LMFDB - Embedded newform 1380.2.p.a.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (of order $2$, degree $1$, 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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.a.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39049 - 0.257970i) q^{2} -1.00000i q^{3} +(1.86690 + 0.717408i) q^{4} -1.00000i q^{5} +(-0.257970 + 1.39049i) q^{6} +2.59830 q^{7} +(-2.41083 - 1.47915i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.39049 - 0.257970i) q^{2} -1.00000i q^{3} +(1.86690 + 0.717408i) q^{4} -1.00000i q^{5} +(-0.257970 + 1.39049i) q^{6} +2.59830 q^{7} +(-2.41083 - 1.47915i) q^{8} -1.00000 q^{9} +(-0.257970 + 1.39049i) q^{10} -1.75416 q^{11} +(0.717408 - 1.86690i) q^{12} -2.03614 q^{13} +(-3.61291 - 0.670285i) q^{14} -1.00000 q^{15} +(2.97065 + 2.67866i) q^{16} +3.95759i q^{17} +(1.39049 + 0.257970i) q^{18} -5.10890 q^{19} +(0.717408 - 1.86690i) q^{20} -2.59830i q^{21} +(2.43913 + 0.452520i) q^{22} +(-4.47835 - 1.71592i) q^{23} +(-1.47915 + 2.41083i) q^{24} -1.00000 q^{25} +(2.83122 + 0.525262i) q^{26} +1.00000i q^{27} +(4.85078 + 1.86404i) q^{28} -7.32394 q^{29} +(1.39049 + 0.257970i) q^{30} +4.91715i q^{31} +(-3.43964 - 4.49098i) q^{32} +1.75416i q^{33} +(1.02094 - 5.50297i) q^{34} -2.59830i q^{35} +(-1.86690 - 0.717408i) q^{36} -0.890633i q^{37} +(7.10385 + 1.31794i) q^{38} +2.03614i q^{39} +(-1.47915 + 2.41083i) q^{40} -10.1575 q^{41} +(-0.670285 + 3.61291i) q^{42} +5.82796 q^{43} +(-3.27484 - 1.25845i) q^{44} +1.00000i q^{45} +(5.78443 + 3.54125i) q^{46} -2.70292i q^{47} +(2.67866 - 2.97065i) q^{48} -0.248811 q^{49} +(1.39049 + 0.257970i) q^{50} +3.95759 q^{51} +(-3.80127 - 1.46074i) q^{52} +2.16224i q^{53} +(0.257970 - 1.39049i) q^{54} +1.75416i q^{55} +(-6.26408 - 3.84328i) q^{56} +5.10890i q^{57} +(10.1838 + 1.88936i) q^{58} -10.3196i q^{59} +(-1.86690 - 0.717408i) q^{60} -7.39410i q^{61} +(1.26848 - 6.83723i) q^{62} -2.59830 q^{63} +(3.62423 + 7.13197i) q^{64} +2.03614i q^{65} +(0.452520 - 2.43913i) q^{66} +8.20400 q^{67} +(-2.83920 + 7.38843i) q^{68} +(-1.71592 + 4.47835i) q^{69} +(-0.670285 + 3.61291i) q^{70} -7.48672i q^{71} +(2.41083 + 1.47915i) q^{72} -13.8075 q^{73} +(-0.229757 + 1.23841i) q^{74} +1.00000i q^{75} +(-9.53782 - 3.66516i) q^{76} -4.55784 q^{77} +(0.525262 - 2.83122i) q^{78} -6.39670 q^{79} +(2.67866 - 2.97065i) q^{80} +1.00000 q^{81} +(14.1239 + 2.62033i) q^{82} +9.80321 q^{83} +(1.86404 - 4.85078i) q^{84} +3.95759 q^{85} +(-8.10369 - 1.50344i) q^{86} +7.32394i q^{87} +(4.22898 + 2.59466i) q^{88} +15.8514i q^{89} +(0.257970 - 1.39049i) q^{90} -5.29050 q^{91} +(-7.12963 - 6.41626i) q^{92} +4.91715 q^{93} +(-0.697273 + 3.75837i) q^{94} +5.10890i q^{95} +(-4.49098 + 3.43964i) q^{96} -0.186909i q^{97} +(0.345968 + 0.0641859i) q^{98} +1.75416 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 - 2 * q^10 + 20 * q^14 - 48 * q^15 - 6 * q^16 + 4 * q^18 + 16 * q^19 + 28 * q^22 + 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 + 4 * q^30 + 16 * q^32 - 28 * q^34 + 2 * q^36 + 2 * q^40 - 8 * q^41 + 14 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 + 16 * q^51 - 16 * q^52 + 2 * q^54 + 40 * q^56 - 8 * q^58 + 2 * q^60 + 24 * q^62 - 26 * q^64 - 48 * q^67 - 44 * q^68 - 8 * q^69 + 4 * q^72 + 20 * q^74 - 64 * q^76 + 32 * q^77 - 64 * q^79 + 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 - 40 * q^86 + 2 * q^90 - 4 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−1.39049	−	0.257970i	−0.983222	−	0.182412i
$2$	−1.39049	−	0.257970i	−0.983222	−	0.182412i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.86690	+	0.717408i	0.933451	+	0.358704i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.257970	+	1.39049i	−0.105316	+	0.567664i
$7$	2.59830			0.982067			0.491033	−	0.871141i	$-0.336619\pi$
$7$	2.59830			0.982067			0.491033	+	0.871141i	$0.336619\pi$
$8$	−2.41083	−	1.47915i	−0.852358	−	0.522959i
$9$	−1.00000			−0.333333
$10$	−0.257970	+	1.39049i	−0.0815773	+	0.439710i
$11$	−1.75416			−0.528898			−0.264449	−	0.964400i	$-0.585190\pi$
$11$	−1.75416			−0.528898			−0.264449	+	0.964400i	$0.585190\pi$
$12$	0.717408	−	1.86690i	0.207098	−	0.538928i
$13$	−2.03614			−0.564722			−0.282361	−	0.959308i	$-0.591118\pi$
$13$	−2.03614			−0.564722			−0.282361	+	0.959308i	$0.591118\pi$
$14$	−3.61291	−	0.670285i	−0.965590	−	0.179141i
$15$	−1.00000			−0.258199
$16$	2.97065	+	2.67866i	0.742663	+	0.669665i
$17$			3.95759i			0.959856i	0.877308	+	0.479928i	$0.159337\pi$
$17$			3.95759i			0.959856i	−0.877308	+	0.479928i	$0.840663\pi$
$18$	1.39049	+	0.257970i	0.327741	+	0.0608042i
$19$	−5.10890			−1.17206			−0.586031	−	0.810289i	$-0.699310\pi$
$19$	−5.10890			−1.17206			−0.586031	+	0.810289i	$0.699310\pi$
$20$	0.717408	−	1.86690i	0.160417	−	0.417452i
$21$		−	2.59830i		−	0.566997i
$22$	2.43913	+	0.452520i	0.520024	+	0.0964776i
$23$	−4.47835	−	1.71592i	−0.933800	−	0.357795i
$23$	−4.47835	−	1.71592i	−0.933800	−	0.357795i
$24$	−1.47915	+	2.41083i	−0.301930	+	0.492109i
$25$	−1.00000			−0.200000
$26$	2.83122	+	0.525262i	0.555247	+	0.103012i
$27$			1.00000i			0.192450i
$28$	4.85078	+	1.86404i	0.916712	+	0.352271i
$29$	−7.32394			−1.36002			−0.680011	−	0.733202i	$-0.738025\pi$
$29$	−7.32394			−1.36002			−0.680011	+	0.733202i	$0.738025\pi$
$30$	1.39049	+	0.257970i	0.253867	+	0.0470987i
$31$			4.91715i			0.883147i	0.897225	+	0.441573i	$0.145580\pi$
$31$			4.91715i			0.883147i	−0.897225	+	0.441573i	$0.854420\pi$
$32$	−3.43964	−	4.49098i	−0.608047	−	0.793901i
$33$			1.75416i			0.305360i
$34$	1.02094	−	5.50297i	0.175090	−	0.943752i
$35$		−	2.59830i		−	0.439194i
$36$	−1.86690	−	0.717408i	−0.311150	−	0.119568i
$37$		−	0.890633i		−	0.146419i	−0.997317	−	0.0732096i	$-0.976676\pi$
$37$		−	0.890633i		−	0.146419i	0.997317	−	0.0732096i	$-0.0233242\pi$
$38$	7.10385	+	1.31794i	1.15240	+	0.213799i
$39$			2.03614i			0.326043i
$40$	−1.47915	+	2.41083i	−0.233874	+	0.381186i
$41$	−10.1575			−1.58634			−0.793168	−	0.609003i	$-0.791570\pi$
$41$	−10.1575			−1.58634			−0.793168	+	0.609003i	$0.791570\pi$
$42$	−0.670285	+	3.61291i	−0.103427	+	0.557484i
$43$	5.82796			0.888755			0.444377	−	0.895840i	$-0.353425\pi$
$43$	5.82796			0.888755			0.444377	+	0.895840i	$0.353425\pi$
$44$	−3.27484	−	1.25845i	−0.493701	−	0.189718i
$45$			1.00000i			0.149071i
$46$	5.78443	+	3.54125i	0.852867	+	0.522128i
$47$		−	2.70292i		−	0.394262i	−0.980377	−	0.197131i	$-0.936838\pi$
$47$		−	2.70292i		−	0.394262i	0.980377	−	0.197131i	$-0.0631624\pi$
$48$	2.67866	−	2.97065i	0.386631	−	0.428777i
$49$	−0.248811			−0.0355445
$50$	1.39049	+	0.257970i	0.196644	+	0.0364825i
$51$	3.95759			0.554173
$52$	−3.80127	−	1.46074i	−0.527141	−	0.202568i
$53$			2.16224i			0.297007i	0.988912	+	0.148504i	$0.0474456\pi$
$53$			2.16224i			0.297007i	−0.988912	+	0.148504i	$0.952554\pi$
$54$	0.257970	−	1.39049i	0.0351053	−	0.189221i
$55$			1.75416i			0.236531i
$56$	−6.26408	−	3.84328i	−0.837073	−	0.513581i
$57$			5.10890i			0.676690i
$58$	10.1838	+	1.88936i	1.33720	+	0.248085i
$59$		−	10.3196i		−	1.34349i	−0.740780	−	0.671747i	$-0.765544\pi$
$59$		−	10.3196i		−	1.34349i	0.740780	−	0.671747i	$-0.234456\pi$
$60$	−1.86690	−	0.717408i	−0.241016	−	0.0926170i
$61$		−	7.39410i		−	0.946717i	−0.880870	−	0.473359i	$-0.843041\pi$
$61$		−	7.39410i		−	0.946717i	0.880870	−	0.473359i	$-0.156959\pi$
$62$	1.26848	−	6.83723i	0.161097	−	0.868330i
$63$	−2.59830			−0.327356
$64$	3.62423	+	7.13197i	0.453028	+	0.891496i
$65$			2.03614i			0.252552i
$66$	0.452520	−	2.43913i	0.0557014	−	0.300236i
$67$	8.20400			1.00228			0.501139	−	0.865367i	$-0.332914\pi$
$67$	8.20400			1.00228			0.501139	+	0.865367i	$0.332914\pi$
$68$	−2.83920	+	7.38843i	−0.344304	+	0.895979i
$69$	−1.71592	+	4.47835i	−0.206573	+	0.539130i
$70$	−0.670285	+	3.61291i	−0.0801144	+	0.431825i
$71$		−	7.48672i		−	0.888511i	−0.895900	−	0.444255i	$-0.853468\pi$
$71$		−	7.48672i		−	0.888511i	0.895900	−	0.444255i	$-0.146532\pi$
$72$	2.41083	+	1.47915i	0.284119	+	0.174320i
$73$	−13.8075			−1.61605			−0.808024	−	0.589150i	$-0.799463\pi$
$73$	−13.8075			−1.61605			−0.808024	+	0.589150i	$0.799463\pi$
$74$	−0.229757	+	1.23841i	−0.0267087	+	0.143963i
$75$			1.00000i			0.115470i
$76$	−9.53782	−	3.66516i	−1.09406	−	0.420423i
$77$	−4.55784			−0.519414
$78$	0.525262	−	2.83122i	0.0594742	−	0.320572i
$79$	−6.39670			−0.719685			−0.359843	−	0.933013i	$-0.617170\pi$
$79$	−6.39670			−0.719685			−0.359843	+	0.933013i	$0.617170\pi$
$80$	2.67866	−	2.97065i	0.299483	−	0.332129i
$81$	1.00000			0.111111
$82$	14.1239	+	2.62033i	1.55972	+	0.289367i
$83$	9.80321			1.07604			0.538021	−	0.842931i	$-0.319172\pi$
$83$	9.80321			1.07604			0.538021	+	0.842931i	$0.319172\pi$
$84$	1.86404	−	4.85078i	0.203384	−	0.529264i
$85$	3.95759			0.429261
$86$	−8.10369	−	1.50344i	−0.873844	−	0.162120i
$87$			7.32394i			0.785209i
$88$	4.22898	+	2.59466i	0.450811	+	0.276592i
$89$			15.8514i			1.68025i	0.542393	+	0.840125i	$0.317518\pi$
$89$			15.8514i			1.68025i	−0.542393	+	0.840125i	$0.682482\pi$
$90$	0.257970	−	1.39049i	0.0271924	−	0.146570i
$91$	−5.29050			−0.554595
$92$	−7.12963	−	6.41626i	−0.743315	−	0.668942i
$93$	4.91715			0.509885
$94$	−0.697273	+	3.75837i	−0.0719182	+	0.387647i
$95$			5.10890i			0.524162i
$96$	−4.49098	+	3.43964i	−0.458359	+	0.351056i
$97$		−	0.186909i		−	0.0189777i	−0.999955	−	0.00948885i	$-0.996980\pi$
$97$		−	0.186909i		−	0.0189777i	0.999955	−	0.00948885i	$-0.00302044\pi$
$98$	0.345968	+	0.0641859i	0.0349481	+	0.00648375i
$99$	1.75416			0.176299
$100$	−1.86690	−	0.717408i	−0.186690	−	0.0717408i
$101$	−9.35168			−0.930527			−0.465264	−	0.885172i	$-0.654040\pi$
$101$	−9.35168			−0.930527			−0.465264	+	0.885172i	$0.654040\pi$
$102$	−5.50297	−	1.02094i	−0.544875	−	0.101088i
$103$	−1.95123			−0.192260			−0.0961302	−	0.995369i	$-0.530647\pi$
$103$	−1.95123			−0.192260			−0.0961302	+	0.995369i	$0.530647\pi$
$104$	4.90878	+	3.01175i	0.481346	+	0.295327i
$105$	−2.59830			−0.253569
$106$	0.557794	−	3.00657i	0.0541778	−	0.292024i
$107$	7.60436			0.735141			0.367570	−	0.929996i	$-0.380190\pi$
$107$	7.60436			0.735141			0.367570	+	0.929996i	$0.380190\pi$
$108$	−0.717408	+	1.86690i	−0.0690326	+	0.179643i
$109$			6.19075i			0.592966i	0.955038	+	0.296483i	$0.0958138\pi$
$109$			6.19075i			0.592966i	−0.955038	+	0.296483i	$0.904186\pi$
$110$	0.452520	−	2.43913i	0.0431461	−	0.232562i
$111$	−0.890633			−0.0845352
$112$	7.71866	+	6.95998i	0.729345	+	0.657656i
$113$		−	8.58491i		−	0.807600i	−0.914847	−	0.403800i	$-0.867689\pi$
$113$		−	8.58491i		−	0.807600i	0.914847	−	0.403800i	$-0.132311\pi$
$114$	1.31794	−	7.10385i	0.123437	−	0.665337i
$115$	−1.71592	+	4.47835i	−0.160011	+	0.417608i
$116$	−13.6731	−	5.25425i	−1.26951	−	0.487845i
$117$	2.03614			0.188241
$118$	−2.66214	+	14.3492i	−0.245070	+	1.32095i
$119$			10.2830i			0.942643i
$120$	2.41083	+	1.47915i	0.220078	+	0.135027i
$121$	−7.92293			−0.720267
$122$	−1.90746	+	10.2814i	−0.172693	+	0.930833i
$123$			10.1575i			0.915871i
$124$	−3.52760	+	9.17985i	−0.316788	+	0.824375i
$125$			1.00000i			0.0894427i
$126$	3.61291	+	0.670285i	0.321863	+	0.0597137i
$127$		−	3.84618i		−	0.341294i	−0.985332	−	0.170647i	$-0.945414\pi$
$127$		−	3.84618i		−	0.341294i	0.985332	−	0.170647i	$-0.0545857\pi$
$128$	−3.19960	−	10.8518i	−0.282807	−	0.959177i
$129$		−	5.82796i		−	0.513123i
$130$	0.525262	−	2.83122i	0.0460685	−	0.248314i
$131$			8.85272i			0.773466i	0.922192	+	0.386733i	$0.126396\pi$
$131$			8.85272i			0.773466i	−0.922192	+	0.386733i	$0.873604\pi$
$132$	−1.25845	+	3.27484i	−0.109534	+	0.285038i
$133$	−13.2745			−1.15104
$134$	−11.4076	−	2.11639i	−0.985462	−	0.182828i
$135$	1.00000			0.0860663
$136$	5.85387	−	9.54108i	0.501965	−	0.818141i
$137$			17.8085i			1.52148i	0.649054	+	0.760742i	$0.275165\pi$
$137$			17.8085i			1.52148i	−0.649054	+	0.760742i	$0.724835\pi$
$138$	3.54125	−	5.78443i	0.301451	−	0.492403i
$139$		−	1.26954i		−	0.107681i	−0.998550	−	0.0538403i	$-0.982854\pi$
$139$		−	1.26954i		−	0.107681i	0.998550	−	0.0538403i	$-0.0171462\pi$
$140$	1.86404	−	4.85078i	0.157540	−	0.409966i
$141$	−2.70292			−0.227627
$142$	−1.93135	+	10.4102i	−0.162075	+	0.873603i
$143$	3.57170			0.298681
$144$	−2.97065	−	2.67866i	−0.247554	−	0.223222i
$145$			7.32394i			0.608220i
$146$	19.1992	+	3.56193i	1.58893	+	0.294787i
$147$			0.248811i			0.0205216i
$148$	0.638947	−	1.66273i	0.0525211	−	0.136675i
$149$		−	10.5890i		−	0.867486i	−0.901037	−	0.433743i	$-0.857193\pi$
$149$		−	10.5890i		−	0.867486i	0.901037	−	0.433743i	$-0.142807\pi$
$150$	0.257970	−	1.39049i	0.0210632	−	0.113533i
$151$			9.56575i			0.778450i	0.921143	+	0.389225i	$0.127257\pi$
$151$			9.56575i			0.778450i	−0.921143	+	0.389225i	$0.872743\pi$
$152$	12.3167	+	7.55683i	0.999016	+	0.612940i
$153$		−	3.95759i		−	0.319952i
$154$	6.33761	+	1.17579i	0.510699	+	0.0947475i
$155$	4.91715			0.394955
$156$	−1.46074	+	3.80127i	−0.116953	+	0.304345i
$157$			14.8452i			1.18477i	0.805653	+	0.592387i	$0.201814\pi$
$157$			14.8452i			1.18477i	−0.805653	+	0.592387i	$0.798186\pi$
$158$	8.89453	+	1.65016i	0.707610	+	0.131280i
$159$	2.16224			0.171477
$160$	−4.49098	+	3.43964i	−0.355043	+	0.271927i
$161$	−11.6361	−	4.45849i	−0.917054	−	0.351378i
$162$	−1.39049	−	0.257970i	−0.109247	−	0.0202681i
$163$			9.70954i			0.760510i	0.924882	+	0.380255i	$0.124164\pi$
$163$			9.70954i			0.760510i	−0.924882	+	0.380255i	$0.875836\pi$
$164$	−18.9631	−	7.28707i	−1.48077	−	0.569025i
$165$	1.75416			0.136561
$166$	−13.6312	−	2.52894i	−1.05799	−	0.196283i
$167$			17.5706i			1.35966i	0.733371	+	0.679829i	$0.237946\pi$
$167$			17.5706i			1.35966i	−0.733371	+	0.679829i	$0.762054\pi$
$168$	−3.84328	+	6.26408i	−0.296516	+	0.483284i
$169$	−8.85415			−0.681089
$170$	−5.50297	−	1.02094i	−0.422059	−	0.0783025i
$171$	5.10890			0.390687
$172$	10.8802	+	4.18102i	0.829610	+	0.318800i
$173$	−3.61225			−0.274635			−0.137317	−	0.990527i	$-0.543848\pi$
$173$	−3.61225			−0.274635			−0.137317	+	0.990527i	$0.543848\pi$
$174$	1.88936	−	10.1838i	0.143232	−	0.772035i
$175$	−2.59830			−0.196413
$176$	−5.21099	−	4.69879i	−0.392793	−	0.354185i
$177$	−10.3196			−0.775667
$178$	4.08920	−	22.0412i	0.306498	−	1.65206i
$179$		−	21.6167i		−	1.61571i	−0.589383	−	0.807854i	$-0.700629\pi$
$179$		−	21.6167i		−	1.61571i	0.589383	−	0.807854i	$-0.299371\pi$
$180$	−0.717408	+	1.86690i	−0.0534724	+	0.139151i
$181$		−	20.6411i		−	1.53424i	−0.641503	−	0.767121i	$-0.721689\pi$
$181$		−	20.6411i		−	1.53424i	0.641503	−	0.767121i	$-0.278311\pi$
$182$	7.35637	+	1.36479i	0.545290	+	0.101165i
$183$	−7.39410			−0.546587
$184$	8.25844	+	10.7610i	0.608820	+	0.793308i
$185$	−0.890633			−0.0654807
$186$	−6.83723	−	1.26848i	−0.501330	−	0.0930094i
$187$		−	6.94223i		−	0.507666i
$188$	1.93910	−	5.04609i	0.141423	−	0.368024i
$189$			2.59830i			0.188999i
$190$	1.31794	−	7.10385i	0.0956137	−	0.515368i
$191$	0.429593			0.0310843			0.0155421	−	0.999879i	$-0.495053\pi$
$191$	0.429593			0.0310843			0.0155421	+	0.999879i	$0.495053\pi$
$192$	7.13197	−	3.62423i	0.514706	−	0.261556i
$193$	8.47229			0.609849			0.304924	−	0.952377i	$-0.401369\pi$
$193$	8.47229			0.609849			0.304924	+	0.952377i	$0.401369\pi$
$194$	−0.0482169	+	0.259894i	−0.00346177	+	0.0186593i
$195$	2.03614			0.145811
$196$	−0.464506	−	0.178499i	−0.0331790	−	0.0127499i
$197$	−12.5408			−0.893497			−0.446748	−	0.894660i	$-0.647418\pi$
$197$	−12.5408			−0.893497			−0.446748	+	0.894660i	$0.647418\pi$
$198$	−2.43913	−	0.452520i	−0.173341	−	0.0321592i
$199$	6.94093			0.492029			0.246015	−	0.969266i	$-0.420879\pi$
$199$	6.94093			0.492029			0.246015	+	0.969266i	$0.420879\pi$
$200$	2.41083	+	1.47915i	0.170472	+	0.104592i
$201$		−	8.20400i		−	0.578666i
$202$	13.0034	+	2.41245i	0.914915	+	0.169740i
$203$	−19.0298			−1.33563
$204$	7.38843	+	2.83920i	0.517294	+	0.198784i
$205$			10.1575i			0.709431i
$206$	2.71316	+	0.503359i	0.189035	+	0.0350707i
$207$	4.47835	+	1.71592i	0.311267	+	0.119265i
$208$	−6.04865	−	5.45412i	−0.419398	−	0.378175i
$209$	8.96181			0.619901
$210$	3.61291	+	0.670285i	0.249314	+	0.0462541i
$211$		−	8.77564i		−	0.604140i	−0.953286	−	0.302070i	$-0.902322\pi$
$211$		−	8.77564i		−	0.604140i	0.953286	−	0.302070i	$-0.0976776\pi$
$212$	−1.55121	+	4.03670i	−0.106538	+	0.277242i
$213$	−7.48672			−0.512982
$214$	−10.5738	−	1.96170i	−0.722807	−	0.134099i
$215$		−	5.82796i		−	0.397463i
$216$	1.47915	−	2.41083i	0.100643	−	0.164036i
$217$			12.7763i			0.867309i
$218$	1.59703	−	8.60815i	0.108164	−	0.583017i
$219$			13.8075i			0.933025i
$220$	−1.25845	+	3.27484i	−0.0848444	+	0.220790i
$221$		−	8.05818i		−	0.542052i
$222$	1.23841	+	0.229757i	0.0831169	+	0.0154203i
$223$		−	12.3863i		−	0.829447i	−0.909948	−	0.414723i	$-0.863878\pi$
$223$		−	12.3863i		−	0.829447i	0.909948	−	0.414723i	$-0.136122\pi$
$224$	−8.93722	−	11.6689i	−0.597143	−	0.779664i
$225$	1.00000			0.0666667
$226$	−2.21465	+	11.9372i	−0.147316	+	0.794050i
$227$	1.51099			0.100288			0.0501438	−	0.998742i	$-0.484032\pi$
$227$	1.51099			0.100288			0.0501438	+	0.998742i	$0.484032\pi$
$228$	−3.66516	+	9.53782i	−0.242731	+	0.631657i
$229$			20.9819i			1.38652i	0.720687	+	0.693260i	$0.243826\pi$
$229$			20.9819i			1.38652i	−0.720687	+	0.693260i	$0.756174\pi$
$230$	3.54125	−	5.78443i	0.233503	−	0.381414i
$231$			4.55784i			0.299884i
$232$	17.6568	+	10.8332i	1.15923	+	0.711236i
$233$	−6.16707			−0.404018			−0.202009	−	0.979384i	$-0.564747\pi$
$233$	−6.16707			−0.404018			−0.202009	+	0.979384i	$0.564747\pi$
$234$	−2.83122	−	0.525262i	−0.185082	−	0.0343375i
$235$	−2.70292			−0.176319
$236$	7.40335	−	19.2656i	0.481917	−	1.25409i
$237$			6.39670i			0.415510i
$238$	2.65271	−	14.2984i	0.171950	−	0.926827i
$239$			20.3266i			1.31482i	0.753535	+	0.657408i	$0.228347\pi$
$239$			20.3266i			1.31482i	−0.753535	+	0.657408i	$0.771653\pi$
$240$	−2.97065	−	2.67866i	−0.191755	−	0.172907i
$241$		−	0.798895i		−	0.0514613i	−0.999669	−	0.0257307i	$-0.991809\pi$
$241$		−	0.798895i		−	0.0514613i	0.999669	−	0.0257307i	$-0.00819123\pi$
$242$	11.0167	+	2.04388i	0.708182	+	0.131386i
$243$		−	1.00000i		−	0.0641500i
$244$	5.30458	−	13.8041i	0.339591	−	0.883715i
$245$			0.248811i			0.0158960i
$246$	2.62033	−	14.1239i	0.167066	−	0.900505i
$247$	10.4024			0.661889
$248$	7.27321	−	11.8544i	0.461849	−	0.752757i
$249$		−	9.80321i		−	0.621253i
$250$	0.257970	−	1.39049i	0.0163155	−	0.0879421i
$251$	−12.7763			−0.806433			−0.403216	−	0.915105i	$-0.632108\pi$
$251$	−12.7763			−0.806433			−0.403216	+	0.915105i	$0.632108\pi$
$252$	−4.85078	−	1.86404i	−0.305571	−	0.117424i
$253$	7.85573	+	3.01000i	0.493885	+	0.189237i
$254$	−0.992201	+	5.34806i	−0.0622562	+	0.335567i
$255$		−	3.95759i		−	0.247834i
$256$	1.64955	+	15.9147i	0.103097	+	0.994671i
$257$	16.6463			1.03837			0.519185	−	0.854662i	$-0.326236\pi$
$257$	16.6463			1.03837			0.519185	+	0.854662i	$0.326236\pi$
$258$	−1.50344	+	8.10369i	−0.0936000	+	0.504514i
$259$		−	2.31414i		−	0.143793i
$260$	−1.46074	+	3.80127i	−0.0905912	+	0.235745i
$261$	7.32394			0.453341
$262$	2.28374	−	12.3096i	0.141090	−	0.760489i
$263$	−10.4192			−0.642474			−0.321237	−	0.946999i	$-0.604099\pi$
$263$	−10.4192			−0.642474			−0.321237	+	0.946999i	$0.604099\pi$
$264$	2.59466	−	4.22898i	0.159690	−	0.260276i
$265$	2.16224			0.132826
$266$	18.4580	+	3.42442i	1.13173	+	0.209965i
$267$	15.8514			0.970093
$268$	15.3161	+	5.88562i	0.935578	+	0.359521i
$269$	18.5876			1.13330			0.566652	−	0.823957i	$-0.308238\pi$
$269$	18.5876			1.13330			0.566652	+	0.823957i	$0.308238\pi$
$270$	−1.39049	−	0.257970i	−0.0846223	−	0.0156996i
$271$		−	17.7596i		−	1.07882i	−0.842043	−	0.539410i	$-0.818647\pi$
$271$		−	17.7596i		−	1.07882i	0.842043	−	0.539410i	$-0.181353\pi$
$272$	−10.6010	+	11.7566i	−0.642782	+	0.712850i
$273$			5.29050i			0.320196i
$274$	4.59407	−	24.7625i	0.277538	−	1.49596i
$275$	1.75416			0.105780
$276$	−6.41626	+	7.12963i	−0.386214	+	0.429153i
$277$	18.4824			1.11050			0.555250	−	0.831683i	$-0.312622\pi$
$277$	18.4824			1.11050			0.555250	+	0.831683i	$0.312622\pi$
$278$	−0.327503	+	1.76527i	−0.0196423	+	0.105874i
$279$		−	4.91715i		−	0.294382i
$280$	−3.84328	+	6.26408i	−0.229680	+	0.374350i
$281$			7.06994i			0.421758i	0.977512	+	0.210879i	$0.0676325\pi$
$281$			7.06994i			0.421758i	−0.977512	+	0.210879i	$0.932367\pi$
$282$	3.75837	+	0.697273i	0.223808	+	0.0415220i
$283$	−20.8787			−1.24111			−0.620554	−	0.784164i	$-0.713092\pi$
$283$	−20.8787			−1.24111			−0.620554	+	0.784164i	$0.713092\pi$
$284$	5.37103	−	13.9770i	0.318712	−	0.829382i
$285$	5.10890			0.302625
$286$	−4.96640	−	0.921392i	−0.293669	−	0.0544831i
$287$	−26.3923			−1.55789
$288$	3.43964	+	4.49098i	0.202682	+	0.264634i
$289$	1.33750			0.0786765
$290$	1.88936	−	10.1838i	0.110947	−	0.598016i
$291$	−0.186909			−0.0109568
$292$	−25.7773	−	9.90562i	−1.50850	−	0.579683i
$293$		−	31.0901i		−	1.81630i	−0.418641	−	0.908152i	$-0.637493\pi$
$293$		−	31.0901i		−	1.81630i	0.418641	−	0.908152i	$-0.362507\pi$
$294$	0.0641859	−	0.345968i	0.00374340	−	0.0201773i
$295$	−10.3196			−0.600829
$296$	−1.31738	+	2.14717i	−0.0765712	+	0.124802i
$297$		−	1.75416i		−	0.101787i
$298$	−2.73165	+	14.7239i	−0.158240	+	0.852932i
$299$	9.11852	+	3.49385i	0.527338	+	0.202055i
$300$	−0.717408	+	1.86690i	−0.0414196	+	0.107786i
$301$	15.1428			0.872817
$302$	2.46768	−	13.3010i	0.141999	−	0.765389i
$303$			9.35168i			0.537240i
$304$	−15.1768	−	13.6850i	−0.870447	−	0.784889i
$305$	−7.39410			−0.423385
$306$	−1.02094	+	5.50297i	−0.0583632	+	0.314584i
$307$		−	18.6521i		−	1.06453i	−0.846578	−	0.532265i	$-0.821341\pi$
$307$		−	18.6521i		−	1.06453i	0.846578	−	0.532265i	$-0.178659\pi$
$308$	−8.50904	−	3.26983i	−0.484847	−	0.186316i
$309$			1.95123i			0.111002i
$310$	−6.83723	−	1.26848i	−0.388329	−	0.0720448i
$311$			8.82536i			0.500440i	0.968189	+	0.250220i	$0.0805030\pi$
$311$			8.82536i			0.500440i	−0.968189	+	0.250220i	$0.919497\pi$
$312$	3.01175	−	4.90878i	0.170507	−	0.277905i
$313$		−	34.9736i		−	1.97682i	−0.151801	−	0.988411i	$-0.548507\pi$
$313$		−	34.9736i		−	1.97682i	0.151801	−	0.988411i	$-0.451493\pi$
$314$	3.82961	−	20.6420i	0.216118	−	1.16490i
$315$			2.59830i			0.146398i
$316$	−11.9420	−	4.58904i	−0.671791	−	0.258154i
$317$	23.4318			1.31606			0.658032	−	0.752990i	$-0.271389\pi$
$317$	23.4318			1.31606			0.658032	+	0.752990i	$0.271389\pi$
$318$	−3.00657	−	0.557794i	−0.168600	−	0.0312796i
$319$	12.8473			0.719313
$320$	7.13197	−	3.62423i	0.398689	−	0.202600i
$321$		−	7.60436i		−	0.424434i
$322$	15.0297	+	9.20124i	0.837572	+	0.512765i
$323$		−	20.2189i		−	1.12501i
$324$	1.86690	+	0.717408i	0.103717	+	0.0398560i
$325$	2.03614			0.112944
$326$	2.50477	−	13.5010i	0.138726	−	0.747750i
$327$	6.19075			0.342349
$328$	24.4880	+	15.0245i	1.35213	+	0.829588i
$329$		−	7.02301i		−	0.387191i
$330$	−2.43913	−	0.452520i	−0.134270	−	0.0249104i
$331$		−	12.3559i		−	0.679143i	−0.940580	−	0.339572i	$-0.889718\pi$
$331$		−	12.3559i		−	0.679143i	0.940580	−	0.339572i	$-0.110282\pi$
$332$	18.3016	+	7.03290i	1.00443	+	0.385981i
$333$			0.890633i			0.0488064i
$334$	4.53270	−	24.4317i	0.248018	−	1.33685i
$335$		−	8.20400i		−	0.448233i
$336$	6.95998	−	7.71866i	0.379698	−	0.421087i
$337$		−	7.53162i		−	0.410274i	−0.978733	−	0.205137i	$-0.934236\pi$
$337$		−	7.53162i		−	0.410274i	0.978733	−	0.205137i	$-0.0657639\pi$
$338$	12.3116	+	2.28411i	0.669661	+	0.124239i
$339$	−8.58491			−0.466268
$340$	7.38843	+	2.83920i	0.400694	+	0.153977i
$341$		−	8.62546i		−	0.467095i
$342$	−7.10385	−	1.31794i	−0.384132	−	0.0712662i
$343$	−18.8346			−1.01697
$344$	−14.0502	−	8.62043i	−0.757537	−	0.464782i
$345$	4.47835	+	1.71592i	0.241106	+	0.0923822i
$346$	5.02279	+	0.931854i	0.270027	+	0.0500968i
$347$		−	23.8968i		−	1.28285i	−0.767187	−	0.641424i	$-0.778344\pi$
$347$		−	23.8968i		−	1.28285i	0.767187	−	0.641424i	$-0.221656\pi$
$348$	−5.25425	+	13.6731i	−0.281658	+	0.732955i
$349$	10.0932			0.540275			0.270137	−	0.962822i	$-0.412931\pi$
$349$	10.0932			0.540275			0.270137	+	0.962822i	$0.412931\pi$
$350$	3.61291	+	0.670285i	0.193118	+	0.0358282i
$351$		−	2.03614i		−	0.108681i
$352$	6.03366	+	7.87789i	0.321595	+	0.419893i
$353$	0.820616			0.0436770			0.0218385	−	0.999762i	$-0.493048\pi$
$353$	0.820616			0.0436770			0.0218385	+	0.999762i	$0.493048\pi$
$354$	14.3492	+	2.66214i	0.762653	+	0.141491i
$355$	−7.48672			−0.397354
$356$	−11.3720	+	29.5931i	−0.602712	+	1.56843i
$357$	10.2830			0.544235
$358$	−5.57646	+	30.0577i	−0.294725	+	1.58860i
$359$	23.8059			1.25643			0.628214	−	0.778041i	$-0.283786\pi$
$359$	23.8059			1.25643			0.628214	+	0.778041i	$0.283786\pi$
$360$	1.47915	−	2.41083i	0.0779581	−	0.127062i
$361$	7.10084			0.373728
$362$	−5.32479	+	28.7012i	−0.279865	+	1.50850i
$363$			7.92293i			0.415846i
$364$	−9.87685	−	3.79545i	−0.517688	−	0.198935i
$365$			13.8075i			0.722718i
$366$	10.2814	+	1.90746i	0.537417	+	0.0997044i
$367$	34.8932			1.82141			0.910704	−	0.413059i	$-0.135540\pi$
$367$	34.8932			1.82141			0.910704	+	0.413059i	$0.135540\pi$
$368$	−8.70724	−	17.0934i	−0.453896	−	0.891054i
$369$	10.1575			0.528778
$370$	1.23841	+	0.229757i	0.0643820	+	0.0119445i
$371$			5.61817i			0.291681i
$372$	9.17985	+	3.52760i	0.475953	+	0.182898i
$373$		−	30.7357i		−	1.59144i	−0.605667	−	0.795718i	$-0.707094\pi$
$373$		−	30.7357i		−	1.59144i	0.605667	−	0.795718i	$-0.292906\pi$
$374$	−1.79089	+	9.65307i	−0.0926046	+	0.499149i
$375$	1.00000			0.0516398
$376$	−3.99803	+	6.51629i	−0.206183	+	0.336052i
$377$	14.9125			0.768035
$378$	0.670285	−	3.61291i	0.0344757	−	0.185828i
$379$	−25.6529			−1.31770			−0.658850	−	0.752274i	$-0.728957\pi$
$379$	−25.6529			−1.31770			−0.658850	+	0.752274i	$0.728957\pi$
$380$	−3.66516	+	9.53782i	−0.188019	+	0.489280i
$381$	−3.84618			−0.197046
$382$	−0.597343	−	0.110822i	−0.0305627	−	0.00567016i
$383$	19.3975			0.991168			0.495584	−	0.868560i	$-0.334954\pi$
$383$	19.3975			0.991168			0.495584	+	0.868560i	$0.334954\pi$
$384$	−10.8518	+	3.19960i	−0.553781	+	0.163279i
$385$			4.55784i			0.232289i
$386$	−11.7806	−	2.18560i	−0.599617	−	0.111244i
$387$	−5.82796			−0.296252
$388$	0.134090	−	0.348940i	0.00680738	−	0.0177148i
$389$		−	5.01904i		−	0.254475i	−0.991872	−	0.127238i	$-0.959389\pi$
$389$		−	5.01904i		−	0.254475i	0.991872	−	0.127238i	$-0.0406111\pi$
$390$	−2.83122	−	0.525262i	−0.143364	−	0.0265977i
$391$	6.79091	−	17.7235i	0.343431	−	0.896314i
$392$	0.599842	+	0.368029i	0.0302966	+	0.0185883i
$393$	8.85272			0.446561
$394$	17.4378	+	3.23516i	0.878506	+	0.162985i
$395$			6.39670i			0.321853i
$396$	3.27484	+	1.25845i	0.164567	+	0.0632393i
$397$	−19.3839			−0.972849			−0.486425	−	0.873723i	$-0.661699\pi$
$397$	−19.3839			−0.972849			−0.486425	+	0.873723i	$0.661699\pi$
$398$	−9.65126	−	1.79055i	−0.483774	−	0.0897523i
$399$			13.2745i			0.664555i
$400$	−2.97065	−	2.67866i	−0.148533	−	0.133933i
$401$			18.9091i			0.944278i	0.881524	+	0.472139i	$0.156518\pi$
$401$			18.9091i			0.944278i	−0.881524	+	0.472139i	$0.843482\pi$
$402$	−2.11639	+	11.4076i	−0.105556	+	0.568957i
$403$		−	10.0120i		−	0.498733i
$404$	−17.4587	−	6.70897i	−0.868602	−	0.333784i
$405$		−	1.00000i		−	0.0496904i
$406$	26.4607	+	4.90913i	1.31322	+	0.243636i
$407$			1.56231i			0.0774409i
$408$	−9.54108	−	5.85387i	−0.472354	−	0.289810i
$409$	−24.6813			−1.22041			−0.610206	−	0.792242i	$-0.708913\pi$
$409$	−24.6813			−1.22041			−0.610206	+	0.792242i	$0.708913\pi$
$410$	2.62033	−	14.1239i	0.129409	−	0.697528i
$411$	17.8085			0.878429
$412$	−3.64276	−	1.39983i	−0.179466	−	0.0689646i
$413$		−	26.8134i		−	1.31940i
$414$	−5.78443	−	3.54125i	−0.284289	−	0.174043i
$415$		−	9.80321i		−	0.481221i
$416$	7.00356	+	9.14424i	0.343378	+	0.448333i
$417$	−1.26954			−0.0621695
$418$	−12.4613	−	2.31188i	−0.609501	−	0.113078i
$419$	24.3020			1.18723			0.593616	−	0.804748i	$-0.297700\pi$
$419$	24.3020			1.18723			0.593616	+	0.804748i	$0.297700\pi$
$420$	−4.85078	−	1.86404i	−0.236694	−	0.0909560i
$421$			7.78410i			0.379374i	0.981845	+	0.189687i	$0.0607473\pi$
$421$			7.78410i			0.379374i	−0.981845	+	0.189687i	$0.939253\pi$
$422$	−2.26385	+	12.2024i	−0.110203	+	0.594004i
$423$			2.70292i			0.131421i
$424$	3.19828	−	5.21281i	0.155322	−	0.253156i
$425$		−	3.95759i		−	0.191971i
$426$	10.4102	+	1.93135i	0.504375	+	0.0935743i
$427$		−	19.2121i		−	0.929740i
$428$	14.1966	+	5.45543i	0.686218	+	0.263698i
$429$		−	3.57170i		−	0.172443i
$430$	−1.50344	+	8.10369i	−0.0725023	+	0.390795i
$431$	−1.36631			−0.0658129			−0.0329065	−	0.999458i	$-0.510476\pi$
$431$	−1.36631			−0.0658129			−0.0329065	+	0.999458i	$0.510476\pi$
$432$	−2.67866	+	2.97065i	−0.128877	+	0.142926i
$433$			29.1429i			1.40052i	0.713889	+	0.700259i	$0.246932\pi$
$433$			29.1429i			1.40052i	−0.713889	+	0.700259i	$0.753068\pi$
$434$	3.29590	−	17.7652i	0.158208	−	0.852758i
$435$	7.32394			0.351156
$436$	−4.44129	+	11.5575i	−0.212699	+	0.553505i
$437$	22.8794	+	8.76647i	1.09447	+	0.419357i
$438$	3.56193	−	19.1992i	0.170195	−	0.917371i
$439$		−	1.78962i		−	0.0854138i	−0.999088	−	0.0427069i	$-0.986402\pi$
$439$		−	1.78962i		−	0.0854138i	0.999088	−	0.0427069i	$-0.0135982\pi$
$440$	2.59466	−	4.22898i	0.123696	−	0.201609i
$441$	0.248811			0.0118482
$442$	−2.07877	+	11.2048i	−0.0988771	+	0.532958i
$443$			31.5079i			1.49699i	0.663143	+	0.748493i	$0.269222\pi$
$443$			31.5079i			1.49699i	−0.663143	+	0.748493i	$0.730778\pi$
$444$	−1.66273	−	0.638947i	−0.0789095	−	0.0303231i
$445$	15.8514			0.751431
$446$	−3.19529	+	17.2229i	−0.151301	+	0.815530i
$447$	−10.5890			−0.500843
$448$	9.41684	+	18.5310i	0.444904	+	0.875509i
$449$	−6.54651			−0.308949			−0.154475	−	0.987997i	$-0.549368\pi$
$449$	−6.54651			−0.308949			−0.154475	+	0.987997i	$0.549368\pi$
$450$	−1.39049	−	0.257970i	−0.0655481	−	0.0121608i
$451$	17.8179			0.839010
$452$	6.15888	−	16.0272i	0.289689	−	0.753855i
$453$	9.56575			0.449438
$454$	−2.10100	−	0.389789i	−0.0986050	−	0.0182937i
$455$			5.29050i			0.248022i
$456$	7.55683	−	12.3167i	0.353881	−	0.576782i
$457$		−	8.53045i		−	0.399038i	−0.979894	−	0.199519i	$-0.936062\pi$
$457$		−	8.53045i		−	0.399038i	0.979894	−	0.199519i	$-0.0639379\pi$
$458$	5.41269	−	29.1750i	0.252919	−	1.36326i
$459$	−3.95759			−0.184724
$460$	−6.41626	+	7.12963i	−0.299160	+	0.332421i
$461$	28.1888			1.31288			0.656441	−	0.754377i	$-0.272061\pi$
$461$	28.1888			1.31288			0.656441	+	0.754377i	$0.272061\pi$
$462$	1.17579	−	6.33761i	0.0547025	−	0.294852i
$463$		−	2.51180i		−	0.116733i	−0.998295	−	0.0583667i	$-0.981411\pi$
$463$		−	2.51180i		−	0.116733i	0.998295	−	0.0583667i	$-0.0185892\pi$
$464$	−21.7569	−	19.6184i	−1.01004	−	0.910760i
$465$		−	4.91715i		−	0.228028i
$466$	8.57522	+	1.59092i	0.397239	+	0.0736979i
$467$	−39.3961			−1.82303			−0.911516	−	0.411264i	$-0.865088\pi$
$467$	−39.3961			−1.82303			−0.911516	+	0.411264i	$0.865088\pi$
$468$	3.80127	+	1.46074i	0.175714	+	0.0675227i
$469$	21.3165			0.984305
$470$	3.75837	+	0.697273i	0.173361	+	0.0321628i
$471$	14.8452			0.684030
$472$	−15.2642	+	24.8788i	−0.702592	+	1.14514i
$473$	−10.2232			−0.470061
$474$	1.65016	−	8.89453i	0.0757943	−	0.408539i
$475$	5.10890			0.234412
$476$	−7.37712	+	19.1974i	−0.338130	+	0.879911i
$477$		−	2.16224i		−	0.0990024i
$478$	5.24364	−	28.2638i	0.239839	−	1.29276i
$479$	−28.5976			−1.30666			−0.653329	−	0.757074i	$-0.726628\pi$
$479$	−28.5976			−1.30666			−0.653329	+	0.757074i	$0.726628\pi$
$480$	3.43964	+	4.49098i	0.156997	+	0.204984i
$481$			1.81345i			0.0826862i
$482$	−0.206091	+	1.11085i	−0.00938719	+	0.0505979i
$483$	−4.45849	+	11.6361i	−0.202868	+	0.529462i
$484$	−14.7913	−	5.68397i	−0.672334	−	0.258362i
$485$	−0.186909			−0.00848709
$486$	−0.257970	+	1.39049i	−0.0117018	+	0.0630737i
$487$		−	23.2007i		−	1.05132i	−0.850694	−	0.525661i	$-0.823818\pi$
$487$		−	23.2007i		−	1.05132i	0.850694	−	0.525661i	$-0.176182\pi$
$488$	−10.9370	+	17.8259i	−0.495094	+	0.806942i
$489$	9.70954			0.439081
$490$	0.0641859	−	0.345968i	0.00289962	−	0.0156293i
$491$		−	10.7234i		−	0.483941i	−0.970284	−	0.241970i	$-0.922206\pi$
$491$		−	10.7234i		−	0.483941i	0.970284	−	0.241970i	$-0.0777937\pi$
$492$	−7.28707	+	18.9631i	−0.328527	+	0.854921i
$493$		−	28.9851i		−	1.30543i
$494$	−14.4644	−	2.68351i	−0.650784	−	0.120737i
$495$		−	1.75416i		−	0.0788435i
$496$	−13.1714	+	14.6072i	−0.591413	+	0.655881i
$497$		−	19.4528i		−	0.872577i
$498$	−2.52894	+	13.6312i	−0.113324	+	0.610830i
$499$		−	21.4690i		−	0.961086i	−0.876971	−	0.480543i	$-0.840440\pi$
$499$		−	21.4690i		−	0.961086i	0.876971	−	0.480543i	$-0.159560\pi$
$500$	−0.717408	+	1.86690i	−0.0320835	+	0.0834904i
$501$	17.5706			0.784999
$502$	17.7653	+	3.29590i	0.792903	+	0.147103i
$503$	37.2965			1.66297			0.831485	−	0.555547i	$-0.187491\pi$
$503$	37.2965			1.66297			0.831485	+	0.555547i	$0.187491\pi$
$504$	6.26408	+	3.84328i	0.279024	+	0.171194i
$505$			9.35168i			0.416144i
$506$	−10.1468	−	6.21190i	−0.451080	−	0.276153i
$507$			8.85415i			0.393227i
$508$	2.75928	−	7.18045i	0.122423	−	0.318581i
$509$	−5.86771			−0.260082			−0.130041	−	0.991509i	$-0.541511\pi$
$509$	−5.86771			−0.260082			−0.130041	+	0.991509i	$0.541511\pi$
$510$	−1.02094	+	5.50297i	−0.0452080	+	0.243676i
$511$	−35.8761			−1.58707
$512$	1.81186	−	22.5548i	0.0800735	−	0.996789i
$513$		−	5.10890i		−	0.225563i
$514$	−23.1465	−	4.29426i	−1.02095	−	0.189412i
$515$			1.95123i			0.0859815i
$516$	4.18102	−	10.8802i	0.184059	−	0.478975i
$517$			4.74135i			0.208524i
$518$	−0.596978	+	3.21778i	−0.0262297	+	0.141381i
$519$			3.61225i			0.158560i
$520$	3.01175	−	4.90878i	0.132074	−	0.215264i
$521$			25.6449i			1.12352i	0.827299	+	0.561762i	$0.189876\pi$
$521$			25.6449i			1.12352i	−0.827299	+	0.561762i	$0.810124\pi$
$522$	−10.1838	−	1.88936i	−0.445735	−	0.0826950i
$523$	−18.7797			−0.821178			−0.410589	−	0.911821i	$-0.634677\pi$
$523$	−18.7797			−0.821178			−0.410589	+	0.911821i	$0.634677\pi$
$524$	−6.35101	+	16.5272i	−0.277445	+	0.721993i
$525$			2.59830i			0.113399i
$526$	14.4877	+	2.68784i	0.631695	+	0.117195i
$527$	−19.4601			−0.847694
$528$	−4.69879	+	5.21099i	−0.204489	+	0.226779i
$529$	17.1112	+	15.3690i	0.743966	+	0.668217i
$530$	−3.00657	−	0.557794i	−0.130597	−	0.0242290i
$531$			10.3196i			0.447832i
$532$	−24.7822	−	9.52321i	−1.07444	−	0.412884i
$533$	20.6821			0.895839
$534$	−22.0412	−	4.08920i	−0.953817	−	0.176957i
$535$		−	7.60436i		−	0.328765i
$536$	−19.7785	−	12.1350i	−0.854300	−	0.524150i
$537$	−21.6167			−0.932829
$538$	−25.8457	−	4.79504i	−1.11429	−	0.206729i
$539$	0.436454			0.0187994
$540$	1.86690	+	0.717408i	0.0803387	+	0.0308723i
$541$	−29.0557			−1.24920			−0.624601	−	0.780944i	$-0.714738\pi$
$541$	−29.0557			−1.24920			−0.624601	+	0.780944i	$0.714738\pi$
$542$	−4.58146	+	24.6945i	−0.196790	+	1.06072i
$543$	−20.6411			−0.885795
$544$	17.7734	−	13.6127i	0.762030	−	0.583638i
$545$	6.19075			0.265182
$546$	1.36479	−	7.35637i	0.0584077	−	0.314823i
$547$			15.5085i			0.663094i	0.943439	+	0.331547i	$0.107571\pi$
$547$			15.5085i			0.663094i	−0.943439	+	0.331547i	$0.892429\pi$
$548$	−12.7760	+	33.2468i	−0.545762	+	1.42023i
$549$			7.39410i			0.315572i
$550$	−2.43913	−	0.452520i	−0.104005	−	0.0192955i
$551$	37.4173			1.59403
$552$	10.7610	−	8.25844i	0.458017	−	0.351503i
$553$	−16.6206			−0.706779
$554$	−25.6995	−	4.76791i	−1.09187	−	0.202569i
$555$			0.890633i			0.0378053i
$556$	0.910775	−	2.37010i	0.0386255	−	0.100515i
$557$			28.2878i			1.19859i	0.800527	+	0.599296i	$0.204553\pi$
$557$			28.2878i			1.19859i	−0.800527	+	0.599296i	$0.795447\pi$
$558$	−1.26848	+	6.83723i	−0.0536990	+	0.289443i
$559$	−11.8665			−0.501900
$560$	6.95998	−	7.71866i	0.294113	−	0.326173i
$561$	−6.94223			−0.293101
$562$	1.82383	−	9.83066i	0.0769338	−	0.414681i
$563$	−6.04537			−0.254782			−0.127391	−	0.991853i	$-0.540660\pi$
$563$	−6.04537			−0.254782			−0.127391	+	0.991853i	$0.540660\pi$
$564$	−5.04609	−	1.93910i	−0.212479	−	0.0816507i
$565$	−8.58491			−0.361170
$566$	29.0315	+	5.38607i	1.22028	+	0.226394i
$567$	2.59830			0.109119
$568$	−11.0740	+	18.0492i	−0.464654	+	0.757329i
$569$			34.8074i			1.45920i	0.683872	+	0.729602i	$0.260294\pi$
$569$			34.8074i			1.45920i	−0.683872	+	0.729602i	$0.739706\pi$
$570$	−7.10385	−	1.31794i	−0.297548	−	0.0552026i
$571$	−34.3474			−1.43739			−0.718697	−	0.695323i	$-0.755261\pi$
$571$	−34.3474			−1.43739			−0.718697	+	0.695323i	$0.755261\pi$
$572$	6.66802	+	2.56237i	0.278804	+	0.107138i
$573$		−	0.429593i		−	0.0179465i
$574$	36.6981	+	6.80842i	1.53175	+	0.284178i
$575$	4.47835	+	1.71592i	0.186760	+	0.0715589i
$576$	−3.62423	−	7.13197i	−0.151009	−	0.297165i
$577$	−29.0033			−1.20742			−0.603712	−	0.797202i	$-0.706312\pi$
$577$	−29.0033			−1.20742			−0.603712	+	0.797202i	$0.706312\pi$
$578$	−1.85978	−	0.345035i	−0.0773565	−	0.0143516i
$579$		−	8.47229i		−	0.352096i
$580$	−5.25425	+	13.6731i	−0.218171	+	0.567744i
$581$	25.4717			1.05675
$582$	0.259894	+	0.0482169i	0.0107730	+	0.00199865i
$583$		−	3.79292i		−	0.157087i
$584$	33.2876	+	20.4234i	1.37745	+	0.845126i
$585$		−	2.03614i		−	0.0841838i
$586$	−8.02032	+	43.2304i	−0.331316	+	1.78583i
$587$			15.8918i			0.655923i	0.944691	+	0.327961i	$0.106362\pi$
$587$			15.8918i			0.655923i	−0.944691	+	0.327961i	$0.893638\pi$
$588$	−0.178499	+	0.464506i	−0.00736118	+	0.0191559i
$589$		−	25.1212i		−	1.03510i
$590$	14.3492	+	2.66214i	0.590748	+	0.109599i
$591$			12.5408i			0.515861i
$592$	2.38571	−	2.64576i	0.0980519	−	0.108740i
$593$	−30.1078			−1.23638			−0.618190	−	0.786029i	$-0.712134\pi$
$593$	−30.1078			−1.23638			−0.618190	+	0.786029i	$0.712134\pi$
$594$	−0.452520	+	2.43913i	−0.0185671	+	0.100079i
$595$	10.2830			0.421563
$596$	7.59664	−	19.7687i	0.311171	−	0.809756i
$597$		−	6.94093i		−	0.284073i
$598$	−11.7779	−	7.21046i	−0.481633	−	0.294858i
$599$			1.22255i			0.0499519i	0.999688	+	0.0249760i	$0.00795092\pi$
$599$			1.22255i			0.0499519i	−0.999688	+	0.0249760i	$0.992049\pi$
$600$	1.47915	−	2.41083i	0.0603861	−	0.0984218i
$601$	−2.02167			−0.0824655			−0.0412327	−	0.999150i	$-0.513129\pi$
$601$	−2.02167			−0.0824655			−0.0412327	+	0.999150i	$0.513129\pi$
$602$	−21.0559	−	3.90639i	−0.858173	−	0.159213i
$603$	−8.20400			−0.334093
$604$	−6.86254	+	17.8583i	−0.279233	+	0.726645i
$605$			7.92293i			0.322113i
$606$	2.41245	−	13.0034i	0.0979993	−	0.528226i
$607$		−	37.5362i		−	1.52355i	−0.647844	−	0.761773i	$-0.724329\pi$
$607$		−	37.5362i		−	1.52355i	0.647844	−	0.761773i	$-0.275671\pi$
$608$	17.5727	+	22.9440i	0.712669	+	0.930501i
$609$			19.0298i			0.771128i
$610$	10.2814	+	1.90746i	0.416281	+	0.0772307i
$611$			5.50351i			0.222648i
$612$	2.83920	−	7.38843i	0.114768	−	0.298660i
$613$		−	10.9310i		−	0.441498i	−0.975331	−	0.220749i	$-0.929150\pi$
$613$		−	10.9310i		−	0.441498i	0.975331	−	0.220749i	$-0.0708501\pi$
$614$	−4.81167	+	25.9354i	−0.194183	+	1.04667i
$615$	10.1575			0.409590
$616$	10.9882	+	6.74173i	0.442726	+	0.271632i
$617$			10.2444i			0.412425i	0.978507	+	0.206212i	$0.0661137\pi$
$617$			10.2444i			0.412425i	−0.978507	+	0.206212i	$0.933886\pi$
$618$	0.503359	−	2.71316i	0.0202481	−	0.109139i
$619$	12.0993			0.486314			0.243157	−	0.969987i	$-0.421817\pi$
$619$	12.0993			0.486314			0.243157	+	0.969987i	$0.421817\pi$
$620$	9.17985	+	3.52760i	0.368672	+	0.141672i
$621$	1.71592	−	4.47835i	0.0688576	−	0.179710i
$622$	2.27668	−	12.2715i	0.0912866	−	0.492044i
$623$			41.1869i			1.65012i
$624$	−5.45412	+	6.04865i	−0.218339	+	0.242140i
$625$	1.00000			0.0400000
$626$	−9.02213	+	48.6302i	−0.360597	+	1.94366i
$627$		−	8.96181i		−	0.357900i
$628$	−10.6500	+	27.7145i	−0.424983	+	1.10593i
$629$	3.52476			0.140541
$630$	0.670285	−	3.61291i	0.0267048	−	0.143942i
$631$	−15.8148			−0.629579			−0.314789	−	0.949162i	$-0.601934\pi$
$631$	−15.8148			−0.629579			−0.314789	+	0.949162i	$0.601934\pi$
$632$	15.4214	+	9.46169i	0.613430	+	0.376366i
$633$	−8.77564			−0.348800
$634$	−32.5817	−	6.04472i	−1.29398	−	0.240066i
$635$	−3.84618			−0.152631
$636$	4.03670	+	1.55121i	0.160066	+	0.0615095i
$637$	0.506613			0.0200727
$638$	−17.8641	−	3.31423i	−0.707245	−	0.131212i
$639$			7.48672i			0.296170i
$640$	−10.8518	+	3.19960i	−0.428957	+	0.126475i
$641$		−	44.2351i		−	1.74718i	−0.486661	−	0.873591i	$-0.661785\pi$
$641$		−	44.2351i		−	1.74718i	0.486661	−	0.873591i	$-0.338215\pi$
$642$	−1.96170	+	10.5738i	−0.0774220	+	0.417313i
$643$	−18.6431			−0.735211			−0.367606	−	0.929982i	$-0.619822\pi$
$643$	−18.6431			−0.735211			−0.367606	+	0.929982i	$0.619822\pi$
$644$	−18.5249	−	16.6714i	−0.729985	−	0.656946i
$645$	−5.82796			−0.229476
$646$	−5.21588	+	28.1141i	−0.205216	+	1.10614i
$647$			19.8452i			0.780194i	0.920774	+	0.390097i	$0.127558\pi$
$647$			19.8452i			0.780194i	−0.920774	+	0.390097i	$0.872442\pi$
$648$	−2.41083	−	1.47915i	−0.0947064	−	0.0581065i
$649$			18.1022i			0.710572i
$650$	−2.83122	−	0.525262i	−0.111049	−	0.0206025i
$651$	12.7763			0.500741
$652$	−6.96570	+	18.1268i	−0.272798	+	0.709899i
$653$	−33.2325			−1.30049			−0.650243	−	0.759726i	$-0.725333\pi$
$653$	−33.2325			−1.30049			−0.650243	+	0.759726i	$0.725333\pi$
$654$	−8.60815	−	1.59703i	−0.336605	−	0.0624487i
$655$	8.85272			0.345904
$656$	−30.1744	−	27.2085i	−1.17811	−	1.06231i
$657$	13.8075			0.538682
$658$	−1.81173	+	9.76540i	−0.0706285	+	0.380695i
$659$	−12.5073			−0.487215			−0.243607	−	0.969874i	$-0.578331\pi$
$659$	−12.5073			−0.487215			−0.243607	+	0.969874i	$0.578331\pi$
$660$	3.27484	+	1.25845i	0.127473	+	0.0489849i
$661$			19.4372i			0.756020i	0.925802	+	0.378010i	$0.123391\pi$
$661$			19.4372i			0.756020i	−0.925802	+	0.378010i	$0.876609\pi$
$662$	−3.18746	+	17.1808i	−0.123884	+	0.667749i
$663$	−8.05818			−0.312954
$664$	−23.6339	−	14.5004i	−0.917173	−	0.562726i
$665$			13.2745i			0.514762i
$666$	0.229757	−	1.23841i	0.00890290	−	0.0479875i
$667$	32.7992	+	12.5673i	1.26999	+	0.486609i
$668$	−12.6053	+	32.8027i	−0.487714	+	1.26917i
$669$	−12.3863			−0.478881
$670$	−2.11639	+	11.4076i	−0.0817632	+	0.440712i
$671$			12.9704i			0.500717i
$672$	−11.6689	+	8.93722i	−0.450139	+	0.344761i
$673$	24.8890			0.959401			0.479700	−	0.877432i	$-0.340745\pi$
$673$	24.8890			0.959401			0.479700	+	0.877432i	$0.340745\pi$
$674$	−1.94293	+	10.4726i	−0.0748390	+	0.403390i
$675$		−	1.00000i		−	0.0384900i
$676$	−16.5298	−	6.35204i	−0.635763	−	0.244309i
$677$			27.4911i			1.05657i	0.849067	+	0.528284i	$0.177165\pi$
$677$			27.4911i			1.05657i	−0.849067	+	0.528284i	$0.822835\pi$
$678$	11.9372	+	2.21465i	0.458445	+	0.0850531i
$679$		−	0.485646i		−	0.0186374i
$680$	−9.54108	−	5.85387i	−0.365884	−	0.224486i
$681$		−	1.51099i		−	0.0579011i
$682$	−2.22511	+	11.9936i	−0.0852039	+	0.459258i
$683$		−	49.4721i		−	1.89300i	−0.322707	−	0.946499i	$-0.604593\pi$
$683$		−	49.4721i		−	1.89300i	0.322707	−	0.946499i	$-0.395407\pi$
$684$	9.53782	+	3.66516i	0.364688	+	0.140141i
$685$	17.8085			0.680428
$686$	26.1893	+	4.85877i	0.999911	+	0.185509i
$687$	20.9819			0.800508
$688$	17.3128	+	15.6111i	0.660045	+	0.595168i
$689$		−	4.40262i		−	0.167727i
$690$	−5.78443	−	3.54125i	−0.220209	−	0.134813i
$691$			48.6195i			1.84957i	0.380487	+	0.924786i	$0.375756\pi$
$691$			48.6195i			1.84957i	−0.380487	+	0.924786i	$0.624244\pi$
$692$	−6.74373	−	2.59146i	−0.256358	−	0.0985125i
$693$	4.55784			0.173138
$694$	−6.16466	+	33.2282i	−0.234007	+	1.26132i
$695$	−1.26954			−0.0481563
$696$	10.8332	−	17.6568i	0.410632	−	0.669279i
$697$		−	40.1992i		−	1.52265i
$698$	−14.0344	−	2.60374i	−0.531210	−	0.0985528i
$699$			6.16707i			0.233260i
$700$	−4.85078	−	1.86404i	−0.183342	−	0.0704543i
$701$		−	16.2570i		−	0.614020i	−0.951706	−	0.307010i	$-0.900672\pi$
$701$		−	16.2570i		−	0.614020i	0.951706	−	0.307010i	$-0.0993285\pi$
$702$	−0.525262	+	2.83122i	−0.0198247	+	0.106857i
$703$			4.55016i			0.171612i
$704$	−6.35746	−	12.5106i	−0.239606	−	0.471511i
$705$			2.70292i			0.101798i
$706$	−1.14106	−	0.211695i	−0.0429442	−	0.00796723i
$707$	−24.2985			−0.913840
$708$	−19.2656	−	7.40335i	−0.724047	−	0.278235i
$709$		−	18.0103i		−	0.676390i	−0.941076	−	0.338195i	$-0.890184\pi$
$709$		−	18.0103i		−	0.676390i	0.941076	−	0.338195i	$-0.109816\pi$
$710$	10.4102	+	1.93135i	0.390687	+	0.0724823i
$711$	6.39670			0.239895
$712$	23.4467	−	38.2152i	0.878701	−	1.43217i
$713$	8.43745	−	22.0207i	0.315985	−	0.824683i
$714$	−14.2984	−	2.65271i	−0.535104	−	0.0992753i
$715$		−	3.57170i		−	0.133574i
$716$	15.5080	−	40.3563i	0.579560	−	1.50818i
$717$	20.3266			0.759109
$718$	−33.1018	−	6.14121i	−1.23535	−	0.229188i
$719$		−	10.5365i		−	0.392946i	−0.980509	−	0.196473i	$-0.937051\pi$
$719$		−	10.5365i		−	0.392946i	0.980509	−	0.196473i	$-0.0629488\pi$
$720$	−2.67866	+	2.97065i	−0.0998278	+	0.110710i
$721$	−5.06989			−0.188813
$722$	−9.87362	−	1.83180i	−0.367458	−	0.0681727i
$723$	−0.798895			−0.0297112
$724$	14.8081	−	38.5349i	0.550338	−	1.43214i
$725$	7.32394			0.272004
$726$	2.04388	−	11.0167i	0.0758555	−	0.408869i
$727$	30.3679			1.12628			0.563142	−	0.826360i	$-0.309592\pi$
$727$	30.3679			1.12628			0.563142	+	0.826360i	$0.309592\pi$
$728$	12.7545	+	7.82545i	0.472714	+	0.290030i
$729$	−1.00000			−0.0370370
$730$	3.56193	−	19.1992i	0.131833	−	0.710593i
$731$			23.0646i			0.853077i
$732$	−13.8041	−	5.30458i	−0.510213	−	0.196063i
$733$			6.62522i			0.244708i	0.992487	+	0.122354i	$0.0390443\pi$
$733$			6.62522i			0.244708i	−0.992487	+	0.122354i	$0.960956\pi$
$734$	−48.5185	−	9.00140i	−1.79085	−	0.332248i
$735$	0.248811			0.00917754
$736$	7.69771	+	26.0143i	0.283741	+	0.958901i
$737$	−14.3911			−0.530103
$738$	−14.1239	−	2.62033i	−0.519907	−	0.0964558i
$739$		−	24.3361i		−	0.895217i	−0.894230	−	0.447608i	$-0.852276\pi$
$739$		−	24.3361i		−	0.895217i	0.894230	−	0.447608i	$-0.147724\pi$
$740$	−1.66273	−	0.638947i	−0.0611230	−	0.0234882i
$741$		−	10.4024i		−	0.382142i
$742$	1.44932	−	7.81199i	0.0532062	−	0.286787i
$743$	30.2508			1.10980			0.554898	−	0.831919i	$-0.312757\pi$
$743$	30.2508			1.10980			0.554898	+	0.831919i	$0.312757\pi$
$744$	−11.8544	−	7.27321i	−0.434605	−	0.266649i
$745$	−10.5890			−0.387952
$746$	−7.92891	+	42.7376i	−0.290298	+	1.56474i
$747$	−9.80321			−0.358681
$748$	4.98041	−	12.9605i	0.182102	−	0.473882i
$749$	19.7584			0.721958
$750$	−1.39049	−	0.257970i	−0.0507734	−	0.00941974i
$751$	−34.2351			−1.24926			−0.624629	−	0.780922i	$-0.714750\pi$
$751$	−34.2351			−1.24926			−0.624629	+	0.780922i	$0.714750\pi$
$752$	7.24021	−	8.02944i	0.264023	−	0.292803i
$753$			12.7763i			0.465594i
$754$	−20.7357	−	3.84699i	−0.755149	−	0.140099i
$755$	9.56575			0.348133
$756$	−1.86404	+	4.85078i	−0.0677946	+	0.176421i
$757$		−	22.6203i		−	0.822147i	−0.911602	−	0.411074i	$-0.865154\pi$
$757$		−	22.6203i		−	0.822147i	0.911602	−	0.411074i	$-0.134846\pi$
$758$	35.6700	+	6.61768i	1.29559	+	0.240365i
$759$	3.01000	−	7.85573i	0.109256	−	0.285145i
$760$	7.55683	−	12.3167i	0.274115	−	0.446774i
$761$	−40.6373			−1.47310			−0.736551	−	0.676382i	$-0.763547\pi$
$761$	−40.6373			−1.47310			−0.736551	+	0.676382i	$0.763547\pi$
$762$	5.34806	+	0.992201i	0.193740	+	0.0359436i
$763$			16.0854i			0.582332i
$764$	0.802009	+	0.308193i	0.0290157	+	0.0111500i
$765$	−3.95759			−0.143087
$766$	−26.9720	−	5.00399i	−0.974538	−	0.180801i
$767$			21.0121i			0.758701i
$768$	15.9147	−	1.64955i	0.574274	−	0.0595229i
$769$			44.9857i			1.62223i	0.584889	+	0.811114i	$0.301138\pi$
$769$			44.9857i			1.62223i	−0.584889	+	0.811114i	$0.698862\pi$
$770$	1.17579	−	6.33761i	0.0423724	−	0.228391i
$771$		−	16.6463i		−	0.599503i
$772$	15.8169	+	6.07809i	0.569264	+	0.218755i
$773$		−	50.2656i		−	1.80793i	−0.427609	−	0.903964i	$-0.640644\pi$
$773$		−	50.2656i		−	1.80793i	0.427609	−	0.903964i	$-0.359356\pi$
$774$	8.10369	+	1.50344i	0.291281	+	0.0540400i
$775$		−	4.91715i		−	0.176629i
$776$	−0.276466	+	0.450606i	−0.00992456	+	0.0161758i
$777$	−2.31414			−0.0830192
$778$	−1.29476	+	6.97890i	−0.0464194	+	0.250206i
$779$	51.8936			1.85928
$780$	3.80127	+	1.46074i	0.136107	+	0.0523029i
$781$			13.1329i			0.469932i
$782$	−14.0148	+	22.8924i	−0.501168	+	0.818629i
$783$		−	7.32394i		−	0.261736i
$784$	−0.739131	−	0.666481i	−0.0263976	−	0.0238029i
$785$	14.8452			0.529847
$786$	−12.3096	−	2.28374i	−0.439068	−	0.0814582i
$787$	13.0884			0.466550			0.233275	−	0.972411i	$-0.425056\pi$
$787$	13.0884			0.466550			0.233275	+	0.972411i	$0.425056\pi$
$788$	−23.4125	−	8.99688i	−0.834036	−	0.320501i
$789$			10.4192i			0.370933i
$790$	1.65016	−	8.89453i	0.0587100	−	0.316453i
$791$		−	22.3062i		−	0.793117i
$792$	−4.22898	−	2.59466i	−0.150270	−	0.0921973i
$793$			15.0554i			0.534632i
$794$	26.9530	+	5.00046i	0.956527	+	0.177460i
$795$		−	2.16224i		−	0.0766869i
$796$	12.9580	+	4.97948i	0.459286	+	0.176493i
$797$		−	28.0520i		−	0.993652i	−0.867850	−	0.496826i	$-0.834499\pi$
$797$		−	28.0520i		−	0.993652i	0.867850	−	0.496826i	$-0.165501\pi$
$798$	3.42442	−	18.4580i	0.121223	−	0.653405i
$799$	10.6970			0.378434
$800$	3.43964	+	4.49098i	0.121609	+	0.158780i
$801$		−	15.8514i		−	0.560083i
$802$	4.87800	−	26.2929i	0.172248	−	0.928435i
$803$	24.2206			0.854725
$804$	5.88562	−	15.3161i	0.207570	−	0.540156i
$805$	−4.45849	+	11.6361i	−0.157141	+	0.410119i
$806$	−2.58279	+	13.9215i	−0.0909751	+	0.490365i
$807$		−	18.5876i		−	0.654313i
$808$	22.5453	+	13.8325i	0.793142	+	0.486627i
$809$	18.9978			0.667928			0.333964	−	0.942586i	$-0.391614\pi$
$809$	18.9978			0.667928			0.333964	+	0.942586i	$0.391614\pi$
$810$	−0.257970	+	1.39049i	−0.00906415	+	0.0488567i
$811$		−	7.94646i		−	0.279038i	−0.990219	−	0.139519i	$-0.955444\pi$
$811$		−	7.94646i		−	0.279038i	0.990219	−	0.139519i	$-0.0445556\pi$
$812$	−35.5269	−	13.6522i	−1.24675	−	0.479097i
$813$	−17.7596			−0.622858
$814$	0.403030	−	2.17237i	0.0141262	−	0.0761416i
$815$	9.70954			0.340110
$816$	11.7566	+	10.6010i	0.411564	+	0.371111i
$817$	−29.7744			−1.04168
$818$	34.3190	+	6.36704i	1.19994	+	0.222618i
$819$	5.29050			0.184865
$820$	−7.28707	+	18.9631i	−0.254476	+	0.662219i
$821$	4.42411			0.154403			0.0772013	−	0.997016i	$-0.475402\pi$
$821$	4.42411			0.154403			0.0772013	+	0.997016i	$0.475402\pi$
$822$	−24.7625	−	4.59407i	−0.863691	−	0.160236i
$823$		−	32.2030i		−	1.12252i	−0.827638	−	0.561262i	$-0.810316\pi$
$823$		−	32.2030i		−	1.12252i	0.827638	−	0.561262i	$-0.189684\pi$
$824$	4.70409	+	2.88616i	0.163875	+	0.100544i
$825$		−	1.75416i		−	0.0610719i
$826$	−6.91706	+	37.2837i	−0.240675	+	1.29726i
$827$	−49.2912			−1.71402			−0.857011	−	0.515298i	$-0.827681\pi$
$827$	−49.2912			−1.71402			−0.857011	+	0.515298i	$0.827681\pi$
$828$	7.12963	+	6.41626i	0.247772	+	0.222981i
$829$	−3.25392			−0.113013			−0.0565067	−	0.998402i	$-0.517996\pi$
$829$	−3.25392			−0.113013			−0.0565067	+	0.998402i	$0.517996\pi$
$830$	−2.52894	+	13.6312i	−0.0877806	+	0.473147i
$831$		−	18.4824i		−	0.641148i
$832$	−7.37941	−	14.5217i	−0.255835	−	0.503448i
$833$		−	0.984692i		−	0.0341176i
$834$	1.76527	+	0.327503i	0.0611264	+	0.0113405i
$835$	17.5706			0.608057
$836$	16.7308	+	6.42927i	0.578648	+	0.222361i
$837$	−4.91715			−0.169962
$838$	−33.7916	−	6.26920i	−1.16731	−	0.216566i
$839$	−9.24797			−0.319275			−0.159638	−	0.987176i	$-0.551033\pi$
$839$	−9.24797			−0.319275			−0.159638	+	0.987176i	$0.551033\pi$
$840$	6.26408	+	3.84328i	0.216131	+	0.132606i
$841$	24.6402			0.849660
$842$	2.00807	−	10.8237i	0.0692025	−	0.373009i
$843$	7.06994			0.243502
$844$	6.29571	−	16.3833i	0.216707	−	0.563935i
$845$			8.85415i			0.304592i
$846$	0.697273	−	3.75837i	0.0239727	−	0.129216i
$847$	−20.5862			−0.707350
$848$	−5.79192	+	6.42327i	−0.198895	+	0.220576i
$849$			20.8787i			0.716554i
$850$	−1.02094	+	5.50297i	−0.0350179	+	0.188750i
$851$	−1.52826	+	3.98857i	−0.0523880	+	0.136726i
$852$	−13.9770	−	5.37103i	−0.478844	−	0.184009i
$853$	30.3727			1.03994			0.519971	−	0.854184i	$-0.325943\pi$
$853$	30.3727			1.03994			0.519971	+	0.854184i	$0.325943\pi$
$854$	−4.95615	+	26.7142i	−0.169596	+	0.914141i
$855$		−	5.10890i		−	0.174721i
$856$	−18.3328	−	11.2480i	−0.626603	−	0.384448i
$857$	−18.2387			−0.623023			−0.311511	−	0.950242i	$-0.600835\pi$
$857$	−18.2387			−0.623023			−0.311511	+	0.950242i	$0.600835\pi$
$858$	−0.921392	+	4.96640i	−0.0314558	+	0.169550i
$859$			46.4910i			1.58625i	0.609058	+	0.793126i	$0.291548\pi$
$859$			46.4910i			1.58625i	−0.609058	+	0.793126i	$0.708452\pi$
$860$	4.18102	−	10.8802i	0.142572	−	0.371013i
$861$			26.3923i			0.899447i
$862$	1.89984	+	0.352468i	0.0647087	+	0.0120051i
$863$			16.0349i			0.545833i	0.962038	+	0.272917i	$0.0879883\pi$
$863$			16.0349i			0.545833i	−0.962038	+	0.272917i	$0.912012\pi$
$864$	4.49098	−	3.43964i	0.152786	−	0.117019i
$865$			3.61225i			0.122820i
$866$	7.51800	−	40.5228i	0.255472	−	1.37702i
$867$		−	1.33750i		−	0.0454239i
$868$	−9.16579	+	23.8520i	−0.311107	+	0.809591i
$869$	11.2208			0.380640
$870$	−10.1838	−	1.88936i	−0.345265	−	0.0640553i
$871$	−16.7045			−0.566009
$872$	9.15705	−	14.9249i	0.310097	−	0.505419i
$873$			0.186909i			0.00632590i
$874$	−29.5520	−	18.0919i	−0.999613	−	0.611967i
$875$			2.59830i			0.0878387i
$876$	−9.90562	+	25.7773i	−0.334680	+	0.870934i
$877$	2.63429			0.0889535			0.0444768	−	0.999010i	$-0.485838\pi$
$877$	2.63429			0.0889535			0.0444768	+	0.999010i	$0.485838\pi$
$878$	−0.461668	+	2.48844i	−0.0155805	+	0.0839808i
$879$	−31.0901			−1.04864
$880$	−4.69879	+	5.21099i	−0.158396	+	0.175662i
$881$		−	23.7900i		−	0.801504i	−0.916187	−	0.400752i	$-0.868749\pi$
$881$		−	23.7900i		−	0.801504i	0.916187	−	0.400752i	$-0.131251\pi$
$882$	−0.345968	−	0.0641859i	−0.0116494	−	0.00216125i
$883$		−	17.2297i		−	0.579826i	−0.957053	−	0.289913i	$-0.906374\pi$
$883$		−	17.2297i		−	0.579826i	0.957053	−	0.289913i	$-0.0936264\pi$
$884$	5.78100	−	15.0438i	0.194436	−	0.505979i
$885$			10.3196i			0.346889i
$886$	8.12810	−	43.8113i	0.273069	−	1.47187i
$887$			39.2819i			1.31896i	0.751723	+	0.659479i	$0.229223\pi$
$887$			39.2819i			1.31896i	−0.751723	+	0.659479i	$0.770777\pi$
$888$	2.14717	+	1.31738i	0.0720542	+	0.0442084i
$889$		−	9.99356i		−	0.335173i
$890$	−22.0412	−	4.08920i	−0.738823	−	0.137070i
$891$	−1.75416			−0.0587665
$892$	8.88601	−	23.1240i	0.297526	−	0.774248i
$893$			13.8089i			0.462099i
$894$	14.7239	+	2.73165i	0.492440	+	0.0913601i
$895$	−21.6167			−0.722566
$896$	−8.31354	−	28.1964i	−0.277736	−	0.941976i
$897$	3.49385	−	9.11852i	0.116656	−	0.304459i
$898$	9.10284	+	1.68881i	0.303766	+	0.0563562i
$899$		−	36.0130i		−	1.20110i
$900$	1.86690	+	0.717408i	0.0622301	+	0.0239136i
$901$	−8.55727			−0.285084
$902$	−24.7755	−	4.59648i	−0.824933	−	0.153046i
$903$		−	15.1428i		−	0.503921i
$904$	−12.6984	+	20.6968i	−0.422341	+	0.688364i
$905$	−20.6411			−0.686134
$906$	−13.3010	−	2.46768i	−0.441897	−	0.0819831i
$907$	−33.4013			−1.10907			−0.554536	−	0.832160i	$-0.687104\pi$
$907$	−33.4013			−1.10907			−0.554536	+	0.832160i	$0.687104\pi$
$908$	2.82086	+	1.08399i	0.0936136	+	0.0359736i
$909$	9.35168			0.310176
$910$	1.36479	−	7.35637i	0.0452424	−	0.243861i
$911$	52.8101			1.74968			0.874838	−	0.484416i	$-0.160968\pi$
$911$	52.8101			1.74968			0.874838	+	0.484416i	$0.160968\pi$
$912$	−13.6850	+	15.1768i	−0.453156	+	0.502553i
$913$	−17.1964			−0.569117
$914$	−2.20060	+	11.8615i	−0.0727894	+	0.392343i
$915$			7.39410i			0.244441i
$916$	−15.0526	+	39.1711i	−0.497350	+	1.29425i
$917$			23.0021i			0.759595i
$918$	5.50297	+	1.02094i	0.181625	+	0.0336960i
$919$	15.4354			0.509168			0.254584	−	0.967051i	$-0.418061\pi$
$919$	15.4354			0.509168			0.254584	+	0.967051i	$0.418061\pi$
$920$	10.7610	−	8.25844i	0.354778	−	0.272273i
$921$	−18.6521			−0.614606
$922$	−39.1961	−	7.27186i	−1.29085	−	0.239486i
$923$			15.2440i			0.501762i
$924$	−3.26983	+	8.50904i	−0.107569	+	0.279927i
$925$			0.890633i			0.0292838i
$926$	−0.647970	+	3.49263i	−0.0212936	+	0.114775i
$927$	1.95123			0.0640868
$928$	25.1917	+	32.8917i	0.826958	+	1.07972i
$929$	16.3559			0.536619			0.268310	−	0.963333i	$-0.413535\pi$
$929$	16.3559			0.536619			0.268310	+	0.963333i	$0.413535\pi$
$930$	−1.26848	+	6.83723i	−0.0415951	+	0.224202i
$931$	1.27115			0.0416603
$932$	−11.5133	−	4.42430i	−0.377131	−	0.144923i
$933$	8.82536			0.288929
$934$	54.7797	+	10.1630i	1.79245	+	0.332544i
$935$	−6.94223			−0.227035
$936$	−4.90878	−	3.01175i	−0.160449	−	0.0984422i
$937$		−	50.5247i		−	1.65057i	−0.564716	−	0.825286i	$-0.691014\pi$
$937$		−	50.5247i		−	1.65057i	0.564716	−	0.825286i	$-0.308986\pi$
$938$	−29.6403	−	5.49902i	−0.967790	−	0.179549i
$939$	−34.9736			−1.14132
$940$	−5.04609	−	1.93910i	−0.164585	−	0.0632464i
$941$			0.921848i			0.0300514i	0.999887	+	0.0150257i	$0.00478300\pi$
$941$			0.921848i			0.0300514i	−0.999887	+	0.0150257i	$0.995217\pi$
$942$	−20.6420	−	3.82961i	−0.672553	−	0.124776i
$943$	45.4888	+	17.4295i	1.48132	+	0.567582i
$944$	27.6427	−	30.6559i	0.899692	−	0.997764i
$945$	2.59830			0.0845229
$946$	14.2151	+	2.63727i	0.462174	+	0.0857450i
$947$			55.9151i			1.81700i	0.417888	+	0.908499i	$0.362771\pi$
$947$			55.9151i			1.81700i	−0.417888	+	0.908499i	$0.637229\pi$
$948$	−4.58904	+	11.9420i	−0.149045	+	0.387859i
$949$	28.1140			0.912618
$950$	−7.10385	−	1.31794i	−0.230479	−	0.0427597i
$951$		−	23.4318i		−	0.759830i
$952$	15.2101	−	24.7906i	0.492963	−	0.803469i
$953$			0.618608i			0.0200387i	0.999950	+	0.0100193i	$0.00318931\pi$
$953$			0.618608i			0.0200387i	−0.999950	+	0.0100193i	$0.996811\pi$
$954$	−0.557794	+	3.00657i	−0.0180593	+	0.0973413i
$955$		−	0.429593i		−	0.0139013i
$956$	−14.5824	+	37.9477i	−0.471629	+	1.22732i
$957$		−	12.8473i		−	0.415296i
$958$	39.7645	+	7.37732i	1.28473	+	0.238351i
$959$			46.2720i			1.49420i
$960$	−3.62423	−	7.13197i	−0.116971	−	0.230183i
$961$	6.82160			0.220052
$962$	0.467816	−	2.52158i	0.0150830	−	0.0812989i
$963$	−7.60436			−0.245047
$964$	0.573133	−	1.49146i	0.0184594	−	0.0480366i
$965$		−	8.47229i		−	0.272733i
$966$	9.20124	−	15.0297i	0.296045	−	0.483573i
$967$			44.5923i			1.43399i	0.697077	+	0.716996i	$0.254484\pi$
$967$			44.5923i			1.43399i	−0.697077	+	0.716996i	$0.745516\pi$
$968$	19.1009	+	11.7192i	0.613925	+	0.376670i
$969$	−20.2189			−0.649525
$970$	0.259894	+	0.0482169i	0.00834469	+	0.00154815i
$971$	−9.61774			−0.308648			−0.154324	−	0.988020i	$-0.549320\pi$
$971$	−9.61774			−0.308648			−0.154324	+	0.988020i	$0.549320\pi$
$972$	0.717408	−	1.86690i	0.0230109	−	0.0598809i
$973$		−	3.29864i		−	0.105750i
$974$	−5.98508	+	32.2602i	−0.191774	+	1.03368i
$975$		−	2.03614i		−	0.0652085i
$976$	19.8063	−	21.9653i	0.633984	−	0.703092i
$977$		−	54.1107i		−	1.73116i	−0.500775	−	0.865578i	$-0.666952\pi$
$977$		−	54.1107i		−	1.73116i	0.500775	−	0.865578i	$-0.333048\pi$
$978$	−13.5010	−	2.50477i	−0.431714	−	0.0800938i
$979$		−	27.8059i		−	0.888681i
$980$	−0.178499	+	0.464506i	−0.00570194	+	0.0148381i
$981$		−	6.19075i		−	0.197655i
$982$	−2.76632	+	14.9108i	−0.0882768	+	0.475821i
$983$	31.0113			0.989108			0.494554	−	0.869147i	$-0.335331\pi$
$983$	31.0113			0.989108			0.494554	+	0.869147i	$0.335331\pi$
$984$	15.0245	−	24.4880i	0.478963	−	0.780650i
$985$			12.5408i			0.399584i
$986$	−7.47730	+	40.3034i	−0.238126	+	1.28352i
$987$	−7.02301			−0.223545
$988$	19.4203	+	7.46277i	0.617842	+	0.237422i
$989$	−26.0996	−	10.0003i	−0.829920	−	0.317992i
$990$	−0.452520	+	2.43913i	−0.0143820	+	0.0775207i
$991$			21.4252i			0.680593i	0.940318	+	0.340297i	$0.110528\pi$
$991$			21.4252i			0.680593i	−0.940318	+	0.340297i	$0.889472\pi$
$992$	22.0828	−	16.9132i	0.701131	−	0.536995i
$993$	−12.3559			−0.392104
$994$	−5.01824	+	27.0488i	−0.159169	+	0.857937i
$995$		−	6.94093i		−	0.220042i
$996$	7.03290	−	18.3016i	0.222846	−	0.579910i
$997$	21.4409			0.679041			0.339521	−	0.940599i	$-0.389735\pi$
$997$	21.4409			0.679041			0.339521	+	0.940599i	$0.389735\pi$
$998$	−5.53837	+	29.8524i	−0.175314	+	0.944961i
$999$	0.890633			0.0281784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.a.91.3	✓	48
4.3	odd	2		1380.2.p.b.91.4	yes	48
23.22	odd	2		1380.2.p.b.91.3	yes	48
92.91	even	2	inner	1380.2.p.a.91.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.3	✓	48	1.1	even	1	trivial
1380.2.p.a.91.4	yes	48	92.91	even	2	inner
1380.2.p.b.91.3	yes	48	23.22	odd	2
1380.2.p.b.91.4	yes	48	4.3	odd	2

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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39049 - 0.257970i) q^{2} -1.00000i q^{3} +(1.86690 + 0.717408i) q^{4} -1.00000i q^{5} +(-0.257970 + 1.39049i) q^{6} +2.59830 q^{7} +(-2.41083 - 1.47915i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.39049 - 0.257970i) q^{2} -1.00000i q^{3} +(1.86690 + 0.717408i) q^{4} -1.00000i q^{5} +(-0.257970 + 1.39049i) q^{6} +2.59830 q^{7} +(-2.41083 - 1.47915i) q^{8} -1.00000 q^{9} +(-0.257970 + 1.39049i) q^{10} -1.75416 q^{11} +(0.717408 - 1.86690i) q^{12} -2.03614 q^{13} +(-3.61291 - 0.670285i) q^{14} -1.00000 q^{15} +(2.97065 + 2.67866i) q^{16} +3.95759i q^{17} +(1.39049 + 0.257970i) q^{18} -5.10890 q^{19} +(0.717408 - 1.86690i) q^{20} -2.59830i q^{21} +(2.43913 + 0.452520i) q^{22} +(-4.47835 - 1.71592i) q^{23} +(-1.47915 + 2.41083i) q^{24} -1.00000 q^{25} +(2.83122 + 0.525262i) q^{26} +1.00000i q^{27} +(4.85078 + 1.86404i) q^{28} -7.32394 q^{29} +(1.39049 + 0.257970i) q^{30} +4.91715i q^{31} +(-3.43964 - 4.49098i) q^{32} +1.75416i q^{33} +(1.02094 - 5.50297i) q^{34} -2.59830i q^{35} +(-1.86690 - 0.717408i) q^{36} -0.890633i q^{37} +(7.10385 + 1.31794i) q^{38} +2.03614i q^{39} +(-1.47915 + 2.41083i) q^{40} -10.1575 q^{41} +(-0.670285 + 3.61291i) q^{42} +5.82796 q^{43} +(-3.27484 - 1.25845i) q^{44} +1.00000i q^{45} +(5.78443 + 3.54125i) q^{46} -2.70292i q^{47} +(2.67866 - 2.97065i) q^{48} -0.248811 q^{49} +(1.39049 + 0.257970i) q^{50} +3.95759 q^{51} +(-3.80127 - 1.46074i) q^{52} +2.16224i q^{53} +(0.257970 - 1.39049i) q^{54} +1.75416i q^{55} +(-6.26408 - 3.84328i) q^{56} +5.10890i q^{57} +(10.1838 + 1.88936i) q^{58} -10.3196i q^{59} +(-1.86690 - 0.717408i) q^{60} -7.39410i q^{61} +(1.26848 - 6.83723i) q^{62} -2.59830 q^{63} +(3.62423 + 7.13197i) q^{64} +2.03614i q^{65} +(0.452520 - 2.43913i) q^{66} +8.20400 q^{67} +(-2.83920 + 7.38843i) q^{68} +(-1.71592 + 4.47835i) q^{69} +(-0.670285 + 3.61291i) q^{70} -7.48672i q^{71} +(2.41083 + 1.47915i) q^{72} -13.8075 q^{73} +(-0.229757 + 1.23841i) q^{74} +1.00000i q^{75} +(-9.53782 - 3.66516i) q^{76} -4.55784 q^{77} +(0.525262 - 2.83122i) q^{78} -6.39670 q^{79} +(2.67866 - 2.97065i) q^{80} +1.00000 q^{81} +(14.1239 + 2.62033i) q^{82} +9.80321 q^{83} +(1.86404 - 4.85078i) q^{84} +3.95759 q^{85} +(-8.10369 - 1.50344i) q^{86} +7.32394i q^{87} +(4.22898 + 2.59466i) q^{88} +15.8514i q^{89} +(0.257970 - 1.39049i) q^{90} -5.29050 q^{91} +(-7.12963 - 6.41626i) q^{92} +4.91715 q^{93} +(-0.697273 + 3.75837i) q^{94} +5.10890i q^{95} +(-4.49098 + 3.43964i) q^{96} -0.186909i q^{97} +(0.345968 + 0.0641859i) q^{98} +1.75416 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 - 2 * q^10 + 20 * q^14 - 48 * q^15 - 6 * q^16 + 4 * q^18 + 16 * q^19 + 28 * q^22 + 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 + 4 * q^30 + 16 * q^32 - 28 * q^34 + 2 * q^36 + 2 * q^40 - 8 * q^41 + 14 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 + 16 * q^51 - 16 * q^52 + 2 * q^54 + 40 * q^56 - 8 * q^58 + 2 * q^60 + 24 * q^62 - 26 * q^64 - 48 * q^67 - 44 * q^68 - 8 * q^69 + 4 * q^72 + 20 * q^74 - 64 * q^76 + 32 * q^77 - 64 * q^79 + 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 - 40 * q^86 + 2 * q^90 - 4 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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