LMFDB - Embedded newform 572.2.bs.a.15.8

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			15.8
Character	$\chi$	$=$	572.15
Dual form			572.2.bs.a.267.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36269 + 0.378247i) q^{2} +(0.565515 + 2.66054i) q^{3} +(1.71386 - 1.03087i) q^{4} +(-0.216128 + 1.36458i) q^{5} +(-1.77696 - 3.41159i) q^{6} +(-3.01627 + 1.95879i) q^{7} +(-1.94554 + 2.05302i) q^{8} +(-4.01801 + 1.78893i) q^{9} +O(q^{10})$	\(q+(-1.36269 + 0.378247i) q^{2} +(0.565515 + 2.66054i) q^{3} +(1.71386 - 1.03087i) q^{4} +(-0.216128 + 1.36458i) q^{5} +(-1.77696 - 3.41159i) q^{6} +(-3.01627 + 1.95879i) q^{7} +(-1.94554 + 2.05302i) q^{8} +(-4.01801 + 1.78893i) q^{9} +(-0.221632 - 1.94125i) q^{10} +(3.25920 - 0.614525i) q^{11} +(3.71188 + 3.97681i) q^{12} +(-2.74884 - 2.33321i) q^{13} +(3.36934 - 3.81012i) q^{14} +(-3.75273 + 0.196672i) q^{15} +(1.87462 - 3.53353i) q^{16} +(-4.32232 + 0.454295i) q^{17} +(4.79865 - 3.95757i) q^{18} +(-0.283108 + 5.40202i) q^{19} +(1.03629 + 2.56149i) q^{20} +(-6.91717 - 6.91717i) q^{21} +(-4.20884 + 2.07019i) q^{22} +(-4.16088 - 7.20685i) q^{23} +(-6.56236 - 4.01516i) q^{24} +(2.93993 + 0.955240i) q^{25} +(4.62836 + 2.13970i) q^{26} +(-2.23549 - 3.07688i) q^{27} +(-3.15020 + 6.46646i) q^{28} +(3.34391 - 3.71379i) q^{29} +(5.03942 - 1.68746i) q^{30} +(0.964315 + 6.08844i) q^{31} +(-1.21798 + 5.52418i) q^{32} +(3.47809 + 8.32369i) q^{33} +(5.71816 - 2.25397i) q^{34} +(-2.02102 - 4.53927i) q^{35} +(-5.04215 + 7.20802i) q^{36} +(5.33715 - 0.279708i) q^{37} +(-1.65751 - 7.46837i) q^{38} +(4.65307 - 8.63286i) q^{39} +(-2.38101 - 3.09855i) q^{40} +(-2.49545 + 3.84266i) q^{41} +(12.0424 + 6.80957i) q^{42} +(-3.11377 + 5.39321i) q^{43} +(4.95231 - 4.41301i) q^{44} +(-1.57273 - 5.86952i) q^{45} +(8.39596 + 8.24687i) q^{46} +(0.710577 + 1.39459i) q^{47} +(10.4612 + 2.98924i) q^{48} +(2.41387 - 5.42164i) q^{49} +(-4.36753 - 0.189679i) q^{50} +(-3.65300 - 11.2428i) q^{51} +(-7.11636 - 1.16509i) q^{52} +(-7.45618 - 5.41723i) q^{53} +(4.21010 + 3.34728i) q^{54} +(0.134163 + 4.58023i) q^{55} +(1.84684 - 10.0034i) q^{56} +(-14.5324 + 2.30170i) q^{57} +(-3.15199 + 6.32558i) q^{58} +(0.416262 - 0.270324i) q^{59} +(-6.22890 + 4.20564i) q^{60} +(-0.325979 - 3.10149i) q^{61} +(-3.61700 - 7.93192i) q^{62} +(8.61526 - 13.2663i) q^{63} +(-0.429767 - 7.98845i) q^{64} +(3.77794 - 3.24673i) q^{65} +(-7.88797 - 10.0270i) q^{66} +(2.51507 - 9.38638i) q^{67} +(-6.93953 + 5.23434i) q^{68} +(16.8211 - 15.1457i) q^{69} +(4.47099 + 5.42119i) q^{70} +(-9.34374 + 11.5386i) q^{71} +(4.14448 - 11.7295i) q^{72} +(2.67119 - 5.24250i) q^{73} +(-7.16710 + 2.39992i) q^{74} +(-0.878880 + 8.36199i) q^{75} +(5.08356 + 9.55014i) q^{76} +(-8.62689 + 8.23765i) q^{77} +(-3.07535 + 13.5239i) q^{78} +(0.634419 - 0.873202i) q^{79} +(4.41660 + 3.32175i) q^{80} +(-1.90707 + 2.11802i) q^{81} +(1.94706 - 6.18026i) q^{82} +(-8.78948 - 1.39212i) q^{83} +(-18.9857 - 4.72436i) q^{84} +(0.314254 - 5.99632i) q^{85} +(2.20314 - 8.52705i) q^{86} +(11.7717 + 6.79640i) q^{87} +(-5.07926 + 7.88677i) q^{88} +(1.54304 - 5.75871i) q^{89} +(4.36328 + 7.40346i) q^{90} +(12.8615 + 1.65318i) q^{91} +(-14.5605 - 8.06220i) q^{92} +(-15.6532 + 6.00870i) q^{93} +(-1.49579 - 1.63162i) q^{94} +(-7.31028 - 1.55385i) q^{95} +(-15.3861 - 0.116489i) q^{96} +(-4.47236 + 11.6509i) q^{97} +(-1.23864 + 8.30107i) q^{98} +(-11.9961 + 8.29966i) 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 $

$2$	−1.36269	+	0.378247i	−0.963569	+	0.267461i
$2$	−1.36269	+	0.378247i	−0.963569	+	0.267461i
$3$	0.565515	+	2.66054i	0.326500	+	1.53606i	0.768974	+	0.639280i	$0.220768\pi$
$3$	0.565515	+	2.66054i	0.326500	+	1.53606i	−0.442474	+	0.896781i	$0.645899\pi$
$4$	1.71386	−	1.03087i	0.856929	−	0.515434i
$5$	−0.216128	+	1.36458i	−0.0966552	+	0.610257i	0.891047	+	0.453911i	$0.149971\pi$
$5$	−0.216128	+	1.36458i	−0.0966552	+	0.610257i	−0.987702	+	0.156346i	$0.950029\pi$
$6$	−1.77696	−	3.41159i	−0.725442	−	1.39277i
$7$	−3.01627	+	1.95879i	−1.14004	+	0.740352i	−0.969523	−	0.245002i	$-0.921211\pi$
$7$	−3.01627	+	1.95879i	−1.14004	+	0.740352i	−0.170520	+	0.985354i	$0.554545\pi$
$8$	−1.94554	+	2.05302i	−0.687851	+	0.725852i
$9$	−4.01801	+	1.78893i	−1.33934	+	0.596311i
$10$	−0.221632	−	1.94125i	−0.0700860	−	0.613876i
$11$	3.25920	−	0.614525i	0.982685	−	0.185286i
$11$	3.25920	−	0.614525i	0.982685	−	0.185286i
$12$	3.71188	+	3.97681i	1.07153	+	1.14801i
$13$	−2.74884	−	2.33321i	−0.762392	−	0.647115i
$13$	−2.74884	−	2.33321i	−0.762392	−	0.647115i
$14$	3.36934	−	3.81012i	0.900494	−	1.01830i
$15$	−3.75273	+	0.196672i	−0.968950	+	0.0507805i
$16$	1.87462	−	3.53353i	0.468655	−	0.883381i
$17$	−4.32232	+	0.454295i	−1.04832	+	0.110183i	−0.612991	−	0.790090i	$-0.710034\pi$
$17$	−4.32232	+	0.454295i	−1.04832	+	0.110183i	−0.435327	+	0.900273i	$0.643367\pi$
$18$	4.79865	−	3.95757i	1.13105	−	0.932808i
$19$	−0.283108	+	5.40202i	−0.0649494	+	1.23931i	0.750654	+	0.660696i	$0.229739\pi$
$19$	−0.283108	+	5.40202i	−0.0649494	+	1.23931i	−0.815603	+	0.578612i	$0.803595\pi$
$20$	1.03629	+	2.56149i	0.231721	+	0.572766i
$21$	−6.91717	−	6.91717i	−1.50945	−	1.50945i
$22$	−4.20884	+	2.07019i	−0.897327	+	0.441366i
$23$	−4.16088	−	7.20685i	−0.867603	−	1.50273i	−0.864439	−	0.502737i	$-0.832326\pi$
$23$	−4.16088	−	7.20685i	−0.867603	−	1.50273i	−0.00316317	−	0.999995i	$-0.501007\pi$
$24$	−6.56236	−	4.01516i	−1.33954	−	0.819592i
$25$	2.93993	+	0.955240i	0.587986	+	0.191048i
$26$	4.62836	+	2.13970i	0.907695	+	0.419630i
$27$	−2.23549	−	3.07688i	−0.430220	−	0.592147i
$28$	−3.15020	+	6.46646i	−0.595333	+	1.22205i
$29$	3.34391	−	3.71379i	0.620949	−	0.689634i	−0.347830	−	0.937557i	$-0.613081\pi$
$29$	3.34391	−	3.71379i	0.620949	−	0.689634i	0.968780	+	0.247923i	$0.0797481\pi$
$30$	5.03942	−	1.68746i	0.920068	−	0.308087i
$31$	0.964315	+	6.08844i	0.173196	+	1.09352i	0.909145	+	0.416480i	$0.136736\pi$
$31$	0.964315	+	6.08844i	0.173196	+	1.09352i	−0.735949	+	0.677037i	$0.763264\pi$
$32$	−1.21798	+	5.52418i	−0.215311	+	0.976545i
$33$	3.47809	+	8.32369i	0.605457	+	1.44897i
$34$	5.71816	−	2.25397i	0.980656	−	0.386553i
$35$	−2.02102	−	4.53927i	−0.341614	−	0.767277i
$36$	−5.04215	+	7.20802i	−0.840358	+	1.20134i
$37$	5.33715	−	0.279708i	0.877422	−	0.0459838i	0.391696	−	0.920095i	$-0.371888\pi$
$37$	5.33715	−	0.279708i	0.877422	−	0.0459838i	0.485726	+	0.874111i	$0.338555\pi$
$38$	−1.65751	−	7.46837i	−0.268884	−	1.21153i
$39$	4.65307	−	8.63286i	0.745088	−	1.38236i
$40$	−2.38101	−	3.09855i	−0.376471	−	0.489923i
$41$	−2.49545	+	3.84266i	−0.389724	+	0.600122i	−0.978017	−	0.208526i	$-0.933134\pi$
$41$	−2.49545	+	3.84266i	−0.389724	+	0.600122i	0.588293	+	0.808648i	$0.299800\pi$
$42$	12.0424	+	6.80957i	1.85818	+	1.05074i
$43$	−3.11377	+	5.39321i	−0.474845	+	0.822456i	−0.999585	−	0.0288066i	$-0.990829\pi$
$43$	−3.11377	+	5.39321i	−0.474845	+	0.822456i	0.524740	+	0.851263i	$0.324163\pi$
$44$	4.95231	−	4.41301i	0.746588	−	0.665286i
$45$	−1.57273	−	5.86952i	−0.234449	−	0.874976i
$46$	8.39596	+	8.24687i	1.23792	+	1.21594i
$47$	0.710577	+	1.39459i	0.103648	+	0.203421i	0.937006	−	0.349312i	$-0.113585\pi$
$47$	0.710577	+	1.39459i	0.103648	+	0.203421i	−0.833358	+	0.552733i	$0.813585\pi$
$48$	10.4612	+	2.98924i	1.50994	+	0.431459i
$49$	2.41387	−	5.42164i	0.344839	−	0.774521i
$50$	−4.36753	−	0.189679i	−0.617662	−	0.0268247i
$51$	−3.65300	−	11.2428i	−0.511523	−	1.57431i
$52$	−7.11636	−	1.16509i	−0.986861	−	0.161569i
$53$	−7.45618	−	5.41723i	−1.02419	−	0.744114i	−0.0570486	−	0.998371i	$-0.518169\pi$
$53$	−7.45618	−	5.41723i	−1.02419	−	0.744114i	−0.967137	+	0.254257i	$0.918169\pi$
$54$	4.21010	+	3.34728i	0.572922	+	0.455507i
$55$	0.134163	+	4.58023i	0.0180906	+	0.617599i
$56$	1.84684	−	10.0034i	0.246794	−	1.33675i
$57$	−14.5324	+	2.30170i	−1.92486	+	0.304868i
$58$	−3.15199	+	6.32558i	−0.413877	+	0.830590i
$59$	0.416262	−	0.270324i	0.0541927	−	0.0351931i	−0.517258	−	0.855829i	$-0.673047\pi$
$59$	0.416262	−	0.270324i	0.0541927	−	0.0351931i	0.571451	+	0.820636i	$0.306381\pi$
$60$	−6.22890	+	4.20564i	−0.804147	+	0.542945i
$61$	−0.325979	−	3.10149i	−0.0417374	−	0.397105i	−0.995369	−	0.0961283i	$-0.969354\pi$
$61$	−0.325979	−	3.10149i	−0.0417374	−	0.397105i	0.953632	−	0.300976i	$-0.0973126\pi$
$62$	−3.61700	−	7.93192i	−0.459360	−	1.00736i
$63$	8.61526	−	13.2663i	1.08542	−	1.67140i
$64$	−0.429767	−	7.98845i	−0.0537208	−	0.998556i
$65$	3.77794	−	3.24673i	0.468596	−	0.402708i
$66$	−7.88797	−	10.0270i	−0.970942	−	1.23424i
$67$	2.51507	−	9.38638i	0.307265	−	1.14673i	−0.623713	−	0.781654i	$-0.714376\pi$
$67$	2.51507	−	9.38638i	0.307265	−	1.14673i	0.930978	−	0.365076i	$-0.118957\pi$
$68$	−6.93953	+	5.23434i	−0.841542	+	0.634757i
$69$	16.8211	−	15.1457i	2.02502	−	1.82333i
$70$	4.47099	+	5.42119i	0.534385	+	0.647956i
$71$	−9.34374	+	11.5386i	−1.10890	+	1.36938i	−0.186810	+	0.982396i	$0.559815\pi$
$71$	−9.34374	+	11.5386i	−1.10890	+	1.36938i	−0.922088	+	0.386979i	$0.873519\pi$
$72$	4.14448	−	11.7295i	0.488432	−	1.38233i
$73$	2.67119	−	5.24250i	0.312639	−	0.613588i	−0.680203	−	0.733024i	$-0.738109\pi$
$73$	2.67119	−	5.24250i	0.312639	−	0.613588i	0.992842	+	0.119436i	$0.0381085\pi$
$74$	−7.16710	+	2.39992i	−0.833158	+	0.278985i
$75$	−0.878880	+	8.36199i	−0.101484	+	0.965559i
$76$	5.08356	+	9.55014i	0.583125	+	1.09548i
$77$	−8.62689	+	8.23765i	−0.983125	+	0.938767i
$78$	−3.07535	+	13.5239i	−0.348215	+	1.53129i
$79$	0.634419	−	0.873202i	0.0713777	−	0.0982429i	−0.771836	−	0.635822i	$-0.780661\pi$
$79$	0.634419	−	0.873202i	0.0713777	−	0.0982429i	0.843213	+	0.537579i	$0.180661\pi$
$80$	4.41660	+	3.32175i	0.493791	+	0.371383i
$81$	−1.90707	+	2.11802i	−0.211897	+	0.235335i
$82$	1.94706	−	6.18026i	0.215016	−	0.682495i
$83$	−8.78948	−	1.39212i	−0.964771	−	0.152805i	−0.345877	−	0.938280i	$-0.612419\pi$
$83$	−8.78948	−	1.39212i	−0.964771	−	0.152805i	−0.618893	+	0.785475i	$0.712419\pi$
$84$	−18.9857	−	4.72436i	−2.07151	−	0.515470i
$85$	0.314254	−	5.99632i	0.0340856	−	0.650393i
$86$	2.20314	−	8.52705i	0.237571	−	0.919496i
$87$	11.7717	+	6.79640i	1.26206	+	0.728651i
$88$	−5.07926	+	7.88677i	−0.541451	+	0.840732i
$89$	1.54304	−	5.75871i	0.163562	−	0.610422i	−0.834657	−	0.550770i	$-0.814334\pi$
$89$	1.54304	−	5.75871i	0.163562	−	0.610422i	0.998219	−	0.0596521i	$-0.0189991\pi$
$90$	4.36328	+	7.40346i	0.459930	+	0.780394i
$91$	12.8615	+	1.65318i	1.34825	+	0.173300i
$92$	−14.5605	−	8.06220i	−1.51803	−	0.840543i
$93$	−15.6532	+	6.00870i	−1.62316	+	0.623073i
$94$	−1.49579	−	1.63162i	−0.154279	−	0.168288i
$95$	−7.31028	−	1.55385i	−0.750018	−	0.159421i
$96$	−15.3861	−	0.116489i	−1.57033	−	0.0118891i
$97$	−4.47236	+	11.6509i	−0.454100	+	1.18297i	0.495251	+	0.868750i	$0.335076\pi$
$97$	−4.47236	+	11.6509i	−0.454100	+	1.18297i	−0.949350	+	0.314220i	$0.898257\pi$
$98$	−1.23864	+	8.30107i	−0.125122	+	0.838535i
$99$	−11.9961	+	8.29966i	−1.20566	+	0.834147i
$100$	6.02335	−	1.39353i	0.602335	−	0.139353i
$101$	1.69859	+	0.178529i	0.169016	+	0.0177643i	0.188658	−	0.982043i	$-0.439586\pi$
$101$	1.69859	+	0.178529i	0.169016	+	0.0177643i	−0.0196426	+	0.999807i	$0.506253\pi$
$102$	9.23047	+	13.9387i	0.913953	+	1.38014i
$103$	4.32453	+	13.3095i	0.426109	+	1.31143i	0.901929	+	0.431885i	$0.142151\pi$
$103$	4.32453	+	13.3095i	0.426109	+	1.31143i	−0.475820	+	0.879543i	$0.657849\pi$
$104$	10.1381	−	1.10408i	0.994122	−	0.108264i
$105$	10.9340	−	7.94401i	1.06705	−	0.775256i
$106$	12.2095	+	4.56174i	1.18589	+	0.443075i
$107$	3.45640	+	16.2611i	0.334143	+	1.57202i	0.749276	+	0.662258i	$0.230402\pi$
$107$	3.45640	+	16.2611i	0.334143	+	1.57202i	−0.415133	+	0.909761i	$0.636265\pi$
$108$	−7.00317	−	2.96885i	−0.673880	−	0.285678i
$109$	−3.51986	+	3.51986i	−0.337142	+	0.337142i	−0.855291	−	0.518149i	$-0.826621\pi$
$109$	−3.51986	+	3.51986i	−0.337142	+	0.337142i	0.518149	+	0.855291i	$0.326621\pi$
$110$	−1.91528	−	6.19070i	−0.182615	−	0.590260i
$111$	3.76241	+	14.0415i	0.357112	+	1.33276i
$112$	1.26707	+	14.3300i	0.119727	+	1.35406i
$113$	−1.85928	−	2.06494i	−0.174906	−	0.194253i	0.649317	−	0.760517i	$-0.275055\pi$
$113$	−1.85928	−	2.06494i	−0.174906	−	0.194253i	−0.824223	+	0.566265i	$0.808388\pi$
$114$	18.9325	−	8.63334i	1.77319	−	0.808586i
$115$	10.7336	−	4.12023i	1.00091	−	0.384214i
$116$	1.90256	−	9.81205i	0.176649	−	0.911026i
$117$	15.2188	+	4.45736i	1.40698	+	0.412083i
$118$	−0.464988	+	0.525818i	−0.0428056	+	0.0484055i
$119$	12.1474	−	9.83679i	1.11355	−	0.901737i
$120$	6.89730	−	8.08705i	0.629634	−	0.738243i
$121$	10.2447	−	4.00571i	0.931338	−	0.364156i
$122$	1.61734	+	4.10307i	0.146427	+	0.371475i
$123$	−11.6347	−	4.46616i	−1.04907	−	0.402700i
$124$	7.92909	+	9.44065i	0.712053	+	0.847795i
$125$	−5.07503	+	9.96031i	−0.453924	+	0.890877i
$126$	−6.72199	+	21.3366i	−0.598843	+	1.90082i
$127$	10.1048	+	4.49893i	0.896652	+	0.399215i	0.802715	−	0.596363i	$-0.203388\pi$
$127$	10.1048	+	4.49893i	0.896652	+	0.399215i	0.0939371	+	0.995578i	$0.470055\pi$
$128$	3.60725	+	10.7232i	0.318839	+	0.947809i
$129$	−16.1097	−	5.23436i	−1.41838	−	0.460860i
$130$	−3.92010	+	5.85329i	−0.343815	+	0.513368i
$131$			1.43171i			0.125089i	0.998042	+	0.0625446i	$0.0199216\pi$
$131$			1.43171i			0.125089i	−0.998042	+	0.0625446i	$0.980078\pi$
$132$	14.5416	+	10.6802i	1.26568	+	0.929590i
$133$	−9.72748	−	16.8485i	−0.843480	−	1.46095i
$134$	0.123102	+	13.7421i	0.0106344	+	1.18713i
$135$	4.68179	−	2.38549i	0.402944	−	0.205310i
$136$	7.47657	−	9.75766i	0.641110	−	0.836712i
$137$	0.327899	−	0.404921i	0.0280143	−	0.0345948i	−0.762946	−	0.646462i	$-0.776248\pi$
$137$	0.327899	−	0.404921i	0.0280143	−	0.0345948i	0.790961	+	0.611867i	$0.209581\pi$
$138$	−17.1931	+	27.0015i	−1.46357	+	2.29852i
$139$	−1.61175	+	7.58268i	−0.136707	+	0.643155i	0.855422	+	0.517932i	$0.173298\pi$
$139$	−1.61175	+	7.58268i	−0.136707	+	0.643155i	−0.992129	+	0.125223i	$0.960035\pi$
$140$	−8.14313	−	5.69627i	−0.688220	−	0.481423i
$141$	−3.30850	+	2.67917i	−0.278626	+	0.225627i
$142$	8.36821	−	19.2577i	0.702245	−	1.61607i
$143$	−10.3928	−	5.91515i	−0.869092	−	0.494650i
$144$	−1.21100	+	17.5513i	−0.100917	+	1.46261i
$145$	4.34504	+	5.36568i	0.360836	+	0.445595i
$146$	−1.65704	+	8.15428i	−0.137138	+	0.674853i
$147$	15.7896	+	3.35618i	1.30230	+	0.276813i
$148$	8.85878	−	5.98128i	0.728187	−	0.491658i
$149$	6.98819	+	5.65893i	0.572495	+	0.463597i	0.871323	−	0.490709i	$-0.163262\pi$
$149$	6.98819	+	5.65893i	0.572495	+	0.463597i	−0.298828	+	0.954307i	$0.596596\pi$
$150$	−1.96525	−	11.7272i	−0.160462	−	0.957526i
$151$	−8.39410	−	16.4744i	−0.683102	−	1.34066i	−0.928533	−	0.371250i	$-0.878929\pi$
$151$	−8.39410	−	16.4744i	−0.683102	−	1.34066i	0.245431	−	0.969414i	$-0.421071\pi$
$152$	−10.5396	−	11.0911i	−0.854878	−	0.899603i
$153$	16.5544	−	9.55772i	1.33835	−	0.772695i
$154$	8.63993	−	14.4885i	0.696225	−	1.16751i
$155$	−8.51656			−0.684066
$156$	−0.924639	−	19.5922i	−0.0740303	−	1.56863i
$157$	−4.76403	+	14.6622i	−0.380211	+	1.17017i	0.559684	+	0.828706i	$0.310922\pi$
$157$	−4.76403	+	14.6622i	−0.380211	+	1.17017i	−0.939895	+	0.341463i	$0.889078\pi$
$158$	−0.534231	+	1.42987i	−0.0425011	+	0.113755i
$159$	10.1962	−	22.9010i	0.808609	−	1.81616i
$160$	−7.27491	−	2.85596i	−0.575132	−	0.225783i
$161$	26.6670	+	13.5875i	2.10165	+	1.07085i
$162$	1.79762	−	3.60755i	0.141234	−	0.283436i
$163$	−5.81024	+	15.1362i	−0.455093	+	1.18556i	0.493693	+	0.869636i	$0.335647\pi$
$163$	−5.81024	+	15.1362i	−0.455093	+	1.18556i	−0.948786	+	0.315921i	$0.897687\pi$
$164$	−0.315575	+	9.15825i	−0.0246422	+	0.715140i
$165$	−12.1100	+	2.94714i	−0.942763	+	0.229434i
$166$	12.5039	−	1.42757i	0.970492	−	0.110801i
$167$	−4.64325	−	5.73393i	−0.359305	−	0.443705i	0.565154	−	0.824985i	$-0.308817\pi$
$167$	−4.64325	−	5.73393i	−0.359305	−	0.443705i	−0.924459	+	0.381280i	$0.875483\pi$
$168$	27.6587	−	0.743461i	2.13391	−	0.0573592i
$169$	2.11228	+	12.8272i	0.162483	+	0.986711i
$170$	1.83986	+	8.29001i	0.141111	+	0.635814i
$171$	−8.52633	−	22.2118i	−0.652025	−	1.69858i
$172$	0.223128	+	12.4531i	0.0170133	+	0.949538i
$173$	7.26707	−	6.54330i	0.552505	−	0.497478i	−0.344928	−	0.938629i	$-0.612097\pi$
$173$	7.26707	−	6.54330i	0.552505	−	0.497478i	0.897433	+	0.441152i	$0.145430\pi$
$174$	−18.6119	−	4.80879i	−1.41097	−	0.364553i
$175$	−10.7387	+	2.87743i	−0.811771	+	0.217513i
$176$	3.93832	−	12.6685i	0.296862	−	0.954920i
$177$	0.954608	+	0.954608i	0.0717528	+	0.0717528i
$178$	0.0755251	+	8.43100i	0.00566084	+	0.631930i
$179$	−14.9450	+	3.17666i	−1.11704	+	0.237435i	−0.729207	−	0.684293i	$-0.760111\pi$
$179$	−14.9450	+	3.17666i	−1.11704	+	0.237435i	−0.387836	+	0.921728i	$0.626777\pi$
$180$	−8.74614	−	8.43824i	−0.651899	−	0.628949i
$181$	9.75760	+	13.4302i	0.725277	+	0.998258i	0.999332	+	0.0365437i	$0.0116348\pi$
$181$	9.75760	+	13.4302i	0.725277	+	0.998258i	−0.274055	+	0.961714i	$0.588365\pi$
$182$	−18.1516	+	2.61206i	−1.34549	+	0.193618i
$183$	8.06727	−	2.62122i	0.596350	−	0.193766i
$184$	22.8909	+	5.47884i	1.68754	+	0.403906i
$185$	−0.771822	+	7.34340i	−0.0567455	+	0.539897i
$186$	19.0577	−	14.1088i	1.39738	−	1.03451i
$187$	−13.8081	+	4.13681i	−1.00975	+	0.302513i
$188$	2.65546	+	1.65761i	0.193669	+	0.120894i
$189$	12.7698	+	4.90186i	0.928866	+	0.356558i
$190$	10.5494	−	0.647676i	0.765333	−	0.0469873i
$191$	3.52861	−	16.6008i	0.255322	−	1.20119i	−0.644386	−	0.764700i	$-0.722887\pi$
$191$	3.52861	−	16.6008i	0.255322	−	1.20119i	0.899708	−	0.436493i	$-0.143780\pi$
$192$	21.0105	−	5.66099i	1.51630	−	0.408547i
$193$	7.86144	+	20.4798i	0.565879	+	1.47416i	0.855898	+	0.517144i	$0.173005\pi$
$193$	7.86144	+	20.4798i	0.565879	+	1.47416i	−0.290020	+	0.957021i	$0.593662\pi$
$194$	1.68753	−	17.5682i	0.121158	−	1.26133i
$195$	10.7745	+	8.21527i	0.771581	+	0.588308i
$196$	−1.45197	−	11.7803i	−0.103712	−	0.841451i
$197$	−4.06688	−	1.08972i	−0.289753	−	0.0776390i	0.111015	−	0.993819i	$-0.464590\pi$
$197$	−4.06688	−	1.08972i	−0.289753	−	0.0776390i	−0.400768	+	0.916180i	$0.631257\pi$
$198$	13.2077	−	15.8474i	0.938633	−	1.12622i
$199$	−9.86089	+	17.0796i	−0.699020	+	1.21074i	0.269787	+	0.962920i	$0.413047\pi$
$199$	−9.86089	+	17.0796i	−0.699020	+	1.21074i	−0.968807	+	0.247818i	$0.920287\pi$
$200$	−7.68087	+	4.17727i	−0.543119	+	0.295377i
$201$	26.3951	+	1.38331i	1.86177	+	0.0975712i
$202$	−2.38218	+	0.399206i	−0.167609	+	0.0280880i
$203$	−2.81161	+	17.7518i	−0.197336	+	1.24593i
$204$	−17.8506	−	15.5028i	−1.24979	−	1.08541i
$205$	−4.70426	−	4.23574i	−0.328560	−	0.295837i
$206$	−10.9273	−	16.5011i	−0.761341	−	1.14968i
$207$	29.6110	+	21.5137i	2.05811	+	1.49530i
$208$	−13.3975	+	5.33923i	−0.928948	+	0.370209i
$209$	2.39697	+	17.7802i	0.165802	+	1.22988i
$210$	−11.8949	+	14.9610i	−0.820824	+	1.03241i
$211$	0.795973	+	0.0836601i	0.0547970	+	0.00575940i	0.131887	−	0.991265i	$-0.457896\pi$
$211$	0.795973	+	0.0836601i	0.0547970	+	0.00575940i	−0.0770903	+	0.997024i	$0.524563\pi$
$212$	−18.3633	−	1.59803i	−1.26120	−	0.109753i
$213$	−35.9828	−	18.3341i	−2.46550	−	1.25623i
$214$	−10.8607	−	20.8515i	−0.742423	−	1.42538i
$215$	−6.68646	−	5.41459i	−0.456013	−	0.369272i
$216$	10.6661	+	1.39670i	0.725738	+	0.0950333i
$217$	−14.8346	−	16.4755i	−1.00704	−	1.11843i
$218$	3.46511	−	6.12787i	0.234687	−	0.415032i
$219$	15.4585	+	4.14208i	1.04459	+	0.279896i
$220$	4.95156	+	7.71157i	0.333834	+	0.519914i
$221$	12.9414	+	8.83609i	0.870530	+	0.594380i
$222$	−10.4382	−	17.7111i	−0.700564	−	1.18869i
$223$	−7.63395	−	4.95754i	−0.511207	−	0.331982i	0.263125	−	0.964762i	$-0.415247\pi$
$223$	−7.63395	−	4.95754i	−0.511207	−	0.331982i	−0.774331	+	0.632780i	$0.781914\pi$
$224$	−7.14692	−	19.0482i	−0.477524	−	1.27271i
$225$	−13.5215	+	1.42117i	−0.901435	+	0.0947447i
$226$	3.31468	+	2.11060i	0.220489	+	0.140395i
$227$	5.48418	+	8.44490i	0.363998	+	0.560508i	0.972458	−	0.233076i	$-0.0748792\pi$
$227$	5.48418	+	8.44490i	0.363998	+	0.560508i	−0.608460	+	0.793584i	$0.708213\pi$
$228$	−22.5337	+	18.9258i	−1.49233	+	1.25339i
$229$	0.806805	+	5.09397i	0.0533152	+	0.336619i	0.999900	+	0.0141629i	$0.00450836\pi$
$229$	0.806805	+	5.09397i	0.0533152	+	0.336619i	−0.946585	+	0.322456i	$0.895492\pi$
$230$	−13.0681	+	9.67455i	−0.861684	+	0.637921i
$231$	−26.7952	−	18.2936i	−1.76299	−	1.20363i
$232$	1.11877	+	14.0904i	0.0734511	+	0.925083i
$233$	11.3137	−	15.5719i	0.741184	−	1.02015i	−0.257366	−	0.966314i	$-0.582855\pi$
$233$	11.3137	−	15.5719i	0.741184	−	1.02015i	0.998550	−	0.0538381i	$-0.0171455\pi$
$234$	−22.4246	−	0.317519i	−1.46594	−	0.0207568i
$235$	−2.05659	+	0.668227i	−0.134157	+	0.0435903i
$236$	0.434746	−	0.892408i	0.0282995	−	0.0580908i
$237$	2.68196	+	1.19409i	0.174212	+	0.0775642i
$238$	−12.8325	+	17.9992i	−0.831805	+	1.16672i
$239$	2.73992	−	1.39606i	0.177231	−	0.0903035i	−0.363124	−	0.931741i	$-0.618290\pi$
$239$	2.73992	−	1.39606i	0.177231	−	0.0903035i	0.540355	+	0.841437i	$0.318290\pi$
$240$	−6.33999	+	13.6290i	−0.409245	+	0.879751i
$241$	4.59775	−	1.23196i	0.296167	−	0.0793577i	−0.107676	−	0.994186i	$-0.534341\pi$
$241$	4.59775	−	1.23196i	0.296167	−	0.0793577i	0.403843	+	0.914828i	$0.367674\pi$
$242$	−12.4452	+	9.33359i	−0.800011	+	0.599986i
$243$	−16.5946	−	9.58092i	−1.06455	−	0.614617i
$244$	−3.75591	−	4.97947i	−0.240447	−	0.318778i
$245$	6.87654	+	4.46568i	0.439326	+	0.285302i
$246$	17.5439	+	1.68519i	1.11856	+	0.107444i
$247$	13.3823	−	14.1888i	0.851492	−	0.902809i
$248$	−14.3758	−	9.86554i	−0.912864	−	0.626463i
$249$	−1.26680	−	24.1720i	−0.0802802	−	1.53184i
$250$	3.14824	−	15.4924i	0.199112	−	0.979828i
$251$	−3.93137	+	1.75036i	−0.248146	+	0.110482i	−0.527041	−	0.849840i	$-0.676699\pi$
$251$	−3.93137	+	1.75036i	−0.248146	+	0.110482i	0.278895	+	0.960322i	$0.410032\pi$
$252$	1.08949	−	31.6178i	0.0686311	−	1.99174i
$253$	−17.9899	−	20.9316i	−1.13102	−	1.31596i
$254$	−15.4714	−	2.30856i	−0.970760	−	0.144852i
$255$	16.1312	−	2.55492i	1.01017	−	0.159996i
$256$	−8.97160	−	13.2480i	−0.560725	−	0.828002i
$257$	16.8795	+	15.1984i	1.05292	+	0.948049i	0.998725	−	0.0504813i	$-0.0160755\pi$
$257$	16.8795	+	15.1984i	1.05292	+	0.948049i	0.0541904	+	0.998531i	$0.482742\pi$
$258$	23.9324	+	1.03937i	1.48997	+	0.0647084i
$259$	−15.5504	+	11.2980i	−0.966255	+	0.702025i
$260$	3.12789	−	9.45900i	0.193984	−	0.586622i
$261$	−6.79216	+	20.9041i	−0.420424	+	1.29393i
$262$	−0.541541	−	1.95098i	−0.0334565	−	0.120532i
$263$	14.1454	−	8.16686i	0.872244	−	0.503590i	0.00415045	−	0.999991i	$-0.498679\pi$
$263$	14.1454	−	8.16686i	0.872244	−	0.503590i	0.868093	+	0.496401i	$0.165346\pi$
$264$	−23.8554	−	9.05347i	−1.46820	−	0.557203i
$265$	9.00371	−	9.00371i	0.553093	−	0.553093i
$266$	19.6285	+	19.2799i	1.20350	+	1.18213i
$267$	16.1939	+	0.848685i	0.991049	+	0.0519387i
$268$	−5.36565	−	18.6796i	−0.327759	−	1.14104i
$269$	−1.17634	−	11.1921i	−0.0717225	−	0.682394i	−0.970023	−	0.243013i	$-0.921864\pi$
$269$	−1.17634	−	11.1921i	−0.0717225	−	0.682394i	0.898301	−	0.439381i	$-0.144802\pi$
$270$	−5.47753	+	5.02156i	−0.333352	+	0.305603i
$271$	0.885058	+	16.8879i	0.0537634	+	1.02587i	0.883713	+	0.468029i	$0.155036\pi$
$271$	0.885058	+	16.8879i	0.0537634	+	1.02587i	−0.829950	+	0.557838i	$0.811631\pi$
$272$	−6.49745	+	16.1247i	−0.393966	+	0.977702i
$273$	2.87503	+	35.1534i	0.174005	+	2.12758i
$274$	−0.293665	+	0.675810i	−0.0177409	+	0.0408272i
$275$	10.1688	+	1.30666i	0.613203	+	0.0787944i
$276$	13.2156	−	43.2979i	0.795487	−	2.60623i
$277$	5.55422	+	12.4750i	0.333721	+	0.749549i	0.999993	+	0.00384030i	$0.00122241\pi$
$277$	5.55422	+	12.4750i	0.333721	+	0.749549i	−0.666272	+	0.745709i	$0.732111\pi$
$278$	−0.671811	−	10.9425i	−0.0402925	−	0.656288i
$279$	−14.7665	−	22.7384i	−0.884045	−	1.36131i
$280$	13.2512	+	4.68215i	0.791909	+	0.279812i
$281$	14.5571	+	2.30562i	0.868406	+	0.137542i	0.574710	−	0.818357i	$-0.305115\pi$
$281$	14.5571	+	2.30562i	0.868406	+	0.137542i	0.293696	+	0.955899i	$0.405115\pi$
$282$	3.49508	−	4.90232i	0.208129	−	0.291929i
$283$	−11.4254	+	2.42855i	−0.679170	+	0.144362i	−0.534565	−	0.845127i	$-0.679525\pi$
$283$	−11.4254	+	2.42855i	−0.679170	+	0.144362i	−0.144605	+	0.989489i	$0.546191\pi$
$284$	−4.11911	+	29.4076i	−0.244424	+	1.74502i
$285$		−	20.3280i		−	1.20413i
$286$	16.3996	+	4.12947i	0.969730	+	0.244180i
$287$		−	16.4786i		−	0.972698i
$288$	−4.98851	−	24.3751i	−0.293951	−	1.43632i
$289$	1.84759	−	0.392718i	0.108682	−	0.0231010i
$290$	−7.95050	−	5.66826i	−0.466869	−	0.332852i
$291$	−33.5268	−	5.31013i	−1.96538	−	0.311285i
$292$	−0.826292	−	11.7385i	−0.0483551	−	0.686946i
$293$	−1.37573	−	2.11844i	−0.0803712	−	0.123761i	0.796199	−	0.605035i	$-0.206841\pi$
$293$	−1.37573	−	2.11844i	−0.0803712	−	0.123761i	−0.876570	+	0.481274i	$0.840174\pi$
$294$	−22.7858	+	1.39892i	−1.32889	+	0.0815869i
$295$	0.278911	+	0.626445i	0.0162388	+	0.0364731i
$296$	−9.80938	+	11.5015i	−0.570159	+	0.668508i
$297$	−9.17671	−	8.65441i	−0.532487	−	0.502180i
$298$	−11.6632	−	5.06811i	−0.675633	−	0.293588i
$299$	−5.37748	+	29.5187i	−0.310987	+	1.70711i
$300$	7.11383	+	15.2373i	0.410717	+	0.879724i
$301$	−1.17218	−	22.3666i	−0.0675635	−	1.28919i
$302$	17.6700	+	19.2744i	1.01679	+	1.10912i
$303$	0.485593	+	4.62011i	0.0278966	+	0.265419i
$304$	18.5575	+	11.1271i	1.06434	+	0.638183i
$305$	4.30267	+	0.225493i	0.246370	+	0.0129117i
$306$	−18.9434	+	19.2859i	−1.08292	+	1.10250i
$307$	19.8008	−	19.8008i	1.13009	−	1.13009i	0.139931	−	0.990161i	$-0.455312\pi$
$307$	19.8008	−	19.8008i	1.13009	−	1.13009i	0.990161	−	0.139931i	$-0.0446880\pi$
$308$	−6.29333	+	23.0113i	−0.358596	+	1.31119i
$309$	−32.9649	+	19.0323i	−1.87531	+	1.08271i
$310$	11.6054	−	3.22136i	0.659145	−	0.182961i
$311$	10.4107	−	32.0408i	0.590336	−	1.81687i	0.0136449	−	0.999907i	$-0.495657\pi$
$311$	10.4107	−	32.0408i	0.590336	−	1.81687i	0.576692	−	0.816962i	$-0.304343\pi$
$312$	8.67069	+	26.3484i	0.490881	+	1.49168i
$313$	5.61302	−	4.07810i	0.317267	−	0.230508i	−0.417742	−	0.908566i	$-0.637178\pi$
$313$	5.61302	−	4.07810i	0.317267	−	0.230508i	0.735008	+	0.678058i	$0.237178\pi$
$314$	0.945979	−	21.7820i	0.0533847	−	1.22923i
$315$	16.2409	+	14.6234i	0.915073	+	0.823935i
$316$	0.187147	−	2.15055i	0.0105278	−	0.120978i
$317$	−0.583774	+	0.0924608i	−0.0327880	+	0.00519312i	−0.172807	−	0.984956i	$-0.555284\pi$
$317$	−0.583774	+	0.0924608i	−0.0327880	+	0.00519312i	0.140019	+	0.990149i	$0.455284\pi$
$318$	−5.23201	+	35.0636i	−0.293397	+	1.96627i
$319$	8.61626	−	14.1589i	0.482418	−	0.792746i
$320$	10.9937	+	1.14007i	0.614568	+	0.0637321i
$321$	−41.3086	+	18.3918i	−2.30562	+	1.02653i
$322$	−41.4784	−	8.42888i	−2.31150	−	0.469723i
$323$	−1.23042	−	23.4779i	−0.0684626	−	1.30634i
$324$	−1.08505	+	5.59593i	−0.0602807	+	0.310885i
$325$	−5.85263	−	9.48527i	−0.324645	−	0.526148i
$326$	2.19234	−	22.8237i	0.121423	−	1.26409i
$327$	−11.3553	−	7.37419i	−0.627947	−	0.407794i
$328$	−3.03405	−	12.5992i	−0.167528	−	0.695677i
$329$	−4.87499	−	2.81457i	−0.268767	−	0.155173i
$330$	15.3875	−	8.59661i	0.847052	−	0.473228i
$331$	−20.7044	+	5.54772i	−1.13802	+	0.304930i	−0.778153	−	0.628075i	$-0.783843\pi$
$331$	−20.7044	+	5.54772i	−1.13802	+	0.304930i	−0.359863	+	0.933005i	$0.617176\pi$
$332$	−16.4990	+	6.67491i	−0.905501	+	0.366333i
$333$	−20.9444	+	10.6717i	−1.14774	+	0.584805i
$334$	8.49615	+	6.05729i	0.464889	+	0.331440i
$335$	12.2649	+	5.46066i	0.670100	+	0.298348i
$336$	−37.4091	+	11.4749i	−2.04083	+	0.626009i
$337$	12.8399	−	4.17194i	0.699435	−	0.227260i	0.0623507	−	0.998054i	$-0.480140\pi$
$337$	12.8399	−	4.17194i	0.699435	−	0.227260i	0.637084	+	0.770794i	$0.280140\pi$
$338$	−7.73026	−	16.6806i	−0.420471	−	0.907306i
$339$	4.44239	−	6.11442i	0.241277	−	0.332090i
$340$	−5.64283	−	10.6008i	−0.306026	−	0.574909i
$341$	6.88439	+	19.2508i	0.372811	+	1.04249i
$342$	20.0203	+	27.0428i	1.08258	+	1.46231i
$343$	−0.599337	−	3.78407i	−0.0323612	−	0.204320i
$344$	−5.01439	−	16.8853i	−0.270358	−	0.910395i
$345$	17.0320	+	26.2270i	0.916973	+	1.41201i
$346$	−7.42779	+	11.6652i	−0.399320	+	0.627127i
$347$	31.8304	−	3.34551i	1.70874	−	0.179596i	0.800869	−	0.598839i	$-0.204371\pi$
$347$	31.8304	−	3.34551i	1.70874	−	0.179596i	0.907874	+	0.419243i	$0.137704\pi$
$348$	27.1812	−	0.487020i	1.45707	−	0.0261070i
$349$	−8.35872	−	5.42822i	−0.447432	−	0.290566i	0.301188	−	0.953565i	$-0.402617\pi$
$349$	−8.35872	−	5.42822i	−0.447432	−	0.290566i	−0.748620	+	0.662999i	$0.769283\pi$
$350$	13.5452	−	7.98295i	0.724021	−	0.426706i
$351$	−1.03400	+	13.6737i	−0.0551911	+	0.729850i
$352$	−0.574907	+	18.7529i	−0.0306426	+	0.999530i
$353$	−18.3385	−	4.91378i	−0.976059	−	0.261534i	−0.264675	−	0.964338i	$-0.585265\pi$
$353$	−18.3385	−	4.91378i	−0.976059	−	0.261534i	−0.711384	+	0.702803i	$0.751931\pi$
$354$	−1.66191	−	0.939759i	−0.0883298	−	0.0499476i
$355$	−13.7258	−	15.2440i	−0.728490	−	0.809070i
$356$	−3.29192	−	11.4603i	−0.174471	−	0.607394i
$357$	33.0407	+	26.7558i	1.74870	+	1.41607i
$358$	19.1639	−	9.98172i	1.01284	−	0.527550i
$359$	−20.3936	−	10.3911i	−1.07633	−	0.548419i	−0.176343	−	0.984329i	$-0.556427\pi$
$359$	−20.3936	−	10.3911i	−1.07633	−	0.548419i	−0.899991	+	0.435910i	$0.856427\pi$
$360$	15.1100	+	8.19052i	0.796369	+	0.431678i
$361$	−10.2057	−	1.07267i	−0.537144	−	0.0564562i
$362$	−18.3765	−	14.6104i	−0.965849	−	0.767906i
$363$	16.4509	+	24.9912i	0.863447	+	1.31170i
$364$	23.7470	−	10.4252i	1.24468	−	0.546430i
$365$	6.57647	+	4.77808i	0.344228	+	0.250096i
$366$	−10.0017	+	6.62333i	−0.522799	+	0.346207i
$367$	22.0676	+	19.8697i	1.15192	+	1.03719i	0.998800	+	0.0489840i	$0.0155983\pi$
$367$	22.0676	+	19.8697i	1.15192	+	1.03719i	0.153119	+	0.988208i	$0.451068\pi$
$368$	−33.2656	+	1.19246i	−1.73409	+	0.0621611i
$369$	3.15249	−	19.9040i	0.164112	−	1.03616i
$370$	−1.72586	−	10.2987i	−0.0897234	−	0.535406i
$371$	33.1011	+	1.73475i	1.71852	+	0.0900639i
$372$	−20.6332	+	26.4344i	−1.06978	+	1.37056i
$373$	3.96515	−	6.86785i	0.205308	−	0.355604i	−0.744923	−	0.667151i	$-0.767514\pi$
$373$	3.96515	−	6.86785i	0.205308	−	0.355604i	0.950231	+	0.311547i	$0.100847\pi$
$374$	17.2515	−	10.8601i	0.892053	−	0.561561i
$375$	−29.3698	−	7.86960i	−1.51665	−	0.406385i
$376$	−4.24556	−	1.25439i	−0.218948	−	0.0646903i
$377$	−17.8569	+	2.40659i	−0.919680	+	0.123946i
$378$	−19.2554	−	1.84959i	−0.990391	−	0.0951328i
$379$	−3.72378	−	9.70078i	−0.191278	−	0.498295i	0.804082	−	0.594518i	$-0.202657\pi$
$379$	−3.72378	−	9.70078i	−0.191278	−	0.498295i	−0.995360	+	0.0962229i	$0.969324\pi$
$380$	−14.1306	+	4.87286i	−0.724884	+	0.249972i
$381$	−6.25517	+	29.4283i	−0.320462	+	1.50766i
$382$	1.47080	+	23.9565i	0.0752527	+	1.22572i
$383$	−1.45599	−	0.558902i	−0.0743976	−	0.0285586i	0.320885	−	0.947118i	$-0.396020\pi$
$383$	−1.45599	−	0.558902i	−0.0743976	−	0.0285586i	−0.395282	+	0.918560i	$0.629353\pi$
$384$	−26.4896	+	15.6614i	−1.35179	+	0.799215i
$385$	−9.37638	−	13.5524i	−0.477865	−	0.690695i
$386$	−18.4591	−	24.9340i	−0.939545	−	1.26911i
$387$	2.86307	−	27.2403i	0.145538	−	1.38470i
$388$	4.34555	+	24.5784i	0.220612	+	1.24778i
$389$	0.415613	−	0.135041i	0.0210724	−	0.00684684i	−0.298462	−	0.954422i	$-0.596474\pi$
$389$	0.415613	−	0.135041i	0.0210724	−	0.00684684i	0.319534	+	0.947575i	$0.396474\pi$
$390$	−17.7898	−	7.11944i	−0.900820	−	0.360507i
$391$	21.2587	+	29.2601i	1.07510	+	1.47975i
$392$	6.43446	+	15.5037i	0.324989	+	0.783057i
$393$	−3.80912	+	0.809653i	−0.192145	+	0.0408416i
$394$	5.95408	−	0.0533368i	0.299962	−	0.00268707i
$395$	1.05444	+	1.05444i	0.0530544	+	0.0530544i
$396$	−12.0038	+	26.5909i	−0.603216	+	1.33624i
$397$	5.54330	−	1.48532i	0.278210	−	0.0745462i	−0.117016	−	0.993130i	$-0.537333\pi$
$397$	5.54330	−	1.48532i	0.278210	−	0.0745462i	0.395226	+	0.918584i	$0.370666\pi$
$398$	6.97706	−	27.0040i	0.349728	−	1.35359i
$399$	39.3250	−	35.4084i	1.96871	−	1.77264i
$400$	8.88661	−	8.59759i	0.444331	−	0.429880i
$401$	3.31079	+	8.62489i	0.165333	+	0.430706i	0.991069	−	0.133350i	$-0.0425734\pi$
$401$	3.31079	+	8.62489i	0.165333	+	0.430706i	−0.825736	+	0.564056i	$0.809240\pi$
$402$	−36.4917	+	8.09886i	−1.82004	+	0.403934i
$403$	11.5549	−	18.9861i	0.575588	−	0.945767i
$404$	3.09518	−	1.44505i	0.153991	−	0.0718938i
$405$	−2.47803	−	3.06011i	−0.123134	−	0.152058i
$406$	−2.88321	−	25.2537i	−0.143091	−	1.25332i
$407$	17.2229	−	4.19144i	0.853709	−	0.207762i
$408$	30.1887	+	14.3736i	1.49456	+	0.711599i
$409$	10.3649	−	27.0014i	0.512510	−	1.33513i	−0.396375	−	0.918089i	$-0.629732\pi$
$409$	10.3649	−	27.0014i	0.512510	−	1.33513i	0.908885	−	0.417046i	$-0.136935\pi$
$410$	8.01261	+	3.99263i	0.395715	+	0.197182i
$411$	1.26274	+	0.643398i	0.0622863	+	0.0317365i
$412$	21.1320	+	18.3526i	1.04110	+	0.904169i
$413$	−0.726051	+	1.63074i	−0.0357266	+	0.0802434i
$414$	−48.4882	−	18.1162i	−2.38306	−	0.890364i
$415$	3.79930	−	11.6930i	0.186500	−	0.573988i
$416$	16.2371	−	12.3433i	0.796089	−	0.605179i
$417$	−21.0855			−1.03256
$418$	−9.99165	−	23.3223i	−0.488707	−	1.14073i
$419$	13.1733	−	7.60559i	0.643556	−	0.371557i	−0.142427	−	0.989805i	$-0.545491\pi$
$419$	13.1733	−	7.60559i	0.643556	−	0.371557i	0.785983	+	0.618248i	$0.212157\pi$
$420$	10.5501	−	24.8864i	0.514791	−	1.21433i
$421$	−3.06152	−	6.00857i	−0.149209	−	0.292840i	0.804289	−	0.594238i	$-0.202546\pi$
$421$	−3.06152	−	6.00857i	−0.149209	−	0.292840i	−0.953498	+	0.301399i	$0.902546\pi$
$422$	−1.11631	+	0.187072i	−0.0543411	+	0.00910650i
$423$	−5.34993	−	4.33229i	−0.260122	−	0.210643i
$424$	25.6280	−	4.76824i	1.24460	−	0.231566i
$425$	−13.1413	−	2.79327i	−0.637446	−	0.135493i
$426$	55.9683	+	11.3734i	2.71167	+	0.551043i
$427$	7.05840	+	8.71640i	0.341580	+	0.421816i
$428$	22.6868	+	24.3061i	1.09661	+	1.17488i
$429$	9.86017	−	30.9956i	0.476054	−	1.49648i
$430$	11.1596	+	4.84928i	0.538166	+	0.233853i
$431$	−19.2887	+	15.6197i	−0.929102	+	0.752372i	−0.969059	−	0.246829i	$-0.920611\pi$
$431$	−19.2887	+	15.6197i	−0.929102	+	0.752372i	0.0399566	+	0.999201i	$0.487278\pi$
$432$	−15.0629	+	2.13116i	−0.724716	+	0.102536i
$433$	2.96554	−	13.9518i	0.142515	−	0.670479i	−0.847648	−	0.530559i	$-0.821982\pi$
$433$	2.96554	−	13.9518i	0.142515	−	0.670479i	0.990163	−	0.139920i	$-0.0446846\pi$
$434$	26.4468	+	16.8399i	1.26949	+	0.808340i
$435$	−11.8184	+	14.5945i	−0.566649	+	0.699753i
$436$	−2.40403	+	9.66106i	−0.115132	+	0.462681i
$437$	40.1095	−	20.4368i	1.91870	−	0.977626i
$438$	−22.6318	+	0.202737i	−1.08139	+	0.00968713i
$439$	−1.65105	−	2.85971i	−0.0788005	−	0.136486i	0.823932	−	0.566688i	$-0.191776\pi$
$439$	−1.65105	−	2.85971i	−0.0788005	−	0.136486i	−0.902733	+	0.430202i	$0.858442\pi$
$440$	−9.66432	−	8.63558i	−0.460729	−	0.411685i
$441$			26.1025i			1.24298i
$442$	−20.9773	−	7.14584i	−0.997789	−	0.339893i
$443$	15.0770	+	4.89881i	0.716329	+	0.232750i	0.644431	−	0.764662i	$-0.277094\pi$
$443$	15.0770	+	4.89881i	0.716329	+	0.232750i	0.0718984	+	0.997412i	$0.477094\pi$
$444$	20.9232	+	20.1866i	0.992971	+	0.958014i
$445$	7.52470	+	3.35021i	0.356705	+	0.158815i
$446$	12.2779	+	3.86809i	0.581375	+	0.183159i
$447$	−11.1039	+	21.7926i	−0.525195	+	1.03075i
$448$	16.9440	+	23.2535i	0.800527	+	1.09862i
$449$	10.0195	+	3.84613i	0.472849	+	0.181510i	0.583111	−	0.812393i	$-0.301835\pi$
$449$	10.0195	+	3.84613i	0.472849	+	0.181510i	−0.110261	+	0.993903i	$0.535169\pi$
$450$	17.8881	−	7.05110i	0.843254	−	0.332392i
$451$	−5.77176	+	14.0575i	−0.271781	+	0.661942i
$452$	−5.31521	−	1.62234i	−0.250007	−	0.0763083i
$453$	39.0836	−	31.6493i	1.83631	−	1.48701i
$454$	−10.6675	−	9.43342i	−0.500651	−	0.442732i
$455$	−5.03561	+	17.1932i	−0.236073	+	0.806030i
$456$	23.5478	−	34.3133i	1.10273	−	1.60687i
$457$	14.4083	−	5.53082i	0.673991	−	0.258721i	0.00278973	−	0.999996i	$-0.499112\pi$
$457$	14.4083	−	5.53082i	0.673991	−	0.258721i	0.671201	+	0.741275i	$0.265779\pi$
$458$	−3.02620	−	6.63633i	−0.141405	−	0.310096i
$459$	11.0603	+	12.2837i	0.516251	+	0.573355i
$460$	14.1484	−	18.1264i	0.659673	−	0.845147i
$461$	−0.408535	−	1.52467i	−0.0190274	−	0.0710111i	0.955759	−	0.294150i	$-0.0950364\pi$
$461$	−0.408535	−	1.52467i	−0.0190274	−	0.0710111i	−0.974787	+	0.223139i	$0.928370\pi$
$462$	43.4331	+	14.7934i	2.02069	+	0.688251i
$463$	20.7999	−	20.7999i	0.966652	−	0.966652i	−0.0328098	−	0.999462i	$-0.510446\pi$
$463$	20.7999	−	20.7999i	0.966652	−	0.966652i	0.999462	+	0.0328098i	$0.0104455\pi$
$464$	−6.85421	−	18.7778i	−0.318199	−	0.871735i
$465$	−4.81624	−	22.6586i	−0.223348	−	1.05077i
$466$	−9.52702	+	25.4991i	−0.441331	+	1.18122i
$467$	−3.31031	+	2.40508i	−0.153183	+	0.111294i	−0.661737	−	0.749736i	$-0.730180\pi$
$467$	−3.31031	+	2.40508i	−0.153183	+	0.111294i	0.508554	+	0.861030i	$0.330180\pi$
$468$	30.6779	−	8.04935i	1.41809	−	0.372081i
$469$	10.7998	+	33.2384i	0.498688	+	1.53480i
$470$	2.54975	−	1.68849i	0.117611	−	0.0778841i
$471$	−41.7034	−	4.38320i	−1.92159	−	0.201967i
$472$	−0.254874	+	1.38052i	−0.0117315	+	0.0635435i
$473$	−6.83413	+	19.4910i	−0.314233	+	0.896197i
$474$	−4.10634	−	0.612727i	−0.188611	−	0.0281435i
$475$	−5.99254	+	15.6111i	−0.274957	+	0.716287i
$476$	10.6785	−	29.3813i	0.489449	−	1.34669i
$477$	39.6501	+	8.42789i	1.81545	+	0.385887i
$478$	−3.20561	+	2.93876i	−0.146621	+	0.134416i
$479$	−15.4740	+	5.93991i	−0.707025	+	0.271402i	−0.685195	−	0.728360i	$-0.740283\pi$
$479$	−15.4740	+	5.93991i	−0.707025	+	0.271402i	−0.0218308	+	0.999762i	$0.506949\pi$
$480$	3.48431	−	20.9703i	0.159036	−	0.957157i
$481$	−15.3236	−	11.6838i	−0.698697	−	0.532736i
$482$	−5.79933	+	3.41787i	−0.264152	+	0.155680i
$483$	−21.0695	+	78.6325i	−0.958696	+	3.57790i
$484$	13.4286	−	17.4262i	0.610392	−	0.792099i
$485$	−14.9319	−	8.62096i	−0.678024	−	0.391457i
$486$	26.2373	+	6.77897i	1.19015	+	0.307500i
$487$	−0.115007	+	2.19447i	−0.00521148	+	0.0994410i	−0.999997	−	0.00255055i	$-0.999188\pi$
$487$	−0.115007	+	2.19447i	−0.00521148	+	0.0994410i	0.994785	+	0.101992i	$0.0325215\pi$
$488$	7.00162	+	5.36482i	0.316948	+	0.242854i
$489$	−43.5561	−	6.89862i	−1.96968	−	0.311966i
$490$	−11.0597	−	3.48431i	−0.499628	−	0.157405i
$491$	−4.38609	+	4.87125i	−0.197942	+	0.219837i	−0.833942	−	0.551853i	$-0.813921\pi$
$491$	−4.38609	+	4.87125i	−0.197942	+	0.219837i	0.636000	+	0.771689i	$0.280588\pi$
$492$	−24.5443	+	4.33953i	−1.10654	+	0.195641i
$493$	−12.7663	+	17.5713i	−0.574966	+	0.791373i
$494$	−12.8690	+	24.3967i	−0.579005	+	1.09766i
$495$	−8.73281	−	18.1634i	−0.392511	−	0.816386i
$496$	23.3214	+	8.00609i	1.04716	+	0.359484i
$497$	5.58165	−	53.1058i	0.250371	−	2.38212i
$498$	10.8692	+	32.4598i	0.487063	+	1.45456i
$499$	17.3008	−	33.9548i	0.774491	−	1.52002i	−0.0778071	−	0.996968i	$-0.524792\pi$
$499$	17.3008	−	33.9548i	0.774491	−	1.52002i	0.852298	−	0.523056i	$-0.175208\pi$
$500$	1.56989	+	22.3022i	0.0702074	+	0.997386i
$501$	12.6295	−	15.5961i	0.564245	−	0.696784i
$502$	4.69518	−	3.87223i	0.209556	−	0.172826i
$503$	−13.6097	+	12.2543i	−0.606828	+	0.546391i	−0.914233	−	0.405188i	$-0.867206\pi$
$503$	−13.6097	+	12.2543i	−0.606828	+	0.546391i	0.307405	+	0.951579i	$0.400539\pi$
$504$	10.4747	+	43.4975i	0.466581	+	1.93753i
$505$	−0.610727	+	2.27926i	−0.0271770	+	0.101426i
$506$	32.4320	+	21.7187i	1.44178	+	0.965512i
$507$	−32.9328	+	12.8738i	−1.46260	+	0.571746i
$508$	21.9559	−	2.70615i	0.974136	−	0.120066i
$509$	−16.3361	+	25.1554i	−0.724084	+	1.11499i	0.264510	+	0.964383i	$0.414790\pi$
$509$	−16.3361	+	25.1554i	−0.724084	+	1.11499i	−0.988593	+	0.150608i	$0.951877\pi$
$510$	−21.0154	+	9.58314i	−0.930577	+	0.424348i
$511$	2.21193	+	21.0451i	0.0978498	+	0.930979i
$512$	17.2366	+	14.6595i	0.761755	+	0.647865i
$513$	17.2543	−	11.2051i	0.761795	−	0.494715i
$514$	−28.7503	−	14.3261i	−1.26812	−	0.631897i
$515$	−19.0965	+	3.02459i	−0.841493	+	0.133279i
$516$	−33.0057	+	7.63604i	−1.45299	+	0.336158i
$517$	3.17292	+	4.10856i	0.139545	+	0.180694i
$518$	16.9170	−	21.2776i	0.743288	−	0.934885i
$519$	21.5183	+	15.6340i	0.944549	+	0.686255i
$520$	−0.684517	+	14.0728i	−0.0300181	+	0.617134i
$521$	−2.11081	−	6.49641i	−0.0924763	−	0.284613i	0.894111	−	0.447845i	$-0.147808\pi$
$521$	−2.11081	−	6.49641i	−0.0924763	−	0.284613i	−0.986588	+	0.163232i	$0.947808\pi$
$522$	1.34870	−	31.0550i	0.0590309	−	1.35924i
$523$	−5.46737	+	12.2799i	−0.239071	+	0.536963i	−0.992738	−	0.120293i	$-0.961616\pi$
$523$	−5.46737	+	12.2799i	−0.239071	+	0.536963i	0.753667	+	0.657256i	$0.228283\pi$
$524$	1.47591	+	2.45375i	0.0644752	+	0.107193i
$525$	−13.7284	−	26.9435i	−0.599157	−	1.17591i
$526$	−16.1868	+	16.4794i	−0.705776	+	0.718535i
$527$	−6.93403	−	25.8781i	−0.302051	−	1.12727i
$528$	35.9321	+	3.31384i	1.56374	+	0.144216i
$529$	−23.1258	+	40.0550i	−1.00547	+	1.74152i
$530$	−8.86365	+	15.6749i	−0.385012	+	0.680874i
$531$	−1.18895	+	1.83083i	−0.0515962	+	0.0794512i
$532$	−34.0401	−	18.8482i	−1.47583	−	0.817172i
$533$	15.8253	−	4.74046i	0.685471	−	0.205332i
$534$	−22.3883	+	4.96879i	−0.968835	+	0.215021i
$535$	−22.9365	+	1.20205i	−0.991631	+	0.0519692i
$536$	14.3772	+	23.4251i	0.621002	+	1.01181i
$537$	−16.9033	−	37.9653i	−0.729429	−	1.63832i
$538$	5.83636	+	14.8064i	0.251623	+	0.638350i
$539$	4.53555	−	19.1536i	0.195360	−	0.825003i
$540$	5.56480	−	8.91471i	0.239471	−	0.383628i
$541$	3.63664	+	22.9608i	0.156351	+	0.987162i	0.933691	+	0.358081i	$0.116569\pi$
$541$	3.63664	+	22.9608i	0.156351	+	0.987162i	−0.777339	+	0.629081i	$0.783431\pi$
$542$	−7.59386	−	22.6782i	−0.326184	−	0.974114i
$543$	−30.2134	+	33.5554i	−1.29658	+	1.44000i
$544$	2.75492	−	24.4306i	0.118116	−	1.04745i
$545$	−4.04238	−	5.56386i	−0.173157	−	0.238330i
$546$	−17.2145	−	46.8158i	−0.736711	−	2.00353i
$547$	−19.3094	−	6.27402i	−0.825612	−	0.268258i	−0.134416	−	0.990925i	$-0.542916\pi$
$547$	−19.3094	−	6.27402i	−0.825612	−	0.268258i	−0.691196	+	0.722667i	$0.742916\pi$
$548$	0.144551	−	1.03200i	0.00617493	−	0.0440848i
$549$	6.85815	+	11.8787i	0.292699	+	0.506969i
$550$	−14.3512	+	2.06575i	−0.611938	+	0.0880841i
$551$	19.1153	+	19.1153i	0.814339	+	0.814339i
$552$	−1.63150	+	64.0005i	−0.0694414	+	2.72404i
$553$	−0.203159	+	3.87650i	−0.00863920	+	0.164846i
$554$	−12.2873	−	14.8987i	−0.522038	−	0.632985i
$555$	−19.9739	+	2.09934i	−0.847843	+	0.0891119i
$556$	5.05444	+	14.6571i	0.214356	+	0.621602i
$557$	−4.84968	+	0.254161i	−0.205488	+	0.0107692i	−0.154802	−	0.987946i	$-0.549474\pi$
$557$	−4.84968	+	0.254161i	−0.205488	+	0.0107692i	−0.0506856	+	0.998715i	$0.516141\pi$
$558$	28.7228	+	25.4000i	1.21594	+	1.07527i
$559$	21.1427	−	7.56001i	0.894242	−	0.319754i
$560$	−19.8283	−	1.36811i	−0.837898	−	0.0578131i
$561$	−18.8148	−	34.3976i	−0.794363	−	1.45227i
$562$	−20.7090	+	2.36434i	−0.873556	+	0.0997336i
$563$	24.6348	−	10.9681i	1.03823	−	0.462251i	0.184428	−	0.982846i	$-0.440957\pi$
$563$	24.6348	−	10.9681i	1.03823	−	0.462251i	0.853803	+	0.520595i	$0.174290\pi$
$564$	−2.90843	+	8.00235i	−0.122467	+	0.336960i
$565$	3.21960	−	2.09083i	0.135450	−	0.0879620i
$566$	14.6507	−	7.63099i	0.615816	−	0.320755i
$567$	1.60349	−	10.1241i	0.0673404	−	0.425171i
$568$	−5.51027	−	41.6316i	−0.231206	−	1.74682i
$569$	3.94885	+	18.5779i	0.165545	+	0.778826i	0.980063	+	0.198688i	$0.0636681\pi$
$569$	3.94885	+	18.5779i	0.165545	+	0.778826i	−0.814518	+	0.580138i	$0.802999\pi$
$570$	7.68900	+	27.7008i	0.322057	+	1.16026i
$571$	−2.37091			−0.0992196			−0.0496098	−	0.998769i	$-0.515798\pi$
$571$	−2.37091			−0.0992196			−0.0496098	+	0.998769i	$0.515798\pi$
$572$	−23.9096	+	0.575920i	−0.999710	+	0.0240804i
$573$	46.1626			1.92847
$574$	6.23296	+	22.4552i	0.260159	+	0.937261i
$575$	−5.34840	−	25.1623i	−0.223044	−	1.04934i
$576$	16.0176	+	31.3289i	0.667401	+	1.30537i
$577$	−3.90474	+	24.6535i	−0.162556	+	1.02634i	0.762632	+	0.646832i	$0.223907\pi$
$577$	−3.90474	+	24.6535i	−0.162556	+	1.02634i	−0.925189	+	0.379508i	$0.876093\pi$
$578$	−2.36915	+	1.23400i	−0.0985438	+	0.0513276i
$579$	−50.0414	+	32.4972i	−2.07965	+	1.35054i
$580$	12.9781	+	4.71684i	0.538886	+	0.195856i
$581$	29.2383	−	13.0177i	1.21301	−	0.540066i
$582$	47.6953	−	5.44536i	1.97703	−	0.225717i
$583$	−27.6302	−	13.0738i	−1.14433	−	0.541462i
$584$	5.56605	+	15.6835i	0.230325	+	0.648987i
$585$	−9.37161	+	19.8039i	−0.387468	+	0.818791i
$586$	2.67599	+	2.36642i	0.110544	+	0.0977558i
$587$	1.85298	−	0.0971108i	0.0764809	−	0.00400819i	−0.0140571	−	0.999901i	$-0.504475\pi$
$587$	1.85298	−	0.0971108i	0.0764809	−	0.00400819i	0.0905380	+	0.995893i	$0.471141\pi$
$588$	30.5208	−	10.5250i	1.25866	−	0.434042i
$589$	−33.1629	+	3.48556i	−1.36645	+	0.143620i
$590$	−0.617021	−	0.748154i	−0.0254024	−	0.0308010i
$591$	0.599352	−	11.4363i	0.0246541	−	0.470427i
$592$	9.01678	−	19.3833i	0.370587	−	0.796649i
$593$	23.3152	+	23.3152i	0.957442	+	0.957442i	0.999131	−	0.0416882i	$-0.0132736\pi$
$593$	23.3152	+	23.3152i	0.957442	+	0.957442i	−0.0416882	+	0.999131i	$0.513274\pi$
$594$	15.7785	+	8.32223i	0.647401	+	0.341465i
$595$	10.7977	+	18.7021i	0.442660	+	0.766710i
$596$	17.8104	+	2.49469i	0.729542	+	0.102187i
$597$	−51.0173	−	16.5765i	−2.08800	−	0.678432i
$598$	−3.83752	−	42.2589i	−0.156928	−	1.72809i
$599$	16.6616	+	22.9328i	0.680776	+	0.937008i	0.999943	−	0.0106909i	$-0.00340308\pi$
$599$	16.6616	+	22.9328i	0.680776	+	0.937008i	−0.319167	+	0.947698i	$0.603403\pi$
$600$	−15.4574	−	18.0729i	−0.631046	−	0.737824i
$601$	26.0646	−	28.9477i	1.06320	−	1.18080i	0.0802763	−	0.996773i	$-0.474420\pi$
$601$	26.0646	−	28.9477i	1.06320	−	1.18080i	0.982921	−	0.184028i	$-0.0589136\pi$
$602$	10.0574	+	30.0354i	0.409910	+	1.22415i
$603$	6.68603	+	42.2139i	0.272276	+	1.71908i
$604$	−31.3692	−	19.5815i	−1.27639	−	0.796760i
$605$	3.25193	+	14.8454i	0.132210	+	0.603553i
$606$	−2.40926	−	6.11211i	−0.0978694	−	0.248288i
$607$	5.13632	+	11.5364i	0.208477	+	0.468246i	0.987274	−	0.159030i	$-0.0508365\pi$
$607$	5.13632	+	11.5364i	0.208477	+	0.468246i	−0.778797	+	0.627276i	$0.784170\pi$
$608$	−29.4969	−	8.14351i	−1.19626	−	0.330263i
$609$	−48.8194	+	2.55851i	−1.97826	+	0.103676i
$610$	−5.94850	+	1.32019i	−0.240848	+	0.0534531i
$611$	1.30059	−	5.49142i	0.0526163	−	0.222159i
$612$	18.5192	−	33.4460i	0.748596	−	1.35198i
$613$	12.6497	−	19.4788i	0.510915	−	0.786741i	−0.485237	−	0.874383i	$-0.661267\pi$
$613$	12.6497	−	19.4788i	0.510915	−	0.786741i	0.996152	+	0.0876421i	$0.0279332\pi$
$614$	−19.4928	+	34.4720i	−0.786666	+	1.39118i
$615$	8.60900	−	14.9112i	0.347149	−	0.601279i
$616$	−0.128099	−	33.7378i	−0.00516126	−	1.35934i
$617$	3.88025	+	14.4813i	0.156213	+	0.582995i	0.998998	+	0.0447453i	$0.0142476\pi$
$617$	3.88025	+	14.4813i	0.156213	+	0.582995i	−0.842785	+	0.538250i	$0.819086\pi$
$618$	37.7221	−	38.4041i	1.51741	−	1.54484i
$619$	5.77616	+	11.3364i	0.232164	+	0.455647i	0.977470	−	0.211076i	$-0.0676966\pi$
$619$	5.77616	+	11.3364i	0.232164	+	0.455647i	−0.745306	+	0.666722i	$0.767697\pi$
$620$	−14.5962	+	8.77945i	−0.586196	+	0.352591i
$621$	−12.8731	+	28.9134i	−0.516578	+	1.16025i
$622$	−2.06722	+	47.5996i	−0.0828880	+	1.90857i
$623$	6.62586	+	20.3923i	0.265460	+	0.817001i
$624$	−21.7817	−	32.6251i	−0.871966	−	1.30605i
$625$	0.00952361	+	0.00691931i	0.000380944	+	0.000276772i
$626$	−6.10629	+	7.68030i	−0.244056	+	0.306967i
$627$	−45.9494	+	16.4322i	−1.83504	+	0.656239i
$628$	6.94990	+	30.0400i	0.277331	+	1.19873i
$629$	−22.9418	+	3.63363i	−0.914751	+	0.144882i
$630$	−27.6626	−	13.7841i	−1.10211	−	0.549172i
$631$	−28.5062	+	18.5121i	−1.13481	+	0.736956i	−0.968474	−	0.249113i	$-0.919861\pi$
$631$	−28.5062	+	18.5121i	−1.13481	+	0.736956i	−0.166338	+	0.986069i	$0.553194\pi$
$632$	0.558415	+	3.00132i	0.0222126	+	0.119386i
$633$	0.227553	+	2.16503i	0.00904444	+	0.0860521i
$634$	0.760532	−	0.346807i	0.0302046	−	0.0137734i
$635$	−8.32304	+	12.8164i	−0.330290	+	0.508602i
$636$	−6.13310	−	49.7599i	−0.243193	−	1.97311i
$637$	−19.2852	+	9.27119i	−0.764107	+	0.367338i
$638$	−6.38574	+	22.5533i	−0.252814	+	0.892893i
$639$	16.9015	−	63.0774i	0.668615	−	2.49530i
$640$	−15.4123	+	2.60477i	−0.609224	+	0.102963i
$641$	−2.30648	+	2.07676i	−0.0911005	+	0.0820273i	−0.713423	−	0.700734i	$-0.752856\pi$
$641$	−2.30648	+	2.07676i	−0.0911005	+	0.0820273i	0.622322	+	0.782761i	$0.286189\pi$
$642$	49.3342	−	40.6872i	1.94707	−	1.60579i
$643$	−3.54186	+	4.37384i	−0.139678	+	0.172487i	−0.842184	−	0.539190i	$-0.818731\pi$
$643$	−3.54186	+	4.37384i	−0.139678	+	0.172487i	0.702507	+	0.711677i	$0.252064\pi$
$644$	59.7104	−	4.20310i	2.35292	−	0.165625i
$645$	10.6244	−	20.8516i	0.418336	−	0.821032i
$646$	10.5571	+	31.5277i	0.415365	+	1.24044i
$647$	−0.302674	+	2.87975i	−0.0118993	+	0.113215i	−0.998859	−	0.0477517i	$-0.984794\pi$
$647$	−0.302674	+	2.87975i	−0.0118993	+	0.113215i	0.986960	+	0.160966i	$0.0514610\pi$
$648$	−0.638049	−	8.03594i	−0.0250649	−	0.315682i
$649$	1.19056	−	1.13684i	0.0467335	−	0.0446249i
$650$	11.5631	+	10.7118i	0.453542	+	0.420150i
$651$	35.4445	−	48.7851i	1.38918	−	1.91204i
$652$	5.64549	+	31.9309i	0.221095	+	1.25051i
$653$	−2.97590	+	3.30507i	−0.116456	+	0.129337i	−0.798554	−	0.601924i	$-0.794401\pi$
$653$	−2.97590	+	3.30507i	−0.116456	+	0.129337i	0.682098	+	0.731261i	$0.261068\pi$
$654$	18.2630	+	5.75366i	0.714139	+	0.224986i
$655$	−1.95368	−	0.309432i	−0.0763365	−	0.0120905i
$656$	8.90011	+	16.0213i	0.347491	+	0.625525i
$657$	−1.35437	+	25.8430i	−0.0528392	+	1.00823i
$658$	7.70771	+	1.99145i	0.300478	+	0.0776347i
$659$	3.88021	+	2.24024i	0.151152	+	0.0872675i	0.573668	−	0.819088i	$-0.305520\pi$
$659$	3.88021	+	2.24024i	0.151152	+	0.0872675i	−0.422517	+	0.906355i	$0.638853\pi$
$660$	−17.7167	+	17.5348i	−0.689623	+	0.682541i
$661$	−4.14376	+	15.4647i	−0.161173	+	0.601508i	0.837324	+	0.546707i	$0.184119\pi$
$661$	−4.14376	+	15.4647i	−0.161173	+	0.601508i	−0.998497	+	0.0548003i	$0.982548\pi$
$662$	26.1153	−	15.3912i	1.01500	−	0.598196i
$663$	−16.1902	+	39.4279i	−0.628776	+	1.53125i
$664$	19.9583	−	15.3365i	0.774532	−	0.595173i
$665$	25.0934	−	9.63246i	0.973081	−	0.373531i
$666$	24.5042	−	22.4644i	0.949518	−	0.870477i
$667$	−40.6784	−	8.64645i	−1.57507	−	0.334792i
$668$	−13.8688	−	5.04057i	−0.536600	−	0.195025i
$669$	8.87262	−	23.1140i	0.343035	−	0.893637i
$670$	−18.7787	−	2.80206i	−0.725484	−	0.108253i
$671$	−2.96837	−	9.90803i	−0.114593	−	0.382495i
$672$	46.6367	−	29.7867i	1.79905	−	1.14905i
$673$	12.8150	+	1.34691i	0.493982	+	0.0519196i	0.348244	−	0.937404i	$-0.386778\pi$
$673$	12.8150	+	1.34691i	0.493982	+	0.0519196i	0.145737	+	0.989323i	$0.453445\pi$
$674$	−15.9188	+	10.5417i	−0.613170	+	0.406052i
$675$	−3.63301	−	11.1812i	−0.139834	−	0.430366i
$676$	16.8434	+	19.8066i	0.647822	+	0.761792i
$677$	−3.56288	+	2.58859i	−0.136933	+	0.0994874i	−0.654143	−	0.756371i	$-0.726971\pi$
$677$	−3.56288	+	2.58859i	−0.136933	+	0.0994874i	0.517210	+	0.855858i	$0.326971\pi$
$678$	−3.74084	+	10.0124i	−0.143666	+	0.384524i
$679$	−9.33180	−	43.9027i	−0.358122	−	1.68483i
$680$	11.6992	+	12.3112i	0.448643	+	0.472115i
$681$	−19.3666	+	19.3666i	−0.742129	+	0.742129i
$682$	−16.6629	−	23.6290i	−0.638055	−	0.904800i
$683$	−12.5015	−	46.6562i	−0.478356	−	1.78525i	−0.608278	−	0.793724i	$-0.708139\pi$
$683$	−12.5015	−	46.6562i	−0.478356	−	1.78525i	0.129922	−	0.991524i	$-0.458527\pi$
$684$	−37.5104	−	29.2784i	−1.43425	−	1.11949i
$685$	0.481678	+	0.534957i	0.0184040	+	0.0204397i
$686$	2.24803	+	4.92982i	0.0858300	+	0.188221i
$687$	−13.0964	+	5.02725i	−0.499660	+	0.191801i
$688$	13.2199	+	21.1128i	0.504004	+	0.804918i
$689$	7.85635	+	32.2879i	0.299303	+	1.23007i
$690$	−33.1297	−	29.2970i	−1.26123	−	1.11532i
$691$	22.7414	−	18.4156i	0.865122	−	0.700562i	−0.0902653	−	0.995918i	$-0.528772\pi$
$691$	22.7414	−	18.4156i	0.865122	−	0.700562i	0.955387	+	0.295356i	$0.0954382\pi$
$692$	5.70944	−	18.7057i	0.217041	−	0.711083i
$693$	19.9263	−	48.5319i	0.756939	−	1.84357i
$694$	−42.1096	+	16.5986i	−1.59846	+	0.630076i
$695$	−9.99880	−	3.83818i	−0.379276	−	0.145590i
$696$	−36.8555	+	10.9449i	−1.39700	+	0.414865i
$697$	9.04045	−	17.7429i	0.342432	−	0.672060i
$698$	13.4436	+	4.23532i	0.508846	+	0.160309i
$699$	47.8278	+	21.2943i	1.80901	+	0.805425i
$700$	−15.4384	+	16.0017i	−0.583517	+	0.604808i
$701$	−32.3216	−	10.5019i	−1.22077	−	0.396652i	−0.373408	−	0.927667i	$-0.621811\pi$
$701$	−32.3216	−	10.5019i	−1.22077	−	0.396652i	−0.847362	+	0.531015i	$0.821811\pi$
$702$	−3.76302	−	19.0242i	−0.142026	−	0.718022i
$703$			28.9106i			1.09038i
$704$	−6.30979	−	25.7718i	−0.237809	−	0.971312i
$705$	−2.94088	−	5.09375i	−0.110760	−	0.191842i
$706$	26.8483	−	0.240508i	1.01045	−	0.00905164i
$707$	−5.47309	+	2.78868i	−0.205837	+	0.104879i
$708$	2.62014	+	0.651988i	0.0984709	+	0.0245032i
$709$	11.5545	−	14.2686i	0.433938	−	0.535869i	−0.512529	−	0.858670i	$-0.671291\pi$
$709$	11.5545	−	14.2686i	0.433938	−	0.535869i	0.946467	+	0.322801i	$0.104624\pi$
$710$	24.4700	+	15.5812i	0.918344	+	0.584752i
$711$	−0.987000	+	4.64347i	−0.0370154	+	0.174144i
$712$	8.82069	+	14.3717i	0.330569	+	0.538601i
$713$	39.8661	−	32.2829i	1.49300	−	1.20901i
$714$	−55.1446	−	23.9624i	−2.06373	−	0.896770i
$715$	10.3178	−	12.9034i	0.385866	−	0.482559i
$716$	−22.3389	+	20.8507i	−0.834845	+	0.779227i
$717$	5.26373	+	6.50017i	0.196578	+	0.242753i
$718$	31.7206	+	6.44599i	1.18380	+	0.240562i
$719$	2.05645	+	0.437111i	0.0766925	+	0.0163015i	0.246098	−	0.969245i	$-0.420851\pi$
$719$	2.05645	+	0.437111i	0.0766925	+	0.0163015i	−0.169406	+	0.985546i	$0.554185\pi$
$720$	−23.6884	−	5.44583i	−0.882813	−	0.202954i
$721$	−39.1145	−	31.6743i	−1.45670	−	1.17961i
$722$	14.3130	−	2.39858i	0.532675	−	0.0892659i
$723$	5.87778	+	11.5358i	0.218597	+	0.429021i
$724$	30.5679	+	12.9586i	1.13605	+	0.481604i
$725$	13.3784	−	7.72404i	0.496862	−	0.286864i
$726$	−31.8703	−	27.8328i	−1.18282	−	1.03297i
$727$	6.25401			0.231948			0.115974	−	0.993252i	$-0.463001\pi$
$727$	6.25401			0.231948			0.115974	+	0.993252i	$0.463001\pi$
$728$	−28.4166	+	23.1886i	−1.05319	+	0.859426i
$729$	13.4637	−	41.4371i	0.498656	−	1.53471i
$730$	−10.7690	−	4.02352i	−0.398578	−	0.148917i
$731$	11.0086	−	24.7257i	0.407168	−	0.914515i
$732$	11.1240	−	12.8087i	0.411156	−	0.473423i
$733$	−13.2395	−	6.74587i	−0.489013	−	0.249164i	0.192056	−	0.981384i	$-0.438484\pi$
$733$	−13.2395	−	6.74587i	−0.489013	−	0.249164i	−0.681069	+	0.732220i	$0.738484\pi$
$734$	−37.5870	−	18.7293i	−1.38736	−	0.691312i
$735$	−7.99231	+	20.8207i	−0.294801	+	0.767983i
$736$	44.8798	−	14.2076i	1.65429	−	0.523698i
$737$	2.42896	−	32.1376i	0.0894717	−	1.18381i
$738$	3.23277	+	28.3155i	0.119000	+	1.04231i
$739$	−15.8447	−	19.5665i	−0.582855	−	0.719766i	0.397368	−	0.917659i	$-0.369924\pi$
$739$	−15.8447	−	19.5665i	−0.582855	−	0.719766i	−0.980224	+	0.197893i	$0.936590\pi$
$740$	6.24729	+	13.3812i	0.229655	+	0.491902i
$741$	45.3176	+	27.5800i	1.66478	+	1.01318i
$742$	−45.7627	+	10.1564i	−1.68000	+	0.372855i
$743$	−2.95057	−	7.68649i	−0.108246	−	0.281990i	0.868749	−	0.495252i	$-0.164924\pi$
$743$	−2.95057	−	7.68649i	−0.108246	−	0.281990i	−0.976995	+	0.213262i	$0.931591\pi$
$744$	18.1179	−	43.8264i	0.664235	−	1.60676i
$745$	−9.23238	+	8.31287i	−0.338248	+	0.304560i
$746$	−2.80554	+	10.8586i	−0.102718	+	0.397560i
$747$	37.8066	−	10.1303i	1.38327	−	0.370647i
$748$	−19.4007	+	21.3243i	−0.709359	+	0.779692i
$749$	−42.2775	−	42.2775i	−1.54478	−	1.54478i
$750$	42.9986	−	0.385182i	1.57009	−	0.0140649i
$751$	42.6432	−	9.06410i	1.55607	−	0.330754i	0.652030	−	0.758193i	$-0.273918\pi$
$751$	42.6432	−	9.06410i	1.55607	−	0.330754i	0.904044	+	0.427439i	$0.140584\pi$
$752$	6.25986	+	0.103477i	0.228274	+	0.00377342i
$753$	−6.88014	−	9.46971i	−0.250726	−	0.345095i
$754$	23.4232	−	10.0338i	0.853024	−	0.365409i
$755$	24.2947	−	7.89383i	0.884175	−	0.287286i
$756$	26.9388	−	4.76288i	0.979755	−	0.173224i
$757$	3.19405	−	30.3894i	0.116090	−	1.10452i	−0.769048	−	0.639191i	$-0.779269\pi$
$757$	3.19405	−	30.3894i	0.116090	−	1.10452i	0.885138	−	0.465329i	$-0.154064\pi$
$758$	8.74365	+	11.8107i	0.317584	+	0.428982i
$759$	45.5157	−	59.6999i	1.65211	−	2.16697i
$760$	17.4125	−	11.9851i	0.631617	−	0.434744i
$761$	3.40344	+	1.30646i	0.123374	+	0.0473590i	0.419272	−	0.907861i	$-0.362285\pi$
$761$	3.40344	+	1.30646i	0.123374	+	0.0473590i	−0.295898	+	0.955220i	$0.595619\pi$
$762$	−2.60729	−	42.4677i	−0.0944521	−	1.53844i
$763$	3.72219	−	17.5115i	0.134752	−	0.633960i
$764$	−11.0657	−	32.0890i	−0.400344	−	1.16094i
$765$	9.46435	+	24.6555i	0.342184	+	0.891421i
$766$	2.19547	+	0.210887i	0.0793255	+	0.00761967i
$767$	−1.77496	−	0.228148i	−0.0640901	−	0.00823795i
$768$	30.1733	−	31.3612i	1.08879	−	1.13165i
$769$	21.8615	+	5.85777i	0.788345	+	0.211237i	0.630461	−	0.776221i	$-0.282866\pi$
$769$	21.8615	+	5.85777i	0.788345	+	0.211237i	0.157885	+	0.987458i	$0.449533\pi$
$770$	17.9033	+	14.9212i	0.645190	+	0.537722i
$771$	−30.8903	+	53.5035i	−1.11249	+	1.92688i
$772$	34.5853	+	26.9953i	1.24475	+	0.971581i
$773$	8.90136	+	0.466501i	0.320160	+	0.0167789i	0.211739	−	0.977326i	$-0.432087\pi$
$773$	8.90136	+	0.466501i	0.320160	+	0.0167789i	0.108421	+	0.994105i	$0.465421\pi$
$774$	6.40208	+	38.2031i	0.230118	+	1.37318i
$775$	−2.98091	+	18.8207i	−0.107078	+	0.676061i
$776$	−15.2184	−	31.8491i	−0.546307	−	1.14332i
$777$	−38.8528	−	34.9832i	−1.39384	−	1.25502i
$778$	−0.515273	+	0.341223i	−0.0184734	+	0.0122334i
$779$	−20.0516	−	14.5684i	−0.718424	−	0.521966i
$780$	26.9349	+	2.97268i	0.964424	+	0.106439i
$781$	−23.3624	+	43.3484i	−0.835971	+	1.55113i
$782$	−40.0366	−	31.8314i	−1.43171	−	1.13829i
$783$	−18.9022	−	1.98670i	−0.675509	−	0.0709989i
$784$	−14.6324	−	18.6930i	−0.522587	−	0.667607i
$785$	−18.9780	−	9.66977i	−0.677354	−	0.345129i
$786$	4.88441	−	2.54410i	0.174221	−	0.0907449i
$787$	14.5485	+	11.7811i	0.518596	+	0.419951i	0.852556	−	0.522636i	$-0.175051\pi$
$787$	14.5485	+	11.7811i	0.518596	+	0.419951i	−0.333959	+	0.942587i	$0.608385\pi$
$788$	−8.09340	+	2.32480i	−0.288315	+	0.0828174i
$789$	29.7277	+	33.0159i	1.05833	+	1.17540i
$790$	−1.83571	−	1.03803i	−0.0653115	−	0.0369316i
$791$	9.65285	+	2.58647i	0.343216	+	0.0919644i
$792$	6.29961	−	40.7756i	0.223847	−	1.44890i
$793$	−6.34035	+	9.28608i	−0.225152	+	0.329758i
$794$	−6.99199	+	4.12077i	−0.248136	+	0.146241i
$795$	29.0464	+	18.8630i	1.03017	+	0.669001i
$796$	0.706616	+	39.4372i	0.0250453	+	1.39782i
$797$	29.6463	−	3.11596i	1.05013	−	0.110373i	0.436290	−	0.899806i	$-0.356292\pi$
$797$	29.6463	−	3.11596i	1.05013	−	0.110373i	0.613837	+	0.789433i	$0.289625\pi$
$798$	−40.1947	+	63.1253i	−1.42288	+	2.23461i
$799$	−3.70489	−	5.70504i	−0.131070	−	0.201830i
$800$	−8.85770	+	15.0772i	−0.313167	+	0.533060i
$801$	4.10199	+	25.8990i	0.144937	+	0.915095i
$802$	−7.77392	−	10.5008i	−0.274507	−	0.370795i
$803$	5.48427	−	18.7278i	0.193536	−	0.660891i
$804$	46.6635	−	24.8391i	1.64570	−	0.876008i
$805$	−24.3047	+	33.4525i	−0.856627	+	1.17905i
$806$	−8.56426	+	30.2428i	−0.301663	+	1.06526i
$807$	29.1117	−	9.45898i	1.02478	−	0.332972i
$808$	−3.67119	+	3.13989i	−0.129152	+	0.110461i
$809$	−41.3000	−	18.3879i	−1.45203	−	0.646486i	−0.479137	−	0.877740i	$-0.659050\pi$
$809$	−41.3000	−	18.3879i	−1.45203	−	0.646486i	−0.972893	+	0.231254i	$0.925717\pi$
$810$	4.53426	+	3.23268i	0.159318	+	0.113585i
$811$	−20.7997	+	10.5980i	−0.730375	+	0.372145i	−0.779295	−	0.626658i	$-0.784422\pi$
$811$	−20.7997	+	10.5980i	−0.730375	+	0.372145i	0.0489190	+	0.998803i	$0.484422\pi$
$812$	13.4811	+	33.3225i	0.473093	+	1.16939i
$813$	−44.4304	+	11.9051i	−1.55824	+	0.417529i
$814$	−21.8842	+	12.2262i	−0.767039	+	0.428527i
$815$	−19.3987	−	11.1999i	−0.679507	−	0.392314i
$816$	−46.5747	−	8.16798i	−1.63044	−	0.285937i
$817$	−28.2527	−	18.3475i	−0.988436	−	0.641898i
$818$	−3.91092	+	40.7151i	−0.136742	+	1.42357i
$819$	−54.6351	+	16.3659i	−1.90911	+	0.571871i
$820$	−12.4289	−	2.40998i	−0.434037	−	0.0841600i
$821$	2.30951	+	44.0681i	0.0806025	+	1.53799i	0.677411	+	0.735604i	$0.263102\pi$
$821$	2.30951	+	44.0681i	0.0806025	+	1.53799i	−0.596809	+	0.802383i	$0.703565\pi$
$822$	−1.96409	−	0.399125i	−0.0685054	−	0.0139211i
$823$	26.6313	−	11.8570i	0.928307	−	0.413309i	0.113827	−	0.993501i	$-0.463689\pi$
$823$	26.6313	−	11.8570i	0.928307	−	0.413309i	0.814480	+	0.580192i	$0.197022\pi$
$824$	−35.7383	−	17.0159i	−1.24500	−	0.592776i
$825$	2.27420	+	27.7935i	0.0791776	+	0.967644i
$826$	0.372562	−	2.49682i	0.0129631	−	0.0868755i
$827$	6.61001	−	1.04692i	0.229853	−	0.0364051i	−0.0404455	−	0.999182i	$-0.512878\pi$
$827$	6.61001	−	1.04692i	0.229853	−	0.0364051i	0.270298	+	0.962777i	$0.412878\pi$
$828$	72.9269	+	6.34631i	2.53438	+	0.220549i
$829$	−14.3310	−	12.9037i	−0.497737	−	0.448165i	0.381625	−	0.924317i	$-0.375364\pi$
$829$	−14.3310	−	12.9037i	−0.497737	−	0.448165i	−0.879363	+	0.476152i	$0.842031\pi$
$830$	−0.754415	+	17.3711i	−0.0261861	+	0.602959i
$831$	−30.0492	+	21.8320i	−1.04239	+	0.757344i
$832$	−17.4573	+	22.9617i	−0.605225	+	0.796055i
$833$	−7.97051	+	24.5307i	−0.276162	+	0.849939i
$834$	28.7330	−	7.97552i	0.994943	−	0.276170i
$835$	8.82791	−	5.09680i	0.305503	−	0.176382i
$836$	22.4371	+	28.0018i	0.776004	+	0.968463i
$837$	16.5777	−	16.5777i	0.573010	−	0.573010i
$838$	−15.0743	+	15.3468i	−0.520733	+	0.530147i
$839$	50.6201	+	2.65289i	1.74760	+	0.0915879i	0.899138	−	0.437666i	$-0.144195\pi$
$839$	50.6201	+	2.65289i	1.74760	+	0.0915879i	0.848464	+	0.529254i	$0.177528\pi$
$840$	−4.96330	+	37.9031i	−0.171250	+	1.30778i
$841$	0.420829	+	4.00392i	0.0145114	+	0.138066i
$842$	6.44463	+	7.02982i	0.222097	+	0.242263i
$843$	2.09807	+	40.0337i	0.0722615	+	1.37883i
$844$	1.45043	−	0.677162i	0.0499258	−	0.0233089i
$845$	−17.9603	+	0.110051i	−0.617852	+	0.00378587i
$846$	8.92898	+	3.87998i	0.306985	+	0.133396i
$847$	−23.0545	+	32.1495i	−0.792162	+	1.10467i
$848$	−33.1194	+	16.1913i	−1.13733	+	0.556013i
$849$	−12.9225	−	29.0244i	−0.443498	−	0.996113i
$850$	18.9641	−	1.16429i	0.650462	−	0.0399349i
$851$	−24.2230	−	37.3002i	−0.830355	−	1.27864i
$852$	−80.5695	+	5.67140i	−2.76027	+	0.194299i
$853$	21.4471	+	3.39688i	0.734334	+	0.116307i	0.512391	−	0.858752i	$-0.328760\pi$
$853$	21.4471	+	3.39688i	0.734334	+	0.116307i	0.221943	+	0.975060i	$0.428760\pi$
$854$	−12.9154	−	9.20794i	−0.441955	−	0.315089i
$855$	32.1525	−	6.83423i	1.09959	−	0.233726i
$856$	−40.1089	−	24.5405i	−1.37089	−	0.838777i
$857$			42.8791i			1.46472i	0.680916	+	0.732361i	$0.261582\pi$
$857$			42.8791i			1.46472i	−0.680916	+	0.732361i	$0.738418\pi$
$858$	−1.71237	+	45.9671i	−0.0584594	+	1.56929i
$859$		−	38.7630i		−	1.32258i	−0.750133	−	0.661288i	$-0.770010\pi$
$859$		−	38.7630i		−	1.32258i	0.750133	−	0.661288i	$-0.229990\pi$
$860$	−17.0414	−	2.38698i	−0.581106	−	0.0813953i
$861$	43.8418	−	9.31886i	1.49412	−	0.317586i
$862$	20.3764	−	28.5807i	0.694024	−	0.973461i
$863$	37.1862	+	5.88972i	1.26583	+	0.200488i	0.753012	−	0.658007i	$-0.228600\pi$
$863$	37.1862	+	5.88972i	1.26583	+	0.200488i	0.512822	+	0.858495i	$0.328600\pi$
$864$	19.7200	−	8.60163i	0.670889	−	0.292633i
$865$	7.35821	+	11.3306i	0.250187	+	0.385254i
$866$	1.23610	+	20.1337i	0.0420043	+	0.684170i
$867$	2.08968	+	4.69350i	0.0709692	+	0.159400i
$868$	−42.4085	−	12.9441i	−1.43944	−	0.439353i
$869$	1.53109	−	3.23580i	0.0519387	−	0.109767i
$870$	10.5845	−	24.3581i	0.358848	−	0.825816i
$871$	−28.8139	+	19.9335i	−0.976323	+	0.675421i
$872$	−0.378317	−	14.0744i	−0.0128114	−	0.476618i
$873$	−2.87269	−	54.8142i	−0.0972259	−	1.85518i
$874$	−46.9267	+	43.0204i	−1.58732	+	1.45519i
$875$	−4.20247	−	39.9839i	−0.142070	−	1.35170i
$876$	30.7635	−	8.83669i	1.03940	−	0.298564i
$877$	12.7010	+	0.665634i	0.428884	+	0.0224768i	0.265557	−	0.964095i	$-0.414444\pi$
$877$	12.7010	+	0.665634i	0.428884	+	0.0224768i	0.163327	+	0.986572i	$0.447777\pi$
$878$	3.33155	+	3.27240i	0.112435	+	0.110438i
$879$	4.85820	−	4.85820i	0.163863	−	0.163863i
$880$	16.4359	+	8.11213i	0.554053	+	0.273460i
$881$	22.1141	−	12.7676i	0.745044	−	0.430151i	−0.0788565	−	0.996886i	$-0.525127\pi$
$881$	22.1141	−	12.7676i	0.745044	−	0.430151i	0.823900	+	0.566735i	$0.191794\pi$
$882$	−9.87319	−	35.5697i	−0.332448	−	1.19769i
$883$	−0.896500	+	2.75914i	−0.0301696	+	0.0928526i	−0.965007	−	0.262222i	$-0.915545\pi$
$883$	−0.896500	+	2.75914i	−0.0301696	+	0.0928526i	0.934838	+	0.355075i	$0.115545\pi$
$884$	31.2885	+	1.80298i	1.05235	+	0.0606406i
$885$	−1.50895	+	1.09632i	−0.0507229	+	0.0368523i
$886$	−22.3983	−	0.972742i	−0.752484	−	0.0326799i
$887$	41.0245	+	36.9386i	1.37747	+	1.24028i	0.940058	+	0.341016i	$0.110771\pi$
$887$	41.0245	+	36.9386i	1.37747	+	1.24028i	0.437411	+	0.899262i	$0.355896\pi$
$888$	−36.1474	−	19.5940i	−1.21303	−	0.657531i
$889$	−39.2911	+	6.22310i	−1.31778	+	0.208716i
$890$	−11.5211	−	1.71911i	−0.386187	−	0.0576247i
$891$	−4.91395	+	8.07498i	−0.164624	+	0.270522i
$892$	−18.1941	−	0.626930i	−0.609183	−	0.0209912i
$893$	−7.73474	+	3.44373i	−0.258833	+	0.115240i
$894$	6.88817	−	33.8965i	0.230375	−	1.13367i
$895$	−1.10476	−	21.0802i	−0.0369282	−	0.704632i
$896$	−31.8850	−	25.2783i	−1.06520	−	0.844490i
$897$	−81.5766	+	2.38628i	−2.72376	+	0.0796755i
$898$	−15.1083	−	1.45124i	−0.504170	−	0.0484284i
$899$	25.8358	+	16.7780i	0.861673	+	0.559577i
$900$	−21.7089	+	16.3746i	−0.723631	+	0.545820i
$901$	34.6890	+	20.0277i	1.15566	+	0.667220i
$902$	2.54792	−	21.3392i	0.0848365	−	0.710517i
$903$	58.8442	−	15.7673i	1.95821	−	0.524701i
$904$	7.85664	+	0.200282i	0.261308	+	0.00666127i
$905$	−20.4354	+	10.4123i	−0.679295	+	0.346118i
$906$	−41.2877	+	57.9115i	−1.37169	+	1.92398i
$907$	−2.59607	−	1.15584i	−0.0862009	−	0.0383791i	0.363183	−	0.931718i	$-0.381690\pi$
$907$	−2.59607	−	1.15584i	−0.0862009	−	0.0383791i	−0.449384	+	0.893339i	$0.648357\pi$
$908$	18.1047	+	8.81989i	0.600825	+	0.292698i
$909$	−7.14432	+	2.32133i	−0.236962	+	0.0769936i
$910$	0.358711	−	25.3337i	0.0118911	−	0.839806i
$911$	−9.40190	+	12.9406i	−0.311499	+	0.428741i	−0.935848	−	0.352404i	$-0.885364\pi$
$911$	−9.40190	+	12.9406i	−0.311499	+	0.428741i	0.624349	+	0.781145i	$0.285364\pi$
$912$	−19.1096	+	55.6653i	−0.632781	+	1.84326i
$913$	−29.5021	+	0.864170i	−0.976378	+	0.0285998i
$914$	−17.5420	+	12.9867i	−0.580239	+	0.429562i
$915$	1.83329	+	11.5749i	0.0606066	+	0.382655i
$916$	6.63396	+	7.89862i	0.219192	+	0.260978i
$917$	−2.80442	−	4.31842i	−0.0926100	−	0.142607i
$918$	−19.7181	−	12.5554i	−0.650794	−	0.414390i
$919$	−19.2629	+	2.02461i	−0.635424	+	0.0667857i	−0.416763	−	0.909015i	$-0.636835\pi$
$919$	−19.2629	+	2.02461i	−0.635424	+	0.0667857i	−0.218661	+	0.975801i	$0.570169\pi$
$920$	−12.4237	+	30.0523i	−0.409596	+	0.990794i
$921$	63.8784	+	41.4831i	2.10487	+	1.36692i
$922$	1.13341	+	1.92313i	0.0373269	+	0.0633350i
$923$	52.6063	−	9.91681i	1.73156	−	0.326416i
$924$	−64.7815	−	3.73040i	−2.13115	−	0.122721i
$925$	15.9580	+	4.27594i	0.524697	+	0.140592i
$926$	−20.4763	+	36.2113i	−0.672894	+	1.18998i
$927$	−41.1859	−	45.7416i	−1.35272	−	1.50235i
$928$	16.4428	+	22.9957i	0.539762	+	0.754871i
$929$	13.0725	+	10.5859i	0.428896	+	0.347313i	0.819335	−	0.573316i	$-0.194343\pi$
$929$	13.0725	+	10.5859i	0.428896	+	0.347313i	−0.390438	+	0.920629i	$0.627676\pi$
$930$	15.1336	+	29.0550i	0.496250	+	0.952750i
$931$	28.6044	+	14.5747i	0.937473	+	0.477666i
$932$	3.33742	−	38.3510i	0.109321	−	1.25623i
$933$	91.1332	+	9.57849i	2.98357	+	0.313586i
$934$	3.60122	−	4.52950i	0.117835	−	0.148210i
$935$	−2.66067	−	19.7363i	−0.0870133	−	0.645446i
$936$	−38.7599	+	22.5726i	−1.26691	+	0.737809i
$937$	−30.2417	−	21.9719i	−0.987952	−	0.717789i	−0.0284804	−	0.999594i	$-0.509067\pi$
$937$	−30.2417	−	21.9719i	−0.987952	−	0.717789i	−0.959472	+	0.281805i	$0.909067\pi$
$938$	−27.2891	−	41.2086i	−0.891021	−	1.34551i
$939$	14.0242	+	12.6274i	0.457662	+	0.412080i
$940$	−2.83585	+	3.26532i	−0.0924953	+	0.106503i
$941$	−3.88031	+	24.4993i	−0.126494	+	0.798654i	0.840117	+	0.542406i	$0.182486\pi$
$941$	−3.88031	+	24.4993i	−0.126494	+	0.798654i	−0.966611	+	0.256248i	$0.917514\pi$
$942$	58.4868	−	9.80123i	1.90560	−	0.319341i
$943$	38.0767	+	1.99552i	1.23995	+	0.0649830i
$944$	−0.174862	−	1.97763i	−0.00569129	−	0.0643663i
$945$	−9.44887	+	16.3659i	−0.307372	+	0.532383i
$946$	1.94039	−	29.1452i	0.0630876	−	0.947593i
$947$	−22.1927	−	5.94653i	−0.721167	−	0.193236i	−0.120475	−	0.992716i	$-0.538442\pi$
$947$	−22.1927	−	5.94653i	−0.721167	−	0.193236i	−0.600692	+	0.799480i	$0.705108\pi$
$948$	5.82744	−	0.718255i	0.189267	−	0.0233278i
$949$	−19.5745	+	8.17838i	−0.635415	+	0.265481i
$950$	2.26113	−	23.5398i	0.0733608	−	0.763732i
$951$	−0.576128	−	1.50087i	−0.0186822	−	0.0486689i
$952$	−3.43816	+	44.0767i	−0.111431	+	1.42853i
$953$	−8.12573	+	38.2285i	−0.263218	+	1.23834i	0.625622	+	0.780126i	$0.284845\pi$
$953$	−8.12573	+	38.2285i	−0.263218	+	1.23834i	−0.888840	+	0.458217i	$0.848488\pi$
$954$	−57.2187	+	3.51292i	−1.85252	+	0.113735i
$955$	21.8905	+	8.40296i	0.708358	+	0.271913i
$956$	3.25668	−	5.21714i	0.105329	−	0.168734i
$957$	42.5429	+	14.9168i	1.37522	+	0.482192i
$958$	18.8395	−	13.9473i	0.608678	−	0.450616i
$959$	−0.195876	+	1.86364i	−0.00632517	+	0.0601799i
$960$	3.18390	+	29.8939i	0.102760	+	0.964823i
$961$	−6.65650	+	2.16283i	−0.214726	+	0.0697687i
$962$	25.3007	+	10.1253i	0.815728	+	0.326453i
$963$	−42.9779	−	59.1540i	−1.38494	−	1.90621i
$964$	6.60990	−	6.85109i	0.212891	−	0.220659i
$965$	−29.6452	+	6.30129i	−0.954314	+	0.202846i
$966$	−1.03126	−	115.121i	−0.0331802	−	3.70397i
$967$	13.9602	+	13.9602i	0.448931	+	0.448931i	0.894999	−	0.446068i	$-0.147176\pi$
$967$	13.9602	+	13.9602i	0.448931	+	0.448931i	−0.446068	+	0.894999i	$0.647176\pi$
$968$	−11.7077	+	28.8259i	−0.376299	+	0.926498i
$969$	61.7680	−	16.5507i	1.98427	−	0.531684i
$970$	23.6085	+	6.09975i	0.758022	+	0.195851i
$971$	−43.5222	+	39.1876i	−1.39669	+	1.25759i	−0.469538	+	0.882912i	$0.655580\pi$
$971$	−43.5222	+	39.1876i	−1.39669	+	1.25759i	−0.927156	+	0.374677i	$0.877754\pi$
$972$	−38.3175	+	0.686554i	−1.22904	+	0.0220212i
$973$	−9.99140	−	26.0285i	−0.320310	−	0.834435i
$974$	−0.673333	−	3.03389i	−0.0215750	−	0.0972121i
$975$	21.9262	−	20.9352i	0.702199	−	0.670463i
$976$	−11.5703	−	4.66225i	−0.370355	−	0.149235i
$977$	−17.9634	−	22.1830i	−0.574701	−	0.709697i	0.404053	−	0.914736i	$-0.367601\pi$
$977$	−17.9634	−	22.1830i	−0.574701	−	0.709697i	−0.978754	+	0.205039i	$0.934268\pi$
$978$	61.9630	−	7.07430i	1.98136	−	0.226211i
$979$	1.49021	−	19.7170i	0.0476272	−	0.630158i
$980$	16.3889	+	0.564729i	0.523525	+	0.0180396i
$981$	7.84605	−	20.4397i	0.250505	−	0.652588i
$982$	4.13436	−	8.29704i	0.131933	−	0.264769i
$983$	−22.3457	−	11.3857i	−0.712717	−	0.363147i	0.0597407	−	0.998214i	$-0.480973\pi$
$983$	−22.3457	−	11.3857i	−0.712717	−	0.363147i	−0.772457	+	0.635067i	$0.780973\pi$
$984$	31.8050	−	15.1973i	1.01390	−	0.484471i
$985$	2.36596	−	5.31404i	0.0753859	−	0.169319i
$986$	10.7503	−	28.7731i	0.342358	−	0.916324i
$987$	4.73140	−	14.5618i	0.150602	−	0.463506i
$988$	8.30854	−	38.1129i	0.264330	−	1.21253i
$989$	51.8240			1.64791
$990$	18.7704	+	21.4480i	0.596562	+	0.681662i
$991$	27.5588	−	15.9111i	0.875435	−	0.505433i	0.00628457	−	0.999980i	$-0.498000\pi$
$991$	27.5588	−	15.9111i	0.875435	−	0.505433i	0.869151	+	0.494548i	$0.164666\pi$
$992$	−34.8082	−	2.08858i	−1.10516	−	0.0663126i
$993$	−26.4685	−	51.9474i	−0.839954	−	1.64850i
$994$	12.4811	+	74.4781i	0.395875	+	2.36230i
$995$	−21.1751	−	17.1473i	−0.671297	−	0.543606i
$996$	−27.0893	−	40.1215i	−0.858356	−	1.27130i
$997$	−31.2997	−	6.65296i	−0.991271	−	0.210701i	−0.316391	−	0.948629i	$-0.602471\pi$
$997$	−31.2997	−	6.65296i	−0.991271	−	0.210701i	−0.674880	+	0.737928i	$0.735805\pi$
$998$	−10.7324	+	52.8139i	−0.339728	+	1.67179i
$999$	−12.7918	−	15.7965i	−0.404714	−	0.499780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bs.a.15.8	✓	1280
4.3	odd	2	inner	572.2.bs.a.15.55	yes	1280
11.3	even	5	inner	572.2.bs.a.223.42	yes	1280
13.7	odd	12	inner	572.2.bs.a.59.23	yes	1280
44.3	odd	10	inner	572.2.bs.a.223.23	yes	1280
52.7	even	12	inner	572.2.bs.a.59.42	yes	1280
143.124	odd	60	inner	572.2.bs.a.267.55	yes	1280
572.267	even	60	inner	572.2.bs.a.267.8	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bs.a.15.8	✓	1280	1.1	even	1	trivial
572.2.bs.a.15.55	yes	1280	4.3	odd	2	inner
572.2.bs.a.59.23	yes	1280	13.7	odd	12	inner
572.2.bs.a.59.42	yes	1280	52.7	even	12	inner
572.2.bs.a.223.23	yes	1280	44.3	odd	10	inner
572.2.bs.a.223.42	yes	1280	11.3	even	5	inner
572.2.bs.a.267.8	yes	1280	572.267	even	60	inner
572.2.bs.a.267.55	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)

\(f(q)\)	\(=\)	\(q+(-1.36269 + 0.378247i) q^{2} +(0.565515 + 2.66054i) q^{3} +(1.71386 - 1.03087i) q^{4} +(-0.216128 + 1.36458i) q^{5} +(-1.77696 - 3.41159i) q^{6} +(-3.01627 + 1.95879i) q^{7} +(-1.94554 + 2.05302i) q^{8} +(-4.01801 + 1.78893i) q^{9} +O(q^{10})\)	\(q+(-1.36269 + 0.378247i) q^{2} +(0.565515 + 2.66054i) q^{3} +(1.71386 - 1.03087i) q^{4} +(-0.216128 + 1.36458i) q^{5} +(-1.77696 - 3.41159i) q^{6} +(-3.01627 + 1.95879i) q^{7} +(-1.94554 + 2.05302i) q^{8} +(-4.01801 + 1.78893i) q^{9} +(-0.221632 - 1.94125i) q^{10} +(3.25920 - 0.614525i) q^{11} +(3.71188 + 3.97681i) q^{12} +(-2.74884 - 2.33321i) q^{13} +(3.36934 - 3.81012i) q^{14} +(-3.75273 + 0.196672i) q^{15} +(1.87462 - 3.53353i) q^{16} +(-4.32232 + 0.454295i) q^{17} +(4.79865 - 3.95757i) q^{18} +(-0.283108 + 5.40202i) q^{19} +(1.03629 + 2.56149i) q^{20} +(-6.91717 - 6.91717i) q^{21} +(-4.20884 + 2.07019i) q^{22} +(-4.16088 - 7.20685i) q^{23} +(-6.56236 - 4.01516i) q^{24} +(2.93993 + 0.955240i) q^{25} +(4.62836 + 2.13970i) q^{26} +(-2.23549 - 3.07688i) q^{27} +(-3.15020 + 6.46646i) q^{28} +(3.34391 - 3.71379i) q^{29} +(5.03942 - 1.68746i) q^{30} +(0.964315 + 6.08844i) q^{31} +(-1.21798 + 5.52418i) q^{32} +(3.47809 + 8.32369i) q^{33} +(5.71816 - 2.25397i) q^{34} +(-2.02102 - 4.53927i) q^{35} +(-5.04215 + 7.20802i) q^{36} +(5.33715 - 0.279708i) q^{37} +(-1.65751 - 7.46837i) q^{38} +(4.65307 - 8.63286i) q^{39} +(-2.38101 - 3.09855i) q^{40} +(-2.49545 + 3.84266i) q^{41} +(12.0424 + 6.80957i) q^{42} +(-3.11377 + 5.39321i) q^{43} +(4.95231 - 4.41301i) q^{44} +(-1.57273 - 5.86952i) q^{45} +(8.39596 + 8.24687i) q^{46} +(0.710577 + 1.39459i) q^{47} +(10.4612 + 2.98924i) q^{48} +(2.41387 - 5.42164i) q^{49} +(-4.36753 - 0.189679i) q^{50} +(-3.65300 - 11.2428i) q^{51} +(-7.11636 - 1.16509i) q^{52} +(-7.45618 - 5.41723i) q^{53} +(4.21010 + 3.34728i) q^{54} +(0.134163 + 4.58023i) q^{55} +(1.84684 - 10.0034i) q^{56} +(-14.5324 + 2.30170i) q^{57} +(-3.15199 + 6.32558i) q^{58} +(0.416262 - 0.270324i) q^{59} +(-6.22890 + 4.20564i) q^{60} +(-0.325979 - 3.10149i) q^{61} +(-3.61700 - 7.93192i) q^{62} +(8.61526 - 13.2663i) q^{63} +(-0.429767 - 7.98845i) q^{64} +(3.77794 - 3.24673i) q^{65} +(-7.88797 - 10.0270i) q^{66} +(2.51507 - 9.38638i) q^{67} +(-6.93953 + 5.23434i) q^{68} +(16.8211 - 15.1457i) q^{69} +(4.47099 + 5.42119i) q^{70} +(-9.34374 + 11.5386i) q^{71} +(4.14448 - 11.7295i) q^{72} +(2.67119 - 5.24250i) q^{73} +(-7.16710 + 2.39992i) q^{74} +(-0.878880 + 8.36199i) q^{75} +(5.08356 + 9.55014i) q^{76} +(-8.62689 + 8.23765i) q^{77} +(-3.07535 + 13.5239i) q^{78} +(0.634419 - 0.873202i) q^{79} +(4.41660 + 3.32175i) q^{80} +(-1.90707 + 2.11802i) q^{81} +(1.94706 - 6.18026i) q^{82} +(-8.78948 - 1.39212i) q^{83} +(-18.9857 - 4.72436i) q^{84} +(0.314254 - 5.99632i) q^{85} +(2.20314 - 8.52705i) q^{86} +(11.7717 + 6.79640i) q^{87} +(-5.07926 + 7.88677i) q^{88} +(1.54304 - 5.75871i) q^{89} +(4.36328 + 7.40346i) q^{90} +(12.8615 + 1.65318i) q^{91} +(-14.5605 - 8.06220i) q^{92} +(-15.6532 + 6.00870i) q^{93} +(-1.49579 - 1.63162i) q^{94} +(-7.31028 - 1.55385i) q^{95} +(-15.3861 - 0.116489i) q^{96} +(-4.47236 + 11.6509i) q^{97} +(-1.23864 + 8.30107i) q^{98} +(-11.9961 + 8.29966i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more