LMFDB - Embedded newform 360.2.bo.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 8, 9]))

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

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

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	360.43
Dual form			360.2.bo.a.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40635 + 0.148909i) q^{2} +(0.312010 - 1.70372i) q^{3} +(1.95565 - 0.418836i) q^{4} +(0.0247121 - 2.23593i) q^{5} +(-0.185098 + 2.44249i) q^{6} +(-0.146504 + 0.0392556i) q^{7} +(-2.68797 + 0.880244i) q^{8} +(-2.80530 - 1.06315i) q^{9} +O(q^{10})$	\(q+(-1.40635 + 0.148909i) q^{2} +(0.312010 - 1.70372i) q^{3} +(1.95565 - 0.418836i) q^{4} +(0.0247121 - 2.23593i) q^{5} +(-0.185098 + 2.44249i) q^{6} +(-0.146504 + 0.0392556i) q^{7} +(-2.68797 + 0.880244i) q^{8} +(-2.80530 - 1.06315i) q^{9} +(0.298195 + 3.14819i) q^{10} +(2.72397 - 4.71805i) q^{11} +(-0.103395 - 3.46256i) q^{12} +(0.241643 + 0.0647480i) q^{13} +(0.200191 - 0.0770229i) q^{14} +(-3.80168 - 0.739735i) q^{15} +(3.64915 - 1.63819i) q^{16} +(-1.30067 + 1.30067i) q^{17} +(4.10355 + 1.07743i) q^{18} +5.98400i q^{19} +(-0.888160 - 4.38306i) q^{20} +(0.0211698 + 0.261849i) q^{21} +(-3.12830 + 7.04087i) q^{22} +(-4.83379 - 1.29521i) q^{23} +(0.661014 + 4.85418i) q^{24} +(-4.99878 - 0.110509i) q^{25} +(-0.349476 - 0.0550758i) q^{26} +(-2.68659 + 4.44772i) q^{27} +(-0.270069 + 0.138131i) q^{28} +(0.859025 - 1.48787i) q^{29} +(5.45666 + 0.474225i) q^{30} +(7.20394 - 4.15920i) q^{31} +(-4.88805 + 2.84727i) q^{32} +(-7.18832 - 6.11295i) q^{33} +(1.63552 - 2.02288i) q^{34} +(0.0841524 + 0.328543i) q^{35} +(-5.93148 - 0.904197i) q^{36} +(-7.18491 - 7.18491i) q^{37} +(-0.891069 - 8.41562i) q^{38} +(0.185707 - 0.391489i) q^{39} +(1.90174 + 6.03186i) q^{40} +(-1.18154 - 2.04648i) q^{41} +(-0.0687637 - 0.365100i) q^{42} +(6.20694 - 1.66314i) q^{43} +(3.35105 - 10.3678i) q^{44} +(-2.44646 + 6.24619i) q^{45} +(6.99089 + 1.10173i) q^{46} +(3.43876 - 0.921412i) q^{47} +(-1.65245 - 6.72826i) q^{48} +(-6.04226 + 3.48850i) q^{49} +(7.04650 - 0.588946i) q^{50} +(1.81015 + 2.62180i) q^{51} +(0.499688 + 0.0254159i) q^{52} +(-0.394816 + 0.394816i) q^{53} +(3.11599 - 6.65512i) q^{54} +(-10.4819 - 6.20720i) q^{55} +(0.359243 - 0.234477i) q^{56} +(10.1950 + 1.86707i) q^{57} +(-0.986534 + 2.22039i) q^{58} +(-0.281358 + 0.162442i) q^{59} +(-7.74460 + 0.145616i) q^{60} +(-0.955824 - 0.551845i) q^{61} +(-9.51194 + 6.92203i) q^{62} +(0.452722 + 0.0456322i) q^{63} +(6.45034 - 4.73213i) q^{64} +(0.150744 - 0.538696i) q^{65} +(11.0196 + 7.52656i) q^{66} +(11.4774 + 3.07537i) q^{67} +(-1.99889 + 3.08843i) q^{68} +(-3.71486 + 7.83130i) q^{69} +(-0.167271 - 0.449516i) q^{70} +11.0915i q^{71} +(8.47639 + 0.388372i) q^{72} +(-0.181440 - 0.181440i) q^{73} +(11.1744 + 9.03461i) q^{74} +(-1.74794 + 8.48202i) q^{75} +(2.50631 + 11.7026i) q^{76} +(-0.213862 + 0.798144i) q^{77} +(-0.202874 + 0.578224i) q^{78} +(6.22715 - 10.7857i) q^{79} +(-3.57271 - 8.19974i) q^{80} +(6.73941 + 5.96492i) q^{81} +(1.96640 + 2.70214i) q^{82} +(4.44406 - 1.19078i) q^{83} +(0.151073 + 0.503219i) q^{84} +(2.87607 + 2.94035i) q^{85} +(-8.48148 + 3.26323i) q^{86} +(-2.26689 - 1.92777i) q^{87} +(-3.16890 + 15.0797i) q^{88} -5.15599i q^{89} +(2.51047 - 9.14863i) q^{90} -0.0379433 q^{91} +(-9.99570 - 0.508418i) q^{92} +(-4.83839 - 13.5712i) q^{93} +(-4.69890 + 1.80789i) q^{94} +(13.3798 + 0.147877i) q^{95} +(3.32582 + 9.21623i) q^{96} +(-1.90774 - 7.11977i) q^{97} +(7.97807 - 5.80580i) q^{98} +(-12.6576 + 10.3396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.40635	+	0.148909i	−0.994441	+	0.105294i
$2$	−1.40635	+	0.148909i	−0.994441	+	0.105294i
$3$	0.312010	−	1.70372i	0.180139	−	0.983641i
$3$	0.312010	−	1.70372i	0.180139	−	0.983641i
$4$	1.95565	−	0.418836i	0.977826	−	0.209418i
$5$	0.0247121	−	2.23593i	0.0110516	−	0.999939i
$5$	0.0247121	−	2.23593i	0.0110516	−	0.999939i
$6$	−0.185098	+	2.44249i	−0.0755658	+	0.997141i
$7$	−0.146504	+	0.0392556i	−0.0553733	+	0.0148372i	−0.286399	−	0.958110i	$-0.592458\pi$
$7$	−0.146504	+	0.0392556i	−0.0553733	+	0.0148372i	0.231026	+	0.972948i	$0.425792\pi$
$8$	−2.68797	+	0.880244i	−0.950340	+	0.311213i
$9$	−2.80530	−	1.06315i	−0.935100	−	0.354384i
$10$	0.298195	+	3.14819i	0.0942977	+	0.995544i
$11$	2.72397	−	4.71805i	0.821308	−	1.42255i	−0.0834013	−	0.996516i	$-0.526578\pi$
$11$	2.72397	−	4.71805i	0.821308	−	1.42255i	0.904709	−	0.426030i	$-0.140088\pi$
$12$	−0.103395	−	3.46256i	−0.0298474	−	0.999554i
$13$	0.241643	+	0.0647480i	0.0670196	+	0.0179579i	0.292173	−	0.956365i	$-0.405622\pi$
$13$	0.241643	+	0.0647480i	0.0670196	+	0.0179579i	−0.225153	+	0.974323i	$0.572288\pi$
$14$	0.200191	−	0.0770229i	0.0535032	−	0.0205852i
$15$	−3.80168	−	0.739735i	−0.981590	−	0.190999i
$16$	3.64915	−	1.63819i	0.912288	−	0.409549i
$17$	−1.30067	+	1.30067i	−0.315459	+	0.315459i	−0.847020	−	0.531561i	$-0.821606\pi$
$17$	−1.30067	+	1.30067i	−0.315459	+	0.315459i	0.531561	+	0.847020i	$0.321606\pi$
$18$	4.10355	+	1.07743i	0.967216	+	0.253954i
$19$			5.98400i			1.37282i	0.727213	+	0.686412i	$0.240815\pi$
$19$			5.98400i			1.37282i	−0.727213	+	0.686412i	$0.759185\pi$
$20$	−0.888160	−	4.38306i	−0.198599	−	0.980081i
$21$	0.0211698	+	0.261849i	0.00461962	+	0.0571402i
$22$	−3.12830	+	7.04087i	−0.666956	+	1.50112i
$23$	−4.83379	−	1.29521i	−1.00792	−	0.270070i	−0.283158	−	0.959073i	$-0.591382\pi$
$23$	−4.83379	−	1.29521i	−1.00792	−	0.270070i	−0.724758	+	0.689003i	$0.758049\pi$
$24$	0.661014	+	4.85418i	0.134929	+	0.990855i
$25$	−4.99878	−	0.110509i	−0.999756	−	0.0221018i
$26$	−0.349476	−	0.0550758i	−0.0685379	−	0.0108012i
$27$	−2.68659	+	4.44772i	−0.517035	+	0.855964i
$28$	−0.270069	+	0.138131i	−0.0510383	+	0.0261044i
$29$	0.859025	−	1.48787i	0.159517	−	0.276291i	−0.775178	−	0.631743i	$-0.782340\pi$
$29$	0.859025	−	1.48787i	0.159517	−	0.276291i	0.934695	+	0.355452i	$0.115673\pi$
$30$	5.45666	+	0.474225i	0.996245	+	0.0865812i
$31$	7.20394	−	4.15920i	1.29387	−	0.747014i	0.314529	−	0.949248i	$-0.398153\pi$
$31$	7.20394	−	4.15920i	1.29387	−	0.747014i	0.979337	+	0.202234i	$0.0648201\pi$
$32$	−4.88805	+	2.84727i	−0.864094	+	0.503331i
$33$	−7.18832	−	6.11295i	−1.25133	−	1.06413i
$34$	1.63552	−	2.02288i	0.280489	−	0.346921i
$35$	0.0841524	+	0.328543i	0.0142244	+	0.0555339i
$36$	−5.93148	−	0.904197i	−0.988580	−	0.150699i
$37$	−7.18491	−	7.18491i	−1.18119	−	1.18119i	−0.979436	−	0.201755i	$-0.935335\pi$
$37$	−7.18491	−	7.18491i	−1.18119	−	1.18119i	−0.201755	−	0.979436i	$-0.564665\pi$
$38$	−0.891069	−	8.41562i	−0.144551	−	1.36519i
$39$	0.185707	−	0.391489i	0.0297369	−	0.0626884i
$40$	1.90174	+	6.03186i	0.300691	+	0.953721i
$41$	−1.18154	−	2.04648i	−0.184525	−	0.319607i	0.758891	−	0.651217i	$-0.225741\pi$
$41$	−1.18154	−	2.04648i	−0.184525	−	0.319607i	−0.943416	+	0.331610i	$0.892408\pi$
$42$	−0.0687637	−	0.365100i	−0.0106105	−	0.0563361i
$43$	6.20694	−	1.66314i	0.946549	−	0.253627i	0.247652	−	0.968849i	$-0.420341\pi$
$43$	6.20694	−	1.66314i	0.946549	−	0.253627i	0.698897	+	0.715222i	$0.253674\pi$
$44$	3.35105	−	10.3678i	0.505189	−	1.56300i
$45$	−2.44646	+	6.24619i	−0.364697	+	0.931126i
$46$	6.99089	+	1.10173i	1.03075	+	0.162441i
$47$	3.43876	−	0.921412i	0.501594	−	0.134402i	0.000854411	−	1.00000i	$-0.499728\pi$
$47$	3.43876	−	0.921412i	0.501594	−	0.134402i	0.500740	+	0.865598i	$0.333061\pi$
$48$	−1.65245	−	6.72826i	−0.238510	−	0.971140i
$49$	−6.04226	+	3.48850i	−0.863179	+	0.498357i
$50$	7.04650	−	0.588946i	0.996525	−	0.0832896i
$51$	1.81015	+	2.62180i	0.253472	+	0.367125i
$52$	0.499688	+	0.0254159i	0.0692942	+	0.00352456i
$53$	−0.394816	+	0.394816i	−0.0542321	+	0.0542321i	−0.733703	−	0.679471i	$-0.762210\pi$
$53$	−0.394816	+	0.394816i	−0.0542321	+	0.0542321i	0.679471	+	0.733703i	$0.262210\pi$
$54$	3.11599	−	6.65512i	0.424032	−	0.905647i
$55$	−10.4819	−	6.20720i	−1.41338	−	0.836979i
$56$	0.359243	−	0.234477i	0.0480059	−	0.0313333i
$57$	10.1950	+	1.86707i	1.35037	+	0.247299i
$58$	−0.986534	+	2.22039i	−0.129538	+	0.291552i
$59$	−0.281358	+	0.162442i	−0.0366297	+	0.0211482i	−0.518203	−	0.855258i	$-0.673399\pi$
$59$	−0.281358	+	0.162442i	−0.0366297	+	0.0211482i	0.481573	+	0.876406i	$0.340066\pi$
$60$	−7.74460	+	0.145616i	−0.999823	+	0.0187990i
$61$	−0.955824	−	0.551845i	−0.122381	−	0.0706566i	0.437560	−	0.899189i	$-0.355843\pi$
$61$	−0.955824	−	0.551845i	−0.122381	−	0.0706566i	−0.559941	+	0.828533i	$0.689176\pi$
$62$	−9.51194	+	6.92203i	−1.20802	+	0.879098i
$63$	0.452722	+	0.0456322i	0.0570376	+	0.00574912i
$64$	6.45034	−	4.73213i	0.806293	−	0.591517i
$65$	0.150744	−	0.538696i	0.0186974	−	0.0668171i
$66$	11.0196	+	7.52656i	1.35642	+	0.926455i
$67$	11.4774	+	3.07537i	1.40219	+	0.375716i	0.879131	−	0.476580i	$-0.158124\pi$
$67$	11.4774	+	3.07537i	1.40219	+	0.375716i	0.523060	+	0.852296i	$0.324790\pi$
$68$	−1.99889	+	3.08843i	−0.242401	+	0.374527i
$69$	−3.71486	+	7.83130i	−0.447217	+	0.942777i
$70$	−0.167271	−	0.449516i	−0.0199927	−	0.0537274i
$71$			11.0915i			1.31632i	0.752876	+	0.658162i	$0.228666\pi$
$71$			11.0915i			1.31632i	−0.752876	+	0.658162i	$0.771334\pi$
$72$	8.47639	+	0.388372i	0.998952	+	0.0457700i
$73$	−0.181440	−	0.181440i	−0.0212360	−	0.0212360i	0.696409	−	0.717645i	$-0.254780\pi$
$73$	−0.181440	−	0.181440i	−0.0212360	−	0.0212360i	−0.717645	+	0.696409i	$0.754780\pi$
$74$	11.1744	+	9.03461i	1.29900	+	1.05025i
$75$	−1.74794	+	8.48202i	−0.201835	+	0.979420i
$76$	2.50631	+	11.7026i	0.287494	+	1.34238i
$77$	−0.213862	+	0.798144i	−0.0243718	+	0.0909570i
$78$	−0.202874	+	0.578224i	−0.0229709	+	0.0654710i
$79$	6.22715	−	10.7857i	0.700609	−	1.21349i	−0.267644	−	0.963518i	$-0.586245\pi$
$79$	6.22715	−	10.7857i	0.700609	−	1.21349i	0.968253	−	0.249973i	$-0.0804217\pi$
$80$	−3.57271	−	8.19974i	−0.399441	−	0.916759i
$81$	6.73941	+	5.96492i	0.748824	+	0.662769i
$82$	1.96640	+	2.70214i	0.217152	+	0.298401i
$83$	4.44406	−	1.19078i	0.487799	−	0.130705i	−0.00653267	−	0.999979i	$-0.502079\pi$
$83$	4.44406	−	1.19078i	0.487799	−	0.130705i	0.494332	+	0.869273i	$0.335413\pi$
$84$	0.151073	+	0.503219i	0.0164834	+	0.0549057i
$85$	2.87607	+	2.94035i	0.311953	+	0.318926i
$86$	−8.48148	+	3.26323i	−0.914582	+	0.351883i
$87$	−2.26689	−	1.92777i	−0.243036	−	0.206678i
$88$	−3.16890	+	15.0797i	−0.337806	+	1.60750i
$89$		−	5.15599i		−	0.546534i	−0.961938	−	0.273267i	$-0.911896\pi$
$89$		−	5.15599i		−	0.546534i	0.961938	−	0.273267i	$-0.0881043\pi$
$90$	2.51047	−	9.14863i	0.264627	−	0.964351i
$91$	−0.0379433			−0.00397754
$92$	−9.99570	−	0.508418i	−1.04212	−	0.0530062i
$93$	−4.83839	−	13.5712i	−0.501718	−	1.40727i
$94$	−4.69890	+	1.80789i	−0.484654	+	0.186470i
$95$	13.3798	+	0.147877i	1.37274	+	0.0151719i
$96$	3.32582	+	9.21623i	0.339440	+	0.940628i
$97$	−1.90774	−	7.11977i	−0.193701	−	0.722903i	−0.992599	−	0.121437i	$-0.961250\pi$
$97$	−1.90774	−	7.11977i	−0.193701	−	0.722903i	0.798898	−	0.601467i	$-0.205417\pi$
$98$	7.97807	−	5.80580i	0.805907	−	0.586474i
$99$	−12.6576	+	10.3396i	−1.27213	+	1.03916i
$100$	−9.82216	+	1.87755i	−0.982216	+	0.187755i
$101$	12.2397	+	7.06657i	1.21789	+	0.703150i	0.964467	−	0.264205i	$-0.0851095\pi$
$101$	12.2397	+	7.06657i	1.21789	+	0.703150i	0.253425	+	0.967355i	$0.418443\pi$
$102$	−2.93612	−	3.41762i	−0.290719	−	0.338395i
$103$	10.1677	+	2.72444i	1.00186	+	0.268447i	0.722223	−	0.691660i	$-0.243120\pi$
$103$	10.1677	+	2.72444i	1.00186	+	0.268447i	0.279634	+	0.960107i	$0.409787\pi$
$104$	−0.706522	+	0.0386640i	−0.0692802	+	0.00379132i
$105$	0.586000	−	0.0408633i	0.0571877	−	0.00398785i
$106$	0.496458	−	0.614041i	0.0482203	−	0.0596409i
$107$	2.52729	−	2.52729i	0.244323	−	0.244323i	−0.574313	−	0.818636i	$-0.694731\pi$
$107$	2.52729	−	2.52729i	0.244323	−	0.244323i	0.818636	+	0.574313i	$0.194731\pi$
$108$	−3.39117	+	9.82344i	−0.326316	+	0.945261i
$109$	12.0059			1.14996			0.574980	−	0.818168i	$-0.305010\pi$
$109$	12.0059			1.14996			0.574980	+	0.818168i	$0.305010\pi$
$110$	15.6656	+	7.16866i	1.49365	+	0.683505i
$111$	−14.4828	+	9.99928i	−1.37465	+	0.949090i
$112$	−0.470307	+	0.383251i	−0.0444398	+	0.0362139i
$113$	1.87681	−	7.00436i	0.176556	−	0.658915i	−0.819726	−	0.572756i	$-0.805874\pi$
$113$	1.87681	−	7.00436i	0.176556	−	0.658915i	0.996281	−	0.0861587i	$-0.0274592\pi$
$114$	−14.6158	−	1.10763i	−1.36890	−	0.103739i
$115$	−3.01546	+	10.7760i	−0.281193	+	1.00487i
$116$	1.05678	−	3.26956i	0.0981195	−	0.303571i
$117$	−0.609043	−	0.438540i	−0.0563061	−	0.0405431i
$118$	0.371500	−	0.270348i	0.0341993	−	0.0248875i
$119$	0.139495	−	0.241612i	0.0127875	−	0.0221485i
$120$	10.8699	−	1.35802i	0.992286	−	0.123970i
$121$	−9.34001	−	16.1774i	−0.849092	−	1.47067i
$122$	1.42640	+	0.633759i	0.129140	+	0.0573778i
$123$	−3.85528	+	1.37448i	−0.347619	+	0.123933i
$124$	12.3464	−	11.1512i	1.10874	−	1.00141i
$125$	−0.370621	+	11.1742i	−0.0331493	+	0.999450i
$126$	−0.643482	+	0.00323918i	−0.0573259	+	0.000288569i
$127$	10.7939	+	10.7939i	0.957806	+	0.957806i	0.999145	−	0.0413396i	$-0.0131625\pi$
$127$	10.7939	+	10.7939i	0.957806	+	0.957806i	−0.0413396	+	0.999145i	$0.513163\pi$
$128$	−8.36680	+	7.61556i	−0.739527	+	0.673127i
$129$	−0.896900	−	11.0938i	−0.0789677	−	0.976753i
$130$	−0.131782	+	0.780044i	−0.0115580	+	0.0684144i
$131$	3.71613	+	6.43653i	0.324680	+	0.562363i	0.981448	−	0.191731i	$-0.0614100\pi$
$131$	3.71613	+	6.43653i	0.324680	+	0.562363i	−0.656767	+	0.754093i	$0.728077\pi$
$132$	−16.6182	−	8.94408i	−1.44643	−	0.778482i
$133$	−0.234906	−	0.876680i	−0.0203689	−	0.0760178i
$134$	−16.5992	−	2.61596i	−1.43396	−	0.225985i
$135$	9.87841	+	6.11695i	0.850198	+	0.526463i
$136$	2.35125	−	4.64107i	0.201618	−	0.397968i
$137$	4.24433	+	15.8401i	0.362618	+	1.35331i	0.870621	+	0.491954i	$0.163717\pi$
$137$	4.24433	+	15.8401i	0.362618	+	1.35331i	−0.508004	+	0.861355i	$0.669616\pi$
$138$	4.05826	−	11.5667i	0.345462	−	0.984626i
$139$	7.44377	−	4.29767i	0.631373	−	0.364523i	−0.149911	−	0.988700i	$-0.547899\pi$
$139$	7.44377	−	4.29767i	0.631373	−	0.364523i	0.781284	+	0.624176i	$0.214565\pi$
$140$	0.302178	+	0.607269i	0.0255387	+	0.0513236i
$141$	−0.496899	−	6.14616i	−0.0418465	−	0.517600i
$142$	−1.65163	−	15.5986i	−0.138601	−	1.30901i
$143$	0.963712	−	0.963712i	0.0805896	−	0.0805896i
$144$	−11.9786	+	0.716019i	−0.998218	+	0.0596683i
$145$	−3.30556	−	1.95749i	−0.274512	−	0.162561i
$146$	0.282187	+	0.228151i	0.0233539	+	0.0188819i
$147$	4.05817	+	11.3827i	0.334712	+	0.938832i
$148$	−17.0605	−	11.0419i	−1.40236	−	0.907637i
$149$	6.42506	+	11.1285i	0.526361	+	0.911684i	0.999528	+	0.0307117i	$0.00977736\pi$
$149$	6.42506	+	11.1285i	0.526361	+	0.911684i	−0.473167	+	0.880973i	$0.656889\pi$
$150$	1.19518	−	12.1890i	0.0975860	−	0.995227i
$151$	−19.2472	−	11.1124i	−1.56631	−	0.904311i	−0.996593	−	0.0824719i	$-0.973719\pi$
$151$	−19.2472	−	11.1124i	−1.56631	−	0.904311i	−0.569719	−	0.821839i	$-0.692948\pi$
$152$	−5.26738	−	16.0848i	−0.427241	−	1.30465i
$153$	5.03158	−	2.26596i	0.406779	−	0.183192i
$154$	0.181915	−	1.15432i	0.0146591	−	0.0930176i
$155$	−9.12166	−	16.2103i	−0.732669	−	1.30204i
$156$	0.199209	−	0.843397i	0.0159495	−	0.0675258i
$157$	5.05037	−	18.8482i	0.403063	−	1.50425i	−0.404537	−	0.914522i	$-0.632567\pi$
$157$	5.05037	−	18.8482i	0.403063	−	1.50425i	0.807600	−	0.589731i	$-0.200766\pi$
$158$	−7.15148	+	16.0958i	−0.568941	+	1.28052i
$159$	0.549467	+	0.795840i	0.0435756	+	0.0631142i
$160$	6.24550	+	10.9997i	0.493750	+	0.869604i
$161$	0.759014			0.0598187
$162$	−10.3662	−	7.38522i	−0.814447	−	0.580238i
$163$	−0.0151370	−	0.0151370i	−0.00118562	−	0.00118562i	0.706514	−	0.707699i	$-0.250267\pi$
$163$	−0.0151370	−	0.0151370i	−0.00118562	−	0.00118562i	−0.707699	+	0.706514i	$0.750267\pi$
$164$	−3.16782	−	3.50734i	−0.247365	−	0.273877i
$165$	−13.8458	+	15.9215i	−1.07789	+	1.23949i
$166$	−6.07260	+	2.33642i	−0.471325	+	0.181341i
$167$	−2.89398	+	10.8005i	−0.223943	+	0.835768i	0.758882	+	0.651228i	$0.225746\pi$
$167$	−2.89398	+	10.8005i	−0.223943	+	0.835768i	−0.982825	+	0.184539i	$0.940921\pi$
$168$	−0.287395	−	0.685208i	−0.0221730	−	0.0528649i
$169$	−11.2041	−	6.46871i	−0.861856	−	0.497593i
$170$	−4.48261	−	3.70690i	−0.343800	−	0.284306i
$171$	6.36191	−	16.7869i	0.486507	−	1.28373i
$172$	11.4420	−	5.85222i	0.872446	−	0.446227i
$173$	−5.16006	−	19.2576i	−0.392312	−	1.46413i	−0.826311	−	0.563215i	$-0.809564\pi$
$173$	−5.16006	−	19.2576i	−0.392312	−	1.46413i	0.433999	−	0.900913i	$-0.357102\pi$
$174$	3.47511	+	2.37356i	0.263447	+	0.179939i
$175$	0.736679	−	0.180040i	0.0556877	−	0.0136097i
$176$	2.21109	−	21.6793i	0.166668	−	1.63414i
$177$	0.188969	+	0.530038i	0.0142038	+	0.0398401i
$178$	0.767772	+	7.25114i	0.0575469	+	0.543496i
$179$		−	22.0358i		−	1.64703i	−0.567295	−	0.823515i	$-0.692010\pi$
$179$		−	22.0358i		−	1.64703i	0.567295	−	0.823515i	$-0.307990\pi$
$180$	−2.16830	+	13.2400i	−0.161616	+	0.986854i
$181$			1.96336i			0.145935i	0.997334	+	0.0729676i	$0.0232470\pi$
$181$			1.96336i			0.145935i	−0.997334	+	0.0729676i	$0.976753\pi$
$182$	0.0533617	−	0.00565008i	0.00395543	−	0.000418812i
$183$	−1.23841	+	1.45627i	−0.0915462	+	0.107651i
$184$	14.1332	−	0.773431i	1.04191	−	0.0570181i
$185$	−16.2425	+	15.8874i	−1.19417	+	1.16807i
$186$	8.82535	+	18.3654i	0.647106	+	1.34662i
$187$	2.59365	+	9.67962i	0.189666	+	0.707844i
$188$	6.33909	−	3.24224i	0.462326	−	0.236464i
$189$	0.218998	−	0.757072i	0.0159298	−	0.0550689i
$190$	−18.8388	+	1.78440i	−1.36671	+	0.129454i
$191$	1.68818	+	0.974669i	0.122152	+	0.0705246i	0.559831	−	0.828607i	$-0.310866\pi$
$191$	1.68818	+	0.974669i	0.122152	+	0.0705246i	−0.437679	+	0.899131i	$0.644199\pi$
$192$	−6.04964	−	12.4660i	−0.436596	−	0.899658i
$193$	−2.94912	+	11.0063i	−0.212283	+	0.792250i	0.774823	+	0.632178i	$0.217839\pi$
$193$	−2.94912	+	11.0063i	−0.212283	+	0.792250i	−0.987105	+	0.160071i	$0.948828\pi$
$194$	3.74315	+	9.72883i	0.268742	+	0.698489i
$195$	−0.870753	−	0.424903i	−0.0623559	−	0.0304279i
$196$	−10.3554	+	9.35300i	−0.739675	+	0.668072i
$197$	7.51592	+	7.51592i	0.535487	+	0.535487i	0.922200	−	0.386713i	$-0.126390\pi$
$197$	7.51592	+	7.51592i	0.535487	+	0.535487i	−0.386713	+	0.922200i	$0.626390\pi$
$198$	16.2613	−	16.4259i	1.15564	−	1.16734i
$199$	−16.4710			−1.16760			−0.583798	−	0.811899i	$-0.698434\pi$
$199$	−16.4710			−1.16760			−0.583798	+	0.811899i	$0.698434\pi$
$200$	13.5338	−	4.10310i	0.956986	−	0.290133i
$201$	8.82062	−	18.5947i	0.622159	−	1.31157i
$202$	−18.2655	−	8.11550i	−1.28516	−	0.571004i
$203$	−0.0674431	+	0.251701i	−0.00473358	+	0.0176659i
$204$	4.63813	+	4.36917i	0.324734	+	0.305903i
$205$	−4.60500	+	2.59127i	−0.321627	+	0.180982i
$206$	−14.7051	−	2.31746i	−1.02455	−	0.161465i
$207$	12.1832	+	8.77252i	0.846793	+	0.609732i
$208$	0.987861	−	0.159582i	0.0684958	−	0.0110650i
$209$	28.2328	+	16.3002i	1.95291	+	1.12751i
$210$	−0.818038	+	0.144729i	−0.0564500	+	0.00998722i
$211$	−9.95971	−	17.2507i	−0.685655	−	1.18759i	−0.973231	−	0.229831i	$-0.926183\pi$
$211$	−9.95971	−	17.2507i	−0.685655	−	1.18759i	0.287576	−	0.957758i	$-0.407151\pi$
$212$	−0.606759	+	0.937485i	−0.0416724	+	0.0643867i
$213$	18.8968	+	3.46067i	1.29479	+	0.237121i
$214$	−3.17793	+	3.93060i	−0.217239	+	0.268690i
$215$	−3.56529	−	13.9194i	−0.243151	−	0.949294i
$216$	3.30639	−	14.3202i	0.224971	−	0.974365i
$217$	−0.892134	+	0.892134i	−0.0605620	+	0.0605620i
$218$	−16.8846	+	1.78779i	−1.14357	+	0.121084i
$219$	−0.365734	+	0.252511i	−0.0247140	+	0.0170631i
$220$	−23.0988	−	7.74892i	−1.55732	−	0.522432i
$221$	−0.398513	+	0.230082i	−0.0268069	+	0.0154770i
$222$	18.8789	−	16.2191i	1.26707	−	1.08856i
$223$	1.29689	+	4.84007i	0.0868463	+	0.324115i	0.995657	−	0.0930930i	$-0.0296754\pi$
$223$	1.29689	+	4.84007i	0.0868463	+	0.324115i	−0.908811	+	0.417208i	$0.863009\pi$
$224$	0.604348	−	0.609019i	0.0403797	−	0.0406918i
$225$	13.9056	+	5.62447i	0.927039	+	0.374965i
$226$	−1.59645	+	10.1301i	−0.106194	+	0.673843i
$227$	−3.99322	−	14.9029i	−0.265039	−	0.989140i	−0.962226	−	0.272251i	$-0.912232\pi$
$227$	−3.99322	−	14.9029i	−0.265039	−	0.989140i	0.697187	−	0.716889i	$-0.254435\pi$
$228$	20.7200	−	0.618713i	1.37221	−	0.0409753i
$229$	10.7333	+	18.5906i	0.709276	+	1.22850i	0.965126	+	0.261786i	$0.0843114\pi$
$229$	10.7333	+	18.5906i	0.709276	+	1.22850i	−0.255850	+	0.966717i	$0.582355\pi$
$230$	2.63615	−	15.6039i	0.173823	−	1.02889i
$231$	1.29308	+	0.613389i	0.0850787	+	0.0403580i
$232$	−0.999339	+	4.75551i	−0.0656098	+	0.312215i
$233$	12.6794	+	12.6794i	0.830654	+	0.830654i	0.987606	−	0.156952i	$-0.0501668\pi$
$233$	12.6794	+	12.6794i	0.830654	+	0.830654i	−0.156952	+	0.987606i	$0.550167\pi$
$234$	0.921832	+	0.526051i	0.0602620	+	0.0343890i
$235$	−1.97524	−	7.71159i	−0.128850	−	0.503049i
$236$	−0.482202	+	0.435523i	−0.0313887	+	0.0283502i
$237$	−16.4329	−	13.9746i	−1.06743	−	0.907745i
$238$	−0.160201	+	0.360563i	−0.0103843	+	0.0233719i
$239$	−3.85635	−	6.67939i	−0.249447	−	0.432054i	0.713926	−	0.700221i	$-0.246915\pi$
$239$	−3.85635	−	6.67939i	−0.249447	−	0.432054i	−0.963372	+	0.268167i	$0.913582\pi$
$240$	−15.0848	+	3.52849i	−0.973717	+	0.227763i
$241$	1.66976	−	2.89212i	0.107559	−	0.186298i	−0.807222	−	0.590248i	$-0.799030\pi$
$241$	1.66976	−	2.89212i	0.107559	−	0.186298i	0.914781	+	0.403951i	$0.132363\pi$
$242$	15.5443	+	21.3603i	0.999225	+	1.37309i
$243$	12.2653	−	9.62094i	0.786819	−	0.617183i
$244$	−2.10039	−	0.678885i	−0.134464	−	0.0434611i
$245$	7.65073	+	13.5963i	0.488787	+	0.868634i
$246$	5.21721	−	2.50709i	0.332637	−	0.159846i
$247$	−0.387452	+	1.44599i	−0.0246530	+	0.0920062i
$248$	−15.7029	+	17.5210i	−0.997132	+	1.11259i
$249$	−0.642166	−	7.94296i	−0.0406956	−	0.503365i
$250$	−1.14271	−	15.7700i	−0.0722713	−	0.997385i
$251$	−5.14442			−0.324713			−0.162357	−	0.986732i	$-0.551909\pi$
$251$	−5.14442			−0.324713			−0.162357	+	0.986732i	$0.551909\pi$
$252$	0.904479	−	0.100375i	0.0569768	−	0.00632305i
$253$	−19.2780	+	19.2780i	−1.21200	+	1.21200i
$254$	−16.7874	−	13.5727i	−1.05333	−	0.851630i
$255$	5.90689	−	3.98259i	0.369904	−	0.249399i
$256$	10.6326	−	11.9560i	0.664540	−	0.747253i
$257$	−7.88339	−	2.11235i	−0.491752	−	0.131765i	0.00441743	−	0.999990i	$-0.498594\pi$
$257$	−7.88339	−	2.11235i	−0.491752	−	0.131765i	−0.496170	+	0.868226i	$0.665261\pi$
$258$	2.91332	+	15.4682i	0.181375	+	0.963008i
$259$	1.33466	+	0.770569i	0.0829320	+	0.0478808i
$260$	0.0691766	−	1.11664i	0.00429015	−	0.0692511i
$261$	−3.99166	+	3.26066i	−0.247078	+	0.201830i
$262$	−6.18465	−	8.49867i	−0.382089	−	0.525050i
$263$	2.78271	+	10.3852i	0.171589	+	0.640380i	0.997107	+	0.0760047i	$0.0242164\pi$
$263$	2.78271	+	10.3852i	0.171589	+	0.640380i	−0.825518	+	0.564376i	$0.809117\pi$
$264$	24.7029	+	10.1039i	1.52036	+	0.621854i
$265$	0.873024	+	0.892537i	0.0536294	+	0.0548281i
$266$	0.460905	+	1.19794i	0.0282599	+	0.0734505i
$267$	−8.78435	−	1.60872i	−0.537594	−	0.0984521i
$268$	23.7339	+	1.20719i	1.44978	+	0.0737411i
$269$	−8.40504			−0.512464			−0.256232	−	0.966615i	$-0.582481\pi$
$269$	−8.40504			−0.512464			−0.256232	+	0.966615i	$0.582481\pi$
$270$	−14.8034	−	7.13160i	−0.900905	−	0.434015i
$271$			22.5479i			1.36969i	0.728689	+	0.684845i	$0.240130\pi$
$271$			22.5479i			1.36969i	−0.728689	+	0.684845i	$0.759870\pi$
$272$	−2.61560	+	6.87710i	−0.158594	+	0.416985i
$273$	−0.0118387	+	0.0646447i	−0.000716510	+	0.00391247i
$274$	−8.32775	−	21.6447i	−0.503098	−	1.30760i
$275$	−14.1379	+	23.2835i	−0.852548	+	1.40405i
$276$	−3.98496	+	16.8712i	−0.239866	+	1.01553i
$277$	−6.62772	+	1.77589i	−0.398221	+	0.106703i	−0.452371	−	0.891830i	$-0.649422\pi$
$277$	−6.62772	+	1.77589i	−0.398221	+	0.106703i	0.0541500	+	0.998533i	$0.482755\pi$
$278$	−9.82861	+	7.15247i	−0.589481	+	0.428977i
$279$	−24.6311	+	4.00891i	−1.47462	+	0.240007i
$280$	−0.515397	−	0.809038i	−0.0308008	−	0.0483492i
$281$	−15.1569	+	26.2526i	−0.904186	+	1.56610i	−0.0821802	+	0.996617i	$0.526188\pi$
$281$	−15.1569	+	26.2526i	−0.904186	+	1.56610i	−0.822006	+	0.569479i	$0.807145\pi$
$282$	1.61403	+	8.56967i	0.0961141	+	0.510316i
$283$	−0.260897	+	0.973682i	−0.0155087	+	0.0578794i	−0.973247	−	0.229763i	$-0.926205\pi$
$283$	−0.260897	+	0.973682i	−0.0155087	+	0.0578794i	0.957738	+	0.287643i	$0.0928715\pi$
$284$	4.64554	+	21.6912i	0.275662	+	1.28714i
$285$	4.42658	−	22.7493i	0.262208	−	1.34755i
$286$	−1.21181	+	1.49882i	−0.0716560	+	0.0886272i
$287$	0.253436	+	0.253436i	0.0149599	+	0.0149599i
$288$	16.7395	−	2.79069i	0.986387	−	0.164443i
$289$			13.6165i			0.800971i
$290$	4.94026	+	2.26069i	0.290102	+	0.132752i
$291$	−12.7253	+	1.02880i	−0.745971	+	0.0603096i
$292$	−0.430827	−	0.278840i	−0.0252123	−	0.0163179i
$293$	−14.2575	−	3.82027i	−0.832929	−	0.223183i	−0.182938	−	0.983124i	$-0.558561\pi$
$293$	−14.2575	−	3.82027i	−0.832929	−	0.223183i	−0.649991	+	0.759942i	$0.725227\pi$
$294$	−7.40220	−	15.4038i	−0.431705	−	0.898370i
$295$	0.356257	+	0.633112i	0.0207421	+	0.0368612i
$296$	25.6373	+	12.9883i	1.49014	+	0.754931i
$297$	13.6664	+	24.7909i	0.793005	+	1.43852i
$298$	−10.6930	−	14.6939i	−0.619430	−	0.851194i
$299$	−1.08419	−	0.625957i	−0.0627003	−	0.0362000i
$300$	0.134203	+	17.3200i	0.00774819	+	0.999970i
$301$	−0.844053	+	0.487314i	−0.0486504	+	0.0280883i
$302$	28.7230	+	12.7618i	1.65282	+	0.734360i
$303$	15.8583	−	18.6481i	0.911037	−	1.07130i
$304$	9.80296	+	21.8365i	0.562238	+	1.25241i
$305$	−1.25751	+	2.12352i	−0.0720048	+	0.121592i
$306$	−6.73876	+	3.93598i	−0.385229	+	0.225005i
$307$	16.2816	−	16.2816i	0.929241	−	0.929241i	−0.0684157	−	0.997657i	$-0.521794\pi$
$307$	16.2816	−	16.2816i	0.929241	−	0.929241i	0.997657	+	0.0684157i	$0.0217944\pi$
$308$	−0.0839487	+	1.65047i	−0.00478342	+	0.0940440i
$309$	7.81410	−	16.4729i	0.444529	−	0.937110i
$310$	15.2421	+	21.4391i	0.865694	+	1.21766i
$311$	14.0776	−	8.12773i	0.798270	−	0.460881i	−0.0445962	−	0.999005i	$-0.514200\pi$
$311$	14.0776	−	8.12773i	0.798270	−	0.460881i	0.842866	+	0.538124i	$0.180867\pi$
$312$	−0.154569	+	1.21578i	−0.00875075	+	0.0688298i
$313$	14.4838	−	3.88092i	0.818673	−	0.219363i	0.174907	−	0.984585i	$-0.444038\pi$
$313$	14.4838	−	3.88092i	0.818673	−	0.219363i	0.643766	+	0.765222i	$0.277371\pi$
$314$	−4.29593	+	27.2593i	−0.242434	+	1.53833i
$315$	0.113218	−	1.01113i	0.00637913	−	0.0569706i
$316$	7.66069	−	23.7013i	0.430948	−	1.33330i
$317$	3.02284	−	0.809968i	0.169780	−	0.0454924i	−0.172928	−	0.984935i	$-0.555323\pi$
$317$	3.02284	−	0.809968i	0.169780	−	0.0454924i	0.342707	+	0.939442i	$0.388656\pi$
$318$	−0.891252	−	1.03741i	−0.0499789	−	0.0581751i
$319$	−4.67991	−	8.10585i	−0.262025	−	0.453840i
$320$	−10.4213	−	14.5395i	−0.582570	−	0.812781i
$321$	−3.51725	−	5.09433i	−0.196314	−	0.284338i
$322$	−1.06744	+	0.113024i	−0.0594862	+	0.00629856i
$323$	−7.78322	−	7.78322i	−0.433070	−	0.433070i
$324$	15.6783	+	8.84261i	0.871015	+	0.491256i
$325$	−1.20076	−	0.350364i	−0.0666064	−	0.0194347i
$326$	0.0235420	+	0.0190339i	0.00130387	+	0.00105419i
$327$	3.74597	−	20.4547i	0.207153	−	1.13115i
$328$	4.97734	+	4.46084i	0.274828	+	0.246309i
$329$	−0.467621	+	0.269981i	−0.0257808	+	0.0148845i
$330$	17.1012	−	24.4530i	0.941389	−	1.34609i
$331$	−13.2160	+	22.8908i	−0.726417	+	1.25819i	0.231971	+	0.972723i	$0.425483\pi$
$331$	−13.2160	+	22.8908i	−0.726417	+	1.25819i	−0.958388	+	0.285469i	$0.907851\pi$
$332$	8.19230	−	4.19009i	0.449611	−	0.229961i
$333$	12.5172	+	27.7945i	0.685936	+	1.52313i
$334$	2.46167	−	15.6202i	0.134697	−	0.854701i
$335$	7.15994	−	25.5867i	0.391189	−	1.39795i
$336$	0.506212	+	0.920848i	0.0276161	+	0.0502364i
$337$	−9.84602	−	2.63823i	−0.536347	−	0.143714i	−0.0195295	−	0.999809i	$-0.506217\pi$
$337$	−9.84602	−	2.63823i	−0.536347	−	0.143714i	−0.516818	+	0.856096i	$0.672883\pi$
$338$	16.7202	+	7.42889i	0.909459	+	0.404078i
$339$	−11.3479	−	5.38299i	−0.616331	−	0.292364i
$340$	6.85612	+	4.54571i	0.371825	+	0.246526i
$341$		−	45.3181i		−	2.45411i
$342$	−6.44737	+	24.5557i	−0.348634	+	1.32782i
$343$	1.49901	−	1.49901i	0.0809389	−	0.0809389i
$344$	−15.2201	+	9.93409i	−0.820611	+	0.535610i
$345$	17.4184	+	8.49971i	0.937777	+	0.457609i
$346$	10.1245	+	26.3146i	0.544295	+	1.41468i
$347$	19.7716	+	5.29778i	1.06139	+	0.284400i	0.746953	−	0.664877i	$-0.231516\pi$
$347$	19.7716	+	5.29778i	1.06139	+	0.284400i	0.314442	+	0.949277i	$0.398183\pi$
$348$	−5.24067	−	2.82059i	−0.280929	−	0.151199i
$349$	10.4555	−	18.1095i	0.559670	−	0.969378i	−0.437853	−	0.899046i	$-0.644261\pi$
$349$	10.4555	−	18.1095i	0.559670	−	0.969378i	0.997524	−	0.0703312i	$-0.0224056\pi$
$350$	−1.00922	+	0.362897i	−0.0539451	+	0.0193977i
$351$	−0.937176	+	0.900808i	−0.0500228	+	0.0480816i
$352$	0.118653	+	30.8180i	0.00632425	+	1.64260i
$353$	−4.48999	+	1.20309i	−0.238978	+	0.0640340i	−0.376320	−	0.926490i	$-0.622811\pi$
$353$	−4.48999	+	1.20309i	−0.238978	+	0.0640340i	0.137342	+	0.990524i	$0.456144\pi$
$354$	−0.344684	−	0.717281i	−0.0183198	−	0.0381231i
$355$	24.7999	+	0.274095i	1.31624	+	0.0145475i
$356$	−2.15951	−	10.0833i	−0.114454	−	0.534416i
$357$	−0.368115	−	0.313045i	−0.0194827	−	0.0165681i
$358$	3.28131	+	30.9900i	0.173423	+	1.63787i
$359$	−17.4595			−0.921476			−0.460738	−	0.887536i	$-0.652415\pi$
$359$	−17.4595			−0.921476			−0.460738	+	0.887536i	$0.652415\pi$
$360$	1.07784	−	18.9430i	0.0568072	−	0.998385i
$361$	−16.8083			−0.884648
$362$	−0.292361	−	2.76117i	−0.0153661	−	0.145124i
$363$	−30.4758	+	10.8652i	−1.59957	+	0.570277i
$364$	−0.0742039	+	0.0158920i	−0.00388934	+	0.000832968i
$365$	−0.410171	+	0.401204i	−0.0214694	+	0.0210000i
$366$	1.52480	−	2.23244i	0.0797023	−	0.116692i
$367$	7.17356	−	1.92215i	0.374457	−	0.100335i	−0.0666819	−	0.997774i	$-0.521241\pi$
$367$	7.17356	−	1.92215i	0.374457	−	0.100335i	0.441139	+	0.897439i	$0.354575\pi$
$368$	−19.7611	+	3.19227i	−1.03012	+	0.166409i
$369$	1.13884	+	6.99716i	0.0592859	+	0.364258i
$370$	20.4769	−	24.7619i	1.06454	−	1.28731i
$371$	0.0423433	−	0.0733407i	0.00219835	−	0.00380766i
$372$	−15.1463	−	24.5140i	−0.785300	−	1.27099i
$373$	−2.90589	−	0.778631i	−0.150461	−	0.0403160i	0.182802	−	0.983150i	$-0.441483\pi$
$373$	−2.90589	−	0.778631i	−0.150461	−	0.0403160i	−0.333264	+	0.942834i	$0.608150\pi$
$374$	−5.08896	−	13.2267i	−0.263144	−	0.683938i
$375$	18.9220	+	4.11789i	0.977129	+	0.212647i
$376$	−8.43220	+	5.50367i	−0.434857	+	0.283830i
$377$	0.303914	−	0.303914i	0.0156524	−	0.0156524i
$378$	−0.195254	+	1.09732i	−0.0100428	+	0.0564401i
$379$		−	1.07451i		−	0.0551937i	−0.999619	−	0.0275969i	$-0.991215\pi$
$379$		−	1.07451i		−	0.0551937i	0.999619	−	0.0275969i	$-0.00878547\pi$
$380$	26.2282	−	5.31475i	1.34548	−	0.272641i
$381$	21.7576	−	15.0220i	1.11468	−	0.769599i
$382$	−2.51931	−	1.11934i	−0.128899	−	0.0572706i
$383$	−11.3814	−	3.04964i	−0.581563	−	0.155829i	−0.0439687	−	0.999033i	$-0.514000\pi$
$383$	−11.3814	−	3.04964i	−0.581563	−	0.155829i	−0.537594	+	0.843204i	$0.680667\pi$
$384$	10.3642	+	16.6308i	0.528897	+	0.848686i
$385$	1.77931	+	0.497905i	0.0906821	+	0.0253756i
$386$	2.50858	−	15.9179i	0.127683	−	0.810198i
$387$	−19.1805	−	1.93330i	−0.974999	−	0.0982753i
$388$	−6.71289	−	13.1248i	−0.340795	−	0.666309i
$389$	−1.71560	+	2.97151i	−0.0869845	+	0.150662i	−0.906235	−	0.422774i	$-0.861056\pi$
$389$	−1.71560	+	2.97151i	−0.0869845	+	0.150662i	0.819251	+	0.573436i	$0.194390\pi$
$390$	1.28786	+	0.467900i	0.0652131	+	0.0236931i
$391$	7.97182	−	4.60253i	0.403152	−	0.232760i
$392$	13.1707	−	14.6956i	0.665219	−	0.742241i
$393$	12.1255	−	4.32298i	0.611651	−	0.218065i
$394$	−11.6892	−	9.45085i	−0.588894	−	0.476127i
$395$	−23.9623	−	14.1900i	−1.20567	−	0.713977i
$396$	−20.4232	+	25.5220i	−1.02630	+	1.28253i
$397$	14.3888	+	14.3888i	0.722155	+	0.722155i	0.969044	−	0.246889i	$-0.0794082\pi$
$397$	14.3888	+	14.3888i	0.722155	+	0.722155i	−0.246889	+	0.969044i	$0.579408\pi$
$398$	23.1640	−	2.45267i	1.16110	−	0.122941i
$399$	−1.56691	+	0.126680i	−0.0784435	+	0.00634193i
$400$	−18.4223	+	7.78571i	−0.921117	+	0.389285i
$401$	−2.12534	−	3.68121i	−0.106135	−	0.183831i	0.808067	−	0.589091i	$-0.200514\pi$
$401$	−2.12534	−	3.68121i	−0.106135	−	0.183831i	−0.914201	+	0.405261i	$0.867181\pi$
$402$	−9.63599	+	27.4642i	−0.480599	+	1.36979i
$403$	2.01008	−	0.538599i	0.100129	−	0.0268295i
$404$	26.8963	+	8.69335i	1.33814	+	0.432510i
$405$	13.5037	−	14.9215i	0.671004	−	0.741453i
$406$	0.0573683	−	0.364023i	0.00284714	−	0.0180662i
$407$	−53.4702	+	14.3273i	−2.65042	+	0.710178i
$408$	−7.17345	−	5.45393i	−0.355139	−	0.270010i
$409$	0.717054	−	0.413991i	0.0354560	−	0.0204705i	−0.482167	−	0.876079i	$-0.660150\pi$
$409$	0.717054	−	0.413991i	0.0354560	−	0.0204705i	0.517623	+	0.855609i	$0.326817\pi$
$410$	6.09039	−	4.32996i	0.300783	−	0.213841i
$411$	28.3113	−	2.28889i	1.39649	−	0.112902i
$412$	21.0257	+	1.06944i	1.03586	+	0.0526876i
$413$	0.0348433	−	0.0348433i	0.00171453	−	0.00171453i
$414$	−18.4402	−	10.5231i	−0.906288	−	0.517180i
$415$	−2.55269	−	9.96605i	−0.125306	−	0.489214i
$416$	−1.36552	+	0.371530i	−0.0669500	+	0.0182158i
$417$	−4.99947	−	14.0230i	−0.244825	−	0.686709i
$418$	−42.1326	−	18.7198i	−2.06077	−	0.915614i
$419$	2.14624	−	1.23913i	0.104851	−	0.0605357i	−0.446658	−	0.894705i	$-0.647386\pi$
$419$	2.14624	−	1.23913i	0.104851	−	0.0605357i	0.551508	+	0.834169i	$0.314052\pi$
$420$	1.12890	−	0.325352i	0.0550846	−	0.0158756i
$421$	−24.5340	−	14.1647i	−1.19572	−	0.690347i	−0.236119	−	0.971724i	$-0.575876\pi$
$421$	−24.5340	−	14.1647i	−1.19572	−	0.690347i	−0.959597	+	0.281377i	$0.909209\pi$
$422$	16.5756	+	22.7775i	0.806889	+	1.10879i
$423$	−10.6263	−	1.07109i	−0.516671	−	0.0520779i
$424$	0.713717	−	1.40879i	0.0346612	−	0.0684167i
$425$	6.64550	−	6.35803i	0.322354	−	0.308410i
$426$	−27.0909	−	2.05302i	−1.31256	−	0.0994691i
$427$	0.161695	+	0.0433260i	0.00782497	+	0.00209669i
$428$	3.88399	−	6.00103i	0.187740	−	0.290071i
$429$	−1.34120	−	1.94258i	−0.0647539	−	0.0937886i
$430$	7.08677	+	19.0447i	0.341754	+	0.918415i
$431$			14.2569i			0.686733i	0.939202	+	0.343366i	$0.111567\pi$
$431$			14.2569i			0.686733i	−0.939202	+	0.343366i	$0.888433\pi$
$432$	−2.51755	+	20.6316i	−0.121126	+	0.992637i
$433$	24.8796	+	24.8796i	1.19564	+	1.19564i	0.975460	+	0.220178i	$0.0706637\pi$
$433$	24.8796	+	24.8796i	1.19564	+	1.19564i	0.220178	+	0.975460i	$0.429336\pi$
$434$	1.12181	−	1.38750i	0.0538485	−	0.0666022i
$435$	−4.36637	+	5.02098i	−0.209352	+	0.240737i
$436$	23.4794	−	5.02851i	1.12446	−	0.240822i
$437$	7.75055	−	28.9255i	0.370759	−	1.38369i
$438$	0.476749	−	0.409581i	0.0227800	−	0.0195705i
$439$	−4.56907	+	7.91386i	−0.218070	+	0.377708i	−0.954218	−	0.299113i	$-0.903309\pi$
$439$	−4.56907	+	7.91386i	−0.218070	+	0.377708i	0.736148	+	0.676820i	$0.236643\pi$
$440$	33.6389	+	7.45810i	1.60367	+	0.355551i
$441$	20.6591	−	3.36244i	0.983769	−	0.160116i
$442$	0.526189	−	0.382918i	0.0250283	−	0.0182136i
$443$	−5.11892	+	1.37161i	−0.243207	+	0.0651671i	−0.378363	−	0.925657i	$-0.623513\pi$
$443$	−5.11892	+	1.37161i	−0.243207	+	0.0651671i	0.135156	+	0.990824i	$0.456846\pi$
$444$	−24.1353	+	25.6210i	−1.14541	+	1.21592i
$445$	−11.5285	−	0.127415i	−0.546501	−	0.00604007i
$446$	−2.54461	−	6.61372i	−0.120491	−	0.313169i
$447$	20.9645	−	7.47427i	0.991588	−	0.353521i
$448$	−0.759237	+	0.946488i	−0.0358706	+	0.0447174i
$449$			4.83011i			0.227947i	0.993484	+	0.113974i	$0.0363579\pi$
$449$			4.83011i			0.227947i	−0.993484	+	0.113974i	$0.963642\pi$
$450$	−20.3937	−	5.83933i	−0.961367	−	0.275269i
$451$	−12.8739			−0.606208
$452$	0.736718	−	14.4842i	0.0346523	−	0.681278i
$453$	−24.9376	+	29.3246i	−1.17167	+	1.37779i
$454$	7.83504	+	20.3641i	0.367717	+	0.955735i
$455$	−0.000937658		0.0848387i	−4.39581e−5		0.00397730i
$456$	−29.0474	+	3.95551i	−1.36027	+	0.185234i
$457$	1.49014	+	5.56129i	0.0697059	+	0.260146i	0.991981	−	0.126389i	$-0.0403386\pi$
$457$	1.49014	+	5.56129i	0.0697059	+	0.260146i	−0.922275	+	0.386535i	$0.873672\pi$
$458$	−17.8631	−	24.5467i	−0.834688	−	1.14699i
$459$	−2.29065	−	9.27939i	−0.106918	−	0.433125i
$460$	−1.38380	+	22.3371i	−0.0645201	+	1.04147i
$461$	−30.5264	−	17.6244i	−1.42176	−	0.820852i	−0.425308	−	0.905049i	$-0.639834\pi$
$461$	−30.5264	−	17.6244i	−1.42176	−	0.820852i	−0.996449	+	0.0841964i	$0.973168\pi$
$462$	−1.90987	−	0.670090i	−0.0888552	−	0.0311754i
$463$	−0.511678	−	0.137104i	−0.0237797	−	0.00637175i	0.246910	−	0.969039i	$-0.420585\pi$
$463$	−0.511678	−	0.137104i	−0.0237797	−	0.00637175i	−0.270689	+	0.962667i	$0.587252\pi$
$464$	0.697286	−	6.83673i	0.0323707	−	0.317387i
$465$	−30.4638	+	10.4829i	−1.41273	+	0.486135i
$466$	−19.7198	−	15.9436i	−0.913500	−	0.738574i
$467$	−14.8255	+	14.8255i	−0.686043	+	0.686043i	−0.961355	−	0.275312i	$-0.911219\pi$
$467$	−14.8255	+	14.8255i	−0.686043	+	0.686043i	0.275312	+	0.961355i	$0.411219\pi$
$468$	−1.37475	−	0.602544i	−0.0635480	−	0.0278526i
$469$	−1.80221			−0.0832185
$470$	3.92620	+	10.5511i	0.181102	+	0.486685i
$471$	−30.5363	−	14.4852i	−1.40704	−	0.667444i
$472$	0.613293	−	0.684303i	0.0282291	−	0.0314976i
$473$	9.06070	−	33.8150i	0.416612	−	1.55482i
$474$	25.1914	+	17.2061i	1.15708	+	0.790305i
$475$	0.661286	−	29.9127i	0.0303419	−	1.37249i
$476$	0.171608	−	0.530934i	0.00786562	−	0.0243353i
$477$	1.52732	−	0.687827i	0.0699314	−	0.0314934i
$478$	6.41801	+	8.81934i	0.293553	+	0.403387i
$479$	0.414869	−	0.718574i	0.0189559	−	0.0328325i	−0.856392	−	0.516326i	$-0.827299\pi$
$479$	0.414869	−	0.718574i	0.0189559	−	0.0328325i	0.875348	+	0.483494i	$0.160632\pi$
$480$	20.6891	−	7.20855i	0.944322	−	0.329024i
$481$	−1.27097	−	2.20139i	−0.0579513	−	0.100375i
$482$	−1.91762	+	4.31598i	−0.0873450	+	0.196587i
$483$	0.236820	−	1.29314i	0.0107757	−	0.0588401i
$484$	−25.0415	−	27.7254i	−1.13825	−	1.26025i
$485$	−15.9665	+	4.08963i	−0.725000	+	0.185700i
$486$	−15.8167	+	15.3568i	−0.717460	+	0.696600i
$487$	20.9797	+	20.9797i	0.950681	+	0.950681i	0.998840	−	0.0481586i	$-0.0153353\pi$
$487$	20.9797	+	20.9797i	0.950681	+	0.950681i	−0.0481586	+	0.998840i	$0.515335\pi$
$488$	3.05498	+	0.641984i	0.138293	+	0.0290613i
$489$	−0.0305120	+	0.0210663i	−0.00137980	+	0.000952649i
$490$	−12.7842	−	17.9819i	−0.577532	−	0.812339i
$491$	12.5709	+	21.7734i	0.567315	+	0.982618i	0.996830	+	0.0795582i	$0.0253509\pi$
$491$	12.5709	+	21.7734i	0.567315	+	0.982618i	−0.429516	+	0.903059i	$0.641316\pi$
$492$	−6.96391	+	4.30274i	−0.313957	+	0.193983i
$493$	0.817927	+	3.05254i	0.0368376	+	0.137480i
$494$	0.329574	−	2.09127i	0.0148282	−	0.0940906i
$495$	22.8057	+	28.5569i	1.02504	+	1.28354i
$496$	19.4747	−	26.9790i	0.874441	−	1.21139i
$497$	−0.435405	−	1.62495i	−0.0195306	−	0.0728892i
$498$	2.08589	+	11.0750i	0.0934708	+	0.496281i
$499$	−25.5535	+	14.7533i	−1.14393	+	0.660450i	−0.947401	−	0.320048i	$-0.896301\pi$
$499$	−25.5535	+	14.7533i	−1.14393	+	0.660450i	−0.196531	+	0.980498i	$0.562968\pi$
$500$	3.95535	+	22.0081i	0.176888	+	0.984231i
$501$	17.4980	+	8.30039i	0.781754	+	0.370834i
$502$	7.23487	−	0.766048i	0.322908	−	0.0341904i
$503$	8.26647	−	8.26647i	0.368584	−	0.368584i	−0.498377	−	0.866961i	$-0.666070\pi$
$503$	8.26647	−	8.26647i	0.368584	−	0.368584i	0.866961	+	0.498377i	$0.166070\pi$
$504$	−1.25707	+	0.275848i	−0.0559943	+	0.0122872i
$505$	16.1028	−	27.1924i	0.716567	−	1.21005i
$506$	24.2410	−	29.9823i	1.07764	−	1.33288i
$507$	−14.5166	+	17.0704i	−0.644707	+	0.758121i
$508$	25.6300	+	16.5883i	1.13715	+	0.735986i
$509$	16.7540	+	29.0188i	0.742608	+	1.28624i	0.951304	+	0.308255i	$0.0997449\pi$
$509$	16.7540	+	29.0188i	0.742608	+	1.28624i	−0.208696	+	0.977981i	$0.566922\pi$
$510$	−7.71413	+	6.48051i	−0.341587	+	0.286962i
$511$	0.0337042	+	0.0194591i	0.00149099	+	0.000860822i
$512$	−13.1729	+	18.3977i	−0.582165	+	0.813071i
$513$	−26.6152	−	16.0766i	−1.17509	−	0.709798i
$514$	11.4014	+	1.79680i	0.502893	+	0.0792534i
$515$	6.34292	−	22.6670i	0.279503	−	0.998829i
$516$	−6.40049	−	21.3199i	−0.281766	−	0.938557i
$517$	5.01980	−	18.7341i	0.220770	−	0.823926i
$518$	−1.99175	−	0.884948i	−0.0875126	−	0.0388824i
$519$	−34.4195	+	2.78272i	−1.51085	+	0.122148i
$520$	0.0689905	+	1.58069i	0.00302543	+	0.0693178i
$521$	16.9914			0.744407			0.372204	−	0.928151i	$-0.378602\pi$
$521$	16.9914			0.744407			0.372204	+	0.928151i	$0.378602\pi$
$522$	5.12814	−	5.18003i	0.224453	−	0.226724i
$523$	19.0915	+	19.0915i	0.834815	+	0.834815i	0.988171	−	0.153356i	$-0.0490082\pi$
$523$	19.0915	+	19.0915i	0.834815	+	0.834815i	−0.153356	+	0.988171i	$0.549008\pi$
$524$	9.96332	+	11.0312i	0.435250	+	0.481899i
$525$	−0.0768863	−	1.31127i	−0.00335559	−	0.0572283i
$526$	−5.45992	−	14.1909i	−0.238064	−	0.618753i
$527$	−3.96021	+	14.7797i	−0.172509	+	0.643814i
$528$	−36.2455	−	10.5312i	−1.57738	−	0.458313i
$529$	1.76942	+	1.02157i	0.0769312	+	0.0444162i
$530$	−1.36069	−	1.12522i	−0.0591044	−	0.0488765i
$531$	0.961995	−	0.156572i	0.0417470	−	0.00679467i
$532$	−0.826579	−	1.61609i	−0.0358367	−	0.0700666i
$533$	−0.153004	−	0.571020i	−0.00662736	−	0.0247336i
$534$	12.5934	+	0.954363i	0.544972	+	0.0412993i
$535$	−5.58840	−	5.71331i	−0.241608	−	0.247008i
$536$	−33.5580	+	1.83645i	−1.44949	+	0.0793224i
$537$	−37.5427	−	6.87537i	−1.62009	−	0.296694i
$538$	11.8204	−	1.25158i	0.509615	−	0.0539595i
$539$			38.0102i			1.63722i
$540$	21.8807	+	7.82519i	0.941597	+	0.336743i
$541$			32.3552i			1.39106i	0.718499	+	0.695528i	$0.244830\pi$
$541$			32.3552i			1.39106i	−0.718499	+	0.695528i	$0.755170\pi$
$542$	−3.35758	−	31.7104i	−0.144220	−	1.36208i
$543$	3.34500	+	0.612587i	0.143548	+	0.0262886i
$544$	2.65439	−	10.0611i	0.113806	−	0.431366i
$545$	0.296692	−	26.8444i	0.0127089	−	1.14989i
$546$	0.00702322	−	0.0926760i	0.000300566	−	0.00396617i
$547$	−0.775291	−	2.89343i	−0.0331491	−	0.123714i	0.947369	−	0.320145i	$-0.103732\pi$
$547$	−0.775291	−	2.89343i	−0.0331491	−	0.123714i	−0.980518	+	0.196431i	$0.937065\pi$
$548$	14.9348	+	29.2000i	0.637984	+	1.24736i
$549$	2.09468	+	2.56428i	0.0893987	+	0.109441i
$550$	16.4158	−	34.8500i	0.699971	−	1.48601i
$551$	8.90345	+	5.14041i	0.379300	+	0.218989i
$552$	3.09198	−	24.3203i	0.131604	−	1.03514i
$553$	−0.488901	+	1.82460i	−0.0207902	+	0.0775900i
$554$	9.05646	−	3.48445i	0.384772	−	0.148040i
$555$	21.9998	+	32.6297i	0.933840	+	1.38505i
$556$	12.7574	−	11.5225i	0.541035	−	0.488661i
$557$	4.11994	+	4.11994i	0.174567	+	0.174567i	0.788983	−	0.614415i	$-0.210608\pi$
$557$	4.11994	+	4.11994i	0.174567	+	0.174567i	−0.614415	+	0.788983i	$0.710608\pi$
$558$	34.0430	−	9.30572i	1.44116	−	0.393942i
$559$	1.60755			0.0679920
$560$	0.845302	+	1.06104i	0.0357205	+	0.0448373i
$561$	17.3006	−	1.39870i	0.730431	−	0.0590533i
$562$	17.4067	−	39.1773i	0.734259	−	1.65260i
$563$	10.0011	−	37.3247i	0.421497	−	1.57305i	−0.349960	−	0.936765i	$-0.613805\pi$
$563$	10.0011	−	37.3247i	0.421497	−	1.57305i	0.771457	−	0.636282i	$-0.219529\pi$
$564$	−3.54599	−	11.8116i	−0.149313	−	0.497359i
$565$	−15.6149	−	4.36952i	−0.656924	−	0.183827i
$566$	0.221924	−	1.40819i	0.00932815	−	0.0591906i
$567$	−1.22151	−	0.609325i	−0.0512985	−	0.0255892i
$568$	−9.76326	−	29.8137i	−0.409657	−	1.25096i
$569$	−3.97619	−	2.29566i	−0.166691	−	0.0962389i	0.414334	−	0.910125i	$-0.364015\pi$
$569$	−3.97619	−	2.29566i	−0.166691	−	0.0962389i	−0.581024	+	0.813886i	$0.697348\pi$
$570$	−2.83776	+	32.6527i	−0.118861	+	1.36767i
$571$	4.69159	+	8.12608i	0.196337	+	0.340066i	0.947338	−	0.320235i	$-0.103762\pi$
$571$	4.69159	+	8.12608i	0.196337	+	0.340066i	−0.751001	+	0.660301i	$0.770429\pi$
$572$	1.48105	−	2.28832i	0.0619257	−	0.0956795i
$573$	2.18729	−	2.57207i	0.0913752	−	0.107450i
$574$	−0.394159	−	0.318681i	−0.0164519	−	0.0133015i
$575$	24.0199	+	7.00865i	1.00170	+	0.292281i
$576$	−23.1261	+	6.41736i	−0.963588	+	0.267390i
$577$	25.0905	−	25.0905i	1.04453	−	1.04453i	0.0455705	−	0.998961i	$-0.485489\pi$
$577$	25.0905	−	25.0905i	1.04453	−	1.04453i	0.998961	−	0.0455705i	$-0.0145106\pi$
$578$	−2.02761	−	19.1496i	−0.0843377	−	0.796519i
$579$	17.8314	+	8.45854i	0.741049	+	0.351525i
$580$	−7.28439	−	2.44368i	−0.302468	−	0.101468i
$581$	−0.604328	+	0.348909i	−0.0250717	+	0.0144752i
$582$	17.7431	−	3.34177i	0.735474	−	0.138521i
$583$	0.787295	+	2.93823i	0.0326064	+	0.121689i
$584$	0.647417	+	0.327994i	0.0267903	+	0.0135725i
$585$	−0.995597	+	1.35094i	−0.0411629	+	0.0558546i
$586$	20.6199	+	3.24959i	0.851799	+	0.134239i
$587$	−6.20734	−	23.1661i	−0.256204	−	0.956167i	−0.967417	−	0.253190i	$-0.918520\pi$
$587$	−6.20734	−	23.1661i	−0.256204	−	0.956167i	0.711212	−	0.702977i	$-0.248146\pi$
$588$	12.7039	+	20.5610i	0.523898	+	0.847920i
$589$	24.8887	+	43.1084i	1.02552	+	1.77625i
$590$	−0.595298	−	0.837328i	−0.0245080	−	0.0344723i
$591$	15.1500	−	10.4600i	0.623189	−	0.430265i
$592$	−37.9891	−	14.4486i	−1.56134	−	0.593832i
$593$	5.16616	+	5.16616i	0.212149	+	0.212149i	0.805180	−	0.593031i	$-0.202069\pi$
$593$	5.16616	+	5.16616i	0.212149	+	0.212149i	−0.593031	+	0.805180i	$0.702069\pi$
$594$	−22.9113	−	32.8297i	−0.940064	−	1.34702i
$595$	−0.536781	−	0.317871i	−0.0220059	−	0.0130315i
$596$	17.2262	+	19.0725i	0.705613	+	0.781239i
$597$	−5.13910	+	28.0618i	−0.210329	+	1.14849i
$598$	1.61796	+	0.718871i	0.0661634	+	0.0293968i
$599$	−5.69334	−	9.86115i	−0.232624	−	0.402916i	0.725956	−	0.687741i	$-0.241398\pi$
$599$	−5.69334	−	9.86115i	−0.232624	−	0.402916i	−0.958579	+	0.284826i	$0.908064\pi$
$600$	−2.76783	−	24.3380i	−0.112996	−	0.993595i
$601$	−15.5362	+	26.9095i	−0.633735	+	1.09766i	0.353047	+	0.935606i	$0.385146\pi$
$601$	−15.5362	+	26.9095i	−0.633735	+	1.09766i	−0.986782	+	0.162055i	$0.948188\pi$
$602$	1.11447	−	0.811022i	0.0454224	−	0.0330548i
$603$	−28.9280	−	20.8296i	−1.17804	−	0.848246i
$604$	−42.2950	−	13.6705i	−1.72096	−	0.556245i
$605$	−36.4023	+	20.4839i	−1.47996	+	0.832787i
$606$	−19.5255	+	28.5872i	−0.793171	+	1.16128i
$607$	−9.69649	+	36.1878i	−0.393568	+	1.46882i	0.430637	+	0.902525i	$0.358289\pi$
$607$	−9.69649	+	36.1878i	−0.393568	+	1.46882i	−0.824205	+	0.566292i	$0.808378\pi$
$608$	−17.0381	−	29.2501i	−0.690985	−	1.18625i
$609$	0.407784	+	0.193437i	0.0165242	+	0.00783846i
$610$	1.45229	−	3.17367i	0.0588015	−	0.128498i
$611$	0.890610			0.0360302
$612$	8.89096	−	6.53884i	0.359396	−	0.264317i
$613$	−8.69624	+	8.69624i	−0.351238	+	0.351238i	−0.860570	−	0.509332i	$-0.829893\pi$
$613$	−8.69624	+	8.69624i	−0.351238	+	0.351238i	0.509332	+	0.860570i	$0.329893\pi$
$614$	−20.4732	+	25.3222i	−0.826232	+	1.02192i
$615$	2.97798	+	8.65411i	0.120084	+	0.348967i
$616$	−0.127707	−	2.33364i	−0.00514546	−	0.0940249i
$617$	−25.3176	−	6.78383i	−1.01925	−	0.273107i	−0.289759	−	0.957100i	$-0.593575\pi$
$617$	−25.3176	−	6.78383i	−1.01925	−	0.273107i	−0.729489	+	0.683993i	$0.760242\pi$
$618$	−8.53643	+	24.3303i	−0.343385	+	0.978707i
$619$	−2.60988	−	1.50681i	−0.104900	−	0.0605640i	0.446632	−	0.894718i	$-0.352623\pi$
$619$	−2.60988	−	1.50681i	−0.104900	−	0.0605640i	−0.551532	+	0.834154i	$0.685957\pi$
$620$	−24.6282	−	27.8812i	−0.989094	−	1.11974i
$621$	18.7472	−	18.0197i	0.752298	−	0.723104i
$622$	−18.5878	+	13.5267i	−0.745304	+	0.542372i
$623$	0.202402	+	0.755373i	0.00810905	+	0.0302634i
$624$	0.0363392	−	1.73283i	0.00145473	−	0.0693686i
$625$	24.9756	+	1.10482i	0.999023	+	0.0441928i
$626$	−19.7914	+	7.61471i	−0.791024	+	0.304345i
$627$	36.5799	−	43.0149i	1.46086	−	1.71785i
$628$	1.98245	−	38.9759i	0.0791085	−	1.55531i
$629$	18.6904			0.745235
$630$	−0.00865918	+	1.43886i	−0.000344990	+	0.0573256i
$631$			11.9919i			0.477389i	0.971095	+	0.238694i	$0.0767194\pi$
$631$			11.9919i			0.477389i	−0.971095	+	0.238694i	$0.923281\pi$
$632$	−7.24430	+	34.4731i	−0.288163	+	1.37127i
$633$	−32.4979	+	11.5861i	−1.29167	+	0.460507i
$634$	−4.13057	+	1.58923i	−0.164046	+	0.0631163i
$635$	24.4012	−	23.8677i	0.968332	−	0.947162i
$636$	1.40789	+	1.32625i	0.0558266	+	0.0525892i
$637$	−1.68594	+	0.451746i	−0.0667994	+	0.0178988i
$638$	7.78864	+	10.7028i	0.308355	+	0.423728i
$639$	11.7920	−	31.1151i	0.466484	−	1.23089i
$640$	16.8211	+	18.8958i	0.664912	+	0.746921i
$641$	−8.63190	+	14.9509i	−0.340939	+	0.590524i	−0.984607	−	0.174780i	$-0.944078\pi$
$641$	−8.63190	+	14.9509i	−0.340939	+	0.590524i	0.643668	+	0.765305i	$0.277412\pi$
$642$	5.70509	+	6.64068i	0.225162	+	0.262087i
$643$	−5.28555	+	19.7259i	−0.208442	+	0.777915i	0.779931	+	0.625865i	$0.215254\pi$
$643$	−5.28555	+	19.7259i	−0.208442	+	0.777915i	−0.988373	+	0.152050i	$0.951413\pi$
$644$	1.48437	−	0.317902i	0.0584923	−	0.0125271i
$645$	−24.8271	+	1.73126i	−0.977566	+	0.0681682i
$646$	12.1049	+	9.78696i	0.476262	+	0.385063i
$647$	−25.6716	−	25.6716i	−1.00925	−	1.00925i	−0.999957	−	0.00929696i	$-0.997041\pi$
$647$	−25.6716	−	25.6716i	−1.00925	−	1.00925i	−0.00929696	−	0.999957i	$-0.502959\pi$
$648$	−23.3659	−	10.1012i	−0.917900	−	0.396812i
$649$			1.76995i			0.0694766i
$650$	1.74087	+	0.313932i	0.0682825	+	0.0123134i
$651$	1.24159	+	1.79830i	0.0486617	+	0.0704808i
$652$	−0.0359426	−	0.0232628i	−0.00140762	−	0.000911041i
$653$	−27.9813	−	7.49758i	−1.09499	−	0.293403i	−0.334270	−	0.942478i	$-0.608490\pi$
$653$	−27.9813	−	7.49758i	−1.09499	−	0.293403i	−0.760725	+	0.649075i	$0.775156\pi$
$654$	−2.22227	+	29.3243i	−0.0868976	+	1.14667i
$655$	14.4835	−	8.14996i	0.565917	−	0.318445i
$656$	−7.66415	−	5.53235i	−0.299235	−	0.216002i
$657$	0.316095	+	0.701892i	0.0123321	+	0.0273834i
$658$	0.617437	−	0.449321i	0.0240702	−	0.0175164i
$659$	32.2837	+	18.6390i	1.25760	+	0.726073i	0.972607	−	0.232457i	$-0.0746766\pi$
$659$	32.2837	+	18.6390i	1.25760	+	0.726073i	0.284989	+	0.958531i	$0.408010\pi$
$660$	−20.4090	+	36.9361i	−0.794420	+	1.43773i
$661$	−4.60573	+	2.65912i	−0.179142	+	0.103428i	−0.586890	−	0.809667i	$-0.699648\pi$
$661$	−4.60573	+	2.65912i	−0.179142	+	0.103428i	0.407747	+	0.913095i	$0.366314\pi$
$662$	15.1777	−	34.1605i	0.589899	−	1.32768i
$663$	0.267654	+	0.750742i	0.0103948	+	0.0291564i
$664$	−10.8973	+	7.11264i	−0.422898	+	0.276024i
$665$	−1.96600	+	0.503568i	−0.0762383	+	0.0195275i
$666$	−21.7424	−	37.2249i	−0.842500	−	1.44244i
$667$	−6.07946	+	6.07946i	−0.235398	+	0.235398i
$668$	−1.13599	+	22.3341i	−0.0439529	+	0.864133i
$669$	8.65074	−	0.699388i	0.334457	−	0.0270399i
$670$	−6.25931	+	37.0501i	−0.241818	+	1.43137i
$671$	−5.20727	+	3.00642i	−0.201024	+	0.116062i
$672$	−0.849034	−	1.21966i	−0.0327522	−	0.0470493i
$673$	−39.7833	+	10.6599i	−1.53353	+	0.410909i	−0.924170	−	0.381981i	$-0.875242\pi$
$673$	−39.7833	+	10.6599i	−1.53353	+	0.410909i	−0.609364	+	0.792890i	$0.708575\pi$
$674$	14.2398	+	2.24413i	0.548498	+	0.0864406i
$675$	13.9212	−	21.9363i	0.535827	−	0.844328i
$676$	−24.6207	−	7.95786i	−0.946951	−	0.306071i
$677$	33.5676	−	8.99442i	1.29011	−	0.345684i	0.452407	−	0.891812i	$-0.350565\pi$
$677$	33.5676	−	8.99442i	1.29011	−	0.345684i	0.837702	+	0.546128i	$0.183899\pi$
$678$	16.7607	+	5.88058i	0.643690	+	0.225842i
$679$	0.558982	+	0.968185i	0.0214518	+	0.0371555i
$680$	−10.3190	−	5.37193i	−0.395716	−	0.206004i
$681$	−26.6362	+	2.15346i	−1.02070	+	0.0825209i
$682$	6.74825	+	63.7332i	0.258404	+	2.44047i
$683$	32.0794	+	32.0794i	1.22748	+	1.22748i	0.964913	+	0.262570i	$0.0845700\pi$
$683$	32.0794	+	32.0794i	1.22748	+	1.22748i	0.262570	+	0.964913i	$0.415430\pi$
$684$	5.41072	−	35.4940i	0.206884	−	1.35715i
$685$	35.5222	−	9.09860i	1.35723	−	0.347640i
$686$	−1.88492	+	2.33135i	−0.0719665	+	0.0890113i
$687$	35.0220	−	12.4860i	1.33617	−	0.476372i
$688$	19.9255	−	16.2372i	0.759653	−	0.619039i
$689$	−0.120968	+	0.0698408i	−0.00460851	+	0.00266072i
$690$	−25.7621	−	9.35983i	−0.980748	−	0.356323i
$691$	14.0756	−	24.3796i	0.535461	−	0.927445i	−0.463680	−	0.886003i	$-0.653471\pi$
$691$	14.0756	−	24.3796i	0.535461	−	0.927445i	0.999141	−	0.0414424i	$-0.0131953\pi$
$692$	−18.1570	−	35.5000i	−0.690227	−	1.34951i
$693$	1.44850	−	2.01167i	0.0550238	−	0.0764169i
$694$	−28.5947	−	4.50639i	−1.08544	−	0.171060i
$695$	−9.42533	−	16.7500i	−0.357523	−	0.635363i
$696$	7.79024	+	3.18636i	0.295288	+	0.120778i
$697$	4.19860	+	1.12501i	0.159033	+	0.0426128i
$698$	−12.0075	+	27.0252i	−0.454489	+	1.02292i
$699$	25.5582	−	17.6460i	0.966699	−	0.667433i
$700$	1.36528	−	0.660643i	0.0516027	−	0.0249700i
$701$		−	4.69063i		−	0.177163i	−0.996069	−	0.0885813i	$-0.971767\pi$
$701$		−	4.69063i		−	0.177163i	0.996069	−	0.0885813i	$-0.0282333\pi$
$702$	1.18386	−	1.40641i	0.0446820	−	0.0530814i
$703$	42.9945	−	42.9945i	1.62157	−	1.62157i
$704$	−4.75593	−	43.3232i	−0.179246	−	1.63281i
$705$	−13.7547	+	0.959148i	−0.518031	+	0.0361236i
$706$	6.13536	−	2.36056i	0.230907	−	0.0888410i
$707$	−2.07056	−	0.554805i	−0.0778714	−	0.0208656i
$708$	0.591556	+	0.957423i	0.0222321	+	0.0359822i
$709$	12.9362	−	22.4062i	0.485830	−	0.841482i	−0.514037	−	0.857768i	$-0.671851\pi$
$709$	12.9362	−	22.4062i	0.485830	−	0.841482i	0.999867	+	0.0162856i	$0.00518409\pi$
$710$	−34.9183	+	3.30745i	−1.31046	+	0.124126i
$711$	−28.9359	+	23.6368i	−1.08518	+	0.886450i
$712$	4.53853	+	13.8591i	0.170089	+	0.519394i
$713$	−40.2094	+	10.7741i	−1.50585	+	0.403493i
$714$	0.564314	+	0.385436i	0.0211189	+	0.0144246i
$715$	−2.13098	−	2.17861i	−0.0796940	−	0.0814753i
$716$	−9.22936	−	43.0943i	−0.344917	−	1.61051i
$717$	−12.5830	+	4.48609i	−0.469921	+	0.167536i
$718$	24.5542	−	2.59986i	0.916353	−	0.0970261i
$719$	39.1266			1.45917			0.729587	−	0.683888i	$-0.239712\pi$
$719$	39.1266			1.45917			0.729587	+	0.683888i	$0.239712\pi$
$720$	1.30495	+	26.8011i	0.0486328	+	0.998817i
$721$	−1.59656			−0.0594591
$722$	23.6384	−	2.50290i	0.879730	−	0.0931483i
$723$	−4.40637	−	3.74717i	−0.163874	−	0.139359i
$724$	0.822324	+	3.83964i	0.0305614	+	0.142699i
$725$	−4.45850	+	7.34263i	−0.165584	+	0.272698i
$726$	41.2418	−	19.8185i	1.53063	−	0.735532i
$727$	−20.7310	+	5.55486i	−0.768871	+	0.206018i	−0.621873	−	0.783118i	$-0.713628\pi$
$727$	−20.7310	+	5.55486i	−0.768871	+	0.206018i	−0.146998	+	0.989137i	$0.546961\pi$
$728$	0.101990	−	0.0333994i	0.00378002	−	0.00123786i
$729$	−12.5645	−	23.8984i	−0.465350	−	0.885127i
$730$	0.517103	−	0.625312i	0.0191388	−	0.0231438i
$731$	−5.90998	+	10.2364i	−0.218588	+	0.378606i
$732$	−1.81197	+	3.36666i	−0.0669723	+	0.124435i
$733$	9.40591	+	2.52031i	0.347415	+	0.0930896i	0.428307	−	0.903633i	$-0.359110\pi$
$733$	9.40591	+	2.52031i	0.347415	+	0.0930896i	−0.0808919	+	0.996723i	$0.525777\pi$
$734$	−9.80233	+	3.77143i	−0.361811	+	0.139206i
$735$	25.5513	−	8.79250i	0.942474	−	0.324316i
$736$	27.3157	−	7.43205i	1.00687	−	0.273949i
$737$	45.7739	−	45.7739i	1.68610	−	1.68610i
$738$	−2.64355	−	9.67088i	−0.0973105	−	0.355990i
$739$			27.9419i			1.02786i	0.857833	+	0.513929i	$0.171810\pi$
$739$			27.9419i			1.02786i	−0.857833	+	0.513929i	$0.828190\pi$
$740$	−25.1105	+	37.8732i	−0.923080	+	1.39225i
$741$	2.34267	+	1.11127i	0.0860601	+	0.0408236i
$742$	−0.0486285	+	0.109448i	−0.00178521	+	0.00401797i
$743$	4.34473	+	1.16417i	0.159393	+	0.0427091i	0.337633	−	0.941278i	$-0.390374\pi$
$743$	4.34473	+	1.16417i	0.159393	+	0.0427091i	−0.178240	+	0.983987i	$0.557040\pi$
$744$	24.9514	+	32.2199i	0.914763	+	1.18124i
$745$	25.0414	−	14.0910i	0.917446	−	0.516254i
$746$	4.20265	+	0.662318i	0.153870	+	0.0242492i
$747$	−13.7329	−	1.38421i	−0.502461	−	0.0506457i
$748$	9.12644	+	17.8437i	0.333696	+	0.652429i
$749$	−0.271048	+	0.469469i	−0.00990388	+	0.0171540i
$750$	−27.2242	−	2.97355i	−0.994088	−	0.108579i
$751$	5.53469	−	3.19545i	0.201964	−	0.116604i	−0.395607	−	0.918420i	$-0.629466\pi$
$751$	5.53469	−	3.19545i	0.201964	−	0.116604i	0.597571	+	0.801816i	$0.296133\pi$
$752$	11.0391	−	8.99572i	0.402554	−	0.328040i
$753$	−1.60511	+	8.76464i	−0.0584935	+	0.319401i
$754$	−0.382155	+	0.472665i	−0.0139173	+	0.0172135i
$755$	−25.3221	+	42.7608i	−0.921566	+	1.55622i
$756$	0.111195	−	1.57229i	0.00404413	−	0.0571838i
$757$	−29.6494	−	29.6494i	−1.07763	−	1.07763i	−0.996722	−	0.0809055i	$-0.974219\pi$
$757$	−29.6494	−	29.6494i	−1.07763	−	1.07763i	−0.0809055	−	0.996722i	$-0.525781\pi$
$758$	0.160003	+	1.51114i	0.00581158	+	0.0548869i
$759$	26.8293	+	38.8591i	0.973842	+	1.41050i
$760$	−36.0947	+	11.3800i	−1.30929	+	0.412797i
$761$	14.3909	+	24.9258i	0.521670	+	0.903559i	0.999682	+	0.0252059i	$0.00802415\pi$
$761$	14.3909	+	24.9258i	0.521670	+	0.903559i	−0.478012	+	0.878353i	$0.658643\pi$
$762$	−28.3619	+	24.3661i	−1.02744	+	0.882690i
$763$	−1.75892	+	0.471300i	−0.0636770	+	0.0170622i
$764$	3.70971	+	1.19905i	0.134213	+	0.0433799i
$765$	−4.94219	−	11.3063i	−0.178685	−	0.408779i
$766$	16.4604	+	2.59408i	0.594738	+	0.0937279i
$767$	−0.0785059	+	0.0210356i	−0.00283469	+	0.000759552i
$768$	−17.0522	−	21.8454i	−0.615319	−	0.788278i
$769$	11.7712	−	6.79611i	0.424481	−	0.245074i	−0.272512	−	0.962152i	$-0.587854\pi$
$769$	11.7712	−	6.79611i	0.424481	−	0.245074i	0.696993	+	0.717078i	$0.254521\pi$
$770$	−2.57648	−	0.435275i	−0.0928499	−	0.0156862i
$771$	−6.05853	+	12.7720i	−0.218193	+	0.459972i
$772$	−1.15764	+	22.7597i	−0.0416643	+	0.819138i
$773$	16.8783	−	16.8783i	0.607070	−	0.607070i	−0.335110	−	0.942179i	$-0.608773\pi$
$773$	16.8783	−	16.8783i	0.607070	−	0.607070i	0.942179	+	0.335110i	$0.108773\pi$
$774$	27.2624	−	0.137235i	0.979927	−	0.00493279i
$775$	−36.4705	+	19.9948i	−1.31006	+	0.718235i
$776$	11.3951	+	17.4584i	0.409059	+	0.626722i
$777$	1.72926	−	2.03346i	0.0620368	−	0.0729501i
$778$	1.97026	−	4.43446i	0.0706372	−	0.158983i
$779$	12.2462	−	7.07033i	0.438765	−	0.253321i
$780$	−1.88085	−	0.466260i	−0.0673454	−	0.0166948i
$781$	52.3305	+	30.2130i	1.87253	+	1.08111i
$782$	−10.5258	+	7.65985i	−0.376403	+	0.273916i
$783$	4.30980	+	7.81801i	0.154020	+	0.279393i
$784$	−16.3343	+	22.6285i	−0.583367	+	0.808159i
$785$	−42.0185	−	11.7581i	−1.49971	−	0.419663i
$786$	−16.4090	+	7.88522i	−0.585289	+	0.281257i
$787$	−2.85024	−	0.763720i	−0.101600	−	0.0272237i	0.207661	−	0.978201i	$-0.433415\pi$
$787$	−2.85024	−	0.763720i	−0.101600	−	0.0272237i	−0.309261	+	0.950977i	$0.600082\pi$
$788$	17.8465	+	11.5506i	0.635754	+	0.411473i
$789$	18.5617	−	1.50066i	0.660815	−	0.0534250i
$790$	35.8124	+	16.3880i	1.27415	+	0.583058i
$791$			1.09984i			0.0391059i
$792$	24.9218	−	38.9341i	0.885557	−	1.38346i
$793$	−0.195237	−	0.195237i	−0.00693307	−	0.00693307i
$794$	−22.3784	−	18.0932i	−0.794180	−	0.642102i
$795$	1.79302	−	1.20890i	0.0635919	−	0.0428754i
$796$	−32.2115	+	6.89863i	−1.14171	+	0.244515i
$797$	−11.7949	+	44.0192i	−0.417797	+	1.55924i	0.361370	+	0.932423i	$0.382309\pi$
$797$	−11.7949	+	44.0192i	−0.417797	+	1.55924i	−0.779167	+	0.626817i	$0.784358\pi$
$798$	2.18476	−	0.411482i	0.0773396	−	0.0145663i
$799$	−3.27424	+	5.67114i	−0.115834	+	0.200631i
$800$	24.7489	−	13.6927i	0.875007	−	0.484110i
$801$	−5.48161	+	14.4641i	−0.193683	+	0.511064i
$802$	3.53715	+	4.86059i	0.124901	+	0.171633i
$803$	−1.35028	+	0.361807i	−0.0476504	+	0.0127679i
$804$	9.46193	−	40.0592i	0.333697	−	1.41278i
$805$	0.0187568	−	1.69710i	0.000661091	−	0.0598150i
$806$	−2.74668	+	1.05678i	−0.0967476	+	0.0372234i
$807$	−2.62245	+	14.3198i	−0.0923147	+	0.504081i
$808$	−39.1201	−	8.22083i	−1.37624	−	0.289208i
$809$		−	39.3114i		−	1.38212i	−0.722800	−	0.691058i	$-0.757145\pi$
$809$		−	39.3114i		−	1.38212i	0.722800	−	0.691058i	$-0.242855\pi$
$810$	−16.7690	+	22.9956i	−0.589204	+	0.807985i
$811$	−11.7992			−0.414327			−0.207164	−	0.978306i	$-0.566423\pi$
$811$	−11.7992			−0.414327			−0.207164	+	0.978306i	$0.566423\pi$
$812$	−0.0264739	+	0.520487i	−0.000929050	+	0.0182655i
$813$	38.4153	+	7.03518i	1.34728	+	0.246735i
$814$	73.0645	−	28.1114i	2.56091	−	0.985304i
$815$	−0.0342193	+	0.0334712i	−0.00119865	+	0.00117245i
$816$	10.9005	+	6.60196i	0.381595	+	0.231115i
$817$	9.95226	+	37.1423i	0.348185	+	1.29945i
$818$	−0.946783	+	0.688993i	−0.0331035	+	0.0240901i
$819$	0.106442	+	0.0403395i	0.00371940	+	0.00140958i
$820$	−7.92046	+	6.99635i	−0.276594	+	0.244323i
$821$	23.5009	+	13.5683i	0.820187	+	0.473535i	0.850481	−	0.526006i	$-0.176311\pi$
$821$	23.5009	+	13.5683i	0.820187	+	0.473535i	−0.0302939	+	0.999541i	$0.509644\pi$
$822$	−39.4748	+	7.43477i	−1.37684	+	0.259317i
$823$	4.25879	+	1.14114i	0.148452	+	0.0397776i	0.332280	−	0.943181i	$-0.392182\pi$
$823$	4.25879	+	1.14114i	0.148452	+	0.0397776i	−0.183828	+	0.982958i	$0.558849\pi$
$824$	−29.7287	+	1.62689i	−1.03565	+	0.0566754i
$825$	35.2573	+	31.3517i	1.22750	+	1.09152i
$826$	−0.0438135	+	0.0541904i	−0.00152447	+	0.00188553i
$827$	−32.5850	+	32.5850i	−1.13309	+	1.13309i	−0.143432	+	0.989660i	$0.545814\pi$
$827$	−32.5850	+	32.5850i	−1.13309	+	1.13309i	−0.989660	+	0.143432i	$0.954186\pi$
$828$	27.5004	+	12.0532i	0.955706	+	0.418878i
$829$	−38.8343			−1.34877			−0.674385	−	0.738380i	$-0.735591\pi$
$829$	−38.8343			−1.34877			−0.674385	+	0.738380i	$0.735591\pi$
$830$	5.07401	+	13.6357i	0.176121	+	0.473300i
$831$	0.957704	+	11.8459i	0.0332224	+	0.410928i
$832$	1.86507	−	0.725839i	0.0646598	−	0.0251639i
$833$	3.32160	−	12.3964i	0.115087	−	0.429509i
$834$	9.11916	+	18.9768i	0.315771	+	0.657113i
$835$	24.0777	+	6.73765i	0.833242	+	0.233166i
$836$	62.0408	+	20.0527i	2.14572	+	0.693537i
$837$	−0.855093	+	43.2152i	−0.0295563	+	1.49374i
$838$	−2.83386	+	2.06225i	−0.0978940	+	0.0712394i
$839$	8.65028	−	14.9827i	0.298641	−	0.517261i	−0.677184	−	0.735813i	$-0.736800\pi$
$839$	8.65028	−	14.9827i	0.298641	−	0.517261i	0.975825	+	0.218552i	$0.0701334\pi$
$840$	−1.53918	+	0.625662i	−0.0531067	+	0.0215874i
$841$	13.0242	+	22.5585i	0.449109	+	0.777879i
$842$	36.6128	+	16.2673i	1.26176	+	0.560608i
$843$	39.9978	+	34.0142i	1.37760	+	1.17151i
$844$	−26.7029	−	29.5649i	−0.919153	−	1.01767i
$845$	−14.7405	+	24.8918i	−0.507087	+	0.856304i
$846$	15.1039	−	0.0760304i	0.519282	−	0.00261398i
$847$	2.00340	+	2.00340i	0.0688377	+	0.0688377i
$848$	−0.793958	+	2.08753i	−0.0272646	+	0.0716860i
$849$	1.57747	+	0.748293i	0.0541388	+	0.0256814i
$850$	−8.39915	+	9.93120i	−0.288088	+	0.340637i
$851$	25.4244	+	44.0363i	0.871537	+	1.50955i
$852$	38.4051	−	1.14681i	1.31574	−	0.0392889i
$853$	−4.51779	−	16.8606i	−0.154686	−	0.577296i	−0.999132	−	0.0416556i	$-0.986737\pi$
$853$	−4.51779	−	16.8606i	−0.154686	−	0.577296i	0.844446	−	0.535641i	$-0.179930\pi$
$854$	−0.233852	−	0.0368539i	−0.00800224	−	0.00126111i
$855$	−37.3772	−	14.6396i	−1.27827	−	0.500665i
$856$	−4.56865	+	9.01792i	−0.156153	+	0.308226i
$857$	−10.6605	−	39.7856i	−0.364156	−	1.35905i	−0.868561	−	0.495582i	$-0.834955\pi$
$857$	−10.6605	−	39.7856i	−0.364156	−	1.35905i	0.504405	−	0.863467i	$-0.331712\pi$
$858$	2.17547	+	2.53223i	0.0742694	+	0.0864490i
$859$	5.92539	−	3.42103i	0.202172	−	0.116724i	−0.395496	−	0.918468i	$-0.629427\pi$
$859$	5.92539	−	3.42103i	0.202172	−	0.116724i	0.597668	+	0.801744i	$0.296094\pi$
$860$	−12.8024	−	25.7282i	−0.436558	−	0.877325i
$861$	0.510858	−	0.352709i	0.0174100	−	0.0120203i
$862$	−2.12298	−	20.0503i	−0.0723090	−	0.682915i
$863$	−14.4519	+	14.4519i	−0.491949	+	0.491949i	−0.908920	−	0.416971i	$-0.863092\pi$
$863$	−14.4519	+	14.4519i	−0.491949	+	0.491949i	0.416971	+	0.908920i	$0.363092\pi$
$864$	0.468347	−	29.3901i	0.0159335	−	0.999873i
$865$	−43.1862	+	11.0616i	−1.46837	+	0.376107i
$866$	−38.6943	−	31.2847i	−1.31488	−	1.06310i
$867$	23.1987	+	4.24848i	0.787868	+	0.144286i
$868$	−1.37105	+	2.11836i	−0.0465363	+	0.0719019i
$869$	−33.9251	−	58.7601i	−1.15083	−	1.99330i
$870$	5.39299	−	7.71145i	0.182840	−	0.261443i
$871$	2.57431	+	1.48628i	0.0872272	+	0.0503607i
$872$	−32.2716	+	10.5681i	−1.09285	+	0.357883i
$873$	−2.21763	+	22.0013i	−0.0750553	+	0.744632i
$874$	−6.59276	+	41.8335i	−0.223003	+	1.41504i
$875$	−0.384352	−	1.65161i	−0.0129935	−	0.0558347i
$876$	−0.609487	+	0.647007i	−0.0205927	+	0.0218603i
$877$	10.6489	−	39.7422i	0.359587	−	1.34200i	−0.515025	−	0.857175i	$-0.672217\pi$
$877$	10.6489	−	39.7422i	0.359587	−	1.34200i	0.874612	−	0.484823i	$-0.161116\pi$
$878$	5.24728	−	11.8100i	0.177087	−	0.398570i
$879$	−10.9571	+	23.0987i	−0.369575	+	0.779100i
$880$	−48.4188	−	5.47960i	−1.63220	−	0.184717i
$881$	11.9791			0.403586			0.201793	−	0.979428i	$-0.435323\pi$
$881$	11.9791			0.403586			0.201793	+	0.979428i	$0.435323\pi$
$882$	−28.5533	+	7.80510i	−0.961441	+	0.262811i
$883$	−10.5762	−	10.5762i	−0.355917	−	0.355917i	0.506388	−	0.862305i	$-0.330980\pi$
$883$	−10.5762	−	10.5762i	−0.355917	−	0.355917i	−0.862305	+	0.506388i	$0.830980\pi$
$884$	−0.682987	+	0.616872i	−0.0229713	+	0.0207476i
$885$	1.18980	−	0.409423i	0.0399946	−	0.0137626i
$886$	6.99476	−	2.69122i	0.234993	−	0.0904132i
$887$	9.91772	−	37.0134i	0.333004	−	1.24279i	−0.573012	−	0.819547i	$-0.694225\pi$
$887$	9.91772	−	37.0134i	0.333004	−	1.24279i	0.906016	−	0.423242i	$-0.139108\pi$
$888$	30.1275	−	39.6261i	1.01101	−	1.32977i
$889$	−2.00507	−	1.15763i	−0.0672480	−	0.0388256i
$890$	16.2320	−	1.53749i	0.544099	−	0.0515369i
$891$	46.5008	−	15.5486i	1.55783	−	0.520899i
$892$	4.56346	+	8.92230i	0.152796	+	0.298741i
$893$	5.51373	+	20.5775i	0.184510	+	0.688601i
$894$	−28.3705	+	13.6333i	−0.948853	+	0.455964i
$895$	−49.2704	−	0.544549i	−1.64693	−	0.0182023i
$896$	0.926815	−	1.44415i	0.0309627	−	0.0482457i
$897$	−1.40473	+	1.65185i	−0.0469026	+	0.0551535i
$898$	−0.719245	−	6.79284i	−0.0240015	−	0.226680i
$899$		−	14.2914i		−	0.476645i
$900$	29.5502	+	5.17536i	0.985007	+	0.172512i
$901$		−	1.02705i		−	0.0342160i
$902$	18.1052	−	1.91703i	0.602838	−	0.0638302i
$903$	0.566892	+	1.59007i	0.0188650	+	0.0529143i
$904$	1.12073	+	20.4796i	0.0372750	+	0.681140i
$905$	4.38993	+	0.0485186i	0.145926	+	0.00161281i
$906$	30.7044	−	44.9541i	1.02009	−	1.49350i
$907$	−7.15665	−	26.7090i	−0.237633	−	0.886857i	−0.976944	−	0.213494i	$-0.931516\pi$
$907$	−7.15665	−	26.7090i	−0.237633	−	0.886857i	0.739312	−	0.673363i	$-0.235151\pi$
$908$	−14.0512	−	27.4724i	−0.466306	−	0.911703i
$909$	−26.8231	−	32.8365i	−0.889665	−	1.08912i
$910$	−0.0113145	−	0.119453i	−0.000375073	−	0.00395982i
$911$	44.5901	+	25.7441i	1.47733	+	0.852939i	0.999672	−	0.0256040i	$-0.00815089\pi$
$911$	44.5901	+	25.7441i	1.47733	+	0.852939i	0.477662	+	0.878543i	$0.341484\pi$
$912$	40.2619	−	9.88825i	1.33321	−	0.327433i
$913$	6.48731	−	24.2110i	0.214699	−	0.801266i
$914$	−2.92379	−	7.59923i	−0.0967103	−	0.251360i
$915$	3.22552	+	2.80500i	0.106632	+	0.0927304i
$916$	28.7770	+	31.8613i	0.950819	+	1.05273i
$917$	−0.797098	−	0.797098i	−0.0263225	−	0.0263225i
$918$	4.60324	+	12.7090i	0.151930	+	0.419459i
$919$	−35.6076			−1.17459			−0.587294	−	0.809374i	$-0.699807\pi$
$919$	−35.6076			−1.17459			−0.587294	+	0.809374i	$0.699807\pi$
$920$	−1.38008	−	31.6200i	−0.0454999	−	1.04248i
$921$	−22.6592	−	32.8193i	−0.746647	−	1.08143i
$922$	45.5553	+	20.2405i	1.50029	+	0.666586i
$923$	−0.718155	+	2.68019i	−0.0236384	+	0.0882196i
$924$	2.78573	+	0.657986i	0.0916439	+	0.0216462i
$925$	35.1218	+	36.7097i	1.15480	+	1.20701i
$926$	0.740016	+	0.116623i	0.0243184	+	0.00383247i
$927$	−25.6271	−	18.4527i	−0.841703	−	0.606067i
$928$	0.0374183	+	9.71868i	0.00122832	+	0.319031i
$929$	−12.7939	−	7.38654i	−0.419753	−	0.242345i	0.275219	−	0.961382i	$-0.411250\pi$
$929$	−12.7939	−	7.38654i	−0.419753	−	0.242345i	−0.694972	+	0.719037i	$0.744583\pi$
$930$	41.2818	−	19.2790i	1.35368	−	0.632184i
$931$	−20.8752	−	36.1569i	−0.684157	−	1.18499i
$932$	30.1071	+	19.4859i	0.986189	+	0.638282i
$933$	−9.45498	−	26.5202i	−0.309542	−	0.868233i
$934$	18.6423	−	23.0575i	0.609993	−	0.754466i
$935$	21.7071	−	5.56001i	0.709897	−	0.181832i
$936$	2.02311	+	0.642676i	0.0661275	+	0.0210065i
$937$	−21.2523	+	21.2523i	−0.694283	+	0.694283i	−0.963171	−	0.268889i	$-0.913344\pi$
$937$	−21.2523	+	21.2523i	−0.694283	+	0.694283i	0.268889	+	0.963171i	$0.413344\pi$
$938$	2.53455	−	0.268365i	0.0827559	−	0.00876242i
$939$	−2.09290	−	25.8872i	−0.0682994	−	0.844796i
$940$	−7.09276	−	14.2539i	−0.231340	−	0.464911i
$941$	2.53780	−	1.46520i	0.0827300	−	0.0477642i	−0.458064	−	0.888919i	$-0.651457\pi$
$941$	2.53780	−	1.46520i	0.0827300	−	0.0477642i	0.540794	+	0.841155i	$0.318124\pi$
$942$	45.1017	+	15.8242i	1.46949	+	0.515581i
$943$	3.06068	+	11.4226i	0.0996696	+	0.371972i
$944$	−0.760607	+	1.05370i	−0.0247557	+	0.0342949i
$945$	−1.68735	−	0.508374i	−0.0548895	−	0.0165374i
$946$	−7.70720	+	48.9050i	−0.250583	+	1.59004i
$947$	10.8646	+	40.5471i	0.353051	+	1.31760i	0.882920	+	0.469524i	$0.155575\pi$
$947$	10.8646	+	40.5471i	0.353051	+	1.31760i	−0.529869	+	0.848080i	$0.677759\pi$
$948$	−37.9901	−	20.4467i	−1.23386	−	0.664078i
$949$	−0.0320958	−	0.0555916i	−0.00104187	−	0.00180458i
$950$	3.52426	+	42.1663i	0.114342	+	1.36805i
$951$	−0.436800	−	5.40279i	−0.0141642	−	0.175197i
$952$	−0.162280	+	0.772235i	−0.00525952	+	0.0250283i
$953$	8.51733	+	8.51733i	0.275904	+	0.275904i	0.831471	−	0.555568i	$-0.187499\pi$
$953$	8.51733	+	8.51733i	0.275904	+	0.275904i	−0.555568	+	0.831471i	$0.687499\pi$
$954$	−2.04553	+	1.19476i	−0.0662266	+	0.0386817i
$955$	2.22101	−	3.75056i	0.0718702	−	0.121365i
$956$	−10.3392	−	11.4474i	−0.334395	−	0.370235i
$957$	−15.2702	+	5.44414i	−0.493617	+	0.175984i
$958$	−0.476450	+	1.07235i	−0.0153934	+	0.0346459i
$959$	−1.24362	−	2.15402i	−0.0401587	−	0.0695569i
$960$	−28.0227	+	13.2185i	−0.904428	+	0.426626i
$961$	19.0979	−	33.0785i	0.616060	−	1.06705i
$962$	2.11524	+	2.90667i	0.0681981	+	0.0937147i
$963$	−9.77672	+	4.40292i	−0.315050	+	0.141882i
$964$	2.05416	−	6.35533i	0.0661600	−	0.204692i
$965$	24.5364	+	6.86603i	0.789855	+	0.221025i
$966$	−0.140492	+	1.85388i	−0.00452025	+	0.0596477i
$967$	−6.47940	+	24.1815i	−0.208364	+	0.777623i	0.780034	+	0.625737i	$0.215202\pi$
$967$	−6.47940	+	24.1815i	−0.208364	+	0.777623i	−0.988398	+	0.151887i	$0.951465\pi$
$968$	39.3457	+	35.2628i	1.26462	+	1.13339i
$969$	−15.6888	+	10.8320i	−0.503998	+	0.347973i
$970$	21.8455	−	8.12900i	0.701417	−	0.261006i
$971$	−33.1458			−1.06370			−0.531850	−	0.846839i	$-0.678503\pi$
$971$	−33.1458			−1.06370			−0.531850	+	0.846839i	$0.678503\pi$
$972$	19.9571	−	23.9524i	0.640123	−	0.768272i
$973$	−0.921835	+	0.921835i	−0.0295527	+	0.0295527i
$974$	−32.6289	−	26.3808i	−1.04550	−	0.845295i
$975$	−0.971572	+	1.93644i	−0.0311152	+	0.0620158i
$976$	−4.39198	−	0.447943i	−0.140584	−	0.0143383i
$977$	−44.2245	−	11.8499i	−1.41487	−	0.379113i	−0.531208	−	0.847242i	$-0.678262\pi$
$977$	−44.2245	−	11.8499i	−1.41487	−	0.379113i	−0.883660	+	0.468129i	$0.844928\pi$
$978$	0.0397737	−	0.0341701i	0.00127182	−	0.00109264i
$979$	−24.3263	−	14.0448i	−0.777470	−	0.448873i
$980$	20.6568	+	23.3852i	0.659856	+	0.747013i
$981$	−33.6802	−	12.7641i	−1.07533	−	0.407527i
$982$	−20.9213	−	28.7491i	−0.667625	−	0.917420i
$983$	8.59814	+	32.0887i	0.274238	+	1.02347i	0.956350	+	0.292223i	$0.0943949\pi$
$983$	8.59814	+	32.0887i	0.274238	+	1.02347i	−0.682112	+	0.731248i	$0.738938\pi$
$984$	9.15299	−	7.08815i	0.291787	−	0.225962i
$985$	16.9908	−	16.6194i	0.541373	−	0.529537i
$986$	−1.60484	−	4.17116i	−0.0511086	−	0.132837i
$987$	0.314069	+	0.880930i	0.00999692	+	0.0280403i
$988$	−0.152089	+	2.99013i	−0.00483860	+	0.0951289i
$989$	−32.1572			−1.02254
$990$	−36.3253	−	36.7651i	−1.15449	−	1.16847i
$991$		−	50.9203i		−	1.61754i	−0.588128	−	0.808768i	$-0.700135\pi$
$991$		−	50.9203i		−	1.61754i	0.588128	−	0.808768i	$-0.299865\pi$
$992$	−23.3709	+	40.8419i	−0.742027	+	1.29673i
$993$	34.8759	+	29.6585i	1.10675	+	0.941183i
$994$	0.854303	+	2.22042i	0.0270968	+	0.0704275i
$995$	−0.407032	+	36.8279i	−0.0129038	+	1.16752i
$996$	−4.58265	−	15.2647i	−0.145207	−	0.483681i
$997$	−49.9272	+	13.3780i	−1.58121	+	0.423684i	−0.939301	−	0.343095i	$-0.888525\pi$
$997$	−49.9272	+	13.3780i	−1.58121	+	0.423684i	−0.641911	+	0.766779i	$0.721858\pi$
$998$	33.7403	−	24.5535i	1.06803	−	0.777228i
$999$	51.2594	−	12.6536i	1.62177	−	0.400341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.43.3	✓	272
5.2	odd	4	inner	360.2.bo.a.187.33	yes	272
8.3	odd	2	inner	360.2.bo.a.43.61	yes	272
9.4	even	3	inner	360.2.bo.a.283.44	yes	272
40.27	even	4	inner	360.2.bo.a.187.44	yes	272
45.22	odd	12	inner	360.2.bo.a.67.61	yes	272
72.67	odd	6	inner	360.2.bo.a.283.33	yes	272
360.67	even	12	inner	360.2.bo.a.67.3	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.3	✓	272	1.1	even	1	trivial
360.2.bo.a.43.61	yes	272	8.3	odd	2	inner
360.2.bo.a.67.3	yes	272	360.67	even	12	inner
360.2.bo.a.67.61	yes	272	45.22	odd	12	inner
360.2.bo.a.187.33	yes	272	5.2	odd	4	inner
360.2.bo.a.187.44	yes	272	40.27	even	4	inner
360.2.bo.a.283.33	yes	272	72.67	odd	6	inner
360.2.bo.a.283.44	yes	272	9.4	even	3	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40635 + 0.148909i) q^{2} +(0.312010 - 1.70372i) q^{3} +(1.95565 - 0.418836i) q^{4} +(0.0247121 - 2.23593i) q^{5} +(-0.185098 + 2.44249i) q^{6} +(-0.146504 + 0.0392556i) q^{7} +(-2.68797 + 0.880244i) q^{8} +(-2.80530 - 1.06315i) q^{9} +O(q^{10})\)	\(q+(-1.40635 + 0.148909i) q^{2} +(0.312010 - 1.70372i) q^{3} +(1.95565 - 0.418836i) q^{4} +(0.0247121 - 2.23593i) q^{5} +(-0.185098 + 2.44249i) q^{6} +(-0.146504 + 0.0392556i) q^{7} +(-2.68797 + 0.880244i) q^{8} +(-2.80530 - 1.06315i) q^{9} +(0.298195 + 3.14819i) q^{10} +(2.72397 - 4.71805i) q^{11} +(-0.103395 - 3.46256i) q^{12} +(0.241643 + 0.0647480i) q^{13} +(0.200191 - 0.0770229i) q^{14} +(-3.80168 - 0.739735i) q^{15} +(3.64915 - 1.63819i) q^{16} +(-1.30067 + 1.30067i) q^{17} +(4.10355 + 1.07743i) q^{18} +5.98400i q^{19} +(-0.888160 - 4.38306i) q^{20} +(0.0211698 + 0.261849i) q^{21} +(-3.12830 + 7.04087i) q^{22} +(-4.83379 - 1.29521i) q^{23} +(0.661014 + 4.85418i) q^{24} +(-4.99878 - 0.110509i) q^{25} +(-0.349476 - 0.0550758i) q^{26} +(-2.68659 + 4.44772i) q^{27} +(-0.270069 + 0.138131i) q^{28} +(0.859025 - 1.48787i) q^{29} +(5.45666 + 0.474225i) q^{30} +(7.20394 - 4.15920i) q^{31} +(-4.88805 + 2.84727i) q^{32} +(-7.18832 - 6.11295i) q^{33} +(1.63552 - 2.02288i) q^{34} +(0.0841524 + 0.328543i) q^{35} +(-5.93148 - 0.904197i) q^{36} +(-7.18491 - 7.18491i) q^{37} +(-0.891069 - 8.41562i) q^{38} +(0.185707 - 0.391489i) q^{39} +(1.90174 + 6.03186i) q^{40} +(-1.18154 - 2.04648i) q^{41} +(-0.0687637 - 0.365100i) q^{42} +(6.20694 - 1.66314i) q^{43} +(3.35105 - 10.3678i) q^{44} +(-2.44646 + 6.24619i) q^{45} +(6.99089 + 1.10173i) q^{46} +(3.43876 - 0.921412i) q^{47} +(-1.65245 - 6.72826i) q^{48} +(-6.04226 + 3.48850i) q^{49} +(7.04650 - 0.588946i) q^{50} +(1.81015 + 2.62180i) q^{51} +(0.499688 + 0.0254159i) q^{52} +(-0.394816 + 0.394816i) q^{53} +(3.11599 - 6.65512i) q^{54} +(-10.4819 - 6.20720i) q^{55} +(0.359243 - 0.234477i) q^{56} +(10.1950 + 1.86707i) q^{57} +(-0.986534 + 2.22039i) q^{58} +(-0.281358 + 0.162442i) q^{59} +(-7.74460 + 0.145616i) q^{60} +(-0.955824 - 0.551845i) q^{61} +(-9.51194 + 6.92203i) q^{62} +(0.452722 + 0.0456322i) q^{63} +(6.45034 - 4.73213i) q^{64} +(0.150744 - 0.538696i) q^{65} +(11.0196 + 7.52656i) q^{66} +(11.4774 + 3.07537i) q^{67} +(-1.99889 + 3.08843i) q^{68} +(-3.71486 + 7.83130i) q^{69} +(-0.167271 - 0.449516i) q^{70} +11.0915i q^{71} +(8.47639 + 0.388372i) q^{72} +(-0.181440 - 0.181440i) q^{73} +(11.1744 + 9.03461i) q^{74} +(-1.74794 + 8.48202i) q^{75} +(2.50631 + 11.7026i) q^{76} +(-0.213862 + 0.798144i) q^{77} +(-0.202874 + 0.578224i) q^{78} +(6.22715 - 10.7857i) q^{79} +(-3.57271 - 8.19974i) q^{80} +(6.73941 + 5.96492i) q^{81} +(1.96640 + 2.70214i) q^{82} +(4.44406 - 1.19078i) q^{83} +(0.151073 + 0.503219i) q^{84} +(2.87607 + 2.94035i) q^{85} +(-8.48148 + 3.26323i) q^{86} +(-2.26689 - 1.92777i) q^{87} +(-3.16890 + 15.0797i) q^{88} -5.15599i q^{89} +(2.51047 - 9.14863i) q^{90} -0.0379433 q^{91} +(-9.99570 - 0.508418i) q^{92} +(-4.83839 - 13.5712i) q^{93} +(-4.69890 + 1.80789i) q^{94} +(13.3798 + 0.147877i) q^{95} +(3.32582 + 9.21623i) q^{96} +(-1.90774 - 7.11977i) q^{97} +(7.97807 - 5.80580i) q^{98} +(-12.6576 + 10.3396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

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