LMFDB - Embedded newform 285.2.bi.a.233.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(17,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("285.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.bi (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$36$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			233.10
Character	$\chi$	$=$	285.233
Dual form			285.2.bi.a.137.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26745 - 0.591021i) q^{2} +(-0.999391 + 1.41464i) q^{3} +(-0.0284545 - 0.0339107i) q^{4} +(-1.43862 + 1.71183i) q^{5} +(2.10276 - 1.20233i) q^{6} +(1.86072 + 0.498578i) q^{7} +(0.739927 + 2.76144i) q^{8} +(-1.00243 - 2.82757i) q^{9} +O(q^{10})$	\(q+(-1.26745 - 0.591021i) q^{2} +(-0.999391 + 1.41464i) q^{3} +(-0.0284545 - 0.0339107i) q^{4} +(-1.43862 + 1.71183i) q^{5} +(2.10276 - 1.20233i) q^{6} +(1.86072 + 0.498578i) q^{7} +(0.739927 + 2.76144i) q^{8} +(-1.00243 - 2.82757i) q^{9} +(2.83511 - 1.31940i) q^{10} +(-2.08354 - 1.20293i) q^{11} +(0.0764087 - 0.00636287i) q^{12} +(0.512857 - 0.732435i) q^{13} +(-2.06369 - 1.73165i) q^{14} +(-0.983881 - 3.74593i) q^{15} +(0.678879 - 3.85011i) q^{16} +(-4.96710 - 2.31620i) q^{17} +(-0.400616 + 4.17625i) q^{18} +(-4.35855 - 0.0553822i) q^{19} +(0.0989847 + 7.55761e-5i) q^{20} +(-2.56490 + 2.13398i) q^{21} +(1.92982 + 2.75607i) q^{22} +(0.205071 - 2.34397i) q^{23} +(-4.64594 - 1.71303i) q^{24} +(-0.860721 - 4.92536i) q^{25} +(-1.08290 + 0.625215i) q^{26} +(5.00182 + 1.40776i) q^{27} +(-0.0360386 - 0.0772851i) q^{28} +(-0.0141094 - 0.00513539i) q^{29} +(-0.966904 + 5.32927i) q^{30} +(-4.78456 - 8.28710i) q^{31} +(0.143605 - 0.205089i) q^{32} +(3.78400 - 1.74527i) q^{33} +(4.92663 + 5.87133i) q^{34} +(-3.53035 + 2.46797i) q^{35} +(-0.0673610 + 0.114450i) q^{36} +(-0.248890 + 0.248890i) q^{37} +(5.49150 + 2.64619i) q^{38} +(0.523591 + 1.45750i) q^{39} +(-5.79160 - 2.70605i) q^{40} +(-4.09982 - 0.722909i) q^{41} +(4.51210 - 1.18880i) q^{42} +(1.01332 + 11.5823i) q^{43} +(0.0184937 + 0.104883i) q^{44} +(6.28244 + 2.35181i) q^{45} +(-1.64525 + 2.84966i) q^{46} +(-0.400436 - 0.858739i) q^{47} +(4.76807 + 4.80814i) q^{48} +(-2.84849 - 1.64457i) q^{49} +(-1.82007 + 6.75134i) q^{50} +(8.24067 - 4.71189i) q^{51} +(-0.0394305 + 0.00344972i) q^{52} +(0.249084 - 2.84705i) q^{53} +(-5.50754 - 4.74044i) q^{54} +(5.05665 - 1.83610i) q^{55} +5.50718i q^{56} +(4.43424 - 6.11044i) q^{57} +(0.0148478 + 0.0148478i) q^{58} +(11.9950 - 4.36582i) q^{59} +(-0.0990313 + 0.139953i) q^{60} +(-4.73372 + 3.97206i) q^{61} +(1.16633 + 13.3312i) q^{62} +(-0.455487 - 5.76109i) q^{63} +(-7.07469 + 4.08457i) q^{64} +(0.515996 + 1.93162i) q^{65} +(-5.82751 - 0.0243825i) q^{66} +(0.928483 - 0.432959i) q^{67} +(0.0627923 + 0.234344i) q^{68} +(3.11094 + 2.63265i) q^{69} +(5.93316 - 1.04151i) q^{70} +(2.91179 - 3.47013i) q^{71} +(7.06643 - 4.86036i) q^{72} +(-7.21804 + 5.05413i) q^{73} +(0.462555 - 0.168356i) q^{74} +(7.82783 + 3.70475i) q^{75} +(0.122142 + 0.149377i) q^{76} +(-3.27713 - 3.27713i) q^{77} +(0.197788 - 2.15676i) q^{78} +(15.0598 + 2.65545i) q^{79} +(5.61408 + 6.70099i) q^{80} +(-6.99025 + 5.66890i) q^{81} +(4.76906 + 3.33933i) q^{82} +(-15.4623 - 4.14311i) q^{83} +(0.145347 + 0.0262562i) q^{84} +(11.1107 - 5.17069i) q^{85} +(5.56103 - 15.2788i) q^{86} +(0.0213655 - 0.0148275i) q^{87} +(1.78017 - 6.64367i) q^{88} +(0.869065 + 4.92871i) q^{89} +(-6.57270 - 6.69385i) q^{90} +(1.31946 - 1.10716i) q^{91} +(-0.0853210 + 0.0597424i) q^{92} +(16.5049 + 1.51361i) q^{93} +1.32507i q^{94} +(6.36512 - 7.38142i) q^{95} +(0.146610 + 0.408114i) q^{96} +(-1.89890 + 4.07220i) q^{97} +(2.63833 + 3.76793i) q^{98} +(-1.31276 + 7.09721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.26745	−	0.591021i	−0.896222	−	0.417915i	−0.0807650	−	0.996733i	$-0.525736\pi$
$2$	−1.26745	−	0.591021i	−0.896222	−	0.417915i	−0.815457	+	0.578818i	$0.803514\pi$
$3$	−0.999391	+	1.41464i	−0.576999	+	0.816745i
$3$	−0.999391	+	1.41464i	−0.576999	+	0.816745i
$4$	−0.0284545	−	0.0339107i	−0.0142272	−	0.0169554i
$5$	−1.43862	+	1.71183i	−0.643372	+	0.765553i
$5$	−1.43862	+	1.71183i	−0.643372	+	0.765553i
$6$	2.10276	−	1.20233i	0.858449	−	0.490848i
$7$	1.86072	+	0.498578i	0.703285	+	0.188445i	0.592702	−	0.805422i	$-0.298061\pi$
$7$	1.86072	+	0.498578i	0.703285	+	0.188445i	0.110584	+	0.993867i	$0.464728\pi$
$8$	0.739927	+	2.76144i	0.261604	+	0.976318i
$9$	−1.00243	−	2.82757i	−0.334145	−	0.942522i
$10$	2.83511	−	1.31940i	0.896541	−	0.417231i
$11$	−2.08354	−	1.20293i	−0.628212	−	0.362698i	0.151847	−	0.988404i	$-0.451478\pi$
$11$	−2.08354	−	1.20293i	−0.628212	−	0.362698i	−0.780059	+	0.625706i	$0.784811\pi$
$12$	0.0764087	−	0.00636287i	0.0220573	−	0.00183680i
$13$	0.512857	−	0.732435i	0.142241	−	0.203141i	−0.741710	−	0.670721i	$-0.765985\pi$
$13$	0.512857	−	0.732435i	0.142241	−	0.203141i	0.883951	+	0.467580i	$0.154874\pi$
$14$	−2.06369	−	1.73165i	−0.551546	−	0.462802i
$15$	−0.983881	−	3.74593i	−0.254037	−	0.967195i
$16$	0.678879	−	3.85011i	0.169720	−	0.962528i
$17$	−4.96710	−	2.31620i	−1.20470	−	0.561761i	−0.286577	−	0.958057i	$-0.592517\pi$
$17$	−4.96710	−	2.31620i	−1.20470	−	0.561761i	−0.918122	+	0.396297i	$0.870295\pi$
$18$	−0.400616	+	4.17625i	−0.0944261	+	0.984353i
$19$	−4.35855	−	0.0553822i	−0.999919	−	0.0127055i
$19$	−4.35855	−	0.0553822i	−0.999919	−	0.0127055i
$20$	0.0989847		7.55761e-5i	0.0221336		1.68993e-5i
$21$	−2.56490	+	2.13398i	−0.559706	+	0.465672i
$22$	1.92982	+	2.75607i	0.411440	+	0.587597i
$23$	0.205071	−	2.34397i	0.0427603	−	0.488752i	−0.944376	−	0.328869i	$-0.893333\pi$
$23$	0.205071	−	2.34397i	0.0427603	−	0.488752i	0.987136	−	0.159883i	$-0.0511118\pi$
$24$	−4.64594	−	1.71303i	−0.948348	−	0.349671i
$25$	−0.860721	−	4.92536i	−0.172144	−	0.985072i
$26$	−1.08290	+	0.625215i	−0.212375	+	0.122615i
$27$	5.00182	+	1.40776i	0.962601	+	0.270923i
$28$	−0.0360386	−	0.0772851i	−0.00681066	−	0.0146055i
$29$	−0.0141094	−	0.00513539i	−0.00262004	−	0.000953618i	0.340710	−	0.940169i	$-0.389333\pi$
$29$	−0.0141094	−	0.00513539i	−0.00262004	−	0.000953618i	−0.343330	+	0.939215i	$0.611555\pi$
$30$	−0.966904	+	5.32927i	−0.176532	+	0.972987i
$31$	−4.78456	−	8.28710i	−0.859332	−	1.48841i	−0.872567	−	0.488494i	$-0.837546\pi$
$31$	−4.78456	−	8.28710i	−0.859332	−	1.48841i	0.0132352	−	0.999912i	$-0.495787\pi$
$32$	0.143605	−	0.205089i	0.0253860	−	0.0362549i
$33$	3.78400	−	1.74527i	0.658709	−	0.303812i
$34$	4.92663	+	5.87133i	0.844910	+	1.00692i
$35$	−3.53035	+	2.46797i	−0.596739	+	0.417162i
$36$	−0.0673610	+	0.114450i	−0.0112268	+	0.0190750i
$37$	−0.248890	+	0.248890i	−0.0409173	+	0.0409173i	−0.727269	−	0.686352i	$-0.759211\pi$
$37$	−0.248890	+	0.248890i	−0.0409173	+	0.0409173i	0.686352	+	0.727269i	$0.259211\pi$
$38$	5.49150	+	2.64619i	0.890840	+	0.429268i
$39$	0.523591	+	1.45750i	0.0838416	+	0.233387i
$40$	−5.79160	−	2.70605i	−0.915732	−	0.427864i
$41$	−4.09982	−	0.722909i	−0.640285	−	0.112899i	−0.155926	−	0.987769i	$-0.549836\pi$
$41$	−4.09982	−	0.722909i	−0.640285	−	0.112899i	−0.484359	+	0.874869i	$0.660947\pi$
$42$	4.51210	−	1.18880i	0.696232	−	0.183436i
$43$	1.01332	+	11.5823i	0.154529	+	1.76628i	0.538208	+	0.842812i	$0.319101\pi$
$43$	1.01332	+	11.5823i	0.154529	+	1.76628i	−0.383679	+	0.923467i	$0.625343\pi$
$44$	0.0184937	+	0.104883i	0.00278804	+	0.0158117i
$45$	6.28244	+	2.35181i	0.936530	+	0.350587i
$46$	−1.64525	+	2.84966i	−0.242579	+	0.420160i
$47$	−0.400436	−	0.858739i	−0.0584097	−	0.125260i	0.874936	−	0.484238i	$-0.160903\pi$
$47$	−0.400436	−	0.858739i	−0.0584097	−	0.125260i	−0.933346	+	0.358978i	$0.883125\pi$
$48$	4.76807	+	4.80814i	0.688212	+	0.693995i
$49$	−2.84849	−	1.64457i	−0.406927	−	0.234939i
$50$	−1.82007	+	6.75134i	−0.257397	+	0.954784i
$51$	8.24067	−	4.71189i	1.15393	−	0.659797i
$52$	−0.0394305	+	0.00344972i	−0.00546802	+	0.000478390i
$53$	0.249084	−	2.84705i	0.0342143	−	0.391072i	−0.959709	−	0.280996i	$-0.909335\pi$
$53$	0.249084	−	2.84705i	0.0342143	−	0.391072i	0.993923	−	0.110076i	$-0.0351093\pi$
$54$	−5.50754	−	4.74044i	−0.749481	−	0.645092i
$55$	5.05665	−	1.83610i	0.681839	−	0.247580i
$56$			5.50718i			0.735928i
$57$	4.43424	−	6.11044i	0.587329	−	0.809348i
$58$	0.0148478	+	0.0148478i	0.00194961	+	0.00194961i
$59$	11.9950	−	4.36582i	1.56161	−	0.568381i	0.590508	−	0.807032i	$-0.298927\pi$
$59$	11.9950	−	4.36582i	1.56161	−	0.568381i	0.971105	+	0.238651i	$0.0767053\pi$
$60$	−0.0990313	+	0.139953i	−0.0127849	+	0.0180678i
$61$	−4.73372	+	3.97206i	−0.606091	+	0.508571i	−0.893397	−	0.449268i	$-0.851685\pi$
$61$	−4.73372	+	3.97206i	−0.606091	+	0.508571i	0.287306	+	0.957839i	$0.407240\pi$
$62$	1.16633	+	13.3312i	0.148124	+	1.69307i
$63$	−0.455487	−	5.76109i	−0.0573859	−	0.725829i
$64$	−7.07469	+	4.08457i	−0.884336	+	0.510572i
$65$	0.515996	+	1.93162i	0.0640015	+	0.239588i
$66$	−5.82751	−	0.0243825i	−0.717317	−	0.00300128i
$67$	0.928483	−	0.432959i	0.113432	−	0.0528943i	−0.365074	−	0.930979i	$-0.618956\pi$
$67$	0.928483	−	0.432959i	0.113432	−	0.0528943i	0.478506	+	0.878084i	$0.341178\pi$
$68$	0.0627923	+	0.234344i	0.00761469	+	0.0284184i
$69$	3.11094	+	2.63265i	0.374513	+	0.316933i
$70$	5.93316	−	1.04151i	0.709149	−	0.124484i
$71$	2.91179	−	3.47013i	0.345566	−	0.411829i	−0.565068	−	0.825045i	$-0.691150\pi$
$71$	2.91179	−	3.47013i	0.345566	−	0.411829i	0.910633	+	0.413216i	$0.135594\pi$
$72$	7.06643	−	4.86036i	0.832787	−	0.572799i
$73$	−7.21804	+	5.05413i	−0.844808	+	0.591541i	−0.913840	−	0.406073i	$-0.866898\pi$
$73$	−7.21804	+	5.05413i	−0.844808	+	0.591541i	0.0690324	+	0.997614i	$0.478009\pi$
$74$	0.462555	−	0.168356i	0.0537710	−	0.0195710i
$75$	7.82783	+	3.70475i	0.903879	+	0.427787i
$76$	0.122142	+	0.149377i	0.0140107	+	0.0171348i
$77$	−3.27713	−	3.27713i	−0.373463	−	0.373463i
$78$	0.197788	−	2.15676i	0.0223951	−	0.244205i
$79$	15.0598	+	2.65545i	1.69436	+	0.298761i	0.935718	−	0.352750i	$-0.114753\pi$
$79$	15.0598	+	2.65545i	1.69436	+	0.298761i	0.758640	+	0.651510i	$0.225864\pi$
$80$	5.61408	+	6.70099i	0.627674	+	0.749193i
$81$	−6.99025	+	5.66890i	−0.776694	+	0.629878i
$82$	4.76906	+	3.33933i	0.526655	+	0.368768i
$83$	−15.4623	−	4.14311i	−1.69721	−	0.454766i	−0.724975	−	0.688775i	$-0.758149\pi$
$83$	−15.4623	−	4.14311i	−1.69721	−	0.454766i	−0.972234	+	0.234009i	$0.924815\pi$
$84$	0.145347	+	0.0262562i	0.0158587	+	0.00286479i
$85$	11.1107	−	5.17069i	1.20513	−	0.560841i
$86$	5.56103	−	15.2788i	0.599662	−	1.64756i
$87$	0.0213655	−	0.0148275i	0.00229063	−	0.00158967i
$88$	1.78017	−	6.64367i	0.189766	−	0.708217i
$89$	0.869065	+	4.92871i	0.0921207	+	0.522442i	0.995592	+	0.0937932i	$0.0298993\pi$
$89$	0.869065	+	4.92871i	0.0921207	+	0.522442i	−0.903471	+	0.428649i	$0.858990\pi$
$90$	−6.57270	−	6.69385i	−0.692823	−	0.705593i
$91$	1.31946	−	1.10716i	0.138317	−	0.116062i
$92$	−0.0853210	+	0.0597424i	−0.00889533	+	0.00622857i
$93$	16.5049	+	1.51361i	1.71148	+	0.156954i
$94$			1.32507i			0.136671i
$95$	6.36512	−	7.38142i	0.653047	−	0.757317i
$96$	0.146610	+	0.408114i	0.0149634	+	0.0416529i
$97$	−1.89890	+	4.07220i	−0.192804	+	0.413469i	−0.978816	−	0.204742i	$-0.934364\pi$
$97$	−1.89890	+	4.07220i	−0.192804	+	0.413469i	0.786012	+	0.618211i	$0.212142\pi$
$98$	2.63833	+	3.76793i	0.266512	+	0.380618i
$99$	−1.31276	+	7.09721i	−0.131937	+	0.713297i
$100$	−0.142531	+	0.169336i	−0.0142531	+	0.0169336i
$101$	−2.22952	+	0.393125i	−0.221846	+	0.0391174i	−0.283466	−	0.958982i	$-0.591484\pi$
$101$	−2.22952	+	0.393125i	−0.221846	+	0.0391174i	0.0616203	+	0.998100i	$0.480373\pi$
$102$	−13.2295	+	1.10167i	−1.30991	+	0.109082i
$103$	−12.5493	+	3.36259i	−1.23652	+	0.331325i	−0.817116	−	0.576473i	$-0.804429\pi$
$103$	−12.5493	+	3.36259i	−1.23652	+	0.331325i	−0.419407	+	0.907798i	$0.637762\pi$
$104$	2.40206	+	0.874277i	0.235541	+	0.0857299i
$105$	0.0369121	−	7.46066i	0.00360225	−	0.728086i
$106$	−1.99837	+	3.46127i	−0.194098	+	0.336188i
$107$	0.213352	−	0.796239i	0.0206255	−	0.0769754i	−0.954846	−	0.297101i	$-0.903980\pi$
$107$	0.213352	−	0.796239i	0.0206255	−	0.0769754i	0.975471	+	0.220126i	$0.0706468\pi$
$108$	−0.0945862	−	0.209672i	−0.00910156	−	0.0201757i
$109$	−3.63523	+	4.33229i	−0.348192	+	0.414959i	−0.911508	−	0.411283i	$-0.865081\pi$
$109$	−3.63523	+	4.33229i	−0.348192	+	0.414959i	0.563316	+	0.826241i	$0.309525\pi$
$110$	−7.49422	−	0.661426i	−0.714546	−	0.0630645i
$111$	−0.103352	−	0.600830i	−0.00980978	−	0.0570283i
$112$	3.18278	−	6.82550i	0.300745	−	0.644949i
$113$	−12.4421	+	12.4421i	−1.17046	+	1.17046i	−0.188357	+	0.982101i	$0.560316\pi$
$113$	−12.4421	+	12.4421i	−1.17046	+	1.17046i	−0.982101	+	0.188357i	$0.939684\pi$
$114$	−9.23157	+	5.12395i	−0.864616	+	0.479901i
$115$	3.71746	+	3.72314i	0.346655	+	0.347185i
$116$	0.000227330	0	0.000624584i	2.11071e−5	0	5.79912e-5i
$117$	−2.58511	−	0.715917i	−0.238994	−	0.0661866i
$118$	−17.7833	−	1.55584i	−1.63709	−	0.143227i
$119$	−8.08757	−	6.78628i	−0.741387	−	0.622097i
$120$	9.61617	−	5.48864i	0.877832	−	0.501042i
$121$	−2.60590	−	4.51355i	−0.236900	−	0.410323i
$122$	8.34732	−	2.23666i	0.755731	−	0.202497i
$123$	5.11999	−	5.07732i	0.461654	−	0.457807i
$124$	−0.144879	+	0.398053i	−0.0130106	+	0.0357462i
$125$	9.66963	+	5.61233i	0.864878	+	0.501982i
$126$	−2.82762	+	7.57109i	−0.251905	+	0.674487i
$127$	1.34474	+	0.941597i	0.119326	+	0.0835532i	0.631716	−	0.775200i	$-0.282351\pi$
$127$	1.34474	+	0.941597i	0.119326	+	0.0835532i	−0.512390	+	0.858753i	$0.671240\pi$
$128$	10.8820	−	0.952055i	0.961846	−	0.0841506i
$129$	−17.3975	−	10.1417i	−1.53176	−	0.892929i
$130$	0.487631	−	2.75320i	0.0427680	−	0.241471i
$131$	−6.23310	−	17.1253i	−0.544589	−	1.49625i	−0.840920	−	0.541160i	$-0.817985\pi$
$131$	−6.23310	−	17.1253i	−0.544589	−	1.49625i	0.296331	−	0.955085i	$-0.404237\pi$
$132$	−0.166855	−	0.0786573i	−0.0145229	−	0.00684624i
$133$	−8.08241	−	2.27613i	−0.700834	−	0.197365i
$134$	−1.43269			−0.123766
$135$	−9.60558	+	6.53704i	−0.826717	+	0.562618i
$136$	2.72076	−	15.4302i	0.233303	−	1.32313i
$137$	−8.36571	−	0.731905i	−0.714731	−	0.0625309i	−0.276011	−	0.961155i	$-0.589013\pi$
$137$	−8.36571	−	0.731905i	−0.714731	−	0.0625309i	−0.438720	+	0.898624i	$0.644568\pi$
$138$	−2.38701	−	5.17538i	−0.203196	−	0.440557i
$139$	−5.97025	+	1.05272i	−0.506390	+	0.0892903i	−0.421006	−	0.907058i	$-0.638323\pi$
$139$	−5.97025	+	1.05272i	−0.506390	+	0.0892903i	−0.0853843	+	0.996348i	$0.527212\pi$
$140$	0.184145	+	0.0494922i	0.0155631	+	0.00418285i
$141$	1.61500	+	0.291741i	0.136008	+	0.0245690i
$142$	−5.74146	+	2.67729i	−0.481813	+	0.224673i
$143$	−1.94963	+	0.909127i	−0.163036	+	0.0760250i
$144$	−11.5670	+	1.93991i	−0.963914	+	0.161659i
$145$	0.0290890	−	0.0167649i	0.00241571	−	0.00139225i
$146$	12.1356	−	2.13983i	1.00435	−	0.177094i
$147$	5.17324	−	2.38602i	0.426682	−	0.196796i
$148$	0.0155221	+	0.00135801i	0.00127591	+	0.000111628i
$149$	−1.15171	+	6.53167i	−0.0943518	+	0.535095i	0.900592	+	0.434665i	$0.143133\pi$
$149$	−1.15171	+	6.53167i	−0.0943518	+	0.535095i	−0.994944	+	0.100431i	$0.967978\pi$
$150$	−7.73179	−	9.32199i	−0.631298	−	0.761137i
$151$	−4.83491			−0.393459			−0.196730	−	0.980458i	$-0.563032\pi$
$151$	−4.83491			−0.393459			−0.196730	+	0.980458i	$0.563032\pi$
$152$	−3.07207	−	12.0769i	−0.249178	−	0.979563i
$153$	−1.57000	+	16.3666i	−0.126927	+	1.32316i
$154$	2.21674	+	6.09045i	0.178630	+	0.490782i
$155$	21.0693	+	3.73167i	1.69233	+	0.299735i
$156$	0.0345263	−	0.0592277i	0.00276432	−	0.00474201i
$157$	−18.0413	+	1.57841i	−1.43985	+	0.125970i	−0.780166	−	0.625573i	$-0.784865\pi$
$157$	−18.0413	+	1.57841i	−1.43985	+	0.125970i	−0.659684	+	0.751544i	$0.729310\pi$
$158$	−17.5181	−	12.2663i	−1.39366	−	0.975854i
$159$	3.77862	+	3.19768i	0.299664	+	0.253592i
$160$	0.144484	+	0.540873i	0.0114225	+	0.0427597i
$161$	1.55023	−	4.25923i	0.122175	−	0.335674i
$162$	12.2102	−	3.05365i	0.959326	−	0.239918i
$163$	12.9502	−	3.47000i	1.01434	−	0.271791i	0.286898	−	0.957961i	$-0.407376\pi$
$163$	12.9502	−	3.47000i	1.01434	−	0.271791i	0.727441	+	0.686170i	$0.240709\pi$
$164$	0.0921439	+	0.159598i	0.00719523	+	0.0124625i
$165$	−2.45615	+	8.98834i	−0.191211	+	0.699742i
$166$	17.1490	+	14.3897i	1.33102	+	1.11686i
$167$	8.44249	+	0.738622i	0.653300	+	0.0571563i	0.408987	−	0.912540i	$-0.365882\pi$
$167$	8.44249	+	0.738622i	0.653300	+	0.0571563i	0.244313	+	0.969697i	$0.421438\pi$
$168$	−7.79070	−	5.50383i	−0.601065	−	0.424629i
$169$	4.17282	+	11.4647i	0.320986	+	0.881903i
$170$	−17.1383	−	0.0130853i	−1.31445	−	0.00100360i
$171$	4.21256	+	12.3796i	0.322143	+	0.946691i
$172$	0.363929	−	0.363929i	0.0277494	−	0.0277494i
$173$	−3.08308	+	6.61169i	−0.234402	+	0.502677i	−0.987961	−	0.154703i	$-0.950558\pi$
$173$	−3.08308	+	6.61169i	−0.234402	+	0.502677i	0.753559	+	0.657381i	$0.228336\pi$
$174$	−0.0358431	+	0.00616558i	−0.00271726	+	0.000467412i
$175$	0.854116	−	9.59384i	0.0645651	−	0.725226i
$176$	−6.04590	+	7.20523i	−0.455727	+	0.543114i
$177$	−5.81160	+	21.3318i	−0.436827	+	1.60339i
$178$	1.81148	−	6.76053i	0.135776	−	0.506723i
$179$	−0.881066	+	1.52605i	−0.0658540	+	0.114062i	−0.897072	−	0.441883i	$-0.854310\pi$
$179$	−0.881066	+	1.52605i	−0.0658540	+	0.114062i	0.831219	+	0.555946i	$0.187644\pi$
$180$	−0.0990120	−	0.279961i	−0.00737992	−	0.0208671i
$181$	−10.3899	−	3.78163i	−0.772278	−	0.281086i	−0.0743289	−	0.997234i	$-0.523681\pi$
$181$	−10.3899	−	3.78163i	−0.772278	−	0.281086i	−0.697949	+	0.716148i	$0.745904\pi$
$182$	−2.32670	+	0.623437i	−0.172466	+	0.0462122i
$183$	−0.888216	−	10.6662i	−0.0656588	−	0.788466i
$184$	6.62448	−	1.16808i	0.488363	−	0.0861117i
$185$	−0.0679982	−	0.784118i	−0.00499933	−	0.0576495i
$186$	−20.0246	−	11.6732i	−1.46827	−	0.855919i
$187$	7.56294	+	10.8010i	0.553057	+	0.789847i
$188$	−0.0177262	+	0.0380140i	−0.00129282	+	0.00277246i
$189$	8.60510	+	5.11323i	0.625929	+	0.371933i
$190$	−12.4300	+	5.59365i	−0.901769	+	0.405806i
$191$			19.9132i			1.44087i	0.693522	+	0.720436i	$0.256058\pi$
$191$			19.9132i			1.44087i	−0.693522	+	0.720436i	$0.743942\pi$
$192$	1.29216	−	14.0902i	0.0932539	−	1.01688i
$193$	10.3573	−	7.25223i	0.745532	−	0.522027i	−0.137981	−	0.990435i	$-0.544061\pi$
$193$	10.3573	−	7.25223i	0.745532	−	0.522027i	0.883512	+	0.468408i	$0.155172\pi$
$194$	4.81351	−	4.03901i	0.345590	−	0.289984i
$195$	−3.24824	−	1.20050i	−0.232611	−	0.0859693i
$196$	0.0252835	+	0.143390i	0.00180596	+	0.0102421i
$197$	1.89398	−	7.06842i	0.134940	−	0.503604i	−0.865058	−	0.501672i	$-0.832718\pi$
$197$	1.89398	−	7.06842i	0.134940	−	0.503604i	0.999998	−	0.00193175i	$-0.000614896\pi$
$198$	5.85846	−	8.21949i	0.416342	−	0.584134i
$199$	8.37734	−	23.0166i	0.593854	−	1.63160i	−0.169434	−	0.985542i	$-0.554194\pi$
$199$	8.37734	−	23.0166i	0.593854	−	1.63160i	0.763288	−	0.646059i	$-0.223584\pi$
$200$	12.9642	−	6.02124i	0.916710	−	0.425766i
$201$	−0.315435	+	1.74617i	−0.0222491	+	0.123165i
$202$	3.05815	+	0.819429i	0.215171	+	0.0576548i
$203$	−0.0236932	−	0.0165901i	−0.00166293	−	0.00116440i
$204$	−0.394268	−	0.145373i	−0.0276043	−	0.0101781i
$205$	7.13560	−	5.97820i	0.498372	−	0.417536i
$206$	17.8930	+	3.15502i	1.24667	+	0.219821i
$207$	−6.83330	+	1.76983i	−0.474947	+	0.123012i
$208$	−2.47179	−	2.47179i	−0.171388	−	0.171388i
$209$	9.01460	+	5.35843i	0.623553	+	0.370651i
$210$	−4.45619	+	9.43419i	−0.307506	+	0.651021i
$211$	16.2512	−	5.91497i	1.11878	−	0.407203i	0.284574	−	0.958654i	$-0.408148\pi$
$211$	16.2512	−	5.91497i	1.11878	−	0.407203i	0.834207	+	0.551451i	$0.185926\pi$
$212$	−0.103633	+	0.0725645i	−0.00711754	+	0.00498375i
$213$	1.99899	+	7.58716i	0.136968	+	0.519864i
$214$	−0.741007	+	0.883097i	−0.0506542	+	0.0603673i
$215$	−21.2846	−	14.9279i	−1.45160	−	1.01807i
$216$	−0.186456	+	14.8539i	−0.0126867	+	1.01068i
$217$	−4.77095	−	17.8054i	−0.323873	−	1.20871i
$218$	7.16794	−	3.34247i	0.485474	−	0.226380i
$219$	0.0638568	−	15.2620i	0.00431504	−	1.03131i
$220$	−0.206148	−	0.119229i	−0.0138985	−	0.00803845i
$221$	−4.24388	+	2.45020i	−0.285474	+	0.164819i
$222$	−0.224109	+	0.822605i	−0.0150412	+	0.0552096i
$223$	−0.336577	−	3.84709i	−0.0225389	−	0.257620i	−0.999101	−	0.0423861i	$-0.986504\pi$
$223$	−0.336577	−	3.84709i	−0.0225389	−	0.257620i	0.976562	−	0.215234i	$-0.0690515\pi$
$224$	0.369461	−	0.310014i	0.0246856	−	0.0207137i
$225$	−13.0640	+	7.37109i	−0.870930	+	0.491406i
$226$	23.1233	−	8.41621i	1.53814	−	0.559838i
$227$	11.6331	+	11.6331i	0.772119	+	0.772119i	0.978477	−	0.206358i	$-0.0661610\pi$
$227$	11.6331	+	11.6331i	0.772119	+	0.772119i	−0.206358	+	0.978477i	$0.566161\pi$
$228$	−0.333383	+	0.0235012i	−0.0220789	+	0.00155640i
$229$		−	8.15460i		−	0.538871i	−0.963018	−	0.269436i	$-0.913163\pi$
$229$		−	8.15460i		−	0.538871i	0.963018	−	0.269436i	$-0.0868371\pi$
$230$	−2.51124	−	6.91599i	−0.165586	−	0.456027i
$231$	7.91110	−	1.36084i	0.520512	−	0.0895365i
$232$	0.00374119	−	0.0427621i	0.000245621	−	0.00280747i
$233$	1.42783	−	0.124919i	0.0935400	−	0.00818369i	−0.0402896	−	0.999188i	$-0.512828\pi$
$233$	1.42783	−	0.124919i	0.0935400	−	0.00818369i	0.133830	+	0.991004i	$0.457273\pi$
$234$	2.85338	+	2.43525i	0.186531	+	0.159197i
$235$	2.04609	+	0.549923i	0.133472	+	0.0358730i
$236$	−0.489359	−	0.282531i	−0.0318545	−	0.0183912i
$237$	−18.8071	+	18.6504i	−1.22165	+	1.21147i
$238$	6.23975	+	13.3812i	0.404463	+	0.867374i
$239$	14.4284	−	24.9908i	0.933299	−	1.61652i	0.155659	−	0.987811i	$-0.450250\pi$
$239$	14.4284	−	24.9908i	0.933299	−	1.61652i	0.777640	−	0.628710i	$-0.216417\pi$
$240$	−15.0902	+	1.24502i	−0.974067	+	0.0803658i
$241$	2.61882	+	14.8521i	0.168693	+	0.956706i	0.945174	+	0.326566i	$0.105892\pi$
$241$	2.61882	+	14.8521i	0.168693	+	0.956706i	−0.776481	+	0.630140i	$0.782997\pi$
$242$	0.635241	+	7.26084i	0.0408348	+	0.466744i
$243$	−1.03348	−	15.5542i	−0.0662977	−	0.997800i
$244$	0.269391	+	0.0475009i	0.0172460	+	0.00304093i
$245$	6.91313	−	2.51020i	0.441664	−	0.160371i
$246$	−9.49012	+	3.40922i	−0.605068	+	0.217364i
$247$	−2.27587	+	3.16395i	−0.144810	+	0.201317i
$248$	19.3441	−	19.3441i	1.22835	−	1.22835i
$249$	21.3139	−	17.7331i	1.35072	−	1.12379i
$250$	−8.93875	−	12.8283i	−0.565336	−	0.811333i
$251$	18.6953	+	22.2802i	1.18004	+	1.40631i	0.893985	+	0.448097i	$0.147898\pi$
$251$	18.6953	+	22.2802i	1.18004	+	1.40631i	0.286050	+	0.958215i	$0.407657\pi$
$252$	−0.182402	+	0.179375i	−0.0114903	+	0.0112995i
$253$	−3.24692	+	4.63708i	−0.204132	+	0.291531i
$254$	−1.14789	−	1.98820i	−0.0720247	−	0.124750i
$255$	−3.78927	+	20.8853i	−0.237294	+	1.30789i
$256$	0.997851	+	0.363188i	0.0623657	+	0.0226993i
$257$	−7.09388	−	15.2129i	−0.442504	−	0.948952i	−0.993435	−	0.114402i	$-0.963505\pi$
$257$	−7.09388	−	15.2129i	−0.442504	−	0.948952i	0.550931	−	0.834551i	$-0.314273\pi$
$258$	16.0564	+	23.1364i	0.999630	+	1.44041i
$259$	−0.587206	+	0.339024i	−0.0364872	+	0.0210659i
$260$	0.0508203	−	0.0724611i	0.00315174	−	0.00449385i
$261$	−0.000376930		0.0450431i	−2.33314e−5		0.00278810i
$262$	−2.22128	+	25.3893i	−0.137231	+	1.56856i
$263$	11.8230	+	16.8850i	0.729039	+	1.04118i	0.996974	+	0.0777382i	$0.0247698\pi$
$263$	11.8230	+	16.8850i	0.729039	+	1.04118i	−0.267935	+	0.963437i	$0.586341\pi$
$264$	7.61934	+	9.15792i	0.468938	+	0.563631i
$265$	4.51532	+	4.52222i	0.277374	+	0.277798i
$266$	8.89881	+	7.66175i	0.545621	+	0.469772i
$267$	−7.84091	−	3.69629i	−0.479856	−	0.226209i
$268$	−0.0411014	−	0.0191659i	−0.00251067	−	0.00117074i
$269$	−2.84883	+	16.1565i	−0.173696	+	0.985081i	0.765941	+	0.642911i	$0.222273\pi$
$269$	−2.84883	+	16.1565i	−0.173696	+	0.985081i	−0.939638	+	0.342171i	$0.888838\pi$
$270$	16.0381	−	2.60826i	0.976048	−	0.158734i
$271$	−4.90136	−	4.11273i	−0.297736	−	0.249830i	0.481665	−	0.876355i	$-0.340032\pi$
$271$	−4.90136	−	4.11273i	−0.297736	−	0.249830i	−0.779401	+	0.626525i	$0.784477\pi$
$272$	−12.2897	+	17.5515i	−0.745171	+	1.06421i
$273$	0.247578	+	2.97305i	0.0149841	+	0.179937i
$274$	10.1705	+	5.87196i	0.614425	+	0.354738i
$275$	−4.13153	+	11.2976i	−0.249141	+	0.681270i
$276$	0.000754820	−	0.180405i	4.54348e−5	−	0.0108591i
$277$	0.379130	+	1.41493i	0.0227797	+	0.0850150i	0.976380	−	0.216061i	$-0.0693209\pi$
$277$	0.379130	+	1.41493i	0.0227797	+	0.0850150i	−0.953600	+	0.301076i	$0.902654\pi$
$278$	8.18917	+	2.19428i	0.491154	+	0.131604i
$279$	−18.6361	+	21.8359i	−1.11571	+	1.30728i
$280$	−9.42735	−	7.92276i	−0.563392	−	0.473476i
$281$	−14.9826	−	17.8555i	−0.893785	−	1.06517i	−0.997507	−	0.0705647i	$-0.977520\pi$
$281$	−14.9826	−	17.8555i	−0.893785	−	1.06517i	0.103723	−	0.994606i	$-0.466925\pi$
$282$	−1.87451	−	1.32427i	−0.111625	−	0.0788589i
$283$	−20.4183	−	9.52120i	−1.21374	−	0.565976i	−0.292985	−	0.956117i	$-0.594649\pi$
$283$	−20.4183	−	9.52120i	−1.21374	−	0.565976i	−0.920755	+	0.390141i	$0.872426\pi$
$284$	−0.200528			−0.0118992
$285$	4.08083	+	16.3813i	0.241728	+	0.970344i
$286$	3.00837			0.177889
$287$	−7.26819	−	3.38921i	−0.429028	−	0.200059i
$288$	−0.723857	−	0.200464i	−0.0426537	−	0.0118124i
$289$	8.37995	+	9.98683i	0.492938	+	0.587461i
$290$	−0.0467773	+	0.00405649i	−0.00274686	+	0.000238206i
$291$	−3.86297	−	6.75598i	−0.226451	−	0.396042i
$292$	0.376775	+	0.100956i	0.0220491	+	0.00590803i
$293$	2.02499	+	7.55736i	0.118301	+	0.441506i	0.999513	−	0.0312165i	$-0.00993812\pi$
$293$	2.02499	+	7.55736i	0.118301	+	0.441506i	−0.881212	+	0.472722i	$0.843271\pi$
$294$	−7.96701	−	0.0333342i	−0.464645	−	0.00194409i
$295$	−9.78274	+	26.8141i	−0.569573	+	1.56118i
$296$	−0.871458	−	0.503136i	−0.0506524	−	0.0292442i
$297$	−8.72807	−	8.94998i	−0.506454	−	0.519330i
$298$	5.32009	−	7.59788i	0.308185	−	0.440133i
$299$	−1.61164	−	1.35232i	−0.0932033	−	0.0782069i
$300$	−0.0971060	−	0.370864i	−0.00560642	−	0.0214118i
$301$	−3.88916	+	22.0565i	−0.224168	+	1.27132i
$302$	6.12800	+	2.85753i	0.352627	+	0.164432i
$303$	1.67203	−	3.54686i	0.0960558	−	0.203762i
$304$	−3.17215	+	16.7433i	−0.181935	+	0.960294i
$305$	0.0105499	−	13.8176i	0.000604088	−	0.791195i
$306$	11.6629	−	19.8160i	0.666726	−	1.13280i
$307$	14.9607	+	21.3660i	0.853850	+	1.21942i	0.973973	+	0.226665i	$0.0727821\pi$
$307$	14.9607	+	21.3660i	0.853850	+	1.21942i	−0.120123	+	0.992759i	$0.538329\pi$
$308$	−0.0178808	+	0.204379i	−0.00101885	+	0.0116456i
$309$	7.78484	−	21.1134i	0.442864	−	1.20110i
$310$	−24.4987	−	17.1821i	−1.39143	−	0.975877i
$311$	−13.9392	+	8.04780i	−0.790419	+	0.456349i	−0.840110	−	0.542416i	$-0.817510\pi$
$311$	−13.9392	+	8.04780i	−0.790419	+	0.456349i	0.0496910	+	0.998765i	$0.484176\pi$
$312$	−3.63738	+	2.52431i	−0.205926	+	0.142911i
$313$	−5.08299	−	10.9005i	−0.287307	−	0.616133i	0.708689	−	0.705521i	$-0.249287\pi$
$313$	−5.08299	−	10.9005i	−0.287307	−	0.616133i	−0.995997	+	0.0893878i	$0.971509\pi$
$314$	23.7992	+	8.66222i	1.34307	+	0.488837i
$315$	10.5173	+	7.50833i	0.592582	+	0.423047i
$316$	−0.338470	−	0.586247i	−0.0190404	−	0.0329790i
$317$	13.5388	−	19.3354i	0.760414	−	1.08598i	−0.233120	−	0.972448i	$-0.574893\pi$
$317$	13.5388	−	19.3354i	0.760414	−	1.08598i	0.993534	−	0.113536i	$-0.0362177\pi$
$318$	−2.89932	−	6.28614i	−0.162586	−	0.352509i
$319$	0.0232199	+	0.0276724i	0.00130007	+	0.00154936i
$320$	3.18572	−	17.9868i	0.178087	−	1.00549i
$321$	0.913173	+	1.09757i	0.0509684	+	0.0612604i
$322$	−4.48213	+	4.48213i	−0.249780	+	0.249780i
$323$	21.5211	+	10.3703i	1.19746	+	0.577022i
$324$	0.391140	+	0.0757389i	0.0217300	+	0.00420771i
$325$	−4.04893	−	1.89558i	−0.224594	−	0.105148i
$326$	−18.4646	−	3.25580i	−1.02266	−	0.180322i
$327$	−2.49564	−	9.47221i	−0.138009	−	0.523814i
$328$	−1.03729	−	11.8563i	−0.0572750	−	0.654656i
$329$	−0.316951	−	1.79752i	−0.0174741	−	0.0991004i
$330$	8.42534	−	9.94063i	0.463800	−	0.547214i
$331$	1.63937	−	2.83947i	0.0901080	−	0.156072i	−0.817448	−	0.576002i	$-0.804612\pi$
$331$	1.63937	−	2.83947i	0.0901080	−	0.156072i	0.907556	+	0.419930i	$0.137945\pi$
$332$	0.299476	+	0.642228i	0.0164359	+	0.0352469i
$333$	0.953250	+	0.454258i	0.0522378	+	0.0248932i
$334$	−10.2639	−	5.92586i	−0.561615	−	0.324248i
$335$	−0.594586	+	2.21227i	−0.0324857	+	0.120869i
$336$	6.47480	+	11.3238i	0.353230	+	0.617766i
$337$	−19.8701	+	1.73841i	−1.08239	+	0.0946972i	−0.614370	−	0.789018i	$-0.710590\pi$
$337$	−19.8701	+	1.73841i	−1.08239	+	0.0946972i	−0.468024	+	0.883715i	$0.655034\pi$
$338$	1.48706	−	16.9972i	0.0808855	−	0.924525i
$339$	−5.16663	−	30.0358i	−0.280613	−	1.63132i
$340$	−0.491492	−	0.229643i	−0.0266549	−	0.0124542i
$341$			23.0220i			1.24671i
$342$	1.97739	−	18.1802i	0.106925	−	0.983073i
$343$	−14.0153	−	14.0153i	−0.756753	−	0.756753i
$344$	−31.2340	+	11.3682i	−1.68402	+	0.612935i
$345$	−8.98212	+	1.53801i	−0.483581	+	0.0828036i
$346$	7.81530	−	6.55781i	0.420153	−	0.352550i
$347$	−0.232291	−	2.65510i	−0.0124700	−	0.142533i	0.987407	−	0.158199i	$-0.0505687\pi$
$347$	−0.232291	−	2.65510i	−0.0124700	−	0.142533i	−0.999877	+	0.0156659i	$0.995013\pi$
$348$	−0.00111076		0.000302613i	−5.95427e−5		1.62217e-5i
$349$	4.59418	−	2.65245i	0.245921	−	0.141982i	−0.371974	−	0.928243i	$-0.621319\pi$
$349$	4.59418	−	2.65245i	0.245921	−	0.141982i	0.617895	+	0.786261i	$0.287986\pi$
$350$	−6.75271	+	11.6549i	−0.360948	+	0.622981i
$351$	3.59631	−	2.94153i	0.191957	−	0.157007i
$352$	−0.545915	+	0.254564i	−0.0290974	+	0.0135683i
$353$	0.692986	+	2.58626i	0.0368839	+	0.137653i	0.981913	−	0.189335i	$-0.0606332\pi$
$353$	0.692986	+	2.58626i	0.0368839	+	0.137653i	−0.945029	+	0.326987i	$0.893966\pi$
$354$	19.9734	−	23.6022i	1.06158	−	1.25444i
$355$	1.75131	+	9.97670i	0.0929498	+	0.529508i
$356$	0.142407	−	0.169715i	0.00754758	−	0.00899485i
$357$	17.6828	−	4.65889i	0.935874	−	0.246574i
$358$	2.01863	−	1.41346i	0.106688	−	0.0747039i
$359$	−10.3413	+	3.76391i	−0.545791	+	0.198652i	−0.600175	−	0.799868i	$-0.704903\pi$
$359$	−10.3413	+	3.76391i	−0.545791	+	0.198652i	0.0543844	+	0.998520i	$0.482680\pi$
$360$	−1.84584	+	19.0888i	−0.0972843	+	1.00607i
$361$	18.9939	+	0.482772i	0.999677	+	0.0254090i
$362$	10.9337	+	10.9337i	0.574662	+	0.574662i
$363$	8.98938	+	0.824383i	0.471820	+	0.0432689i
$364$	−0.0750889	−	0.0132402i	−0.00393573	−	0.000693975i
$365$	1.73225	−	19.6271i	0.0906699	−	1.02733i
$366$	−5.17816	+	14.0438i	−0.270667	+	0.734080i
$367$	−8.17461	−	5.72392i	−0.426711	−	0.298786i	0.340424	−	0.940272i	$-0.389429\pi$
$367$	−8.17461	−	5.72392i	−0.426711	−	0.298786i	−0.767135	+	0.641486i	$0.778318\pi$
$368$	−8.88534	−	2.38082i	−0.463180	−	0.124109i
$369$	2.06573	+	12.3172i	0.107538	+	0.641207i
$370$	−0.377246	+	1.03402i	−0.0196121	+	0.0537560i
$371$	1.88295	−	5.17336i	0.0977578	−	0.268587i
$372$	−0.418312	−	0.602763i	−0.0216885	−	0.0312518i
$373$	−5.87262	+	21.9169i	−0.304073	+	1.13481i	0.629668	+	0.776864i	$0.283191\pi$
$373$	−5.87262	+	21.9169i	−0.304073	+	1.13481i	−0.933741	+	0.357950i	$0.883476\pi$
$374$	−3.20202	−	18.1596i	−0.165573	−	0.939009i
$375$	−17.6032	+	8.07016i	−0.909025	+	0.416742i
$376$	2.07506	−	1.74119i	0.107013	−	0.0897948i
$377$	−0.0109974	+	0.00770048i	−0.000566396	+	0.000396595i
$378$	−7.88450	−	11.5666i	−0.405535	−	0.594920i
$379$		−	23.2760i		−	1.19561i	−0.801643	−	0.597803i	$-0.796040\pi$
$379$		−	23.2760i		−	1.19561i	0.801643	−	0.597803i	$-0.203960\pi$
$380$	−0.431425	−	0.00581139i	−0.0221316	−	0.000298118i
$381$	−2.67594	+	0.961304i	−0.137093	+	0.0492491i
$382$	11.7691	−	25.2390i	0.602162	−	1.29134i
$383$	−16.9282	−	24.1760i	−0.864993	−	1.23534i	−0.970544	−	0.240924i	$-0.922550\pi$
$383$	−16.9282	−	24.1760i	−0.864993	−	1.23534i	0.105551	−	0.994414i	$-0.466339\pi$
$384$	−9.52860	+	16.3457i	−0.486254	+	0.834138i
$385$	10.3244	−	0.895329i	0.526182	−	0.0456302i
$386$	−17.4135	+	3.07047i	−0.886325	+	0.156283i
$387$	31.7338	−	14.4757i	1.61312	−	0.735840i
$388$	0.192123	−	0.0514792i	0.00975357	−	0.00261346i
$389$	−20.5370	−	7.47485i	−1.04127	−	0.378990i	−0.235906	−	0.971776i	$-0.575806\pi$
$389$	−20.5370	−	7.47485i	−1.04127	−	0.378990i	−0.805360	+	0.592786i	$0.798028\pi$
$390$	3.40746	+	3.44134i	0.172543	+	0.174259i
$391$	−6.44771	+	11.1678i	−0.326075	+	0.564778i
$392$	2.43373	−	9.08280i	0.122922	−	0.458751i
$393$	30.4555	+	8.29726i	1.53628	+	0.418541i
$394$	−6.57810	+	7.83948i	−0.331400	+	0.394947i
$395$	−26.2110	+	21.9596i	−1.31882	+	1.10491i
$396$	0.278025	−	0.157431i	0.0139713	−	0.00791120i
$397$	−1.56363	+	3.35322i	−0.0784763	+	0.168293i	−0.941631	−	0.336646i	$-0.890707\pi$
$397$	−1.56363	+	3.35322i	−0.0784763	+	0.168293i	0.863155	+	0.504939i	$0.168485\pi$
$398$	−24.2211	+	24.2211i	−1.21409	+	1.21409i
$399$	11.2974	−	9.15900i	0.565577	−	0.458523i
$400$	−19.5475	−	0.0298496i	−0.977375	−	0.00149248i
$401$	−8.13769	−	22.3581i	−0.406377	−	1.11651i	−0.959081	−	0.283133i	$-0.908626\pi$
$401$	−8.13769	−	22.3581i	−0.406377	−	1.11651i	0.552704	−	0.833378i	$-0.313596\pi$
$402$	1.43182	−	2.02675i	0.0714127	−	0.101085i
$403$	−8.52355	−	0.745714i	−0.424588	−	0.0371467i
$404$	0.0767710	+	0.0644185i	0.00381950	+	0.00320494i
$405$	0.352154	−	20.1215i	0.0174987	−	0.999847i
$406$	0.0202248	+	0.0350303i	0.00100374	+	0.00173853i
$407$	0.817973	−	0.219175i	0.0405454	−	0.0108641i
$408$	19.1091	+	19.2697i	0.946043	+	0.953992i
$409$	8.05830	−	22.1400i	0.398458	−	1.09475i	−0.564578	−	0.825380i	$-0.690961\pi$
$409$	8.05830	−	22.1400i	0.398458	−	1.09475i	0.963036	−	0.269374i	$-0.0868166\pi$
$410$	−12.5773	+	3.35977i	−0.621146	+	0.165927i
$411$	9.39600	−	11.1030i	0.463471	−	0.547673i
$412$	0.471113	+	0.329877i	0.0232101	+	0.0162519i
$413$	24.4960	−	2.14312i	1.20537	−	0.105456i
$414$	9.70687	+	1.79546i	0.477067	+	0.0882421i
$415$	29.3368	−	20.5085i	1.44009	−	1.00672i
$416$	−0.0765657	−	0.210362i	−0.00375394	−	0.0103139i
$417$	4.47740	−	9.49786i	0.219259	−	0.465112i
$418$	−8.25859	−	12.1194i	−0.403941	−	0.592777i
$419$	−12.4814			−0.609757			−0.304879	−	0.952391i	$-0.598616\pi$
$419$	−12.4814			−0.609757			−0.304879	+	0.952391i	$0.598616\pi$
$420$	−0.254047	+	0.211037i	−0.0123962	+	0.0102976i
$421$	−4.50993	+	25.5771i	−0.219801	+	1.24655i	0.652579	+	0.757721i	$0.273687\pi$
$421$	−4.50993	+	25.5771i	−0.219801	+	1.24655i	−0.872379	+	0.488830i	$0.837424\pi$
$422$	−24.0935	−	2.10791i	−1.17285	−	0.102611i
$423$	−2.02673	+	1.99309i	−0.0985429	+	0.0969073i
$424$	8.04626	−	1.41877i	0.390761	−	0.0689017i
$425$	−7.13282	+	26.4584i	−0.345992	+	1.28342i
$426$	1.95056	−	10.7978i	0.0945049	−	0.523154i
$427$	−10.7885	+	5.03076i	−0.522092	+	0.243456i
$428$	−0.0330719	+	0.0154217i	−0.00159859	+	0.000745434i
$429$	0.662351	−	3.66661i	0.0319786	−	0.177025i
$430$	18.1545	+	31.5000i	0.875487	+	1.51907i
$431$	−36.3208	+	6.40433i	−1.74951	+	0.308486i	−0.954522	−	0.298139i	$-0.903634\pi$
$431$	−36.3208	+	6.40433i	−1.74951	+	0.308486i	−0.794988	+	0.606625i	$0.792523\pi$
$432$	8.81565	−	18.3019i	0.424143	−	0.880550i
$433$	33.2636	+	2.91019i	1.59855	+	0.139855i	0.851295	−	0.524687i	$-0.175818\pi$
$433$	33.2636	+	2.91019i	1.59855	+	0.139855i	0.747251	+	0.664542i	$0.231373\pi$
$434$	−4.47645	+	25.3872i	−0.214876	+	1.21862i
$435$	−0.00535487	+	0.0579053i	−0.000256746	+	0.00277635i
$436$	0.250350			0.0119896
$437$	−1.02363	+	10.2050i	−0.0489667	+	0.488169i
$438$	−9.10111	+	19.3061i	−0.434868	+	0.922480i
$439$	2.45042	+	6.73248i	0.116952	+	0.321324i	0.984332	−	0.176322i	$-0.0564201\pi$
$439$	2.45042	+	6.73248i	0.116952	+	0.321324i	−0.867380	+	0.497646i	$0.834198\pi$
$440$	8.81184	+	12.6051i	0.420088	+	0.600924i
$441$	−1.79472	+	9.70286i	−0.0854628	+	0.462041i
$442$	6.82702	−	0.597287i	0.324728	−	0.0284100i
$443$	8.29510	+	5.80829i	0.394112	+	0.275960i	0.753789	−	0.657117i	$-0.228224\pi$
$443$	8.29510	+	5.80829i	0.394112	+	0.275960i	−0.359677	+	0.933077i	$0.617113\pi$
$444$	−0.0174337	+	0.0206011i	−0.000827369	+	0.000977683i
$445$	−9.68737	−	5.60287i	−0.459225	−	0.265602i
$446$	−1.84712	+	5.07492i	−0.0874636	+	0.240304i
$447$	−8.08898	−	8.15696i	−0.382596	−	0.385811i
$448$	−15.2005	+	4.07295i	−0.718155	+	0.192429i
$449$	2.74373	+	4.75227i	0.129484	+	0.224274i	0.923477	−	0.383654i	$-0.125334\pi$
$449$	2.74373	+	4.75227i	0.129484	+	0.224274i	−0.793993	+	0.607928i	$0.792001\pi$
$450$	20.9144	−	1.62141i	0.985913	−	0.0764341i
$451$	7.67254	+	6.43803i	0.361286	+	0.303155i
$452$	0.775956	+	0.0678874i	0.0364979	+	0.00319315i
$453$	4.83196	−	6.83967i	0.227025	−	0.321356i
$454$	−7.86898	−	21.6199i	−0.369310	−	1.01467i
$455$	−0.00294065	+	3.85147i	−0.000137860	+	0.180560i
$456$	20.1547	+	7.72362i	0.943828	+	0.361692i
$457$	26.5689	−	26.5689i	1.24284	−	1.24284i	0.284021	−	0.958818i	$-0.408331\pi$
$457$	26.5689	−	26.5689i	1.24284	−	1.24284i	0.958818	−	0.284021i	$-0.0916687\pi$
$458$	−4.81954	+	10.3355i	−0.225202	+	0.482948i
$459$	−21.5839	−	18.5777i	−1.00745	−	0.867132i
$460$	0.0204760	−	0.232002i	0.000954700	−	0.0108171i
$461$	16.2108	−	19.3192i	0.755011	−	0.899787i	−0.242511	−	0.970149i	$-0.577971\pi$
$461$	16.2108	−	19.3192i	0.755011	−	0.899787i	0.997522	+	0.0703620i	$0.0224154\pi$
$462$	−10.8312	−	2.95084i	−0.503913	−	0.137285i
$463$	1.42366	−	5.31319i	0.0661633	−	0.246925i	−0.924921	−	0.380159i	$-0.875869\pi$
$463$	1.42366	−	5.31319i	0.0661633	−	0.246925i	0.991085	+	0.133234i	$0.0425361\pi$
$464$	−0.0293504	+	0.0508364i	−0.00136256	+	0.00236002i
$465$	−26.3354	+	26.0761i	−1.22128	+	1.20925i
$466$	−1.88353	−	0.685548i	−0.0872527	−	0.0317574i
$467$	16.5169	−	4.42569i	0.764311	−	0.204797i	0.144454	−	0.989511i	$-0.453857\pi$
$467$	16.5169	−	4.42569i	0.764311	−	0.204797i	0.619857	+	0.784715i	$0.287191\pi$
$468$	0.0492808	+	0.108034i	0.00227800	+	0.00499388i
$469$	1.94351	−	0.342693i	0.0897429	−	0.0158241i
$470$	−2.26830	−	1.90628i	−0.104629	−	0.0879303i
$471$	15.7974	−	27.0994i	0.727905	−	1.24867i
$472$	20.9314	+	29.8931i	0.963444	+	1.37594i
$473$	11.8214	−	25.3511i	0.543549	−	1.16564i
$474$	34.8598	−	12.5230i	1.60117	−	0.575201i
$475$	3.47871	+	21.5151i	0.159614	+	0.987179i
$476$			0.467355i			0.0214212i
$477$	−8.29990	+	2.14968i	−0.380026	+	0.0984269i
$478$	−33.0574	+	23.1471i	−1.51201	+	1.05872i
$479$	−2.07556	+	1.74160i	−0.0948346	+	0.0795757i	−0.688972	−	0.724788i	$-0.741938\pi$
$479$	−2.07556	+	1.74160i	−0.0948346	+	0.0795757i	0.594138	+	0.804363i	$0.297493\pi$
$480$	−0.909538	−	0.336150i	−0.0415146	−	0.0153431i
$481$	0.0546510	+	0.309941i	0.00249187	+	0.0141321i
$482$	5.45867	−	20.3720i	0.248636	−	0.927920i
$483$	4.47600	+	6.44966i	0.203665	+	0.293470i
$484$	−0.0789083	+	0.216799i	−0.00358674	+	0.00985449i
$485$	−4.23911	−	9.10894i	−0.192488	−	0.413616i
$486$	−7.88296	+	20.3249i	−0.357578	+	0.921957i
$487$	−32.6618	−	8.75171i	−1.48005	−	0.396578i	−0.573685	−	0.819076i	$-0.694487\pi$
$487$	−32.6618	−	8.75171i	−1.48005	−	0.396578i	−0.906364	+	0.422498i	$0.861153\pi$
$488$	−14.4712	−	10.1329i	−0.655082	−	0.458693i
$489$	−8.03352	+	21.7878i	−0.363288	+	0.985280i
$490$	−10.2456	−	0.904259i	−0.462850	−	0.0408503i
$491$	15.6025	+	2.75115i	0.704133	+	0.124158i	0.514239	−	0.857647i	$-0.328075\pi$
$491$	15.6025	+	2.75115i	0.704133	+	0.124158i	0.189894	+	0.981805i	$0.439186\pi$
$492$	−0.317862	−	0.0291499i	−0.0143303	−	0.00131418i
$493$	0.0581881	+	0.0581881i	0.00262066	+	0.00262066i
$494$	4.75452	−	2.66506i	0.213916	−	0.119907i
$495$	−10.2607	−	12.4574i	−0.461182	−	0.559920i
$496$	−35.1544	+	12.7951i	−1.57848	+	0.574519i
$497$	7.14815	−	5.00519i	0.320638	−	0.224513i
$498$	−37.4949	+	9.87878i	−1.68019	+	0.442679i
$499$	−1.14070	+	1.35943i	−0.0510646	+	0.0608564i	−0.790972	−	0.611852i	$-0.790425\pi$
$499$	−1.14070	+	1.35943i	−0.0510646	+	0.0608564i	0.739908	+	0.672709i	$0.234869\pi$
$500$	−0.0848259	−	0.487600i	−0.00379353	−	0.0218061i
$501$	−9.48224	+	11.2049i	−0.423635	+	0.500600i
$502$	−10.5273	−	39.2883i	−0.469855	−	1.75352i
$503$	−5.26478	+	2.45501i	−0.234745	+	0.109463i	−0.536432	−	0.843944i	$-0.680228\pi$
$503$	−5.26478	+	2.45501i	−0.234745	+	0.109463i	0.301687	+	0.953407i	$0.402450\pi$
$504$	15.5719	−	5.52059i	0.693628	−	0.245907i
$505$	2.53448	−	4.38212i	0.112783	−	0.195002i
$506$	6.85591	−	3.95826i	0.304783	−	0.175966i
$507$	−20.3888	−	5.55470i	−0.905498	−	0.246693i
$508$	−0.00633363	−	0.0723937i	−0.000281009	−	0.00321195i
$509$	−21.6014	+	18.1258i	−0.957467	+	0.803410i	−0.980539	−	0.196324i	$-0.937100\pi$
$509$	−21.6014	+	18.1258i	−0.957467	+	0.803410i	0.0230724	+	0.999734i	$0.492655\pi$
$510$	17.1463	−	24.2315i	0.759253	−	1.07299i
$511$	−15.9506	+	5.80555i	−0.705614	+	0.256822i
$512$	−16.4984	−	16.4984i	−0.729133	−	0.729133i
$513$	−21.7227	−	6.41278i	−0.959081	−	0.283131i
$514$			23.4742i			1.03540i
$515$	12.2976	−	26.3198i	0.541898	−	1.15979i
$516$	0.151123	+	0.878538i	0.00665281	+	0.0386755i
$517$	−0.198679	+	2.27092i	−0.00873791	+	0.0998748i
$518$	0.944624	−	0.0826439i	0.0415044	−	0.00363116i
$519$	−6.27198	−	10.9691i	−0.275309	−	0.481491i
$520$	−4.95227	+	2.85415i	−0.217171	+	0.125163i
$521$	9.96478	+	5.75317i	0.436565	+	0.252051i	0.702139	−	0.712039i	$-0.252228\pi$
$521$	9.96478	+	5.75317i	0.436565	+	0.252051i	−0.265575	+	0.964090i	$0.585562\pi$
$522$	0.0270991	−	0.0568670i	0.00118610	−	0.00248900i
$523$	12.1467	+	26.0486i	0.531137	+	1.13903i	0.970585	+	0.240759i	$0.0773964\pi$
$523$	12.1467	+	26.0486i	0.531137	+	1.13903i	−0.439448	+	0.898268i	$0.644826\pi$
$524$	−0.403372	+	0.698661i	−0.0176214	+	0.0305211i
$525$	12.7183	+	10.7963i	0.555071	+	0.471188i
$526$	−5.00567	−	28.3886i	−0.218258	−	1.23780i
$527$	4.57083	+	52.2448i	0.199109	+	2.27582i
$528$	−4.15061	−	15.7536i	−0.180632	−	0.685589i
$529$	17.1984	+	3.03255i	0.747758	+	0.131850i
$530$	−3.05021	−	8.40033i	−0.132493	−	0.364887i
$531$	−24.3688	−	29.5401i	−1.05752	−	1.28193i
$532$	0.152796	+	0.338846i	0.00662454	+	0.0146909i
$533$	−2.63211	+	2.63211i	−0.114009	+	0.114009i
$534$	7.75336	+	9.31901i	0.335521	+	0.403273i
$535$	1.05609	+	1.51071i	0.0456589	+	0.0653137i
$536$	1.88260	+	2.24359i	0.0813159	+	0.0969085i
$537$	−1.27829	−	2.77152i	−0.0551623	−	0.119600i
$538$	13.1596	−	18.7939i	0.567351	−	0.810261i
$539$	3.95663	+	6.85308i	0.170424	+	0.295183i
$540$	0.494997	+	0.139724i	0.0213013	+	0.00601277i
$541$	12.4563	+	4.53370i	0.535536	+	0.194919i	0.595609	−	0.803275i	$-0.296911\pi$
$541$	12.4563	+	4.53370i	0.535536	+	0.194919i	−0.0600725	+	0.998194i	$0.519133\pi$
$542$	3.78151	+	8.10948i	0.162430	+	0.348332i
$543$	15.7333	−	10.9187i	0.675179	−	0.468568i
$544$	−1.18833	+	0.686080i	−0.0509491	+	0.0294155i
$545$	−2.18642	−	12.4554i	−0.0936561	−	0.533532i
$546$	1.44334	−	3.91451i	0.0617693	−	0.167525i
$547$	1.51067	−	17.2670i	0.0645916	−	0.738285i	−0.892981	−	0.450094i	$-0.851391\pi$
$547$	1.51067	−	17.2670i	0.0645916	−	0.738285i	0.957573	−	0.288191i	$-0.0930539\pi$
$548$	0.213222	+	0.304513i	0.00910841	+	0.0130082i
$549$	15.9765	+	9.40317i	0.681861	+	0.401317i
$550$	11.9136	−	11.8773i	0.507998	−	0.506449i
$551$	0.0612120	+	0.0231643i	0.00260772	+	0.000986830i
$552$	−4.96804	+	10.5387i	−0.211454	+	0.448555i
$553$	26.6981	+	12.4495i	1.13532	+	0.529407i
$554$	0.355727	−	2.01743i	0.0151134	−	0.0857122i
$555$	1.17720	+	0.687447i	0.0499695	+	0.0291805i
$556$	0.205579	+	0.172501i	0.00871848	+	0.00731568i
$557$	−15.9725	+	22.8111i	−0.676775	+	0.966535i	0.323022	+	0.946392i	$0.395301\pi$
$557$	−15.9725	+	22.8111i	−0.676775	+	0.966535i	−0.999797	+	0.0201438i	$0.993588\pi$
$558$	36.5258	−	16.6616i	1.54626	−	0.705341i
$559$	9.00294	+	5.19785i	0.380784	+	0.219846i
$560$	7.10526	+	15.2677i	0.300252	+	0.645178i
$561$	−22.8379	−	0.0955545i	−0.964216	−	0.00403432i
$562$	8.43664	+	31.4860i	0.355878	+	1.32816i
$563$	7.11394	+	1.90617i	0.299817	+	0.0803357i	0.405591	−	0.914054i	$-0.367066\pi$
$563$	7.11394	+	1.90617i	0.299817	+	0.0803357i	−0.105775	+	0.994390i	$0.533732\pi$
$564$	−0.0360609	−	0.0630672i	−0.00151844	−	0.00265561i
$565$	−3.39926	−	39.1984i	−0.143008	−	1.64909i
$566$	20.2519	+	24.1353i	0.851250	+	1.01448i
$567$	−15.8333	+	7.06304i	−0.664935	+	0.296620i
$568$	11.7371	+	5.47309i	0.492477	+	0.229646i
$569$	−21.3161			−0.893616			−0.446808	−	0.894630i	$-0.647439\pi$
$569$	−21.3161			−0.893616			−0.446808	+	0.894630i	$0.647439\pi$
$570$	4.50944	−	23.1743i	0.188880	−	0.970665i
$571$	−13.3133			−0.557146			−0.278573	−	0.960415i	$-0.589861\pi$
$571$	−13.3133			−0.557146			−0.278573	+	0.960415i	$0.589861\pi$
$572$	0.0863048	+	0.0402446i	0.00360859	+	0.00168271i
$573$	−28.1702	−	19.9011i	−1.17682	−	0.831381i
$574$	7.20896	+	8.59130i	0.300896	+	0.358594i
$575$	−11.7214	+	1.00746i	−0.488817	+	0.0420139i
$576$	18.6413	+	15.9096i	0.776721	+	0.662901i
$577$	−20.9188	−	5.60517i	−0.870860	−	0.233346i	−0.204400	−	0.978887i	$-0.565524\pi$
$577$	−20.9188	−	5.60517i	−0.870860	−	0.233346i	−0.666459	+	0.745541i	$0.732191\pi$
$578$	−4.71873	−	17.6105i	−0.196273	−	0.732501i
$579$	−0.0916289	+	21.8996i	−0.00380797	+	0.910118i
$580$	−0.00139622		0.000509391i	−5.79750e−5		2.11513e-5i
$581$	−26.7053	−	15.4183i	−1.10792	−	0.639660i
$582$	0.903187	+	10.8460i	0.0374383	+	0.449579i
$583$	−3.94378	+	5.63231i	−0.163335	+	0.233266i
$584$	−19.2975	−	16.1925i	−0.798537	−	0.670052i
$585$	4.94454	−	3.39534i	0.204431	−	0.140380i
$586$	1.89999	−	10.7754i	0.0784879	−	0.445127i
$587$	−4.44406	−	2.07230i	−0.183426	−	0.0855329i	0.328736	−	0.944422i	$-0.393377\pi$
$587$	−4.44406	−	2.07230i	−0.183426	−	0.0855329i	−0.512162	+	0.858889i	$0.671155\pi$
$588$	−0.228113	−	0.107535i	−0.00940724	−	0.00443468i
$589$	20.3948	+	36.3847i	0.840352	+	1.49920i
$590$	28.2468	−	28.2037i	1.16290	−	1.16113i
$591$	8.10647	+	9.74341i	0.333456	+	0.400790i
$592$	0.789290	+	1.12722i	0.0324396	+	0.0463286i
$593$	1.54115	−	17.6154i	0.0632874	−	0.723379i	−0.896572	−	0.442898i	$-0.853950\pi$
$593$	1.54115	−	17.6154i	0.0632874	−	0.723379i	0.959860	−	0.280481i	$-0.0904940\pi$
$594$	5.77276	+	16.5021i	0.236859	+	0.677090i
$595$	23.2519	−	4.08164i	0.953236	−	0.167331i
$596$	0.254265	−	0.146800i	0.0104151	−	0.00601316i
$597$	24.1880	+	34.8535i	0.989948	+	1.42646i
$598$	1.24341	+	2.66651i	0.0508470	+	0.109042i
$599$	36.0983	+	13.1387i	1.47494	+	0.536833i	0.949436	−	0.313959i	$-0.101656\pi$
$599$	36.0983	+	13.1387i	1.47494	+	0.536833i	0.525501	+	0.850793i	$0.323878\pi$
$600$	−4.43843	+	24.3573i	−0.181198	+	0.994384i
$601$	−6.44473	−	11.1626i	−0.262886	−	0.455332i	0.704122	−	0.710080i	$-0.251341\pi$
$601$	−6.44473	−	11.1626i	−0.262886	−	0.455332i	−0.967008	+	0.254747i	$0.918008\pi$
$602$	17.9652	−	25.6570i	0.732207	−	1.04570i
$603$	−2.15496	−	2.19133i	−0.0877568	−	0.0892380i
$604$	0.137575	+	0.163955i	0.00559784	+	0.00667124i
$605$	11.4753	+	2.03245i	0.466539	+	0.0826308i
$606$	−4.21549	+	3.50726i	−0.171242	+	0.142473i
$607$	−11.7756	+	11.7756i	−0.477956	+	0.477956i	−0.904478	−	0.426521i	$-0.859739\pi$
$607$	−11.7756	+	11.7756i	−0.477956	+	0.477956i	0.426521	+	0.904478i	$0.359739\pi$
$608$	−0.637267	+	0.885936i	−0.0258446	+	0.0359295i
$609$	0.0471479	−	0.0169374i	0.00191053	−	0.000686337i
$610$	−8.17988	+	17.5069i	−0.331194	+	0.708834i
$611$	−0.834337	−	0.147116i	−0.0337537	−	0.00595168i
$612$	0.599678	−	0.412464i	0.0242406	−	0.0166729i
$613$	−1.45228	−	16.5996i	−0.0586570	−	0.670452i	−0.967426	−	0.253153i	$-0.918532\pi$
$613$	−1.45228	−	16.5996i	−0.0586570	−	0.670452i	0.908769	−	0.417299i	$-0.137023\pi$
$614$	−6.33409	−	35.9224i	−0.255623	−	1.44971i
$615$	1.32577	+	16.0689i	0.0534602	+	0.647961i
$616$	6.62477	−	11.4744i	0.266920	−	0.462318i
$617$	11.7584	+	25.2160i	0.473375	+	1.01516i	0.987526	+	0.157456i	$0.0503293\pi$
$617$	11.7584	+	25.2160i	0.473375	+	1.01516i	−0.514151	+	0.857700i	$0.671893\pi$
$618$	−22.3453	+	22.1591i	−0.898862	+	0.891371i
$619$	−35.6353	−	20.5740i	−1.43230	−	0.826941i	−0.435007	−	0.900427i	$-0.643254\pi$
$619$	−35.6353	−	20.5740i	−1.43230	−	0.826941i	−0.997296	+	0.0734864i	$0.976587\pi$
$620$	−0.472972	−	0.820657i	−0.0189950	−	0.0329584i
$621$	4.32547	−	11.4354i	0.173575	−	0.458888i
$622$	22.4236	−	1.96181i	0.899106	−	0.0786615i
$623$	−0.840262	+	9.60424i	−0.0336644	+	0.384786i
$624$	5.96699	−	1.02642i	0.238871	−	0.0410896i
$625$	−23.5183	+	8.47872i	−0.940733	+	0.339149i
$626$			16.8200i			0.672262i
$627$	−16.5894	+	7.39727i	−0.662516	+	0.295419i
$628$	0.566879	+	0.566879i	0.0226209	+	0.0226209i
$629$	1.81274	−	0.659785i	0.0722788	−	0.0263073i
$630$	−8.89254	−	15.7324i	−0.354287	−	0.626792i
$631$	24.9583	−	20.9425i	0.993574	−	0.833708i	0.00749276	−	0.999972i	$-0.497615\pi$
$631$	24.9583	−	20.9425i	0.993574	−	0.833708i	0.986081	+	0.166264i	$0.0531705\pi$
$632$	3.81027	+	43.5516i	0.151564	+	1.73239i
$633$	−7.87377	+	28.9011i	−0.312954	+	1.14871i
$634$	−28.5873	+	16.5049i	−1.13535	+	0.655494i
$635$	−3.54643	+	0.947361i	−0.140736	+	0.0375949i
$636$	0.000916823	−	0.219124i	3.63544e−5	−	0.00868883i
$637$	−2.66541	+	1.24290i	−0.105607	+	0.0492455i
$638$	−0.0130751	−	0.0487969i	−0.000517648	−	0.00193189i
$639$	−12.7309	−	4.75469i	−0.503627	−	0.188093i
$640$	−14.0254	+	19.9979i	−0.554403	+	0.790485i
$641$	24.9369	−	29.7186i	0.984948	−	1.17382i	0.000169427	−	1.00000i	$-0.499946\pi$
$641$	24.9369	−	29.7186i	0.984948	−	1.17382i	0.984778	−	0.173815i	$-0.0556095\pi$
$642$	−0.508713	−	1.93082i	−0.0200773	−	0.0762034i
$643$	5.77545	−	4.04402i	0.227762	−	0.159480i	−0.454126	−	0.890938i	$-0.650048\pi$
$643$	5.77545	−	4.04402i	0.227762	−	0.159480i	0.681887	+	0.731457i	$0.261159\pi$
$644$	−0.188544	+	0.0686246i	−0.00742969	+	0.00270419i
$645$	42.3893	−	15.1914i	1.66908	−	0.598160i
$646$	−21.1478	−	25.8633i	−0.832048	−	1.01758i
$647$	12.8078	+	12.8078i	0.503526	+	0.503526i	0.912532	−	0.409006i	$-0.134124\pi$
$647$	12.8078	+	12.8078i	0.503526	+	0.503526i	−0.409006	+	0.912532i	$0.634124\pi$
$648$	−20.8266	−	15.1086i	−0.818147	−	0.593522i
$649$	−30.2438	−	5.33280i	−1.18717	−	0.209331i
$650$	4.01149	+	4.79556i	0.157343	+	0.188097i
$651$	29.9564	+	11.0454i	1.17408	+	0.432903i
$652$	−0.486162	−	0.340414i	−0.0190396	−	0.0133316i
$653$	−28.3895	−	7.60695i	−1.11097	−	0.297683i	−0.343745	−	0.939063i	$-0.611695\pi$
$653$	−28.3895	−	7.60695i	−1.11097	−	0.297683i	−0.767223	+	0.641380i	$0.778362\pi$
$654$	−2.43518	+	13.4805i	−0.0952230	+	0.527130i
$655$	38.2827	+	13.9669i	1.49583	+	0.545731i
$656$	−5.56656	+	15.2940i	−0.217338	+	0.597131i
$657$	21.5265	+	15.3431i	0.839829	+	0.598590i
$658$	−0.660652	+	2.46559i	−0.0257549	+	0.0961186i
$659$	0.572710	+	3.24800i	0.0223096	+	0.126524i	0.993929	−	0.110027i	$-0.0350939\pi$
$659$	0.572710	+	3.24800i	0.0223096	+	0.126524i	−0.971619	+	0.236552i	$0.923983\pi$
$660$	0.374690	−	0.172469i	0.0145848	−	0.00671334i
$661$	13.6642	−	11.4657i	0.531477	−	0.445962i	−0.337134	−	0.941457i	$-0.609458\pi$
$661$	13.6642	−	11.4657i	0.531477	−	0.445962i	0.868611	+	0.495495i	$0.165013\pi$
$662$	−3.75601	+	2.62998i	−0.145981	+	0.102217i
$663$	0.775128	−	8.45229i	0.0301035	−	0.328260i
$664$		−	45.7639i		−	1.77598i
$665$	15.5239	−	10.5612i	0.601991	−	0.409547i
$666$	−0.939720	−	1.13914i	−0.0364134	−	0.0441408i
$667$	−0.0149306	+	0.0320189i	−0.000578117	+	0.00123978i
$668$	−0.215179	−	0.307308i	−0.00832554	−	0.0118901i
$669$	5.77864	+	3.36861i	0.223415	+	0.130238i
$670$	2.06111	−	2.45252i	0.0796274	−	0.0947493i
$671$	14.6410	−	2.58161i	0.565211	−	0.0996619i
$672$	0.0693242	+	0.832481i	0.00267424	+	0.0321137i
$673$	−10.4056	+	2.78816i	−0.401105	+	0.107476i	−0.453731	−	0.891139i	$-0.649907\pi$
$673$	−10.4056	+	2.78816i	−0.401105	+	0.107476i	0.0526266	+	0.998614i	$0.483241\pi$
$674$	26.2118	+	9.54031i	1.00964	+	0.367479i
$675$	2.62853	−	25.8475i	0.101172	−	0.994869i
$676$	0.270042	−	0.467726i	0.0103862	−	0.0179895i
$677$	4.84363	−	18.0767i	0.186156	−	0.694743i	−0.808224	−	0.588875i	$-0.799571\pi$
$677$	4.84363	−	18.0767i	0.186156	−	0.694743i	0.994380	−	0.105868i	$-0.0337622\pi$
$678$	−11.2033	+	41.1224i	−0.430261	+	1.57930i
$679$	−5.56362	+	6.63046i	−0.213512	+	0.254454i
$680$	22.4997	+	26.8557i	0.862824	+	1.02987i
$681$	−28.0828	+	4.83070i	−1.07614	+	0.185113i
$682$	13.6065	−	29.1792i	0.521020	−	1.11733i
$683$	18.3632	−	18.3632i	0.702647	−	0.702647i	−0.262331	−	0.964978i	$-0.584491\pi$
$683$	18.3632	−	18.3632i	0.702647	−	0.702647i	0.964978	+	0.262331i	$0.0844913\pi$
$684$	0.299935	−	0.495106i	0.0114683	−	0.0189308i
$685$	13.2880	−	13.2677i	0.507709	−	0.506934i
$686$	9.48031	+	26.0469i	0.361960	+	0.994477i
$687$	11.5359	+	8.14964i	0.440120	+	0.310928i
$688$	45.2809	+	3.96157i	1.72632	+	0.151033i
$689$	−1.95753	−	1.64256i	−0.0745760	−	0.0625767i
$690$	12.2934	+	3.35927i	0.468001	+	0.127885i
$691$	−8.44269	−	14.6232i	−0.321175	−	0.556291i	0.659556	−	0.751656i	$-0.270744\pi$
$691$	−8.44269	−	14.6232i	−0.321175	−	0.556291i	−0.980731	+	0.195364i	$0.937411\pi$
$692$	0.311935	−	0.0835826i	0.0118580	−	0.00317733i
$693$	−5.98119	+	12.5514i	−0.227207	+	0.476788i
$694$	−1.27480	+	3.50249i	−0.0483908	+	0.132953i
$695$	6.78688	−	11.7345i	0.257441	−	0.445116i
$696$	0.0567542	+	0.0480285i	0.00215126	+	0.00182051i
$697$	18.6898	+	13.0868i	0.707928	+	0.495697i
$698$	−7.39054	+	0.646588i	−0.279736	+	0.0244737i
$699$	−1.25024	+	2.14471i	−0.0472885	+	0.0811203i
$700$	−0.349637	+	0.244024i	−0.0132151	+	0.00922324i
$701$	12.6567	+	34.7741i	0.478038	+	1.31340i	0.911156	+	0.412062i	$0.135191\pi$
$701$	12.6567	+	34.7741i	0.478038	+	1.31340i	−0.433118	+	0.901337i	$0.642587\pi$
$702$	−6.29665	+	1.60275i	−0.237652	+	0.0604919i
$703$	1.09858	−	1.07102i	0.0414339	−	0.0403942i
$704$	19.6539			0.740733
$705$	−2.82279	+	2.34490i	−0.106312	+	0.0883141i
$706$	0.650209	−	3.68752i	0.0244709	−	0.138782i
$707$	−4.34451	−	0.380096i	−0.163392	−	0.0142950i
$708$	0.888742	−	0.409909i	0.0334010	−	0.0154053i
$709$	−29.9666	+	5.28392i	−1.12542	+	0.198442i	−0.705218	−	0.708990i	$-0.749151\pi$
$709$	−29.9666	+	5.28392i	−1.12542	+	0.198442i	−0.420200	+	0.907432i	$0.638040\pi$
$710$	3.67675	−	13.6800i	0.137986	−	0.513402i
$711$	−7.58800	−	45.2444i	−0.284572	−	1.69680i
$712$	−12.9673	+	6.04676i	−0.485971	+	0.226612i
$713$	−20.4059	+	9.51543i	−0.764207	+	0.356356i
$714$	−25.1656	−	4.54602i	−0.941798	−	0.170130i
$715$	1.24851	−	4.64533i	0.0466918	−	0.173725i
$716$	0.0768198	−	0.0135454i	0.00287089	−	0.000506215i
$717$	20.9334	+	45.3867i	0.781773	+	1.69500i
$718$	15.3316	+	1.34134i	0.572169	+	0.0500583i
$719$	−5.17529	+	29.3505i	−0.193006	+	1.09459i	0.722225	+	0.691659i	$0.243120\pi$
$719$	−5.17529	+	29.3505i	−0.193006	+	1.09459i	−0.915230	+	0.402931i	$0.867991\pi$
$720$	13.3197	−	22.5915i	0.496397	−	0.841935i
$721$	−25.0273			−0.932065
$722$	−23.7884	−	11.8377i	−0.885314	−	0.440552i
$723$	−23.6276	−	11.1383i	−0.878721	−	0.414239i
$724$	0.167402	+	0.459934i	0.00622146	+	0.0170933i
$725$	−0.0131494	+	0.0739139i	−0.000488357	+	0.00274509i
$726$	−10.9064	−	6.35778i	−0.404773	−	0.235959i
$727$	44.4681	−	3.89046i	1.64923	−	0.144289i	0.775715	−	0.631083i	$-0.217389\pi$
$727$	44.4681	−	3.89046i	1.64923	−	0.144289i	0.873517	+	0.486794i	$0.161834\pi$
$728$	4.03365	+	2.82439i	0.149497	+	0.104679i
$729$	23.0364	+	14.0827i	0.853202	+	0.521581i
$730$	−13.7955	+	23.8525i	−0.510596	+	0.882820i
$731$	21.7936	−	59.8773i	0.806064	−	2.21464i
$732$	−0.336424	+	0.333620i	−0.0124346	+	0.0123310i
$733$	35.5048	−	9.51347i	1.31140	−	0.351388i	0.465650	−	0.884969i	$-0.345821\pi$
$733$	35.5048	−	9.51347i	1.31140	−	0.351388i	0.845749	+	0.533581i	$0.179154\pi$
$734$	6.97794	+	12.0861i	0.257560	+	0.446108i
$735$	−3.35789	+	12.2883i	−0.123858	+	0.453260i
$736$	−0.451273	−	0.378663i	−0.0166342	−	0.0139577i
$737$	−2.45535	−	0.214816i	−0.0904441	−	0.00791283i
$738$	4.66151	−	16.8323i	0.171592	−	0.619605i
$739$	2.13226	+	5.85834i	0.0784365	+	0.215502i	0.972713	−	0.232013i	$-0.0745312\pi$
$739$	2.13226	+	5.85834i	0.0784365	+	0.215502i	−0.894276	+	0.447515i	$0.852309\pi$
$740$	−0.0246551	+	0.0246175i	−0.000906341	+	0.000904958i
$741$	−2.20137	−	6.38158i	−0.0808695	−	0.234433i
$742$	−5.44411	+	5.44411i	−0.199859	+	0.199859i
$743$	−13.1685	+	28.2400i	−0.483106	+	1.03602i	0.502125	+	0.864795i	$0.332552\pi$
$743$	−13.1685	+	28.2400i	−0.483106	+	1.03602i	−0.985231	+	0.171230i	$0.945226\pi$
$744$	8.03270	+	46.6974i	0.294493	+	1.71201i
$745$	−9.52423	−	11.3682i	−0.348941	−	0.416497i
$746$	20.3966	−	24.3077i	0.746772	−	0.889969i
$747$	3.78503	+	47.8739i	0.138487	+	1.75161i
$748$	0.151070	−	0.563801i	0.00552367	−	0.0206146i
$749$	0.793975	−	1.37520i	0.0290112	−	0.0502489i
$750$	27.0808	+	0.175338i	0.988851	+	0.00640245i
$751$	2.99601	+	1.09046i	0.109326	+	0.0397914i	0.396104	−	0.918206i	$-0.370362\pi$
$751$	2.99601	+	1.09046i	0.109326	+	0.0397914i	−0.286778	+	0.957997i	$0.592584\pi$
$752$	−3.57809	+	0.958746i	−0.130479	+	0.0349619i
$753$	−50.2024	+	4.18056i	−1.82948	+	0.152348i
$754$	0.0184898	−	0.00326026i	0.000673360	−	0.000118731i
$755$	6.95561	−	8.27654i	0.253141	−	0.301214i
$756$	−0.0714603	−	0.437300i	−0.00259898	−	0.0159044i
$757$	−28.7312	−	41.0324i	−1.04425	−	1.49135i	−0.861215	−	0.508241i	$-0.830296\pi$
$757$	−28.7312	−	41.0324i	−1.04425	−	1.49135i	−0.183037	−	0.983106i	$-0.558593\pi$
$758$	−13.7566	+	29.5011i	−0.499662	+	1.07153i
$759$	−3.31487	−	9.22749i	−0.120322	−	0.334937i
$760$	25.0931	+	12.1152i	0.910222	+	0.439465i
$761$		−	35.8730i		−	1.30040i	−0.759765	−	0.650198i	$-0.774686\pi$
$761$		−	35.8730i		−	1.30040i	0.759765	−	0.650198i	$-0.225314\pi$
$762$	3.95977	+	0.363136i	0.143447	+	0.0131550i
$763$	−8.92412	+	6.24873i	−0.323075	+	0.226219i
$764$	0.675272	−	0.566621i	0.0244305	−	0.0204996i
$765$	−25.7583	−	26.2330i	−0.931292	−	0.948457i
$766$	7.16713	+	40.6468i	0.258959	+	1.46863i
$767$	2.95403	−	11.0246i	0.106664	−	0.398075i
$768$	−1.51103	+	1.04864i	−0.0545244	+	0.0378394i
$769$	8.10125	−	22.2580i	0.292139	−	0.802644i	−0.703615	−	0.710582i	$-0.748432\pi$
$769$	8.10125	−	22.2580i	0.292139	−	0.802644i	0.995753	−	0.0920625i	$-0.0293459\pi$
$770$	−13.6149	−	4.96718i	−0.490646	−	0.179005i
$771$	28.6103	+	5.16830i	1.03038	+	0.186132i
$772$	−0.540639	−	0.144864i	−0.0194580	−	0.00521376i
$773$	8.44159	+	5.91087i	0.303623	+	0.212599i	0.715452	−	0.698662i	$-0.246221\pi$
$773$	8.44159	+	5.91087i	0.303623	+	0.212599i	−0.411829	+	0.911261i	$0.635110\pi$
$774$	−48.7764	−	0.408172i	−1.75323	−	0.0146714i
$775$	−36.6988	+	30.6985i	−1.31826	+	1.10272i
$776$	−12.6502	−	2.23057i	−0.454115	−	0.0800727i
$777$	0.107251	−	1.16950i	0.00384761	−	0.0419558i
$778$	21.6118	+	21.6118i	0.774820	+	0.774820i
$779$	17.8292	+	3.37789i	0.638799	+	0.121026i
$780$	0.0517173	+	0.144310i	0.00185178	+	0.00516711i
$781$	−10.2412	+	3.72748i	−0.366458	+	0.133380i
$782$	14.7725	−	10.3438i	0.528265	−	0.369895i
$783$	−0.0633432	−	0.0455489i	−0.00226370	−	0.00162778i
$784$	−8.26557	+	9.85052i	−0.295199	+	0.351804i
$785$	23.2526	−	33.1543i	0.829922	−	1.18333i
$786$	−33.6970	−	28.5162i	−1.20193	−	1.01714i
$787$	6.92819	+	25.8563i	0.246963	+	0.921679i	0.972387	+	0.233376i	$0.0749773\pi$
$787$	6.92819	+	25.8563i	0.246963	+	0.921679i	−0.725423	+	0.688303i	$0.758356\pi$
$788$	−0.293587	+	0.136902i	−0.0104586	+	0.00487693i
$789$	−35.7021	−	0.149379i	−1.27103	−	0.00531803i
$790$	46.1997	−	12.3414i	1.64371	−	0.439087i
$791$	−29.3547	+	16.9479i	−1.04373	+	0.602599i
$792$	−20.5699	+	1.62631i	−0.730920	+	0.0577884i
$793$	0.481559	+	5.50424i	0.0171007	+	0.195461i
$794$	3.96364	−	3.32589i	0.140664	−	0.118031i
$795$	−10.9099	+	1.86810i	−0.386934	+	0.0662547i
$796$	−1.01888	+	0.370842i	−0.0361133	+	0.0131442i
$797$	−33.2197	−	33.2197i	−1.17670	−	1.17670i	−0.980579	−	0.196122i	$-0.937165\pi$
$797$	−33.2197	−	33.2197i	−1.17670	−	1.17670i	−0.196122	−	0.980579i	$-0.562835\pi$
$798$	−19.7320	+	4.93156i	−0.698507	+	0.174575i
$799$			5.19293i			0.183713i
$800$	−1.13374	−	0.530781i	−0.0400838	−	0.0187659i
$801$	13.0651	−	7.39805i	0.461632	−	0.261397i
$802$	−2.90001	+	33.1473i	−0.102403	+	1.17047i
$803$	21.1189	−	1.84766i	0.745269	−	0.0652026i
$804$	0.0681893	−	0.0389896i	0.00240485	−	0.00137506i
$805$	5.06087	+	8.78116i	0.178372	+	0.309495i
$806$	10.3624	+	5.98276i	0.365001	+	0.210734i
$807$	−20.0086	−	20.1768i	−0.704338	−	0.710256i
$808$	−2.73527	−	5.86581i	−0.0962266	−	0.206359i
$809$	17.0654	−	29.5581i	0.599987	−	1.03921i	−0.392835	−	0.919609i	$-0.628506\pi$
$809$	17.0654	−	29.5581i	0.599987	−	1.03921i	0.992822	−	0.119600i	$-0.0381611\pi$
$810$	−12.3386	+	25.2949i	−0.433534	+	0.888772i
$811$	1.98894	+	11.2798i	0.0698411	+	0.396088i	0.999610	+	0.0279435i	$0.00889585\pi$
$811$	1.98894	+	11.2798i	0.0698411	+	0.396088i	−0.929768	+	0.368145i	$0.879993\pi$
$812$	0.000111593		0.00127552i	3.91615e−6		4.47618e-5i
$813$	10.7164	−	2.82345i	0.375841	−	0.0990228i
$814$	−1.16628	−	0.205646i	−0.0408779	−	0.00720788i
$815$	−12.6904	+	27.1606i	−0.444527	+	0.951394i
$816$	−12.5469	−	34.9263i	−0.439229	−	1.22267i
$817$	−3.77514	−	50.5380i	−0.132075	−	1.76810i
$818$	−23.2987	+	23.2987i	−0.814620	+	0.814620i
$819$	−4.45323	−	2.62100i	−0.155608	−	0.0915852i
$820$	−0.405765	−	0.0718668i	−0.0141699	−	0.00250970i
$821$	25.9563	+	30.9335i	0.905882	+	1.07959i	0.996491	+	0.0837013i	$0.0266742\pi$
$821$	25.9563	+	30.9335i	0.905882	+	1.07959i	−0.0906091	+	0.995887i	$0.528881\pi$
$822$	−18.4711	+	8.51930i	−0.644253	+	0.297145i
$823$	−11.3399	+	16.1950i	−0.395284	+	0.564523i	−0.966627	−	0.256188i	$-0.917534\pi$
$823$	−11.3399	+	16.1950i	−0.395284	+	0.564523i	0.571343	+	0.820711i	$0.306422\pi$
$824$	−18.5712	−	32.1662i	−0.646958	−	1.12056i
$825$	−11.8530	−	17.1354i	−0.412670	−	0.596576i
$826$	−32.3140	−	11.7613i	−1.12435	−	0.409229i
$827$	−4.77562	−	10.2413i	−0.166064	−	0.356126i	0.805611	−	0.592445i	$-0.201837\pi$
$827$	−4.77562	−	10.2413i	−0.166064	−	0.356126i	−0.971676	+	0.236318i	$0.924059\pi$
$828$	0.254454	+	0.181363i	0.00884289	+	0.00630279i
$829$	7.75697	−	4.47849i	0.269411	−	0.155544i	−0.359209	−	0.933257i	$-0.616953\pi$
$829$	7.75697	−	4.47849i	0.269411	−	0.155544i	0.628620	+	0.777713i	$0.283620\pi$
$830$	−49.3038	+	8.65478i	−1.71136	+	0.300412i
$831$	−2.38052	−	0.877736i	−0.0825794	−	0.0304483i
$832$	−0.636616	+	7.27655i	−0.0220707	+	0.252269i
$833$	10.3396	+	14.7664i	0.358245	+	0.511626i
$834$	−11.2883	+	9.39181i	−0.390882	+	0.325212i
$835$	−13.4100	+	13.3895i	−0.464071	+	0.463363i
$836$	−0.0747972	−	0.458163i	−0.00258692	−	0.0158459i
$837$	−12.2653	−	48.1861i	−0.423951	−	1.66555i
$838$	15.8196	+	7.37678i	0.546478	+	0.254827i
$839$	0.322295	−	1.82782i	0.0111268	−	0.0631035i	−0.978739	−	0.205111i	$-0.934245\pi$
$839$	0.322295	−	1.82782i	0.0111268	−	0.0631035i	0.989866	+	0.142007i	$0.0453556\pi$
$840$	20.6295	−	5.41841i	0.711785	−	0.186953i
$841$	−22.2151	−	18.6407i	−0.766038	−	0.642783i
$842$	20.8327	−	29.7522i	0.717942	−	1.02533i
$843$	40.2326	−	3.35034i	1.38569	−	0.115392i
$844$	−0.663001	−	0.382784i	−0.0228214	−	0.0131760i
$845$	−25.6288	−	9.35029i	−0.881657	−	0.321660i
$846$	3.74673	−	1.32830i	0.128815	−	0.0456679i
$847$	−2.59849	−	9.69769i	−0.0892851	−	0.333217i
$848$	−10.7923	−	2.89180i	−0.370611	−	0.0993048i
$849$	33.8749	−	19.3692i	1.16259	−	0.664749i
$850$	24.6779	−	29.3190i	0.846446	−	1.00563i
$851$	0.532352	+	0.634432i	0.0182488	+	0.0217481i
$852$	0.200406	−	0.283676i	0.00686580	−	0.00971857i
$853$	−42.7323	−	19.9264i	−1.46313	−	0.682266i	−0.482094	−	0.876119i	$-0.660124\pi$
$853$	−42.7323	−	19.9264i	−1.46313	−	0.682266i	−0.981031	+	0.193853i	$0.937902\pi$
$854$	16.6472			0.569654
$855$	−27.2520	−	10.5984i	−0.932000	−	0.362457i
$856$	2.35663			0.0805481
$857$	43.6873	+	20.3717i	1.49233	+	0.695885i	0.986045	−	0.166481i	$-0.0532405\pi$
$857$	43.6873	+	20.3717i	1.49233	+	0.695885i	0.506285	+	0.862366i	$0.331018\pi$
$858$	−3.00654	+	4.25577i	−0.102642	+	0.145290i
$859$	−0.381678	−	0.454866i	−0.0130227	−	0.0155198i	0.759494	−	0.650515i	$-0.225447\pi$
$859$	−0.381678	−	0.454866i	−0.0130227	−	0.0155198i	−0.772516	+	0.634995i	$0.781002\pi$
$860$	0.0994275	+	1.14654i	0.00339045	+	0.0390968i
$861$	12.0583	−	6.89475i	0.410945	−	0.234972i
$862$	49.8198	+	13.3492i	1.69687	+	0.454675i
$863$	−7.54815	−	28.1701i	−0.256942	−	0.958920i	−0.967000	−	0.254777i	$-0.917998\pi$
$863$	−7.54815	−	28.1701i	−0.256942	−	0.958920i	0.710058	−	0.704143i	$-0.248669\pi$
$864$	1.00700	−	0.823658i	0.0342589	−	0.0280214i
$865$	−6.88269	−	14.7894i	−0.234018	−	0.502856i
$866$	−40.4399	−	23.3480i	−1.37420	−	0.793397i
$867$	−22.5027	+	1.87389i	−0.764230	+	0.0636406i
$868$	−0.468040	+	0.668430i	−0.0158863	+	0.0226880i
$869$	−28.1834	−	23.6486i	−0.956055	−	0.802225i
$870$	0.0410103	−	0.0702272i	0.00139038	−	0.00238092i
$871$	0.159064	−	0.902099i	0.00538969	−	0.0305665i
$872$	−14.6532	−	6.83289i	−0.496220	−	0.231391i
$873$	13.4179	+	1.28714i	0.454128	+	0.0435632i
$874$	7.32874	−	12.3293i	0.247898	−	0.417044i
$875$	15.1943	+	15.2640i	0.513660	+	0.516018i
$876$	−0.519363	+	0.432107i	−0.0175476	+	0.0145995i
$877$	−5.95755	−	8.50826i	−0.201172	−	0.287303i	0.705872	−	0.708340i	$-0.250555\pi$
$877$	−5.95755	−	8.50826i	−0.201172	−	0.287303i	−0.907044	+	0.421036i	$0.861667\pi$
$878$	0.873253	−	9.98132i	0.0294708	−	0.336853i
$879$	−12.7147	−	4.68812i	−0.428857	−	0.158126i
$880$	−3.63634	−	20.7152i	−0.122581	−	0.698308i
$881$	14.8328	−	8.56375i	0.499731	−	0.288520i	−0.228871	−	0.973457i	$-0.573503\pi$
$881$	14.8328	−	8.56375i	0.499731	−	0.288520i	0.728603	+	0.684937i	$0.240170\pi$
$882$	8.00931	−	11.2372i	0.269688	−	0.378375i
$883$	8.26817	+	17.7311i	0.278246	+	0.596700i	0.994916	−	0.100712i	$-0.0321122\pi$
$883$	8.26817	+	17.7311i	0.278246	+	0.596700i	−0.716670	+	0.697413i	$0.754334\pi$
$884$	0.203845	+	0.0741937i	0.00685606	+	0.00249540i
$885$	−28.1557	−	40.6369i	−0.946442	−	1.36599i
$886$	−7.08079	−	12.2643i	−0.237884	−	0.412027i
$887$	−28.9298	+	41.3160i	−0.971368	+	1.38726i	−0.0499202	+	0.998753i	$0.515897\pi$
$887$	−28.9298	+	41.3160i	−0.971368	+	1.38726i	−0.921447	+	0.388503i	$0.872992\pi$
$888$	1.58269	−	0.729972i	0.0531115	−	0.0244963i
$889$	2.03272	+	2.42250i	0.0681753	+	0.0812482i
$890$	8.96683	+	12.8268i	0.300569	+	0.429955i
$891$	21.3838	−	3.40258i	0.716384	−	0.113991i
$892$	−0.120881	+	0.120881i	−0.00404738	+	0.00404738i
$893$	1.69776	+	3.76503i	0.0568134	+	0.125992i
$894$	5.43144	+	15.1193i	0.181654	+	0.505664i
$895$	−1.34482	−	3.70365i	−0.0449523	−	0.123799i
$896$	20.7231	+	3.65404i	0.692310	+	0.122073i
$897$	3.52371	−	0.928391i	0.117653	−	0.0309981i
$898$	−0.668839	−	7.64486i	−0.0223194	−	0.255112i
$899$	0.0249496	+	0.141496i	0.000832116	+	0.00471917i
$900$	0.621687	+	0.233268i	0.0207229	+	0.00777559i
$901$	−7.83155	+	13.5646i	−0.260907	+	0.451904i
$902$	−5.91955	−	12.6945i	−0.197099	−	0.422681i
$903$	−27.3154	−	27.5449i	−0.908998	−	0.916637i
$904$	−43.5645	−	25.1520i	−1.44893	−	0.836543i
$905$	21.4207	−	12.3455i	0.712049	−	0.410377i
$906$	−10.1667	+	5.81314i	−0.337765	+	0.193129i
$907$	−19.4206	+	1.69908i	−0.644851	+	0.0564171i	−0.404890	−	0.914365i	$-0.632690\pi$
$907$	−19.4206	+	1.69908i	−0.644851	+	0.0564171i	−0.239961	+	0.970783i	$0.577135\pi$
$908$	0.0634733	−	0.725503i	0.00210644	−	0.0240767i
$909$	3.34654	+	5.91004i	0.110998	+	0.196024i
$910$	2.28003	−	4.87980i	0.0755821	−	0.161764i
$911$		−	0.266585i		−	0.00883236i	−0.999990	−	0.00441618i	$-0.998594\pi$
$911$		−	0.266585i		−	0.00883236i	0.999990	−	0.00441618i	$-0.00140572\pi$
$912$	−20.5156	−	21.2206i	−0.679339	−	0.702683i
$913$	27.2325	+	27.2325i	0.901264	+	0.901264i
$914$	−49.3774	+	17.9719i	−1.63326	+	0.594458i
$915$	19.5365	+	13.8241i	0.645856	+	0.457012i
$916$	−0.276528	+	0.232035i	−0.00913675	+	0.00766665i
$917$	−3.05975	−	34.9731i	−0.101042	−	1.15491i
$918$	16.3767	+	36.3028i	0.540512	+	1.19817i
$919$	−3.77776	+	2.18109i	−0.124617	+	0.0719475i	−0.561013	−	0.827807i	$-0.689588\pi$
$919$	−3.77776	+	2.18109i	−0.124617	+	0.0719475i	0.436396	+	0.899755i	$0.356255\pi$
$920$	−7.53060	+	13.0204i	−0.248276	+	0.429270i
$921$	−45.1769	−	0.189022i	−1.48863	−	0.00622847i
$922$	−31.9644	+	14.9052i	−1.05269	+	0.490878i
$923$	−1.04832	−	3.91238i	−0.0345058	−	0.128777i
$924$	−0.271253	−	0.229549i	−0.00892358	−	0.00755162i
$925$	1.44010	+	1.01165i	0.0473502	+	0.0332628i
$926$	−4.94463	+	5.89278i	−0.162491	+	0.193649i
$927$	22.0878	+	32.1133i	0.725459	+	1.05474i
$928$	−0.00307939	+	0.00215621i	−0.000101086	+	7.07810e-5i
$929$	−17.5647	+	6.39303i	−0.576280	+	0.209749i	−0.613684	−	0.789552i	$-0.710313\pi$
$929$	−17.5647	+	6.39303i	−0.576280	+	0.209749i	0.0374046	+	0.999300i	$0.488091\pi$
$930$	48.7904	−	17.4854i	1.59990	−	0.573368i
$931$	12.3242	+	7.32571i	0.403909	+	0.240090i
$932$	−0.0448641	−	0.0448641i	−0.00146957	−	0.00146957i
$933$	2.54594	−	27.7619i	0.0833503	−	0.908883i
$934$	−23.5500	−	4.15250i	−0.770580	−	0.135874i
$935$	−29.3697	−	2.59211i	−0.960491	−	0.0847711i
$936$	0.0641706	−	7.66837i	0.00209748	−	0.250649i
$937$	44.2466	+	30.9818i	1.44547	+	1.01213i	0.992713	+	0.120499i	$0.0384496\pi$
$937$	44.2466	+	30.9818i	1.44547	+	1.01213i	0.452760	+	0.891632i	$0.350439\pi$
$938$	−2.66584	−	0.714308i	−0.0870426	−	0.0233230i
$939$	20.5002	+	3.70325i	0.668999	+	0.120851i
$940$	−0.0395722	−	0.0850322i	−0.00129070	−	0.00277345i
$941$	0.0759340	−	0.208627i	0.00247538	−	0.00680104i	−0.938449	−	0.345418i	$-0.887737\pi$
$941$	0.0759340	−	0.208627i	0.00247538	−	0.00680104i	0.940924	+	0.338617i	$0.109959\pi$
$942$	−36.0387	+	25.0105i	−1.17420	+	0.814887i
$943$	−2.53523	+	9.46162i	−0.0825586	+	0.308113i
$944$	−8.66574	−	49.1459i	−0.282046	−	1.59956i
$945$	−21.1325	+	7.37445i	−0.687440	+	0.239891i
$946$	−29.9661	+	25.1445i	−0.974281	+	0.817518i
$947$	−13.3270	+	9.33170i	−0.433071	+	0.303239i	−0.769709	−	0.638395i	$-0.779599\pi$
$947$	−13.3270	+	9.33170i	−0.433071	+	0.303239i	0.336639	+	0.941634i	$0.390710\pi$
$948$	1.16759	+	0.107076i	0.0379217	+	0.00347766i
$949$			7.87879i			0.255756i
$950$	8.30677	−	29.3253i	0.269507	−	0.951437i
$951$	13.8221	+	38.4762i	0.448214	+	1.24768i
$952$	12.7557	−	27.3547i	0.413415	−	0.886572i
$953$	−9.53896	−	13.6231i	−0.308997	−	0.441294i	0.634377	−	0.773024i	$-0.281257\pi$
$953$	−9.53896	−	13.6231i	−0.308997	−	0.441294i	−0.943374	+	0.331730i	$0.892368\pi$
$954$	11.7902	+	2.18081i	0.381722	+	0.0706064i
$955$	−34.0881	−	28.6477i	−1.10306	−	0.927017i
$956$	−1.25801	+	0.221821i	−0.0406870	+	0.00717421i
$957$	−0.0623525	+	0.00519235i	−0.00201557	+	0.000167845i
$958$	3.65998	−	0.980690i	0.118249	−	0.0316846i
$959$	−15.2013	−	5.53283i	−0.490876	−	0.178664i
$960$	22.2612	+	22.4825i	0.718476	+	0.725621i
$961$	−30.2840	+	52.4534i	−0.976903	+	1.69205i
$962$	0.113914	−	0.425135i	0.00367275	−	0.0137069i
$963$	−2.46529	+	0.194912i	−0.0794428	+	0.00628096i
$964$	0.429127	−	0.511414i	0.0138213	−	0.0164715i
$965$	−2.48562	+	28.1631i	−0.0800150	+	0.906602i
$966$	−1.86122	−	10.8200i	−0.0598837	−	0.348129i
$967$	16.0065	−	34.3260i	0.514733	−	1.10385i	−0.461503	−	0.887139i	$-0.652690\pi$
$967$	16.0065	−	34.3260i	0.514733	−	1.10385i	0.976236	−	0.216710i	$-0.0695326\pi$
$968$	10.5357	−	10.5357i	0.338632	−	0.338632i
$969$	−36.1783	+	20.0806i	−1.16222	+	0.645083i
$970$	−0.0107278	+	14.0505i	−0.000344448	+	0.451135i
$971$	18.8621	+	51.8232i	0.605314	+	1.66309i	0.740330	+	0.672243i	$0.234669\pi$
$971$	18.8621	+	51.8232i	0.605314	+	1.66309i	−0.135016	+	0.990843i	$0.543109\pi$
$972$	−0.498046	+	0.477631i	−0.0159748	+	0.0153200i
$973$	−11.6338	−	1.01783i	−0.372963	−	0.0326300i
$974$	36.2248	+	30.3962i	1.16072	+	0.973957i
$975$	6.72804	−	3.83337i	0.215470	−	0.122766i
$976$	12.0793	+	20.9219i	0.386648	+	0.669694i
$977$	22.6643	−	6.07289i	0.725096	−	0.194289i	0.122652	−	0.992450i	$-0.460860\pi$
$977$	22.6643	−	6.07289i	0.725096	−	0.194289i	0.602444	+	0.798161i	$0.294194\pi$
$978$	23.0591	−	22.8670i	0.737350	−	0.731205i
$979$	4.11818	−	11.3146i	0.131618	−	0.361616i
$980$	−0.281832	−	0.163003i	−0.00900280	−	0.00520694i
$981$	15.8939	+	5.93600i	0.507454	+	0.189522i
$982$	−18.1494	−	12.7084i	−0.579172	−	0.405540i
$983$	28.3226	−	2.47791i	0.903352	−	0.0790330i	0.373993	−	0.927431i	$-0.377988\pi$
$983$	28.3226	−	2.47791i	0.903352	−	0.0790330i	0.529358	+	0.848398i	$0.322433\pi$
$984$	17.8091	+	10.3817i	0.567735	+	0.330957i
$985$	9.37520	+	13.4110i	0.298719	+	0.427309i
$986$	−0.0393601	−	0.108141i	−0.00125348	−	0.00344391i
$987$	2.85961	+	1.34805i	0.0910223	+	0.0429090i
$988$	0.172051	−	0.0128520i	0.00547366	−	0.000408877i
$989$	27.3563			0.869880
$990$	5.64224	+	21.8534i	0.179322	+	0.694548i
$991$	2.98244	−	16.9142i	0.0947402	−	0.537298i	−0.900086	−	0.435711i	$-0.856497\pi$
$991$	2.98244	−	16.9142i	0.0947402	−	0.537298i	0.994827	−	0.101587i	$-0.0323920\pi$
$992$	−2.38668	−	0.208807i	−0.0757771	−	0.00662963i
$993$	2.37847	+	5.15687i	0.0754785	+	0.163648i
$994$	−12.0181	+	2.11911i	−0.381190	+	0.0672142i
$995$	27.3486	+	47.4527i	0.867008	+	1.50435i
$996$	−1.20782	−	0.218185i	−0.0382712	−	0.00691347i
$997$	−9.19948	+	4.28979i	−0.291351	+	0.135859i	−0.562798	−	0.826594i	$-0.690275\pi$
$997$	−9.19948	+	4.28979i	−0.291351	+	0.135859i	0.271448	+	0.962453i	$0.412498\pi$
$998$	2.24923	−	1.04883i	0.0711980	−	0.0332002i
$999$	−1.59528	+	0.894529i	−0.0504725	+	0.0283016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.bi.a.233.10	yes	432
3.2	odd	2	inner	285.2.bi.a.233.27	yes	432
5.2	odd	4	inner	285.2.bi.a.62.27	yes	432
15.2	even	4	inner	285.2.bi.a.62.10	yes	432
19.4	even	9	inner	285.2.bi.a.23.10	✓	432
57.23	odd	18	inner	285.2.bi.a.23.27	yes	432
95.42	odd	36	inner	285.2.bi.a.137.27	yes	432
285.137	even	36	inner	285.2.bi.a.137.10	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.bi.a.23.10	✓	432	19.4	even	9	inner
285.2.bi.a.23.27	yes	432	57.23	odd	18	inner
285.2.bi.a.62.10	yes	432	15.2	even	4	inner
285.2.bi.a.62.27	yes	432	5.2	odd	4	inner
285.2.bi.a.137.10	yes	432	285.137	even	36	inner
285.2.bi.a.137.27	yes	432	95.42	odd	36	inner
285.2.bi.a.233.10	yes	432	1.1	even	1	trivial
285.2.bi.a.233.27	yes	432	3.2	odd	2	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26745 - 0.591021i) q^{2} +(-0.999391 + 1.41464i) q^{3} +(-0.0284545 - 0.0339107i) q^{4} +(-1.43862 + 1.71183i) q^{5} +(2.10276 - 1.20233i) q^{6} +(1.86072 + 0.498578i) q^{7} +(0.739927 + 2.76144i) q^{8} +(-1.00243 - 2.82757i) q^{9} +O(q^{10})\)	\(q+(-1.26745 - 0.591021i) q^{2} +(-0.999391 + 1.41464i) q^{3} +(-0.0284545 - 0.0339107i) q^{4} +(-1.43862 + 1.71183i) q^{5} +(2.10276 - 1.20233i) q^{6} +(1.86072 + 0.498578i) q^{7} +(0.739927 + 2.76144i) q^{8} +(-1.00243 - 2.82757i) q^{9} +(2.83511 - 1.31940i) q^{10} +(-2.08354 - 1.20293i) q^{11} +(0.0764087 - 0.00636287i) q^{12} +(0.512857 - 0.732435i) q^{13} +(-2.06369 - 1.73165i) q^{14} +(-0.983881 - 3.74593i) q^{15} +(0.678879 - 3.85011i) q^{16} +(-4.96710 - 2.31620i) q^{17} +(-0.400616 + 4.17625i) q^{18} +(-4.35855 - 0.0553822i) q^{19} +(0.0989847 + 7.55761e-5i) q^{20} +(-2.56490 + 2.13398i) q^{21} +(1.92982 + 2.75607i) q^{22} +(0.205071 - 2.34397i) q^{23} +(-4.64594 - 1.71303i) q^{24} +(-0.860721 - 4.92536i) q^{25} +(-1.08290 + 0.625215i) q^{26} +(5.00182 + 1.40776i) q^{27} +(-0.0360386 - 0.0772851i) q^{28} +(-0.0141094 - 0.00513539i) q^{29} +(-0.966904 + 5.32927i) q^{30} +(-4.78456 - 8.28710i) q^{31} +(0.143605 - 0.205089i) q^{32} +(3.78400 - 1.74527i) q^{33} +(4.92663 + 5.87133i) q^{34} +(-3.53035 + 2.46797i) q^{35} +(-0.0673610 + 0.114450i) q^{36} +(-0.248890 + 0.248890i) q^{37} +(5.49150 + 2.64619i) q^{38} +(0.523591 + 1.45750i) q^{39} +(-5.79160 - 2.70605i) q^{40} +(-4.09982 - 0.722909i) q^{41} +(4.51210 - 1.18880i) q^{42} +(1.01332 + 11.5823i) q^{43} +(0.0184937 + 0.104883i) q^{44} +(6.28244 + 2.35181i) q^{45} +(-1.64525 + 2.84966i) q^{46} +(-0.400436 - 0.858739i) q^{47} +(4.76807 + 4.80814i) q^{48} +(-2.84849 - 1.64457i) q^{49} +(-1.82007 + 6.75134i) q^{50} +(8.24067 - 4.71189i) q^{51} +(-0.0394305 + 0.00344972i) q^{52} +(0.249084 - 2.84705i) q^{53} +(-5.50754 - 4.74044i) q^{54} +(5.05665 - 1.83610i) q^{55} +5.50718i q^{56} +(4.43424 - 6.11044i) q^{57} +(0.0148478 + 0.0148478i) q^{58} +(11.9950 - 4.36582i) q^{59} +(-0.0990313 + 0.139953i) q^{60} +(-4.73372 + 3.97206i) q^{61} +(1.16633 + 13.3312i) q^{62} +(-0.455487 - 5.76109i) q^{63} +(-7.07469 + 4.08457i) q^{64} +(0.515996 + 1.93162i) q^{65} +(-5.82751 - 0.0243825i) q^{66} +(0.928483 - 0.432959i) q^{67} +(0.0627923 + 0.234344i) q^{68} +(3.11094 + 2.63265i) q^{69} +(5.93316 - 1.04151i) q^{70} +(2.91179 - 3.47013i) q^{71} +(7.06643 - 4.86036i) q^{72} +(-7.21804 + 5.05413i) q^{73} +(0.462555 - 0.168356i) q^{74} +(7.82783 + 3.70475i) q^{75} +(0.122142 + 0.149377i) q^{76} +(-3.27713 - 3.27713i) q^{77} +(0.197788 - 2.15676i) q^{78} +(15.0598 + 2.65545i) q^{79} +(5.61408 + 6.70099i) q^{80} +(-6.99025 + 5.66890i) q^{81} +(4.76906 + 3.33933i) q^{82} +(-15.4623 - 4.14311i) q^{83} +(0.145347 + 0.0262562i) q^{84} +(11.1107 - 5.17069i) q^{85} +(5.56103 - 15.2788i) q^{86} +(0.0213655 - 0.0148275i) q^{87} +(1.78017 - 6.64367i) q^{88} +(0.869065 + 4.92871i) q^{89} +(-6.57270 - 6.69385i) q^{90} +(1.31946 - 1.10716i) q^{91} +(-0.0853210 + 0.0597424i) q^{92} +(16.5049 + 1.51361i) q^{93} +1.32507i q^{94} +(6.36512 - 7.38142i) q^{95} +(0.146610 + 0.408114i) q^{96} +(-1.89890 + 4.07220i) q^{97} +(2.63833 + 3.76793i) q^{98} +(-1.31276 + 7.09721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Introduction

L-functions

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