LMFDB - Embedded newform 572.2.bk.a.31.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(31,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 12, 15]))

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

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

chi := DirichletCharacter("572.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			31.14
Character	$\chi$	$=$	572.31
Dual form			572.2.bk.a.203.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25415 - 0.653531i) q^{2} +(0.738802 + 1.01687i) q^{3} +(1.14579 + 1.63925i) q^{4} +(-3.61425 - 1.84155i) q^{5} +(-0.262011 - 1.75814i) q^{6} +(-0.636645 + 0.100835i) q^{7} +(-0.365696 - 2.80469i) q^{8} +(0.438847 - 1.35063i) q^{9} +O(q^{10})$	\(q+(-1.25415 - 0.653531i) q^{2} +(0.738802 + 1.01687i) q^{3} +(1.14579 + 1.63925i) q^{4} +(-3.61425 - 1.84155i) q^{5} +(-0.262011 - 1.75814i) q^{6} +(-0.636645 + 0.100835i) q^{7} +(-0.365696 - 2.80469i) q^{8} +(0.438847 - 1.35063i) q^{9} +(3.32931 + 4.67161i) q^{10} +(1.27580 + 3.06143i) q^{11} +(-0.820401 + 2.37621i) q^{12} +(-0.569996 + 3.56021i) q^{13} +(0.864348 + 0.289605i) q^{14} +(-0.797589 - 5.03578i) q^{15} +(-1.37431 + 3.75650i) q^{16} +(2.90053 - 0.942440i) q^{17} +(-1.43306 + 1.40710i) q^{18} +(1.77622 + 0.281325i) q^{19} +(-1.12241 - 8.03472i) q^{20} +(-0.572891 - 0.572891i) q^{21} +(0.400692 - 4.67327i) q^{22} +3.31914 q^{23} +(2.58184 - 2.44398i) q^{24} +(6.73256 + 9.26658i) q^{25} +(3.04157 - 4.09254i) q^{26} +(5.28387 - 1.71683i) q^{27} +(-0.894757 - 0.928087i) q^{28} +(3.02044 + 2.19447i) q^{29} +(-2.29074 + 6.83688i) q^{30} +(-4.53314 + 2.30975i) q^{31} +(4.17858 - 3.81306i) q^{32} +(-2.17052 + 3.55912i) q^{33} +(-4.25362 - 0.713625i) q^{34} +(2.48669 + 0.807973i) q^{35} +(2.71686 - 0.828164i) q^{36} +(1.20916 + 7.63435i) q^{37} +(-2.04379 - 1.51364i) q^{38} +(-4.04140 + 2.05068i) q^{39} +(-3.84326 + 10.8103i) q^{40} +(0.921914 - 5.82073i) q^{41} +(0.344090 + 1.09289i) q^{42} +7.77044 q^{43} +(-3.55666 + 5.59912i) q^{44} +(-4.07336 + 4.07336i) q^{45} +(-4.16271 - 2.16916i) q^{46} +(-1.37914 + 8.70752i) q^{47} +(-4.83523 + 1.37781i) q^{48} +(-6.26225 + 2.03473i) q^{49} +(-2.38766 - 16.0216i) q^{50} +(3.10126 + 2.25320i) q^{51} +(-6.48919 + 3.14490i) q^{52} +(-2.08960 + 6.43114i) q^{53} +(-7.74877 - 1.30000i) q^{54} +(1.02672 - 13.4142i) q^{55} +(0.515628 + 1.74871i) q^{56} +(1.02620 + 2.01403i) q^{57} +(-2.35393 - 4.72615i) q^{58} +(4.40916 - 0.698342i) q^{59} +(7.34105 - 7.07742i) q^{60} +(0.113802 + 0.350246i) q^{61} +(7.19474 + 0.0657708i) q^{62} +(-0.143199 + 0.904123i) q^{63} +(-7.73253 + 2.05132i) q^{64} +(8.61642 - 11.8178i) q^{65} +(5.04816 - 3.04517i) q^{66} +(11.0749 + 11.0749i) q^{67} +(4.86831 + 3.67487i) q^{68} +(2.45219 + 3.37515i) q^{69} +(-2.59065 - 2.63845i) q^{70} +(5.34642 - 10.4929i) q^{71} +(-3.94858 - 0.736908i) q^{72} +(-1.21729 - 7.68566i) q^{73} +(3.47281 - 10.3649i) q^{74} +(-4.44891 + 13.6923i) q^{75} +(1.57401 + 3.23401i) q^{76} +(-1.12093 - 1.82040i) q^{77} +(6.40871 + 0.0693206i) q^{78} +(6.12212 + 1.98920i) q^{79} +(11.8849 - 11.0460i) q^{80} +(2.20279 + 1.60042i) q^{81} +(-4.96025 + 6.69758i) q^{82} +(0.306517 - 0.601574i) q^{83} +(0.282699 - 1.59553i) q^{84} +(-12.2188 - 1.93527i) q^{85} +(-9.74531 - 5.07822i) q^{86} +4.69269i q^{87} +(8.11979 - 4.69777i) q^{88} +(-6.49354 - 6.49354i) q^{89} +(7.77068 - 2.44655i) q^{90} +(0.00389267 - 2.32406i) q^{91} +(3.80305 + 5.44092i) q^{92} +(-5.69782 - 2.90318i) q^{93} +(7.42028 - 10.0192i) q^{94} +(-5.90161 - 4.28777i) q^{95} +(6.96455 + 1.43200i) q^{96} +(6.17163 + 12.1125i) q^{97} +(9.18357 + 1.54072i) q^{98} +(4.69474 - 0.379637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−1.25415	−	0.653531i	−0.886819	−	0.462116i
$2$	−1.25415	−	0.653531i	−0.886819	−	0.462116i
$3$	0.738802	+	1.01687i	0.426548	+	0.587093i	0.967157	−	0.254182i	$-0.0818061\pi$
$3$	0.738802	+	1.01687i	0.426548	+	0.587093i	−0.540609	+	0.841274i	$0.681806\pi$
$4$	1.14579	+	1.63925i	0.572897	+	0.819627i
$5$	−3.61425	−	1.84155i	−1.61634	−	0.823567i	−0.999329	−	0.0366137i	$-0.988343\pi$
$5$	−3.61425	−	1.84155i	−1.61634	−	0.823567i	−0.617012	−	0.786954i	$-0.711657\pi$
$6$	−0.262011	−	1.75814i	−0.106966	−	0.717760i
$7$	−0.636645	+	0.100835i	−0.240629	+	0.0381119i	−0.275584	−	0.961277i	$-0.588871\pi$
$7$	−0.636645	+	0.100835i	−0.240629	+	0.0381119i	0.0349550	+	0.999389i	$0.488871\pi$
$8$	−0.365696	−	2.80469i	−0.129293	−	0.991606i
$9$	0.438847	−	1.35063i	0.146282	−	0.450211i
$10$	3.32931	+	4.67161i	1.05282	+	1.47729i
$11$	1.27580	+	3.06143i	0.384668	+	0.923055i
$11$	1.27580	+	3.06143i	0.384668	+	0.923055i
$12$	−0.820401	+	2.37621i	−0.236829	+	0.685954i
$13$	−0.569996	+	3.56021i	−0.158089	+	0.987425i
$13$	−0.569996	+	3.56021i	−0.158089	+	0.987425i
$14$	0.864348	+	0.289605i	0.231007	+	0.0774003i
$15$	−0.797589	−	5.03578i	−0.205937	−	1.30023i
$16$	−1.37431	+	3.75650i	−0.343578	+	0.939124i
$17$	2.90053	−	0.942440i	0.703482	−	0.228575i	0.0646353	−	0.997909i	$-0.479412\pi$
$17$	2.90053	−	0.942440i	0.703482	−	0.228575i	0.638847	+	0.769334i	$0.279412\pi$
$18$	−1.43306	+	1.40710i	−0.337776	+	0.331656i
$19$	1.77622	+	0.281325i	0.407492	+	0.0645404i	0.356816	−	0.934175i	$-0.383862\pi$
$19$	1.77622	+	0.281325i	0.407492	+	0.0645404i	0.0506760	+	0.998715i	$0.483862\pi$
$20$	−1.12241	−	8.03472i	−0.250979	−	1.79662i
$21$	−0.572891	−	0.572891i	−0.125015	−	0.125015i
$22$	0.400692	−	4.67327i	0.0854279	−	0.996344i
$23$	3.31914			0.692089			0.346044	−	0.938218i	$-0.387525\pi$
$23$	3.31914			0.692089			0.346044	+	0.938218i	$0.387525\pi$
$24$	2.58184	−	2.44398i	0.527015	−	0.498874i
$25$	6.73256	+	9.26658i	1.34651	+	1.85332i
$26$	3.04157	−	4.09254i	0.596501	−	0.802612i
$27$	5.28387	−	1.71683i	1.01688	−	0.330404i
$28$	−0.894757	−	0.928087i	−0.169093	−	0.175392i
$29$	3.02044	+	2.19447i	0.560881	+	0.407504i	0.831781	−	0.555104i	$-0.187321\pi$
$29$	3.02044	+	2.19447i	0.560881	+	0.407504i	−0.270900	+	0.962607i	$0.587321\pi$
$30$	−2.29074	+	6.83688i	−0.418230	+	1.24824i
$31$	−4.53314	+	2.30975i	−0.814176	+	0.414843i	−0.810924	−	0.585152i	$-0.801035\pi$
$31$	−4.53314	+	2.30975i	−0.814176	+	0.414843i	−0.00325165	+	0.999995i	$0.501035\pi$
$32$	4.17858	−	3.81306i	0.738676	−	0.674060i
$33$	−2.17052	+	3.55912i	−0.377840	+	0.619563i
$34$	−4.25362	−	0.713625i	−0.729490	−	0.122386i
$35$	2.48669	+	0.807973i	0.420326	+	0.136572i
$36$	2.71686	−	0.828164i	0.452810	−	0.138027i
$37$	1.20916	+	7.63435i	0.198785	+	1.25508i	0.862099	+	0.506739i	$0.169149\pi$
$37$	1.20916	+	7.63435i	0.198785	+	1.25508i	−0.663314	+	0.748341i	$0.730851\pi$
$38$	−2.04379	−	1.51364i	−0.331546	−	0.245544i
$39$	−4.04140	+	2.05068i	−0.647142	+	0.328371i
$40$	−3.84326	+	10.8103i	−0.607673	+	1.70926i
$41$	0.921914	−	5.82073i	0.143979	−	0.909046i	−0.804901	−	0.593409i	$-0.797782\pi$
$41$	0.921914	−	5.82073i	0.143979	−	0.909046i	0.948880	−	0.315637i	$-0.102218\pi$
$42$	0.344090	+	1.09289i	0.0530942	+	0.168637i
$43$	7.77044			1.18498			0.592490	−	0.805578i	$-0.298145\pi$
$43$	7.77044			1.18498			0.592490	+	0.805578i	$0.298145\pi$
$44$	−3.55666	+	5.59912i	−0.536186	+	0.844100i
$45$	−4.07336	+	4.07336i	−0.607221	+	0.607221i
$46$	−4.16271	−	2.16916i	−0.613758	−	0.319826i
$47$	−1.37914	+	8.70752i	−0.201168	+	1.27012i	0.655872	+	0.754872i	$0.272301\pi$
$47$	−1.37914	+	8.70752i	−0.201168	+	1.27012i	−0.857040	+	0.515250i	$0.827699\pi$
$48$	−4.83523	+	1.37781i	−0.697905	+	0.198869i
$49$	−6.26225	+	2.03473i	−0.894607	+	0.290675i
$50$	−2.38766	−	16.0216i	−0.337666	−	2.26580i
$51$	3.10126	+	2.25320i	0.434264	+	0.315511i
$52$	−6.48919	+	3.14490i	−0.899889	+	0.436119i
$53$	−2.08960	+	6.43114i	−0.287029	+	0.883385i	0.698754	+	0.715362i	$0.253738\pi$
$53$	−2.08960	+	6.43114i	−0.287029	+	0.883385i	−0.985783	+	0.168023i	$0.946262\pi$
$54$	−7.74877	−	1.30000i	−1.05447	−	0.176908i
$55$	1.02672	−	13.4142i	0.138443	−	1.80877i
$56$	0.515628	+	1.74871i	0.0689036	+	0.233682i
$57$	1.02620	+	2.01403i	0.135924	+	0.266765i
$58$	−2.35393	−	4.72615i	−0.309086	−	0.620574i
$59$	4.40916	−	0.698342i	0.574023	−	0.0909164i	0.137328	−	0.990526i	$-0.456149\pi$
$59$	4.40916	−	0.698342i	0.574023	−	0.0909164i	0.436696	+	0.899609i	$0.356149\pi$
$60$	7.34105	−	7.07742i	0.947726	−	0.913691i
$61$	0.113802	+	0.350246i	0.0145709	+	0.0448445i	0.958078	−	0.286509i	$-0.0924948\pi$
$61$	0.113802	+	0.350246i	0.0145709	+	0.0448445i	−0.943507	+	0.331353i	$0.892495\pi$
$62$	7.19474	+	0.0657708i	0.913733	+	0.00835290i
$63$	−0.143199	+	0.904123i	−0.0180414	+	0.113909i
$64$	−7.73253	+	2.05132i	−0.966567	+	0.256415i
$65$	8.61642	−	11.8178i	1.06874	−	1.46582i
$66$	5.04816	−	3.04517i	0.621385	−	0.374834i
$67$	11.0749	+	11.0749i	1.35301	+	1.35301i	0.882276	+	0.470732i	$0.156010\pi$
$67$	11.0749	+	11.0749i	1.35301	+	1.35301i	0.470732	+	0.882276i	$0.343990\pi$
$68$	4.86831	+	3.67487i	0.590370	+	0.445643i
$69$	2.45219	+	3.37515i	0.295209	+	0.406320i
$70$	−2.59065	−	2.63845i	−0.309641	−	0.315355i
$71$	5.34642	−	10.4929i	0.634504	−	1.24528i	−0.320094	−	0.947386i	$-0.603715\pi$
$71$	5.34642	−	10.4929i	0.634504	−	1.24528i	0.954598	−	0.297898i	$-0.0962855\pi$
$72$	−3.94858	−	0.736908i	−0.465345	−	0.0868454i
$73$	−1.21729	−	7.68566i	−0.142473	−	0.899539i	−0.950575	−	0.310496i	$-0.899505\pi$
$73$	−1.21729	−	7.68566i	−0.142473	−	0.899539i	0.808102	−	0.589043i	$-0.200495\pi$
$74$	3.47281	−	10.3649i	0.403707	−	1.20489i
$75$	−4.44891	+	13.6923i	−0.513716	+	1.58105i
$76$	1.57401	+	3.23401i	0.180552	+	0.370966i
$77$	−1.12093	−	1.82040i	−0.127742	−	0.207453i
$78$	6.40871	+	0.0693206i	0.725644	+	0.00784901i
$79$	6.12212	+	1.98920i	0.688792	+	0.223802i	0.632441	−	0.774609i	$-0.282053\pi$
$79$	6.12212	+	1.98920i	0.688792	+	0.223802i	0.0563517	+	0.998411i	$0.482053\pi$
$80$	11.8849	−	11.0460i	1.32877	−	1.23499i
$81$	2.20279	+	1.60042i	0.244754	+	0.177824i
$82$	−4.96025	+	6.69758i	−0.547768	+	0.739625i
$83$	0.306517	−	0.601574i	0.0336447	−	0.0660314i	−0.873572	−	0.486694i	$-0.838203\pi$
$83$	0.306517	−	0.601574i	0.0336447	−	0.0660314i	0.907217	+	0.420663i	$0.138203\pi$
$84$	0.282699	−	1.59553i	0.0308450	−	0.174086i
$85$	−12.2188	−	1.93527i	−1.32532	−	0.209909i
$86$	−9.74531	−	5.07822i	−1.05086	−	0.547599i
$87$			4.69269i			0.503109i
$88$	8.11979	−	4.69777i	0.865572	−	0.500784i
$89$	−6.49354	−	6.49354i	−0.688314	−	0.688314i	0.273546	−	0.961859i	$-0.411804\pi$
$89$	−6.49354	−	6.49354i	−0.688314	−	0.688314i	−0.961859	+	0.273546i	$0.911804\pi$
$90$	7.77068	−	2.44655i	0.819102	−	0.257888i
$91$	0.00389267	−	2.32406i	0.000408063	−	0.243628i
$92$	3.80305	+	5.44092i	0.396496	+	0.567255i
$93$	−5.69782	−	2.90318i	−0.590836	−	0.301046i
$94$	7.42028	−	10.0192i	0.765344	−	1.03341i
$95$	−5.90161	−	4.28777i	−0.605493	−	0.439916i
$96$	6.96455	+	1.43200i	0.710816	+	0.146152i
$97$	6.17163	+	12.1125i	0.626634	+	1.22984i	0.958117	+	0.286378i	$0.0924512\pi$
$97$	6.17163	+	12.1125i	0.626634	+	1.22984i	−0.331483	+	0.943461i	$0.607549\pi$
$98$	9.18357	+	1.54072i	0.927680	+	0.155636i
$99$	4.69474	−	0.379637i	0.471839	−	0.0381550i
$100$	−7.47615	+	21.6540i	−0.747615	+	2.16540i
$101$	−5.82095	−	1.89134i	−0.579206	−	0.188195i	0.00473889	−	0.999989i	$-0.498492\pi$
$101$	−5.82095	−	1.89134i	−0.579206	−	0.188195i	−0.583945	+	0.811793i	$0.698492\pi$
$102$	−2.41692	−	4.85263i	−0.239311	−	0.480482i
$103$	−7.87662	−	5.72270i	−0.776107	−	0.563875i	0.127701	−	0.991813i	$-0.459240\pi$
$103$	−7.87662	−	5.72270i	−0.776107	−	0.563875i	−0.903808	+	0.427938i	$0.859240\pi$
$104$	10.1937	+	0.296708i	0.999577	+	0.0290946i
$105$	1.01556	+	3.12558i	0.0991087	+	0.305025i
$106$	6.82363	−	6.70000i	0.662769	−	0.650762i
$107$	−9.24099	−	12.7191i	−0.893360	−	1.22960i	−0.972538	−	0.232744i	$-0.925229\pi$
$107$	−9.24099	−	12.7191i	−0.893360	−	1.22960i	0.0791778	−	0.996861i	$-0.474771\pi$
$108$	8.86855	+	6.69447i	0.853376	+	0.644175i
$109$	8.35234	−	8.35234i	0.800009	−	0.800009i	−0.183087	−	0.983097i	$-0.558609\pi$
$109$	8.35234	−	8.35234i	0.800009	−	0.800009i	0.983097	+	0.183087i	$0.0586091\pi$
$110$	−10.0543	+	16.1525i	−0.958637	+	1.54008i
$111$	−6.86985	+	6.86985i	−0.652057	+	0.652057i
$112$	0.496164	−	2.53013i	0.0468831	−	0.239075i
$113$	−10.1832	+	7.39856i	−0.957959	+	0.695998i	−0.952676	−	0.303988i	$-0.901682\pi$
$113$	−10.1832	+	7.39856i	−0.957959	+	0.695998i	−0.00528309	+	0.999986i	$0.501682\pi$
$114$	0.0292213	−	3.19655i	0.00273683	−	0.299385i
$115$	−11.9962	−	6.11237i	−1.11865	−	0.569982i
$116$	−0.136507	+	7.46568i	−0.0126743	+	0.693171i
$117$	4.55839	+	2.33224i	0.421424	+	0.215616i
$118$	−5.98614	−	2.00569i	−0.551069	−	0.184639i
$119$	−1.75158	+	0.892474i	−0.160567	+	0.0818129i
$120$	−13.8321	+	4.07855i	−1.26269	+	0.372319i
$121$	−7.74467	+	7.81153i	−0.704061	+	0.710139i
$122$	0.0861720	−	0.513635i	0.00780165	−	0.0465024i
$123$	6.60007	−	3.36290i	0.595108	−	0.303223i
$124$	−8.98031	−	4.78447i	−0.806456	−	0.429658i
$125$	−4.09550	−	25.8579i	−0.366312	−	2.31281i
$126$	0.770466	−	1.04032i	0.0686386	−	0.0926793i
$127$	1.32051	+	4.06410i	0.117176	+	0.360630i	0.992395	−	0.123097i	$-0.0392826\pi$
$127$	1.32051	+	4.06410i	0.117176	+	0.360630i	−0.875219	+	0.483727i	$0.839283\pi$
$128$	11.0384	+	2.48078i	0.975664	+	0.219272i
$129$	5.74082	+	7.90155i	0.505451	+	0.695693i
$130$	−18.5296	+	9.19023i	−1.62515	+	0.806037i
$131$			16.5774i			1.44837i	0.689605	+	0.724186i	$0.257784\pi$
$131$			16.5774i			1.44837i	−0.689605	+	0.724186i	$0.742216\pi$
$132$	−8.32127	+	0.519975i	−0.724274	+	0.0452580i
$133$	−1.15919			−0.100514
$134$	−6.65179	−	21.1273i	−0.574627	−	1.82512i
$135$	−22.2588	−	3.52545i	−1.91574	−	0.303423i
$136$	−3.70396	−	7.79044i	−0.317612	−	0.668025i
$137$	0.908540	−	1.78311i	0.0776218	−	0.152341i	−0.848934	−	0.528499i	$-0.822755\pi$
$137$	0.908540	−	1.78311i	0.0776218	−	0.152341i	0.926556	+	0.376158i	$0.122755\pi$
$138$	−0.869653	−	5.83553i	−0.0740298	−	0.496753i
$139$	9.15620	−	12.6024i	0.776619	−	1.06892i	−0.219028	−	0.975719i	$-0.570289\pi$
$139$	9.15620	−	12.6024i	0.776619	−	1.06892i	0.995647	−	0.0932053i	$-0.0297113\pi$
$140$	1.52476	+	5.00208i	0.128865	+	0.422753i
$141$	−9.87336	+	5.03073i	−0.831487	+	0.423664i
$142$	−13.5627	+	9.66569i	−1.13816	+	0.811127i
$143$	−11.6265	+	2.79711i	−0.972259	+	0.233906i
$144$	4.47053	+	3.50472i	0.372544	+	0.292060i
$145$	−6.87537	−	13.4937i	−0.570968	−	1.12059i
$146$	−3.49615	+	10.4345i	−0.289344	+	0.863567i
$147$	−6.69562	−	4.86466i	−0.552246	−	0.401230i
$148$	−11.1292	+	10.7295i	−0.914815	+	0.881961i
$149$	1.61571	+	0.823245i	0.132364	+	0.0674429i	0.518918	−	0.854824i	$-0.326335\pi$
$149$	1.61571	+	0.823245i	0.132364	+	0.0674429i	−0.386554	+	0.922267i	$0.626335\pi$
$150$	14.5280	−	14.2648i	1.18620	−	1.16471i
$151$	1.36894	−	8.64317i	0.111403	−	0.703372i	−0.867253	−	0.497867i	$-0.834117\pi$
$151$	1.36894	−	8.64317i	0.111403	−	0.703372i	0.978656	−	0.205504i	$-0.0658834\pi$
$152$	0.139474	−	5.08461i	0.0113128	−	0.412416i
$153$		−	4.33114i		−	0.350152i
$154$	0.216129	+	3.01562i	0.0174161	+	0.243005i
$155$	20.6374			1.65764
$156$	−7.99220	−	4.27523i	−0.639888	−	0.342293i
$157$	10.6967	−	7.77164i	0.853693	−	0.620245i	−0.0724684	−	0.997371i	$-0.523088\pi$
$157$	10.6967	−	7.77164i	0.853693	−	0.620245i	0.926162	+	0.377126i	$0.123088\pi$
$158$	−6.37807	−	6.49575i	−0.507412	−	0.516774i
$159$	−8.08346	+	2.62648i	−0.641060	+	0.208293i
$160$	−22.1244	+	6.08627i	−1.74909	+	0.481162i
$161$	−2.11311	+	0.334684i	−0.166537	+	0.0263768i
$162$	−1.71671	−	3.44676i	−0.134877	−	0.270803i
$163$	0.524137	+	1.02868i	0.0410536	+	0.0805722i	0.910622	−	0.413240i	$-0.135603\pi$
$163$	0.524137	+	1.02868i	0.0410536	+	0.0805722i	−0.869569	+	0.493812i	$0.835603\pi$
$164$	10.5980	−	5.15811i	0.827564	−	0.402781i
$165$	14.3991	−	8.86641i	1.12097	−	0.690249i
$166$	−0.777567	+	0.554147i	−0.0603509	+	0.0430101i
$167$	9.06529	+	17.7916i	0.701493	+	1.37676i	0.916456	+	0.400135i	$0.131037\pi$
$167$	9.06529	+	17.7916i	0.701493	+	1.37676i	−0.214963	+	0.976622i	$0.568963\pi$
$168$	−1.39728	+	1.81628i	−0.107802	+	0.140129i
$169$	−12.3502	−	4.05862i	−0.950016	−	0.312201i
$170$	14.0595	+	10.4125i	1.07831	+	0.798601i
$171$	1.15945	−	2.27555i	0.0886656	−	0.174016i
$172$	8.90332	+	12.7377i	0.678872	+	0.971242i
$173$	−7.36810	−	10.1413i	−0.560186	−	0.771030i	0.431164	−	0.902274i	$-0.358103\pi$
$173$	−7.36810	−	10.1413i	−0.560186	−	0.771030i	−0.991350	+	0.131243i	$0.958103\pi$
$174$	3.06682	−	5.88534i	0.232495	−	0.446167i
$175$	−5.22064	−	5.22064i	−0.394643	−	0.394643i
$176$	−13.2536	+	0.585178i	−0.999027	+	0.0441094i
$177$	3.96762	+	3.96762i	0.298225	+	0.298225i
$178$	3.90015	+	12.3876i	0.292329	+	0.928491i
$179$	−17.3291	+	12.5903i	−1.29524	+	0.941044i	−0.999897	−	0.0143479i	$-0.995433\pi$
$179$	−17.3291	+	12.5903i	−1.29524	+	0.941044i	−0.295339	+	0.955392i	$0.595433\pi$
$180$	−11.3445	−	2.01004i	−0.845570	−	0.149820i
$181$	−2.81648	+	0.915130i	−0.209347	+	0.0680210i	−0.411813	−	0.911268i	$-0.635104\pi$
$181$	−2.81648	+	0.915130i	−0.209347	+	0.0680210i	0.202466	+	0.979289i	$0.435104\pi$
$182$	−1.52373	+	2.91219i	−0.112946	+	0.215866i
$183$	−0.272079	+	0.374485i	−0.0201127	+	0.0276827i
$184$	−1.21380	−	9.30915i	−0.0894822	−	0.686280i
$185$	9.68885	−	29.8192i	0.712338	−	2.19235i
$186$	5.24861	+	7.36473i	0.384847	+	0.540008i
$187$	6.58571	+	7.67740i	0.481595	+	0.561427i
$188$	−15.8541	+	7.71627i	−1.15628	+	0.562767i
$189$	−3.19083	+	1.62581i	−0.232099	+	0.118260i
$190$	4.59933	+	9.23441i	0.333670	+	0.669934i
$191$	−9.18339	+	12.6398i	−0.664487	+	0.914587i	−0.999620	−	0.0275836i	$-0.991219\pi$
$191$	−9.18339	+	12.6398i	−0.664487	+	0.914587i	0.335133	+	0.942171i	$0.391219\pi$
$192$	−7.79875	−	6.34749i	−0.562826	−	0.458091i
$193$	−0.695391	+	1.36478i	−0.0500554	+	0.0982392i	−0.914679	−	0.404181i	$-0.867557\pi$
$193$	−0.695391	+	1.36478i	−0.0500554	+	0.0982392i	0.864624	+	0.502420i	$0.167557\pi$
$194$	0.175739	−	19.2243i	0.0126173	−	1.38022i
$195$	18.3831	+	0.0307906i	1.31644	+	0.00220496i
$196$	−10.5107	−	7.93404i	−0.750763	−	0.566717i
$197$	−13.1479	+	13.1479i	−0.936752	+	0.936752i	−0.998115	−	0.0613633i	$-0.980455\pi$
$197$	−13.1479	+	13.1479i	−0.936752	+	0.936752i	0.0613633	+	0.998115i	$0.480455\pi$
$198$	−6.13602	−	2.59204i	−0.436068	−	0.184208i
$199$	2.78020			0.197083			0.0985414	−	0.995133i	$-0.468582\pi$
$199$	2.78020			0.197083			0.0985414	+	0.995133i	$0.468582\pi$
$200$	23.5278	−	22.2715i	1.66366	−	1.57483i
$201$	−3.07960	+	19.4439i	−0.217219	+	1.37146i
$202$	6.06430	+	6.17620i	0.426683	+	0.434556i
$203$	−2.14422	−	1.09254i	−0.150495	−	0.0766810i
$204$	−0.140160	+	7.66546i	−0.00981313	+	0.536690i
$205$	−14.0512	+	19.3398i	−0.981379	+	1.35075i
$206$	6.13852	+	12.3248i	0.427691	+	0.858706i
$207$	1.45659	−	4.48294i	0.101240	−	0.311586i
$208$	−12.5906	−	7.03403i	−0.872999	−	0.487722i
$209$	1.40484	+	5.79667i	0.0971747	+	0.400964i
$210$	0.768994	−	4.58365i	0.0530656	−	0.316302i
$211$	−0.128771	−	0.0418403i	−0.00886497	−	0.00288040i	0.304581	−	0.952486i	$-0.401484\pi$
$211$	−0.128771	−	0.0418403i	−0.00886497	−	0.00288040i	−0.313446	+	0.949606i	$0.601484\pi$
$212$	−12.9365	+	3.94337i	−0.888484	+	0.270832i
$213$	14.6200	−	2.31557i	1.00174	−	0.158660i
$214$	3.27726	+	21.9910i	0.224029	+	1.50327i
$215$	−28.0843	−	14.3097i	−1.91533	−	0.975911i
$216$	−6.74746	−	14.1917i	−0.459107	−	0.965626i
$217$	2.65310	−	1.92759i	0.180104	−	0.130853i
$218$	−15.9336	+	5.01659i	−1.07916	+	0.339766i
$219$	6.91602	−	6.91602i	0.467341	−	0.467341i
$220$	23.1657	−	13.6869i	1.56183	−	0.922768i
$221$	1.70199	+	10.8637i	0.114488	+	0.730771i
$222$	13.1055	−	4.12617i	0.879583	−	0.276930i
$223$	1.98260	+	0.314013i	0.132765	+	0.0210279i	0.222463	−	0.974941i	$-0.428590\pi$
$223$	1.98260	+	0.314013i	0.132765	+	0.0210279i	−0.0896984	+	0.995969i	$0.528590\pi$
$224$	−2.27578	+	2.84891i	−0.152057	+	0.190351i
$225$	15.4703	−	5.02660i	1.03135	−	0.335107i
$226$	17.6065	−	2.62385i	1.17117	−	0.174536i
$227$	2.75289	+	17.3811i	0.182716	+	1.15362i	0.893117	+	0.449825i	$0.148514\pi$
$227$	2.75289	+	17.3811i	0.182716	+	1.15362i	−0.710401	+	0.703798i	$0.751486\pi$
$228$	−2.12570	+	3.98987i	−0.140778	+	0.264235i
$229$	14.1099	−	7.18933i	0.932406	−	0.475085i	0.0793167	−	0.996849i	$-0.474726\pi$
$229$	14.1099	−	7.18933i	0.932406	−	0.475085i	0.853089	+	0.521765i	$0.174726\pi$
$230$	11.0504	+	15.5057i	0.728644	+	1.02242i
$231$	1.02297	−	2.48476i	0.0673065	−	0.163485i
$232$	5.05025	−	9.27388i	0.331565	−	0.608860i
$233$	17.5398	+	5.69904i	1.14907	+	0.373357i	0.820794	−	0.571224i	$-0.193531\pi$
$233$	17.5398	+	5.69904i	1.14907	+	0.373357i	0.328279	+	0.944581i	$0.393531\pi$
$234$	−4.19272	−	5.90404i	−0.274087	−	0.385959i
$235$	21.0199	−	28.9314i	1.37119	−	1.88728i
$236$	6.19675	+	6.42758i	0.403374	+	0.418400i
$237$	2.50027	+	7.69505i	0.162410	+	0.499847i
$238$	2.78000	+	0.0254134i	0.180201	+	0.00164731i
$239$	14.5797	+	2.30919i	0.943080	+	0.149369i	0.608995	−	0.793174i	$-0.291573\pi$
$239$	14.5797	+	2.30919i	0.943080	+	0.149369i	0.334085	+	0.942543i	$0.391573\pi$
$240$	20.0130	+	3.92459i	1.29184	+	0.253331i
$241$	−10.4660	−	10.4660i	−0.674173	−	0.674173i	0.284503	−	0.958675i	$-0.408172\pi$
$241$	−10.4660	−	10.4660i	−0.674173	−	0.674173i	−0.958675	+	0.284503i	$0.908172\pi$
$242$	14.8181	−	4.73546i	0.952542	−	0.304407i
$243$		−	13.2450i		−	0.849668i
$244$	−0.443750	+	0.587861i	−0.0284082	+	0.0376339i
$245$	26.3804	+	4.17824i	1.68538	+	0.266938i
$246$	−10.4752	−	0.0957596i	−0.667877	−	0.00610541i
$247$	−2.01401	+	6.16335i	−0.128149	+	0.392164i
$248$	8.13587	+	11.8694i	0.516628	+	0.753706i
$249$	0.838181	−	0.132755i	0.0531176	−	0.00841300i
$250$	−11.7626	+	35.1063i	−0.743932	+	2.22032i
$251$	3.89301	−	11.9814i	0.245725	−	0.756262i	−0.749792	−	0.661674i	$-0.769846\pi$
$251$	3.89301	−	11.9814i	0.245725	−	0.756262i	0.995516	−	0.0945887i	$-0.0301536\pi$
$252$	−1.64617	+	0.801199i	−0.103699	+	0.0504708i
$253$	4.23456	+	10.1613i	0.266224	+	0.638836i
$254$	0.999900	−	5.95999i	0.0627393	−	0.373963i
$255$	−7.05935	−	13.8548i	−0.442074	−	0.867619i
$256$	−12.2225	−	10.3252i	−0.763908	−	0.645325i
$257$	−0.657157	+	0.904500i	−0.0409924	+	0.0564211i	−0.829021	−	0.559217i	$-0.811102\pi$
$257$	−0.657157	+	0.904500i	−0.0409924	+	0.0564211i	0.788029	+	0.615638i	$0.211102\pi$
$258$	−2.03594	−	13.6616i	−0.126752	−	0.850531i
$259$	−1.53961	−	4.73845i	−0.0956670	−	0.294433i
$260$	29.2451	+	0.583734i	1.81370	+	0.0362017i
$261$	4.28944	−	3.11646i	0.265509	−	0.192904i
$262$	10.8338	−	20.7905i	0.669316	−	1.28444i
$263$		−	19.1082i		−	1.17826i	−0.808037	−	0.589132i	$-0.799470\pi$
$263$		−	19.1082i		−	1.17826i	0.808037	−	0.589132i	$-0.200530\pi$
$264$	10.7760	+	4.78608i	0.663214	+	0.294563i
$265$	19.3956	−	19.3956i	1.19146	−	1.19146i
$266$	1.45379	+	0.757564i	0.0891379	+	0.0464492i
$267$	1.80567	−	11.4005i	0.110505	−	0.697702i
$268$	−5.46501	+	30.8440i	−0.333828	+	1.88410i
$269$	−6.49993	−	20.0047i	−0.396308	−	1.21971i	−0.927938	−	0.372734i	$-0.878420\pi$
$269$	−6.49993	−	20.0047i	−0.396308	−	1.21971i	0.531630	−	0.846977i	$-0.321580\pi$
$270$	25.6120	+	18.9683i	1.55870	+	1.15437i
$271$	10.2995	−	1.63128i	0.625650	−	0.0990933i	0.164444	−	0.986386i	$-0.447417\pi$
$271$	10.2995	−	1.63128i	0.625650	−	0.0990933i	0.461206	+	0.887293i	$0.347417\pi$
$272$	−0.445965	+	12.1910i	−0.0270406	+	0.739191i
$273$	2.36616	−	1.71307i	0.143206	−	0.103679i
$274$	−2.30476	+	1.64253i	−0.139236	+	0.0992290i
$275$	−19.7796	+	32.4335i	−1.19275	+	1.95582i
$276$	−2.72303	+	7.88699i	−0.163907	+	0.474741i
$277$	18.5788	+	6.03662i	1.11629	+	0.362705i	0.808351	−	0.588700i	$-0.200360\pi$
$277$	18.5788	+	6.03662i	1.11629	+	0.362705i	0.307941	+	0.951406i	$0.400360\pi$
$278$	−19.7193	+	9.82150i	−1.18269	+	0.589054i
$279$	1.13027	+	7.13623i	0.0676673	+	0.427235i
$280$	1.35674	−	7.26984i	0.0810808	−	0.434456i
$281$	−2.52158	+	4.94887i	−0.150425	+	0.295225i	−0.953906	−	0.300105i	$-0.902978\pi$
$281$	−2.52158	+	4.94887i	−0.150425	+	0.295225i	0.803482	+	0.595329i	$0.202978\pi$
$282$	15.6704	+	0.143251i	0.933161	+	0.00853050i
$283$	−11.1487	+	8.09999i	−0.662720	+	0.481494i	−0.867580	−	0.497297i	$-0.834326\pi$
$283$	−11.1487	+	8.09999i	−0.662720	+	0.481494i	0.204860	+	0.978791i	$0.434326\pi$
$284$	23.3265	−	3.25860i	1.38417	−	0.193363i
$285$		−	9.16901i		−	0.543125i
$286$	16.4094	+	4.09030i	0.970310	+	0.241864i
$287$			3.79870i			0.224230i
$288$	−3.31628	−	7.31708i	−0.195414	−	0.431163i
$289$	−6.22839	+	4.52519i	−0.366376	+	0.266188i
$290$	−0.195778	+	21.4164i	−0.0114965	+	1.25761i
$291$	−7.75728	+	15.2245i	−0.454740	+	0.892477i
$292$	11.2040	−	10.8016i	0.655664	−	0.632118i
$293$	−2.16863	−	13.6922i	−0.126693	−	0.799907i	−0.966433	−	0.256919i	$-0.917293\pi$
$293$	−2.16863	−	13.6922i	−0.126693	−	0.799907i	0.839740	−	0.542989i	$-0.182707\pi$
$294$	5.21813	+	10.4768i	0.304327	+	0.611020i
$295$	−17.2218	−	5.59571i	−1.00269	−	0.325795i
$296$	20.9698	−	6.18317i	1.21884	−	0.359390i
$297$	11.9971	+	13.9858i	0.696143	+	0.811540i
$298$	−1.48833	−	2.08839i	−0.0862166	−	0.120977i
$299$	−1.89190	+	11.8168i	−0.109411	+	0.683386i
$300$	−27.5428	+	8.39570i	−1.59018	+	0.484726i
$301$	−4.94701	+	0.783529i	−0.285141	+	0.0451618i
$302$	−7.36545	+	9.94521i	−0.423834	+	0.572282i
$303$	−2.37727	−	7.31650i	−0.136571	−	0.420322i
$304$	−3.49787	+	6.28572i	−0.200617	+	0.360511i
$305$	0.233688	−	1.47545i	0.0133810	−	0.0844841i
$306$	−2.83053	+	5.43191i	−0.161811	+	0.310521i
$307$	−6.18430	+	6.18430i	−0.352957	+	0.352957i	−0.861208	−	0.508252i	$-0.830292\pi$
$307$	−6.18430	+	6.18430i	−0.352957	+	0.352957i	0.508252	+	0.861208i	$0.330292\pi$
$308$	1.69974	−	3.92329i	0.0968517	−	0.223550i
$309$		−	12.2375i		−	0.696166i
$310$	−25.8825	−	13.4872i	−1.47002	−	0.766021i
$311$	8.67371	−	6.30182i	0.491841	−	0.357343i	−0.314051	−	0.949406i	$-0.601686\pi$
$311$	8.67371	−	6.30182i	0.491841	−	0.357343i	0.805892	+	0.592063i	$0.201686\pi$
$312$	7.22943	+	10.5849i	0.409286	+	0.599254i
$313$	5.26957	+	16.2181i	0.297854	+	0.916700i	0.982248	+	0.187588i	$0.0600669\pi$
$313$	5.26957	+	16.2181i	0.297854	+	0.916700i	−0.684394	+	0.729112i	$0.739933\pi$
$314$	−18.4944	+	2.75616i	−1.04370	+	0.155539i
$315$	2.18255	−	3.00402i	0.122973	−	0.169257i
$316$	3.75389	+	12.3149i	0.211173	+	0.692769i
$317$	8.64731	+	16.9713i	0.485681	+	0.953203i	0.995664	+	0.0930188i	$0.0296517\pi$
$317$	8.64731	+	16.9713i	0.485681	+	0.953203i	−0.509983	+	0.860184i	$0.670348\pi$
$318$	11.8544	+	1.98879i	0.664760	+	0.111526i
$319$	−2.86476	+	12.0466i	−0.160396	+	0.674477i
$320$	31.7249	+	6.82587i	1.77348	+	0.381578i
$321$	6.10649	−	18.7938i	0.340831	−	1.04897i
$322$	2.86889	+	0.961241i	0.159877	+	0.0535678i
$323$	5.41710	−	0.857985i	0.301416	−	0.0477395i
$324$	−0.0995534	+	5.44468i	−0.00553075	+	0.302482i
$325$	−36.8285	+	18.6874i	−2.04288	+	1.03659i
$326$	0.0149249	−	1.63266i	0.000826616	−	0.0904245i
$327$	14.6640	+	2.32255i	0.810922	+	0.128437i
$328$	−16.6625	−	0.457062i	−0.920031	−	0.0252370i
$329$		−	5.68266i		−	0.313295i
$330$	−23.8531	+	1.70955i	−1.31307	+	0.0941077i
$331$	8.42150	+	8.42150i	0.462888	+	0.462888i	0.899601	−	0.436713i	$-0.143858\pi$
$331$	8.42150	+	8.42150i	0.462888	+	0.462888i	−0.436713	+	0.899601i	$0.643858\pi$
$332$	1.33734	−	0.186820i	0.0733960	−	0.0102531i
$333$	10.8418	+	1.71718i	0.594129	+	0.0941008i
$334$	0.258137	−	28.2379i	0.0141246	−	1.54511i
$335$	−19.6324	−	60.4222i	−1.07263	−	3.30122i
$336$	2.93939	−	1.36473i	0.160357	−	0.0744522i
$337$	11.6001	−	15.9661i	0.631896	−	0.869730i	−0.366255	−	0.930515i	$-0.619360\pi$
$337$	11.6001	−	15.9661i	0.631896	−	0.869730i	0.998151	+	0.0607844i	$0.0193602\pi$
$338$	12.8366	+	13.1614i	0.698219	+	0.715884i
$339$	−15.0468	−	4.88900i	−0.817230	−	0.265534i
$340$	−10.8278	−	22.2471i	−0.587222	−	1.20652i
$341$	−12.8545	−	10.9311i	−0.696110	−	0.591952i
$342$	−2.94128	+	2.09615i	−0.159046	+	0.113347i
$343$	7.80193	−	3.97528i	0.421265	−	0.214645i
$344$	−2.84161	−	21.7936i	−0.153210	−	1.17503i
$345$	−2.64731	−	16.7145i	−0.142526	−	0.899877i
$346$	2.61305	+	17.5340i	0.140478	+	0.942636i
$347$	−2.08787	+	0.678391i	−0.112083	+	0.0364179i	−0.364521	−	0.931195i	$-0.618767\pi$
$347$	−2.08787	+	0.678391i	−0.112083	+	0.0364179i	0.252439	+	0.967613i	$0.418767\pi$
$348$	−7.69251	+	5.37685i	−0.412362	+	0.288229i
$349$	2.12842	+	0.337109i	0.113932	+	0.0180450i	0.213140	−	0.977022i	$-0.431631\pi$
$349$	2.12842	+	0.337109i	0.113932	+	0.0180450i	−0.0992081	+	0.995067i	$0.531631\pi$
$350$	3.13562	+	9.95933i	0.167606	+	0.532348i
$351$	3.10050	+	19.7903i	0.165492	+	1.05633i
$352$	17.0044	+	7.92773i	0.906340	+	0.422549i
$353$	−14.8805	+	14.8805i	−0.792010	+	0.792010i	−0.981821	−	0.189811i	$-0.939213\pi$
$353$	−14.8805	+	14.8805i	−0.792010	+	0.792010i	0.189811	+	0.981821i	$0.439213\pi$
$354$	−2.38304	−	7.56896i	−0.126657	−	0.402286i
$355$	−38.6466	+	28.0784i	−2.05115	+	1.49025i
$356$	3.20431	−	18.0848i	0.169828	−	0.958493i
$357$	−2.20160	−	1.12177i	−0.116521	−	0.0593705i
$358$	29.9615	−	4.46507i	1.58351	−	0.235986i
$359$	−24.3449	+	3.85586i	−1.28488	+	0.203504i	−0.761258	−	0.648449i	$-0.775418\pi$
$359$	−24.3449	+	3.85586i	−1.28488	+	0.203504i	−0.523618	+	0.851953i	$0.675418\pi$
$360$	12.9141	+	9.93489i	0.680633	+	0.523615i
$361$	−14.9943	−	4.87194i	−0.789172	−	0.256418i
$362$	4.13036	+	0.692946i	0.217087	+	0.0364204i
$363$	−13.6651	−	2.10418i	−0.717233	−	0.110441i
$364$	3.81419	−	2.65652i	0.199918	−	0.139239i
$365$	−9.75396	+	30.0196i	−0.510546	+	1.57130i
$366$	0.585967	−	0.291849i	0.0306290	−	0.0152552i
$367$	0.0965936	−	0.132950i	0.00504215	−	0.00693992i	−0.806488	−	0.591250i	$-0.798635\pi$
$367$	0.0965936	−	0.132950i	0.00504215	−	0.00693992i	0.811531	+	0.584310i	$0.198635\pi$
$368$	−4.56154	+	12.4683i	−0.237787	+	0.649957i
$369$	−7.45709	−	3.79958i	−0.388201	−	0.197798i
$370$	−31.6391	+	31.0658i	−1.64484	+	1.61504i
$371$	0.681853	−	4.30505i	0.0354001	−	0.223507i
$372$	−1.76947	−	12.6666i	−0.0917426	−	0.656734i
$373$	−11.7018			−0.605896			−0.302948	−	0.953007i	$-0.597971\pi$
$373$	−11.7018			−0.605896			−0.302948	+	0.953007i	$0.597971\pi$
$374$	−3.24206	−	13.9326i	−0.167643	−	0.720437i
$375$	23.2685	−	23.2685i	1.20158	−	1.20158i
$376$	24.9262	+	0.683742i	1.28547	+	0.0352613i
$377$	−9.53443	+	9.50255i	−0.491048	+	0.489406i
$378$	5.06430	+	0.0462954i	0.260479	+	0.00238118i
$379$	−15.3797	+	30.1843i	−0.790000	+	1.55046i	0.0442150	+	0.999022i	$0.485921\pi$
$379$	−15.3797	+	30.1843i	−0.790000	+	1.55046i	−0.834215	+	0.551440i	$0.814079\pi$
$380$	0.266719	−	14.5871i	0.0136824	−	0.748305i
$381$	−3.15708	+	4.34535i	−0.161742	+	0.222619i
$382$	19.7779	−	9.85066i	1.01193	−	0.504004i
$383$	9.34161	−	4.75979i	0.477334	−	0.243214i	−0.198733	−	0.980054i	$-0.563683\pi$
$383$	9.34161	−	4.75979i	0.477334	−	0.243214i	0.676067	+	0.736840i	$0.263683\pi$
$384$	5.63253	+	13.0574i	0.287434	+	0.666335i
$385$	0.698960	+	8.64362i	0.0356223	+	0.440519i
$386$	1.76405	−	1.25718i	0.0897880	−	0.0639890i
$387$	3.41003	−	10.4950i	0.173342	−	0.533491i
$388$	−12.7841	+	23.9953i	−0.649013	+	1.21818i
$389$	0.521580	−	0.717893i	0.0264451	−	0.0363986i	−0.795590	−	0.605836i	$-0.792839\pi$
$389$	0.521580	−	0.717893i	0.0264451	−	0.0363986i	0.822035	+	0.569437i	$0.192839\pi$
$390$	−23.0350	−	12.0525i	−1.16642	−	0.610303i
$391$	9.62728	−	3.12809i	0.486872	−	0.158194i
$392$	7.99685	+	16.8195i	0.403902	+	0.849516i
$393$	−16.8571	+	12.2474i	−0.850328	+	0.617800i
$394$	25.0821	−	7.89693i	1.26362	−	0.397841i
$395$	−18.4637	−	18.4637i	−0.929008	−	0.929008i
$396$	6.00153	+	7.26089i	0.301588	+	0.364873i
$397$	3.05953	+	3.05953i	0.153554	+	0.153554i	0.779703	−	0.626149i	$-0.215370\pi$
$397$	3.05953	+	3.05953i	0.153554	+	0.153554i	−0.626149	+	0.779703i	$0.715370\pi$
$398$	−3.48679	−	1.81694i	−0.174777	−	0.0910752i
$399$	−0.856409	−	1.17875i	−0.0428741	−	0.0590111i
$400$	−44.0625	+	12.5557i	−2.20313	+	0.627784i
$401$	2.26580	−	4.44689i	0.113149	−	0.222067i	−0.827487	−	0.561485i	$-0.810230\pi$
$401$	2.26580	−	4.44689i	0.113149	−	0.222067i	0.940636	+	0.339418i	$0.110230\pi$
$402$	16.5695	−	22.3729i	0.826409	−	1.11586i
$403$	−5.63932	−	17.4555i	−0.280915	−	0.869519i
$404$	−3.56922	−	11.7091i	−0.177575	−	0.582550i
$405$	−5.01417	−	9.84085i	−0.249156	−	0.488996i
$406$	1.97517	+	2.77152i	0.0980263	+	0.137548i
$407$	−21.8294	+	13.4417i	−1.08204	+	0.666279i
$408$	5.18540	−	9.52206i	0.256716	−	0.471412i
$409$	−14.7273	−	28.9040i	−0.728219	−	1.42921i	−0.896305	−	0.443437i	$-0.853759\pi$
$409$	−14.7273	−	28.9040i	−0.728219	−	1.42921i	0.168087	−	0.985772i	$-0.446241\pi$
$410$	30.2615	−	15.0722i	1.49451	−	0.744362i
$411$	2.48443	−	0.393495i	0.122548	−	0.0194097i
$412$	0.355979	−	19.4688i	0.0175378	−	0.959160i
$413$	−2.73665	+	0.889191i	−0.134662	+	0.0437542i
$414$	−4.75653	+	4.67035i	−0.233771	+	0.229535i
$415$	−2.21566	+	1.60977i	−0.108763	+	0.0790206i
$416$	11.1935	+	17.0501i	0.548808	+	0.835949i
$417$	19.5797			0.958822
$418$	2.02642	−	8.18801i	0.0991156	−	0.400489i
$419$			6.19164i			0.302481i	0.988497	+	0.151241i	$0.0483269\pi$
$419$			6.19164i			0.302481i	−0.988497	+	0.151241i	$0.951673\pi$
$420$	−3.95999	+	5.24603i	−0.193228	+	0.255980i
$421$	2.60731	−	16.4619i	0.127073	−	0.802305i	−0.839018	−	0.544103i	$-0.816870\pi$
$421$	2.60731	−	16.4619i	0.127073	−	0.802305i	0.966091	−	0.258202i	$-0.0831300\pi$
$422$	0.134155	+	0.136630i	0.00653055	+	0.00665105i
$423$	11.1554	+	5.68397i	0.542395	+	0.276364i
$424$	18.8015	+	3.50884i	0.913081	+	0.170405i
$425$	28.2612	+	20.5330i	1.37087	+	0.995995i
$426$	−19.8489	−	6.65052i	−0.961684	−	0.322219i
$427$	−0.107768	−	0.211507i	−0.00521528	−	0.0102356i
$428$	10.2616	−	29.7218i	0.496014	−	1.43666i
$429$	−11.4340	−	9.75620i	−0.552040	−	0.471034i
$430$	25.8702	+	36.3005i	1.24757	+	1.75056i
$431$	28.5236	−	14.5335i	1.37393	−	0.700053i	0.397849	−	0.917451i	$-0.369757\pi$
$431$	28.5236	−	14.5335i	1.37393	−	0.700053i	0.976083	+	0.217398i	$0.0697570\pi$
$432$	−0.812409	+	22.2083i	−0.0390870	+	1.06850i
$433$	0.687886	−	0.946794i	0.0330577	−	0.0455000i	−0.792168	−	0.610303i	$-0.791048\pi$
$433$	0.687886	−	0.946794i	0.0330577	−	0.0455000i	0.825226	+	0.564803i	$0.191048\pi$
$434$	−4.58712	+	0.683606i	−0.220189	+	0.0328141i
$435$	8.64183	−	16.9605i	0.414344	−	0.813196i
$436$	23.2617	+	4.12155i	1.11403	+	0.197387i
$437$	5.89551	+	0.933757i	0.282021	+	0.0446677i
$438$	−13.1936	+	4.15390i	−0.630413	+	0.198481i
$439$	31.9741			1.52604			0.763021	−	0.646374i	$-0.223715\pi$
$439$	31.9741			1.52604			0.763021	+	0.646374i	$0.223715\pi$
$440$	−37.9981	+	2.02589i	−1.81149	+	0.0965804i
$441$			9.35092i			0.445282i
$442$	4.96521	−	14.7370i	0.236171	−	0.700969i
$443$	−0.0110336	−	0.0151864i	−0.000524220	−	0.000721527i	0.808755	−	0.588146i	$-0.200142\pi$
$443$	−0.0110336	−	0.0151864i	−0.000524220	−	0.000721527i	−0.809279	+	0.587424i	$0.800142\pi$
$444$	−19.1329	−	3.39000i	−0.908005	−	0.160882i
$445$	11.5111	+	35.4275i	0.545677	+	1.67942i
$446$	−2.28126	−	1.68951i	−0.108021	−	0.0800007i
$447$	0.356553	+	2.25119i	0.0168644	+	0.106478i
$448$	4.71603	−	2.08567i	0.222812	−	0.0985387i
$449$	25.3980	−	12.9409i	1.19860	−	0.610719i	0.263351	−	0.964700i	$-0.415172\pi$
$449$	25.3980	−	12.9409i	1.19860	−	0.610719i	0.935253	+	0.353981i	$0.115172\pi$
$450$	−22.6871	−	3.80620i	−1.06948	−	0.179426i
$451$	18.9959	−	4.60372i	0.894483	−	0.216781i
$452$	−23.7960	−	8.21571i	−1.11927	−	0.386434i
$453$	9.80040	−	4.99355i	0.460463	−	0.234618i
$454$	7.90653	−	23.5976i	0.371072	−	1.10749i
$455$	−4.29396	+	8.39258i	−0.201304	+	0.393450i
$456$	5.27345	−	3.61469i	0.246952	−	0.169273i
$457$	−29.1671	−	14.8614i	−1.36438	−	0.695185i	−0.390149	−	0.920752i	$-0.627577\pi$
$457$	−29.1671	−	14.8614i	−1.36438	−	0.695185i	−0.974228	+	0.225567i	$0.927577\pi$
$458$	−22.3944	−	0.204718i	−1.04642	−	0.00956586i
$459$	13.7080	−	9.95945i	0.639835	−	0.464867i
$460$	−3.72545	−	26.6684i	−0.173700	−	1.24342i
$461$	−24.9259	+	24.9259i	−1.16092	+	1.16092i	−0.176640	+	0.984276i	$0.556523\pi$
$461$	−24.9259	+	24.9259i	−1.16092	+	1.16092i	−0.984276	+	0.176640i	$0.943477\pi$
$462$	−2.90682	+	2.44772i	−0.135238	+	0.113878i
$463$	4.49951	−	4.49951i	0.209110	−	0.209110i	−0.594779	−	0.803889i	$-0.702761\pi$
$463$	4.49951	−	4.49951i	0.209110	−	0.209110i	0.803889	+	0.594779i	$0.202761\pi$
$464$	−12.3946	+	8.33036i	−0.575403	+	0.386727i
$465$	15.2470	+	20.9857i	0.707061	+	0.973187i
$466$	−18.2731	−	18.6103i	−0.846486	−	0.862105i
$467$	10.7485	+	33.0805i	0.497381	+	1.53078i	0.813213	+	0.581966i	$0.197716\pi$
$467$	10.7485	+	33.0805i	0.497381	+	1.53078i	−0.315832	+	0.948815i	$0.602284\pi$
$468$	1.39984	+	10.1446i	0.0647076	+	0.468936i
$469$	−8.16747	−	5.93402i	−0.377139	−	0.274007i
$470$	−45.2697	+	22.5472i	−2.08814	+	1.04003i
$471$	15.8056	+	5.13554i	0.728282	+	0.236633i
$472$	−3.57104	−	12.1109i	−0.164370	−	0.557450i
$473$	9.91352	+	23.7886i	0.455824	+	1.09380i
$474$	1.89323	−	11.2848i	0.0869591	−	0.518327i
$475$	9.35156	+	18.3535i	0.429079	+	0.842115i
$476$	−3.46994	−	1.84869i	−0.159044	−	0.0847346i
$477$	7.76908	+	5.64457i	0.355722	+	0.258447i
$478$	−16.7760	−	12.4243i	−0.767316	−	0.568276i
$479$	−13.1958	−	6.72360i	−0.602932	−	0.307209i	0.125749	−	0.992062i	$-0.459866\pi$
$479$	−13.1958	−	6.72360i	−0.602932	−	0.307209i	−0.728681	+	0.684853i	$0.759866\pi$
$480$	−22.5345	−	18.0012i	−1.02856	−	0.821637i
$481$	−27.8691	−	0.0466792i	−1.27072	−	0.00212839i
$482$	6.28608	+	19.9658i	0.286323	+	0.909416i
$483$	−1.90150	−	1.90150i	−0.0865215	−	0.0865215i
$484$	−21.6789	−	3.74508i	−0.985404	−	0.170231i
$485$		−	55.1430i		−	2.50392i
$486$	−8.65602	+	16.6112i	−0.392645	+	0.753502i
$487$	−2.00949	−	0.318273i	−0.0910589	−	0.0144223i	0.110739	−	0.993850i	$-0.464678\pi$
$487$	−2.00949	−	0.318273i	−0.0910589	−	0.0144223i	−0.201798	+	0.979427i	$0.564678\pi$
$488$	0.940715	−	0.447262i	0.0425842	−	0.0202466i
$489$	−0.658801	+	1.29297i	−0.0297920	+	0.0584701i
$490$	−30.3544	−	22.4806i	−1.37127	−	1.01557i
$491$	26.3676	+	19.1572i	1.18995	+	0.864552i	0.993259	−	0.115913i	$-0.0369792\pi$
$491$	26.3676	+	19.1572i	1.18995	+	0.864552i	0.196695	+	0.980465i	$0.436979\pi$
$492$	13.0750	+	6.96600i	0.589465	+	0.314051i
$493$	10.8290	+	3.51857i	0.487715	+	0.158468i
$494$	6.55382	−	6.41355i	0.294870	−	0.288559i
$495$	−17.6671	−	7.27351i	−0.794077	−	0.326920i
$496$	−2.44662	−	20.2030i	−0.109856	−	0.907143i
$497$	−2.34572	+	7.21938i	−0.105220	+	0.323834i
$498$	−1.13797	−	0.381283i	−0.0509935	−	0.0170857i
$499$	−0.448191	−	2.82977i	−0.0200638	−	0.126678i	0.975623	−	0.219451i	$-0.0704267\pi$
$499$	−0.448191	−	2.82977i	−0.0200638	−	0.126678i	−0.995687	+	0.0927735i	$0.970427\pi$
$500$	37.6952	−	36.3414i	1.68578	−	1.62524i
$501$	−11.3944	+	22.3628i	−0.509064	+	0.999094i
$502$	−12.7127	+	12.4824i	−0.567394	+	0.557115i
$503$	−4.66060	−	6.41477i	−0.207806	−	0.286020i	0.692374	−	0.721539i	$-0.256565\pi$
$503$	−4.66060	−	6.41477i	−0.207806	−	0.286020i	−0.900180	+	0.435519i	$0.856565\pi$
$504$	2.58815	+	0.0709946i	0.115285	+	0.00316235i
$505$	17.5554	+	17.5554i	0.781203	+	0.781203i
$506$	1.32995	−	15.5112i	0.0591237	−	0.689559i
$507$	−4.99726	−	15.5571i	−0.221936	−	0.690916i
$508$	−5.14906	+	6.82126i	−0.228453	+	0.302645i
$509$	2.86414	−	18.0835i	0.126951	−	0.801535i	−0.839250	−	0.543745i	$-0.817006\pi$
$509$	2.86414	−	18.0835i	0.126951	−	0.801535i	0.966201	−	0.257790i	$-0.0829943\pi$
$510$	−0.201017	+	21.9895i	−0.00890119	+	0.973711i
$511$	1.54996	+	4.77029i	0.0685663	+	0.211025i
$512$	8.58107	+	20.9372i	0.379233	+	0.925301i
$513$	9.86827	−	1.56298i	0.435695	−	0.0690073i
$514$	1.41529	−	0.704907i	0.0624259	−	0.0310921i
$515$	17.9294	+	35.1885i	0.790065	+	1.55059i
$516$	−6.37487	+	18.4642i	−0.280638	+	0.812842i
$517$	−28.4169	+	6.88692i	−1.24978	+	0.302887i
$518$	−1.16581	+	6.94892i	−0.0512228	+	0.305318i
$519$	4.86888	−	14.9849i	0.213720	−	0.657762i
$520$	−36.2963	−	19.8446i	−1.59170	−	0.870245i
$521$	−21.9413	−	15.9413i	−0.961266	−	0.698401i	−0.00782189	−	0.999969i	$-0.502490\pi$
$521$	−21.9413	−	15.9413i	−0.961266	−	0.698401i	−0.953445	+	0.301568i	$0.902490\pi$
$522$	−7.41631	+	1.10523i	−0.324603	+	0.0483746i
$523$	35.3993	−	11.5019i	1.54790	−	0.502944i	0.594358	−	0.804200i	$-0.297406\pi$
$523$	35.3993	−	11.5019i	1.54790	−	0.502944i	0.953543	+	0.301257i	$0.0974061\pi$
$524$	−27.1745	+	18.9943i	−1.18713	+	0.829768i
$525$	1.45171	−	9.16576i	0.0633580	−	0.400026i
$526$	−12.4878	+	23.9646i	−0.544495	+	1.04491i
$527$	−10.9717	+	10.9717i	−0.477935	+	0.477935i
$528$	−10.3868	−	13.0449i	−0.452029	−	0.567706i
$529$	−11.9833			−0.521013
$530$	−37.0007	+	11.6494i	−1.60721	+	0.506018i
$531$	0.991742	−	6.26161i	0.0430379	−	0.271731i
$532$	−1.32819	−	1.90020i	−0.0575842	−	0.0823841i
$533$	20.1976	+	6.60000i	0.874853	+	0.285878i
$534$	−9.71520	+	13.1180i	−0.420418	+	0.567670i
$535$	9.97630	+	62.9879i	0.431313	+	2.72320i
$536$	27.0115	−	35.1115i	1.16672	−	1.51659i
$537$	−25.6055	−	8.31974i	−1.10496	−	0.359023i
$538$	−4.92182	+	29.3369i	−0.212195	+	1.26480i
$539$	−14.2185	−	16.5755i	−0.612436	−	0.713958i
$540$	−19.7249	−	40.5274i	−0.848826	−	1.74402i
$541$	7.25537	−	3.69680i	0.311933	−	0.158938i	−0.291015	−	0.956719i	$-0.593993\pi$
$541$	7.25537	−	3.69680i	0.311933	−	0.158938i	0.602948	+	0.797781i	$0.293993\pi$
$542$	−13.9832	−	4.68517i	−0.600631	−	0.201245i
$543$	−3.01139	−	2.18790i	−0.129231	−	0.0938920i
$544$	8.52654	−	14.9980i	0.365572	−	0.643033i
$545$	−45.5687	+	14.8062i	−1.95195	+	0.634227i
$546$	−4.08706	+	0.602087i	−0.174910	+	0.0257670i
$547$	−7.51145	−	10.3386i	−0.321166	−	0.442047i	0.617657	−	0.786448i	$-0.288082\pi$
$547$	−7.51145	−	10.3386i	−0.321166	−	0.442047i	−0.938823	+	0.344401i	$0.888082\pi$
$548$	3.96397	−	0.553748i	0.169332	−	0.0236550i
$549$	0.522996			0.0223209
$550$	46.0029	−	27.7500i	1.96157	−	1.18327i
$551$	4.74758	+	4.74758i	0.202254	+	0.202254i
$552$	8.56948	−	8.11190i	0.364741	−	0.345265i
$553$	−4.09820	−	0.649090i	−0.174273	−	0.0276021i
$554$	−19.3555	−	19.7127i	−0.822337	−	0.837511i
$555$	37.4805	−	12.1782i	1.59096	−	0.516934i
$556$	31.1497	+	0.569558i	1.32104	+	0.0241547i
$557$	−1.33844	−	8.45058i	−0.0567116	−	0.358063i	−0.999683	−	0.0251883i	$-0.991981\pi$
$557$	−1.33844	−	8.45058i	−0.0567116	−	0.358063i	0.942971	−	0.332874i	$-0.108019\pi$
$558$	3.24622	−	9.68858i	0.137423	−	0.410150i
$559$	−4.42912	+	27.6644i	−0.187332	+	1.17008i
$560$	−6.45263	+	8.23082i	−0.272673	+	0.347815i
$561$	−2.94142	+	12.3689i	−0.124187	+	0.522216i
$562$	6.39668	−	4.55871i	0.269828	−	0.192297i
$563$	−7.67884	+	23.6330i	−0.323624	+	0.996013i	0.648433	+	0.761271i	$0.275424\pi$
$563$	−7.67884	+	23.6330i	−0.323624	+	0.996013i	−0.972058	+	0.234742i	$0.924576\pi$
$564$	−19.5595	−	10.4208i	−0.823603	−	0.438794i
$565$	50.4296	−	7.98727i	2.12159	−	0.336027i
$566$	19.2757	−	2.87261i	0.810219	−	0.120745i
$567$	−1.56377	−	0.796780i	−0.0656721	−	0.0334616i
$568$	−31.3846	−	11.1578i	−1.31687	−	0.468172i
$569$	−15.5766	−	21.4394i	−0.653006	−	0.898786i	0.346219	−	0.938154i	$-0.387465\pi$
$569$	−15.5766	−	21.4394i	−0.653006	−	0.898786i	−0.999225	+	0.0393681i	$0.987465\pi$
$570$	−5.99224	+	11.4993i	−0.250987	+	0.481654i
$571$	2.90514			0.121576			0.0607882	−	0.998151i	$-0.480639\pi$
$571$	2.90514			0.121576			0.0607882	+	0.998151i	$0.480639\pi$
$572$	−17.9068	−	15.8539i	−0.748720	−	0.662886i
$573$	−19.6378			−0.820383
$574$	2.48257	−	4.76415i	0.103620	−	0.198852i
$575$	22.3463	+	30.7571i	0.931906	+	1.28266i
$576$	−0.622816	+	11.3440i	−0.0259507	+	0.472668i
$577$	−1.14905	−	0.585472i	−0.0478357	−	0.0243735i	0.429909	−	0.902872i	$-0.358546\pi$
$577$	−1.14905	−	0.585472i	−0.0478357	−	0.0243735i	−0.477745	+	0.878499i	$0.658546\pi$
$578$	10.7687	−	1.60483i	0.447919	−	0.0667521i
$579$	−1.90157	+	0.301179i	−0.0790265	+	0.0125166i
$580$	14.2418	−	26.7314i	0.591359	−	1.10996i
$581$	−0.134483	+	0.413897i	−0.00557930	+	0.0171713i
$582$	19.6785	−	14.0242i	0.815700	−	0.581323i
$583$	−22.3544	+	1.80767i	−0.925824	+	0.0748661i
$584$	−21.1107	+	6.22473i	−0.873568	+	0.257581i
$585$	−12.1802	−	16.8238i	−0.503590	−	0.695580i
$586$	−6.22849	+	18.5894i	−0.257297	+	0.767920i
$587$	1.64806	+	10.4054i	0.0680227	+	0.429479i	0.998073	+	0.0620469i	$0.0197628\pi$
$587$	1.64806	+	10.4054i	0.0680227	+	0.429479i	−0.930050	+	0.367432i	$0.880237\pi$
$588$	0.302604	−	16.5497i	0.0124792	−	0.682499i
$589$	−8.70162	+	2.82733i	−0.358544	+	0.116498i
$590$	17.9418	+	18.2729i	0.738653	+	0.752282i
$591$	−23.0835	−	3.65607i	−0.949530	−	0.150391i
$592$	−30.3402	−	5.94977i	−1.24697	−	0.244534i
$593$	−11.0124	−	11.0124i	−0.452224	−	0.452224i	0.443868	−	0.896092i	$-0.353606\pi$
$593$	−11.0124	−	11.0124i	−0.452224	−	0.452224i	−0.896092	+	0.443868i	$0.853606\pi$
$594$	−5.90601	−	25.3808i	−0.242327	−	1.04139i
$595$	7.97418			0.326909
$596$	0.501762	+	3.59183i	0.0205530	+	0.147127i
$597$	2.05401	+	2.82711i	0.0840652	+	0.115706i
$598$	10.0954	−	13.5837i	0.412832	−	0.555479i
$599$	42.0364	−	13.6584i	1.71756	−	0.558069i	0.725997	−	0.687698i	$-0.241379\pi$
$599$	42.0364	−	13.6584i	1.71756	−	0.558069i	0.991563	+	0.129629i	$0.0413785\pi$
$600$	40.0297	+	7.47057i	1.63420	+	0.304985i
$601$	34.0378	+	24.7299i	1.38843	+	1.00875i	0.996036	+	0.0889560i	$0.0283530\pi$
$601$	34.0378	+	24.7299i	1.38843	+	1.00875i	0.392394	+	0.919797i	$0.371647\pi$
$602$	6.71636	+	2.25036i	0.273738	+	0.0917178i
$603$	19.8182	−	10.0979i	0.807060	−	0.411218i
$604$	15.7369	−	7.65925i	0.640325	−	0.311650i
$605$	42.3765	−	13.9706i	1.72285	−	0.567986i
$606$	−1.80010	+	10.7296i	−0.0731239	+	0.435861i
$607$	−21.2538	−	6.90577i	−0.862664	−	0.280296i	−0.155923	−	0.987769i	$-0.549835\pi$
$607$	−21.2538	−	6.90577i	−0.862664	−	0.280296i	−0.706741	+	0.707473i	$0.749835\pi$
$608$	8.49477	−	5.59728i	0.344509	−	0.227000i
$609$	−0.473185	−	2.98757i	−0.0191744	−	0.121063i
$610$	−1.25733	+	1.69772i	−0.0509080	+	0.0687385i
$611$	−30.2145	−	9.87327i	−1.22235	−	0.399430i
$612$	7.09984	−	4.96259i	0.286994	−	0.200601i
$613$	−2.31514	+	14.6172i	−0.0935075	+	0.590383i	0.895791	+	0.444476i	$0.146610\pi$
$613$	−2.31514	+	14.6172i	−0.0935075	+	0.590383i	−0.989298	+	0.145907i	$0.953390\pi$
$614$	11.7977	−	3.71442i	0.476116	−	0.149902i
$615$	−30.0472			−1.21162
$616$	−4.69572	+	3.80956i	−0.189196	+	0.153492i
$617$	27.3319	−	27.3319i	1.10034	−	1.10034i	0.105973	−	0.994369i	$-0.466204\pi$
$617$	27.3319	−	27.3319i	1.10034	−	1.10034i	0.994369	−	0.105973i	$-0.0337957\pi$
$618$	−7.99757	+	15.3477i	−0.321710	+	0.617373i
$619$	−2.67828	+	16.9100i	−0.107649	+	0.679669i	0.873559	+	0.486718i	$0.161806\pi$
$619$	−2.67828	+	16.9100i	−0.107649	+	0.679669i	−0.981208	+	0.192951i	$0.938194\pi$
$620$	23.6462	+	33.8300i	0.949655	+	1.35864i
$621$	17.5379	−	5.69841i	0.703772	−	0.228669i
$622$	−14.9966	+	2.23490i	−0.601308	+	0.0896113i
$623$	4.78885	+	3.47930i	0.191861	+	0.139395i
$624$	−2.14922	−	17.9998i	−0.0860375	−	0.720568i
$625$	−15.1190	+	46.5316i	−0.604761	+	1.86126i
$626$	3.99018	−	23.7838i	0.159479	−	0.950590i
$627$	−4.85658	+	5.71114i	−0.193953	+	0.228081i
$628$	24.9960	+	8.62999i	0.997448	+	0.344374i
$629$	10.7021	+	21.0041i	0.426722	+	0.837489i
$630$	−4.70047	+	2.34113i	−0.187271	+	0.0932730i
$631$	12.5978	−	1.99529i	0.501509	−	0.0794312i	0.0994453	−	0.995043i	$-0.468293\pi$
$631$	12.5978	−	1.99529i	0.501509	−	0.0794312i	0.402063	+	0.915612i	$0.368293\pi$
$632$	3.34024	−	17.8981i	0.132868	−	0.711947i
$633$	−0.0525901	−	0.161856i	−0.00209027	−	0.00643319i
$634$	0.246235	−	26.9359i	0.00977923	−	1.06976i
$635$	2.71161	−	17.1204i	0.107607	−	0.679404i
$636$	−13.5674	−	10.2415i	−0.537984	−	0.406100i
$637$	−3.67460	−	23.4547i	−0.145593	−	0.929309i
$638$	11.4656	−	13.2360i	0.453929	−	0.524018i
$639$	−11.8258	−	11.8258i	−0.467823	−	0.467823i
$640$	−35.3270	−	29.2939i	−1.39642	−	1.15794i
$641$	−5.41494	−	7.45303i	−0.213877	−	0.294377i	0.688576	−	0.725164i	$-0.258236\pi$
$641$	−5.41494	−	7.45303i	−0.213877	−	0.294377i	−0.902454	+	0.430787i	$0.858236\pi$
$642$	−19.9408	+	19.5796i	−0.787002	+	0.772743i
$643$	−0.533060	+	1.04619i	−0.0210218	+	0.0412577i	−0.901279	−	0.433240i	$-0.857370\pi$
$643$	−0.533060	+	1.04619i	−0.0210218	+	0.0412577i	0.880257	+	0.474498i	$0.157370\pi$
$644$	−2.96983	−	3.08045i	−0.117028	−	0.121387i
$645$	−6.19762	−	39.1302i	−0.244031	−	1.54075i
$646$	−7.35459	−	2.46420i	−0.289362	−	0.0969527i
$647$	8.19564	−	25.2236i	0.322204	−	0.991642i	−0.650483	−	0.759521i	$-0.725433\pi$
$647$	8.19564	−	25.2236i	0.322204	−	0.991642i	0.972687	−	0.232121i	$-0.0745665\pi$
$648$	3.68312	−	6.76339i	0.144687	−	0.265691i
$649$	7.76312	+	12.6074i	0.304729	+	0.494882i
$650$	58.4014	+	0.631705i	2.29069	+	0.0247775i
$651$	3.92023	+	1.27376i	0.153646	+	0.0499225i
$652$	−1.08571	+	2.03784i	−0.0425197	+	0.0798082i
$653$	13.6741	+	9.93480i	0.535108	+	0.388779i	0.822265	−	0.569105i	$-0.192710\pi$
$653$	13.6741	+	9.93480i	0.535108	+	0.388779i	−0.287157	+	0.957884i	$0.592710\pi$
$654$	−16.8730	−	12.4962i	−0.659788	−	0.488641i
$655$	30.5281	−	59.9148i	1.19283	−	2.34106i
$656$	20.5986	+	11.4627i	0.804239	+	0.447542i
$657$	−10.9147	−	1.72872i	−0.425823	−	0.0674438i
$658$	−3.71380	+	7.12692i	−0.144779	+	0.277836i
$659$			7.61848i			0.296774i	0.988929	+	0.148387i	$0.0474081\pi$
$659$			7.61848i			0.296774i	−0.988929	+	0.148387i	$0.952592\pi$
$660$	31.0327	+	13.4447i	1.20795	+	0.523336i
$661$	−8.53718	−	8.53718i	−0.332058	−	0.332058i	0.521310	−	0.853368i	$-0.325444\pi$
$661$	−8.53718	−	8.53718i	−0.332058	−	0.332058i	−0.853368	+	0.521310i	$0.825444\pi$
$662$	−5.05813	−	16.0656i	−0.196590	−	0.624406i
$663$	−9.78957	+	9.75684i	−0.380196	+	0.378924i
$664$	−1.79932	−	0.639692i	−0.0698271	−	0.0248249i
$665$	4.18959	+	2.13470i	0.162465	+	0.0827801i
$666$	−12.4751	−	9.23908i	−0.483400	−	0.358007i
$667$	10.0253	+	7.28377i	0.388179	+	0.282029i
$668$	−18.7781	+	35.2459i	−0.726545	+	1.36370i
$669$	1.14544	+	2.24805i	0.0442852	+	0.0869146i
$670$	−14.8658	+	88.6090i	−0.574317	+	3.42326i
$671$	−0.927066	+	0.795241i	−0.0357890	+	0.0306999i
$672$	−4.57834	−	0.209405i	−0.176613	−	0.00807796i
$673$	25.0402	+	8.13606i	0.965230	+	0.313622i	0.748889	−	0.662696i	$-0.230588\pi$
$673$	25.0402	+	8.13606i	0.965230	+	0.313622i	0.216341	+	0.976318i	$0.430588\pi$
$674$	−24.9826	+	12.4429i	−0.962294	+	0.479284i
$675$	51.4831	+	37.4047i	1.98159	+	1.43971i
$676$	−7.49769	−	24.8955i	−0.288373	−	0.957518i
$677$	−3.27070	−	10.0662i	−0.125703	−	0.386874i	0.868325	−	0.495995i	$-0.165197\pi$
$677$	−3.27070	−	10.0662i	−0.125703	−	0.386874i	−0.994029	+	0.109121i	$0.965197\pi$
$678$	15.6759	+	15.9651i	0.602028	+	0.613136i
$679$	−5.15050	−	7.08905i	−0.197658	−	0.272053i
$680$	−0.959459	+	34.9776i	−0.0367936	+	1.34133i
$681$	−15.6405	+	15.6405i	−0.599346	+	0.599346i
$682$	8.97769	+	22.1101i	0.343773	+	0.846638i
$683$	−36.5255	+	36.5255i	−1.39761	+	1.39761i	−0.590767	+	0.806842i	$0.701175\pi$
$683$	−36.5255	+	36.5255i	−1.39761	+	1.39761i	−0.806842	+	0.590767i	$0.798825\pi$
$684$	5.05871	−	0.706678i	0.193425	−	0.0270205i
$685$	−6.56738	+	4.77148i	−0.250927	+	0.182309i
$686$	−12.3828	−	0.113197i	−0.472777	−	0.00432189i
$687$	17.7350	+	9.03646i	0.676634	+	0.344762i
$688$	−10.6790	+	29.1896i	−0.407133	+	1.11284i
$689$	−21.7051	−	11.1052i	−0.826900	−	0.423073i
$690$	−7.60329	+	22.6926i	−0.289452	+	0.863892i
$691$	−7.16995	+	3.65327i	−0.272758	+	0.138977i	−0.585020	−	0.811019i	$-0.698913\pi$
$691$	−7.16995	+	3.65327i	−0.272758	+	0.138977i	0.312262	+	0.949996i	$0.398913\pi$
$692$	8.18188	−	23.6981i	0.311028	−	0.900865i
$693$	−2.95060	+	0.715086i	−0.112084	+	0.0271639i
$694$	3.06186	+	0.513684i	0.116227	+	0.0194992i
$695$	−56.3008	+	28.6867i	−2.13561	+	1.08815i
$696$	13.1615	−	1.71609i	0.498886	−	0.0650484i
$697$	−2.81165	−	17.7521i	−0.106499	−	0.672408i
$698$	−2.44905	−	1.81378i	−0.0926980	−	0.0686524i
$699$	7.16327	+	22.0463i	0.270940	+	0.833867i
$700$	2.57618	−	14.5397i	0.0973705	−	0.549550i
$701$	−9.84589	−	13.5517i	−0.371874	−	0.511841i	0.581535	−	0.813522i	$-0.302452\pi$
$701$	−9.84589	−	13.5517i	−0.371874	−	0.511841i	−0.953409	+	0.301680i	$0.902452\pi$
$702$	9.04506	−	26.8463i	0.341384	−	1.01325i
$703$			13.9004i			0.524265i
$704$	−16.1451	−	21.0555i	−0.608493	−	0.793559i
$705$	44.9491			1.69288
$706$	28.3873	−	8.93755i	1.06837	−	0.336369i
$707$	3.89659	+	0.617159i	0.146546	+	0.0232106i
$708$	−1.95787	+	11.0500i	−0.0735811	+	0.415285i
$709$	1.73163	−	3.39852i	0.0650327	−	0.127634i	−0.856202	−	0.516642i	$-0.827182\pi$
$709$	1.73163	−	3.39852i	0.0650327	−	0.127634i	0.921235	+	0.389008i	$0.127182\pi$
$710$	66.8188	−	9.95782i	2.50767	−	0.373710i
$711$	5.37335	−	7.39578i	0.201516	−	0.277363i
$712$	−15.8377	+	20.5870i	−0.593542	+	0.771530i
$713$	−15.0461	+	7.66638i	−0.563482	+	0.287108i
$714$	2.02803	+	2.84569i	0.0758972	+	0.106497i
$715$	47.1722	+	11.3014i	1.76414	+	0.422648i
$716$	−40.4943	−	13.9809i	−1.51334	−	0.522490i
$717$	8.42333	+	16.5317i	0.314575	+	0.617388i
$718$	33.0522	+	11.0743i	1.23350	+	0.413291i
$719$	−32.8655	−	23.8782i	−1.22568	−	0.890506i	−0.229118	−	0.973399i	$-0.573584\pi$
$719$	−32.8655	−	23.8782i	−1.22568	−	0.890506i	−0.996559	+	0.0828924i	$0.973584\pi$
$720$	−9.70350	−	20.8996i	−0.361628	−	0.778883i
$721$	5.59166	+	2.84909i	0.208244	+	0.106106i
$722$	15.6211	+	15.9094i	0.581359	+	0.592086i
$723$	2.91029	−	18.3749i	0.108235	−	0.683369i
$724$	−4.72724	−	3.56838i	−0.175686	−	0.132618i
$725$			42.7635i			1.58820i
$726$	15.7630	+	11.5695i	0.585020	+	0.429386i
$727$	−25.9213			−0.961369			−0.480685	−	0.876894i	$-0.659612\pi$
$727$	−25.9213			−0.961369			−0.480685	+	0.876894i	$0.659612\pi$
$728$	−6.51970	+	0.838982i	−0.241636	+	0.0310948i
$729$	20.0769	−	14.5867i	0.743587	−	0.540248i
$730$	31.8517	−	31.2746i	1.17888	−	1.15753i
$731$	22.5384	−	7.32317i	0.833613	−	0.270857i
$732$	−0.925624	−	0.0169246i	−0.0342120	−	0.000625552i
$733$	−4.23225	+	0.670322i	−0.156322	+	0.0247589i	−0.234105	−	0.972211i	$-0.575216\pi$
$733$	−4.23225	+	0.670322i	−0.156322	+	0.0247589i	0.0777830	+	0.996970i	$0.475216\pi$
$734$	−0.208030	+	0.103612i	−0.00767852	+	0.00382440i
$735$	15.2411	+	29.9124i	0.562178	+	1.10334i
$736$	13.8693	−	12.6561i	0.511230	−	0.466510i
$737$	−19.7756	+	48.0341i	−0.728442	+	1.76936i
$738$	6.86918	+	9.63869i	0.252858	+	0.354805i
$739$	−21.1700	−	41.5485i	−0.778751	−	1.52839i	−0.847526	−	0.530753i	$-0.821909\pi$
$739$	−21.1700	−	41.5485i	−0.778751	−	1.52839i	0.0687750	−	0.997632i	$-0.478091\pi$
$740$	59.9827	−	18.2842i	2.20501	−	0.672140i
$741$	−7.75531	+	2.50550i	−0.284898	+	0.0920418i
$742$	−3.66863	+	4.95358i	−0.134680	+	0.181852i
$743$	15.8115	−	31.0318i	0.580068	−	1.13845i	−0.395442	−	0.918491i	$-0.629408\pi$
$743$	15.8115	−	31.0318i	0.580068	−	1.13845i	0.975510	−	0.219956i	$-0.0705915\pi$
$744$	−6.05885	+	17.0423i	−0.222128	+	0.624800i
$745$	−4.32353	−	5.95083i	−0.158402	−	0.218021i
$746$	14.6758	+	7.64749i	0.537321	+	0.279995i
$747$	−0.677991	−	0.677991i	−0.0248064	−	0.0248064i
$748$	−5.03936	+	19.5924i	−0.184257	+	0.716368i
$749$	7.16576	+	7.16576i	0.261831	+	0.261831i
$750$	−44.3890	+	13.9756i	−1.62086	+	0.510315i
$751$	−14.6638	+	10.6539i	−0.535089	+	0.388765i	−0.822258	−	0.569115i	$-0.807286\pi$
$751$	−14.6638	+	10.6539i	−0.535089	+	0.388765i	0.287169	+	0.957880i	$0.407286\pi$
$752$	−30.8144	−	17.1476i	−1.12369	−	0.625308i
$753$	15.0598	−	4.89322i	0.548809	−	0.178319i
$754$	18.1678	−	5.68659i	0.661634	−	0.207093i
$755$	−20.8646	+	28.7176i	−0.759339	+	1.04514i
$756$	−6.32115	−	3.36774i	−0.229898	−	0.122483i
$757$	6.82115	−	20.9933i	0.247919	−	0.763016i	−0.747224	−	0.664573i	$-0.768614\pi$
$757$	6.82115	−	20.9933i	0.247919	−	0.763016i	0.995143	−	0.0984435i	$-0.0313864\pi$
$758$	39.0148	−	27.8046i	1.41708	−	1.00991i
$759$	−7.20427	+	11.8132i	−0.261498	+	0.428792i
$760$	−9.86766	+	18.1202i	−0.357938	+	0.657288i
$761$	8.91594	−	4.54290i	0.323203	−	0.164680i	−0.284860	−	0.958569i	$-0.591947\pi$
$761$	8.91594	−	4.54290i	0.323203	−	0.164680i	0.608062	+	0.793889i	$0.291947\pi$
$762$	6.79929	−	3.38648i	0.246312	−	0.122679i
$763$	−4.47527	+	6.15968i	−0.162016	+	0.222995i
$764$	−31.2422	−	0.571250i	−1.13030	−	0.0206671i
$765$	−7.97602	+	15.6538i	−0.288374	+	0.565965i
$766$	−14.8265	−	0.135536i	−0.535702	−	0.00489713i
$767$	−0.0269592	+	16.0956i	−0.000973439	+	0.581178i
$768$	1.46939	−	20.0571i	0.0530222	−	0.723747i
$769$	12.4478	−	12.4478i	0.448878	−	0.448878i	−0.446104	−	0.894981i	$-0.647189\pi$
$769$	12.4478	−	12.4478i	0.448878	−	0.448878i	0.894981	+	0.446104i	$0.147189\pi$
$770$	4.77227	−	11.2972i	0.171981	−	0.407123i
$771$	−1.40527			−0.0506096
$772$	−3.03400	+	0.423836i	−0.109196	+	0.0152542i
$773$	5.93332	−	37.4615i	0.213407	−	1.34740i	−0.615556	−	0.788093i	$-0.711069\pi$
$773$	5.93332	−	37.4615i	0.213407	−	1.34740i	0.828963	−	0.559304i	$-0.188931\pi$
$774$	−11.1355	+	10.9338i	−0.400257	+	0.393006i
$775$	−51.9231	−	26.4561i	−1.86513	−	0.950333i
$776$	31.7149	−	21.7390i	1.13850	−	0.780384i
$777$	3.68093	−	5.06637i	0.132053	−	0.181755i
$778$	−1.12331	+	0.559478i	−0.0402725	+	0.0200583i
$779$	3.27503	−	10.0795i	0.117340	−	0.361136i
$780$	21.0127	+	30.1698i	0.752376	+	1.08025i
$781$	38.9444	+	2.98079i	1.39354	+	0.106661i
$782$	−14.1184	−	2.36862i	−0.504872	−	0.0847018i
$783$	19.7271	+	6.40973i	0.704990	+	0.229065i
$784$	0.962837	−	26.3205i	0.0343870	−	0.940016i
$785$	−52.9726	+	8.39004i	−1.89067	+	0.299453i
$786$	29.1454	−	4.34346i	1.03958	−	0.154926i
$787$	−40.8510	−	20.8146i	−1.45618	−	0.741960i	−0.466401	−	0.884573i	$-0.654450\pi$
$787$	−40.8510	−	20.8146i	−1.45618	−	0.741960i	−0.989779	+	0.142613i	$0.954450\pi$
$788$	−36.6177	−	6.48799i	−1.30445	−	0.231125i
$789$	19.4307	−	14.1172i	0.691750	−	0.502586i
$790$	11.0897	+	35.2228i	0.394552	+	1.25317i
$791$	5.73708	−	5.73708i	0.203987	−	0.203987i
$792$	−2.78161	−	13.0284i	−0.0988402	−	0.462946i
$793$	−1.31182	+	0.205520i	−0.0465840	+	0.00729822i
$794$	−1.83762	−	5.83662i	−0.0652147	−	0.207134i
$795$	34.0524	+	5.39338i	1.20772	+	0.191283i
$796$	3.18553	+	4.55745i	0.112908	+	0.161535i
$797$	−44.3541	+	14.4115i	−1.57110	+	0.510482i	−0.959745	−	0.280873i	$-0.909376\pi$
$797$	−44.3541	+	14.4115i	−1.57110	+	0.510482i	−0.611357	+	0.791355i	$0.709376\pi$
$798$	0.303720	+	2.03802i	0.0107516	+	0.0721450i
$799$	4.20609	+	26.5562i	0.148801	+	0.939491i
$800$	63.4666	+	13.0495i	2.24388	+	0.461369i
$801$	−11.6200	+	5.92071i	−0.410574	+	0.209198i
$802$	−5.74784	+	4.09630i	−0.202963	+	0.144645i
$803$	21.9761	−	13.5320i	0.775519	−	0.477534i
$804$	−35.4020	+	17.2304i	−1.24853	+	0.607669i
$805$	8.25366	+	2.68178i	0.290903	+	0.0945202i
$806$	−4.33513	+	25.5773i	−0.152699	+	0.900922i
$807$	15.5401	−	21.3892i	0.547039	−	0.752934i
$808$	−3.17592	+	17.0176i	−0.111729	+	0.598677i
$809$	4.24935	+	13.0782i	0.149399	+	0.459804i	0.997550	−	0.0699505i	$-0.0222841\pi$
$809$	4.24935	+	13.0782i	0.149399	+	0.459804i	−0.848151	+	0.529754i	$0.822284\pi$
$810$	−0.142780	+	15.6188i	−0.00501677	+	0.548790i
$811$	7.60481	+	1.20448i	0.267041	+	0.0422951i	0.288519	−	0.957474i	$-0.406837\pi$
$811$	7.60481	+	1.20448i	0.267041	+	0.0422951i	−0.0214780	+	0.999769i	$0.506837\pi$
$812$	−0.665893	−	4.76675i	−0.0233682	−	0.167280i
$813$	9.26811	+	9.26811i	0.325047	+	0.325047i
$814$	36.1619	−	2.59172i	1.26747	−	0.0908397i
$815$		−	4.68312i		−	0.164043i
$816$	−12.7262	+	8.55328i	−0.445508	+	0.299425i
$817$	13.8020	+	2.18602i	0.482870	+	0.0764791i
$818$	−0.419364	+	45.8747i	−0.0146627	+	1.60397i
$819$	−3.13725	−	1.02517i	−0.109624	−	0.0358222i
$820$	−47.8027	−	0.874051i	−1.66934	−	0.0305232i
$821$	−43.1920	+	6.84094i	−1.50741	+	0.238750i	−0.854806	−	0.518948i	$-0.826324\pi$
$821$	−43.1920	+	6.84094i	−1.50741	+	0.238750i	−0.652605	+	0.757698i	$0.726324\pi$
$822$	−3.37301	−	1.13015i	−0.117647	−	0.0394185i
$823$	6.73667	−	20.7333i	0.234825	−	0.722718i	−0.762319	−	0.647201i	$-0.775939\pi$
$823$	6.73667	−	20.7333i	0.234825	−	0.722718i	0.997145	−	0.0755171i	$-0.0240607\pi$
$824$	−13.1699	+	24.1842i	−0.458797	+	0.842497i
$825$	−47.5940	+	3.84866i	−1.65701	+	0.133993i
$826$	4.01329	+	0.673305i	0.139640	+	0.0234273i
$827$	−1.19987	−	2.35488i	−0.0417237	−	0.0818873i	0.869203	−	0.494455i	$-0.164632\pi$
$827$	−1.19987	−	2.35488i	−0.0417237	−	0.0818873i	−0.910927	+	0.412567i	$0.864632\pi$
$828$	9.01763	−	2.74879i	0.313384	−	0.0955272i
$829$	6.37854	−	8.77931i	0.221536	−	0.304918i	−0.683754	−	0.729713i	$-0.739654\pi$
$829$	6.37854	−	8.77931i	0.221536	−	0.304918i	0.905290	+	0.424795i	$0.139654\pi$
$830$	3.83081	−	0.570895i	0.132969	−	0.0198161i
$831$	7.58758	+	23.3522i	0.263210	+	0.810078i
$832$	−2.89563	−	28.6987i	−0.100388	−	0.994948i
$833$	−16.2462	+	11.8036i	−0.562899	+	0.408970i
$834$	−24.5559	−	12.7959i	−0.850302	−	0.443087i
$835$		−	80.9976i		−	2.80304i
$836$	−7.89256	+	8.94468i	−0.272970	+	0.309358i
$837$	−19.9870	+	19.9870i	−0.690853	+	0.690853i
$838$	4.04643	−	7.76526i	0.139782	−	0.268246i
$839$	7.19465	−	45.4252i	0.248387	−	1.56825i	−0.476368	−	0.879246i	$-0.658047\pi$
$839$	7.19465	−	45.4252i	0.248387	−	1.56825i	0.724755	−	0.689007i	$-0.241953\pi$
$840$	8.39488	−	3.99134i	0.289651	−	0.137714i
$841$	−4.65418	−	14.3241i	−0.160489	−	0.493935i
$842$	−14.0283	+	18.9418i	−0.483449	+	0.652777i
$843$	−6.89532	+	1.09211i	−0.237488	+	0.0376143i
$844$	−0.0789583	−	0.259029i	−0.00271786	−	0.00891615i
$845$	37.1626	+	37.4124i	1.27843	+	1.28703i
$846$	−10.2759	−	14.4190i	−0.353294	−	0.495735i
$847$	4.14293	−	5.75410i	0.142353	−	0.197713i
$848$	−21.2868	−	16.6880i	−0.730991	−	0.573068i
$849$	−16.4733	−	5.35251i	−0.565363	−	0.183698i
$850$	−22.0249	−	44.2210i	−0.755448	−	1.51677i
$851$	4.01338	+	25.3395i	0.137577	+	0.868627i
$852$	20.5473	+	21.3127i	0.703938	+	0.730160i
$853$	9.97970	−	19.5863i	0.341698	−	0.670621i	−0.654657	−	0.755926i	$-0.727187\pi$
$853$	9.97970	−	19.5863i	0.341698	−	0.670621i	0.996355	+	0.0853059i	$0.0271867\pi$
$854$	−0.00306874	+	0.335692i	−0.000105010	+	0.0114872i
$855$	−8.38111	+	6.08923i	−0.286628	+	0.208247i
$856$	−32.2938	+	30.5694i	−1.10378	+	1.04484i
$857$			46.5503i			1.59013i	0.606526	+	0.795064i	$0.292563\pi$
$857$			46.5503i			1.59013i	−0.606526	+	0.795064i	$0.707437\pi$
$858$	7.96401	+	19.7082i	0.271887	+	0.672828i
$859$		−	34.0928i		−	1.16323i	−0.813464	−	0.581616i	$-0.802421\pi$
$859$		−	34.0928i		−	1.16323i	0.813464	−	0.581616i	$-0.197579\pi$
$860$	−8.72163	−	62.4332i	−0.297405	−	2.12896i
$861$	−3.86280	+	2.80649i	−0.131644	+	0.0956449i
$862$	−45.2710	−	0.413845i	−1.54194	−	0.0140956i
$863$	2.55078	−	5.00620i	0.0868297	−	0.170413i	−0.843508	−	0.537116i	$-0.819514\pi$
$863$	2.55078	−	5.00620i	0.0868297	−	0.170413i	0.930338	+	0.366703i	$0.119514\pi$
$864$	15.5327	−	27.3216i	0.528433	−	0.929501i
$865$	7.95438	+	50.2220i	0.270457	+	1.70760i
$866$	−1.48147	+	0.737869i	−0.0503425	+	0.0250738i
$867$	−9.20310	−	2.99027i	−0.312554	−	0.101555i
$868$	6.19971	+	2.14048i	0.210432	+	0.0726527i
$869$	1.72081	+	21.2802i	0.0583746	+	0.721883i
$870$	−21.9224	+	15.6234i	−0.743239	+	0.529682i
$871$	−45.7414	+	33.1162i	−1.54989	+	1.12210i
$872$	−26.4801	−	20.3713i	−0.896730	−	0.689859i
$873$	19.0679	−	3.02007i	0.645352	−	0.102214i
$874$	−6.78363	−	5.02397i	−0.229460	−	0.169938i
$875$	5.21475	+	16.0494i	0.176291	+	0.542567i
$876$	19.2614	+	3.41278i	0.650784	+	0.115307i
$877$	0.286150	−	1.80668i	0.00966260	−	0.0610073i	−0.982386	−	0.186863i	$-0.940168\pi$
$877$	0.286150	−	1.80668i	0.00966260	−	0.0610073i	0.992048	+	0.125856i	$0.0401678\pi$
$878$	−40.1004	−	20.8961i	−1.35332	−	0.705209i
$879$	12.3211	−	12.3211i	0.415579	−	0.415579i
$880$	48.9794	+	22.2922i	1.65110	+	0.751470i
$881$		−	40.1466i		−	1.35257i	−0.736639	−	0.676286i	$-0.763588\pi$
$881$		−	40.1466i		−	1.35257i	0.736639	−	0.676286i	$-0.236412\pi$
$882$	6.11112	−	11.7275i	0.205772	−	0.394885i
$883$	22.1084	−	16.0627i	0.744007	−	0.540553i	−0.149957	−	0.988693i	$-0.547913\pi$
$883$	22.1084	−	16.0627i	0.744007	−	0.540553i	0.893963	+	0.448140i	$0.147913\pi$
$884$	−15.8582	+	15.2376i	−0.533370	+	0.512495i
$885$	−7.03339	−	21.6466i	−0.236425	−	0.727641i
$886$	0.00391298	+	0.0262568i	0.000131459	+	0.000882114i
$887$	6.12980	−	8.43695i	0.205819	−	0.283285i	−0.693612	−	0.720349i	$-0.743982\pi$
$887$	6.12980	−	8.43695i	0.205819	−	0.283285i	0.899430	+	0.437064i	$0.143982\pi$
$888$	21.7800	+	16.7555i	0.730890	+	0.562277i
$889$	−1.25049	−	2.45423i	−0.0419402	−	0.0823123i
$890$	8.71631	−	51.9543i	0.292171	−	1.74151i
$891$	−2.08925	+	8.78548i	−0.0699925	+	0.294325i
$892$	1.75690	+	3.60978i	0.0588255	+	0.120864i
$893$	−4.89928	+	15.0784i	−0.163948	+	0.504581i
$894$	1.02405	−	3.05635i	0.0342494	−	0.102220i
$895$	85.8174	−	13.5921i	2.86856	−	0.454335i
$896$	−7.27767	−	0.466326i	−0.243130	−	0.0155789i
$897$	−13.4140	+	6.80649i	−0.447880	+	0.227262i
$898$	−40.3102	−	0.368496i	−1.34517	−	0.0122969i
$899$	−18.7607	−	2.97141i	−0.625706	−	0.0991020i
$900$	25.9657	+	19.6003i	0.865522	+	0.653343i
$901$			20.6230i			0.687053i
$902$	−26.8325	−	6.64067i	−0.893423	−	0.221110i
$903$	−4.45161	−	4.45161i	−0.148140	−	0.148140i
$904$	24.4746	+	25.8552i	0.814013	+	0.859931i
$905$	11.8647	+	1.87919i	0.394397	+	0.0624663i
$906$	−15.5546	−	0.142193i	−0.516768	−	0.00472404i
$907$	15.5838	+	47.9619i	0.517451	+	1.59255i	0.778778	+	0.627300i	$0.215840\pi$
$907$	15.5838	+	47.9619i	0.517451	+	1.59255i	−0.261327	+	0.965250i	$0.584160\pi$
$908$	−25.3378	+	24.4278i	−0.840864	+	0.810666i
$909$	−5.10901	+	7.03195i	−0.169455	+	0.233235i
$910$	10.8701	−	7.71934i	0.360340	−	0.255894i
$911$	−26.1231	−	8.48790i	−0.865496	−	0.281217i	−0.157574	−	0.987507i	$-0.550367\pi$
$911$	−26.1231	−	8.48790i	−0.865496	−	0.281217i	−0.707922	+	0.706290i	$0.750367\pi$
$912$	−8.97602	+	1.08701i	−0.297226	+	0.0359945i
$913$	2.23273	+	0.170893i	0.0738926	+	0.00565572i
$914$	26.8676	+	37.7000i	0.888700	+	1.24700i
$915$	1.67300	−	0.852435i	0.0553076	−	0.0281806i
$916$	27.9521	+	14.8922i	0.923565	+	0.492051i
$917$	−1.67157	−	10.5539i	−0.0552002	−	0.348520i
$918$	−23.7007	+	3.53205i	−0.782241	+	0.116575i
$919$	−44.5802	+	14.4850i	−1.47056	+	0.477815i	−0.931279	−	0.364308i	$-0.881306\pi$
$919$	−44.5802	+	14.4850i	−1.47056	+	0.477815i	−0.539286	+	0.842123i	$0.681306\pi$
$920$	−12.7563	+	35.8809i	−0.420564	+	1.18296i
$921$	−10.8576	−	1.71968i	−0.357771	−	0.0566653i
$922$	47.5507	−	14.9710i	1.56600	−	0.493044i
$923$	34.3097	+	25.0153i	1.12932	+	0.823390i
$924$	5.24526	−	1.17011i	0.172556	−	0.0384938i
$925$	−62.6036	+	62.6036i	−2.05839	+	2.05839i
$926$	−8.58364	+	2.70250i	−0.282076	+	0.0888096i
$927$	−11.1859	+	8.12703i	−0.367393	+	0.266927i
$928$	20.9888	−	2.34731i	0.688991	−	0.0770541i
$929$	−13.9295	−	7.09745i	−0.457013	−	0.232860i	0.210300	−	0.977637i	$-0.432556\pi$
$929$	−13.9295	−	7.09745i	−0.457013	−	0.232860i	−0.667313	+	0.744777i	$0.732556\pi$
$930$	−5.40724	−	36.2836i	−0.177310	−	1.18979i
$931$	−11.6955	+	1.85239i	−0.383305	+	0.0607096i
$932$	10.7549	+	35.2822i	0.352287	+	1.15571i
$933$	12.8163	+	4.16427i	0.419587	+	0.136332i
$934$	8.13887	−	48.5124i	0.266312	−	1.58737i
$935$	−9.66406	−	39.8760i	−0.316048	−	1.30408i
$936$	4.87423	−	13.6378i	0.159319	−	0.445764i
$937$	2.61541	−	8.04939i	0.0854416	−	0.262962i	−0.899203	−	0.437531i	$-0.855853\pi$
$937$	2.61541	−	8.04939i	0.0854416	−	0.262962i	0.984645	+	0.174569i	$0.0558531\pi$
$938$	6.36519	+	12.7799i	0.207831	+	0.417277i
$939$	−12.5986	+	17.3404i	−0.411139	+	0.565884i
$940$	71.5104	+	1.30754i	2.33241	+	0.0426471i
$941$	−17.8170	−	9.07821i	−0.580817	−	0.295941i	0.138791	−	0.990322i	$-0.455678\pi$
$941$	−17.8170	−	9.07821i	−0.580817	−	0.295941i	−0.719608	+	0.694381i	$0.755678\pi$
$942$	−16.4663	−	16.7702i	−0.536502	−	0.546402i
$943$	3.05996	−	19.3198i	0.0996461	−	0.629140i
$944$	−3.43624	+	17.5227i	−0.111840	+	0.570316i
$945$	14.5265			0.472546
$946$	3.11355	−	36.3133i	0.101230	−	1.18065i
$947$	21.1645	−	21.1645i	0.687754	−	0.687754i	−0.273981	−	0.961735i	$-0.588341\pi$
$947$	21.1645	−	21.1645i	0.687754	−	0.687754i	0.961735	+	0.273981i	$0.0883405\pi$
$948$	−9.74935	+	12.9155i	−0.316644	+	0.419477i
$949$	28.0564	+	0.0469929i	0.910750	+	0.00152545i
$950$	0.266288	−	29.1296i	0.00863954	−	0.945088i
$951$	−10.8690	+	21.3317i	−0.352452	+	0.691727i
$952$	3.14365	+	4.58625i	0.101886	+	0.148641i
$953$	19.1631	−	26.3757i	0.620753	−	0.854393i	−0.376655	−	0.926354i	$-0.622926\pi$
$953$	19.1631	−	26.3757i	0.620753	−	0.854393i	0.997407	+	0.0719609i	$0.0229257\pi$
$954$	−6.05471	−	12.1565i	−0.196028	−	0.393581i
$955$	56.4680	−	28.7719i	1.82726	−	0.931036i
$956$	12.9199	+	26.5456i	0.417861	+	0.858547i
$957$	−14.3663	+	5.98692i	−0.464397	+	0.193530i
$958$	12.1555	+	17.0563i	0.392725	+	0.551064i
$959$	−0.398618	+	1.22682i	−0.0128720	+	0.0396161i
$960$	16.4974	+	37.3032i	0.532451	+	1.20396i
$961$	−3.00694	+	4.13870i	−0.0969982	+	0.133507i
$962$	34.9216	+	18.2719i	1.12592	+	0.589109i
$963$	−21.2342	+	6.89942i	−0.684264	+	0.222331i
$964$	5.16455	−	29.1483i	0.166339	−	0.938802i
$965$	5.02664	−	3.65206i	0.161813	−	0.117564i
$966$	1.14208	+	3.62747i	0.0367459	+	0.116712i
$967$	22.5423	+	22.5423i	0.724911	+	0.724911i	0.969601	−	0.244690i	$-0.0786863\pi$
$967$	22.5423	+	22.5423i	0.724911	+	0.724911i	−0.244690	+	0.969601i	$0.578686\pi$
$968$	24.7411	+	18.8647i	0.795209	+	0.606336i
$969$	4.87463	+	4.87463i	0.156596	+	0.156596i
$970$	−36.0377	+	69.1577i	−1.15710	+	2.22052i
$971$	−11.4899	−	15.8145i	−0.368729	−	0.507511i	0.583826	−	0.811879i	$-0.301555\pi$
$971$	−11.4899	−	15.8145i	−0.368729	−	0.507511i	−0.952555	+	0.304367i	$0.901555\pi$
$972$	21.7119	−	15.1760i	0.696411	−	0.486772i
$973$	−4.55848	+	8.94653i	−0.146138	+	0.286813i
$974$	2.31221	+	1.71243i	0.0740880	+	0.0548698i
$975$	−46.2117	−	23.6436i	−1.47996	−	0.757202i
$976$	−1.47210	−	0.0538513i	−0.0471207	−	0.00172374i
$977$	7.03541	+	13.8078i	0.225083	+	0.441749i	0.975737	−	0.218945i	$-0.0702617\pi$
$977$	7.03541	+	13.8078i	0.225083	+	0.441749i	−0.750654	+	0.660695i	$0.770262\pi$
$978$	1.67123	−	1.19103i	0.0534401	−	0.0380850i
$979$	11.5950	−	28.1639i	0.370579	−	0.900123i
$980$	23.3773	+	48.0316i	0.746760	+	1.53431i
$981$	−7.61554	−	14.9463i	−0.243145	−	0.477200i
$982$	−20.5492	−	41.2581i	−0.655751	−	1.31660i
$983$	−26.2755	+	4.16163i	−0.838059	+	0.132736i	−0.560688	−	0.828027i	$-0.689463\pi$
$983$	−26.2755	+	4.16163i	−0.838059	+	0.132736i	−0.277371	+	0.960763i	$0.589463\pi$
$984$	−11.8455	−	17.2813i	−0.377621	−	0.550908i
$985$	71.7326	−	23.3073i	2.28559	−	0.742633i
$986$	−11.2818	−	11.4899i	−0.359284	−	0.365914i
$987$	5.77855	−	4.19836i	0.183933	−	0.133635i
$988$	−12.4109	+	3.76045i	−0.394845	+	0.119636i
$989$	25.7912			0.820112
$990$	17.4037	+	20.6681i	0.553127	+	0.656875i
$991$			12.9572i			0.411598i	0.978594	+	0.205799i	$0.0659794\pi$
$991$			12.9572i			0.411598i	−0.978594	+	0.205799i	$0.934021\pi$
$992$	−10.1349	+	26.9366i	−0.321783	+	0.855238i
$993$	−2.34178	+	14.7854i	−0.0743142	+	0.469202i
$994$	7.65998	−	7.52120i	0.242960	−	0.238558i
$995$	−10.0483	−	5.11988i	−0.318553	−	0.162311i
$996$	1.17800	+	1.22188i	0.0373264	+	0.0387168i
$997$	−24.2555	−	17.6226i	−0.768179	−	0.558115i	0.133229	−	0.991085i	$-0.457465\pi$
$997$	−24.2555	−	17.6226i	−0.768179	−	0.558115i	−0.901408	+	0.432970i	$0.857465\pi$
$998$	−1.28724	+	3.84187i	−0.0407469	+	0.121612i
$999$	19.4960	+	38.2630i	0.616825	+	1.21059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bk.a.31.14	✓	640
4.3	odd	2	inner	572.2.bk.a.31.44	yes	640
11.5	even	5	inner	572.2.bk.a.291.78	yes	640
13.8	odd	4	inner	572.2.bk.a.515.52	yes	640
44.27	odd	10	inner	572.2.bk.a.291.52	yes	640
52.47	even	4	inner	572.2.bk.a.515.78	yes	640
143.60	odd	20	inner	572.2.bk.a.203.44	yes	640
572.203	even	20	inner	572.2.bk.a.203.14	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bk.a.31.14	✓	640	1.1	even	1	trivial
572.2.bk.a.31.44	yes	640	4.3	odd	2	inner
572.2.bk.a.203.14	yes	640	572.203	even	20	inner
572.2.bk.a.203.44	yes	640	143.60	odd	20	inner
572.2.bk.a.291.52	yes	640	44.27	odd	10	inner
572.2.bk.a.291.78	yes	640	11.5	even	5	inner
572.2.bk.a.515.52	yes	640	13.8	odd	4	inner
572.2.bk.a.515.78	yes	640	52.47	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25415 - 0.653531i) q^{2} +(0.738802 + 1.01687i) q^{3} +(1.14579 + 1.63925i) q^{4} +(-3.61425 - 1.84155i) q^{5} +(-0.262011 - 1.75814i) q^{6} +(-0.636645 + 0.100835i) q^{7} +(-0.365696 - 2.80469i) q^{8} +(0.438847 - 1.35063i) q^{9} +O(q^{10})\)	\(q+(-1.25415 - 0.653531i) q^{2} +(0.738802 + 1.01687i) q^{3} +(1.14579 + 1.63925i) q^{4} +(-3.61425 - 1.84155i) q^{5} +(-0.262011 - 1.75814i) q^{6} +(-0.636645 + 0.100835i) q^{7} +(-0.365696 - 2.80469i) q^{8} +(0.438847 - 1.35063i) q^{9} +(3.32931 + 4.67161i) q^{10} +(1.27580 + 3.06143i) q^{11} +(-0.820401 + 2.37621i) q^{12} +(-0.569996 + 3.56021i) q^{13} +(0.864348 + 0.289605i) q^{14} +(-0.797589 - 5.03578i) q^{15} +(-1.37431 + 3.75650i) q^{16} +(2.90053 - 0.942440i) q^{17} +(-1.43306 + 1.40710i) q^{18} +(1.77622 + 0.281325i) q^{19} +(-1.12241 - 8.03472i) q^{20} +(-0.572891 - 0.572891i) q^{21} +(0.400692 - 4.67327i) q^{22} +3.31914 q^{23} +(2.58184 - 2.44398i) q^{24} +(6.73256 + 9.26658i) q^{25} +(3.04157 - 4.09254i) q^{26} +(5.28387 - 1.71683i) q^{27} +(-0.894757 - 0.928087i) q^{28} +(3.02044 + 2.19447i) q^{29} +(-2.29074 + 6.83688i) q^{30} +(-4.53314 + 2.30975i) q^{31} +(4.17858 - 3.81306i) q^{32} +(-2.17052 + 3.55912i) q^{33} +(-4.25362 - 0.713625i) q^{34} +(2.48669 + 0.807973i) q^{35} +(2.71686 - 0.828164i) q^{36} +(1.20916 + 7.63435i) q^{37} +(-2.04379 - 1.51364i) q^{38} +(-4.04140 + 2.05068i) q^{39} +(-3.84326 + 10.8103i) q^{40} +(0.921914 - 5.82073i) q^{41} +(0.344090 + 1.09289i) q^{42} +7.77044 q^{43} +(-3.55666 + 5.59912i) q^{44} +(-4.07336 + 4.07336i) q^{45} +(-4.16271 - 2.16916i) q^{46} +(-1.37914 + 8.70752i) q^{47} +(-4.83523 + 1.37781i) q^{48} +(-6.26225 + 2.03473i) q^{49} +(-2.38766 - 16.0216i) q^{50} +(3.10126 + 2.25320i) q^{51} +(-6.48919 + 3.14490i) q^{52} +(-2.08960 + 6.43114i) q^{53} +(-7.74877 - 1.30000i) q^{54} +(1.02672 - 13.4142i) q^{55} +(0.515628 + 1.74871i) q^{56} +(1.02620 + 2.01403i) q^{57} +(-2.35393 - 4.72615i) q^{58} +(4.40916 - 0.698342i) q^{59} +(7.34105 - 7.07742i) q^{60} +(0.113802 + 0.350246i) q^{61} +(7.19474 + 0.0657708i) q^{62} +(-0.143199 + 0.904123i) q^{63} +(-7.73253 + 2.05132i) q^{64} +(8.61642 - 11.8178i) q^{65} +(5.04816 - 3.04517i) q^{66} +(11.0749 + 11.0749i) q^{67} +(4.86831 + 3.67487i) q^{68} +(2.45219 + 3.37515i) q^{69} +(-2.59065 - 2.63845i) q^{70} +(5.34642 - 10.4929i) q^{71} +(-3.94858 - 0.736908i) q^{72} +(-1.21729 - 7.68566i) q^{73} +(3.47281 - 10.3649i) q^{74} +(-4.44891 + 13.6923i) q^{75} +(1.57401 + 3.23401i) q^{76} +(-1.12093 - 1.82040i) q^{77} +(6.40871 + 0.0693206i) q^{78} +(6.12212 + 1.98920i) q^{79} +(11.8849 - 11.0460i) q^{80} +(2.20279 + 1.60042i) q^{81} +(-4.96025 + 6.69758i) q^{82} +(0.306517 - 0.601574i) q^{83} +(0.282699 - 1.59553i) q^{84} +(-12.2188 - 1.93527i) q^{85} +(-9.74531 - 5.07822i) q^{86} +4.69269i q^{87} +(8.11979 - 4.69777i) q^{88} +(-6.49354 - 6.49354i) q^{89} +(7.77068 - 2.44655i) q^{90} +(0.00389267 - 2.32406i) q^{91} +(3.80305 + 5.44092i) q^{92} +(-5.69782 - 2.90318i) q^{93} +(7.42028 - 10.0192i) q^{94} +(-5.90161 - 4.28777i) q^{95} +(6.96455 + 1.43200i) q^{96} +(6.17163 + 12.1125i) q^{97} +(9.18357 + 1.54072i) q^{98} +(4.69474 - 0.379637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Introduction

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