LMFDB - Embedded newform 572.2.bs.a.15.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(15,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 12, 5]))

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

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

chi := DirichletCharacter("572.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bs (of order $60$, degree $16$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$80$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			15.12
Character	$\chi$	$=$	572.15
Dual form			572.2.bs.a.267.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31691 - 0.515500i) q^{2} +(0.427935 + 2.01327i) q^{3} +(1.46852 + 1.35774i) q^{4} +(-0.499033 + 3.15077i) q^{5} +(0.474290 - 2.87191i) q^{6} +(-3.19451 + 2.07454i) q^{7} +(-1.23400 - 2.54504i) q^{8} +(-1.12951 + 0.502889i) q^{9} +O(q^{10})$	\(q+(-1.31691 - 0.515500i) q^{2} +(0.427935 + 2.01327i) q^{3} +(1.46852 + 1.35774i) q^{4} +(-0.499033 + 3.15077i) q^{5} +(0.474290 - 2.87191i) q^{6} +(-3.19451 + 2.07454i) q^{7} +(-1.23400 - 2.54504i) q^{8} +(-1.12951 + 0.502889i) q^{9} +(2.28140 - 3.89204i) q^{10} +(-3.11853 + 1.12905i) q^{11} +(-2.10507 + 3.53756i) q^{12} +(3.55672 + 0.591412i) q^{13} +(5.27632 - 1.08522i) q^{14} +(-6.55692 + 0.343633i) q^{15} +(0.313100 + 3.98773i) q^{16} +(-2.53431 + 0.266367i) q^{17} +(1.74670 - 0.0800002i) q^{18} +(0.206486 - 3.93998i) q^{19} +(-5.01076 + 3.94941i) q^{20} +(-5.54366 - 5.54366i) q^{21} +(4.68886 + 0.120750i) q^{22} +(2.62437 + 4.54555i) q^{23} +(4.59580 - 3.57349i) q^{24} +(-4.92304 - 1.59959i) q^{25} +(-4.37901 - 2.61233i) q^{26} +(2.13362 + 2.93668i) q^{27} +(-7.50788 - 1.29080i) q^{28} +(5.02466 - 5.58045i) q^{29} +(8.81203 + 2.92755i) q^{30} +(-1.25024 - 7.89372i) q^{31} +(1.64335 - 5.41289i) q^{32} +(-3.60761 - 5.79531i) q^{33} +(3.47478 + 0.955656i) q^{34} +(-4.94223 - 11.1004i) q^{35} +(-2.34150 - 0.795072i) q^{36} +(7.50091 - 0.393106i) q^{37} +(-2.30298 + 5.08217i) q^{38} +(0.331367 + 7.41373i) q^{39} +(8.63465 - 2.61799i) q^{40} +(-2.82108 + 4.34409i) q^{41} +(4.44276 + 10.1583i) q^{42} +(-1.20439 + 2.08607i) q^{43} +(-6.11258 - 2.57612i) q^{44} +(-1.02083 - 3.80978i) q^{45} +(-1.11284 - 7.33895i) q^{46} +(2.48365 + 4.87443i) q^{47} +(-7.89440 + 2.33684i) q^{48} +(3.05402 - 6.85945i) q^{49} +(5.65862 + 4.64435i) q^{50} +(-1.62079 - 4.98828i) q^{51} +(4.42013 + 5.69759i) q^{52} +(-10.5114 - 7.63699i) q^{53} +(-1.29594 - 4.96723i) q^{54} +(-2.00111 - 10.3892i) q^{55} +(9.22181 + 5.57019i) q^{56} +(8.02063 - 1.27034i) q^{57} +(-9.49377 + 4.75876i) q^{58} +(-9.26691 + 6.01800i) q^{59} +(-10.0955 - 8.39794i) q^{60} +(0.626157 + 5.95748i) q^{61} +(-2.42275 + 11.0398i) q^{62} +(2.56496 - 3.94969i) q^{63} +(-4.95449 + 6.28116i) q^{64} +(-3.63832 + 10.9113i) q^{65} +(1.76342 + 9.49164i) q^{66} +(-1.33576 + 4.98511i) q^{67} +(-4.08334 - 3.04977i) q^{68} +(-8.02837 + 7.22878i) q^{69} +(0.786215 + 17.1660i) q^{70} +(0.0737360 - 0.0910564i) q^{71} +(2.67369 + 2.25408i) q^{72} +(-2.27999 + 4.47474i) q^{73} +(-10.0807 - 3.34903i) q^{74} +(1.11368 - 10.5959i) q^{75} +(5.65269 - 5.50559i) q^{76} +(7.61994 - 10.0763i) q^{77} +(3.38540 - 9.93406i) q^{78} +(-3.65141 + 5.02574i) q^{79} +(-12.7207 - 1.00350i) q^{80} +(-7.48122 + 8.30874i) q^{81} +(5.95450 - 4.26652i) q^{82} +(-2.92787 - 0.463729i) q^{83} +(-0.614140 - 15.6678i) q^{84} +(0.425444 - 8.11796i) q^{85} +(2.66144 - 2.12630i) q^{86} +(13.3852 + 7.72795i) q^{87} +(6.72174 + 6.54356i) q^{88} +(-3.71455 + 13.8629i) q^{89} +(-0.619600 + 5.54338i) q^{90} +(-12.5889 + 5.48927i) q^{91} +(-2.31771 + 10.2384i) q^{92} +(15.3572 - 5.89507i) q^{93} +(-0.757977 - 7.69952i) q^{94} +(12.3109 + 2.61677i) q^{95} +(11.6009 + 0.992146i) q^{96} +(5.22038 - 13.5996i) q^{97} +(-7.55793 + 7.45895i) q^{98} +(2.95462 - 2.84354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.31691	−	0.515500i	−0.931198	−	0.364514i
$2$	−1.31691	−	0.515500i	−0.931198	−	0.364514i
$3$	0.427935	+	2.01327i	0.247068	+	1.16236i	0.910300	+	0.413950i	$0.135851\pi$
$3$	0.427935	+	2.01327i	0.247068	+	1.16236i	−0.663231	+	0.748414i	$0.730816\pi$
$4$	1.46852	+	1.35774i	0.734260	+	0.678869i
$5$	−0.499033	+	3.15077i	−0.223174	+	1.40907i	0.580627	+	0.814170i	$0.302807\pi$
$5$	−0.499033	+	3.15077i	−0.223174	+	1.40907i	−0.803801	+	0.594898i	$0.797193\pi$
$6$	0.474290	−	2.87191i	0.193628	−	1.17245i
$7$	−3.19451	+	2.07454i	−1.20741	+	0.784102i	−0.981763	−	0.190107i	$-0.939116\pi$
$7$	−3.19451	+	2.07454i	−1.20741	+	0.784102i	−0.225648	+	0.974209i	$0.572450\pi$
$8$	−1.23400	−	2.54504i	−0.436285	−	0.899809i
$9$	−1.12951	+	0.502889i	−0.376503	+	0.167630i
$10$	2.28140	−	3.89204i	0.721444	−	1.23077i
$11$	−3.11853	+	1.12905i	−0.940273	+	0.340420i
$11$	−3.11853	+	1.12905i	−0.940273	+	0.340420i
$12$	−2.10507	+	3.53756i	−0.607680	+	1.02120i
$13$	3.55672	+	0.591412i	0.986456	+	0.164028i
$13$	3.55672	+	0.591412i	0.986456	+	0.164028i
$14$	5.27632	−	1.08522i	1.41015	−	0.290037i
$15$	−6.55692	+	0.343633i	−1.69299	+	0.0887258i
$16$	0.313100	+	3.98773i	0.0782749	+	0.996932i
$17$	−2.53431	+	0.266367i	−0.614661	+	0.0646035i	−0.406743	−	0.913543i	$-0.633335\pi$
$17$	−2.53431	+	0.266367i	−0.614661	+	0.0646035i	−0.207918	+	0.978146i	$0.566669\pi$
$18$	1.74670	−	0.0800002i	0.411702	−	0.0188562i
$19$	0.206486	−	3.93998i	0.0473711	−	0.903894i	−0.866823	−	0.498616i	$-0.833842\pi$
$19$	0.206486	−	3.93998i	0.0473711	−	0.903894i	0.914194	−	0.405277i	$-0.132825\pi$
$20$	−5.01076	+	3.94941i	−1.12044	+	0.883115i
$21$	−5.54366	−	5.54366i	−1.20972	−	1.20972i
$22$	4.68886	+	0.120750i	0.999669	+	0.0257439i
$23$	2.62437	+	4.54555i	0.547219	+	0.947812i	0.998464	+	0.0554113i	$0.0176470\pi$
$23$	2.62437	+	4.54555i	0.547219	+	0.947812i	−0.451244	+	0.892400i	$0.649020\pi$
$24$	4.59580	−	3.57349i	0.938114	−	0.729436i
$25$	−4.92304	−	1.59959i	−0.984607	−	0.319918i
$26$	−4.37901	−	2.61233i	−0.858795	−	0.512319i
$27$	2.13362	+	2.93668i	0.410615	+	0.565164i
$28$	−7.50788	−	1.29080i	−1.41886	−	0.243939i
$29$	5.02466	−	5.58045i	0.933057	−	1.03626i	−0.0662037	−	0.997806i	$-0.521089\pi$
$29$	5.02466	−	5.58045i	0.933057	−	1.03626i	0.999260	−	0.0384582i	$-0.0122446\pi$
$30$	8.81203	+	2.92755i	1.60885	+	0.534496i
$31$	−1.25024	−	7.89372i	−0.224550	−	1.41775i	−0.800041	−	0.599945i	$-0.795189\pi$
$31$	−1.25024	−	7.89372i	−0.224550	−	1.41775i	0.575491	−	0.817808i	$-0.304811\pi$
$32$	1.64335	−	5.41289i	0.290506	−	0.956873i
$33$	−3.60761	−	5.79531i	−0.628004	−	1.00883i
$34$	3.47478	+	0.955656i	0.595920	+	0.163894i
$35$	−4.94223	−	11.1004i	−0.835389	−	1.87631i
$36$	−2.34150	−	0.795072i	−0.390249	−	0.132512i
$37$	7.50091	−	0.393106i	1.23314	−	0.0646262i	0.575402	−	0.817871i	$-0.304846\pi$
$37$	7.50091	−	0.393106i	1.23314	−	0.0646262i	0.657740	+	0.753245i	$0.271512\pi$
$38$	−2.30298	+	5.08217i	−0.373593	+	0.824437i
$39$	0.331367	+	7.41373i	0.0530612	+	1.18715i
$40$	8.63465	−	2.61799i	1.36526	−	0.413940i
$41$	−2.82108	+	4.34409i	−0.440579	+	0.678433i	−0.987297	−	0.158884i	$-0.949210\pi$
$41$	−2.82108	+	4.34409i	−0.440579	+	0.678433i	0.546718	+	0.837317i	$0.315877\pi$
$42$	4.44276	+	10.1583i	0.685532	+	1.56745i
$43$	−1.20439	+	2.08607i	−0.183668	+	0.318122i	−0.943127	−	0.332433i	$-0.892130\pi$
$43$	−1.20439	+	2.08607i	−0.183668	+	0.318122i	0.759459	+	0.650555i	$0.225464\pi$
$44$	−6.11258	−	2.57612i	−0.921505	−	0.388365i
$45$	−1.02083	−	3.80978i	−0.152176	−	0.567928i
$46$	−1.11284	−	7.33895i	−0.164079	−	1.08207i
$47$	2.48365	+	4.87443i	0.362277	+	0.711008i	0.998151	−	0.0607845i	$-0.0193602\pi$
$47$	2.48365	+	4.87443i	0.362277	+	0.711008i	−0.635874	+	0.771793i	$0.719360\pi$
$48$	−7.89440	+	2.33684i	−1.13946	+	0.337294i
$49$	3.05402	−	6.85945i	0.436289	−	0.979921i
$50$	5.65862	+	4.64435i	0.800250	+	0.656810i
$51$	−1.62079	−	4.98828i	−0.226956	−	0.698499i
$52$	4.42013	+	5.69759i	0.612961	+	0.790113i
$53$	−10.5114	−	7.63699i	−1.44385	−	1.04902i	−0.987220	−	0.159366i	$-0.949055\pi$
$53$	−10.5114	−	7.63699i	−1.44385	−	1.04902i	−0.456634	−	0.889655i	$-0.650945\pi$
$54$	−1.29594	−	4.96723i	−0.176355	−	0.675954i
$55$	−2.00111	−	10.3892i	−0.269830	−	1.40088i
$56$	9.22181	+	5.57019i	1.23232	+	0.744347i
$57$	8.02063	−	1.27034i	1.06236	−	0.168261i
$58$	−9.49377	+	4.75876i	−1.24659	+	0.624856i
$59$	−9.26691	+	6.01800i	−1.20645	+	0.783477i	−0.981606	−	0.190917i	$-0.938854\pi$
$59$	−9.26691	+	6.01800i	−1.20645	+	0.783477i	−0.224843	+	0.974395i	$0.572187\pi$
$60$	−10.0955	−	8.39794i	−1.30333	−	1.08417i
$61$	0.626157	+	5.95748i	0.0801711	+	0.762777i	0.958572	+	0.284852i	$0.0919444\pi$
$61$	0.626157	+	5.95748i	0.0801711	+	0.762777i	−0.878400	+	0.477925i	$0.841389\pi$
$62$	−2.42275	+	11.0398i	−0.307690	+	1.40206i
$63$	2.56496	−	3.94969i	0.323155	−	0.497614i
$64$	−4.95449	+	6.28116i	−0.619312	+	0.785145i
$65$	−3.63832	+	10.9113i	−0.451278	+	1.35338i
$66$	1.76342	+	9.49164i	0.217062	+	1.16834i
$67$	−1.33576	+	4.98511i	−0.163189	+	0.609028i	0.835076	+	0.550135i	$0.185424\pi$
$67$	−1.33576	+	4.98511i	−0.163189	+	0.609028i	−0.998264	+	0.0588929i	$0.981243\pi$
$68$	−4.08334	−	3.04977i	−0.495178	−	0.369838i
$69$	−8.02837	+	7.22878i	−0.966502	+	0.870242i
$70$	0.786215	+	17.1660i	0.0939707	+	2.05173i
$71$	0.0737360	−	0.0910564i	0.00875085	−	0.0108064i	−0.772752	−	0.634708i	$-0.781120\pi$
$71$	0.0737360	−	0.0910564i	0.00875085	−	0.0108064i	0.781503	+	0.623902i	$0.214454\pi$
$72$	2.67369	+	2.25408i	0.315097	+	0.265646i
$73$	−2.27999	+	4.47474i	−0.266853	+	0.523728i	−0.985084	−	0.172077i	$-0.944952\pi$
$73$	−2.27999	+	4.47474i	−0.266853	+	0.523728i	0.718231	+	0.695805i	$0.244952\pi$
$74$	−10.0807	−	3.34903i	−1.17186	−	0.389317i
$75$	1.11368	−	10.5959i	0.128596	−	1.22351i
$76$	5.65269	−	5.50559i	0.648408	−	0.631534i
$77$	7.61994	−	10.0763i	0.868373	−	1.14830i
$78$	3.38540	−	9.93406i	0.383321	−	1.12481i
$79$	−3.65141	+	5.02574i	−0.410816	+	0.565439i	−0.963417	−	0.268006i	$-0.913635\pi$
$79$	−3.65141	+	5.02574i	−0.410816	+	0.565439i	0.552601	+	0.833446i	$0.313635\pi$
$80$	−12.7207	−	1.00350i	−1.42221	−	0.112195i
$81$	−7.48122	+	8.30874i	−0.831247	+	0.923194i
$82$	5.95450	−	4.26652i	0.657565	−	0.471158i
$83$	−2.92787	−	0.463729i	−0.321375	−	0.0509008i	−0.00633731	−	0.999980i	$-0.502017\pi$
$83$	−2.92787	−	0.463729i	−0.321375	−	0.0509008i	−0.315038	+	0.949079i	$0.602017\pi$
$84$	−0.614140	−	15.6678i	−0.0670082	−	1.70950i
$85$	0.425444	−	8.11796i	0.0461459	−	0.880517i
$86$	2.66144	−	2.12630i	0.286991	−	0.229285i
$87$	13.3852	+	7.72795i	1.43505	+	0.828524i
$88$	6.72174	+	6.54356i	0.716540	+	0.697546i
$89$	−3.71455	+	13.8629i	−0.393741	+	1.46946i	0.430173	+	0.902747i	$0.358453\pi$
$89$	−3.71455	+	13.8629i	−0.393741	+	1.46946i	−0.823914	+	0.566715i	$0.808214\pi$
$90$	−0.619600	+	5.54338i	−0.0653116	+	0.584324i
$91$	−12.5889	+	5.48927i	−1.31967	+	0.575432i
$92$	−2.31771	+	10.2384i	−0.241638	+	1.06743i
$93$	15.3572	−	5.89507i	1.59247	−	0.611291i
$94$	−0.757977	−	7.69952i	−0.0781794	−	0.794144i
$95$	12.3109	+	2.61677i	1.26308	+	0.268475i
$96$	11.6009	+	0.992146i	1.18401	+	0.101260i
$97$	5.22038	−	13.5996i	0.530049	−	1.38083i	−0.363388	−	0.931638i	$-0.618380\pi$
$97$	5.22038	−	13.5996i	0.530049	−	1.38083i	0.893437	−	0.449188i	$-0.148286\pi$
$98$	−7.55793	+	7.45895i	−0.763466	+	0.753467i
$99$	2.95462	−	2.84354i	0.296951	−	0.285787i
$100$	−5.05775	−	9.03322i	−0.505775	−	0.903322i
$101$	−4.60715	−	0.484231i	−0.458429	−	0.0481828i	−0.127500	−	0.991839i	$-0.540695\pi$
$101$	−4.60715	−	0.484231i	−0.458429	−	0.0481828i	−0.330929	+	0.943656i	$0.607362\pi$
$102$	−0.437018	+	7.40465i	−0.0432712	+	0.733169i
$103$	−1.03718	−	3.19211i	−0.102196	−	0.314528i	0.886866	−	0.462027i	$-0.152878\pi$
$103$	−1.03718	−	3.19211i	−0.102196	−	0.314528i	−0.989062	+	0.147499i	$0.952878\pi$
$104$	−2.88382	−	9.78180i	−0.282781	−	0.959184i
$105$	20.2333	−	14.7003i	1.97456	−	1.43460i
$106$	9.90575	+	15.4759i	0.962131	+	1.50315i
$107$	0.538438	+	2.53315i	0.0520528	+	0.244889i	0.996480	−	0.0838317i	$-0.0267158\pi$
$107$	0.538438	+	2.53315i	0.0520528	+	0.244889i	−0.944427	+	0.328721i	$0.893382\pi$
$108$	−0.853971	+	7.20946i	−0.0821734	+	0.693731i
$109$	1.68218	−	1.68218i	0.161124	−	0.161124i	−0.621941	−	0.783064i	$-0.713655\pi$
$109$	1.68218	−	1.68218i	0.161124	−	0.161124i	0.783064	+	0.621941i	$0.213655\pi$
$110$	−2.72035	+	14.7133i	−0.259375	+	1.40285i
$111$	4.00133	+	14.9332i	0.379789	+	1.41739i
$112$	−9.27289	−	12.0893i	−0.876206	−	1.14233i
$113$	5.56319	+	6.17855i	0.523341	+	0.581229i	0.945635	−	0.325230i	$-0.105442\pi$
$113$	5.56319	+	6.17855i	0.523341	+	0.581229i	−0.422294	+	0.906459i	$0.638775\pi$
$114$	−11.2173	−	2.46170i	−1.05060	−	0.230560i
$115$	−15.6316	+	6.00042i	−1.45766	+	0.559542i
$116$	14.9556	−	1.37283i	1.38859	−	0.127464i
$117$	−4.31475	+	1.12063i	−0.398899	+	0.103602i
$118$	15.3060	−	3.14809i	1.40903	−	0.289806i
$119$	7.54330	−	6.10844i	0.691493	−	0.559960i
$120$	8.96579	+	16.2636i	0.818461	+	1.48466i
$121$	8.45051	−	7.04193i	0.768228	−	0.640176i
$122$	2.24649	−	8.16827i	0.203387	−	0.739520i
$123$	−9.95308	−	3.82063i	−0.897439	−	0.344495i
$124$	8.88159	−	13.2896i	0.797590	−	1.19344i
$125$	0.255451	−	0.501350i	0.0228482	−	0.0448421i
$126$	−5.41390	+	3.87916i	−0.482308	+	0.345583i
$127$	6.38115	+	2.84107i	0.566235	+	0.252104i	0.669829	−	0.742516i	$-0.266367\pi$
$127$	6.38115	+	2.84107i	0.566235	+	0.252104i	−0.103594	+	0.994620i	$0.533034\pi$
$128$	9.76257	−	5.71770i	0.862898	−	0.505378i
$129$	−4.71522	−	1.53207i	−0.415152	−	0.134891i
$130$	10.4161	−	12.4936i	0.913553	−	1.09576i
$131$		−	9.73118i		−	0.850217i	−0.905142	−	0.425109i	$-0.860236\pi$
$131$		−	9.73118i		−	0.850217i	0.905142	−	0.425109i	$-0.139764\pi$
$132$	2.57066	−	13.4087i	0.223747	−	1.16708i
$133$	7.51402	+	13.0147i	0.651549	+	1.12852i
$134$	4.32890	−	5.87637i	0.373960	−	0.507641i
$135$	−10.3175	+	5.25705i	−0.887992	+	0.452455i
$136$	3.80526	+	6.12124i	0.326298	+	0.524892i
$137$	−7.86746	+	9.71550i	−0.672162	+	0.830051i	−0.993127	−	0.117040i	$-0.962660\pi$
$137$	−7.86746	+	9.71550i	−0.672162	+	0.830051i	0.320965	+	0.947091i	$0.395993\pi$
$138$	14.2991	−	5.38105i	1.21722	−	0.458065i
$139$	−1.35135	+	6.35761i	−0.114620	+	0.539245i	0.882943	+	0.469480i	$0.155558\pi$
$139$	−1.35135	+	6.35761i	−0.114620	+	0.539245i	−0.997563	+	0.0697656i	$0.977775\pi$
$140$	7.81370	−	23.0114i	0.660378	−	1.94482i
$141$	−8.75072	+	7.08619i	−0.736944	+	0.596765i
$142$	−0.144043	+	0.0819024i	−0.0120879	+	0.00687310i
$143$	−11.7595	+	2.17135i	−0.983377	+	0.181578i
$144$	−2.35903	−	4.34671i	−0.196586	−	0.362226i
$145$	15.0753	+	18.6164i	1.25193	+	1.54601i
$146$	5.30928	−	4.71750i	0.439399	−	0.390423i
$147$	15.1169	+	3.21319i	1.24682	+	0.265019i
$148$	11.5490	+	9.60698i	0.949319	+	0.789689i
$149$	−10.9663	−	8.88032i	−0.898393	−	0.727504i	0.0643484	−	0.997927i	$-0.479503\pi$
$149$	−10.9663	−	8.88032i	−0.898393	−	0.727504i	−0.962742	+	0.270423i	$0.912836\pi$
$150$	−6.92882	+	13.3798i	−0.565736	+	1.09246i
$151$	−2.34100	−	4.59447i	−0.190508	−	0.373893i	0.775920	−	0.630832i	$-0.217286\pi$
$151$	−2.34100	−	4.59447i	−0.190508	−	0.373893i	−0.966428	+	0.256939i	$0.917286\pi$
$152$	−10.2822	+	4.33642i	−0.833999	+	0.351730i
$153$	2.72857	−	1.57534i	0.220592	−	0.127359i
$154$	−15.2291	+	9.34149i	−1.22720	+	0.752758i
$155$	25.4952			2.04782
$156$	−9.57928	+	11.3371i	−0.766956	+	0.907696i
$157$	1.15352	−	3.55017i	0.0920609	−	0.283334i	−0.894416	−	0.447237i	$-0.852408\pi$
$157$	1.15352	−	3.55017i	0.0920609	−	0.283334i	0.986477	+	0.163902i	$0.0524082\pi$
$158$	7.39936	−	4.73615i	0.588661	−	0.376788i
$159$	10.8772	−	24.4305i	0.862614	−	1.93746i
$160$	16.2347	+	7.87902i	1.28347	+	0.622892i
$161$	−17.8135	−	9.07643i	−1.40390	−	0.715323i
$162$	14.1353	−	7.08532i	1.11057	−	0.556675i
$163$	8.25578	−	21.5070i	0.646643	−	1.68456i	−0.0793386	−	0.996848i	$-0.525281\pi$
$163$	8.25578	−	21.5070i	0.646643	−	1.68456i	0.725981	−	0.687714i	$-0.241386\pi$
$164$	−10.0409	+	2.54909i	−0.784066	+	0.199050i
$165$	20.0600	−	8.47469i	1.56167	−	0.659754i
$166$	3.61670	+	2.12001i	0.280710	+	0.164544i
$167$	7.76916	+	9.59412i	0.601196	+	0.742415i	0.983358	−	0.181680i	$-0.0581536\pi$
$167$	7.76916	+	9.59412i	0.601196	+	0.742415i	−0.382162	+	0.924095i	$0.624820\pi$
$168$	−7.26798	+	20.9497i	−0.560737	+	1.61631i
$169$	12.3005	+	4.20697i	0.946189	+	0.323613i
$170$	−4.74508	+	10.4713i	−0.363931	+	0.803115i
$171$	1.74815	+	4.55408i	0.133684	+	0.348259i
$172$	−4.60100	+	1.42818i	−0.350823	+	0.108898i
$173$	−13.0241	+	11.7269i	−0.990203	+	0.891582i	−0.994106	−	0.108410i	$-0.965424\pi$
$173$	−13.0241	+	11.7269i	−0.990203	+	0.891582i	0.00390369	+	0.999992i	$0.498757\pi$
$174$	−13.6434	−	17.0771i	−1.03430	−	1.29461i
$175$	19.0451	−	5.10312i	1.43967	−	0.385759i
$176$	−5.47874	−	12.0824i	−0.412975	−	0.910742i
$177$	−16.0815	−	16.0815i	−1.20876	−	1.20876i
$178$	12.0380	−	16.3414i	0.902290	−	1.22484i
$179$	−3.36701	+	0.715680i	−0.251662	+	0.0534924i	−0.332015	−	0.943274i	$-0.607729\pi$
$179$	−3.36701	+	0.715680i	−0.251662	+	0.0534924i	0.0803531	+	0.996766i	$0.474395\pi$
$180$	3.67357	−	6.98075i	0.273812	−	0.520314i
$181$	7.66709	+	10.5528i	0.569890	+	0.784386i	0.992542	−	0.121906i	$-0.0389006\pi$
$181$	7.66709	+	10.5528i	0.569890	+	0.784386i	−0.422652	+	0.906292i	$0.638901\pi$
$182$	19.4082	−	0.739333i	1.43863	−	0.0548030i
$183$	−11.7261	+	3.81004i	−0.866817	+	0.281646i
$184$	8.33014	−	12.2883i	0.614106	−	0.905908i
$185$	−2.50461	+	23.8298i	−0.184143	+	1.75200i
$186$	−23.2630	−	0.153332i	−1.70573	−	0.0112429i
$187$	7.60260	−	3.69203i	0.555957	−	0.269988i
$188$	−2.97091	+	10.5303i	−0.216676	+	0.768003i
$189$	−12.9081	−	4.95496i	−0.938928	−	0.360421i
$190$	−14.8635	−	9.79234i	−1.07831	−	0.710411i
$191$	4.99095	−	23.4806i	0.361132	−	1.69899i	−0.304334	−	0.952565i	$-0.598434\pi$
$191$	4.99095	−	23.4806i	0.361132	−	1.69899i	0.665466	−	0.746428i	$-0.268233\pi$
$192$	−14.7659	−	7.28682i	−1.06564	−	0.525881i
$193$	4.99825	+	13.0209i	0.359782	+	0.937264i	0.987329	+	0.158686i	$0.0507256\pi$
$193$	4.99825	+	13.0209i	0.359782	+	0.937264i	−0.627547	+	0.778579i	$0.715941\pi$
$194$	−13.8854	+	15.2183i	−0.996910	+	1.09261i
$195$	−23.5243	−	2.65563i	−1.68461	−	0.190174i
$196$	13.7982	−	5.92667i	0.985587	−	0.423334i
$197$	14.6202	+	3.91748i	1.04165	+	0.279109i	0.738796	−	0.673929i	$-0.235395\pi$
$197$	14.6202	+	3.91748i	1.04165	+	0.279109i	0.302852	+	0.953038i	$0.402061\pi$
$198$	−5.35683	+	2.22159i	−0.380693	+	0.157882i
$199$	5.16156	−	8.94009i	0.365893	−	0.633746i	−0.623026	−	0.782201i	$-0.714097\pi$
$199$	5.16156	−	8.94009i	0.365893	−	0.633746i	0.988919	+	0.148455i	$0.0474301\pi$
$200$	2.00399	+	14.5032i	0.141704	+	1.02553i
$201$	−10.6080	−	0.555942i	−0.748231	−	0.0392131i
$202$	5.81759	+	3.01268i	0.409325	+	0.211971i
$203$	−4.47447	+	28.2507i	−0.314046	+	1.98281i
$204$	4.39261	−	9.52599i	0.307544	−	0.666953i
$205$	−12.2794	−	11.0564i	−0.857631	−	0.772215i
$206$	−0.279658	+	4.73840i	−0.0194847	+	0.330140i
$207$	−5.25015	−	3.81446i	−0.364911	−	0.265123i
$208$	−1.24478	+	14.3684i	−0.0863102	+	0.996268i
$209$	3.80449	+	12.5201i	0.263162	+	0.866034i
$210$	−34.2234	+	8.92880i	−2.36164	+	0.616146i
$211$	6.53082	+	0.686417i	0.449600	+	0.0472549i	0.326623	−	0.945155i	$-0.394089\pi$
$211$	6.53082	+	0.686417i	0.449600	+	0.0472549i	0.122977	+	0.992410i	$0.460756\pi$
$212$	−5.06719	−	25.4868i	−0.348016	−	1.75044i
$213$	0.214876	+	0.109485i	0.0147230	+	0.00750176i
$214$	0.596764	−	3.61351i	0.0407939	−	0.247014i
$215$	−5.97168	−	4.83577i	−0.407265	−	0.329797i
$216$	4.84108	−	9.05401i	0.329394	−	0.616048i
$217$	20.3697	+	22.6229i	1.38279	+	1.53574i
$218$	−3.08245	+	1.34812i	−0.208770	+	0.0913064i
$219$	−9.98456	−	2.67535i	−0.674694	−	0.180784i
$220$	11.1672	−	17.9737i	0.752889	−	1.21179i
$221$	−9.17137	−	0.551432i	−0.616933	−	0.0370933i
$222$	2.42864	−	21.7284i	0.163000	−	1.45831i
$223$	13.4206	+	8.71547i	0.898713	+	0.583631i	0.909221	−	0.416314i	$-0.136678\pi$
$223$	13.4206	+	8.71547i	0.898713	+	0.583631i	−0.0105079	+	0.999945i	$0.503345\pi$
$224$	5.97956	+	20.7007i	0.399526	+	1.38313i
$225$	6.36502	−	0.668991i	0.424335	−	0.0445994i
$226$	−4.14119	−	11.0044i	−0.275468	−	0.732004i
$227$	4.63670	+	7.13989i	0.307748	+	0.473891i	0.958377	−	0.285505i	$-0.0921613\pi$
$227$	4.63670	+	7.13989i	0.307748	+	0.473891i	−0.650629	+	0.759396i	$0.725495\pi$
$228$	13.5032	+	9.02438i	0.894274	+	0.597654i
$229$	0.827071	+	5.22192i	0.0546544	+	0.345074i	0.999829	+	0.0185080i	$0.00589161\pi$
$229$	0.827071	+	5.22192i	0.0546544	+	0.345074i	−0.945174	+	0.326566i	$0.894108\pi$
$230$	23.6787	+	0.156072i	1.56133	+	0.0102911i
$231$	23.5471	+	11.0290i	1.54929	+	0.725658i
$232$	−20.4029	−	5.90171i	−1.33952	−	0.387466i
$233$	−4.09659	+	5.63847i	−0.268377	+	0.369389i	−0.921841	−	0.387569i	$-0.873315\pi$
$233$	−4.09659	+	5.63847i	−0.268377	+	0.369389i	0.653464	+	0.756957i	$0.273315\pi$
$234$	6.25984	+	0.748484i	0.409219	+	0.0489299i
$235$	−16.5976	+	5.39289i	−1.08271	+	0.351794i
$236$	−21.7795	−	3.74448i	−1.41773	−	0.243745i
$237$	−11.6807	−	5.20060i	−0.758746	−	0.337815i
$238$	−13.0828	+	4.15572i	−0.848030	+	0.269375i
$239$	16.8620	−	8.59162i	1.09071	−	0.555746i	0.186338	−	0.982486i	$-0.440338\pi$
$239$	16.8620	−	8.59162i	1.09071	−	0.555746i	0.904374	+	0.426740i	$0.140338\pi$
$240$	−3.42329	−	26.0396i	−0.220972	−	1.68085i
$241$	−21.1081	+	5.65589i	−1.35969	+	0.364328i	−0.863703	−	0.504001i	$-0.831861\pi$
$241$	−21.1081	+	5.65589i	−1.35969	+	0.364328i	−0.495988	+	0.868329i	$0.665194\pi$
$242$	−14.7587	+	4.91737i	−0.948726	+	0.316101i
$243$	−10.4984	−	6.06126i	−0.673473	−	0.388830i
$244$	−7.16917	+	9.59883i	−0.458959	+	0.614502i
$245$	20.0885	+	13.0456i	1.28341	+	0.833454i
$246$	11.1378	+	10.1623i	0.710121	+	0.647921i
$247$	3.06456	−	13.8913i	0.194994	−	0.883881i
$248$	−18.5471	+	12.9228i	−1.17774	+	0.820596i
$249$	−0.319323	−	6.09305i	−0.0202363	−	0.386131i
$250$	−0.594852	+	0.528550i	−0.0376218	+	0.0334284i
$251$	−11.1861	+	4.98037i	−0.706060	+	0.314358i	−0.728169	−	0.685398i	$-0.759628\pi$
$251$	−11.1861	+	4.98037i	−0.706060	+	0.314358i	0.0221094	+	0.999756i	$0.492962\pi$
$252$	9.12934	−	2.31766i	0.575094	−	0.145999i
$253$	−13.3163	−	11.2124i	−0.837190	−	0.704918i
$254$	−6.93884	−	7.03092i	−0.435382	−	0.441159i
$255$	16.5257	−	2.61742i	1.03488	−	0.163909i
$256$	−15.8039	+	2.49711i	−0.987746	+	0.156070i
$257$	21.4571	+	19.3201i	1.33846	+	1.20515i	0.960154	+	0.279472i	$0.0901593\pi$
$257$	21.4571	+	19.3201i	1.33846	+	1.20515i	0.378304	+	0.925681i	$0.376507\pi$
$258$	5.41975	+	4.44830i	0.337419	+	0.276939i
$259$	−23.1462	+	16.8167i	−1.43824	+	1.04494i
$260$	−20.1576	+	11.0835i	−1.25012	+	0.687370i
$261$	−2.86905	+	8.83002i	−0.177590	+	0.546564i
$262$	−5.01642	+	12.8151i	−0.309916	+	0.791721i
$263$	−13.6766	+	7.89621i	−0.843338	+	0.486901i	−0.858397	−	0.512985i	$-0.828540\pi$
$263$	−13.6766	+	7.89621i	−0.843338	+	0.486901i	0.0150594	+	0.999887i	$0.495206\pi$
$264$	−10.2975	+	16.3329i	−0.633769	+	1.00522i
$265$	29.3079	−	29.3079i	1.80037	−	1.80037i
$266$	−3.18625	−	21.0127i	−0.195362	−	1.28837i
$267$	−29.4993	−	1.54600i	−1.80533	−	0.0946134i
$268$	−8.73005	+	5.50712i	−0.533273	+	0.336401i
$269$	−1.67807	−	15.9658i	−0.102314	−	0.973452i	−0.918435	−	0.395571i	$-0.870547\pi$
$269$	−1.67807	−	15.9658i	−0.102314	−	0.973452i	0.816121	−	0.577880i	$-0.196120\pi$
$270$	16.2973	−	1.60439i	0.991823	−	0.0976398i
$271$	1.21066	+	23.1007i	0.0735423	+	1.40327i	0.747383	+	0.664393i	$0.231310\pi$
$271$	1.21066	+	23.1007i	0.0735423	+	1.40327i	−0.673841	+	0.738876i	$0.735357\pi$
$272$	−1.85569	−	10.0227i	−0.112518	−	0.607718i
$273$	−16.4386	−	22.9958i	−0.994911	−	1.39177i
$274$	15.3691	−	8.73880i	0.928481	−	0.527930i
$275$	17.1587	−	0.569950i	1.03471	−	0.0343693i
$276$	−21.6046	−	0.284815i	−1.30044	−	0.0171439i
$277$	−5.56020	−	12.4884i	−0.334080	−	0.750356i	−0.999991	−	0.00432430i	$-0.998624\pi$
$277$	−5.56020	−	12.4884i	−0.334080	−	0.750356i	0.665911	−	0.746031i	$-0.268043\pi$
$278$	5.05696	−	7.67580i	0.303296	−	0.460364i
$279$	5.38182	+	8.28728i	0.322201	+	0.496146i
$280$	−22.1524	+	26.2761i	−1.32386	+	1.57030i
$281$	7.00993	+	1.11026i	0.418178	+	0.0662328i	0.361978	−	0.932187i	$-0.382102\pi$
$281$	7.00993	+	1.11026i	0.418178	+	0.0662328i	0.0561998	+	0.998420i	$0.482102\pi$
$282$	15.1769	−	4.82091i	0.903770	−	0.287081i
$283$	−3.16124	+	0.671943i	−0.187916	+	0.0399429i	−0.300909	−	0.953653i	$-0.597290\pi$
$283$	−3.16124	+	0.671943i	−0.187916	+	0.0399429i	0.112992	+	0.993596i	$0.463957\pi$
$284$	0.231913	−	0.0336040i	0.0137615	−	0.00199403i
$285$			25.9051i			1.53449i
$286$	16.6055	+	3.20252i	0.981906	+	0.189369i
$287$		−	19.7297i		−	1.16461i
$288$	0.865911	+	6.94033i	0.0510243	+	0.408963i
$289$	−10.2767	+	2.18438i	−0.604513	+	0.128493i
$290$	−10.2561	−	32.2875i	−0.602256	−	1.89598i
$291$	29.6136	+	4.69033i	1.73598	+	0.274952i
$292$	−9.42373	+	3.47561i	−0.551482	+	0.203395i
$293$	0.534726	+	0.823406i	0.0312390	+	0.0481039i	0.853945	−	0.520363i	$-0.174203\pi$
$293$	0.534726	+	0.823406i	0.0312390	+	0.0481039i	−0.822706	+	0.568467i	$0.807537\pi$
$294$	−18.2512	−	12.0242i	−1.06443	−	0.701268i
$295$	−14.3369	−	32.2011i	−0.834724	−	1.87482i
$296$	−10.2566	−	18.6050i	−0.596152	−	1.08140i
$297$	−9.96941	−	6.74917i	−0.578484	−	0.391627i
$298$	9.86384	+	17.3477i	0.571397	+	1.00493i
$299$	6.64586	+	17.7193i	0.384340	+	1.02473i
$300$	16.0220	−	14.0483i	0.925028	−	0.811077i
$301$	−0.480187	−	9.16251i	−0.0276775	−	0.528118i
$302$	0.714444	+	7.25730i	0.0411116	+	0.417611i
$303$	−0.996669	−	9.48267i	−0.0572572	−	0.544765i
$304$	15.7762	−	0.410199i	0.904829	−	0.0235265i
$305$	−19.0831	−	1.00010i	−1.09270	−	0.0572658i
$306$	−4.40538	+	0.668010i	−0.251839	+	0.0381876i
$307$	−0.366840	+	0.366840i	−0.0209367	+	0.0209367i	−0.717498	−	0.696561i	$-0.754713\pi$
$307$	−0.366840	+	0.366840i	−0.0209367	+	0.0209367i	0.696561	+	0.717498i	$0.254713\pi$
$308$	24.8709	−	4.45132i	1.41715	−	0.253637i
$309$	5.98275	−	3.45414i	0.340347	−	0.196499i
$310$	−33.5750	−	13.1428i	−1.90693	−	0.746459i
$311$	3.75939	−	11.5702i	0.213176	−	0.656087i	−0.786102	−	0.618096i	$-0.787904\pi$
$311$	3.75939	−	11.5702i	0.213176	−	0.656087i	0.999278	−	0.0379909i	$-0.0120958\pi$
$312$	18.4594	−	9.99188i	1.04506	−	0.565679i
$313$	−12.3999	+	9.00904i	−0.700882	+	0.509221i	−0.880219	−	0.474567i	$-0.842605\pi$
$313$	−12.3999	+	9.00904i	−0.700882	+	0.509221i	0.179337	+	0.983788i	$0.442605\pi$
$314$	−3.34920	+	4.08062i	−0.189006	+	0.230283i
$315$	11.1646	+	10.0526i	0.629052	+	0.566401i
$316$	−12.1858	+	2.42274i	−0.685505	+	0.136290i
$317$	2.52545	−	0.399993i	0.141844	−	0.0224658i	−0.0851088	−	0.996372i	$-0.527124\pi$
$317$	2.52545	−	0.399993i	0.141844	−	0.0224658i	0.226952	+	0.973906i	$0.427124\pi$
$318$	−26.9182	+	26.5656i	−1.50950	+	1.48973i
$319$	−9.36900	+	23.0759i	−0.524563	+	1.29200i
$320$	−17.3180	−	18.7450i	−0.968108	−	1.04788i
$321$	−4.86952	+	2.16805i	−0.271790	+	0.121009i
$322$	18.7799	+	21.1357i	1.04656	+	1.17785i
$323$	0.526182	+	10.0401i	0.0292775	+	0.558649i
$324$	−22.2674	+	2.04401i	−1.23708	+	0.113556i
$325$	−16.5638	−	8.60084i	−0.918796	−	0.477089i
$326$	−21.9590	+	24.0671i	−1.21620	+	1.33295i
$327$	4.10656	+	2.66683i	0.227093	+	0.147476i
$328$	14.5371	+	1.81918i	0.802678	+	0.100447i
$329$	−18.0462	−	10.4190i	−0.994920	−	0.574417i
$330$	−30.7860	+	0.819503i	−1.69471	+	0.0451122i
$331$	12.1238	−	3.24856i	0.666383	−	0.178557i	0.0902583	−	0.995918i	$-0.471231\pi$
$331$	12.1238	−	3.24856i	0.666383	−	0.178557i	0.576125	+	0.817361i	$0.304564\pi$
$332$	−3.67001	−	4.65627i	−0.201418	−	0.255546i
$333$	−8.27465	+	4.21614i	−0.453448	+	0.231043i
$334$	−5.28554	−	16.6396i	−0.289212	−	0.910479i
$335$	−15.0403	−	6.69639i	−0.821742	−	0.365863i
$336$	20.3709	−	23.8423i	1.11132	−	1.30070i
$337$	−11.8492	+	3.85005i	−0.645468	+	0.209725i	−0.613415	−	0.789761i	$-0.710205\pi$
$337$	−11.8492	+	3.85005i	−0.645468	+	0.209725i	−0.0320535	+	0.999486i	$0.510205\pi$
$338$	−14.0299	−	11.8811i	−0.763128	−	0.646247i
$339$	−10.0584	+	13.8442i	−0.546299	+	0.751916i
$340$	11.6468	−	11.3437i	0.631638	−	0.615201i
$341$	12.8113	+	23.2052i	0.693770	+	1.25663i
$342$	0.0454698	−	6.89850i	0.00245873	−	0.373028i
$343$	0.303054	+	1.91341i	0.0163634	+	0.103314i
$344$	6.79534	+	0.491023i	0.366380	+	0.0264742i
$345$	−18.7698	−	28.9029i	−1.01053	−	1.55608i
$346$	23.1968	−	8.72944i	1.24707	−	0.469298i
$347$	24.8860	−	2.61562i	1.33595	−	0.140414i	0.590534	−	0.807013i	$-0.298917\pi$
$347$	24.8860	−	2.61562i	1.33595	−	0.140414i	0.745417	+	0.666599i	$0.232250\pi$
$348$	9.16391	+	29.5223i	0.491237	+	1.58256i
$349$	−18.3507	−	11.9171i	−0.982293	−	0.637908i	−0.0496717	−	0.998766i	$-0.515817\pi$
$349$	−18.3507	−	11.9171i	−0.982293	−	0.637908i	−0.932621	+	0.360857i	$0.882484\pi$
$350$	−27.7114	−	3.09738i	−1.48124	−	0.165562i
$351$	5.85190	+	11.7068i	0.312351	+	0.624861i
$352$	0.986564	+	18.7357i	0.0525840	+	0.998617i
$353$	19.9320	+	5.34077i	1.06088	+	0.284261i	0.746739	−	0.665117i	$-0.231618\pi$
$353$	19.9320	+	5.34077i	1.06088	+	0.284261i	0.314136	+	0.949378i	$0.398285\pi$
$354$	12.8879	+	29.4680i	0.684987	+	1.56621i
$355$	0.250101	+	0.277765i	0.0132740	+	0.0147422i
$356$	−24.2770	+	15.3145i	−1.28668	+	0.811668i
$357$	15.5260	+	12.5727i	0.821723	+	0.665418i
$358$	4.80299	+	0.793205i	0.253846	+	0.0419222i
$359$	11.3282	+	5.77200i	0.597879	+	0.304634i	0.726615	−	0.687044i	$-0.241092\pi$
$359$	11.3282	+	5.77200i	0.597879	+	0.304634i	−0.128737	+	0.991679i	$0.541092\pi$
$360$	−8.43635	+	7.29931i	−0.444635	+	0.384708i
$361$	3.41509	+	0.358941i	0.179742	+	0.0188916i
$362$	−4.65690	−	17.8496i	−0.244761	−	0.938152i
$363$	17.7936	+	13.9997i	0.933922	+	0.734794i
$364$	−25.9400	−	9.03127i	−1.35963	−	0.473367i
$365$	−12.9611	−	9.41677i	−0.678414	−	0.492896i
$366$	17.4063	+	1.02731i	0.909843	+	0.0536984i
$367$	22.0006	+	19.8095i	1.14842	+	1.03405i	0.998974	+	0.0452768i	$0.0144170\pi$
$367$	22.0006	+	19.8095i	1.14842	+	1.03405i	0.149450	+	0.988769i	$0.452250\pi$
$368$	−17.3047	+	11.8885i	−0.902070	+	0.619730i
$369$	1.00184	−	6.32538i	0.0521538	−	0.329286i
$370$	15.5826	−	30.0907i	0.810102	−	1.56434i
$371$	49.4220	+	2.59010i	2.56586	+	0.134471i
$372$	30.5563	+	12.1940i	1.58427	+	0.632229i
$373$	−10.2809	+	17.8070i	−0.532323	+	0.922011i	0.466964	+	0.884276i	$0.345348\pi$
$373$	−10.2809	+	17.8070i	−0.532323	+	0.922011i	−0.999288	+	0.0377351i	$0.987986\pi$
$374$	−11.9152	+	0.942940i	−0.616121	+	0.0487583i
$375$	1.11867	+	0.299747i	0.0577679	+	0.0154789i
$376$	9.34081	−	12.3360i	0.481716	−	0.636182i
$377$	21.1717	−	16.8764i	1.09040	−	0.869181i
$378$	14.4446	+	13.1794i	0.742949	+	0.677875i
$379$	4.07098	+	10.6053i	0.209112	+	0.544756i	0.997519	−	0.0703984i	$-0.0224271\pi$
$379$	4.07098	+	10.6053i	0.209112	+	0.544756i	−0.788407	+	0.615154i	$0.789094\pi$
$380$	14.5260	+	20.5578i	0.745166	+	1.05459i
$381$	−2.98914	+	14.0628i	−0.153138	+	0.720458i
$382$	−18.6769	+	28.3490i	−0.955591	+	1.45046i
$383$	15.4940	+	5.94757i	0.791704	+	0.303907i	0.720410	−	0.693549i	$-0.243954\pi$
$383$	15.4940	+	5.94757i	0.791704	+	0.303907i	0.0712941	+	0.997455i	$0.477287\pi$
$384$	15.6890	+	17.2079i	0.800628	+	0.878139i
$385$	27.9454	+	29.0371i	1.42423	+	1.47987i
$386$	0.130006	−	19.7240i	0.00661712	−	1.00392i
$387$	0.311308	−	2.96190i	0.0158247	−	0.150562i
$388$	26.1308	−	12.8833i	1.32659	−	0.654051i
$389$	14.9583	−	4.86024i	0.758414	−	0.246424i	0.0958164	−	0.995399i	$-0.469454\pi$
$389$	14.9583	−	4.86024i	0.758414	−	0.246424i	0.662598	+	0.748975i	$0.269454\pi$
$390$	29.6105	+	15.6240i	1.49939	+	0.791153i
$391$	−7.86176	−	10.8208i	−0.397586	−	0.547231i
$392$	−21.2262	+	0.691932i	−1.07209	+	0.0349478i
$393$	19.5915	−	4.16431i	0.988262	−	0.210062i
$394$	−17.2341	−	12.6957i	−0.868242	−	0.639600i
$395$	−14.0128	−	14.0128i	−0.705059	−	0.705059i
$396$	8.19971	−	0.164196i	0.412051	−	0.00825115i
$397$	11.7071	−	3.13691i	0.587563	−	0.157437i	0.0472238	−	0.998884i	$-0.484963\pi$
$397$	11.7071	−	3.13691i	0.587563	−	0.157437i	0.540339	+	0.841447i	$0.318296\pi$
$398$	−11.4059	+	9.11253i	−0.571728	+	0.456770i
$399$	−22.9866	+	20.6972i	−1.15077	+	1.03616i
$400$	4.83733	−	20.1326i	0.241867	−	1.00663i
$401$	−13.8374	−	36.0477i	−0.691007	−	1.80013i	−0.593398	−	0.804910i	$-0.702214\pi$
$401$	−13.8374	−	36.0477i	−0.691007	−	1.80013i	−0.0976093	−	0.995225i	$-0.531120\pi$
$402$	13.6832	+	6.20055i	0.682458	+	0.309255i
$403$	0.221685	−	28.8151i	0.0110429	−	1.43538i
$404$	−6.10823	−	6.96640i	−0.303896	−	0.346591i
$405$	−22.4456	−	27.7180i	−1.11533	−	1.37732i
$406$	20.4557	−	34.8971i	1.01520	−	1.73191i
$407$	−22.9480	+	9.69478i	−1.13749	+	0.480553i
$408$	−10.6953	+	10.2805i	−0.529498	+	0.508961i
$409$	2.50498	−	6.52569i	0.123863	−	0.322675i	−0.857602	−	0.514313i	$-0.828047\pi$
$409$	2.50498	−	6.52569i	0.123863	−	0.322675i	0.981466	+	0.191639i	$0.0613802\pi$
$410$	10.4713	+	20.8904i	0.517142	+	1.03170i
$411$	−22.9267	−	11.6817i	−1.13089	−	0.576218i
$412$	2.81093	−	6.09590i	0.138485	−	0.300323i
$413$	17.1187	−	38.4491i	0.842354	−	1.89196i
$414$	4.94764	+	7.72977i	0.243163	+	0.379897i
$415$	2.92221	−	8.99362i	0.143445	−	0.441480i
$416$	9.04617	−	18.2802i	0.443525	−	0.896262i
$417$	−13.3779			−0.655118
$418$	1.44393	−	18.4491i	0.0706252	−	0.902375i
$419$	−0.108932	+	0.0628921i	−0.00532169	+	0.00307248i	−0.502658	−	0.864485i	$-0.667645\pi$
$419$	−0.108932	+	0.0628921i	−0.00532169	+	0.00307248i	0.497337	+	0.867558i	$0.334311\pi$
$420$	49.6721	+	5.88373i	2.42375	+	0.287097i
$421$	10.9124	+	21.4168i	0.531837	+	1.04379i	0.988081	+	0.153934i	$0.0491945\pi$
$421$	10.9124	+	21.4168i	0.531837	+	1.04379i	−0.456244	+	0.889855i	$0.650806\pi$
$422$	−8.24668	−	4.27059i	−0.401442	−	0.207889i
$423$	−5.25659	−	4.25671i	−0.255584	−	0.206968i
$424$	−6.46539	+	36.1760i	−0.313987	+	1.75686i
$425$	12.9026	+	2.74253i	0.625868	+	0.133032i
$426$	−0.226533	−	0.254950i	−0.0109756	−	0.0123524i
$427$	−14.3593	−	17.7322i	−0.694895	−	0.858123i
$428$	−2.64865	+	4.45104i	−0.128027	+	0.215149i
$429$	−9.40382	−	22.7458i	−0.454021	−	1.09818i
$430$	5.37134	+	9.44669i	0.259029	+	0.455560i
$431$	14.2343	−	11.5267i	0.685640	−	0.555221i	−0.221960	−	0.975056i	$-0.571245\pi$
$431$	14.2343	−	11.5267i	0.685640	−	0.555221i	0.907600	+	0.419835i	$0.137912\pi$
$432$	−11.0426	+	9.42777i	−0.531289	+	0.453594i
$433$	0.273572	−	1.28706i	0.0131470	−	0.0618520i	−0.971085	−	0.238734i	$-0.923268\pi$
$433$	0.273572	−	1.28706i	0.0131470	−	0.0618520i	0.984232	+	0.176882i	$0.0566010\pi$
$434$	−15.1631	−	40.2929i	−0.727850	−	1.93412i
$435$	−31.0287	+	38.3172i	−1.48771	+	1.83717i
$436$	4.75428	−	0.186356i	0.227689	−	0.00892485i
$437$	18.4513	−	9.40139i	0.882644	−	0.449729i
$438$	11.7697	+	8.67025i	0.562376	+	0.414281i
$439$	−6.53760	−	11.3235i	−0.312023	−	0.540439i	0.666777	−	0.745257i	$-0.267673\pi$
$439$	−6.53760	−	11.3235i	−0.312023	−	0.540439i	−0.978800	+	0.204818i	$0.934340\pi$
$440$	−23.9716	+	17.9132i	−1.14280	+	0.853978i
$441$			9.28363i			0.442078i
$442$	11.7936	+	5.45403i	0.560966	+	0.259422i
$443$	−24.8809	−	8.08430i	−1.18213	−	0.384097i	−0.348971	−	0.937134i	$-0.613469\pi$
$443$	−24.8809	−	8.08430i	−1.18213	−	0.384097i	−0.833157	+	0.553037i	$0.813469\pi$
$444$	−14.3993	+	27.3624i	−0.683360	+	1.29856i
$445$	−41.8250	−	18.6217i	−1.98270	−	0.882754i
$446$	−13.1810	−	18.3959i	−0.624139	−	0.871069i
$447$	13.1857	−	25.8783i	0.623661	−	1.22400i
$448$	2.79666	−	30.3435i	0.132130	−	1.43360i
$449$	14.4278	+	5.53830i	0.680888	+	0.261368i	0.674134	−	0.738609i	$-0.264517\pi$
$449$	14.4278	+	5.53830i	0.680888	+	0.261368i	0.00675361	+	0.999977i	$0.497850\pi$
$450$	−8.72705	−	2.40017i	−0.411397	−	0.113145i
$451$	3.89298	−	16.7323i	0.183313	−	0.787894i
$452$	−0.219191	+	16.6267i	−0.0103099	+	0.782052i
$453$	8.24814	−	6.67921i	0.387531	−	0.313817i
$454$	−2.42552	−	11.7928i	−0.113835	−	0.553465i
$455$	−11.0132	−	42.4040i	−0.516306	−	1.98793i
$456$	−13.1305	−	18.8452i	−0.614893	−	0.882509i
$457$	−26.9185	+	10.3331i	−1.25920	+	0.483360i	−0.894208	−	0.447652i	$-0.852260\pi$
$457$	−26.9185	+	10.3331i	−1.25920	+	0.483360i	−0.364988	+	0.931012i	$0.618927\pi$
$458$	1.60272	−	7.30317i	0.0748901	−	0.341255i
$459$	−6.18950	−	6.87413i	−0.288901	−	0.320857i
$460$	−31.1023	−	12.4119i	−1.45015	−	0.578708i
$461$	2.54888	+	9.51254i	0.118713	+	0.443043i	0.999538	−	0.0303992i	$-0.00967787\pi$
$461$	2.54888	+	9.51254i	0.118713	+	0.443043i	−0.880825	+	0.473442i	$0.843011\pi$
$462$	−25.3240	−	26.6628i	−1.17818	−	1.24047i
$463$	−25.1016	+	25.1016i	−1.16657	+	1.16657i	−0.183561	+	0.983008i	$0.558762\pi$
$463$	−25.1016	+	25.1016i	−1.16657	+	1.16657i	−0.983008	+	0.183561i	$0.941238\pi$
$464$	23.8265	+	18.2897i	1.10612	+	0.849080i
$465$	10.9103	+	51.3288i	0.505952	+	2.38032i
$466$	8.30149	−	5.31359i	0.384559	−	0.246147i
$467$	5.44235	−	3.95410i	0.251842	−	0.182974i	−0.454701	−	0.890644i	$-0.650254\pi$
$467$	5.44235	−	3.95410i	0.251842	−	0.182974i	0.706543	+	0.707670i	$0.250254\pi$
$468$	−7.85782	−	4.21264i	−0.363228	−	0.194729i
$469$	−6.07471	−	18.6961i	−0.280504	−	0.863303i
$470$	24.6377	+	1.45410i	1.13645	+	0.0670727i
$471$	7.64109	+	0.803111i	0.352083	+	0.0370054i
$472$	26.7514	+	16.1585i	1.23134	+	0.743755i
$473$	1.40067	−	7.86528i	0.0644029	−	0.361646i
$474$	12.7016	+	12.8702i	0.583405	+	0.591146i
$475$	−7.31890	+	19.0664i	−0.335814	+	0.874825i
$476$	19.3711	+	1.27145i	0.887875	+	0.0582767i
$477$	15.7133	+	3.33996i	0.719462	+	0.152926i
$478$	−26.6348	+	2.62205i	−1.21825	+	0.119930i
$479$	32.5567	−	12.4973i	1.48755	−	0.571018i	0.527184	−	0.849751i	$-0.323248\pi$
$479$	32.5567	−	12.4973i	1.48755	−	0.571018i	0.960369	+	0.278733i	$0.0899145\pi$
$480$	−8.91525	+	36.0566i	−0.406923	+	1.64575i
$481$	26.9111	+	3.03796i	1.22704	+	0.138519i
$482$	30.7131	+	3.43290i	1.39894	+	0.156364i
$483$	10.6503	−	39.7476i	0.484607	−	1.80858i
$484$	21.9708	+	1.13236i	0.998674	+	0.0514708i
$485$	40.2439	+	23.2348i	1.82738	+	1.05504i
$486$	10.7009	+	13.3941i	0.485403	+	0.607568i
$487$	0.952471	−	18.1742i	0.0431606	−	0.823553i	−0.888200	−	0.459456i	$-0.848044\pi$
$487$	0.952471	−	18.1742i	0.0431606	−	0.823553i	0.931361	−	0.364097i	$-0.118622\pi$
$488$	14.3894	−	8.94512i	0.651376	−	0.404927i
$489$	46.8325	+	7.41754i	2.11784	+	0.335433i
$490$	−19.7298	−	27.5355i	−0.891300	−	1.24393i
$491$	−0.634219	+	0.704371i	−0.0286219	+	0.0317878i	−0.757286	−	0.653084i	$-0.773475\pi$
$491$	−0.634219	+	0.704371i	−0.0286219	+	0.0317878i	0.728664	+	0.684871i	$0.240142\pi$
$492$	−9.42888	−	19.1243i	−0.425087	−	0.862192i
$493$	−11.2476	+	15.4810i	−0.506567	+	0.697230i
$494$	−11.1967	+	16.7138i	−0.503764	+	0.751991i
$495$	7.48490	+	10.7284i	0.336421	+	0.482204i
$496$	31.0865	−	7.45714i	1.39583	−	0.334836i
$497$	−0.0466504	+	0.443849i	−0.00209255	+	0.0199093i
$498$	−2.72044	+	8.18862i	−0.121906	+	0.366941i
$499$	−9.54978	+	18.7425i	−0.427507	+	0.839030i	0.572313	+	0.820036i	$0.306046\pi$
$499$	−9.54978	+	18.7425i	−0.427507	+	0.839030i	−0.999820	+	0.0189942i	$0.993954\pi$
$500$	1.05584	−	0.389408i	0.0472184	−	0.0174148i
$501$	−15.9909	+	19.7471i	−0.714420	+	0.882236i
$502$	17.2985	−	0.792283i	0.772069	−	0.0353613i
$503$	−9.10489	+	8.19808i	−0.405967	+	0.365534i	−0.846670	−	0.532119i	$-0.821396\pi$
$503$	−9.10489	+	8.19808i	−0.405967	+	0.365534i	0.440703	+	0.897653i	$0.354729\pi$
$504$	−13.2173	−	1.65402i	−0.588745	−	0.0736758i
$505$	3.82482	−	14.2744i	0.170202	−	0.635203i
$506$	11.7564	+	21.6303i	0.522638	+	0.961585i
$507$	−3.20599	+	26.5645i	−0.142383	+	1.17977i
$508$	5.51341	+	12.8361i	0.244618	+	0.569509i
$509$	−1.63695	+	2.52068i	−0.0725565	+	0.111727i	−0.873086	−	0.487566i	$-0.837885\pi$
$509$	−1.63695	+	2.52068i	−0.0725565	+	0.111727i	0.800530	+	0.599293i	$0.204552\pi$
$510$	−23.1123	−	5.07211i	−1.02343	−	0.224597i
$511$	−1.99956	−	19.0245i	−0.0884552	−	0.841595i
$512$	22.0997	+	4.85845i	0.976677	+	0.214715i
$513$	12.0110	−	7.80004i	0.530299	−	0.344380i
$514$	−18.2977	−	36.5040i	−0.807075	−	1.61012i
$515$	10.5752	−	1.67495i	0.465999	−	0.0738070i
$516$	−4.84425	−	8.65190i	−0.213256	−	0.380879i
$517$	−13.2488	−	12.3969i	−0.582681	−	0.545216i
$518$	39.1506	−	10.2143i	1.72018	−	0.448789i
$519$	−29.1830	−	21.2027i	−1.28099	−	0.930695i
$520$	32.2593	−	4.20480i	1.41466	−	0.184393i
$521$	3.43161	+	10.5614i	0.150342	+	0.462704i	0.997659	−	0.0683824i	$-0.0217838\pi$
$521$	3.43161	+	10.5614i	0.150342	+	0.462704i	−0.847317	+	0.531087i	$0.821784\pi$
$522$	8.33016	−	10.1494i	0.364601	−	0.444226i
$523$	0.513183	−	1.15263i	0.0224399	−	0.0504009i	−0.901978	−	0.431782i	$-0.857885\pi$
$523$	0.513183	−	1.15263i	0.0224399	−	0.0504009i	0.924418	+	0.381381i	$0.124552\pi$
$524$	13.2124	−	14.2904i	0.577186	−	0.624280i
$525$	18.4240	+	36.1592i	0.804091	+	1.57812i
$526$	22.0814	−	3.34832i	0.962797	−	0.145994i
$527$	5.27113	+	19.6721i	0.229614	+	0.856931i
$528$	21.9806	−	16.2007i	0.956581	−	0.705043i
$529$	−2.27466	+	3.93982i	−0.0988981	+	0.171296i
$530$	−53.7042	+	23.4878i	−2.33276	+	1.02024i
$531$	7.44066	−	11.4576i	0.322897	−	0.497218i
$532$	−6.63601	+	29.3144i	−0.287708	+	1.27094i
$533$	−12.6029	+	13.7823i	−0.545894	+	0.596976i
$534$	38.0511	+	17.2429i	1.64663	+	0.746171i
$535$	−8.25008	+	0.432368i	−0.356682	+	0.0186929i
$536$	14.3356	−	2.75206i	0.619205	−	0.118871i
$537$	−2.88172	−	6.47245i	−0.124355	−	0.279307i
$538$	−6.02049	+	21.8906i	−0.259562	+	0.943771i
$539$	−1.77945	+	24.8395i	−0.0766462	+	1.06992i
$540$	−22.2892	−	6.28843i	−0.959175	−	0.270611i
$541$	4.83643	+	30.5360i	0.207934	+	1.31285i	0.841963	+	0.539536i	$0.181400\pi$
$541$	4.83643	+	30.5360i	0.207934	+	1.31285i	−0.634028	+	0.773310i	$0.718600\pi$
$542$	10.3141	−	31.0458i	0.443028	−	1.33353i
$543$	−17.9647	+	19.9519i	−0.770941	+	0.856217i
$544$	−2.72294	+	14.1557i	−0.116745	+	0.606921i
$545$	4.46071	+	6.13963i	0.191076	+	0.262993i
$546$	9.79391	+	38.7576i	0.419140	+	1.65867i
$547$	5.60188	+	1.82016i	0.239519	+	0.0778245i	0.426317	−	0.904574i	$-0.359811\pi$
$547$	5.60188	+	1.82016i	0.239519	+	0.0778245i	−0.186798	+	0.982398i	$0.559811\pi$
$548$	−24.7446	+	3.58546i	−1.05704	+	0.153163i
$549$	−3.70320	−	6.41414i	−0.158049	−	0.273749i
$550$	−22.8903	−	8.09472i	−0.976045	−	0.345160i
$551$	−20.9494	−	20.9494i	−0.892473	−	0.892473i
$552$	28.3045	+	11.5122i	1.20472	+	0.489994i
$553$	1.23838	−	23.6297i	0.0526614	−	1.00484i
$554$	0.884523	+	19.3124i	0.0375798	+	0.820506i
$555$	−49.0478	+	5.15513i	−2.08196	+	0.218823i
$556$	−10.6164	+	7.50149i	−0.450238	+	0.318134i
$557$	16.9189	−	0.886683i	0.716878	−	0.0375700i	0.309590	−	0.950870i	$-0.399808\pi$
$557$	16.9189	−	0.886683i	0.716878	−	0.0375700i	0.407287	+	0.913300i	$0.366475\pi$
$558$	−2.81530	−	13.6880i	−0.119181	−	0.579457i
$559$	−5.51740	+	6.70725i	−0.233361	+	0.283686i
$560$	42.7181	−	23.1838i	1.80517	−	0.979694i
$561$	10.6865	+	13.7262i	0.451184	+	0.579520i
$562$	−8.65913	−	5.07574i	−0.365263	−	0.214107i
$563$	12.4739	−	5.55372i	0.525710	−	0.234061i	−0.126681	−	0.991944i	$-0.540432\pi$
$563$	12.4739	−	5.55372i	0.525710	−	0.234061i	0.652392	+	0.757882i	$0.273766\pi$
$564$	−22.4718	−	1.47496i	−0.946233	−	0.0621072i
$565$	−22.2434	+	14.4450i	−0.935787	+	0.607707i
$566$	4.50947	+	0.744731i	0.189547	+	0.0313034i
$567$	6.66204	−	42.0624i	0.279779	−	1.76646i
$568$	−0.322733	−	0.0752978i	−0.0135416	−	0.00315943i
$569$	−5.60889	−	26.3877i	−0.235137	−	1.10623i	−0.924312	−	0.381637i	$-0.875360\pi$
$569$	−5.60889	−	26.3877i	−0.235137	−	1.10623i	0.689175	−	0.724594i	$-0.257973\pi$
$570$	13.3541	−	34.1147i	0.559341	−	1.42891i
$571$	−22.9312			−0.959640			−0.479820	−	0.877367i	$-0.659298\pi$
$571$	−22.9312			−0.959640			−0.479820	+	0.877367i	$0.659298\pi$
$572$	−20.2171	−	12.7776i	−0.845321	−	0.534258i
$573$	49.4086			2.06407
$574$	−10.1707	+	25.9823i	−0.424515	+	1.08448i
$575$	−5.64886	−	26.5758i	−0.235574	−	1.10829i
$576$	2.43741	−	9.58618i	0.101559	−	0.399424i
$577$	−1.14517	+	7.23033i	−0.0476741	+	0.301002i	−0.999992	−	0.00410650i	$-0.998693\pi$
$577$	−1.14517	+	7.23033i	−0.0476741	+	0.301002i	0.952317	+	0.305109i	$0.0986929\pi$
$578$	14.6596	+	2.42100i	0.609759	+	0.100700i
$579$	−24.0757	+	15.6349i	−1.00055	+	0.649766i
$580$	−3.13786	+	47.8068i	−0.130292	+	1.98507i
$581$	10.3151	−	4.59259i	0.427943	−	0.190533i
$582$	−36.5807	−	21.4426i	−1.51632	−	0.888823i
$583$	41.4027	+	11.9483i	1.71472	+	0.494850i
$584$	14.2019	+	0.280858i	0.587679	+	0.0116220i
$585$	−1.37764	−	14.1540i	−0.0569585	−	0.585197i
$586$	−0.279722	−	1.36000i	−0.0115552	−	0.0561813i
$587$	−8.15221	+	0.427239i	−0.336478	+	0.0176340i	−0.219827	−	0.975539i	$-0.570549\pi$
$587$	−8.15221	+	0.427239i	−0.336478	+	0.0176340i	−0.116651	+	0.993173i	$0.537216\pi$
$588$	17.8367	+	25.2434i	0.735575	+	1.04102i
$589$	−31.3593	+	3.29599i	−1.29214	+	0.135809i
$590$	2.28072	+	49.7967i	0.0938959	+	2.05010i
$591$	−1.63046	+	31.1109i	−0.0670680	+	1.27973i
$592$	3.91613	+	29.7885i	0.160952	+	1.22430i
$593$	−33.8348	−	33.8348i	−1.38943	−	1.38943i	−0.826519	−	0.562909i	$-0.809682\pi$
$593$	−33.8348	−	33.8348i	−1.38943	−	1.38943i	−0.562909	−	0.826519i	$-0.690318\pi$
$594$	9.64965	+	14.0273i	0.395930	+	0.575547i
$595$	15.4819	+	26.8155i	0.634698	+	1.09933i
$596$	−4.04706	−	27.9303i	−0.165774	−	1.14407i
$597$	20.2077	+	6.56587i	0.827044	+	0.268723i
$598$	0.382286	−	26.7607i	0.0156328	−	1.09433i
$599$	10.0325	+	13.8086i	0.409918	+	0.564204i	0.963198	−	0.268791i	$-0.0866242\pi$
$599$	10.0325	+	13.8086i	0.409918	+	0.564204i	−0.553280	+	0.832995i	$0.686624\pi$
$600$	−28.3414	+	10.2410i	−1.15703	+	0.418088i
$601$	4.89408	−	5.43543i	0.199634	−	0.221716i	−0.635013	−	0.772502i	$-0.719005\pi$
$601$	4.89408	−	5.43543i	0.199634	−	0.221716i	0.834647	+	0.550786i	$0.185672\pi$
$602$	−4.09091	+	12.3138i	−0.166733	+	0.501871i
$603$	−0.998211	−	6.30246i	−0.0406503	−	0.256656i
$604$	2.80028	−	9.92553i	0.113942	−	0.403864i
$605$	17.9704	+	30.1398i	0.730602	+	1.22536i
$606$	−3.57579	+	13.0016i	−0.145257	+	0.528156i
$607$	11.5162	+	25.8657i	0.467426	+	1.04986i	0.981387	+	0.192042i	$0.0615111\pi$
$607$	11.5162	+	25.8657i	0.467426	+	1.04986i	−0.513960	+	0.857814i	$0.671822\pi$
$608$	−20.9874	−	7.59245i	−0.851150	−	0.307914i
$609$	−58.7911	+	3.08111i	−2.38234	+	0.124853i
$610$	24.6153	+	11.1544i	0.996643	+	0.451629i
$611$	5.95082	+	18.8058i	0.240745	+	0.760802i
$612$	6.14586	+	1.39126i	0.248432	+	0.0562385i
$613$	−9.27982	+	14.2897i	−0.374808	+	0.577154i	−0.974863	−	0.222805i	$-0.928479\pi$
$613$	−9.27982	+	14.2897i	−0.374808	+	0.577154i	0.600055	+	0.799959i	$0.295145\pi$
$614$	0.672202	−	0.293990i	0.0271279	−	0.0118645i
$615$	17.0048	−	29.4533i	0.685701	−	1.18767i
$616$	−35.0475	−	6.95897i	−1.41211	−	0.280385i
$617$	−6.90754	−	25.7793i	−0.278087	−	1.03783i	−0.953744	−	0.300619i	$-0.902807\pi$
$617$	−6.90754	−	25.7793i	−0.278087	−	1.03783i	0.675657	−	0.737216i	$-0.263860\pi$
$618$	−9.65937	+	1.46470i	−0.388557	+	0.0589188i
$619$	0.728253	+	1.42928i	0.0292709	+	0.0574475i	0.905179	−	0.425031i	$-0.139737\pi$
$619$	0.728253	+	1.42928i	0.0292709	+	0.0574475i	−0.875908	+	0.482478i	$0.839737\pi$
$620$	37.4402	+	34.6158i	1.50363	+	1.39020i
$621$	−7.74938	+	17.4054i	−0.310972	+	0.698455i
$622$	−10.9152	+	13.2990i	−0.437661	+	0.533242i
$623$	−16.8929	−	51.9910i	−0.676800	−	2.08298i
$624$	−29.4602	+	3.64264i	−1.17935	+	0.145822i
$625$	−19.4868	−	14.1580i	−0.779470	−	0.566318i
$626$	20.9737	−	5.47198i	0.838278	−	0.218704i
$627$	−23.5783	+	13.0173i	−0.941628	+	0.519859i
$628$	6.51416	−	3.64732i	0.259943	−	0.145544i
$629$	−18.9049	+	2.99425i	−0.753789	+	0.119389i
$630$	−9.52064	−	18.9938i	−0.379311	−	0.756730i
$631$	−6.42444	+	4.17208i	−0.255753	+	0.166088i	−0.666147	−	0.745820i	$-0.732058\pi$
$631$	−6.42444	+	4.17208i	−0.255753	+	0.166088i	0.410394	+	0.911908i	$0.365391\pi$
$632$	17.2966	+	3.09124i	0.688020	+	0.122963i
$633$	1.41282	+	13.4421i	0.0561545	+	0.534275i
$634$	−3.53200	−	0.775116i	−0.140274	−	0.0307838i
$635$	−12.1360	+	18.6877i	−0.481601	+	0.741600i
$636$	49.1435	−	21.1083i	1.94867	−	0.837000i
$637$	14.9191	−	22.5909i	0.591114	−	0.895085i
$638$	24.2338	−	25.5592i	0.959425	−	1.01190i
$639$	−0.0374941	+	0.139930i	−0.00148324	+	0.00553554i
$640$	13.1433	+	33.6129i	0.519536	+	1.32867i
$641$	−32.5624	+	29.3193i	−1.28614	+	1.15804i	−0.307704	+	0.951482i	$0.599561\pi$
$641$	−32.5624	+	29.3193i	−1.28614	+	1.15804i	−0.978434	+	0.206561i	$0.933773\pi$
$642$	7.53036	−	0.344896i	0.297199	−	0.0136119i
$643$	5.08183	−	6.27554i	0.200408	−	0.247483i	−0.667027	−	0.745033i	$-0.732434\pi$
$643$	5.08183	−	6.27554i	0.200408	−	0.247483i	0.867435	+	0.497550i	$0.165767\pi$
$644$	−13.8361	−	37.5149i	−0.545217	−	1.47830i
$645$	7.18025	−	14.0920i	0.282722	−	0.554873i
$646$	4.48276	−	13.4932i	0.176372	−	0.530885i
$647$	−1.59800	+	15.2040i	−0.0628240	+	0.597730i	0.917141	+	0.398562i	$0.130491\pi$
$647$	−1.59800	+	15.2040i	−0.0628240	+	0.597730i	−0.979965	+	0.199168i	$0.936176\pi$
$648$	30.3779	+	8.78706i	1.19336	+	0.345188i
$649$	22.1046	−	29.2301i	0.867681	−	1.14738i
$650$	17.3794	+	19.8652i	0.681675	+	0.779177i
$651$	−36.8291	+	50.6909i	−1.44345	+	1.98673i
$652$	41.3247	−	20.3743i	1.61840	−	0.797921i
$653$	7.91465	−	8.79011i	0.309724	−	0.343984i	−0.568106	−	0.822955i	$-0.692324\pi$
$653$	7.91465	−	8.79011i	0.309724	−	0.343984i	0.877830	+	0.478972i	$0.158990\pi$
$654$	−4.03323	−	5.62891i	−0.157712	−	0.220108i
$655$	30.6607	+	4.85618i	1.19801	+	0.189747i
$656$	−18.2063	−	9.88958i	−0.710838	−	0.386123i
$657$	0.324972	−	6.20084i	0.0126784	−	0.241918i
$658$	18.3943	+	23.0237i	0.717085	+	0.897558i
$659$	−38.0454	−	21.9655i	−1.48204	−	0.855656i	−0.482248	−	0.876035i	$-0.660179\pi$
$659$	−38.0454	−	21.9655i	−1.48204	−	0.855656i	−0.999792	+	0.0203787i	$0.993513\pi$
$660$	40.9649	+	14.7910i	1.59456	+	0.575737i
$661$	−1.68607	+	6.29248i	−0.0655804	+	0.244749i	−0.990933	−	0.134359i	$-0.957102\pi$
$661$	−1.68607	+	6.29248i	−0.0655804	+	0.244749i	0.925352	+	0.379108i	$0.123769\pi$
$662$	−17.6406	−	1.97174i	−0.685621	−	0.0766339i
$663$	−2.81456	−	18.7004i	−0.109309	−	0.726265i
$664$	2.43278	+	8.02379i	0.0944100	+	0.311384i
$665$	−44.7560	+	17.1802i	−1.73556	+	0.666220i
$666$	13.0704	−	1.28671i	0.506468	−	0.0498592i
$667$	38.5528	+	8.19465i	1.49277	+	0.317298i
$668$	−1.61712	+	24.6376i	−0.0625683	+	0.953258i
$669$	−11.8035	+	30.7491i	−0.456349	+	1.18883i
$670$	16.3548	+	16.5719i	0.631842	+	0.640227i
$671$	−8.67896	−	17.8717i	−0.335047	−	0.689927i
$672$	−39.1174	+	20.8971i	−1.50899	+	0.806121i
$673$	−20.5378	−	2.15861i	−0.791674	−	0.0832082i	−0.299945	−	0.953957i	$-0.596968\pi$
$673$	−20.5378	−	2.15861i	−0.791674	−	0.0832082i	−0.491729	+	0.870748i	$0.663635\pi$
$674$	17.5891	+	1.03810i	0.677507	+	0.0399861i
$675$	−5.80641	−	17.8703i	−0.223489	−	0.687828i
$676$	12.3515	+	22.8788i	0.475058	+	0.879954i
$677$	−5.19884	+	3.77718i	−0.199807	+	0.145169i	−0.683190	−	0.730241i	$-0.739408\pi$
$677$	−5.19884	+	3.77718i	−0.199807	+	0.145169i	0.483383	+	0.875409i	$0.339408\pi$
$678$	20.3828	−	13.0465i	0.782796	−	0.501049i
$679$	11.5362	+	54.2738i	0.442720	+	2.08284i
$680$	−21.1856	+	8.93479i	−0.812429	+	0.342633i
$681$	−12.3903	+	12.3903i	−0.474799	+	0.474799i
$682$	−4.90904	−	37.1635i	−0.187977	−	1.42306i
$683$	−6.27876	−	23.4327i	−0.240250	−	0.896625i	−0.975712	−	0.219059i	$-0.929701\pi$
$683$	−6.27876	−	23.4327i	−0.240250	−	0.896625i	0.735462	−	0.677566i	$-0.236965\pi$
$684$	−3.61605	+	9.06128i	−0.138263	+	0.346467i
$685$	−26.6852	−	29.6369i	−1.01959	−	1.13237i
$686$	0.587266	−	2.67602i	0.0224219	−	0.102171i
$687$	−10.1592	+	3.89976i	−0.387599	+	0.148785i
$688$	−8.69575	−	4.14963i	−0.331522	−	0.158203i
$689$	−32.8695	−	33.3792i	−1.25223	−	1.27165i
$690$	9.81872	+	47.7385i	0.373792	+	1.81737i
$691$	3.92578	−	3.17904i	0.149344	−	0.120936i	−0.551737	−	0.834018i	$-0.686035\pi$
$691$	3.92578	−	3.17904i	0.149344	−	0.120936i	0.701081	+	0.713082i	$0.252701\pi$
$692$	−35.0482	−	0.462044i	−1.33233	−	0.0175643i
$693$	−3.53953	+	15.2132i	−0.134456	+	0.577902i
$694$	−34.1211	−	9.38418i	−1.29522	−	0.356219i
$695$	−19.3570	−	7.43045i	−0.734253	−	0.281853i
$696$	3.15064	−	43.6022i	0.119425	−	1.65274i
$697$	5.99239	−	11.7607i	0.226978	−	0.445469i
$698$	18.0231	+	25.1536i	0.682183	+	0.952078i
$699$	−13.1049	−	5.83466i	−0.495671	−	0.220687i
$700$	34.8968	+	18.3642i	1.31897	+	0.694102i
$701$	−18.4299	−	5.98825i	−0.696089	−	0.226173i	−0.0604635	−	0.998170i	$-0.519258\pi$
$701$	−18.4299	−	5.98825i	−0.696089	−	0.226173i	−0.635626	+	0.771997i	$0.719258\pi$
$702$	−1.67160	−	18.4335i	−0.0630903	−	0.695726i
$703$		−	29.6346i		−	1.11769i
$704$	8.35904	−	25.1819i	0.315043	−	0.949077i
$705$	−17.9601	−	31.1078i	−0.676415	−	1.17159i
$706$	−23.4956	−	17.3083i	−0.884268	−	0.651407i
$707$	15.7221	−	8.01083i	0.591292	−	0.301278i
$708$	−1.78155	−	45.4505i	−0.0669548	−	1.70814i
$709$	18.9299	−	23.3765i	0.710927	−	0.877922i	−0.285839	−	0.958278i	$-0.592272\pi$
$709$	18.9299	−	23.3765i	0.710927	−	0.877922i	0.996766	+	0.0803560i	$0.0256057\pi$
$710$	−0.186173	−	0.494720i	−0.00698696	−	0.0185665i
$711$	1.59691	−	7.51286i	0.0598887	−	0.281754i
$712$	39.8654	−	7.65309i	1.49402	−	0.286812i
$713$	32.6001	−	26.3991i	1.22088	−	0.988653i
$714$	−13.9652	−	24.5608i	−0.522633	−	0.919166i
$715$	−0.973074	−	38.1350i	−0.0363909	−	1.42617i
$716$	−5.91623	−	3.52052i	−0.221100	−	0.131568i
$717$	24.5131	+	30.2712i	0.915459	+	1.13050i
$718$	−11.9428	−	13.4409i	−0.445700	−	0.501610i
$719$	45.1257	+	9.59177i	1.68290	+	0.357712i	0.947461	−	0.319873i	$-0.103640\pi$
$719$	45.1257	+	9.59177i	1.68290	+	0.357712i	0.735444	+	0.677585i	$0.236973\pi$
$720$	14.8727	−	5.26362i	0.554274	−	0.196164i
$721$	9.93544	+	8.04556i	0.370015	+	0.299632i
$722$	−4.31235	−	2.23317i	−0.160489	−	0.0831102i
$723$	−20.4197	−	40.0760i	−0.759418	−	1.49044i
$724$	−3.06871	+	25.9069i	−0.114048	+	0.962824i
$725$	−33.6630	+	19.4354i	−1.25021	+	0.721811i
$726$	−16.2158	−	27.6090i	−0.601824	−	1.02467i
$727$	−19.4588			−0.721689			−0.360844	−	0.932626i	$-0.617511\pi$
$727$	−19.4588			−0.721689			−0.360844	+	0.932626i	$0.617511\pi$
$728$	29.5051	+	25.2655i	1.09353	+	0.936400i
$729$	−2.65456	+	8.16991i	−0.0983172	+	0.302589i
$730$	12.2143	+	19.0825i	0.452070	+	0.706275i
$731$	2.49664	−	5.60755i	0.0923417	−	0.207403i
$732$	−22.3930	−	10.3258i	−0.827670	−	0.381654i
$733$	44.3520	+	22.5985i	1.63818	+	0.834694i	0.997776	+	0.0666548i	$0.0212326\pi$
$733$	44.3520	+	22.5985i	1.63818	+	0.834694i	0.640403	+	0.768039i	$0.278767\pi$
$734$	−18.7612	−	37.4287i	−0.692487	−	1.38152i
$735$	−17.6678	+	46.0263i	−0.651688	+	1.69771i
$736$	28.9173	−	6.73553i	1.06591	−	0.248275i
$737$	−1.46281	−	17.0544i	−0.0538834	−	0.628205i
$738$	−4.58007	+	7.81352i	−0.168595	+	0.287620i
$739$	−8.12065	−	10.0282i	−0.298723	−	0.368892i	0.605579	−	0.795785i	$-0.292941\pi$
$739$	−8.12065	−	10.0282i	−0.298723	−	0.368892i	−0.904302	+	0.426893i	$0.859608\pi$
$740$	−36.0327	+	31.5939i	−1.32459	+	1.16142i
$741$	29.2784	+	0.225249i	1.07557	+	0.00827474i
$742$	−63.7493	−	28.8880i	−2.34031	−	1.06051i
$743$	−4.32262	−	11.2608i	−0.158582	−	0.413120i	0.831152	−	0.556046i	$-0.187682\pi$
$743$	−4.32262	−	11.2608i	−0.158582	−	0.413120i	−0.989733	+	0.142926i	$0.954349\pi$
$744$	−33.9540	−	31.8102i	−1.24481	−	1.16622i
$745$	33.4524	−	30.1207i	1.22560	−	1.10354i
$746$	22.7185	−	18.1505i	0.831784	−	0.664536i
$747$	3.54025	−	0.948608i	0.129531	−	0.0347078i
$748$	16.1774	+	4.90052i	0.591503	+	0.179181i
$749$	−6.97517	−	6.97517i	−0.254867	−	0.254867i
$750$	−1.31867	−	0.971416i	−0.0481511	−	0.0354711i
$751$	34.9379	−	7.42628i	1.27490	−	0.270989i	0.479753	−	0.877403i	$-0.340726\pi$
$751$	34.9379	−	7.42628i	1.27490	−	0.270989i	0.795149	+	0.606415i	$0.207393\pi$
$752$	−18.6603	+	11.4303i	−0.680470	+	0.416819i
$753$	−14.8138	−	20.3894i	−0.539843	−	0.743031i
$754$	−36.5810	+	11.3108i	−1.33220	+	0.411916i
$755$	15.6444	−	5.08316i	0.569357	−	0.184995i
$756$	−12.2283	−	24.8023i	−0.444739	−	0.902051i
$757$	−3.39929	+	32.3421i	−0.123549	+	1.17549i	0.740490	+	0.672068i	$0.234594\pi$
$757$	−3.39929	+	32.3421i	−0.123549	+	1.17549i	−0.864039	+	0.503425i	$0.832073\pi$
$758$	0.105887	−	16.0648i	0.00384600	−	0.583500i
$759$	16.8751	−	31.6076i	0.612528	−	1.14728i
$760$	−8.53189	−	34.5610i	−0.309484	−	1.25366i
$761$	4.05891	+	1.55807i	0.147135	+	0.0564799i	0.430821	−	0.902437i	$-0.358224\pi$
$761$	4.05891	+	1.55807i	0.147135	+	0.0564799i	−0.283686	+	0.958917i	$0.591557\pi$
$762$	11.1858	−	16.9786i	0.405219	−	0.615069i
$763$	−1.88399	+	8.86350i	−0.0682052	+	0.320880i
$764$	39.2097	−	27.7053i	1.41856	−	1.00234i
$765$	3.60189	+	9.38326i	0.130227	+	0.339252i
$766$	−17.3382	−	15.8196i	−0.626455	−	0.571584i
$767$	−36.5189	+	15.9238i	−1.31862	+	0.574974i
$768$	−11.7904	−	30.7491i	−0.425450	−	1.10956i
$769$	29.2079	+	7.82623i	1.05326	+	0.282221i	0.743600	−	0.668625i	$-0.233117\pi$
$769$	29.2079	+	7.82623i	1.05326	+	0.282221i	0.309664	+	0.950846i	$0.399784\pi$
$770$	−21.8330	−	52.6451i	−0.786808	−	1.89720i
$771$	−29.7144	+	51.4668i	−1.07014	+	1.85353i
$772$	−10.3389	+	25.9077i	−0.372106	+	0.932440i
$773$	24.3066	+	1.27386i	0.874249	+	0.0458175i	0.484180	−	0.874968i	$-0.339118\pi$
$773$	24.3066	+	1.27386i	0.874249	+	0.0458175i	0.390069	+	0.920786i	$0.372451\pi$
$774$	−1.93683	+	3.74009i	−0.0696178	+	0.134435i
$775$	−6.47173	+	40.8609i	−0.232472	+	1.46777i
$776$	−41.0534	+	3.49574i	−1.47373	+	0.125490i
$777$	−43.7617	−	39.4032i	−1.56994	−	1.41358i
$778$	−22.2042	−	1.31048i	−0.796059	−	0.0469829i
$779$	16.5331	+	12.0120i	0.592361	+	0.430375i
$780$	−30.9403	−	35.8397i	−1.10784	−	1.28327i
$781$	−0.127141	+	0.367214i	−0.00454948	+	0.0131399i
$782$	4.77514	+	18.3028i	0.170759	+	0.654506i
$783$	27.1087	+	2.84924i	0.968786	+	0.101824i
$784$	28.3098	+	10.0309i	1.01106	+	0.358247i
$785$	10.6101	+	5.40613i	0.378691	+	0.192953i
$786$	−27.9470	−	4.61540i	−0.996838	−	0.164626i
$787$	−32.6828	−	26.4660i	−1.16502	−	0.943411i	−0.165928	−	0.986138i	$-0.553062\pi$
$787$	−32.6828	−	26.4660i	−1.16502	−	0.943411i	−0.999087	+	0.0427272i	$0.986395\pi$
$788$	16.1512	+	25.6033i	0.575362	+	0.912080i
$789$	−21.7500	−	24.1558i	−0.774319	−	0.859968i
$790$	11.2300	+	25.6772i	0.399546	+	0.913553i
$791$	−30.5893	−	8.19637i	−1.08763	−	0.291430i
$792$	−10.8829	−	4.01072i	−0.386709	−	0.142515i
$793$	−1.29627	+	21.5594i	−0.0460318	+	0.765596i
$794$	−17.0343	−	1.90398i	−0.604525	−	0.0675696i
$795$	71.5468	+	46.4630i	2.53750	+	1.64787i
$796$	19.7181	−	6.12065i	0.698891	−	0.216941i
$797$	29.7389	−	3.12568i	1.05341	−	0.110717i	0.438037	−	0.898957i	$-0.355674\pi$
$797$	29.7389	−	3.12568i	1.05341	−	0.110717i	0.615369	+	0.788239i	$0.289007\pi$
$798$	40.9408	−	15.4068i	1.44929	−	0.545397i
$799$	−7.59272	−	11.6918i	−0.268611	−	0.413625i
$800$	−16.7487	+	24.0192i	−0.592155	+	0.849206i
$801$	−2.77588	−	17.5262i	−0.0980810	−	0.619259i
$802$	−0.359915	+	54.6048i	−0.0127090	+	1.92816i
$803$	2.05805	−	16.5288i	0.0726271	−	0.583290i
$804$	−14.8232	−	15.2193i	−0.522775	−	0.536743i
$805$	37.4872	−	51.5968i	1.32125	−	1.81855i
$806$	−15.1461	+	37.8327i	−0.533500	+	1.33260i
$807$	31.4254	−	10.2107i	1.10623	−	0.359435i
$808$	4.45283	+	12.3229i	0.156650	+	0.433519i
$809$	37.7242	+	16.7959i	1.32631	+	0.590512i	0.942903	−	0.333067i	$-0.108084\pi$
$809$	37.7242	+	16.7959i	1.32631	+	0.590512i	0.383408	+	0.923579i	$0.374750\pi$
$810$	15.2702	+	48.0728i	0.536542	+	1.68911i
$811$	−9.69443	+	4.93956i	−0.340417	+	0.173451i	−0.615839	−	0.787872i	$-0.711183\pi$
$811$	−9.69443	+	4.93956i	−0.340417	+	0.173451i	0.275421	+	0.961324i	$0.411183\pi$
$812$	−44.9278	+	35.4115i	−1.57666	+	1.24270i
$813$	−45.9900	+	12.3230i	−1.61294	+	0.432186i
$814$	35.2182	−	0.937486i	1.23440	−	0.0328589i
$815$	63.6439	+	36.7448i	2.22935	+	1.28711i
$816$	19.3844	−	8.02510i	0.678591	−	0.280935i
$817$	7.97037	+	5.17602i	0.278848	+	0.181086i
$818$	−6.66283	+	7.30245i	−0.232961	+	0.255324i
$819$	11.4587	−	12.5310i	0.400400	−	0.437868i
$820$	−3.02083	−	32.9088i	−0.105492	−	1.14923i
$821$	−2.73480	−	52.1831i	−0.0954452	−	1.82120i	−0.457682	−	0.889116i	$-0.651320\pi$
$821$	−2.73480	−	52.1831i	−0.0954452	−	1.82120i	0.362236	−	0.932086i	$-0.382013\pi$
$822$	24.1706	+	27.2026i	0.843045	+	0.948799i
$823$	−42.7888	+	19.0508i	−1.49152	+	0.664068i	−0.980682	−	0.195607i	$-0.937332\pi$
$823$	−42.7888	+	19.0508i	−1.49152	+	0.664068i	−0.510840	+	0.859676i	$0.670665\pi$
$824$	−6.84418	+	6.57873i	−0.238428	+	0.229181i
$825$	8.49025	+	34.3012i	0.295593	+	1.19421i
$826$	−42.3643	+	41.8095i	−1.47404	+	1.45474i
$827$	16.8776	−	2.67314i	0.586890	−	0.0929543i	0.144074	−	0.989567i	$-0.453980\pi$
$827$	16.8776	−	2.67314i	0.586890	−	0.0929543i	0.442816	+	0.896613i	$0.353980\pi$
$828$	−2.53092	−	12.7299i	−0.0879556	−	0.442396i
$829$	−10.7061	−	9.63983i	−0.371839	−	0.334805i	0.461932	−	0.886915i	$-0.347156\pi$
$829$	−10.7061	−	9.63983i	−0.371839	−	0.334805i	−0.833771	+	0.552110i	$0.813823\pi$
$830$	−8.48450	+	10.3374i	−0.294501	+	0.358817i
$831$	22.7632	−	16.5384i	0.789646	−	0.573712i
$832$	−21.3365	+	19.4102i	−0.739709	+	0.672926i
$833$	−5.91272	+	18.1975i	−0.204864	+	0.630505i
$834$	17.6175	+	6.89631i	0.610045	+	0.238800i
$835$	−34.1059	+	19.6911i	−1.18028	+	0.681437i
$836$	−11.4120	+	23.5515i	−0.394694	+	0.814546i
$837$	20.5137	−	20.5137i	0.709059	−	0.709059i
$838$	0.175875	−	0.0266688i	0.00607551	−	0.000921260i
$839$	24.4701	+	1.28242i	0.844803	+	0.0442742i	0.469825	−	0.882760i	$-0.344317\pi$
$839$	24.4701	+	1.28242i	0.844803	+	0.0442742i	0.374978	+	0.927034i	$0.377650\pi$
$840$	−62.3808	−	33.3543i	−2.15234	−	1.15083i
$841$	−2.86290	−	27.2387i	−0.0987207	−	0.939264i
$842$	−3.33032	−	33.8294i	−0.114771	−	1.16584i
$843$	0.764527	+	14.5880i	0.0263317	+	0.502439i
$844$	8.65867	+	9.87516i	0.298044	+	0.339917i
$845$	−19.3935	+	36.6565i	−0.667158	+	1.26102i
$846$	4.72815	+	8.31549i	0.162557	+	0.285892i
$847$	−12.3865	+	40.0264i	−0.425604	+	1.37532i
$848$	27.1631	−	44.3078i	0.932785	−	1.52154i
$849$	−2.70561	−	6.07690i	−0.0928564	−	0.208559i
$850$	−15.5778	−	10.2630i	−0.534315	−	0.352017i
$851$	21.4721	+	33.0641i	0.736053	+	1.13342i
$852$	0.166898	+	0.452525i	0.00571782	+	0.0155032i
$853$	25.8615	+	4.09606i	0.885481	+	0.140246i	0.582578	−	0.812775i	$-0.302044\pi$
$853$	25.8615	+	4.09606i	0.885481	+	0.140246i	0.302903	+	0.953021i	$0.402044\pi$
$854$	9.76896	+	30.7540i	0.334287	+	1.05238i
$855$	−15.2212	+	3.23538i	−0.520556	+	0.110647i
$856$	5.78255	−	4.49626i	0.197644	−	0.153679i
$857$			15.1103i			0.516160i	0.966124	+	0.258080i	$0.0830897\pi$
$857$			15.1103i			0.516160i	−0.966124	+	0.258080i	$0.916910\pi$
$858$	0.658527	+	34.8020i	0.0224818	+	1.18812i
$859$			23.2363i			0.792811i	0.918076	+	0.396405i	$0.129743\pi$
$859$			23.2363i			0.792811i	−0.918076	+	0.396405i	$0.870257\pi$
$860$	−2.20382	−	15.2094i	−0.0751498	−	0.518636i
$861$	39.7213	−	8.44301i	1.35370	−	0.287737i
$862$	−24.6873	+	7.84187i	−0.840852	+	0.267095i
$863$	−2.31362	−	0.366441i	−0.0787564	−	0.0124738i	0.116932	−	0.993140i	$-0.462694\pi$
$863$	−2.31362	−	0.366441i	−0.0787564	−	0.0124738i	−0.195688	+	0.980666i	$0.562694\pi$
$864$	19.4022	−	6.72308i	0.660076	−	0.228724i
$865$	−30.4494	−	46.8880i	−1.03531	−	1.59424i
$866$	−1.02375	+	1.55391i	−0.0347884	+	0.0528042i
$867$	−8.79553	−	19.7551i	−0.298712	−	0.670918i
$868$	−0.802572	+	60.8789i	−0.0272411	+	2.06636i
$869$	5.71277	−	19.7955i	0.193792	−	0.671518i
$870$	60.6146	−	34.4652i	2.05503	−	1.16848i
$871$	−7.69916	+	16.9406i	−0.260876	+	0.574011i
$872$	−6.35704	−	2.20542i	−0.215276	−	0.0746848i
$873$	0.942610	+	17.9861i	0.0319025	+	0.608736i
$874$	−29.1451	+	2.86918i	−0.985848	+	0.0970516i
$875$	0.224031	+	2.13151i	0.00757362	+	0.0720582i
$876$	−11.0301	−	17.4852i	−0.372672	−	0.590771i
$877$	7.82394	+	0.410035i	0.264196	+	0.0138459i	0.183974	−	0.982931i	$-0.441104\pi$
$877$	7.82394	+	0.410035i	0.264196	+	0.0138459i	0.0802218	+	0.996777i	$0.474437\pi$
$878$	2.77221	+	18.2821i	0.0935576	+	0.616993i
$879$	−1.42891	+	1.42891i	−0.0481961	+	0.0481961i
$880$	40.8028	−	11.2327i	1.37546	−	0.378656i
$881$	2.76419	−	1.59591i	0.0931280	−	0.0537675i	−0.452713	−	0.891656i	$-0.649544\pi$
$881$	2.76419	−	1.59591i	0.0931280	−	0.0537675i	0.545841	+	0.837889i	$0.316210\pi$
$882$	4.78571	−	12.2257i	0.161143	−	0.411662i
$883$	−0.274376	+	0.844442i	−0.00923348	+	0.0284177i	−0.955567	−	0.294774i	$-0.904756\pi$
$883$	−0.274376	+	0.844442i	−0.00923348	+	0.0284177i	0.946334	+	0.323191i	$0.104756\pi$
$884$	−12.7196	−	13.2621i	−0.427807	−	0.446052i
$885$	58.6944	−	42.6440i	1.97299	−	1.43346i
$886$	28.5985	+	23.4724i	0.960787	+	0.788571i
$887$	8.03570	+	7.23538i	0.269812	+	0.242940i	0.792919	−	0.609327i	$-0.208560\pi$
$887$	8.03570	+	7.23538i	0.269812	+	0.242940i	−0.523107	+	0.852267i	$0.675227\pi$
$888$	33.0679	−	28.6111i	1.10969	−	0.960125i
$889$	−26.2785	+	4.16211i	−0.881354	+	0.139593i
$890$	45.4805	+	46.0840i	1.52451	+	1.54474i
$891$	13.9495	−	34.3577i	0.467326	−	1.15103i
$892$	7.87517	+	31.0206i	0.263680	+	1.03865i
$893$	19.7180	−	8.77902i	0.659838	−	0.293779i
$894$	−30.7047	+	27.2823i	−1.02692	+	0.912457i
$895$	−0.574694	−	10.9658i	−0.0192099	−	0.366547i
$896$	−19.3250	+	38.5181i	−0.645604	+	1.28680i
$897$	−32.8298	+	20.9626i	−1.09616	+	0.699922i
$898$	−16.1451	−	14.7310i	−0.538769	−	0.491579i
$899$	−50.3326	−	32.6863i	−1.67868	−	1.09015i
$900$	10.2555	+	7.65960i	0.341849	+	0.255320i
$901$	28.6734	+	16.5546i	0.955251	+	0.551514i
$902$	−13.7522	+	20.0282i	−0.457899	+	0.666866i
$903$	18.2412	−	4.88770i	0.607028	−	0.162653i
$904$	8.85970	−	21.7829i	0.294669	−	0.724488i
$905$	−37.0757	+	18.8910i	−1.23244	+	0.627958i
$906$	−14.3052	+	4.54402i	−0.475259	+	0.150965i
$907$	−29.8092	−	13.2719i	−0.989798	−	0.440686i	−0.153017	−	0.988224i	$-0.548899\pi$
$907$	−29.8092	−	13.2719i	−0.989798	−	0.440686i	−0.836781	+	0.547537i	$0.815565\pi$
$908$	−2.88501	+	16.7805i	−0.0957424	+	0.556880i
$909$	5.44733	−	1.76994i	0.180676	−	0.0587053i
$910$	−7.35585	+	61.5196i	−0.243844	+	2.03936i
$911$	−5.29095	+	7.28237i	−0.175297	+	0.241276i	−0.887620	−	0.460576i	$-0.847643\pi$
$911$	−5.29095	+	7.28237i	−0.175297	+	0.241276i	0.712323	+	0.701851i	$0.247643\pi$
$912$	7.57703	+	31.5863i	0.250901	+	1.04593i
$913$	9.65423	−	1.85954i	0.319508	−	0.0615418i
$914$	40.7761	+	0.268766i	1.34875	+	0.00888998i
$915$	−6.15285	−	38.8475i	−0.203407	−	1.28426i
$916$	−5.87542	+	8.79144i	−0.194130	+	0.290477i
$917$	20.1877	+	31.0863i	0.666657	+	1.02656i
$918$	4.60741	+	12.2433i	0.152067	+	0.404090i
$919$	44.9630	−	4.72580i	1.48319	−	0.155890i	0.671949	−	0.740598i	$-0.265457\pi$
$919$	44.9630	−	4.72580i	1.48319	−	0.155890i	0.811244	+	0.584708i	$0.198791\pi$
$920$	34.5607	+	32.3786i	1.13943	+	1.06749i
$921$	−0.895533	−	0.581566i	−0.0295088	−	0.0191632i
$922$	1.54706	−	13.8411i	0.0509498	−	0.455833i
$923$	0.316110	−	0.280253i	0.0104049	−	0.00922465i
$924$	19.6049	+	48.1672i	0.644953	+	1.58458i
$925$	−37.5561	−	10.0631i	−1.23484	−	0.330873i
$926$	45.9965	−	20.1167i	1.51154	−	0.661077i
$927$	2.77678	+	3.08393i	0.0912015	+	0.101290i
$928$	−21.9491	−	36.3686i	−0.720515	−	1.19386i
$929$	14.9324	+	12.0920i	0.489915	+	0.396725i	0.842198	−	0.539168i	$-0.181261\pi$
$929$	14.9324	+	12.0920i	0.489915	+	0.396725i	−0.352283	+	0.935893i	$0.614595\pi$
$930$	12.0921	−	73.2198i	0.396516	−	2.40097i
$931$	−26.3955	−	13.4492i	−0.865077	−	0.440779i
$932$	−13.6715	+	2.71812i	−0.447824	+	0.0890348i
$933$	24.9028	+	2.61739i	0.815281	+	0.0856895i
$934$	−9.20543	+	2.40167i	−0.301211	+	0.0785851i
$935$	7.83879	+	25.7965i	0.256356	+	0.843636i
$936$	8.17645	+	9.59838i	0.267256	+	0.313733i
$937$	−25.1094	−	18.2431i	−0.820290	−	0.595975i	0.0965056	−	0.995332i	$-0.469233\pi$
$937$	−25.1094	−	18.2431i	−0.820290	−	0.595975i	−0.916796	+	0.399357i	$0.869233\pi$
$938$	−1.63794	+	27.7526i	−0.0534807	+	0.906154i
$939$	−23.4440	−	21.1091i	−0.765066	−	0.688868i
$940$	−31.6961	−	14.6156i	−1.03381	−	0.476709i
$941$	−2.01172	+	12.7015i	−0.0655801	+	0.414056i	0.932957	+	0.359988i	$0.117219\pi$
$941$	−2.01172	+	12.7015i	−0.0655801	+	0.414056i	−0.998537	+	0.0540689i	$0.982781\pi$
$942$	−9.64865	−	4.99661i	−0.314370	−	0.162798i
$943$	−27.1498	−	1.42286i	−0.884120	−	0.0463348i
$944$	−26.8996	−	35.0697i	−0.875508	−	1.14142i
$945$	22.0535	−	38.1978i	0.717401	−	1.24258i
$946$	−5.89911	+	9.63584i	−0.191797	+	0.313288i
$947$	−9.29848	−	2.49152i	−0.302160	−	0.0809635i	0.104554	−	0.994519i	$-0.466659\pi$
$947$	−9.29848	−	2.49152i	−0.302160	−	0.0809635i	−0.406714	+	0.913556i	$0.633325\pi$
$948$	−10.0924	−	23.4966i	−0.327784	−	0.763133i
$949$	−10.7557	+	14.5670i	−0.349145	+	0.472863i
$950$	19.4671	−	21.3359i	0.631595	−	0.692227i
$951$	1.88602	+	4.91326i	0.0611585	+	0.159323i
$952$	−24.8547	−	11.6602i	−0.805545	−	0.377910i
$953$	−10.6550	+	50.1279i	−0.345150	+	1.62380i	0.372942	+	0.927855i	$0.378349\pi$
$953$	−10.6550	+	50.1279i	−0.345150	+	1.62380i	−0.718092	+	0.695948i	$0.754984\pi$
$954$	−18.9713	−	12.4986i	−0.614218	−	0.404658i
$955$	71.4912	+	27.4429i	2.31340	+	0.888031i
$956$	36.4273	+	10.2772i	1.17814	+	0.332389i
$957$	−50.4675	−	8.98738i	−1.63138	−	0.290521i
$958$	−49.3167	−	0.325059i	−1.59335	−	0.0105022i
$959$	4.97748	−	47.3576i	0.160731	−	1.52926i
$960$	30.3278	−	42.8876i	0.978825	−	1.38419i
$961$	−31.2649	+	10.1586i	−1.00854	+	0.327696i
$962$	−33.8735	−	17.8734i	−1.09213	−	0.576262i
$963$	−1.88207	−	2.59044i	−0.0606487	−	0.0834758i
$964$	−38.6768	−	20.3534i	−1.24570	−	0.655540i
$965$	−43.5201	+	9.25049i	−1.40096	+	0.297784i
$966$	−34.5154	+	46.8538i	−1.11052	+	1.50750i
$967$	26.5428	+	26.5428i	0.853559	+	0.853559i	0.990570	−	0.137011i	$-0.0437495\pi$
$967$	26.5428	+	26.5428i	0.853559	+	0.853559i	−0.137011	+	0.990570i	$0.543749\pi$
$968$	−28.3500	−	12.8172i	−0.911202	−	0.411960i
$969$	−19.9884	+	5.35588i	−0.642120	+	0.172056i
$970$	−41.0202	−	51.3440i	−1.31708	−	1.64856i
$971$	14.2965	−	12.8726i	0.458797	−	0.413103i	−0.407054	−	0.913404i	$-0.633444\pi$
$971$	14.2965	−	12.8726i	0.458797	−	0.413103i	0.865851	+	0.500301i	$0.166777\pi$
$972$	−7.18752	−	23.1552i	−0.230540	−	0.742702i
$973$	−8.87220	−	23.1129i	−0.284430	−	0.740965i
$974$	−10.6231	+	23.4429i	−0.340387	+	0.751159i
$975$	10.2276	−	37.0281i	0.327546	−	1.18585i
$976$	−23.5608	+	4.36223i	−0.754162	+	0.139632i
$977$	19.5031	+	24.0843i	0.623959	+	0.770526i	0.986908	−	0.161283i	$-0.0515633\pi$
$977$	19.5031	+	24.0843i	0.623959	+	0.770526i	−0.362949	+	0.931809i	$0.618230\pi$
$978$	−57.8506	−	33.9104i	−1.84986	−	1.08434i
$979$	−4.06787	−	47.4257i	−0.130010	−	1.51573i
$980$	11.7878	+	46.4326i	0.376548	+	1.48324i
$981$	−1.05409	+	2.74599i	−0.0336544	+	0.0876727i
$982$	1.19831	−	0.600656i	0.0382397	−	0.0191677i
$983$	35.9380	+	18.3113i	1.14625	+	0.584041i	0.920731	−	0.390199i	$-0.127594\pi$
$983$	35.9380	+	18.3113i	1.14625	+	0.584041i	0.225515	+	0.974240i	$0.427594\pi$
$984$	2.55842	+	30.0457i	0.0815596	+	0.957821i
$985$	−19.6390	+	44.1100i	−0.625752	+	1.40546i
$986$	22.7926	−	14.5890i	0.725864	−	0.464609i
$987$	13.2537	−	40.7906i	0.421869	−	1.29838i
$988$	23.3611	−	16.2387i	0.743215	−	0.516623i
$989$	−12.6431			−0.402026
$990$	−4.32649	−	17.9868i	−0.137505	−	0.571658i
$991$	−27.7988	+	16.0496i	−0.883058	+	0.509834i	−0.871666	−	0.490101i	$-0.836960\pi$
$991$	−27.7988	+	16.0496i	−0.883058	+	0.509834i	−0.0113927	+	0.999935i	$0.503626\pi$
$992$	−44.7824	−	6.20470i	−1.42184	−	0.196999i
$993$	11.7284	+	23.0183i	0.372190	+	0.730465i
$994$	0.290238	−	0.560462i	0.00920580	−	0.0177768i
$995$	25.5924	+	20.7243i	0.811333	+	0.657004i
$996$	7.80382	−	9.38131i	0.247274	−	0.297258i
$997$	−25.0741	−	5.32967i	−0.794106	−	0.168792i	−0.207041	−	0.978332i	$-0.566383\pi$
$997$	−25.0741	−	5.32967i	−0.794106	−	0.168792i	−0.587065	+	0.809540i	$0.699717\pi$
$998$	22.2380	−	19.7593i	0.703931	−	0.625471i
$999$	17.1585	+	21.1890i	0.542872	+	0.670391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bs.a.15.12	✓	1280
4.3	odd	2	inner	572.2.bs.a.15.37	yes	1280
11.3	even	5	inner	572.2.bs.a.223.24	yes	1280
13.7	odd	12	inner	572.2.bs.a.59.5	yes	1280
44.3	odd	10	inner	572.2.bs.a.223.5	yes	1280
52.7	even	12	inner	572.2.bs.a.59.24	yes	1280
143.124	odd	60	inner	572.2.bs.a.267.37	yes	1280
572.267	even	60	inner	572.2.bs.a.267.12	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bs.a.15.12	✓	1280	1.1	even	1	trivial
572.2.bs.a.15.37	yes	1280	4.3	odd	2	inner
572.2.bs.a.59.5	yes	1280	13.7	odd	12	inner
572.2.bs.a.59.24	yes	1280	52.7	even	12	inner
572.2.bs.a.223.5	yes	1280	44.3	odd	10	inner
572.2.bs.a.223.24	yes	1280	11.3	even	5	inner
572.2.bs.a.267.12	yes	1280	572.267	even	60	inner
572.2.bs.a.267.37	yes	1280	143.124	odd	60	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31691 - 0.515500i) q^{2} +(0.427935 + 2.01327i) q^{3} +(1.46852 + 1.35774i) q^{4} +(-0.499033 + 3.15077i) q^{5} +(0.474290 - 2.87191i) q^{6} +(-3.19451 + 2.07454i) q^{7} +(-1.23400 - 2.54504i) q^{8} +(-1.12951 + 0.502889i) q^{9} +O(q^{10})\)	\(q+(-1.31691 - 0.515500i) q^{2} +(0.427935 + 2.01327i) q^{3} +(1.46852 + 1.35774i) q^{4} +(-0.499033 + 3.15077i) q^{5} +(0.474290 - 2.87191i) q^{6} +(-3.19451 + 2.07454i) q^{7} +(-1.23400 - 2.54504i) q^{8} +(-1.12951 + 0.502889i) q^{9} +(2.28140 - 3.89204i) q^{10} +(-3.11853 + 1.12905i) q^{11} +(-2.10507 + 3.53756i) q^{12} +(3.55672 + 0.591412i) q^{13} +(5.27632 - 1.08522i) q^{14} +(-6.55692 + 0.343633i) q^{15} +(0.313100 + 3.98773i) q^{16} +(-2.53431 + 0.266367i) q^{17} +(1.74670 - 0.0800002i) q^{18} +(0.206486 - 3.93998i) q^{19} +(-5.01076 + 3.94941i) q^{20} +(-5.54366 - 5.54366i) q^{21} +(4.68886 + 0.120750i) q^{22} +(2.62437 + 4.54555i) q^{23} +(4.59580 - 3.57349i) q^{24} +(-4.92304 - 1.59959i) q^{25} +(-4.37901 - 2.61233i) q^{26} +(2.13362 + 2.93668i) q^{27} +(-7.50788 - 1.29080i) q^{28} +(5.02466 - 5.58045i) q^{29} +(8.81203 + 2.92755i) q^{30} +(-1.25024 - 7.89372i) q^{31} +(1.64335 - 5.41289i) q^{32} +(-3.60761 - 5.79531i) q^{33} +(3.47478 + 0.955656i) q^{34} +(-4.94223 - 11.1004i) q^{35} +(-2.34150 - 0.795072i) q^{36} +(7.50091 - 0.393106i) q^{37} +(-2.30298 + 5.08217i) q^{38} +(0.331367 + 7.41373i) q^{39} +(8.63465 - 2.61799i) q^{40} +(-2.82108 + 4.34409i) q^{41} +(4.44276 + 10.1583i) q^{42} +(-1.20439 + 2.08607i) q^{43} +(-6.11258 - 2.57612i) q^{44} +(-1.02083 - 3.80978i) q^{45} +(-1.11284 - 7.33895i) q^{46} +(2.48365 + 4.87443i) q^{47} +(-7.89440 + 2.33684i) q^{48} +(3.05402 - 6.85945i) q^{49} +(5.65862 + 4.64435i) q^{50} +(-1.62079 - 4.98828i) q^{51} +(4.42013 + 5.69759i) q^{52} +(-10.5114 - 7.63699i) q^{53} +(-1.29594 - 4.96723i) q^{54} +(-2.00111 - 10.3892i) q^{55} +(9.22181 + 5.57019i) q^{56} +(8.02063 - 1.27034i) q^{57} +(-9.49377 + 4.75876i) q^{58} +(-9.26691 + 6.01800i) q^{59} +(-10.0955 - 8.39794i) q^{60} +(0.626157 + 5.95748i) q^{61} +(-2.42275 + 11.0398i) q^{62} +(2.56496 - 3.94969i) q^{63} +(-4.95449 + 6.28116i) q^{64} +(-3.63832 + 10.9113i) q^{65} +(1.76342 + 9.49164i) q^{66} +(-1.33576 + 4.98511i) q^{67} +(-4.08334 - 3.04977i) q^{68} +(-8.02837 + 7.22878i) q^{69} +(0.786215 + 17.1660i) q^{70} +(0.0737360 - 0.0910564i) q^{71} +(2.67369 + 2.25408i) q^{72} +(-2.27999 + 4.47474i) q^{73} +(-10.0807 - 3.34903i) q^{74} +(1.11368 - 10.5959i) q^{75} +(5.65269 - 5.50559i) q^{76} +(7.61994 - 10.0763i) q^{77} +(3.38540 - 9.93406i) q^{78} +(-3.65141 + 5.02574i) q^{79} +(-12.7207 - 1.00350i) q^{80} +(-7.48122 + 8.30874i) q^{81} +(5.95450 - 4.26652i) q^{82} +(-2.92787 - 0.463729i) q^{83} +(-0.614140 - 15.6678i) q^{84} +(0.425444 - 8.11796i) q^{85} +(2.66144 - 2.12630i) q^{86} +(13.3852 + 7.72795i) q^{87} +(6.72174 + 6.54356i) q^{88} +(-3.71455 + 13.8629i) q^{89} +(-0.619600 + 5.54338i) q^{90} +(-12.5889 + 5.48927i) q^{91} +(-2.31771 + 10.2384i) q^{92} +(15.3572 - 5.89507i) q^{93} +(-0.757977 - 7.69952i) q^{94} +(12.3109 + 2.61677i) q^{95} +(11.6009 + 0.992146i) q^{96} +(5.22038 - 13.5996i) q^{97} +(-7.55793 + 7.45895i) q^{98} +(2.95462 - 2.84354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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