LMFDB - Embedded newform 855.2.ci.a.182.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(182,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 8]))

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

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

chi := DirichletCharacter("855.182");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.ci (of order $12$, degree $4$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			182.15
Character	$\chi$	$=$	855.182
Dual form			855.2.ci.a.653.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14510 - 0.574778i) q^{2} +(-1.63225 - 0.579449i) q^{3} +(2.53904 + 1.46592i) q^{4} +(-1.44202 + 1.70897i) q^{5} +(3.16829 + 2.18116i) q^{6} +(2.12013 - 0.568087i) q^{7} +(-1.46328 - 1.46328i) q^{8} +(2.32848 + 1.89161i) q^{9} +O(q^{10})$	\(q+(-2.14510 - 0.574778i) q^{2} +(-1.63225 - 0.579449i) q^{3} +(2.53904 + 1.46592i) q^{4} +(-1.44202 + 1.70897i) q^{5} +(3.16829 + 2.18116i) q^{6} +(2.12013 - 0.568087i) q^{7} +(-1.46328 - 1.46328i) q^{8} +(2.32848 + 1.89161i) q^{9} +(4.07556 - 2.83707i) q^{10} +(2.83218 + 1.63516i) q^{11} +(-3.29493 - 3.86399i) q^{12} +(-1.22318 - 4.56495i) q^{13} -4.87442 q^{14} +(3.34400 - 1.95389i) q^{15} +(-0.634011 - 1.09814i) q^{16} +(0.489798 + 1.82795i) q^{17} +(-3.90757 - 5.39606i) q^{18} +(1.32239 + 4.15346i) q^{19} +(-6.16656 + 2.22526i) q^{20} +(-3.78976 - 0.301247i) q^{21} +(-5.13546 - 5.13546i) q^{22} +(-1.83145 + 0.490736i) q^{23} +(1.54054 + 3.23633i) q^{24} +(-0.841145 - 4.92874i) q^{25} +10.4953i q^{26} +(-2.70457 - 4.43681i) q^{27} +(6.21587 + 1.66554i) q^{28} -3.10920 q^{29} +(-8.29627 + 2.26922i) q^{30} +(-0.0902853 - 0.156379i) q^{31} +(1.80003 + 6.71779i) q^{32} +(-3.67533 - 4.31009i) q^{33} -4.20267i q^{34} +(-2.08643 + 4.44243i) q^{35} +(3.13916 + 8.21623i) q^{36} +(3.17454 + 3.17454i) q^{37} +(-0.449350 - 9.66969i) q^{38} +(-0.648628 + 8.15991i) q^{39} +(4.61078 - 0.390617i) q^{40} +2.02814i q^{41} +(7.95627 + 2.82448i) q^{42} +(1.07680 + 0.288527i) q^{43} +(4.79401 + 8.30348i) q^{44} +(-6.59042 + 1.25155i) q^{45} +4.21072 q^{46} +(-3.05579 + 3.05579i) q^{47} +(0.398549 + 2.15981i) q^{48} +(-1.88995 + 1.09116i) q^{49} +(-1.02859 + 11.0561i) q^{50} +(0.259731 - 3.26749i) q^{51} +(3.58615 - 13.3837i) q^{52} +(3.57658 - 13.3480i) q^{53} +(3.25139 + 11.0719i) q^{54} +(-6.87850 + 2.48217i) q^{55} +(-3.93361 - 2.27107i) q^{56} +(0.248241 - 7.54575i) q^{57} +(6.66955 + 1.78710i) q^{58} +4.50615 q^{59} +(11.3548 - 0.0589728i) q^{60} +15.0970 q^{61} +(0.103788 + 0.387343i) q^{62} +(6.01128 + 2.68768i) q^{63} -12.9089i q^{64} +(9.56521 + 4.49239i) q^{65} +(5.40662 + 11.3581i) q^{66} +(-7.01556 + 1.87981i) q^{67} +(-1.43601 + 5.35925i) q^{68} +(3.27375 + 0.260229i) q^{69} +(7.02902 - 8.33023i) q^{70} +(-7.99302 - 4.61477i) q^{71} +(-0.639261 - 6.17517i) q^{72} +(2.38999 + 8.91957i) q^{73} +(-4.98506 - 8.63437i) q^{74} +(-1.48299 + 8.53233i) q^{75} +(-2.73102 + 12.4843i) q^{76} +(6.93350 + 1.85783i) q^{77} +(6.08151 - 17.1310i) q^{78} +(1.13720 - 0.656565i) q^{79} +(2.79094 + 0.500036i) q^{80} +(1.84362 + 8.80915i) q^{81} +(1.16573 - 4.35056i) q^{82} +(4.52482 - 1.21242i) q^{83} +(-9.18076 - 6.32035i) q^{84} +(-3.83021 - 1.79890i) q^{85} +(-2.14400 - 1.23784i) q^{86} +(5.07499 + 1.80162i) q^{87} +(-1.75157 - 6.53696i) q^{88} +(8.09858 + 14.0272i) q^{89} +(14.8565 + 1.10332i) q^{90} +(-5.18658 - 8.98343i) q^{91} +(-5.36952 - 1.43876i) q^{92} +(0.0567547 + 0.307565i) q^{93} +(8.31139 - 4.79858i) q^{94} +(-9.00506 - 3.72946i) q^{95} +(0.954522 - 12.0081i) q^{96} +(-2.87504 + 10.7298i) q^{97} +(4.68131 - 1.25435i) q^{98} +(3.50158 + 9.16481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7}+O(q^{10}) $ 464 * q - 6 * q^2 - 2 * q^3 - 4 * q^6 - 4 * q^7	$ 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7} - 4 q^{10} - 24 q^{11} + 2 q^{12} + 2 q^{13} + 10 q^{15} + 212 q^{16} + 18 q^{17} - 24 q^{18} - 12 q^{20} - 4 q^{21} - 20 q^{22} + 18 q^{23} - 4 q^{25} - 2 q^{27} - 20 q^{28} + 2 q^{30} - 8 q^{31} - 30 q^{32} + 10 q^{33} - 68 q^{36} - 16 q^{37} + 30 q^{38} - 36 q^{40} - 14 q^{42} + 2 q^{43} + 6 q^{45} - 56 q^{46} + 42 q^{48} - 108 q^{50} + 12 q^{51} - 34 q^{52} - 14 q^{55} - 24 q^{56} - 78 q^{57} - 12 q^{58} - 42 q^{60} - 8 q^{61} - 12 q^{62} + 92 q^{63} - 84 q^{65} - 52 q^{66} + 2 q^{67} - 60 q^{68} - 84 q^{70} - 118 q^{72} - 4 q^{73} + 98 q^{75} - 60 q^{76} - 12 q^{77} + 92 q^{78} + 120 q^{80} - 12 q^{81} + 4 q^{82} - 12 q^{83} + 2 q^{85} - 264 q^{86} + 102 q^{87} + 48 q^{88} - 34 q^{90} - 8 q^{91} + 54 q^{92} - 52 q^{93} - 36 q^{95} + 96 q^{96} + 2 q^{97} + 42 q^{98}+O(q^{100}) $ 464 * q - 6 * q^2 - 2 * q^3 - 4 * q^6 - 4 * q^7 - 4 * q^10 - 24 * q^11 + 2 * q^12 + 2 * q^13 + 10 * q^15 + 212 * q^16 + 18 * q^17 - 24 * q^18 - 12 * q^20 - 4 * q^21 - 20 * q^22 + 18 * q^23 - 4 * q^25 - 2 * q^27 - 20 * q^28 + 2 * q^30 - 8 * q^31 - 30 * q^32 + 10 * q^33 - 68 * q^36 - 16 * q^37 + 30 * q^38 - 36 * q^40 - 14 * q^42 + 2 * q^43 + 6 * q^45 - 56 * q^46 + 42 * q^48 - 108 * q^50 + 12 * q^51 - 34 * q^52 - 14 * q^55 - 24 * q^56 - 78 * q^57 - 12 * q^58 - 42 * q^60 - 8 * q^61 - 12 * q^62 + 92 * q^63 - 84 * q^65 - 52 * q^66 + 2 * q^67 - 60 * q^68 - 84 * q^70 - 118 * q^72 - 4 * q^73 + 98 * q^75 - 60 * q^76 - 12 * q^77 + 92 * q^78 + 120 * q^80 - 12 * q^81 + 4 * q^82 - 12 * q^83 + 2 * q^85 - 264 * q^86 + 102 * q^87 + 48 * q^88 - 34 * q^90 - 8 * q^91 + 54 * q^92 - 52 * q^93 - 36 * q^95 + 96 * q^96 + 2 * q^97 + 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.14510	−	0.574778i	−1.51682	−	0.406430i	−0.598124	−	0.801404i	$-0.704087\pi$
$2$	−2.14510	−	0.574778i	−1.51682	−	0.406430i	−0.918692	+	0.394974i	$0.870754\pi$
$3$	−1.63225	−	0.579449i	−0.942380	−	0.334545i
$3$	−1.63225	−	0.579449i	−0.942380	−	0.334545i
$4$	2.53904	+	1.46592i	1.26952	+	0.732958i
$5$	−1.44202	+	1.70897i	−0.644892	+	0.764274i
$5$	−1.44202	+	1.70897i	−0.644892	+	0.764274i
$6$	3.16829	+	2.18116i	1.29345	+	0.890454i
$7$	2.12013	−	0.568087i	0.801334	−	0.214717i	0.165164	−	0.986266i	$-0.447185\pi$
$7$	2.12013	−	0.568087i	0.801334	−	0.214717i	0.636170	+	0.771549i	$0.280518\pi$
$8$	−1.46328	−	1.46328i	−0.517347	−	0.517347i
$9$	2.32848	+	1.89161i	0.776159	+	0.630537i
$10$	4.07556	−	2.83707i	1.28881	−	0.897160i
$11$	2.83218	+	1.63516i	0.853934	+	0.493019i	0.861976	−	0.506949i	$-0.169227\pi$
$11$	2.83218	+	1.63516i	0.853934	+	0.493019i	−0.00804212	+	0.999968i	$0.502560\pi$
$12$	−3.29493	−	3.86399i	−0.951163	−	1.11544i
$13$	−1.22318	−	4.56495i	−0.339248	−	1.26609i	−0.899190	−	0.437559i	$-0.855843\pi$
$13$	−1.22318	−	4.56495i	−0.339248	−	1.26609i	0.559942	−	0.828532i	$-0.310823\pi$
$14$	−4.87442			−1.30274
$15$	3.34400	−	1.95389i	0.863417	−	0.504491i
$16$	−0.634011	−	1.09814i	−0.158503	−	0.274535i
$17$	0.489798	+	1.82795i	0.118793	+	0.443343i	0.999543	−	0.0302397i	$-0.00962708\pi$
$17$	0.489798	+	1.82795i	0.118793	+	0.443343i	−0.880749	+	0.473583i	$0.842960\pi$
$18$	−3.90757	−	5.39606i	−0.921022	−	1.27186i
$19$	1.32239	+	4.15346i	0.303378	+	0.952870i
$19$	1.32239	+	4.15346i	0.303378	+	0.952870i
$20$	−6.16656	+	2.22526i	−1.37888	+	0.497583i
$21$	−3.78976	−	0.301247i	−0.826993	−	0.0657374i
$22$	−5.13546	−	5.13546i	−1.09488	−	1.09488i
$23$	−1.83145	+	0.490736i	−0.381884	+	0.102326i	−0.444654	−	0.895702i	$-0.646673\pi$
$23$	−1.83145	+	0.490736i	−0.381884	+	0.102326i	0.0627696	+	0.998028i	$0.480007\pi$
$24$	1.54054	+	3.23633i	0.314462	+	0.660614i
$25$	−0.841145	−	4.92874i	−0.168229	−	0.985748i
$26$			10.4953i			2.05831i
$27$	−2.70457	−	4.43681i	−0.520494	−	0.853865i
$28$	6.21587	+	1.66554i	1.17469	+	0.314757i
$29$	−3.10920			−0.577364			−0.288682	−	0.957425i	$-0.593217\pi$
$29$	−3.10920			−0.577364			−0.288682	+	0.957425i	$0.593217\pi$
$30$	−8.29627	+	2.26922i	−1.51468	+	0.414302i
$31$	−0.0902853	−	0.156379i	−0.0162157	−	0.0280865i	0.857804	−	0.513977i	$-0.171829\pi$
$31$	−0.0902853	−	0.156379i	−0.0162157	−	0.0280865i	−0.874019	+	0.485891i	$0.838495\pi$
$32$	1.80003	+	6.71779i	0.318203	+	1.18755i
$33$	−3.67533	−	4.31009i	−0.639793	−	0.750291i
$34$		−	4.20267i		−	0.720751i
$35$	−2.08643	+	4.44243i	−0.352671	+	0.750908i
$36$	3.13916	+	8.21623i	0.523194	+	1.36937i
$37$	3.17454	+	3.17454i	0.521891	+	0.521891i	0.918142	−	0.396251i	$-0.129689\pi$
$37$	3.17454	+	3.17454i	0.521891	+	0.521891i	−0.396251	+	0.918142i	$0.629689\pi$
$38$	−0.449350	−	9.66969i	−0.0728943	−	1.56863i
$39$	−0.648628	+	8.15991i	−0.103864	+	1.30663i
$40$	4.61078	−	0.390617i	0.729028	−	0.0617620i
$41$			2.02814i			0.316742i	0.987380	+	0.158371i	$0.0506242\pi$
$41$			2.02814i			0.316742i	−0.987380	+	0.158371i	$0.949376\pi$
$42$	7.95627	+	2.82448i	1.22768	+	0.435826i
$43$	1.07680	+	0.288527i	0.164210	+	0.0440000i	0.339988	−	0.940430i	$-0.389577\pi$
$43$	1.07680	+	0.288527i	0.164210	+	0.0440000i	−0.175777	+	0.984430i	$0.556244\pi$
$44$	4.79401	+	8.30348i	0.722725	+	1.25180i
$45$	−6.59042	+	1.25155i	−0.982442	+	0.186570i
$46$	4.21072			0.620837
$47$	−3.05579	+	3.05579i	−0.445733	+	0.445733i	−0.893933	−	0.448200i	$-0.852065\pi$
$47$	−3.05579	+	3.05579i	−0.445733	+	0.445733i	0.448200	+	0.893933i	$0.352065\pi$
$48$	0.398549	+	2.15981i	0.0575256	+	0.311742i
$49$	−1.88995	+	1.09116i	−0.269993	+	0.155880i
$50$	−1.02859	+	11.0561i	−0.145465	+	1.56357i
$51$	0.259731	−	3.26749i	0.0363696	−	0.457539i
$52$	3.58615	−	13.3837i	0.497309	−	1.85598i
$53$	3.57658	−	13.3480i	0.491282	−	1.83349i	−0.0586507	−	0.998279i	$-0.518680\pi$
$53$	3.57658	−	13.3480i	0.491282	−	1.83349i	0.549932	−	0.835209i	$-0.314654\pi$
$54$	3.25139	+	11.0719i	0.442458	+	1.50670i
$55$	−6.87850	+	2.48217i	−0.927497	+	0.334696i
$56$	−3.93361	−	2.27107i	−0.525651	−	0.303485i
$57$	0.248241	−	7.54575i	0.0328803	−	0.999459i
$58$	6.66955	+	1.78710i	0.875755	+	0.234658i
$59$	4.50615			0.586650			0.293325	−	0.956013i	$-0.405238\pi$
$59$	4.50615			0.586650			0.293325	+	0.956013i	$0.405238\pi$
$60$	11.3548	−	0.0589728i	1.46590	−	0.00761336i
$61$	15.0970			1.93297			0.966487	−	0.256715i	$-0.0826402\pi$
$61$	15.0970			1.93297			0.966487	+	0.256715i	$0.0826402\pi$
$62$	0.103788	+	0.387343i	0.0131811	+	0.0491926i
$63$	6.01128	+	2.68768i	0.757350	+	0.338616i
$64$		−	12.9089i		−	1.61361i
$65$	9.56521	+	4.49239i	1.18642	+	0.557213i
$66$	5.40662	+	11.3581i	0.665509	+	1.39808i
$67$	−7.01556	+	1.87981i	−0.857088	+	0.229656i	−0.660496	−	0.750830i	$-0.729654\pi$
$67$	−7.01556	+	1.87981i	−0.857088	+	0.229656i	−0.196592	+	0.980485i	$0.562987\pi$
$68$	−1.43601	+	5.35925i	−0.174141	+	0.649904i
$69$	3.27375	+	0.260229i	0.394113	+	0.0313279i
$70$	7.02902	−	8.33023i	0.840129	−	0.995653i
$71$	−7.99302	−	4.61477i	−0.948597	−	0.547673i	−0.0559524	−	0.998433i	$-0.517820\pi$
$71$	−7.99302	−	4.61477i	−0.948597	−	0.547673i	−0.892645	+	0.450761i	$0.851153\pi$
$72$	−0.639261	−	6.17517i	−0.0753376	−	0.727751i
$73$	2.38999	+	8.91957i	0.279727	+	1.04396i	0.952607	+	0.304205i	$0.0983907\pi$
$73$	2.38999	+	8.91957i	0.279727	+	1.04396i	−0.672879	+	0.739752i	$0.734943\pi$
$74$	−4.98506	−	8.63437i	−0.579501	−	1.00373i
$75$	−1.48299	+	8.53233i	−0.171241	+	0.985229i
$76$	−2.73102	+	12.4843i	−0.313269	+	1.43205i
$77$	6.93350	+	1.85783i	0.790146	+	0.211719i
$78$	6.08151	−	17.1310i	0.688596	−	1.93971i
$79$	1.13720	−	0.656565i	0.127946	−	0.0738694i	−0.434661	−	0.900594i	$-0.643132\pi$
$79$	1.13720	−	0.656565i	0.127946	−	0.0738694i	0.562607	+	0.826725i	$0.309799\pi$
$80$	2.79094	+	0.500036i	0.312037	+	0.0559057i
$81$	1.84362	+	8.80915i	0.204847	+	0.978794i
$82$	1.16573	−	4.35056i	0.128733	−	0.480439i
$83$	4.52482	−	1.21242i	0.496664	−	0.133081i	−0.00178737	−	0.999998i	$-0.500569\pi$
$83$	4.52482	−	1.21242i	0.496664	−	0.133081i	0.498451	+	0.866918i	$0.333902\pi$
$84$	−9.18076	−	6.32035i	−1.00170	−	0.689607i
$85$	−3.83021	−	1.79890i	−0.415445	−	0.195118i
$86$	−2.14400	−	1.23784i	−0.231194	−	0.133480i
$87$	5.07499	+	1.80162i	0.544096	+	0.193154i
$88$	−1.75157	−	6.53696i	−0.186718	−	0.696843i
$89$	8.09858	+	14.0272i	0.858448	+	1.48688i	0.873409	+	0.486987i	$0.161904\pi$
$89$	8.09858	+	14.0272i	0.858448	+	1.48688i	−0.0149613	+	0.999888i	$0.504763\pi$
$90$	14.8565	+	1.10332i	1.56601	+	0.116300i
$91$	−5.18658	−	8.98343i	−0.543702	−	0.941719i
$92$	−5.36952	−	1.43876i	−0.559811	−	0.150001i
$93$	0.0567547	+	0.307565i	0.00588519	+	0.0318930i
$94$	8.31139	−	4.79858i	0.857254	−	0.494936i
$95$	−9.00506	−	3.72946i	−0.923900	−	0.382634i
$96$	0.954522	−	12.0081i	0.0974205	−	1.22557i
$97$	−2.87504	+	10.7298i	−0.291916	+	1.08944i	0.651720	+	0.758459i	$0.274048\pi$
$97$	−2.87504	+	10.7298i	−0.291916	+	1.08944i	−0.943636	+	0.330985i	$0.892619\pi$
$98$	4.68131	−	1.25435i	0.472884	−	0.126709i
$99$	3.50158	+	9.16481i	0.351923	+	0.921098i
$100$	5.08942	−	13.7473i	0.508942	−	1.37473i
$101$			6.32014i			0.628878i	0.949278	+	0.314439i	$0.101816\pi$
$101$			6.32014i			0.628878i	−0.949278	+	0.314439i	$0.898184\pi$
$102$	−2.43523	+	6.85980i	−0.241124	+	0.679222i
$103$	12.5875	+	3.37280i	1.24028	+	0.332332i	0.818574	−	0.574401i	$-0.194765\pi$
$103$	12.5875	+	3.37280i	1.24028	+	0.332332i	0.421705	+	0.906733i	$0.361432\pi$
$104$	−4.88995	+	8.46965i	−0.479499	+	0.830517i
$105$	5.97974	−	6.04217i	0.583563	−	0.589656i
$106$	−15.3443	+	26.5771i	−1.49037	+	2.58139i
$107$	8.08989	−	8.08989i	0.782079	−	0.782079i	−0.198102	−	0.980181i	$-0.563478\pi$
$107$	8.08989	−	8.08989i	0.782079	−	0.782079i	0.980181	+	0.198102i	$0.0634777\pi$
$108$	−0.363012	−	15.2299i	−0.0349308	−	1.46550i
$109$	12.5052	+	7.21988i	1.19778	+	0.691539i	0.960060	−	0.279794i	$-0.0902661\pi$
$109$	12.5052	+	7.21988i	1.19778	+	0.691539i	0.237721	+	0.971333i	$0.423599\pi$
$110$	16.1818	−	1.37089i	1.54287	−	0.130709i
$111$	−3.34216	−	7.02113i	−0.317224	−	0.666416i
$112$	−1.96802	−	1.96802i	−0.185961	−	0.185961i
$113$	−2.86491	+	10.6920i	−0.269508	+	1.00582i	0.689925	+	0.723881i	$0.257644\pi$
$113$	−2.86491	+	10.6920i	−0.269508	+	1.00582i	−0.959433	+	0.281937i	$0.909023\pi$
$114$	−4.86964	+	16.0437i	−0.456083	+	1.50263i
$115$	1.80234	−	3.83755i	0.168069	−	0.357853i
$116$	−7.89439	−	4.55783i	−0.732975	−	0.423184i
$117$	5.78697	−	12.9432i	0.535006	−	1.19660i
$118$	−9.66614	−	2.59004i	−0.889841	−	0.238432i
$119$	2.07687	+	3.59725i	0.190386	+	0.329759i
$120$	−7.75229	−	2.03413i	−0.707684	−	0.185689i
$121$	−0.152507	−	0.264149i	−0.0138642	−	0.0240136i
$122$	−32.3846	−	8.67744i	−2.93197	−	0.785618i
$123$	1.17520	−	3.31043i	0.105964	−	0.298491i
$124$		−	0.529403i		−	0.0475418i
$125$	9.63601	+	5.66986i	0.861871	+	0.507128i
$126$	−11.3500	−	9.22050i	−1.01114	−	0.821428i
$127$	−2.30086	+	8.58694i	−0.204169	+	0.761968i	0.785533	+	0.618820i	$0.212389\pi$
$127$	−2.30086	+	8.58694i	−0.204169	+	0.761968i	−0.989701	+	0.143148i	$0.954278\pi$
$128$	−3.81971	+	14.2554i	−0.337618	+	1.26001i
$129$	−1.59042	−	1.09490i	−0.140029	−	0.0964005i
$130$	−17.9362	−	15.1345i	−1.57311	−	1.32739i
$131$		−	11.7912i		−	1.03020i	−0.857130	−	0.515100i	$-0.827755\pi$
$131$		−	11.7912i		−	1.03020i	0.857130	−	0.515100i	$-0.172245\pi$
$132$	−3.01359	−	16.3312i	−0.262299	−	1.42145i
$133$	5.16318	+	8.05465i	0.447704	+	0.698427i
$134$	16.1296			1.39338
$135$	11.4824	+	1.77596i	0.988249	+	0.152851i
$136$	1.95809	−	3.39151i	0.167905	−	0.290820i
$137$	−13.5265	+	13.5265i	−1.15565	+	1.15565i	−0.170249	+	0.985401i	$0.554457\pi$
$137$	−13.5265	+	13.5265i	−1.15565	+	1.15565i	−0.985401	+	0.170249i	$0.945543\pi$
$138$	−6.87295	−	2.43990i	−0.585064	−	0.207698i
$139$	18.3502	+	10.5945i	1.55644	+	0.898612i	0.997593	+	0.0693415i	$0.0220898\pi$
$139$	18.3502	+	10.5945i	1.55644	+	0.898612i	0.558848	+	0.829270i	$0.311244\pi$
$140$	−11.8098	+	8.22098i	−0.998107	+	0.694800i
$141$	6.75849	−	3.21714i	0.569168	−	0.270932i
$142$	14.4934	+	14.4934i	1.21626	+	1.21626i
$143$	4.00017	−	14.9289i	0.334511	−	1.24841i
$144$	0.600970	−	3.75629i	0.0500808	−	0.313024i
$145$	4.48353	−	5.31352i	0.372337	−	0.441264i
$146$		−	20.5071i		−	1.69718i
$147$	3.71714	−	0.685921i	0.306585	−	0.0565738i
$148$	3.40668	+	12.7139i	0.280027	+	1.04508i
$149$	−9.78150			−0.801332			−0.400666	−	0.916224i	$-0.631221\pi$
$149$	−9.78150			−0.801332			−0.400666	+	0.916224i	$0.631221\pi$
$150$	8.08537	−	17.4503i	0.660168	−	1.42481i
$151$	−8.19097	+	14.1872i	−0.666572	+	1.15454i	0.312285	+	0.949988i	$0.398906\pi$
$151$	−8.19097	+	14.1872i	−0.666572	+	1.15454i	−0.978857	+	0.204547i	$0.934428\pi$
$152$	4.14265	−	8.01271i	0.336013	−	0.649917i
$153$	−2.31729	+	5.18285i	−0.187341	+	0.419009i
$154$	−13.8052	−	7.97045i	−1.11246	−	0.642278i
$155$	0.397440	+	0.0712069i	0.0319231	+	0.00571947i
$156$	−13.6086	+	19.7675i	−1.08956	+	1.58267i
$157$	8.78545	+	8.78545i	0.701155	+	0.701155i	0.964658	−	0.263504i	$-0.0848781\pi$
$157$	8.78545	+	8.78545i	0.701155	+	0.701155i	−0.263504	+	0.964658i	$0.584878\pi$
$158$	−2.81680	+	0.754759i	−0.224093	+	0.0600454i
$159$	−13.5724	+	19.7148i	−1.07636	+	1.56349i
$160$	−14.0762	−	6.61101i	−1.11282	−	0.522646i
$161$	−3.60414	+	2.08085i	−0.284046	+	0.163994i
$162$	1.10855	−	19.9562i	0.0870955	−	1.56791i
$163$	−2.80233	+	2.80233i	−0.219495	+	0.219495i	−0.808286	−	0.588790i	$-0.799604\pi$
$163$	−2.80233	+	2.80233i	−0.219495	+	0.219495i	0.588790	+	0.808286i	$0.299604\pi$
$164$	−2.97308	+	5.14953i	−0.232159	+	0.402111i
$165$	12.6657	−	0.0657813i	0.986025	−	0.00512107i
$166$	−10.4031			−0.807436
$167$	−2.97323	−	11.0962i	−0.230075	−	0.858652i	−0.980307	−	0.197478i	$-0.936725\pi$
$167$	−2.97323	−	11.0962i	−0.230075	−	0.858652i	0.750232	−	0.661174i	$-0.229942\pi$
$168$	5.10467	+	5.98628i	0.393834	+	0.461852i
$169$	−8.08431	+	4.66748i	−0.621870	+	0.359037i
$170$	7.18222	+	6.06034i	0.550851	+	0.464807i
$171$	−4.77757	+	12.1727i	−0.365350	+	0.930870i
$172$	2.31108	+	2.31108i	0.176218	+	0.176218i
$173$	−3.55769	+	13.2775i	−0.270486	+	1.00947i	0.688320	+	0.725407i	$0.258348\pi$
$173$	−3.55769	+	13.2775i	−0.270486	+	1.00947i	−0.958806	+	0.284061i	$0.908318\pi$
$174$	−9.85084	−	6.78166i	−0.746790	−	0.514116i
$175$	−4.58329	−	9.97173i	−0.346464	−	0.753792i
$176$		−	4.14684i		−	0.312579i
$177$	−7.35516	−	2.61108i	−0.552847	−	0.196261i
$178$	−9.30978	−	34.7446i	−0.697797	−	2.60422i
$179$	5.19064			0.387966			0.193983	−	0.981005i	$-0.437859\pi$
$179$	5.19064			0.387966			0.193983	+	0.981005i	$0.437859\pi$
$180$	−18.5680	−	6.48326i	−1.38398	−	0.483234i
$181$	−8.14237	−	14.1030i	−0.605218	−	1.04827i	−0.992017	−	0.126104i	$-0.959753\pi$
$181$	−8.14237	−	14.1030i	−0.605218	−	1.04827i	0.386799	−	0.922164i	$-0.373581\pi$
$182$	5.96227	+	22.2515i	0.441953	+	1.64939i
$183$	−24.6421	−	8.74794i	−1.82160	−	0.646667i
$184$	3.39801	+	1.96184i	0.250505	+	0.144629i
$185$	−10.0029	+	0.847432i	−0.735431	+	0.0623044i
$186$	0.0550370	−	0.692380i	0.00403551	−	0.0507677i
$187$	−1.60180	+	5.97798i	−0.117135	+	0.437153i
$188$	−12.2383	+	3.27925i	−0.892571	+	0.239164i
$189$	−8.25453	−	7.87019i	−0.600429	−	0.572472i
$190$	17.1732	+	13.1760i	1.24587	+	0.955886i
$191$	−9.06490	−	5.23362i	−0.655913	−	0.378692i	0.134805	−	0.990872i	$-0.456959\pi$
$191$	−9.06490	−	5.23362i	−0.655913	−	0.378692i	−0.790718	+	0.612181i	$0.790293\pi$
$192$	−7.48005	+	21.0706i	−0.539826	+	1.52064i
$193$	−8.25595	+	8.25595i	−0.594276	+	0.594276i	−0.938784	−	0.344508i	$-0.888046\pi$
$193$	−8.25595	+	8.25595i	−0.594276	+	0.594276i	0.344508	+	0.938784i	$0.388046\pi$
$194$	12.3345	−	21.3640i	0.885565	−	1.53384i
$195$	−13.0097	−	12.8753i	−0.931644	−	0.922016i
$196$	−6.39821			−0.457015
$197$	−10.1952	+	10.1952i	−0.726380	+	0.726380i	−0.969897	−	0.243517i	$-0.921699\pi$
$197$	−10.1952	+	10.1952i	−0.726380	+	0.726380i	0.243517	+	0.969897i	$0.421699\pi$
$198$	−2.24352	−	21.6721i	−0.159440	−	1.54017i
$199$	6.77858	−	3.91361i	0.480521	−	0.277429i	−0.240113	−	0.970745i	$-0.577184\pi$
$199$	6.77858	−	3.91361i	0.480521	−	0.277429i	0.720633	+	0.693316i	$0.243851\pi$
$200$	−5.98129	+	8.44295i	−0.422941	+	0.597007i
$201$	12.5404	+	0.996832i	0.884532	+	0.0703111i
$202$	3.63268	−	13.5574i	0.255595	−	0.953892i
$203$	−6.59191	+	1.76630i	−0.462661	+	0.123970i
$204$	5.44933	−	7.91554i	0.381529	−	0.554198i
$205$	−3.46602	−	2.92462i	−0.242078	−	0.204264i
$206$	−25.0628	−	14.4700i	−1.74621	−	1.00817i
$207$	−5.19278	−	2.32173i	−0.360923	−	0.161371i
$208$	−4.23745	+	4.23745i	−0.293814	+	0.293814i
$209$	−3.04632	+	13.9257i	−0.210718	+	0.963260i
$210$	−16.3001	+	9.52406i	−1.12481	+	0.657222i
$211$	−14.3826			−0.990136			−0.495068	−	0.868854i	$-0.664857\pi$
$211$	−14.3826			−0.990136			−0.495068	+	0.868854i	$0.664857\pi$
$212$	28.6481	−	28.6481i	1.96756	−	1.96756i
$213$	10.3726	+	12.1640i	0.710718	+	0.833464i
$214$	−22.0035	+	12.7037i	−1.50413	+	0.868410i
$215$	−2.04585	+	1.42415i	−0.139526	+	0.0971264i
$216$	−2.53476	+	10.4498i	−0.172469	+	0.711021i
$217$	−0.280253	−	0.280253i	−0.0190248	−	0.0190248i
$218$	−22.6751	−	22.6751i	−1.53575	−	1.53575i
$219$	1.26737	−	15.9438i	0.0856410	−	1.07739i
$220$	−21.1035	−	3.78098i	−1.42279	−	0.254913i
$221$	7.74540	−	4.47181i	0.521012	−	0.300806i
$222$	3.13368	+	16.9820i	0.210319	+	1.13976i
$223$	−0.209687	−	0.0561855i	−0.0140417	−	0.00376246i	0.251791	−	0.967782i	$-0.418980\pi$
$223$	−0.209687	−	0.0561855i	−0.0140417	−	0.00376246i	−0.265833	+	0.964019i	$0.585647\pi$
$224$	7.63258	+	13.2200i	0.509973	+	0.883299i
$225$	7.36466	−	13.0676i	0.490978	−	0.871172i
$226$	12.2911	−	21.2887i	0.817589	−	1.41611i
$227$	5.77380	+	21.5481i	0.383221	+	1.43020i	0.840953	+	0.541108i	$0.181995\pi$
$227$	5.77380	+	21.5481i	0.383221	+	1.43020i	−0.457732	+	0.889090i	$0.651338\pi$
$228$	11.6917	−	18.7951i	0.774304	−	1.24473i
$229$	1.22718	−	0.708512i	0.0810943	−	0.0468198i	−0.458905	−	0.888486i	$-0.651758\pi$
$229$	1.22718	−	0.708512i	0.0810943	−	0.0468198i	0.539999	+	0.841666i	$0.318425\pi$
$230$	−6.07195	+	7.19599i	−0.400372	+	0.474489i
$231$	−10.2407	−	7.05005i	−0.673788	−	0.463859i
$232$	4.54963	+	4.54963i	0.298698	+	0.298698i
$233$	26.6203	−	7.13288i	1.74395	−	0.467290i	0.760633	−	0.649182i	$-0.224889\pi$
$233$	26.6203	−	7.13288i	1.74395	−	0.467290i	0.983319	+	0.181892i	$0.0582221\pi$
$234$	−19.8531	+	24.4382i	−1.29784	+	1.59757i
$235$	−0.815733	−	9.62877i	−0.0532125	−	0.628112i
$236$	11.4413	+	6.60563i	0.744765	+	0.429990i
$237$	−2.23665	+	0.412727i	−0.145286	+	0.0268095i
$238$	−2.38748	−	8.91020i	−0.154757	−	0.577562i
$239$	0.626928	+	1.08587i	0.0405526	+	0.0702392i	0.885589	−	0.464469i	$-0.153755\pi$
$239$	0.626928	+	1.08587i	0.0405526	+	0.0702392i	−0.845037	+	0.534708i	$0.820421\pi$
$240$	−4.26577	−	2.43339i	−0.275354	−	0.157075i
$241$	11.5474			0.743832			0.371916	−	0.928266i	$-0.378701\pi$
$241$	11.5474			0.743832			0.371916	+	0.928266i	$0.378701\pi$
$242$	0.175315	+	0.654284i	0.0112697	+	0.0420590i
$243$	2.09519	−	15.4470i	0.134407	−	0.990926i
$244$	38.3319	+	22.1310i	2.45395	+	1.41679i
$245$	0.860586	−	4.80334i	0.0549808	−	0.306874i
$246$	−4.42369	+	6.42573i	−0.282044	+	0.409689i
$247$	17.3429	−	11.1171i	1.10350	−	0.707363i
$248$	−0.0967132	+	0.360939i	−0.00614129	+	0.0229196i
$249$	−8.08818	−	0.642926i	−0.512568	−	0.0407438i
$250$	−17.4113	−	17.7010i	−1.10119	−	1.11951i
$251$	16.6850	−	9.63306i	1.05314	−	0.608034i	0.129617	−	0.991564i	$-0.458625\pi$
$251$	16.6850	−	9.63306i	1.05314	−	0.608034i	0.923528	+	0.383531i	$0.125292\pi$
$252$	11.3230	+	15.6362i	0.713280	+	0.984986i
$253$	−5.98944	−	1.60486i	−0.376553	−	0.100897i
$254$	9.87118	−	17.0974i	0.619373	−	1.07279i
$255$	5.20949	+	5.15566i	0.326231	+	0.322860i
$256$	3.47843	−	6.02482i	0.217402	−	0.376551i
$257$	1.03672	+	3.86908i	0.0646686	+	0.241346i	0.990693	−	0.136118i	$-0.0434627\pi$
$257$	1.03672	+	3.86908i	0.0646686	+	0.241346i	−0.926024	+	0.377465i	$0.876796\pi$
$258$	2.78229	+	3.26281i	0.173218	+	0.203134i
$259$	8.53386	+	4.92702i	0.530268	+	0.306150i
$260$	17.7010	+	25.4282i	1.09777	+	1.57699i
$261$	−7.23970	−	5.88139i	−0.448126	−	0.364049i
$262$	−6.77731	+	25.2933i	−0.418704	+	1.56262i
$263$	−2.06371	+	7.70188i	−0.127254	+	0.474918i	−0.999910	−	0.0134171i	$-0.995729\pi$
$263$	−2.06371	+	7.70188i	−0.127254	+	0.474918i	0.872656	+	0.488335i	$0.162396\pi$
$264$	−0.928829	+	11.6849i	−0.0571655	+	0.719156i
$265$	17.6538	+	25.3604i	1.08446	+	1.55787i
$266$	−6.44591	−	20.2457i	−0.395224	−	1.24135i
$267$	−5.09089	−	27.5885i	−0.311557	−	1.68839i
$268$	−20.5685	−	5.51130i	−1.25642	−	0.336656i
$269$	10.8142	−	18.7308i	0.659354	−	1.14204i	−0.321429	−	0.946934i	$-0.604163\pi$
$269$	10.8142	−	18.7308i	0.659354	−	1.14204i	0.980783	−	0.195101i	$-0.0625036\pi$
$270$	−23.6102	−	10.4095i	−1.43687	−	0.633500i
$271$	0.627457	−	1.08679i	0.0381153	−	0.0660176i	−0.846338	−	0.532645i	$-0.821198\pi$
$271$	0.627457	−	1.08679i	0.0381153	−	0.0660176i	0.884454	+	0.466628i	$0.154531\pi$
$272$	1.69681	−	1.69681i	0.102884	−	0.102884i
$273$	3.26036	+	17.6686i	0.197326	+	1.06935i
$274$	36.7906	−	21.2410i	2.22260	−	1.28322i
$275$	5.67700	−	15.3345i	0.342336	−	0.924704i
$276$	7.93070	+	5.45977i	0.477372	+	0.328640i
$277$	−2.36693	+	0.634218i	−0.142215	+	0.0381065i	−0.329224	−	0.944252i	$-0.606787\pi$
$277$	−2.36693	+	0.634218i	−0.142215	+	0.0381065i	0.187009	+	0.982358i	$0.440121\pi$
$278$	−33.2735	−	33.2735i	−1.99561	−	1.99561i
$279$	0.0855802	−	0.534909i	0.00512355	−	0.0320242i
$280$	9.55355	−	3.44748i	0.570934	−	0.206027i
$281$			17.1923i			1.02560i	0.858507	+	0.512802i	$0.171393\pi$
$281$			17.1923i			1.02560i	−0.858507	+	0.512802i	$0.828607\pi$
$282$	−16.3468	+	3.01646i	−0.973438	+	0.179628i
$283$	−2.74571	+	2.74571i	−0.163215	+	0.163215i	−0.783989	−	0.620774i	$-0.786818\pi$
$283$	−2.74571	+	2.74571i	−0.163215	+	0.163215i	0.620774	+	0.783989i	$0.286818\pi$
$284$	−13.5297	−	23.4342i	−0.802843	−	1.39056i
$285$	12.5375	+	11.3054i	0.742656	+	0.669673i
$286$	−17.1616	+	29.7247i	−1.01478	+	1.75766i
$287$	1.15216	+	4.29992i	0.0680098	+	0.253816i
$288$	−8.51611	+	19.0472i	−0.501817	+	1.12237i
$289$	11.6209	−	6.70935i	0.683584	−	0.394667i
$290$	−12.6717	+	8.82101i	−0.744110	+	0.517988i
$291$	10.9101	−	15.8477i	0.639563	−	0.929011i
$292$	−7.00706	+	26.1507i	−0.410057	+	1.53035i
$293$	−0.815233	+	3.04249i	−0.0476264	+	0.177744i	−0.985642	−	0.168849i	$-0.945995\pi$
$293$	−0.815233	+	3.04249i	−0.0476264	+	0.177744i	0.938016	+	0.346593i	$0.112662\pi$
$294$	−8.36790	−	0.665161i	−0.488026	−	0.0387930i
$295$	−6.49796	+	7.70086i	−0.378326	+	0.448362i
$296$		−	9.29048i		−	0.539998i
$297$	−0.404922	−	16.9883i	−0.0234960	−	0.985758i
$298$	20.9823	+	5.62219i	1.21547	+	0.325685i
$299$	4.48038	+	7.76024i	0.259107	+	0.448786i
$300$	−16.2731	+	19.4900i	−0.939526	+	1.12526i
$301$	2.44686			0.141035
$302$	25.7249	−	25.7249i	1.48030	−	1.48030i
$303$	3.66220	−	10.3161i	0.210388	−	0.592642i
$304$	3.72267	−	4.08551i	0.213510	−	0.234320i
$305$	−21.7702	+	25.8003i	−1.24656	+	1.47732i
$306$	7.94981	−	9.78582i	0.454460	−	0.559418i
$307$	9.18996	−	2.46244i	0.524499	−	0.140539i	0.0131521	−	0.999914i	$-0.495813\pi$
$307$	9.18996	−	2.46244i	0.524499	−	0.140539i	0.511347	+	0.859374i	$0.329147\pi$
$308$	14.8810	+	14.8810i	0.847926	+	0.847926i
$309$	−18.5915	−	12.7990i	−1.05763	−	0.728112i
$310$	−0.811621	−	0.381186i	−0.0460970	−	0.0216499i
$311$	−4.81882	+	2.78214i	−0.273250	+	0.157761i	−0.630364	−	0.776300i	$-0.717094\pi$
$311$	−4.81882	+	2.78214i	−0.273250	+	0.157761i	0.357114	+	0.934061i	$0.383761\pi$
$312$	12.8894	−	10.9911i	0.729716	−	0.622249i
$313$	−21.9657	+	21.9657i	−1.24158	+	1.24158i	−0.282228	+	0.959347i	$0.591074\pi$
$313$	−21.9657	+	21.9657i	−1.24158	+	1.24158i	−0.959347	+	0.282228i	$0.908926\pi$
$314$	−13.7960	−	23.8954i	−0.778553	−	1.34849i
$315$	−13.2616	+	6.39739i	−0.747204	+	0.360452i
$316$	3.84988			0.216573
$317$	15.6730	−	15.6730i	0.880283	−	0.880283i	−0.113280	−	0.993563i	$-0.536136\pi$
$317$	15.6730	−	15.6730i	0.880283	−	0.880283i	0.993563	+	0.113280i	$0.0361356\pi$
$318$	40.4457	−	34.4892i	2.26808	−	1.93406i
$319$	−8.80581	−	5.08404i	−0.493031	−	0.284651i
$320$	22.0609	+	18.6149i	1.23324	+	1.04061i
$321$	−17.8924	+	8.51705i	−0.998656	+	0.475375i
$322$	8.92727	−	2.39206i	0.497497	−	0.133304i
$323$	−6.94462	+	4.45163i	−0.386409	+	0.247695i
$324$	−8.23243	+	25.0694i	−0.457357	+	1.39274i
$325$	−21.4706	+	9.86850i	−1.19097	+	0.547406i
$326$	7.62200	−	4.40057i	0.422144	−	0.243725i
$327$	−16.2281	−	19.0308i	−0.897414	−	1.05240i
$328$	2.96773	−	2.96773i	0.163866	−	0.163866i
$329$	−4.74272	+	8.21463i	−0.261475	+	0.452887i
$330$	−27.2071	−	7.13887i	−1.49770	−	0.392982i
$331$	2.93796	−	5.08870i	0.161485	−	0.279700i	−0.773916	−	0.633288i	$-0.781705\pi$
$331$	2.93796	−	5.08870i	0.161485	−	0.279700i	0.935402	+	0.353587i	$0.115038\pi$
$332$	13.2660	+	3.55462i	0.728068	+	0.195085i
$333$	1.38686	+	13.3968i	0.0759993	+	0.734142i
$334$			25.5115i			1.39593i
$335$	6.90405	−	14.7001i	0.377209	−	0.803153i
$336$	2.07194	+	4.35268i	0.113033	+	0.237458i
$337$	0.459709	+	0.459709i	0.0250420	+	0.0250420i	0.719517	−	0.694475i	$-0.244363\pi$
$337$	0.459709	+	0.459709i	0.0250420	+	0.0250420i	−0.694475	+	0.719517i	$0.744363\pi$
$338$	20.0244	−	5.36553i	1.08919	−	0.291846i
$339$	10.8717	−	15.7919i	0.590470	−	0.857700i
$340$	−7.08803	−	10.1822i	−0.384402	−	0.552209i
$341$		−	0.590524i		−	0.0319787i
$342$	17.2450	−	23.3657i	0.932502	−	1.26347i
$343$	−14.2514	+	14.2514i	−0.769501	+	0.769501i
$344$	−1.15346	−	1.99785i	−0.0621905	−	0.107717i
$345$	−5.16554	+	5.21947i	−0.278103	+	0.281007i
$346$	15.2632	−	26.4366i	0.820555	−	1.42124i
$347$	−15.1720	+	15.1720i	−0.814473	+	0.814473i	−0.985301	−	0.170828i	$-0.945356\pi$
$347$	−15.1720	+	15.1720i	−0.814473	+	0.814473i	0.170828	+	0.985301i	$0.445356\pi$
$348$	10.2446	+	12.0139i	0.549167	+	0.644013i
$349$	−7.40948	−	4.27787i	−0.396620	−	0.228989i	0.288404	−	0.957509i	$-0.406875\pi$
$349$	−7.40948	−	4.27787i	−0.396620	−	0.228989i	−0.685025	+	0.728520i	$0.740209\pi$
$350$	4.10010	+	24.0247i	0.219159	+	1.28418i
$351$	−16.9457	+	17.7732i	−0.904494	+	0.948665i
$352$	−5.88666	+	21.9693i	−0.313760	+	1.17097i
$353$	30.9917	−	8.30420i	1.64952	−	0.441988i	0.690043	−	0.723769i	$-0.257592\pi$
$353$	30.9917	−	8.30420i	1.64952	−	0.441988i	0.959479	+	0.281781i	$0.0909251\pi$
$354$	14.2768	+	9.82862i	0.758802	+	0.522385i
$355$	19.4126	−	7.00522i	1.03031	−	0.371798i
$356$			47.4874i			2.51683i
$357$	−1.30555	−	7.07504i	−0.0690972	−	0.374451i
$358$	−11.1344	−	2.98347i	−0.588474	−	0.157681i
$359$	9.60747	−	16.6406i	0.507063	−	0.878259i	−0.492904	−	0.870084i	$-0.664065\pi$
$359$	9.60747	−	16.6406i	0.507063	−	0.878259i	0.999967	−	0.00817470i	$-0.00260212\pi$
$360$	11.4750	+	7.81225i	0.604785	+	0.411742i
$361$	−15.5025	+	10.9850i	−0.815923	+	0.578160i
$362$	9.36012	+	34.9324i	0.491957	+	1.83601i
$363$	0.0958680	+	0.519527i	0.00503176	+	0.0272681i
$364$		−	30.4124i		−	1.59404i
$365$	−18.6897	−	8.77780i	−0.978263	−	0.459451i
$366$	47.8317	+	32.9290i	2.50020	+	1.72123i
$367$	10.7617	+	10.7617i	0.561756	+	0.561756i	0.929806	−	0.368050i	$-0.119975\pi$
$367$	10.7617	+	10.7617i	0.561756	+	0.561756i	−0.368050	+	0.929806i	$0.619975\pi$
$368$	1.70006	+	1.70006i	0.0886216	+	0.0886216i
$369$	−3.83645	+	4.72248i	−0.199717	+	0.245842i
$370$	21.9444	+	3.93165i	1.14084	+	0.204397i
$371$		−	30.3313i		−	1.57472i
$372$	−0.306762	+	0.864118i	−0.0159049	+	0.0448024i
$373$	0.631000	+	0.169076i	0.0326719	+	0.00875442i	0.275118	−	0.961410i	$-0.411283\pi$
$373$	0.631000	+	0.169076i	0.0326719	+	0.00875442i	−0.242446	+	0.970165i	$0.577950\pi$
$374$	6.87203	−	11.9027i	0.355344	−	0.615474i
$375$	−12.4430	−	14.8382i	−0.642553	−	0.766241i
$376$	8.94296			0.461198
$377$	3.80310	+	14.1933i	0.195869	+	0.730995i
$378$	13.1832	+	21.6269i	0.678071	+	1.11237i
$379$			23.7632i			1.22063i	0.792158	+	0.610316i	$0.208958\pi$
$379$			23.7632i			1.22063i	−0.792158	+	0.610316i	$0.791042\pi$
$380$	−17.3972	−	22.6699i	−0.892455	−	1.16294i
$381$	8.73128	−	12.6828i	0.447317	−	0.649760i
$382$	16.4370	+	16.4370i	0.840988	+	0.840988i
$383$	14.2706	+	14.2706i	0.729191	+	0.729191i	0.970459	−	0.241267i	$-0.0775631\pi$
$383$	14.2706	+	14.2706i	0.729191	+	0.729191i	−0.241267	+	0.970459i	$0.577563\pi$
$384$	14.4950	−	21.0550i	0.739694	−	1.07446i
$385$	−13.1732	+	9.17011i	−0.671370	+	0.467352i
$386$	22.4552	−	12.9645i	1.14294	−	0.659876i
$387$	1.96152	+	2.70871i	0.0997098	+	0.137692i
$388$	−23.0288	+	23.0288i	−1.16911	+	1.16911i
$389$	13.9130			0.705418			0.352709	−	0.935733i	$-0.385260\pi$
$389$	13.9130			0.705418			0.352709	+	0.935733i	$0.385260\pi$
$390$	20.5067	+	35.0964i	1.03840	+	1.77718i
$391$	−1.79408	−	3.10745i	−0.0907307	−	0.157150i
$392$	4.36220	+	1.16885i	0.220324	+	0.0590357i
$393$	−6.83238	+	19.2461i	−0.344648	+	0.970840i
$394$	27.7298	−	16.0098i	1.39701	−	0.806562i
$395$	−0.517825	+	2.89023i	−0.0260546	+	0.145423i
$396$	−4.54418	+	28.4029i	−0.228354	+	1.42730i
$397$	16.7491	−	4.48791i	0.840614	−	0.225242i	0.187275	−	0.982307i	$-0.440034\pi$
$397$	16.7491	−	4.48791i	0.840614	−	0.225242i	0.653339	+	0.757066i	$0.273368\pi$
$398$	−16.7902	+	4.49892i	−0.841617	+	0.225510i
$399$	−3.76034	−	16.1390i	−0.188253	−	0.807961i
$400$	−4.87915	+	4.04857i	−0.243957	+	0.202428i
$401$			10.9107i			0.544854i	0.962176	+	0.272427i	$0.0878263\pi$
$401$			10.9107i			0.544854i	−0.962176	+	0.272427i	$0.912174\pi$
$402$	−26.3275	−	9.34626i	−1.31310	−	0.466149i
$403$	−0.603427	+	0.603427i	−0.0300588	+	0.0300588i
$404$	−9.26480	+	16.0471i	−0.460941	+	0.798374i
$405$	−17.7131	−	9.55229i	−0.880171	−	0.474657i
$406$	15.1555			0.752157
$407$	3.79999	+	14.1818i	0.188358	+	0.702963i
$408$	−5.16130	+	4.40118i	−0.255523	+	0.217891i
$409$	−15.0810	−	8.70704i	−0.745709	−	0.430535i	0.0784324	−	0.996919i	$-0.475009\pi$
$409$	−15.0810	−	8.70704i	−0.745709	−	0.430535i	−0.824141	+	0.566384i	$0.808342\pi$
$410$	5.75397	+	8.26580i	0.284168	+	0.408219i
$411$	29.9166	−	14.2407i	1.47568	−	0.702444i
$412$	27.0158	+	27.0158i	1.33098	+	1.33098i
$413$	9.55362	−	2.55988i	0.470103	−	0.125964i
$414$	9.80457	+	7.96504i	0.481868	+	0.391460i
$415$	−4.45290	+	9.48112i	−0.218584	+	0.465410i
$416$	28.4646	−	16.4341i	1.39559	−	0.805747i
$417$	−23.8131	−	27.9258i	−1.16613	−	1.36753i
$418$	14.5388	−	28.1211i	0.711118	−	1.37545i
$419$	−19.8920	−	34.4540i	−0.971789	−	1.68319i	−0.690149	−	0.723667i	$-0.742455\pi$
$419$	−19.8920	−	34.4540i	−0.971789	−	1.68319i	−0.281639	−	0.959520i	$-0.590878\pi$
$420$	24.0401	−	6.57554i	1.17304	−	0.320853i
$421$	−2.07173	−	3.58833i	−0.100970	−	0.174885i	0.811115	−	0.584887i	$-0.198861\pi$
$421$	−2.07173	−	3.58833i	−0.100970	−	0.174885i	−0.912084	+	0.410002i	$0.865528\pi$
$422$	30.8521	+	8.26678i	1.50185	+	0.402421i
$423$	−12.8957	+	1.33498i	−0.627011	+	0.0649089i
$424$	−24.7654	+	14.2983i	−1.20271	+	0.694387i
$425$	8.59750	−	3.95166i	0.417040	−	0.191684i
$426$	−15.2586	−	32.0550i	−0.739284	−	1.55307i
$427$	32.0076	−	8.57642i	1.54896	−	0.415042i
$428$	32.3997	−	8.68147i	1.56610	−	0.419635i
$429$	−15.1798	+	22.0497i	−0.732887	+	1.06457i
$430$	5.20713	−	1.87904i	0.251110	−	0.0906154i
$431$	−9.69666	+	5.59837i	−0.467072	+	0.269664i	−0.715013	−	0.699111i	$-0.753579\pi$
$431$	−9.69666	+	5.59837i	−0.467072	+	0.269664i	0.247941	+	0.968775i	$0.420246\pi$
$432$	−3.15751	+	5.78298i	−0.151916	+	0.278234i
$433$	23.8099	+	6.37984i	1.14423	+	0.306596i	0.780651	−	0.624967i	$-0.214888\pi$
$433$	23.8099	+	6.37984i	1.14423	+	0.306596i	0.363580	+	0.931563i	$0.381554\pi$
$434$	0.440089	+	0.762256i	0.0211249	+	0.0365895i
$435$	−10.3972	+	6.07502i	−0.498506	+	0.291275i
$436$	21.1675	+	36.6632i	1.01374	+	1.75585i
$437$	−4.46016	−	6.95793i	−0.213358	−	0.332843i
$438$	−11.8828	+	33.4727i	−0.567783	+	1.59939i
$439$	26.8365	−	15.4941i	1.28084	−	0.739491i	0.303835	−	0.952725i	$-0.401733\pi$
$439$	26.8365	−	15.4941i	1.28084	−	0.739491i	0.977001	+	0.213234i	$0.0683996\pi$
$440$	13.6973	+	6.43306i	0.652992	+	0.306684i
$441$	−6.46476	−	1.03430i	−0.307846	−	0.0492523i
$442$	−19.1850	+	5.14060i	−0.912536	+	0.244513i
$443$	16.4211	+	16.4211i	0.780189	+	0.780189i	0.979862	−	0.199674i	$-0.0639882\pi$
$443$	16.4211	+	16.4211i	0.780189	+	0.780189i	−0.199674	+	0.979862i	$0.563988\pi$
$444$	1.80650	−	22.7263i	0.0857328	−	1.07854i
$445$	−35.6503	−	6.38724i	−1.68999	−	0.302784i
$446$	0.417506	+	0.241047i	0.0197695	+	0.0114139i
$447$	15.9658	+	5.66788i	0.755159	+	0.268081i
$448$	−7.33339	−	27.3686i	−0.346470	−	1.29304i
$449$	36.8818			1.74056			0.870279	−	0.492558i	$-0.163938\pi$
$449$	36.8818			1.74056			0.870279	+	0.492558i	$0.163938\pi$
$450$	−23.3089	+	23.7982i	−1.09879	+	1.12186i
$451$	−3.31633	+	5.74405i	−0.156160	+	0.270477i
$452$	−22.9477	+	22.9477i	−1.07937	+	1.07937i
$453$	21.5904	−	18.4108i	1.01441	−	0.865013i
$454$		−	49.5416i		−	2.32510i
$455$	22.8316	+	4.09059i	1.07036	+	0.191770i
$456$	−11.4048	+	10.6783i	−0.534078	+	0.500057i
$457$	−9.92642	+	2.65978i	−0.464338	+	0.124419i	−0.483401	−	0.875399i	$-0.660599\pi$
$457$	−9.92642	+	2.65978i	−0.464338	+	0.124419i	0.0190624	+	0.999818i	$0.493932\pi$
$458$	−3.03966	+	0.814475i	−0.142034	+	0.0380579i
$459$	6.78559	−	7.11696i	0.316724	−	0.332191i
$460$	10.2017	−	7.10161i	0.475659	−	0.331114i
$461$	4.56325	−	2.63460i	0.212532	−	0.122705i	−0.389956	−	0.920834i	$-0.627510\pi$
$461$	4.56325	−	2.63460i	0.212532	−	0.122705i	0.602488	+	0.798128i	$0.294176\pi$
$462$	17.9151	+	21.0092i	0.833487	+	0.977436i
$463$	−10.2732	−	2.75269i	−0.477436	−	0.127929i	0.0120726	−	0.999927i	$-0.496157\pi$
$463$	−10.2732	−	2.75269i	−0.477436	−	0.127929i	−0.489508	+	0.871999i	$0.662824\pi$
$464$	1.97127	+	3.41433i	0.0915137	+	0.158506i
$465$	−0.607460	−	0.346523i	−0.0281703	−	0.0160696i
$466$	−61.2030			−2.83517
$467$	−25.2931	+	25.2931i	−1.17043	+	1.17043i	−0.188317	+	0.982108i	$0.560303\pi$
$467$	−25.2931	+	25.2931i	−1.17043	+	1.17043i	−0.982108	+	0.188317i	$0.939697\pi$
$468$	33.6670	−	24.3800i	1.55626	−	1.12697i
$469$	−13.8060	+	7.97090i	−0.637502	+	0.368062i
$470$	−3.78458	+	21.1236i	−0.174570	+	0.974357i
$471$	−9.24933	−	19.4308i	−0.426186	−	0.895322i
$472$	−6.59375	−	6.59375i	−0.303502	−	0.303502i
$473$	2.57790	+	2.57790i	0.118532	+	0.118532i
$474$	5.03506	+	0.400235i	0.231268	+	0.0183834i
$475$	19.3590	−	10.0114i	0.888253	−	0.459355i
$476$			12.1781i			0.558181i
$477$	33.5772	−	24.3150i	1.53739	−	1.11331i
$478$	−0.720689	−	2.68965i	−0.0329636	−	0.123022i
$479$	−12.2743			−0.560828			−0.280414	−	0.959879i	$-0.590472\pi$
$479$	−12.2743			−0.560828			−0.280414	+	0.959879i	$0.590472\pi$
$480$	19.1451	+	18.9472i	0.873849	+	0.864819i
$481$	10.6086	−	18.3747i	0.483711	−	0.837812i
$482$	−24.7703	−	6.63718i	−1.12826	−	0.302315i
$483$	7.08860	−	1.30805i	0.322542	−	0.0595185i
$484$		−	0.894248i		−	0.0406476i
$485$	−14.1910	−	20.3859i	−0.644380	−	0.925677i
$486$	−13.3730	+	31.9311i	−0.606612	+	1.44843i
$487$	−19.8447	−	19.8447i	−0.899250	−	0.899250i	0.0961194	−	0.995370i	$-0.469357\pi$
$487$	−19.8447	−	19.8447i	−0.899250	−	0.899250i	−0.995370	+	0.0961194i	$0.969357\pi$
$488$	−22.0911	−	22.0911i	−1.00002	−	1.00002i
$489$	6.19791	−	2.95030i	0.280279	−	0.133417i
$490$	−4.60690	+	9.80901i	−0.208119	+	0.443126i
$491$		−	3.74830i		−	0.169158i	−0.996417	−	0.0845792i	$-0.973045\pi$
$491$		−	3.74830i		−	0.169158i	0.996417	−	0.0845792i	$-0.0269546\pi$
$492$	7.83670	−	6.68257i	0.353306	−	0.301273i
$493$	−1.52288	−	5.68346i	−0.0685870	−	0.255970i
$494$	−43.5921	+	13.8790i	−1.96130	+	0.624445i
$495$	−20.7117	−	7.23176i	−0.930923	−	0.325044i
$496$	−0.114484	+	0.198292i	−0.00514047	+	0.00890356i
$497$	−19.5678	−	5.24319i	−0.877738	−	0.235189i
$498$	16.9804	+	6.02805i	0.760911	+	0.270124i
$499$		−	27.1532i		−	1.21555i	−0.794111	−	0.607773i	$-0.792063\pi$
$499$		−	27.1532i		−	1.21555i	0.794111	−	0.607773i	$-0.207937\pi$
$500$	16.1547	+	28.5216i	0.722460	+	1.27552i
$501$	−1.57665	+	19.8346i	−0.0704394	+	0.886147i
$502$	−41.3278	+	11.0738i	−1.84455	+	0.494246i
$503$	9.68063	−	36.1286i	0.431638	−	1.61089i	−0.317348	−	0.948309i	$-0.602792\pi$
$503$	9.68063	−	36.1286i	0.431638	−	1.61089i	0.748986	−	0.662585i	$-0.230541\pi$
$504$	−4.86335	−	12.7290i	−0.216631	−	0.566995i
$505$	−10.8009	−	9.11379i	−0.480635	−	0.405558i
$506$	11.9255	+	6.88520i	0.530154	+	0.306084i
$507$	15.9002	−	2.93405i	0.706152	−	0.130306i
$508$	−18.4297	+	18.4297i	−0.817687	+	0.817687i
$509$	−13.5095	+	23.3992i	−0.598799	+	1.03715i	0.394199	+	0.919025i	$0.371022\pi$
$509$	−13.5095	+	23.3992i	−0.598799	+	1.03715i	−0.992999	+	0.118126i	$0.962311\pi$
$510$	−8.21153	−	14.0537i	−0.363613	−	0.622309i
$511$	10.1342	+	17.5529i	0.448310	+	0.776496i
$512$	9.94677	−	9.94677i	0.439589	−	0.439589i
$513$	14.8516	−	17.1005i	0.655716	−	0.755008i
$514$		−	8.89545i		−	0.392361i
$515$	−23.9154	+	16.6479i	−1.05384	+	0.733595i
$516$	−2.43311	−	5.11141i	−0.107112	−	0.225017i
$517$	−13.6513	+	3.65784i	−0.600382	+	0.160872i
$518$	−15.4740	−	15.4740i	−0.679891	−	0.679891i
$519$	13.5006	−	19.6107i	0.592613	−	0.860812i
$520$	−7.42294	−	20.5702i	−0.325517	−	0.902063i
$521$		−	34.1973i		−	1.49821i	−0.662451	−	0.749105i	$-0.730484\pi$
$521$		−	34.1973i		−	1.49821i	0.662451	−	0.749105i	$-0.269516\pi$
$522$	12.1494	+	16.7774i	0.531765	+	0.734327i
$523$	−40.6040	−	10.8798i	−1.77549	−	0.475741i	−0.785739	−	0.618558i	$-0.787717\pi$
$523$	−40.6040	−	10.8798i	−1.77549	−	0.475741i	−0.989749	+	0.142818i	$0.954384\pi$
$524$	17.2849	−	29.9383i	0.755093	−	1.30786i
$525$	1.70297	+	18.9321i	0.0743238	+	0.826266i
$526$	8.85375	−	15.3351i	0.386042	−	0.668644i
$527$	0.241631	−	0.241631i	0.0105256	−	0.0105256i
$528$	−2.40288	+	6.76867i	−0.104572	+	0.294569i
$529$	−16.8052	+	9.70248i	−0.730660	+	0.421847i
$530$	−23.2926	−	64.5476i	−1.01176	−	2.80377i
$531$	10.4925	+	8.52387i	0.455334	+	0.369905i
$532$	1.30208	+	28.0199i	0.0564525	+	1.21482i
$533$	9.25836	−	2.48077i	0.401024	−	0.107454i
$534$	−4.93681	+	62.1063i	−0.213637	+	2.68760i
$535$	2.15957	+	25.4912i	0.0933662	+	1.10208i
$536$	13.0164	+	7.51504i	0.562224	+	0.324600i
$537$	−8.47242	−	3.00771i	−0.365612	−	0.129792i
$538$	−33.9636	+	33.9636i	−1.46428	+	1.46428i
$539$	−7.13690			−0.307408
$540$	26.5509	+	21.3415i	1.14257	+	0.918392i
$541$	5.90587	+	10.2293i	0.253913	+	0.439791i	0.964600	−	0.263718i	$-0.0849489\pi$
$541$	5.90587	+	10.2293i	0.253913	+	0.439791i	−0.710686	+	0.703509i	$0.751616\pi$
$542$	−1.97062	+	1.97062i	−0.0846454	+	0.0846454i
$543$	5.11842	+	27.7377i	0.219652	+	1.19034i
$544$	−11.3981	+	6.58072i	−0.488691	+	0.282146i
$545$	−30.3713	+	10.9598i	−1.30097	+	0.469465i
$546$	3.16169	−	39.7748i	0.135308	−	1.70221i
$547$	−23.0019	−	23.0019i	−0.983492	−	0.983492i	0.0163742	−	0.999866i	$-0.494788\pi$
$547$	−23.0019	−	23.0019i	−0.983492	−	0.983492i	−0.999866	+	0.0163742i	$0.994788\pi$
$548$	−54.1732	+	14.5157i	−2.31416	+	0.620079i
$549$	35.1531	+	28.5577i	1.50030	+	1.21881i
$550$	−20.9917	+	29.6310i	−0.895088	+	1.26347i
$551$	−4.11159	−	12.9140i	−0.175160	−	0.550153i
$552$	−4.40962	−	5.17119i	−0.187686	−	0.220101i
$553$	2.03804	−	2.03804i	0.0866661	−	0.0866661i
$554$	5.44185			0.231202
$555$	16.8184	+	4.41297i	0.713899	+	0.187320i
$556$	31.0612	+	53.7996i	1.31729	+	2.28161i
$557$	−11.6951	−	3.13368i	−0.495536	−	0.132778i	0.00239156	−	0.999997i	$-0.499239\pi$
$557$	−11.6951	−	3.13368i	−0.495536	−	0.132778i	−0.497927	+	0.867219i	$0.665905\pi$
$558$	−0.491033	+	1.09825i	−0.0207871	+	0.0464924i
$559$		−	5.26846i		−	0.222832i
$560$	6.20122	−	0.525357i	0.262050	−	0.0222004i
$561$	6.07846	−	8.82940i	0.256633	−	0.372778i
$562$	9.88174	−	36.8791i	0.416836	−	1.55565i
$563$	6.50975	−	24.2947i	0.274353	−	1.02390i	−0.681920	−	0.731427i	$-0.738855\pi$
$563$	6.50975	−	24.2947i	0.274353	−	1.02390i	0.956274	−	0.292474i	$-0.0944784\pi$
$564$	21.8762	+	1.73893i	0.921152	+	0.0732220i
$565$	−14.1410	−	20.3141i	−0.594917	−	0.854622i
$566$	7.46799	−	4.31165i	0.313903	−	0.181232i
$567$	8.91309	+	17.6292i	0.374314	+	0.740357i
$568$	4.94332	+	18.4487i	0.207417	+	0.774091i
$569$	3.30474	−	5.72398i	0.138542	−	0.239962i	−0.788403	−	0.615159i	$-0.789092\pi$
$569$	3.30474	−	5.72398i	0.138542	−	0.239962i	0.926945	+	0.375197i	$0.122425\pi$
$570$	−20.3961	−	31.4575i	−0.854298	−	1.31761i
$571$	5.71449	+	9.89778i	0.239144	+	0.414209i	0.960469	−	0.278387i	$-0.0897999\pi$
$571$	5.71449	+	9.89778i	0.239144	+	0.414209i	−0.721325	+	0.692597i	$0.756467\pi$
$572$	32.0411	−	32.0411i	1.33970	−	1.33970i
$573$	11.7636	+	13.7952i	0.491430	+	0.576304i
$574$		−	9.88600i		−	0.412634i
$575$	3.95923	+	8.61398i	0.165111	+	0.359228i
$576$	24.4186	−	30.0581i	1.01744	−	1.25242i
$577$	−12.5872	−	12.5872i	−0.524012	−	0.524012i	0.394768	−	0.918781i	$-0.370825\pi$
$577$	−12.5872	−	12.5872i	−0.524012	−	0.524012i	−0.918781	+	0.394768i	$0.870825\pi$
$578$	−28.7845	+	7.71277i	−1.19728	+	0.320809i
$579$	18.2597	−	8.69187i	0.758846	−	0.361222i
$580$	19.1731	−	6.91877i	0.796118	−	0.287286i
$581$	8.90445	−	5.14099i	0.369419	−	0.213284i
$582$	−32.5123	+	27.7241i	−1.34768	+	1.14920i
$583$	31.9556	−	31.9556i	1.32347	−	1.32347i
$584$	9.55460	−	16.5491i	0.395372	−	0.684805i
$585$	13.7745	+	28.5541i	0.569506	+	1.18057i
$586$	3.49751	−	6.05787i	0.144481	−	0.250248i
$587$	−13.9044	−	3.72566i	−0.573895	−	0.153775i	−0.0398125	−	0.999207i	$-0.512676\pi$
$587$	−13.9044	−	3.72566i	−0.573895	−	0.153775i	−0.534082	+	0.845433i	$0.679343\pi$
$588$	10.4435	+	3.70744i	0.430682	+	0.152892i
$589$	0.530121	−	0.581792i	0.0218433	−	0.0239723i
$590$	18.3651	−	12.7842i	0.756078	−	0.526319i
$591$	22.5488	−	10.7335i	0.927532	−	0.441519i
$592$	1.47339	−	5.49878i	0.0605561	−	0.225998i
$593$	−0.515547	+	1.92405i	−0.0211710	+	0.0790112i	−0.975703	−	0.219097i	$-0.929689\pi$
$593$	−0.515547	+	1.92405i	−0.0211710	+	0.0790112i	0.954532	+	0.298108i	$0.0963556\pi$
$594$	−8.89588	+	36.6743i	−0.365002	+	1.50476i
$595$	−9.14247	−	1.63800i	−0.374805	−	0.0671515i
$596$	−24.8356	−	14.3389i	−1.01731	−	0.587343i
$597$	−13.3321	+	2.46016i	−0.545645	+	0.100688i
$598$	−5.15045	−	19.2217i	−0.210618	−	0.786035i
$599$	−15.3321	+	26.5560i	−0.626453	+	1.08505i	0.361805	+	0.932254i	$0.382161\pi$
$599$	−15.3321	+	26.5560i	−0.626453	+	1.08505i	−0.988258	+	0.152795i	$0.951173\pi$
$600$	14.6552	−	10.3152i	0.598297	−	0.421115i
$601$	−12.5409	+	21.7215i	−0.511555	+	0.886039i	0.488355	+	0.872645i	$0.337597\pi$
$601$	−12.5409	+	21.7215i	−0.511555	+	0.886039i	−0.999910	+	0.0133945i	$0.995736\pi$
$602$	−5.24877	−	1.40640i	−0.213924	−	0.0573208i
$603$	−19.8915	−	8.89360i	−0.810043	−	0.362176i
$604$	−41.5944	+	24.0146i	−1.69245	+	0.977138i
$605$	0.671340	+	0.120280i	0.0272939	+	0.00489008i
$606$	−13.7852	+	20.0240i	−0.559987	+	0.813421i
$607$	4.91168	−	18.3306i	0.199359	−	0.744018i	−0.791736	−	0.610863i	$-0.790823\pi$
$607$	4.91168	−	18.3306i	0.199359	−	0.744018i	0.991095	−	0.133155i	$-0.0425107\pi$
$608$	−25.5218	+	16.3599i	−1.03504	+	0.663482i
$609$	11.7831	+	0.936635i	0.477476	+	0.0379544i
$610$	61.5288	−	42.8313i	2.49123	−	1.73419i
$611$	17.6873	+	10.2118i	0.715552	+	0.413124i
$612$	−13.4813	+	9.76253i	−0.544950	+	0.394627i
$613$	−3.17625	−	11.8539i	−0.128287	−	0.478775i	0.871648	−	0.490132i	$-0.163052\pi$
$613$	−3.17625	−	11.8539i	−0.128287	−	0.478775i	−0.999936	+	0.0113571i	$0.996385\pi$
$614$	−21.1288			−0.852688
$615$	3.96275	+	6.78209i	0.159794	+	0.273480i
$616$	−7.42713	−	12.8642i	−0.299248	−	0.518312i
$617$	0.552305	+	2.06123i	0.0222350	+	0.0829820i	0.976152	−	0.217089i	$-0.0696562\pi$
$617$	0.552305	+	2.06123i	0.0222350	+	0.0829820i	−0.953917	+	0.300071i	$0.902990\pi$
$618$	32.5241	+	38.1412i	1.30831	+	1.53427i
$619$	−21.6969	−	12.5267i	−0.872072	−	0.503491i	−0.00403578	−	0.999992i	$-0.501285\pi$
$619$	−21.6969	−	12.5267i	−0.872072	−	0.503491i	−0.868036	+	0.496501i	$0.834618\pi$
$620$	0.904733	+	0.763411i	0.0363350	+	0.0306593i
$621$	7.13060	+	6.79859i	0.286141	+	0.272818i
$622$	11.9360	−	3.19823i	0.478589	−	0.128237i
$623$	25.1387	+	25.1387i	1.00716	+	1.00716i
$624$	9.37195	−	4.46119i	0.375178	−	0.178590i
$625$	−23.5849	+	8.29157i	−0.943398	+	0.331663i
$626$	59.7441	−	34.4933i	2.38786	−	1.37863i
$627$	13.0416	−	20.9650i	0.520830	−	0.837262i
$628$	9.42788	+	35.1853i	0.376214	+	1.40405i
$629$	−4.24802	+	7.35779i	−0.169380	+	0.293374i
$630$	32.1245	−	6.10059i	1.27987	−	0.243053i
$631$	4.80778	+	8.32733i	0.191395	+	0.331506i	0.945713	−	0.325004i	$-0.105366\pi$
$631$	4.80778	+	8.32733i	0.191395	+	0.331506i	−0.754318	+	0.656509i	$0.772032\pi$
$632$	−2.62479	−	0.703309i	−0.104408	−	0.0279761i
$633$	23.4759	+	8.33395i	0.933084	+	0.331245i
$634$	−42.6287	+	24.6117i	−1.69300	+	0.977455i
$635$	−11.3569	−	16.3147i	−0.450685	−	0.647428i
$636$	−63.3610	+	30.1608i	−2.51243	+	1.19595i
$637$	7.29284	+	7.29284i	0.288953	+	0.288953i
$638$	15.9672	+	15.9672i	0.632146	+	0.632146i
$639$	−9.88223	−	25.8651i	−0.390935	−	1.02321i
$640$	−18.8539	−	27.0843i	−0.745264	−	1.07060i
$641$	−23.1003	+	13.3369i	−0.912406	+	0.526778i	−0.881204	−	0.472735i	$-0.843267\pi$
$641$	−23.1003	+	13.3369i	−0.912406	+	0.526778i	−0.0312014	+	0.999513i	$0.509933\pi$
$642$	43.2764	−	7.98577i	1.70798	−	0.315173i
$643$	33.6147	−	33.6147i	1.32563	−	1.32563i	0.416494	−	0.909138i	$-0.363259\pi$
$643$	33.6147	−	33.6147i	1.32563	−	1.32563i	0.909138	−	0.416494i	$-0.136741\pi$
$644$	−12.2014			−0.480803
$645$	4.16457	−	1.13911i	0.163980	−	0.0448523i
$646$	17.4556	−	5.55758i	0.686782	−	0.218660i
$647$	32.9655	−	32.9655i	1.29601	−	1.29601i	0.364999	−	0.931008i	$-0.381069\pi$
$647$	32.9655	−	32.9655i	1.29601	−	1.29601i	0.931008	−	0.364999i	$-0.118931\pi$
$648$	10.1925	−	15.5880i	0.400399	−	0.612354i
$649$	12.7622	+	7.36827i	0.500961	+	0.289230i
$650$	51.7288	−	8.82811i	2.02897	−	0.346267i
$651$	0.295051	+	0.619836i	0.0115640	+	0.0242933i
$652$	−11.2232	+	3.00725i	−0.439535	+	0.117773i
$653$	−7.27233	+	27.1407i	−0.284588	+	1.06210i	0.664552	+	0.747242i	$0.268623\pi$
$653$	−7.27233	+	27.1407i	−0.284588	+	1.06210i	−0.949140	+	0.314855i	$0.898044\pi$
$654$	23.8724	+	50.1505i	0.933484	+	1.96104i
$655$	20.1507	+	17.0031i	0.787355	+	0.664367i
$656$	2.22718	−	1.28586i	0.0869567	−	0.0502045i
$657$	−11.3073	+	25.2900i	−0.441140	+	0.986656i
$658$	14.8952	−	14.8952i	0.580676	−	0.580676i
$659$	−26.4350			−1.02976			−0.514880	−	0.857262i	$-0.672164\pi$
$659$	−26.4350			−1.02976			−0.514880	+	0.857262i	$0.672164\pi$
$660$	32.2552	+	18.3999i	1.25553	+	0.716214i
$661$	−19.4784	+	33.7375i	−0.757620	+	1.31224i	0.186441	+	0.982466i	$0.440305\pi$
$661$	−19.4784	+	33.7375i	−0.757620	+	1.31224i	−0.944061	+	0.329771i	$0.893028\pi$
$662$	−9.22711	+	9.22711i	−0.358622	+	0.358622i
$663$	−15.2336	+	2.81105i	−0.591625	+	0.109172i
$664$	−8.39519	−	4.84697i	−0.325797	−	0.188099i
$665$	−21.2106	−	2.79127i	−0.822510	−	0.108241i
$666$	4.72527	−	29.5347i	0.183100	−	1.14445i
$667$	5.69435	−	1.52580i	0.220486	−	0.0590791i
$668$	8.71700	−	32.5323i	0.337271	−	1.25871i
$669$	0.309705	+	0.213212i	0.0119739	+	0.00824325i
$670$	−23.2592	+	27.5649i	−0.898582	+	1.06493i
$671$	42.7574	+	24.6860i	1.65063	+	0.952993i
$672$	−4.79796	−	26.0011i	−0.185085	−	1.00301i
$673$	−2.20235	−	8.21927i	−0.0848942	−	0.316830i	0.910400	−	0.413729i	$-0.135774\pi$
$673$	−2.20235	−	8.21927i	−0.0848942	−	0.316830i	−0.995294	+	0.0968998i	$0.969107\pi$
$674$	−0.721892	−	1.25035i	−0.0278063	−	0.0481618i
$675$	−19.5930	+	17.0621i	−0.754134	+	0.656721i
$676$	−27.3685			−1.05264
$677$	−2.79049	−	10.4142i	−0.107247	−	0.400252i	0.891343	−	0.453329i	$-0.149764\pi$
$677$	−2.79049	−	10.4142i	−0.107247	−	0.400252i	−0.998590	+	0.0530774i	$0.983097\pi$
$678$	−32.3978	+	27.6265i	−1.24423	+	1.06099i
$679$			24.3818i			0.935688i
$680$	2.97238	+	8.23695i	0.113986	+	0.315873i
$681$	3.06174	−	38.5175i	0.117326	−	1.47599i
$682$	−0.339420	+	1.26673i	−0.0129971	+	0.0485057i
$683$	−29.6790	−	29.6790i	−1.13563	−	1.13563i	−0.989224	−	0.146410i	$-0.953228\pi$
$683$	−29.6790	−	29.6790i	−1.13563	−	1.13563i	−0.146410	−	0.989224i	$-0.546772\pi$
$684$	−29.9746	+	23.9035i	−1.14611	+	0.913973i
$685$	−3.61086	−	42.6220i	−0.137964	−	1.62850i
$686$	38.7620	−	22.3793i	1.47994	−	0.854444i
$687$	−2.41361	+	0.445382i	−0.0920849	+	0.0169924i
$688$	−0.365859	−	1.36540i	−0.0139482	−	0.0520556i
$689$	−65.3078			−2.48803
$690$	14.0806	−	8.22726i	0.536041	−	0.313207i
$691$	17.1567	−	29.7164i	0.652673	−	1.13046i	−0.329798	−	0.944051i	$-0.606981\pi$
$691$	17.1567	−	29.7164i	0.652673	−	1.13046i	0.982472	−	0.186412i	$-0.0596859\pi$
$692$	−28.4968	+	28.4968i	−1.08329	+	1.08329i
$693$	12.6302	+	17.4414i	0.479783	+	0.662544i
$694$	41.2659	−	23.8249i	1.56643	−	0.904380i
$695$	−44.5670	+	16.0824i	−1.69052	+	0.610040i
$696$	−4.78985	−	10.0624i	−0.181559	−	0.381414i
$697$	−3.70734	+	0.993378i	−0.140425	+	0.0376269i
$698$	13.4353	+	13.4353i	0.508532	+	0.508532i
$699$	−47.5841	−	3.78244i	−1.79979	−	0.143065i
$700$	2.98055	−	32.0374i	0.112654	−	1.21090i
$701$	9.11803	+	5.26430i	0.344383	+	0.198830i	0.662209	−	0.749320i	$-0.269619\pi$
$701$	9.11803	+	5.26430i	0.344383	+	0.198830i	−0.317825	+	0.948149i	$0.602953\pi$
$702$	46.5659	−	28.3854i	1.75752	−	1.07134i
$703$	−8.98735	+	17.3833i	−0.338964	+	0.655625i
$704$	21.1081	−	36.5604i	0.795543	−	1.37792i
$705$	−4.24790	+	16.1892i	−0.159985	+	0.609722i
$706$	−71.2534			−2.68166
$707$	3.59039	+	13.3995i	0.135031	+	0.503941i
$708$	−14.8474	−	17.4117i	−0.558000	−	0.654371i
$709$			23.7445i			0.891742i	0.895097	+	0.445871i	$0.147106\pi$
$709$			23.7445i			0.891742i	−0.895097	+	0.445871i	$0.852894\pi$
$710$	−45.6685	+	3.86895i	−1.71391	+	0.145199i
$711$	3.88992	+	0.622349i	0.145883	+	0.0233399i
$712$	8.67516	−	32.3761i	0.325115	−	1.21335i
$713$	0.242094	+	0.242094i	0.00906650	+	0.00906650i
$714$	−1.26604	+	15.9271i	−0.0473803	+	0.596057i
$715$	19.7446	+	28.3639i	0.738406	+	1.06075i
$716$	13.1792	+	7.60904i	0.492531	+	0.284363i
$717$	−0.394096	−	2.13569i	−0.0147178	−	0.0797586i
$718$	−30.1737	+	30.1737i	−1.12607	+	1.12607i
$719$	−14.6912	+	25.4459i	−0.547888	+	0.948971i	0.450531	+	0.892761i	$0.351235\pi$
$719$	−14.6912	+	25.4459i	−0.547888	+	0.948971i	−0.998419	+	0.0562096i	$0.982099\pi$
$720$	5.55278	+	6.44370i	0.206940	+	0.240142i
$721$	28.6031			1.06524
$722$	39.5685	−	14.6535i	1.47259	−	0.545347i
$723$	−18.8482	−	6.69111i	−0.700972	−	0.248845i
$724$		−	47.7442i		−	1.77440i
$725$	2.61529	+	15.3244i	0.0971294	+	0.569135i
$726$	0.0929664	−	1.16954i	0.00345031	−	0.0434058i
$727$	−1.54918	+	5.78162i	−0.0574560	+	0.214429i	−0.988685	−	0.150005i	$-0.952071\pi$
$727$	−1.54918	+	5.78162i	−0.0574560	+	0.214429i	0.931229	+	0.364434i	$0.118738\pi$
$728$	−5.55584	+	20.7347i	−0.205913	+	0.768478i
$729$	−12.3706	+	23.9993i	−0.458171	+	0.888864i
$730$	35.0460	+	29.5717i	1.29711	+	1.09450i
$731$			2.10966i			0.0780285i
$732$	−49.7436	−	58.3346i	−1.83857	−	2.15611i
$733$	51.0133	+	13.6690i	1.88422	+	0.504875i	0.999229	+	0.0392641i	$0.0125014\pi$
$733$	51.0133	+	13.6690i	1.88422	+	0.504875i	0.884990	+	0.465611i	$0.154165\pi$
$734$	−16.8993	−	29.2705i	−0.623766	−	1.08039i
$735$	−4.18798	+	7.34159i	−0.154476	+	0.270799i
$736$	−6.59333	−	11.4200i	−0.243033	−	0.420946i
$737$	−22.9431	−	6.14759i	−0.845121	−	0.226450i
$738$	10.9439	−	7.92509i	0.402852	−	0.291727i
$739$	−1.10601	−	0.638555i	−0.0406852	−	0.0234896i	0.479519	−	0.877531i	$-0.340811\pi$
$739$	−1.10601	−	0.638555i	−0.0406852	−	0.0234896i	−0.520205	+	0.854042i	$0.674144\pi$
$740$	−26.6402	−	12.5118i	−0.979312	−	0.459944i
$741$	−34.7496	+	8.09657i	−1.27656	+	0.297435i
$742$	−17.4338	+	65.0637i	−0.640014	+	2.38856i
$743$	0.184064	+	0.184064i	0.00675265	+	0.00675265i	0.710475	−	0.703722i	$-0.248480\pi$
$743$	0.184064	+	0.184064i	0.00675265	+	0.00675265i	−0.703722	+	0.710475i	$0.748480\pi$
$744$	0.367005	−	0.533102i	0.0134551	−	0.0195445i
$745$	14.1051	−	16.7163i	0.516772	−	0.612437i
$746$	−1.25638	−	0.725370i	−0.0459993	−	0.0265577i
$747$	12.8294	+	5.73610i	0.469403	+	0.209873i
$748$	−12.8302	+	12.8302i	−0.469120	+	0.469120i
$749$	12.5559	−	21.7474i	0.458781	−	0.794632i
$750$	18.1628	+	38.9814i	0.663211	+	1.42340i
$751$	−0.0379751	+	0.0657749i	−0.00138573	+	0.00240016i	−0.866717	−	0.498799i	$-0.833774\pi$
$751$	−0.0379751	+	0.0657749i	−0.00138573	+	0.00240016i	0.865332	+	0.501200i	$0.167108\pi$
$752$	5.29309	+	1.41828i	0.193019	+	0.0517193i
$753$	−32.8159	+	6.05549i	−1.19588	+	0.220674i
$754$		−	32.6321i		−	1.18839i
$755$	−12.4339	−	34.4563i	−0.452515	−	1.25399i
$756$	−9.42156	−	32.0832i	−0.342659	−	1.16685i
$757$	46.2638	−	12.3964i	1.68149	−	0.450553i	0.713317	−	0.700842i	$-0.247192\pi$
$757$	46.2638	−	12.3964i	1.68149	−	0.450553i	0.968171	+	0.250288i	$0.0805255\pi$
$758$	13.6586	−	50.9744i	0.496101	−	1.85148i
$759$	8.84632	+	6.09011i	0.321101	+	0.221057i
$760$	7.71969	+	18.6342i	0.280022	+	0.675932i
$761$	42.8887	−	24.7618i	1.55472	−	0.897615i	0.556967	−	0.830534i	$-0.311965\pi$
$761$	42.8887	−	24.7618i	1.55472	−	0.897615i	0.997748	−	0.0670808i	$-0.0213685\pi$
$762$	−26.0193	+	22.1874i	−0.942579	+	0.803763i
$763$	30.6142	+	8.20305i	1.10831	+	0.296970i
$764$	−15.3441	−	26.5768i	−0.555130	−	0.961514i
$765$	−5.51575	−	11.4340i	−0.199422	−	0.413395i
$766$	−22.4094	−	38.8142i	−0.809684	−	1.40241i
$767$	−5.51181	−	20.5703i	−0.199020	−	0.742752i
$768$	−9.16875	+	7.81844i	−0.330849	+	0.282124i
$769$	−29.1978	−	16.8574i	−1.05290	−	0.607893i	−0.129441	−	0.991587i	$-0.541318\pi$
$769$	−29.1978	−	16.8574i	−1.05290	−	0.607893i	−0.923460	+	0.383694i	$0.874652\pi$
$770$	33.5287	−	12.0991i	1.20829	−	0.436023i
$771$	0.549752	−	6.91603i	0.0197988	−	0.249075i
$772$	−33.0647	+	8.85967i	−1.19003	+	0.318866i
$773$	−5.99660	+	22.3796i	−0.215683	+	0.804938i	0.770243	+	0.637751i	$0.220135\pi$
$773$	−5.99660	+	22.3796i	−0.215683	+	0.804938i	−0.985925	+	0.167187i	$0.946532\pi$
$774$	−2.65076	−	6.93791i	−0.0952794	−	0.249378i
$775$	−0.694807	+	0.576530i	−0.0249582	+	0.0207096i
$776$	19.9076	−	11.4937i	0.714643	−	0.412599i
$777$	−11.0744	−	12.9871i	−0.397293	−	0.465908i
$778$	−29.8449	−	7.99691i	−1.06999	−	0.286703i
$779$	−8.42380	+	2.68200i	−0.301814	+	0.0960926i
$780$	−14.1581	−	51.7619i	−0.506942	−	1.85337i
$781$	−15.0918	−	26.1397i	−0.540026	−	0.935353i
$782$	2.06240	+	7.69699i	0.0737513	+	0.275244i
$783$	8.40904	+	13.7949i	0.300515	+	0.492991i
$784$	2.39650	+	1.38362i	0.0855891	+	0.0494149i
$785$	−27.6829	+	2.34524i	−0.988043	+	0.0837053i
$786$	25.7184	−	37.3578i	0.917346	−	1.33251i
$787$	−2.47215	+	9.22619i	−0.0881226	+	0.328878i	−0.995887	−	0.0906019i	$-0.971121\pi$
$787$	−2.47215	+	9.22619i	−0.0881226	+	0.328878i	0.907765	+	0.419480i	$0.137788\pi$
$788$	−40.8315	+	10.9408i	−1.45456	+	0.389748i
$789$	7.83134	−	11.3756i	0.278803	−	0.404981i
$790$	2.77203	−	5.90220i	0.0986243	−	0.209991i
$791$			24.2959i			0.863864i
$792$	8.28688	−	18.5345i	0.294462	−	0.658594i
$793$	−18.4663	−	68.9172i	−0.655757	−	2.44732i
$794$	−38.5081			−1.36660
$795$	−14.1204	−	51.6239i	−0.500797	−	1.83091i
$796$	22.9481			0.813374
$797$	−7.98314	−	2.13908i	−0.282777	−	0.0757700i	0.114643	−	0.993407i	$-0.463428\pi$
$797$	−7.98314	−	2.13908i	−0.282777	−	0.0757700i	−0.397420	+	0.917637i	$0.630094\pi$
$798$	−1.21003	+	36.7812i	−0.0428346	+	1.30204i
$799$	−7.08256	−	4.08912i	−0.250563	−	0.144663i
$800$	31.5961	−	14.5225i	1.11709	−	0.513448i
$801$	−7.67653	+	47.9813i	−0.271237	+	1.69534i
$802$	6.27123	−	23.4045i	0.221445	−	0.826443i
$803$	−7.81604	+	29.1699i	−0.275822	+	1.02938i
$804$	30.3794	+	20.9142i	1.07140	+	0.737587i
$805$	1.64114	−	9.15999i	0.0578426	−	0.322847i
$806$	1.64125	−	0.947576i	0.0578106	−	0.0333769i
$807$	−28.5050	+	24.3070i	−1.00342	+	0.855647i
$808$	9.24814	−	9.24814i	0.325348	−	0.325348i
$809$	7.58353			0.266623			0.133311	−	0.991074i	$-0.457439\pi$
$809$	7.58353			0.266623			0.133311	+	0.991074i	$0.457439\pi$
$810$	32.5060	+	30.6717i	1.14214	+	1.07769i
$811$	27.2072	+	47.1243i	0.955374	+	1.65476i	0.733510	+	0.679679i	$0.237881\pi$
$811$	27.2072	+	47.1243i	0.955374	+	1.65476i	0.221864	+	0.975078i	$0.428786\pi$
$812$	−19.3264	−	5.17849i	−0.678223	−	0.181729i
$813$	−1.65390	+	1.41033i	−0.0580050	+	0.0494624i
$814$		−	32.6055i		−	1.14282i
$815$	−0.748072	−	8.83012i	−0.0262038	−	0.309305i
$816$	−3.75282	+	1.78640i	−0.131375	+	0.0625365i
$817$	0.225565	+	4.85400i	0.00789152	+	0.169820i
$818$	27.3457	+	27.3457i	0.956121	+	0.956121i
$819$	4.91629	−	30.7287i	0.171789	−	1.07375i
$820$	−4.51313	−	12.5066i	−0.157605	−	0.436751i
$821$			22.2172i			0.775387i	0.921788	+	0.387694i	$0.126728\pi$
$821$			22.2172i			0.775387i	−0.921788	+	0.387694i	$0.873272\pi$
$822$	−72.3595	+	13.3524i	−2.52383	+	0.465720i
$823$	−7.52969	−	28.1012i	−0.262469	−	0.979546i	−0.963782	−	0.266693i	$-0.914069\pi$
$823$	−7.52969	−	28.1012i	−0.262469	−	0.979546i	0.701313	−	0.712853i	$-0.252598\pi$
$824$	−13.4836	−	23.3543i	−0.469724	−	0.813586i
$825$	−18.1518	+	21.7402i	−0.631966	+	0.756896i
$826$	−21.9649			−0.764255
$827$	−30.1573	−	8.08062i	−1.04867	−	0.280991i	−0.306969	−	0.951720i	$-0.599315\pi$
$827$	−30.1573	−	8.08062i	−1.04867	−	0.280991i	−0.741703	+	0.670729i	$0.765981\pi$
$828$	−9.78123	−	13.5071i	−0.339921	−	0.469406i
$829$			33.9871i			1.18042i	0.807250	+	0.590210i	$0.200955\pi$
$829$			33.9871i			1.18042i	−0.807250	+	0.590210i	$0.799045\pi$
$830$	15.0015	−	17.7785i	0.520709	−	0.617102i
$831$	4.23092	+	0.336315i	0.146769	+	0.0116666i
$832$	−58.9286	+	15.7899i	−2.04298	+	0.547415i
$833$	−2.92028	−	2.92028i	−0.101182	−	0.101182i
$834$	35.0304	+	73.5910i	1.21300	+	2.54825i
$835$	23.2506	+	10.9199i	0.804619	+	0.377897i
$836$	−28.1486	+	30.8922i	−0.973540	+	1.06843i
$837$	−0.449641	+	0.823516i	−0.0155419	+	0.0284649i
$838$	22.8670	+	85.3408i	0.789927	+	2.94805i
$839$	−20.6849	−	35.8274i	−0.714123	−	1.23690i	−0.963297	−	0.268439i	$-0.913492\pi$
$839$	−20.6849	−	35.8274i	−0.714123	−	1.23690i	0.249173	−	0.968459i	$-0.419841\pi$
$840$	−17.5914	+	0.0913637i	−0.606961	+	0.00315235i
$841$	−19.3329			−0.666651
$842$	2.38157	+	8.88813i	0.0820742	+	0.306305i
$843$	9.96203	−	28.0621i	0.343111	−	0.966509i
$844$	−36.5179	−	21.0836i	−1.25700	−	0.725728i
$845$	3.68118	−	20.5464i	0.126636	−	0.706819i
$846$	28.4299	+	4.54851i	0.977441	+	0.156381i
$847$	−0.473394	−	0.473394i	−0.0162660	−	0.0162660i
$848$	−16.9255	+	4.53519i	−0.581226	+	0.155739i
$849$	6.07267	−	2.89068i	0.208414	−	0.0992079i
$850$	−20.7138	+	3.53505i	−0.710479	+	0.121251i
$851$	−7.37189	−	4.25616i	−0.252705	−	0.145899i
$852$	8.50500	+	46.0903i	0.291377	+	1.57903i
$853$	20.8897	+	5.59737i	0.715248	+	0.191650i	0.598051	−	0.801458i	$-0.295942\pi$
$853$	20.8897	+	5.59737i	0.715248	+	0.191650i	0.117198	+	0.993109i	$0.462609\pi$
$854$	−73.5892			−2.51817
$855$	−13.9134	−	25.7180i	−0.475829	−	0.879538i
$856$	−23.6755			−0.809213
$857$	−7.80715	−	2.09192i	−0.266687	−	0.0714586i	0.122997	−	0.992407i	$-0.460749\pi$
$857$	−7.80715	−	2.09192i	−0.266687	−	0.0714586i	−0.389685	+	0.920948i	$0.627416\pi$
$858$	45.2359	−	38.5739i	1.54433	−	1.31689i
$859$	10.4079	+	6.00899i	0.355112	+	0.205024i	0.666935	−	0.745116i	$-0.267606\pi$
$859$	10.4079	+	6.00899i	0.355112	+	0.205024i	−0.311822	+	0.950140i	$0.600939\pi$
$860$	−7.28219	+	0.616935i	−0.248321	+	0.0210373i
$861$	0.610970	−	7.68616i	0.0208218	−	0.261944i
$862$	24.0182	−	6.43565i	0.818062	−	0.219199i
$863$	11.8866	+	11.8866i	0.404626	+	0.404626i	0.879860	−	0.475233i	$-0.157636\pi$
$863$	11.8866	+	11.8866i	0.404626	+	0.404626i	−0.475233	+	0.879860i	$0.657636\pi$
$864$	24.9373	−	26.1551i	0.848384	−	0.889814i
$865$	−17.5605	−	25.2264i	−0.597075	−	0.857723i
$866$	−47.4077	−	27.3708i	−1.61098	−	0.930099i
$867$	−22.8560	+	4.21760i	−0.776230	+	0.143237i
$868$	−0.300747	−	1.12240i	−0.0102080	−	0.0380969i
$869$	4.29436			0.145676
$870$	25.7948	−	7.05547i	0.874524	−	0.239203i
$871$	17.1625	+	29.7264i	0.581530	+	1.00724i
$872$	−7.73390	−	28.8633i	−0.261903	−	0.977435i
$873$	−26.9910	+	19.5456i	−0.913507	+	0.661519i
$874$	5.56823	+	17.4891i	0.188348	+	0.591577i
$875$	23.6506	+	6.54675i	0.799535	+	0.221320i
$876$	26.5903	−	38.6242i	0.898402	−	1.30499i
$877$	20.7365	+	20.7365i	0.700223	+	0.700223i	0.964458	−	0.264235i	$-0.0851196\pi$
$877$	20.7365	+	20.7365i	0.700223	+	0.700223i	−0.264235	+	0.964458i	$0.585120\pi$
$878$	−66.4727	+	17.8113i	−2.24334	+	0.601102i
$879$	3.09363	−	4.49372i	0.104346	−	0.151569i
$880$	7.08681	+	5.97983i	0.238896	+	0.201580i
$881$			57.1468i			1.92533i	0.270704	+	0.962663i	$0.412743\pi$
$881$			57.1468i			1.92533i	−0.270704	+	0.962663i	$0.587257\pi$
$882$	13.2731	+	5.93448i	0.446928	+	0.199824i
$883$	−50.4261	−	13.5116i	−1.69697	−	0.454702i	−0.724798	−	0.688961i	$-0.758067\pi$
$883$	−50.4261	−	13.5116i	−1.69697	−	0.454702i	−0.972174	+	0.234258i	$0.924734\pi$
$884$	26.2212			0.881914
$885$	15.0686	−	8.80449i	0.506524	−	0.295960i
$886$	−25.7864	−	44.6634i	−0.866311	−	1.50049i
$887$	−2.70827	−	10.1074i	−0.0909347	−	0.339373i	0.905437	−	0.424481i	$-0.139543\pi$
$887$	−2.70827	−	10.1074i	−0.0909347	−	0.339373i	−0.996372	+	0.0851075i	$0.972877\pi$
$888$	−5.38336	+	15.1644i	−0.180654	+	0.508883i
$889$			19.5125i			0.654429i
$890$	72.8023	+	34.1923i	2.44034	+	1.14613i
$891$	−9.18289	+	27.9637i	−0.307638	+	0.936819i
$892$	−0.450041	−	0.450041i	−0.0150685	−	0.0150685i
$893$	−16.7331	−	8.65116i	−0.559952	−	0.289500i
$894$	−30.9906	−	21.3350i	−1.03648	−	0.713549i
$895$	−7.48501	+	8.87063i	−0.250196	+	0.296513i
$896$			32.3932i			1.08218i
$897$	−2.81643	−	15.2628i	−0.0940380	−	0.509610i
$898$	−79.1152	−	21.1989i	−2.64011	−	0.707415i
$899$	0.280715	+	0.486213i	0.00936237	+	0.0162161i
$900$	37.8552	−	22.3832i	1.26184	−	0.746105i
$901$	26.1513			0.871225
$902$	10.4154	−	10.4154i	0.346796	−	0.346796i
$903$	−3.99389	−	1.41783i	−0.132908	−	0.0471825i
$904$	19.8375	−	11.4532i	0.659787	−	0.380928i
$905$	35.8431	+	6.42179i	1.19146	+	0.213467i
$906$	−56.8958	+	27.0832i	−1.89024	+	0.899781i
$907$	11.6360	−	43.4263i	0.386368	−	1.44195i	−0.449631	−	0.893214i	$-0.648444\pi$
$907$	11.6360	−	43.4263i	0.386368	−	1.44195i	0.835999	−	0.548731i	$-0.184889\pi$
$908$	−16.9278	+	63.1755i	−0.561769	+	2.09655i
$909$	−11.9552	+	14.7163i	−0.396531	+	0.488110i
$910$	−46.6248	−	21.8978i	−1.54560	−	0.725906i
$911$	−12.5680	−	7.25615i	−0.416397	−	0.240407i	0.277138	−	0.960830i	$-0.410614\pi$
$911$	−12.5680	−	7.25615i	−0.416397	−	0.240407i	−0.693535	+	0.720423i	$0.743948\pi$
$912$	−8.44367	+	4.51149i	−0.279598	+	0.149390i
$913$	14.7976	+	3.96501i	0.489730	+	0.131223i
$914$	22.8220			0.754883
$915$	50.4844	−	29.4978i	1.66896	−	0.975168i
$916$	4.15448			0.137268
$917$	−6.69842	−	24.9988i	−0.221201	−	0.825534i
$918$	−18.6464	+	11.3664i	−0.615424	+	0.375147i
$919$		−	23.1931i		−	0.765070i	−0.923941	−	0.382535i	$-0.875051\pi$
$919$		−	23.1931i		−	0.765070i	0.923941	−	0.382535i	$-0.124949\pi$
$920$	−8.25274	+	2.97807i	−0.272085	+	0.0981842i
$921$	−16.4272	−	1.30579i	−0.541294	−	0.0430272i
$922$	−11.3030	+	3.02862i	−0.372243	+	0.0997422i
$923$	−11.2894	+	42.1325i	−0.371594	+	1.38681i
$924$	−15.6668	−	32.9124i	−0.515399	−	1.08274i
$925$	12.9762	−	18.3167i	0.426656	−	0.602251i
$926$	20.4549	+	11.8096i	0.672188	+	0.388088i
$927$	22.9296	+	31.6641i	0.753107	+	1.03998i
$928$	−5.59664	−	20.8869i	−0.183719	−	0.685648i
$929$	29.6941	+	51.4317i	0.974232	+	1.68742i	0.682447	+	0.730935i	$0.260916\pi$
$929$	29.6941	+	51.4317i	0.974232	+	1.68742i	0.291785	+	0.956484i	$0.405751\pi$
$930$	1.10389	+	1.09248i	0.0361980	+	0.0358239i
$931$	−7.03136	−	6.40689i	−0.230444	−	0.209977i
$932$	78.0462	+	20.9124i	2.55649	+	0.685009i
$933$	9.47762	−	1.74890i	0.310283	−	0.0572564i
$934$	68.7942	−	39.7184i	2.25102	−	1.29962i
$935$	−7.90636	−	11.3578i	−0.258566	−	0.371440i
$936$	−27.4074	+	10.4715i	−0.895840	+	0.342272i
$937$	8.28790	−	30.9309i	0.270754	−	1.01047i	−0.687880	−	0.725825i	$-0.741458\pi$
$937$	8.28790	−	30.9309i	0.270754	−	1.01047i	0.958634	−	0.284643i	$-0.0918750\pi$
$938$	34.1968	−	9.16301i	1.11657	−	0.299183i
$939$	48.5815	−	23.1255i	1.58540	−	0.754673i
$940$	12.0438	−	25.6437i	0.392825	−	0.836404i
$941$	−32.3194	−	18.6596i	−1.05358	−	0.608286i	−0.129932	−	0.991523i	$-0.541476\pi$
$941$	−32.3194	−	18.6596i	−1.05358	−	0.608286i	−0.923650	+	0.383237i	$0.874809\pi$
$942$	8.67237	+	46.9973i	0.282561	+	1.53125i
$943$	−0.995281	−	3.71444i	−0.0324108	−	0.120959i
$944$	−2.85695	−	4.94837i	−0.0929857	−	0.161056i
$945$	25.3531	−	2.75774i	0.824737	−	0.0897094i
$946$	−4.04814	−	7.01158i	−0.131616	−	0.227966i
$947$	−18.9241	−	5.07069i	−0.614949	−	0.164775i	−0.0621186	−	0.998069i	$-0.519786\pi$
$947$	−18.9241	−	5.07069i	−0.614949	−	0.164775i	−0.552831	+	0.833294i	$0.686452\pi$
$948$	−6.28397	−	2.23081i	−0.204094	−	0.0724533i
$949$	37.7941	−	21.8204i	1.22685	−	0.708320i
$950$	−47.2814	+	10.3483i	−1.53401	+	0.335745i
$951$	−34.6640	+	16.5006i	−1.12406	+	0.535067i
$952$	2.22473	−	8.30282i	0.0721040	−	0.269096i
$953$	1.84352	−	0.493971i	0.0597176	−	0.0160013i	−0.228837	−	0.973465i	$-0.573492\pi$
$953$	1.84352	−	0.493971i	0.0597176	−	0.0160013i	0.288554	+	0.957464i	$0.406825\pi$
$954$	−86.0023	+	32.8587i	−2.78443	+	1.06384i
$955$	22.0159	−	7.94463i	0.712417	−	0.257082i
$956$			3.67610i			0.118893i
$957$	11.4273	+	13.4009i	0.369394	+	0.433191i
$958$	26.3296	+	7.05501i	0.850672	+	0.227937i
$959$	−20.9938	+	36.3623i	−0.677924	+	1.17420i
$960$	−25.2225	−	43.1674i	−0.814054	−	1.39322i
$961$	15.4837	−	26.8186i	0.499474	−	0.865115i
$962$	−33.3179	+	33.3179i	−1.07421	+	1.07421i
$963$	34.1401	−	3.53422i	1.10015	−	0.113889i
$964$	29.3193	+	16.9275i	0.944310	+	0.545198i
$965$	−2.20389	−	26.0144i	−0.0709459	−	0.837433i
$966$	−15.9576	−	1.26846i	−0.513428	−	0.0408122i
$967$	3.81832	+	3.81832i	0.122789	+	0.122789i	0.765831	−	0.643042i	$-0.222328\pi$
$967$	3.81832	+	3.81832i	0.122789	+	0.122789i	−0.643042	+	0.765831i	$0.722328\pi$
$968$	−0.163364	+	0.609684i	−0.00525073	+	0.0195960i
$969$	13.9149	−	3.24212i	0.447009	−	0.104152i
$970$	18.7237	+	51.8866i	0.601183	+	1.66598i
$971$	−35.6284	−	20.5701i	−1.14337	−	0.660125i	−0.196107	−	0.980583i	$-0.562830\pi$
$971$	−35.6284	−	20.5701i	−1.14337	−	0.660125i	−0.947263	+	0.320458i	$0.896163\pi$
$972$	27.9638	−	36.1492i	0.896940	−	1.15949i
$973$	44.9233	+	12.0372i	1.44018	+	0.385894i
$974$	31.1626	+	53.9753i	0.998516	+	1.72948i
$975$	40.7637	−	3.66675i	1.30548	−	0.117430i
$976$	−9.57167	−	16.5786i	−0.306382	−	0.530669i
$977$	35.6933	+	9.56398i	1.14193	+	0.305979i	0.779726	−	0.626121i	$-0.215358\pi$
$977$	35.6933	+	9.56398i	1.14193	+	0.305979i	0.362203	+	0.932099i	$0.382025\pi$
$978$	−14.9909	+	2.76626i	−0.479357	+	0.0884553i
$979$			52.9699i			1.69292i
$980$	9.22636	−	10.9343i	0.294725	−	0.349285i
$981$	15.4609	+	40.4663i	0.493628	+	1.29199i
$982$	−2.15444	+	8.04049i	−0.0687510	+	0.256582i
$983$	−5.68058	+	21.2002i	−0.181182	+	0.676182i	0.814233	+	0.580538i	$0.197158\pi$
$983$	−5.68058	+	21.2002i	−0.181182	+	0.676182i	−0.995416	+	0.0956441i	$0.969509\pi$
$984$	−6.56373	+	3.12443i	−0.209244	+	0.0996033i
$985$	−2.72158	−	32.1251i	−0.0867167	−	1.02359i
$986$			13.0669i			0.416136i
$987$	12.5013	−	10.6602i	0.397920	−	0.339317i
$988$	60.3310	−	2.80358i	1.91938	−	0.0891937i
$989$	−2.11370			−0.0672117
$990$	40.2721	+	27.4175i	1.27993	+	0.871386i
$991$	−2.07425	+	3.59270i	−0.0658906	+	0.114126i	−0.897089	−	0.441851i	$-0.854322\pi$
$991$	−2.07425	+	3.59270i	−0.0658906	+	0.114126i	0.831198	+	0.555976i	$0.187655\pi$
$992$	0.888004	−	0.888004i	0.0281942	−	0.0281942i
$993$	−7.74413	+	6.60363i	−0.245753	+	0.209560i
$994$	38.9614	+	22.4943i	1.23578	+	0.713477i
$995$	−3.08662	+	17.2279i	−0.0978523	+	0.546161i
$996$	−19.5937	−	13.4890i	−0.620852	−	0.427416i
$997$	−9.78360	−	9.78360i	−0.309850	−	0.309850i	0.535001	−	0.844851i	$-0.320311\pi$
$997$	−9.78360	−	9.78360i	−0.309850	−	0.309850i	−0.844851	+	0.535001i	$0.820311\pi$
$998$	−15.6071	+	58.2464i	−0.494034	+	1.84376i
$999$	5.49909	−	22.6706i	0.173983	−	0.717266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.ci.a.182.15	yes	464
5.3	odd	4	inner	855.2.ci.a.353.15	yes	464
9.5	odd	6		855.2.bx.a.752.15	yes	464
19.7	even	3		855.2.bx.a.767.102	yes	464
45.23	even	12		855.2.bx.a.68.102	✓	464
95.83	odd	12		855.2.bx.a.83.15	yes	464
171.140	odd	6	inner	855.2.ci.a.482.15	yes	464
855.653	even	12	inner	855.2.ci.a.653.15	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.bx.a.68.102	✓	464	45.23	even	12
855.2.bx.a.83.15	yes	464	95.83	odd	12
855.2.bx.a.752.15	yes	464	9.5	odd	6
855.2.bx.a.767.102	yes	464	19.7	even	3
855.2.ci.a.182.15	yes	464	1.1	even	1	trivial
855.2.ci.a.353.15	yes	464	5.3	odd	4	inner
855.2.ci.a.482.15	yes	464	171.140	odd	6	inner
855.2.ci.a.653.15	yes	464	855.653	even	12	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.ci (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14510 - 0.574778i) q^{2} +(-1.63225 - 0.579449i) q^{3} +(2.53904 + 1.46592i) q^{4} +(-1.44202 + 1.70897i) q^{5} +(3.16829 + 2.18116i) q^{6} +(2.12013 - 0.568087i) q^{7} +(-1.46328 - 1.46328i) q^{8} +(2.32848 + 1.89161i) q^{9} +O(q^{10})\)	\(q+(-2.14510 - 0.574778i) q^{2} +(-1.63225 - 0.579449i) q^{3} +(2.53904 + 1.46592i) q^{4} +(-1.44202 + 1.70897i) q^{5} +(3.16829 + 2.18116i) q^{6} +(2.12013 - 0.568087i) q^{7} +(-1.46328 - 1.46328i) q^{8} +(2.32848 + 1.89161i) q^{9} +(4.07556 - 2.83707i) q^{10} +(2.83218 + 1.63516i) q^{11} +(-3.29493 - 3.86399i) q^{12} +(-1.22318 - 4.56495i) q^{13} -4.87442 q^{14} +(3.34400 - 1.95389i) q^{15} +(-0.634011 - 1.09814i) q^{16} +(0.489798 + 1.82795i) q^{17} +(-3.90757 - 5.39606i) q^{18} +(1.32239 + 4.15346i) q^{19} +(-6.16656 + 2.22526i) q^{20} +(-3.78976 - 0.301247i) q^{21} +(-5.13546 - 5.13546i) q^{22} +(-1.83145 + 0.490736i) q^{23} +(1.54054 + 3.23633i) q^{24} +(-0.841145 - 4.92874i) q^{25} +10.4953i q^{26} +(-2.70457 - 4.43681i) q^{27} +(6.21587 + 1.66554i) q^{28} -3.10920 q^{29} +(-8.29627 + 2.26922i) q^{30} +(-0.0902853 - 0.156379i) q^{31} +(1.80003 + 6.71779i) q^{32} +(-3.67533 - 4.31009i) q^{33} -4.20267i q^{34} +(-2.08643 + 4.44243i) q^{35} +(3.13916 + 8.21623i) q^{36} +(3.17454 + 3.17454i) q^{37} +(-0.449350 - 9.66969i) q^{38} +(-0.648628 + 8.15991i) q^{39} +(4.61078 - 0.390617i) q^{40} +2.02814i q^{41} +(7.95627 + 2.82448i) q^{42} +(1.07680 + 0.288527i) q^{43} +(4.79401 + 8.30348i) q^{44} +(-6.59042 + 1.25155i) q^{45} +4.21072 q^{46} +(-3.05579 + 3.05579i) q^{47} +(0.398549 + 2.15981i) q^{48} +(-1.88995 + 1.09116i) q^{49} +(-1.02859 + 11.0561i) q^{50} +(0.259731 - 3.26749i) q^{51} +(3.58615 - 13.3837i) q^{52} +(3.57658 - 13.3480i) q^{53} +(3.25139 + 11.0719i) q^{54} +(-6.87850 + 2.48217i) q^{55} +(-3.93361 - 2.27107i) q^{56} +(0.248241 - 7.54575i) q^{57} +(6.66955 + 1.78710i) q^{58} +4.50615 q^{59} +(11.3548 - 0.0589728i) q^{60} +15.0970 q^{61} +(0.103788 + 0.387343i) q^{62} +(6.01128 + 2.68768i) q^{63} -12.9089i q^{64} +(9.56521 + 4.49239i) q^{65} +(5.40662 + 11.3581i) q^{66} +(-7.01556 + 1.87981i) q^{67} +(-1.43601 + 5.35925i) q^{68} +(3.27375 + 0.260229i) q^{69} +(7.02902 - 8.33023i) q^{70} +(-7.99302 - 4.61477i) q^{71} +(-0.639261 - 6.17517i) q^{72} +(2.38999 + 8.91957i) q^{73} +(-4.98506 - 8.63437i) q^{74} +(-1.48299 + 8.53233i) q^{75} +(-2.73102 + 12.4843i) q^{76} +(6.93350 + 1.85783i) q^{77} +(6.08151 - 17.1310i) q^{78} +(1.13720 - 0.656565i) q^{79} +(2.79094 + 0.500036i) q^{80} +(1.84362 + 8.80915i) q^{81} +(1.16573 - 4.35056i) q^{82} +(4.52482 - 1.21242i) q^{83} +(-9.18076 - 6.32035i) q^{84} +(-3.83021 - 1.79890i) q^{85} +(-2.14400 - 1.23784i) q^{86} +(5.07499 + 1.80162i) q^{87} +(-1.75157 - 6.53696i) q^{88} +(8.09858 + 14.0272i) q^{89} +(14.8565 + 1.10332i) q^{90} +(-5.18658 - 8.98343i) q^{91} +(-5.36952 - 1.43876i) q^{92} +(0.0567547 + 0.307565i) q^{93} +(8.31139 - 4.79858i) q^{94} +(-9.00506 - 3.72946i) q^{95} +(0.954522 - 12.0081i) q^{96} +(-2.87504 + 10.7298i) q^{97} +(4.68131 - 1.25435i) q^{98} +(3.50158 + 9.16481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7}+O(q^{10}) \) 464 * q - 6 * q^2 - 2 * q^3 - 4 * q^6 - 4 * q^7	\( 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7} - 4 q^{10} - 24 q^{11} + 2 q^{12} + 2 q^{13} + 10 q^{15} + 212 q^{16} + 18 q^{17} - 24 q^{18} - 12 q^{20} - 4 q^{21} - 20 q^{22} + 18 q^{23} - 4 q^{25} - 2 q^{27} - 20 q^{28} + 2 q^{30} - 8 q^{31} - 30 q^{32} + 10 q^{33} - 68 q^{36} - 16 q^{37} + 30 q^{38} - 36 q^{40} - 14 q^{42} + 2 q^{43} + 6 q^{45} - 56 q^{46} + 42 q^{48} - 108 q^{50} + 12 q^{51} - 34 q^{52} - 14 q^{55} - 24 q^{56} - 78 q^{57} - 12 q^{58} - 42 q^{60} - 8 q^{61} - 12 q^{62} + 92 q^{63} - 84 q^{65} - 52 q^{66} + 2 q^{67} - 60 q^{68} - 84 q^{70} - 118 q^{72} - 4 q^{73} + 98 q^{75} - 60 q^{76} - 12 q^{77} + 92 q^{78} + 120 q^{80} - 12 q^{81} + 4 q^{82} - 12 q^{83} + 2 q^{85} - 264 q^{86} + 102 q^{87} + 48 q^{88} - 34 q^{90} - 8 q^{91} + 54 q^{92} - 52 q^{93} - 36 q^{95} + 96 q^{96} + 2 q^{97} + 42 q^{98}+O(q^{100}) \) 464 * q - 6 * q^2 - 2 * q^3 - 4 * q^6 - 4 * q^7 - 4 * q^10 - 24 * q^11 + 2 * q^12 + 2 * q^13 + 10 * q^15 + 212 * q^16 + 18 * q^17 - 24 * q^18 - 12 * q^20 - 4 * q^21 - 20 * q^22 + 18 * q^23 - 4 * q^25 - 2 * q^27 - 20 * q^28 + 2 * q^30 - 8 * q^31 - 30 * q^32 + 10 * q^33 - 68 * q^36 - 16 * q^37 + 30 * q^38 - 36 * q^40 - 14 * q^42 + 2 * q^43 + 6 * q^45 - 56 * q^46 + 42 * q^48 - 108 * q^50 + 12 * q^51 - 34 * q^52 - 14 * q^55 - 24 * q^56 - 78 * q^57 - 12 * q^58 - 42 * q^60 - 8 * q^61 - 12 * q^62 + 92 * q^63 - 84 * q^65 - 52 * q^66 + 2 * q^67 - 60 * q^68 - 84 * q^70 - 118 * q^72 - 4 * q^73 + 98 * q^75 - 60 * q^76 - 12 * q^77 + 92 * q^78 + 120 * q^80 - 12 * q^81 + 4 * q^82 - 12 * q^83 + 2 * q^85 - 264 * q^86 + 102 * q^87 + 48 * q^88 - 34 * q^90 - 8 * q^91 + 54 * q^92 - 52 * q^93 - 36 * q^95 + 96 * q^96 + 2 * q^97 + 42 * q^98

Introduction

L-functions

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