1.43799	−	0.269998i
$203$	0.0574726	+	0.214491i	0.00403378	+	0.0150543i
$204$	−15.2370	−	17.4921i	−1.06680	−	1.22469i
$205$	7.29878	+	4.33732i	0.509769	+	0.302931i
$206$	−7.89162	−	3.78680i	−0.549835	−	0.263839i
$207$	−21.2486	−	3.87959i	−1.47688	−	0.269650i
$208$	0.850433	−	0.541030i	0.0589669	−	0.0375137i
$209$	−2.27098	+	1.31115i	−0.157087	+	0.0906942i
$210$	−3.94484	−	10.2920i	−0.272220	−	0.710217i
$211$	1.15287	−	1.99683i	0.0793669	−	0.137468i	−0.823610	−	0.567157i	$-0.808043\pi$
$211$	1.15287	−	1.99683i	0.0793669	−	0.137468i	0.902977	+	0.429689i	$0.141377\pi$
$212$	14.0700	−	19.1763i	0.966329	−	1.31703i
$213$	−22.3176	−	5.01868i	−1.52918	−	0.343874i
$214$	−0.212317	−	2.78091i	−0.0145137	−	0.190099i
$215$	1.04041	−	3.69619i	0.0709557	−	0.252078i
$216$	5.04524	+	13.8038i	0.343285	+	0.939231i
$217$	4.53181	+	4.53181i	0.307639	+	0.307639i
$218$	−9.35319	−	8.02630i	−0.633478	−	0.543609i
$219$	−12.3794	−	19.5622i	−0.836520	−	1.32189i
$220$	3.63802	+	4.65463i	0.245275	+	0.313815i
$221$	1.46138	+	0.843729i	0.0983032	+	0.0567554i
$222$	1.28310	−	8.78715i	0.0861160	−	0.589755i
$223$	3.54029	−	13.2125i	0.237075	−	0.884776i	−0.740127	−	0.672467i	$-0.765235\pi$
$223$	3.54029	−	13.2125i	0.237075	−	0.884776i	0.977202	−	0.212310i	$-0.0680985\pi$
$224$	−8.94955	−	7.03508i	−0.597967	−	0.470051i
$225$	13.3901	+	6.76063i	0.892671	+	0.450709i
$226$	−6.87580	+	14.3290i	−0.457371	+	0.953153i
$227$	5.26075	−	19.6334i	0.349168	−	1.30311i	−0.538499	−	0.842626i	$-0.681008\pi$
$227$	5.26075	−	19.6334i	0.349168	−	1.30311i	0.887667	−	0.460487i	$-0.152325\pi$
$228$	−0.472700	+	6.86028i	−0.0313053	+	0.454333i
$229$	5.54146	−	9.59810i	0.366190	−	0.634260i	−0.622776	−	0.782400i	$-0.713995\pi$
$229$	5.54146	−	9.59810i	0.366190	−	0.634260i	0.988966	+	0.148140i	$0.0473286\pi$
$230$	−10.1076	+	20.4017i	−0.666474	+	1.34525i
$231$	−4.60056	+	0.186904i	−0.302695	+	0.0122973i
$232$	−0.311935	−	0.0103597i	−0.0204796	−	0.000680148i
$233$	−9.55795	+	9.55795i	−0.626162	+	0.626162i	−0.947100	−	0.320938i	$-0.896002\pi$
$233$	−9.55795	+	9.55795i	−0.626162	+	0.626162i	0.320938	+	0.947100i	$0.396002\pi$
$234$	−0.673070	−	0.830615i	−0.0440000	−	0.0542990i
$235$	2.25064	−	7.99566i	0.146816	−	0.521579i
$236$	−4.34222	+	11.1556i	−0.282654	+	0.726165i
$237$	4.45059	−	1.38846i	0.289097	−	0.0901900i
$238$	3.51688	−	18.7307i	0.227965	−	1.21413i
$239$	−14.5422	+	25.1878i	−0.940656	+	1.62926i	−0.176431	+	0.984313i	$0.556455\pi$
$239$	−14.5422	+	25.1878i	−0.940656	+	1.62926i	−0.764224	+	0.644950i	$0.776878\pi$
$240$	15.4529	−	1.09933i	0.997479	−	0.0709616i
$241$	−2.10611	−	3.64790i	−0.135667	−	0.234982i	0.790185	−	0.612868i	$-0.209984\pi$
$241$	−2.10611	−	3.64790i	−0.135667	−	0.234982i	−0.925852	+	0.377886i	$0.876651\pi$
$242$	−12.3479	+	4.34015i	−0.793756	+	0.278995i
$243$	13.9346	−	6.98770i	0.893903	−	0.448261i
$244$	11.4207	+	14.2390i	0.731132	+	0.911562i
$245$	−3.37030	+	5.67149i	−0.215320	+	0.362338i
$246$	−1.08388	−	9.23724i	−0.0691057	−	0.588945i
$247$	−0.129465	−	0.483170i	−0.00823766	−	0.0307434i
$248$	−7.94631	+	4.24255i	−0.504591	+	0.269402i
$249$	−8.96804	+	17.1008i	−0.568326	+	1.08372i
$250$	10.7423	−	11.6018i	0.679404	−	0.733764i
$251$	29.1014			1.83687			0.918433	−	0.395577i	$-0.129455\pi$
$251$	29.1014			1.83687			0.918433	+	0.395577i	$0.129455\pi$
$252$	−6.32942	+	10.2822i	−0.398716	+	0.647718i
$253$	6.72539	+	6.72539i	0.422822	+	0.422822i
$254$	28.0810	−	2.14393i	1.76196	−	0.134522i
$255$	13.5922	+	22.0891i	0.851175	+	1.38327i
$256$	13.1180	−	9.16065i	0.819876	−	0.572541i
$257$	13.8479	−	3.71055i	0.863811	−	0.231458i	0.200402	−	0.979714i	$-0.435775\pi$
$257$	13.8479	−	3.71055i	0.863811	−	0.231458i	0.663410	+	0.748256i	$0.269109\pi$
$258$	−3.90844	+	1.55475i	−0.243329	+	0.0967947i
$259$	6.31815	−	3.64778i	0.392591	−	0.226662i
$260$	−1.03725	+	0.440518i	−0.0643273	+	0.0273198i
$261$	0.0268535	+	0.329949i	0.00166219	+	0.0204233i
$262$	14.5406	−	5.11083i	0.898319	−	0.315748i
$263$	−3.60452	+	13.4523i	−0.222264	+	0.829502i	0.761218	+	0.648497i	$0.224602\pi$
$263$	−3.60452	+	13.4523i	−0.222264	+	0.829502i	−0.983482	+	0.181006i	$0.942065\pi$
$264$	1.62863	−	6.26327i	0.100235	−	0.385478i
$265$	−19.0383	+	18.5651i	−1.16951	+	1.14044i
$266$	−4.66327	+	3.18894i	−0.285923	+	0.195526i
$267$	−27.4846	−	6.18061i	−1.68203	−	0.378247i
$268$	9.15405	+	20.8220i	0.559173	+	1.27191i
$269$	11.9082			0.726054			0.363027	−	0.931779i	$-0.381743\pi$
$269$	11.9082			0.726054			0.363027	+	0.931779i	$0.381743\pi$
$270$	−3.02946	−	16.1500i	−0.184367	−	0.982857i
$271$		−	19.8861i		−	1.20799i	−0.796987	−	0.603996i	$-0.793574\pi$
$271$		−	19.8861i		−	1.20799i	0.796987	−	0.603996i	$-0.206426\pi$
$272$	23.7521	+	12.3837i	1.44019	+	0.750870i
$273$	0.192695	−	0.856900i	0.0116625	−	0.0518619i
$274$	−19.7546	+	13.5090i	−1.19342	+	0.816109i
$275$	−3.15751	−	5.80139i	−0.190405	−	0.349837i
$276$	24.4783	−	4.78396i	1.47342	−	0.287961i
$277$	−1.09667	−	0.293851i	−0.0658923	−	0.0176558i	0.225722	−	0.974192i	$-0.427526\pi$
$277$	−1.09667	−	0.293851i	−0.0658923	−	0.0176558i	−0.291615	+	0.956536i	$0.594192\pi$
$278$	−6.31590	−	17.9691i	−0.378803	−	1.07771i
$279$	5.43265	+	7.85954i	0.325244	+	0.470539i
$280$	8.57823	+	9.40199i	0.512647	+	0.561876i
$281$	11.2231	+	19.4390i	0.669514	+	1.15963i	0.978040	+	0.208416i	$0.0668308\pi$
$281$	11.2231	+	19.4390i	0.669514	+	1.15963i	−0.308527	+	0.951216i	$0.599836\pi$
$282$	−8.45479	+	3.36327i	−0.503476	+	0.200280i
$283$	2.96727	+	11.0740i	0.176386	+	0.658280i	0.996311	+	0.0858104i	$0.0273479\pi$
$283$	2.96727	+	11.0740i	0.176386	+	0.658280i	−0.819926	+	0.572470i	$0.805985\pi$
$284$	26.1076	−	4.00990i	1.54920	−	0.237944i
$285$	1.78102	−	7.47908i	0.105499	−	0.443022i
$286$	0.0358368	+	0.469388i	0.00211908	+	0.0277555i
$287$	5.40289	−	5.40289i	0.318923	−	0.318923i
$288$	−11.2412	−	12.7136i	−0.662393	−	0.749157i
$289$			27.8450i			1.63794i
$290$	0.342116	+	0.0687036i	0.0200898	+	0.00403441i
$291$	11.8981	+	6.23964i	0.697479	+	0.365774i
$292$	21.5525	+	15.8134i	1.26126	+	0.925409i
$293$	8.67781	−	2.32521i	0.506963	−	0.135840i	0.00373326	−	0.999993i	$-0.498812\pi$
$293$	8.67781	−	2.32521i	0.506963	−	0.135840i	0.503230	+	0.864153i	$0.332145\pi$
$294$	7.17776	−	0.842226i	0.418616	−	0.0491196i
$295$	6.83724	−	11.5056i	0.398079	−	0.669882i
$296$	2.32374	+	9.98736i	0.135064	+	0.580504i
$297$	−6.79697	−	0.957756i	−0.394400	−	0.0555746i
$298$	3.50443	−	1.23176i	0.203006	−	0.0713541i
$299$	−1.57122	+	0.907144i	−0.0908660	+	0.0524615i
$300$	−17.2441	−	1.62509i	−0.995589	−	0.0938249i
$301$	−2.99270	−	1.72783i	−0.172496	−	0.0995907i
$302$	4.51743	+	0.848193i	0.259949	+	0.0488080i
$303$	−7.58488	−	24.3127i	−0.435740	−	1.39673i
$304$	−2.38293	−	7.57436i	−0.136670	−	0.434419i
$305$	−9.98068	−	17.8007i	−0.571492	−	1.01926i
$306$	10.1730	−	26.5277i	0.581554	−	1.51649i
$307$	−2.70573	−	2.70573i	−0.154424	−	0.154424i	0.625667	−	0.780091i	$-0.284827\pi$
$307$	−2.70573	−	2.70573i	−0.154424	−	0.154424i	−0.780091	+	0.625667i	$0.784827\pi$
$308$	4.86707	−	2.13973i	0.277327	−	0.121922i
$309$	−0.435169	−	10.7115i	−0.0247559	−	0.609358i
$310$	9.54264	−	3.21979i	0.541985	−	0.182872i
$311$	14.3079	+	8.26068i	0.811327	+	0.468420i	0.847417	−	0.530929i	$-0.178157\pi$
$311$	14.3079	+	8.26068i	0.811327	+	0.468420i	−0.0360894	+	0.999349i	$0.511490\pi$
$312$	1.07363	+	0.609303i	0.0607822	+	0.0344950i
$313$	−12.4176	−	3.32727i	−0.701882	−	0.188069i	−0.109808	−	0.993953i	$-0.535024\pi$
$313$	−12.4176	−	3.32727i	−0.701882	−	0.188069i	−0.592073	+	0.805884i	$0.701690\pi$
$314$	3.46250	−	7.21578i	0.195400	−	0.407210i
$315$	8.86846	−	10.1775i	0.499681	−	0.573438i
$316$	−4.19948	+	3.36826i	−0.236239	+	0.189479i
$317$	−17.0599	−	4.57119i	−0.958179	−	0.256743i	−0.254350	−	0.967112i	$-0.581861\pi$
$317$	−17.0599	−	4.57119i	−0.958179	−	0.256743i	−0.703830	+	0.710369i	$0.748528\pi$
$318$	28.8241	+	4.20889i	1.61637	+	0.236023i
$319$	0.0728839	−	0.126239i	0.00408072	−	0.00706801i
$320$	−16.1493	+	7.69408i	−0.902775	+	0.430112i
$321$	2.88641	−	1.82658i	0.161104	−	0.101950i
$322$	15.5498	+	13.3439i	0.866559	+	0.743625i
$323$	9.39987	−	9.39987i	0.523023	−	0.523023i
$324$	−12.0356	+	13.3845i	−0.668642	+	0.743584i
$325$	1.22482	−	0.295364i	0.0679408	−	0.0163839i
$326$	−18.6531	+	1.42413i	−1.03310	+	0.0788753i
$327$	3.31176	−	14.7271i	0.183141	−	0.814411i
$328$	5.05804	+	9.47372i	0.279284	+	0.523099i
$329$	−6.47385	−	3.73768i	−0.356915	−	0.206065i
$330$	−2.94621	+	6.60841i	−0.162184	+	0.363781i
$331$	−2.40477	−	4.16518i	−0.132178	−	0.228939i	0.792338	−	0.610082i	$-0.208864\pi$
$331$	−2.40477	−	4.16518i	−0.132178	−	0.228939i	−0.924516	+	0.381144i	$0.875530\pi$
$332$	2.43439	−	22.1635i	0.133605	−	1.21638i
$333$	10.2426	−	3.65787i	0.561290	−	0.200450i
$334$	−14.4191	+	30.0492i	−0.788980	+	1.64422i
$335$	−6.27218	−	24.6445i	−0.342686	−	1.34647i
$336$	2.47126	−	13.7213i	0.134818	−	0.748556i
$337$	−21.7702	+	5.83331i	−1.18590	+	0.317761i	−0.797264	−	0.603631i	$-0.793720\pi$
$337$	−21.7702	+	5.83331i	−1.18590	+	0.317761i	−0.388636	+	0.921392i	$0.627054\pi$
$338$	17.9808	+	3.37607i	0.978025	+	0.183634i
$339$	−19.4492	+	0.790149i	−1.05634	+	0.0429150i
$340$	−23.9212	−	18.0188i	−1.29731	−	0.977205i
$341$		−	4.20711i		−	0.227828i
$342$	−7.69277	+	3.42807i	−0.415977	+	0.185369i
$343$	14.1590	+	14.1590i	0.764512	+	0.764512i
$344$	3.54655	−	3.31856i	0.191217	−	0.178925i
$345$	−27.8744	+	0.781242i	−1.50071	+	0.0420607i
$346$	15.8352	−	10.8287i	0.851303	−	0.582157i
$347$	−15.4801	+	4.14789i	−0.831017	+	0.222670i	−0.649157	−	0.760654i	$-0.724878\pi$
$347$	−15.4801	+	4.14789i	−0.831017	+	0.222670i	−0.181860	+	0.983324i	$0.558212\pi$
$348$	−0.167918	−	0.343395i	−0.00900134	−	0.0184079i
$349$	−0.583898	−	1.01134i	−0.0312553	−	0.0541358i	0.849975	−	0.526824i	$-0.176617\pi$
$349$	−0.583898	−	1.01134i	−0.0312553	−	0.0541358i	−0.881230	+	0.472688i	$0.843284\pi$
$350$	−7.73410	−	11.9442i	−0.413405	−	0.638442i
$351$	0.512042	−	1.20508i	0.0273308	−	0.0643227i
$352$	0.888650	+	7.41968i	0.0473652	+	0.395470i
$353$	−9.31553	−	2.49609i	−0.495816	−	0.132853i	0.00224172	−	0.999997i	$-0.499286\pi$
$353$	−9.31553	−	2.49609i	−0.495816	−	0.132853i	−0.498057	+	0.867144i	$0.665953\pi$
$354$	−14.5613	+	1.70860i	−0.773927	+	0.0908112i
$355$	−29.5291	−	0.371614i	−1.56724	−	0.0197232i
$356$	32.1520	−	4.93827i	1.70405	−	0.261728i
$357$	22.2820	−	6.95136i	1.17929	−	0.367905i
$358$	16.2672	−	18.9565i	0.859751	−	1.00188i
$359$	5.86290			0.309432			0.154716	−	0.987959i	$-0.450554\pi$
$359$	5.86290			0.309432			0.154716	+	0.987959i	$0.450554\pi$
$360$	10.0629	+	16.0854i	0.530359	+	0.847773i
$361$	15.0594			0.792601
$362$	13.8315	−	16.1181i	0.726967	−	0.847148i
$363$	−11.7857	−	10.8655i	−0.618591	−	0.570291i
$364$	0.153963	+	1.00242i	0.00806983	+	0.0525409i
$365$	−20.8655	−	21.3974i	−1.09215	−	1.11999i
$366$	−8.84538	+	20.5312i	−0.462356	+	1.07319i
$367$	−10.2268	−	2.74026i	−0.533834	−	0.143040i	−0.0181756	−	0.999835i	$-0.505786\pi$
$367$	−10.2268	−	2.74026i	−0.533834	−	0.143040i	−0.515658	+	0.856795i	$0.672452\pi$
$368$	−24.2993	+	15.4588i	−1.26669	+	0.805845i
$369$	9.37027	−	6.47689i	0.487797	−	0.337173i
$370$	−0.728834	−	11.4413i	−0.0378903	−	0.594804i
$371$	11.9657	+	20.7251i	0.621226	+	1.07599i
$372$	−9.15258	−	6.15995i	−0.474539	−	0.319378i
$373$	16.2385	−	4.35110i	0.840798	−	0.225291i	0.187379	−	0.982288i	$-0.440001\pi$
$373$	16.2385	−	4.35110i	0.840798	−	0.225291i	0.653419	+	0.756996i	$0.273334\pi$
$374$	−10.3268	+	7.06188i	−0.533985	+	0.365161i
$375$	18.7193	+	4.95864i	0.966660	+	0.256063i
$376$	7.67196	−	7.17875i	0.395651	−	0.370216i
$377$	0.0196617	+	0.0196617i	0.00101263	+	0.00101263i
$378$	−14.7577	−	0.942633i	−0.759053	−	0.0484838i
$379$			0.705705i			0.0362497i	0.999836	+	0.0181248i	$0.00576963\pi$
$379$			0.705705i			0.0362497i	−0.999836	+	0.0181248i	$0.994230\pi$
$380$	1.23719	+	8.79096i	0.0634666	+	0.450967i
$381$	18.4444	+	29.1464i	0.944936	+	1.49321i
$382$	10.7038	+	2.00975i	0.547655	+	0.102828i
$383$	6.24315	−	1.67285i	0.319010	−	0.0854785i	−0.0957609	−	0.995404i	$-0.530528\pi$
$383$	6.24315	−	1.67285i	0.319010	−	0.0854785i	0.414771	+	0.909926i	$0.363862\pi$
$384$	17.4427	+	8.93045i	0.890118	+	0.455730i
$385$	−5.76056	+	1.46610i	−0.293585	+	0.0747193i
$386$	10.8869	−	22.6882i	0.554130	−	1.15480i
$387$	−3.92627	−	3.33528i	−0.199584	−	0.169542i
$388$	−15.4206	−	1.69376i	−0.782862	−	0.0859877i
$389$	−1.44864	−	2.50911i	−0.0734488	−	0.127217i	0.826962	−	0.562258i	$-0.190067\pi$
$389$	−1.44864	−	2.50911i	−0.0734488	−	0.127217i	−0.900411	+	0.435041i	$0.856734\pi$
$390$	−1.07217	−	0.869114i	−0.0542914	−	0.0440093i
$391$	−41.7559	−	24.1078i	−2.11168	−	1.21918i
$392$	−7.36152	+	3.93033i	−0.371813	+	0.198512i
$393$	13.8785	+	12.7949i	0.700079	+	0.645417i
$394$	25.7233	−	1.96392i	1.29592	−	0.0989409i
$395$	5.24989	−	2.94357i	0.264151	−	0.148107i
$396$	7.71071	−	1.83478i	0.387478	−	0.0922013i
$397$	17.6468	−	17.6468i	0.885669	−	0.885669i	−0.108435	−	0.994104i	$-0.534584\pi$
$397$	17.6468	−	17.6468i	0.885669	−	0.885669i	0.994104	+	0.108435i	$0.0345839\pi$
$398$	−7.08846	−	6.08285i	−0.355312	−	0.304906i
$399$	−6.12756	−	3.21343i	−0.306762	−	0.160873i
$400$	19.2231	−	5.52005i	0.961157	−	0.276003i
$401$	5.89944	−	10.2181i	0.294604	−	0.510269i	−0.680289	−	0.732944i	$-0.738146\pi$
$401$	5.89944	−	10.2181i	0.294604	−	0.510269i	0.974893	+	0.222675i	$0.0714790\pi$
$402$	−17.2683	+	21.8594i	−0.861263	+	1.09025i
$403$	0.775177	+	0.207708i	0.0386143	+	0.0103467i
$404$	18.4002	+	22.9410i	0.915442	+	1.14136i
$405$	15.7311	−	12.5511i	0.781687	−	0.623671i
$406$	0.135859	−	0.283127i	0.00674256	−	0.0140514i
$407$	−4.62594	−	1.23952i	−0.229300	−	0.0614406i
$408$	0.242934	+	32.8058i	0.0120270	+	1.62413i
$409$	−2.02564	−	1.16950i	−0.100161	−	0.0578281i	0.449083	−	0.893490i	$-0.351751\pi$
$409$	−2.02564	−	1.16950i	−0.100161	−	0.0578281i	−0.549244	+	0.835662i	$0.685084\pi$
$410$	−3.83868	−	11.3769i	−0.189579	−	0.561864i
$411$	−25.9576	−	13.6128i	−1.28039	−	0.671469i
$412$	4.98195	+	11.3320i	0.245443	+	0.558290i
$413$	−8.51698	−	8.51698i	−0.419093	−	0.419093i
$414$	19.2315	+	23.7330i	0.945179	+	1.16642i
$415$	−6.75450	+	23.9961i	−0.331565	+	1.17792i
$416$	−1.41098	−	0.202578i	−0.0691790	−	0.00993218i
$417$	15.8118	−	17.1509i	0.774306	−	0.839885i
$418$	3.64481	+	0.684349i	0.178273	+	0.0334726i
$419$	−6.68840	−	3.86155i	−0.326750	−	0.188649i	0.327647	−	0.944800i	$-0.393744\pi$
$419$	−6.68840	−	3.86155i	−0.326750	−	0.188649i	−0.654397	+	0.756151i	$0.727078\pi$
$420$	−5.24497	+	14.6787i	−0.255928	+	0.716249i
$421$	7.20368	−	4.15905i	0.351086	−	0.202700i	−0.314078	−	0.949397i	$-0.601695\pi$
$421$	7.20368	−	4.15905i	0.351086	−	0.202700i	0.665163	+	0.746698i	$0.268362\pi$
$422$	−3.07631	+	1.08129i	−0.149753	+	0.0526362i
$423$	−8.49338	−	7.21493i	−0.412962	−	0.350802i
$424$	−32.7611	+	7.62244i	−1.59102	+	0.370179i
$425$	23.0729	+	24.2645i	1.11920	+	1.17700i
$426$	19.3298	+	25.9401i	0.936531	+	1.25680i
$427$	−17.7403	+	4.75349i	−0.858511	+	0.230037i
$428$	−2.33327	+	3.18007i	−0.112783	+	0.153715i
$429$	−0.487197	+	0.308308i	−0.0235221	+	0.0148852i
$430$	−4.52068	+	3.00865i	−0.218007	+	0.145090i
$431$			19.8626i			0.956749i	0.878156	+	0.478375i	$0.158774\pi$
$431$			19.8626i			0.956749i	−0.878156	+	0.478375i	$0.841226\pi$
$432$	7.29826	−	19.4611i	0.351137	−	0.936324i
$433$	1.10504	−	1.10504i	0.0531050	−	0.0531050i	−0.680056	−	0.733161i	$-0.738044\pi$
$433$	1.10504	−	1.10504i	0.0531050	−	0.0531050i	0.733161	+	0.680056i	$0.238044\pi$
$434$	−0.689981	−	9.03731i	−0.0331201	−	0.433805i
$435$	0.122134	+	0.409547i	0.00585586	+	0.0196363i
$436$	2.64608	+	17.2280i	0.126724	+	0.825073i
$437$	3.69919	+	13.8055i	0.176956	+	0.660409i
$438$	−4.73042	+	32.3957i	−0.226028	+	1.54793i
$439$	−2.98308	−	5.16684i	−0.142374	−	0.246600i	0.786016	−	0.618206i	$-0.212140\pi$
$439$	−2.98308	−	5.16684i	−0.142374	−	0.246600i	−0.928390	+	0.371607i	$0.878807\pi$
$440$	0.382370	−	8.34598i	0.0182288	−	0.397879i
$441$	5.03284	+	7.28114i	0.239659	+	0.346721i
$442$	−0.791340	−	2.25140i	−0.0376402	−	0.107088i
$443$	−24.7333	−	6.62726i	−1.17511	−	0.314871i	−0.382127	−	0.924110i	$-0.624808\pi$
$443$	−24.7333	−	6.62726i	−1.17511	−	0.314871i	−0.792986	+	0.609239i	$0.791475\pi$
$444$	−9.46977	+	8.24889i	−0.449416	+	0.391475i
$445$	−36.3657	−	0.457650i	−1.72390	−	0.0216947i
$446$	−15.9679	+	10.9195i	−0.756101	+	0.517054i
$447$	3.34487	+	3.08370i	0.158207	+	0.145854i
$448$	3.12577	+	15.7925i	0.147679	+	0.746126i
$449$			22.4854i			1.06115i	0.847638	+	0.530575i	$0.178024\pi$
$449$			22.4854i			1.06115i	−0.847638	+	0.530575i	$0.821976\pi$
$450$	−8.14420	−	19.5875i	−0.383921	−	0.923366i
$451$	−5.01578			−0.236184
$452$	20.5759	−	9.04586i	0.967810	−	0.425481i
$453$	1.67652	+	5.37394i	0.0787696	+	0.252490i
$454$	−23.7277	+	16.2260i	−1.11360	+	0.761525i
$455$	0.0142684	−	1.13379i	0.000668911	−	0.0531529i
$456$	6.82544	−	6.92728i	0.319631	−	0.324400i
$457$	−0.558443	+	2.08414i	−0.0261229	+	0.0974919i	−0.977756	−	0.209743i	$-0.932737\pi$
$457$	−0.558443	+	2.08414i	−0.0261229	+	0.0974919i	0.951634	+	0.307235i	$0.0994038\pi$
$458$	−14.7868	+	5.19738i	−0.690942	+	0.242858i
$459$	34.5389	−	4.22818i	1.61214	−	0.197355i
$460$	29.6371	−	12.5869i	1.38184	−	0.586865i
$461$	17.5506	−	10.1329i	0.817414	−	0.471934i	−0.0321098	−	0.999484i	$-0.510223\pi$
$461$	17.5506	−	10.1329i	0.817414	−	0.471934i	0.849524	+	0.527550i	$0.176889\pi$
$462$	5.10957	+	4.03640i	0.237719	+	0.187790i
$463$	−32.6266	+	8.74228i	−1.51629	+	0.406288i	−0.918518	−	0.395379i	$-0.870613\pi$
$463$	−32.6266	+	8.74228i	−1.51629	+	0.406288i	−0.597770	+	0.801667i	$0.703946\pi$
$464$	0.325236	+	0.298402i	0.0150987	+	0.0138530i
$465$	8.96284	+	8.47413i	0.415642	+	0.392978i
$466$	19.0604	−	1.45523i	0.882957	−	0.0674120i
$467$	21.4579	+	21.4579i	0.992952	+	0.992952i	0.999975	−	0.00702358i	$-0.00223569\pi$
$467$	21.4579	+	21.4579i	0.992952	+	0.992952i	−0.00702358	+	0.999975i	$0.502236\pi$
$468$	−0.0426170	+	1.51131i	−0.00196997	+	0.0698605i
$469$	−22.8859			−1.05677
$470$	−9.77922	+	6.50836i	−0.451082	+	0.300208i
$471$	9.79420	−	0.397902i	0.451293	−	0.0183343i
$472$	14.9341	−	7.97336i	0.687399	−	0.367004i
$473$	0.587119	+	2.19116i	0.0269957	+	0.100749i
$474$	−6.05522	−	2.60874i	−0.278125	−	0.119824i
$475$	0.249777	−	9.92230i	0.0114606	−	0.455266i
$476$	−21.0248	+	16.8633i	−0.963672	+	0.772928i
$477$	11.9987	+	33.5983i	0.549385	+	1.53836i
$478$	38.8043	−	13.6392i	1.77487	−	0.623844i
$479$	−9.57868	−	16.5908i	−0.437661	−	0.758051i	0.559848	−	0.828596i	$-0.310860\pi$
$479$	−9.57868	−	16.5908i	−0.437661	−	0.758051i	−0.997509	+	0.0705445i	$0.977526\pi$
$480$	−17.5969	−	13.0518i	−0.803183	−	0.595732i
$481$	0.456773	−	0.791153i	0.0208270	−	0.0360735i
$482$	−1.09928	+	5.85468i	−0.0500707	+	0.266674i
$483$	−5.50586	+	24.4841i	−0.250525	+	1.11406i
$484$	17.2493	+	6.71415i	0.784058	+	0.305189i
$485$	16.6956	+	4.69954i	0.758109	+	0.213395i
$486$	−21.3904	−	5.33397i	−0.970288	−	0.241954i
$487$	12.0743	−	12.0743i	0.547137	−	0.547137i	−0.378475	−	0.925612i	$-0.623551\pi$
$487$	12.0743	−	12.0743i	0.547137	−	0.547137i	0.925612	+	0.378475i	$0.123551\pi$
$488$	0.856838	−	25.7998i	0.0387872	−	1.16790i
$489$	−12.2519	−	19.3608i	−0.554051	−	0.875528i
$490$	8.84037	−	2.98283i	0.399367	−	0.134751i
$491$	−3.11268	+	5.39133i	−0.140473	+	0.243307i	−0.927675	−	0.373389i	$-0.878196\pi$
$491$	−3.11268	+	5.39133i	−0.140473	+	0.243307i	0.787202	+	0.616696i	$0.211529\pi$
$492$	−7.34399	+	10.9119i	−0.331093	+	0.491945i
$493$	−0.191255	+	0.713772i	−0.00861368	+	0.0321467i
$494$	−0.306041	+	0.637784i	−0.0137694	+	0.0286952i
$495$	−8.84068	+	0.607636i	−0.397359	+	0.0273112i
$496$	12.4355	+	2.76512i	0.558368	+	0.124157i
$497$	−6.87862	+	25.6714i	−0.308548	+	1.15152i
$498$	25.3740	−	10.0937i	1.13704	−	0.452307i
$499$	1.67316	+	0.965997i	0.0749007	+	0.0432440i	0.536983	−	0.843593i	$-0.319564\pi$
$499$	1.67316	+	0.965997i	0.0749007	+	0.0432440i	−0.462082	+	0.886837i	$0.652897\pi$
$500$	−22.2139	+	2.55800i	−0.993435	+	0.114397i
$501$	−40.7867	+	1.65701i	−1.82222	+	0.0740298i
$502$	−31.2324	−	26.8016i	−1.39397	−	1.19621i
$503$	7.62368	+	7.62368i	0.339923	+	0.339923i	0.856338	−	0.516415i	$-0.172734\pi$
$503$	7.62368	+	7.62368i	0.339923	+	0.339923i	−0.516415	+	0.856338i	$0.672734\pi$
$504$	16.2625	−	5.20589i	0.724389	−	0.231889i
$505$	−16.0802	−	28.6792i	−0.715558	−	1.27621i
$506$	−1.02396	−	13.4118i	−0.0455206	−	0.596225i
$507$	6.67305	+	21.3899i	0.296361	+	0.949961i
$508$	−32.1117	−	23.5609i	−1.42473	−	1.04535i
$509$	2.00222	−	3.46795i	0.0887470	−	0.153714i	−0.818235	−	0.574884i	$-0.805047\pi$
$509$	2.00222	−	3.46795i	0.0887470	−	0.153714i	0.906982	+	0.421170i	$0.138380\pi$
$510$	5.75596	−	36.2245i	0.254878	−	1.60405i
$511$	−23.2932	+	13.4483i	−1.03043	+	0.594919i
$512$	−22.5153	−	2.24989i	−0.995044	−	0.0994319i
$513$	−8.12590	−	6.35338i	−0.358767	−	0.280508i
$514$	−18.2793	−	8.77132i	−0.806264	−	0.386886i
$515$	−3.41353	−	13.4124i	−0.150418	−	0.591020i
$516$	5.62651	+	1.93096i	0.247693	+	0.0850057i
$517$	1.27006	+	4.73995i	0.0558574	+	0.208463i
$518$	−10.1403	−	1.90394i	−0.445539	−	0.0836545i
$519$	20.8075	+	10.9119i	0.913347	+	0.478980i
$520$	1.51890	+	0.482501i	0.0666083	+	0.0211591i
$521$	2.56116			0.112206			0.0561032	−	0.998425i	$-0.482132\pi$
$521$	2.56116			0.112206			0.0561032	+	0.998425i	$0.482132\pi$
$522$	0.275054	−	0.378841i	0.0120388	−	0.0165814i
$523$	−5.64399	+	5.64399i	−0.246795	+	0.246795i	−0.819654	−	0.572859i	$-0.805834\pi$
$523$	−5.64399	+	5.64399i	−0.246795	+	0.246795i	0.572859	+	0.819654i	$0.305834\pi$
$524$	−20.3122	−	7.90638i	−0.887343	−	0.345392i
$525$	8.47977	−	15.2254i	0.370088	−	0.664491i
$526$	16.2576	−	11.1176i	0.708866	−	0.484752i
$527$	5.51994	+	20.6007i	0.240452	+	0.897380i
$528$	−7.51618	+	5.22198i	−0.327100	+	0.227257i
$529$	24.9757	−	14.4197i	1.08590	−	0.626943i
$530$	37.5303	−	2.39076i	1.63021	−	0.103848i
$531$	−10.2100	−	14.7711i	−0.443076	−	0.641009i
$532$	7.94166	+	0.872292i	0.344315	+	0.0378187i
$533$	0.247633	−	0.924179i	0.0107262	−	0.0400306i
$534$	23.8050	+	31.9458i	1.03014	+	1.38243i
$535$	3.15719	−	3.07871i	0.136497	−	0.133104i
$536$	9.35212	−	30.7773i	0.403950	−	1.32938i
$537$	29.8481	+	6.71208i	1.28804	+	0.289648i
$538$	−12.7801	−	10.9671i	−0.550991	−	0.472825i
$539$		−	3.89750i		−	0.167877i
$540$	−11.6224	+	20.1226i	−0.500148	+	0.865940i
$541$		−	32.8804i		−	1.41364i	−0.707393	−	0.706820i	$-0.750129\pi$
$541$		−	32.8804i		−	1.41364i	0.707393	−	0.706820i	$-0.249871\pi$
$542$	−18.3145	+	21.3422i	−0.786675	+	0.916726i
$543$	25.3788	+	5.70706i	1.08911	+	0.244913i
$544$	−14.0864	−	35.1655i	−0.603949	−	1.50771i
$545$	0.245223	−	19.4859i	0.0105042	−	0.834682i
$546$	−0.995986	+	0.742179i	−0.0426243	+	0.0317623i
$547$	−5.98385	+	22.3320i	−0.255851	+	0.954849i	0.711764	+	0.702418i	$0.247896\pi$
$547$	−5.98385	+	22.3320i	−0.255851	+	0.954849i	−0.967615	+	0.252430i	$0.918770\pi$
$548$	33.6425	+	3.69521i	1.43714	+	0.157852i
$549$	−27.2897	+	2.22102i	−1.16469	+	0.0947908i
$550$	−1.95421	+	9.13417i	−0.0833277	+	0.389482i
$551$	0.189701	−	0.109524i	0.00808153	−	0.00466588i
$552$	−30.6766	−	17.4095i	−1.30568	−	0.740999i
$553$	−1.40193	−	5.23208i	−0.0596162	−	0.222491i
$554$	0.906341	+	1.32537i	0.0385067	+	0.0563094i
$555$	11.9584	−	7.35844i	0.507608	−	0.312348i
$556$	−9.77061	+	25.1016i	−0.414366	+	1.06455i
$557$	−32.9080	+	32.9080i	−1.39436	+	1.39436i	−0.579095	+	0.815260i	$0.696594\pi$
$557$	−32.9080	+	32.9080i	−1.39436	+	1.39436i	−0.815260	+	0.579095i	$0.803406\pi$
$558$	1.40797	−	13.4384i	0.0596040	−	0.568892i
$559$	−0.432716			−0.0183019
$560$	−0.547400	−	17.9908i	−0.0231319	−	0.760248i
$561$	−13.5694	−	7.11613i	−0.572902	−	0.300443i
$562$	5.85784	−	31.1985i	0.247098	−	1.31603i
$563$	−0.277375	−	1.03518i	−0.0116900	−	0.0436276i	0.959834	−	0.280567i	$-0.0905224\pi$
$563$	−0.277375	−	1.03518i	−0.0116900	−	0.0436276i	−0.971524	+	0.236939i	$0.923856\pi$
$564$	12.1714	+	4.17708i	0.512507	+	0.175887i
$565$	−24.3532	+	6.19805i	−1.02455	+	0.260754i
$566$	7.01429	−	14.6176i	0.294832	−	0.614425i
$567$	−7.45468	−	16.5059i	−0.313067	−	0.693182i
$568$	−31.7123	−	19.7408i	−1.33062	−	0.828307i
$569$	3.51094	−	2.02704i	0.147186	−	0.0849781i	−0.424598	−	0.905382i	$-0.639585\pi$
$569$	3.51094	−	2.02704i	0.147186	−	0.0849781i	0.571785	+	0.820404i	$0.306251\pi$
$570$	−8.79946	+	6.38646i	−0.368569	+	0.267500i
$571$	0.902766	−	1.56364i	0.0377796	−	0.0654362i	−0.846517	−	0.532361i	$-0.821305\pi$
$571$	0.902766	−	1.56364i	0.0377796	−	0.0654362i	0.884297	+	0.466925i	$0.154638\pi$
$572$	0.393832	−	0.536763i	0.0164669	−	0.0224432i
$573$	3.97242	+	12.7333i	0.165950	+	0.531940i
$574$	−10.7744	+	0.822606i	−0.449716	+	0.0343349i
$575$	−34.9966	+	8.43940i	−1.45946	+	0.351947i
$576$	0.355431	+	23.9974i	0.0148096	+	0.999890i
$577$	−18.1272	−	18.1272i	−0.754644	−	0.754644i	0.220698	−	0.975342i	$-0.429166\pi$
$577$	−18.1272	−	18.1272i	−0.754644	−	0.754644i	−0.975342	+	0.220698i	$0.929166\pi$
$578$	25.6444	−	29.8839i	1.06667	−	1.24301i
$579$	30.7953	−	1.25110i	1.27981	−	0.0519939i
$580$	−0.303894	−	0.388814i	−0.0126185	−	0.0161446i
$581$	19.4290	+	11.2173i	0.806049	+	0.465372i
$582$	−7.02280	−	17.6543i	−0.291104	−	0.731796i
$583$	4.06593	−	15.1743i	0.168394	−	0.628454i
$584$	−8.56695	−	36.8205i	−0.354503	−	1.52365i
$585$	0.324512	−	1.65893i	0.0134169	−	0.0685884i
$586$	−11.4547	−	5.49654i	−0.473189	−	0.227060i
$587$	4.75315	−	17.7390i	0.196183	−	0.732166i	−0.795774	−	0.605594i	$-0.792936\pi$
$587$	4.75315	−	17.7390i	0.196183	−	0.732166i	0.991957	−	0.126573i	$-0.0403977\pi$
$588$	−8.47902	−	5.70662i	−0.349669	−	0.235337i
$589$	3.16105	−	5.47509i	0.130249	−	0.225597i
$590$	−17.9342	+	6.05120i	−0.738340	+	0.249124i
$591$	16.8958	+	26.6992i	0.695000	+	1.09826i
$592$	6.70419	−	12.8588i	0.275540	−	0.528493i
$593$	6.27001	−	6.27001i	0.257478	−	0.257478i	−0.566549	−	0.824028i	$-0.691722\pi$
$593$	6.27001	−	6.27001i	0.257478	−	0.257478i	0.824028	+	0.566549i	$0.191722\pi$
$594$	6.41261	+	7.28770i	0.263113	+	0.299018i
$595$	26.2838	−	14.7371i	1.07753	−	0.604162i
$596$	−4.89546	−	1.90552i	−0.200526	−	0.0780531i
$597$	2.50987	−	11.1612i	0.102722	−	0.456796i
$598$	2.52173	+	0.473479i	0.103121	+	0.0193620i
$599$	2.03465	−	3.52412i	0.0831336	−	0.143992i	−0.821461	−	0.570265i	$-0.806841\pi$
$599$	2.03465	−	3.52412i	0.0831336	−	0.143992i	0.904594	+	0.426273i	$0.140174\pi$
$600$	17.0101	+	17.6254i	0.694436	+	0.719555i
$601$	−0.616995	−	1.06867i	−0.0251678	−	0.0435918i	0.853167	−	0.521638i	$-0.174679\pi$
$601$	−0.616995	−	1.06867i	−0.0251678	−	0.0435918i	−0.878335	+	0.478046i	$0.841345\pi$
$602$	1.62055	+	4.61054i	0.0660487	+	0.187912i
$603$	−33.5632	−	6.12800i	−1.36680	−	0.249551i
$604$	−4.06706	−	5.07073i	−0.165486	−	0.206325i
$605$	−17.7905	−	10.5721i	−0.723288	−	0.429816i
$606$	−14.2511	+	33.0785i	−0.578910	+	1.34372i
$607$	6.00311	+	22.4039i	0.243659	+	0.909346i	0.974053	+	0.226320i	$0.0726696\pi$
$607$	6.00311	+	22.4039i	0.243659	+	0.909346i	−0.730394	+	0.683026i	$0.760664\pi$
$608$	−4.41836	+	10.3236i	−0.179188	+	0.418677i
$609$	0.384297	−	0.0156125i	0.0155725	−	0.000632652i
$610$	−5.68239	+	28.2960i	−0.230073	+	1.14567i
$611$	−0.936059			−0.0378689
$612$	−35.3492	+	19.1011i	−1.42891	+	0.772116i
$613$	13.3544	+	13.3544i	0.539381	+	0.539381i	0.923347	−	0.383966i	$-0.125442\pi$
$613$	13.3544	+	13.3544i	0.539381	+	0.539381i	−0.383966	+	0.923347i	$0.625442\pi$
$614$	0.411955	+	5.39575i	0.0166251	+	0.217755i
$615$	10.1030	−	10.6856i	0.407392	−	0.430887i
$616$	−7.19408	−	2.18603i	−0.289858	−	0.0880775i
$617$	23.2851	−	6.23923i	0.937424	−	0.251182i	0.242406	−	0.970175i	$-0.422063\pi$
$617$	23.2851	−	6.23923i	0.937424	−	0.251182i	0.695017	+	0.718993i	$0.255397\pi$
$618$	−9.39798	+	11.8967i	−0.378042	+	0.478554i
$619$	−8.68281	+	5.01302i	−0.348991	+	0.201490i	−0.664241	−	0.747519i	$-0.731245\pi$
$619$	−8.68281	+	5.01302i	−0.348991	+	0.201490i	0.315250	+	0.949009i	$0.397912\pi$
$620$	−13.2067	−	5.33294i	−0.530395	−	0.214176i
$621$	−14.6305	+	34.4327i	−0.587102	+	1.38174i
$622$	−7.74775	−	22.0427i	−0.310657	−	0.883833i
$623$	−8.47117	+	31.6148i	−0.339390	+	1.26662i
$624$	−0.591092	−	1.64270i	−0.0236626	−	0.0657606i
$625$	24.9683	+	1.25787i	0.998733	+	0.0503147i
$626$	10.2625	+	15.0071i	0.410172	+	0.599805i
$627$	1.35267	+	4.33586i	0.0540203	+	0.173158i
$628$	−10.3616	+	4.55529i	−0.413472	+	0.181776i
$629$	24.2779			0.968022
$630$	−18.8911	+	2.75517i	−0.752638	+	0.109769i
$631$		−	17.6619i		−	0.703110i	−0.936167	−	0.351555i	$-0.885653\pi$
$631$		−	17.6619i		−	0.703110i	0.936167	−	0.351555i	$-0.114347\pi$
$632$	7.60906	+	0.252705i	0.302672	+	0.0100521i
$633$	−2.93625	−	2.70699i	−0.116705	−	0.107593i
$634$	14.0992	+	20.6176i	0.559950	+	0.818829i
$635$	31.0882	+	31.8806i	1.23370	+	1.26514i
$636$	−27.0584	−	31.0632i	−1.07294	−	1.23174i
$637$	0.718130	+	0.192422i	0.0284533	+	0.00762405i
$638$	−0.194483	+	0.0683584i	−0.00769966	+	0.00270634i
$639$	−16.9616	+	35.8064i	−0.670992	+	1.41648i
$640$	24.4179	+	6.61561i	0.965202	+	0.261505i
$641$	5.76308	+	9.98194i	0.227628	+	0.394263i	0.957105	−	0.289743i	$-0.0935697\pi$
$641$	5.76308	+	9.98194i	0.227628	+	0.394263i	−0.729477	+	0.684006i	$0.760236\pi$
$642$	−4.78000	−	0.697975i	−0.188651	−	0.0275469i
$643$	11.4755	+	42.8272i	0.452550	+	1.68894i	0.695191	+	0.718825i	$0.255320\pi$
$643$	11.4755	+	42.8272i	0.452550	+	1.68894i	−0.242641	+	0.970116i	$0.578014\pi$
$644$	−4.39915	−	28.6419i	−0.173351	−	1.12865i
$645$	−5.85065	−	3.16272i	−0.230369	−	0.124532i
$646$	−18.7452	+	1.43116i	−0.737519	+	0.0563081i
$647$	33.6355	−	33.6355i	1.32235	−	1.32235i	0.410475	−	0.911872i	$-0.365363\pi$
$647$	33.6355	−	33.6355i	1.32235	−	1.32235i	0.911872	−	0.410475i	$-0.134637\pi$
$648$	25.2436	−	3.28018i	0.991663	−	0.128858i
$649$			7.90675i			0.310367i
$650$	−1.58653	−	0.811032i	−0.0622288	−	0.0318113i
$651$	9.38019	−	5.93597i	0.367639	−	0.232649i
$652$	21.3306	+	15.6506i	0.835371	+	0.612925i
$653$	−24.2446	+	6.49633i	−0.948766	+	0.254221i	−0.699839	−	0.714301i	$-0.746745\pi$
$653$	−24.2446	+	6.49633i	−0.948766	+	0.254221i	−0.248928	+	0.968522i	$0.580078\pi$
$654$	−17.1175	+	12.7555i	−0.669347	+	0.498778i
$655$	20.9496	+	12.4493i	0.818568	+	0.486436i
$656$	3.29662	−	14.8257i	0.128711	−	0.578848i
$657$	−37.7615	+	13.4855i	−1.47322	+	0.526121i
$658$	3.50560	+	9.97360i	0.136663	+	0.388812i
$659$	11.0808	−	6.39752i	0.431648	−	0.249212i	−0.268401	−	0.963307i	$-0.586495\pi$
$659$	11.0808	−	6.39752i	0.431648	−	0.249212i	0.700048	+	0.714095i	$0.253162\pi$
$660$	9.24810	−	4.37893i	0.359982	−	0.170450i
$661$	−18.0929	−	10.4459i	−0.703732	−	0.406300i	0.105004	−	0.994472i	$-0.466514\pi$
$661$	−18.0929	−	10.4459i	−0.703732	−	0.406300i	−0.808736	+	0.588172i	$0.799848\pi$
$662$	−1.25516	+	6.68490i	−0.0487831	+	0.259816i
$663$	1.98111	−	2.14890i	0.0769399	−	0.0834562i
$664$	−23.0246	+	21.5445i	−0.893530	+	0.836087i
$665$	−8.59830	−	2.42028i	−0.333428	−	0.0938543i
$666$	−14.3614	−	5.50741i	−0.556493	−	0.213408i
$667$	−0.561790	−	0.561790i	−0.0217526	−	0.0217526i
$668$	43.1495	−	18.9699i	1.66950	−	0.733969i
$669$	−20.9819	−	11.0034i	−0.811206	−	0.425416i
$670$	−15.9654	+	32.2256i	−0.616798	+	1.24498i
$671$	10.4410	+	6.02814i	0.403072	+	0.232714i
$672$	−15.2891	+	12.4500i	−0.589790	+	0.480271i
$673$	14.0287	+	3.75898i	0.540767	+	0.144898i	0.518855	−	0.854862i	$-0.326358\pi$
$673$	14.0287	+	3.75898i	0.540767	+	0.144898i	0.0219111	+	0.999760i	$0.493025\pi$
$674$	28.7367	+	13.7893i	1.10689	+	0.531144i
$675$	16.5127	−	20.0581i	0.635576	−	0.772038i
$676$	−16.1881	−	20.1831i	−0.622621	−	0.776272i
$677$	34.5042	+	9.24538i	1.32611	+	0.355329i	0.851262	−	0.524741i	$-0.175838\pi$
$677$	34.5042	+	9.24538i	1.32611	+	0.355329i	0.474844	+	0.880070i	$0.342505\pi$
$678$	21.6011	+	17.0642i	0.829585	+	0.655346i
$679$	7.80460	−	13.5180i	0.299513	−	0.518772i
$680$	9.07802	+	41.3689i	0.348126	+	1.58643i
$681$	−31.1784	−	16.3507i	−1.19476	−	0.626559i
$682$	−3.87463	+	4.51517i	−0.148367	+	0.172895i
$683$	8.67115	−	8.67115i	0.331792	−	0.331792i	−0.521475	−	0.853267i	$-0.674618\pi$
$683$	8.67115	−	8.67115i	0.331792	−	0.331792i	0.853267	+	0.521475i	$0.174618\pi$
$684$	11.4132	+	3.40574i	0.436396	+	0.130222i
$685$	−36.4242	−	10.2528i	−1.39170	−	0.391739i
$686$	−2.15574	−	28.2358i	−0.0823067	−	1.07805i
$687$	−14.1136	−	13.0116i	−0.538466	−	0.496422i
$688$	−6.86254	+	0.295281i	−0.261632	+	0.0112575i
$689$	2.59518	+	1.49833i	0.0988686	+	0.0570818i
$690$	30.6350	+	24.8331i	1.16625	+	0.945378i
$691$	4.38363	+	7.59267i	0.166761	+	0.288839i	0.937279	−	0.348579i	$-0.113336\pi$
$691$	4.38363	+	7.59267i	0.166761	+	0.288839i	−0.770518	+	0.637418i	$0.780002\pi$
$692$	−26.9676	−	2.96206i	−1.02516	−	0.112601i
$693$	−1.43240	+	7.84528i	−0.0544123	+	0.298018i
$694$	20.4337	+	9.80515i	0.775655	+	0.372198i
$695$	15.3848	−	25.8893i	0.583577	−	0.982036i
$696$	−0.136043	+	0.523188i	−0.00515671	+	0.0198314i
$697$	24.5605	−	6.58096i	0.930294	−	0.249271i
$698$	−0.304763	+	1.62315i	−0.0115354	+	0.0614371i
$699$	12.5194	+	19.7836i	0.473529	+	0.748284i
$700$	−2.69981	+	19.9417i	−0.102043	+	0.753724i
$701$		−	6.19195i		−	0.233867i	−0.993140	−	0.116933i	$-0.962694\pi$
$701$		−	6.19195i		−	0.233867i	0.993140	−	0.116933i	$-0.0373064\pi$
$702$	−1.65939	+	0.821750i	−0.0626295	+	0.0310150i
$703$	−5.08884	−	5.08884i	−0.191929	−	0.191929i
$704$	5.87959	−	8.78140i	0.221595	−	0.330962i
$705$	−12.6562	−	6.84164i	−0.476661	−	0.257671i
$706$	7.69883	+	11.2582i	0.289749	+	0.423708i
$707$	−28.5819	+	7.65848i	−1.07493	+	0.288027i
$708$	17.2012	+	11.5769i	0.646459	+	0.435086i
$709$	−3.44549	−	5.96777i	−0.129398	−	0.224124i	0.794045	−	0.607858i	$-0.207971\pi$
$709$	−3.44549	−	5.96777i	−0.129398	−	0.224124i	−0.923444	+	0.383734i	$0.874638\pi$
$710$	31.3491	+	27.5943i	1.17651	+	1.03560i
$711$	−0.655039	−	8.04846i	−0.0245659	−	0.301841i
$712$	−39.0544	−	24.3112i	−1.46362	−	0.911102i
$713$	−22.1490	−	5.93482i	−0.829488	−	0.222261i
$714$	−30.3156	−	13.0608i	−1.13453	−	0.488787i
$715$	−0.532900	+	0.519654i	−0.0199293	+	0.0194340i
$716$	−34.9168	+	5.36292i	−1.30490	+	0.200422i
$717$	37.0375	+	34.1456i	1.38319	+	1.27519i
$718$	−6.29220	−	5.39956i	−0.234823	−	0.201510i
$719$	9.40925			0.350906			0.175453	−	0.984488i	$-0.443861\pi$
$719$	9.40925			0.350906			0.175453	+	0.984488i	$0.443861\pi$
$720$	4.01447	−	26.5308i	0.149610	−	0.988745i
$721$	−12.4553			−0.463860
$722$	−16.1621	−	13.8693i	−0.601493	−	0.516162i
$723$	−6.96474	+	2.17280i	−0.259021	+	0.0808073i
$724$	−29.6886	+	4.55991i	−1.10337	+	0.169468i
$725$	0.263755	+	0.484606i	0.00979561	+	0.0179978i
$726$	2.64192	+	22.5155i	0.0980510	+	0.835627i
$727$	47.6245	+	12.7610i	1.76630	+	0.473278i	0.987978	−	0.154592i	$-0.0494063\pi$
$727$	47.6245	+	12.7610i	1.76630	+	0.473278i	0.778318	+	0.627870i	$0.216073\pi$
$728$	0.757962	−	1.21761i	0.0280919	−	0.0451278i
$729$	−6.51296	−	26.2027i	−0.241221	−	0.970470i
$730$	2.68700	+	42.1807i	0.0994504	+	1.56118i
$731$	−5.74981	−	9.95897i	−0.212664	−	0.368346i
$732$	28.4018	−	13.8883i	1.04976	−	0.513326i
$733$	27.9428	−	7.48726i	1.03209	−	0.276548i	0.297259	−	0.954797i	$-0.403927\pi$
$733$	27.9428	−	7.48726i	1.03209	−	0.276548i	0.734832	+	0.678249i	$0.237261\pi$
$734$	8.45193	+	12.3595i	0.311966	+	0.456197i
$735$	8.30324	+	7.85049i	0.306270	+	0.289570i
$736$	40.3157	+	5.78822i	1.48606	+	0.213357i
$737$	10.6231	+	10.6231i	0.391307	+	0.391307i
$738$	−16.0214	−	1.67860i	−0.589757	−	0.0617902i
$739$			17.5090i			0.644079i	0.946726	+	0.322039i	$0.104368\pi$
$739$			17.5090i			0.644079i	−0.946726	+	0.322039i	$0.895632\pi$
$740$	−9.75489	+	12.9503i	−0.358597	+	0.476062i
$741$	−0.865683	+	0.0351694i	−0.0318016	+	0.00129198i
$742$	6.24542	−	33.2627i	0.229276	−	1.22111i
$743$	−5.41032	+	1.44969i	−0.198485	+	0.0531840i	−0.356692	−	0.934222i	$-0.616095\pi$
$743$	−5.41032	+	1.44969i	−0.198485	+	0.0531840i	0.158207	+	0.987406i	$0.449429\pi$
$744$	4.14964	+	15.0403i	0.152133	+	0.551403i
$745$	5.04907	+	3.00042i	0.184984	+	0.109927i
$746$	−21.4348	−	10.2855i	−0.784784	−	0.376579i
$747$	25.4898	+	21.6530i	0.932624	+	0.792243i
$748$	17.5867	+	1.93169i	0.643035	+	0.0706294i
$749$	−1.98431	−	3.43692i	−0.0725050	−	0.125582i
$750$	−15.5232	−	22.5617i	−0.566828	−	0.823836i
$751$	19.6052	+	11.3191i	0.715403	+	0.413038i	0.813058	−	0.582182i	$-0.197801\pi$
$751$	19.6052	+	11.3191i	0.715403	+	0.413038i	−0.0976554	+	0.995220i	$0.531134\pi$
$752$	−14.8452	+	0.638756i	−0.541348	+	0.0232930i
$753$	11.0587	−	49.1771i	0.403001	−	1.79211i
$754$	−0.00299355	−	0.0392092i	−0.000109019	−	0.00142792i
$755$	3.55426	+	6.33906i	0.129353	+	0.230702i
$756$	14.9702	+	14.6031i	0.544460	+	0.531108i
$757$	2.02607	−	2.02607i	0.0736387	−	0.0736387i	−0.669328	−	0.742967i	$-0.733418\pi$
$757$	2.02607	−	2.02607i	0.0736387	−	0.0736387i	0.742967	+	0.669328i	$0.233418\pi$
$758$	0.649935	−	0.757381i	0.0236067	−	0.0275093i
$759$	13.9206	−	8.80923i	0.505286	−	0.319755i
$760$	6.76844	−	10.5741i	0.245517	−	0.383563i
$761$	14.6870	−	25.4386i	0.532402	−	0.922147i	−0.466883	−	0.884319i	$-0.654623\pi$
$761$	14.6870	−	25.4386i	0.532402	−	0.922147i	0.999284	−	0.0378275i	$-0.0120437\pi$
$762$	7.04801	−	48.2674i	0.255322	−	1.74854i
$763$	−16.9402	−	4.53911i	−0.613276	−	0.164327i
$764$	−9.63668	−	12.0148i	−0.348643	−	0.434681i
$765$	42.4923	−	14.5748i	1.53631	−	0.526952i
$766$	−8.24094	−	3.95442i	−0.297757	−	0.142879i
$767$	−1.45685	−	0.390362i	−0.0526039	−	0.0140952i
$768$	−10.4952	−	25.6486i	−0.378714	−	0.925514i
$769$	−15.2348	−	8.79582i	−0.549381	−	0.317185i	0.199491	−	0.979900i	$-0.436071\pi$
$769$	−15.2348	−	8.79582i	−0.549381	−	0.317185i	−0.748872	+	0.662714i	$0.769404\pi$
$770$	7.53261	+	3.73186i	0.271456	+	0.134487i
$771$	−1.00798	−	24.8110i	−0.0363014	−	0.893546i
$772$	−32.5793	+	14.3229i	−1.17255	+	0.515494i
$773$	0.834126	+	0.834126i	0.0300014	+	0.0300014i	0.721948	−	0.691947i	$-0.243247\pi$
$773$	0.834126	+	0.834126i	0.0300014	+	0.0300014i	−0.691947	+	0.721948i	$0.743247\pi$
$774$	1.14208	+	7.19549i	0.0410511	+	0.258637i
$775$	13.5858	+	8.30650i	0.488017	+	0.298378i
$776$	14.9899	+	16.0197i	0.538105	+	0.575075i
$777$	−3.76328	−	12.0629i	−0.135007	−	0.432754i
$778$	−0.756109	+	4.02699i	−0.0271078	+	0.144375i
$779$	−6.52749	−	3.76865i	−0.233872	−	0.135026i
$780$	0.350250	+	1.92019i	0.0125410	+	0.0687539i
$781$	15.1089	−	8.72313i	0.540639	−	0.312138i
$782$	22.6109	+	64.3290i	0.808563	+	2.30040i
$783$	0.567769	+	0.0800039i	0.0202904	+	0.00285911i
$784$	11.5203	+	2.56162i	0.411439	+	0.0914866i
$785$	12.2637	−	3.12120i	0.437711	−	0.111400i
$786$	−3.11105	−	26.5135i	−0.110967	−	0.945706i
$787$	30.2424	−	8.10344i	1.07803	−	0.288856i	0.324239	−	0.945975i	$-0.394892\pi$
$787$	30.2424	−	8.10344i	1.07803	−	0.288856i	0.753787	+	0.657119i	$0.228225\pi$
$788$	−29.4156	−	21.5827i	−1.04789	−	0.768851i
$789$	21.3626	+	11.2030i	0.760528	+	0.398839i
$790$	−8.34526	−	1.67589i	−0.296911	−	0.0596255i
$791$			22.6155i			0.804113i
$792$	−9.96511	−	5.13221i	−0.354095	−	0.182365i
$793$	−1.62619	+	1.62619i	−0.0577478	+	0.0577478i
$794$	−35.1912	+	2.68678i	−1.24889	+	0.0953503i
$795$	24.1375	+	39.2267i	0.856071	+	1.39123i
$796$	2.00537	+	13.0565i	0.0710785	+	0.462777i
$797$	−1.31195	−	4.89626i	−0.0464716	−	0.173434i	0.938790	−	0.344491i	$-0.111949\pi$
$797$	−1.31195	−	4.89626i	−0.0464716	−	0.173434i	−0.985261	+	0.171057i	$0.945282\pi$
$798$	3.61676	+	9.09205i	0.128032	+	0.321855i
$799$	−12.4381	−	21.5434i	−0.440028	−	0.762151i
$800$	−25.7146	−	11.7797i	−0.909147	−	0.416476i
$801$	−20.8886	+	44.0963i	−0.738063	+	1.55807i
$802$	−15.7420	+	5.53313i	−0.555870	+	0.195382i
$803$	17.0545	+	4.56975i	0.601841	+	0.161263i
$804$	38.6647	−	7.55651i	1.36360	−	0.266498i
$805$	−0.407688	+	32.3956i	−0.0143691	+	1.14179i
$806$	−0.640646	−	0.936834i	−0.0225658	−	0.0329986i
$807$	4.52517	−	20.1230i	0.159293	−	0.708364i
$808$	1.38048	−	41.5668i	0.0485650	−	1.46232i
$809$		−	14.3924i		−	0.506010i	−0.967465	−	0.253005i	$-0.918581\pi$
$809$		−	14.3924i		−	0.506010i	0.967465	−	0.253005i	$-0.0814190\pi$
$810$	−28.4423	−	1.01774i	−0.999360	−	0.0357599i
$811$	−2.34663			−0.0824014			−0.0412007	−	0.999151i	$-0.513118\pi$
$811$	−2.34663			−0.0824014			−0.0412007	+	0.999151i	$0.513118\pi$
$812$	−0.406559	+	0.178737i	−0.0142674	+	0.00627244i
$813$	−33.6045	−	7.55680i	−1.17856	−	0.265029i
$814$	3.82312	+	5.59064i	0.134000	+	0.195952i
$815$	−20.6507	−	21.1771i	−0.723362	−	0.741801i
$816$	29.9525	−	35.4317i	1.04855	−	1.24036i
$817$	−0.882273	+	3.29269i	−0.0308668	+	0.115197i
$818$	1.09688	+	3.12069i	0.0383517	+	0.109112i
$819$	−1.37481	−	0.651253i	−0.0480397	−	0.0227566i
$820$	−6.35802	+	15.7453i	−0.222032	+	0.549849i
$821$	34.6998	−	20.0339i	1.21103	−	0.699189i	0.248046	−	0.968748i	$-0.420211\pi$
$821$	34.6998	−	20.0339i	1.21103	−	0.699189i	0.962984	+	0.269560i	$0.0868781\pi$
$822$	15.3214	+	38.5158i	0.534394	+	1.34339i
$823$	−14.7029	+	3.93962i	−0.512510	+	0.137327i	−0.505800	−	0.862651i	$-0.668803\pi$
$823$	−14.7029	+	3.93962i	−0.512510	+	0.137327i	−0.00670995	+	0.999977i	$0.502136\pi$
$824$	5.08975	−	16.7501i	0.177310	−	0.583516i
$825$	−11.0034	+	3.13115i	−0.383088	+	0.109013i
$826$	1.29673	+	16.9845i	0.0451192	+	0.590967i
$827$	−20.3139	−	20.3139i	−0.706385	−	0.706385i	0.259388	−	0.965773i	$-0.416479\pi$
$827$	−20.3139	−	20.3139i	−0.706385	−	0.706385i	−0.965773	+	0.259388i	$0.916479\pi$
$828$	1.21769	−	43.1826i	0.0423177	−	1.50070i
$829$	−8.86162			−0.307777			−0.153888	−	0.988088i	$-0.549180\pi$
$829$	−8.86162			−0.307777			−0.153888	+	0.988088i	$0.549180\pi$
$830$	29.3488	−	19.5325i	1.01871	−	0.677983i
$831$	−0.913303	+	1.74154i	−0.0316821	+	0.0604133i
$832$	1.32773	+	1.51688i	0.0460307	+	0.0525885i
$833$	5.11371	+	19.0846i	0.177179	+	0.661243i
$834$	−32.7651	+	3.84460i	−1.13456	+	0.133128i
$835$	−51.0708	+	12.9978i	−1.76738	+	0.449809i
$836$	−3.28143	−	4.09122i	−0.113491	−	0.141498i
$837$	15.3459	−	6.19369i	0.530432	−	0.214085i
$838$	3.62178	+	10.3041i	0.125112	+	0.355950i
$839$	−19.2036	−	33.2616i	−0.662981	−	1.14832i	−0.979828	−	0.199841i	$-0.935958\pi$
$839$	−19.2036	−	33.2616i	−0.662981	−	1.14832i	0.316847	−	0.948477i	$-0.397376\pi$
$840$	19.1477	−	10.9231i	0.660660	−	0.376884i
$841$	14.4939	−	25.1042i	0.499790	−	0.865662i
$842$	−11.5615	−	2.17079i	−0.398437	−	0.0748105i
$843$	37.1138	−	11.5784i	1.27827	−	0.398783i
$844$	4.29741	+	1.67274i	0.147923	+	0.0575779i
$845$	14.1471	+	25.2315i	0.486674	+	0.867988i
$846$	2.47056	+	15.5654i	0.0849395	+	0.535150i
$847$	−13.1694	+	13.1694i	−0.452505	+	0.452505i
$848$	42.1800	+	21.9914i	1.44847	+	0.755189i
$849$	19.8410	−	0.806064i	0.680940	−	0.0276640i
$850$	−2.41545	−	47.2907i	−0.0828491	−	1.62206i
$851$	−13.0513	+	22.6055i	−0.447393	+	0.774907i
$852$	3.14489	−	45.6417i	0.107742	−	1.56366i
$853$	−12.5843	+	46.9654i	−0.430880	+	1.60807i	0.319858	+	0.947465i	$0.396365\pi$
$853$	−12.5843	+	46.9654i	−0.430880	+	1.60807i	−0.750738	+	0.660600i	$0.770302\pi$
$854$	23.4171	+	11.2367i	0.801317	+	0.384512i
$855$	−11.9617	−	5.85175i	−0.409083	−	0.200126i
$856$	5.43288	−	1.26406i	0.185692	−	0.0432045i
$857$	−10.7582	+	40.1502i	−0.367494	+	1.37151i	0.496515	+	0.868028i	$0.334613\pi$
$857$	−10.7582	+	40.1502i	−0.367494	+	1.37151i	−0.864009	+	0.503477i	$0.832054\pi$
$858$	0.806814	+	0.117811i	0.0275442	+	0.00402200i
$859$	−15.7308	−	9.08219i	−0.536729	−	0.309880i	0.207023	−	0.978336i	$-0.433622\pi$
$859$	−15.7308	−	9.08219i	−0.536729	−	0.309880i	−0.743752	+	0.668456i	$0.766956\pi$
$860$	7.62259	+	0.934466i	0.259928	+	0.0318650i
$861$	−7.07696	−	11.1832i	−0.241182	−	0.381123i
$862$	18.2929	−	21.3171i	0.623059	−	0.726062i
$863$	−15.3762	−	15.3762i	−0.523413	−	0.523413i	0.395187	−	0.918601i	$-0.370680\pi$
$863$	−15.3762	−	15.3762i	−0.523413	−	0.523413i	−0.918601	+	0.395187i	$0.870680\pi$
$864$	−25.7558	+	14.1647i	−0.876231	+	0.481892i
$865$	29.1974	+	8.21858i	0.992742	+	0.279440i
$866$	−2.20368	+	0.168246i	−0.0748839	+	0.00571724i
$867$	47.0538	+	10.5812i	1.59803	+	0.359357i
$868$	−7.58260	+	10.3345i	−0.257370	+	0.350776i
$869$	−1.77786	+	3.07935i	−0.0603098	+	0.104460i
$870$	0.246105	−	0.552018i	0.00834373	−	0.0187152i
$871$	−2.48182	+	1.43288i	−0.0840932	+	0.0485513i
$872$	13.0267	−	20.9265i	0.441140	−	0.708661i
$873$	15.0654	−	17.7349i	0.509887	−	0.600236i
$874$	8.74446	−	18.2233i	0.295786	−	0.616412i
$875$	6.63922	−	21.4970i	0.224447	−	0.726730i
$876$	34.9123	−	30.4113i	1.17958	−	1.02750i
$877$	−13.0996	−	48.8883i	−0.442341	−	1.65084i	−0.722863	−	0.690992i	$-0.757174\pi$
$877$	−13.0996	−	48.8883i	−0.442341	−	1.65084i	0.280522	−	0.959848i	$-0.409493\pi$
$878$	−1.55700	+	8.29251i	−0.0525463	+	0.279859i
$879$	−0.631649	−	15.5478i	−0.0213050	−	0.524414i
$880$	−8.09678	+	8.60496i	−0.272942	+	0.290073i
$881$	−11.9316			−0.401985			−0.200993	−	0.979593i	$-0.564417\pi$
$881$	−11.9316			−0.401985			−0.200993	+	0.979593i	$0.564417\pi$
$882$	1.30435	−	12.4494i	0.0439198	−	0.419193i
$883$	−23.7691	+	23.7691i	−0.799895	+	0.799895i	−0.983079	−	0.183184i	$-0.941360\pi$
$883$	−23.7691	+	23.7691i	−0.799895	+	0.799895i	0.183184	+	0.983079i	$0.441360\pi$
$884$	−1.22419	+	3.14506i	−0.0411740	+	0.105780i
$885$	−16.8446	−	15.9261i	−0.566224	−	0.535350i
$886$	20.4408	+	29.8912i	0.686723	+	1.00421i
$887$	3.08826	+	11.5255i	0.103693	+	0.386989i	0.998194	−	0.0600782i	$-0.0191350\pi$
$887$	3.08826	+	11.5255i	0.103693	+	0.386989i	−0.894500	+	0.447068i	$0.852468\pi$
$888$	17.7602	−	0.131518i	0.595993	−	0.00441346i
$889$	34.7053	−	20.0371i	1.16398	−	0.672023i
$890$	38.6071	+	33.9830i	1.29411	+	1.13911i
$891$	−4.20135	+	11.1219i	−0.140750	+	0.372598i
$892$	27.1937	+	2.98689i	0.910512	+	0.100008i
$893$	−1.90855	+	7.12280i	−0.0638671	+	0.238355i
$894$	−0.749795	−	6.39004i	−0.0250769	−	0.213715i
$895$	39.4928	+	0.497004i	1.32010	+	0.0166130i
$896$	11.1898	−	19.8276i	0.373825	−	0.662395i
$897$	0.935867	+	2.99985i	0.0312477	+	0.100162i
$898$	20.7084	−	24.1319i	0.691048	−	0.805290i
$899$			0.351431i			0.0117209i
$900$	−9.29902	+	28.5224i	−0.309967	+	0.950747i
$901$			79.6376i			2.65311i
$902$	5.38306	+	4.61939i	0.179236	+	0.153809i
$903$	−4.05702	+	4.40063i	−0.135009	+	0.146444i
$904$	−30.4136	−	9.24159i	−1.01154	−	0.307371i
$905$	33.5795	+	0.422586i	1.11622	+	0.0140472i
$906$	3.14997	−	7.31147i	0.104651	−	0.242907i
$907$	−12.0095	+	44.8199i	−0.398767	+	1.48822i	0.416500	+	0.909136i	$0.363257\pi$
$907$	−12.0095	+	44.8199i	−0.398767	+	1.48822i	−0.815267	+	0.579085i	$0.803410\pi$
$908$	40.4089	+	4.43842i	1.34102	+	0.147294i
$909$	−43.9672	+	3.57835i	−1.45830	+	0.118686i
$910$	−1.05950	+	1.20367i	−0.0351221	+	0.0399013i
$911$	−11.5629	+	6.67583i	−0.383095	+	0.221180i	−0.679164	−	0.733986i	$-0.737658\pi$
$911$	−11.5629	+	6.67583i	−0.383095	+	0.221180i	0.296069	+	0.955167i	$0.404324\pi$
$912$	−13.7051	+	1.14849i	−0.453820	+	0.0380304i
$913$	−3.81164	−	14.2253i	−0.126147	−	0.470787i
$914$	2.51877	−	1.72244i	0.0833135	−	0.0569732i
$915$	−33.8732	+	10.1015i	−1.11981	+	0.333946i
$916$	20.6562	+	8.04027i	0.682500	+	0.265658i
$917$	15.5078	−	15.5078i	0.512114	−	0.512114i
$918$	−40.9620	−	27.2716i	−1.35195	−	0.900096i
$919$	25.9978			0.857588			0.428794	−	0.903402i	$-0.358939\pi$
$919$	25.9978			0.857588			0.428794	+	0.903402i	$0.358939\pi$
$920$	−43.3994	−	13.7864i	−1.43084	−	0.454525i
$921$	−5.60046	+	3.54408i	−0.184542	+	0.116782i
$922$	−28.1678	−	5.28880i	−0.927658	−	0.174177i
$923$	0.861335	+	3.21455i	0.0283512	+	0.105808i
$924$	−1.76631	−	9.03773i	−0.0581072	−	0.297319i
$925$	13.1362	−	12.4910i	0.431914	−	0.410703i
$926$	43.0671	+	20.6658i	1.41527	+	0.679120i
$927$	−18.2663	−	3.33507i	−0.599943	−	0.109538i
$928$	−0.0742313	−	0.619785i	−0.00243676	−	0.0203454i
$929$	0.631009	−	0.364313i	0.0207027	−	0.0119527i	−0.489613	−	0.871940i	$-0.662862\pi$
$929$	0.631009	−	0.364313i	0.0207027	−	0.0119527i	0.510316	+	0.859987i	$0.329529\pi$
$930$	−1.81471	−	17.3492i	−0.0595066	−	0.568902i
$931$	2.92842	−	5.07216i	0.0959749	−	0.166233i
$932$	−21.7963	−	15.9923i	−0.713963	−	0.523846i
$933$	19.3964	−	21.0391i	0.635009	−	0.688790i
$934$	−3.26702	−	42.7912i	−0.106900	−	1.40017i
$935$	−19.0409	−	5.35969i	−0.622703	−	0.175280i
$936$	1.43762	−	1.58273i	0.0469899	−	0.0517332i
$937$	−26.9782	−	26.9782i	−0.881338	−	0.881338i	0.112333	−	0.993671i	$-0.464168\pi$
$937$	−26.9782	−	26.9782i	−0.881338	−	0.881338i	−0.993671	+	0.112333i	$0.964168\pi$
$938$	24.5617	+	21.0773i	0.801969	+	0.688198i
$939$	−10.3413	+	19.7194i	−0.337477	+	0.643519i
$940$	16.4893	+	2.02145i	0.537822	+	0.0659325i
$941$	−48.4091	−	27.9490i	−1.57809	−	0.911112i	−0.995126	−	0.0986151i	$-0.968559\pi$
$941$	−48.4091	−	27.9490i	−1.57809	−	0.911112i	−0.582966	−	0.812497i	$-0.698108\pi$
$942$	−10.8778	−	8.59314i	−0.354419	−	0.279980i
$943$	−7.07558	+	26.4064i	−0.230413	+	0.859912i
$944$	−23.3709	−	5.19670i	−0.760659	−	0.169138i
$945$	−13.8284	−	18.8539i	−0.449839	−	0.613317i
$946$	1.38788	−	2.89232i	0.0451240	−	0.0940375i
$947$	12.1360	−	45.2921i	0.394366	−	1.47179i	−0.428491	−	0.903546i	$-0.640955\pi$
$947$	12.1360	−	45.2921i	0.394366	−	1.47179i	0.822857	−	0.568248i	$-0.192379\pi$
$948$	4.09603	+	8.37645i	0.133033	+	0.272054i
$949$	−1.68399	+	2.91676i	−0.0546646	+	0.0946819i
$950$	−9.40623	+	10.4188i	−0.305178	+	0.338031i
$951$	−14.2075	+	27.0916i	−0.460709	+	0.878506i
$952$	38.0950	+	1.26517i	1.23467	+	0.0410045i
$953$	−11.8743	+	11.8743i	−0.384647	+	0.384647i	−0.872773	−	0.488126i	$-0.837681\pi$
$953$	−11.8743	+	11.8743i	−0.384647	+	0.384647i	0.488126	+	0.872773i	$0.337681\pi$
$954$	18.0657	−	47.1090i	0.584899	−	1.52521i
$955$	8.42164	+	15.0201i	0.272518	+	0.486038i
$956$	−54.2071	−	21.0997i	−1.75318	−	0.682413i
$957$	−0.185628	−	0.171134i	−0.00600051	−	0.00553199i
$958$	−4.99954	+	26.6273i	−0.161528	+	0.860289i
$959$	−17.0270	+	29.4916i	−0.549830	+	0.952334i
$960$	6.86502	+	30.2138i	0.221568	+	0.975145i
$961$	−10.4286	−	18.0628i	−0.336405	−	0.582670i
$962$	−1.21885	+	0.428411i	−0.0392973	+	0.0138125i
$963$	−1.98979	−	5.57172i	−0.0641202	−	0.179546i
$964$	6.57177	−	5.27099i	0.211662	−	0.169767i
$965$	38.5602	−	9.81380i	1.24130	−	0.315918i
$966$	28.4582	−	21.2062i	0.915626	−	0.682298i
$967$	7.58370	+	28.3027i	0.243875	+	0.910155i	0.973945	+	0.226783i	$0.0728207\pi$
$967$	7.58370	+	28.3027i	0.243875	+	0.910155i	−0.730070	+	0.683372i	$0.760513\pi$
$968$	−12.3288	−	23.0919i	−0.396263	−	0.742201i
$969$	−12.3124	−	19.4564i	−0.395531	−	0.625029i
$970$	−13.5900	−	20.4199i	−0.436349	−	0.655642i
$971$	−32.8220			−1.05331			−0.526655	−	0.850079i	$-0.676554\pi$
$971$	−32.8220			−1.05331			−0.526655	+	0.850079i	$0.676554\pi$
$972$	18.0443	+	25.4245i	0.578770	+	0.815491i
$973$	−19.1644	−	19.1644i	−0.614383	−	0.614383i
$974$	−24.0784	+	1.83834i	−0.771523	+	0.0589042i
$975$	−0.0336839	−	2.18200i	−0.00107875	−	0.0698800i
$976$	−24.6805	+	26.8999i	−0.790002	+	0.861043i
$977$	−27.5968	+	7.39454i	−0.882900	+	0.236572i	−0.671658	−	0.740862i	$-0.734417\pi$
$977$	−27.5968	+	7.39454i	−0.882900	+	0.236572i	−0.211242	+	0.977434i	$0.567751\pi$
$978$	−4.68172	+	32.0622i	−0.149705	+	1.02524i
$979$	18.6069	−	10.7427i	0.594681	−	0.343339i
$980$	−12.2348	−	4.94048i	−0.390826	−	0.157818i
$981$	−23.6281	−	11.1928i	−0.754388	−	0.357357i
$982$	8.30587	−	2.91941i	0.265051	−	0.0931622i
$983$	−12.9714	+	48.4099i	−0.413723	+	1.54404i	0.373657	+	0.927567i	$0.378104\pi$
$983$	−12.9714	+	48.4099i	−0.413723	+	1.54404i	−0.787380	+	0.616468i	$0.788563\pi$
$984$	17.9313	−	4.94727i	0.571628	−	0.157713i
$985$	28.4779	+	29.2039i	0.907383	+	0.930512i
$986$	0.862623	−	0.589898i	0.0274715	−	0.0187862i
$987$	−8.77622	+	9.51951i	−0.279350	+	0.303009i
$988$	0.915831	−	0.402630i	0.0291365	−	0.0128094i
$989$	12.3639			0.393150
$990$	10.0477	+	7.48989i	0.319335	+	0.238044i
$991$		−	35.5644i		−	1.12974i	−0.825180	−	0.564870i	$-0.808926\pi$
$991$		−	35.5644i		−	1.12974i	0.825180	−	0.564870i	$-0.191074\pi$
$992$	−10.7994	−	14.4203i	−0.342882	−	0.457845i
$993$	−7.95236	+	2.48091i	−0.252360	+	0.0787293i
$994$	31.0249	−	21.2161i	0.984050	−	0.672935i
$995$	0.185846	−	14.7677i	0.00589172	−	0.468166i
$996$	−36.5280	−	12.5360i	−1.15743	−	0.397219i
$997$	−47.2239	−	12.6536i	−1.49559	−	0.400743i	−0.583973	−	0.811773i	$-0.698503\pi$
$997$	−47.2239	−	12.6536i	−1.49559	−	0.400743i	−0.911622	+	0.411030i	$0.865169\pi$
$998$	−0.906016	−	2.57766i	−0.0286794	−	0.0815944i
$999$	−2.28902	−	18.6985i	−0.0724215	−	0.591593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.67.17	yes	272
5.3	odd	4	inner	360.2.bo.a.283.18	yes	272
8.3	odd	2	inner	360.2.bo.a.67.63	yes	272
9.7	even	3	inner	360.2.bo.a.187.30	yes	272
40.3	even	4	inner	360.2.bo.a.283.30	yes	272
45.43	odd	12	inner	360.2.bo.a.43.63	yes	272
72.43	odd	6	inner	360.2.bo.a.187.18	yes	272
360.43	even	12	inner	360.2.bo.a.43.17	✓	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.17	✓	272	360.43	even	12	inner
360.2.bo.a.43.63	yes	272	45.43	odd	12	inner
360.2.bo.a.67.17	yes	272	1.1	even	1	trivial
360.2.bo.a.67.63	yes	272	8.3	odd	2	inner
360.2.bo.a.187.18	yes	272	72.43	odd	6	inner
360.2.bo.a.187.30	yes	272	9.7	even	3	inner
360.2.bo.a.283.18	yes	272	5.3	odd	4	inner
360.2.bo.a.283.30	yes	272	40.3	even	4	inner

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07322 - 0.920972i) q^{2} +(0.380005 - 1.68985i) q^{3} +(0.303622 + 1.97682i) q^{4} +(0.0281379 - 2.23589i) q^{5} +(-1.96414 + 1.46362i) q^{6} +(-1.94379 - 0.520837i) q^{7} +(1.49474 - 2.40120i) q^{8} +(-2.71119 - 1.28430i) q^{9} +O(q^{10})\)	\(q+(-1.07322 - 0.920972i) q^{2} +(0.380005 - 1.68985i) q^{3} +(0.303622 + 1.97682i) q^{4} +(0.0281379 - 2.23589i) q^{5} +(-1.96414 + 1.46362i) q^{6} +(-1.94379 - 0.520837i) q^{7} +(1.49474 - 2.40120i) q^{8} +(-2.71119 - 1.28430i) q^{9} +(-2.08939 + 2.37370i) q^{10} +(0.660500 + 1.14402i) q^{11} +(3.45591 + 0.238125i) q^{12} +(-0.243400 + 0.0652188i) q^{13} +(1.60645 + 2.34915i) q^{14} +(-3.76763 - 0.897199i) q^{15} +(-3.81563 + 1.20041i) q^{16} +(-4.73524 - 4.73524i) q^{17} +(1.72691 + 3.87528i) q^{18} +1.98509i q^{19} +(4.42850 - 0.623243i) q^{20} +(-1.61879 + 3.08679i) q^{21} +(0.344745 - 1.83609i) q^{22} +(6.95463 - 1.86349i) q^{23} +(-3.48966 - 3.43835i) q^{24} +(-4.99842 - 0.125827i) q^{25} +(0.321287 + 0.154170i) q^{26} +(-3.20055 + 4.09347i) q^{27} +(0.439422 - 4.00066i) q^{28} +(-0.0551733 - 0.0955630i) q^{29} +(3.21722 + 4.43278i) q^{30} +(-2.75811 - 1.59240i) q^{31} +(5.20057 + 2.22577i) q^{32} +(2.18422 - 0.681413i) q^{33} +(0.720954 + 9.44299i) q^{34} +(-1.21923 + 4.33145i) q^{35} +(1.71566 - 5.74948i) q^{36} +(-2.56353 + 2.56353i) q^{37} +(1.82821 - 2.13045i) q^{38} +(0.0177168 + 0.436093i) q^{39} +(-5.32676 - 3.40964i) q^{40} +(-1.89848 + 3.28826i) q^{41} +(4.58017 - 1.82197i) q^{42} +(1.65871 + 0.444450i) q^{43} +(-2.06098 + 1.65304i) q^{44} +(-2.94785 + 6.02579i) q^{45} +(-9.18009 - 4.40507i) q^{46} +(3.58815 + 0.961442i) q^{47} +(0.578560 + 6.90400i) q^{48} +(-2.55513 - 1.47521i) q^{49} +(5.24854 + 4.73844i) q^{50} +(-9.80126 + 6.20243i) q^{51} +(-0.202827 - 0.461355i) q^{52} +(-8.40903 - 8.40903i) q^{53} +(7.20488 - 1.44559i) q^{54} +(2.57649 - 1.44462i) q^{55} +(-4.15609 + 3.88891i) q^{56} +(3.35450 + 0.754344i) q^{57} +(-0.0287974 + 0.153374i) q^{58} +(5.18353 + 2.99271i) q^{59} +(0.629664 - 7.72033i) q^{60} +(7.90390 - 4.56332i) q^{61} +(1.49352 + 4.24914i) q^{62} +(4.60107 + 3.90851i) q^{63} +(-3.53151 - 7.17833i) q^{64} +(0.138973 + 0.546050i) q^{65} +(-2.97172 - 1.28029i) q^{66} +(10.9852 - 2.94347i) q^{67} +(7.92299 - 10.7984i) q^{68} +(-0.506220 - 12.4604i) q^{69} +(5.29764 - 3.52574i) q^{70} -13.2069i q^{71} +(-7.13640 + 4.59041i) q^{72} +(9.45101 - 9.45101i) q^{73} +(5.11219 - 0.390305i) q^{74} +(-2.11205 + 8.39876i) q^{75} +(-3.92416 + 0.602717i) q^{76} +(-0.688025 - 2.56775i) q^{77} +(0.382615 - 0.484342i) q^{78} +(1.34585 + 2.33107i) q^{79} +(2.57663 + 8.56510i) q^{80} +(5.70112 + 6.96399i) q^{81} +(5.06589 - 1.78060i) q^{82} +(-10.7685 - 2.88542i) q^{83} +(-6.59353 - 2.26283i) q^{84} +(-10.7207 + 10.4542i) q^{85} +(-1.37084 - 2.00462i) q^{86} +(-0.182453 + 0.0569202i) q^{87} +(3.73429 + 0.124020i) q^{88} -16.2645i q^{89} +(8.71329 - 3.75214i) q^{90} +0.507086 q^{91} +(5.79535 + 13.1822i) q^{92} +(-3.73901 + 4.05568i) q^{93} +(-2.96543 - 4.33643i) q^{94} +(4.43844 + 0.0558563i) q^{95} +(5.73747 - 7.94238i) q^{96} +(-2.00757 + 7.49237i) q^{97} +(1.38361 + 3.93643i) q^{98} +(-0.321473 - 3.94994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

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