LMFDB - Embedded newform 966.2.be.b.493.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.12
Character	$\chi$	$=$	966.493
Dual form			966.2.be.b.145.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.464807 + 0.0443837i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.63637 + 0.222555i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.464807 + 0.0443837i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.63637 + 0.222555i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(0.110081 - 0.453760i) q^{10} +(3.00724 - 1.04081i) q^{11} +(0.189251 - 0.981929i) q^{12} +(-1.51689 - 5.16605i) q^{13} +(0.651959 - 2.56417i) q^{14} +(-0.252437 - 0.392799i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-1.56954 - 0.628349i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(-1.06848 + 0.427753i) q^{19} +(0.392799 + 0.252437i) q^{20} +(-1.40587 - 2.24132i) q^{21} +3.18226i q^{22} +(-3.55532 - 3.21865i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.69557 + 0.904996i) q^{25} +(5.37804 + 0.256188i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(2.20990 + 1.45476i) q^{28} +(-1.27396 - 8.86061i) q^{29} +(0.453760 - 0.110081i) q^{30} +(8.62160 - 0.410698i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(2.30311 + 2.19601i) q^{33} +(1.10714 - 1.27770i) q^{34} +(1.21553 - 0.220457i) q^{35} +(0.959493 - 0.281733i) q^{36} +(0.911093 + 0.648786i) q^{37} +(-0.0547629 - 1.14962i) q^{38} +(3.89669 - 3.71548i) q^{39} +(-0.367025 + 0.288632i) q^{40} +(5.51363 + 2.51799i) q^{41} +(2.57787 - 0.595485i) q^{42} +(2.36073 - 3.67337i) q^{43} +(-3.00724 - 1.04081i) q^{44} +(0.233461 - 0.404366i) q^{45} +(4.20446 - 2.30706i) q^{46} +(0.907054 - 0.523688i) q^{47} +(-0.755750 + 0.654861i) q^{48} +(6.90094 - 1.17348i) q^{49} +(0.680547 - 4.73331i) q^{50} +(-0.160706 - 1.68299i) q^{51} +(-2.00108 + 4.99847i) q^{52} +(-3.97311 - 4.16688i) q^{53} +(0.458227 - 0.888835i) q^{54} +(-1.35159 + 0.617251i) q^{55} +(-2.09754 + 1.61256i) q^{56} +(-0.869806 - 0.753692i) q^{57} +(8.78995 + 1.69412i) q^{58} +(-3.90391 - 0.947077i) q^{59} +(-0.0443837 + 0.464807i) q^{60} +(-0.553604 - 0.285402i) q^{61} +(-2.43174 + 8.28175i) q^{62} +(1.34796 - 2.27662i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.934349 + 2.33389i) q^{65} +(-2.82850 + 1.45820i) q^{66} +(0.331436 + 1.71966i) q^{67} +(0.845322 + 1.46414i) q^{68} +(1.23171 - 4.63496i) q^{69} +(-0.189228 + 1.22078i) q^{70} +(-7.33701 - 8.46736i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(-3.36782 + 4.28253i) q^{73} +(-0.911093 + 0.648786i) q^{74} +(-2.95603 - 3.75889i) q^{75} +(1.10430 + 0.324251i) q^{76} +(-7.69656 + 3.41325i) q^{77} +(2.23665 + 4.89759i) q^{78} +(4.54873 - 4.77057i) q^{79} +(-0.152715 - 0.441241i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-4.18284 + 4.38683i) q^{82} +(-5.22557 - 11.4424i) q^{83} +(-0.280404 + 2.63085i) q^{84} +(0.757422 + 0.222399i) q^{85} +(2.69921 + 3.43233i) q^{86} +(7.29186 - 5.19251i) q^{87} +(1.96714 - 2.50142i) q^{88} +(-0.287508 + 6.03554i) q^{89} +(0.305769 + 0.352876i) q^{90} +(5.14881 + 13.2820i) q^{91} +(0.805032 + 4.72778i) q^{92} +(4.31569 + 7.47499i) q^{93} +(0.198217 + 1.02845i) q^{94} +(0.477650 - 0.246246i) q^{95} +(-0.371662 - 0.928368i) q^{96} +(-2.09999 + 4.59834i) q^{97} +(-1.14814 + 6.90520i) q^{98} +(-0.896546 + 3.05335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$3$	0.458227	+	0.888835i	0.264557	+	0.513169i
$3$	0.458227	+	0.888835i	0.264557	+	0.513169i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−0.464807	+	0.0443837i	−0.207868	+	0.0198490i	−0.198471	−	0.980107i	$-0.563597\pi$
$5$	−0.464807	+	0.0443837i	−0.207868	+	0.0198490i	−0.00939755	+	0.999956i	$0.502991\pi$
$6$	−0.989821	+	0.142315i	−0.404093	+	0.0580998i
$7$	−2.63637	+	0.222555i	−0.996456	+	0.0841178i
$7$	−2.63637	+	0.222555i	−0.996456	+	0.0841178i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	0.110081	−	0.453760i	0.0348107	−	0.143491i
$11$	3.00724	−	1.04081i	0.906716	−	0.313817i	0.166386	−	0.986061i	$-0.446790\pi$
$11$	3.00724	−	1.04081i	0.906716	−	0.313817i	0.740330	+	0.672243i	$0.234669\pi$
$12$	0.189251	−	0.981929i	0.0546321	−	0.283458i
$13$	−1.51689	−	5.16605i	−0.420709	−	1.43280i	−0.848630	−	0.528987i	$-0.822572\pi$
$13$	−1.51689	−	5.16605i	−0.420709	−	1.43280i	0.427921	−	0.903816i	$-0.359246\pi$
$14$	0.651959	−	2.56417i	0.174243	−	0.685302i
$15$	−0.252437	−	0.392799i	−0.0651789	−	0.101420i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−1.56954	−	0.628349i	−0.380670	−	0.152397i	0.173433	−	0.984846i	$-0.444514\pi$
$17$	−1.56954	−	0.628349i	−0.380670	−	0.152397i	−0.554102	+	0.832449i	$0.686938\pi$
$18$	−0.580057	−	0.814576i	−0.136721	−	0.191997i
$19$	−1.06848	+	0.427753i	−0.245125	+	0.0981333i	−0.490972	−	0.871175i	$-0.663358\pi$
$19$	−1.06848	+	0.427753i	−0.245125	+	0.0981333i	0.245847	+	0.969309i	$0.420934\pi$
$20$	0.392799	+	0.252437i	0.0878326	+	0.0564466i
$21$	−1.40587	−	2.24132i	−0.306786	−	0.489097i
$22$			3.18226i			0.678460i
$23$	−3.55532	−	3.21865i	−0.741335	−	0.671135i
$23$	−3.55532	−	3.21865i	−0.741335	−	0.671135i
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−4.69557	+	0.904996i	−0.939114	+	0.180999i
$26$	5.37804	+	0.256188i	1.05472	+	0.0502426i
$27$	−0.989821	−	0.142315i	−0.190491	−	0.0273885i
$28$	2.20990	+	1.45476i	0.417633	+	0.274924i
$29$	−1.27396	−	8.86061i	−0.236569	−	1.64537i	−0.668678	−	0.743552i	$-0.733140\pi$
$29$	−1.27396	−	8.86061i	−0.236569	−	1.64537i	0.432109	−	0.901821i	$-0.357769\pi$
$30$	0.453760	−	0.110081i	0.0828448	−	0.0200979i
$31$	8.62160	−	0.410698i	1.54849	−	0.0737635i	0.744180	−	0.667979i	$-0.232840\pi$
$31$	8.62160	−	0.410698i	1.54849	−	0.0737635i	0.804306	+	0.594216i	$0.202537\pi$
$32$	−0.995472	−	0.0950560i	−0.175976	−	0.0168037i
$33$	2.30311	+	2.19601i	0.400920	+	0.382276i
$34$	1.10714	−	1.27770i	0.189872	−	0.219124i
$35$	1.21553	−	0.220457i	0.205462	−	0.0372641i
$36$	0.959493	−	0.281733i	0.159915	−	0.0469554i
$37$	0.911093	+	0.648786i	0.149783	+	0.106660i	0.652492	−	0.757796i	$-0.273724\pi$
$37$	0.911093	+	0.648786i	0.149783	+	0.106660i	−0.502709	+	0.864456i	$0.667663\pi$
$38$	−0.0547629	−	1.14962i	−0.00888372	−	0.186492i
$39$	3.89669	−	3.71548i	0.623969	−	0.594954i
$40$	−0.367025	+	0.288632i	−0.0580318	+	0.0456367i
$41$	5.51363	+	2.51799i	0.861085	+	0.393244i	0.796479	−	0.604667i	$-0.206694\pi$
$41$	5.51363	+	2.51799i	0.861085	+	0.393244i	0.0646060	+	0.997911i	$0.479421\pi$
$42$	2.57787	−	0.595485i	0.397774	−	0.0918853i
$43$	2.36073	−	3.67337i	0.360008	−	0.560183i	−0.613253	−	0.789887i	$-0.710139\pi$
$43$	2.36073	−	3.67337i	0.360008	−	0.560183i	0.973261	+	0.229704i	$0.0737757\pi$
$44$	−3.00724	−	1.04081i	−0.453358	−	0.156909i
$45$	0.233461	−	0.404366i	0.0348023	−	0.0602793i
$46$	4.20446	−	2.30706i	0.619913	−	0.340158i
$47$	0.907054	−	0.523688i	0.132307	−	0.0763878i	−0.432385	−	0.901689i	$-0.642328\pi$
$47$	0.907054	−	0.523688i	0.132307	−	0.0763878i	0.564693	+	0.825301i	$0.308995\pi$
$48$	−0.755750	+	0.654861i	−0.109083	+	0.0945210i
$49$	6.90094	−	1.17348i	0.985848	−	0.167639i
$50$	0.680547	−	4.73331i	0.0962439	−	0.669391i
$51$	−0.160706	−	1.68299i	−0.0225033	−	0.235666i
$52$	−2.00108	+	4.99847i	−0.277500	+	0.693162i
$53$	−3.97311	−	4.16688i	−0.545749	−	0.572365i	0.391874	−	0.920019i	$-0.371827\pi$
$53$	−3.97311	−	4.16688i	−0.545749	−	0.572365i	−0.937623	+	0.347654i	$0.886978\pi$
$54$	0.458227	−	0.888835i	0.0623567	−	0.120955i
$55$	−1.35159	+	0.617251i	−0.182248	+	0.0832301i
$56$	−2.09754	+	1.61256i	−0.280295	+	0.215487i
$57$	−0.869806	−	0.753692i	−0.115209	−	0.0998289i
$58$	8.78995	+	1.69412i	1.15418	+	0.222449i
$59$	−3.90391	−	0.947077i	−0.508245	−	0.123299i	−0.0265668	−	0.999647i	$-0.508457\pi$
$59$	−3.90391	−	0.947077i	−0.508245	−	0.123299i	−0.481678	+	0.876348i	$0.659973\pi$
$60$	−0.0443837	+	0.464807i	−0.00572991	+	0.0600064i
$61$	−0.553604	−	0.285402i	−0.0708817	−	0.0365420i	0.422421	−	0.906400i	$-0.361180\pi$
$61$	−0.553604	−	0.285402i	−0.0708817	−	0.0365420i	−0.493303	+	0.869858i	$0.664211\pi$
$62$	−2.43174	+	8.28175i	−0.308831	+	1.05178i
$63$	1.34796	−	2.27662i	0.169827	−	0.286827i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.934349	+	2.33389i	0.115892	+	0.289484i
$66$	−2.82850	+	1.45820i	−0.348165	+	0.179491i
$67$	0.331436	+	1.71966i	0.0404914	+	0.210089i	0.996540	−	0.0831205i	$-0.0264887\pi$
$67$	0.331436	+	1.71966i	0.0404914	+	0.210089i	−0.956048	+	0.293210i	$0.905277\pi$
$68$	0.845322	+	1.46414i	0.102510	+	0.177553i
$69$	1.23171	−	4.63496i	0.148280	−	0.557984i
$70$	−0.189228	+	1.22078i	−0.0226171	+	0.145911i
$71$	−7.33701	−	8.46736i	−0.870743	−	1.00489i	−0.999912	−	0.0132684i	$-0.995776\pi$
$71$	−7.33701	−	8.46736i	−0.870743	−	1.00489i	0.129169	−	0.991623i	$-0.458769\pi$
$72$	−0.0475819	+	0.998867i	−0.00560758	+	0.117718i
$73$	−3.36782	+	4.28253i	−0.394174	+	0.501233i	−0.942118	−	0.335282i	$-0.891168\pi$
$73$	−3.36782	+	4.28253i	−0.394174	+	0.501233i	0.547944	+	0.836515i	$0.315411\pi$
$74$	−0.911093	+	0.648786i	−0.105912	+	0.0754199i
$75$	−2.95603	−	3.75889i	−0.341333	−	0.434040i
$76$	1.10430	+	0.324251i	0.126672	+	0.0371942i
$77$	−7.69656	+	3.41325i	−0.877105	+	0.388976i
$78$	2.23665	+	4.89759i	0.253251	+	0.554543i
$79$	4.54873	−	4.77057i	0.511772	−	0.536731i	−0.416253	−	0.909249i	$-0.636657\pi$
$79$	4.54873	−	4.77057i	0.511772	−	0.536731i	0.928025	+	0.372518i	$0.121505\pi$
$80$	−0.152715	−	0.441241i	−0.0170741	−	0.0493323i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	−4.18284	+	4.38683i	−0.461917	+	0.484445i
$83$	−5.22557	−	11.4424i	−0.573581	−	1.25597i	−0.944869	−	0.327449i	$-0.893811\pi$
$83$	−5.22557	−	11.4424i	−0.573581	−	1.25597i	0.371288	−	0.928518i	$-0.378916\pi$
$84$	−0.280404	+	2.63085i	−0.0305946	+	0.287049i
$85$	0.757422	+	0.222399i	0.0821540	+	0.0241226i
$86$	2.69921	+	3.43233i	0.291064	+	0.370118i
$87$	7.29186	−	5.19251i	0.781769	−	0.556695i
$88$	1.96714	−	2.50142i	0.209698	−	0.266653i
$89$	−0.287508	+	6.03554i	−0.0304758	+	0.639766i	0.931024	+	0.364959i	$0.118917\pi$
$89$	−0.287508	+	6.03554i	−0.0304758	+	0.639766i	−0.961499	+	0.274807i	$0.911386\pi$
$90$	0.305769	+	0.352876i	0.0322308	+	0.0371964i
$91$	5.14881	+	13.2820i	0.539742	+	1.39234i
$92$	0.805032	+	4.72778i	0.0839304	+	0.492905i
$93$	4.31569	+	7.47499i	0.447516	+	0.775121i
$94$	0.198217	+	1.02845i	0.0204445	+	0.106076i
$95$	0.477650	−	0.246246i	0.0490059	−	0.0252643i
$96$	−0.371662	−	0.928368i	−0.0379326	−	0.0947512i
$97$	−2.09999	+	4.59834i	−0.213222	+	0.466890i	−0.985777	−	0.168057i	$-0.946251\pi$
$97$	−2.09999	+	4.59834i	−0.213222	+	0.466890i	0.772556	+	0.634947i	$0.218978\pi$
$98$	−1.14814	+	6.90520i	−0.115980	+	0.697530i
$99$	−0.896546	+	3.05335i	−0.0901062	+	0.306874i
$100$	4.25040	+	2.19123i	0.425040	+	0.219123i
$101$	1.28250	−	13.4309i	0.127613	−	1.33643i	−0.674065	−	0.738672i	$-0.735453\pi$
$101$	1.28250	−	13.4309i	0.127613	−	1.33643i	0.801678	−	0.597756i	$-0.203941\pi$
$102$	1.64299	+	0.398585i	0.162680	+	0.0394658i
$103$	9.44935	+	1.82121i	0.931072	+	0.179449i	0.632166	−	0.774833i	$-0.282166\pi$
$103$	9.44935	+	1.82121i	0.931072	+	0.179449i	0.298906	+	0.954283i	$0.403378\pi$
$104$	−4.06906	−	3.52586i	−0.399005	−	0.345739i
$105$	0.752938	+	0.979385i	0.0734792	+	0.0955782i
$106$	5.23718	−	2.39174i	0.508680	−	0.232306i
$107$	1.88020	−	3.64708i	0.181766	−	0.352576i	−0.780295	−	0.625412i	$-0.784931\pi$
$107$	1.88020	−	3.64708i	0.181766	−	0.352576i	0.962061	+	0.272835i	$0.0879614\pi$
$108$	0.690079	+	0.723734i	0.0664029	+	0.0696413i
$109$	−5.64819	+	14.1085i	−0.540998	+	1.35135i	0.366157	+	0.930553i	$0.380673\pi$
$109$	−5.64819	+	14.1085i	−0.540998	+	1.35135i	−0.907155	+	0.420796i	$0.861751\pi$
$110$	−0.141240	−	1.47914i	−0.0134668	−	0.141030i
$111$	−0.159177	+	1.10710i	−0.0151084	+	0.105082i
$112$	−0.837830	−	2.50959i	−0.0791675	−	0.237134i
$113$	7.22709	−	6.26231i	0.679867	−	0.589109i	−0.244943	−	0.969538i	$-0.578769\pi$
$113$	7.22709	−	6.26231i	0.679867	−	0.589109i	0.924810	+	0.380429i	$0.124224\pi$
$114$	0.996725	−	0.575459i	0.0933518	−	0.0538967i
$115$	1.79539	+	1.33825i	0.167421	+	0.124793i
$116$	−4.47586	+	7.75242i	−0.415573	+	0.719794i
$117$	5.08802	+	1.76098i	0.470388	+	0.162803i
$118$	2.17183	−	3.37944i	0.199933	−	0.311102i
$119$	4.27774	+	1.30725i	0.392140	+	0.119836i
$120$	−0.424727	−	0.193966i	−0.0387721	−	0.0177066i
$121$	−0.686406	+	0.539795i	−0.0624005	+	0.0490723i
$122$	0.450772	−	0.429810i	0.0408109	−	0.0389131i
$123$	0.288412	+	6.05452i	0.0260053	+	0.545918i
$124$	−7.03091	−	5.00669i	−0.631395	−	0.449614i
$125$	4.38241	−	1.28679i	0.391974	−	0.115094i
$126$	1.71053	+	2.01843i	0.152387	+	0.179816i
$127$	−2.84537	+	3.28374i	−0.252486	+	0.291385i	−0.867817	−	0.496885i	$-0.834477\pi$
$127$	−2.84537	+	3.28374i	−0.252486	+	0.291385i	0.615330	+	0.788269i	$0.289023\pi$
$128$	0.723734	+	0.690079i	0.0639697	+	0.0609949i
$129$	4.34677	+	0.415066i	0.382711	+	0.0365445i
$130$	−2.51113	+	0.119620i	−0.220240	+	0.0104913i
$131$	−12.1980	+	2.95921i	−1.06575	+	0.258547i	−0.730030	−	0.683415i	$-0.760494\pi$
$131$	−12.1980	+	2.95921i	−1.06575	+	0.258547i	−0.335717	+	0.941963i	$0.608979\pi$
$132$	−0.452883	−	3.14987i	−0.0394184	−	0.274161i
$133$	2.72170	−	1.36551i	0.236002	−	0.118405i
$134$	−1.73348	−	0.249237i	−0.149750	−	0.0215308i
$135$	0.466393	+	0.0222170i	0.0401407	+	0.00191214i
$136$	−1.66009	+	0.319957i	−0.142352	+	0.0274361i
$137$	−5.34351	−	3.08508i	−0.456527	−	0.263576i	0.254056	−	0.967190i	$-0.418235\pi$
$137$	−5.34351	−	3.08508i	−0.456527	−	0.263576i	−0.710583	+	0.703614i	$0.751569\pi$
$138$	3.97719	+	2.67991i	0.338561	+	0.228129i
$139$			10.2401i			0.868550i	0.900780	+	0.434275i	$0.142995\pi$
$139$			10.2401i			0.868550i	−0.900780	+	0.434275i	$0.857005\pi$
$140$	−1.09175	−	0.578099i	−0.0922695	−	0.0488583i
$141$	0.881109	+	0.566254i	0.0742027	+	0.0476872i
$142$	10.4014	−	4.16408i	0.872863	−	0.349442i
$143$	−9.93854	−	13.9567i	−0.831103	−	1.16712i
$144$	−0.928368	−	0.371662i	−0.0773640	−	0.0309719i
$145$	0.985414	+	4.06193i	0.0818342	+	0.337325i
$146$	−2.94549	−	4.58327i	−0.243771	−	0.379314i
$147$	4.20522	+	5.59608i	0.346841	+	0.461557i
$148$	−0.315114	−	1.07318i	−0.0259022	−	0.0882149i
$149$	−1.29136	+	6.70023i	−0.105793	+	0.548904i	0.889897	+	0.456161i	$0.150776\pi$
$149$	−1.29136	+	6.70023i	−0.105793	+	0.548904i	−0.995690	+	0.0927433i	$0.970436\pi$
$150$	4.51898	−	1.56403i	0.368973	−	0.127703i
$151$	3.62676	−	14.9497i	0.295141	−	1.21659i	−0.610318	−	0.792156i	$-0.708959\pi$
$151$	3.62676	−	14.9497i	0.295141	−	1.21659i	0.905460	−	0.424432i	$-0.139526\pi$
$152$	−0.667598	+	0.937511i	−0.0541494	+	0.0760422i
$153$	1.42226	−	0.914032i	0.114983	−	0.0738951i
$154$	−0.708227	−	8.38962i	−0.0570706	−	0.676055i
$155$	−3.98916	+	0.573554i	−0.320417	+	0.0460690i
$156$	−5.35976	+	0.511795i	−0.429124	+	0.0409764i
$157$	−13.8326	−	10.8781i	−1.10396	−	0.868163i	−0.111873	−	0.993722i	$-0.535685\pi$
$157$	−13.8326	−	10.8781i	−1.10396	−	0.868163i	−0.992086	+	0.125559i	$0.959927\pi$
$158$	3.02045	+	5.85886i	0.240294	+	0.466106i
$159$	1.88308	−	5.44081i	0.149338	−	0.431485i
$160$	0.466922			0.0369134
$161$	10.0895	+	7.69431i	0.795162	+	0.606397i
$162$	1.00000			0.0785674
$163$	0.930967	−	2.68985i	0.0729190	−	0.210686i	−0.902651	−	0.430372i	$-0.858382\pi$
$163$	0.930967	−	2.68985i	0.0729190	−	0.210686i	0.975570	+	0.219687i	$0.0705035\pi$
$164$	−2.77749	−	5.38758i	−0.216885	−	0.420699i
$165$	−1.16797	−	0.918501i	−0.0909263	−	0.0715052i
$166$	12.5222	−	1.19572i	0.971911	−	0.0928062i
$167$	−10.3774	+	1.49205i	−0.803030	+	0.115458i	−0.531595	−	0.846999i	$-0.678407\pi$
$167$	−10.3774	+	1.49205i	−0.803030	+	0.115458i	−0.271435	+	0.962457i	$0.587498\pi$
$168$	−2.39444	−	1.12545i	−0.184735	−	0.0868303i
$169$	−13.4508	+	8.64430i	−1.03468	+	0.664946i
$170$	−0.457896	+	0.643025i	−0.0351190	+	0.0493178i
$171$	0.271339	−	1.11848i	0.0207498	−	0.0855320i
$172$	−4.12638	+	1.42815i	−0.314634	+	0.108896i
$173$	−3.43735	+	17.8347i	−0.261337	+	1.35595i	0.579639	+	0.814873i	$0.303194\pi$
$173$	−3.43735	+	17.8347i	−0.261337	+	1.35595i	−0.840976	+	0.541072i	$0.818019\pi$
$174$	2.52199	+	8.58911i	0.191192	+	0.651139i
$175$	12.1779	−	3.43093i	0.920560	−	0.259354i
$176$	1.72046	+	2.67709i	0.129684	+	0.201793i
$177$	−0.947077	−	3.90391i	−0.0711867	−	0.293435i
$178$	−5.60956	−	2.24573i	−0.420454	−	0.168324i
$179$	−8.57004	−	12.0349i	−0.640555	−	0.899533i	0.358872	−	0.933387i	$-0.383161\pi$
$179$	−8.57004	−	12.0349i	−0.640555	−	0.899533i	−0.999427	+	0.0338537i	$0.989222\pi$
$180$	−0.433475	+	0.173537i	−0.0323093	+	0.0129347i
$181$	−4.90846	−	3.15447i	−0.364843	−	0.234470i	0.345356	−	0.938472i	$-0.387758\pi$
$181$	−4.90846	−	3.15447i	−0.364843	−	0.234470i	−0.710198	+	0.704002i	$0.751395\pi$
$182$	−14.2356	+	0.521503i	−1.05521	+	0.0386564i
$183$		−	0.622841i		−	0.0460418i
$184$	−4.73106	−	0.785550i	−0.348778	−	0.0579115i
$185$	−0.452278	−	0.261123i	−0.0332522	−	0.0191981i
$186$	−8.47540	+	1.63350i	−0.621446	+	0.119774i
$187$	−5.37398	−	0.255994i	−0.392984	−	0.0187201i
$188$	−1.03672	−	0.149057i	−0.0756102	−	0.0108711i
$189$	2.64121	+	0.154906i	0.192120	+	0.0112677i
$190$	0.0764784	+	0.531919i	0.00554833	+	0.0385895i
$191$	16.2893	−	3.95174i	1.17865	−	0.285938i	0.401863	−	0.915700i	$-0.368363\pi$
$191$	16.2893	−	3.95174i	1.17865	−	0.285938i	0.776788	+	0.629762i	$0.216848\pi$
$192$	0.998867	−	0.0475819i	0.0720870	−	0.00343393i
$193$	−22.8776	−	2.18455i	−1.64677	−	0.157247i	−0.769962	−	0.638090i	$-0.779725\pi$
$193$	−22.8776	−	2.18455i	−1.64677	−	0.157247i	−0.876807	+	0.480843i	$0.840331\pi$
$194$	−3.65859	−	3.48846i	−0.262672	−	0.250457i
$195$	−1.64630	+	1.89993i	−0.117894	+	0.136057i
$196$	−6.14990	−	3.34346i	−0.439278	−	0.238819i
$197$	−6.28916	+	1.84666i	−0.448084	+	0.131569i	−0.497987	−	0.867185i	$-0.665927\pi$
$197$	−6.28916	+	1.84666i	−0.448084	+	0.131569i	0.0499025	+	0.998754i	$0.484109\pi$
$198$	−2.59219	−	1.84589i	−0.184219	−	0.131182i
$199$	1.21286	+	25.4610i	0.0859772	+	1.80488i	0.471165	+	0.882045i	$0.343834\pi$
$199$	1.21286	+	25.4610i	0.0859772	+	1.80488i	−0.385187	+	0.922838i	$0.625863\pi$
$200$	−3.46088	+	3.29995i	−0.244722	+	0.233341i
$201$	−1.37662	+	1.08258i	−0.0970991	+	0.0763596i
$202$	12.2728	+	5.60479i	0.863510	+	0.394352i
$203$	5.33061	+	23.0763i	0.374136	+	1.61964i
$204$	−0.914032	+	1.42226i	−0.0639950	+	0.0995782i
$205$	−2.67453	−	0.925665i	−0.186798	−	0.0646513i
$206$	−4.81163	+	8.33398i	−0.335242	+	0.580656i
$207$	4.68412	−	1.02908i	0.325569	−	0.0715258i
$208$	4.66280	−	2.69207i	0.323307	−	0.186662i
$209$	−2.76795	+	2.39844i	−0.191463	+	0.165904i
$210$	−1.17178	+	0.391201i	−0.0808606	+	0.0269954i
$211$	2.96190	−	20.6005i	0.203906	−	1.41819i	−0.588647	−	0.808390i	$-0.700339\pi$
$211$	2.96190	−	20.6005i	0.203906	−	1.41819i	0.792552	−	0.609804i	$-0.208752\pi$
$212$	0.547282	+	5.73140i	0.0375875	+	0.393634i
$213$	4.16408	−	10.4014i	0.285318	−	0.712690i
$214$	2.83154	+	2.96963i	0.193560	+	0.203000i
$215$	−0.934246	+	1.81219i	−0.0637151	+	0.123590i
$216$	−0.909632	+	0.415415i	−0.0618926	+	0.0282654i
$217$	−22.6384	+	3.00153i	−1.53679	+	0.203757i
$218$	−11.4852	−	9.95198i	−0.777876	−	0.674033i
$219$	−5.34969	−	1.03107i	−0.361499	−	0.0696732i
$220$	1.44398	+	0.350306i	0.0973532	+	0.0236176i
$221$	−0.865264	+	9.06146i	−0.0582040	+	0.609540i
$222$	−0.994151	−	0.512520i	−0.0667230	−	0.0343981i
$223$	2.68046	−	9.12882i	0.179497	−	0.611311i	−0.819758	−	0.572711i	$-0.805892\pi$
$223$	2.68046	−	9.12882i	0.179497	−	0.611311i	0.999255	−	0.0386003i	$-0.0122899\pi$
$224$	2.64559	+	0.0290562i	0.176766	+	0.00194140i
$225$	1.98651	−	4.34985i	0.132434	−	0.289990i
$226$	3.55414	+	8.87781i	0.236418	+	0.590543i
$227$	−7.94933	+	4.09817i	−0.527616	+	0.272005i	−0.701386	−	0.712781i	$-0.747435\pi$
$227$	−7.94933	+	4.09817i	−0.527616	+	0.272005i	0.173771	+	0.984786i	$0.444405\pi$
$228$	0.217813	+	1.13012i	0.0144250	+	0.0748440i
$229$	13.0591	+	22.6190i	0.862967	+	1.49470i	0.869052	+	0.494721i	$0.164730\pi$
$229$	13.0591	+	22.6190i	0.862967	+	1.49470i	−0.00608470	+	0.999981i	$0.501937\pi$
$230$	−1.85187	+	1.25895i	−0.122108	+	0.0830126i
$231$	−6.56059	−	5.27694i	−0.431655	−	0.347197i
$232$	−5.86213	−	6.76526i	−0.384868	−	0.444161i
$233$	0.422343	−	8.86606i	0.0276686	−	0.580835i	−0.941882	−	0.335944i	$-0.890945\pi$
$233$	0.422343	−	8.86606i	0.0276686	−	0.580835i	0.969551	−	0.244891i	$-0.0787522\pi$
$234$	−3.32826	+	4.23222i	−0.217575	+	0.276669i
$235$	−0.398362	+	0.283672i	−0.0259863	+	0.0185048i
$236$	2.48323	+	3.15769i	0.161645	+	0.205548i
$237$	6.32460	+	1.85707i	0.410827	+	0.120630i
$238$	−2.63447	+	3.61491i	−0.170767	+	0.234320i
$239$	−2.64051	−	5.78191i	−0.170800	−	0.374000i	0.804803	−	0.593542i	$-0.202271\pi$
$239$	−2.64051	−	5.78191i	−0.170800	−	0.374000i	−0.975603	+	0.219542i	$0.929544\pi$
$240$	0.322213	−	0.337927i	0.0207987	−	0.0218131i
$241$	5.83563	+	16.8609i	0.375906	+	1.08611i	0.961334	+	0.275385i	$0.0888053\pi$
$241$	5.83563	+	16.8609i	0.375906	+	1.08611i	−0.585428	+	0.810724i	$0.699074\pi$
$242$	−0.285606	−	0.825204i	−0.0183594	−	0.0530461i
$243$	0.690079	−	0.723734i	0.0442686	−	0.0464276i
$244$	0.258738	+	0.566556i	0.0165640	+	0.0362701i
$245$	−3.15552	+	0.851730i	−0.201599	+	0.0544150i
$246$	−5.81586	−	1.70769i	−0.370806	−	0.108878i
$247$	3.83055	+	4.87094i	0.243732	+	0.309931i
$248$	7.03091	−	5.00669i	0.446464	−	0.317925i
$249$	7.77592	−	9.88788i	0.492779	−	0.626619i
$250$	−0.217327	+	4.56225i	−0.0137449	+	0.288542i
$251$	−2.93192	−	3.38362i	−0.185061	−	0.213572i	0.655637	−	0.755077i	$-0.272400\pi$
$251$	−2.93192	−	3.38362i	−0.185061	−	0.213572i	−0.840698	+	0.541504i	$0.817855\pi$
$252$	−2.46688	+	0.956292i	−0.155399	+	0.0602408i
$253$	−14.0417	−	5.97881i	−0.882794	−	0.375885i
$254$	−2.17250	−	3.76289i	−0.136315	−	0.236105i
$255$	0.149395	+	0.775133i	0.00935546	+	0.0485407i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	8.72768	+	21.8007i	0.544417	+	1.35989i	0.904302	+	0.426892i	$0.140392\pi$
$257$	8.72768	+	21.8007i	0.544417	+	1.35989i	−0.359885	+	0.932997i	$0.617184\pi$
$258$	−1.81393	+	3.97194i	−0.112930	+	0.247282i
$259$	−2.54637	−	1.50768i	−0.158224	−	0.0936824i
$260$	0.708268	−	2.41214i	0.0439249	−	0.149595i
$261$	7.95661	+	4.10192i	0.492502	+	0.253902i
$262$	1.19313	−	12.4950i	0.0737118	−	0.771945i
$263$	2.69133	+	0.652911i	0.165955	+	0.0402602i	0.317875	−	0.948133i	$-0.397031\pi$
$263$	2.69133	+	0.652911i	0.165955	+	0.0402602i	−0.151921	+	0.988393i	$0.548546\pi$
$264$	3.12475	+	0.602246i	0.192315	+	0.0370657i
$265$	2.03167	+	1.76045i	0.124805	+	0.108144i
$266$	0.400228	+	3.01863i	0.0245396	+	0.185084i
$267$	−5.49635	+	2.51010i	−0.336371	+	0.153615i
$268$	0.802494	−	1.55662i	0.0490201	−	0.0950858i
$269$	−5.37188	−	5.63387i	−0.327529	−	0.343503i	0.539295	−	0.842117i	$-0.318691\pi$
$269$	−5.37188	−	5.63387i	−0.327529	−	0.343503i	−0.866824	+	0.498614i	$0.833842\pi$
$270$	−0.173537	+	0.433475i	−0.0105611	+	0.0263805i
$271$	−0.905855	−	9.48655i	−0.0550268	−	0.576267i	−0.980374	−	0.197146i	$-0.936833\pi$
$271$	−0.905855	−	9.48655i	−0.0550268	−	0.576267i	0.925347	−	0.379120i	$-0.123773\pi$
$272$	0.240604	−	1.67344i	0.0145888	−	0.101467i
$273$	−9.44623	+	10.6626i	−0.571712	+	0.645332i
$274$	4.66309	−	4.04059i	0.281708	−	0.244101i
$275$	−13.1788	+	7.60876i	−0.794709	+	0.458825i
$276$	−3.83333	+	2.88194i	−0.230740	+	0.173472i
$277$	8.50990	−	14.7396i	0.511310	−	0.885615i	−0.488604	−	0.872506i	$-0.662494\pi$
$277$	8.50990	−	14.7396i	0.511310	−	0.885615i	0.999914	−	0.0131094i	$-0.00417297\pi$
$278$	−9.67686	−	3.34919i	−0.580379	−	0.200871i
$279$	−4.66648	+	7.26118i	−0.279375	+	0.434715i
$280$	0.903379	−	0.842625i	0.0539872	−	0.0503565i
$281$	−24.4578	−	11.1695i	−1.45903	−	0.666317i	−0.481372	−	0.876516i	$-0.659861\pi$
$281$	−24.4578	−	11.1695i	−1.45903	−	0.666317i	−0.977659	+	0.210199i	$0.932589\pi$
$282$	−0.823293	+	0.647445i	−0.0490264	+	0.0385548i
$283$	12.2955	−	11.7238i	0.730893	−	0.696905i	−0.230196	−	0.973144i	$-0.573937\pi$
$283$	12.2955	−	11.7238i	0.730893	−	0.696905i	0.961089	+	0.276239i	$0.0890882\pi$
$284$	0.533104	+	11.1912i	0.0316339	+	0.664078i
$285$	0.437744	+	0.311716i	0.0259297	+	0.0184645i
$286$	16.4397	−	4.82713i	0.972100	−	0.285434i
$287$	−15.0964	−	5.41128i	−0.891112	−	0.319418i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	−10.2348	−	9.75890i	−0.602050	−	0.574053i
$290$	−4.16083	−	0.397311i	−0.244332	−	0.0233309i
$291$	−5.04944	+	0.240534i	−0.296003	+	0.0141004i
$292$	5.29457	−	1.28445i	0.309842	−	0.0751667i
$293$	−3.81973	−	26.5668i	−0.223151	−	1.55205i	−0.726012	−	0.687682i	$-0.758629\pi$
$293$	−3.81973	−	26.5668i	−0.223151	−	1.55205i	0.502861	−	0.864367i	$-0.332281\pi$
$294$	−6.66369	+	2.14364i	−0.388635	+	0.125019i
$295$	1.85660	+	0.266939i	0.108095	+	0.0155418i
$296$	1.11722	+	0.0532198i	0.0649371	+	0.00309334i
$297$	−3.12475	+	0.602246i	−0.181316	+	0.0349459i
$298$	−5.90936	−	3.41177i	−0.342320	−	0.197638i
$299$	−11.2347	+	23.2493i	−0.649718	+	1.34454i
$300$			4.78198i			0.276088i
$301$	−5.40624	+	10.2098i	−0.311610	+	0.588481i
$302$	12.9413	+	8.31685i	0.744687	+	0.478581i
$303$	12.5256	−	5.01448i	0.719575	−	0.288074i
$304$	−0.667598	−	0.937511i	−0.0382894	−	0.0537699i
$305$	0.269986	+	0.108086i	0.0154594	+	0.00618900i
$306$	0.398585	+	1.64299i	0.0227856	+	0.0939234i
$307$	−1.04175	−	1.62100i	−0.0594561	−	0.0925154i	0.810253	−	0.586081i	$-0.199330\pi$
$307$	−1.04175	−	1.62100i	−0.0594561	−	0.0925154i	−0.869709	+	0.493565i	$0.835693\pi$
$308$	8.15984	+	2.07470i	0.464950	+	0.118217i
$309$	2.71118	+	9.23344i	0.154234	+	0.525272i
$310$	0.762716	−	3.95735i	0.0433194	−	0.224762i
$311$	20.4666	−	7.08354i	1.16055	−	0.401671i	0.322132	−	0.946695i	$-0.395601\pi$
$311$	20.4666	−	7.08354i	1.16055	−	0.401671i	0.838420	+	0.545024i	$0.183479\pi$
$312$	1.26936	−	5.23237i	0.0718634	−	0.296225i
$313$	−14.2144	+	19.9614i	−0.803447	+	1.12828i	0.185881	+	0.982572i	$0.440486\pi$
$313$	−14.2144	+	19.9614i	−0.803447	+	1.12828i	−0.989327	+	0.145711i	$0.953453\pi$
$314$	14.8040	−	9.51393i	0.835436	−	0.536902i
$315$	−0.525496	+	1.11802i	−0.0296084	+	0.0629932i
$316$	−6.52452	+	0.938084i	−0.367033	+	0.0527713i
$317$	8.69248	−	0.830031i	0.488218	−	0.0466192i	0.151955	−	0.988387i	$-0.451443\pi$
$317$	8.69248	−	0.830031i	0.488218	−	0.0466192i	0.336263	+	0.941768i	$0.390837\pi$
$318$	4.52568	+	3.55903i	0.253787	+	0.199581i
$319$	−13.0534	−	25.3200i	−0.730848	−	1.41765i
$320$	−0.152715	+	0.441241i	−0.00853703	+	0.0246661i
$321$	4.10321			0.229019
$322$	−10.5711	+	7.01800i	−0.589103	+	0.391098i
$323$	1.94580			0.108267
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	11.7979	+	22.8847i	0.654430	+	1.26942i
$326$	2.23742	+	1.75953i	0.123919	+	0.0974513i
$327$	−15.1283	+	1.44458i	−0.836596	+	0.0798852i
$328$	5.99969	−	0.862625i	0.331278	−	0.0476305i
$329$	−2.27479	+	1.58251i	−0.125413	+	0.0872464i
$330$	1.24999	−	0.803319i	0.0688097	−	0.0442213i
$331$	−5.17730	+	7.27050i	−0.284570	+	0.399623i	−0.931974	−	0.362524i	$-0.881915\pi$
$331$	−5.17730	+	7.27050i	−0.284570	+	0.399623i	0.647404	+	0.762147i	$0.275854\pi$
$332$	−2.96565	+	12.2246i	−0.162761	+	0.670910i
$333$	−1.05697	+	0.365821i	−0.0579217	+	0.0200469i
$334$	1.98414	−	10.2947i	0.108567	−	0.563300i
$335$	−0.230379	−	0.784598i	−0.0125869	−	0.0428672i
$336$	1.84670	−	1.89465i	0.100746	−	0.103362i
$337$	5.40366	+	8.40826i	0.294356	+	0.458027i	0.956660	−	0.291209i	$-0.0940574\pi$
$337$	5.40366	+	8.40826i	0.294356	+	0.458027i	−0.662303	+	0.749236i	$0.730421\pi$
$338$	−3.76955	−	15.5383i	−0.205036	−	0.845172i
$339$	8.87781	+	3.55414i	0.482176	+	0.193034i
$340$	−0.457896	−	0.643025i	−0.0248329	−	0.0348729i
$341$	25.4997	−	10.2086i	1.38089	−	0.552824i
$342$	0.968215	+	0.622234i	0.0523550	+	0.0336465i
$343$	−17.9323	+	4.62956i	−0.968253	+	0.249973i
$344$		−	4.36654i		−	0.235428i
$345$	−0.366790	+	2.20903i	−0.0197473	+	0.118930i
$346$	−15.7295	−	9.08145i	−0.845625	−	0.488222i
$347$	2.14324	−	0.413077i	0.115055	−	0.0221751i	−0.131398	−	0.991330i	$-0.541947\pi$
$347$	2.14324	−	0.413077i	0.115055	−	0.0221751i	0.246454	+	0.969155i	$0.420735\pi$
$348$	−8.94158	−	0.425940i	−0.479319	−	0.0228328i
$349$	18.6544	+	2.68210i	0.998548	+	0.143570i	0.622158	−	0.782892i	$-0.286256\pi$
$349$	18.6544	+	2.68210i	0.998548	+	0.143570i	0.376390	+	0.926461i	$0.377165\pi$
$350$	−0.740756	+	12.6302i	−0.0395951	+	0.675115i
$351$	0.766243	+	5.32934i	0.0408990	+	0.284459i
$352$	−3.09256	+	0.750246i	−0.164834	+	0.0399882i
$353$	21.8464	−	1.04067i	1.16277	−	0.0553895i	0.542692	−	0.839931i	$-0.317405\pi$
$353$	21.8464	−	1.04067i	1.16277	−	0.0553895i	0.620076	+	0.784542i	$0.287102\pi$
$354$	3.99895	+	0.381854i	0.212542	+	0.0202953i
$355$	3.78611	+	3.61005i	0.200946	+	0.191601i
$356$	3.95692	−	4.56653i	0.209716	−	0.242026i
$357$	0.798239	+	4.40122i	0.0422473	+	0.232938i
$358$	14.1760	−	4.16245i	0.749225	−	0.219992i
$359$	27.1853	+	19.3586i	1.43479	+	1.02171i	0.992156	+	0.125002i	$0.0398939\pi$
$359$	27.1853	+	19.3586i	1.43479	+	1.02171i	0.442630	+	0.896704i	$0.354046\pi$
$360$	−0.0222170	−	0.466393i	−0.00117094	−	0.0245811i
$361$	−12.7923	+	12.1974i	−0.673278	+	0.641969i
$362$	4.58638	−	3.60677i	0.241055	−	0.189568i
$363$	−0.794319	−	0.362753i	−0.0416909	−	0.0190396i
$364$	4.16317	−	13.6232i	0.218210	−	0.714049i
$365$	1.37531	−	2.14003i	0.0719872	−	0.112014i
$366$	0.588586	+	0.203711i	0.0307659	+	0.0106482i
$367$	−7.27056	+	12.5930i	−0.379520	+	0.657348i	−0.990992	−	0.133918i	$-0.957244\pi$
$367$	−7.27056	+	12.5930i	−0.379520	+	0.657348i	0.611472	+	0.791266i	$0.290578\pi$
$368$	2.28972	−	4.21393i	0.119360	−	0.219666i
$369$	−5.24932	+	3.03069i	−0.273268	+	0.157772i
$370$	0.394687	−	0.341998i	0.0205188	−	0.0177796i
$371$	11.4020	+	10.1012i	0.591960	+	0.524429i
$372$	1.22837	−	8.54352i	0.0636882	−	0.442961i
$373$	−2.29796	−	24.0653i	−0.118984	−	1.24605i	−0.835895	−	0.548889i	$-0.815051\pi$
$373$	−2.29796	−	24.0653i	−0.118984	−	1.24605i	0.716911	−	0.697164i	$-0.245555\pi$
$374$	1.99957	−	4.99468i	0.103395	−	0.258269i
$375$	3.15188	+	3.30560i	0.162762	+	0.170700i
$376$	0.479935	−	0.930945i	0.0247508	−	0.0480098i
$377$	−43.8418	+	20.0219i	−2.25797	+	1.03118i
$378$	−1.01024	+	2.44528i	−0.0519612	+	0.125772i
$379$	27.2245	+	23.5902i	1.39843	+	1.21175i	0.947732	+	0.319068i	$0.103370\pi$
$379$	27.2245	+	23.5902i	1.39843	+	1.21175i	0.450697	+	0.892677i	$0.351176\pi$
$380$	−0.527678	−	0.101702i	−0.0270693	−	0.00521718i
$381$	−4.22253	−	1.02437i	−0.216327	−	0.0524803i
$382$	−1.59331	+	16.6859i	−0.0815207	+	0.853723i
$383$	17.1894	+	8.86177i	0.878339	+	0.452815i	0.837555	−	0.546353i	$-0.183984\pi$
$383$	17.1894	+	8.86177i	0.878339	+	0.452815i	0.0407841	+	0.999168i	$0.487014\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	3.42593	−	1.92811i	0.174601	−	0.0982654i
$386$	9.54694	−	20.9049i	0.485927	−	1.06403i
$387$	1.62288	+	4.05375i	0.0824955	+	0.206064i
$388$	4.49321	−	2.31641i	0.228108	−	0.117598i
$389$	3.38960	+	17.5869i	0.171860	+	0.891692i	0.960804	+	0.277228i	$0.0894157\pi$
$389$	3.38960	+	17.5869i	0.171860	+	0.891692i	−0.788945	+	0.614464i	$0.789372\pi$
$390$	−1.25699	−	2.17716i	−0.0636500	−	0.110245i
$391$	3.55778	+	7.28578i	0.179925	+	0.368458i
$392$	5.17101	−	4.71812i	0.261175	−	0.238301i
$393$	−8.21971	−	9.48606i	−0.414630	−	0.478508i
$394$	0.311884	−	6.54725i	0.0157125	−	0.329846i
$395$	−1.90255	+	2.41929i	−0.0957276	+	0.121728i
$396$	2.59219	−	1.84589i	0.130263	−	0.0927595i
$397$	4.72072	+	6.00289i	0.236926	+	0.301276i	0.889947	−	0.456064i	$-0.150741\pi$
$397$	4.72072	+	6.00289i	0.236926	+	0.301276i	−0.653021	+	0.757340i	$0.726499\pi$
$398$	−24.4574	−	7.18133i	−1.22594	−	0.359968i
$399$	2.46087	+	1.79343i	0.123198	+	0.0897840i
$400$	−1.98651	−	4.34985i	−0.0993254	−	0.217492i
$401$	1.47754	−	1.54960i	0.0737847	−	0.0773831i	−0.685807	−	0.727784i	$-0.740550\pi$
$401$	1.47754	−	1.54960i	0.0737847	−	0.0773831i	0.759591	+	0.650401i	$0.225399\pi$
$402$	−0.572795	−	1.65498i	−0.0285684	−	0.0825431i
$403$	−15.1997	−	43.9166i	−0.757151	−	2.18764i
$404$	−9.31056	+	9.76464i	−0.463218	+	0.485809i
$405$	0.193966	+	0.424727i	0.00963826	+	0.0211048i
$406$	−23.5506	−	2.51010i	−1.16880	−	0.124574i
$407$	3.41514	+	1.00278i	0.169282	+	0.0497057i
$408$	−1.04509	−	1.32894i	−0.0517395	−	0.0657922i
$409$	27.9208	−	19.8823i	1.38059	−	0.983116i	0.382341	−	0.924021i	$-0.375118\pi$
$409$	27.9208	−	19.8823i	1.38059	−	0.983116i	0.998252	−	0.0590948i	$-0.0188214\pi$
$410$	1.74951	−	2.22468i	0.0864021	−	0.109869i
$411$	0.293588	−	6.16317i	0.0144816	−	0.304007i
$412$	−6.30189	−	7.27277i	−0.310472	−	0.358304i
$413$	10.5029	+	1.62802i	0.516816	+	0.0801095i
$414$	−0.559547	+	4.76308i	−0.0275002	+	0.234092i
$415$	2.93674	+	5.08658i	0.144159	+	0.249691i
$416$	1.01896	+	5.28684i	0.0499584	+	0.259209i
$417$	−9.10172	+	4.69226i	−0.445713	+	0.229781i
$418$	−1.36122	−	3.40017i	−0.0665795	−	0.166308i
$419$	10.6855	−	23.3980i	0.522020	−	1.14307i	−0.446649	−	0.894709i	$-0.647383\pi$
$419$	10.6855	−	23.3980i	0.522020	−	1.14307i	0.968669	−	0.248356i	$-0.0798901\pi$
$420$	0.0135670	−	1.23528i	0.000661999	−	0.0602757i
$421$	−9.87197	+	33.6208i	−0.481130	+	1.63858i	0.258825	+	0.965924i	$0.416665\pi$
$421$	−9.87197	+	33.6208i	−0.481130	+	1.63858i	−0.739956	+	0.672656i	$0.765154\pi$
$422$	18.4987	+	9.53675i	0.900503	+	0.464242i
$423$	−0.0995594	+	1.04263i	−0.00484074	+	0.0506946i
$424$	−5.59518	−	1.35737i	−0.271726	−	0.0659200i
$425$	7.93854	+	1.53003i	0.385076	+	0.0742172i
$426$	8.46736	+	7.33701i	0.410245	+	0.355479i
$427$	1.52302	+	0.629220i	0.0737043	+	0.0304501i
$428$	−3.73241	+	1.70453i	−0.180413	+	0.0823918i
$429$	7.85113	−	15.2291i	0.379056	−	0.735266i
$430$	−1.40695	−	1.47557i	−0.0678494	−	0.0711584i
$431$	8.66400	−	21.6416i	0.417330	−	1.04244i	−0.559577	−	0.828778i	$-0.689037\pi$
$431$	8.66400	−	21.6416i	0.417330	−	1.04244i	0.976908	−	0.213662i	$-0.0685392\pi$
$432$	−0.0950560	−	0.995472i	−0.00457339	−	0.0478947i
$433$	1.12135	−	7.79917i	0.0538887	−	0.374804i	−0.944975	−	0.327143i	$-0.893914\pi$
$433$	1.12135	−	7.79917i	0.0538887	−	0.374804i	0.998864	−	0.0476613i	$-0.0151768\pi$
$434$	4.56784	−	22.3750i	0.219263	−	1.07403i
$435$	−3.15885	+	2.73716i	−0.151455	+	0.131237i
$436$	13.1611	−	7.59855i	0.630301	−	0.363904i
$437$	5.17556	+	1.91825i	0.247581	+	0.0917624i
$438$	2.72407	−	4.71824i	0.130161	−	0.225446i
$439$	7.58333	+	2.62462i	0.361933	+	0.125266i	0.501981	−	0.864879i	$-0.332605\pi$
$439$	7.58333	+	2.62462i	0.361933	+	0.125266i	−0.140049	+	0.990145i	$0.544726\pi$
$440$	−0.803319	+	1.24999i	−0.0382968	+	0.0595909i
$441$	−3.04705	+	6.30202i	−0.145098	+	0.300096i
$442$	−8.28008	−	3.78139i	−0.393843	−	0.179862i
$443$	−2.63713	+	2.07386i	−0.125294	+	0.0985320i	−0.678839	−	0.734287i	$-0.737517\pi$
$443$	−2.63713	+	2.07386i	−0.125294	+	0.0985320i	0.553546	+	0.832819i	$0.313274\pi$
$444$	0.809487	−	0.771845i	0.0384166	−	0.0366301i
$445$	−0.134244	−	2.81812i	−0.00636377	−	0.133592i
$446$	7.75005	+	5.51878i	0.366975	+	0.261322i
$447$	−6.54714	+	1.92241i	−0.309669	+	0.0909270i
$448$	−0.892746	+	2.49058i	−0.0421783	+	0.117669i
$449$	−7.68018	+	8.86341i	−0.362450	+	0.418290i	−0.907459	−	0.420140i	$-0.861981\pi$
$449$	−7.68018	+	8.86341i	−0.362450	+	0.418290i	0.545009	+	0.838430i	$0.316526\pi$
$450$	3.46088	+	3.29995i	0.163148	+	0.155561i
$451$	19.2016	+	1.83353i	0.904166	+	0.0863374i
$452$	−9.55198	+	0.455017i	−0.449287	+	0.0214022i
$453$	14.9497	−	3.62676i	0.702398	−	0.170400i
$454$	−1.27280	−	8.85250i	−0.0597354	−	0.415469i
$455$	−2.98271	−	5.94507i	−0.139832	−	0.278709i
$456$	−1.13920	−	0.163793i	−0.0533481	−	0.00767030i
$457$	29.4878	+	1.40468i	1.37938	+	0.0657080i	0.724109	−	0.689686i	$-0.242251\pi$
$457$	29.4878	+	1.40468i	1.37938	+	0.0657080i	0.655271	+	0.755394i	$0.272554\pi$
$458$	−25.6461	+	4.94289i	−1.19837	+	0.230966i
$459$	1.46414	+	0.845322i	0.0683403	+	0.0394563i
$460$	−0.584021	−	2.16178i	−0.0272301	−	0.100793i
$461$			12.6317i			0.588318i	0.955757	+	0.294159i	$0.0950395\pi$
$461$			12.6317i			0.588318i	−0.955757	+	0.294159i	$0.904961\pi$
$462$	7.13247	−	4.47385i	0.331832	−	0.208142i
$463$	−5.58952	−	3.59217i	−0.259767	−	0.166942i	0.404275	−	0.914638i	$-0.367524\pi$
$463$	−5.58952	−	3.59217i	−0.259767	−	0.166942i	−0.664042	+	0.747695i	$0.731160\pi$
$464$	8.31049	−	3.32702i	0.385805	−	0.154453i
$465$	−2.33773	−	3.28289i	−0.108410	−	0.152240i
$466$	8.24030	+	3.29892i	0.381725	+	0.152819i
$467$	−3.65989	−	15.0863i	−0.169359	−	0.698109i	−0.991641	−	0.129028i	$-0.958814\pi$
$467$	−3.65989	−	15.0863i	−0.169359	−	0.698109i	0.822282	−	0.569081i	$-0.192701\pi$
$468$	−2.91089	−	4.52943i	−0.134556	−	0.209373i
$469$	−1.25651	−	4.45989i	−0.0580202	−	0.205939i
$470$	−0.137779	−	0.469233i	−0.00635528	−	0.0216441i
$471$	3.33035	−	17.2795i	0.153454	−	0.796197i
$472$	−3.79620	+	1.31388i	−0.174734	+	0.0604762i
$473$	3.27598	−	13.5038i	0.150630	−	0.620904i
$474$	−3.82351	+	5.36937i	−0.175620	+	0.246623i
$475$	4.62999	−	2.97551i	0.212438	−	0.136526i
$476$	−2.55444	−	3.67189i	−0.117082	−	0.168301i
$477$	5.69887	−	0.819373i	0.260933	−	0.0375165i
$478$	6.32753	−	0.604206i	0.289415	−	0.0276357i
$479$	8.25712	+	6.49347i	0.377278	+	0.296694i	0.788734	−	0.614735i	$-0.210737\pi$
$479$	8.25712	+	6.49347i	0.377278	+	0.296694i	−0.411456	+	0.911430i	$0.634980\pi$
$480$	0.213956	+	0.415016i	0.00976570	+	0.0189428i
$481$	1.96963	−	5.69088i	0.0898076	−	0.259482i
$482$	−17.8423			−0.812693
$483$	−2.21571	+	12.4936i	−0.100818	+	0.568480i
$484$	0.873231			0.0396923
$485$	0.772000	−	2.23055i	0.0350547	−	0.101284i
$486$	0.458227	+	0.888835i	0.0207856	+	0.0403184i
$487$	−30.6052	−	24.0682i	−1.38685	−	1.09063i	−0.984545	−	0.175130i	$-0.943965\pi$
$487$	−30.6052	−	24.0682i	−1.38685	−	1.09063i	−0.402309	−	0.915504i	$-0.631792\pi$
$488$	−0.620021	+	0.0592048i	−0.0280670	+	0.00268008i
$489$	2.81743	−	0.405085i	0.127409	−	0.0183186i
$490$	0.227186	−	3.26055i	0.0102632	−	0.147296i
$491$	36.8816	−	23.7024i	1.66444	−	1.06967i	0.753212	−	0.657778i	$-0.228504\pi$
$491$	36.8816	−	23.7024i	1.66444	−	1.06967i	0.911232	−	0.411894i	$-0.135133\pi$
$492$	3.51595	−	4.93746i	0.158511	−	0.222598i
$493$	−3.56802	+	14.7076i	−0.160695	+	0.662396i
$494$	−5.85590	+	2.02675i	−0.263469	+	0.0911876i
$495$	0.281202	−	1.45901i	0.0126391	−	0.0655778i
$496$	2.43174	+	8.28175i	0.109188	+	0.371861i
$497$	21.2276	+	20.6902i	0.952186	+	0.928084i
$498$	6.80081	+	10.5823i	0.304751	+	0.474202i
$499$	−4.94180	−	20.3704i	−0.221226	−	0.911904i	−0.968823	−	0.247752i	$-0.920308\pi$
$499$	−4.94180	−	20.3704i	−0.221226	−	0.911904i	0.747598	−	0.664152i	$-0.231207\pi$
$500$	−4.24025	−	1.69754i	−0.189630	−	0.0759162i
$501$	−6.08140	−	8.54014i	−0.271697	−	0.381545i
$502$	4.15646	−	1.66400i	0.185512	−	0.0742678i
$503$	−17.8140	−	11.4484i	−0.794287	−	0.510458i	0.0794596	−	0.996838i	$-0.474681\pi$
$503$	−17.8140	−	11.4484i	−0.794287	−	0.510458i	−0.873747	+	0.486381i	$0.838317\pi$
$504$	−0.0968591	−	2.64398i	−0.00431445	−	0.117772i
$505$			6.29972i			0.280334i
$506$	10.2426	−	11.3139i	0.455338	−	0.502966i
$507$	−13.8469	−	7.99450i	−0.614961	−	0.355048i
$508$	4.26649	−	0.822298i	0.189295	−	0.0364836i
$509$	35.2639	+	1.67982i	1.56304	+	0.0744569i	0.811154	−	0.584833i	$-0.198840\pi$
$509$	35.2639	+	1.67982i	1.56304	+	0.0744569i	0.751889	+	0.659290i	$0.229143\pi$
$510$	−0.781364	−	0.112343i	−0.0345994	−	0.00497464i
$511$	7.92574	−	12.0399i	0.350614	−	0.532613i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	1.11848	−	0.271339i	0.0493819	−	0.0119799i
$514$	−23.4562	+	1.11736i	−1.03461	+	0.0492845i
$515$	−4.47296	−	0.427116i	−0.197102	−	0.0188210i
$516$	−3.16021	−	3.01326i	−0.139121	−	0.132651i
$517$	2.18266	−	2.51893i	0.0959935	−	0.110782i
$518$	2.25759	−	1.91321i	0.0991929	−	0.0840617i
$519$	−17.4272	+	5.11708i	−0.764968	+	0.224615i
$520$	2.04782	+	1.45825i	0.0898029	+	0.0639484i
$521$	1.06720	+	22.4032i	0.0467547	+	0.981501i	0.893377	+	0.449307i	$0.148329\pi$
$521$	1.06720	+	22.4032i	0.0467547	+	0.981501i	−0.846623	+	0.532194i	$0.821368\pi$
$522$	−6.47866	+	6.17739i	−0.283563	+	0.270377i
$523$	16.7524	−	13.1742i	0.732532	−	0.576069i	−0.180686	−	0.983541i	$-0.557832\pi$
$523$	16.7524	−	13.1742i	0.732532	−	0.576069i	0.913218	+	0.407471i	$0.133589\pi$
$524$	11.4176	+	5.21423i	0.498779	+	0.227785i
$525$	8.62975	+	9.25197i	0.376633	+	0.403789i
$526$	−1.49725	+	2.32977i	−0.0652832	+	0.101583i
$527$	−13.7900	−	4.77277i	−0.600703	−	0.207905i
$528$	−1.59113	+	2.75592i	−0.0692450	+	0.119936i
$529$	2.28059	+	22.8867i	0.0991560	+	0.995072i
$530$	−2.32812	+	1.34414i	−0.101127	+	0.0583859i
$531$	3.03595	−	2.63067i	0.131749	−	0.114161i
$532$	−2.98351	−	0.609081i	−0.129351	−	0.0264070i
$533$	4.64450	−	32.3032i	0.201176	−	1.39921i
$534$	−0.574365	−	6.01502i	−0.0248552	−	0.260296i
$535$	−0.712059	+	1.77864i	−0.0307850	+	0.0768972i
$536$	1.20854	+	1.26748i	0.0522009	+	0.0547467i
$537$	6.77006	−	13.1321i	0.292149	−	0.566691i
$538$	7.08098	−	3.23378i	0.305283	−	0.139418i
$539$	19.5314	−	10.7115i	0.841276	−	0.461378i
$540$	−0.352876	−	0.305769i	−0.0151854	−	0.0131582i
$541$	4.63362	+	0.893058i	0.199215	+	0.0383956i	0.287883	−	0.957666i	$-0.407049\pi$
$541$	4.63362	+	0.893058i	0.199215	+	0.0383956i	−0.0886675	+	0.996061i	$0.528261\pi$
$542$	9.26107	+	2.24671i	0.397797	+	0.0965045i
$543$	0.554623	−	5.80827i	0.0238011	−	0.249257i
$544$	1.50271	+	0.774698i	0.0644280	+	0.0332149i
$545$	1.99913	−	6.80842i	0.0856334	−	0.291641i
$546$	−6.98664	−	12.4141i	−0.299001	−	0.531274i
$547$	9.08773	−	19.8994i	0.388563	−	0.850835i	−0.609740	−	0.792602i	$-0.708726\pi$
$547$	9.08773	−	19.8994i	0.388563	−	0.850835i	0.998303	−	0.0582334i	$-0.0185468\pi$
$548$	2.29322	+	5.72818i	0.0979613	+	0.244696i
$549$	0.553604	−	0.285402i	0.0236272	−	0.0121807i
$550$	−2.87993	−	14.9425i	−0.122801	−	0.637151i
$551$	5.15135	+	8.92240i	0.219455	+	0.380107i
$552$	−1.46967	−	4.56509i	−0.0625534	−	0.194303i
$553$	−10.9304	+	13.5894i	−0.464810	+	0.577878i
$554$	11.1456	+	12.8627i	0.473531	+	0.546484i
$555$	0.0248495	−	0.521654i	0.00105480	−	0.0221430i
$556$	6.32998	−	8.04923i	0.268451	−	0.341363i
$557$	6.94768	−	4.94742i	0.294383	−	0.209629i	−0.423317	−	0.905982i	$-0.639134\pi$
$557$	6.94768	−	4.94742i	0.294383	−	0.209629i	0.717700	+	0.696353i	$0.245195\pi$
$558$	−5.33557	−	6.78472i	−0.225872	−	0.287220i
$559$	−22.5577	−	6.62355i	−0.954091	−	0.280146i
$560$	0.500815	+	1.12929i	0.0211633	+	0.0477212i
$561$	−2.23496	−	4.89388i	−0.0943602	−	0.206620i
$562$	18.5546	−	19.4595i	0.782677	−	0.820848i
$563$	9.97743	+	28.8279i	0.420499	+	1.21495i	0.934128	+	0.356939i	$0.116180\pi$
$563$	9.97743	+	28.8279i	0.420499	+	1.21495i	−0.513629	+	0.858012i	$0.671699\pi$
$564$	−0.342563	−	0.989771i	−0.0144245	−	0.0416769i
$565$	−3.08126	+	3.23153i	−0.129630	+	0.135952i
$566$	7.05749	+	15.4537i	0.296648	+	0.649569i
$567$	1.07259	+	2.41859i	0.0450445	+	0.101571i
$568$	−10.7501	−	3.15651i	−0.451064	−	0.132444i
$569$	−4.00357	−	5.09095i	−0.167838	−	0.213424i	0.694857	−	0.719148i	$-0.255468\pi$
$569$	−4.00357	−	5.09095i	−0.167838	−	0.213424i	−0.862695	+	0.505724i	$0.831225\pi$
$570$	−0.437744	+	0.311716i	−0.0183351	+	0.0130564i
$571$	−13.9824	+	17.7800i	−0.585144	+	0.744071i	−0.985009	−	0.172503i	$-0.944815\pi$
$571$	−13.9824	+	17.7800i	−0.585144	+	0.744071i	0.399865	+	0.916574i	$0.369057\pi$
$572$	−0.815256	+	17.1143i	−0.0340876	+	0.715586i
$573$	10.9766	+	12.6677i	0.458555	+	0.529201i
$574$	10.0512	−	12.4962i	0.419529	−	0.521583i
$575$	19.6071	+	11.8958i	0.817673	+	0.496091i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	0.431227	+	2.23742i	0.0179522	+	0.0931449i	0.989800	−	0.142466i	$-0.0455031\pi$
$577$	0.431227	+	2.23742i	0.0179522	+	0.0931449i	−0.971848	+	0.235611i	$0.924291\pi$
$578$	12.5697	−	6.48011i	0.522829	−	0.269537i
$579$	−8.54144	−	21.3355i	−0.354970	−	0.886672i
$580$	1.73633	−	3.80204i	0.0720972	−	0.157871i
$581$	16.3231	+	29.0035i	0.677197	+	1.20327i
$582$	1.42420	−	4.85039i	0.0590352	−	0.201055i
$583$	−16.2850	−	8.39552i	−0.674457	−	0.347707i
$584$	−0.517879	+	5.42348i	−0.0214300	+	0.224425i
$585$	−2.44311	−	0.592692i	−0.101010	−	0.0245048i
$586$	26.3550	+	5.07950i	1.08871	+	0.209832i
$587$	−5.84961	−	5.06872i	−0.241439	−	0.209208i	0.525733	−	0.850650i	$-0.323791\pi$
$587$	−5.84961	−	5.06872i	−0.241439	−	0.209208i	−0.767172	+	0.641441i	$0.778337\pi$
$588$	0.153741	−	6.99831i	0.00634019	−	0.288606i
$589$	−9.03630	+	4.12674i	−0.372334	+	0.170039i
$590$	−0.859491	+	1.66718i	−0.0353847	+	0.0686367i
$591$	−4.52324	−	4.74384i	−0.186061	−	0.195135i
$592$	−0.415700	+	1.03837i	−0.0170852	+	0.0426766i
$593$	2.18652	+	22.8982i	0.0897894	+	0.940318i	0.922343	+	0.386373i	$0.126272\pi$
$593$	2.18652	+	22.8982i	0.0897894	+	0.940318i	−0.832553	+	0.553945i	$0.813122\pi$
$594$	0.452883	−	3.14987i	0.0185820	−	0.129241i
$595$	−2.04635	−	0.417760i	−0.0838920	−	0.0171265i
$596$	5.15688	−	4.46847i	0.211234	−	0.183035i
$597$	−22.0749	+	12.7449i	−0.903465	+	0.521616i
$598$	−18.2961	−	18.2209i	−0.748183	−	0.745107i
$599$	9.36973	−	16.2288i	0.382837	−	0.663092i	−0.608630	−	0.793454i	$-0.708281\pi$
$599$	9.36973	−	16.2288i	0.382837	−	0.663092i	0.991466	+	0.130362i	$0.0416139\pi$
$600$	−4.51898	−	1.56403i	−0.184487	−	0.0638514i
$601$	−19.8442	+	30.8781i	−0.809461	+	1.25955i	0.153028	+	0.988222i	$0.451098\pi$
$601$	−19.8442	+	30.8781i	−0.809461	+	1.25955i	−0.962488	+	0.271323i	$0.912539\pi$
$602$	−7.88002	−	8.44818i	−0.321166	−	0.344322i
$603$	−1.59304	−	0.727518i	−0.0648737	−	0.0296268i
$604$	−12.0921	+	9.50934i	−0.492021	+	0.386930i
$605$	0.295088	−	0.281366i	0.0119970	−	0.0114392i
$606$	0.641976	+	13.4767i	0.0260785	+	0.547455i
$607$	−4.45637	−	3.17337i	−0.180879	−	0.128803i	0.486031	−	0.873941i	$-0.338444\pi$
$607$	−4.45637	−	3.17337i	−0.180879	−	0.128803i	−0.666910	+	0.745138i	$0.732383\pi$
$608$	1.10430	−	0.324251i	0.0447852	−	0.0131501i
$609$	−18.0684	+	15.3122i	−0.732170	+	0.620483i
$610$	−0.190445	+	0.219786i	−0.00771091	+	0.00889886i
$611$	−4.08130	−	3.89151i	−0.165112	−	0.157434i
$612$	−1.68299	−	0.160706i	−0.0680308	−	0.00649616i
$613$	−8.97369	+	0.427470i	−0.362444	+	0.0172653i	−0.228014	−	0.973658i	$-0.573223\pi$
$613$	−8.97369	+	0.427470i	−0.362444	+	0.0172653i	−0.134430	+	0.990923i	$0.542920\pi$
$614$	1.87257	−	0.454281i	0.0755709	−	0.0183333i
$615$	−0.402778	−	2.80139i	−0.0162416	−	0.112963i
$616$	−4.62942	+	7.03249i	−0.186525	+	0.283347i
$617$	46.1867	+	6.64064i	1.85940	+	0.267342i	0.978545	−	0.206035i	$-0.0660560\pi$
$617$	46.1867	+	6.64064i	1.85940	+	0.267342i	0.880860	+	0.473377i	$0.156965\pi$
$618$	−9.61235	−	0.457893i	−0.386666	−	0.0184191i
$619$	26.4086	−	5.08984i	1.06145	−	0.204578i	0.371499	−	0.928433i	$-0.378844\pi$
$619$	26.4086	−	5.08984i	1.06145	−	0.204578i	0.689952	+	0.723856i	$0.257632\pi$
$620$	3.49024	+	2.01509i	0.140171	+	0.0809279i
$621$	3.06107	+	3.69186i	0.122836	+	0.148149i
$622$			21.6577i			0.868395i
$623$	−0.585260	−	15.9759i	−0.0234479	−	0.640062i
$624$	4.52943	+	2.91089i	0.181322	+	0.116529i
$625$	20.2173	−	8.09380i	0.808694	−	0.323752i
$626$	−14.2144	−	19.9614i	−0.568123	−	0.797816i
$627$	−3.40017	−	1.36122i	−0.135790	−	0.0543620i
$628$	4.14877	+	17.1015i	0.165554	+	0.682422i
$629$	−1.02233	−	1.59078i	−0.0407631	−	0.0634286i
$630$	−0.884655	−	0.862262i	−0.0352455	−	0.0343534i
$631$	−7.12945	−	24.2807i	−0.283819	−	0.966598i	−0.970793	−	0.239917i	$-0.922880\pi$
$631$	−7.12945	−	24.2807i	−0.283819	−	0.966598i	0.686975	−	0.726681i	$-0.258938\pi$
$632$	1.24747	−	6.47249i	0.0496217	−	0.257462i
$633$	19.6676	−	6.80704i	0.781718	−	0.270555i
$634$	−2.05865	+	8.48588i	−0.0817595	+	0.337017i
$635$	1.17681	−	1.65259i	0.0467001	−	0.0655812i
$636$	−4.84349	+	3.11272i	−0.192057	+	0.123428i
$637$	−16.5302	−	33.8705i	−0.654950	−	1.34200i
$638$	28.1967	−	4.05408i	1.11632	−	0.160503i
$639$	11.1532	−	1.06500i	0.441213	−	0.0421308i
$640$	−0.367025	−	0.288632i	−0.0145079	−	0.0114092i
$641$	−8.90975	−	17.2825i	−0.351914	−	0.682618i	0.644736	−	0.764406i	$-0.276967\pi$
$641$	−8.90975	−	17.2825i	−0.351914	−	0.682618i	−0.996650	+	0.0817876i	$0.973937\pi$
$642$	−1.34203	+	3.87753i	−0.0529656	+	0.153034i
$643$	38.7970			1.53001			0.765003	−	0.644027i	$-0.222737\pi$
$643$	38.7970			1.53001			0.765003	+	0.644027i	$0.222737\pi$
$644$	−3.17456	−	12.2850i	−0.125095	−	0.484098i
$645$	−2.03883			−0.0802789
$646$	−0.636407	+	1.83878i	−0.0250391	+	0.0723458i
$647$	−19.5910	−	38.0012i	−0.770201	−	1.49398i	−0.866798	−	0.498659i	$-0.833826\pi$
$647$	−19.5910	−	38.0012i	−0.770201	−	1.49398i	0.0965971	−	0.995324i	$-0.469204\pi$
$648$	−0.786053	−	0.618159i	−0.0308791	−	0.0242836i
$649$	−12.7257	+	1.21516i	−0.499527	+	0.0476991i
$650$	−25.4848	+	3.66416i	−0.999597	+	0.143720i
$651$	−13.0414	−	18.7464i	−0.511132	−	0.734730i
$652$	−2.39455	+	1.53888i	−0.0937777	+	0.0602673i
$653$	3.98518	−	5.59641i	0.155952	−	0.219004i	−0.729206	−	0.684294i	$-0.760110\pi$
$653$	3.98518	−	5.59641i	0.155952	−	0.219004i	0.885158	+	0.465290i	$0.154050\pi$
$654$	3.58285	−	14.7687i	0.140101	−	0.577502i
$655$	5.53840	−	1.91686i	0.216403	−	0.0748978i
$656$	−1.14713	+	5.95185i	−0.0447877	+	0.232381i
$657$	−1.53492	−	5.22746i	−0.0598830	−	0.203943i
$658$	−0.751461	−	2.66726i	−0.0292950	−	0.103981i
$659$	11.7403	+	18.2682i	0.457337	+	0.711630i	0.990970	−	0.134086i	$-0.0428099\pi$
$659$	11.7403	+	18.2682i	0.457337	+	0.711630i	−0.533633	+	0.845716i	$0.679174\pi$
$660$	0.350306	+	1.44398i	0.0136356	+	0.0562069i
$661$	8.23916	+	3.29846i	0.320466	+	0.128295i	0.526318	−	0.850288i	$-0.323572\pi$
$661$	8.23916	+	3.29846i	0.320466	+	0.128295i	−0.205852	+	0.978583i	$0.565996\pi$
$662$	−5.17730	−	7.27050i	−0.201221	−	0.282576i
$663$	−8.45063	+	3.38312i	−0.328195	+	0.131390i
$664$	−10.5823	−	6.80081i	−0.410671	−	0.263922i
$665$	−1.20446	+	0.755500i	−0.0467070	+	0.0292970i
$666$		−	1.11849i		−	0.0433405i
$667$	−23.9898	+	35.6027i	−0.928890	+	1.37854i
$668$	9.07954	+	5.24207i	0.351298	+	0.202822i
$669$	9.34227	−	1.80058i	0.361193	−	0.0696143i
$670$	0.816795	+	0.0389088i	0.0315556	+	0.00150318i
$671$	−1.96187	−	0.282074i	−0.0757371	−	0.0108893i
$672$	1.18645	+	2.36481i	0.0457685	+	0.0912245i
$673$	1.31243	+	9.12817i	0.0505906	+	0.351865i	0.999356	+	0.0358837i	$0.0114246\pi$
$673$	1.31243	+	9.12817i	0.0505906	+	0.351865i	−0.948765	+	0.315981i	$0.897666\pi$
$674$	−9.71317	+	2.35639i	−0.374137	+	0.0907648i
$675$	4.77657	−	0.227536i	0.183850	−	0.00875786i
$676$	15.9166	+	1.51985i	0.612177	+	0.0584558i
$677$	−27.9860	−	26.6846i	−1.07559	−	1.02557i	−0.999595	−	0.0284634i	$-0.990939\pi$
$677$	−27.9860	−	26.6846i	−1.07559	−	1.02557i	−0.0759938	−	0.997108i	$-0.524213\pi$
$678$	−6.26231	+	7.22709i	−0.240503	+	0.277555i
$679$	4.51298	−	12.5903i	0.173192	−	0.483171i
$680$	0.757422	−	0.222399i	0.0290458	−	0.00852862i
$681$	−7.28519	−	5.18776i	−0.279169	−	0.198795i
$682$	1.30695	+	27.4362i	0.0500455	+	1.05059i
$683$	5.66611	−	5.40262i	0.216808	−	0.206726i	−0.573890	−	0.818932i	$-0.694566\pi$
$683$	5.66611	−	5.40262i	0.216808	−	0.206726i	0.790698	+	0.612207i	$0.209718\pi$
$684$	−0.904683	+	0.711451i	−0.0345914	+	0.0272030i
$685$	2.62063	+	1.19680i	0.100129	+	0.0457275i
$686$	1.49014	−	18.4602i	0.0568939	−	0.704814i
$687$	−14.1205	+	21.9720i	−0.538732	+	0.838283i
$688$	4.12638	+	1.42815i	0.157317	+	0.0544479i
$689$	−15.4995	+	26.8460i	−0.590485	+	1.02275i
$690$	−1.96757	−	1.06912i	−0.0749042	−	0.0407007i
$691$	−13.4328	+	7.75541i	−0.511006	+	0.295030i	−0.733247	−	0.679962i	$-0.761996\pi$
$691$	−13.4328	+	7.75541i	−0.511006	+	0.295030i	0.222241	+	0.974992i	$0.428663\pi$
$692$	13.7266	−	11.8942i	0.521807	−	0.452149i
$693$	1.68409	−	8.24932i	0.0639733	−	0.313366i
$694$	−0.310629	+	2.16047i	−0.0117913	+	0.0820104i
$695$	−0.454492	−	4.75965i	−0.0172399	−	0.180544i
$696$	3.32702	−	8.31049i	0.126110	−	0.315008i
$697$	−7.07169	−	7.41658i	−0.267859	−	0.280923i
$698$	−8.63585	+	16.7512i	−0.326872	+	0.634043i
$699$	8.07400	−	3.68727i	0.305387	−	0.139465i
$700$	−11.6933	−	4.83096i	−0.441965	−	0.182593i
$701$	33.5198	+	29.0451i	1.26603	+	1.09702i	0.990757	+	0.135651i	$0.0433126\pi$
$701$	33.5198	+	29.0451i	1.26603	+	1.09702i	0.275270	+	0.961367i	$0.411233\pi$
$702$	−5.28684	−	1.01896i	−0.199539	−	0.0384580i
$703$	−1.25100	−	0.303490i	−0.0471824	−	0.0114463i
$704$	0.302493	−	3.16785i	0.0114006	−	0.119393i
$705$	−0.434678	−	0.224092i	−0.0163709	−	0.00843980i
$706$	−6.16183	+	20.9853i	−0.231904	+	0.789791i
$707$	−0.392027	+	35.6944i	−0.0147437	+	1.34243i
$708$	−1.66878	+	3.65412i	−0.0627166	+	0.137330i
$709$	−7.20976	−	18.0091i	−0.270768	−	0.676346i	0.729200	−	0.684300i	$-0.239892\pi$
$709$	−7.20976	−	18.0091i	−0.270768	−	0.676346i	−0.999968	+	0.00795441i	$0.997468\pi$
$710$	−4.64981	+	2.39715i	−0.174504	+	0.0899633i
$711$	1.24747	+	6.47249i	0.0467838	+	0.242737i
$712$	3.02119	+	5.23286i	0.113224	+	0.196110i
$713$	−31.9744	−	26.2898i	−1.19745	−	0.984559i
$714$	−4.42024	−	0.685163i	−0.165423	−	0.0256416i
$715$	5.23896	+	6.04608i	0.195926	+	0.226111i
$716$	−0.702998	+	14.7577i	−0.0262723	+	0.551523i
$717$	3.92921	−	4.99640i	0.146739	−	0.186594i
$718$	−27.1853	+	19.3586i	−1.01455	+	0.722456i
$719$	0.0758955	+	0.0965090i	0.00283043	+	0.00359918i	0.787466	−	0.616358i	$-0.211392\pi$
$719$	0.0758955	+	0.0965090i	0.00283043	+	0.00359918i	−0.784636	+	0.619957i	$0.787150\pi$
$720$	0.448008	+	0.131547i	0.0166963	+	0.00490247i
$721$	−25.3173	−	2.69840i	−0.942867	−	0.100494i
$722$	−7.34262	−	16.0781i	−0.273264	−	0.598365i
$723$	−12.3126	+	12.9130i	−0.457909	+	0.480241i
$724$	1.90834	+	5.51379i	0.0709229	+	0.204918i
$725$	14.0008	+	40.4526i	0.519976	+	1.50237i
$726$	0.602598	−	0.631987i	0.0223645	−	0.0234552i
$727$	19.0154	+	41.6379i	0.705242	+	1.54427i	0.833497	+	0.552524i	$0.186335\pi$
$727$	19.0154	+	41.6379i	0.705242	+	1.54427i	−0.128254	+	0.991741i	$0.540937\pi$
$728$	11.5123	+	8.38991i	0.426673	+	0.310951i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	1.57251	+	1.99961i	0.0582012	+	0.0740088i
$731$	−6.01342	+	4.28213i	−0.222414	+	0.158380i
$732$	−0.385015	+	0.489586i	−0.0142306	+	0.0180956i
$733$	−1.41008	+	29.6012i	−0.0520824	+	1.09334i	0.809952	+	0.586496i	$0.199493\pi$
$733$	−1.41008	+	29.6012i	−0.0520824	+	1.09334i	−0.862035	+	0.506849i	$0.830810\pi$
$734$	−9.52240	−	10.9894i	−0.351478	−	0.405628i
$735$	−2.20299	−	2.41446i	−0.0812586	−	0.0890586i
$736$	3.23327	+	3.54203i	0.119180	+	0.130561i
$737$	2.78655	+	4.82645i	0.102644	+	0.177784i
$738$	−1.14713	−	5.95185i	−0.0422263	−	0.219091i
$739$	31.7925	−	16.3902i	1.16950	−	0.602922i	0.239654	−	0.970858i	$-0.422966\pi$
$739$	31.7925	−	16.3902i	1.16950	−	0.602922i	0.929851	+	0.367937i	$0.119936\pi$
$740$	0.194099	+	0.484836i	0.00713523	+	0.0178229i
$741$	−2.57421	+	5.63673i	−0.0945659	+	0.207070i
$742$	−13.2749	+	7.47108i	−0.487336	+	0.274272i
$743$	1.98902	−	6.77398i	0.0729701	−	0.248513i	−0.914928	−	0.403617i	$-0.867753\pi$
$743$	1.98902	−	6.77398i	0.0729701	−	0.248513i	0.987898	+	0.155103i	$0.0495711\pi$
$744$	7.67188	+	3.95513i	0.281265	+	0.145002i
$745$	0.302854	−	3.17163i	0.0110957	−	0.116200i
$746$	23.4933	+	5.69942i	0.860151	+	0.208670i
$747$	12.3518	+	2.38062i	0.451930	+	0.0871024i
$748$	4.06599	+	3.52320i	0.148667	+	0.128821i
$749$	−4.14523	+	10.0335i	−0.151463	+	0.366616i
$750$	−4.15467	+	1.89737i	−0.151707	+	0.0692823i
$751$	−7.05679	+	13.6883i	−0.257506	+	0.499492i	−0.981780	−	0.190020i	$-0.939145\pi$
$751$	−7.05679	+	13.6883i	−0.257506	+	0.499492i	0.724274	+	0.689512i	$0.242175\pi$
$752$	0.722772	+	0.758022i	0.0263568	+	0.0276422i
$753$	1.66400	−	4.15646i	0.0606394	−	0.151470i
$754$	−4.58145	−	47.9791i	−0.166847	−	1.74730i
$755$	−1.02222	+	7.10969i	−0.0372024	+	0.258748i
$756$	−1.98038	−	1.75445i	−0.0720256	−	0.0638089i
$757$	−36.6466	+	31.7545i	−1.33194	+	1.15414i	−0.356400	+	0.934333i	$0.615996\pi$
$757$	−36.6466	+	31.7545i	−1.33194	+	1.15414i	−0.975544	+	0.219803i	$0.929458\pi$
$758$	−31.1970	+	18.0116i	−1.13313	+	0.654210i
$759$	−1.12010	−	15.2204i	−0.0406571	−	0.552466i
$760$	0.268694	−	0.465392i	0.00974657	−	0.0168816i
$761$	−1.08503	−	0.375533i	−0.0393324	−	0.0136131i	0.307331	−	0.951603i	$-0.400564\pi$
$761$	−1.08503	−	0.375533i	−0.0393324	−	0.0136131i	−0.346663	+	0.937990i	$0.612685\pi$
$762$	2.34909	−	3.65525i	0.0850985	−	0.132416i
$763$	11.7508	−	38.4523i	0.425409	−	1.39207i
$764$	−15.2470	−	6.96309i	−0.551619	−	0.251916i
$765$	−0.620509	+	0.487974i	−0.0224346	+	0.0176427i
$766$	−13.9965	+	13.3456i	−0.505714	+	0.482197i
$767$	1.02914	+	21.6044i	0.0371602	+	0.780089i
$768$	−0.814576	−	0.580057i	−0.0293935	−	0.0209310i
$769$	15.3479	−	4.50655i	0.553459	−	0.162510i	0.00696895	−	0.999976i	$-0.497782\pi$
$769$	15.3479	−	4.50655i	0.553459	−	0.162510i	0.546490	+	0.837465i	$0.315964\pi$
$770$	0.701552	+	3.86813i	0.0252822	+	0.139398i
$771$	−15.3780	+	17.7471i	−0.553824	+	0.639147i
$772$	16.6326	+	15.8592i	0.598622	+	0.570785i
$773$	32.5054	+	3.10389i	1.16914	+	0.111639i	0.661510	−	0.749936i	$-0.269916\pi$
$773$	32.5054	+	3.10389i	1.16914	+	0.111639i	0.507629	+	0.861576i	$0.330522\pi$
$774$	−4.36159	+	0.207768i	−0.156774	+	0.00746808i
$775$	−40.1116	+	9.73098i	−1.44085	+	0.349547i
$776$	0.719425	+	5.00371i	0.0258258	+	0.179623i
$777$	0.173260	−	2.95416i	0.00621566	−	0.105980i
$778$	−17.7283	−	2.54894i	−0.635590	−	0.0913840i
$779$	−6.96826	−	0.331939i	−0.249664	−	0.0118930i
$780$	2.46854	−	0.475772i	0.0883880	−	0.0170354i
$781$	−30.8771	−	17.8269i	−1.10487	−	0.637896i
$782$	−8.04871	+	0.979160i	−0.287821	+	0.0350147i
$783$			8.95172i			0.319908i
$784$	2.76736	+	6.42975i	0.0988341	+	0.229634i
$785$	6.91229	+	4.44226i	0.246710	+	0.158551i
$786$	11.6527	−	4.66505i	0.415639	−	0.166397i
$787$	−0.696966	−	0.978752i	−0.0248442	−	0.0348887i	0.801967	−	0.597368i	$-0.203787\pi$
$787$	−0.696966	−	0.978752i	−0.0248442	−	0.0348887i	−0.826811	+	0.562480i	$0.809848\pi$
$788$	6.08515	+	2.43613i	0.216774	+	0.0867834i
$789$	0.652911	+	2.69133i	0.0232442	+	0.0958140i
$790$	−1.66397	−	2.58918i	−0.0592012	−	0.0921189i
$791$	−17.6596	+	18.1182i	−0.627903	+	0.644210i
$792$	0.896546	+	3.05335i	0.0318574	+	0.108496i
$793$	−0.634648	+	3.29287i	−0.0225370	+	0.116933i
$794$	−7.21673	+	2.49774i	−0.256112	+	0.0886413i
$795$	−0.633788	+	2.61251i	−0.0224781	+	0.0926561i
$796$	14.7856	−	20.7635i	0.524061	−	0.735941i
$797$	−21.2319	+	13.6449i	−0.752073	+	0.483328i	−0.859659	−	0.510868i	$-0.829324\pi$
$797$	−21.2319	+	13.6449i	−0.752073	+	0.483328i	0.107586	+	0.994196i	$0.465688\pi$
$798$	−2.49967	+	1.73895i	−0.0884873	+	0.0615582i
$799$	−1.75272	+	0.252003i	−0.0620067	+	0.00891522i
$800$	4.76033	−	0.454556i	0.168303	−	0.0160710i
$801$	−4.74964	−	3.73515i	−0.167820	−	0.131975i
$802$	0.981114	+	1.90310i	0.0346444	+	0.0672007i
$803$	−5.67051	+	16.3839i	−0.200108	+	0.578174i
$804$	1.75130			0.0617637
$805$	−5.03117	−	3.12856i	−0.177325	−	0.110267i
$806$	46.4726			1.63693
$807$	2.54604	−	7.35631i	0.0896249	−	0.258954i
$808$	−6.18240	−	11.9922i	−0.217496	−	0.421884i
$809$	−28.6606	−	22.5389i	−1.00765	−	0.792426i	−0.0293413	−	0.999569i	$-0.509341\pi$
$809$	−28.6606	−	22.5389i	−1.00765	−	0.792426i	−0.978311	+	0.207143i	$0.933583\pi$
$810$	−0.464807	+	0.0443837i	−0.0163317	+	0.00155948i
$811$	−22.7116	+	3.26543i	−0.797511	+	0.114665i	−0.529011	−	0.848615i	$-0.677437\pi$
$811$	−22.7116	+	3.26543i	−0.797511	+	0.114665i	−0.268500	+	0.963280i	$0.586528\pi$
$812$	10.0747	−	21.4344i	0.353553	−	0.752200i
$813$	8.01689	−	5.15214i	0.281165	−	0.180694i
$814$	−2.06461	+	2.89933i	−0.0723644	+	0.101622i
$815$	−0.313335	+	1.29158i	−0.0109756	+	0.0452422i
$816$	1.59766	−	0.552956i	0.0559293	−	0.0193573i
$817$	−0.951088	+	4.93471i	−0.0332744	+	0.172644i
$818$	9.65679	+	32.8880i	0.337642	+	1.14990i
$819$	−13.8058	−	3.51024i	−0.482415	−	0.122658i
$820$	1.53012	+	2.38091i	0.0534340	+	0.0831450i
$821$	−10.3833	−	42.8004i	−0.362379	−	1.49375i	−0.802960	−	0.596033i	$-0.796743\pi$
$821$	−10.3833	−	42.8004i	−0.362379	−	1.49375i	0.440582	−	0.897713i	$-0.354772\pi$
$822$	5.72818	+	2.29322i	0.199793	+	0.0799851i
$823$	31.9807	+	44.9107i	1.11478	+	1.56549i	0.782881	+	0.622171i	$0.213749\pi$
$823$	31.9807	+	44.9107i	1.11478	+	1.56549i	0.331897	+	0.943316i	$0.392311\pi$
$824$	8.93392	−	3.57660i	0.311228	−	0.124597i
$825$	−12.8018	−	8.22721i	−0.445701	−	0.286435i
$826$	−4.97365	+	9.39281i	−0.173055	+	0.326818i
$827$		−	30.2255i		−	1.05104i	−0.850780	−	0.525522i	$-0.823870\pi$
$827$		−	30.2255i		−	1.05104i	0.850780	−	0.525522i	$-0.176130\pi$
$828$	−4.31810	−	2.08662i	−0.150064	−	0.0725152i
$829$	−32.7139	−	18.8874i	−1.13620	−	0.655986i	−0.190714	−	0.981646i	$-0.561080\pi$
$829$	−32.7139	−	18.8874i	−1.13620	−	0.655986i	−0.945487	+	0.325660i	$0.894414\pi$
$830$	−5.76734	+	1.11156i	−0.200187	+	0.0385829i
$831$	17.0005	+	0.809834i	0.589741	+	0.0280928i
$832$	−5.32934	−	0.766243i	−0.184762	−	0.0265647i
$833$	−11.5687	−	2.49438i	−0.400830	−	0.0864252i
$834$	−1.45731	−	10.1358i	−0.0504626	−	0.350975i
$835$	4.75729	−	1.15410i	0.164633	−	0.0399394i
$836$	3.65837	−	0.174270i	0.126527	−	0.00602725i
$837$	−8.59230	−	0.820465i	−0.296993	−	0.0283594i
$838$	18.6162	+	17.7505i	0.643086	+	0.613181i
$839$	12.3128	−	14.2097i	0.425084	−	0.490573i	−0.502295	−	0.864696i	$-0.667511\pi$
$839$	12.3128	−	14.2097i	0.425084	−	0.490573i	0.927379	+	0.374123i	$0.122056\pi$
$840$	1.16291	+	0.416843i	0.0401241	+	0.0143824i
$841$	−49.0620	+	14.4059i	−1.69179	+	0.496756i
$842$	−28.5429	−	20.3253i	−0.983654	−	0.700457i
$843$	−1.27936	−	26.8571i	−0.0440636	−	0.925009i
$844$	−15.0626	+	14.3621i	−0.518475	+	0.494365i
$845$	5.86836	−	4.61493i	0.201878	−	0.158759i
$846$	−0.952727	−	0.435096i	−0.0327554	−	0.0149589i
$847$	1.68949	−	1.57587i	0.0580515	−	0.0541474i
$848$	3.11272	−	4.84349i	0.106891	−	0.166326i
$849$	16.0546	+	5.55656i	0.550993	+	0.190701i
$850$	−4.04232	+	7.00150i	−0.138650	+	0.240150i
$851$	−1.15101	−	5.23913i	−0.0394561	−	0.179595i
$852$	−9.70288	+	5.60196i	−0.332415	+	0.191920i
$853$	19.8969	−	17.2408i	0.681258	−	0.590313i	−0.243944	−	0.969789i	$-0.578441\pi$
$853$	19.8969	−	17.2408i	0.681258	−	0.590313i	0.925202	+	0.379476i	$0.123896\pi$
$854$	−1.09275	+	1.23346i	−0.0373930	+	0.0422082i
$855$	−0.0764784	+	0.531919i	−0.00261551	+	0.0181912i
$856$	−0.390035	−	4.08463i	−0.0133311	−	0.139610i
$857$	−16.4641	+	41.1253i	−0.562402	+	1.40481i	0.325834	+	0.945427i	$0.394355\pi$
$857$	−16.4641	+	41.1253i	−0.562402	+	1.40481i	−0.888237	+	0.459386i	$0.848069\pi$
$858$	11.8236	+	12.4003i	0.403652	+	0.423338i
$859$	−2.85617	+	5.54019i	−0.0974511	+	0.189029i	−0.932522	−	0.361114i	$-0.882396\pi$
$859$	−2.85617	+	5.54019i	−0.0974511	+	0.189029i	0.835071	+	0.550143i	$0.185427\pi$
$860$	1.85459	−	0.846961i	0.0632409	−	0.0288811i
$861$	−2.10783	−	15.8978i	−0.0718345	−	0.541796i
$862$	17.6176	+	15.2658i	0.600059	+	0.519954i
$863$	−23.0457	−	4.44169i	−0.784484	−	0.151197i	−0.218746	−	0.975782i	$-0.570196\pi$
$863$	−23.0457	−	4.44169i	−0.784484	−	0.151197i	−0.565738	+	0.824585i	$0.691409\pi$
$864$	0.971812	+	0.235759i	0.0330617	+	0.00802068i
$865$	0.806137	−	8.44225i	0.0274095	−	0.287045i
$866$	7.00347	+	3.61054i	0.237988	+	0.122691i
$867$	3.98418	−	13.5689i	0.135310	−	0.460823i
$868$	19.6504	+	11.6347i	0.666978	+	0.394909i
$869$	8.71383	−	19.0806i	0.295596	−	0.647266i
$870$	−1.55346	−	3.88035i	−0.0526671	−	0.131556i
$871$	8.38107	−	4.32074i	0.283982	−	0.146403i
$872$	2.87607	+	14.9225i	0.0973960	+	0.505338i
$873$	−2.52758	−	4.37790i	−0.0855457	−	0.148169i
$874$	−3.50551	+	4.26351i	−0.118576	+	0.144215i
$875$	−11.2673	+	4.36779i	−0.380904	+	0.147658i
$876$	3.56778	+	4.11744i	0.120544	+	0.139115i
$877$	2.51734	−	52.8455i	0.0850046	−	1.78447i	−0.406559	−	0.913624i	$-0.633272\pi$
$877$	2.51734	−	52.8455i	0.0850046	−	1.78447i	0.491564	−	0.870842i	$-0.336425\pi$
$878$	−4.96053	+	6.30782i	−0.167410	+	0.212879i
$879$	21.8632	−	15.5687i	0.737428	−	0.525120i
$880$	−0.918501	−	1.16797i	−0.0309627	−	0.0393722i
$881$	11.0441	+	3.24283i	0.372084	+	0.109254i	0.462428	−	0.886657i	$-0.346978\pi$
$881$	11.0441	+	3.24283i	0.372084	+	0.109254i	−0.0903438	+	0.995911i	$0.528797\pi$
$882$	−4.95882	−	4.94066i	−0.166972	−	0.166361i
$883$	21.5120	+	47.1047i	0.723936	+	1.58520i	0.808304	+	0.588765i	$0.200386\pi$
$883$	21.5120	+	47.1047i	0.723936	+	1.58520i	−0.0843681	+	0.996435i	$0.526887\pi$
$884$	6.28156	−	6.58792i	0.211272	−	0.221576i
$885$	0.613478	+	1.77253i	0.0206218	+	0.0595829i
$886$	−1.09728	−	3.17038i	−0.0368638	−	0.106511i
$887$	18.8736	−	19.7941i	0.633713	−	0.664619i	−0.326075	−	0.945344i	$-0.605726\pi$
$887$	18.8736	−	19.7941i	0.633713	−	0.664619i	0.959788	+	0.280725i	$0.0905748\pi$
$888$	0.464636	+	1.01741i	0.0155922	+	0.0341421i
$889$	6.77066	−	9.29041i	0.227081	−	0.311590i
$890$	2.70704	+	0.794858i	0.0907401	+	0.0266437i
$891$	−1.96714	−	2.50142i	−0.0659017	−	0.0838009i
$892$	−7.75005	+	5.51878i	−0.259491	+	0.184783i
$893$	−0.745157	+	0.947544i	−0.0249357	+	0.0317083i
$894$	0.324677	−	6.81581i	0.0108588	−	0.227955i
$895$	4.51757	+	5.21355i	0.151006	+	0.174270i
$896$	−2.06161	−	1.65824i	−0.0688737	−	0.0553978i
$897$	−25.8128	+	0.667659i	−0.861865	+	0.0222925i
$898$	−5.86398	−	10.1567i	−0.195684	−	0.338934i
$899$	−14.6226	−	75.8694i	−0.487692	−	2.53039i
$900$	−4.25040	+	2.19123i	−0.141680	+	0.0730411i
$901$	3.61770	+	9.03658i	0.120523	+	0.301052i
$902$	−8.01290	+	17.5458i	−0.266800	+	0.584211i
$903$	−11.5521	−	0.126875i	−0.384429	−	0.00422213i
$904$	2.69416	−	9.17545i	0.0896063	−	0.305171i
$905$	2.42149	+	1.24837i	0.0804932	+	0.0414971i
$906$	−1.46228	+	15.3137i	−0.0485809	+	0.508762i
$907$	51.5436	+	12.5044i	1.71148	+	0.415200i	0.967473	−	0.252974i	$-0.0814086\pi$
$907$	51.5436	+	12.5044i	1.71148	+	0.415200i	0.744005	+	0.668174i	$0.232924\pi$
$908$	8.78192	+	1.69258i	0.291438	+	0.0561701i
$909$	10.1966	+	8.83540i	0.338200	+	0.293052i
$910$	6.59364	−	0.874225i	0.218577	−	0.0289803i
$911$	−44.5444	+	20.3428i	−1.47582	+	0.673986i	−0.980822	−	0.194907i	$-0.937559\pi$
$911$	−44.5444	+	20.3428i	−1.47582	+	0.673986i	−0.495001	+	0.868893i	$0.664832\pi$
$912$	0.527382	−	1.02298i	0.0174633	−	0.0338742i
$913$	−27.6239	−	28.9712i	−0.914219	−	0.958806i
$914$	−10.9719	+	27.4066i	−0.362919	+	0.906528i
$915$	0.0276440	+	0.289501i	0.000913883	+	0.00957062i
$916$	3.71700	−	25.8523i	0.122813	−	0.854183i
$917$	31.5000	−	10.5163i	1.04022	−	0.347279i
$918$	−1.27770	+	1.10714i	−0.0421705	+	0.0365410i
$919$	12.3134	−	7.10915i	0.406182	−	0.234509i	−0.282966	−	0.959130i	$-0.591318\pi$
$919$	12.3134	−	7.10915i	0.406182	−	0.234509i	0.689148	+	0.724621i	$0.257985\pi$
$920$	2.23390	+	0.155147i	0.0736494	+	0.00511506i
$921$	0.963444	−	1.66873i	0.0317466	−	0.0549867i
$922$	−11.9370	−	4.13143i	−0.393124	−	0.136061i
$923$	−32.6134	+	50.7474i	−1.07348	+	1.67037i
$924$	1.89499	+	8.20344i	0.0623405	+	0.269873i
$925$	−4.86525	−	2.22188i	−0.159968	−	0.0730551i
$926$	5.22276	−	4.10722i	0.171630	−	0.134972i
$927$	−6.96468	+	6.64080i	−0.228750	+	0.218113i
$928$	0.425940	+	8.94158i	0.0139822	+	0.293522i
$929$	−17.0201	−	12.1200i	−0.558411	−	0.397643i	0.265713	−	0.964052i	$-0.414393\pi$
$929$	−17.0201	−	12.1200i	−0.558411	−	0.397643i	−0.824124	+	0.566409i	$0.808332\pi$
$930$	3.86693	−	1.13543i	0.126802	−	0.0372323i
$931$	−6.87153	+	4.20573i	−0.225205	+	0.137837i
$932$	−5.81262	+	6.70812i	−0.190399	+	0.219732i
$933$	15.6744	+	14.9455i	0.513158	+	0.489295i
$934$	15.4536	+	1.47564i	0.505656	+	0.0482843i
$935$	2.50923	−	0.119529i	0.0820604	−	0.00390902i
$936$	5.23237	−	1.26936i	0.171025	−	0.0414903i
$937$	6.44423	+	44.8206i	0.210524	+	1.46422i	0.771414	+	0.636334i	$0.219550\pi$
$937$	6.44423	+	44.8206i	0.210524	+	1.46422i	−0.560890	+	0.827890i	$0.689541\pi$
$938$	4.62557	+	0.271287i	0.151030	+	0.00885783i
$939$	−24.2558	−	3.48746i	−0.791558	−	0.113809i
$940$	0.488489	+	0.0232696i	0.0159327	+	0.000758970i
$941$	14.6276	−	2.81924i	0.476847	−	0.0919047i	0.0548358	−	0.998495i	$-0.482536\pi$
$941$	14.6276	−	2.81924i	0.476847	−	0.0919047i	0.422011	+	0.906591i	$0.361324\pi$
$942$	15.2399	+	8.79875i	0.496542	+	0.286679i
$943$	−11.4982	−	26.6987i	−0.374433	−	0.869430i
$944$		−	4.01714i		−	0.130747i
$945$	−1.23453	+	0.0452256i	−0.0401593	+	0.00147119i
$946$	11.6896	+	7.51245i	0.380062	+	0.244251i
$947$	−35.3292	+	14.1437i	−1.14804	+	0.459607i	−0.866123	−	0.499830i	$-0.833396\pi$
$947$	−35.3292	+	14.1437i	−1.14804	+	0.459607i	−0.281920	+	0.959438i	$0.590971\pi$
$948$	−3.82351	−	5.36937i	−0.124182	−	0.174389i
$949$	27.2324	+	10.9022i	0.884001	+	0.353900i
$950$	1.29754	+	5.34854i	0.0420978	+	0.173529i
$951$	4.72089	+	7.34584i	0.153085	+	0.238205i
$952$	4.30542	−	1.21299i	0.139539	−	0.0393131i
$953$	−12.0798	−	41.1399i	−0.391302	−	1.33265i	−0.886040	−	0.463609i	$-0.846554\pi$
$953$	−12.0798	−	41.1399i	−0.391302	−	1.33265i	0.494738	−	0.869042i	$-0.335264\pi$
$954$	−1.08961	+	5.65343i	−0.0352774	+	0.183036i
$955$	−7.39598	+	2.55978i	−0.239328	+	0.0828324i
$956$	−1.49856	+	6.17714i	−0.0484668	+	0.199783i
$957$	16.5239	−	23.2046i	0.534142	−	0.750097i
$958$	−8.83698	+	5.67918i	−0.285510	+	0.183486i
$959$	14.7741	+	6.94420i	0.477081	+	0.224240i
$960$	−0.462169	+	0.0664499i	−0.0149164	+	0.00214466i
$961$	43.3037	−	4.13501i	1.39690	−	0.133387i
$962$	4.73369	+	3.72261i	0.152620	+	0.120022i
$963$	1.88020	+	3.64708i	0.0605886	+	0.117525i
$964$	5.83563	−	16.8609i	0.187953	−	0.543055i
$965$	10.7307			0.345432
$966$	−11.0818	−	6.18011i	−0.356551	−	0.198842i
$967$	−32.3335			−1.03977			−0.519887	−	0.854235i	$-0.674026\pi$
$967$	−32.3335			−1.03977			−0.519887	+	0.854235i	$0.674026\pi$
$968$	−0.285606	+	0.825204i	−0.00917972	+	0.0265231i
$969$	0.891615	+	1.72949i	0.0286428	+	0.0555593i
$970$	1.85537	+	1.45908i	0.0595724	+	0.0468483i
$971$	−0.905597	+	0.0864741i	−0.0290620	+	0.00277508i	−0.109577	−	0.993978i	$-0.534950\pi$
$971$	−0.905597	+	0.0864741i	−0.0290620	+	0.00277508i	0.0805149	+	0.996753i	$0.474344\pi$
$972$	−0.989821	+	0.142315i	−0.0317485	+	0.00456475i
$973$	−2.27897	−	26.9966i	−0.0730605	−	0.865472i
$974$	32.7545	−	21.0500i	1.04952	−	0.674486i
$975$	−14.9347	+	20.9728i	−0.478292	+	0.671667i
$976$	0.146840	−	0.605284i	0.00470025	−	0.0193747i
$977$	−25.3680	+	8.77996i	−0.811595	+	0.280896i	−0.701175	−	0.712989i	$-0.747341\pi$
$977$	−25.3680	+	8.77996i	−0.811595	+	0.280896i	−0.110420	+	0.993885i	$0.535220\pi$
$978$	−0.538685	+	2.79497i	−0.0172253	+	0.0893731i
$979$	5.41728	+	18.4495i	0.173137	+	0.589650i
$980$	3.00691	+	1.28111i	0.0960523	+	0.0409236i
$981$	−8.21617	−	12.7846i	−0.262322	−	0.408181i
$982$	10.3360	+	42.6054i	0.329834	+	1.35959i
$983$	−23.9038	−	9.56963i	−0.762412	−	0.305224i	−0.0423219	−	0.999104i	$-0.513476\pi$
$983$	−23.9038	−	9.56963i	−0.762412	−	0.305224i	−0.720091	+	0.693880i	$0.755900\pi$
$984$	3.51595	+	4.93746i	0.112084	+	0.157400i
$985$	2.84129	−	1.13748i	0.0905309	−	0.0362431i
$986$	−12.7317	−	8.18216i	−0.405459	−	0.260573i
$987$	−2.44896	−	1.29676i	−0.0779511	−	0.0412764i
$988$		−	6.19671i		−	0.197144i
$989$	−20.2164	+	5.46163i	−0.642845	+	0.173670i
$990$	1.28680	+	0.742933i	0.0408971	+	0.0236119i
$991$	−39.9449	+	7.69876i	−1.26889	+	0.244559i	−0.778889	−	0.627161i	$-0.784217\pi$
$991$	−39.9449	+	7.69876i	−1.26889	+	0.244559i	−0.490003	+	0.871720i	$0.663004\pi$
$992$	−8.62160	−	0.410698i	−0.273736	−	0.0130397i
$993$	−8.83465	−	1.27023i	−0.280359	−	0.0403096i
$994$	−26.4952	+	13.2929i	−0.840375	+	0.421627i
$995$	−1.69380	−	11.7806i	−0.0536971	−	0.373471i
$996$	−12.2246	+	2.96565i	−0.387350	+	0.0939702i
$997$	40.0540	−	1.90801i	1.26852	−	0.0604272i	0.597503	−	0.801867i	$-0.296160\pi$
$997$	40.0540	−	1.90801i	1.26852	−	0.0604272i	0.671020	+	0.741439i	$0.265857\pi$
$998$	20.8663	+	1.99249i	0.660513	+	0.0630713i
$999$	−0.809487	−	0.771845i	−0.0256110	−	0.0244201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.493.12	yes	320
7.5	odd	6	inner	966.2.be.b.355.12	yes	320
23.7	odd	22	inner	966.2.be.b.283.12	yes	320
161.145	even	66	inner	966.2.be.b.145.12	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.145.12	✓	320	161.145	even	66	inner
966.2.be.b.283.12	yes	320	23.7	odd	22	inner
966.2.be.b.355.12	yes	320	7.5	odd	6	inner
966.2.be.b.493.12	yes	320	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.464807 + 0.0443837i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.63637 + 0.222555i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.464807 + 0.0443837i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.63637 + 0.222555i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(0.110081 - 0.453760i) q^{10} +(3.00724 - 1.04081i) q^{11} +(0.189251 - 0.981929i) q^{12} +(-1.51689 - 5.16605i) q^{13} +(0.651959 - 2.56417i) q^{14} +(-0.252437 - 0.392799i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-1.56954 - 0.628349i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(-1.06848 + 0.427753i) q^{19} +(0.392799 + 0.252437i) q^{20} +(-1.40587 - 2.24132i) q^{21} +3.18226i q^{22} +(-3.55532 - 3.21865i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.69557 + 0.904996i) q^{25} +(5.37804 + 0.256188i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(2.20990 + 1.45476i) q^{28} +(-1.27396 - 8.86061i) q^{29} +(0.453760 - 0.110081i) q^{30} +(8.62160 - 0.410698i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(2.30311 + 2.19601i) q^{33} +(1.10714 - 1.27770i) q^{34} +(1.21553 - 0.220457i) q^{35} +(0.959493 - 0.281733i) q^{36} +(0.911093 + 0.648786i) q^{37} +(-0.0547629 - 1.14962i) q^{38} +(3.89669 - 3.71548i) q^{39} +(-0.367025 + 0.288632i) q^{40} +(5.51363 + 2.51799i) q^{41} +(2.57787 - 0.595485i) q^{42} +(2.36073 - 3.67337i) q^{43} +(-3.00724 - 1.04081i) q^{44} +(0.233461 - 0.404366i) q^{45} +(4.20446 - 2.30706i) q^{46} +(0.907054 - 0.523688i) q^{47} +(-0.755750 + 0.654861i) q^{48} +(6.90094 - 1.17348i) q^{49} +(0.680547 - 4.73331i) q^{50} +(-0.160706 - 1.68299i) q^{51} +(-2.00108 + 4.99847i) q^{52} +(-3.97311 - 4.16688i) q^{53} +(0.458227 - 0.888835i) q^{54} +(-1.35159 + 0.617251i) q^{55} +(-2.09754 + 1.61256i) q^{56} +(-0.869806 - 0.753692i) q^{57} +(8.78995 + 1.69412i) q^{58} +(-3.90391 - 0.947077i) q^{59} +(-0.0443837 + 0.464807i) q^{60} +(-0.553604 - 0.285402i) q^{61} +(-2.43174 + 8.28175i) q^{62} +(1.34796 - 2.27662i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.934349 + 2.33389i) q^{65} +(-2.82850 + 1.45820i) q^{66} +(0.331436 + 1.71966i) q^{67} +(0.845322 + 1.46414i) q^{68} +(1.23171 - 4.63496i) q^{69} +(-0.189228 + 1.22078i) q^{70} +(-7.33701 - 8.46736i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(-3.36782 + 4.28253i) q^{73} +(-0.911093 + 0.648786i) q^{74} +(-2.95603 - 3.75889i) q^{75} +(1.10430 + 0.324251i) q^{76} +(-7.69656 + 3.41325i) q^{77} +(2.23665 + 4.89759i) q^{78} +(4.54873 - 4.77057i) q^{79} +(-0.152715 - 0.441241i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-4.18284 + 4.38683i) q^{82} +(-5.22557 - 11.4424i) q^{83} +(-0.280404 + 2.63085i) q^{84} +(0.757422 + 0.222399i) q^{85} +(2.69921 + 3.43233i) q^{86} +(7.29186 - 5.19251i) q^{87} +(1.96714 - 2.50142i) q^{88} +(-0.287508 + 6.03554i) q^{89} +(0.305769 + 0.352876i) q^{90} +(5.14881 + 13.2820i) q^{91} +(0.805032 + 4.72778i) q^{92} +(4.31569 + 7.47499i) q^{93} +(0.198217 + 1.02845i) q^{94} +(0.477650 - 0.246246i) q^{95} +(-0.371662 - 0.928368i) q^{96} +(-2.09999 + 4.59834i) q^{97} +(-1.14814 + 6.90520i) q^{98} +(-0.896546 + 3.05335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

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