LMFDB - Embedded newform 54.3.f.a.11.4

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			11.4
Character	$\chi$	$=$	54.11
Dual form			54.3.f.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909039 - 1.08335i) q^{2} +(-2.95590 - 0.512490i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.71293 - 7.45370i) q^{5} +(-3.24224 + 2.73640i) q^{6} +(0.0787775 - 0.446769i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(8.47471 + 3.02974i) q^{9} +O(q^{10})$	\(q+(0.909039 - 1.08335i) q^{2} +(-2.95590 - 0.512490i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.71293 - 7.45370i) q^{5} +(-3.24224 + 2.73640i) q^{6} +(0.0787775 - 0.446769i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(8.47471 + 3.02974i) q^{9} +(-5.60882 - 9.71475i) q^{10} +(4.82381 + 13.2533i) q^{11} +(0.0171659 + 5.99998i) q^{12} +(-9.80599 + 8.22820i) q^{13} +(-0.412396 - 0.491475i) q^{14} +(-11.8391 + 20.6421i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(28.5583 - 16.4882i) q^{17} +(10.9861 - 6.42693i) q^{18} +(0.202792 - 0.351246i) q^{19} +(-15.6231 - 2.75478i) q^{20} +(-0.461823 + 1.28023i) q^{21} +(18.7430 + 6.82189i) q^{22} +(14.2603 - 2.51448i) q^{23} +(6.51568 + 5.43561i) q^{24} +(-29.0466 - 24.3730i) q^{25} +18.1031i q^{26} +(-23.4977 - 13.2988i) q^{27} -0.907323 q^{28} +(-16.8547 + 20.0866i) q^{29} +(11.6004 + 31.5903i) q^{30} +(4.33881 + 24.6066i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(-7.46652 - 41.6476i) q^{33} +(8.09818 - 45.9270i) q^{34} +(-3.11637 - 1.79924i) q^{35} +(3.02419 - 17.7441i) q^{36} +(3.84477 + 6.65933i) q^{37} +(-0.196177 - 0.538991i) q^{38} +(33.2024 - 19.2963i) q^{39} +(-17.1864 + 14.4211i) q^{40} +(-15.9304 - 18.9851i) q^{41} +(0.967127 + 1.66410i) q^{42} +(-16.8662 + 6.13880i) q^{43} +(24.4286 - 14.1039i) q^{44} +(45.5740 - 54.9485i) q^{45} +(10.2391 - 17.7347i) q^{46} +(-46.7491 - 8.24313i) q^{47} +(11.8117 - 2.11758i) q^{48} +(45.8515 + 16.6886i) q^{49} +(-52.8090 + 9.31165i) q^{50} +(-92.8656 + 34.1015i) q^{51} +(19.6120 + 16.4564i) q^{52} +0.261457i q^{53} +(-35.7676 + 13.3671i) q^{54} +111.873 q^{55} +(-0.824792 + 0.982949i) q^{56} +(-0.779443 + 0.934320i) q^{57} +(6.43929 + 36.5190i) q^{58} +(18.8461 - 51.7793i) q^{59} +(44.7686 + 16.1495i) q^{60} +(-18.1761 + 103.082i) q^{61} +(30.6018 + 17.6679i) q^{62} +(2.02121 - 3.54757i) q^{63} +(4.00000 + 6.92820i) q^{64} +(34.7276 + 95.4134i) q^{65} +(-51.9063 - 29.7704i) q^{66} +(-49.4929 + 41.5295i) q^{67} +(-42.3935 - 50.5226i) q^{68} +(-43.4407 + 0.124283i) q^{69} +(-4.78210 + 1.74054i) q^{70} +(-94.6180 + 54.6277i) q^{71} +(-16.4740 - 19.4064i) q^{72} +(31.4705 - 54.5085i) q^{73} +(10.7094 + 1.88836i) q^{74} +(73.3680 + 86.9302i) q^{75} +(-0.762248 - 0.277436i) q^{76} +(6.30118 - 1.11107i) q^{77} +(9.27764 - 53.5109i) q^{78} +(-14.7532 - 12.3794i) q^{79} +31.7283i q^{80} +(62.6414 + 51.3523i) q^{81} -35.0489 q^{82} +(36.7220 - 43.7636i) q^{83} +(2.68196 + 0.464994i) q^{84} +(-45.4212 - 257.596i) q^{85} +(-8.68158 + 23.8524i) q^{86} +(60.1149 - 50.7362i) q^{87} +(6.92713 - 39.2857i) q^{88} +(89.7902 + 51.8404i) q^{89} +(-18.0999 - 99.3230i) q^{90} +(2.90362 + 5.02921i) q^{91} +(-9.90511 - 27.2141i) q^{92} +(-0.214455 - 74.9584i) q^{93} +(-51.4269 + 43.1523i) q^{94} +(-2.06792 - 2.46445i) q^{95} +(8.44320 - 14.7212i) q^{96} +(-52.8231 + 19.2260i) q^{97} +(59.7604 - 34.5027i) q^{98} +(0.726312 + 126.933i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$3$	−2.95590	−	0.512490i	−0.985301	−	0.170830i
$3$	−2.95590	−	0.512490i	−0.985301	−	0.170830i
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	2.71293	−	7.45370i	0.542585	−	1.49074i	−0.300936	−	0.953644i	$-0.597299\pi$
$5$	2.71293	−	7.45370i	0.542585	−	1.49074i	0.843521	−	0.537096i	$-0.180479\pi$
$6$	−3.24224	+	2.73640i	−0.540373	+	0.456067i
$7$	0.0787775	−	0.446769i	0.0112539	−	0.0638242i	−0.978664	−	0.205469i	$-0.934128\pi$
$7$	0.0787775	−	0.446769i	0.0112539	−	0.0638242i	0.989918	+	0.141645i	$0.0452391\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$	8.47471	+	3.02974i	0.941634	+	0.336638i
$10$	−5.60882	−	9.71475i	−0.560882	−	0.971475i
$11$	4.82381	+	13.2533i	0.438528	+	1.20485i	0.940450	+	0.339933i	$0.110404\pi$
$11$	4.82381	+	13.2533i	0.438528	+	1.20485i	−0.501922	+	0.864913i	$0.667373\pi$
$12$	0.0171659	+	5.99998i	0.00143049	+	0.499998i
$13$	−9.80599	+	8.22820i	−0.754307	+	0.632939i	−0.936638	−	0.350299i	$-0.886080\pi$
$13$	−9.80599	+	8.22820i	−0.754307	+	0.632939i	0.182331	+	0.983237i	$0.441636\pi$
$14$	−0.412396	−	0.491475i	−0.0294569	−	0.0351053i
$15$	−11.8391	+	20.6421i	−0.789273	+	1.37614i
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	28.5583	−	16.4882i	1.67990	−	0.969891i	0.718182	−	0.695856i	$-0.244975\pi$
$17$	28.5583	−	16.4882i	1.67990	−	0.969891i	0.961720	−	0.274036i	$-0.0883586\pi$
$18$	10.9861	−	6.42693i	0.610339	−	0.357052i
$19$	0.202792	−	0.351246i	0.0106733	−	0.0184866i	−0.860639	−	0.509215i	$-0.829936\pi$
$19$	0.202792	−	0.351246i	0.0106733	−	0.0184866i	0.871313	+	0.490728i	$0.163269\pi$
$20$	−15.6231	−	2.75478i	−0.781156	−	0.137739i
$21$	−0.461823	+	1.28023i	−0.0219916	+	0.0609635i
$22$	18.7430	+	6.82189i	0.851955	+	0.310086i
$23$	14.2603	−	2.51448i	0.620013	−	0.109325i	0.145187	−	0.989404i	$-0.453622\pi$
$23$	14.2603	−	2.51448i	0.620013	−	0.109325i	0.474827	+	0.880079i	$0.342511\pi$
$24$	6.51568	+	5.43561i	0.271487	+	0.226484i
$25$	−29.0466	−	24.3730i	−1.16186	−	0.974920i
$26$			18.1031i			0.696272i
$27$	−23.4977	−	13.2988i	−0.870285	−	0.492549i
$28$	−0.907323			−0.0324044
$29$	−16.8547	+	20.0866i	−0.581195	+	0.692642i	−0.973888	−	0.227028i	$-0.927099\pi$
$29$	−16.8547	+	20.0866i	−0.581195	+	0.692642i	0.392693	+	0.919670i	$0.371544\pi$
$30$	11.6004	+	31.5903i	0.386680	+	1.05301i
$31$	4.33881	+	24.6066i	0.139962	+	0.793762i	0.971275	+	0.237959i	$0.0764783\pi$
$31$	4.33881	+	24.6066i	0.139962	+	0.793762i	−0.831314	+	0.555804i	$0.812411\pi$
$32$	−1.93476	+	5.31570i	−0.0604612	+	0.166116i
$33$	−7.46652	−	41.6476i	−0.226258	−	1.26205i
$34$	8.09818	−	45.9270i	0.238182	−	1.35080i
$35$	−3.11637	−	1.79924i	−0.0890391	−	0.0514068i
$36$	3.02419	−	17.7441i	0.0840052	−	0.492893i
$37$	3.84477	+	6.65933i	0.103913	+	0.179982i	0.913293	−	0.407302i	$-0.133530\pi$
$37$	3.84477	+	6.65933i	0.103913	+	0.179982i	−0.809381	+	0.587284i	$0.800197\pi$
$38$	−0.196177	−	0.538991i	−0.00516254	−	0.0141840i
$39$	33.2024	−	19.2963i	0.851344	−	0.494777i
$40$	−17.1864	+	14.4211i	−0.429660	+	0.360528i
$41$	−15.9304	−	18.9851i	−0.388547	−	0.463052i	0.535946	−	0.844253i	$-0.319955\pi$
$41$	−15.9304	−	18.9851i	−0.388547	−	0.463052i	−0.924492	+	0.381200i	$0.875511\pi$
$42$	0.967127	+	1.66410i	0.0230268	+	0.0396214i
$43$	−16.8662	+	6.13880i	−0.392238	+	0.142763i	−0.530607	−	0.847618i	$-0.678036\pi$
$43$	−16.8662	+	6.13880i	−0.392238	+	0.142763i	0.138369	+	0.990381i	$0.455814\pi$
$44$	24.4286	−	14.1039i	0.555196	−	0.320543i
$45$	45.5740	−	54.9485i	1.01276	−	1.22108i
$46$	10.2391	−	17.7347i	0.222589	−	0.385536i
$47$	−46.7491	−	8.24313i	−0.994662	−	0.175386i	−0.347452	−	0.937698i	$-0.612953\pi$
$47$	−46.7491	−	8.24313i	−0.994662	−	0.175386i	−0.647210	+	0.762312i	$0.724064\pi$
$48$	11.8117	−	2.11758i	0.246077	−	0.0441162i
$49$	45.8515	+	16.6886i	0.935746	+	0.340584i
$50$	−52.8090	+	9.31165i	−1.05618	+	0.186233i
$51$	−92.8656	+	34.1015i	−1.82089	+	0.668657i
$52$	19.6120	+	16.4564i	0.377153	+	0.316469i
$53$			0.261457i			0.00493315i	0.999997	+	0.00246657i	$0.000785136\pi$
$53$			0.261457i			0.00493315i	−0.999997	+	0.00246657i	$0.999215\pi$
$54$	−35.7676	+	13.3671i	−0.662363	+	0.247539i
$55$	111.873			2.03405
$56$	−0.824792	+	0.982949i	−0.0147284	+	0.0175527i
$57$	−0.779443	+	0.934320i	−0.0136744	+	0.0163916i
$58$	6.43929	+	36.5190i	0.111022	+	0.629638i
$59$	18.8461	−	51.7793i	0.319426	−	0.877615i	−0.671232	−	0.741247i	$-0.734235\pi$
$59$	18.8461	−	51.7793i	0.319426	−	0.877615i	0.990658	−	0.136368i	$-0.0435430\pi$
$60$	44.7686	+	16.1495i	0.746143	+	0.269159i
$61$	−18.1761	+	103.082i	−0.297969	+	1.68987i	0.356916	+	0.934137i	$0.383828\pi$
$61$	−18.1761	+	103.082i	−0.297969	+	1.68987i	−0.654885	+	0.755729i	$0.727283\pi$
$62$	30.6018	+	17.6679i	0.493577	+	0.284967i
$63$	2.02121	−	3.54757i	0.0320827	−	0.0563106i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	34.7276	+	95.4134i	0.534271	+	1.46790i
$66$	−51.9063	−	29.7704i	−0.786459	−	0.451067i
$67$	−49.4929	+	41.5295i	−0.738700	+	0.619843i	−0.932488	−	0.361200i	$-0.882367\pi$
$67$	−49.4929	+	41.5295i	−0.738700	+	0.619843i	0.193788	+	0.981043i	$0.437923\pi$
$68$	−42.3935	−	50.5226i	−0.623434	−	0.742980i
$69$	−43.4407	+	0.124283i	−0.629576	+	0.00180121i
$70$	−4.78210	+	1.74054i	−0.0683158	+	0.0248649i
$71$	−94.6180	+	54.6277i	−1.33265	+	0.769405i	−0.985705	−	0.168481i	$-0.946114\pi$
$71$	−94.6180	+	54.6277i	−1.33265	+	0.769405i	−0.346943	+	0.937886i	$0.612780\pi$
$72$	−16.4740	−	19.4064i	−0.228806	−	0.269533i
$73$	31.4705	−	54.5085i	0.431103	−	0.746692i	−0.565866	−	0.824497i	$-0.691458\pi$
$73$	31.4705	−	54.5085i	0.431103	−	0.746692i	0.996969	+	0.0778057i	$0.0247914\pi$
$74$	10.7094	+	1.88836i	0.144722	+	0.0255184i
$75$	73.3680	+	86.9302i	0.978240	+	1.15907i
$76$	−0.762248	−	0.277436i	−0.0100296	−	0.00365047i
$77$	6.30118	−	1.11107i	0.0818335	−	0.0144295i
$78$	9.27764	−	53.5109i	0.118944	−	0.686037i
$79$	−14.7532	−	12.3794i	−0.186750	−	0.156702i	0.544620	−	0.838683i	$-0.316674\pi$
$79$	−14.7532	−	12.3794i	−0.186750	−	0.156702i	−0.731369	+	0.681981i	$0.761118\pi$
$80$			31.7283i			0.396603i
$81$	62.6414	+	51.3523i	0.773350	+	0.633979i
$82$	−35.0489			−0.427426
$83$	36.7220	−	43.7636i	0.442434	−	0.527273i	−0.498033	−	0.867158i	$-0.665944\pi$
$83$	36.7220	−	43.7636i	0.442434	−	0.527273i	0.940467	+	0.339886i	$0.110388\pi$
$84$	2.68196	+	0.464994i	0.0319281	+	0.00553564i
$85$	−45.4212	−	257.596i	−0.534367	−	3.03055i
$86$	−8.68158	+	23.8524i	−0.100949	+	0.277354i
$87$	60.1149	−	50.7362i	0.690976	−	0.583175i
$88$	6.92713	−	39.2857i	0.0787174	−	0.446429i
$89$	89.7902	+	51.8404i	1.00888	+	0.582476i	0.910863	−	0.412709i	$-0.135417\pi$
$89$	89.7902	+	51.8404i	1.00888	+	0.582476i	0.0980154	+	0.995185i	$0.468751\pi$
$90$	−18.0999	−	99.3230i	−0.201110	−	1.10359i
$91$	2.90362	+	5.02921i	0.0319079	+	0.0552661i
$92$	−9.90511	−	27.2141i	−0.107664	−	0.295805i
$93$	−0.214455	−	74.9584i	−0.00230597	−	0.806004i
$94$	−51.4269	+	43.1523i	−0.547095	+	0.459067i
$95$	−2.06792	−	2.46445i	−0.0217676	−	0.0259416i
$96$	8.44320	−	14.7212i	0.0879500	−	0.153345i
$97$	−52.8231	+	19.2260i	−0.544568	+	0.198207i	−0.599631	−	0.800276i	$-0.704686\pi$
$97$	−52.8231	+	19.2260i	−0.544568	+	0.198207i	0.0550633	+	0.998483i	$0.482464\pi$
$98$	59.7604	−	34.5027i	0.609800	−	0.352068i
$99$	0.726312	+	126.933i	0.00733649	+	1.28215i
$100$	−37.9176	+	65.6753i	−0.379176	+	0.656753i
$101$	−44.2921	−	7.80990i	−0.438536	−	0.0773258i	−0.0499788	−	0.998750i	$-0.515915\pi$
$101$	−44.2921	−	7.80990i	−0.438536	−	0.0773258i	−0.388557	+	0.921425i	$0.627026\pi$
$102$	−47.4746	+	131.606i	−0.465437	+	1.29025i
$103$	85.6429	+	31.1715i	0.831485	+	0.302636i	0.722468	−	0.691404i	$-0.243008\pi$
$103$	85.6429	+	31.1715i	0.831485	+	0.302636i	0.109017	+	0.994040i	$0.465230\pi$
$104$	35.6561	−	6.28713i	0.342847	−	0.0604532i
$105$	8.28959	+	6.91547i	0.0789485	+	0.0658617i
$106$	0.283249	+	0.237674i	0.00267216	+	0.00224221i
$107$		−	206.049i		−	1.92569i	−0.270046	−	0.962847i	$-0.587039\pi$
$107$		−	206.049i		−	1.92569i	0.270046	−	0.962847i	$-0.412961\pi$
$108$	−18.0329	+	50.9000i	−0.166971	+	0.471297i
$109$	−140.161			−1.28588			−0.642942	−	0.765915i	$-0.722286\pi$
$109$	−140.161			−1.28588			−0.642942	+	0.765915i	$0.722286\pi$
$110$	101.697	−	121.197i	0.924516	−	1.10180i
$111$	−7.95191	−	21.6547i	−0.0716388	−	0.195088i
$112$	0.315110	+	1.78708i	0.00281348	+	0.0159561i
$113$	−24.9375	+	68.5153i	−0.220686	+	0.606330i	−0.999788	−	0.0205666i	$-0.993453\pi$
$113$	−24.9375	+	68.5153i	−0.220686	+	0.606330i	0.779102	+	0.626897i	$0.215675\pi$
$114$	0.303651	+	1.69374i	0.00266361	+	0.0148574i
$115$	19.9450	−	113.114i	0.173435	−	0.983597i
$116$	45.4165	+	26.2212i	0.391521	+	0.226045i
$117$	−108.032	+	40.0220i	−0.923352	+	0.342069i
$118$	−38.9633	−	67.4864i	−0.330197	−	0.571918i
$119$	−5.11665	−	14.0579i	−0.0429971	−	0.118133i
$120$	58.1920	−	33.8195i	0.484933	−	0.281829i
$121$	−59.6896	+	50.0855i	−0.493302	+	0.413930i
$122$	95.1509	+	113.396i	0.779925	+	0.929479i
$123$	37.3591	+	64.2824i	0.303732	+	0.522621i
$124$	46.9588	−	17.0916i	0.378700	−	0.137835i
$125$	−88.7360	+	51.2318i	−0.709888	+	0.409854i
$126$	−2.00590	−	5.41456i	−0.0159198	−	0.0429727i
$127$	−5.49347	+	9.51497i	−0.0432557	+	0.0749210i	−0.886843	−	0.462072i	$-0.847106\pi$
$127$	−5.49347	+	9.51497i	−0.0432557	+	0.0749210i	0.843587	+	0.536993i	$0.180440\pi$
$128$	11.1418	+	1.96460i	0.0870455	+	0.0153485i
$129$	53.0010	−	9.50193i	0.410860	−	0.0736584i
$130$	134.935	+	49.1123i	1.03796	+	0.377787i
$131$	36.9106	−	6.50833i	0.281760	−	0.0496819i	−0.0309820	−	0.999520i	$-0.509863\pi$
$131$	36.9106	−	6.50833i	0.281760	−	0.0496819i	0.312742	+	0.949838i	$0.398752\pi$
$132$	−79.4367	+	29.1702i	−0.601793	+	0.220987i
$133$	−0.140951	−	0.118272i	−0.00105978	−	0.000889260i
$134$			91.3701i			0.681866i
$135$	−162.873	+	139.066i	−1.20647	+	1.03012i
$136$	−93.2711			−0.685817
$137$	−27.2090	+	32.4264i	−0.198606	+	0.236689i	−0.856151	−	0.516726i	$-0.827150\pi$
$137$	−27.2090	+	32.4264i	−0.198606	+	0.236689i	0.657545	+	0.753415i	$0.271595\pi$
$138$	−39.3547	+	47.1745i	−0.285179	+	0.341844i
$139$	−28.2955	−	160.472i	−0.203565	−	1.15447i	−0.899682	−	0.436545i	$-0.856202\pi$
$139$	−28.2955	−	160.472i	−0.203565	−	1.15447i	0.696117	−	0.717928i	$-0.254909\pi$
$140$	−2.46150	+	6.76292i	−0.0175821	+	0.0483066i
$141$	133.961	+	48.3243i	0.950079	+	0.342726i
$142$	−26.8305	+	152.163i	−0.188947	+	1.07157i
$143$	−156.353	−	90.2705i	−1.09338	−	0.631262i
$144$	−35.9994	+	0.205990i	−0.249996	+	0.00143048i
$145$	103.994	+	180.123i	0.717201	+	1.24223i
$146$	−30.4439	−	83.6439i	−0.208520	−	0.572903i
$147$	−126.980	−	72.8283i	−0.863809	−	0.495431i
$148$	11.7810	−	9.88547i	0.0796017	−	0.0667937i
$149$	115.419	+	137.551i	0.774624	+	0.923161i	0.998677	−	0.0514163i	$-0.0163735\pi$
$149$	115.419	+	137.551i	0.774624	+	0.923161i	−0.224054	+	0.974577i	$0.571929\pi$
$150$	160.870	−	0.460248i	1.07247	−	0.00306832i
$151$	151.225	−	55.0415i	1.00149	−	0.364514i	0.211333	−	0.977414i	$-0.432220\pi$
$151$	151.225	−	55.0415i	1.00149	−	0.364514i	0.790160	+	0.612901i	$0.209997\pi$
$152$	−0.993473	+	0.573582i	−0.00653601	+	0.00377357i
$153$	291.978	−	53.2080i	1.90835	−	0.347765i
$154$	4.52434	−	7.83639i	0.0293788	−	0.0508856i
$155$	195.181	+	34.4157i	1.25923	+	0.222037i
$156$	−49.5373	−	58.6945i	−0.317547	−	0.376246i
$157$	−72.6336	−	26.4365i	−0.462635	−	0.168385i	0.100178	−	0.994969i	$-0.468059\pi$
$157$	−72.6336	−	26.4365i	−0.462635	−	0.168385i	−0.562813	+	0.826584i	$0.690281\pi$
$158$	−26.8225	+	4.72954i	−0.169763	+	0.0299338i
$159$	0.133994	−	0.772841i	0.000842730	−	0.00486063i
$160$	34.3728	+	28.8422i	0.214830	+	0.180264i
$161$		−	6.56915i		−	0.0408022i
$162$	112.576	−	21.1813i	0.694913	−	0.130749i
$163$	−2.14092			−0.0131345			−0.00656723	−	0.999978i	$-0.502090\pi$
$163$	−2.14092			−0.0131345			−0.00656723	+	0.999978i	$0.502090\pi$
$164$	−31.8608	+	37.9703i	−0.194273	+	0.231526i
$165$	−330.685	−	57.3337i	−2.00415	−	0.347477i
$166$	−14.0296	−	79.5657i	−0.0845155	−	0.479311i
$167$	30.6994	−	84.3460i	0.183829	−	0.505066i	−0.813209	−	0.581971i	$-0.802282\pi$
$167$	30.6994	−	84.3460i	0.183829	−	0.505066i	0.997038	+	0.0769052i	$0.0245039\pi$
$168$	2.94176	−	2.48280i	0.0175105	−	0.0147786i
$169$	−0.892424	+	5.06119i	−0.00528061	+	0.0299479i
$170$	−320.357	−	184.958i	−1.88445	−	1.08799i
$171$	2.78279	−	2.36230i	0.0162736	−	0.0138146i
$172$	17.9487	+	31.0880i	0.104353	+	0.180744i
$173$	−62.3682	−	171.355i	−0.360510	−	0.990492i	−0.978850	−	0.204581i	$-0.934417\pi$
$173$	−62.3682	−	171.355i	−0.360510	−	0.990492i	0.618340	−	0.785911i	$-0.287805\pi$
$174$	−0.318275	−	111.247i	−0.00182917	−	0.639349i
$175$	−13.1773	+	11.0571i	−0.0752990	+	0.0631834i
$176$	−36.2632	−	43.2168i	−0.206041	−	0.245550i
$177$	−82.2436	+	143.396i	−0.464653	+	0.810147i
$178$	137.784	−	50.1493i	0.774068	−	0.281738i
$179$	−104.032	+	60.0628i	−0.581183	+	0.335546i	−0.761604	−	0.648043i	$-0.775588\pi$
$179$	−104.032	+	60.0628i	−0.581183	+	0.335546i	0.180420	+	0.983590i	$0.442254\pi$
$180$	−124.055	−	70.6799i	−0.689195	−	0.392666i
$181$	−79.9928	+	138.552i	−0.441949	+	0.765478i	−0.997834	−	0.0657809i	$-0.979046\pi$
$181$	−79.9928	+	138.552i	−0.441949	+	0.765478i	0.555885	+	0.831259i	$0.312380\pi$
$182$	8.08790	+	1.42612i	0.0444390	+	0.00783580i
$183$	106.555	−	295.385i	0.582268	−	1.61412i
$184$	−38.4865	−	14.0079i	−0.209166	−	0.0761301i
$185$	60.0672	−	10.5915i	0.324688	−	0.0572512i
$186$	−81.4012	−	67.9078i	−0.437641	−	0.365096i
$187$	356.282	+	298.956i	1.90525	+	1.59870i
$188$			94.9406i			0.505003i
$189$	−7.79259	+	9.45040i	−0.0412307	+	0.0500021i
$190$	−4.54969			−0.0239457
$191$	−82.0805	+	97.8197i	−0.429741	+	0.512145i	−0.936847	−	0.349738i	$-0.886271\pi$
$191$	−82.0805	+	97.8197i	−0.429741	+	0.512145i	0.507107	+	0.861883i	$0.330715\pi$
$192$	−8.27297	−	22.5290i	−0.0430884	−	0.117339i
$193$	17.3129	+	98.1865i	0.0897043	+	0.508738i	0.996242	+	0.0866135i	$0.0276045\pi$
$193$	17.3129	+	98.1865i	0.0897043	+	0.508738i	−0.906538	+	0.422125i	$0.861284\pi$
$194$	−27.1897	+	74.7032i	−0.140153	+	0.385068i
$195$	−53.7531	−	299.830i	−0.275657	−	1.53759i
$196$	16.9460	−	96.1058i	0.0864594	−	0.490336i
$197$	−32.9869	−	19.0450i	−0.167446	−	0.0966751i	0.413935	−	0.910306i	$-0.364154\pi$
$197$	−32.9869	−	19.0450i	−0.167446	−	0.0966751i	−0.581381	+	0.813631i	$0.697487\pi$
$198$	138.173	+	114.600i	0.697843	+	0.578788i
$199$	−192.718	−	333.797i	−0.968430	−	1.67737i	−0.700102	−	0.714043i	$-0.746862\pi$
$199$	−192.718	−	333.797i	−0.968430	−	1.67737i	−0.268329	−	0.963327i	$-0.586471\pi$
$200$	36.6807	+	100.779i	0.183404	+	0.503897i
$201$	167.580	−	97.3925i	0.833730	−	0.484540i
$202$	−48.7241	+	40.8844i	−0.241209	+	0.202398i
$203$	7.64631	+	9.11252i	0.0376666	+	0.0448893i
$204$	99.4187	+	171.066i	0.487347	+	0.838560i
$205$	−184.728	+	67.2354i	−0.901110	+	0.327977i
$206$	111.622	−	64.4452i	0.541856	−	0.312841i
$207$	128.470	+	21.8956i	0.620629	+	0.105776i
$208$	25.6016	−	44.3433i	0.123085	−	0.213189i
$209$	5.63340	+	0.993320i	0.0269541	+	0.00475273i
$210$	15.0274	−	2.69410i	0.0715592	−	0.0128290i
$211$	320.622	+	116.697i	1.51953	+	0.553065i	0.961032	−	0.276439i	$-0.0891542\pi$
$211$	320.622	+	116.697i	1.51953	+	0.553065i	0.558502	+	0.829503i	$0.311376\pi$
$212$	0.514970	−	0.0908030i	0.00242910	−	0.000428316i
$213$	307.678	−	112.983i	1.44450	−	0.530439i
$214$	−223.224	−	187.307i	−1.04310	−	0.875266i
$215$			142.370i			0.662186i
$216$	38.7500	+	65.8061i	0.179398	+	0.304658i
$217$	11.3353			0.0522364
$218$	−127.412	+	151.844i	−0.584459	+	0.696532i
$219$	−120.959	+	144.993i	−0.552323	+	0.662070i
$220$	−38.8530	−	220.346i	−0.176605	−	1.00157i
$221$	−144.375	+	396.666i	−0.653279	+	1.79487i
$222$	−30.6883	−	11.0703i	−0.138235	−	0.0498661i
$223$	−10.1542	+	57.5872i	−0.0455344	+	0.258238i	−0.999074	−	0.0430300i	$-0.986299\pi$
$223$	−10.1542	+	57.5872i	−0.0455344	+	0.258238i	0.953539	+	0.301268i	$0.0974100\pi$
$224$	2.22248	+	1.28315i	0.00992178	+	0.00572834i
$225$	−172.318	−	294.558i	−0.765856	−	1.30914i
$226$	51.5569	+	89.2992i	0.228128	+	0.395129i
$227$	14.3644	+	39.4658i	0.0632792	+	0.173858i	0.967303	−	0.253624i	$-0.0816227\pi$
$227$	14.3644	+	39.4658i	0.0632792	+	0.173858i	−0.904024	+	0.427483i	$0.859400\pi$
$228$	2.11095	+	1.21072i	0.00925854	+	0.00531016i
$229$	68.1857	−	57.2146i	0.297754	−	0.249845i	−0.481655	−	0.876361i	$-0.659964\pi$
$229$	68.1857	−	57.2146i	0.297754	−	0.249845i	0.779409	+	0.626516i	$0.215520\pi$
$230$	−104.411	−	124.432i	−0.453961	−	0.541009i
$231$	−19.1951	+	0.0549169i	−0.0830956	+	0.000237735i
$232$	69.6921	−	25.3658i	0.300397	−	0.109336i
$233$	121.622	−	70.2184i	0.521982	−	0.301367i	−0.215763	−	0.976446i	$-0.569224\pi$
$233$	121.622	−	70.2184i	0.521982	−	0.301367i	0.737745	+	0.675079i	$0.235891\pi$
$234$	−54.8476	+	153.418i	−0.234391	+	0.655634i
$235$	−188.269	+	326.091i	−0.801143	+	1.38762i
$236$	−108.530	−	19.1369i	−0.459875	−	0.0810884i
$237$	37.2648	+	44.1533i	0.157235	+	0.186301i
$238$	−19.8808	−	7.23604i	−0.0835330	−	0.0304035i
$239$	−28.6122	+	5.04510i	−0.119716	+	0.0211092i	−0.233185	−	0.972432i	$-0.574915\pi$
$239$	−28.6122	+	5.04510i	−0.119716	+	0.0211092i	0.113469	+	0.993542i	$0.463804\pi$
$240$	16.2604	−	93.7856i	0.0677517	−	0.390773i
$241$	−113.719	−	95.4212i	−0.471861	−	0.395938i	0.375612	−	0.926777i	$-0.377433\pi$
$241$	−113.719	−	95.4212i	−0.471861	−	0.395938i	−0.847473	+	0.530839i	$0.821877\pi$
$242$			110.194i			0.455349i
$243$	−158.844	−	183.895i	−0.653680	−	0.756771i
$244$	209.344			0.857967
$245$	248.784	−	296.489i	1.01544	−	1.21016i
$246$	103.601	+	17.9622i	0.421143	+	0.0730172i
$247$	0.901547	+	5.11293i	0.00364999	+	0.0207001i
$248$	24.1712	−	66.4097i	0.0974643	−	0.267781i
$249$	−130.975	+	110.541i	−0.526005	+	0.443941i
$250$	−25.1625	+	142.704i	−0.100650	+	0.570816i
$251$	270.246	+	156.027i	1.07668	+	0.621621i	0.929999	−	0.367563i	$-0.119808\pi$
$251$	270.246	+	156.027i	1.07668	+	0.621621i	0.146680	+	0.989184i	$0.453141\pi$
$252$	−7.68930	−	2.74895i	−0.0305131	−	0.0109085i
$253$	102.114	+	176.867i	0.403613	+	0.699078i
$254$	5.31427	+	14.6008i	0.0209223	+	0.0574836i
$255$	2.24504	+	784.707i	0.00880407	+	3.07728i
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	−33.8555	−	40.3474i	−0.131733	−	0.156994i	0.696145	−	0.717901i	$-0.254897\pi$
$257$	−33.8555	−	40.3474i	−0.131733	−	0.156994i	−0.827879	+	0.560907i	$0.810452\pi$
$258$	37.8860	−	66.0563i	0.146845	−	0.256032i
$259$	3.27807	−	1.19312i	0.0126566	−	0.00460664i
$260$	175.867	−	101.537i	0.676411	−	0.390526i
$261$	−203.696	+	119.163i	−0.780443	+	0.456563i
$262$	26.5024	−	45.9034i	0.101154	−	0.175204i
$263$	−15.7913	−	2.78443i	−0.0600429	−	0.0105872i	0.143546	−	0.989644i	$-0.454149\pi$
$263$	−15.7913	−	2.78443i	−0.0600429	−	0.0105872i	−0.203589	+	0.979056i	$0.565261\pi$
$264$	−40.6095	+	112.575i	−0.153824	+	0.426419i
$265$	1.94882	+	0.709313i	0.00735404	+	0.00267665i
$266$	−0.256259	+	0.0451854i	−0.000963380	+	0.000169870i
$267$	−238.843	−	199.252i	−0.894544	−	0.746261i
$268$	98.9858	+	83.0590i	0.369350	+	0.309922i
$269$		−	233.865i		−	0.869388i	−0.900578	−	0.434694i	$-0.856857\pi$
$269$		−	233.865i		−	0.869388i	0.900578	−	0.434694i	$-0.143143\pi$
$270$	2.59954	+	302.865i	0.00962791	+	1.12172i
$271$	−229.874			−0.848243			−0.424122	−	0.905605i	$-0.639417\pi$
$271$	−229.874			−0.848243			−0.424122	+	0.905605i	$0.639417\pi$
$272$	−84.7870	+	101.045i	−0.311717	+	0.371490i
$273$	−6.00539	−	16.3539i	−0.0219978	−	0.0599045i
$274$	10.3951	+	58.9537i	0.0379384	+	0.215159i
$275$	182.907	−	502.534i	0.665118	−	1.82740i
$276$	15.3316	+	85.5183i	0.0555492	+	0.309849i
$277$	45.6767	−	259.046i	0.164898	−	0.935183i	−0.784272	−	0.620418i	$-0.786963\pi$
$277$	45.6767	−	259.046i	0.164898	−	0.935183i	0.949170	−	0.314765i	$-0.101926\pi$
$278$	−199.569	−	115.221i	−0.717874	−	0.414465i
$279$	−37.7815	+	221.680i	−0.135418	+	0.794550i
$280$	5.08901	+	8.81442i	0.0181750	+	0.0314801i
$281$	−168.471	−	462.870i	−0.599540	−	1.64722i	−0.752193	−	0.658943i	$-0.771004\pi$
$281$	−168.471	−	462.870i	−0.599540	−	1.64722i	0.152653	−	0.988280i	$-0.451218\pi$
$282$	174.128	−	101.198i	0.617476	−	0.358859i
$283$	−375.336	+	314.944i	−1.32628	+	1.11288i	−0.341343	+	0.939939i	$0.610882\pi$
$283$	−375.336	+	314.944i	−1.32628	+	1.11288i	−0.984933	+	0.172938i	$0.944674\pi$
$284$	140.456	+	167.389i	0.494564	+	0.589398i
$285$	4.84957	+	8.34447i	0.0170160	+	0.0292789i
$286$	−239.926	+	87.3258i	−0.838901	+	0.305335i
$287$	−9.73694	+	5.62162i	−0.0339266	+	0.0195875i
$288$	−32.5017	+	39.1872i	−0.112853	+	0.136067i
$289$	399.218	−	691.467i	1.38138	−	2.39262i
$290$	289.671	+	51.0768i	0.998866	+	0.176127i
$291$	165.993	−	29.7590i	0.570423	−	0.102265i
$292$	−118.290	−	43.0542i	−0.405104	−	0.147446i
$293$	−149.954	+	26.4409i	−0.511788	+	0.0902420i	−0.423578	−	0.905860i	$-0.639226\pi$
$293$	−149.954	+	26.4409i	−0.511788	+	0.0902420i	−0.0882105	+	0.996102i	$0.528115\pi$
$294$	−194.328	+	71.3600i	−0.660980	+	0.242721i
$295$	−334.819	−	280.947i	−1.13498	−	0.952362i
$296$		−	21.7493i		−	0.0734773i
$297$	62.9048	−	375.573i	0.211801	−	1.26456i
$298$	253.936			0.852135
$299$	−119.147	+	141.994i	−0.398484	+	0.474895i
$300$	145.739	−	174.697i	0.485796	−	0.582324i
$301$	1.41395	+	8.01892i	0.00469751	+	0.0266409i
$302$	77.8405	−	213.865i	0.257750	−	0.708162i
$303$	126.921	+	45.7846i	0.418880	+	0.151104i
$304$	−0.281716	+	1.59769i	−0.000926696	+	0.00525555i
$305$	719.030	+	415.132i	2.35748	+	1.36109i
$306$	207.777	−	364.683i	0.679009	−	1.19177i
$307$	−152.701	−	264.487i	−0.497399	−	0.861520i	0.502597	−	0.864521i	$-0.332378\pi$
$307$	−152.701	−	264.487i	−0.497399	−	0.861520i	−0.999995	+	0.00300104i	$0.999045\pi$
$308$	−4.37675	−	12.0250i	−0.0142102	−	0.0390423i
$309$	−237.177	−	136.031i	−0.767563	−	0.440230i
$310$	214.712	−	180.165i	0.692619	−	0.581176i
$311$	−227.448	−	271.062i	−0.731344	−	0.871582i	0.264336	−	0.964431i	$-0.414847\pi$
$311$	−227.448	−	271.062i	−0.731344	−	0.871582i	−0.995680	+	0.0928489i	$0.970403\pi$
$312$	−108.618	+	0.310755i	−0.348135	+	0.000996009i
$313$	−109.151	+	39.7277i	−0.348725	+	0.126926i	−0.510443	−	0.859911i	$-0.670519\pi$
$313$	−109.151	+	39.7277i	−0.348725	+	0.126926i	0.161718	+	0.986837i	$0.448297\pi$
$314$	−94.6668	+	54.6559i	−0.301487	+	0.174063i
$315$	−20.9591	−	24.6898i	−0.0665368	−	0.0783803i
$316$	−19.2590	+	33.3575i	−0.0609462	+	0.105562i
$317$	223.759	+	39.4548i	0.705866	+	0.124463i	0.515047	−	0.857162i	$-0.327775\pi$
$317$	223.759	+	39.4548i	0.705866	+	0.124463i	0.190819	+	0.981625i	$0.438886\pi$
$318$	−0.715452	−	0.847705i	−0.00224985	−	0.00266574i
$319$	−347.518	−	126.486i	−1.08940	−	0.396508i
$320$	62.4925	−	11.0191i	0.195289	−	0.0344347i
$321$	−105.598	+	609.062i	−0.328966	+	1.89739i
$322$	−7.11670	−	5.97162i	−0.0221015	−	0.0185454i
$323$		−	13.3747i		−	0.0414076i
$324$	79.3892	−	141.214i	0.245028	−	0.435845i
$325$	485.376			1.49347
$326$	−1.94618	+	2.31936i	−0.00596987	+	0.00711461i
$327$	414.303	+	71.8313i	1.26698	+	0.219668i
$328$	12.1724	+	69.0329i	0.0371109	+	0.210466i
$329$	−7.36556	+	20.2367i	−0.0223877	+	0.0615097i
$330$	−362.718	+	306.129i	−1.09915	+	0.927664i
$331$	−16.3581	+	92.7715i	−0.0494203	+	0.280276i	−0.999496	−	0.0317429i	$-0.989894\pi$
$331$	−16.3581	+	92.7715i	−0.0494203	+	0.280276i	0.950076	+	0.312019i	$0.101005\pi$
$332$	−98.9509	−	57.1293i	−0.298045	−	0.172076i
$333$	12.4072	+	68.0845i	0.0372590	+	0.204458i
$334$	−63.4693	−	109.932i	−0.190028	−	0.329138i
$335$	175.278	+	481.572i	0.523217	+	1.43753i
$336$	−0.0155750	−	5.44392i	−4.63541e−5	−	0.0162021i
$337$	55.5042	−	46.5735i	0.164701	−	0.138200i	−0.556712	−	0.830705i	$-0.687937\pi$
$337$	55.5042	−	46.5735i	0.164701	−	0.138200i	0.721413	+	0.692505i	$0.243493\pi$
$338$	4.67179	+	5.56762i	0.0138219	+	0.0164723i
$339$	108.826	−	189.744i	0.321021	−	0.559718i
$340$	−491.591	+	178.925i	−1.44586	+	0.526249i
$341$	−305.190	+	176.201i	−0.894984	+	0.516719i
$342$	−0.0295380	−	5.16216i	−8.63684e−5	−	0.0150940i
$343$	22.1827	−	38.4216i	0.0646727	−	0.112016i
$344$	49.9952	+	8.81551i	0.145335	+	0.0256265i
$345$	−116.925	+	324.131i	−0.338913	+	0.939511i
$346$	−242.333	−	88.2019i	−0.700384	−	0.254919i
$347$	−407.086	+	71.7802i	−1.17316	+	0.206859i	−0.726063	−	0.687628i	$-0.758652\pi$
$347$	−407.086	+	71.7802i	−1.17316	+	0.206859i	−0.447094	+	0.894487i	$0.647541\pi$
$348$	−120.808	−	100.783i	−0.347151	−	0.289606i
$349$	−53.8823	−	45.2127i	−0.154391	−	0.129549i	0.562320	−	0.826920i	$-0.309909\pi$
$349$	−53.8823	−	45.2127i	−0.154391	−	0.129549i	−0.716711	+	0.697370i	$0.754353\pi$
$350$			24.3270i			0.0695057i
$351$	339.843	−	62.9357i	0.968215	−	0.179304i
$352$	−79.7835			−0.226658
$353$	−318.904	+	380.055i	−0.903411	+	1.07664i	0.0933029	+	0.995638i	$0.470257\pi$
$353$	−318.904	+	380.055i	−0.903411	+	1.07664i	−0.996714	+	0.0810052i	$0.974187\pi$
$354$	80.5855	+	219.451i	0.227643	+	0.619919i
$355$	150.487	+	853.456i	0.423908	+	2.40410i
$356$	70.9218	−	194.856i	0.199219	−	0.547349i
$357$	7.91979	+	44.1759i	0.0221843	+	0.123742i
$358$	−29.4999	+	167.302i	−0.0824020	+	0.467325i
$359$	251.693	+	145.315i	0.701094	+	0.404777i	0.807755	−	0.589519i	$-0.200683\pi$
$359$	251.693	+	145.315i	0.701094	+	0.404777i	−0.106661	+	0.994295i	$0.534016\pi$
$360$	−189.342	+	70.1444i	−0.525950	+	0.194845i
$361$	180.418	+	312.493i	0.499772	+	0.865631i
$362$	77.3834	+	212.609i	0.213766	+	0.587318i
$363$	202.105	−	117.457i	0.556762	−	0.323574i
$364$	8.89720	−	7.46564i	0.0244429	−	0.0205100i
$365$	−320.913	−	382.449i	−0.879213	−	1.04781i
$366$	−223.142	−	383.953i	−0.609678	−	1.04905i
$367$	536.255	−	195.181i	1.46119	−	0.531828i	0.515495	−	0.856893i	$-0.327608\pi$
$367$	536.255	−	195.181i	1.46119	−	0.531828i	0.945692	+	0.325065i	$0.105386\pi$
$368$	−50.1612	+	28.9606i	−0.136308	+	0.0786973i
$369$	−77.4857	−	209.159i	−0.209988	−	0.566825i
$370$	43.1292	−	74.7019i	0.116565	−	0.201897i
$371$	0.116811	+	0.0205969i	0.000314854	+	5.55173e-5i
$372$	−147.565	+	26.4552i	−0.396679	+	0.0711161i
$373$	18.7449	+	6.82259i	0.0502545	+	0.0182911i	0.367025	−	0.930211i	$-0.380376\pi$
$373$	18.7449	+	6.82259i	0.0502545	+	0.0182911i	−0.316771	+	0.948502i	$0.602599\pi$
$374$	647.749	−	114.216i	1.73195	−	0.305389i
$375$	288.551	−	105.960i	0.769469	−	0.282559i
$376$	102.854	+	86.3047i	0.273548	+	0.229534i
$377$		−	335.653i		−	0.890325i
$378$	3.15433	+	17.0329i	0.00834479	+	0.0450606i
$379$	−37.0647			−0.0977961			−0.0488981	−	0.998804i	$-0.515571\pi$
$379$	−37.0647			−0.0977961			−0.0488981	+	0.998804i	$0.515571\pi$
$380$	−4.13585	+	4.92891i	−0.0108838	+	0.0129708i
$381$	21.1145	−	25.3100i	0.0554186	−	0.0664304i
$382$	31.3587	+	177.844i	0.0820908	+	0.465560i
$383$	−139.086	+	382.135i	−0.363148	+	0.997740i	0.614762	+	0.788713i	$0.289252\pi$
$383$	−139.086	+	382.135i	−0.363148	+	0.997740i	−0.977910	+	0.209028i	$0.932970\pi$
$384$	−31.9273	−	11.5173i	−0.0831440	−	0.0299928i
$385$	8.81306	−	49.9814i	0.0228911	−	0.129822i
$386$	122.109	+	70.4994i	0.316343	+	0.182641i
$387$	−161.535	+	0.924309i	−0.417404	+	0.00238840i
$388$	56.2132	+	97.3641i	0.144879	+	0.250938i
$389$	−53.2715	−	146.362i	−0.136945	−	0.376253i	0.852196	−	0.523222i	$-0.175270\pi$
$389$	−53.2715	−	146.362i	−0.136945	−	0.376253i	−0.989141	+	0.146970i	$0.953048\pi$
$390$	−373.685	−	214.324i	−0.958166	−	0.549549i
$391$	365.791	−	306.935i	0.935528	−	0.785001i
$392$	−88.7116	−	105.722i	−0.226305	−	0.269700i
$393$	−112.440	+	0.321688i	−0.286106	+	0.000818545i
$394$	−50.6188	+	18.4237i	−0.128474	+	0.0467607i
$395$	−132.297	+	76.3818i	−0.334929	+	0.193372i
$396$	249.756	−	45.5138i	0.630698	−	0.114934i
$397$	−203.720	+	352.853i	−0.513147	+	0.888797i	0.486736	+	0.873549i	$0.338187\pi$
$397$	−203.720	+	352.853i	−0.513147	+	0.888797i	−0.999884	+	0.0152485i	$0.995146\pi$
$398$	−536.807	−	94.6535i	−1.34876	−	0.237823i
$399$	0.356023	+	0.421835i	0.000892288	+	0.00105723i
$400$	142.524	+	51.8744i	0.356309	+	0.129686i
$401$	−57.1810	+	10.0826i	−0.142596	+	0.0251435i	−0.244491	−	0.969652i	$-0.578621\pi$
$401$	−57.1810	+	10.0826i	−0.142596	+	0.0251435i	0.101894	+	0.994795i	$0.467510\pi$
$402$	46.8262	−	270.081i	0.116483	−	0.671843i
$403$	−245.015	−	205.592i	−0.607977	−	0.510153i
$404$			89.9509i			0.222651i
$405$	552.706	−	327.595i	1.36471	−	0.808877i
$406$	16.8229			0.0414356
$407$	−69.7117	+	83.0792i	−0.171282	+	0.204126i
$408$	275.700	+	47.8005i	0.675736	+	0.117158i
$409$	50.2599	+	285.038i	0.122885	+	0.696915i	0.982542	+	0.186043i	$0.0595664\pi$
$409$	50.2599	+	285.038i	0.122885	+	0.696915i	−0.859657	+	0.510872i	$0.829323\pi$
$410$	−95.0851	+	261.244i	−0.231915	+	0.637181i
$411$	97.0452	−	81.9049i	0.236120	−	0.199282i
$412$	31.6524	−	179.509i	0.0768261	−	0.435702i
$413$	−21.6488	−	12.4989i	−0.0524183	−	0.0302637i
$414$	140.505	−	119.274i	0.339384	−	0.288102i
$415$	−226.577	−	392.443i	−0.545968	−	0.945645i
$416$	−24.7665	−	68.0453i	−0.0595348	−	0.163570i
$417$	1.39857	+	488.840i	0.00335387	+	1.17228i
$418$	6.19709	−	5.19998i	0.0148256	−	0.0124401i
$419$	432.059	+	514.908i	1.03117	+	1.22890i	0.973052	+	0.230587i	$0.0740648\pi$
$419$	432.059	+	514.908i	1.03117	+	1.22890i	0.0581156	+	0.998310i	$0.481491\pi$
$420$	10.7419	−	18.7290i	0.0255759	−	0.0445929i
$421$	211.095	−	76.8324i	0.501414	−	0.182500i	−0.0789157	−	0.996881i	$-0.525146\pi$
$421$	211.095	−	76.8324i	0.501414	−	0.182500i	0.580330	+	0.814381i	$0.302924\pi$
$422$	417.881	−	241.264i	0.990239	−	0.571715i
$423$	−371.210	−	211.496i	−0.877566	−	0.499990i
$424$	0.369756	−	0.640436i	0.000872066	−	0.00151046i
$425$	−1231.39	−	217.127i	−2.89738	−	0.510887i
$426$	157.290	−	436.029i	0.369226	−	1.02354i
$427$	44.6219	+	16.2411i	0.104501	+	0.0380353i
$428$	−405.838	+	71.5602i	−0.948220	+	0.167197i
$429$	415.902	+	346.960i	0.969468	+	0.808765i
$430$	154.237	+	129.420i	0.358690	+	0.300976i
$431$		−	189.283i		−	0.439171i	−0.975593	−	0.219585i	$-0.929530\pi$
$431$		−	189.283i		−	0.439171i	0.975593	−	0.219585i	$-0.0704705\pi$
$432$	106.516	+	17.8404i	0.246565	+	0.0412973i
$433$	−364.876			−0.842669			−0.421334	−	0.906905i	$-0.638438\pi$
$433$	−364.876			−0.842669			−0.421334	+	0.906905i	$0.638438\pi$
$434$	10.3042	−	12.2801i	0.0237425	−	0.0282952i
$435$	−215.085	−	585.722i	−0.494449	−	1.34649i
$436$	48.6775	+	276.064i	0.111646	+	0.633174i
$437$	2.00868	−	5.51879i	0.00459651	−	0.0126288i
$438$	47.1225	+	262.845i	0.107586	+	0.600104i
$439$	73.6423	−	417.646i	0.167750	−	0.951358i	−0.778433	−	0.627727i	$-0.783985\pi$
$439$	73.6423	−	417.646i	0.167750	−	0.951358i	0.946183	−	0.323631i	$-0.104904\pi$
$440$	−274.031	−	158.212i	−0.622798	−	0.359573i
$441$	338.016	+	280.349i	0.766477	+	0.635712i
$442$	298.486	+	516.994i	0.675308	+	1.16967i
$443$	61.4880	+	168.937i	0.138799	+	0.381348i	0.989544	−	0.144231i	$-0.0460710\pi$
$443$	61.4880	+	168.937i	0.138799	+	0.381348i	−0.850745	+	0.525579i	$0.823849\pi$
$444$	−39.8898	+	23.1828i	−0.0898419	+	0.0522135i
$445$	629.997	−	528.630i	1.41572	−	1.18793i
$446$	53.1565	+	63.3495i	0.119185	+	0.142039i
$447$	−270.674	−	465.738i	−0.605534	−	1.04192i
$448$	3.41042	−	1.24129i	0.00761254	−	0.00277074i
$449$	558.134	−	322.239i	1.24306	−	0.717681i	0.273343	−	0.961917i	$-0.411871\pi$
$449$	558.134	−	322.239i	1.24306	−	0.717681i	0.969716	+	0.244236i	$0.0785372\pi$
$450$	−475.753	−	81.0839i	−1.05723	−	0.180187i
$451$	174.770	−	302.711i	0.387518	−	0.671200i
$452$	143.610	+	25.3222i	0.317720	+	0.0560226i
$453$	−475.216	+	85.1959i	−1.04904	+	0.188070i
$454$	55.8131	+	20.3143i	0.122936	+	0.0447452i
$455$	45.3636	−	7.99882i	0.0997001	−	0.0175798i
$456$	3.23056	−	1.18631i	0.00708457	−	0.00260155i
$457$	198.907	+	166.903i	0.435246	+	0.365215i	0.833927	−	0.551875i	$-0.186088\pi$
$457$	198.907	+	166.903i	0.435246	+	0.365215i	−0.398681	+	0.917090i	$0.630532\pi$
$458$		−	125.879i		−	0.274846i
$459$	−890.327	+	7.64182i	−1.93971	+	0.0166488i
$460$	−229.717			−0.499385
$461$	313.010	−	373.031i	0.678981	−	0.809178i	−0.310996	−	0.950411i	$-0.600662\pi$
$461$	313.010	−	373.031i	0.678981	−	0.809178i	0.989976	+	0.141234i	$0.0451069\pi$
$462$	−17.3896	+	20.8449i	−0.0376398	+	0.0451189i
$463$	104.106	+	590.412i	0.224850	+	1.27519i	0.862972	+	0.505252i	$0.168601\pi$
$463$	104.106	+	590.412i	0.224850	+	1.27519i	−0.638121	+	0.769936i	$0.720288\pi$
$464$	35.8727	−	98.5595i	0.0773119	−	0.212413i
$465$	−559.299	−	201.758i	−1.20279	−	0.433888i
$466$	34.4879	−	195.590i	0.0740083	−	0.419722i
$467$	−551.534	−	318.428i	−1.18102	−	0.681860i	−0.224766	−	0.974413i	$-0.572162\pi$
$467$	−551.534	−	318.428i	−1.18102	−	0.681860i	−0.956249	+	0.292553i	$0.905495\pi$
$468$	116.347	+	198.882i	0.248605	+	0.424962i
$469$	14.6552	+	25.3835i	0.0312477	+	0.0541226i
$470$	182.127	+	500.390i	0.387505	+	1.06466i
$471$	201.149	+	115.368i	0.427069	+	0.244942i
$472$	−119.390	+	100.180i	−0.252946	+	0.212247i
$473$	−162.719	−	193.921i	−0.344015	−	0.409981i
$474$	81.7086	−	0.233767i	0.172381	−	0.000493180i
$475$	−14.4513	+	5.25985i	−0.0304238	+	0.0110734i
$476$	−25.9116	+	14.9601i	−0.0544362	+	0.0314288i
$477$	−0.792146	+	2.21577i	−0.00166068	+	0.00464522i
$478$	−20.5440	+	35.5832i	−0.0429790	+	0.0744419i
$479$	393.091	+	69.3125i	0.820649	+	0.144703i	0.568182	−	0.822903i	$-0.307647\pi$
$479$	393.091	+	69.3125i	0.820649	+	0.144703i	0.252467	+	0.967605i	$0.418758\pi$
$480$	−86.8213	−	102.870i	−0.180878	−	0.214314i
$481$	−92.4960	−	33.6658i	−0.192299	−	0.0699913i
$482$	−206.749	+	36.4555i	−0.428940	+	0.0756337i
$483$	−3.36663	+	19.4178i	−0.00697024	+	0.0402024i
$484$	119.379	+	100.171i	0.246651	+	0.206965i
$485$			445.886i			0.919354i
$486$	−343.619	+	4.91577i	−0.707034	+	0.0101147i
$487$	−379.619			−0.779505			−0.389753	−	0.920920i	$-0.627440\pi$
$487$	−379.619			−0.779505			−0.389753	+	0.920920i	$0.627440\pi$
$488$	190.302	−	226.793i	0.389963	−	0.464740i
$489$	6.32834	+	1.09720i	0.0129414	+	0.00224376i
$490$	−95.0473	−	539.040i	−0.193974	−	1.10008i
$491$	204.694	−	562.393i	0.416893	−	1.14540i	−0.536561	−	0.843862i	$-0.680277\pi$
$491$	204.694	−	562.393i	0.416893	−	1.14540i	0.953453	−	0.301541i	$-0.0975010\pi$
$492$	113.637	−	95.9080i	0.230969	−	0.194935i
$493$	−150.150	+	851.542i	−0.304564	+	1.72727i
$494$	6.35863	+	3.67116i	0.0128717	+	0.00743149i
$495$	948.089	+	338.945i	1.91533	+	0.684738i
$496$	−49.9725	−	86.5549i	−0.100751	−	0.174506i
$497$	16.9522	+	46.5759i	0.0341091	+	0.0937141i
$498$	0.693442	+	242.378i	0.00139245	+	0.486703i
$499$	−35.4771	+	29.7688i	−0.0710964	+	0.0596569i	−0.677643	−	0.735391i	$-0.736999\pi$
$499$	−35.4771	+	29.7688i	−0.0710964	+	0.0596569i	0.606547	+	0.795048i	$0.292554\pi$
$500$	131.725	+	156.983i	0.263449	+	0.313966i
$501$	−133.971	+	233.585i	−0.267407	+	0.466238i
$502$	414.696	−	150.937i	0.826088	−	0.300672i
$503$	−728.991	+	420.883i	−1.44929	+	0.836745i	−0.998439	−	0.0558562i	$-0.982211\pi$
$503$	−728.991	+	420.883i	−1.44929	+	0.836745i	−0.450847	+	0.892601i	$0.648878\pi$
$504$	−9.96795	+	5.83130i	−0.0197777	+	0.0115700i
$505$	−178.374	+	308.953i	−0.353216	+	0.611788i
$506$	284.434	+	50.1535i	0.562123	+	0.0991175i
$507$	5.23172	−	14.5030i	0.0103190	−	0.0286055i
$508$	20.6487	+	7.51551i	0.0406470	+	0.0147943i
$509$	503.035	−	88.6986i	0.988281	−	0.174261i	0.343934	−	0.938994i	$-0.388240\pi$
$509$	503.035	−	88.6986i	0.988281	−	0.174261i	0.644347	+	0.764733i	$0.277129\pi$
$510$	852.154	+	710.897i	1.67089	+	1.39392i
$511$	−21.8736	−	18.3541i	−0.0428054	−	0.0359180i
$512$		−	22.6274i		−	0.0441942i
$513$	−9.43630	+	5.55658i	−0.0183943	+	0.0108315i
$514$	−74.4863			−0.144915
$515$	464.686	−	553.791i	0.902303	−	1.07532i
$516$	−37.1222	−	101.092i	−0.0719423	−	0.195914i
$517$	−116.260	−	659.343i	−0.224874	−	1.27533i
$518$	1.68732	−	4.63589i	0.00325738	−	0.00894959i
$519$	96.5364	+	538.472i	0.186005	+	1.03752i
$520$	49.8699	−	282.827i	0.0959037	−	0.543897i
$521$	−496.828	−	286.844i	−0.953604	−	0.550563i	−0.0594053	−	0.998234i	$-0.518920\pi$
$521$	−496.828	−	286.844i	−0.953604	−	0.550563i	−0.894199	+	0.447670i	$0.852254\pi$
$522$	−56.0720	+	328.997i	−0.107418	+	0.630263i
$523$	257.403	+	445.835i	0.492166	+	0.852457i	0.999959	−	0.00902213i	$-0.00287187\pi$
$523$	257.403	+	445.835i	0.492166	+	0.852457i	−0.507793	+	0.861479i	$0.669539\pi$
$524$	−25.6378	−	70.4394i	−0.0489272	−	0.134426i
$525$	44.6175	−	25.9304i	0.0849858	−	0.0493913i
$526$	−17.3714	+	14.5763i	−0.0330255	+	0.0277117i
$527$	529.627	+	631.185i	1.00499	+	1.19769i
$528$	85.0422	+	146.329i	0.161065	+	0.277138i
$529$	−300.064	+	109.214i	−0.567228	+	0.206454i
$530$	2.53999	−	1.46646i	0.00479243	−	0.00276691i
$531$	316.593	−	381.716i	0.596221	−	0.718862i
$532$	−0.183998	+	0.318694i	−0.000345861	+	0.000599048i
$533$	312.427	+	55.0893i	0.586167	+	0.103357i
$534$	−432.977	+	77.6235i	−0.810819	+	0.145362i
$535$	−1535.83	−	558.997i	−2.87071	−	1.04485i
$536$	179.964	−	31.7325i	0.335754	−	0.0592024i
$537$	338.289	−	124.224i	0.629962	−	0.231331i
$538$	−253.358	−	212.593i	−0.470926	−	0.395154i
$539$			688.187i			1.27678i
$540$	330.472	+	272.500i	0.611985	+	0.504629i
$541$	104.119			0.192457			0.0962284	−	0.995359i	$-0.469322\pi$
$541$	104.119			0.192457			0.0962284	+	0.995359i	$0.469322\pi$
$542$	−208.964	+	249.034i	−0.385543	+	0.459472i
$543$	307.457	−	368.549i	0.566219	−	0.678728i
$544$	32.3927	+	183.708i	0.0595454	+	0.337699i
$545$	−380.247	+	1044.72i	−0.697702	+	1.91692i
$546$	−23.1762	−	8.36043i	−0.0424472	−	0.0153121i
$547$	−34.7198	+	196.906i	−0.0634732	+	0.359974i	0.936484	+	0.350711i	$0.114060\pi$
$547$	−34.7198	+	196.906i	−0.0634732	+	0.359974i	−0.999957	+	0.00926380i	$0.997051\pi$
$548$	73.3171	+	42.3296i	0.133790	+	0.0772439i
$549$	−466.348	+	818.519i	−0.849450	+	1.49093i
$550$	−378.150	−	654.976i	−0.687546	−	1.19087i
$551$	3.63735	+	9.99353i	0.00660136	+	0.0181371i
$552$	106.583	+	61.1300i	0.193086	+	0.110743i
$553$	−6.69298	+	5.61608i	−0.0121030	+	0.0101557i
$554$	−239.115	−	284.966i	−0.431616	−	0.514380i
$555$	−182.981	+	0.523506i	−0.329695	+	0.000943254i
$556$	−306.241	+	111.463i	−0.550793	+	0.200472i
$557$	289.044	−	166.880i	0.518930	−	0.299604i	−0.217567	−	0.976045i	$-0.569812\pi$
$557$	289.044	−	166.880i	0.518930	−	0.299604i	0.736497	+	0.676441i	$0.236479\pi$
$558$	205.812	+	242.446i	0.368838	+	0.434491i
$559$	114.879	−	198.976i	0.205508	−	0.355950i
$560$	14.1752	+	2.49947i	0.0253129	+	0.00446334i
$561$	−899.923	−	1066.28i	−1.60414	−	1.90067i
$562$	−654.597	−	238.254i	−1.16476	−	0.423939i
$563$	989.177	−	174.419i	1.75697	−	0.309802i	0.800006	−	0.599992i	$-0.204830\pi$
$563$	989.177	−	174.419i	1.75697	−	0.309802i	0.956969	+	0.290190i	$0.0937187\pi$
$564$	48.6561	−	280.635i	0.0862696	−	0.497580i
$565$	443.039	+	371.754i	0.784140	+	0.657971i
$566$			692.917i			1.22423i
$567$	27.8774	−	23.9408i	0.0491664	−	0.0422237i
$568$	309.021			0.544051
$569$	441.594	−	526.272i	0.776089	−	0.924906i	−0.222661	−	0.974896i	$-0.571474\pi$
$569$	441.594	−	526.272i	0.776089	−	0.924906i	0.998750	+	0.0499895i	$0.0159188\pi$
$570$	13.4484	+	2.33167i	0.0235937	+	0.00409065i
$571$	−67.2813	−	381.571i	−0.117831	−	0.668251i	−0.985310	−	0.170777i	$-0.945372\pi$
$571$	−67.2813	−	381.571i	−0.117831	−	0.668251i	0.867479	−	0.497474i	$-0.165739\pi$
$572$	−123.497	+	339.306i	−0.215904	+	0.593192i
$573$	292.753	−	247.080i	0.510914	−	0.431204i
$574$	−2.76107	+	15.6588i	−0.00481022	+	0.0272801i
$575$	−475.499	−	274.529i	−0.826954	−	0.477442i
$576$	12.9082	+	70.8335i	0.0224100	+	0.122975i
$577$	−279.632	−	484.337i	−0.484631	−	0.839406i	0.515213	−	0.857062i	$-0.327713\pi$
$577$	−279.632	−	484.337i	−0.484631	−	0.839406i	−0.999844	+	0.0176564i	$0.994379\pi$
$578$	−386.196	−	1061.06i	−0.668158	−	1.83575i
$579$	−0.855729	−	299.102i	−0.00147794	−	0.516584i
$580$	318.656	−	267.385i	0.549408	−	0.461008i
$581$	−16.6594	−	19.8539i	−0.0286736	−	0.0341719i
$582$	118.655	−	206.881i	0.203874	−	0.355465i
$583$	−3.46517	+	1.26122i	−0.00594368	+	0.00216332i
$584$	−154.173	+	89.0120i	−0.263995	+	0.152418i
$585$	5.22888	+	913.817i	0.00893826	+	1.56208i
$586$	−107.669	+	186.488i	−0.183736	+	0.318240i
$587$	499.131	+	88.0103i	0.850309	+	0.149932i	0.581787	−	0.813341i	$-0.302354\pi$
$587$	499.131	+	88.0103i	0.850309	+	0.149932i	0.268522	+	0.963274i	$0.413465\pi$
$588$	−99.3441	+	275.395i	−0.168953	+	0.468358i
$589$	9.52286	+	3.46604i	0.0161678	+	0.00588461i
$590$	−608.728	+	107.335i	−1.03174	+	0.181924i
$591$	87.7456	+	73.2005i	0.148470	+	0.123859i
$592$	−23.5621	−	19.7709i	−0.0398008	−	0.0333969i
$593$		−	598.516i		−	1.00930i	−0.863324	−	0.504651i	$-0.831621\pi$
$593$		−	598.516i		−	1.00930i	0.863324	−	0.504651i	$-0.168379\pi$
$594$	−349.694	−	409.558i	−0.588711	−	0.689492i
$595$	−118.664			−0.199436
$596$	230.838	−	275.102i	0.387312	−	0.461580i
$597$	398.587	+	1085.44i	0.667650	+	1.81815i
$598$	45.5198	+	258.155i	0.0761200	+	0.431698i
$599$	264.288	−	726.125i	0.441215	−	1.21223i	−0.497478	−	0.867477i	$-0.665741\pi$
$599$	264.288	−	726.125i	0.441215	−	1.21223i	0.938694	−	0.344753i	$-0.112037\pi$
$600$	−56.7762	−	316.693i	−0.0946269	−	0.527821i
$601$	−22.6179	+	128.272i	−0.0376337	+	0.213431i	−0.997826	−	0.0659100i	$-0.979005\pi$
$601$	−22.6179	+	128.272i	−0.0376337	+	0.213431i	0.960192	+	0.279341i	$0.0901161\pi$
$602$	9.97263	+	5.75770i	0.0165658	+	0.00956429i
$603$	−545.262	+	202.000i	−0.904248	+	0.334991i
$604$	−160.931	−	278.740i	−0.266442	−	0.461490i
$605$	211.389	+	580.786i	0.349403	+	0.959978i
$606$	164.977	−	95.8797i	0.272239	−	0.158217i
$607$	485.221	−	407.149i	0.799376	−	0.670756i	−0.148671	−	0.988887i	$-0.547500\pi$
$607$	485.221	−	407.149i	0.799376	−	0.670756i	0.948047	+	0.318131i	$0.103055\pi$
$608$	1.47477	+	1.75756i	0.00242560	+	0.00289072i
$609$	−17.9317	−	30.8544i	−0.0294445	−	0.0506640i
$610$	1103.36	−	401.590i	1.80879	−	0.658345i
$611$	526.247	−	303.829i	0.861288	−	0.497265i
$612$	−206.202	−	556.606i	−0.336932	−	0.909487i
$613$	−388.396	+	672.722i	−0.633599	+	1.09743i	0.353211	+	0.935544i	$0.385090\pi$
$613$	−388.396	+	672.722i	−0.633599	+	1.09743i	−0.986810	+	0.161883i	$0.948243\pi$
$614$	−425.343	−	74.9995i	−0.692741	−	0.122149i
$615$	580.494	−	104.070i	0.943893	−	0.169220i
$616$	−17.0060	−	6.18966i	−0.0276071	−	0.0100482i
$617$	−360.546	+	63.5740i	−0.584353	+	0.103037i	−0.458006	−	0.888949i	$-0.651436\pi$
$617$	−360.546	+	63.5740i	−0.584353	+	0.103037i	−0.126347	+	0.991986i	$0.540325\pi$
$618$	−362.972	+	133.288i	−0.587334	+	0.215677i
$619$	341.806	+	286.809i	0.552190	+	0.463343i	0.875682	−	0.482888i	$-0.160412\pi$
$619$	341.806	+	286.809i	0.552190	+	0.463343i	−0.323492	+	0.946231i	$0.604857\pi$
$620$		−	396.385i		−	0.639330i
$621$	−368.524	−	130.561i	−0.593436	−	0.210243i
$622$	−500.414			−0.804524
$623$	30.2342	−	36.0317i	0.0485299	−	0.0578357i
$624$	−98.4014	+	117.954i	−0.157694	+	0.189029i
$625$	−23.4761	−	133.140i	−0.0375618	−	0.213024i
$626$	−56.1835	+	154.363i	−0.0897500	+	0.246586i
$627$	−16.1427	−	5.82322i	−0.0257459	−	0.00928743i
$628$	−26.8443	+	152.242i	−0.0427457	+	0.242423i
$629$	219.600	+	126.786i	0.349126	+	0.201568i
$630$	−45.8003	+	0.262071i	−0.0726989	+	0.000415985i
$631$	444.799	+	770.415i	0.704911	+	1.22094i	0.966723	+	0.255824i	$0.0823466\pi$
$631$	444.799	+	770.415i	0.704911	+	1.22094i	−0.261812	+	0.965119i	$0.584320\pi$
$632$	18.6307	+	51.1875i	0.0294790	+	0.0809929i
$633$	−887.920	−	509.259i	−1.40272	−	0.804517i
$634$	246.150	−	206.544i	0.388248	−	0.325779i
$635$	56.0184	+	66.7601i	0.0882179	+	0.105134i
$636$	−1.56873	+	0.00448813i	−0.00246656	+	7.05681e-6i
$637$	−586.937	+	213.628i	−0.921408	+	0.335365i
$638$	−452.936	+	261.503i	−0.709931	+	0.409879i
$639$	−967.368	+	176.286i	−1.51388	+	0.275878i
$640$	44.8705	−	77.7180i	0.0701102	−	0.121434i
$641$	460.754	+	81.2433i	0.718805	+	0.126745i	0.521074	−	0.853512i	$-0.325532\pi$
$641$	460.754	+	81.2433i	0.718805	+	0.126745i	0.197731	+	0.980256i	$0.436643\pi$
$642$	563.834	+	668.061i	0.878246	+	1.04059i
$643$	367.369	+	133.711i	0.571336	+	0.207949i	0.611501	−	0.791244i	$-0.290566\pi$
$643$	367.369	+	133.711i	0.571336	+	0.207949i	−0.0401649	+	0.999193i	$0.512788\pi$
$644$	−12.9387	+	2.28144i	−0.0200912	+	0.00354261i
$645$	72.9632	−	420.832i	0.113121	−	0.652452i
$646$	−14.4894	−	12.1581i	−0.0224295	−	0.0188206i
$647$		−	343.874i		−	0.531490i	−0.964043	−	0.265745i	$-0.914382\pi$
$647$		−	343.874i		−	0.531490i	0.964043	−	0.265745i	$-0.0856180\pi$
$648$	−80.8162	−	214.375i	−0.124716	−	0.330826i
$649$	777.157			1.19747
$650$	441.226	−	525.833i	0.678809	−	0.808974i
$651$	−33.5060	−	5.80922i	−0.0514685	−	0.00892354i
$652$	0.743533	+	4.21678i	0.00114039	+	0.00646746i
$653$	40.4063	−	111.015i	0.0618779	−	0.170008i	−0.904901	−	0.425622i	$-0.860055\pi$
$653$	40.4063	−	111.015i	0.0618779	−	0.170008i	0.966779	+	0.255614i	$0.0822776\pi$
$654$	454.436	−	383.538i	0.694857	−	0.586450i
$655$	51.6245	−	292.777i	0.0788161	−	0.446988i
$656$	85.8520	+	49.5667i	0.130872	+	0.0755590i
$657$	431.850	−	366.596i	0.657306	−	0.557985i
$658$	15.2279	+	26.3754i	0.0231426	+	0.0400842i
$659$	−236.242	−	649.069i	−0.358485	−	0.984930i	−0.979555	−	0.201175i	$-0.935524\pi$
$659$	−236.242	−	649.069i	−0.358485	−	0.984930i	0.621070	−	0.783755i	$-0.286698\pi$
$660$	1.92039	+	671.234i	0.00290969	+	1.01702i
$661$	767.161	−	643.724i	1.16061	−	0.973864i	0.160692	−	0.987005i	$-0.448627\pi$
$661$	767.161	−	643.724i	1.16061	−	0.973864i	0.999914	+	0.0131403i	$0.00418282\pi$
$662$	85.6338	+	102.054i	0.129356	+	0.154161i
$663$	630.045	−	1098.52i	0.950294	−	1.65689i
$664$	−151.841	+	55.2657i	−0.228677	+	0.0832315i
$665$	−1.26395	+	0.729741i	−0.00190068	+	0.00109736i
$666$	85.0380	+	48.4501i	0.127685	+	0.0727479i
$667$	−189.845	+	328.822i	−0.284626	+	0.492986i
$668$	−176.791	−	31.1730i	−0.264657	−	0.0466662i
$669$	59.5276	−	165.018i	0.0889799	−	0.246664i
$670$	681.045	+	247.880i	1.01649	+	0.369971i
$671$	−1453.85	+	256.353i	−2.16669	+	0.382047i
$672$	−5.91183	−	4.93186i	−0.00879736	−	0.00733908i
$673$	−122.061	−	102.421i	−0.181368	−	0.152186i	0.547584	−	0.836751i	$-0.315548\pi$
$673$	−122.061	−	102.421i	−0.181368	−	0.152186i	−0.728952	+	0.684565i	$0.759992\pi$
$674$		−	102.468i		−	0.152029i
$675$	358.396	+	958.994i	0.530957	+	1.42073i
$676$	10.2785			0.0152049
$677$	−657.379	+	783.434i	−0.971018	+	1.15721i	0.0165244	+	0.999863i	$0.494740\pi$
$677$	−657.379	+	783.434i	−0.971018	+	1.15721i	−0.987543	+	0.157351i	$0.949705\pi$
$678$	−106.632	−	290.382i	−0.157275	−	0.428292i
$679$	4.42833	+	25.1143i	0.00652185	+	0.0369872i
$680$	−253.038	+	695.215i	−0.372114	+	1.02237i
$681$	−22.2339	−	124.019i	−0.0326489	−	0.182113i
$682$	−86.5415	+	490.801i	−0.126894	+	0.719650i
$683$	376.428	+	217.331i	0.551139	+	0.318200i	0.749581	−	0.661912i	$-0.230255\pi$
$683$	376.428	+	217.331i	0.551139	+	0.318200i	−0.198442	+	0.980113i	$0.563588\pi$
$684$	−5.61927	−	4.66060i	−0.00821531	−	0.00681374i
$685$	167.881	+	290.778i	0.245081	+	0.424493i
$686$	−21.4591	−	58.9584i	−0.0312815	−	0.0859452i
$687$	−230.872	+	134.176i	−0.336058	+	0.195307i
$688$	54.9979	−	46.1487i	0.0799388	−	0.0670766i
$689$	−2.15132	−	2.56384i	−0.00312238	−	0.00372111i
$690$	244.858	+	421.319i	0.354867	+	0.610607i
$691$	−576.062	+	209.669i	−0.833664	+	0.303429i	−0.723362	−	0.690469i	$-0.757404\pi$
$691$	−576.062	+	209.669i	−0.833664	+	0.303429i	−0.110302	+	0.993898i	$0.535182\pi$
$692$	−315.843	+	182.352i	−0.456421	+	0.263515i
$693$	56.7669	+	9.67495i	0.0819147	+	0.0139610i
$694$	−292.294	+	506.267i	−0.421172	+	0.729492i
$695$	−1272.87	−	224.442i	−1.83147	−	0.322938i
$696$	−219.003	+	39.2624i	−0.314659	+	0.0564116i
$697$	−767.976	−	279.520i	−1.10183	−	0.401034i
$698$	−97.9623	+	17.2734i	−0.140347	+	0.0247470i
$699$	−395.489	+	145.229i	−0.565792	+	0.207766i
$700$	26.3547	+	22.1142i	0.0376495	+	0.0315917i
$701$			644.120i			0.918859i	0.888214	+	0.459430i	$0.151946\pi$
$701$			644.120i			0.918859i	−0.888214	+	0.459430i	$0.848054\pi$
$702$	240.749	−	425.381i	0.342948	−	0.605955i
$703$	3.11875			0.00443634
$704$	−72.5264	+	86.4335i	−0.103020	+	0.122775i
$705$	723.622	−	867.407i	1.02641	−	1.23036i
$706$	121.837	+	690.970i	0.172573	+	0.978710i
$707$	−6.97845	+	19.1731i	−0.00987051	+	0.0271190i
$708$	310.998	+	112.187i	0.439263	+	0.158457i
$709$	54.3773	−	308.389i	0.0766958	−	0.434963i	−0.922146	−	0.386843i	$-0.873566\pi$
$709$	54.3773	−	308.389i	0.0766958	−	0.434963i	0.998842	−	0.0481207i	$-0.0153232\pi$
$710$	1061.39	+	612.794i	1.49492	+	0.863090i
$711$	−87.5229	−	149.611i	−0.123098	−	0.210423i
$712$	−146.627	−	253.965i	−0.205936	−	0.356692i
$713$	123.746	+	339.988i	0.173556	+	0.476842i
$714$	55.0574	+	31.5777i	0.0771112	+	0.0442265i
$715$	−1097.02	+	920.512i	−1.53430	+	1.28743i
$716$	154.431	+	184.043i	0.215685	+	0.257043i
$717$	87.1604	−	0.249365i	0.121563	−	0.000347789i
$718$	386.226	−	140.575i	0.537919	−	0.195786i
$719$	−1134.61	+	655.066i	−1.57804	+	0.911079i	−0.582902	+	0.812543i	$0.698083\pi$
$719$	−1134.61	+	655.066i	−1.57804	+	0.911079i	−0.995133	+	0.0985362i	$0.968584\pi$
$720$	−96.1283	+	268.888i	−0.133512	+	0.373455i
$721$	20.6732	−	35.8070i	0.0286730	−	0.0496630i
$722$	502.546	+	88.6124i	0.696047	+	0.122732i
$723$	287.238	+	340.335i	0.397287	+	0.470726i
$724$	300.675	+	109.437i	0.415296	+	0.151156i
$725$	979.141	−	172.649i	1.35054	−	0.238137i
$726$	56.4735	−	325.724i	0.0777872	−	0.448655i
$727$	965.609	+	810.242i	1.32821	+	1.11450i	0.984492	+	0.175428i	$0.0561308\pi$
$727$	965.609	+	810.242i	1.32821	+	1.11450i	0.343718	+	0.939073i	$0.388314\pi$
$728$		−	16.4253i		−	0.0225623i
$729$	375.283	+	624.983i	0.514792	+	0.857315i
$730$	−706.049			−0.967190
$731$	−380.454	+	453.407i	−0.520456	+	0.620256i
$732$	−618.800	−	107.287i	−0.845355	−	0.146566i
$733$	36.7966	+	208.684i	0.0502000	+	0.284698i	0.999566	−	0.0294754i	$-0.00938366\pi$
$733$	36.7966	+	208.684i	0.0502000	+	0.284698i	−0.949365	+	0.314174i	$0.898273\pi$
$734$	276.028	−	758.380i	0.376059	−	1.03321i
$735$	−887.327	+	748.893i	−1.20725	+	1.01890i
$736$	−14.2240	+	80.6685i	−0.0193261	+	0.109604i
$737$	−789.147	−	455.614i	−1.07076	−	0.618201i
$738$	−297.029	−	106.189i	−0.402479	−	0.143888i
$739$	26.2115	+	45.3996i	0.0354688	+	0.0614338i	0.883215	−	0.468968i	$-0.155374\pi$
$739$	26.2115	+	45.3996i	0.0354688	+	0.0614338i	−0.847746	+	0.530402i	$0.822041\pi$
$740$	−41.7223	−	114.631i	−0.0563814	−	0.154907i
$741$	−0.0445609	−	15.5753i	−6.01361e−5	−	0.0210194i
$742$	0.128499	−	0.107824i	0.000173180	−	0.000145315i
$743$	−12.7448	−	15.1886i	−0.0171531	−	0.0204423i	0.757400	−	0.652952i	$-0.226469\pi$
$743$	−12.7448	−	15.1886i	−0.0171531	−	0.0204423i	−0.774553	+	0.632509i	$0.782025\pi$
$744$	−105.482	+	183.913i	−0.141777	+	0.247195i
$745$	1338.39	−	487.133i	1.79649	−	0.653870i
$746$	24.4311	−	14.1053i	0.0327495	−	0.0189079i
$747$	443.801	−	259.626i	0.594111	−	0.347558i
$748$	465.094	−	805.566i	0.621783	−	1.07696i
$749$	−92.0566	−	16.2321i	−0.122906	−	0.0216716i
$750$	147.512	−	408.923i	0.196683	−	0.545231i
$751$	1260.89	+	458.927i	1.67895	+	0.611088i	0.993165	−	0.116716i	$-0.0372368\pi$
$751$	1260.89	+	458.927i	1.67895	+	0.611088i	0.685785	+	0.727804i	$0.259459\pi$
$752$	186.996	−	32.9725i	0.248665	−	0.0438464i
$753$	−718.860	−	599.699i	−0.954661	−	0.796412i
$754$	−363.629	−	305.121i	−0.482267	−	0.404670i
$755$		−	1276.51i		−	1.69075i
$756$	21.3200	+	12.0663i	0.0282011	+	0.0159607i
$757$	1369.68			1.80935			0.904675	−	0.426102i	$-0.140114\pi$
$757$	1369.68			1.80935			0.904675	+	0.426102i	$0.140114\pi$
$758$	−33.6933	+	40.1541i	−0.0444503	+	0.0529738i
$759$	−211.197	−	575.133i	−0.278257	−	0.757752i
$760$	1.58009	+	8.96114i	0.00207907	+	0.0117910i
$761$	−18.9789	+	52.1440i	−0.0249394	+	0.0685204i	−0.951538	−	0.307533i	$-0.900497\pi$
$761$	−18.9789	+	52.1440i	−0.0249394	+	0.0685204i	0.926598	+	0.376053i	$0.122719\pi$
$762$	−8.22567	−	45.8821i	−0.0107948	−	0.0602128i
$763$	−11.0416	+	62.6198i	−0.0144712	+	0.0820705i
$764$	221.174	+	127.695i	0.289494	+	0.167140i
$765$	395.518	−	2320.67i	0.517018	−	3.03355i
$766$	287.551	+	498.054i	0.375393

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)

\(f(q)\)	\(=\)	\(q+(0.909039 - 1.08335i) q^{2} +(-2.95590 - 0.512490i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.71293 - 7.45370i) q^{5} +(-3.24224 + 2.73640i) q^{6} +(0.0787775 - 0.446769i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(8.47471 + 3.02974i) q^{9} +O(q^{10})\)	\(q+(0.909039 - 1.08335i) q^{2} +(-2.95590 - 0.512490i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.71293 - 7.45370i) q^{5} +(-3.24224 + 2.73640i) q^{6} +(0.0787775 - 0.446769i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(8.47471 + 3.02974i) q^{9} +(-5.60882 - 9.71475i) q^{10} +(4.82381 + 13.2533i) q^{11} +(0.0171659 + 5.99998i) q^{12} +(-9.80599 + 8.22820i) q^{13} +(-0.412396 - 0.491475i) q^{14} +(-11.8391 + 20.6421i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(28.5583 - 16.4882i) q^{17} +(10.9861 - 6.42693i) q^{18} +(0.202792 - 0.351246i) q^{19} +(-15.6231 - 2.75478i) q^{20} +(-0.461823 + 1.28023i) q^{21} +(18.7430 + 6.82189i) q^{22} +(14.2603 - 2.51448i) q^{23} +(6.51568 + 5.43561i) q^{24} +(-29.0466 - 24.3730i) q^{25} +18.1031i q^{26} +(-23.4977 - 13.2988i) q^{27} -0.907323 q^{28} +(-16.8547 + 20.0866i) q^{29} +(11.6004 + 31.5903i) q^{30} +(4.33881 + 24.6066i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(-7.46652 - 41.6476i) q^{33} +(8.09818 - 45.9270i) q^{34} +(-3.11637 - 1.79924i) q^{35} +(3.02419 - 17.7441i) q^{36} +(3.84477 + 6.65933i) q^{37} +(-0.196177 - 0.538991i) q^{38} +(33.2024 - 19.2963i) q^{39} +(-17.1864 + 14.4211i) q^{40} +(-15.9304 - 18.9851i) q^{41} +(0.967127 + 1.66410i) q^{42} +(-16.8662 + 6.13880i) q^{43} +(24.4286 - 14.1039i) q^{44} +(45.5740 - 54.9485i) q^{45} +(10.2391 - 17.7347i) q^{46} +(-46.7491 - 8.24313i) q^{47} +(11.8117 - 2.11758i) q^{48} +(45.8515 + 16.6886i) q^{49} +(-52.8090 + 9.31165i) q^{50} +(-92.8656 + 34.1015i) q^{51} +(19.6120 + 16.4564i) q^{52} +0.261457i q^{53} +(-35.7676 + 13.3671i) q^{54} +111.873 q^{55} +(-0.824792 + 0.982949i) q^{56} +(-0.779443 + 0.934320i) q^{57} +(6.43929 + 36.5190i) q^{58} +(18.8461 - 51.7793i) q^{59} +(44.7686 + 16.1495i) q^{60} +(-18.1761 + 103.082i) q^{61} +(30.6018 + 17.6679i) q^{62} +(2.02121 - 3.54757i) q^{63} +(4.00000 + 6.92820i) q^{64} +(34.7276 + 95.4134i) q^{65} +(-51.9063 - 29.7704i) q^{66} +(-49.4929 + 41.5295i) q^{67} +(-42.3935 - 50.5226i) q^{68} +(-43.4407 + 0.124283i) q^{69} +(-4.78210 + 1.74054i) q^{70} +(-94.6180 + 54.6277i) q^{71} +(-16.4740 - 19.4064i) q^{72} +(31.4705 - 54.5085i) q^{73} +(10.7094 + 1.88836i) q^{74} +(73.3680 + 86.9302i) q^{75} +(-0.762248 - 0.277436i) q^{76} +(6.30118 - 1.11107i) q^{77} +(9.27764 - 53.5109i) q^{78} +(-14.7532 - 12.3794i) q^{79} +31.7283i q^{80} +(62.6414 + 51.3523i) q^{81} -35.0489 q^{82} +(36.7220 - 43.7636i) q^{83} +(2.68196 + 0.464994i) q^{84} +(-45.4212 - 257.596i) q^{85} +(-8.68158 + 23.8524i) q^{86} +(60.1149 - 50.7362i) q^{87} +(6.92713 - 39.2857i) q^{88} +(89.7902 + 51.8404i) q^{89} +(-18.0999 - 99.3230i) q^{90} +(2.90362 + 5.02921i) q^{91} +(-9.90511 - 27.2141i) q^{92} +(-0.214455 - 74.9584i) q^{93} +(-51.4269 + 43.1523i) q^{94} +(-2.06792 - 2.46445i) q^{95} +(8.44320 - 14.7212i) q^{96} +(-52.8231 + 19.2260i) q^{97} +(59.7604 - 34.5027i) q^{98} +(0.726312 + 126.933i) 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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