LMFDB - Embedded newform 260.2.bj.c.3.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(3,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("260.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bj (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			3.20
Character	$\chi$	$=$	260.3
Dual form			260.2.bj.c.87.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0703644 + 1.41246i) q^{2} +(-0.124346 - 0.0333185i) q^{3} +(-1.99010 - 0.198774i) q^{4} +(-1.85457 - 1.24923i) q^{5} +(0.0558107 - 0.173290i) q^{6} +(-0.462161 + 0.123836i) q^{7} +(0.420793 - 2.79695i) q^{8} +(-2.58372 - 1.49171i) q^{9} +O(q^{10})$	\(q+(-0.0703644 + 1.41246i) q^{2} +(-0.124346 - 0.0333185i) q^{3} +(-1.99010 - 0.198774i) q^{4} +(-1.85457 - 1.24923i) q^{5} +(0.0558107 - 0.173290i) q^{6} +(-0.462161 + 0.123836i) q^{7} +(0.420793 - 2.79695i) q^{8} +(-2.58372 - 1.49171i) q^{9} +(1.89498 - 2.53161i) q^{10} +(-3.02041 + 1.74383i) q^{11} +(0.240839 + 0.0910240i) q^{12} +(-0.965152 - 3.47397i) q^{13} +(-0.142393 - 0.661498i) q^{14} +(0.188987 + 0.217129i) q^{15} +(3.92098 + 0.791159i) q^{16} +(0.0874092 + 0.326216i) q^{17} +(2.28879 - 3.54445i) q^{18} +(0.935831 - 1.62091i) q^{19} +(3.44246 + 2.85473i) q^{20} +0.0615941 q^{21} +(-2.25057 - 4.38891i) q^{22} +(-7.16439 - 1.91969i) q^{23} +(-0.145514 + 0.333771i) q^{24} +(1.87885 + 4.63356i) q^{25} +(4.97477 - 1.11880i) q^{26} +(0.544659 + 0.544659i) q^{27} +(0.944360 - 0.154579i) q^{28} +(4.31388 - 2.49062i) q^{29} +(-0.319984 + 0.251658i) q^{30} +8.66885i q^{31} +(-1.39338 + 5.48256i) q^{32} +(0.433679 - 0.116204i) q^{33} +(-0.466918 + 0.100508i) q^{34} +(1.01181 + 0.347683i) q^{35} +(4.84535 + 3.48223i) q^{36} +(-1.14494 - 0.306785i) q^{37} +(2.22362 + 1.43588i) q^{38} +(0.00426563 + 0.464134i) q^{39} +(-4.27442 + 4.66147i) q^{40} +(0.581422 + 1.00705i) q^{41} +(-0.00433403 + 0.0869993i) q^{42} +(-1.36753 - 5.10370i) q^{43} +(6.35753 - 2.87002i) q^{44} +(2.92820 + 5.99415i) q^{45} +(3.21561 - 9.98435i) q^{46} +(-5.87046 - 5.87046i) q^{47} +(-0.461199 - 0.229019i) q^{48} +(-5.86392 + 3.38554i) q^{49} +(-6.67694 + 2.32777i) q^{50} -0.0434761i q^{51} +(1.23021 + 7.10539i) q^{52} +(-1.80694 - 1.80694i) q^{53} +(-0.807635 + 0.730986i) q^{54} +(7.78000 + 0.539121i) q^{55} +(0.151888 + 1.34475i) q^{56} +(-0.170373 + 0.170373i) q^{57} +(3.21436 + 6.26844i) q^{58} +(-6.64587 + 11.5110i) q^{59} +(-0.332942 - 0.469673i) q^{60} +(5.69767 - 9.86866i) q^{61} +(-12.2444 - 0.609978i) q^{62} +(1.37882 + 0.369455i) q^{63} +(-7.64587 - 2.35387i) q^{64} +(-2.54984 + 7.64842i) q^{65} +(0.133618 + 0.620732i) q^{66} +(2.09306 - 7.81142i) q^{67} +(-0.109110 - 0.666576i) q^{68} +(0.826905 + 0.477414i) q^{69} +(-0.562284 + 1.40468i) q^{70} +(-1.63374 - 0.943240i) q^{71} +(-5.25946 + 6.59885i) q^{72} +(0.703943 + 0.703943i) q^{73} +(0.513886 - 1.59560i) q^{74} +(-0.0792453 - 0.638768i) q^{75} +(-2.18459 + 3.03974i) q^{76} +(1.17997 - 1.17997i) q^{77} +(-0.655871 - 0.0266334i) q^{78} +12.6068 q^{79} +(-6.28339 - 6.36546i) q^{80} +(4.42556 + 7.66530i) q^{81} +(-1.46334 + 0.750376i) q^{82} +(-6.52171 + 6.52171i) q^{83} +(-0.122578 - 0.0122433i) q^{84} +(0.245412 - 0.714184i) q^{85} +(7.30500 - 1.57247i) q^{86} +(-0.619399 + 0.165967i) q^{87} +(3.60645 + 9.18172i) q^{88} +(0.0310852 - 0.0179471i) q^{89} +(-8.67255 + 3.71420i) q^{90} +(0.876257 + 1.48601i) q^{91} +(13.8762 + 5.24447i) q^{92} +(0.288833 - 1.07794i) q^{93} +(8.70488 - 7.87873i) q^{94} +(-3.76045 + 1.83702i) q^{95} +(0.355933 - 0.635312i) q^{96} +(1.23898 + 4.62394i) q^{97} +(-4.36933 - 8.52079i) q^{98} +10.4052 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 24 q^{5} - 4 q^{6} - 24 q^{8}+O(q^{10}) $ 144 * q - 6 * q^2 - 24 * q^5 - 4 * q^6 - 24 * q^8	$ 144 q - 6 q^{2} - 24 q^{5} - 4 q^{6} - 24 q^{8} - 16 q^{10} + 20 q^{12} - 12 q^{13} - 28 q^{16} - 4 q^{18} + 30 q^{20} - 32 q^{21} - 28 q^{22} - 24 q^{25} - 12 q^{26} + 14 q^{28} - 4 q^{30} + 4 q^{32} - 28 q^{33} + 4 q^{36} + 20 q^{40} + 24 q^{41} - 56 q^{42} - 4 q^{46} + 12 q^{48} + 20 q^{50} - 2 q^{52} + 24 q^{53} - 20 q^{56} - 24 q^{57} - 42 q^{58} + 88 q^{60} - 32 q^{61} - 128 q^{66} - 32 q^{68} + 108 q^{70} + 2 q^{72} - 8 q^{73} + 60 q^{76} - 72 q^{77} - 120 q^{78} - 64 q^{80} - 32 q^{81} - 42 q^{82} - 48 q^{85} - 24 q^{86} - 42 q^{88} - 56 q^{90} - 84 q^{92} + 8 q^{93} + 160 q^{96} + 68 q^{97} + 98 q^{98}+O(q^{100}) $ 144 * q - 6 * q^2 - 24 * q^5 - 4 * q^6 - 24 * q^8 - 16 * q^10 + 20 * q^12 - 12 * q^13 - 28 * q^16 - 4 * q^18 + 30 * q^20 - 32 * q^21 - 28 * q^22 - 24 * q^25 - 12 * q^26 + 14 * q^28 - 4 * q^30 + 4 * q^32 - 28 * q^33 + 4 * q^36 + 20 * q^40 + 24 * q^41 - 56 * q^42 - 4 * q^46 + 12 * q^48 + 20 * q^50 - 2 * q^52 + 24 * q^53 - 20 * q^56 - 24 * q^57 - 42 * q^58 + 88 * q^60 - 32 * q^61 - 128 * q^66 - 32 * q^68 + 108 * q^70 + 2 * q^72 - 8 * q^73 + 60 * q^76 - 72 * q^77 - 120 * q^78 - 64 * q^80 - 32 * q^81 - 42 * q^82 - 48 * q^85 - 24 * q^86 - 42 * q^88 - 56 * q^90 - 84 * q^92 + 8 * q^93 + 160 * q^96 + 68 * q^97 + 98 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0703644	+	1.41246i	−0.0497551	+	0.998761i
$2$	−0.0703644	+	1.41246i	−0.0497551	+	0.998761i
$3$	−0.124346	−	0.0333185i	−0.0717915	−	0.0192365i	0.222745	−	0.974877i	$-0.428498\pi$
$3$	−0.124346	−	0.0333185i	−0.0717915	−	0.0192365i	−0.294536	+	0.955640i	$0.595165\pi$
$4$	−1.99010	−	0.198774i	−0.995049	−	0.0993870i
$5$	−1.85457	−	1.24923i	−0.829389	−	0.558672i
$5$	−1.85457	−	1.24923i	−0.829389	−	0.558672i
$6$	0.0558107	−	0.173290i	0.0227846	−	0.0707454i
$7$	−0.462161	+	0.123836i	−0.174680	+	0.0468055i	−0.345099	−	0.938566i	$-0.612155\pi$
$7$	−0.462161	+	0.123836i	−0.174680	+	0.0468055i	0.170419	+	0.985372i	$0.445488\pi$
$8$	0.420793	−	2.79695i	0.148773	−	0.988871i
$9$	−2.58372	−	1.49171i	−0.861241	−	0.497238i
$10$	1.89498	−	2.53161i	0.599247	−	0.800565i
$11$	−3.02041	+	1.74383i	−0.910687	+	0.525785i	−0.880652	−	0.473763i	$-0.842895\pi$
$11$	−3.02041	+	1.74383i	−0.910687	+	0.525785i	−0.0300349	+	0.999549i	$0.509562\pi$
$12$	0.240839	+	0.0910240i	0.0695242	+	0.0262764i
$13$	−0.965152	−	3.47397i	−0.267685	−	0.963506i
$13$	−0.965152	−	3.47397i	−0.267685	−	0.963506i
$14$	−0.142393	−	0.661498i	−0.0380562	−	0.176793i
$15$	0.188987	+	0.217129i	0.0487961	+	0.0560624i
$16$	3.92098	+	0.791159i	0.980244	+	0.197790i
$17$	0.0874092	+	0.326216i	0.0211999	+	0.0791189i	0.975715	−	0.219042i	$-0.0702933\pi$
$17$	0.0874092	+	0.326216i	0.0211999	+	0.0791189i	−0.954515	+	0.298161i	$0.903627\pi$
$18$	2.28879	−	3.54445i	0.539473	−	0.835435i
$19$	0.935831	−	1.62091i	0.214694	−	0.371861i	−0.738484	−	0.674271i	$-0.764458\pi$
$19$	0.935831	−	1.62091i	0.214694	−	0.371861i	0.953178	+	0.302410i	$0.0977912\pi$
$20$	3.44246	+	2.85473i	0.769757	+	0.638337i
$21$	0.0615941			0.0134409
$22$	−2.25057	−	4.38891i	−0.479823	−	0.935720i
$23$	−7.16439	−	1.91969i	−1.49388	−	0.400283i	−0.582834	−	0.812591i	$-0.698056\pi$
$23$	−7.16439	−	1.91969i	−1.49388	−	0.400283i	−0.911045	+	0.412308i	$0.864723\pi$
$24$	−0.145514	+	0.333771i	−0.0297030	+	0.0681307i
$25$	1.87885	+	4.63356i	0.375771	+	0.926713i
$26$	4.97477	−	1.11880i	0.975632	−	0.219414i
$27$	0.544659	+	0.544659i	0.104820	+	0.104820i
$28$	0.944360	−	0.154579i	0.178467	−	0.0292128i
$29$	4.31388	−	2.49062i	0.801067	−	0.462496i	−0.0427773	−	0.999085i	$-0.513621\pi$
$29$	4.31388	−	2.49062i	0.801067	−	0.462496i	0.843844	+	0.536589i	$0.180287\pi$
$30$	−0.319984	+	0.251658i	−0.0584208	+	0.0459463i
$31$			8.66885i			1.55697i	0.627663	+	0.778485i	$0.284012\pi$
$31$			8.66885i			1.55697i	−0.627663	+	0.778485i	$0.715988\pi$
$32$	−1.39338	+	5.48256i	−0.246317	+	0.969189i
$33$	0.433679	−	0.116204i	0.0754938	−	0.0202285i
$34$	−0.466918	+	0.100508i	−0.0800757	+	0.0172370i
$35$	1.01181	+	0.347683i	0.171027	+	0.0587691i
$36$	4.84535	+	3.48223i	0.807558	+	0.580372i
$37$	−1.14494	−	0.306785i	−0.188227	−	0.0504352i	0.163474	−	0.986548i	$-0.447730\pi$
$37$	−1.14494	−	0.306785i	−0.188227	−	0.0504352i	−0.351701	+	0.936112i	$0.614397\pi$
$38$	2.22362	+	1.43588i	0.360719	+	0.232930i
$39$	0.00426563	+	0.464134i	0.000683047	+	0.0743209i
$40$	−4.27442	+	4.66147i	−0.675845	+	0.737043i
$41$	0.581422	+	1.00705i	0.0908029	+	0.157275i	0.907849	−	0.419297i	$-0.137723\pi$
$41$	0.581422	+	1.00705i	0.0908029	+	0.157275i	−0.817046	+	0.576572i	$0.804390\pi$
$42$	−0.00433403	+	0.0869993i	−0.000668755	+	0.0134243i
$43$	−1.36753	−	5.10370i	−0.208547	−	0.778306i	−0.988339	−	0.152268i	$-0.951342\pi$
$43$	−1.36753	−	5.10370i	−0.208547	−	0.778306i	0.779793	−	0.626038i	$-0.215324\pi$
$44$	6.35753	−	2.87002i	0.958434	−	0.432672i
$45$	2.92820	+	5.99415i	0.436511	+	0.893555i
$46$	3.21561	−	9.98435i	0.474116	−	1.47211i
$47$	−5.87046	−	5.87046i	−0.856295	−	0.856295i	0.134604	−	0.990899i	$-0.457024\pi$
$47$	−5.87046	−	5.87046i	−0.856295	−	0.856295i	−0.990899	+	0.134604i	$0.957024\pi$
$48$	−0.461199	−	0.229019i	−0.0665684	−	0.0330561i
$49$	−5.86392	+	3.38554i	−0.837703	+	0.483648i
$50$	−6.67694	+	2.32777i	−0.944261	+	0.329197i
$51$		−	0.0434761i		−	0.00608787i
$52$	1.23021	+	7.10539i	0.170600	+	0.985340i
$53$	−1.80694	−	1.80694i	−0.248202	−	0.248202i	0.572030	−	0.820232i	$-0.306156\pi$
$53$	−1.80694	−	1.80694i	−0.248202	−	0.248202i	−0.820232	+	0.572030i	$0.806156\pi$
$54$	−0.807635	+	0.730986i	−0.109905	+	0.0994745i
$55$	7.78000	+	0.539121i	1.04906	+	0.0726951i
$56$	0.151888	+	1.34475i	0.0202969	+	0.179700i
$57$	−0.170373	+	0.170373i	−0.0225665	+	0.0225665i
$58$	3.21436	+	6.26844i	0.422066	+	0.823086i
$59$	−6.64587	+	11.5110i	−0.865218	+	1.49860i	0.00161221	+	0.999999i	$0.499487\pi$
$59$	−6.64587	+	11.5110i	−0.865218	+	1.49860i	−0.866830	+	0.498603i	$0.833847\pi$
$60$	−0.332942	−	0.469673i	−0.0429827	−	0.0606345i
$61$	5.69767	−	9.86866i	0.729512	−	1.26355i	−0.227578	−	0.973760i	$-0.573081\pi$
$61$	5.69767	−	9.86866i	0.729512	−	1.26355i	0.957090	−	0.289792i	$-0.0935862\pi$
$62$	−12.2444	−	0.609978i	−1.55504	−	0.0774673i
$63$	1.37882	+	0.369455i	0.173715	+	0.0465469i
$64$	−7.64587	−	2.35387i	−0.955733	−	0.294234i
$65$	−2.54984	+	7.64842i	−0.316269	+	0.948669i
$66$	0.133618	+	0.620732i	0.0164472	+	0.0764068i
$67$	2.09306	−	7.81142i	0.255708	−	0.954316i	−0.711987	−	0.702193i	$-0.752204\pi$
$67$	2.09306	−	7.81142i	0.255708	−	0.954316i	0.967695	−	0.252123i	$-0.0811289\pi$
$68$	−0.109110	−	0.666576i	−0.0132315	−	0.0808342i
$69$	0.826905	+	0.477414i	0.0995477	+	0.0574739i
$70$	−0.562284	+	1.40468i	−0.0672058	+	0.167891i
$71$	−1.63374	−	0.943240i	−0.193889	−	0.111942i	0.399913	−	0.916553i	$-0.369040\pi$
$71$	−1.63374	−	0.943240i	−0.193889	−	0.111942i	−0.593802	+	0.804611i	$0.702374\pi$
$72$	−5.25946	+	6.59885i	−0.619834	+	0.777682i
$73$	0.703943	+	0.703943i	0.0823903	+	0.0823903i	0.747101	−	0.664711i	$-0.231445\pi$
$73$	0.703943	+	0.703943i	0.0823903	+	0.0823903i	−0.664711	+	0.747101i	$0.731445\pi$
$74$	0.513886	−	1.59560i	0.0597380	−	0.185484i
$75$	−0.0792453	−	0.638768i	−0.00915046	−	0.0737586i
$76$	−2.18459	+	3.03974i	−0.250589	+	0.348682i
$77$	1.17997	−	1.17997i	0.134470	−	0.134470i
$78$	−0.655871	−	0.0266334i	−0.0742628	−	0.00301564i
$79$	12.6068			1.41838			0.709190	−	0.705018i	$-0.249061\pi$
$79$	12.6068			1.41838			0.709190	+	0.705018i	$0.249061\pi$
$80$	−6.28339	−	6.36546i	−0.702504	−	0.711680i
$81$	4.42556	+	7.66530i	0.491729	+	0.851700i
$82$	−1.46334	+	0.750376i	−0.161598	+	0.0828652i
$83$	−6.52171	+	6.52171i	−0.715851	+	0.715851i	−0.967753	−	0.251902i	$-0.918944\pi$
$83$	−6.52171	+	6.52171i	−0.715851	+	0.715851i	0.251902	+	0.967753i	$0.418944\pi$
$84$	−0.122578	−	0.0122433i	−0.0133744	−	0.00133585i
$85$	0.245412	−	0.714184i	0.0266186	−	0.0774641i
$86$	7.30500	−	1.57247i	0.787719	−	0.169564i
$87$	−0.619399	+	0.165967i	−0.0664066	+	0.0177936i
$88$	3.60645	+	9.18172i	0.384449	+	0.978775i
$89$	0.0310852	−	0.0179471i	0.00329503	−	0.00190238i	−0.498352	−	0.866975i	$-0.666061\pi$
$89$	0.0310852	−	0.0179471i	0.00329503	−	0.00190238i	0.501647	+	0.865073i	$0.332728\pi$
$90$	−8.67255	+	3.71420i	−0.914167	+	0.391511i
$91$	0.876257	+	1.48601i	0.0918567	+	0.155777i
$92$	13.8762	+	5.24447i	1.44670	+	0.546774i
$93$	0.288833	−	1.07794i	0.0299506	−	0.111777i
$94$	8.70488	−	7.87873i	0.897839	−	0.812629i
$95$	−3.76045	+	1.83702i	−0.385814	+	0.188474i
$96$	0.355933	−	0.635312i	0.0363272	−	0.0648413i
$97$	1.23898	+	4.62394i	0.125799	+	0.469490i	0.999867	−	0.0163149i	$-0.00519341\pi$
$97$	1.23898	+	4.62394i	0.125799	+	0.469490i	−0.874068	+	0.485804i	$0.838527\pi$
$98$	−4.36933	−	8.52079i	−0.441369	−	0.860729i
$99$	10.4052			1.04576
$100$	−2.81807	−	9.59471i	−0.281807	−	0.959471i
$101$	−2.51945	−	4.36381i	−0.250695	−	0.434216i	0.713023	−	0.701141i	$-0.247326\pi$
$101$	−2.51945	−	4.36381i	−0.250695	−	0.434216i	−0.963717	+	0.266925i	$0.913992\pi$
$102$	0.0614084	+	0.00305917i	0.00608033	+	0.000302903i
$103$	7.21738	−	7.21738i	0.711150	−	0.711150i	−0.255626	−	0.966776i	$-0.582282\pi$
$103$	7.21738	−	7.21738i	0.711150	−	0.711150i	0.966776	+	0.255626i	$0.0822815\pi$
$104$	−10.1227	+	1.23766i	−0.992608	+	0.121363i
$105$	−0.114231	−	0.0769451i	−0.0111478	−	0.00750907i
$106$	2.67938	−	2.42509i	0.260244	−	0.235545i
$107$	2.35808	−	8.80047i	0.227964	−	0.850773i	−0.753231	−	0.657756i	$-0.771506\pi$
$107$	2.35808	−	8.80047i	0.227964	−	0.850773i	0.981195	−	0.193018i	$-0.0618275\pi$
$108$	−0.975661	−	1.19219i	−0.0938830	−	0.114718i
$109$		−	14.0800i		−	1.34862i	−0.738448	−	0.674310i	$-0.764441\pi$
$109$		−	14.0800i		−	1.34862i	0.738448	−	0.674310i	$-0.235559\pi$
$110$	−1.30892	+	10.9510i	−0.124801	+	1.04414i
$111$	0.132147	+	0.0762953i	0.0125429	+	0.00724163i
$112$	−1.91010	+	0.119914i	−0.180487	+	0.0113308i
$113$	−9.63578	+	2.58190i	−0.906458	+	0.242885i	−0.681788	−	0.731550i	$-0.738797\pi$
$113$	−9.63578	+	2.58190i	−0.906458	+	0.242885i	−0.224671	+	0.974435i	$0.572131\pi$
$114$	−0.228658	−	0.252634i	−0.0214158	−	0.0236614i
$115$	10.8887	+	12.5102i	1.01538	+	1.16658i
$116$	−9.08011	+	4.09909i	−0.843067	+	0.380591i
$117$	−2.68848	+	10.4155i	−0.248551	+	0.962915i
$118$	−15.7912	−	10.1970i	−1.45370	−	0.938710i
$119$	−0.0807942	−	0.139940i	−0.00740640	−	0.0128283i
$120$	0.686823	−	0.437220i	0.0626980	−	0.0399126i
$121$	0.581907	−	1.00789i	0.0529006	−	0.0916265i
$122$	13.5382	+	8.74215i	1.22569	+	0.791477i
$123$	−0.0387443	−	0.144596i	−0.00349345	−	0.0130377i
$124$	1.72314	−	17.2519i	0.154743	−	1.54926i
$125$	2.30392	−	10.9404i	0.206069	−	0.978538i
$126$	−0.618861	+	1.92154i	−0.0551325	+	0.171184i
$127$	5.18626	−	19.3554i	0.460206	−	1.71751i	−0.212109	−	0.977246i	$-0.568033\pi$
$127$	5.18626	−	19.3554i	0.460206	−	1.71751i	0.672314	−	0.740266i	$-0.265300\pi$
$128$	3.86275	−	10.6339i	0.341422	−	0.939910i
$129$			0.680191i			0.0598874i
$130$	−10.6237	−	4.13973i	−0.931758	−	0.363079i
$131$		−	10.5834i		−	0.924676i	−0.886704	−	0.462338i	$-0.847011\pi$
$131$		−	10.5834i		−	0.924676i	0.886704	−	0.462338i	$-0.152989\pi$
$132$	−0.886162	+	0.145053i	−0.0771305	+	0.0126252i
$133$	−0.231778	+	0.865008i	−0.0200977	+	0.0750057i
$134$	10.8861	+	3.50602i	0.940412	+	0.302874i
$135$	−0.329704	−	1.69051i	−0.0283764	−	0.145496i
$136$	0.949190	−	0.107210i	0.0813924	−	0.00919319i
$137$	0.428112	+	1.59774i	0.0365761	+	0.136504i	0.981800	−	0.189920i	$-0.0608229\pi$
$137$	0.428112	+	1.59774i	0.0365761	+	0.136504i	−0.945223	+	0.326424i	$0.894156\pi$
$138$	−0.732514	+	1.13438i	−0.0623557	+	0.0965648i
$139$	4.95700	−	8.58578i	0.420447	−	0.728236i	−0.575536	−	0.817776i	$-0.695207\pi$
$139$	4.95700	−	8.58578i	0.420447	−	0.728236i	0.995983	+	0.0895405i	$0.0285399\pi$
$140$	−1.94449	−	0.893044i	−0.164339	−	0.0754760i
$141$	0.534376	+	0.925567i	0.0450026	+	0.0779468i
$142$	1.44725	−	2.24123i	0.121450	−	0.188079i
$143$	8.97318	+	8.80975i	0.750375	+	0.736708i
$144$	−8.95054	−	7.89311i	−0.745879	−	0.657760i
$145$	−11.1117	−	0.769997i	−0.922779	−	0.0639447i
$146$	−1.04383	+	0.944760i	−0.0863876	+	0.0781889i
$147$	0.841959	−	0.225602i	0.0694436	−	0.0186074i
$148$	2.21756	+	0.838117i	0.182282	+	0.0688928i
$149$	10.7837	+	6.22596i	0.883434	+	0.510051i	0.871789	−	0.489881i	$-0.162960\pi$
$149$	10.7837	+	6.22596i	0.883434	+	0.510051i	0.0116448	+	0.999932i	$0.496293\pi$
$150$	0.907811	−	0.0669845i	0.0741225	−	0.00546926i
$151$			12.2435i			0.996360i	0.867074	+	0.498180i	$0.165998\pi$
$151$			12.2435i			0.996360i	−0.867074	+	0.498180i	$0.834002\pi$
$152$	−4.13980	−	3.29954i	−0.335782	−	0.267628i
$153$	0.260779	−	0.973241i	0.0210827	−	0.0786819i
$154$	1.58363	+	1.74968i	0.127612	+	0.140994i
$155$	10.8294	−	16.0770i	0.869836	−	1.29133i
$156$	0.0837687	−	0.924519i	0.00670686	−	0.0740208i
$157$	14.0200	−	14.0200i	1.11892	−	1.11892i	0.127019	−	0.991900i	$-0.459459\pi$
$157$	14.0200	−	14.0200i	1.11892	−	1.11892i	0.991900	−	0.127019i	$-0.0405409\pi$
$158$	−0.887072	+	17.8067i	−0.0705717	+	1.41662i
$159$	0.164482	+	0.284891i	0.0130443	+	0.0225933i
$160$	9.43310	−	8.42714i	0.745752	−	0.666224i
$161$	3.54883			0.279687
$162$	−11.1383	+	5.71157i	−0.875111	+	0.448744i
$163$	3.00034	+	11.1974i	0.235005	+	0.877049i	0.978147	+	0.207916i	$0.0666679\pi$
$163$	3.00034	+	11.1974i	0.235005	+	0.877049i	−0.743142	+	0.669134i	$0.766665\pi$
$164$	−0.956911	−	2.11971i	−0.0747222	−	0.165521i
$165$	−0.949453	−	0.326256i	−0.0739148	−	0.0253990i
$166$	−8.75278	−	9.67057i	−0.679347	−	0.750582i
$167$	0.103335	−	0.385651i	0.00799629	−	0.0298426i	−0.961812	−	0.273709i	$-0.911749\pi$
$167$	0.103335	−	0.385651i	0.00799629	−	0.0298426i	0.969809	+	0.243867i	$0.0784160\pi$
$168$	0.0259183	−	0.172276i	0.00199964	−	0.0132914i
$169$	−11.1370	+	6.70582i	−0.856689	+	0.515833i
$170$	0.991489	+	0.396888i	0.0760437	+	0.0304399i
$171$	−4.83586	+	2.79198i	−0.369807	+	0.213508i
$172$	1.70704	+	10.4287i	0.130160	+	0.795180i
$173$	−7.40562	+	1.98433i	−0.563039	+	0.150866i	−0.529102	−	0.848558i	$-0.677471\pi$
$173$	−7.40562	+	1.98433i	−0.563039	+	0.150866i	−0.0339369	+	0.999424i	$0.510805\pi$
$174$	−0.190839	−	0.886556i	−0.0144675	−	0.0672096i
$175$	−1.44213	−	1.90878i	−0.109015	−	0.144290i
$176$	−13.2226	+	4.44791i	−0.996691	+	0.335274i
$177$	1.20992	−	1.20992i	0.0909431	−	0.0909431i
$178$	0.0231622	+	0.0451695i	0.00173608	+	0.00338560i
$179$	−6.31792	−	10.9430i	−0.472223	−	0.817915i	0.527271	−	0.849697i	$-0.323215\pi$
$179$	−6.31792	−	10.9430i	−0.472223	−	0.817915i	−0.999495	+	0.0317821i	$0.989882\pi$
$180$	−4.63593	−	12.5110i	−0.345542	−	0.932514i
$181$	−17.8541			−1.32709			−0.663544	−	0.748137i	$-0.730948\pi$
$181$	−17.8541			−1.32709			−0.663544	+	0.748137i	$0.730948\pi$
$182$	−2.16059	+	1.13312i	−0.160154	+	0.0839922i
$183$	−1.03729	+	1.03729i	−0.0766790	+	0.0766790i
$184$	−8.38401	+	19.2306i	−0.618077	+	1.41770i
$185$	1.74012	+	1.99924i	0.127936	+	0.146987i
$186$	1.50223	+	0.483815i	0.110149	+	0.0354750i
$187$	−0.832877	−	0.832877i	−0.0609060	−	0.0609060i
$188$	10.5159	+	12.8497i	0.766951	+	0.937160i
$189$	−0.319168	−	0.184272i	−0.0232161	−	0.0134038i
$190$	−2.33011	−	5.44075i	−0.169044	−	0.394713i
$191$	−14.5826	−	8.41925i	−1.05516	−	0.609195i	−0.131068	−	0.991373i	$-0.541841\pi$
$191$	−14.5826	−	8.41925i	−1.05516	−	0.609195i	−0.924089	+	0.382178i	$0.875174\pi$
$192$	0.872309	+	0.547445i	0.0629535	+	0.0395084i
$193$	2.45900	−	9.17710i	0.177002	−	0.660582i	−0.819199	−	0.573509i	$-0.805582\pi$
$193$	2.45900	−	9.17710i	0.177002	−	0.660582i	0.996202	−	0.0870734i	$-0.0277515\pi$
$194$	−6.61831	+	1.42465i	−0.475167	+	0.102284i
$195$	0.571898	−	0.866097i	0.0409545	−	0.0620225i
$196$	12.3427	−	5.57195i	0.881624	−	0.397997i
$197$	4.58380	+	1.22822i	0.326582	+	0.0875074i	0.418385	−	0.908270i	$-0.362596\pi$
$197$	4.58380	+	1.22822i	0.326582	+	0.0875074i	−0.0918029	+	0.995777i	$0.529263\pi$
$198$	−0.732155	+	14.6969i	−0.0520320	+	1.04447i
$199$	−10.0010	+	17.3222i	−0.708949	+	1.22794i	0.256299	+	0.966598i	$0.417497\pi$
$199$	−10.0010	+	17.3222i	−0.708949	+	1.22794i	−0.965247	+	0.261337i	$0.915836\pi$
$200$	13.7505	−	3.30529i	0.972304	−	0.233719i
$201$	−0.520530	+	0.901584i	−0.0367153	+	0.0635928i
$202$	6.34100	−	3.25157i	0.446151	−	0.228780i
$203$	−1.68528	+	1.68528i	−0.118283	+	0.118283i
$204$	−0.00864192	+	0.0865217i	−0.000605056	+	0.00605773i
$205$	0.179752	−	2.59398i	0.0125544	−	0.181171i
$206$	9.68643	+	10.7021i	0.674886	+	0.745652i
$207$	15.6472	+	15.6472i	1.08755	+	1.08755i
$208$	−1.03588	−	14.3850i	−0.0718250	−	0.997417i
$209$			6.52773i			0.451532i
$210$	0.116720	−	0.155932i	0.00805443	−	0.0107603i
$211$	−17.5973	+	10.1598i	−1.21145	+	0.699431i	−0.963075	−	0.269233i	$-0.913230\pi$
$211$	−17.5973	+	10.1598i	−1.21145	+	0.699431i	−0.248375	+	0.968664i	$0.579897\pi$
$212$	3.23681	+	3.95516i	0.222305	+	0.271641i
$213$	0.171722	+	0.171722i	0.0117662	+	0.0117662i
$214$	12.2644	+	3.94994i	0.838377	+	0.270012i
$215$	−3.83950	+	11.1735i	−0.261852	+	0.762027i
$216$	1.75257	−	1.29420i	0.119247	−	0.0880589i
$217$	−1.07351	−	4.00640i	−0.0728747	−	0.271972i
$218$	19.8875	+	0.990731i	1.34695	+	0.0671008i
$219$	−0.0640785	−	0.110987i	−0.00433002	−	0.00749982i
$220$	−15.3758	−	2.61937i	−1.03664	−	0.176598i
$221$	1.04890	−	0.618505i	0.0705567	−	0.0416052i
$222$	−0.117063	+	0.181285i	−0.00785674	+	0.0121670i
$223$	−25.0163	−	6.70309i	−1.67521	−	0.448872i	−0.708704	−	0.705506i	$-0.750720\pi$
$223$	−25.0163	−	6.70309i	−1.67521	−	0.448872i	−0.966509	+	0.256634i	$0.917386\pi$
$224$	−0.0349710	−	2.70638i	−0.00233660	−	0.180827i
$225$	2.05751	−	14.7746i	0.137167	−	0.984971i
$226$	−2.96882	−	13.7919i	−0.197483	−	0.917420i
$227$	−12.4828	+	3.34476i	−0.828515	+	0.222000i	−0.648066	−	0.761584i	$-0.724422\pi$
$227$	−12.4828	+	3.34476i	−0.828515	+	0.222000i	−0.180449	+	0.983584i	$0.557755\pi$
$228$	0.372926	−	0.305194i	0.0246976	−	0.0202120i
$229$			12.4530i			0.822920i	0.911428	+	0.411460i	$0.134981\pi$
$229$			12.4530i			0.822920i	−0.911428	+	0.411460i	$0.865019\pi$
$230$	−18.4363	+	14.4996i	−1.21565	+	0.956077i
$231$	−0.186039	+	0.107410i	−0.0122405	+	0.00706705i
$232$	−5.15089	−	13.1137i	−0.338172	−	0.860959i
$233$	17.3862	+	17.3862i	1.13901	+	1.13901i	0.988629	+	0.150377i	$0.0480489\pi$
$233$	17.3862	+	17.3862i	1.13901	+	1.13901i	0.150377	+	0.988629i	$0.451951\pi$
$234$	−14.5223	−	4.53026i	−0.949356	−	0.296153i
$235$	3.55363	+	18.2207i	0.231813	+	1.18859i
$236$	15.5140	−	21.5869i	1.00988	−	1.40519i
$237$	−1.56762	−	0.420041i	−0.101828	−	0.0272846i
$238$	0.203345	−	0.104272i	0.0131809	−	0.00675895i
$239$	−13.7087			−0.886742			−0.443371	−	0.896338i	$-0.646218\pi$
$239$	−13.7087			−0.886742			−0.443371	+	0.896338i	$0.646218\pi$
$240$	0.569229	+	1.00088i	0.0367436	+	0.0646062i
$241$	−4.45424	+	7.71498i	−0.286923	+	0.496965i	−0.973074	−	0.230494i	$-0.925966\pi$
$241$	−4.45424	+	7.71498i	−0.286923	+	0.496965i	0.686151	+	0.727460i	$0.259299\pi$
$242$	1.38266	+	0.892841i	0.0888810	+	0.0573940i
$243$	−0.892984	−	3.33266i	−0.0572849	−	0.213790i
$244$	−13.3006	+	18.5070i	−0.851481	+	1.18479i
$245$	15.1044	+	1.04667i	0.964982	+	0.0668692i
$246$	0.206962	−	0.0445504i	0.0131954	−	0.00284043i
$247$	−6.53420	−	1.68663i	−0.415761	−	0.107318i
$248$	24.2463	+	3.64779i	1.53964	+	0.231635i
$249$	1.02825	−	0.593658i	0.0651625	−	0.0376216i
$250$	15.2908	+	4.02401i	0.967073	+	0.254501i
$251$	18.7955	+	10.8516i	1.18636	+	0.684948i	0.957478	−	0.288505i	$-0.0931583\pi$
$251$	18.7955	+	10.8516i	1.18636	+	0.684948i	0.228886	+	0.973453i	$0.426492\pi$
$252$	−2.67056	−	1.00933i	−0.168229	−	0.0635815i
$253$	24.9870	−	6.69524i	1.57092	−	0.420926i
$254$	26.9738	+	8.68732i	1.69249	+	0.545091i
$255$	−0.0543116	+	0.0806295i	−0.00340113	+	0.00504921i
$256$	14.7481	+	6.20424i	0.921758	+	0.387765i
$257$	−20.8831	−	5.59562i	−1.30265	−	0.349045i	−0.460201	−	0.887815i	$-0.652223\pi$
$257$	−20.8831	−	5.59562i	−1.30265	−	0.349045i	−0.842453	+	0.538770i	$0.818889\pi$
$258$	−0.960743	−	0.0478612i	−0.0598133	−	0.00297971i
$259$	0.567137			0.0352402
$260$	6.59475	−	14.7143i	0.408989	−	0.912539i
$261$	−14.8612			−0.919883
$262$	14.9487	+	0.744695i	0.923531	+	0.0460074i
$263$	−11.8004	−	3.16191i	−0.727645	−	0.194972i	−0.124065	−	0.992274i	$-0.539593\pi$
$263$	−11.8004	−	3.16191i	−0.727645	−	0.194972i	−0.603580	+	0.797302i	$0.706260\pi$
$264$	−0.142528	−	1.26188i	−0.00877197	−	0.0776631i
$265$	1.09381	+	5.60837i	0.0671924	+	0.344520i
$266$	−1.20548	−	0.388244i	−0.0739129	−	0.0238048i
$267$	−0.00446331	+	0.00119594i	−0.000273150	+	7.31903e-5i
$268$	−5.71811	+	15.1294i	−0.349289	+	0.924177i
$269$	2.34395	+	1.35328i	0.142913	+	0.0825110i	0.569752	−	0.821817i	$-0.307039\pi$
$269$	2.34395	+	1.35328i	0.142913	+	0.0825110i	−0.426838	+	0.904328i	$0.640373\pi$
$270$	2.41098	−	0.346743i	0.146728	−	0.0211021i
$271$	7.04827	−	4.06932i	0.428152	−	0.247194i	−0.270407	−	0.962746i	$-0.587158\pi$
$271$	7.04827	−	4.06932i	0.428152	−	0.247194i	0.698559	+	0.715552i	$0.253825\pi$
$272$	0.0846410	+	1.34824i	0.00513212	+	0.0817490i
$273$	−0.0594477	−	0.213976i	−0.00359794	−	0.0129504i
$274$	−2.28687	+	0.492269i	−0.138155	+	0.0297390i
$275$	−13.7551	−	10.7188i	−0.829462	−	0.646370i
$276$	−1.55072	−	1.11447i	−0.0933426	−	0.0670831i
$277$	4.09806	+	15.2942i	0.246229	+	0.918938i	0.972762	+	0.231807i	$0.0744637\pi$
$277$	4.09806	+	15.2942i	0.246229	+	0.918938i	−0.726533	+	0.687131i	$0.758870\pi$
$278$	11.7783	+	7.60571i	0.706415	+	0.456160i
$279$	12.9314	−	22.3979i	0.774185	−	1.34093i
$280$	1.39821	−	2.68368i	0.0835592	−	0.160380i
$281$	−2.04246			−0.121843			−0.0609213	−	0.998143i	$-0.519404\pi$
$281$	−2.04246			−0.121843			−0.0609213	+	0.998143i	$0.519404\pi$
$282$	−1.34493	+	0.689659i	−0.0800893	+	0.0410686i
$283$	−20.3021	−	5.43994i	−1.20684	−	0.323371i	−0.401317	−	0.915939i	$-0.631447\pi$
$283$	−20.3021	−	5.43994i	−1.20684	−	0.323371i	−0.805520	+	0.592568i	$0.798114\pi$
$284$	3.06381	+	2.20189i	0.181804	+	0.130658i
$285$	0.528805	−	0.103134i	0.0313237	−	0.00610913i
$286$	−13.0748	+	12.0544i	−0.773130	+	0.712791i
$287$	−0.393420	−	0.393420i	−0.0232228	−	0.0232228i
$288$	11.7785	−	12.0869i	0.694056	−	0.712228i
$289$	14.6237	−	8.44297i	0.860215	−	0.496645i
$290$	1.86946	−	15.6407i	0.109779	−	0.918455i
$291$		−	0.616251i		−	0.0361253i
$292$	−1.26099	−	1.54084i	−0.0737938	−	0.0901709i
$293$	−9.51518	+	2.54959i	−0.555883	+	0.148948i	−0.525814	−	0.850599i	$-0.676239\pi$
$293$	−9.51518	+	2.54959i	−0.555883	+	0.148948i	−0.0300687	+	0.999548i	$0.509573\pi$
$294$	0.259411	+	1.20511i	0.0151291	+	0.0702834i
$295$	26.7051	−	13.0457i	1.55483	−	0.759550i
$296$	−1.33985	+	3.07324i	−0.0778769	+	0.178629i
$297$	−2.59489	−	0.695298i	−0.150571	−	0.0403453i
$298$	−9.55272	+	14.7935i	−0.553374	+	0.856962i
$299$	0.245770	+	26.7417i	0.0142132	+	1.54651i
$300$	0.0307355	+	1.28696i	0.00177451	+	0.0743028i
$301$	1.26404	+	2.18938i	0.0728580	+	0.126194i
$302$	−17.2935	−	0.861505i	−0.995126	−	0.0495740i
$303$	0.167889	+	0.626569i	0.00964495	+	0.0359955i
$304$	4.95177	−	5.61515i	0.284003	−	0.322051i
$305$	−22.8949	+	11.1844i	−1.31096	+	0.640418i
$306$	1.35632	+	0.436822i	0.0775354	+	0.0249715i
$307$	−5.38133	−	5.38133i	−0.307129	−	0.307129i	0.536666	−	0.843795i	$-0.319684\pi$
$307$	−5.38133	−	5.38133i	−0.307129	−	0.307129i	−0.843795	+	0.536666i	$0.819684\pi$
$308$	−2.58279	+	2.11370i	−0.147168	+	0.120439i
$309$	−1.13793	+	0.656983i	−0.0647345	+	0.0373745i
$310$	21.9461	+	16.4273i	1.24646	+	0.933009i
$311$		−	14.9090i		−	0.845412i	−0.906267	−	0.422706i	$-0.861080\pi$
$311$		−	14.9090i		−	0.845412i	0.906267	−	0.422706i	$-0.138920\pi$
$312$	1.29995	+	0.183373i	0.0735954	+	0.0103815i
$313$	3.58511	+	3.58511i	0.202642	+	0.202642i	0.801131	−	0.598489i	$-0.204232\pi$
$313$	3.58511	+	3.58511i	0.202642	+	0.202642i	−0.598489	+	0.801131i	$0.704232\pi$
$314$	18.8162	+	20.7893i	1.06186	+	1.17321i
$315$	−2.09559	−	2.40765i	−0.118073	−	0.135655i
$316$	−25.0888	−	2.50591i	−1.41136	−	0.140968i
$317$	23.3009	−	23.3009i	1.30871	−	1.30871i	0.386363	−	0.922347i	$-0.373731\pi$
$317$	23.3009	−	23.3009i	1.30871	−	1.30871i	0.922347	−	0.386363i	$-0.126269\pi$
$318$	−0.413971	+	0.212278i	−0.0232144	+	0.0119040i
$319$	−8.68644	+	15.0454i	−0.486347	+	0.842378i
$320$	11.2393	+	13.9169i	0.628294	+	0.777976i
$321$	−0.586438	+	1.01574i	−0.0327318	+	0.0566931i
$322$	−0.249711	+	5.01258i	−0.0139158	+	0.279340i
$323$	0.610565	+	0.163600i	0.0339728	+	0.00910297i
$324$	−7.28364	−	16.1344i	−0.404647	−	0.896355i
$325$	14.2835	−	10.9992i	0.792305	−	0.610125i
$326$	−16.0270	+	3.44996i	−0.887656	+	0.191076i
$327$	−0.469125	+	1.75080i	−0.0259427	+	0.0968194i
$328$	3.06134	−	1.20245i	0.169034	−	0.0663941i
$329$	3.44007	+	1.98613i	0.189657	+	0.109499i
$330$	0.527632	−	1.31811i	0.0290452	−	0.0725595i
$331$	−3.95572	−	2.28384i	−0.217426	−	0.125531i	0.387332	−	0.921940i	$-0.373397\pi$
$331$	−3.95572	−	2.28384i	−0.217426	−	0.125531i	−0.604758	+	0.796409i	$0.706730\pi$
$332$	14.2752	−	11.6825i	0.783453	−	0.641161i
$333$	2.50057	+	2.50057i	0.137030	+	0.137030i
$334$	0.537446	+	0.173093i	0.0294077	+	0.00947120i
$335$	−13.6400	+	11.8721i	−0.745232	+	0.648642i
$336$	0.241509	+	0.0487307i	0.0131754	+	0.00265848i
$337$	−10.0791	+	10.0791i	−0.549044	+	0.549044i	−0.926164	−	0.377120i	$-0.876914\pi$
$337$	−10.0791	+	10.0791i	−0.549044	+	0.549044i	0.377120	+	0.926164i	$0.376914\pi$
$338$	−8.68808	−	16.2024i	−0.472569	−	0.881294i
$339$	1.28420			0.0697482
$340$	−0.630354	+	1.37251i	−0.0341858	+	0.0744350i
$341$	−15.1170	−	26.1834i	−0.818633	−	1.41791i
$342$	−3.60330	−	7.02692i	−0.194844	−	0.379972i
$343$	4.65910	−	4.65910i	0.251568	−	0.251568i
$344$	−14.8502	+	1.67732i	−0.800671	+	0.0904350i
$345$	−0.937153	−	1.91839i	−0.0504546	−	0.103283i
$346$	−2.28170	−	10.5998i	−0.122665	−	0.569848i
$347$	7.11565	−	1.90663i	0.381988	−	0.102353i	−0.0627149	−	0.998031i	$-0.519976\pi$
$347$	7.11565	−	1.90663i	0.381988	−	0.102353i	0.444703	+	0.895678i	$0.353309\pi$
$348$	1.26565	−	0.207171i	0.0678462	−	0.0111055i
$349$	−16.9307	+	9.77496i	−0.906281	+	0.523241i	−0.879233	−	0.476393i	$-0.841944\pi$
$349$	−16.9307	+	9.77496i	−0.906281	+	0.523241i	−0.0270482	+	0.999634i	$0.508611\pi$
$350$	2.79756	−	1.90265i	0.149536	−	0.101701i
$351$	1.36645	−	2.41781i	0.0729358	−	0.129053i
$352$	−5.35210	−	18.9894i	−0.285268	−	1.01214i
$353$	2.85398	−	10.6512i	0.151902	−	0.566906i	−0.847449	−	0.530877i	$-0.821863\pi$
$353$	2.85398	−	10.6512i	0.151902	−	0.566906i	0.999351	−	0.0360287i	$-0.0114708\pi$
$354$	1.62383	+	1.79410i	0.0863056	+	0.0953553i
$355$	1.85156	+	3.79022i	0.0982707	+	0.201164i
$356$	−0.0654300	+	0.0295375i	−0.00346778	+	0.00156548i
$357$	0.00538389	+	0.0200930i	0.000284946	+	0.00106343i
$358$	15.9011	−	8.15382i	0.840397	−	0.430943i
$359$	5.55317			0.293085			0.146543	−	0.989204i	$-0.453185\pi$
$359$	5.55317			0.293085			0.146543	+	0.989204i	$0.453185\pi$
$360$	17.9975	−	5.66775i	0.948552	−	0.298716i
$361$	7.74844	+	13.4207i	0.407813	+	0.706352i
$362$	1.25630	−	25.2183i	0.0660294	−	1.32544i
$363$	−0.105940	+	0.105940i	−0.00556038	+	0.00556038i
$364$	−1.44846	−	3.13149i	−0.0759197	−	0.164135i
$365$	−0.426125	−	2.18490i	−0.0223044	−	0.114363i
$366$	−1.39215	−	1.53813i	−0.0727689	−	0.0803992i
$367$	−6.46243	+	24.1181i	−0.337336	+	1.25895i	0.563979	+	0.825789i	$0.309270\pi$
$367$	−6.46243	+	24.1181i	−0.337336	+	1.25895i	−0.901314	+	0.433165i	$0.857397\pi$
$368$	−26.5726	−	13.1952i	−1.38519	−	0.687850i
$369$		−	3.46926i		−	0.180603i
$370$	−2.94630	+	2.31718i	−0.153171	+	0.120465i
$371$	1.05886	+	0.611333i	0.0549732	+	0.0317388i
$372$	−0.789073	+	2.08779i	−0.0409115	+	0.108247i
$373$	−3.79520	+	1.01692i	−0.196508	+	0.0526542i	−0.355731	−	0.934589i	$-0.615768\pi$
$373$	−3.79520	+	1.01692i	−0.196508	+	0.0526542i	0.159223	+	0.987243i	$0.449101\pi$
$374$	1.23501	−	1.11780i	0.0638610	−	0.0578002i
$375$	−0.651001	+	1.28363i	−0.0336176	+	0.0662866i
$376$	−18.8896	+	13.9491i	−0.974159	+	0.719372i
$377$	−12.8159	−	12.5825i	−0.660052	−	0.648030i
$378$	0.282735	−	0.437847i	0.0145423	−	0.0225204i
$379$	−3.40304	−	5.89424i	−0.174803	−	0.302767i	0.765290	−	0.643685i	$-0.222595\pi$
$379$	−3.40304	−	5.89424i	−0.174803	−	0.302767i	−0.940093	+	0.340918i	$0.889262\pi$
$380$	7.84881	−	2.90836i	0.402635	−	0.149196i
$381$	−1.28979	+	2.23397i	−0.0660777	+	0.114450i
$382$	12.9180	−	20.0049i	0.660940	−	1.02354i
$383$	1.76074	+	6.57115i	0.0899694	+	0.335770i	0.996209	−	0.0869946i	$-0.0277263\pi$
$383$	1.76074	+	6.57115i	0.0899694	+	0.335770i	−0.906239	+	0.422765i	$0.861060\pi$
$384$	−0.834625	+	1.19358i	−0.0425918	+	0.0609098i
$385$	−3.66237	+	0.714280i	−0.186652	+	0.0364031i
$386$	12.7893	+	4.11898i	0.650957	+	0.209651i
$387$	−4.07993	+	15.2265i	−0.207395	+	0.774007i
$388$	−1.54657	−	9.44836i	−0.0785153	−	0.479668i
$389$		−	18.6437i		−	0.945274i	−0.881257	−	0.472637i	$-0.843302\pi$
$389$		−	18.6437i		−	0.945274i	0.881257	−	0.472637i	$-0.156698\pi$
$390$	1.18309	+	0.868727i	0.0599080	+	0.0439897i
$391$		−	2.50493i		−	0.126680i
$392$	7.00168	+	17.8257i	0.353638	+	0.900334i
$393$	−0.352623	+	1.31601i	−0.0177875	+	0.0663839i
$394$	−2.05736	+	6.38802i	−0.103648	+	0.321824i
$395$	−23.3802	−	15.7488i	−1.17639	−	0.792409i
$396$	−20.7074	−	2.06828i	−1.04058	−	0.103935i
$397$	−2.95391	−	11.0241i	−0.148253	−	0.553286i	−0.999589	−	0.0286659i	$-0.990874\pi$
$397$	−2.95391	−	11.0241i	−0.148253	−	0.553286i	0.851337	−	0.524620i	$-0.175793\pi$
$398$	−23.7632	−	15.3448i	−1.19114	−	0.769167i
$399$	0.0576416	−	0.0998382i	0.00288569	−	0.00499816i
$400$	3.70106	+	19.6546i	0.185053	+	0.982729i
$401$	12.0555	+	20.8808i	0.602024	+	1.04274i	0.992514	+	0.122129i	$0.0389722\pi$
$401$	12.0555	+	20.8808i	0.602024	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$402$	−1.23683	−	0.798668i	−0.0616873	−	0.0398339i
$403$	30.1153	−	8.36676i	1.50015	−	0.416778i
$404$	4.14654	+	9.18522i	0.206298	+	0.456982i
$405$	1.36820	−	19.7444i	0.0679865	−	0.981106i
$406$	−2.26181	−	2.49897i	−0.112252	−	0.124022i
$407$	3.99316	−	1.06996i	0.197934	−	0.0530362i
$408$	−0.121601	−	0.0182944i	−0.00602012	−	0.000905709i
$409$	−20.5507	−	11.8650i	−1.01617	−	0.586684i	−0.103176	−	0.994663i	$-0.532900\pi$
$409$	−20.5507	−	11.8650i	−1.01617	−	0.586684i	−0.912991	+	0.407979i	$0.866234\pi$
$410$	3.65125	+	0.436416i	0.180322	+	0.0215531i
$411$		−	0.212937i		−	0.0105034i
$412$	−15.7979	+	12.9287i	−0.778308	+	0.636950i
$413$	1.64599	−	6.14292i	0.0809939	−	0.302273i
$414$	−23.2020	+	21.0000i	−1.14032	+	1.03210i
$415$	20.2421	−	3.94786i	0.993645	−	0.193793i
$416$	20.3911	−	0.450946i	0.999756	−	0.0221094i
$417$	−0.902451	+	0.902451i	−0.0441932	+	0.0441932i
$418$	−9.22017	−	0.459320i	−0.450973	−	0.0224661i
$419$	−4.91668	−	8.51595i	−0.240196	−	0.416031i	0.720574	−	0.693378i	$-0.243878\pi$
$419$	−4.91668	−	8.51595i	−0.240196	−	0.416031i	−0.960770	+	0.277347i	$0.910545\pi$
$420$	0.212035	+	0.175834i	0.0103463	+	0.00857984i
$421$	−27.2170			−1.32647			−0.663237	−	0.748409i	$-0.730818\pi$
$421$	−27.2170			−1.32647			−0.663237	+	0.748409i	$0.730818\pi$
$422$	−13.1121	−	25.5704i	−0.638289	−	1.24475i
$423$	6.41061	+	23.9247i	0.311694	+	1.16326i
$424$	−5.81426	+	4.29357i	−0.282366	+	0.208514i
$425$	−1.34731	+	1.01793i	−0.0653542	+	0.0493768i
$426$	−0.254635	+	0.230468i	−0.0123371	+	0.0111662i
$427$	−1.41115	+	5.26648i	−0.0682903	+	0.254863i
$428$	−6.44211	+	17.0451i	−0.311391	+	0.823905i
$429$	−0.822255	−	1.39443i	−0.0396989	−	0.0673239i
$430$	−15.5120	−	6.20937i	−0.748055	−	0.299442i
$431$	23.9758	−	13.8425i	1.15488	−	0.666767i	0.204805	−	0.978803i	$-0.434344\pi$
$431$	23.9758	−	13.8425i	1.15488	−	0.666767i	0.950070	+	0.312035i	$0.101011\pi$
$432$	1.70468	+	2.56651i	0.0820166	+	0.123481i
$433$	−21.3816	+	5.72918i	−1.02753	+	0.275327i	−0.732938	−	0.680296i	$-0.761851\pi$
$433$	−21.3816	+	5.72918i	−1.02753	+	0.275327i	−0.294595	+	0.955622i	$0.595185\pi$
$434$	5.73443	−	1.23439i	0.275261	−	0.0592525i
$435$	1.35605	+	0.465973i	0.0650176	+	0.0223417i
$436$	−2.79874	+	28.0206i	−0.134035	+	1.34194i
$437$	−9.81629	+	9.81629i	−0.469577	+	0.469577i
$438$	0.161274	−	0.0826989i	0.00770597	−	0.00395150i
$439$	−12.6462	−	21.9038i	−0.603570	−	1.04541i	−0.992276	−	0.124052i	$-0.960411\pi$
$439$	−12.6462	−	21.9038i	−0.603570	−	1.04541i	0.388706	−	0.921362i	$-0.372922\pi$
$440$	4.78166	−	21.5334i	0.227957	−	1.02657i
$441$	20.2010			0.961953
$442$	0.799810	+	1.52505i	0.0380431	+	0.0725394i
$443$	12.4615	−	12.4615i	0.592063	−	0.592063i	−0.346125	−	0.938188i	$-0.612503\pi$
$443$	12.4615	−	12.4615i	0.592063	−	0.592063i	0.938188	+	0.346125i	$0.112503\pi$
$444$	−0.247821	−	0.178103i	−0.0117611	−	0.00845238i
$445$	−0.0800697	−	0.00554849i	−0.00379567	−	0.000263024i
$446$	11.2281	−	34.8629i	0.531666	−	1.65080i
$447$	−1.13347	−	1.13347i	−0.0536114	−	0.0536114i
$448$	3.82511	+	0.141037i	0.180720	+	0.00666338i
$449$	17.6268	+	10.1768i	0.831860	+	0.480274i	0.854489	−	0.519470i	$-0.173870\pi$
$449$	17.6268	+	10.1768i	0.831860	+	0.480274i	−0.0226294	+	0.999744i	$0.507204\pi$
$450$	20.7237	+	3.94576i	0.976926	+	0.186005i
$451$	−3.51226	−	2.02781i	−0.165386	−	0.0954857i
$452$	19.6894	−	3.22289i	0.926110	−	0.151592i
$453$	0.407935	−	1.52243i	0.0191665	−	0.0715302i
$454$	−3.84601	−	17.8669i	−0.180502	−	0.838534i
$455$	0.231292	−	3.85056i	0.0108431	−	0.180517i
$456$	0.404834	+	0.548218i	0.0189581	+	0.0256727i
$457$	19.6887	+	5.27556i	0.920997	+	0.246780i	0.688011	−	0.725700i	$-0.258484\pi$
$457$	19.6887	+	5.27556i	0.920997	+	0.246780i	0.232985	+	0.972480i	$0.425151\pi$
$458$	−17.5894	−	0.876250i	−0.821901	−	0.0409445i
$459$	−0.130068	+	0.225285i	−0.00607106	+	0.0105154i
$460$	−19.1829	−	27.0608i	−0.894408	−	1.26172i
$461$	2.48508	−	4.30428i	0.115742	−	0.200470i	−0.802334	−	0.596875i	$-0.796409\pi$
$461$	2.48508	−	4.30428i	0.115742	−	0.200470i	0.918076	+	0.396405i	$0.129742\pi$
$462$	−0.138622	−	0.270331i	−0.00644927	−	0.0125769i
$463$	26.5609	−	26.5609i	1.23439	−	1.23439i	0.272128	−	0.962261i	$-0.412272\pi$
$463$	26.5609	−	26.5609i	1.23439	−	1.23439i	0.962261	−	0.272128i	$-0.0877276\pi$
$464$	18.8851	−	6.35269i	0.876718	−	0.294916i
$465$	−1.88226	+	1.63830i	−0.0872875	+	0.0759742i
$466$	−25.7807	+	23.3339i	−1.19427	+	1.08092i
$467$	20.5114	+	20.5114i	0.949154	+	0.949154i	0.998768	−	0.0496140i	$-0.0157991\pi$
$467$	20.5114	+	20.5114i	0.949154	+	0.949154i	−0.0496140	+	0.998768i	$0.515799\pi$
$468$	7.42068	−	20.1935i	0.343021	−	0.933445i
$469$			3.86933i			0.178669i
$470$	−25.9861	+	3.73727i	−1.19865	+	0.172388i
$471$	−2.21047	+	1.27621i	−0.101853	+	0.0588048i
$472$	29.3991	+	23.4319i	1.35320	+	1.07854i
$473$	13.0305	+	13.0305i	0.599143	+	0.599143i
$474$	0.703597	−	2.18464i	0.0323173	−	0.100344i
$475$	9.26886	+	1.29078i	0.425284	+	0.0592252i
$476$	0.132972	+	0.294554i	0.00609476	+	0.0135008i
$477$	1.97320	+	7.36407i	0.0903464	+	0.337177i
$478$	0.964604	−	19.3630i	0.0441200	−	0.885644i
$479$	0.169656	+	0.293853i	0.00775179	+	0.0134265i	0.869875	−	0.493272i	$-0.164199\pi$
$479$	0.169656	+	0.293853i	0.00775179	+	0.0134265i	−0.862123	+	0.506698i	$0.830866\pi$
$480$	−1.45375	+	0.733588i	−0.0663544	+	0.0334836i
$481$	0.0392764	+	4.27358i	0.00179085	+	0.194858i
$482$	−10.5837	−	6.83431i	−0.482074	−	0.311294i
$483$	−0.441284	−	0.118242i	−0.0200791	−	0.00538018i
$484$	−1.35839	+	1.89014i	−0.0617452	+	0.0859152i
$485$	3.47858	−	10.1232i	0.157954	−	0.459670i
$486$	4.77009	−	1.02680i	0.216376	−	0.0465768i
$487$	1.33724	−	0.358312i	0.0605961	−	0.0162367i	−0.228394	−	0.973569i	$-0.573347\pi$
$487$	1.33724	−	0.358312i	0.0605961	−	0.0162367i	0.288990	+	0.957332i	$0.406681\pi$
$488$	−25.2046	−	20.0888i	−1.14096	−	0.909376i
$489$		−	1.49233i		−	0.0674853i
$490$	−2.54119	+	21.2607i	−0.114799	+	0.960460i
$491$	15.0179	−	8.67057i	0.677747	−	0.391297i	−0.121259	−	0.992621i	$-0.538693\pi$
$491$	15.0179	−	8.67057i	0.677747	−	0.391297i	0.799006	+	0.601324i	$0.205360\pi$
$492$	0.0483631	+	0.295461i	0.00218037	+	0.0133204i
$493$	1.18955	+	1.18955i	0.0535747	+	0.0535747i
$494$	2.84207	−	9.11063i	0.127871	−	0.409907i
$495$	−19.2972	−	12.9985i	−0.867343	−	0.584238i
$496$	−6.85844	+	33.9904i	−0.307953	+	1.52621i
$497$	0.871857	+	0.233614i	0.0391082	+	0.0104790i
$498$	0.766168	+	1.49413i	0.0343328	+	0.0669536i
$499$	−2.68600			−0.120242			−0.0601208	−	0.998191i	$-0.519149\pi$
$499$	−2.68600			−0.120242			−0.0601208	+	0.998191i	$0.519149\pi$
$500$	−6.75968	+	21.3145i	−0.302302	+	0.953212i
$501$	−0.0256986	+	0.0445113i	−0.00114813	+	0.00198862i
$502$	−16.6500	+	25.7844i	−0.743127	+	1.15082i
$503$	7.44505	+	27.7853i	0.331958	+	1.23889i	0.907129	+	0.420852i	$0.138269\pi$
$503$	7.44505	+	27.7853i	0.331958	+	1.23889i	−0.575171	+	0.818033i	$0.695064\pi$
$504$	1.61355	−	3.70104i	0.0718730	−	0.164857i
$505$	−0.778910	+	11.2404i	−0.0346610	+	0.500190i
$506$	7.69858	+	35.7643i	0.342244	+	1.58992i
$507$	1.60827	−	0.462778i	0.0714258	−	0.0205527i
$508$	−14.1685	+	37.4882i	−0.628626	+	1.66327i
$509$	−10.9012	+	6.29382i	−0.483188	+	0.278969i	−0.721744	−	0.692160i	$-0.756659\pi$
$509$	−10.9012	+	6.29382i	−0.483188	+	0.278969i	0.238556	+	0.971129i	$0.423326\pi$
$510$	−0.110064	−	0.0823866i	−0.00487374	−	0.00364814i
$511$	−0.412508	−	0.238162i	−0.0182483	−	0.0105357i
$512$	−9.80099	+	20.3946i	−0.433147	+	0.901323i
$513$	1.39255	−	0.373133i	0.0614826	−	0.0164742i
$514$	9.37302	−	29.1029i	0.413426	−	1.28367i
$515$	−22.4013	+	4.36897i	−0.987119	+	0.192520i
$516$	0.135204	−	1.35365i	0.00595203	−	0.0595909i
$517$	27.9683	+	7.49408i	1.23004	+	0.329589i
$518$	−0.0399062	+	0.801059i	−0.00175338	+	0.0351965i
$519$	0.986978			0.0433235
$520$	20.3193	+	10.3502i	0.891060	+	0.453886i
$521$	25.8522			1.13260			0.566302	−	0.824198i	$-0.308373\pi$
$521$	25.8522			1.13260			0.566302	+	0.824198i	$0.308373\pi$
$522$	1.04570	−	20.9908i	0.0457689	−	0.918743i
$523$	35.5862	+	9.53530i	1.55608	+	0.416950i	0.931419	−	0.363948i	$-0.118572\pi$
$523$	35.5862	+	9.53530i	1.55608	+	0.416950i	0.624658	+	0.780898i	$0.285238\pi$
$524$	−2.10371	+	21.0620i	−0.0919008	+	0.920098i
$525$	0.115726	+	0.285400i	0.00505071	+	0.0124559i
$526$	5.29641	−	16.4451i	0.230934	−	0.717043i
$527$	−2.82791	+	0.757737i	−0.123186	+	0.0330076i
$528$	1.79238	−	0.112524i	0.0780034	−	0.00489697i
$529$	27.7247	+	16.0068i	1.20542	+	0.695949i
$530$	−7.99858	+	1.15034i	−0.347436	+	0.0499675i
$531$	34.3422	−	19.8275i	1.49032	−	0.860439i
$532$	0.633203	−	1.67538i	0.0274528	−	0.0726369i
$533$	2.93731	−	2.99180i	0.127229	−	0.129589i
$534$	−0.00137516	−	0.00638840i	−5.95090e−5	−	0.000276453i
$535$	−15.3670	+	13.3753i	−0.664374	+	0.578265i
$536$	−20.9674	−	9.14118i	−0.905654	−	0.394839i
$537$	0.421008	+	1.57122i	0.0181678	+	0.0678032i
$538$	−2.07639	+	3.21552i	−0.0895195	+	0.138631i
$539$	11.8076	−	20.4514i	0.508590	−	0.880904i
$540$	0.320113	+	3.42982i	0.0137755	+	0.147596i
$541$	21.5054			0.924591			0.462296	−	0.886726i	$-0.347026\pi$
$541$	21.5054			0.924591			0.462296	+	0.886726i	$0.347026\pi$
$542$	5.25181	+	10.2417i	0.225585	+	0.439921i
$543$	2.22010	+	0.594874i	0.0952736	+	0.0255285i
$544$	−1.91029	+	0.0246842i	−0.0819031	+	0.00105833i
$545$	−17.5892	+	26.1124i	−0.753437	+	1.11853i
$546$	0.306416	−	0.0689113i	0.0131134	−	0.00294913i
$547$	3.00823	+	3.00823i	0.128623	+	0.128623i	0.768488	−	0.639865i	$-0.221010\pi$
$547$	3.00823	+	3.00823i	0.128623	+	0.128623i	−0.639865	+	0.768488i	$0.721010\pi$
$548$	−0.534397	−	3.26475i	−0.0228283	−	0.139463i
$549$	−29.4424	+	16.9986i	−1.25657	+	0.725482i
$550$	16.1078	−	18.6743i	0.686840	−	0.796274i
$551$		−	9.32319i		−	0.397181i
$552$	1.68326	−	2.11192i	0.0716442	−	0.0898893i
$553$	−5.82638	+	1.56117i	−0.247763	+	0.0663879i
$554$	−21.8908	+	4.71219i	−0.930051	+	0.200202i
$555$	−0.149766	−	0.306577i	−0.00635722	−	0.0130135i
$556$	−11.5715	+	16.1012i	−0.490743	+	0.682843i
$557$	−25.8299	−	6.92109i	−1.09445	−	0.293256i	−0.333945	−	0.942593i	$-0.608380\pi$
$557$	−25.8299	−	6.92109i	−1.09445	−	0.293256i	−0.760501	+	0.649337i	$0.775047\pi$
$558$	30.7263	+	19.8412i	1.30075	+	0.839944i
$559$	−16.4102	+	9.67661i	−0.694078	+	0.409277i
$560$	3.69221	+	2.16376i	0.156024	+	0.0914355i
$561$	0.0758151	+	0.131316i	0.00320092	+	0.00554415i
$562$	0.143716	−	2.88489i	0.00606230	−	0.121692i
$563$	−2.32261	−	8.66811i	−0.0978865	−	0.365317i	0.899555	−	0.436808i	$-0.143891\pi$
$563$	−2.32261	−	8.66811i	−0.0978865	−	0.365317i	−0.997441	+	0.0714906i	$0.977224\pi$
$564$	−0.879482	−	1.94819i	−0.0370329	−	0.0820335i
$565$	21.0956	+	7.24899i	0.887499	+	0.304967i
$566$	9.11226	−	28.2932i	0.383017	−	1.18925i
$567$	−2.99456	−	2.99456i	−0.125760	−	0.125760i
$568$	−3.32566	+	4.17258i	−0.139542	+	0.175078i
$569$	25.5353	−	14.7428i	1.07049	−	0.618050i	0.142178	−	0.989841i	$-0.454589\pi$
$569$	25.5353	−	14.7428i	1.07049	−	0.618050i	0.928317	+	0.371791i	$0.121256\pi$
$570$	0.108464	+	0.754174i	0.00454304	+	0.0315889i
$571$		−	21.9871i		−	0.920130i	−0.887885	−	0.460065i	$-0.847826\pi$
$571$		−	21.9871i		−	0.920130i	0.887885	−	0.460065i	$-0.152174\pi$
$572$	−16.1064	−	19.3159i	−0.673441	−	0.807638i
$573$	1.53277	+	1.53277i	0.0640325	+	0.0640325i
$574$	0.583373	−	0.528008i	0.0243495	−	0.0220386i
$575$	−4.56582	−	36.8035i	−0.190408	−	1.53481i
$576$	16.2435	+	17.4872i	0.676813	+	0.728634i
$577$	−24.1574	+	24.1574i	−1.00569	+	1.00569i	−0.00570302	+	0.999984i	$0.501815\pi$
$577$	−24.1574	+	24.1574i	−1.00569	+	1.00569i	−0.999984	+	0.00570302i	$0.998185\pi$
$578$	10.8964	+	21.2494i	0.453230	+	0.883860i
$579$	−0.611535	+	1.05921i	−0.0254145	+	0.0440193i
$580$	21.9604	+	3.74109i	0.911855	+	0.155340i
$581$	2.20646	−	3.82170i	0.0915394	−	0.158551i
$582$	0.870431	+	0.0433621i	0.0360805	+	0.00179742i
$583$	8.60869	+	2.30669i	0.356535	+	0.0955334i
$584$	2.26511	−	1.67268i	0.0937308	−	0.0692160i
$585$	17.9973	−	15.9578i	0.744099	−	0.659772i
$586$	−2.93166	−	13.6192i	−0.121106	−	0.562605i
$587$	−0.734777	+	2.74223i	−0.0303275	+	0.113184i	−0.979430	−	0.201783i	$-0.935327\pi$
$587$	−0.734777	+	2.74223i	−0.0303275	+	0.113184i	0.949103	+	0.314966i	$0.101993\pi$
$588$	−1.72042	+	0.281611i	−0.0709491	+	0.0116134i
$589$	14.0514	+	8.11257i	0.578977	+	0.334273i
$590$	16.5475	+	38.6378i	0.681248	+	1.59069i
$591$	−0.529056	−	0.305451i	−0.0217625	−	0.0125646i
$592$	−4.24656	−	2.10873i	−0.174533	−	0.0866682i
$593$	−32.3945	−	32.3945i	−1.33028	−	1.33028i	−0.905113	−	0.425171i	$-0.860214\pi$
$593$	−32.3945	−	32.3945i	−1.33028	−	1.33028i	−0.425171	−	0.905113i	$-0.639786\pi$
$594$	1.16467	−	3.61625i	0.0477870	−	0.148377i
$595$	−0.0249783	+	0.360458i	−0.00102401	+	0.0147774i
$596$	−20.2230	−	14.5338i	−0.828368	−	0.595327i
$597$	1.82073	−	1.82073i	0.0745176	−	0.0745176i
$598$	−37.7889	−	1.53452i	−1.54530	−	0.0627512i
$599$	15.2583			0.623435			0.311718	−	0.950175i	$-0.399096\pi$
$599$	15.2583			0.623435			0.311718	+	0.950175i	$0.399096\pi$
$600$	−1.81995	−	0.0471436i	−0.0742991	−	0.00192463i
$601$	−2.22869	−	3.86020i	−0.0909100	−	0.157461i	0.816984	−	0.576660i	$-0.195644\pi$
$601$	−2.22869	−	3.86020i	−0.0909100	−	0.157461i	−0.907894	+	0.419199i	$0.862311\pi$
$602$	−3.18136	+	1.63135i	−0.129662	+	0.0664890i
$603$	−17.0603	+	17.0603i	−0.694749	+	0.694749i
$604$	2.43369	−	24.3657i	0.0990253	−	0.991427i
$605$	−2.33827	+	1.14227i	−0.0950644	+	0.0464399i
$606$	−0.896818	+	0.193048i	−0.0364308	+	0.00784205i
$607$	−5.42551	+	1.45376i	−0.220214	+	0.0590063i	−0.367239	−	0.930127i	$-0.619697\pi$
$607$	−5.42551	+	1.45376i	−0.220214	+	0.0590063i	0.147025	+	0.989133i	$0.453030\pi$
$608$	7.58275	+	7.38929i	0.307521	+	0.299675i
$609$	0.265709	−	0.153407i	0.0107671	−	0.00621638i
$610$	−14.1866	−	33.1252i	−0.574397	−	1.34120i
$611$	−14.7279	+	26.0597i	−0.595828	+	1.05426i
$612$	−0.712431	+	1.88501i	−0.0287983	+	0.0761970i
$613$	−10.3691	+	38.6979i	−0.418803	+	1.56299i	0.358291	+	0.933610i	$0.383359\pi$
$613$	−10.3691	+	38.6979i	−0.418803	+	1.56299i	−0.777094	+	0.629384i	$0.783307\pi$
$614$	7.97958	−	7.22227i	0.322030	−	0.291467i
$615$	−0.108779	+	0.316563i	−0.00438640	+	0.0127651i
$616$	−2.80378	−	3.79683i	−0.112968	−	0.152978i
$617$	−11.8396	−	44.1860i	−0.476644	−	1.77886i	−0.615054	−	0.788485i	$-0.710866\pi$
$617$	−11.8396	−	44.1860i	−0.476644	−	1.77886i	0.138410	−	0.990375i	$-0.455801\pi$
$618$	−0.847895	−	1.65351i	−0.0341073	−	0.0665139i
$619$	8.70809			0.350007			0.175004	−	0.984568i	$-0.444006\pi$
$619$	8.70809			0.350007			0.175004	+	0.984568i	$0.444006\pi$
$620$	−24.7472	+	29.8422i	−0.993871	+	1.19849i
$621$	−2.85657	−	4.94773i	−0.114630	−	0.198545i
$622$	21.0584	+	1.04906i	0.844365	+	0.0420636i
$623$	−0.0121439	+	0.0121439i	−0.000486534	+	0.000486534i
$624$	−0.350478	+	1.82323i	−0.0140304	+	0.0729877i
$625$	−17.9398	+	17.4116i	−0.717593	+	0.696463i
$626$	−5.31610	+	4.81157i	−0.212474	+	0.192309i
$627$	0.217494	−	0.811700i	0.00868589	−	0.0324162i
$628$	−30.6880	+	25.1144i	−1.22459	+	1.00217i
$629$		−	0.400313i		−	0.0159615i
$630$	3.54816	−	2.79053i	0.141362	−	0.111177i
$631$	11.5208	+	6.65153i	0.458635	+	0.264793i	0.711470	−	0.702716i	$-0.248030\pi$
$631$	11.5208	+	6.65153i	0.458635	+	0.264793i	−0.252835	+	0.967509i	$0.581363\pi$
$632$	5.30486	−	35.2607i	0.211016	−	1.40259i
$633$	2.52668	−	0.677021i	0.100426	−	0.0269092i
$634$	31.2721	+	34.5512i	1.24197	+	1.37220i
$635$	−33.7976	+	29.4171i	−1.34122	+	1.16738i
$636$	−0.270706	−	0.599656i	−0.0107342	−	0.0237779i
$637$	17.4208	+	17.1035i	0.690239	+	0.677667i
$638$	−20.6398	−	13.3279i	−0.817137	−	0.527658i
$639$	2.81409	+	4.87415i	0.111324	+	0.192818i
$640$	−20.4479	+	14.8958i	−0.808273	+	0.588807i
$641$	9.28669	−	16.0850i	0.366802	−	0.635320i	−0.622261	−	0.782810i	$-0.713786\pi$
$641$	9.28669	−	16.0850i	0.366802	−	0.635320i	0.989064	+	0.147489i	$0.0471192\pi$
$642$	−1.39343	−	0.899793i	−0.0549943	−	0.0355120i
$643$	−4.25591	−	15.8833i	−0.167837	−	0.626374i	−0.997661	−	0.0683505i	$-0.978226\pi$
$643$	−4.25591	−	15.8833i	−0.167837	−	0.626374i	0.829825	−	0.558024i	$-0.188440\pi$
$644$	−7.06251	−	0.705414i	−0.278302	−	0.0277972i
$645$	0.849714	−	1.26146i	0.0334575	−	0.0496700i
$646$	−0.274041	+	0.850889i	−0.0107820	+	0.0334778i
$647$	−8.22107	+	30.6815i	−0.323204	+	1.20621i	0.592902	+	0.805275i	$0.297982\pi$
$647$	−8.22107	+	30.6815i	−0.323204	+	1.20621i	−0.916105	+	0.400938i	$0.868684\pi$
$648$	23.3017	−	9.15258i	0.915378	−	0.359547i
$649$		−	46.3571i		−	1.81968i
$650$	14.5309	+	20.9488i	0.569948	+	0.821681i
$651$			0.533950i			0.0209271i
$652$	−3.74521	−	22.8803i	−0.146674	−	0.896063i
$653$	−12.3930	+	46.2514i	−0.484977	+	1.80996i	0.0951898	+	0.995459i	$0.469654\pi$
$653$	−12.3930	+	46.2514i	−0.484977	+	1.80996i	−0.580166	+	0.814498i	$0.697012\pi$
$654$	−2.43993	−	0.785816i	−0.0954087	−	0.0307278i
$655$	−13.2211	+	19.6277i	−0.516591	+	0.766916i
$656$	1.48300	+	4.40863i	0.0579016	+	0.172128i
$657$	−0.768713	−	2.86888i	−0.0299904	−	0.111926i
$658$	−3.04739	+	4.71922i	−0.118799	+	0.183974i
$659$	−9.71504	+	16.8270i	−0.378444	+	0.655485i	−0.990836	−	0.135070i	$-0.956874\pi$
$659$	−9.71504	+	16.8270i	−0.378444	+	0.655485i	0.612392	+	0.790554i	$0.290208\pi$
$660$	1.82465	+	0.838008i	0.0710245	+	0.0326194i
$661$	6.53882	+	11.3256i	0.254331	+	0.440513i	0.964713	−	0.263302i	$-0.0848115\pi$
$661$	6.53882	+	11.3256i	0.254331	+	0.440513i	−0.710383	+	0.703815i	$0.751478\pi$
$662$	3.50417	−	5.42660i	0.136194	−	0.210911i
$663$	−0.151035	+	0.0419611i	−0.00586571	+	0.00162963i
$664$	15.4966	+	20.9852i	0.601386	+	0.814384i
$665$	1.51044	−	1.31467i	0.0585725	−	0.0509809i
$666$	−3.70791	+	3.35601i	−0.143679	+	0.130043i
$667$	−35.6875	+	9.56244i	−1.38183	+	0.370259i
$668$	−0.282304	+	0.746942i	−0.0109227	+	0.0289001i
$669$	2.88735	+	1.66701i	0.111631	+	0.0644503i
$670$	−15.8091	−	20.1013i	−0.610759	−	0.776582i
$671$			39.7432i			1.53427i
$672$	−0.0858240	+	0.337693i	−0.00331073	+	0.0130268i
$673$	8.57330	−	31.9960i	0.330477	−	1.23336i	−0.578214	−	0.815885i	$-0.696250\pi$
$673$	8.57330	−	31.9960i	0.330477	−	1.23336i	0.908691	−	0.417470i	$-0.137083\pi$
$674$	−13.5271	−	14.9456i	−0.521046	−	0.575682i
$675$	−1.50038	+	3.54705i	−0.0577496	+	0.136526i
$676$	23.4966	−	11.1315i	0.903715	−	0.428135i
$677$	−27.8575	+	27.8575i	−1.07065	+	1.07065i	−0.0733431	+	0.997307i	$0.523367\pi$
$677$	−27.8575	+	27.8575i	−1.07065	+	1.07065i	−0.997307	+	0.0733431i	$0.976633\pi$
$678$	−0.0903620	+	1.81388i	−0.00347033	+	0.0696618i
$679$	−1.14522	−	1.98357i	−0.0439493	−	0.0761225i
$680$	−1.89427	−	0.986928i	−0.0726419	−	0.0378469i
$681$	1.66364			0.0637508
$682$	38.0468	−	19.5098i	1.45689	−	0.747070i
$683$	−1.95187	−	7.28447i	−0.0746862	−	0.278733i	0.918476	−	0.395477i	$-0.129421\pi$
$683$	−1.95187	−	7.28447i	−0.0746862	−	0.278733i	−0.993162	+	0.116745i	$0.962754\pi$
$684$	10.1788	−	4.59508i	0.389196	−	0.175697i
$685$	1.20198	−	3.49792i	0.0459251	−	0.133649i
$686$	6.25297	+	6.90864i	0.238739	+	0.263773i
$687$	0.414917	−	1.54849i	0.0158301	−	0.0590786i
$688$	−1.32422	−	21.0934i	−0.0504855	−	0.804179i
$689$	−4.53328	+	8.02122i	−0.172704	+	0.305584i
$690$	2.77560	−	1.18871i	0.105665	−	0.0452533i
$691$	9.33909	−	5.39193i	0.355276	−	0.205119i	−0.311731	−	0.950171i	$-0.600909\pi$
$691$	9.33909	−	5.39193i	0.355276	−	0.205119i	0.667006	+	0.745052i	$0.267575\pi$
$692$	15.1323	−	2.47697i	0.575246	−	0.0941602i
$693$	−4.80888	+	1.28853i	−0.182674	+	0.0489474i
$694$	2.19236	+	10.1847i	0.0832208	+	0.386608i
$695$	−19.9187	+	9.73049i	−0.755559	+	0.369098i
$696$	0.203564	+	1.80227i	0.00771608	+	0.0683147i
$697$	−0.277695	+	0.277695i	−0.0105184	+	0.0105184i
$698$	−12.6154	−	24.6018i	−0.477501	−	0.931192i
$699$	−1.58263	−	2.74119i	−0.0598605	−	0.103681i
$700$	2.49057	+	4.08532i	0.0941347	+	0.154411i
$701$	11.4291			0.431670			0.215835	−	0.976430i	$-0.430753\pi$
$701$	11.4291			0.431670			0.215835	+	0.976430i	$0.430753\pi$
$702$	3.31891	+	2.10019i	0.125264	+	0.0792665i
$703$	−1.56874	+	1.56874i	−0.0591661	+	0.0591661i
$704$	27.1984	−	6.22346i	1.02508	−	0.234555i
$705$	0.165207	−	2.38409i	0.00622206	−	0.0897898i
$706$	14.8436	+	4.78060i	0.558646	+	0.179920i
$707$	1.70479	+	1.70479i	0.0641151	+	0.0641151i
$708$	−2.64836	+	2.16736i	−0.0995314	+	0.0814543i
$709$	−40.0705	−	23.1347i	−1.50488	−	0.868842i	−0.999984	−	0.00566008i	$-0.998198\pi$
$709$	−40.0705	−	23.1347i	−1.50488	−	0.868842i	−0.504894	−	0.863181i	$-0.668468\pi$
$710$	−5.48383	+	2.34856i	−0.205804	+	0.0881400i
$711$	−32.5726	−	18.8058i	−1.22157	−	0.705272i
$712$	−0.0371166	−	0.0944958i	−0.00139100	−	0.00354138i
$713$	16.6415	−	62.1070i	0.623230	−	2.32592i
$714$	−0.0287594	+	0.00619071i	−0.00107629	+	0.000231682i
$715$	−5.63599	−	27.5478i	−0.210774	−	1.03023i
$716$	10.3981	+	23.0334i	0.388595	+	0.860798i
$717$	1.70463	+	0.456754i	0.0636605	+	0.0170578i
$718$	−0.390745	+	7.84364i	−0.0145825	+	0.292722i
$719$	13.1111	−	22.7090i	0.488960	−	0.846904i	−0.510959	−	0.859605i	$-0.670710\pi$
$719$	13.1111	−	22.7090i	0.488960	−	0.846904i	0.999919	+	0.0127012i	$0.00404301\pi$
$720$	6.73909	+	25.8196i	0.251151	+	0.962240i
$721$	−2.44182	+	4.22936i	−0.0909382	+	0.157510i
$722$	−19.5014	+	10.0000i	−0.725768	+	0.372163i
$723$	0.810921	−	0.810921i	0.0301585	−	0.0301585i
$724$	35.5315	+	3.54894i	1.32052	+	0.131895i
$725$	19.6456	+	15.3091i	0.729619	+	0.568566i
$726$	−0.142181	−	0.157090i	−0.00527684	−	0.00583015i
$727$	−2.39430	−	2.39430i	−0.0887997	−	0.0887997i	0.661312	−	0.750111i	$-0.270000\pi$
$727$	−2.39430	−	2.39430i	−0.0887997	−	0.0887997i	−0.750111	+	0.661312i	$0.770000\pi$
$728$	4.52503	−	1.82554i	0.167709	−	0.0676592i
$729$		−	26.1092i		−	0.967008i
$730$	3.11607	−	0.448147i	0.115331	−	0.0165866i
$731$	1.54537	−	0.892220i	0.0571576	−	0.0330000i
$732$	2.27050	−	1.85813i	0.0839203	−	0.0686785i
$733$	18.2323	+	18.2323i	0.673424	+	0.673424i	0.958504	−	0.285080i	$-0.0920200\pi$
$733$	18.2323	+	18.2323i	0.673424	+	0.673424i	−0.285080	+	0.958504i	$0.592020\pi$
$734$	−33.6112	−	10.8250i	−1.24061	−	0.399558i
$735$	−1.84330	−	0.633405i	−0.0679911	−	0.0233635i
$736$	20.5075	−	36.6043i	0.755918	−	1.34925i
$737$	7.29990	+	27.2436i	0.268895	+	1.00353i
$738$	4.90020	+	0.244113i	0.180379	+	0.00898591i
$739$	−16.0575	−	27.8124i	−0.590684	−	1.02309i	−0.994140	−	0.108096i	$-0.965525\pi$
$739$	−16.0575	−	27.8124i	−0.590684	−	1.02309i	0.403457	−	0.914999i	$-0.367809\pi$
$740$	−3.06562	−	4.32458i	−0.112694	−	0.158975i
$741$	0.756309	+	0.427436i	0.0277837	+	0.0157023i
$742$	−0.937990	+	1.45258i	−0.0344347	+	0.0533260i
$743$	−1.29144	−	0.346039i	−0.0473782	−	0.0126949i	0.235052	−	0.971983i	$-0.424474\pi$
$743$	−1.29144	−	0.346039i	−0.0473782	−	0.0126949i	−0.282430	+	0.959288i	$0.591141\pi$
$744$	−2.89341	−	1.26144i	−0.106077	−	0.0462467i
$745$	−12.2214	−	25.0178i	−0.447759	−	0.916580i
$746$	−1.16932	−	5.43213i	−0.0428117	−	0.198884i
$747$	26.5788	−	7.12178i	0.972469	−	0.260572i
$748$	1.49195	+	1.82306i	0.0545512	+	0.0666577i
$749$			4.35925i			0.159283i
$750$	−1.76728	−	1.00984i	−0.0645319	−	0.0368740i
$751$	12.1968	−	7.04182i	0.445067	−	0.256960i	−0.260677	−	0.965426i	$-0.583946\pi$
$751$	12.1968	−	7.04182i	0.445067	−	0.256960i	0.705745	+	0.708466i	$0.250613\pi$
$752$	−18.3735	−	27.6624i	−0.670012	−	1.00874i
$753$	−1.97560	−	1.97560i	−0.0719949	−	0.0719949i
$754$	18.6740	−	17.2166i	0.680068	−	0.626991i
$755$	15.2949	−	22.7064i	0.556639	−	0.826370i
$756$	0.598548	+	0.430161i	0.0217690	+	0.0156448i
$757$	−7.02805	−	1.88316i	−0.255439	−	0.0684446i	0.128827	−	0.991667i	$-0.458879\pi$
$757$	−7.02805	−	1.88316i	−0.255439	−	0.0684446i	−0.384266	+	0.923222i	$0.625545\pi$
$758$	8.56485	−	4.39193i	0.311089	−	0.159522i
$759$	−3.33012			−0.120876
$760$	3.55568	+	11.2908i	0.128978	+	0.409560i
$761$	7.99444	−	13.8468i	0.289798	−	0.501945i	−0.683963	−	0.729516i	$-0.739745\pi$
$761$	7.99444	−	13.8468i	0.289798	−	0.501945i	0.973761	+	0.227571i	$0.0730785\pi$
$762$	−3.06465	−	1.97897i	−0.111021	−	0.0716903i
$763$	1.74361	+	6.50723i	0.0631228	+	0.235577i
$764$	27.3472	+	19.6538i	0.989387	+	0.711048i
$765$	−1.69943	+	1.47917i	−0.0614432	+	0.0534795i
$766$	−9.40540	+	2.02460i	−0.339831	+	0.0731517i
$767$	46.4031	+	11.9777i	1.67552	+	0.432490i
$768$	−1.62716	−	1.26286i	−0.0587152	−	0.0455696i
$769$	20.5940	−	11.8900i	0.742640	−	0.428763i	−0.0803883	−	0.996764i	$-0.525616\pi$
$769$	20.5940	−	11.8900i	0.742640	−	0.428763i	0.823028	+	0.568000i	$0.192283\pi$
$770$	−0.751193	−	5.22322i	−0.0270711	−	0.188232i
$771$	2.41030	+	1.39159i	0.0868050	+	0.0501169i
$772$	−6.71781	+	17.7745i	−0.241779	+	0.639720i
$773$	−31.6973	+	8.49326i	−1.14007	+	0.305481i	−0.778980	−	0.627049i	$-0.784263\pi$
$773$	−31.6973	+	8.49326i	−1.14007	+	0.305481i	−0.361092	+	0.932530i	$0.617596\pi$
$774$	−21.2198	−	6.83415i	−0.762729	−	0.245648i
$775$	−40.1676	+	16.2875i	−1.44286	+	0.585064i
$776$	13.4543	−	1.51965i	0.482980	−	0.0545521i
$777$	−0.0705214	−	0.0188962i	−0.00252994	−	0.000677896i
$778$	26.3336	+	1.31185i	0.944104	+	0.0470323i
$779$	2.17645			0.0779795
$780$	−1.31029	+	1.60994i	−0.0469159	+	0.0576450i
$781$	6.57941			0.235430
$782$	3.53813	+	0.176258i	0.126523	+	0.00630298i
$783$	3.70613	+	0.993054i	0.132446	+	0.0354889i
$784$	−25.6708	+	8.63532i	−0.916814	+	0.308404i
$785$	−43.5153	+	8.48688i	−1.55313	+	0.302910i
$786$	−1.83400	−	0.590667i	−0.0654166	−	0.0210684i
$787$	−23.1933	+	6.21462i	−0.826751	+	0.221527i	−0.647296	−	0.762239i	$-0.724100\pi$
$787$	−23.1933	+	6.21462i	−0.826751	+	0.221527i	−0.179455	+	0.983766i	$0.557434\pi$
$788$	−8.87807	−	3.35543i	−0.316268	−	0.119532i
$789$	1.36199	+	0.786345i	0.0484881	+	0.0279946i
$790$	23.8897	−	31.9155i	0.849959	−	1.13550i
$791$	4.13355	−	2.38651i	0.146972	−	0.0848544i
$792$	4.37843	−	29.1028i	0.155581	−	1.03412i
$793$	−39.7826	−	10.2688i	−1.41272	−	0.364656i
$794$	15.7790	−	3.39658i	0.559977	−	0.120540i
$795$	0.0508510	−	0.733826i	0.00180350	−	0.0260261i
$796$	23.3461	−	32.4849i	0.827479	−	1.15140i
$797$	4.87331	+	18.1874i	0.172621	+	0.644232i	0.996945	+	0.0781122i	$0.0248892\pi$
$797$	4.87331	+	18.1874i	0.172621	+	0.644232i	−0.824323	+	0.566119i	$0.808444\pi$
$798$	0.136962	+	0.0884417i	0.00484840	+	0.00313080i
$799$	1.40190	−	2.42817i	0.0495958	−	0.0859025i
$800$	−28.0218	+	3.84462i	−0.990719	+	0.135928i
$801$	−0.107087			−0.00378375
$802$	−30.3416	+	15.5587i	−1.07140	+	0.549397i
$803$	−3.35375	−	0.898636i	−0.118351	−	0.0317122i
$804$	1.21512	−	1.69077i	0.0428539	−	0.0596290i
$805$	−6.58154	−	4.43330i	−0.231969	−	0.156253i
$806$	9.69868	+	43.1255i	0.341621	+	1.51903i
$807$	−0.246373	−	0.246373i	−0.00867273	−	0.00867273i
$808$	−13.2655	+	5.21051i	−0.466680	+	0.183305i
$809$	42.2537	−	24.3952i	1.48556	−	0.857689i	0.485697	−	0.874127i	$-0.338566\pi$
$809$	42.2537	−	24.3952i	1.48556	−	0.857689i	0.999865	+	0.0164381i	$0.00523266\pi$
$810$	27.7919	+	3.32183i	0.976508	+	0.116717i
$811$			39.8115i			1.39797i	0.715136	+	0.698985i	$0.246365\pi$
$811$			39.8115i			1.39797i	−0.715136	+	0.698985i	$0.753635\pi$
$812$	3.68886	−	3.01888i	0.129453	−	0.105942i
$813$	−1.01201	+	0.271168i	−0.0354928	+	0.00951026i
$814$	1.23031	+	5.71548i	0.0431223	+	0.200327i
$815$	8.42380	−	24.5145i	0.295073	−	0.858705i
$816$	0.0343965	−	0.170469i	0.00120412	−	0.00596761i
$817$	−9.55239	−	2.55955i	−0.334196	−	0.0895475i
$818$	18.2048	−	28.1922i	0.636517	−	0.985718i
$819$	−0.0472997	−	5.14657i	−0.00165278	−	0.179836i
$820$	−0.873339	+	5.12654i	−0.0304983	+	0.179027i
$821$	−18.1132	−	31.3730i	−0.632155	−	1.09492i	−0.987110	−	0.160041i	$-0.948837\pi$
$821$	−18.1132	−	31.3730i	−0.632155	−	1.09492i	0.354956	−	0.934883i	$-0.384496\pi$
$822$	0.300766	+	0.0149832i	0.0104904	+	0.000522599i
$823$	−11.4470	−	42.7207i	−0.399016	−	1.48915i	−0.814830	−	0.579700i	$-0.803170\pi$
$823$	−11.4470	−	42.7207i	−0.399016	−	1.48915i	0.415814	−	0.909450i	$-0.363497\pi$
$824$	−17.1496	−	23.2237i	−0.597436	−	0.809035i
$825$	1.35326	+	1.79115i	0.0471144	+	0.0623598i
$826$	8.56082	+	2.75714i	0.297869	+	0.0959332i
$827$	8.73298	+	8.73298i	0.303675	+	0.303675i	0.842450	−	0.538775i	$-0.181113\pi$
$827$	8.73298	+	8.73298i	0.303675	+	0.303675i	−0.538775	+	0.842450i	$0.681113\pi$
$828$	−28.0292	−	34.2497i	−0.974080	−	1.19026i
$829$	−6.73529	+	3.88862i	−0.233926	+	0.135057i	−0.612382	−	0.790562i	$-0.709789\pi$
$829$	−6.73529	+	3.88862i	−0.233926	+	0.135057i	0.378456	+	0.925619i	$0.376455\pi$
$830$	4.15188	+	28.8690i	0.144114	+	1.00206i
$831$		−	2.03832i		−	0.0707085i
$832$	−0.797862	+	28.8334i	−0.0276609	+	0.999617i
$833$	−1.61698	−	1.61698i	−0.0560249	−	0.0560249i
$834$	−1.21118	−	1.33818i	−0.0419396	−	0.0463373i
$835$	−0.673408	+	0.586127i	−0.0233042	+	0.0202838i
$836$	1.29754	−	12.9908i	0.0448765	−	0.449297i
$837$	−4.72157	+	4.72157i	−0.163201	+	0.163201i
$838$	12.3744	−	6.34541i	0.427467	−	0.219199i
$839$	19.7258	−	34.1661i	0.681011	−	1.17955i	−0.293662	−	0.955909i	$-0.594874\pi$
$839$	19.7258	−	34.1661i	0.681011	−	1.17955i	0.974673	−	0.223636i	$-0.0717926\pi$
$840$	−0.263279	+	0.287119i	−0.00908399	+	0.00990655i
$841$	−2.09365	+	3.62630i	−0.0721947	+	0.125045i
$842$	1.91511	−	38.4430i	0.0659989	−	1.32483i
$843$	0.253972	+	0.0680516i	0.00874727	+	0.00234382i
$844$	37.0399	−	16.7211i	1.27497	−	0.575566i
$845$	29.0314	+	1.47620i	0.998710	+	0.0507828i
$846$	−34.2438	+	7.37129i	−1.17733	+	0.253430i
$847$	−0.144122	+	0.537869i	−0.00495207	+	0.0184814i
$848$	−5.65539	−	8.51454i	−0.194207	−	0.292391i
$849$	2.34325	+	1.35288i	0.0804201	+	0.0464306i
$850$	−1.34298	−	1.97465i	−0.0460639	−	0.0677300i
$851$	7.61385	+	4.39586i	0.260999	+	0.150688i
$852$	−0.307610	−	0.375878i	−0.0105386	−	0.0128774i
$853$	28.6881	+	28.6881i	0.982261	+	0.982261i	0.999845	−	0.0175843i	$-0.00559754\pi$
$853$	28.6881	+	28.6881i	0.982261	+	0.982261i	−0.0175843	+	0.999845i	$0.505598\pi$
$854$	−7.33941	−	2.36377i	−0.251149	−	0.0808865i
$855$	12.4563	+	0.863166i	0.425995	+	0.0295197i
$856$	−23.6222	−	10.2986i	−0.807391	−	0.351999i
$857$	25.4840	−	25.4840i	0.870517	−	0.870517i	−0.122011	−	0.992529i	$-0.538934\pi$
$857$	25.4840	−	25.4840i	0.870517	−	0.870517i	0.992529	+	0.122011i	$0.0389344\pi$
$858$	2.02744	−	1.06329i	0.0692157	−	0.0363000i
$859$	−34.6071			−1.18078			−0.590389	−	0.807119i	$-0.701026\pi$
$859$	−34.6071			−1.18078			−0.590389	+	0.807119i	$0.701026\pi$
$860$	9.86199	−	21.4732i	0.336291	−	0.732230i
$861$	0.0358122	+	0.0620285i	0.00122048	+	0.00211393i
$862$	17.8649	+	34.8390i	0.608481	+	1.18662i
$863$	−2.25618	+	2.25618i	−0.0768014	+	0.0768014i	−0.744464	−	0.667663i	$-0.767295\pi$
$863$	−2.25618	+	2.25618i	−0.0768014	+	0.0768014i	0.667663	+	0.744464i	$0.267295\pi$
$864$	−3.74504	+	2.22721i	−0.127409	+	0.0757712i
$865$	16.2131	+	5.57124i	0.551263	+	0.189428i
$866$	−6.58774	−	30.6038i	−0.223861	−	1.03996i
$867$	−2.09971	+	0.562615i	−0.0713098	+	0.0191074i
$868$	1.34003	+	8.18652i	0.0454834	+	0.277868i
$869$	−38.0778	+	21.9842i	−1.29170	+	0.745763i
$870$	−0.753587	+	1.88258i	−0.0255490	+	0.0638255i
$871$	−29.1568	+	0.267966i	−0.987939	+	0.00907967i
$872$	−39.3811	−	5.92477i	−1.33361	−	0.200638i
$873$	3.69641	−	13.7952i	0.125104	−	0.466896i
$874$	−13.1744	−	14.5559i	−0.445632	−	0.492359i
$875$	0.290029	+	5.34152i	0.00980477	+	0.180576i
$876$	0.105461	+	0.233612i	0.00356320	+	0.00789303i
$877$	−12.1925	−	45.5030i	−0.411711	−	1.53653i	−0.791333	−	0.611385i	$-0.790613\pi$
$877$	−12.1925	−	45.5030i	−0.411711	−	1.53653i	0.379622	−	0.925142i	$-0.376054\pi$
$878$	31.8282	−	16.3210i	1.07415	−	0.550808i
$879$	1.26813			0.0427729
$880$	30.0787	+	8.26910i	1.01395	+	0.278751i
$881$	17.4663	+	30.2525i	0.588455	+	1.01923i	0.994435	+	0.105352i	$0.0335969\pi$
$881$	17.4663	+	30.2525i	0.588455	+	1.01923i	−0.405980	+	0.913882i	$0.633070\pi$
$882$	−1.42143	+	28.5332i	−0.0478621	+	0.960761i
$883$	−24.6607	+	24.6607i	−0.829900	+	0.829900i	−0.987503	−	0.157603i	$-0.949624\pi$
$883$	−24.6607	+	24.6607i	−0.829900	+	0.829900i	0.157603	+	0.987503i	$0.449624\pi$
$884$	−2.21036	+	1.02239i	−0.0743424	+	0.0343867i
$885$	−3.75534	+	0.732413i	−0.126235	+	0.0246198i
$886$	16.7245	+	18.4782i	0.561872	+	0.620788i
$887$	3.56420	−	13.3018i	0.119674	−	0.446631i	−0.879920	−	0.475122i	$-0.842404\pi$
$887$	3.56420	−	13.3018i	0.119674	−	0.446631i	0.999594	+	0.0284918i	$0.00907046\pi$
$888$	0.269001	−	0.337505i	0.00902708	−	0.0113259i
$889$			9.58754i			0.321556i
$890$	0.0134711	−	0.112705i	0.000451552	−	0.00377788i
$891$	−26.7340	−	15.4349i	−0.895623	−	0.517088i
$892$	48.4524	+	18.3124i	1.62231	+	0.613144i
$893$	−15.0092	+	4.02171i	−0.502265	+	0.134581i
$894$	1.68074	−	1.52123i	0.0562125	−	0.0508776i
$895$	−1.95324	+	28.1870i	−0.0652896	+	0.942187i
$896$	−0.468361	+	5.39290i	−0.0156469	+	0.180164i
$897$	0.860433	−	3.33342i	0.0287290	−	0.111300i
$898$	−15.6147	+	24.1811i	−0.521069	+	0.806933i
$899$	21.5908	+	37.3963i	0.720093	+	1.24724i
$900$	−7.03145	+	28.9938i	−0.234382	+	0.966461i
$901$	0.431509	−	0.747395i	0.0143756	−	0.0248993i
$902$	3.11134	−	4.81825i	0.103596	−	0.160430i
$903$	−0.0842318	−	0.314357i	−0.00280306	−	0.0104612i
$904$	3.16678	+	28.0373i	0.105326	+	0.932505i
$905$	33.1117	+	22.3039i	1.10067	+	0.741407i
$906$	2.12168	+	0.683318i	0.0704879	+	0.0227017i
$907$	−0.977113	+	3.64663i	−0.0324445	+	0.121085i	−0.980249	−	0.197768i	$-0.936631\pi$
$907$	−0.977113	+	3.64663i	−0.0324445	+	0.121085i	0.947804	+	0.318852i	$0.103297\pi$
$908$	25.5069	−	4.17515i	0.846476	−	0.138557i
$909$			15.0332i			0.498619i
$910$	5.42250	+	0.597633i	0.179754	+	0.0198113i
$911$			16.1407i			0.534764i	0.963591	+	0.267382i	$0.0861585\pi$
$911$			16.1407i			0.534764i	−0.963591	+	0.267382i	$0.913841\pi$
$912$	−0.802823	+	0.533238i	−0.0265841	+	0.0176573i
$913$	8.32545	−	31.0710i	0.275532	−	1.02830i
$914$	−8.83691	+	27.4383i	−0.292299	+	0.907578i
$915$	3.21955	−	0.627916i	0.106435	−	0.0207583i
$916$	2.47534	−	24.7828i	0.0817876	−	0.818846i
$917$	1.31060	+	4.89123i	0.0432799	+	0.161523i
$918$	−0.309054	−	0.199568i	−0.0102003	−	0.00658673i
$919$	−27.3331	+	47.3423i	−0.901636	+	1.56168i	−0.0762664	+	0.997087i	$0.524300\pi$
$919$	−27.3331	+	47.3423i	−0.901636	+	1.56168i	−0.825370	+	0.564592i	$0.809033\pi$
$920$	39.5722	−	25.1910i	1.30466	−	0.830523i
$921$	0.489852	+	0.848448i	0.0161412	+	0.0279573i
$922$	5.90477	+	3.81294i	0.194463	+	0.125573i
$923$	−1.69998	+	6.58594i	−0.0559556	+	0.216779i
$924$	0.391587	−	0.176776i	0.0128823	−	0.00581551i
$925$	−0.729663	−	5.88155i	−0.0239912	−	0.193384i
$926$	35.6473	+	39.3852i	1.17144	+	1.29428i
$927$	−29.4140	+	7.88146i	−0.966082	+	0.258861i
$928$	7.64410	+	27.1215i	0.250930	+	0.890306i
$929$	−17.8598	−	10.3114i	−0.585963	−	0.338306i	0.177537	−	0.984114i	$-0.443187\pi$
$929$	−17.8598	−	10.3114i	−0.585963	−	0.338306i	−0.763499	+	0.645808i	$0.776520\pi$
$930$	−2.18159	−	2.77389i	−0.0715371	−	0.0909595i
$931$			12.6732i			0.415346i
$932$	−31.1443	−	38.0561i	−1.02016	−	1.24657i
$933$	−0.496746	+	1.85388i	−0.0162627	+	0.0606934i
$934$	−30.4148	+	27.5283i	−0.995204	+	0.900754i
$935$	0.504174	+	2.58508i	0.0164883	+	0.0845412i
$936$	28.0004	+	11.9023i	0.915221	+	0.389040i
$937$	−7.24525	+	7.24525i	−0.236692	+	0.236692i	−0.815479	−	0.578787i	$-0.803526\pi$
$937$	−7.24525	+	7.24525i	−0.236692	+	0.236692i	0.578787	+	0.815479i	$0.303526\pi$
$938$	−5.46528	−	0.272263i	−0.178448	−	0.00888969i
$939$	−0.326345	−	0.565246i	−0.0106499	−	0.0184461i
$940$	−3.45026	−	36.9674i	−0.112535	−	1.20574i
$941$	5.62676			0.183427			0.0917136	−	0.995785i	$-0.470766\pi$
$941$	5.62676			0.183427			0.0917136	+	0.995785i	$0.470766\pi$
$942$	−1.64706	−	3.21200i	−0.0536643	−	0.104653i
$943$	−2.23230	−	8.33107i	−0.0726938	−	0.271297i
$944$	−35.1653	+	39.8764i	−1.14453	+	1.29786i
$945$	0.361722	+	0.740459i	0.0117668	+	0.0240871i
$946$	−19.3220	+	17.4882i	−0.628211	+	0.568590i
$947$	−2.27295	+	8.48275i	−0.0738608	+	0.275652i	−0.992973	−	0.118345i	$-0.962241\pi$
$947$	−2.27295	+	8.48275i	−0.0738608	+	0.275652i	0.919112	+	0.393997i	$0.128908\pi$
$948$	3.03621	+	1.14752i	0.0986116	+	0.0372699i
$949$	1.76607	−	3.12489i	0.0573289	−	0.101438i
$950$	−2.47538	+	13.0011i	−0.0803120	+	0.421811i
$951$	−3.67374	+	2.12103i	−0.119129	+	0.0687793i
$952$	−0.425402	+	0.167092i	−0.0137874	+	0.00541548i
$953$	10.8599	−	2.90991i	0.351787	−	0.0942612i	−0.0785979	−	0.996906i	$-0.525044\pi$
$953$	10.8599	−	2.90991i	0.351787	−	0.0942612i	0.430385	+	0.902645i	$0.358378\pi$
$954$	−10.5403	+	2.26890i	−0.341255	+	0.0734582i
$955$	16.5268	+	33.8310i	0.534795	+	1.09475i
$956$	27.2817	+	2.72493i	0.882352	+	0.0881306i
$957$	1.58142	−	1.58142i	0.0511200	−	0.0511200i
$958$	−0.426994	+	0.218956i	−0.0137956	+	0.00707416i
$959$	−0.395714	−	0.685396i	−0.0127783	−	0.0221326i
$960$	−0.933873	−	2.10499i	−0.0301406	−	0.0679382i
$961$	−44.1489			−1.42416
$962$	−6.03903	−	0.245231i	−0.194706	−	0.00790657i
$963$	−19.2204	+	19.2204i	−0.619369	+	0.619369i
$964$	10.3979	−	14.4682i	0.334894	−	0.465988i
$965$	−16.0247	+	13.9477i	−0.515853	+	0.448993i
$966$	0.198063	−	0.614977i	0.00637256	−	0.0197866i
$967$	−2.79314	−	2.79314i	−0.0898213	−	0.0898213i	0.660768	−	0.750590i	$-0.270231\pi$
$967$	−2.79314	−	2.79314i	−0.0898213	−	0.0898213i	−0.750590	+	0.660768i	$0.770231\pi$
$968$	−2.57416	−	2.05168i	−0.0827367	−	0.0659434i
$969$	−0.0704707	−	0.0406863i	−0.00226385	−	0.00130703i
$970$	14.0538	+	5.62567i	0.451241	+	0.180629i
$971$	−35.8935	−	20.7231i	−1.15188	−	0.665037i	−0.202534	−	0.979275i	$-0.564918\pi$
$971$	−35.8935	−	20.7231i	−1.15188	−	0.665037i	−0.949344	+	0.314238i	$0.898251\pi$
$972$	1.11468	+	6.80982i	0.0357533	+	0.218425i
$973$	−1.22771	+	4.58186i	−0.0393585	+	0.146888i
$974$	0.412008	+	1.91401i	0.0132016	+	0.0613289i
$975$	−2.14258	+	0.891804i	−0.0686174	+	0.0285606i
$976$	30.1481	−	34.1870i	0.965018	−	1.09430i
$977$	13.0724	+	3.50273i	0.418223	+	0.112062i	0.461793	−	0.886988i	$-0.347206\pi$
$977$	13.0724	+	3.50273i	0.418223	+	0.112062i	−0.0435699	+	0.999050i	$0.513873\pi$
$978$	2.10785	+	0.105007i	0.0674017	+	0.00335774i
$979$	−0.0625933	+	0.108415i	−0.00200049	+	0.00346495i
$980$	−29.8511	−	5.08533i	−0.953558	−	0.162445i
$981$	−21.0033	+	36.3789i	−0.670585	+	1.16149i
$982$	11.1901	+	21.8223i	0.357091	+	0.696376i
$983$	22.7007	−	22.7007i	0.724041	−	0.724041i	−0.245385	−	0.969426i	$-0.578914\pi$
$983$	22.7007	−	22.7007i	0.724041	−	0.724041i	0.969426	+	0.245385i	$0.0789144\pi$
$984$	−0.420730	+	0.0475211i	−0.0134124	+	0.00151492i
$985$	−6.96664	−	8.00404i	−0.221975	−	0.255030i
$986$	−1.76390	+	1.59649i	−0.0561740	+	0.0508427i
$987$	−0.361586	−	0.361586i	−0.0115094	−	0.0115094i
$988$	12.6684	+	4.65538i	0.403037	+	0.148107i
$989$			39.1901i			1.24617i
$990$	19.7177	−	26.3419i	0.626669	−	0.837200i
$991$	28.1145	−	16.2319i	0.893086	−	0.515624i	0.0181357	−	0.999836i	$-0.494227\pi$
$991$	28.1145	−	16.2319i	0.893086	−	0.515624i	0.874951	+	0.484212i	$0.160894\pi$
$992$	−47.5275	−	12.0790i	−1.50900	−	0.383508i
$993$	0.415786	+	0.415786i	0.0131946	+	0.0131946i
$994$	−0.391318	+	1.21503i	−0.0124119	+	0.0385383i
$995$	40.1868	−	19.6317i	1.27401	−	0.622365i
$996$	−2.16431	+	0.977049i	−0.0685789	+	0.0309590i
$997$	−5.19332	−	19.3817i	−0.164474	−	0.613826i	−0.998107	−	0.0615065i	$-0.980410\pi$
$997$	−5.19332	−	19.3817i	−0.164474	−	0.613826i	0.833632	−	0.552320i	$-0.186257\pi$
$998$	0.188998	−	3.79387i	0.00598264	−	0.120093i
$999$	−0.456508	−	0.790695i	−0.0144433	−	0.0250165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bj.c.3.20	✓	144
4.3	odd	2	inner	260.2.bj.c.3.25	yes	144
5.2	odd	4	inner	260.2.bj.c.107.1	yes	144
13.9	even	3	inner	260.2.bj.c.243.30	yes	144
20.7	even	4	inner	260.2.bj.c.107.30	yes	144
52.35	odd	6	inner	260.2.bj.c.243.1	yes	144
65.22	odd	12	inner	260.2.bj.c.87.25	yes	144
260.87	even	12	inner	260.2.bj.c.87.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bj.c.3.20	✓	144	1.1	even	1	trivial
260.2.bj.c.3.25	yes	144	4.3	odd	2	inner
260.2.bj.c.87.20	yes	144	260.87	even	12	inner
260.2.bj.c.87.25	yes	144	65.22	odd	12	inner
260.2.bj.c.107.1	yes	144	5.2	odd	4	inner
260.2.bj.c.107.30	yes	144	20.7	even	4	inner
260.2.bj.c.243.1	yes	144	52.35	odd	6	inner
260.2.bj.c.243.30	yes	144	13.9	even	3	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0703644 + 1.41246i) q^{2} +(-0.124346 - 0.0333185i) q^{3} +(-1.99010 - 0.198774i) q^{4} +(-1.85457 - 1.24923i) q^{5} +(0.0558107 - 0.173290i) q^{6} +(-0.462161 + 0.123836i) q^{7} +(0.420793 - 2.79695i) q^{8} +(-2.58372 - 1.49171i) q^{9} +O(q^{10})\)	\(q+(-0.0703644 + 1.41246i) q^{2} +(-0.124346 - 0.0333185i) q^{3} +(-1.99010 - 0.198774i) q^{4} +(-1.85457 - 1.24923i) q^{5} +(0.0558107 - 0.173290i) q^{6} +(-0.462161 + 0.123836i) q^{7} +(0.420793 - 2.79695i) q^{8} +(-2.58372 - 1.49171i) q^{9} +(1.89498 - 2.53161i) q^{10} +(-3.02041 + 1.74383i) q^{11} +(0.240839 + 0.0910240i) q^{12} +(-0.965152 - 3.47397i) q^{13} +(-0.142393 - 0.661498i) q^{14} +(0.188987 + 0.217129i) q^{15} +(3.92098 + 0.791159i) q^{16} +(0.0874092 + 0.326216i) q^{17} +(2.28879 - 3.54445i) q^{18} +(0.935831 - 1.62091i) q^{19} +(3.44246 + 2.85473i) q^{20} +0.0615941 q^{21} +(-2.25057 - 4.38891i) q^{22} +(-7.16439 - 1.91969i) q^{23} +(-0.145514 + 0.333771i) q^{24} +(1.87885 + 4.63356i) q^{25} +(4.97477 - 1.11880i) q^{26} +(0.544659 + 0.544659i) q^{27} +(0.944360 - 0.154579i) q^{28} +(4.31388 - 2.49062i) q^{29} +(-0.319984 + 0.251658i) q^{30} +8.66885i q^{31} +(-1.39338 + 5.48256i) q^{32} +(0.433679 - 0.116204i) q^{33} +(-0.466918 + 0.100508i) q^{34} +(1.01181 + 0.347683i) q^{35} +(4.84535 + 3.48223i) q^{36} +(-1.14494 - 0.306785i) q^{37} +(2.22362 + 1.43588i) q^{38} +(0.00426563 + 0.464134i) q^{39} +(-4.27442 + 4.66147i) q^{40} +(0.581422 + 1.00705i) q^{41} +(-0.00433403 + 0.0869993i) q^{42} +(-1.36753 - 5.10370i) q^{43} +(6.35753 - 2.87002i) q^{44} +(2.92820 + 5.99415i) q^{45} +(3.21561 - 9.98435i) q^{46} +(-5.87046 - 5.87046i) q^{47} +(-0.461199 - 0.229019i) q^{48} +(-5.86392 + 3.38554i) q^{49} +(-6.67694 + 2.32777i) q^{50} -0.0434761i q^{51} +(1.23021 + 7.10539i) q^{52} +(-1.80694 - 1.80694i) q^{53} +(-0.807635 + 0.730986i) q^{54} +(7.78000 + 0.539121i) q^{55} +(0.151888 + 1.34475i) q^{56} +(-0.170373 + 0.170373i) q^{57} +(3.21436 + 6.26844i) q^{58} +(-6.64587 + 11.5110i) q^{59} +(-0.332942 - 0.469673i) q^{60} +(5.69767 - 9.86866i) q^{61} +(-12.2444 - 0.609978i) q^{62} +(1.37882 + 0.369455i) q^{63} +(-7.64587 - 2.35387i) q^{64} +(-2.54984 + 7.64842i) q^{65} +(0.133618 + 0.620732i) q^{66} +(2.09306 - 7.81142i) q^{67} +(-0.109110 - 0.666576i) q^{68} +(0.826905 + 0.477414i) q^{69} +(-0.562284 + 1.40468i) q^{70} +(-1.63374 - 0.943240i) q^{71} +(-5.25946 + 6.59885i) q^{72} +(0.703943 + 0.703943i) q^{73} +(0.513886 - 1.59560i) q^{74} +(-0.0792453 - 0.638768i) q^{75} +(-2.18459 + 3.03974i) q^{76} +(1.17997 - 1.17997i) q^{77} +(-0.655871 - 0.0266334i) q^{78} +12.6068 q^{79} +(-6.28339 - 6.36546i) q^{80} +(4.42556 + 7.66530i) q^{81} +(-1.46334 + 0.750376i) q^{82} +(-6.52171 + 6.52171i) q^{83} +(-0.122578 - 0.0122433i) q^{84} +(0.245412 - 0.714184i) q^{85} +(7.30500 - 1.57247i) q^{86} +(-0.619399 + 0.165967i) q^{87} +(3.60645 + 9.18172i) q^{88} +(0.0310852 - 0.0179471i) q^{89} +(-8.67255 + 3.71420i) q^{90} +(0.876257 + 1.48601i) q^{91} +(13.8762 + 5.24447i) q^{92} +(0.288833 - 1.07794i) q^{93} +(8.70488 - 7.87873i) q^{94} +(-3.76045 + 1.83702i) q^{95} +(0.355933 - 0.635312i) q^{96} +(1.23898 + 4.62394i) q^{97} +(-4.36933 - 8.52079i) q^{98} +10.4052 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 24 q^{5} - 4 q^{6} - 24 q^{8}+O(q^{10}) \) 144 * q - 6 * q^2 - 24 * q^5 - 4 * q^6 - 24 * q^8	\( 144 q - 6 q^{2} - 24 q^{5} - 4 q^{6} - 24 q^{8} - 16 q^{10} + 20 q^{12} - 12 q^{13} - 28 q^{16} - 4 q^{18} + 30 q^{20} - 32 q^{21} - 28 q^{22} - 24 q^{25} - 12 q^{26} + 14 q^{28} - 4 q^{30} + 4 q^{32} - 28 q^{33} + 4 q^{36} + 20 q^{40} + 24 q^{41} - 56 q^{42} - 4 q^{46} + 12 q^{48} + 20 q^{50} - 2 q^{52} + 24 q^{53} - 20 q^{56} - 24 q^{57} - 42 q^{58} + 88 q^{60} - 32 q^{61} - 128 q^{66} - 32 q^{68} + 108 q^{70} + 2 q^{72} - 8 q^{73} + 60 q^{76} - 72 q^{77} - 120 q^{78} - 64 q^{80} - 32 q^{81} - 42 q^{82} - 48 q^{85} - 24 q^{86} - 42 q^{88} - 56 q^{90} - 84 q^{92} + 8 q^{93} + 160 q^{96} + 68 q^{97} + 98 q^{98}+O(q^{100}) \) 144 * q - 6 * q^2 - 24 * q^5 - 4 * q^6 - 24 * q^8 - 16 * q^10 + 20 * q^12 - 12 * q^13 - 28 * q^16 - 4 * q^18 + 30 * q^20 - 32 * q^21 - 28 * q^22 - 24 * q^25 - 12 * q^26 + 14 * q^28 - 4 * q^30 + 4 * q^32 - 28 * q^33 + 4 * q^36 + 20 * q^40 + 24 * q^41 - 56 * q^42 - 4 * q^46 + 12 * q^48 + 20 * q^50 - 2 * q^52 + 24 * q^53 - 20 * q^56 - 24 * q^57 - 42 * q^58 + 88 * q^60 - 32 * q^61 - 128 * q^66 - 32 * q^68 + 108 * q^70 + 2 * q^72 - 8 * q^73 + 60 * q^76 - 72 * q^77 - 120 * q^78 - 64 * q^80 - 32 * q^81 - 42 * q^82 - 48 * q^85 - 24 * q^86 - 42 * q^88 - 56 * q^90 - 84 * q^92 + 8 * q^93 + 160 * q^96 + 68 * q^97 + 98 * q^98

Introduction

L-functions

Modular forms

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