LMFDB - Embedded newform 115.2.l.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	115.17
Dual form			115.2.l.a.88.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07057 + 0.399303i) q^{2} +(-0.256216 + 0.139905i) q^{3} +(-0.524814 + 0.454754i) q^{4} +(-1.94143 + 1.10943i) q^{5} +(0.218434 - 0.252086i) q^{6} +(-1.96263 - 2.62176i) q^{7} +(1.47546 - 2.70211i) q^{8} +(-1.57585 + 2.45207i) q^{9} +O(q^{10})$	\(q+(-1.07057 + 0.399303i) q^{2} +(-0.256216 + 0.139905i) q^{3} +(-0.524814 + 0.454754i) q^{4} +(-1.94143 + 1.10943i) q^{5} +(0.218434 - 0.252086i) q^{6} +(-1.96263 - 2.62176i) q^{7} +(1.47546 - 2.70211i) q^{8} +(-1.57585 + 2.45207i) q^{9} +(1.63545 - 1.96295i) q^{10} +(-4.61502 + 2.10761i) q^{11} +(0.0708436 - 0.189939i) q^{12} +(1.66196 + 1.24413i) q^{13} +(3.14801 + 2.02311i) q^{14} +(0.342212 - 0.555869i) q^{15} +(-0.302976 + 2.10724i) q^{16} +(0.000724021 + 0.0101231i) q^{17} +(0.707943 - 3.25436i) q^{18} +(0.119065 + 0.137408i) q^{19} +(0.514374 - 1.46512i) q^{20} +(0.869653 + 0.397157i) q^{21} +(4.09915 - 4.09915i) q^{22} +(-1.87965 + 4.41213i) q^{23} +0.898747i q^{24} +(2.53833 - 4.30777i) q^{25} +(-2.27604 - 0.668305i) q^{26} +(0.123179 - 1.72227i) q^{27} +(2.22227 + 0.483425i) q^{28} +(5.07075 + 4.39383i) q^{29} +(-0.144403 + 0.731745i) q^{30} +(6.87834 - 2.01966i) q^{31} +(0.791777 + 3.63974i) q^{32} +(0.887578 - 1.18567i) q^{33} +(-0.00481732 - 0.0105485i) q^{34} +(6.71897 + 2.91258i) q^{35} +(-0.288060 - 2.00350i) q^{36} +(-7.95454 + 1.73040i) q^{37} +(-0.182336 - 0.0995627i) q^{38} +(-0.599880 - 0.0862498i) q^{39} +(0.133288 + 6.88289i) q^{40} +(-6.41335 + 4.12161i) q^{41} +(-1.08961 - 0.0779307i) q^{42} +(-2.53456 - 4.64170i) q^{43} +(1.46358 - 3.20480i) q^{44} +(0.339006 - 6.50882i) q^{45} +(0.250526 - 5.47406i) q^{46} +(-4.98615 - 4.98615i) q^{47} +(-0.217186 - 0.582297i) q^{48} +(-1.04961 + 3.57463i) q^{49} +(-0.997360 + 5.62535i) q^{50} +(-0.00160178 - 0.00249242i) q^{51} +(-1.43799 + 0.102847i) q^{52} +(-3.19353 + 2.39065i) q^{53} +(0.555836 + 1.89300i) q^{54} +(6.62151 - 9.21183i) q^{55} +(-9.98007 + 1.43492i) q^{56} +(-0.0497304 - 0.0185485i) q^{57} +(-7.18308 - 2.67915i) q^{58} +(-9.60547 + 1.38106i) q^{59} +(0.0731861 + 0.447350i) q^{60} +(2.58654 + 8.80896i) q^{61} +(-6.55731 + 4.90874i) q^{62} +(9.52154 - 0.680994i) q^{63} +(-4.60297 - 7.16236i) q^{64} +(-4.60686 - 0.571563i) q^{65} +(-0.476778 + 1.62376i) q^{66} +(3.10249 + 8.31810i) q^{67} +(-0.00498351 - 0.00498351i) q^{68} +(-0.135681 - 1.39343i) q^{69} +(-8.35616 - 0.435223i) q^{70} +(4.48898 - 9.82949i) q^{71} +(4.30065 + 7.87605i) q^{72} +(-3.76794 - 0.269488i) q^{73} +(7.82497 - 5.02880i) q^{74} +(-0.0476836 + 1.45884i) q^{75} +(-0.124974 - 0.0179686i) q^{76} +(14.5832 + 7.96304i) q^{77} +(0.676656 - 0.147198i) q^{78} +(-0.0456137 - 0.317250i) q^{79} +(-1.74963 - 4.42720i) q^{80} +(-3.42314 - 7.49563i) q^{81} +(5.22019 - 6.97336i) q^{82} +(-0.751981 - 3.45680i) q^{83} +(-0.637015 + 0.187044i) q^{84} +(-0.0126366 - 0.0188501i) q^{85} +(4.56688 + 3.95722i) q^{86} +(-1.91392 - 0.416348i) q^{87} +(-1.11430 + 15.5800i) q^{88} +(-1.61512 - 0.474243i) q^{89} +(2.23606 + 7.10354i) q^{90} -6.79903i q^{91} +(-1.01997 - 3.17033i) q^{92} +(-1.47978 + 1.47978i) q^{93} +(7.32904 + 3.34706i) q^{94} +(-0.383602 - 0.134675i) q^{95} +(-0.712082 - 0.821787i) q^{96} +(-1.05513 + 4.85033i) q^{97} +(-0.303681 - 4.24601i) q^{98} +(2.10457 - 14.6376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

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 $

$2$	−1.07057	+	0.399303i	−0.757010	+	0.282350i	−0.698184	−	0.715918i	$-0.746008\pi$
$2$	−1.07057	+	0.399303i	−0.757010	+	0.282350i	−0.0588257	+	0.998268i	$0.518736\pi$
$3$	−0.256216	+	0.139905i	−0.147926	+	0.0807739i	−0.551507	−	0.834170i	$-0.685947\pi$
$3$	−0.256216	+	0.139905i	−0.147926	+	0.0807739i	0.403581	+	0.914944i	$0.367765\pi$
$4$	−0.524814	+	0.454754i	−0.262407	+	0.227377i
$5$	−1.94143	+	1.10943i	−0.868235	+	0.496152i
$5$	−1.94143	+	1.10943i	−0.868235	+	0.496152i
$6$	0.218434	−	0.252086i	0.0891752	−	0.102914i
$7$	−1.96263	−	2.62176i	−0.741803	−	0.990933i	−0.999693	−	0.0247587i	$-0.992118\pi$
$7$	−1.96263	−	2.62176i	−0.741803	−	0.990933i	0.257890	−	0.966174i	$-0.416973\pi$
$8$	1.47546	−	2.70211i	0.521655	−	0.955339i
$9$	−1.57585	+	2.45207i	−0.525283	+	0.817356i
$10$	1.63545	−	1.96295i	0.517174	−	0.620739i
$11$	−4.61502	+	2.10761i	−1.39148	+	0.635468i	−0.963350	−	0.268248i	$-0.913555\pi$
$11$	−4.61502	+	2.10761i	−1.39148	+	0.635468i	−0.428132	+	0.903716i	$0.640828\pi$
$12$	0.0708436	−	0.189939i	0.0204508	−	0.0548307i
$13$	1.66196	+	1.24413i	0.460945	+	0.345059i	0.804378	−	0.594118i	$-0.202499\pi$
$13$	1.66196	+	1.24413i	0.460945	+	0.345059i	−0.343433	+	0.939177i	$0.611590\pi$
$14$	3.14801	+	2.02311i	0.841342	+	0.540698i
$15$	0.342212	−	0.555869i	0.0883588	−	0.143525i
$16$	−0.302976	+	2.10724i	−0.0757439	+	0.526811i
$17$	0.000724021		0.0101231i	0.000175601		0.00245522i	0.997539	−	0.0701115i	$-0.0223355\pi$
$17$	0.000724021		0.0101231i	0.000175601		0.00245522i	−0.997364	+	0.0725667i	$0.976881\pi$
$18$	0.707943	−	3.25436i	0.166864	−	0.767061i
$19$	0.119065	+	0.137408i	0.0273154	+	0.0315236i	0.769243	−	0.638956i	$-0.220634\pi$
$19$	0.119065	+	0.137408i	0.0273154	+	0.0315236i	−0.741927	+	0.670480i	$0.766088\pi$
$20$	0.514374	−	1.46512i	0.115017	−	0.327611i
$21$	0.869653	+	0.397157i	0.189774	+	0.0866668i
$22$	4.09915	−	4.09915i	0.873941	−	0.873941i
$23$	−1.87965	+	4.41213i	−0.391934	+	0.919993i
$23$	−1.87965	+	4.41213i	−0.391934	+	0.919993i
$24$			0.898747i			0.183456i
$25$	2.53833	−	4.30777i	0.507666	−	0.861554i
$26$	−2.27604	−	0.668305i	−0.446368	−	0.131065i
$27$	0.123179	−	1.72227i	0.0237058	−	0.331451i
$28$	2.22227	+	0.483425i	0.419970	+	0.0913588i
$29$	5.07075	+	4.39383i	0.941614	+	0.815913i	0.983071	−	0.183227i	$-0.0586543\pi$
$29$	5.07075	+	4.39383i	0.941614	+	0.815913i	−0.0414565	+	0.999140i	$0.513200\pi$
$30$	−0.144403	+	0.731745i	−0.0263642	+	0.133598i
$31$	6.87834	−	2.01966i	1.23539	−	0.362742i	0.402106	−	0.915593i	$-0.368278\pi$
$31$	6.87834	−	2.01966i	1.23539	−	0.362742i	0.833280	+	0.552851i	$0.186460\pi$
$32$	0.791777	+	3.63974i	0.139968	+	0.643421i
$33$	0.887578	−	1.18567i	0.154508	−	0.206398i
$34$	−0.00481732	−	0.0105485i	−0.000826163	−	0.00180905i
$35$	6.71897	+	2.91258i	1.13571	+	0.492316i
$36$	−0.288060	−	2.00350i	−0.0480101	−	0.333917i
$37$	−7.95454	+	1.73040i	−1.30772	+	0.284477i	−0.811822	−	0.583905i	$-0.801524\pi$
$37$	−7.95454	+	1.73040i	−1.30772	+	0.284477i	−0.495896	+	0.868382i	$0.665160\pi$
$38$	−0.182336	−	0.0995627i	−0.0295787	−	0.0161512i
$39$	−0.599880	−	0.0862498i	−0.0960578	−	0.0138110i
$40$	0.133288	+	6.88289i	0.0210748	+	1.08828i
$41$	−6.41335	+	4.12161i	−1.00160	+	0.643687i	−0.935205	−	0.354106i	$-0.884785\pi$
$41$	−6.41335	+	4.12161i	−1.00160	+	0.643687i	−0.0663919	+	0.997794i	$0.521149\pi$
$42$	−1.08961	−	0.0779307i	−0.168131	−	0.0120250i
$43$	−2.53456	−	4.64170i	−0.386517	−	0.707853i	0.609896	−	0.792482i	$-0.291211\pi$
$43$	−2.53456	−	4.64170i	−0.386517	−	0.707853i	−0.996413	+	0.0846290i	$0.973029\pi$
$44$	1.46358	−	3.20480i	0.220644	−	0.483142i
$45$	0.339006	−	6.50882i	0.0505360	−	0.970278i
$46$	0.250526	−	5.47406i	0.0369380	−	0.807107i
$47$	−4.98615	−	4.98615i	−0.727305	−	0.727305i	0.242777	−	0.970082i	$-0.421942\pi$
$47$	−4.98615	−	4.98615i	−0.727305	−	0.727305i	−0.970082	+	0.242777i	$0.921942\pi$
$48$	−0.217186	−	0.582297i	−0.0313480	−	0.0840473i
$49$	−1.04961	+	3.57463i	−0.149944	+	0.510661i
$50$	−0.997360	+	5.62535i	−0.141048	+	0.795545i
$51$	−0.00160178	−	0.00249242i	−0.000224294	−	0.000349008i
$52$	−1.43799	+	0.102847i	−0.199414	+	0.0142624i
$53$	−3.19353	+	2.39065i	−0.438665	+	0.328381i	−0.795679	−	0.605718i	$-0.792886\pi$
$53$	−3.19353	+	2.39065i	−0.438665	+	0.328381i	0.357014	+	0.934099i	$0.383795\pi$
$54$	0.555836	+	1.89300i	0.0756397	+	0.257605i
$55$	6.62151	−	9.21183i	0.892844	−	1.24212i
$56$	−9.98007	+	1.43492i	−1.33364	+	0.191749i
$57$	−0.0497304	−	0.0185485i	−0.00658696	−	0.00245681i
$58$	−7.18308	−	2.67915i	−0.943184	−	0.351790i
$59$	−9.60547	+	1.38106i	−1.25053	+	0.179799i	−0.735588	−	0.677429i	$-0.763094\pi$
$59$	−9.60547	+	1.38106i	−1.25053	+	0.179799i	−0.514938	+	0.857227i	$0.672185\pi$
$60$	0.0731861	+	0.447350i	0.00944828	+	0.0577527i
$61$	2.58654	+	8.80896i	0.331173	+	1.12787i	0.941862	+	0.336001i	$0.109074\pi$
$61$	2.58654	+	8.80896i	0.331173	+	1.12787i	−0.610689	+	0.791871i	$0.709107\pi$
$62$	−6.55731	+	4.90874i	−0.832779	+	0.623411i
$63$	9.52154	−	0.680994i	1.19960	−	0.0857972i
$64$	−4.60297	−	7.16236i	−0.575371	−	0.895295i
$65$	−4.60686	−	0.571563i	−0.571411	−	0.0708936i
$66$	−0.476778	+	1.62376i	−0.0586873	+	0.199871i
$67$	3.10249	+	8.31810i	0.379030	+	1.01622i	0.976725	+	0.214495i	$0.0688105\pi$
$67$	3.10249	+	8.31810i	0.379030	+	1.01622i	−0.597695	+	0.801723i	$0.703917\pi$
$68$	−0.00498351	−	0.00498351i	−0.000604340	−	0.000604340i
$69$	−0.135681	−	1.39343i	−0.0163340	−	0.167749i
$70$	−8.35616	−	0.435223i	−0.998752	−	0.0520191i
$71$	4.48898	−	9.82949i	0.532743	−	1.16655i	−0.431642	−	0.902045i	$-0.642066\pi$
$71$	4.48898	−	9.82949i	0.532743	−	1.16655i	0.964386	−	0.264500i	$-0.0852070\pi$
$72$	4.30065	+	7.87605i	0.506836	+	0.928201i
$73$	−3.76794	−	0.269488i	−0.441004	−	0.0315412i	−0.150928	−	0.988545i	$-0.548226\pi$
$73$	−3.76794	−	0.269488i	−0.441004	−	0.0315412i	−0.290076	+	0.957004i	$0.593681\pi$
$74$	7.82497	−	5.02880i	0.909634	−	0.584586i
$75$	−0.0476836	+	1.45884i	−0.00550603	+	0.168453i
$76$	−0.124974	−	0.0179686i	−0.0143355	−	0.00206113i
$77$	14.5832	+	7.96304i	1.66191	+	0.907472i
$78$	0.676656	−	0.147198i	0.0766162	−	0.0166668i
$79$	−0.0456137	−	0.317250i	−0.00513194	−	0.0356934i	0.987095	−	0.160138i	$-0.0511941\pi$
$79$	−0.0456137	−	0.317250i	−0.00513194	−	0.0356934i	−0.992227	+	0.124445i	$0.960285\pi$
$80$	−1.74963	−	4.42720i	−0.195615	−	0.494976i
$81$	−3.42314	−	7.49563i	−0.380349	−	0.832847i
$82$	5.22019	−	6.97336i	0.576474	−	0.770079i
$83$	−0.751981	−	3.45680i	−0.0825406	−	0.379433i	0.917283	−	0.398237i	$-0.130378\pi$
$83$	−0.751981	−	3.45680i	−0.0825406	−	0.379433i	−0.999823	+	0.0188039i	$0.994014\pi$
$84$	−0.637015	+	0.187044i	−0.0695040	+	0.0204082i
$85$	−0.0126366	−	0.0188501i	−0.00137063	−	0.00204458i
$86$	4.56688	+	3.95722i	0.492459	+	0.426718i
$87$	−1.91392	−	0.416348i	−0.205194	−	0.0446372i
$88$	−1.11430	+	15.5800i	−0.118785	+	1.66083i
$89$	−1.61512	−	0.474243i	−0.171203	−	0.0502697i	0.195008	−	0.980802i	$-0.437527\pi$
$89$	−1.61512	−	0.474243i	−0.171203	−	0.0502697i	−0.366211	+	0.930532i	$0.619345\pi$
$90$	2.23606	+	7.10354i	0.235702	+	0.748779i
$91$		−	6.79903i		−	0.712732i
$92$	−1.01997	−	3.17033i	−0.106339	−	0.330530i
$93$	−1.47978	+	1.47978i	−0.153446	+	0.153446i
$94$	7.32904	+	3.34706i	0.755932	+	0.345223i
$95$	−0.383602	−	0.134675i	−0.0393567	−	0.0138173i
$96$	−0.712082	−	0.821787i	−0.0726766	−	0.0838733i
$97$	−1.05513	+	4.85033i	−0.107132	+	0.492477i	0.892046	+	0.451944i	$0.149269\pi$
$97$	−1.05513	+	4.85033i	−0.107132	+	0.492477i	−0.999178	+	0.0405331i	$0.987094\pi$
$98$	−0.303681	−	4.24601i	−0.0306764	−	0.428912i
$99$	2.10457	−	14.6376i	0.211518	−	1.47114i
$100$	0.626826	+	3.41509i	0.0626826	+	0.341509i
$101$	15.5616	+	10.0009i	1.54844	+	0.995122i	0.985704	+	0.168485i	$0.0538876\pi$
$101$	15.5616	+	10.0009i	1.54844	+	0.995122i	0.562736	+	0.826637i	$0.309749\pi$
$102$	0.00271005	+	0.00202872i	0.000268335	+	0.000200873i
$103$	−3.86539	+	10.3635i	−0.380868	+	1.02115i	0.595180	+	0.803593i	$0.297081\pi$
$103$	−3.86539	+	10.3635i	−0.380868	+	1.02115i	−0.976048	+	0.217555i	$0.930192\pi$
$104$	5.81393	−	2.65513i	0.570103	−	0.260357i
$105$	−2.12899	+	0.193765i	−0.207768	+	0.0189095i
$106$	2.46432	−	3.83455i	0.239356	−	0.372445i
$107$	7.92335	−	14.5105i	0.765979	−	1.40279i	−0.144617	−	0.989488i	$-0.546195\pi$
$107$	7.92335	−	14.5105i	0.765979	−	1.40279i	0.910596	−	0.413298i	$-0.135623\pi$
$108$	0.718563	+	0.959888i	0.0691438	+	0.0923653i
$109$	−4.82733	+	5.57104i	−0.462374	+	0.533609i	−0.938275	−	0.345891i	$-0.887577\pi$
$109$	−4.82733	+	5.57104i	−0.462374	+	0.533609i	0.475900	+	0.879499i	$0.342122\pi$
$110$	−3.41050	+	12.5059i	−0.325179	+	1.19239i
$111$	1.79599	−	1.55623i	0.170468	−	0.147711i
$112$	6.11932	−	3.34140i	0.578221	−	0.315733i
$113$	0.388569	−	0.144929i	0.0365535	−	0.0136338i	−0.331121	−	0.943588i	$-0.607427\pi$
$113$	0.388569	−	0.144929i	0.0365535	−	0.0136338i	0.367674	+	0.929955i	$0.380154\pi$
$114$	0.0606466			0.00568007
$115$	−1.24574	−	10.6512i	−0.116166	−	0.993230i
$116$	−4.65931			−0.432606
$117$	−5.66969	+	2.11469i	−0.524163	+	0.195503i
$118$	9.73191	−	5.31402i	0.895895	−	0.489196i
$119$	0.0251195	−	0.0217661i	0.00230270	−	0.00199530i
$120$	−0.997098	−	1.74486i	−0.0910221	−	0.159283i
$121$	9.65294	−	11.1401i	0.877540	−	1.01273i
$122$	−6.28653	−	8.39782i	−0.569156	−	0.760303i
$123$	1.06657	−	1.95328i	0.0961695	−	0.176121i
$124$	−2.69140	+	4.18790i	−0.241695	+	0.376085i
$125$	−0.148823	+	11.1793i	−0.0133111	+	0.999911i
$126$	−9.92159	+	4.53104i	−0.883886	+	0.403657i
$127$	−0.596781	+	1.60003i	−0.0529558	+	0.141980i	−0.960734	−	0.277470i	$-0.910504\pi$
$127$	−0.596781	+	1.60003i	−0.0529558	+	0.141980i	0.907779	+	0.419450i	$0.137777\pi$
$128$	1.82396	+	1.36540i	0.161216	+	0.120685i
$129$	1.29879	+	0.834682i	0.114352	+	0.0734896i
$130$	5.16021	−	1.22764i	0.452581	−	0.107671i
$131$	−1.81181	+	12.6014i	−0.158298	+	1.10099i	0.743471	+	0.668769i	$0.233178\pi$
$131$	−1.81181	+	12.6014i	−0.158298	+	1.10099i	−0.901769	+	0.432219i	$0.857731\pi$
$132$	0.0733727	+	1.02588i	0.00638627	+	0.0892917i
$133$	0.126572	−	0.581842i	0.0109752	−	0.0504521i
$134$	−6.64289	−	7.66631i	−0.573859	−	0.662268i
$135$	1.67159	+	3.48033i	0.143868	+	0.299539i
$136$	0.0284221	+	0.0129799i	0.00243717	+	0.00111302i
$137$	9.31134	−	9.31134i	0.795521	−	0.795521i	−0.186865	−	0.982386i	$-0.559833\pi$
$137$	9.31134	−	9.31134i	0.795521	−	0.795521i	0.982386	+	0.186865i	$0.0598326\pi$
$138$	0.701658	+	1.43759i	0.0597291	+	0.122376i
$139$			0.885678i			0.0751223i	0.999294	+	0.0375611i	$0.0119589\pi$
$139$			0.885678i			0.0751223i	−0.999294	+	0.0375611i	$0.988041\pi$
$140$	−4.85072	+	1.52692i	−0.409961	+	0.129048i
$141$	1.97512	+	0.579947i	0.166335	+	0.0488404i
$142$	−0.880833	+	12.3157i	−0.0739178	+	1.03351i
$143$	−10.2921	−	2.23892i	−0.860671	−	0.187227i
$144$	−4.68966	−	4.06361i	−0.390805	−	0.338634i
$145$	−14.7192	−	2.90468i	−1.22236	−	0.241221i
$146$	4.14146	−	1.21604i	0.342750	−	0.100641i
$147$	−0.231181	−	1.06272i	−0.0190675	−	0.0876518i
$148$	3.38775	−	4.52550i	0.278471	−	0.371994i
$149$	−2.93367	−	6.42384i	−0.240336	−	0.526262i	0.750575	−	0.660786i	$-0.229777\pi$
$149$	−2.93367	−	6.42384i	−0.240336	−	0.526262i	−0.990910	+	0.134524i	$0.957049\pi$
$150$	−0.531472	−	1.58084i	−0.0433945	−	0.129075i
$151$	1.00907	+	7.01824i	0.0821170	+	0.571137i	0.988791	+	0.149305i	$0.0477036\pi$
$151$	1.00907	+	7.01824i	0.0821170	+	0.571137i	−0.906674	+	0.421832i	$0.861387\pi$
$152$	0.546968	−	0.118986i	0.0443650	−	0.00965101i
$153$	−0.0259636	−	0.0141772i	−0.00209903	−	0.00114616i
$154$	−18.7921	−	2.70189i	−1.51431	−	0.217725i
$155$	−11.1132	+	11.5521i	−0.892631	+	0.927885i
$156$	0.354048	−	0.227533i	0.0283465	−	0.0182172i
$157$	1.52318	+	0.108940i	0.121563	+	0.00869436i	0.131988	−	0.991251i	$-0.457864\pi$
$157$	1.52318	+	0.108940i	0.121563	+	0.00869436i	−0.0104251	+	0.999946i	$0.503318\pi$
$158$	0.175512	+	0.321426i	0.0139630	+	0.0255713i
$159$	0.483772	−	1.05931i	0.0383656	−	0.0840089i
$160$	−5.57522	−	6.18789i	−0.440760	−	0.489196i
$161$	15.2566	−	3.73137i	1.20239	−	0.294073i
$162$	6.65775	+	6.65775i	0.523082	+	0.523082i
$163$	1.42025	+	3.80783i	0.111242	+	0.298253i	0.980627	−	0.195883i	$-0.0627573\pi$
$163$	1.42025	+	3.80783i	0.111242	+	0.298253i	−0.869385	+	0.494136i	$0.835485\pi$
$164$	1.49150	−	5.07958i	0.116466	−	0.396648i
$165$	−0.407760	+	3.28660i	−0.0317441	+	0.255861i
$166$	2.18536	+	3.40049i	0.169617	+	0.263929i
$167$	0.0802897	−	0.00574243i	0.00621300	−	0.000444363i	−0.0682323	−	0.997669i	$-0.521736\pi$
$167$	0.0802897	−	0.00574243i	0.00621300	−	0.000444363i	0.0744453	+	0.997225i	$0.476281\pi$
$168$	2.35630	−	1.76391i	0.181793	−	0.136088i
$169$	−2.44826	−	8.33802i	−0.188328	−	0.641386i
$170$	0.0210553	+	0.0151346i	0.00161487	+	0.00116077i
$171$	−0.524563	+	0.0754208i	−0.0401144	+	0.00576757i
$172$	3.44101	+	1.28343i	0.262374	+	0.0978605i
$173$	6.39869	+	2.38659i	0.486483	+	0.181449i	0.580724	−	0.814101i	$-0.302770\pi$
$173$	6.39869	+	2.38659i	0.486483	+	0.181449i	−0.0942407	+	0.995549i	$0.530042\pi$
$174$	2.21525	−	0.318504i	0.167937	−	0.0241457i
$175$	−16.2757	+	1.79965i	−1.23033	+	0.136041i
$176$	−3.04300	−	10.3635i	−0.229375	−	0.781180i
$177$	2.26786	−	1.69770i	0.170463	−	0.127607i
$178$	1.91848	−	0.137212i	0.143796	−	0.0102845i
$179$	3.80357	+	5.91846i	0.284292	+	0.442367i	0.953802	−	0.300436i	$-0.0971323\pi$
$179$	3.80357	+	5.91846i	0.284292	+	0.442367i	−0.669510	+	0.742803i	$0.733496\pi$
$180$	2.78200	+	3.57009i	0.207358	+	0.266099i
$181$	−5.11190	+	17.4095i	−0.379965	+	1.29404i	0.518531	+	0.855059i	$0.326479\pi$
$181$	−5.11190	+	17.4095i	−0.379965	+	1.29404i	−0.898496	+	0.438982i	$0.855339\pi$
$182$	2.71487	+	7.27886i	0.201240	+	0.539545i
$183$	−1.89513	−	1.89513i	−0.140092	−	0.140092i
$184$	9.14870	+	11.5890i	0.674451	+	0.854349i
$185$	13.5234	−	12.1845i	0.994264	−	0.895820i
$186$	0.993333	−	2.17510i	0.0728347	−	0.159486i
$187$	−0.0246770	−	0.0451925i	−0.00180456	−	0.00330480i
$188$	4.88428	+	0.349331i	0.356223	+	0.0254775i
$189$	−4.75714	+	3.05723i	−0.346031	+	0.222380i
$190$	0.464450	−	0.00899417i	0.0336948	−	0.000652506i
$191$	−4.43991	−	0.638363i	−0.321261	−	0.0461904i	−0.0202021	−	0.999796i	$-0.506431\pi$
$191$	−4.43991	−	0.638363i	−0.321261	−	0.0461904i	−0.301059	+	0.953606i	$0.597340\pi$
$192$	2.18140	+	1.19114i	0.157429	+	0.0859628i
$193$	−24.6615	+	5.36478i	−1.77517	+	0.386166i	−0.976486	−	0.215580i	$-0.930836\pi$
$193$	−24.6615	+	5.36478i	−1.77517	+	0.386166i	−0.798688	+	0.601745i	$0.794472\pi$
$194$	−0.807165	−	5.61396i	−0.0579511	−	0.403059i
$195$	1.26032	−	0.498077i	0.0902531	−	0.0356681i
$196$	−1.07473	−	2.35333i	−0.0767664	−	0.168095i
$197$	−7.06862	+	9.44257i	−0.503618	+	0.672755i	−0.978250	−	0.207429i	$-0.933490\pi$
$197$	−7.06862	+	9.44257i	−0.503618	+	0.672755i	0.474632	+	0.880185i	$0.342581\pi$
$198$	3.59175	+	16.5110i	0.255255	+	1.17339i
$199$	−11.3212	+	3.32420i	−0.802539	+	0.235647i	−0.657181	−	0.753733i	$-0.728251\pi$
$199$	−11.3212	+	3.32420i	−0.802539	+	0.235647i	−0.145357	+	0.989379i	$0.546433\pi$
$200$	−7.89485	−	13.2148i	−0.558250	−	0.934427i
$201$	−1.95865	−	1.69718i	−0.138152	−	0.119710i
$202$	−20.6532	−	4.49284i	−1.45316	−	0.316115i
$203$	1.56759	−	21.9177i	0.110023	−	1.53832i
$204$	0.00197407		0.000579640i	0.000138213		4.05829e-5i
$205$	7.87845	−	15.1170i	0.550255	−	1.05582i
$206$		−	12.6384i		−	0.880557i
$207$	−7.85681	−	11.5619i	−0.546086	−	0.803607i
$208$	−3.12521	+	3.12521i	−0.216695	+	0.216695i
$209$	−0.839091	−	0.383200i	−0.0580411	−	0.0265065i
$210$	2.20187	−	1.05755i	0.151944	−	0.0729781i
$211$	5.84909	+	6.75021i	0.402668	+	0.464704i	0.920479	−	0.390791i	$-0.127799\pi$
$211$	5.84909	+	6.75021i	0.402668	+	0.464704i	−0.517811	+	0.855495i	$0.673253\pi$
$212$	0.588854	−	2.70692i	0.0404426	−	0.185912i
$213$	0.225042	+	3.14650i	0.0154196	+	0.215595i
$214$	−2.68843	+	18.6984i	−0.183777	+	1.27820i
$215$	10.0703	+	6.19963i	0.686790	+	0.422812i
$216$	−4.47201	−	2.87399i	−0.304282	−	0.195550i
$217$	−18.7947	−	14.0695i	−1.27587	−	0.955102i
$218$	2.94348	−	7.89178i	0.199358	−	0.534499i
$219$	1.00311	−	0.458105i	0.0677838	−	0.0309558i
$220$	0.714054	+	7.84566i	0.0481415	+	0.528954i
$221$	−0.0113912	+	0.0177250i	−0.000766254	+	0.00119231i
$222$	−1.30133	+	2.38321i	−0.0873395	+	0.159950i
$223$	15.4152	+	20.5923i	1.03228	+	1.37896i	0.922934	+	0.384957i	$0.125784\pi$
$223$	15.4152	+	20.5923i	1.03228	+	1.37896i	0.109343	+	0.994004i	$0.465125\pi$
$224$	7.98857	−	9.21930i	0.533759	−	0.615991i
$225$	6.56293	+	13.0126i	0.437529	+	0.867503i
$226$	−0.358121	+	0.310314i	−0.0238219	+	0.0206418i
$227$	11.2462	−	6.14091i	0.746439	−	0.407587i	−0.0605406	−	0.998166i	$-0.519282\pi$
$227$	11.2462	−	6.14091i	0.746439	−	0.407587i	0.806980	+	0.590579i	$0.201101\pi$
$228$	0.0345342	−	0.0128806i	0.00228709	−	0.000853039i
$229$	24.2907			1.60518			0.802588	−	0.596534i	$-0.203456\pi$
$229$	24.2907			1.60518			0.802588	+	0.596534i	$0.203456\pi$
$230$	5.58671	+	10.9055i	0.368377	+	0.719086i
$231$	−4.85052			−0.319141
$232$	19.3543	−	7.21878i	1.27067	−	0.473936i
$233$	−16.4667	+	8.99151i	−1.07877	+	0.589053i	−0.917451	−	0.397849i	$-0.869757\pi$
$233$	−16.4667	+	8.99151i	−1.07877	+	0.589053i	−0.161320	+	0.986902i	$0.551575\pi$
$234$	5.22542	−	4.52785i	0.341596	−	0.295995i
$235$	15.2121	+	4.14850i	0.992327	+	0.270618i
$236$	4.41305	−	5.09293i	0.287265	−	0.331521i
$237$	0.0560717	+	0.0749030i	0.00364225	+	0.00486547i
$238$	−0.0182009	+	0.0333325i	−0.00117979	+	0.00216063i
$239$	0.945717	−	1.47156i	0.0611733	−	0.0951876i	−0.809319	−	0.587369i	$-0.800164\pi$
$239$	0.945717	−	1.47156i	0.0611733	−	0.0951876i	0.870493	+	0.492181i	$0.163800\pi$
$240$	1.06767	+	0.889538i	0.0689177	+	0.0574195i
$241$	−1.83140	+	0.836372i	−0.117971	+	0.0538755i	−0.473526	−	0.880780i	$-0.657019\pi$
$241$	−1.83140	+	0.836372i	−0.117971	+	0.0538755i	0.355555	+	0.934655i	$0.384292\pi$
$242$	−5.88591	+	15.7807i	−0.378361	+	1.01442i
$243$	6.07254	+	4.54585i	0.389554	+	0.291616i
$244$	−5.36336	−	3.44682i	−0.343354	−	0.220660i
$245$	−1.92806	−	8.10437i	−0.123179	−	0.517769i
$246$	−0.361892	+	2.51702i	−0.0230734	+	0.160479i
$247$	0.0269278	+	0.376500i	0.00171337	+	0.0239561i
$248$	4.69139	−	21.5660i	0.297903	−	1.36944i
$249$	0.676291	+	0.780482i	0.0428582	+	0.0494610i
$250$	−4.30463	−	12.0277i	−0.272248	−	0.760701i
$251$	−21.8602	−	9.98322i	−1.37980	−	0.630135i	−0.419159	−	0.907913i	$-0.637675\pi$
$251$	−21.8602	−	9.98322i	−1.37980	−	0.630135i	−0.960645	+	0.277777i	$0.910402\pi$
$252$	−4.68736	+	4.68736i	−0.295276	+	0.295276i
$253$	−0.624423	−	24.3237i	−0.0392571	−	1.52922i
$254$		−	1.95125i		−	0.122432i
$255$	0.00587491	+	0.00306180i	0.000367901	+	0.000191737i
$256$	13.8402	+	4.06385i	0.865012	+	0.253991i
$257$	−1.30222	+	18.2075i	−0.0812304	+	1.13575i	0.779402	+	0.626524i	$0.215523\pi$
$257$	−1.30222	+	18.2075i	−0.0812304	+	1.13575i	−0.860633	+	0.509226i	$0.829932\pi$
$258$	−1.72374	−	0.374977i	−0.107315	−	0.0233450i
$259$	20.1485	+	17.4588i	1.25197	+	1.08484i
$260$	2.67767	−	1.79503i	0.166062	−	0.111323i
$261$	−18.7647	+	5.50981i	−1.16151	+	0.341049i
$262$	−3.09210	−	14.2142i	−0.191031	−	0.878154i
$263$	0.659304	−	0.880727i	0.0406544	−	0.0543080i	−0.779753	−	0.626087i	$-0.784656\pi$
$263$	0.659304	−	0.880727i	0.0406544	−	0.0543080i	0.820408	+	0.571779i	$0.193746\pi$
$264$	−1.89421	−	4.14774i	−0.116580	−	0.255276i
$265$	3.54777	−	8.18429i	0.217938	−	0.502757i
$266$	0.0968268	+	0.673445i	0.00593683	+	0.0412916i
$267$	0.480170	−	0.104454i	0.0293859	−	0.00639251i
$268$	−5.41092	−	2.95459i	−0.330525	−	0.180480i
$269$	16.6206	+	2.38969i	1.01338	+	0.145702i	0.628944	−	0.777451i	$-0.283488\pi$
$269$	16.6206	+	2.38969i	1.01338	+	0.145702i	0.384434	+	0.923153i	$0.374397\pi$
$270$	−3.17927	−	3.05848i	−0.193484	−	0.186133i
$271$	4.66608	−	2.99871i	0.283444	−	0.182158i	−0.391192	−	0.920309i	$-0.627937\pi$
$271$	4.66608	−	2.99871i	0.283444	−	0.182158i	0.674636	+	0.738151i	$0.264301\pi$
$272$	−0.0215513	−	0.00154138i	−0.00130674	−	9.34597e-5i
$273$	0.951215	+	1.74202i	0.0575701	+	0.105432i
$274$	−6.25042	+	13.6865i	−0.377602	+	0.826833i
$275$	−2.63534	+	25.2303i	−0.158917	+	1.52144i
$276$	0.704875	+	0.669591i	0.0424285	+	0.0403046i
$277$	4.23651	+	4.23651i	0.254547	+	0.254547i	0.822832	−	0.568285i	$-0.192393\pi$
$277$	4.23651	+	4.23651i	0.254547	+	0.254547i	−0.568285	+	0.822832i	$0.692393\pi$
$278$	−0.353654	−	0.948184i	−0.0212108	−	0.0568683i
$279$	−5.88687	+	20.0488i	−0.352438	+	1.20029i
$280$	17.7837	−	13.8580i	1.06278	−	0.828173i
$281$	−11.1596	−	17.3647i	−0.665726	−	1.03589i	−0.995766	−	0.0919225i	$-0.970699\pi$
$281$	−11.1596	−	17.3647i	−0.665726	−	1.03589i	0.330041	−	0.943967i	$-0.392938\pi$
$282$	−2.34608	+	0.167795i	−0.139707	+	0.00999206i
$283$	2.02033	−	1.51240i	0.120096	−	0.0899028i	−0.537541	−	0.843237i	$-0.680647\pi$
$283$	2.02033	−	1.51240i	0.120096	−	0.0899028i	0.657637	+	0.753335i	$0.271556\pi$
$284$	2.11412	+	7.20003i	0.125450	+	0.427243i
$285$	0.117127	−	0.0191618i	0.00693798	−	0.00113505i
$286$	11.9125	−	1.71276i	0.704400	−	0.101277i
$287$	23.3929	+	8.72510i	1.38084	+	0.515026i
$288$	−10.1726	−	3.79419i	−0.599427	−	0.223575i
$289$	16.8269	−	2.41934i	0.989815	−	0.142314i
$290$	16.9178	−	2.76774i	0.993447	−	0.162527i
$291$	−0.408244	−	1.39035i	−0.0239317	−	0.0815038i
$292$	2.10002	−	1.57205i	0.122894	−	0.0919975i
$293$	19.5179	−	1.39595i	1.14025	−	0.0815522i	0.511587	−	0.859231i	$-0.329058\pi$
$293$	19.5179	−	1.39595i	1.14025	−	0.0815522i	0.628661	+	0.777679i	$0.283603\pi$
$294$	0.671845	+	1.04541i	0.0391828	+	0.0609696i
$295$	17.1162	−	13.3378i	0.996544	−	0.776559i
$296$	−7.06089	+	24.0472i	−0.410406	+	1.39771i
$297$	3.06140	+	8.20793i	0.177640	+	0.476272i
$298$	5.70577	+	5.70577i	0.330526	+	0.330526i
$299$	−8.61317	+	4.99427i	−0.498112	+	0.288826i
$300$	−0.638390	−	0.787306i	−0.0368575	−	0.0454551i
$301$	−7.19504	+	15.7549i	−0.414715	+	0.908100i
$302$	−3.88269	−	7.11062i	−0.223424	−	0.409170i
$303$	−5.38630	−	0.385236i	−0.309435	−	0.0221312i
$304$	−0.325627	+	0.209267i	−0.0186760	+	0.0120023i
$305$	−14.7945	−	14.2324i	−0.847132	−	0.814946i
$306$	0.0334569	+	0.00481038i	0.00191260	+	0.000274991i
$307$	−9.91150	−	5.41209i	−0.565679	−	0.308884i	0.170842	−	0.985298i	$-0.445351\pi$
$307$	−9.91150	−	5.41209i	−0.565679	−	0.308884i	−0.736521	+	0.676414i	$0.763533\pi$
$308$	−11.2747	+	2.45266i	−0.642436	+	0.139753i
$309$	−0.459528	−	3.19609i	−0.0261416	−	0.181819i
$310$	7.28468	−	16.8049i	0.413742	−	0.954453i
$311$	−8.67600	−	18.9978i	−0.491971	−	1.07727i	−0.978996	−	0.203878i	$-0.934646\pi$
$311$	−8.67600	−	18.9978i	−0.491971	−	1.07727i	0.487026	−	0.873388i	$-0.338082\pi$
$312$	−1.11816	+	1.49368i	−0.0633032	+	0.0845632i
$313$	−3.29730	−	15.1575i	−0.186375	−	0.856750i	−0.971430	−	0.237325i	$-0.923729\pi$
$313$	−3.29730	−	15.1575i	−0.186375	−	0.856750i	0.785056	−	0.619425i	$-0.212634\pi$
$314$	−1.67418	+	0.491583i	−0.0944793	+	0.0277416i
$315$	−17.7299	+	11.8856i	−0.998968	+	0.669678i
$316$	0.168210	+	0.145754i	0.00946253	+	0.00819933i
$317$	−22.5147	−	4.89778i	−1.26455	−	0.275087i	−0.470209	−	0.882555i	$-0.655822\pi$
$317$	−22.5147	−	4.89778i	−1.26455	−	0.275087i	−0.794344	+	0.607468i	$0.792185\pi$
$318$	−0.0949263	+	1.32724i	−0.00532320	+	0.0744281i
$319$	−32.6621	−	9.59045i	−1.82873	−	0.536962i
$320$	16.8825	+	8.79857i	0.943761	+	0.491855i
$321$			4.82634i			0.269380i
$322$	−14.8434	+	10.0867i	−0.827189	+	0.562111i
$323$	−0.00130480	+	0.00130480i	−7.26009e−5	+	7.26009e-5i
$324$	5.20518	+	2.37712i	0.289176	+	0.132062i
$325$	9.57803	−	4.00134i	0.531293	−	0.221955i
$326$	−3.04096	−	3.50946i	−0.168423	−	0.194371i
$327$	0.457426	−	2.10275i	0.0252957	−	0.116283i
$328$	1.67438	+	23.4108i	0.0924520	+	1.29265i
$329$	−3.28655	+	22.8585i	−0.181193	+	1.26023i
$330$	−0.875812	−	3.68137i	−0.0482119	−	0.202653i
$331$	5.80446	+	3.73030i	0.319042	+	0.205036i	0.690353	−	0.723473i	$-0.257455\pi$
$331$	5.80446	+	3.73030i	0.319042	+	0.205036i	−0.371311	+	0.928509i	$0.621092\pi$
$332$	1.96664	+	1.47221i	0.107934	+	0.0807981i
$333$	8.29208	−	22.2319i	0.454403	−	1.21830i
$334$	−0.0836631	+	0.0382076i	−0.00457784	+	0.00209063i
$335$	−15.2516	−	12.7070i	−0.833286	−	0.694260i
$336$	−1.10039	+	1.71224i	−0.0600312	+	0.0934104i
$337$	3.67782	−	6.73542i	0.200344	−	0.366902i	−0.758121	−	0.652114i	$-0.773882\pi$
$337$	3.67782	−	6.73542i	0.200344	−	0.366902i	0.958464	+	0.285212i	$0.0920641\pi$
$338$	5.95045	+	7.94887i	0.323662	+	0.432361i
$339$	−0.0792814	+	0.0914957i	−0.00430598	+	0.00496936i
$340$	0.0152040	+	0.00414630i	0.000824554	+	0.000224865i
$341$	−27.4870	+	23.8176i	−1.48851	+	1.28980i
$342$	0.531468	−	0.290203i	0.0287385	−	0.0156924i
$343$	−10.0477	+	3.74759i	−0.542524	+	0.202351i
$344$	−16.2820			−0.877868
$345$	1.80933	+	2.55472i	0.0974110	+	0.137542i
$346$	−7.80324			−0.419505
$347$	−15.7973	+	5.89208i	−0.848043	+	0.316304i	−0.735651	−	0.677360i	$-0.763124\pi$
$347$	−15.7973	+	5.89208i	−0.848043	+	0.316304i	−0.112392	+	0.993664i	$0.535851\pi$
$348$	1.19379	−	0.651859i	0.0639939	−	0.0349433i
$349$	10.7242	−	9.29255i	0.574052	−	0.497419i	−0.318768	−	0.947833i	$-0.603269\pi$
$349$	10.7242	−	9.29255i	0.574052	−	0.497419i	0.892820	+	0.450414i	$0.148724\pi$
$350$	16.7058	−	8.42562i	0.892961	−	0.450368i
$351$	2.34745	−	2.70910i	0.125297	−	0.144601i
$352$	−11.3252	−	15.1287i	−0.603636	−	0.806364i
$353$	−0.243587	+	0.446096i	−0.0129648	+	0.0237433i	−0.884081	−	0.467334i	$-0.845215\pi$
$353$	−0.243587	+	0.446096i	−0.0129648	+	0.0237433i	0.871116	+	0.491077i	$0.163397\pi$
$354$	−1.75001	+	2.72308i	−0.0930122	+	0.144730i
$355$	2.19008	+	24.0635i	0.116238	+	1.27716i
$356$	1.06330	−	0.485595i	0.0563550	−	0.0257365i
$357$	−0.00339083	+	0.00909116i	−0.000179462	+	0.000481155i
$358$	−6.43526	−	4.81738i	−0.340114	−	0.254606i
$359$	−1.13207	−	0.727539i	−0.0597485	−	0.0383980i	0.510426	−	0.859922i	$-0.329488\pi$
$359$	−1.13207	−	0.727539i	−0.0597485	−	0.0383980i	−0.570174	+	0.821524i	$0.693124\pi$
$360$	−17.0874	−	10.5196i	−0.900583	−	0.554429i
$361$	2.69928	−	18.7739i	0.142067	−	0.988099i
$362$	−1.47902	−	20.6794i	−0.0777355	−	1.08688i
$363$	−0.914689	+	4.20476i	−0.0480087	+	0.220693i
$364$	3.09189	+	3.56823i	0.162059	+	0.187026i
$365$	7.61418	−	3.65707i	0.398545	−	0.191420i
$366$	2.78560	+	1.27214i	0.145606	+	0.0664960i
$367$	−16.5849	+	16.5849i	−0.865726	+	0.865726i	−0.991996	−	0.126269i	$-0.959700\pi$
$367$	−16.5849	+	16.5849i	−0.865726	+	0.865726i	0.126269	+	0.991996i	$0.459700\pi$
$368$	−8.72794	−	5.29765i	−0.454975	−	0.276159i
$369$		−	22.2210i		−	1.15678i
$370$	−9.61255	+	18.4443i	−0.499733	+	0.958875i
$371$	12.5354	+	3.68073i	0.650807	+	0.191094i
$372$	0.103674	−	1.44955i	0.00537523	−	0.0751555i
$373$	−20.5178	−	4.46338i	−1.06237	−	0.231105i	−0.352772	−	0.935709i	$-0.614761\pi$
$373$	−20.5178	−	4.46338i	−1.06237	−	0.231105i	−0.709600	+	0.704604i	$0.751125\pi$
$374$	0.0444641	+	0.0385283i	0.00229918	+	0.00199225i
$375$	−1.52591	−	2.88515i	−0.0787977	−	0.148988i
$376$	−20.8300	+	6.11624i	−1.07423	+	0.315421i
$377$	2.96090	+	13.6110i	0.152494	+	0.701004i
$378$	3.87211	−	5.17253i	0.199160	−	0.266046i
$379$	−2.46273	−	5.39263i	−0.126502	−	0.277001i	0.835775	−	0.549072i	$-0.185019\pi$
$379$	−2.46273	−	5.39263i	−0.126502	−	0.277001i	−0.962277	+	0.272071i	$0.912291\pi$
$380$	0.262564	−	0.103765i	0.0134692	−	0.00532305i
$381$	−0.0709469	−	0.493447i	−0.00363472	−	0.0252800i
$382$	5.00816	−	1.08946i	0.256240	−	0.0557415i
$383$	7.78859	+	4.25289i	0.397978	+	0.217313i	0.665758	−	0.746168i	$-0.268108\pi$
$383$	7.78859	+	4.25289i	0.397978	+	0.217313i	−0.267780	+	0.963480i	$0.586290\pi$
$384$	−0.658352	−	0.0946567i	−0.0335964	−	0.00483043i
$385$	−37.1468	+	0.719355i	−1.89318	+	0.0366617i
$386$	24.2598	−	15.5908i	1.23479	−	0.793552i
$387$	15.3759	+	1.09970i	0.781599	+	0.0559010i
$388$	−1.65196	−	3.02535i	−0.0838658	−	0.153589i
$389$	9.46281	−	20.7207i	0.479783	−	1.05058i	−0.502740	−	0.864438i	$-0.667675\pi$
$389$	9.46281	−	20.7207i	0.479783	−	1.05058i	0.982523	−	0.186141i	$-0.0595982\pi$
$390$	−1.15038	+	1.03648i	−0.0582516	+	0.0524841i
$391$	−0.0460255	−	0.0158335i	−0.00232761	−	0.000800734i
$392$	8.11038	+	8.11038i	0.409636	+	0.409636i
$393$	−1.29878	−	3.48216i	−0.0655146	−	0.175652i
$394$	3.79703	−	12.9315i	0.191292	−	0.651479i
$395$	0.440523	+	0.565315i	0.0221651	+	0.0284441i
$396$	5.55201	+	8.63910i	0.278999	+	0.434131i
$397$	−28.0955	+	2.00943i	−1.41007	+	0.100850i	−0.755499	−	0.655149i	$-0.772606\pi$
$397$	−28.0955	+	2.00943i	−1.41007	+	0.100850i	−0.654572	+	0.756000i	$0.727151\pi$
$398$	10.7928	−	8.07940i	0.540995	−	0.404984i
$399$	0.0489725	+	0.166785i	0.00245169	+	0.00834970i
$400$	8.30847	+	6.65402i	0.415423	+	0.332701i
$401$	16.0724	−	2.31086i	0.802617	−	0.115399i	0.271215	−	0.962519i	$-0.412575\pi$
$401$	16.0724	−	2.31086i	0.802617	−	0.115399i	0.531402	+	0.847120i	$0.321665\pi$
$402$	2.77457	+	1.03486i	0.138383	+	0.0516141i
$403$	13.9443	+	5.20094i	0.694613	+	0.259077i
$404$	−12.7149	+	1.82813i	−0.632590	+	0.0909526i
$405$	14.9617	+	10.7545i	0.743451	+	0.534397i
$406$	7.07361	+	24.0905i	0.351057	+	1.19559i
$407$	33.0634	−	24.7509i	1.63889	−	1.22686i
$408$	−0.00909814		0.000650712i	−0.000450425		3.22150e-5i
$409$	16.3945	+	25.5103i	0.810656	+	1.26141i	0.962034	+	0.272929i	$0.0879926\pi$
$409$	16.3945	+	25.5103i	0.810656	+	1.26141i	−0.151378	+	0.988476i	$0.548371\pi$
$410$	−2.39820	+	19.3298i	−0.118439	+	0.954629i
$411$	−1.08302	+	3.68841i	−0.0534212	+	0.181936i
$412$	−2.68424	−	7.19673i	−0.132243	−	0.354557i
$413$	22.4728	+	22.4728i	1.10581	+	1.10581i
$414$	13.0280	+	9.24061i	0.640291	+	0.454151i
$415$	5.29500	+	5.87688i	0.259921	+	0.288484i
$416$	−3.21240	+	7.03418i	−0.157501	+	0.344879i
$417$	−0.123910	−	0.226925i	−0.00606792	−	0.0111126i
$418$	1.05132	+	0.0751920i	0.0514218	+	0.00367776i
$419$	−31.2410	+	20.0774i	−1.52622	+	0.980845i	−0.535564	+	0.844495i	$0.679901\pi$
$419$	−31.2410	+	20.0774i	−1.52622	+	0.980845i	−0.990661	+	0.136351i	$0.956463\pi$
$420$	1.02921	−	1.06986i	0.0502203	−	0.0522037i
$421$	33.9875	+	4.88666i	1.65645	+	0.238161i	0.906156	−	0.422944i	$-0.139003\pi$
$421$	33.9875	+	4.88666i	1.65645	+	0.238161i	0.750293	+	0.661106i	$0.229912\pi$
$422$	−8.95727	−	4.89104i	−0.436033	−	0.238092i
$423$	20.0838	−	4.36897i	0.976509	−	0.212427i
$424$	1.74785	+	12.1566i	0.0848832	+	0.590376i
$425$	0.0454459	+	0.0225769i	0.00220445	+	0.00109514i
$426$	−1.49733	−	3.27870i	−0.0725460	−	0.158854i
$427$	18.0186	−	24.0700i	0.871980	−	1.16483i
$428$	2.44044	+	11.2185i	0.117963	+	0.542267i
$429$	2.95024	−	0.866269i	0.142439	−	0.0418239i
$430$	−13.2566	−	2.61605i	−0.639288	−	0.126157i
$431$	6.53576	+	5.66327i	0.314816	+	0.272790i	0.797907	−	0.602780i	$-0.205940\pi$
$431$	6.53576	+	5.66327i	0.314816	+	0.272790i	−0.483091	+	0.875570i	$0.660486\pi$
$432$	3.59192	+	0.781374i	0.172816	+	0.0375939i
$433$	1.24020	−	17.3403i	0.0596002	−	0.833319i	−0.876459	−	0.481477i	$-0.840101\pi$
$433$	1.24020	−	17.3403i	0.0596002	−	0.833319i	0.936059	−	0.351843i	$-0.114445\pi$
$434$	25.7391	+	7.55768i	1.23552	+	0.362780i
$435$	4.17766	−	1.31505i	0.200304	−	0.0630519i
$436$		−	5.11901i		−	0.245156i
$437$	−0.830065	+	0.267051i	−0.0397074	+	0.0127748i
$438$	−0.890980	+	0.890980i	−0.0425727	+	0.0425727i
$439$	−10.0260	−	4.57874i	−0.478516	−	0.218531i	0.161529	−	0.986868i	$-0.448357\pi$
$439$	−10.0260	−	4.57874i	−0.478516	−	0.218531i	−0.640046	+	0.768337i	$0.721085\pi$
$440$	−15.1216	−	31.4837i	−0.720892	−	1.50093i
$441$	−7.11122	−	8.20678i	−0.338629	−	0.390799i
$442$	0.00511744	−	0.0235245i	0.000243412	−	0.00111895i
$443$	−1.60679	−	22.4658i	−0.0763407	−	1.06738i	−0.880835	−	0.473423i	$-0.843018\pi$
$443$	−1.60679	−	22.4658i	−0.0763407	−	1.06738i	0.804495	−	0.593960i	$-0.202436\pi$
$444$	−0.234857	+	1.63347i	−0.0111458	+	0.0775209i
$445$	3.66180	−	0.871156i	0.173586	−	0.0412968i
$446$	−24.7257	−	15.8902i	−1.17079	−	0.752424i
$447$	1.65038	+	1.23546i	0.0780602	+	0.0584351i
$448$	−9.74410	+	26.1249i	−0.460365	+	1.23429i
$449$	17.2029	−	7.85629i	0.811853	−	0.370761i	0.0341692	−	0.999416i	$-0.489122\pi$
$449$	17.2029	−	7.85629i	0.811853	−	0.370761i	0.777684	+	0.628655i	$0.216394\pi$
$450$	−12.2221	−	11.3103i	−0.576153	−	0.533173i
$451$	20.9110	−	32.5382i	0.984661	−	1.53216i
$452$	−0.138020	+	0.252764i	−0.00649190	+	0.0118890i
$453$	−1.24042	−	1.65701i	−0.0582802	−	0.0778532i
$454$	−9.58784	+	11.0650i	−0.449980	+	0.519304i
$455$	7.54305	+	13.1999i	0.353624	+	0.618819i
$456$	−0.123495	+	0.107009i	−0.00578320	+	0.00501117i
$457$	26.2573	−	14.3376i	1.22826	−	0.670683i	0.271750	−	0.962368i	$-0.412398\pi$
$457$	26.2573	−	14.3376i	1.22826	−	0.670683i	0.956514	+	0.291685i	$0.0942159\pi$
$458$	−26.0050	+	9.69936i	−1.21513	+	0.453222i
$459$	0.0175240			0.000817948
$460$	5.49746	+	5.02340i	0.256320	+	0.234217i
$461$	7.18959			0.334853			0.167426	−	0.985885i	$-0.446454\pi$
$461$	7.18959			0.334853			0.167426	+	0.985885i	$0.446454\pi$
$462$	5.19284	−	1.93683i	0.241593	−	0.0901094i
$463$	−4.91028	+	2.68122i	−0.228200	+	0.124607i	−0.589282	−	0.807927i	$-0.700589\pi$
$463$	−4.91028	+	2.68122i	−0.228200	+	0.124607i	0.361082	+	0.932534i	$0.382407\pi$
$464$	−10.7952	+	9.35407i	−0.501153	+	0.434252i
$465$	1.23118	−	4.51461i	0.0570947	−	0.209360i
$466$	14.0385	−	16.2013i	0.650321	−	0.750510i
$467$	9.35929	+	12.5025i	0.433096	+	0.578549i	0.962997	−	0.269511i	$-0.0868619\pi$
$467$	9.35929	+	12.5025i	0.433096	+	0.578549i	−0.529901	+	0.848059i	$0.677771\pi$
$468$	2.01387	−	3.68813i	0.0930913	−	0.170484i
$469$	15.7191	−	24.4593i	0.725838	−	1.12943i
$470$	−17.9422	+	1.63296i	−0.827610	+	0.0753230i
$471$	−0.405505	+	0.185188i	−0.0186847	+	0.00853300i
$472$	−10.4407	+	27.9927i	−0.480574	+	1.28847i
$473$	21.4799	+	16.0797i	0.987649	+	0.739345i
$474$	−0.0899379	−	0.0577996i	−0.00413099	−	0.00265482i
$475$	0.894150	−	0.164117i	0.0410264	−	0.00753022i
$476$	−0.00328481	+	0.0228464i	−0.000150559	+	0.00104716i
$477$	−0.829510	−	11.5981i	−0.0379806	−	0.531039i
$478$	−0.424859	+	1.95305i	−0.0194326	+	0.0893302i
$479$	−9.82943	−	11.3438i	−0.449118	−	0.518310i	0.485368	−	0.874310i	$-0.338686\pi$
$479$	−9.82943	−	11.3438i	−0.449118	−	0.518310i	−0.934486	+	0.356000i	$0.884140\pi$
$480$	2.29418	+	0.805439i	0.104714	+	0.0367631i
$481$	−15.3730	−	7.02061i	−0.700948	−	0.320112i
$482$	1.62668	−	1.62668i	0.0740933	−	0.0740933i
$483$	−3.38695	+	3.09051i	−0.154112	+	0.140623i
$484$			10.2362i			0.465281i
$485$	−3.33265	−	10.5872i	−0.151328	−	0.480740i
$486$	−8.31628	−	2.44188i	−0.377234	−	0.110766i
$487$	0.785712	−	10.9857i	0.0356040	−	0.497809i	−0.948095	−	0.317987i	$-0.896993\pi$
$487$	0.785712	−	10.9857i	0.0356040	−	0.497809i	0.983699	−	0.179822i	$-0.0575522\pi$
$488$	27.6191	+	6.00817i	1.25026	+	0.271977i
$489$	−0.896624	−	0.776929i	−0.0405467	−	0.0351339i
$490$	5.30023	+	7.90644i	0.239440	+	0.357177i
$491$	−31.1378	+	9.14290i	−1.40523	+	0.412613i	−0.894477	−	0.447114i	$-0.852452\pi$
$491$	−31.1378	+	9.14290i	−1.40523	+	0.412613i	−0.510754	+	0.859727i	$0.670634\pi$
$492$	0.328510	+	1.51014i	0.0148104	+	0.0680822i
$493$	−0.0408080	+	0.0545131i	−0.00183790	+	0.00245515i
$494$	−0.179166	−	0.392318i	−0.00806105	−	0.0176512i
$495$	12.1535	+	30.7529i	0.546261	+	1.38224i
$496$	2.17195	+	15.1062i	0.0975234	+	0.678290i
$497$	−34.5808	+	7.52258i	−1.55116	+	0.337434i
$498$	−1.03567	−	0.565518i	−0.0464094	−	0.0253415i
$499$	−7.71513	−	1.10927i	−0.345377	−	0.0496577i	−0.0325562	−	0.999470i	$-0.510365\pi$
$499$	−7.71513	−	1.10927i	−0.345377	−	0.0496577i	−0.312821	+	0.949812i	$0.601274\pi$
$500$	−5.00575	−	5.93476i	−0.223864	−	0.265410i
$501$	−0.0197681	+	0.0127042i	−0.000883174	+	0.000567582i
$502$	27.3893	+	1.95892i	1.22244	+	0.0874309i
$503$	14.9423	+	27.3648i	0.666244	+	1.22013i	0.964104	+	0.265525i	$0.0855453\pi$
$503$	14.9423	+	27.3648i	0.666244	+	1.22013i	−0.297860	+	0.954610i	$0.596273\pi$
$504$	12.2086	−	26.7330i	0.543813	−	1.19078i
$505$	−41.3071	−	2.15144i	−1.83814	−	0.0957380i
$506$	10.3810	+	25.7909i	0.461492	+	1.14655i
$507$	1.79381	+	1.79381i	0.0796659	+	0.0796659i
$508$	−0.414422	−	1.11111i	−0.0183870	−	0.0492975i
$509$	4.71980	−	16.0742i	0.209202	−	0.712475i	−0.786310	−	0.617833i	$-0.788011\pi$
$509$	4.71980	−	16.0742i	0.209202	−	0.712475i	0.995511	−	0.0946428i	$-0.0301709\pi$
$510$	−0.00751211		0.000932009i	−0.000332642		4.12701e-5i
$511$	6.68852	+	10.4075i	0.295883	+	0.460403i
$512$	−20.9849	+	1.50087i	−0.927408	+	0.0663296i
$513$	0.251321	−	0.188136i	0.0110961	−	0.00830642i
$514$	−5.87617	−	20.0124i	−0.259187	−	0.882709i
$515$	−3.99320	−	24.4085i	−0.175961	−	1.07557i
$516$	−1.06120	+	0.152577i	−0.0467166	+	0.00671684i
$517$	33.5201	+	12.5023i	1.47421	+	0.549852i
$518$	−28.5418	−	10.6455i	−1.25405	−	0.467738i
$519$	−1.97334	+	0.283724i	−0.0866200	+	0.0124541i
$520$	−8.34168	+	11.6049i	−0.365807	+	0.508909i
$521$	5.04756	+	17.1904i	0.221138	+	0.753125i	0.993081	+	0.117434i	$0.0374668\pi$
$521$	5.04756	+	17.1904i	0.221138	+	0.753125i	−0.771943	+	0.635692i	$0.780715\pi$
$522$	17.8889	−	13.3915i	0.782976	−	0.586129i
$523$	−13.1685	+	0.941829i	−0.575818	+	0.0411833i	−0.356212	−	0.934405i	$-0.615932\pi$
$523$	−13.1685	+	0.941829i	−0.575818	+	0.0411833i	−0.219606	+	0.975589i	$0.570477\pi$
$524$	−4.77967	−	7.43731i	−0.208801	−	0.324900i
$525$	3.91833	−	2.73815i	0.171010	−	0.119503i
$526$	−0.354156	+	1.20615i	−0.0154419	+	0.0525905i
$527$	0.0254254	+	0.0681681i	0.00110755	+	0.00296945i
$528$	2.22957	+	2.22957i	0.0970296	+	0.0970296i
$529$	−15.9338	−	16.5865i	−0.692775	−	0.721154i
$530$	−0.530139	+	10.1785i	−0.0230278	+	0.442127i
$531$	11.7503	−	25.7296i	0.509921	−	1.11657i
$532$	0.198168	+	0.362918i	0.00859168	+	0.0157345i
$533$	−15.7866	−	1.12908i	−0.683792	−	0.0489057i
$534$	−0.472348	+	0.303560i	−0.0204405	+	0.0131363i
$535$	0.715769	+	36.9616i	0.0309454	+	1.59799i
$536$	27.0540	+	3.88978i	1.16856	+	0.168013i
$537$	−1.80255	−	0.984269i	−0.0777860	−	0.0424744i
$538$	−18.7478	+	4.07834i	−0.808276	+	0.175830i
$539$	−2.68997	−	18.7091i	−0.115865	−	0.805860i
$540$	−2.45997	−	1.06636i	−0.105860	−	0.0458889i
$541$	−4.38382	−	9.59922i	−0.188475	−	0.412703i	0.791680	−	0.610936i	$-0.209207\pi$
$541$	−4.38382	−	9.59922i	−0.188475	−	0.412703i	−0.980155	+	0.198234i	$0.936480\pi$
$542$	−3.79799	+	5.07352i	−0.163138	+	0.217926i
$543$	−1.12592	−	5.17578i	−0.0483179	−	0.222114i
$544$	−0.0362723	+	0.0106505i	−0.00155516	+	0.000456637i
$545$	3.19126	−	16.1714i	0.136699	−	0.692706i
$546$	−1.71394	−	1.48514i	−0.0733499	−	0.0635580i
$547$	7.80744	+	1.69840i	0.333822	+	0.0726185i	0.376352	−	0.926477i	$-0.377178\pi$
$547$	7.80744	+	1.69840i	0.333822	+	0.0726185i	−0.0425302	+	0.999095i	$0.513542\pi$
$548$	−0.652353	+	9.12109i	−0.0278671	+	0.389634i
$549$	−25.6762	−	7.53921i	−1.09583	−	0.321765i
$550$	−7.25320	−	28.0632i	−0.309278	−	1.19662i
$551$			1.21991i			0.0519701i
$552$	−3.96539	−	1.68933i	−0.168778	−	0.0719027i
$553$	−0.742232	+	0.742232i	−0.0315629	+	0.0315629i
$554$	−6.22714	−	2.84384i	−0.264566	−	0.120823i
$555$	−1.76026	+	5.01385i	−0.0747189	+	0.212826i
$556$	−0.402766	−	0.464817i	−0.0170811	−	0.0197126i
$557$	−1.74969	+	8.04318i	−0.0741366	+	0.340800i	−0.999243	−	0.0389081i	$-0.987612\pi$
$557$	−1.74969	+	8.04318i	−0.0741366	+	0.340800i	0.925106	+	0.379708i	$0.123976\pi$
$558$	−1.70324	−	23.8144i	−0.0721039	−	1.00814i
$559$	1.56253	−	10.8676i	0.0660881	−	0.459653i
$560$	−8.17319	+	13.2761i	−0.345381	+	0.561016i
$561$	0.0126453	+	0.00812663i	0.000533884	+	0.000343106i
$562$	18.8809	+	14.1341i	0.796444	+	0.596211i
$563$	−12.3138	+	33.0146i	−0.518965	+	1.39140i	0.368114	+	0.929781i	$0.380004\pi$
$563$	−12.3138	+	33.0146i	−0.518965	+	1.39140i	−0.887079	+	0.461618i	$0.847269\pi$
$564$	−1.30030	+	0.593829i	−0.0547527	+	0.0250047i
$565$	−0.593593	+	0.712460i	−0.0249726	+	0.0299734i
$566$	−1.55900	+	2.42586i	−0.0655298	+	0.101966i
$567$	−12.9334	+	23.6858i	−0.543152	+	0.994709i
$568$	−19.9370	−	26.6327i	−0.836539	−	1.11748i
$569$	5.10865	−	5.89569i	0.214166	−	0.247160i	−0.638494	−	0.769627i	$-0.720442\pi$
$569$	5.10865	−	5.89569i	0.214166	−	0.247160i	0.852660	+	0.522466i	$0.174988\pi$
$570$	−0.117741	+	0.0672831i	−0.00493164	+	0.00281818i
$571$	1.97337	−	1.70994i	0.0825830	−	0.0715586i	−0.612591	−	0.790400i	$-0.709873\pi$
$571$	1.97337	−	1.70994i	0.0825830	−	0.0715586i	0.695174	+	0.718841i	$0.255327\pi$
$572$	6.41961	−	3.50537i	0.268417	−	0.146567i
$573$	1.22689	−	0.457605i	0.0512540	−	0.0191167i
$574$	−28.5278			−1.19073
$575$	14.2353	+	19.2965i	0.593652	+	0.804722i
$576$	24.8162			1.03401
$577$	−17.0326	+	6.35284i	−0.709077	+	0.264472i	−0.678018	−	0.735046i	$-0.737161\pi$
$577$	−17.0326	+	6.35284i	−0.709077	+	0.264472i	−0.0310591	+	0.999518i	$0.509888\pi$
$578$	−17.0483	+	9.30910i	−0.709118	+	0.387208i
$579$	5.56812	−	4.82480i	0.231403	−	0.200512i
$580$	9.04574	−	5.16918i	0.375604	−	0.214639i
$581$	−7.58705	+	8.75592i	−0.314764	+	0.363257i
$582$	0.992227	+	1.32546i	0.0411291	+	0.0549421i
$583$	9.69967	−	17.7636i	0.401719	−	0.735694i
$584$	−6.28764	+	9.78376i	−0.260184	+	0.404855i
$585$	8.66123	−	10.3956i	0.358098	−	0.429807i
$586$	−20.3379	+	9.28803i	−0.840153	+	0.383685i
$587$	−16.0464	+	43.0221i	−0.662306	+	1.77571i	−0.0318404	+	0.999493i	$0.510137\pi$
$587$	−16.0464	+	43.0221i	−0.662306	+	1.77571i	−0.630465	+	0.776217i	$0.717136\pi$
$588$	0.604604	+	0.452601i	0.0249335	+	0.0186649i
$589$	1.09649	+	0.704670i	0.0451800	+	0.0290354i
$590$	−12.9983	+	21.1137i	−0.535132	+	0.869237i
$591$	0.490035	−	3.40827i	0.0201574	−	0.140198i
$592$	−1.23635	−	17.2864i	−0.0508136	−	0.710467i
$593$	7.38140	−	33.9317i	0.303118	−	1.39341i	−0.533583	−	0.845748i	$-0.679155\pi$
$593$	7.38140	−	33.9317i	0.303118	−	1.39341i	0.836700	−	0.547661i	$-0.184482\pi$
$594$	−6.55491	−	7.56476i	−0.268951	−	0.310386i
$595$	−0.0246198	+	0.0701258i	−0.00100931	+	0.00287488i
$596$	4.46090	+	2.03722i	0.182726	+	0.0834480i
$597$	2.43560	−	2.43560i	0.0996825	−	0.0996825i
$598$	7.22681	−	8.78600i	0.295526	−	0.359286i
$599$		−	0.783929i		−	0.0320305i	−0.999872	−	0.0160152i	$-0.994902\pi$
$599$		−	0.783929i		−	0.0320305i	0.999872	−	0.0160152i	$-0.00509802\pi$
$600$	3.87160	+	2.28132i	0.158057	+	0.0931343i
$601$	−31.7856	−	9.33311i	−1.29656	−	0.380705i	−0.440582	−	0.897712i	$-0.645228\pi$
$601$	−31.7856	−	9.33311i	−1.29656	−	0.380705i	−0.855981	+	0.517007i	$0.827046\pi$
$602$	1.41182	−	19.7398i	0.0575415	−	0.804535i
$603$	−25.2856	−	5.50055i	−1.02971	−	0.224000i
$604$	−3.72115	−	3.22439i	−0.151411	−	0.131199i
$605$	−6.38139	+	32.3370i	−0.259440	+	1.31469i
$606$	5.92026	−	1.73835i	0.240494	−	0.0706155i
$607$	3.57556	+	16.4366i	0.145128	+	0.667141i	0.991012	+	0.133775i	$0.0427098\pi$
$607$	3.57556	+	16.4366i	0.145128	+	0.667141i	−0.845884	+	0.533367i	$0.820927\pi$
$608$	−0.405858	+	0.542163i	−0.0164597	+	0.0219876i
$609$	2.66475	+	5.83499i	0.107981	+	0.236446i
$610$	21.5217	+	9.32935i	0.871388	+	0.377734i
$611$	−2.08338	−	14.4902i	−0.0842845	−	0.586211i
$612$	0.0200732	−	0.00436665i	0.000811410	−	0.000176511i
$613$	36.0867	+	19.7048i	1.45753	+	0.795871i	0.995835	−	0.0911693i	$-0.0290604\pi$
$613$	36.0867	+	19.7048i	1.45753	+	0.795871i	0.461693	+	0.887040i	$0.347242\pi$
$614$	12.7721	+	1.83634i	0.515438	+	0.0741088i
$615$	0.0963506	+	4.97545i	0.00388523	+	0.200629i
$616$	43.0340	−	27.6563i	1.73389	−	1.11430i
$617$	−3.70694	−	0.265125i	−0.149236	−	0.0106735i	−0.00347857	−	0.999994i	$-0.501107\pi$
$617$	−3.70694	−	0.265125i	−0.149236	−	0.0106735i	−0.145757	+	0.989320i	$0.546562\pi$
$618$	1.76817	+	3.23815i	0.0711261	+	0.130258i
$619$	−14.4653	+	31.6746i	−0.581409	+	1.27311i	0.359087	+	0.933304i	$0.383088\pi$
$619$	−14.4653	+	31.6746i	−0.581409	+	1.27311i	−0.940496	+	0.339804i	$0.889639\pi$
$620$	0.578990	−	11.1165i	0.0232528	−	0.446447i
$621$	7.36735	+	3.78075i	0.295642	+	0.151716i
$622$	16.8742	+	16.8742i	0.676593	+	0.676593i
$623$	1.92653	+	5.16523i	0.0771849	+	0.206941i
$624$	0.363498	−	1.23796i	0.0145516	−	0.0495581i
$625$	−12.1138	−	21.8691i	−0.484551	−	0.874763i
$626$	9.58243	+	14.9105i	0.382991	+	0.595945i
$627$	0.268600	−	0.0192107i	0.0107269	−	0.000767199i
$628$	−0.848928	+	0.635499i	−0.0338759	+	0.0253592i
$629$	−0.0232764	−	0.0792720i	−0.000928090	−	0.00316078i
$630$	14.2352	−	19.8040i	0.567145	−	0.789011i
$631$	−27.1783	+	3.90765i	−1.08195	+	0.155561i	−0.660155	−	0.751130i	$-0.729509\pi$
$631$	−27.1783	+	3.90765i	−1.08195	+	0.155561i	−0.421796	+	0.906691i	$0.638600\pi$
$632$	−0.924546	−	0.344838i	−0.0367765	−	0.0137169i
$633$	−2.44302	−	0.911198i	−0.0971012	−	0.0362169i
$634$	26.0594	−	3.74677i	1.03495	−	0.148803i
$635$	−0.616514	−	3.76845i	−0.0244656	−	0.149546i
$636$	0.227836	+	0.775939i	0.00903429	+	0.0307680i
$637$	−6.19170	+	4.63505i	−0.245324	+	0.183647i
$638$	38.7967	−	2.77479i	1.53597	−	0.109855i
$639$	17.0286	+	26.4971i	0.673642	+	1.04821i
$640$	−5.05590	−	0.627274i	−0.199852	−	0.0247952i
$641$	5.48637	−	18.6849i	0.216699	−	0.738008i	−0.777350	−	0.629069i	$-0.783436\pi$
$641$	5.48637	−	18.6849i	0.216699	−	0.738008i	0.994048	−	0.108939i	$-0.0347454\pi$
$642$	−1.92718	−	5.16696i	−0.0760595	−	0.203923i
$643$	−1.22544	−	1.22544i	−0.0483265	−	0.0483265i	0.682531	−	0.730857i	$-0.260879\pi$
$643$	−1.22544	−	1.22544i	−0.0483265	−	0.0483265i	−0.730857	+	0.682531i	$0.760879\pi$
$644$	−6.31003	+	8.89628i	−0.248650	+	0.350563i
$645$	−3.44754	−	0.179562i	−0.135747	−	0.00707023i
$646$	0.000875872	−	0.00191789i	3.44607e−5	−	7.54585e-5i
$647$	1.41599	+	2.59319i	0.0556682	+	0.101949i	0.904032	−	0.427466i	$-0.140594\pi$
$647$	1.41599	+	2.59319i	0.0556682	+	0.101949i	−0.848363	+	0.529414i	$0.822412\pi$
$648$	−25.3047	−	1.80983i	−0.994062	−	0.0710968i
$649$	41.4187	−	26.6182i	1.62583	−	1.04486i
$650$	−8.65623	+	8.10827i	−0.339525	+	0.318033i
$651$	6.78389	+	0.975376i	0.265882	+	0.0382280i
$652$	−2.47700	−	1.35254i	−0.0970066	−	0.0529696i
$653$	19.4496	−	4.23101i	0.761123	−	0.165572i	0.184780	−	0.982780i	$-0.440843\pi$
$653$	19.4496	−	4.23101i	0.761123	−	0.165572i	0.576343	+	0.817208i	$0.304479\pi$
$654$	0.349928	+	2.43381i	0.0136833	+	0.0951693i
$655$	−10.4629	−	26.4748i	−0.408818	−	1.03446i
$656$	−6.74214	−	14.7632i	−0.263236	−	0.576407i
$657$	6.59851	−	8.81458i	0.257432	−	0.343889i
$658$	−5.60897	−	25.7840i	−0.218660	−	1.00517i
$659$	−12.0052	+	3.52504i	−0.467656	+	0.137316i	−0.507066	−	0.861907i	$-0.669270\pi$
$659$	−12.0052	+	3.52504i	−0.467656	+	0.137316i	0.0394107	+	0.999223i	$0.487452\pi$
$660$	−1.28060	−	1.91028i	−0.0498471	−	0.0743577i
$661$	−5.99322	−	5.19315i	−0.233109	−	0.201990i	0.530471	−	0.847703i	$-0.322015\pi$
$661$	−5.99322	−	5.19315i	−0.233109	−	0.201990i	−0.763581	+	0.645713i	$0.776560\pi$
$662$	−7.70363	−	1.67582i	−0.299410	−	0.0651326i
$663$	0.000438792	−	0.00613512i	1.70413e−5	−	0.000238268i
$664$	−10.4502	−	3.06844i	−0.405545	−	0.119079i
$665$	0.399782	+	1.27003i	0.0155029	+	0.0492496i
$666$			27.1120i			1.05057i
$667$	−28.9174	+	14.1139i	−1.11969	+	0.546494i
$668$	−0.0395258	+	0.0395258i	−0.00152930	+	0.00152930i
$669$	−6.83057	−	3.11942i	−0.264085	−	0.120604i
$670$	21.4020	+	7.51380i	0.826830	+	0.290283i
$671$	−30.5028	−	35.2021i	−1.17755	−	1.35896i
$672$	−0.756978	+	3.47977i	−0.0292011	+	0.134235i
$673$	2.56219	+	35.8241i	0.0987653	+	1.38092i	0.769227	+	0.638975i	$0.220641\pi$
$673$	2.56219	+	35.8241i	0.0987653	+	1.38092i	−0.670462	+	0.741944i	$0.733904\pi$
$674$	−1.24790	+	8.67933i	−0.0480673	+	0.334315i
$675$	−7.10648	−	4.90231i	−0.273528	−	0.188690i
$676$	5.07663	+	3.26255i	0.195255	+	0.125483i
$677$	37.5834	+	28.1346i	1.44445	+	1.08130i	0.980741	+	0.195313i	$0.0625722\pi$
$677$	37.5834	+	28.1346i	1.44445	+	1.08130i	0.463708	+	0.885988i	$0.346519\pi$
$678$	0.0483421	−	0.129610i	0.00185657	−	0.00497765i
$679$	14.7872	−	6.75311i	0.567482	−	0.259160i
$680$	−0.0695799	+	0.00633265i	−0.00266827	+	0.000242846i
$681$	−2.02233	+	3.14680i	−0.0774957	+	0.120586i
$682$	19.9164	−	36.4742i	0.762639	−	1.39667i
$683$	11.9715	+	15.9920i	0.458076	+	0.611918i	0.968805	−	0.247824i	$-0.0797155\pi$
$683$	11.9715	+	15.9920i	0.458076	+	0.611918i	−0.510729	+	0.859742i	$0.670625\pi$
$684$	0.241000	−	0.278129i	0.00921488	−	0.0106345i
$685$	−7.74706	+	28.4076i	−0.296000	+	1.08540i
$686$	9.26035	−	8.02414i	0.353562	−	0.306363i
$687$	−6.22367	+	3.39838i	−0.237448	+	0.129656i
$688$	10.5491	−	3.93461i	0.402181	−	0.150006i
$689$	−8.28180			−0.315512
$690$	−2.95713	−	2.01255i	−0.112576	−	0.0766165i
$691$	−20.9055			−0.795281			−0.397641	−	0.917541i	$-0.630171\pi$
$691$	−20.9055			−0.795281			−0.397641	+	0.917541i	$0.630171\pi$
$692$	−4.44343	+	1.65731i	−0.168914	+	0.0630016i
$693$	−42.5069	+	23.2105i	−1.61470	+	0.881694i
$694$	14.5594	−	12.6158i	0.552669	−	0.478890i
$695$	−0.982599	−	1.71949i	−0.0372721	−	0.0652238i
$696$	−3.94894	+	4.55732i	−0.149684	+	0.172745i
$697$	−0.0463670	−	0.0619391i	−0.00175628	−	0.00234611i
$698$	−7.77047	+	14.2306i	−0.294117	+	0.538634i
$699$	2.96108	−	4.60754i	0.111998	−	0.174273i
$700$	7.72334	−	8.34594i	0.291915	−	0.315447i
$701$	−19.2641	+	8.79763i	−0.727596	+	0.332282i	−0.744543	−	0.667575i	$-0.767333\pi$
$701$	−19.2641	+	8.79763i	−0.727596	+	0.332282i	0.0169472	+	0.999856i	$0.494605\pi$
$702$	−1.43136	+	3.83763i	−0.0540233	+	0.144842i
$703$	−1.18488	−	0.886990i	−0.0446886	−	0.0334535i
$704$	36.3383	+	23.3532i	1.36955	+	0.880156i
$705$	−4.47797	+	1.06533i	−0.168650	+	0.0401226i
$706$	0.0826500	−	0.574844i	0.00311057	−	0.0216345i
$707$	−4.32181	−	60.4268i	−0.162538	−	2.27258i
$708$	−0.418170	+	1.92230i	−0.0157158	+	0.0722443i
$709$	−0.798970	−	0.922061i	−0.0300060	−	0.0346287i	0.740548	−	0.672003i	$-0.234566\pi$
$709$	−0.798970	−	0.922061i	−0.0300060	−	0.0346287i	−0.770554	+	0.637374i	$0.780020\pi$
$710$	−11.9533	−	24.8872i	−0.448599	−	0.934002i
$711$	0.849800	+	0.388091i	0.0318700	+	0.0145545i
$712$	−3.66451	+	3.66451i	−0.137333	+	0.137333i
$713$	−4.01786	+	34.1444i	−0.150470	+	1.27872i
$714$		−	0.0110867i		−	0.000414910i
$715$	22.4654	−	7.07169i	0.840158	−	0.264466i
$716$	−4.68761	−	1.37641i	−0.175184	−	0.0514387i
$717$	−0.0364293	+	0.509348i	−0.00136048	+	0.0190220i
$718$	1.50248	+	0.326844i	0.0560719	+	0.0121977i
$719$	0.924542	+	0.801120i	0.0344796	+	0.0298767i	0.671930	−	0.740615i	$-0.265466\pi$
$719$	0.924542	+	0.801120i	0.0344796	+	0.0298767i	−0.637451	+	0.770491i	$0.720011\pi$
$720$	13.6130	+	2.68638i	0.507325	+	0.100116i
$721$	34.7570	−	10.2056i	1.29442	−	0.380076i
$722$	4.60670	+	21.1767i	0.171444	+	0.788114i
$723$	0.352222	−	0.470513i	0.0130993	−	0.0174986i
$724$	−5.23426	−	11.4614i	−0.194530	−	0.425961i
$725$	31.7988	−	10.6906i	1.18098	−	0.397040i
$726$	−0.699732	−	4.86674i	−0.0259695	−	0.180622i
$727$	41.1203	−	8.94517i	1.52507	−	0.331758i	0.629612	−	0.776910i	$-0.283214\pi$
$727$	41.1203	−	8.94517i	1.52507	−	0.331758i	0.895455	+	0.445152i	$0.146850\pi$
$728$	−18.3717	−	10.0317i	−0.680901	−	0.371800i
$729$	22.2774	+	3.20300i	0.825087	+	0.118630i
$730$	−6.69126	+	6.95554i	−0.247655	+	0.257436i
$731$	0.0451535	−	0.0290184i	0.00167006	−	0.00107328i
$732$	1.85641	+	0.132773i	0.0686148	+	0.00490742i
$733$	−20.7449	−	37.9914i	−0.766229	−	1.40324i	−0.910417	−	0.413693i	$-0.864239\pi$
$733$	−20.7449	−	37.9914i	−0.766229	−	1.40324i	0.144188	−	0.989550i	$-0.453943\pi$
$734$	11.1330	−	24.3778i	0.410926	−	0.899802i
$735$	1.62784	+	1.80672i	0.0600437	+	0.0666420i
$736$	−17.5473	−	3.34802i	−0.646802	−	0.123410i
$737$	−31.8494	−	31.8494i	−1.17319	−	1.17319i
$738$	8.87293	+	23.7892i	0.326617	+	0.875694i
$739$	4.63699	−	15.7921i	0.170575	−	0.580924i	−0.829185	−	0.558975i	$-0.811195\pi$
$739$	4.63699	−	15.7921i	0.170575	−	0.580924i	0.999759	−	0.0219486i	$-0.00698702\pi$
$740$	−1.55636	+	12.5444i	−0.0572128	+	0.461142i
$741$	−0.0595734	−	0.0926979i	−0.00218848	−	0.00340534i
$742$	−14.8898	+	1.06494i	−0.546622	+	0.0390952i
$743$	6.66520	−	4.98950i	0.244522	−	0.183047i	−0.469986	−	0.882674i	$-0.655741\pi$
$743$	6.66520	−	4.98950i	0.244522	−	0.183047i	0.714509	+	0.699627i	$0.246650\pi$
$744$	1.81517	+	6.18189i	0.0665472	+	0.226639i
$745$	12.8223	+	9.21676i	0.469774	+	0.337676i
$746$	23.7481	−	3.41446i	0.869479	−	0.125012i
$747$	9.66132	+	3.60349i	0.353489	+	0.131845i
$748$	0.0335023	+	0.0124957i	0.00122497	+	0.000456889i
$749$	−53.5937	+	7.70562i	−1.95827	+	0.281557i
$750$	2.78565	+	2.47946i	0.101718	+	0.0905372i
$751$	8.38304	+	28.5500i	0.305901	+	1.04180i	0.958735	+	0.284303i	$0.0917621\pi$
$751$	8.38304	+	28.5500i	0.305901	+	1.04180i	−0.652833	+	0.757502i	$0.726420\pi$
$752$	12.0177	−	8.99635i	0.438241	−	0.328063i
$753$	6.99763	−	0.500481i	0.255008	−	0.0182385i
$754$	−8.60479	−	13.3893i	−0.313368	−	0.487610i
$755$	−9.74530	−	12.5060i	−0.354668	−	0.455138i
$756$	1.10633	−	3.76780i	0.0402367	−	0.137034i
$757$	16.0823	+	43.1184i	0.584522	+	1.56716i	0.805948	+	0.591987i	$0.201656\pi$
$757$	16.0823	+	43.1184i	0.584522	+	1.56716i	−0.221426	+	0.975177i	$0.571071\pi$
$758$	4.78983	+	4.78983i	0.173975	+	0.173975i
$759$	3.56298	+	6.14475i	0.129328	+	0.223040i
$760$	−0.929896	+	0.837826i	−0.0337309	+	0.0303911i
$761$	−4.41186	+	9.66062i	−0.159930	+	0.350197i	−0.972585	−	0.232547i	$-0.925294\pi$
$761$	−4.41186	+	9.66062i	−0.159930	+	0.350197i	0.812655	+	0.582745i	$0.198021\pi$
$762$	0.272989	+	0.499942i	0.00988934	+	0.0181110i
$763$	24.0802	+	1.72225i	0.871761	+	0.0623496i
$764$	2.62043	−	1.68405i	0.0948038	−	0.0609267i
$765$	0.0661351	−	0.00128072i	0.00239112	−	4.63045e-5i
$766$	−10.0365	−	1.44302i	−0.362632	−	0.0521386i
$767$	−17.6821	−	9.65518i	−0.638465	−	0.348628i
$768$	−4.11463	+	0.895083i	−0.148474	+	0.0322985i
$769$	6.84136	+	47.5827i	0.246706	+	1.71588i	0.617001	+	0.786962i	$0.288347\pi$
$769$	6.84136	+	47.5827i	0.246706	+	1.71588i	−0.370296	+	0.928914i	$0.620744\pi$
$770$	39.4811	−	15.6030i	1.42280	−	0.562292i
$771$	−2.21365	−	4.84723i	−0.0797228	−	0.174569i
$772$	10.5031	−	14.0304i	0.378013	−	0.504966i
$773$	−3.85314	−	17.7126i	−0.138588	−	0.637078i	−0.993063	−	0.117586i	$-0.962485\pi$
$773$	−3.85314	−	17.7126i	−0.138588	−	0.637078i	0.854475	−	0.519493i	$-0.173879\pi$
$774$	−16.9001	+	4.96232i	−0.607462	+	0.178367i
$775$	8.75924	−	34.7569i	0.314641	−	1.24850i
$776$	11.5493	+	10.0076i	0.414597	+	0.359250i
$777$	−7.60493	−	1.65435i	−0.272825	−	0.0593495i
$778$	−1.85680	+	25.9615i	−0.0665697	+	0.930766i
$779$	−1.32995	−	0.390508i	−0.0476504	−	0.0139914i
$780$	−0.434929	+	0.834532i	−0.0155730	+	0.0298810i
$781$			54.8243i			1.96177i
$782$	0.0555961	−	0.00142723i	0.00198811	−	5.10377e-5i
$783$	8.19197	−	8.19197i	0.292757	−	0.292757i
$784$	−7.21460	−	3.29480i	−0.257664	−	0.117671i
$785$	−3.07802	+	1.47836i	−0.109859	+	0.0527650i
$786$	2.78087	+	3.20930i	0.0991904	+	0.114472i
$787$	−3.68856	+	16.9560i	−0.131483	+	0.604417i	0.863498	+	0.504352i	$0.168269\pi$
$787$	−3.68856	+	16.9560i	−0.131483	+	0.604417i	−0.994981	+	0.100065i	$0.968095\pi$
$788$	−0.584336	−	8.17008i	−0.0208161	−	0.291047i
$789$	−0.0457065	+	0.317896i	−0.00162720	+	0.0113174i
$790$	−0.697345	−	0.429309i	−0.0248104	−	0.0152741i
$791$	−1.14258	−	0.734295i	−0.0406256	−	0.0261085i
$792$	−36.4472	−	27.2841i	−1.29510	−	0.969497i
$793$	−6.66074	+	17.8581i	−0.236530	+	0.634161i
$794$	29.2759	−	13.3699i	1.03896	−	0.474478i
$795$	0.236023	+	2.59329i	0.00837086	+	0.0919747i
$796$	4.42983	−	6.89295i	0.157011	−	0.244314i
$797$	8.05695	−	14.7552i	0.285392	−	0.522656i	−0.695175	−	0.718840i	$-0.744673\pi$
$797$	8.05695	−	14.7552i	0.285392	−	0.522656i	0.980567	+	0.196184i	$0.0628551\pi$
$798$	−0.119027	−	0.159001i	−0.00421349	−	0.00562857i
$799$	0.0468654	−	0.0540856i	0.00165798	−	0.00191341i
$800$	17.6890	+	5.82806i	0.625399	+	0.206053i
$801$	3.70807	−	3.21306i	0.131018	−	0.113528i
$802$	−16.2839	+	8.89170i	−0.575006	+	0.313977i
$803$	17.9571	−	6.69765i	0.633692	−	0.236355i
$804$	1.79973			0.0634714
$805$	−25.4800	+	24.1704i	−0.898052	+	0.851893i
$806$	−17.0051			−0.598979
$807$	−4.59280	+	1.71303i	−0.161674	+	0.0603014i
$808$	49.9840	−	27.2933i	1.75843	−	0.960176i
$809$	−32.0557	+	27.7764i	−1.12702	+	0.976567i	−0.999883	−	0.0153188i	$-0.995124\pi$
$809$	−32.0557	+	27.7764i	−1.12702	+	0.976567i	−0.127135	+	0.991885i	$0.540578\pi$
$810$	−20.3119	−	5.53927i	−0.713687	−	0.194630i
$811$	−1.29964	+	1.49986i	−0.0456364	+	0.0526672i	−0.778109	−	0.628129i	$-0.783821\pi$
$811$	−1.29964	+	1.49986i	−0.0456364	+	0.0526672i	0.732472	+	0.680797i	$0.238366\pi$
$812$	9.14449	+	12.2156i	0.320909	+	0.428684i
$813$	−0.775991	+	1.42112i	−0.0272152	+	0.0498409i
$814$	−25.5136	+	39.7000i	−0.894253	+	1.39148i
$815$	−6.98185	−	5.81699i	−0.244563	−	0.203760i
$816$	0.00573742	−	0.00262019i	0.000200850	−	9.17251e-5i
$817$	0.336031	−	0.900934i	0.0117562	−	0.0315197i
$818$	−27.7379	−	20.7643i	−0.969833	−	0.726008i
$819$	16.6717	+	10.7142i	0.582556	+	0.374386i
$820$	2.73979	+	11.5164i	0.0956777	+	0.402169i
$821$	−0.250173	+	1.73999i	−0.00873111	+	0.0607262i	−0.993721	−	0.111885i	$-0.964311\pi$
$821$	−0.250173	+	1.73999i	−0.00873111	+	0.0607262i	0.984990	+	0.172611i	$0.0552203\pi$
$822$	−0.313347	−	4.38117i	−0.0109292	−	0.152811i
$823$	8.34124	−	38.3440i	0.290757	−	1.33659i	−0.567502	−	0.823372i	$-0.692090\pi$
$823$	8.34124	−	38.3440i	0.290757	−	1.33659i	0.858259	−	0.513217i	$-0.171546\pi$
$824$	22.3001	+	25.7357i	0.776861	+	0.896545i
$825$	−2.85461	−	6.83309i	−0.0993848	−	0.237898i
$826$	−33.0322	−	15.0853i	−1.14934	−	0.524885i
$827$	1.49928	−	1.49928i	0.0521350	−	0.0521350i	−0.680559	−	0.732694i	$-0.738263\pi$
$827$	1.49928	−	1.49928i	0.0521350	−	0.0521350i	0.732694	+	0.680559i	$0.238263\pi$
$828$	9.38118	+	2.49493i	0.326019	+	0.0867048i
$829$			50.2498i			1.74525i	0.488393	+	0.872624i	$0.337583\pi$
$829$			50.2498i			1.74525i	−0.488393	+	0.872624i	$0.662417\pi$
$830$	−8.01534	−	4.17732i	−0.278217	−	0.144997i
$831$	−1.67817	−	0.492754i	−0.0582150	−	0.0170935i
$832$	1.26094	−	17.6303i	0.0437153	−	0.611219i
$833$	−0.0369464	−	0.00803719i	−0.00128012	−	0.000278472i
$834$	0.223267	+	0.193462i	0.00773111	+	0.00669904i
$835$	−0.149506	+	0.100224i	−0.00517388	+	0.00346841i
$836$	0.614629	−	0.180471i	0.0212574	−	0.00624173i
$837$	−2.63114	−	12.0951i	−0.0909454	−	0.418069i
$838$	25.4289	−	33.9690i	0.878426	−	1.17344i
$839$	−9.37375	−	20.5256i	−0.323618	−	0.708624i	0.675982	−	0.736918i	$-0.263720\pi$
$839$	−9.37375	−	20.5256i	−0.323618	−	0.708624i	−0.999600	+	0.0282943i	$0.990992\pi$
$840$	−2.61767	+	6.03866i	−0.0903183	+	0.208353i
$841$	2.27963	+	15.8552i	0.0786078	+	0.546729i
$842$	−38.3374	+	8.33978i	−1.32119	+	0.287408i
$843$	5.28866	+	2.88783i	0.182151	+	0.0994621i
$844$	−6.13937	−	0.882709i	−0.211326	−	0.0303841i
$845$	14.0036	+	13.4715i	0.481738	+	0.463435i
$846$	−19.7567	+	12.6968i	−0.679248	+	0.436526i
$847$	−48.1518	−	3.44388i	−1.65451	−	0.118333i
$848$	−4.07011	−	7.45385i	−0.139768	−	0.255966i
$849$	−0.306049	+	0.670154i	−0.0105036	+	0.0229996i
$850$	−0.0576683	−	0.00602354i	−0.00197801	−	0.000206606i
$851$	7.31699	−	38.3490i	0.250823	−	1.31459i
$852$	−1.54899	−	1.54899i	−0.0530675	−	0.0530675i
$853$	−2.41416	−	6.47261i	−0.0826592	−	0.221618i	0.889045	−	0.457821i	$-0.151370\pi$
$853$	−2.41416	−	6.47261i	−0.0826592	−	0.221618i	−0.971704	+	0.236203i	$0.924097\pi$
$854$	−9.67898	+	32.9636i	−0.331208	+	1.12799i
$855$	0.934731	−	0.728391i	0.0319671	−	0.0249105i
$856$	−27.5184	−	42.8195i	−0.940560	−	1.46354i
$857$	−10.8559	+	0.776429i	−0.370831	+	0.0265223i	−0.255511	−	0.966806i	$-0.582244\pi$
$857$	−10.8559	+	0.776429i	−0.370831	+	0.0265223i	−0.115319	+	0.993328i	$0.536789\pi$
$858$	−2.81255	+	2.10545i	−0.0960188	+	0.0718788i
$859$	−14.3091	−	48.7323i	−0.488220	−	1.66272i	−0.723134	−	0.690707i	$-0.757299\pi$
$859$	−14.3091	−	48.7323i	−0.488220	−	1.66272i	0.234915	−	0.972016i	$-0.424519\pi$
$860$	−8.10436	+	1.32586i	−0.276356	+	0.0452116i
$861$	−7.21431	+	1.03726i	−0.245863	+	0.0353498i
$862$	−9.25837	−	3.45319i	−0.315341	−	0.117616i
$863$	−28.2167	−	10.5243i	−0.960508	−	0.358251i	−0.180189	−	0.983632i	$-0.557671\pi$
$863$	−28.2167	−	10.5243i	−0.960508	−	0.358251i	−0.780320	+	0.625381i	$0.784944\pi$
$864$	6.36615	−	0.915314i	0.216581	−	0.0311396i
$865$	−15.0704	+	2.46550i	−0.512408	+	0.0838295i
$866$	5.59630	+	19.0592i	0.190170	+	0.647659i
$867$	−3.97284	+	2.97403i	−0.134925	+	0.101003i
$868$	16.2619	−	1.16307i	0.551965	−	0.0394773i
$869$	0.879148	+	1.36798i	0.0298231	+	0.0464056i
$870$	−3.94739	+	3.07602i	−0.133829	+	0.104287i
$871$	−5.19257	+	17.6843i	−0.175944	+	0.599209i
$872$	7.93100	+	21.2638i	0.268577	+	0.720084i
$873$	−10.2306	−	10.2306i	−0.346255	−	0.346255i
$874$	0.782011	−	0.617345i	0.0264519	−	0.0208820i
$875$	29.6017	−	21.5507i	1.00072	−	0.728547i
$876$	−0.318121	+	0.696588i	−0.0107483	+	0.0235355i
$877$	−16.4780	−	30.1773i	−0.556423	−	1.01901i	−0.992861	−	0.119279i	$-0.961942\pi$
$877$	−16.4780	−	30.1773i	−0.556423	−	1.01901i	0.436437	−	0.899735i	$-0.356240\pi$
$878$	12.5619	+	0.898446i	0.423944	+	0.0303211i
$879$	−4.80550	+	3.08831i	−0.162086	+	0.104166i
$880$	17.4054	+	16.7441i	0.586736	+	0.564443i
$881$	43.4518	+	6.24742i	1.46393	+	0.210481i	0.827765	−	0.561075i	$-0.189612\pi$
$881$	43.4518	+	6.24742i	1.46393	+	0.210481i	0.636162	+	0.771556i	$0.280521\pi$
$882$	10.8901	+	5.94643i	0.366688	+	0.200227i
$883$	−8.00385	+	1.74113i	−0.269351	+	0.0585937i	−0.345212	−	0.938525i	$-0.612193\pi$
$883$	−8.00385	+	1.74113i	−0.269351	+	0.0585937i	0.0758612	+	0.997118i	$0.475829\pi$
$884$	−0.00208227	−	0.0144825i	−7.00345e−5	−	0.000487100i
$885$	−2.51942	+	5.81200i	−0.0846894	+	0.195368i
$886$	10.6909	+	23.4097i	0.359166	+	0.786464i
$887$	22.1398	−	29.5753i	0.743382	−	0.993042i	−0.256269	−	0.966606i	$-0.582493\pi$
$887$	22.1398	−	29.5753i	0.743382	−	0.993042i	0.999651	−	0.0264363i	$-0.00841590\pi$
$888$	−1.55520	−	7.14912i	−0.0521890	−	0.239909i
$889$	5.36616	−	1.57565i	0.179975	−	0.0528455i
$890$	−3.57237	+	2.39481i	−0.119746	+	0.0802740i
$891$	31.5957	+	27.3778i	1.05850	+	0.917192i
$892$	−17.4545	−	3.79700i	−0.584421	−	0.127133i
$893$	0.0914627	−	1.27882i	0.00306068	−	0.0427940i
$894$	−2.26017	−	0.663647i	−0.0755915	−	0.0221957i
$895$	−13.9505	−	7.27051i	−0.466314	−	0.243026i
$896$		−	7.46174i		−	0.249279i
$897$	1.50811	−	2.48463i	0.0503544	−	0.0829595i
$898$	−15.2799	+	15.2799i	−0.509897	+	0.509897i
$899$	43.7524	+	19.9810i	1.45922	+	0.666405i
$900$	−9.36183	−	3.84465i	−0.312061	−	0.128155i
$901$	−0.0265130	−	0.0305977i	−0.000883277	−	0.00101936i
$902$	−9.39418	+	43.1843i	−0.312792	+	1.43788i
$903$	−0.360703	−	5.04329i	−0.0120034	−	0.167830i
$904$	0.181706	−	1.26379i	0.00604345	−	0.0420331i
$905$	−9.39025	−	39.4708i	−0.312143	−	1.31205i
$906$	1.98962	+	1.27865i	0.0661006	+	0.0424803i
$907$	−37.8833	−	28.3591i	−1.25789	−	0.941648i	−0.258193	−	0.966093i	$-0.583127\pi$
$907$	−37.8833	−	28.3591i	−1.25789	−	0.941648i	−0.999701	+	0.0244459i	$0.992218\pi$
$908$	−3.10958	+	8.33711i	−0.103195	+	0.276677i
$909$	−49.0456	+	22.3984i	−1.62674	+	0.742907i
$910$	−13.3461	−	11.1195i	−0.442420	−	0.368607i
$911$	−19.1244	+	29.7581i	−0.633619	+	0.985931i	0.364874	+	0.931057i	$0.381112\pi$
$911$	−19.1244	+	29.7581i	−0.633619	+	0.985931i	−0.998493	+	0.0548738i	$0.982524\pi$
$912$	0.0541533	−	0.0991743i	0.00179319	−	0.00328399i
$913$	10.7560	+	14.3683i	0.355971	+	0.475522i
$914$	−22.3853	+	25.8340i	−0.740441	+	0.854514i
$915$	5.78178	+	1.57675i	0.191140	+	0.0521258i
$916$	−12.7481	+	11.0463i	−0.421209	+	0.364980i
$917$	36.5937	−	19.9817i	1.20843	−	0.659853i
$918$	−0.0187607	+	0.00699737i	−0.000619195	+	0.000230948i
$919$	45.4238			1.49839			0.749196	−	0.662348i	$-0.230440\pi$
$919$	45.4238			1.49839			0.749196	+	0.662348i	$0.230440\pi$
$920$	−30.6187	−	12.3493i	−1.00947	−	0.407146i
$921$	3.29666			0.108629
$922$	−7.69699	+	2.87083i	−0.253487	+	0.0945457i
$923$	19.6897	−	10.7514i	0.648093	−	0.353885i
$924$	2.54562	−	2.20579i	0.0837448	−	0.0725653i
$925$	−12.7370	+	38.6587i	−0.418792	+	1.27109i
$926$	4.18620	−	4.83113i	0.137567	−	0.158761i
$927$	−19.3208	−	25.8096i	−0.634578	−	0.847697i
$928$	−11.9775	+	21.9351i	−0.393180	+	0.720056i
$929$	12.8434	−	19.9847i	0.421377	−	0.655676i	−0.564056	−	0.825736i	$-0.690760\pi$
$929$	12.8434	−	19.9847i	0.421377	−	0.655676i	0.985434	+	0.170061i	$0.0543963\pi$
$930$	0.484628	+	5.32484i	0.0158916	+	0.174608i
$931$	−0.616155	+	0.281389i	−0.0201937	+	0.00922214i
$932$	4.55304	−	12.2072i	0.149140	−	0.399859i
$933$	4.88080	+	3.65372i	0.159790	+	0.119618i
$934$	−15.0121	−	9.64770i	−0.491211	−	0.315682i
$935$	0.0980467	+	0.0603609i	0.00320647	+	0.00197401i
$936$	−2.65131	+	18.4403i	−0.0866607	+	0.602739i
$937$	1.17029	+	16.3627i	0.0382316	+	0.534547i	0.980092	+	0.198543i	$0.0636210\pi$
$937$	1.17029	+	16.3627i	0.0382316	+	0.534547i	−0.941861	+	0.336004i	$0.890924\pi$
$938$	−7.06172	+	32.4622i	−0.230573	+	1.05993i
$939$	2.96542	+	3.42227i	0.0967728	+	0.111682i
$940$	−9.87006	+	4.74057i	−0.321926	+	0.154620i
$941$	−12.7532	−	5.82418i	−0.415741	−	0.189863i	0.196552	−	0.980493i	$-0.437026\pi$
$941$	−12.7532	−	5.82418i	−0.415741	−	0.189863i	−0.612293	+	0.790631i	$0.709753\pi$
$942$	0.360176	−	0.360176i	0.0117352	−	0.0117352i
$943$	−6.13023	−	36.0437i	−0.199628	−	1.17375i
$944$		−	20.6595i		−	0.672409i
$945$	5.84388	−	11.2131i	0.190102	−	0.364763i
$946$	−29.4165	−	8.63747i	−0.956414	−	0.280829i
$947$	−0.268052	+	3.74785i	−0.00871051	+	0.121789i	−0.999947	−	0.0103117i	$-0.996718\pi$
$947$	−0.268052	+	3.74785i	−0.00871051	+	0.121789i	0.991236	+	0.132101i	$0.0421722\pi$
$948$	−0.0634897	−	0.0138113i	−0.00206205	−	0.000448571i
$949$	−5.92689	−	5.13568i	−0.192395	−	0.166711i
$950$	−0.891721	+	0.532737i	−0.0289312	+	0.0172843i
$951$	6.45386	−	1.89502i	0.209281	−	0.0614503i
$952$	−0.0217516	−	0.0999906i	−0.000704974	−	0.00324071i
$953$	13.3156	−	17.7876i	0.431335	−	0.576197i	−0.531236	−	0.847224i	$-0.678272\pi$
$953$	13.3156	−	17.7876i	0.431335	−	0.576197i	0.962572	+	0.271027i	$0.0873633\pi$
$954$	5.51920	+	12.0854i	0.178691	+	0.391278i
$955$	9.32802	−	3.68644i	0.301848	−	0.119290i
$956$	0.172874	+	1.20237i	0.00559115	+	0.0388873i
$957$	9.71030	−	2.11235i	0.313889	−	0.0682824i
$958$	15.0527	+	8.21942i	0.486332	+	0.265557i
$959$	−42.6868	−	6.13743i	−1.37843	−	0.198188i
$960$	−5.55653	+	0.107603i	−0.179336	+	0.00347288i
$961$	17.1537	−	11.0240i	0.553344	−	0.355612i
$962$	19.2613	+	1.37759i	0.621008	+	0.0444154i
$963$	23.0948	+	42.2950i	0.744220	+	1.36294i
$964$	0.580801	−	1.27178i	0.0187063	−	0.0409612i
$965$	41.9268	−	37.7756i	1.34967	−	1.21604i
$966$	2.39193	−	4.66104i	0.0769592	−	0.149966i
$967$	32.1848	+	32.1848i	1.03499	+	1.03499i	0.999365	+	0.0356268i	$0.0113428\pi$
$967$	32.1848	+	32.1848i	1.03499	+	1.03499i	0.0356268	+	0.999365i	$0.488657\pi$
$968$	−15.8592	−	42.5201i	−0.509733	−	1.36665i
$969$	0.000151763	0	0.000516857i	4.87533e−6	0	1.66038e-5i
$970$	7.79535	+	10.0036i	0.250294	+	0.321197i
$971$	−11.4675	−	17.8438i	−0.368010	−	0.572635i	0.607026	−	0.794682i	$-0.292362\pi$
$971$	−11.4675	−	17.8438i	−0.368010	−	0.572635i	−0.975036	+	0.222047i	$0.928726\pi$
$972$	−5.25420	+	0.375788i	−0.168529	+	0.0120534i
$973$	2.32204	−	1.73826i	0.0744411	−	0.0557259i
$974$	3.54546	+	12.0747i	0.113604	+	0.386899i
$975$	−1.89424	+	2.36522i	−0.0606642	+	0.0757476i
$976$	−19.3463	+	2.78157i	−0.619259	+	0.0890360i
$977$	2.76598	+	1.03166i	0.0884915	+	0.0330056i	0.393320	−	0.919402i	$-0.371326\pi$
$977$	2.76598	+	1.03166i	0.0884915	+	0.0330056i	−0.304829	+	0.952407i	$0.598599\pi$
$978$	1.27013	+	0.473735i	0.0406144	+	0.0151484i
$979$	8.45335	−	1.21541i	0.270170	−	0.0388446i
$980$	4.69737	+	3.37649i	0.150052	+	0.107858i
$981$	−6.05342	−	20.6161i	−0.193271	−	0.658220i
$982$	29.6846	−	22.2216i	0.947273	−	0.709120i
$983$	−33.1552	+	2.37131i	−1.05749	+	0.0756329i	−0.589234	−	0.807962i	$-0.700571\pi$
$983$	−33.1552	+	2.37131i	−1.05749	+	0.0756329i	−0.468252	+	0.883595i	$0.655116\pi$
$984$	−3.70429	−	5.76398i	−0.118088	−	0.183749i
$985$	3.24738	−	26.1743i	0.103470	−	0.833982i
$986$	0.0219207	−	0.0746550i	0.000698097	−	0.00237750i
$987$	−2.35594	−	6.31651i	−0.0749903	−	0.201057i
$988$	−0.185347	−	0.185347i	−0.00589667	−	0.00589667i
$989$	25.2439	−	2.45804i	0.802709	−	0.0781611i
$990$	−25.2910	−	28.0703i	−0.803800	−	0.892131i
$991$	1.31650	−	2.88273i	0.0418200	−	0.0915729i	−0.887569	−	0.460675i	$-0.847607\pi$
$991$	1.31650	−	2.88273i	0.0418200	−	0.0915729i	0.929389	+	0.369102i	$0.120335\pi$
$992$	12.7972	+	23.4363i	0.406310	+	0.744102i
$993$	−2.00908	−	0.143692i	−0.0637563	−	0.00455994i
$994$	34.0175	−	21.8617i	1.07897	−	0.693411i
$995$	18.2914	−	19.0138i	0.579876	−	0.602778i
$996$	−0.709855	−	0.102062i	−0.0224926	−	0.00323395i
$997$	22.5931	+	12.3368i	0.715531	+	0.390710i	0.795391	−	0.606097i	$-0.207265\pi$
$997$	22.5931	+	12.3368i	0.715531	+	0.390710i	−0.0798599	+	0.996806i	$0.525447\pi$
$998$	8.70255	−	1.89312i	0.275475	−	0.0599258i
$999$	2.00039	+	13.9130i	0.0632895	+	0.440188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.17.4	✓	200
5.2	odd	4		575.2.r.b.293.4		200
5.3	odd	4	inner	115.2.l.a.63.7	yes	200
5.4	even	2		575.2.r.b.132.7		200
23.19	odd	22	inner	115.2.l.a.42.7	yes	200
115.19	odd	22		575.2.r.b.157.4		200
115.42	even	44		575.2.r.b.318.7		200
115.88	even	44	inner	115.2.l.a.88.4	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.17.4	✓	200	1.1	even	1	trivial
115.2.l.a.42.7	yes	200	23.19	odd	22	inner
115.2.l.a.63.7	yes	200	5.3	odd	4	inner
115.2.l.a.88.4	yes	200	115.88	even	44	inner
575.2.r.b.132.7		200	5.4	even	2
575.2.r.b.157.4		200	115.19	odd	22
575.2.r.b.293.4		200	5.2	odd	4
575.2.r.b.318.7		200	115.42	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07057 + 0.399303i) q^{2} +(-0.256216 + 0.139905i) q^{3} +(-0.524814 + 0.454754i) q^{4} +(-1.94143 + 1.10943i) q^{5} +(0.218434 - 0.252086i) q^{6} +(-1.96263 - 2.62176i) q^{7} +(1.47546 - 2.70211i) q^{8} +(-1.57585 + 2.45207i) q^{9} +O(q^{10})\)	\(q+(-1.07057 + 0.399303i) q^{2} +(-0.256216 + 0.139905i) q^{3} +(-0.524814 + 0.454754i) q^{4} +(-1.94143 + 1.10943i) q^{5} +(0.218434 - 0.252086i) q^{6} +(-1.96263 - 2.62176i) q^{7} +(1.47546 - 2.70211i) q^{8} +(-1.57585 + 2.45207i) q^{9} +(1.63545 - 1.96295i) q^{10} +(-4.61502 + 2.10761i) q^{11} +(0.0708436 - 0.189939i) q^{12} +(1.66196 + 1.24413i) q^{13} +(3.14801 + 2.02311i) q^{14} +(0.342212 - 0.555869i) q^{15} +(-0.302976 + 2.10724i) q^{16} +(0.000724021 + 0.0101231i) q^{17} +(0.707943 - 3.25436i) q^{18} +(0.119065 + 0.137408i) q^{19} +(0.514374 - 1.46512i) q^{20} +(0.869653 + 0.397157i) q^{21} +(4.09915 - 4.09915i) q^{22} +(-1.87965 + 4.41213i) q^{23} +0.898747i q^{24} +(2.53833 - 4.30777i) q^{25} +(-2.27604 - 0.668305i) q^{26} +(0.123179 - 1.72227i) q^{27} +(2.22227 + 0.483425i) q^{28} +(5.07075 + 4.39383i) q^{29} +(-0.144403 + 0.731745i) q^{30} +(6.87834 - 2.01966i) q^{31} +(0.791777 + 3.63974i) q^{32} +(0.887578 - 1.18567i) q^{33} +(-0.00481732 - 0.0105485i) q^{34} +(6.71897 + 2.91258i) q^{35} +(-0.288060 - 2.00350i) q^{36} +(-7.95454 + 1.73040i) q^{37} +(-0.182336 - 0.0995627i) q^{38} +(-0.599880 - 0.0862498i) q^{39} +(0.133288 + 6.88289i) q^{40} +(-6.41335 + 4.12161i) q^{41} +(-1.08961 - 0.0779307i) q^{42} +(-2.53456 - 4.64170i) q^{43} +(1.46358 - 3.20480i) q^{44} +(0.339006 - 6.50882i) q^{45} +(0.250526 - 5.47406i) q^{46} +(-4.98615 - 4.98615i) q^{47} +(-0.217186 - 0.582297i) q^{48} +(-1.04961 + 3.57463i) q^{49} +(-0.997360 + 5.62535i) q^{50} +(-0.00160178 - 0.00249242i) q^{51} +(-1.43799 + 0.102847i) q^{52} +(-3.19353 + 2.39065i) q^{53} +(0.555836 + 1.89300i) q^{54} +(6.62151 - 9.21183i) q^{55} +(-9.98007 + 1.43492i) q^{56} +(-0.0497304 - 0.0185485i) q^{57} +(-7.18308 - 2.67915i) q^{58} +(-9.60547 + 1.38106i) q^{59} +(0.0731861 + 0.447350i) q^{60} +(2.58654 + 8.80896i) q^{61} +(-6.55731 + 4.90874i) q^{62} +(9.52154 - 0.680994i) q^{63} +(-4.60297 - 7.16236i) q^{64} +(-4.60686 - 0.571563i) q^{65} +(-0.476778 + 1.62376i) q^{66} +(3.10249 + 8.31810i) q^{67} +(-0.00498351 - 0.00498351i) q^{68} +(-0.135681 - 1.39343i) q^{69} +(-8.35616 - 0.435223i) q^{70} +(4.48898 - 9.82949i) q^{71} +(4.30065 + 7.87605i) q^{72} +(-3.76794 - 0.269488i) q^{73} +(7.82497 - 5.02880i) q^{74} +(-0.0476836 + 1.45884i) q^{75} +(-0.124974 - 0.0179686i) q^{76} +(14.5832 + 7.96304i) q^{77} +(0.676656 - 0.147198i) q^{78} +(-0.0456137 - 0.317250i) q^{79} +(-1.74963 - 4.42720i) q^{80} +(-3.42314 - 7.49563i) q^{81} +(5.22019 - 6.97336i) q^{82} +(-0.751981 - 3.45680i) q^{83} +(-0.637015 + 0.187044i) q^{84} +(-0.0126366 - 0.0188501i) q^{85} +(4.56688 + 3.95722i) q^{86} +(-1.91392 - 0.416348i) q^{87} +(-1.11430 + 15.5800i) q^{88} +(-1.61512 - 0.474243i) q^{89} +(2.23606 + 7.10354i) q^{90} -6.79903i q^{91} +(-1.01997 - 3.17033i) q^{92} +(-1.47978 + 1.47978i) q^{93} +(7.32904 + 3.34706i) q^{94} +(-0.383602 - 0.134675i) q^{95} +(-0.712082 - 0.821787i) q^{96} +(-1.05513 + 4.85033i) q^{97} +(-0.303681 - 4.24601i) q^{98} +(2.10457 - 14.6376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more