LMFDB - Embedded newform 54.3.f.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,3,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, 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:	$1.47139342755$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	54.47
Dual form			54.3.f.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483690 - 1.32893i) q^{2} +(-0.570511 - 2.94525i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(3.98669 - 0.702961i) q^{5} +(-3.63807 + 2.18276i) q^{6} +(-10.1193 - 8.49107i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-8.34903 + 3.36060i) q^{9} +O(q^{10})$	\(q+(-0.483690 - 1.32893i) q^{2} +(-0.570511 - 2.94525i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(3.98669 - 0.702961i) q^{5} +(-3.63807 + 2.18276i) q^{6} +(-10.1193 - 8.49107i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-8.34903 + 3.36060i) q^{9} +(-2.86250 - 4.95800i) q^{10} +(13.3731 + 2.35805i) q^{11} +(4.66042 + 3.77895i) q^{12} +(17.4463 + 6.34995i) q^{13} +(-6.38942 + 17.5548i) q^{14} +(-4.34485 - 11.3408i) q^{15} +(0.694593 - 3.93923i) q^{16} +(13.8790 - 8.01304i) q^{17} +(8.50433 + 9.46976i) q^{18} +(0.327006 - 0.566391i) q^{19} +(-5.20426 + 6.20219i) q^{20} +(-19.2352 + 34.6480i) q^{21} +(-3.33478 - 18.9125i) q^{22} +(4.24411 + 5.05793i) q^{23} +(2.76776 - 8.02119i) q^{24} +(-8.09277 + 2.94553i) q^{25} -26.2563i q^{26} +(14.6610 + 22.6728i) q^{27} +26.4195 q^{28} +(0.466584 + 1.28193i) q^{29} +(-12.9695 + 11.2594i) q^{30} +(-14.3033 + 12.0019i) q^{31} +(-5.57091 + 0.982302i) q^{32} +(-0.684487 - 40.7326i) q^{33} +(-17.3619 - 14.5683i) q^{34} +(-46.3112 - 26.7378i) q^{35} +(8.47116 - 15.8820i) q^{36} +(-8.43940 - 14.6175i) q^{37} +(-0.910861 - 0.160609i) q^{38} +(8.74887 - 55.0066i) q^{39} +(10.7595 + 3.91614i) q^{40} +(-14.6609 + 40.2805i) q^{41} +(55.3485 + 8.80326i) q^{42} +(0.0113866 - 0.0645766i) q^{43} +(-23.5203 + 13.5794i) q^{44} +(-30.9226 + 19.2667i) q^{45} +(4.66878 - 8.08657i) q^{46} +(30.0861 - 35.8552i) q^{47} +(-11.9983 + 0.201624i) q^{48} +(21.7924 + 123.591i) q^{49} +(7.82877 + 9.32997i) q^{50} +(-31.5186 - 36.3056i) q^{51} +(-34.8927 + 12.6999i) q^{52} -14.3109i q^{53} +(23.0390 - 30.4500i) q^{54} +54.9722 q^{55} +(-12.7788 - 35.1096i) q^{56} +(-1.85472 - 0.639983i) q^{57} +(1.47791 - 1.24011i) q^{58} +(-4.79039 + 0.844675i) q^{59} +(21.2361 + 11.7894i) q^{60} +(-12.0703 - 10.1282i) q^{61} +(22.8680 + 13.2029i) q^{62} +(113.021 + 36.8854i) q^{63} +(4.00000 + 6.92820i) q^{64} +(74.0169 + 13.0512i) q^{65} +(-53.7995 + 20.6116i) q^{66} +(-37.1304 - 13.5143i) q^{67} +(-10.9625 + 30.1192i) q^{68} +(12.4756 - 15.3856i) q^{69} +(-13.1323 + 74.4770i) q^{70} +(-60.9106 + 35.1667i) q^{71} +(-25.2035 - 3.57556i) q^{72} +(-34.1753 + 59.1934i) q^{73} +(-15.3435 + 18.2857i) q^{74} +(13.2923 + 22.1548i) q^{75} +(0.227136 + 1.28815i) q^{76} +(-115.304 - 137.414i) q^{77} +(-77.3315 + 14.9795i) q^{78} +(47.4059 - 17.2543i) q^{79} -16.1928i q^{80} +(58.4127 - 56.1155i) q^{81} +60.6211 q^{82} +(50.2457 + 138.049i) q^{83} +(-15.0726 - 77.8122i) q^{84} +(49.6984 - 41.7019i) q^{85} +(-0.0913252 + 0.0161031i) q^{86} +(3.50941 - 2.10556i) q^{87} +(29.4226 + 24.6885i) q^{88} +(-17.2957 - 9.98568i) q^{89} +(40.5610 + 31.7748i) q^{90} +(-122.626 - 212.395i) q^{91} +(-13.0047 - 2.29308i) q^{92} +(43.5089 + 35.2797i) q^{93} +(-62.2012 - 22.6394i) q^{94} +(0.905521 - 2.48790i) q^{95} +(6.07140 + 15.8473i) q^{96} +(18.3596 - 104.122i) q^{97} +(153.703 - 88.7402i) q^{98} +(-119.577 + 25.2544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	−0.483690	−	1.32893i	−0.241845	−	0.664463i
$2$	−0.483690	−	1.32893i	−0.241845	−	0.664463i
$3$	−0.570511	−	2.94525i	−0.190170	−	0.981751i
$3$	−0.570511	−	2.94525i	−0.190170	−	0.981751i
$4$	−1.53209	+	1.28558i	−0.383022	+	0.321394i
$5$	3.98669	−	0.702961i	0.797338	−	0.140592i	0.239886	−	0.970801i	$-0.422890\pi$
$5$	3.98669	−	0.702961i	0.797338	−	0.140592i	0.557452	+	0.830209i	$0.311779\pi$
$6$	−3.63807	+	2.18276i	−0.606346	+	0.363793i
$7$	−10.1193	−	8.49107i	−1.44561	−	1.21301i	−0.935708	−	0.352776i	$-0.885238\pi$
$7$	−10.1193	−	8.49107i	−1.44561	−	1.21301i	−0.509901	−	0.860233i	$-0.670318\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$	−8.34903	+	3.36060i	−0.927670	+	0.373400i
$10$	−2.86250	−	4.95800i	−0.286250	−	0.495800i
$11$	13.3731	+	2.35805i	1.21574	+	0.214368i	0.744491	−	0.667632i	$-0.232692\pi$
$11$	13.3731	+	2.35805i	1.21574	+	0.214368i	0.471249	+	0.882000i	$0.343803\pi$
$12$	4.66042	+	3.77895i	0.388368	+	0.314913i
$13$	17.4463	+	6.34995i	1.34203	+	0.488458i	0.910450	−	0.413619i	$-0.135735\pi$
$13$	17.4463	+	6.34995i	1.34203	+	0.488458i	0.431576	+	0.902077i	$0.357958\pi$
$14$	−6.38942	+	17.5548i	−0.456387	+	1.25391i
$15$	−4.34485	−	11.3408i	−0.289657	−	0.756051i
$16$	0.694593	−	3.93923i	0.0434120	−	0.246202i
$17$	13.8790	−	8.01304i	0.816411	−	0.471355i	−0.0327659	−	0.999463i	$-0.510432\pi$
$17$	13.8790	−	8.01304i	0.816411	−	0.471355i	0.849177	+	0.528108i	$0.177098\pi$
$18$	8.50433	+	9.46976i	0.472463	+	0.526098i
$19$	0.327006	−	0.566391i	0.0172108	−	0.0298100i	−0.857292	−	0.514831i	$-0.827855\pi$
$19$	0.327006	−	0.566391i	0.0172108	−	0.0298100i	0.874503	+	0.485021i	$0.161188\pi$
$20$	−5.20426	+	6.20219i	−0.260213	+	0.310109i
$21$	−19.2352	+	34.6480i	−0.915962	+	1.64991i
$22$	−3.33478	−	18.9125i	−0.151581	−	0.859658i
$23$	4.24411	+	5.05793i	0.184526	+	0.219910i	0.850375	−	0.526177i	$-0.176375\pi$
$23$	4.24411	+	5.05793i	0.184526	+	0.219910i	−0.665849	+	0.746087i	$0.731930\pi$
$24$	2.76776	−	8.02119i	0.115323	−	0.334216i
$25$	−8.09277	+	2.94553i	−0.323711	+	0.117821i
$26$		−	26.2563i		−	1.00986i
$27$	14.6610	+	22.6728i	0.543001	+	0.839732i
$28$	26.4195			0.943554
$29$	0.466584	+	1.28193i	0.0160891	+	0.0442044i	0.947477	−	0.319823i	$-0.103624\pi$
$29$	0.466584	+	1.28193i	0.0160891	+	0.0442044i	−0.931388	+	0.364028i	$0.881401\pi$
$30$	−12.9695	+	11.2594i	−0.432316	+	0.375313i
$31$	−14.3033	+	12.0019i	−0.461397	+	0.387158i	−0.843645	−	0.536902i	$-0.819595\pi$
$31$	−14.3033	+	12.0019i	−0.461397	+	0.387158i	0.382247	+	0.924060i	$0.375150\pi$
$32$	−5.57091	+	0.982302i	−0.174091	+	0.0306970i
$33$	−0.684487	−	40.7326i	−0.0207420	−	1.23432i
$34$	−17.3619	−	14.5683i	−0.510643	−	0.428480i
$35$	−46.3112	−	26.7378i	−1.32318	−	0.763937i
$36$	8.47116	−	15.8820i	0.235310	−	0.441168i
$37$	−8.43940	−	14.6175i	−0.228092	−	0.395067i	0.729151	−	0.684353i	$-0.239915\pi$
$37$	−8.43940	−	14.6175i	−0.228092	−	0.395067i	−0.957243	+	0.289286i	$0.906582\pi$
$38$	−0.910861	−	0.160609i	−0.0239700	−	0.00422656i
$39$	8.74887	−	55.0066i	0.224330	−	1.41043i
$40$	10.7595	+	3.91614i	0.268987	+	0.0979034i
$41$	−14.6609	+	40.2805i	−0.357583	+	0.982450i	0.622283	+	0.782792i	$0.286205\pi$
$41$	−14.6609	+	40.2805i	−0.357583	+	0.982450i	−0.979866	+	0.199658i	$0.936017\pi$
$42$	55.3485	+	8.80326i	1.31782	+	0.209601i
$43$	0.0113866	−	0.0645766i	0.000264805	−	0.00150178i	−0.984675	−	0.174399i	$-0.944202\pi$
$43$	0.0113866	−	0.0645766i	0.000264805	−	0.00150178i	0.984940	+	0.172897i	$0.0553129\pi$
$44$	−23.5203	+	13.5794i	−0.534552	+	0.308624i
$45$	−30.9226	+	19.2667i	−0.687170	+	0.428149i
$46$	4.66878	−	8.08657i	0.101495	−	0.175795i
$47$	30.0861	−	35.8552i	0.640129	−	0.762876i	−0.344262	−	0.938874i	$-0.611871\pi$
$47$	30.0861	−	35.8552i	0.640129	−	0.762876i	0.984391	+	0.175998i	$0.0563152\pi$
$48$	−11.9983	+	0.201624i	−0.249965	+	0.00420051i
$49$	21.7924	+	123.591i	0.444744	+	2.52227i
$50$	7.82877	+	9.32997i	0.156575	+	0.186599i
$51$	−31.5186	−	36.3056i	−0.618011	−	0.711875i
$52$	−34.8927	+	12.6999i	−0.671013	+	0.244229i
$53$		−	14.3109i		−	0.270017i	−0.990844	−	0.135008i	$-0.956894\pi$
$53$		−	14.3109i		−	0.270017i	0.990844	−	0.135008i	$-0.0431061\pi$
$54$	23.0390	−	30.4500i	0.426649	−	0.563889i
$55$	54.9722			0.999494
$56$	−12.7788	−	35.1096i	−0.228194	−	0.626957i
$57$	−1.85472	−	0.639983i	−0.0325390	−	0.0112278i
$58$	1.47791	−	1.24011i	0.0254811	−	0.0213812i
$59$	−4.79039	+	0.844675i	−0.0811930	+	0.0143165i	−0.214097	−	0.976812i	$-0.568681\pi$
$59$	−4.79039	+	0.844675i	−0.0811930	+	0.0143165i	0.132904	+	0.991129i	$0.457570\pi$
$60$	21.2361	+	11.7894i	0.353935	+	0.196490i
$61$	−12.0703	−	10.1282i	−0.197874	−	0.166036i	0.538467	−	0.842646i	$-0.319004\pi$
$61$	−12.0703	−	10.1282i	−0.197874	−	0.166036i	−0.736341	+	0.676611i	$0.763448\pi$
$62$	22.8680	+	13.2029i	0.368839	+	0.212949i
$63$	113.021	+	36.8854i	1.79399	+	0.585483i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	74.0169	+	13.0512i	1.13872	+	0.200787i
$66$	−53.7995	+	20.6116i	−0.815144	+	0.312296i
$67$	−37.1304	−	13.5143i	−0.554185	−	0.201707i	0.0497202	−	0.998763i	$-0.484167\pi$
$67$	−37.1304	−	13.5143i	−0.554185	−	0.201707i	−0.603905	+	0.797056i	$0.706389\pi$
$68$	−10.9625	+	30.1192i	−0.161213	+	0.442929i
$69$	12.4756	−	15.3856i	0.180805	−	0.222979i
$70$	−13.1323	+	74.4770i	−0.187604	+	1.06396i
$71$	−60.9106	+	35.1667i	−0.857896	+	0.495306i	−0.863307	−	0.504679i	$-0.831611\pi$
$71$	−60.9106	+	35.1667i	−0.857896	+	0.495306i	0.00541136	+	0.999985i	$0.498278\pi$
$72$	−25.2035	−	3.57556i	−0.350048	−	0.0496606i
$73$	−34.1753	+	59.1934i	−0.468155	+	0.810868i	−0.999338	−	0.0363890i	$-0.988414\pi$
$73$	−34.1753	+	59.1934i	−0.468155	+	0.810868i	0.531183	+	0.847257i	$0.321748\pi$
$74$	−15.3435	+	18.2857i	−0.207344	+	0.247103i
$75$	13.2923	+	22.1548i	0.177231	+	0.295397i
$76$	0.227136	+	1.28815i	0.00298863	+	0.0169494i
$77$	−115.304	−	137.414i	−1.49745	−	1.78460i
$78$	−77.3315	+	14.9795i	−0.991429	+	0.192045i
$79$	47.4059	−	17.2543i	0.600074	−	0.218409i	−0.0240804	−	0.999710i	$-0.507666\pi$
$79$	47.4059	−	17.2543i	0.600074	−	0.218409i	0.624155	+	0.781301i	$0.285444\pi$
$80$		−	16.1928i		−	0.202410i
$81$	58.4127	−	56.1155i	0.721145	−	0.692784i
$82$	60.6211			0.739281
$83$	50.2457	+	138.049i	0.605370	+	1.66324i	0.740211	+	0.672374i	$0.234725\pi$
$83$	50.2457	+	138.049i	0.605370	+	1.66324i	−0.134841	+	0.990867i	$0.543052\pi$
$84$	−15.0726	−	77.8122i	−0.179436	−	0.926335i
$85$	49.6984	−	41.7019i	0.584687	−	0.490611i
$86$	−0.0913252	+	0.0161031i	−0.00106192	+	0.000187245i
$87$	3.50941	−	2.10556i	0.0403381	−	0.0242019i
$88$	29.4226	+	24.6885i	0.334348	+	0.280551i
$89$	−17.2957	−	9.98568i	−0.194334	−	0.112199i	0.399676	−	0.916656i	$-0.369123\pi$
$89$	−17.2957	−	9.98568i	−0.194334	−	0.112199i	−0.594010	+	0.804458i	$0.702456\pi$
$90$	40.5610	+	31.7748i	0.450678	+	0.353053i
$91$	−122.626	−	212.395i	−1.34754	−	2.33401i
$92$	−13.0047	−	2.29308i	−0.141355	−	0.0249248i
$93$	43.5089	+	35.2797i	0.467837	+	0.379351i
$94$	−62.2012	−	22.6394i	−0.661715	−	0.240844i
$95$	0.905521	−	2.48790i	0.00953180	−	0.0261884i
$96$	6.07140	+	15.8473i	0.0632437	+	0.165076i
$97$	18.3596	−	104.122i	0.189274	−	1.07343i	−0.731066	−	0.682307i	$-0.760977\pi$
$97$	18.3596	−	104.122i	0.189274	−	1.07343i	0.920340	−	0.391120i	$-0.127912\pi$
$98$	153.703	−	88.7402i	1.56839	−	0.905513i
$99$	−119.577	+	25.2544i	−1.20785	+	0.255095i
$100$	8.61214	−	14.9167i	0.0861214	−	0.149167i
$101$	38.7455	−	46.1751i	0.383619	−	0.457179i	−0.539334	−	0.842092i	$-0.681324\pi$
$101$	38.7455	−	46.1751i	0.383619	−	0.457179i	0.922953	+	0.384913i	$0.125768\pi$
$102$	−33.0023	+	59.4465i	−0.323552	+	0.582809i
$103$	−16.6921	−	94.6657i	−0.162059	−	0.919085i	−0.952045	−	0.305959i	$-0.901023\pi$
$103$	−16.6921	−	94.6657i	−0.162059	−	0.919085i	0.789985	−	0.613126i	$-0.210088\pi$
$104$	33.7544	+	40.2270i	0.324562	+	0.386798i
$105$	−52.3285	+	151.653i	−0.498367	+	1.44431i
$106$	−19.0181	+	6.92202i	−0.179416	+	0.0653021i
$107$			107.330i			1.00308i	0.865133	+	0.501542i	$0.167234\pi$
$107$			107.330i			1.00308i	−0.865133	+	0.501542i	$0.832766\pi$
$108$	−51.6095	−	15.8888i	−0.477866	−	0.147119i
$109$	85.1199			0.780917			0.390458	−	0.920621i	$-0.372317\pi$
$109$	85.1199			0.780917			0.390458	+	0.920621i	$0.372317\pi$
$110$	−26.5895	−	73.0540i	−0.241722	−	0.664127i
$111$	−38.2374	+	33.1956i	−0.344481	+	0.299059i
$112$	−40.4770	+	33.9643i	−0.361402	+	0.303252i
$113$	165.620	−	29.2032i	1.46566	−	0.258436i	0.616828	−	0.787098i	$-0.288417\pi$
$113$	165.620	−	29.2032i	1.46566	−	0.258436i	0.848832	+	0.528662i	$0.177306\pi$
$114$	0.0466212	+	2.77435i	0.000408958	+	0.0243364i
$115$	20.4755	+	17.1810i	0.178047	+	0.149400i
$116$	−2.36286	−	1.36420i	−0.0203695	−	0.0117603i
$117$	−167.000	+	5.61425i	−1.42735	+	0.0479850i
$118$	3.43957	+	5.95751i	0.0291489	+	0.0504874i
$119$	−208.484	−	36.7614i	−1.75197	−	0.308920i
$120$	5.39560	−	33.9236i	0.0449633	−	0.282697i
$121$	59.5777	+	21.6845i	0.492378	+	0.179211i
$122$	−7.62133	+	20.9394i	−0.0624699	+	0.171635i
$123$	127.000	+	20.1996i	1.03252	+	0.164224i
$124$	6.48460	−	36.7760i	0.0522952	−	0.296581i
$125$	−117.839	+	68.0342i	−0.942710	+	0.544274i
$126$	−5.64915	−	168.038i	−0.0448345	−	1.33363i
$127$	−85.8323	+	148.666i	−0.675845	+	1.17060i	0.300377	+	0.953821i	$0.402888\pi$
$127$	−85.8323	+	148.666i	−0.675845	+	1.17060i	−0.976221	+	0.216777i	$0.930446\pi$
$128$	7.27231	−	8.66680i	0.0568149	−	0.0677094i
$129$	−0.196691	+	0.00330527i	−0.00152473	+	2.56223e-5i
$130$	−18.4572	−	104.676i	−0.141978	−	0.805198i
$131$	112.534	+	134.113i	0.859038	+	1.02376i	0.999433	+	0.0336659i	$0.0107182\pi$
$131$	112.534	+	134.113i	0.859038	+	1.02376i	−0.140395	+	0.990096i	$0.544837\pi$
$132$	53.4135	+	61.5260i	0.404648	+	0.466106i
$133$	−8.11832	+	2.95483i	−0.0610400	+	0.0222167i
$134$			55.8803i			0.417017i
$135$	74.3871	+	80.0831i	0.551015	+	0.593208i
$136$	45.3286			0.333299
$137$	16.7909	+	46.1327i	0.122561	+	0.336735i	0.985767	−	0.168118i	$-0.0537690\pi$
$137$	16.7909	+	46.1327i	0.122561	+	0.336735i	−0.863205	+	0.504853i	$0.831547\pi$
$138$	−26.4806	−	9.13727i	−0.191888	−	0.0662121i
$139$	−107.159	+	89.9168i	−0.770926	+	0.646884i	−0.940946	−	0.338557i	$-0.890061\pi$
$139$	−107.159	+	89.9168i	−0.770926	+	0.646884i	0.170020	+	0.985441i	$0.445617\pi$
$140$	105.326	−	18.5719i	0.752332	−	0.132656i
$141$	−122.767	−	68.1553i	−0.870688	−	0.483371i
$142$	76.1958	+	63.9359i	0.536590	+	0.450253i
$143$	218.339	+	126.058i	1.52685	+	0.881525i
$144$	7.43900	+	35.2230i	0.0516597	+	0.244604i
$145$	2.76127	+	4.78266i	0.0190432	+	0.0329839i
$146$	95.1939	+	16.7853i	0.652013	+	0.114967i
$147$	351.574	−	134.694i	2.39166	−	0.916288i
$148$	31.7218	+	11.5458i	0.214336	+	0.0780120i
$149$	82.1753	−	225.775i	0.551512	−	1.51527i	−0.280134	−	0.959961i	$-0.590379\pi$
$149$	82.1753	−	225.775i	0.551512	−	1.51527i	0.831646	−	0.555306i	$-0.187399\pi$
$150$	23.0127	−	28.3806i	0.153418	−	0.189204i
$151$	3.53844	−	20.0675i	0.0234334	−	0.132897i	−0.970847	−	0.239701i	$-0.922951\pi$
$151$	3.53844	−	20.0675i	0.0234334	−	0.132897i	0.994280	+	0.106804i	$0.0340617\pi$
$152$	1.60200	−	0.924912i	0.0105394	−	0.00608495i
$153$	−88.9476	+	113.543i	−0.581357	+	0.742111i
$154$	−126.842	+	219.696i	−0.823647	+	1.42660i
$155$	−48.5860	+	57.9026i	−0.313458	+	0.373565i
$156$	57.3111	+	95.5223i	0.367379	+	0.612323i
$157$	−39.0295	−	221.347i	−0.248596	−	1.40986i	−0.811992	−	0.583669i	$-0.801617\pi$
$157$	−39.0295	−	221.347i	−0.248596	−	1.40986i	0.563396	−	0.826187i	$-0.309495\pi$
$158$	−45.8594	−	54.6531i	−0.290250	−	0.345906i
$159$	−42.1492	+	8.16452i	−0.265089	+	0.0513492i
$160$	−21.5190	+	7.83227i	−0.134494	+	0.0489517i
$161$		−	87.2195i		−	0.541736i
$162$	−102.827	−	50.4837i	−0.634735	−	0.311628i
$163$	−155.441			−0.953626			−0.476813	−	0.879005i	$-0.658208\pi$
$163$	−155.441			−0.953626			−0.476813	+	0.879005i	$0.658208\pi$
$164$	−29.3218	−	80.5609i	−0.178791	−	0.491225i
$165$	−31.3623	−	161.907i	−0.190074	−	0.981255i
$166$	159.154	−	133.546i	0.958757	−	0.804493i
$167$	−316.191	+	55.7529i	−1.89336	+	0.333850i	−0.994530	−	0.104454i	$-0.966690\pi$
$167$	−316.191	+	55.7529i	−1.89336	+	0.333850i	−0.898827	+	0.438304i	$0.855579\pi$
$168$	−96.1161	+	57.6673i	−0.572120	+	0.343258i
$169$	134.591	+	112.936i	0.796399	+	0.668258i
$170$	−79.4574	−	45.8747i	−0.467396	−	0.269851i
$171$	−0.826770	+	5.82775i	−0.00483491	+	0.0340804i
$172$	0.0655728	+	0.113575i	0.000381237	+	0.000660323i
$173$	−140.320	−	24.7423i	−0.811100	−	0.143019i	−0.247309	−	0.968937i	$-0.579546\pi$
$173$	−140.320	−	24.7423i	−0.811100	−	0.143019i	−0.563791	+	0.825918i	$0.690658\pi$
$174$	−4.49560	−	3.64531i	−0.0258368	−	0.0209501i
$175$	106.903	+	38.9097i	0.610877	+	0.222341i
$176$	18.5778	−	51.0420i	0.105556	−	0.290011i
$177$	5.22075	+	13.6270i	0.0294958	+	0.0769888i
$178$	−4.90448	+	27.8147i	−0.0275533	+	0.156262i
$179$	186.101	−	107.445i	1.03967	−	0.600253i	0.119930	−	0.992782i	$-0.461733\pi$
$179$	186.101	−	107.445i	1.03967	−	0.600253i	0.919740	+	0.392529i	$0.128400\pi$
$180$	22.6074	−	69.2717i	0.125597	−	0.384843i
$181$	−150.873	+	261.319i	−0.833550	+	1.44375i	0.0616551	+	0.998098i	$0.480362\pi$
$181$	−150.873	+	261.319i	−0.833550	+	1.44375i	−0.895205	+	0.445654i	$0.852971\pi$
$182$	−222.944	+	265.694i	−1.22497	+	1.45986i
$183$	−22.9438	+	41.3283i	−0.125376	+	0.225838i
$184$	3.24290	+	18.3914i	0.0176245	+	0.0999533i
$185$	−43.9208	−	52.3427i	−0.237410	−	0.282934i
$186$	25.8393	−	74.8845i	0.138921	−	0.402605i
$187$	204.501	−	74.4322i	1.09359	−	0.398033i
$188$			93.6112i			0.497932i
$189$	44.1571	−	353.919i	0.233635	−	1.87259i
$190$	−3.74422			−0.0197064
$191$	−101.886	−	279.928i	−0.533433	−	1.46559i	−0.854960	−	0.518694i	$-0.826418\pi$
$191$	−101.886	−	279.928i	−0.533433	−	1.46559i	0.321527	−	0.946900i	$-0.395804\pi$
$192$	18.1233	−	15.7336i	0.0943920	−	0.0819460i
$193$	96.4229	−	80.9084i	0.499601	−	0.419215i	−0.357852	−	0.933778i	$-0.616491\pi$
$193$	96.4229	−	80.9084i	0.499601	−	0.419215i	0.857452	+	0.514564i	$0.172046\pi$
$194$	−147.251	+	25.9644i	−0.759027	+	0.133837i
$195$	−3.78846	−	225.444i	−0.0194280	−	1.15613i
$196$	−192.274	−	161.337i	−0.980987	−	0.823146i
$197$	−37.5877	−	21.7013i	−0.190801	−	0.110159i	0.401557	−	0.915834i	$-0.368469\pi$
$197$	−37.5877	−	21.7013i	−0.190801	−	0.110159i	−0.592357	+	0.805675i	$0.701803\pi$
$198$	91.3995	+	146.694i	0.461613	+	0.740879i
$199$	37.8343	+	65.5310i	0.190122	+	0.329301i	0.945291	−	0.326230i	$-0.105778\pi$
$199$	37.8343	+	65.5310i	0.190122	+	0.329301i	−0.755168	+	0.655531i	$0.772445\pi$
$200$	−23.9888	−	4.22986i	−0.119944	−	0.0211493i
$201$	−18.6199	+	117.068i	−0.0926362	+	0.582430i
$202$	−80.1041	−	29.1555i	−0.396555	−	0.144334i
$203$	6.16346	−	16.9340i	0.0303619	−	0.0834185i
$204$	94.9628	+	15.1040i	0.465504	+	0.0740390i
$205$	−30.1328	+	170.892i	−0.146989	+	0.833618i
$206$	−117.730	+	67.9714i	−0.571505	+	0.329958i
$207$	−52.4319	−	27.9661i	−0.253294	−	0.135102i
$208$	37.1320	−	64.3145i	0.178519	−	0.309205i
$209$	5.70867	−	6.80333i	0.0273142	−	0.0325518i
$210$	226.846	−	3.81201i	1.08022	−	0.0181524i
$211$	37.4085	+	212.154i	0.177291	+	1.00547i	0.935466	+	0.353418i	$0.114981\pi$
$211$	37.4085	+	212.154i	0.177291	+	1.00547i	−0.758174	+	0.652052i	$0.773908\pi$
$212$	18.3977	+	21.9255i	0.0867817	+	0.103422i
$213$	138.325	+	159.334i	0.649414	+	0.748047i
$214$	142.634	−	51.9144i	0.666512	−	0.242591i
$215$		−	0.265451i		−	0.00123466i
$216$	3.84794	+	76.2705i	0.0178145	+	0.353104i
$217$	246.648			1.13663
$218$	−41.1716	−	113.118i	−0.188861	−	0.518890i
$219$	193.837	+	66.8845i	0.885100	+	0.305409i
$220$	−84.2223	+	70.6709i	−0.382829	+	0.321231i
$221$	293.020	−	51.6673i	1.32588	−	0.233789i
$222$	62.6095	+	34.7583i	0.282025	+	0.156569i
$223$	−63.7410	−	53.4851i	−0.285834	−	0.239843i	0.488585	−	0.872516i	$-0.337513\pi$
$223$	−63.7410	−	53.4851i	−0.285834	−	0.239843i	−0.774419	+	0.632673i	$0.781958\pi$
$224$	64.7143	+	37.3628i	0.288903	+	0.166798i
$225$	57.6681	−	51.7889i	0.256302	−	0.230173i
$226$	−118.917	−	205.971i	−0.526183	−	0.911376i
$227$	−61.5724	−	10.8569i	−0.271244	−	0.0478276i	0.0363717	−	0.999338i	$-0.488420\pi$
$227$	−61.5724	−	10.8569i	−0.271244	−	0.0478276i	−0.307616	+	0.951511i	$0.599531\pi$
$228$	3.66435	−	1.40388i	0.0160717	−	0.00615736i
$229$	−136.445	−	49.6621i	−0.595831	−	0.216865i	0.0264609	−	0.999650i	$-0.491576\pi$
$229$	−136.445	−	49.6621i	−0.595831	−	0.216865i	−0.622292	+	0.782785i	$0.713798\pi$
$230$	12.9284	−	35.5206i	0.0562106	−	0.154437i
$231$	−338.937	+	417.996i	−1.46726	+	1.80950i
$232$	−0.670028	+	3.79992i	−0.00288805	+	0.0163790i
$233$	−117.176	+	67.6517i	−0.502902	+	0.290351i	−0.729911	−	0.683542i	$-0.760439\pi$
$233$	−117.176	+	67.6517i	−0.502902	+	0.290351i	0.227009	+	0.973893i	$0.427105\pi$
$234$	88.2369	+	219.215i	0.377081	+	0.936815i
$235$	94.7390	−	164.093i	0.403145	−	0.698267i
$236$	6.25341	−	7.45252i	0.0264975	−	0.0315785i
$237$	−77.8639	−	129.778i	−0.328540	−	0.547588i
$238$	51.9885	+	294.842i	0.218439	+	1.23883i
$239$	94.2026	+	112.266i	0.394153	+	0.469733i	0.926228	−	0.376964i	$-0.123032\pi$
$239$	94.2026	+	112.266i	0.394153	+	0.469733i	−0.532075	+	0.846697i	$0.678588\pi$
$240$	−47.6918	+	9.23816i	−0.198716	+	0.0384923i
$241$	−298.014	+	108.468i	−1.23657	+	0.450075i	−0.875843	−	0.482596i	$-0.839694\pi$
$241$	−298.014	+	108.468i	−1.23657	+	0.450075i	−0.360728	+	0.932671i	$0.617472\pi$
$242$		−	89.6629i		−	0.370508i
$243$	−198.600	−	140.026i	−0.817282	−	0.576238i
$244$	31.5133			0.129153
$245$	173.759	+	477.400i	0.709222	+	1.94857i
$246$	−34.5850	−	178.544i	−0.140589	−	0.725790i
$247$	9.30161	−	7.80498i	0.0376583	−	0.0315991i
$248$	−52.0091	+	9.17061i	−0.209714	+	0.0369783i
$249$	377.924	−	226.745i	1.51777	−	0.910623i
$250$	147.410	+	123.691i	0.589639	+	0.494766i
$251$	−137.930	−	79.6340i	−0.549522	−	0.317267i	0.199407	−	0.979917i	$-0.436098\pi$
$251$	−137.930	−	79.6340i	−0.549522	−	0.317267i	−0.748929	+	0.662650i	$0.769432\pi$
$252$	−220.577	+	88.7854i	−0.875307	+	0.352323i
$253$	44.8302	+	77.6482i	0.177194	+	0.306910i
$254$	239.082	+	42.1566i	0.941268	+	0.165971i
$255$	−151.176	−	122.583i	−0.592848	−	0.480718i
$256$	−15.0351	−	5.47232i	−0.0587308	−	0.0213763i
$257$	−20.7153	+	56.9148i	−0.0806043	+	0.221458i	−0.973448	−	0.228908i	$-0.926484\pi$
$257$	−20.7153	+	56.9148i	−0.0806043	+	0.221458i	0.892844	+	0.450367i	$0.148707\pi$
$258$	0.0995297	+	0.259789i	0.000385774	+	0.00100693i
$259$	−38.7174	+	219.577i	−0.149488	+	0.847789i
$260$	−130.179	+	75.1588i	−0.500688	+	0.289072i
$261$	−8.20357	−	9.13486i	−0.0314313	−	0.0349995i
$262$	123.794	−	214.418i	0.472498	−	0.818390i
$263$	217.155	−	258.796i	0.825686	−	0.984014i	−0.174314	−	0.984690i	$-0.555771\pi$
$263$	217.155	−	258.796i	0.825686	−	0.984014i	1.00000		0.000676331i	$0.000215283\pi$
$264$	55.9279	−	100.742i	0.211848	−	0.381599i
$265$	−10.0600	−	57.0530i	−0.0379622	−	0.215295i
$266$	7.85349	+	9.35943i	0.0295244	+	0.0351858i
$267$	−19.5430	+	56.6372i	−0.0731946	+	0.212124i
$268$	74.2607	−	27.0287i	0.277092	−	0.100853i
$269$			39.0580i			0.145197i	0.997361	+	0.0725986i	$0.0231292\pi$
$269$			39.0580i			0.145197i	−0.997361	+	0.0725986i	$0.976871\pi$
$270$	70.4443	−	137.590i	0.260905	−	0.509594i
$271$	247.005			0.911459			0.455730	−	0.890118i	$-0.349378\pi$
$271$	247.005			0.911459			0.455730	+	0.890118i	$0.349378\pi$
$272$	−21.9250	−	60.2384i	−0.0806065	−	0.221465i
$273$	−555.597	+	482.339i	−2.03515	+	1.76681i
$274$	53.1853	−	44.6278i	0.194107	−	0.162875i
$275$	−115.171	+	20.3078i	−0.418805	+	0.0738466i
$276$	0.665628	+	39.6103i	0.00241170	+	0.143516i
$277$	−146.095	−	122.589i	−0.527420	−	0.442558i	0.339789	−	0.940502i	$-0.389644\pi$
$277$	−146.095	−	122.589i	−0.527420	−	0.442558i	−0.867209	+	0.497943i	$0.834089\pi$
$278$	171.324	+	98.9142i	0.616275	+	0.355806i
$279$	79.0853	−	148.272i	0.283460	−	0.531441i
$280$	−75.6260	−	130.988i	−0.270093	−	0.467814i
$281$	133.542	+	23.5471i	0.475239	+	0.0837975i	0.406137	−	0.913812i	$-0.366876\pi$
$281$	133.542	+	23.5471i	0.475239	+	0.0837975i	0.0691020	+	0.997610i	$0.477987\pi$
$282$	−31.1922	+	196.114i	−0.110611	+	0.695441i
$283$	−436.119	−	158.734i	−1.54106	−	0.560898i	−0.574758	−	0.818324i	$-0.694904\pi$
$283$	−436.119	−	158.734i	−1.54106	−	0.560898i	−0.966298	+	0.257425i	$0.917126\pi$
$284$	48.1109	−	132.184i	0.169405	−	0.465436i
$285$	−7.84410	−	1.24761i	−0.0275231	−	0.00437759i
$286$	61.9136	−	351.129i	0.216481	−	1.22772i
$287$	490.381	−	283.122i	1.70865	−	0.986487i
$288$	43.2106	−	26.9229i	0.150037	−	0.0934823i
$289$	−16.0823	+	27.8554i	−0.0556482	+	0.0963855i
$290$	5.02021	−	5.98285i	0.0173111	−	0.0206305i
$291$	−317.141	+	5.32937i	−1.08983	+	0.0183140i
$292$	−23.7379	−	134.624i	−0.0812943	−	0.461043i
$293$	86.9857	+	103.665i	0.296879	+	0.353807i	0.893778	−	0.448510i	$-0.148045\pi$
$293$	86.9857	+	103.665i	0.296879	+	0.353807i	−0.596899	+	0.802317i	$0.703601\pi$
$294$	−349.052	−	402.066i	−1.18725	−	1.36757i
$295$	−18.5040	+	6.73492i	−0.0627255	+	0.0228302i
$296$		−	47.7404i		−	0.161285i
$297$	142.601	+	337.777i	0.480137	+	1.13730i
$298$	−339.785			−1.14022
$299$	41.9265	+	115.192i	0.140222	+	0.385258i
$300$	−48.8467	−	16.8548i	−0.162822	−	0.0561827i
$301$	−0.663549	+	0.556783i	−0.00220448	+	0.00184978i
$302$	−28.3797	+	5.00411i	−0.0939726	+	0.0165699i
$303$	−158.102	−	87.7719i	−0.521789	−	0.289676i
$304$	−2.00401	−	1.68156i	−0.00659213	−	0.00553146i
$305$	−55.2403	−	31.8930i	−0.181116	−	0.104567i
$306$	193.913	+	63.2852i	0.633703	+	0.206814i
$307$	−174.308	−	301.910i	−0.567778	−	0.983421i	−0.996785	−	0.0801195i	$-0.974470\pi$
$307$	−174.308	−	301.910i	−0.567778	−	0.983421i	0.429007	−	0.903301i	$-0.358864\pi$
$308$	353.312	+	62.2984i	1.14712	+	0.202268i
$309$	−269.291	+	103.170i	−0.871493	+	0.333885i
$310$	100.449	+	36.5604i	0.324028	+	0.117937i
$311$	−74.9120	+	205.819i	−0.240875	+	0.661798i	0.759067	+	0.651012i	$0.225655\pi$
$311$	−74.9120	+	205.819i	−0.240875	+	0.661798i	−0.999942	+	0.0107853i	$0.996567\pi$
$312$	99.2214	−	122.365i	0.318017	−	0.392197i
$313$	47.2508	−	267.973i	0.150961	−	0.856143i	−0.811425	−	0.584457i	$-0.801308\pi$
$313$	47.2508	−	267.973i	0.150961	−	0.856143i	0.962386	−	0.271686i	$-0.0875813\pi$
$314$	−275.276	+	158.931i	−0.876676	+	0.506149i
$315$	476.509	+	67.6013i	1.51273	+	0.214607i
$316$	−50.4483	+	87.3789i	−0.159646	+	0.276516i
$317$	300.183	−	357.744i	0.946949	−	1.12853i	−0.0446266	−	0.999004i	$-0.514210\pi$
$317$	300.183	−	357.744i	0.946949	−	1.12853i	0.991576	−	0.129527i	$-0.0413457\pi$
$318$	31.2371	+	52.0640i	0.0982300	+	0.163723i
$319$	3.21684	+	18.2436i	0.0100842	+	0.0571901i
$320$	20.8170	+	24.8088i	0.0650532	+	0.0775274i
$321$	316.114	−	61.2330i	0.984779	−	0.190757i
$322$	−115.908	+	42.1871i	−0.359963	+	0.131016i
$323$		−	10.4812i		−	0.0324497i
$324$	−17.3528	+	161.068i	−0.0535579	+	0.497123i
$325$	−159.893			−0.491979
$326$	75.1852	+	206.570i	0.230630	+	0.633650i
$327$	−48.5619	−	250.700i	−0.148507	−	0.766666i
$328$	−92.8768	+	77.9329i	−0.283161	+	0.237600i
$329$	−608.897	+	107.365i	−1.85075	+	0.326337i
$330$	−199.993	+	119.991i	−0.606039	+	0.363609i
$331$	79.5802	+	66.7757i	0.240423	+	0.201739i	0.755036	−	0.655684i	$-0.227620\pi$
$331$	79.5802	+	66.7757i	0.240423	+	0.201739i	−0.514612	+	0.857423i	$0.672064\pi$
$332$	−254.453	−	146.909i	−0.766426	−	0.442496i
$333$	119.584	+	93.6803i	0.359112	+	0.281322i
$334$	227.030	+	393.227i	0.679729	+	1.17733i
$335$	−157.527	−	27.7763i	−0.470231	−	0.0829144i
$336$	123.126	+	99.8381i	0.366446	+	0.297137i
$337$	529.219	+	192.620i	1.57038	+	0.571573i	0.973085	−	0.230447i	$-0.0740189\pi$
$337$	529.219	+	192.620i	1.57038	+	0.571573i	0.597298	+	0.802020i	$0.296241\pi$
$338$	84.9826	−	233.488i	0.251428	−	0.690792i
$339$	−180.499	−	471.131i	−0.532445	−	1.38977i
$340$	−22.5314	+	127.782i	−0.0662689	+	0.375830i
$341$	−219.581	+	126.775i	−0.643934	+	0.371775i
$342$	8.14455	−	1.72011i	0.0238145	−	0.00502955i
$343$	505.258	−	875.132i	1.47305	−	2.55140i
$344$	0.119217	−	0.142077i	0.000346560	−	0.000413014i
$345$	38.9208	−	70.1073i	0.112814	−	0.203210i
$346$	34.9908	+	198.443i	0.101130	+	0.573534i
$347$	174.719	+	208.222i	0.503512	+	0.600062i	0.956600	−	0.291403i	$-0.0941222\pi$
$347$	174.719	+	208.222i	0.503512	+	0.600062i	−0.453088	+	0.891466i	$0.649678\pi$
$348$	−2.66987	+	7.73752i	−0.00767205	+	0.0222343i
$349$	−75.3775	+	27.4352i	−0.215981	+	0.0786108i	−0.447745	−	0.894161i	$-0.647773\pi$
$349$	−75.3775	+	27.4352i	−0.215981	+	0.0786108i	0.231763	+	0.972772i	$0.425550\pi$
$350$		−	160.887i		−	0.459677i
$351$	111.811	+	488.654i	0.318549	+	1.39218i
$352$	−76.8169			−0.218230
$353$	−40.8280	−	112.174i	−0.115660	−	0.317773i	0.868333	−	0.495982i	$-0.165192\pi$
$353$	−40.8280	−	112.174i	−0.115660	−	0.317773i	−0.983993	+	0.178209i	$0.942970\pi$
$354$	15.5841	−	13.5292i	0.0440228	−	0.0382182i
$355$	−218.111	+	183.017i	−0.614397	+	0.515540i
$356$	39.3359	−	6.93598i	0.110494	−	0.0194831i
$357$	10.6710	+	635.012i	0.0298908	+	1.77875i
$358$	−232.802	−	195.344i	−0.650285	−	0.545654i
$359$	−225.320	−	130.089i	−0.627633	−	0.362364i	0.152202	−	0.988349i	$-0.451364\pi$
$359$	−225.320	−	130.089i	−0.627633	−	0.362364i	−0.779835	+	0.625985i	$0.784697\pi$
$360$	−102.992	+	3.46241i	−0.286089	+	0.00961782i
$361$	180.286	+	312.265i	0.499408	+	0.864999i
$362$	420.249	+	74.1013i	1.16091	+	0.204700i
$363$	29.8766	−	187.843i	0.0823047	−	0.517473i
$364$	460.924	+	167.763i	1.26627	+	0.460886i
$365$	−94.6358	+	260.010i	−0.259276	+	0.712355i
$366$	66.0200	+	10.5006i	0.180382	+	0.0286901i
$367$	−68.0453	+	385.904i	−0.185410	+	1.05151i	0.740018	+	0.672587i	$0.234817\pi$
$367$	−68.0453	+	385.904i	−0.185410	+	1.05151i	−0.925428	+	0.378924i	$0.876294\pi$
$368$	22.8723	−	13.2053i	0.0621529	−	0.0358840i
$369$	−12.9623	−	385.572i	−0.0351281	−	1.04491i
$370$	−48.3156	+	83.6851i	−0.130583	+	0.226176i
$371$	−121.515	+	144.815i	−0.327533	+	0.390338i
$372$	−112.014	+	1.88233i	−0.301113	+	0.00506003i
$373$	−19.2839	−	109.365i	−0.0516996	−	0.293203i	0.947985	−	0.318315i	$-0.103117\pi$
$373$	−19.2839	−	109.365i	−0.0516996	−	0.293203i	−0.999685	+	0.0251119i	$0.992006\pi$
$374$	−197.830	−	235.764i	−0.528957	−	0.630386i
$375$	267.606	+	308.251i	0.713617	+	0.822001i
$376$	124.402	−	45.2788i	0.330857	−	0.120422i
$377$			25.3277i			0.0671823i
$378$	−491.691	+	112.506i	−1.30077	+	0.297634i
$379$	396.757			1.04685			0.523427	−	0.852071i	$-0.324653\pi$
$379$	396.757			1.04685			0.523427	+	0.852071i	$0.324653\pi$
$380$	1.81104	+	4.97579i	0.00476590	+	0.0130942i
$381$	486.827	+	167.982i	1.27776	+	0.440898i
$382$	−322.723	+	270.797i	−0.844825	+	0.708893i
$383$	222.640	−	39.2574i	0.581305	−	0.102500i	0.124739	−	0.992190i	$-0.460191\pi$
$383$	222.640	−	39.2574i	0.581305	−	0.102500i	0.456566	+	0.889690i	$0.349079\pi$
$384$	−29.6749	−	16.4743i	−0.0772783	−	0.0429018i
$385$	−556.278	−	466.773i	−1.44488	−	1.21240i
$386$	−154.160	−	89.0043i	−0.399378	−	0.230581i
$387$	0.121949	+	0.577418i	0.000315114	+	0.00149204i
$388$	105.729	+	183.127i	0.272497	+	0.471978i
$389$	−637.851	−	112.470i	−1.63972	−	0.289127i	−0.723657	−	0.690160i	$-0.757540\pi$
$389$	−637.851	−	112.470i	−1.63972	−	0.289127i	−0.916063	+	0.401033i	$0.868651\pi$
$390$	−297.767	+	114.080i	−0.763504	+	0.292512i
$391$	99.4333	+	36.1908i	0.254305	+	0.0925595i
$392$	−121.404	+	333.554i	−0.309704	+	0.850904i
$393$	330.794	−	407.954i	0.841715	−	1.03805i
$394$	−10.6586	+	60.4480i	−0.0270523	+	0.153421i
$395$	176.863	−	102.112i	0.447755	−	0.258512i
$396$	150.737	−	192.418i	0.380648	−	0.485903i
$397$	180.080	−	311.908i	0.453602	−	0.785662i	−0.545005	−	0.838433i	$-0.683472\pi$
$397$	180.080	−	311.908i	0.453602	−	0.785662i	0.998607	+	0.0527712i	$0.0168054\pi$
$398$	68.7858	−	81.9757i	0.172829	−	0.205969i
$399$	13.3343	+	22.2247i	0.0334193	+	0.0557011i
$400$	5.98193	+	33.9252i	0.0149548	+	0.0848131i
$401$	158.429	+	188.808i	0.395084	+	0.470843i	0.926514	−	0.376259i	$-0.122790\pi$
$401$	158.429	+	188.808i	0.395084	+	0.470843i	−0.531431	+	0.847102i	$0.678345\pi$
$402$	164.582	−	31.8803i	0.409407	−	0.0793043i
$403$	−325.752	+	118.564i	−0.808318	+	0.294204i
$404$			120.555i			0.298402i
$405$	193.426	−	264.777i	0.477596	−	0.653771i
$406$	−25.4852			−0.0627714
$407$	−78.3926	−	215.382i	−0.192611	−	0.529194i
$408$	−25.8605	−	133.504i	−0.0633835	−	0.327216i
$409$	33.7067	−	28.2832i	0.0824124	−	0.0691522i	−0.600651	−	0.799511i	$-0.705092\pi$
$409$	33.7067	−	28.2832i	0.0824124	−	0.0691522i	0.683063	+	0.730359i	$0.260647\pi$
$410$	241.677	−	42.6142i	0.589457	−	0.103937i
$411$	126.293	−	75.7727i	0.307282	−	0.184362i
$412$	147.274	+	123.577i	0.357460	+	0.299945i
$413$	55.6474	+	32.1280i	0.134739	+	0.0777918i
$414$	−11.8041	+	83.2049i	−0.0285123	+	0.200978i
$415$	297.357	+	515.038i	0.716524	+	1.24106i
$416$	−103.430	−	18.2374i	−0.248629	−	0.0438400i
$417$	325.963	+	264.311i	0.781686	+	0.633839i
$418$	−11.8023	−	4.29570i	−0.0282353	−	0.0102768i
$419$	−102.584	+	281.846i	−0.244830	+	0.672664i	0.755027	+	0.655694i	$0.227624\pi$
$419$	−102.584	+	281.846i	−0.244830	+	0.672664i	−0.999856	+	0.0169693i	$0.994598\pi$
$420$	−114.789	−	299.618i	−0.273307	−	0.713375i
$421$	65.6847	−	372.517i	0.156021	−	0.884837i	−0.801826	−	0.597558i	$-0.796138\pi$
$421$	65.6847	−	372.517i	0.156021	−	0.884837i	0.957847	−	0.287280i	$-0.0927509\pi$
$422$	263.843	−	152.330i	0.625220	−	0.360971i
$423$	−130.695	+	400.463i	−0.308971	+	0.946722i
$424$	20.2386	−	35.0543i	0.0477326	−	0.0826754i
$425$	−88.7169	+	105.729i	−0.208746	+	0.248773i
$426$	144.837	−	260.892i	0.339992	−	0.612423i
$427$	36.1434	+	204.979i	0.0846450	+	0.480046i
$428$	−137.981	−	164.439i	−0.322385	−	0.384203i
$429$	246.708	−	714.981i	0.575077	−	1.66662i
$430$	−0.352765	+	0.128396i	−0.000820385	+	0.000298596i
$431$		−	739.788i		−	1.71645i	−0.513278	−	0.858223i	$-0.671569\pi$
$431$		−	739.788i		−	1.71645i	0.513278	−	0.858223i	$-0.328431\pi$
$432$	99.4967	−	42.0049i	0.230316	−	0.0972335i
$433$	−856.804			−1.97876			−0.989381	−	0.145344i	$-0.953571\pi$
$433$	−856.804			−1.97876			−0.989381	+	0.145344i	$0.953571\pi$
$434$	−119.301	−	327.777i	−0.274887	−	0.755247i
$435$	12.5108	−	10.8612i	0.0287605	−	0.0249683i
$436$	−130.411	+	109.428i	−0.299108	+	0.250982i
$437$	4.25261	−	0.749850i	0.00973138	−	0.00171590i
$438$	−4.87237	−	289.946i	−0.0111241	−	0.661978i
$439$	614.827	+	515.901i	1.40052	+	1.17517i	0.960869	+	0.277003i	$0.0893413\pi$
$439$	614.827	+	515.901i	1.40052	+	1.17517i	0.439648	+	0.898170i	$0.355103\pi$
$440$	134.654	+	77.7424i	0.306031	+	0.176687i
$441$	−597.286	−	958.630i	−1.35439	−	2.17376i
$442$	−210.393	−	364.411i	−0.476002	−	0.824459i
$443$	−301.057	−	53.0845i	−0.679587	−	0.119829i	−0.176809	−	0.984245i	$-0.556577\pi$
$443$	−301.057	−	53.0845i	−0.679587	−	0.119829i	−0.502778	+	0.864416i	$0.667689\pi$
$444$	15.9076	−	100.016i	0.0358280	−	0.225260i
$445$	−75.9722	−	27.6516i	−0.170724	−	0.0621385i
$446$	−40.2468	+	110.577i	−0.0902396	+	0.247931i
$447$	−711.846	−	113.220i	−1.59250	−	0.253289i
$448$	18.3508	−	104.073i	0.0409616	−	0.232305i
$449$	−357.480	+	206.391i	−0.796169	+	0.459668i	−0.842130	−	0.539275i	$-0.818698\pi$
$449$	−357.480	+	206.391i	−0.796169	+	0.459668i	0.0459609	+	0.998943i	$0.485365\pi$
$450$	−96.7170	−	51.5868i	−0.214927	−	0.114637i
$451$	−291.045	+	504.105i	−0.645333	+	1.11775i
$452$	−216.201	+	257.658i	−0.478321	+	0.570041i
$453$	−61.1226	+	1.02713i	−0.134928	+	0.00226739i
$454$	15.3539	+	87.0765i	0.0338192	+	0.191798i
$455$	−638.178	−	760.551i	−1.40259	−	1.67154i
$456$	−3.63806	−	4.19061i	−0.00797820	−	0.00918993i
$457$	−465.412	+	169.396i	−1.01841	+	0.370670i	−0.796656	−	0.604433i	$-0.793400\pi$
$457$	−465.412	+	169.396i	−1.01841	+	0.370670i	−0.221752	+	0.975103i	$0.571177\pi$
$458$			205.347i			0.448356i
$459$	385.158	+	197.196i	0.839125	+	0.429620i
$460$	−53.4576			−0.116212
$461$	278.892	+	766.250i	0.604972	+	1.66215i	0.741051	+	0.671449i	$0.234328\pi$
$461$	278.892	+	766.250i	0.604972	+	1.66215i	−0.136079	+	0.990698i	$0.543450\pi$
$462$	719.425	+	248.242i	1.55720	+	0.537319i
$463$	318.881	−	267.573i	0.688727	−	0.577910i	−0.229815	−	0.973234i	$-0.573812\pi$
$463$	318.881	−	267.573i	0.688727	−	0.577910i	0.918542	+	0.395324i	$0.129368\pi$
$464$	5.37390	−	0.947563i	0.0115817	−	0.00204216i
$465$	198.257	+	110.064i	0.426358	+	0.236697i
$466$	146.581	+	122.996i	0.314552	+	0.263940i
$467$	123.567	+	71.3412i	0.264597	+	0.152765i	0.626430	−	0.779478i	$-0.284516\pi$
$467$	123.567	+	71.3412i	0.264597	+	0.152765i	−0.361833	+	0.932243i	$0.617849\pi$
$468$	248.641	−	223.292i	0.531284	−	0.477120i
$469$	260.981	+	452.032i	0.556462	+	0.963820i
$470$	−263.891	−	46.5312i	−0.561471	−	0.0990025i
$471$	−629.657	+	241.233i	−1.33685	+	0.512172i
$472$	−12.9286	−	4.70561i	−0.0273910	−	0.00996952i
$473$	0.304549	−	0.836742i	0.000643868	−	0.00176901i
$474$	−134.804	+	166.248i	−0.284397	+	0.350734i
$475$	−0.978063	+	5.54687i	−0.00205908	+	0.0116776i
$476$	366.676	−	211.701i	0.770328	−	0.444749i
$477$	48.0931	+	119.482i	0.100824	+	0.250486i
$478$	103.629	−	179.490i	0.216797	−	0.375503i
$479$	66.5425	−	79.3023i	0.138920	−	0.165558i	−0.692099	−	0.721803i	$-0.743314\pi$
$479$	66.5425	−	79.3023i	0.138920	−	0.165558i	0.831019	+	0.556245i	$0.187758\pi$
$480$	35.3449	+	58.9105i	0.0736351	+	0.122730i
$481$	−54.4165	−	308.611i	−0.113132	−	0.641603i
$482$	288.292	+	343.573i	0.598116	+	0.712807i
$483$	−256.883	+	49.7597i	−0.531850	+	0.103022i
$484$	−119.155	+	43.3690i	−0.246189	+	0.0896054i
$485$		−	428.010i		−	0.882495i
$486$	−90.0233	+	331.653i	−0.185233	+	0.682414i
$487$	−757.163			−1.55475			−0.777374	−	0.629038i	$-0.783449\pi$
$487$	−757.163			−1.55475			−0.777374	+	0.629038i	$0.783449\pi$
$488$	−15.2427	−	41.8789i	−0.0312350	−	0.0858173i
$489$	88.6809	+	457.813i	0.181352	+	0.936224i
$490$	550.384	−	461.827i	1.12323	−	0.942504i
$491$	559.039	−	98.5737i	1.13857	−	0.200761i	0.427592	−	0.903972i	$-0.359362\pi$
$491$	559.039	−	98.5737i	1.13857	−	0.200761i	0.710981	+	0.703211i	$0.248251\pi$
$492$	−220.544	+	132.321i	−0.448260	+	0.268945i
$493$	16.7479	+	14.0531i	0.0339713	+	0.0285053i
$494$	−14.8713	−	8.58596i	−0.0301039	−	0.0173805i
$495$	−458.965	+	184.740i	−0.927201	+	0.373211i
$496$	37.3433	+	64.6805i	0.0752889	+	0.130404i
$497$	914.973	+	161.334i	1.84099	+	0.324617i
$498$	−484.125	−	392.558i	−0.972139	−	0.788270i
$499$	−436.182	−	158.757i	−0.874113	−	0.318151i	−0.134282	−	0.990943i	$-0.542873\pi$
$499$	−436.182	−	158.757i	−0.874113	−	0.318151i	−0.739832	+	0.672792i	$0.765095\pi$
$500$	93.0763	−	255.725i	0.186153	−	0.511450i
$501$	344.597	+	899.454i	0.687818	+	1.79532i
$502$	−39.1123	+	221.817i	−0.0779130	+	0.441866i
$503$	−6.81535	+	3.93484i	−0.0135494	+	0.00782275i	−0.506759	−	0.862088i	$-0.669157\pi$
$503$	−6.81535	+	3.93484i	−0.0135494	+	0.00782275i	0.493210	+	0.869910i	$0.335823\pi$
$504$	224.680	+	250.186i	0.445794	+	0.496402i
$505$	122.007	−	211.322i	0.241598	−	0.418460i
$506$	81.5048	−	97.1336i	0.161077	−	0.191964i
$507$	255.838	−	460.837i	0.504612	−	0.908949i
$508$	−59.6185	−	338.113i	−0.117359	−	0.665577i
$509$	39.3894	+	46.9424i	0.0773858	+	0.0922248i	0.803348	−	0.595510i	$-0.203050\pi$
$509$	39.3894	+	46.9424i	0.0773858	+	0.0922248i	−0.725962	+	0.687734i	$0.758605\pi$
$510$	−89.7814	+	260.194i	−0.176042	+	0.510184i
$511$	848.444	−	308.808i	1.66036	−	0.604322i
$512$			22.6274i			0.0441942i
$513$	17.6359	−	0.889752i	0.0343779	−	0.00173441i
$514$	85.6553			0.166645
$515$	−133.093	−	365.669i	−0.258432	−	0.710037i
$516$	0.297099	−	0.257925i	0.000575772	−	0.000499854i
$517$	486.893	−	408.552i	0.941766	−	0.790236i
$518$	310.529	−	54.7547i	0.599478	−	0.105704i
$519$	7.18211	+	427.395i	0.0138384	+	0.823496i
$520$	162.847	+	136.644i	0.313166	+	0.262778i
$521$	838.293	+	483.988i	1.60901	+	0.928961i	0.989593	+	0.143896i	$0.0459631\pi$
$521$	838.293	+	483.988i	1.60901	+	0.928961i	0.619414	+	0.785064i	$0.287370\pi$
$522$	−8.17157	+	15.3204i	−0.0156544	+	0.0293494i
$523$	182.559	+	316.201i	0.349061	+	0.604591i	0.986083	−	0.166255i	$-0.0531674\pi$
$523$	182.559	+	316.201i	0.349061	+	0.604591i	−0.637022	+	0.770845i	$0.719834\pi$
$524$	−344.824	−	60.8018i	−0.658061	−	0.116034i
$525$	53.6092	−	337.056i	0.102113	−	0.642012i
$526$	−448.956	−	163.407i	−0.853528	−	0.310659i
$527$	−102.344	+	281.188i	−0.194201	+	0.533563i
$528$	−160.930	−	25.5962i	−0.304793	−	0.0484777i
$529$	84.2897	−	478.031i	0.159338	−	0.903649i
$530$	−70.9534	+	40.9649i	−0.133874	+	0.0772923i
$531$	37.1565	−	23.1508i	0.0699746	−	0.0435985i
$532$	8.63934	−	14.9638i	0.0162394	−	0.0281274i
$533$	−511.558	+	609.651i	−0.959770	+	1.14381i
$534$	84.7194	−	1.42366i	0.158651	−	0.00266603i
$535$	75.4488	+	427.891i	0.141026	+	0.799797i
$536$	−71.8383	−	85.6135i	−0.134027	−	0.159727i
$537$	−422.626	−	486.815i	−0.787014	−	0.906546i
$538$	51.9052	−	18.8920i	0.0964781	−	0.0351152i
$539$			1704.19i			3.16176i
$540$	−216.921	−	27.0643i	−0.401705	−	0.0501190i
$541$	1.90773			0.00352630			0.00176315	−	0.999998i	$-0.499439\pi$
$541$	1.90773			0.00352630			0.00176315	+	0.999998i	$0.499439\pi$
$542$	−119.474	−	328.252i	−0.220432	−	0.605631i
$543$	855.725	+	295.273i	1.57592	+	0.543780i
$544$	−69.4475	+	58.2733i	−0.127661	+	0.107120i
$545$	339.347	−	59.8360i	0.622655	−	0.109791i
$546$	909.729	+	505.045i	1.66617	+	0.924991i
$547$	−0.552346	−	0.463474i	−0.00100977	−	0.000847301i	0.642283	−	0.766468i	$-0.277988\pi$
$547$	−0.552346	−	0.463474i	−0.00100977	−	0.000847301i	−0.643292	+	0.765621i	$0.722432\pi$
$548$	−85.0322	−	49.0934i	−0.155168	−	0.0895864i
$549$	134.812	+	43.9971i	0.245559	+	0.0801404i
$550$	82.6948	+	143.232i	0.150354	+	0.260421i
$551$	0.878648	+	0.154929i	0.00159464	+	0.000281179i
$552$	52.3173	−	20.0437i	0.0947776	−	0.0363110i
$553$	−626.220	−	227.925i	−1.13240	−	0.412162i
$554$	−92.2464	+	253.445i	−0.166510	+	0.457482i
$555$	−129.105	+	159.220i	−0.232622	+	0.286883i
$556$	48.5818	−	275.521i	0.0873774	−	0.495542i
$557$	−550.670	+	317.930i	−0.988636	+	0.570789i	−0.904866	−	0.425696i	$-0.860029\pi$
$557$	−550.670	+	317.930i	−0.988636	+	0.570789i	−0.0837699	+	0.996485i	$0.526696\pi$
$558$	−235.295	−	33.3808i	−0.421676	−	0.0598223i
$559$	0.608713	−	1.05432i	0.00108893	−	0.00188609i
$560$	−137.494	+	163.859i	−0.245525	+	0.292605i
$561$	−335.892	−	559.842i	−0.598738	−	0.997937i
$562$	−33.3006	−	188.857i	−0.0592538	−	0.336045i
$563$	61.9267	+	73.8014i	0.109994	+	0.131086i	0.818232	−	0.574888i	$-0.194954\pi$
$563$	61.9267	+	73.8014i	0.109994	+	0.131086i	−0.708238	+	0.705973i	$0.750510\pi$
$564$	275.709	−	53.4062i	0.488845	−	0.0946919i
$565$	639.746	−	232.848i	1.13229	−	0.412121i
$566$			656.348i			1.15962i
$567$	−1067.57	+	71.8613i	−1.88285	+	0.126739i
$568$	−198.933			−0.350234
$569$	−356.298	−	978.920i	−0.626182	−	1.72042i	−0.691324	−	0.722545i	$-0.742972\pi$
$569$	−356.298	−	978.920i	−0.626182	−	1.72042i	0.0651419	−	0.997876i	$-0.479250\pi$
$570$	2.13612	+	11.0277i	0.00374758	+	0.0193468i
$571$	−199.435	+	167.346i	−0.349274	+	0.293075i	−0.800498	−	0.599335i	$-0.795432\pi$
$571$	−199.435	+	167.346i	−0.349274	+	0.293075i	0.451225	+	0.892410i	$0.350987\pi$
$572$	−496.572	+	87.5590i	−0.868132	+	0.153075i
$573$	−766.333	+	459.781i	−1.33741	+	0.802411i
$574$	−613.440	−	514.737i	−1.06871	−	0.896755i
$575$	−49.2448	−	28.4315i	−0.0856432	−	0.0494461i
$576$	−56.6791	−	44.4014i	−0.0984011	−	0.0770858i
$577$	−192.470	−	333.369i	−0.333571	−	0.577762i	0.649638	−	0.760243i	$-0.274920\pi$
$577$	−192.470	−	333.369i	−0.333571	−	0.577762i	−0.983209	+	0.182482i	$0.941587\pi$
$578$	44.7966	+	7.89885i	0.0775028	+	0.0136658i
$579$	−293.306	−	237.831i	−0.506574	−	0.410761i
$580$	−10.3790	−	3.77764i	−0.0178948	−	0.00651317i
$581$	663.734	−	1823.59i	1.14240	−	3.13872i
$582$	160.480	+	418.879i	0.275739	+	0.719724i
$583$	33.7457	−	191.381i	0.0578828	−	0.328270i
$584$	−167.424	+	96.6624i	−0.286685	+	0.165518i
$585$	−661.830	+	139.777i	−1.13133	+	0.238934i
$586$	95.6897	−	165.739i	0.163293	−	0.282832i
$587$	667.584	−	795.596i	1.13728	−	1.35536i	0.211465	−	0.977385i	$-0.432176\pi$
$587$	667.584	−	795.596i	1.13728	−	1.35536i	0.925816	−	0.377974i	$-0.123379\pi$
$588$	−365.483	+	658.339i	−0.621570	+	1.11962i
$589$	2.12050	+	12.0260i	0.00360017	+	0.0204176i
$590$	17.9004	+	21.3329i	0.0303397	+	0.0361574i
$591$	−42.4715	+	123.086i	−0.0718639	+	0.208268i
$592$	−63.4435	+	23.0916i	−0.107168	+	0.0390060i
$593$		−	464.135i		−	0.782690i	−0.920244	−	0.391345i	$-0.872010\pi$
$593$		−	464.135i		−	0.782690i	0.920244	−	0.391345i	$-0.127990\pi$
$594$	379.907	−	352.885i	0.639574	−	0.594083i
$595$	−857.005			−1.44034
$596$	164.351	+	451.549i	0.275756	+	0.757633i
$597$	171.420	−	148.818i	0.287136	−	0.249276i
$598$	132.802	−	111.434i	0.222078	−	0.186345i
$599$	804.360	−	141.830i	1.34284	−	0.236778i	0.544385	−	0.838836i	$-0.316763\pi$
$599$	804.360	−	141.830i	1.34284	−	0.236778i	0.798453	+	0.602057i	$0.205652\pi$
$600$	1.22783	+	73.0661i	0.00204639	+	0.121777i
$601$	184.846	+	155.104i	0.307563	+	0.258076i	0.783484	−	0.621412i	$-0.213441\pi$
$601$	184.846	+	155.104i	0.307563	+	0.258076i	−0.475921	+	0.879488i	$0.657885\pi$
$602$	1.06088	+	0.612497i	0.00176225	+	0.00101744i
$603$	355.419	−	11.9486i	0.589418	−	0.0198152i
$604$	20.3771	+	35.2941i	0.0337369	+	0.0584340i
$605$	252.761	+	44.5686i	0.417787	+	0.0736671i
$606$	−40.1701	+	252.560i	−0.0662872	+	0.416766i
$607$	492.438	+	179.233i	0.811266	+	0.295277i	0.714147	−	0.699996i	$-0.246815\pi$
$607$	492.438	+	179.233i	0.811266	+	0.295277i	0.0971191	+	0.995273i	$0.469037\pi$
$608$	−1.26535	+	3.47653i	−0.00208118	+	0.00571798i
$609$	−53.3911	−	8.49193i	−0.0876701	−	0.0139441i
$610$	−15.6643	+	88.8365i	−0.0256791	+	0.145634i
$611$	752.570	−	434.497i	1.23170	−	0.711124i
$612$	−9.69238	−	288.307i	−0.0158372	−	0.471089i
$613$	164.324	−	284.617i	0.268064	−	0.464301i	−0.700297	−	0.713851i	$-0.746949\pi$
$613$	164.324	−	284.617i	0.268064	−	0.464301i	0.968362	+	0.249550i	$0.0802826\pi$
$614$	−316.905	+	377.673i	−0.516132	+	0.615103i
$615$	520.511	−	8.74687i	0.846359	−	0.0142226i
$616$	−88.1033	−	499.658i	−0.143025	−	0.811134i
$617$	−538.270	−	641.486i	−0.872399	−	1.03968i	−0.998861	−	0.0477134i	$-0.984807\pi$
$617$	−538.270	−	641.486i	−0.872399	−	1.03968i	0.126462	−	0.991971i	$-0.459638\pi$
$618$	267.359	+	307.966i	0.432620	+	0.498327i
$619$	193.537	−	70.4416i	0.312660	−	0.113799i	−0.180924	−	0.983497i	$-0.557909\pi$
$619$	193.537	−	70.4416i	0.312660	−	0.113799i	0.493584	+	0.869698i	$0.335687\pi$
$620$		−	151.173i		−	0.243827i
$621$	−52.4542	+	170.380i	−0.0844673	+	0.274364i
$622$	309.752			0.497994
$623$	90.2307	+	247.907i	0.144833	+	0.397924i
$624$	−210.607	−	72.6710i	−0.337511	−	0.116460i
$625$	−257.029	+	215.673i	−0.411246	+	0.345077i
$626$	−378.971	+	66.8228i	−0.605384	+	0.106746i
$627$	−23.2944	−	12.9321i	−0.0371521	−	0.0206254i
$628$	344.355	+	288.948i	0.548337	+	0.460109i
$629$	−234.261	−	135.251i	−0.372434	−	0.215025i
$630$	−140.645	−	665.944i	−0.223247	−	1.05705i
$631$	−189.681	−	328.538i	−0.300604	−	0.520662i	0.675669	−	0.737205i	$-0.263855\pi$
$631$	−189.681	−	328.538i	−0.300604	−	0.520662i	−0.976273	+	0.216544i	$0.930522\pi$
$632$	140.521	+	24.7777i	0.222344	+	0.0392053i
$633$	603.506	−	231.214i	0.953405	−	0.365267i
$634$	−620.611	−	225.884i	−0.978881	−	0.356284i
$635$	−237.680	+	653.022i	−0.374300	+	1.02838i
$636$	54.0802	−	66.6947i	0.0850317	−	0.104866i
$637$	−404.599	+	2294.59i	−0.635163	+	3.60219i
$638$	22.6885	−	13.0992i	0.0355619	−	0.0205317i
$639$	390.363	−	498.305i	0.610897	−	0.779819i
$640$	22.9000	−	39.6640i	0.0357813	−	0.0619750i
$641$	−567.812	+	676.691i	−0.885821	+	1.05568i	0.112255	+	0.993679i	$0.464193\pi$
$641$	−567.812	+	676.691i	−0.885821	+	1.05568i	−0.998076	+	0.0620014i	$0.980252\pi$
$642$	−234.275	−	390.474i	−0.364915	−	0.608216i
$643$	−167.973	−	952.623i	−0.261233	−	1.48153i	−0.779550	−	0.626340i	$-0.784552\pi$
$643$	−167.973	−	952.623i	−0.261233	−	1.48153i	0.518317	−	0.855189i	$-0.326559\pi$
$644$	112.127	+	133.628i	0.174111	+	0.207497i
$645$	−0.781822	+	0.151443i	−0.00121213	+	0.000234795i
$646$	−13.9288	+	5.06967i	−0.0215616	+	0.00784779i
$647$			199.904i			0.308971i	0.987995	+	0.154485i	$0.0493719\pi$
$647$			199.904i			0.308971i	−0.987995	+	0.154485i	$0.950628\pi$
$648$	222.441	−	54.8464i	0.343273	−	0.0846394i
$649$	−66.0543			−0.101779
$650$	77.3386	+	212.486i	0.118983	+	0.326902i
$651$	−140.716	−	726.441i	−0.216153	−	1.11588i
$652$	238.150	−	199.831i	0.365260	−	0.306490i
$653$	−164.505	+	29.0068i	−0.251923	+	0.0444208i	−0.298183	−	0.954509i	$-0.596381\pi$
$653$	−164.505	+	29.0068i	−0.251923	+	0.0444208i	0.0462606	+	0.998929i	$0.485270\pi$
$654$	−309.673	+	185.796i	−0.473505	+	0.284092i
$655$	542.914	+	455.559i	0.828877	+	0.695510i
$656$	148.491	+	85.7311i	0.226358	+	0.130688i
$657$	86.4056	−	609.057i	0.131515	−	0.927028i
$658$	437.197	+	757.248i	0.664434	+	1.15083i
$659$	−126.902	−	22.3762i	−0.192567	−	0.0339548i	0.0765325	−	0.997067i	$-0.475615\pi$
$659$	−126.902	−	22.3762i	−0.192567	−	0.0339548i	−0.269100	+	0.963112i	$0.586726\pi$
$660$	256.193	+	207.737i	0.388172	+	0.314754i
$661$	273.433	+	99.5215i	0.413666	+	0.150562i	0.540465	−	0.841366i	$-0.318248\pi$
$661$	273.433	+	99.5215i	0.413666	+	0.150562i	−0.126799	+	0.991928i	$0.540470\pi$
$662$	50.2479	−	138.055i	0.0759031	−	0.208542i
$663$	−319.345	−	833.542i	−0.481666	−	1.25723i
$664$	−72.1544	+	409.208i	−0.108666	+	0.616277i
$665$	−30.2881	+	17.4868i	−0.0455460	+	0.0262960i
$666$	66.6525	−	204.231i	0.100079	−	0.306653i
$667$	−4.50367	+	7.80058i	−0.00675213	+	0.0116950i
$668$	412.757	−	491.905i	0.617900	−	0.736385i
$669$	−121.162	+	218.247i	−0.181109	+	0.326229i
$670$	39.2817	+	222.777i	0.0586293	+	0.332503i
$671$	−137.535	−	163.908i	−0.204970	−	0.244274i
$672$	73.1227	−	211.916i	0.108814	−	0.315351i
$673$	422.325	−	153.714i	0.627525	−	0.228401i	−0.00862844	−	0.999963i	$-0.502747\pi$
$673$	422.325	−	153.714i	0.627525	−	0.228401i	0.636154	+	0.771562i	$0.280524\pi$
$674$		−	796.461i		−	1.18169i
$675$	−185.432	−	140.301i	−0.274713	−	0.207853i
$676$	−351.393			−0.519813
$677$	389.411	+	1069.90i	0.575202	+	1.58035i	0.796170	+	0.605073i	$0.206856\pi$
$677$	389.411	+	1069.90i	0.575202	+	1.58035i	−0.220969	+	0.975281i	$0.570922\pi$
$678$	−538.793	+	467.751i	−0.794680	+	0.689898i
$679$	−1069.90	+	897.749i	−1.57569	+	1.32216i
$680$	180.711	−	31.8642i	0.265752	−	0.0468592i
$681$	3.15150	+	187.540i	0.00462776	+	0.275389i
$682$	274.684	+	230.487i	0.402763	+	0.337958i
$683$	93.9542	+	54.2445i	0.137561	+	0.0794209i	0.567201	−	0.823579i	$-0.308026\pi$
$683$	93.9542	+	54.2445i	0.137561	+	0.0794209i	−0.429640	+	0.903000i	$0.641360\pi$
$684$	−6.22533	−	9.99151i	−0.00910136	−	0.0146075i
$685$	99.3697	+	172.113i	0.145065	+	0.251260i
$686$	−1407.37	−	248.158i	−2.05156	−	0.361746i
$687$	−68.4237	+	430.199i	−0.0995978	+	0.626199i
$688$	−0.246473	−	0.0897089i	−0.000358246	−	0.000130391i
$689$	90.8733	−	249.672i	0.131892	−	0.362369i
$690$	−111.993	−	17.8126i	−0.162309	−	0.0258154i
$691$	195.940	−	1111.23i	0.283560	−	1.60815i	−0.426825	−	0.904334i	$-0.640368\pi$
$691$	195.940	−	1111.23i	0.283560	−	1.60815i	0.710385	−	0.703813i	$-0.248521\pi$
$692$	246.791	−	142.485i	0.356635	−	0.205903i
$693$	1424.47	+	759.783i	2.05551	+	1.09637i
$694$	192.202	−	332.903i	0.276947	−	0.479687i
$695$	−364.001	+	433.799i	−0.523742	+	0.624171i
$696$	11.5740	−	0.194494i	0.0166293	−	0.000279445i
$697$	119.291	+	676.530i	0.171149	+	0.970632i
$698$	72.9187	+	86.9011i	0.104468	+	0.124500i
$699$	266.102	+	306.518i	0.380689	+	0.438509i
$700$	−213.807	+	77.8194i	−0.305439	+	0.111171i
$701$			778.410i			1.11043i	0.831707	+	0.555214i	$0.187364\pi$
$701$			778.410i			1.11043i	−0.831707	+	0.555214i	$0.812636\pi$
$702$	595.303	−	384.945i	0.848010	−	0.548354i
$703$	−11.0389			−0.0157026
$704$	37.1555	+	102.084i	0.0527778	+	0.145006i
$705$	−537.344	−	185.414i	−0.762191	−	0.262998i
$706$	−129.323	+	108.515i	−0.183177	+	0.153704i
$707$	−784.152	+	138.267i	−1.10913	+	0.195569i
$708$	−25.5172	−	14.1661i	−0.0360413	−	0.0200087i
$709$	−263.186	−	220.839i	−0.371207	−	0.311480i	0.438032	−	0.898959i	$-0.355676\pi$
$709$	−263.186	−	220.839i	−0.371207	−	0.311480i	−0.809239	+	0.587480i	$0.800120\pi$
$710$	348.714	+	201.330i	0.491146	+	0.283563i
$711$	−337.808	+	303.369i	−0.475117	+	0.426679i
$712$	−28.2438	−	48.9197i	−0.0396682	−	0.0687074i
$713$	−121.410	−	21.4078i	−0.170280	−	0.0300249i
$714$	838.723	−	321.330i	1.17468	−	0.450042i
$715$	959.064	+	349.071i	1.34135	+	0.488211i
$716$	−146.994	+	403.862i	−0.205299	+	0.564054i
$717$	276.909	−	341.500i	0.386205	−	0.476290i
$718$	−63.8933	+	362.357i	−0.0889878	+	0.504675i
$719$	−528.455	+	305.104i	−0.734986	+	0.424344i	−0.820243	−	0.572015i	$-0.806162\pi$
$719$	−528.455	+	305.104i	−0.734986	+	0.424344i	0.0852574	+	0.996359i	$0.472829\pi$
$720$	54.4174	+	135.194i	0.0755798	+	0.187769i
$721$	−634.901	+	1099.68i	−0.880584	+	1.52522i
$722$	327.774	−	390.626i	0.453981	−	0.541033i
$723$	489.486	+	815.843i	0.677021	+	1.12841i
$724$	−104.795	−	594.322i	−0.144744	−	0.820887i
$725$	−7.55191	−	9.00001i	−0.0104164	−	0.0124138i
$726$	−264.080	+	51.1537i	−0.363747	+	0.0704597i
$727$	−195.866	+	71.2895i	−0.269417	+	0.0980599i	−0.473196	−	0.880957i	$-0.656900\pi$
$727$	−195.866	+	71.2895i	−0.269417	+	0.0980599i	0.203779	+	0.979017i	$0.434678\pi$
$728$		−	693.679i		−	0.952855i
$729$	−299.108	+	664.812i	−0.410299	+	0.911951i
$730$	391.308			0.536038
$731$	−0.359421	−	0.987500i	−0.000491684	−	0.00135089i
$732$	−17.9787	−	92.8147i	−0.0245611	−	0.126796i
$733$	−191.068	+	160.325i	−0.260665	+	0.218724i	−0.763749	−	0.645514i	$-0.776643\pi$
$733$	−191.068	+	160.325i	−0.260665	+	0.218724i	0.503083	+	0.864238i	$0.332199\pi$
$734$	545.751	−	96.2306i	0.743530	−	0.131104i
$735$	1306.93	−	784.128i	1.77814	−	1.06684i
$736$	−28.6120	−	24.0083i	−0.0388749	−	0.0326200i
$737$	−464.682	−	268.284i	−0.630505	−	0.364022i
$738$	−506.127	+	203.723i	−0.685809	+	0.276048i
$739$	−87.7232	−	151.941i	−0.118705	−	0.205604i	0.800550	−	0.599267i	$-0.204541\pi$
$739$	−87.7232	−	151.941i	−0.118705	−	0.205604i	−0.919255	+	0.393663i	$0.871208\pi$
$740$	134.581	+	23.7303i	0.181866	+	0.0320679i
$741$	−28.2943	−	22.9428i	−0.0381839	−	0.0309619i
$742$	251.224	+	91.4382i	0.338577	+	0.123232i
$743$	228.605	−	628.087i	0.307678	−	0.845340i	−0.685430	−	0.728139i	$-0.740386\pi$
$743$	228.605	−	628.087i	0.307678	−	0.845340i	0.993108	−	0.117201i	$-0.0373921\pi$
$744$	56.6815	+	147.948i	0.0761849	+	0.198855i
$745$	168.897	−	957.860i	0.226707	−	1.28572i
$746$	−136.010	+	78.5255i	−0.182319	+	0.105262i
$747$	−883.431	−	983.720i	−1.18264	−	1.31689i
$748$	−217.625	+	376.938i	−0.290943	+	0.503928i
$749$	911.346	−	1086.10i	1.21675	−	1.45007i
$750$	280.204	−	504.726i	0.373605	−	0.672969i
$751$	73.4096	+	416.327i	0.0977491	+	0.554363i	0.993870	+	0.110553i	$0.0352623\pi$
$751$	73.4096	+	416.327i	0.0977491	+	0.554363i	−0.896121	+	0.443810i	$0.853627\pi$
$752$	−120.344	−	143.421i	−0.160032	−	0.190719i
$753$	−155.852	+	451.671i	−0.206974	+	0.599829i
$754$	33.6587	−	12.2508i	0.0446402	−	0.0162477i
$755$		−	82.4903i		−	0.109259i
$756$	387.337	+	599.003i	0.512351	+	0.792332i
$757$	938.792			1.24015			0.620074	−	0.784543i	$-0.287103\pi$
$757$	938.792			1.24015			0.620074	+	0.784543i	$0.287103\pi$
$758$	−191.907	−	527.261i	−0.253176	−	0.695595i
$759$	203.117	−	176.335i	0.267612	−	0.232326i
$760$	5.73648	−	4.81348i	0.00754800	−	0.00633353i
$761$	−708.743	+	124.971i	−0.931331	+	0.164219i	−0.618675	−	0.785647i	$-0.712330\pi$
$761$	−708.743	+	124.971i	−0.931331	+	0.164219i	−0.312657	+	0.949866i	$0.601219\pi$
$762$	−12.2371	−	728.208i	−0.0160592	−	0.955654i
$763$	−861.351	−	722.759i	−1.12890	−	0.947259i
$764$	515.967	+	297.894i	0.675349	+	0.389913i
$765$	−274.790	+	515.187i	−0.359203	+	0.673447i
$766$	−159.859	−	276.883i	−0.208693

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.483690 - 1.32893i) q^{2} +(-0.570511 - 2.94525i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(3.98669 - 0.702961i) q^{5} +(-3.63807 + 2.18276i) q^{6} +(-10.1193 - 8.49107i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-8.34903 + 3.36060i) q^{9} +O(q^{10})\)	\(q+(-0.483690 - 1.32893i) q^{2} +(-0.570511 - 2.94525i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(3.98669 - 0.702961i) q^{5} +(-3.63807 + 2.18276i) q^{6} +(-10.1193 - 8.49107i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-8.34903 + 3.36060i) q^{9} +(-2.86250 - 4.95800i) q^{10} +(13.3731 + 2.35805i) q^{11} +(4.66042 + 3.77895i) q^{12} +(17.4463 + 6.34995i) q^{13} +(-6.38942 + 17.5548i) q^{14} +(-4.34485 - 11.3408i) q^{15} +(0.694593 - 3.93923i) q^{16} +(13.8790 - 8.01304i) q^{17} +(8.50433 + 9.46976i) q^{18} +(0.327006 - 0.566391i) q^{19} +(-5.20426 + 6.20219i) q^{20} +(-19.2352 + 34.6480i) q^{21} +(-3.33478 - 18.9125i) q^{22} +(4.24411 + 5.05793i) q^{23} +(2.76776 - 8.02119i) q^{24} +(-8.09277 + 2.94553i) q^{25} -26.2563i q^{26} +(14.6610 + 22.6728i) q^{27} +26.4195 q^{28} +(0.466584 + 1.28193i) q^{29} +(-12.9695 + 11.2594i) q^{30} +(-14.3033 + 12.0019i) q^{31} +(-5.57091 + 0.982302i) q^{32} +(-0.684487 - 40.7326i) q^{33} +(-17.3619 - 14.5683i) q^{34} +(-46.3112 - 26.7378i) q^{35} +(8.47116 - 15.8820i) q^{36} +(-8.43940 - 14.6175i) q^{37} +(-0.910861 - 0.160609i) q^{38} +(8.74887 - 55.0066i) q^{39} +(10.7595 + 3.91614i) q^{40} +(-14.6609 + 40.2805i) q^{41} +(55.3485 + 8.80326i) q^{42} +(0.0113866 - 0.0645766i) q^{43} +(-23.5203 + 13.5794i) q^{44} +(-30.9226 + 19.2667i) q^{45} +(4.66878 - 8.08657i) q^{46} +(30.0861 - 35.8552i) q^{47} +(-11.9983 + 0.201624i) q^{48} +(21.7924 + 123.591i) q^{49} +(7.82877 + 9.32997i) q^{50} +(-31.5186 - 36.3056i) q^{51} +(-34.8927 + 12.6999i) q^{52} -14.3109i q^{53} +(23.0390 - 30.4500i) q^{54} +54.9722 q^{55} +(-12.7788 - 35.1096i) q^{56} +(-1.85472 - 0.639983i) q^{57} +(1.47791 - 1.24011i) q^{58} +(-4.79039 + 0.844675i) q^{59} +(21.2361 + 11.7894i) q^{60} +(-12.0703 - 10.1282i) q^{61} +(22.8680 + 13.2029i) q^{62} +(113.021 + 36.8854i) q^{63} +(4.00000 + 6.92820i) q^{64} +(74.0169 + 13.0512i) q^{65} +(-53.7995 + 20.6116i) q^{66} +(-37.1304 - 13.5143i) q^{67} +(-10.9625 + 30.1192i) q^{68} +(12.4756 - 15.3856i) q^{69} +(-13.1323 + 74.4770i) q^{70} +(-60.9106 + 35.1667i) q^{71} +(-25.2035 - 3.57556i) q^{72} +(-34.1753 + 59.1934i) q^{73} +(-15.3435 + 18.2857i) q^{74} +(13.2923 + 22.1548i) q^{75} +(0.227136 + 1.28815i) q^{76} +(-115.304 - 137.414i) q^{77} +(-77.3315 + 14.9795i) q^{78} +(47.4059 - 17.2543i) q^{79} -16.1928i q^{80} +(58.4127 - 56.1155i) q^{81} +60.6211 q^{82} +(50.2457 + 138.049i) q^{83} +(-15.0726 - 77.8122i) q^{84} +(49.6984 - 41.7019i) q^{85} +(-0.0913252 + 0.0161031i) q^{86} +(3.50941 - 2.10556i) q^{87} +(29.4226 + 24.6885i) q^{88} +(-17.2957 - 9.98568i) q^{89} +(40.5610 + 31.7748i) q^{90} +(-122.626 - 212.395i) q^{91} +(-13.0047 - 2.29308i) q^{92} +(43.5089 + 35.2797i) q^{93} +(-62.2012 - 22.6394i) q^{94} +(0.905521 - 2.48790i) q^{95} +(6.07140 + 15.8473i) q^{96} +(18.3596 - 104.122i) q^{97} +(153.703 - 88.7402i) q^{98} +(-119.577 + 25.2544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) \) 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	\( 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) \) 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Introduction

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