LMFDB - Embedded newform 162.3.h.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(5,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([23]))

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

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

chi := DirichletCharacter("162.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.h (of order $54$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	162.5
Dual form			162.3.h.a.65.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.326140 - 1.37609i) q^{2} +(2.89210 + 0.797352i) q^{3} +(-1.78727 + 0.897598i) q^{4} +(-7.40578 + 5.51340i) q^{5} +(0.154002 - 4.23984i) q^{6} +(-1.07376 + 0.706223i) q^{7} +(1.81808 + 2.16670i) q^{8} +(7.72846 + 4.61204i) q^{9} +O(q^{10})$	\(q+(-0.326140 - 1.37609i) q^{2} +(2.89210 + 0.797352i) q^{3} +(-1.78727 + 0.897598i) q^{4} +(-7.40578 + 5.51340i) q^{5} +(0.154002 - 4.23984i) q^{6} +(-1.07376 + 0.706223i) q^{7} +(1.81808 + 2.16670i) q^{8} +(7.72846 + 4.61204i) q^{9} +(10.0023 + 8.39290i) q^{10} +(-1.07678 + 9.21247i) q^{11} +(-5.88465 + 1.17086i) q^{12} +(4.35535 + 14.5479i) q^{13} +(1.32203 + 1.24727i) q^{14} +(-25.8144 + 10.0403i) q^{15} +(2.38863 - 3.20849i) q^{16} +(0.471048 + 0.0830584i) q^{17} +(3.82604 - 12.1393i) q^{18} +(-3.61111 - 20.4796i) q^{19} +(8.28728 - 16.5013i) q^{20} +(-3.66853 + 1.18630i) q^{21} +(13.0284 - 1.52280i) q^{22} +(-15.9635 + 24.2713i) q^{23} +(3.53043 + 7.71596i) q^{24} +(17.2779 - 57.7123i) q^{25} +(18.5988 - 10.7380i) q^{26} +(18.6740 + 19.5008i) q^{27} +(1.28519 - 2.22601i) q^{28} +(-7.55899 + 7.13154i) q^{29} +(22.2354 + 32.2484i) q^{30} +(-0.914886 + 15.7080i) q^{31} +(-5.19421 - 2.24057i) q^{32} +(-10.4597 + 25.7848i) q^{33} +(-0.0393314 - 0.675294i) q^{34} +(4.05834 - 11.1502i) q^{35} +(-17.9526 - 1.30589i) q^{36} +(61.2478 - 22.2924i) q^{37} +(-27.0042 + 11.6485i) q^{38} +(0.996308 + 45.5466i) q^{39} +(-25.4102 - 6.02232i) q^{40} +(8.54541 - 36.0559i) q^{41} +(2.82891 + 4.66134i) q^{42} +(-12.7320 - 29.5161i) q^{43} +(-6.34460 - 17.4316i) q^{44} +(-82.6633 + 8.45430i) q^{45} +(38.6059 + 14.0514i) q^{46} +(10.0825 - 0.587238i) q^{47} +(9.46646 - 7.37469i) q^{48} +(-18.7537 + 43.4760i) q^{49} +(-85.0525 - 4.95375i) q^{50} +(1.29609 + 0.615804i) q^{51} +(-20.8423 - 22.0915i) q^{52} +(14.3946 + 8.31072i) q^{53} +(20.7445 - 32.0572i) q^{54} +(-42.8176 - 74.1622i) q^{55} +(-3.48235 - 1.04255i) q^{56} +(5.88580 - 62.1084i) q^{57} +(12.2790 + 8.07600i) q^{58} +(-8.16985 - 69.8975i) q^{59} +(37.1250 - 41.1156i) q^{60} +(67.7959 + 34.0484i) q^{61} +(21.9140 - 3.86403i) q^{62} +(-11.5556 + 0.505789i) q^{63} +(-1.38919 + 7.87846i) q^{64} +(-112.463 - 83.7255i) q^{65} +(38.8936 + 5.98413i) q^{66} +(27.1526 - 28.7800i) q^{67} +(-0.916440 + 0.274364i) q^{68} +(-65.5207 + 57.4665i) q^{69} +(-16.6673 - 1.94813i) q^{70} +(-57.4122 + 68.4212i) q^{71} +(4.05802 + 25.1303i) q^{72} +(-97.8021 + 82.0657i) q^{73} +(-50.6518 - 77.0123i) q^{74} +(95.9865 - 153.133i) q^{75} +(24.8365 + 33.3612i) q^{76} +(-5.34985 - 10.6524i) q^{77} +(62.3514 - 16.2256i) q^{78} +(115.638 - 27.4066i) q^{79} +36.9309i q^{80} +(38.4581 + 71.2880i) q^{81} -52.4033 q^{82} +(9.97925 + 42.1058i) q^{83} +(5.49181 - 5.41310i) q^{84} +(-3.94641 + 1.98196i) q^{85} +(-36.4644 + 27.1468i) q^{86} +(-27.5477 + 14.5979i) q^{87} +(-21.9183 + 14.4159i) q^{88} +(52.4426 + 62.4987i) q^{89} +(38.5937 + 110.995i) q^{90} +(-14.9506 - 12.5451i) q^{91} +(6.74510 - 57.7081i) q^{92} +(-15.1707 + 44.6995i) q^{93} +(-4.09640 - 13.6829i) q^{94} +(139.655 + 131.758i) q^{95} +(-13.2357 - 10.6216i) q^{96} +(-83.7265 + 112.464i) q^{97} +(65.9433 + 11.6276i) q^{98} +(-50.8102 + 66.2320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q + 72 q^{18} + 108 q^{20} + 270 q^{21} + 162 q^{23} - 54 q^{27} - 162 q^{29} - 216 q^{30} - 378 q^{33} - 486 q^{35} - 180 q^{36} - 108 q^{38} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 1728 q^{65} - 1008 q^{66} + 702 q^{67} - 216 q^{68} - 1872 q^{69} + 540 q^{70} - 1296 q^{71} - 576 q^{72} - 864 q^{74} - 900 q^{75} + 108 q^{76} - 864 q^{77} - 288 q^{78} + 108 q^{79} + 144 q^{81} + 432 q^{83} + 144 q^{84} - 540 q^{85} + 864 q^{86} + 2016 q^{87} - 216 q^{88} + 1782 q^{89} + 1440 q^{90} + 864 q^{92} + 2124 q^{93} - 756 q^{94} + 2808 q^{95} + 288 q^{96} - 918 q^{97} + 1296 q^{98} + 1800 q^{99}+O(q^{100}) $ 324 * q + 72 * q^18 + 108 * q^20 + 270 * q^21 + 162 * q^23 - 54 * q^27 - 162 * q^29 - 216 * q^30 - 378 * q^33 - 486 * q^35 - 180 * q^36 - 108 * q^38 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 1728 * q^65 - 1008 * q^66 + 702 * q^67 - 216 * q^68 - 1872 * q^69 + 540 * q^70 - 1296 * q^71 - 576 * q^72 - 864 * q^74 - 900 * q^75 + 108 * q^76 - 864 * q^77 - 288 * q^78 + 108 * q^79 + 144 * q^81 + 432 * q^83 + 144 * q^84 - 540 * q^85 + 864 * q^86 + 2016 * q^87 - 216 * q^88 + 1782 * q^89 + 1440 * q^90 + 864 * q^92 + 2124 * q^93 - 756 * q^94 + 2808 * q^95 + 288 * q^96 - 918 * q^97 + 1296 * q^98 + 1800 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{23}{54}\right)$

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 $

$2$	−0.326140	−	1.37609i	−0.163070	−	0.688047i
$2$	−0.326140	−	1.37609i	−0.163070	−	0.688047i
$3$	2.89210	+	0.797352i	0.964033	+	0.265784i
$3$	2.89210	+	0.797352i	0.964033	+	0.265784i
$4$	−1.78727	+	0.897598i	−0.446816	+	0.224400i
$5$	−7.40578	+	5.51340i	−1.48116	+	1.10268i	−0.511181	+	0.859473i	$0.670792\pi$
$5$	−7.40578	+	5.51340i	−1.48116	+	1.10268i	−0.969974	+	0.243207i	$0.921801\pi$
$6$	0.154002	−	4.23984i	0.0256670	−	0.706641i
$7$	−1.07376	+	0.706223i	−0.153394	+	0.100889i	−0.623886	−	0.781515i	$-0.714447\pi$
$7$	−1.07376	+	0.706223i	−0.153394	+	0.100889i	0.470492	+	0.882404i	$0.344077\pi$
$8$	1.81808	+	2.16670i	0.227260	+	0.270838i
$9$	7.72846	+	4.61204i	0.858718	+	0.512449i
$10$	10.0023	+	8.39290i	1.00023	+	0.839290i
$11$	−1.07678	+	9.21247i	−0.0978894	+	0.837497i	0.851706	+	0.524020i	$0.175568\pi$
$11$	−1.07678	+	9.21247i	−0.0978894	+	0.837497i	−0.949596	+	0.313478i	$0.898506\pi$
$12$	−5.88465	+	1.17086i	−0.490387	+	0.0975718i
$13$	4.35535	+	14.5479i	0.335027	+	1.11907i	0.945116	+	0.326734i	$0.105948\pi$
$13$	4.35535	+	14.5479i	0.335027	+	1.11907i	−0.610090	+	0.792332i	$0.708867\pi$
$14$	1.32203	+	1.24727i	0.0944304	+	0.0890904i
$15$	−25.8144	+	10.0403i	−1.72096	+	0.669351i
$16$	2.38863	−	3.20849i	0.149290	−	0.200531i
$17$	0.471048	+	0.0830584i	0.0277087	+	0.00488579i	0.187485	−	0.982267i	$-0.439966\pi$
$17$	0.471048	+	0.0830584i	0.0277087	+	0.00488579i	−0.159777	+	0.987153i	$0.551077\pi$
$18$	3.82604	−	12.1393i	0.212558	−	0.674403i
$19$	−3.61111	−	20.4796i	−0.190059	−	1.07788i	−0.919282	−	0.393600i	$-0.871230\pi$
$19$	−3.61111	−	20.4796i	−0.190059	−	1.07788i	0.729223	−	0.684276i	$-0.239882\pi$
$20$	8.28728	−	16.5013i	0.414364	−	0.825066i
$21$	−3.66853	+	1.18630i	−0.174692	+	0.0564905i
$22$	13.0284	−	1.52280i	0.592200	−	0.0692182i
$23$	−15.9635	+	24.2713i	−0.694065	+	1.05527i	0.300763	+	0.953699i	$0.402759\pi$
$23$	−15.9635	+	24.2713i	−0.694065	+	1.05527i	−0.994828	+	0.101575i	$0.967612\pi$
$24$	3.53043	+	7.71596i	0.147101	+	0.321498i
$25$	17.2779	−	57.7123i	0.691117	−	2.30849i
$26$	18.5988	−	10.7380i	0.715337	−	0.413000i
$27$	18.6740	+	19.5008i	0.691631	+	0.722251i
$28$	1.28519	−	2.22601i	0.0458996	−	0.0795005i
$29$	−7.55899	+	7.13154i	−0.260655	+	0.245915i	−0.805464	−	0.592645i	$-0.798084\pi$
$29$	−7.55899	+	7.13154i	−0.260655	+	0.245915i	0.544809	+	0.838560i	$0.316602\pi$
$30$	22.2354	+	32.2484i	0.741182	+	1.07495i
$31$	−0.914886	+	15.7080i	−0.0295124	+	0.506709i	0.950868	+	0.309596i	$0.100194\pi$
$31$	−0.914886	+	15.7080i	−0.0295124	+	0.506709i	−0.980381	+	0.197113i	$0.936843\pi$
$32$	−5.19421	−	2.24057i	−0.162319	−	0.0700177i
$33$	−10.4597	+	25.7848i	−0.316962	+	0.781357i
$34$	−0.0393314	−	0.675294i	−0.00115681	−	0.0198616i
$35$	4.05834	−	11.1502i	0.115953	−	0.318577i
$36$	−17.9526	−	1.30589i	−0.498682	−	0.0362748i
$37$	61.2478	−	22.2924i	1.65535	−	0.602497i	0.665725	−	0.746197i	$-0.268122\pi$
$37$	61.2478	−	22.2924i	1.65535	−	0.602497i	0.989621	+	0.143700i	$0.0459001\pi$
$38$	−27.0042	+	11.6485i	−0.710636	+	0.306538i
$39$	0.996308	+	45.5466i	0.0255464	+	1.16786i
$40$	−25.4102	−	6.02232i	−0.635254	−	0.150558i
$41$	8.54541	−	36.0559i	0.208425	−	0.879413i	−0.763817	−	0.645433i	$-0.776677\pi$
$41$	8.54541	−	36.0559i	0.208425	−	0.879413i	0.972241	−	0.233980i	$-0.0751750\pi$
$42$	2.82891	+	4.66134i	0.0673551	+	0.110984i
$43$	−12.7320	−	29.5161i	−0.296093	−	0.686420i	0.703615	−	0.710581i	$-0.251568\pi$
$43$	−12.7320	−	29.5161i	−0.296093	−	0.686420i	−0.999708	+	0.0241609i	$0.992309\pi$
$44$	−6.34460	−	17.4316i	−0.144195	−	0.396174i
$45$	−82.6633	+	8.45430i	−1.83696	+	0.187873i
$46$	38.6059	+	14.0514i	0.839259	+	0.305465i
$47$	10.0825	−	0.587238i	0.214521	−	0.0124944i	0.0494523	−	0.998776i	$-0.484252\pi$
$47$	10.0825	−	0.587238i	0.214521	−	0.0124944i	0.165069	+	0.986282i	$0.447215\pi$
$48$	9.46646	−	7.37469i	0.197218	−	0.153639i
$49$	−18.7537	+	43.4760i	−0.382729	+	0.887265i
$50$	−85.0525	−	4.95375i	−1.70105	−	0.0990749i
$51$	1.29609	+	0.615804i	0.0254135	+	0.0120746i
$52$	−20.8423	−	22.0915i	−0.400813	−	0.424837i
$53$	14.3946	+	8.31072i	0.271596	+	0.156806i	0.629613	−	0.776909i	$-0.283214\pi$
$53$	14.3946	+	8.31072i	0.271596	+	0.156806i	−0.358017	+	0.933715i	$0.616547\pi$
$54$	20.7445	−	32.0572i	0.384158	−	0.593652i
$55$	−42.8176	−	74.1622i	−0.778502	−	1.34840i
$56$	−3.48235	−	1.04255i	−0.0621849	−	0.0186169i
$57$	5.88580	−	62.1084i	0.103260	−	1.08962i
$58$	12.2790	+	8.07600i	0.211706	+	0.139241i
$59$	−8.16985	−	69.8975i	−0.138472	−	1.18470i	−0.866507	−	0.499164i	$-0.833640\pi$
$59$	−8.16985	−	69.8975i	−0.138472	−	1.18470i	0.728036	−	0.685539i	$-0.240434\pi$
$60$	37.1250	−	41.1156i	0.618750	−	0.685259i
$61$	67.7959	+	34.0484i	1.11141	+	0.558170i	0.907176	−	0.420752i	$-0.138234\pi$
$61$	67.7959	+	34.0484i	1.11141	+	0.558170i	0.204233	+	0.978922i	$0.434530\pi$
$62$	21.9140	−	3.86403i	0.353452	−	0.0623231i
$63$	−11.5556	+	0.505789i	−0.183423	+	0.00802840i
$64$	−1.38919	+	7.87846i	−0.0217060	+	0.123101i
$65$	−112.463	−	83.7255i	−1.73020	−	1.28809i
$66$	38.8936	+	5.98413i	0.589297	+	0.0906687i
$67$	27.1526	−	28.7800i	0.405262	−	0.429553i	−0.492310	−	0.870420i	$-0.663847\pi$
$67$	27.1526	−	28.7800i	0.405262	−	0.429553i	0.897572	+	0.440867i	$0.145329\pi$
$68$	−0.916440	+	0.274364i	−0.0134771	+	0.00403477i
$69$	−65.5207	+	57.4665i	−0.949576	+	0.832847i
$70$	−16.6673	−	1.94813i	−0.238104	−	0.0278304i
$71$	−57.4122	+	68.4212i	−0.808623	+	0.963679i	−0.999840	−	0.0178683i	$-0.994312\pi$
$71$	−57.4122	+	68.4212i	−0.808623	+	0.963679i	0.191217	+	0.981548i	$0.438756\pi$
$72$	4.05802	+	25.1303i	0.0563614	+	0.349032i
$73$	−97.8021	+	82.0657i	−1.33975	+	1.12419i	−0.358066	+	0.933696i	$0.616564\pi$
$73$	−97.8021	+	82.0657i	−1.33975	+	1.12419i	−0.981689	+	0.190491i	$0.938992\pi$
$74$	−50.6518	−	77.0123i	−0.684483	−	1.04071i
$75$	95.9865	−	153.133i	1.27982	−	2.04177i
$76$	24.8365	+	33.3612i	0.326796	+	0.438963i
$77$	−5.34985	−	10.6524i	−0.0694786	−	0.138343i
$78$	62.3514	−	16.2256i	0.799377	−	0.208020i
$79$	115.638	−	27.4066i	1.46377	−	0.346919i	0.579912	−	0.814679i	$-0.303087\pi$
$79$	115.638	−	27.4066i	1.46377	−	0.346919i	0.883856	+	0.467760i	$0.154939\pi$
$80$			36.9309i			0.461636i
$81$	38.4581	+	71.2880i	0.474792	+	0.880098i
$82$	−52.4033			−0.639065
$83$	9.97925	+	42.1058i	0.120232	+	0.507298i	0.999519	+	0.0310065i	$0.00987125\pi$
$83$	9.97925	+	42.1058i	0.120232	+	0.507298i	−0.879287	+	0.476292i	$0.841981\pi$
$84$	5.49181	−	5.41310i	0.0653787	−	0.0644417i
$85$	−3.94641	+	1.98196i	−0.0464283	+	0.0233172i
$86$	−36.4644	+	27.1468i	−0.424005	+	0.315660i
$87$	−27.5477	+	14.5979i	−0.316640	+	0.167792i
$88$	−21.9183	+	14.4159i	−0.249072	+	0.163817i
$89$	52.4426	+	62.4987i	0.589243	+	0.702233i	0.975460	−	0.220175i	$-0.0706629\pi$
$89$	52.4426	+	62.4987i	0.589243	+	0.702233i	−0.386217	+	0.922408i	$0.626219\pi$
$90$	38.5937	+	110.995i	0.428819	+	1.23328i
$91$	−14.9506	−	12.5451i	−0.164293	−	0.137858i
$92$	6.74510	−	57.7081i	0.0733164	−	0.627261i
$93$	−15.1707	+	44.6995i	−0.163126	+	0.480640i
$94$	−4.09640	−	13.6829i	−0.0435787	−	0.145563i
$95$	139.655	+	131.758i	1.47006	+	1.38693i
$96$	−13.2357	−	10.6216i	−0.137871	−	0.110641i
$97$	−83.7265	+	112.464i	−0.863160	+	1.15942i	0.122799	+	0.992432i	$0.460813\pi$
$97$	−83.7265	+	112.464i	−0.863160	+	1.15942i	−0.985958	+	0.166993i	$0.946594\pi$
$98$	65.9433	+	11.6276i	0.672891	+	0.118649i
$99$	−50.8102	+	66.2320i	−0.513234	+	0.669010i
$100$	20.9222	+	118.656i	0.209222	+	1.18656i
$101$	70.2092	−	139.798i	0.695141	−	1.38414i	−0.217778	−	0.975998i	$-0.569881\pi$
$101$	70.2092	−	139.798i	0.695141	−	1.38414i	0.912919	−	0.408141i	$-0.133823\pi$
$102$	0.424697	−	1.98438i	0.00416370	−	0.0194547i
$103$	128.865	−	15.0622i	1.25112	−	0.146235i	0.535384	−	0.844609i	$-0.320167\pi$
$103$	128.865	−	15.0622i	1.25112	−	0.146235i	0.715733	+	0.698374i	$0.246093\pi$
$104$	−23.6025	+	35.8859i	−0.226947	+	0.345057i
$105$	20.6278	−	29.0115i	0.196455	−	0.276300i
$106$	6.74167	−	22.5188i	0.0636007	−	0.212441i
$107$	153.633	−	88.7002i	1.43583	−	0.828974i	0.438269	−	0.898844i	$-0.355592\pi$
$107$	153.633	−	88.7002i	1.43583	−	0.828974i	0.997556	+	0.0698694i	$0.0222583\pi$
$108$	−50.8793	−	18.0913i	−0.471105	−	0.167512i
$109$	−16.4515	+	28.4948i	−0.150931	+	0.261420i	−0.931570	−	0.363562i	$-0.881560\pi$
$109$	−16.4515	+	28.4948i	−0.150931	+	0.261420i	0.780639	+	0.624982i	$0.214894\pi$
$110$	−88.0896	+	83.1083i	−0.800815	+	0.755530i
$111$	194.910	−	15.6357i	1.75594	−	0.140862i
$112$	−0.298908	+	5.13206i	−0.00266883	+	0.0458220i
$113$	25.9180	+	11.1799i	0.229362	+	0.0989373i	0.507660	−	0.861558i	$-0.330511\pi$
$113$	25.9180	+	11.1799i	0.229362	+	0.0989373i	−0.278297	+	0.960495i	$0.589770\pi$
$114$	−87.3866	+	12.1566i	−0.766549	+	0.106637i
$115$	−15.5953	−	267.761i	−0.135611	−	2.32836i
$116$	7.10867	−	19.5309i	0.0612816	−	0.168370i
$117$	−33.4353	+	132.520i	−0.285772	+	1.13265i
$118$	−93.5210	+	34.0389i	−0.792551	+	0.288465i
$119$	−0.564450	+	0.243480i	−0.00474328	+	0.00204605i
$120$	−68.6868	−	37.6780i	−0.572390	−	0.313983i
$121$	34.0283	+	8.06486i	0.281226	+	0.0666517i
$122$	24.7428	−	104.398i	0.202810	−	0.855722i
$123$	53.4635	−	97.4636i	0.434662	−	0.792387i
$124$	−12.4643	−	28.8955i	−0.100519	−	0.233028i
$125$	111.290	+	305.767i	0.890320	+	2.44613i
$126$	4.46477	+	15.7367i	0.0354347	+	0.124894i
$127$	−227.754	−	82.8957i	−1.79334	−	0.652722i	−0.998974	−	0.0452829i	$-0.985581\pi$
$127$	−227.754	−	82.8957i	−1.79334	−	0.652722i	−0.794366	−	0.607440i	$-0.792197\pi$
$128$	11.2946	−	0.657834i	0.0882388	−	0.00513933i
$129$	−13.2874	−	95.5152i	−0.103003	−	0.740428i
$130$	−78.5355	+	182.066i	−0.604119	+	1.40051i
$131$	136.773	+	7.96613i	1.04407	+	0.0608101i	0.571597	−	0.820535i	$-0.306324\pi$
$131$	136.773	+	7.96613i	1.04407	+	0.0608101i	0.472473	+	0.881345i	$0.343361\pi$
$132$	−4.45004	−	55.4729i	−0.0337124	−	0.420249i
$133$	18.3407	+	19.4400i	0.137900	+	0.146165i
$134$	−48.4595	−	27.9781i	−0.361638	−	0.208792i
$135$	−245.811	−	41.4611i	−1.82082	−	0.307119i
$136$	0.676439	+	1.17163i	0.00497381	+	0.00861490i
$137$	69.5450	+	20.8204i	0.507628	+	0.151974i	0.530368	−	0.847768i	$-0.322054\pi$
$137$	69.5450	+	20.8204i	0.507628	+	0.151974i	−0.0227399	+	0.999741i	$0.507239\pi$
$138$	100.448	+	71.4205i	0.727885	+	0.517540i
$139$	66.1114	+	43.4822i	0.475622	+	0.312821i	0.764590	−	0.644517i	$-0.222942\pi$
$139$	66.1114	+	43.4822i	0.475622	+	0.312821i	−0.288968	+	0.957339i	$0.593312\pi$
$140$	2.75507	+	23.5711i	0.0196791	+	0.168365i
$141$	29.6278	+	6.34095i	0.210126	+	0.0449713i
$142$	112.878	+	56.6897i	0.794919	+	0.399223i
$143$	−138.712	+	24.4586i	−0.970011	+	0.171039i
$144$	33.2582	−	13.7802i	0.230959	−	0.0956960i
$145$	16.6612	−	94.4904i	0.114905	−	0.651658i
$146$	144.827	+	107.820i	0.991967	+	0.738492i
$147$	−88.9032	+	110.783i	−0.604784	+	0.753629i
$148$	−89.4565	+	94.8183i	−0.604436	+	0.640664i
$149$	−269.084	+	80.5586i	−1.80593	+	0.540661i	−0.998766	−	0.0496594i	$-0.984186\pi$
$149$	−269.084	+	80.5586i	−1.80593	+	0.540661i	−0.807169	+	0.590321i	$0.799001\pi$
$150$	−242.030	−	82.1435i	−1.61354	−	0.547624i
$151$	−132.995	−	15.5449i	−0.880764	−	0.102947i	−0.336324	−	0.941746i	$-0.609184\pi$
$151$	−132.995	−	15.5449i	−0.880764	−	0.102947i	−0.544440	+	0.838800i	$0.683258\pi$
$152$	37.8080	−	45.0578i	0.248737	−	0.296433i
$153$	3.25740	+	2.81440i	0.0212902	+	0.0183948i
$154$	−12.9139	+	10.8361i	−0.0838567	+	0.0703641i
$155$	−79.8289	−	121.374i	−0.515025	−	0.783058i
$156$	−42.6632	−	80.5096i	−0.273482	−	0.516087i
$157$	33.7863	+	45.3829i	0.215199	+	0.289063i	0.896594	−	0.442853i	$-0.146034\pi$
$157$	33.7863	+	45.3829i	0.215199	+	0.289063i	−0.681395	+	0.731916i	$0.738626\pi$
$158$	−75.4282	−	150.190i	−0.477393	−	0.950568i
$159$	35.0040	+	35.5130i	0.220151	+	0.223352i
$160$	50.8203	−	12.0446i	0.317627	−	0.0752790i
$161$		−	37.3353i		−	0.231897i
$162$	85.5561	−	76.1718i	0.528124	−	0.470197i
$163$	76.9281			0.471951			0.235976	−	0.971759i	$-0.424171\pi$
$163$	76.9281			0.471951			0.235976	+	0.971759i	$0.424171\pi$
$164$	17.0908	+	72.1119i	0.104212	+	0.439706i
$165$	−64.6992	−	248.625i	−0.392116	−	1.50682i
$166$	54.6868	−	27.4648i	0.329439	−	0.165450i
$167$	78.1853	−	58.2068i	0.468175	−	0.348544i	−0.337076	−	0.941478i	$-0.609438\pi$
$167$	78.1853	−	58.2068i	0.468175	−	0.348544i	0.805251	+	0.592934i	$0.202030\pi$
$168$	−9.24003	−	5.79181i	−0.0550002	−	0.0344751i
$169$	−51.4740	+	33.8550i	−0.304580	+	0.200325i
$170$	4.01445	+	4.78423i	0.0236144	+	0.0281425i
$171$	66.5446	−	174.931i	0.389150	−	1.02299i
$172$	49.2490	+	41.3248i	0.286331	+	0.240261i
$173$	4.06737	−	34.7986i	0.0235108	−	0.201148i	−0.976378	−	0.216070i	$-0.930676\pi$
$173$	4.06737	−	34.7986i	0.0235108	−	0.201148i	0.999889	+	0.0149224i	$0.00475011\pi$
$174$	29.0725	+	33.1472i	0.167084	+	0.190501i
$175$	22.2054	+	74.1712i	0.126888	+	0.423836i
$176$	26.9861	+	25.4601i	0.153330	+	0.144659i
$177$	32.1050	−	208.665i	0.181384	−	1.17890i
$178$	68.9004	−	92.5493i	0.387081	−	0.519940i
$179$	111.920	+	19.7345i	0.625251	+	0.110249i	0.477292	−	0.878745i	$-0.341619\pi$
$179$	111.920	+	19.7345i	0.625251	+	0.110249i	0.147959	+	0.988994i	$0.452730\pi$
$180$	140.153	−	89.3085i	0.778626	−	0.496158i
$181$	29.1494	+	165.315i	0.161047	+	0.913340i	0.953048	+	0.302821i	$0.0979283\pi$
$181$	29.1494	+	165.315i	0.161047	+	0.913340i	−0.792001	+	0.610520i	$0.790961\pi$
$182$	−12.3872	+	24.6649i	−0.0680615	+	0.135522i
$183$	168.924	+	152.528i	0.923081	+	0.833489i
$184$	−81.6115	+	9.53902i	−0.443541	+	0.0518425i
$185$	−330.681	+	502.776i	−1.78747	+	2.71771i
$186$	66.4585	+	6.29804i	0.357304	+	0.0338604i
$187$	−1.27239	+	4.25008i	−0.00680422	+	0.0227277i
$188$	−17.4930	+	10.0996i	−0.0930478	+	0.0537212i
$189$	−33.8233	−	7.75113i	−0.178959	−	0.0410112i
$190$	135.764	−	235.151i	0.714549	−	1.23763i
$191$	65.3364	−	61.6418i	0.342076	−	0.322732i	−0.495962	−	0.868344i	$-0.665184\pi$
$191$	65.3364	−	61.6418i	0.342076	−	0.322732i	0.838038	+	0.545613i	$0.183703\pi$
$192$	−10.2996	+	21.6776i	−0.0536436	+	0.112904i
$193$	16.5515	−	284.178i	0.0857591	−	1.47243i	−0.631367	−	0.775484i	$-0.717506\pi$
$193$	16.5515	−	284.178i	0.0857591	−	1.47243i	0.717126	−	0.696943i	$-0.245457\pi$
$194$	182.068	+	78.5364i	0.938494	+	0.404827i
$195$	−258.495	−	331.815i	−1.32562	−	1.70162i
$196$	−5.50612	−	94.5364i	−0.0280924	−	0.482328i
$197$	95.3202	−	261.890i	0.483859	−	1.32939i	−0.422301	−	0.906456i	$-0.638777\pi$
$197$	95.3202	−	261.890i	0.483859	−	1.32939i	0.906160	−	0.422936i	$-0.139000\pi$
$198$	107.713	+	48.3186i	0.544003	+	0.244033i
$199$	−218.760	+	79.6221i	−1.09930	+	0.400111i	−0.827057	−	0.562118i	$-0.809987\pi$
$199$	−218.760	+	79.6221i	−1.09930	+	0.400111i	−0.272240	+	0.962229i	$0.587764\pi$
$200$	156.458	−	67.4893i	0.782289	−	0.337447i
$201$	101.476	−	61.5845i	0.504854	−	0.306391i
$202$	−215.273	−	51.0207i	−1.06571	−	0.252578i
$203$	3.08009	−	12.9959i	0.0151728	−	0.0640192i
$204$	−2.86920	+	0.0627622i	−0.0140647	+	0.000307658i
$205$	135.505	+	314.137i	0.661001	+	1.53237i
$206$	−62.7550	−	172.418i	−0.304636	−	0.836980i
$207$	−235.313	+	113.955i	−1.13678	+	0.550510i
$208$	57.0801	+	20.7754i	0.274423	+	0.0998819i
$209$	192.556	−	11.2151i	0.921322	−	0.0536609i
$210$	−46.6501	−	18.9239i	−0.222143	−	0.0901138i
$211$	−53.3102	+	123.587i	−0.252655	+	0.585720i	−0.996588	−	0.0825340i	$-0.973699\pi$
$211$	−53.3102	+	123.587i	−0.252655	+	0.585720i	0.743933	+	0.668254i	$0.232958\pi$
$212$	−33.1866	−	1.93290i	−0.156541	−	0.00911746i
$213$	−220.598	+	152.103i	−1.03567	+	0.714099i
$214$	−172.166	−	182.485i	−0.804513	−	0.852734i
$215$	257.024	+	148.393i	1.19546	+	0.690200i
$216$	−8.30151	+	75.9150i	−0.0384329	+	0.351458i
$217$	−10.1110	−	17.5127i	−0.0465943	−	0.0807037i
$218$	44.5769	+	13.3455i	0.204481	+	0.0612177i
$219$	−348.288	+	159.359i	−1.59036	+	0.727668i
$220$	143.094	+	94.1146i	0.650429	+	0.427794i
$221$	0.843252	+	7.21449i	0.00381562	+	0.0326447i
$222$	−85.0839	−	263.114i	−0.383261	−	1.18520i
$223$	−166.127	−	83.4320i	−0.744963	−	0.374135i	0.0354724	−	0.999371i	$-0.488706\pi$
$223$	−166.127	−	83.4320i	−0.744963	−	0.374135i	−0.780436	+	0.625236i	$0.785003\pi$
$224$	7.15968	−	1.26244i	0.0319629	−	0.00563591i
$225$	399.703	−	366.341i	1.77646	−	1.62818i
$226$	6.93172	−	39.3117i	0.0306713	−	0.173946i
$227$	79.2204	+	58.9774i	0.348989	+	0.259812i	0.757352	−	0.653007i	$-0.226493\pi$
$227$	79.2204	+	58.9774i	0.348989	+	0.259812i	−0.408363	+	0.912820i	$0.633900\pi$
$228$	45.2289	+	116.287i	0.198373	+	0.510032i
$229$	−173.425	+	183.820i	−0.757314	+	0.802706i	−0.985277	−	0.170964i	$-0.945312\pi$
$229$	−173.425	+	183.820i	−0.757314	+	0.802706i	0.227963	+	0.973670i	$0.426793\pi$
$230$	−363.378	+	108.788i	−1.57990	+	0.472992i
$231$	−6.97855	−	35.0736i	−0.0302102	−	0.151834i
$232$	−29.1948	−	3.41238i	−0.125839	−	0.0147085i
$233$	53.6571	−	63.9461i	0.230288	−	0.274447i	−0.638510	−	0.769614i	$-0.720449\pi$
$233$	53.6571	−	63.9461i	0.230288	−	0.274447i	0.868798	+	0.495167i	$0.164893\pi$
$234$	193.264	+	2.79009i	0.825914	+	0.0119235i
$235$	−71.4310	+	59.9378i	−0.303962	+	0.255054i
$236$	77.3416	+	117.592i	0.327719	+	0.498272i
$237$	356.288	+	12.9413i	1.50333	+	0.0546047i
$238$	0.519141	+	0.697327i	0.00218126	+	0.00292995i
$239$	−53.7072	−	106.940i	−0.224716	−	0.447447i	0.752816	−	0.658231i	$-0.228695\pi$
$239$	−53.7072	−	106.940i	−0.224716	−	0.447447i	−0.977533	+	0.210783i	$0.932399\pi$
$240$	−29.4469	+	106.808i	−0.122696	+	0.445032i
$241$	−27.5511	+	6.52973i	−0.114320	+	0.0270943i	−0.287378	−	0.957817i	$-0.592783\pi$
$241$	−27.5511	+	6.52973i	−0.114320	+	0.0270943i	0.173058	+	0.984912i	$0.444635\pi$
$242$		−	49.4564i		−	0.204365i
$243$	54.3831	+	236.836i	0.223799	+	0.974635i
$244$	−151.731			−0.621849
$245$	−100.815	−	425.370i	−0.411488	−	1.73620i
$246$	−151.556	−	41.7839i	−0.616079	−	0.169853i
$247$	282.207	−	141.730i	1.14254	−	0.573805i
$248$	−35.6978	+	26.5760i	−0.143943	+	0.107161i
$249$	−4.71217	+	129.731i	−0.0189244	+	0.521008i
$250$	384.467	−	252.868i	1.53787	−	1.01147i
$251$	−273.161	−	325.540i	−1.08829	−	1.29697i	−0.951931	−	0.306313i	$-0.900905\pi$
$251$	−273.161	−	325.540i	−1.08829	−	1.29697i	−0.136358	−	0.990660i	$-0.543540\pi$
$252$	20.1990	−	11.2763i	0.0801548	−	0.0447472i
$253$	−206.409	−	173.198i	−0.815847	−	0.684577i
$254$	−39.7925	+	340.447i	−0.156663	+	1.34034i
$255$	−12.9937	+	2.58535i	−0.0509558	+	0.0101386i
$256$	−4.58885	−	15.3278i	−0.0179252	−	0.0598743i
$257$	42.8142	+	40.3931i	0.166592	+	0.157172i	0.765023	−	0.644003i	$-0.222727\pi$
$257$	42.8142	+	40.3931i	0.166592	+	0.157172i	−0.598431	+	0.801174i	$0.704209\pi$
$258$	−127.104	+	49.4361i	−0.492652	+	0.191613i
$259$	−50.0221	+	67.1913i	−0.193135	+	0.259426i
$260$	276.153	+	48.6932i	1.06213	+	0.187282i
$261$	−91.3104	+	20.2534i	−0.349848	+	0.0775994i
$262$	−33.6451	−	190.811i	−0.128416	−	0.728285i
$263$	117.631	−	234.223i	0.447267	−	0.890581i	−0.551154	−	0.834403i	$-0.685812\pi$
$263$	117.631	−	234.223i	0.447267	−	0.890581i	0.998421	−	0.0561776i	$-0.0178913\pi$
$264$	−74.8845	+	24.2156i	−0.283654	+	0.0917258i
$265$	−152.423	+	17.8157i	−0.575183	+	0.0672292i
$266$	20.7696	−	31.5786i	0.0780811	−	0.118717i
$267$	101.836	+	222.568i	0.381407	+	0.833586i
$268$	−22.6959	+	75.8096i	−0.0846863	+	0.282872i
$269$	−363.749	+	210.011i	−1.35223	+	0.780709i	−0.988561	−	0.150821i	$-0.951808\pi$
$269$	−363.749	+	210.011i	−1.35223	+	0.780709i	−0.363666	+	0.931529i	$0.618475\pi$
$270$	23.1146	+	351.781i	0.0856096	+	1.30289i
$271$	−10.8189	+	18.7390i	−0.0399223	+	0.0691475i	−0.885296	−	0.465028i	$-0.846044\pi$
$271$	−10.8189	+	18.7390i	−0.0399223	+	0.0691475i	0.845374	+	0.534175i	$0.179378\pi$
$272$	1.39165	−	1.31296i	0.00511637	−	0.00482705i
$273$	−33.2359	−	48.2025i	−0.121743	−	0.176566i
$274$	5.96941	−	102.491i	0.0217862	−	0.374054i
$275$	513.068	+	221.316i	1.86570	+	0.804785i
$276$	65.5212	−	161.519i	0.237396	−	0.585214i
$277$	0.735914	+	12.6352i	0.00265673	+	0.0456143i	0.999376	−	0.0353225i	$-0.0112458\pi$
$277$	0.735914	+	12.6352i	0.00265673	+	0.0456143i	−0.996719	+	0.0809368i	$0.974209\pi$
$278$	38.2739	−	105.157i	0.137676	−	0.378262i
$279$	−79.5165	+	117.179i	−0.285005	+	0.419996i
$280$	31.5375	−	11.4787i	0.112634	−	0.0409954i
$281$	−231.321	+	99.7821i	−0.823206	+	0.355096i	−0.765659	−	0.643246i	$-0.777587\pi$
$281$	−231.321	+	99.7821i	−0.823206	+	0.355096i	−0.0575468	+	0.998343i	$0.518328\pi$
$282$	−0.937073	−	42.8386i	−0.00332295	−	0.151910i
$283$	412.784	+	97.8317i	1.45860	+	0.345695i	0.881969	−	0.471308i	$-0.156218\pi$
$283$	412.784	+	97.8317i	1.45860	+	0.345695i	0.576633	+	0.817003i	$0.304366\pi$
$284$	41.1961	−	173.820i	0.145057	−	0.612042i
$285$	298.840	+	492.412i	1.04856	+	1.72776i
$286$	78.8967	+	182.903i	0.275863	+	0.639521i
$287$	16.2878	+	44.7504i	0.0567519	+	0.155925i
$288$	−29.8097	−	41.2721i	−0.103506	−	0.143306i
$289$	−271.356	−	98.7656i	−0.938949	−	0.341749i
$290$	−135.461	+	7.88973i	−0.467109	+	0.0272060i
$291$	−331.819	+	258.498i	−1.14027	+	0.888309i
$292$	101.136	−	234.460i	0.346357	−	0.802946i
$293$	−105.493	−	6.14426i	−0.360044	−	0.0209702i	−0.122830	−	0.992428i	$-0.539197\pi$
$293$	−105.493	−	6.14426i	−0.360044	−	0.0209702i	−0.237214	+	0.971458i	$0.576234\pi$
$294$	181.443	+	86.2082i	0.617154	+	0.293225i
$295$	445.877	+	472.602i	1.51145	+	1.60204i
$296$	159.654	+	92.1764i	0.539372	+	0.311407i
$297$	−199.758	+	151.036i	−0.672587	+	0.508538i
$298$	198.615	+	344.012i	0.666494	+	1.15440i
$299$	−422.622	−	126.525i	−1.41345	−	0.423160i
$300$	−34.1014	+	359.847i	−0.113671	+	1.19949i
$301$	34.5160	+	22.7015i	0.114671	+	0.0754204i
$302$	21.9839	+	188.084i	0.0727942	+	0.622794i
$303$	314.520	−	348.328i	1.03802	−	1.14960i
$304$	−74.3344	−	37.3321i	−0.244521	−	0.122803i
$305$	−689.804	+	121.631i	−2.26165	+	0.398790i
$306$	2.81051	−	5.40038i	0.00918469	−	0.0176483i
$307$	−41.8453	+	237.317i	−0.136304	+	0.773018i	0.837639	+	0.546224i	$0.183935\pi$
$307$	−41.8453	+	237.317i	−0.136304	+	0.773018i	−0.973943	+	0.226794i	$0.927176\pi$
$308$	19.1232	+	14.2367i	0.0620883	+	0.0462231i
$309$	384.700	+	59.1896i	1.24498	+	0.191552i
$310$	−140.986	+	149.437i	−0.454795	+	0.482055i
$311$	−199.675	+	59.7789i	−0.642043	+	0.192215i	−0.591243	−	0.806494i	$-0.701362\pi$
$311$	−199.675	+	59.7789i	−0.642043	+	0.192215i	−0.0508004	+	0.998709i	$0.516177\pi$
$312$	−96.8745	+	84.9660i	−0.310495	+	0.272327i
$313$	−11.5518	−	1.35021i	−0.0369067	−	0.00431377i	0.0976195	−	0.995224i	$-0.468877\pi$
$313$	−11.5518	−	1.35021i	−0.0369067	−	0.00431377i	−0.134526	+	0.990910i	$0.542951\pi$
$314$	51.4320	−	61.2943i	0.163796	−	0.195205i
$315$	82.7899	−	67.4566i	0.262825	−	0.214148i
$316$	−182.075	+	152.779i	−0.576187	+	0.483478i
$317$	−251.024	−	381.663i	−0.791873	−	1.20398i	−0.975286	−	0.220948i	$-0.929085\pi$
$317$	−251.024	−	381.663i	−0.791873	−	1.20398i	0.183413	−	0.983036i	$-0.441286\pi$
$318$	37.4530	−	59.7510i	0.117777	−	0.187896i
$319$	−57.5597	−	77.3161i	−0.180438	−	0.242370i
$320$	−33.1491	−	66.0053i	−0.103591	−	0.206267i
$321$	515.048	−	134.030i	1.60451	−	0.417539i
$322$	−51.3769	+	12.1766i	−0.159556	+	0.0378154i
$323$		−	9.94682i		−	0.0307951i
$324$	−132.723	−	92.8905i	−0.409638	−	0.286699i
$325$	914.842			2.81490
$326$	−25.0893	−	105.860i	−0.0769611	−	0.324725i
$327$	−70.2996	+	69.2920i	−0.214983	+	0.211902i
$328$	93.6586	−	47.0371i	0.285545	−	0.143406i
$329$	−10.4115	+	7.75104i	−0.0316458	+	0.0235594i
$330$	−321.030	+	170.119i	−0.972819	+	0.515511i
$331$	−26.1929	+	17.2273i	−0.0791326	+	0.0520464i	−0.588459	−	0.808527i	$-0.700265\pi$
$331$	−26.1929	+	17.2273i	−0.0791326	+	0.0520464i	0.509326	+	0.860574i	$0.329895\pi$
$332$	−55.6296	−	66.2968i	−0.167559	−	0.199689i
$333$	576.165	+	110.192i	1.73022	+	0.330906i
$334$	−105.597	−	88.6067i	−0.316160	−	0.265290i
$335$	−42.4101	+	362.841i	−0.126597	+	1.08311i
$336$	−4.95653	+	14.6041i	−0.0147516	+	0.0434645i
$337$	51.5282	+	172.116i	0.152903	+	0.510731i	0.999778	−	0.0210607i	$-0.00670431\pi$
$337$	51.5282	+	172.116i	0.152903	+	0.510731i	−0.846876	+	0.531791i	$0.821519\pi$
$338$	63.3753	+	59.7915i	0.187501	+	0.176898i
$339$	66.0429	+	52.9991i	0.194817	+	0.156340i
$340$	5.27427	−	7.08458i	0.0155126	−	0.0208370i
$341$	−143.724	−	25.3424i	−0.421478	−	0.0743180i
$342$	−262.424	−	34.5197i	−0.767321	−	0.100935i
$343$	−21.5021	−	121.945i	−0.0626884	−	0.355524i
$344$	40.8047	−	81.2489i	0.118618	−	0.236189i
$345$	168.397	−	786.826i	0.488106	−	2.28065i
$346$	−49.2126	+	5.75213i	−0.142233	+	0.0166246i
$347$	236.896	−	360.183i	0.682699	−	1.03799i	−0.313389	−	0.949625i	$-0.601464\pi$
$347$	236.896	−	360.183i	0.682699	−	1.03799i	0.996088	−	0.0883681i	$-0.0281652\pi$
$348$	36.1320	−	50.8172i	0.103827	−	0.146026i
$349$	−71.6709	+	239.397i	−0.205361	+	0.685952i	0.791809	+	0.610769i	$0.209139\pi$
$349$	−71.6709	+	239.397i	−0.205361	+	0.685952i	−0.997170	+	0.0751836i	$0.976046\pi$
$350$	94.8244	−	54.7469i	0.270927	−	0.156420i
$351$	−202.363	+	356.600i	−0.576532	+	1.01595i
$352$	26.2342	−	45.4389i	0.0745289	−	0.129088i
$353$	−146.063	+	137.803i	−0.413776	+	0.390378i	−0.864786	−	0.502141i	$-0.832546\pi$
$353$	−146.063	+	137.803i	−0.413776	+	0.390378i	0.451009	+	0.892519i	$0.351064\pi$
$354$	−297.613	+	23.8745i	−0.840714	+	0.0674421i
$355$	47.9488	−	823.249i	0.135067	−	2.31901i
$356$	−149.828	−	64.6293i	−0.420864	−	0.181543i
$357$	−1.82658	+	0.254102i	−0.00511648	+	0.000711771i
$358$	−9.34505	−	160.448i	−0.0261035	−	0.448180i
$359$	47.7911	−	131.305i	0.133123	−	0.365752i	−0.855164	−	0.518357i	$-0.826544\pi$
$359$	47.7911	−	131.305i	0.133123	−	0.365752i	0.988287	+	0.152605i	$0.0487661\pi$
$360$	−168.606	−	163.736i	−0.468351	−	0.454822i
$361$	−67.1462	+	24.4392i	−0.186001	+	0.0676987i
$362$	217.982	−	94.0281i	0.602159	−	0.259746i
$363$	91.9827	+	50.4569i	0.253396	+	0.139000i
$364$	37.9812	+	9.00171i	0.104344	+	0.0247300i
$365$	271.840	−	1146.98i	0.744767	−	3.14242i
$366$	154.801	−	282.201i	0.422952	−	0.771040i
$367$	147.218	+	341.290i	0.401140	+	0.929946i	0.992353	+	0.123431i	$0.0393898\pi$
$367$	147.218	+	341.290i	0.401140	+	0.929946i	−0.591213	+	0.806515i	$0.701351\pi$
$368$	39.7434	+	109.194i	0.107998	+	0.296723i
$369$	232.334	−	239.245i	0.629632	−	0.648360i
$370$	799.715	+	291.073i	2.16139	+	0.786682i
$371$	−21.3256	+	1.24207i	−0.0574813	+	0.00334790i
$372$	−13.0081	−	93.5071i	−0.0349680	−	0.251363i
$373$	144.432	−	334.831i	0.387217	−	0.897670i	−0.607433	−	0.794371i	$-0.707801\pi$
$373$	144.432	−	334.831i	0.387217	−	0.897670i	0.994650	−	0.103299i	$-0.0329399\pi$
$374$	6.26348	+	0.364806i	0.0167473	+	0.000975417i
$375$	78.0576	+	973.044i	0.208154	+	2.59478i
$376$	19.6031	+	20.7781i	0.0521360	+	0.0552609i
$377$	−136.671	−	78.9069i	−0.362522	−	0.209302i
$378$	0.364873	+	49.0720i	0.000965272	+	0.129820i
$379$	−323.872	−	560.962i	−0.854543	−	1.48011i	−0.877069	−	0.480365i	$-0.840504\pi$
$379$	−323.872	−	560.962i	−0.854543	−	1.48011i	0.0225260	−	0.999746i	$-0.492829\pi$
$380$	−367.867	−	110.132i	−0.968072	−	0.289822i
$381$	−592.590	−	421.343i	−1.55536	−	1.10589i
$382$	−106.134	−	69.8052i	−0.277837	−	0.182736i
$383$	−40.5347	−	346.797i	−0.105835	−	0.905475i	−0.936971	−	0.349406i	$-0.886383\pi$
$383$	−40.5347	−	346.797i	−0.105835	−	0.905475i	0.831136	−	0.556069i	$-0.187691\pi$
$384$	33.1895	+	7.10323i	0.0864310	+	0.0184980i
$385$	98.3509	+	49.3937i	0.255457	+	0.128295i
$386$	−396.454	+	69.9056i	−1.02708	+	0.181102i
$387$	37.7307	−	286.834i	0.0974954	−	0.741174i
$388$	48.6938	−	276.156i	0.125499	−	0.711742i
$389$	362.665	+	269.994i	0.932300	+	0.694072i	0.952118	−	0.305732i	$-0.0989012\pi$
$389$	362.665	+	269.994i	0.932300	+	0.694072i	−0.0198177	+	0.999804i	$0.506309\pi$
$390$	−372.303	+	463.931i	−0.954623	+	1.18957i
$391$	−9.53550	+	10.1070i	−0.0243875	+	0.0258492i
$392$	−128.295	+	38.4090i	−0.327283	+	0.0979822i
$393$	389.210	+	132.095i	0.990355	+	0.336120i
$394$	−391.473	−	45.7566i	−0.993586	−	0.116134i
$395$	−705.283	+	840.524i	−1.78553	+	2.12791i
$396$	31.3615	−	163.981i	0.0791957	−	0.414094i
$397$	2.65467	−	2.22753i	0.00668683	−	0.00561091i	−0.639438	−	0.768843i	$-0.720833\pi$
$397$	2.65467	−	2.22753i	0.00668683	−	0.00561091i	0.646125	+	0.763232i	$0.276389\pi$
$398$	180.914	+	275.066i	0.454557	+	0.691121i
$399$	37.5425	+	70.8462i	0.0940914	+	0.177559i
$400$	−143.899	−	193.290i	−0.359747	−	0.483224i
$401$	74.6610	+	148.662i	0.186187	+	0.370729i	0.967290	−	0.253674i	$-0.0816389\pi$
$401$	74.6610	+	148.662i	0.186187	+	0.370729i	−0.781103	+	0.624402i	$0.785343\pi$
$402$	−117.841	−	119.555i	−0.293138	−	0.297400i
$403$	−232.502	+	55.1040i	−0.576929	+	0.136735i
$404$			312.876i			0.774445i
$405$	−677.851	−	315.908i	−1.67371	−	0.780019i
$406$	−18.8881			−0.0465224
$407$	139.417	+	588.248i	0.342549	+	1.44533i
$408$	1.02213	+	3.92782i	0.00250521	+	0.00962700i
$409$	−63.8997	+	32.0917i	−0.156234	+	0.0784637i	−0.525198	−	0.850980i	$-0.676009\pi$
$409$	−63.8997	+	32.0917i	−0.156234	+	0.0784637i	0.368964	+	0.929444i	$0.379713\pi$
$410$	388.087	−	288.920i	0.946555	−	0.704684i
$411$	184.530	+	115.667i	0.448978	+	0.281427i
$412$	−216.796	+	142.589i	−0.526204	+	0.346090i
$413$	58.1357	+	69.2834i	0.140764	+	0.167756i
$414$	233.558	+	286.648i	0.564151	+	0.692386i
$415$	−306.050	−	256.806i	−0.737470	−	0.618811i
$416$	9.97285	−	85.3232i	0.0239732	−	0.205104i
$417$	156.530	+	178.469i	0.375372	+	0.427983i
$418$	−78.2334	−	261.318i	−0.187161	−	0.625162i
$419$	−75.3841	−	71.1212i	−0.179914	−	0.169740i	0.591016	−	0.806660i	$-0.298727\pi$
$419$	−75.3841	−	71.1212i	−0.179914	−	0.169740i	−0.770930	+	0.636919i	$0.780208\pi$
$420$	−10.8266	+	70.3668i	−0.0257775	+	0.167540i
$421$	313.478	−	421.074i	0.744604	−	1.00018i	−0.254845	−	0.966982i	$-0.582024\pi$
$421$	313.478	−	421.074i	0.744604	−	1.00018i	0.999449	−	0.0331946i	$-0.0105681\pi$
$422$	187.454	+	33.0531i	0.444203	+	0.0783250i
$423$	80.6305	+	41.9624i	0.190616	+	0.0992020i
$424$	8.16364	+	46.2983i	0.0192539	+	0.109194i
$425$	12.9322	−	25.7502i	0.0304287	−	0.0605886i
$426$	281.254	+	253.956i	0.660220	+	0.596141i
$427$	−96.8423	+	11.3192i	−0.226797	+	0.0265088i
$428$	−194.966	+	296.432i	−0.455529	+	0.692598i
$429$	−420.669	−	39.8654i	−0.980581	−	0.0929262i
$430$	120.377	−	402.086i	0.279946	−	0.935084i
$431$	153.358	−	88.5410i	0.355818	−	0.205432i	−0.311427	−	0.950270i	$-0.600807\pi$
$431$	153.358	−	88.5410i	0.355818	−	0.205432i	0.667245	+	0.744839i	$0.267474\pi$
$432$	107.174	−	13.3353i	0.248087	−	0.0308687i
$433$	209.442	−	362.764i	0.483699	−	0.837791i	−0.516126	−	0.856513i	$-0.672626\pi$
$433$	209.442	−	362.764i	0.483699	−	0.837791i	0.999825	+	0.0187215i	$0.00595958\pi$
$434$	−20.8015	+	19.6252i	−0.0479298	+	0.0452194i
$435$	123.528	−	259.991i	0.283972	−	0.597679i
$436$	3.82627	−	65.6945i	0.00877585	−	0.150675i
$437$	554.713	+	239.280i	1.26937	+	0.547551i
$438$	332.884	+	427.304i	0.760009	+	0.975580i
$439$	−14.7253	−	252.824i	−0.0335429	−	0.575909i	−0.972649	−	0.232281i	$-0.925381\pi$
$439$	−14.7253	−	252.824i	−0.0335429	−	0.575909i	0.939106	−	0.343628i	$-0.111656\pi$
$440$	82.8417	−	227.606i	0.188277	−	0.517286i
$441$	−345.450	+	249.509i	−0.783334	+	0.565781i
$442$	9.65279	−	3.51333i	0.0218389	−	0.00794870i
$443$	147.773	−	63.7430i	0.333573	−	0.143889i	−0.222704	−	0.974886i	$-0.571488\pi$
$443$	147.773	−	63.7430i	0.333573	−	0.143889i	0.556278	+	0.830997i	$0.312229\pi$
$444$	−334.321	+	202.896i	−0.752974	+	0.456972i
$445$	−732.959	−	173.714i	−1.64710	−	0.390369i
$446$	−60.6296	+	255.817i	−0.135941	+	0.573580i
$447$	−842.452	+	18.4282i	−1.88468	+	0.0412264i
$448$	−4.07230	−	9.44065i	−0.00908996	−	0.0210729i
$449$	−200.378	−	550.534i	−0.446276	−	1.22613i	−0.935298	−	0.353862i	$-0.884868\pi$
$449$	−200.378	−	550.534i	−0.446276	−	1.22613i	0.489022	−	0.872272i	$-0.337354\pi$
$450$	−634.478	−	430.551i	−1.40995	−	0.956779i
$451$	322.963	+	117.549i	0.716103	+	0.260640i
$452$	−56.3573	+	3.28244i	−0.124684	+	0.00726204i
$453$	−372.241	−	151.002i	−0.821724	−	0.333337i
$454$	55.3215	−	128.250i	0.121853	−	0.282488i
$455$	179.887	+	10.4772i	0.395356	+	0.0230269i
$456$	145.271	−	100.165i	0.318577	−	0.219661i
$457$	419.468	+	444.610i	0.917873	+	0.972889i	0.999718	−	0.0237563i	$-0.00756257\pi$
$457$	419.468	+	444.610i	0.917873	+	0.972889i	−0.0818445	+	0.996645i	$0.526081\pi$
$458$	309.514	+	178.698i	0.675794	+	0.390170i
$459$	7.17665	+	10.7368i	0.0156354	+	0.0233918i
$460$	268.215	+	464.562i	0.583076	+	1.00992i
$461$	199.763	+	59.8051i	0.433325	+	0.129729i	0.496034	−	0.868303i	$-0.334789\pi$
$461$	199.763	+	59.8051i	0.433325	+	0.129729i	−0.0627094	+	0.998032i	$0.519974\pi$
$462$	−45.9885	+	21.0420i	−0.0995423	+	0.0455455i
$463$	192.773	+	126.789i	0.416355	+	0.273841i	0.740355	−	0.672216i	$-0.234657\pi$
$463$	192.773	+	126.789i	0.416355	+	0.273841i	−0.324000	+	0.946057i	$0.605028\pi$
$464$	4.82583	+	41.2876i	0.0104005	+	0.0889820i
$465$	−134.095	−	414.677i	−0.288377	−	0.891779i
$466$	−105.495	−	52.9818i	−0.226385	−	0.113695i
$467$	282.995	−	49.8997i	0.605986	−	0.106852i	0.137768	−	0.990465i	$-0.456007\pi$
$467$	282.995	−	49.8997i	0.605986	−	0.106852i	0.468218	+	0.883613i	$0.344896\pi$
$468$	−59.1917	−	266.859i	−0.126478	−	0.570212i
$469$	−8.83021	+	50.0786i	−0.0188277	+	0.106777i
$470$	105.776	+	78.7477i	0.225056	+	0.167548i
$471$	61.5271	+	158.191i	0.130631	+	0.335863i
$472$	136.594	−	144.781i	0.289393	−	0.306739i
$473$	285.625	−	85.5106i	0.603859	−	0.180784i
$474$	−98.3914	−	494.506i	−0.207577	−	1.04326i
$475$	−1244.32	−	145.440i	−2.61962	−	0.306190i
$476$	0.790274	−	0.941812i	0.00166024	−	0.00197860i
$477$	72.9186	+	130.618i	0.152869	+	0.273831i
$478$	−129.643	+	108.784i	−0.271220	+	0.227581i
$479$	93.8272	+	142.657i	0.195882	+	0.297823i	0.920051	−	0.391799i	$-0.128147\pi$
$479$	93.8272	+	142.657i	0.195882	+	0.297823i	−0.724169	+	0.689622i	$0.757777\pi$
$480$	156.581	+	5.68744i	0.326211	+	0.0118488i
$481$	591.062	+	793.934i	1.22882	+	1.65059i
$482$	17.9710	+	35.7833i	0.0372843	+	0.0742392i
$483$	29.7694	−	107.977i	0.0616344	−	0.223556i
$484$	−68.0566	+	16.1297i	−0.140613	+	0.0333259i
$485$		−	1294.50i		−	2.66908i
$486$	308.172	−	152.078i	0.634100	−	0.312918i
$487$	319.557			0.656174			0.328087	−	0.944647i	$-0.393596\pi$
$487$	319.557			0.656174			0.328087	+	0.944647i	$0.393596\pi$
$488$	49.4856	+	208.796i	0.101405	+	0.427861i
$489$	222.483	+	61.3388i	0.454976	+	0.125437i
$490$	−552.469	+	277.460i	−1.12749	+	0.566246i
$491$	147.406	−	109.740i	0.300217	−	0.223503i	−0.436501	−	0.899704i	$-0.643782\pi$
$491$	147.406	−	109.740i	0.300217	−	0.223503i	0.736717	+	0.676201i	$0.236375\pi$
$492$	−8.07023	+	222.182i	−0.0164029	+	0.451589i
$493$	−4.15298	+	2.73146i	−0.00842390	+	0.00554048i
$494$	−287.073	−	342.120i	−0.581119	−	0.692550i
$495$	11.1254	−	770.636i	0.0224756	−	1.55684i
$496$	48.2136	+	40.4560i	0.0972049	+	0.0815646i
$497$	13.3263	−	114.014i	0.0268135	−	0.229404i
$498$	180.059	−	35.8261i	0.361564	−	0.0719399i
$499$	−202.950	−	677.900i	−0.406713	−	1.35852i	−0.878895	−	0.477015i	$-0.841719\pi$
$499$	−202.950	−	677.900i	−0.406713	−	1.35852i	0.472182	−	0.881501i	$-0.343467\pi$
$500$	−473.360	−	446.592i	−0.946721	−	0.893185i
$501$	272.531	−	105.999i	0.543974	−	0.211574i
$502$	−358.885	+	482.066i	−0.714910	+	0.960291i
$503$	299.434	+	52.7983i	0.595296	+	0.104967i	0.463175	−	0.886267i	$-0.346710\pi$
$503$	299.434	+	52.7983i	0.595296	+	0.104967i	0.132121	+	0.991234i	$0.457821\pi$
$504$	−22.1049	−	24.1181i	−0.0438590	−	0.0478533i
$505$	250.808	+	1422.40i	0.496650	+	2.81664i
$506$	−171.018	+	340.525i	−0.337981	+	0.672975i
$507$	−175.862	+	56.8690i	−0.346868	+	0.112168i
$508$	481.464	−	56.2751i	0.947764	−	0.110778i
$509$	−364.645	+	554.416i	−0.716395	+	1.08923i	0.275393	+	0.961332i	$0.411192\pi$
$509$	−364.645	+	554.416i	−0.716395	+	1.08923i	−0.991788	+	0.127894i	$0.959178\pi$
$510$	7.79545	+	17.0374i	0.0152852	+	0.0334066i
$511$	47.0593	−	157.189i	0.0920925	−	0.307610i
$512$	−19.5959	+	11.3137i	−0.0382733	+	0.0220971i
$513$	331.935	−	452.857i	0.647046	−	0.882762i
$514$	41.6212	−	72.0901i	0.0809752	−	0.140253i
$515$	−871.302	+	822.031i	−1.69185	+	1.59618i
$516$	109.483	+	158.784i	0.212175	+	0.307721i
$517$	−5.44674	+	93.5170i	−0.0105353	+	0.180884i
$518$	108.776	+	46.9212i	0.209992	+	0.0905816i
$519$	39.5099	−	97.3977i	0.0761270	−	0.187664i
$520$	−23.0581	−	395.893i	−0.0443426	−	0.761333i
$521$	−168.127	+	461.925i	−0.322700	+	0.886612i	0.667204	+	0.744875i	$0.267491\pi$
$521$	−168.127	+	461.925i	−0.322700	+	0.886612i	−0.989904	+	0.141737i	$0.954731\pi$
$522$	57.6506	+	119.046i	0.110442	+	0.228058i
$523$	592.196	−	215.542i	1.13231	−	0.412126i	0.293177	−	0.956058i	$-0.405288\pi$
$523$	592.196	−	215.542i	1.13231	−	0.412126i	0.839129	+	0.543933i	$0.183065\pi$
$524$	−251.600	+	108.530i	−0.480153	+	0.207118i
$525$	5.07960	+	232.216i	0.00967543	+	0.442316i
$526$	−360.677	−	85.4819i	−0.685697	−	0.162513i
$527$	−1.73563	+	7.32322i	−0.00329342	+	0.0138960i
$528$	57.7458	+	95.1504i	0.109367	+	0.180209i
$529$	−124.737	−	289.173i	−0.235798	−	0.546641i
$530$	74.2275	+	203.938i	0.140052	+	0.384790i
$531$	259.230	−	577.880i	0.488192	−	1.08829i
$532$	−50.2289	−	18.2818i	−0.0944152	−	0.0343643i
$533$	561.755	−	32.7185i	1.05395	−	0.0613856i
$534$	273.061	−	212.724i	0.511350	−	0.398359i
$535$	−648.735	+	1503.94i	−1.21259	+	2.81110i
$536$	111.723	+	6.50713i	0.208439	+	0.0121402i
$537$	307.948	+	146.314i	0.573460	+	0.272465i
$538$	407.627	+	432.060i	0.757672	+	0.803085i
$539$	−380.327	−	219.582i	−0.705616	−	0.407388i
$540$	476.546	−	146.538i	0.882492	−	0.271366i
$541$	253.875	+	439.724i	0.469270	+	0.812799i	0.999383	−	0.0351278i	$-0.0111838\pi$
$541$	253.875	+	439.724i	0.469270	+	0.812799i	−0.530113	+	0.847927i	$0.677850\pi$
$542$	29.3151	+	8.77635i	0.0540868	+	0.0161925i
$543$	−47.5110	+	501.348i	−0.0874973	+	0.923294i
$544$	−2.26062	−	1.48684i	−0.00415556	−	0.00273315i
$545$	−35.2671	−	301.729i	−0.0647103	−	0.553632i
$546$	−55.4916	+	61.4564i	−0.101633	+	0.112558i
$547$	−379.035	−	190.359i	−0.692934	−	0.348005i	0.0672283	−	0.997738i	$-0.478584\pi$
$547$	−379.035	−	190.359i	−0.692934	−	0.348005i	−0.760162	+	0.649733i	$0.774881\pi$
$548$	−142.984	+	25.2119i	−0.260919	+	0.0460071i
$549$	366.925	+	575.819i	0.668352	+	1.04885i
$550$	137.219	−	778.210i	0.249490	−	1.41493i
$551$	173.348	+	129.053i	0.314606	+	0.234215i
$552$	−243.634	−	37.4854i	−0.441367	−	0.0679083i
$553$	−104.812	+	111.094i	−0.189533	+	0.200894i
$554$	17.1471	−	5.13352i	0.0309515	−	0.00926627i
$555$	−1357.25	+	1190.41i	−2.44550	+	2.14488i
$556$	−157.188	−	18.3727i	−0.282713	−	0.0330444i
$557$	−123.616	+	147.319i	−0.221931	+	0.264487i	−0.865509	−	0.500893i	$-0.833005\pi$
$557$	−123.616	+	147.319i	−0.221931	+	0.264487i	0.643578	+	0.765381i	$0.277449\pi$
$558$	187.183	+	71.2054i	0.335453	+	0.127608i
$559$	373.944	−	313.776i	0.668951	−	0.561317i
$560$	−26.0814	−	39.6549i	−0.0465740	−	0.0708123i
$561$	−7.06868	+	11.2771i	−0.0126001	+	0.0201018i
$562$	212.752	+	285.776i	0.378563	+	0.508499i
$563$	256.994	+	511.718i	0.456473	+	0.908913i	0.997684	+	0.0680255i	$0.0216699\pi$
$563$	256.994	+	511.718i	0.456473	+	0.908913i	−0.541210	+	0.840887i	$0.682034\pi$
$564$	−58.6443	+	15.2609i	−0.103979	+	0.0270583i
$565$	−253.582	+	60.1000i	−0.448818	+	0.106372i
$566$		−	599.937i		−	1.05996i
$567$	−91.6400	−	49.3861i	−0.161623	−	0.0871008i
$568$	−252.628			−0.444768
$569$	226.892	+	957.333i	0.398756	+	1.68248i	0.688386	+	0.725344i	$0.258320\pi$
$569$	226.892	+	957.333i	0.398756	+	1.68248i	−0.289630	+	0.957139i	$0.593532\pi$
$570$	580.141	−	571.827i	1.01779	−	1.00320i
$571$	−17.2215	+	8.64899i	−0.0301603	+	0.0151471i	−0.463815	−	0.885932i	$-0.653520\pi$
$571$	−17.2215	+	8.64899i	−0.0301603	+	0.0151471i	0.433655	+	0.901079i	$0.357224\pi$
$572$	225.960	−	168.221i	0.395036	−	0.294093i
$573$	238.110	−	126.178i	0.415549	−	0.220206i
$574$	56.2686	−	37.0084i	0.0980289	−	0.0644746i
$575$	1124.94	+	1340.65i	1.95641	+	2.33156i
$576$	−47.0721	+	54.4814i	−0.0817223	+	0.0945857i
$577$	284.913	+	239.070i	0.493783	+	0.414333i	0.855380	−	0.518001i	$-0.173324\pi$
$577$	284.913	+	239.070i	0.493783	+	0.414333i	−0.361597	+	0.932335i	$0.617768\pi$
$578$	−47.4105	+	405.623i	−0.0820251	+	0.701770i
$579$	274.459	−	808.674i	0.474022	−	1.39667i
$580$	55.0364	+	183.834i	0.0948904	+	0.316956i
$581$	−40.4514	−	38.1639i	−0.0696237	−	0.0656866i
$582$	463.937	+	372.307i	0.797142	+	0.639703i
$583$	−92.0621	+	123.661i	−0.157911	+	0.212111i
$584$	−355.624	−	62.7060i	−0.608945	−	0.107373i
$585$	−483.019	−	1165.75i	−0.825674	−	1.99274i
$586$	25.9504	+	147.172i	0.0442839	+	0.251147i
$587$	395.573	−	787.652i	0.673890	−	1.34183i	−0.253356	−	0.967373i	$-0.581534\pi$
$587$	395.573	−	787.652i	0.673890	−	1.34183i	0.927246	−	0.374452i	$-0.122169\pi$
$588$	59.4546	−	277.799i	0.101113	−	0.472447i
$589$	324.997	−	37.9867i	0.551778	−	0.0644936i
$590$	504.926	−	767.703i	0.855807	−	1.30119i
$591$	484.494	−	681.408i	0.819787	−	1.15297i
$592$	74.7737	−	249.762i	0.126307	−	0.421894i
$593$	226.200	−	130.597i	0.381450	−	0.220230i	−0.296999	−	0.954878i	$-0.595986\pi$
$593$	226.200	−	130.597i	0.381450	−	0.220230i	0.678449	+	0.734648i	$0.262652\pi$
$594$	272.989	+	225.627i	0.459577	+	0.379844i
$595$	2.83779	−	4.91520i	0.00476939	−	0.00826083i
$596$	408.616	−	385.509i	0.685597	−	0.646827i
$597$	−696.162	+	55.8462i	−1.16610	+	0.0935447i
$598$	−36.2759	+	622.832i	−0.0606620	+	1.04153i
$599$	−910.950	−	392.945i	−1.52078	−	0.656002i	−0.538368	−	0.842710i	$-0.680959\pi$
$599$	−910.950	−	392.945i	−1.52078	−	0.656002i	−0.982416	+	0.186707i	$0.940218\pi$
$600$	506.304	−	70.4337i	0.843840	−	0.117390i
$601$	28.7286	+	493.251i	0.0478014	+	0.820718i	0.933969	+	0.357353i	$0.116321\pi$
$601$	28.7286	+	493.251i	0.0478014	+	0.820718i	−0.886168	+	0.463364i	$0.846642\pi$
$602$	19.9824	−	54.9012i	0.0331933	−	0.0911979i
$603$	342.582	−	97.1965i	0.568130	−	0.161188i
$604$	251.651	−	91.5935i	0.416641	−	0.151645i
$605$	−296.471	+	127.885i	−0.490035	+	0.211380i
$606$	−581.910	−	319.205i	−0.960247	−	0.526741i
$607$	−785.689	−	186.212i	−1.29438	−	0.306774i	−0.474981	−	0.879996i	$-0.657545\pi$
$607$	−785.689	−	186.212i	−1.29438	−	0.306774i	−0.819400	+	0.573222i	$0.805693\pi$
$608$	−27.1291	+	114.467i	−0.0446202	+	0.188267i
$609$	19.2702	−	35.1295i	0.0316424	−	0.0576839i
$610$	392.348	+	909.566i	0.643194	+	1.49109i
$611$	52.4558	+	144.121i	0.0858524	+	0.235877i
$612$	−8.34805	−	2.10625i	−0.0136406	−	0.00344158i
$613$	−781.441	−	284.421i	−1.27478	−	0.463982i	−0.386078	−	0.922466i	$-0.626170\pi$
$613$	−781.441	−	284.421i	−1.27478	−	0.463982i	−0.888703	+	0.458484i	$0.848393\pi$
$614$	340.217	−	19.8154i	0.554100	−	0.0322726i
$615$	141.417	+	1016.56i	0.229946	+	1.65294i
$616$	13.3542	−	30.9585i	0.0216789	−	0.0502573i
$617$	−428.414	−	24.9523i	−0.694351	−	0.0404413i	−0.292660	−	0.956217i	$-0.594540\pi$
$617$	−428.414	−	24.9523i	−0.694351	−	0.0404413i	−0.401691	+	0.915775i	$0.631577\pi$
$618$	−44.0157	−	548.687i	−0.0712228	−	0.887843i
$619$	249.491	+	264.445i	0.403055	+	0.427214i	0.896829	−	0.442376i	$-0.145864\pi$
$619$	249.491	+	264.445i	0.403055	+	0.427214i	−0.493774	+	0.869590i	$0.664383\pi$
$620$	251.620	+	145.273i	0.405840	+	0.234312i
$621$	−771.412	+	141.943i	−1.24221	+	0.228571i
$622$	147.383	+	255.276i	0.236951	+	0.410411i
$623$	−100.449	−	30.0724i	−0.161234	−	0.0482703i
$624$	148.516	+	105.598i	0.238006	+	0.169227i
$625$	−1251.69	−	823.251i	−2.00271	−	1.31720i
$626$	1.90949	+	16.3367i	0.00305030	+	0.0260970i
$627$	565.834	+	121.100i	0.902447	+	0.193142i
$628$	−101.121	−	50.7847i	−0.161020	−	0.0808674i
$629$	30.7022	−	5.41363i	0.0488111	−	0.00860672i
$630$	−119.828	−	91.9263i	−0.190203	−	0.145915i
$631$	26.3829	−	149.625i	0.0418112	−	0.237123i	−0.956739	−	0.290947i	$-0.906030\pi$
$631$	26.3829	−	149.625i	0.0418112	−	0.237123i	0.998550	+	0.0538237i	$0.0171409\pi$
$632$	269.620	+	200.725i	0.426614	+	0.317603i
$633$	−252.721	+	314.918i	−0.399243	+	0.497501i
$634$	−443.335	+	469.908i	−0.699267	+	0.741179i
$635$	2143.73	−	641.792i	3.37596	−	1.01070i
$636$	−94.4378	−	32.0516i	−0.148487	−	0.0503956i
$637$	−714.161	−	83.4735i	−1.12113	−	0.131042i
$638$	−87.6217	+	104.423i	−0.137338	+	0.163673i
$639$	−759.270	+	264.003i	−1.18822	+	0.413150i
$640$	−80.0182	+	67.1432i	−0.125028	+	0.104911i
$641$	59.5235	+	90.5010i	0.0928603	+	0.141187i	0.878930	−	0.476950i	$-0.158258\pi$
$641$	59.5235	+	90.5010i	0.0928603	+	0.141187i	−0.786070	+	0.618138i	$0.787887\pi$
$642$	−352.415	−	665.042i	−0.548934	−	1.03589i
$643$	−248.096	−	333.251i	−0.385842	−	0.518275i	0.566190	−	0.824275i	$-0.308417\pi$
$643$	−248.096	−	333.251i	−0.385842	−	0.518275i	−0.952032	+	0.305999i	$0.901009\pi$
$644$	33.5121	+	66.7282i	0.0520375	+	0.103615i
$645$	625.017	+	634.106i	0.969019	+	0.983110i
$646$	−13.6877	+	3.24406i	−0.0211885	+	0.00502176i
$647$			299.044i			0.462201i	0.972930	+	0.231100i	$0.0742326\pi$
$647$			299.044i			0.462201i	−0.972930	+	0.231100i	$0.925767\pi$
$648$	−84.5398	+	212.934i	−0.130463	+	0.328602i
$649$	652.726			1.00574
$650$	−298.367	−	1258.91i	−0.459026	−	1.93678i
$651$	−15.2781	−	58.7105i	−0.0234687	−	0.0901851i
$652$	−137.491	+	69.0505i	−0.210876	+	0.105906i
$653$	−246.801	+	183.736i	−0.377949	+	0.281373i	−0.769324	−	0.638858i	$-0.779407\pi$
$653$	−246.801	+	183.736i	−0.377949	+	0.281373i	0.391375	+	0.920231i	$0.372000\pi$
$654$	118.280	+	74.1399i	0.180856	+	0.113364i
$655$	−1056.83	+	695.090i	−1.61348	+	1.06121i
$656$	−95.2733	−	113.542i	−0.145234	−	0.173083i
$657$	−1134.35	+	183.174i	−1.72656	+	0.278804i
$658$	14.0617	+	11.7992i	0.0213704	+	0.0179319i
$659$	−14.9611	+	128.001i	−0.0227028	+	0.194234i	−0.999830	−	0.0184194i	$-0.994137\pi$
$659$	−14.9611	+	128.001i	−0.0227028	+	0.194234i	0.977128	+	0.212654i	$0.0682107\pi$
$660$	338.800	+	386.285i	0.513334	+	0.585281i
$661$	−268.576	−	897.105i	−0.406317	−	1.35719i	−0.879361	−	0.476155i	$-0.842030\pi$
$661$	−268.576	−	897.105i	−0.406317	−	1.35719i	0.473044	−	0.881039i	$-0.343155\pi$
$662$	32.2490	+	30.4253i	0.0487145	+	0.0459597i
$663$	−3.31372	+	21.5374i	−0.00499807	+	0.0324847i
$664$	−73.0875	+	98.1736i	−0.110072	+	0.147852i
$665$	−243.007	−	42.8487i	−0.365424	−	0.0644342i
$666$	−36.2762	−	828.794i	−0.0544688	−	1.24444i
$667$	−52.4239	−	297.311i	−0.0785966	−	0.445744i
$668$	−87.4916	+	174.210i	−0.130975	+	0.260793i
$669$	−413.930	−	373.755i	−0.618730	−	0.558677i
$670$	513.135	−	59.9769i	0.765874	−	0.0895178i
$671$	−386.671	+	587.905i	−0.576261	+	0.876162i
$672$	21.7131	+	2.05767i	0.0323112	+	0.00306202i
$673$	136.270	−	455.174i	0.202482	−	0.676336i	−0.795077	−	0.606508i	$-0.792570\pi$
$673$	136.270	−	455.174i	0.202482	−	0.676336i	0.997559	−	0.0698280i	$-0.0222450\pi$
$674$	220.043	−	127.042i	0.326473	−	0.188489i
$675$	1448.08	−	740.788i	2.14531	−	1.09746i
$676$	61.6095	−	106.711i	0.0911383	−	0.157856i
$677$	461.324	−	435.237i	0.681424	−	0.642890i	−0.265589	−	0.964086i	$-0.585566\pi$
$677$	461.324	−	435.237i	0.681424	−	0.642890i	0.947013	+	0.321196i	$0.104085\pi$
$678$	51.3925	−	108.166i	0.0758002	−	0.159537i
$679$	10.4773	−	179.889i	0.0154306	−	0.264932i
$680$	−11.4692	−	4.94733i	−0.0168665	−	0.00727548i
$681$	182.087	+	233.735i	0.267382	+	0.343223i
$682$	12.0006	+	206.043i	0.0175962	+	0.302116i
$683$	333.383	−	915.962i	0.488116	−	1.34109i	−0.414268	−	0.910155i	$-0.635963\pi$
$683$	333.383	−	915.962i	0.488116	−	1.34109i	0.902384	−	0.430932i	$-0.141815\pi$
$684$	38.0846	+	372.378i	0.0556792	+	0.544412i
$685$	−629.827	+	229.238i	−0.919455	+	0.334654i
$686$	−160.794	+	69.3600i	−0.234394	+	0.101108i
$687$	−648.131	+	393.344i	−0.943422	+	0.572553i
$688$	−125.114	−	29.6526i	−0.181852	−	0.0430997i
$689$	−58.2098	+	245.607i	−0.0844845	+	0.356468i
$690$	−1137.67	+	24.8859i	−1.64879	+	0.0360665i
$691$	230.766	+	534.975i	0.333959	+	0.774204i	0.999610	+	0.0279405i	$0.00889488\pi$
$691$	230.766	+	534.975i	0.333959	+	0.774204i	−0.665651	+	0.746264i	$0.731846\pi$
$692$	23.9657	+	65.8451i	0.0346325	+	0.0951519i
$693$	7.78335	−	107.001i	0.0112314	−	0.154402i
$694$	−572.908	−	208.521i	−0.825515	−	0.300463i
$695$	−729.341	+	42.4793i	−1.04941	+	0.0611213i
$696$	−81.7132	−	33.1474i	−0.117404	−	0.0476256i
$697$	7.02004	−	16.2743i	0.0100718	−	0.0233491i
$698$	352.808	+	20.5487i	0.505455	+	0.0294394i
$699$	206.169	−	142.155i	0.294949	−	0.203369i
$700$	−106.263	−	112.632i	−0.151804	−	0.160903i
$701$	20.0883	+	11.5980i	0.0286567	+	0.0165449i	0.514260	−	0.857634i	$-0.328067\pi$
$701$	20.0883	+	11.5980i	0.0286567	+	0.0165449i	−0.485603	+	0.874179i	$0.661400\pi$
$702$	556.714	+	162.169i	0.793039	+	0.231010i
$703$	−677.713	−	1173.83i	−0.964029	−	1.66975i
$704$	−71.0842	−	21.2812i	−0.100972	−	0.0302290i
$705$	−254.377	+	116.390i	−0.360818	+	0.165092i
$706$	237.267	+	156.053i	0.336073	+	0.221039i
$707$	23.3408	+	199.693i	0.0330138	+	0.282451i
$708$	129.917	+	401.756i	0.183499	+	0.567453i
$709$	446.038	+	224.009i	0.629108	+	0.315950i	0.734631	−	0.678467i	$-0.237355\pi$
$709$	446.038	+	224.009i	0.629108	+	0.315950i	−0.105523	+	0.994417i	$0.533652\pi$
$710$	−1148.51	+	202.513i	−1.61761	+	0.285229i
$711$	1020.10	+	321.515i	1.43474	+	0.452201i
$712$	−40.0712	+	227.255i	−0.0562798	+	0.319178i
$713$	−366.648	−	272.960i	−0.514233	−	0.382832i
$714$	0.945390	+	2.43068i	0.00132408	+	0.00340431i
$715$	892.417	−	945.907i	1.24814	−	1.32295i
$716$	−217.744	+	65.1883i	−0.304112	+	0.0910451i
$717$	−70.0578	−	352.104i	−0.0977096	−	0.491080i
$718$	−196.275	−	22.9412i	−0.273363	−	0.0319515i
$719$	−644.746	+	768.379i	−0.896726	+	1.06868i	0.100551	+	0.994932i	$0.467940\pi$
$719$	−644.746	+	768.379i	−0.896726	+	1.06868i	−0.997277	+	0.0737450i	$0.976505\pi$
$720$	−170.327	+	285.419i	−0.236565	+	0.396415i
$721$	−127.733	+	107.181i	−0.177161	+	0.148655i
$722$	55.5297	+	84.4289i	0.0769110	+	0.116937i
$723$	−84.8870	−	3.08332i	−0.117409	−	0.00426462i
$724$	−200.484	−	269.297i	−0.276911	−	0.371957i
$725$	280.974	+	559.465i	0.387550	+	0.771676i
$726$	39.4342	−	143.033i	0.0543171	−	0.197015i
$727$	1086.94	−	257.610i	1.49510	−	0.354346i	0.599926	−	0.800056i	$-0.295197\pi$
$727$	1086.94	−	257.610i	1.49510	−	0.354346i	0.895178	+	0.445710i	$0.147049\pi$
$728$		−	55.2015i		−	0.0758262i
$729$	−31.5609	+	728.316i	−0.0432935	+	0.999062i
$730$	−1667.01			−2.28358
$731$	−3.54582	−	14.9610i	−0.00485064	−	0.0204664i
$732$	−438.821	−	120.983i	−0.599482	−	0.165277i
$733$	718.190	−	360.689i	0.979795	−	0.492072i	0.114548	−	0.993418i	$-0.463458\pi$
$733$	718.190	−	360.689i	0.979795	−	0.492072i	0.865247	+	0.501346i	$0.167162\pi$
$734$	421.634	−	313.895i	0.574433	−	0.427649i
$735$	47.6043	−	1310.60i	0.0647677	−	1.78312i
$736$	137.299	−	90.3031i	0.186548	−	0.122694i
$737$	235.898	+	281.132i	0.320078	+	0.381454i
$738$	−404.997	−	241.686i	−0.548776	−	0.327488i
$739$	−112.239	−	94.1800i	−0.151880	−	0.127443i	0.563681	−	0.825992i	$-0.309385\pi$
$739$	−112.239	−	94.1800i	−0.151880	−	0.127443i	−0.715561	+	0.698550i	$0.753829\pi$
$740$	139.724	−	1195.41i	0.188816	−	1.61542i
$741$	929.180	−	184.878i	1.25395	−	0.249498i
$742$	8.66433	+	28.9409i	0.0116770	+	0.0390039i
$743$	−864.334	−	815.457i	−1.16330	−	1.09752i	−0.993708	−	0.112006i	$-0.964272\pi$
$743$	−864.334	−	815.457i	−1.16330	−	1.09752i	−0.169595	−	0.985514i	$-0.554246\pi$
$744$	−124.432	+	48.3968i	−0.167247	+	0.0650494i
$745$	1548.63	−	2080.17i	2.07869	−	2.79217i
$746$	−507.864	−	89.5500i	−0.680782	−	0.120040i
$747$	−117.069	+	371.437i	−0.156719	+	0.497239i
$748$	−1.54076	−	8.73811i	−0.00205984	−	0.0116820i
$749$	−102.323	+	203.742i	−0.136613	+	0.272019i
$750$	1313.54	−	424.763i	1.75139	−	0.566351i
$751$	485.615	−	56.7603i	0.646625	−	0.0755796i	0.213542	−	0.976934i	$-0.431500\pi$
$751$	485.615	−	56.7603i	0.646625	−	0.0755796i	0.433082	+	0.901354i	$0.357426\pi$
$752$	22.1992	−	33.7523i	0.0295203	−	0.0448834i
$753$	−530.437	−	1159.30i	−0.704431	−	1.53957i
$754$	−64.0094	+	213.806i	−0.0848932	+	0.283563i
$755$	1070.64	−	618.134i	1.41807	−	0.818721i
$756$	67.4087	−	16.5064i	0.0891649	−	0.0218339i
$757$	−294.470	+	510.038i	−0.388997	+	0.673762i	−0.992315	−	0.123739i	$-0.960512\pi$
$757$	−294.470	+	510.038i	−0.388997	+	0.673762i	0.603318	+	0.797501i	$0.293845\pi$
$758$	−666.309	+	628.630i	−0.879035	+	0.829327i
$759$	−458.856	−	665.487i	−0.604554	−	0.876794i
$760$	−31.5760	+	542.138i	−0.0415473	+	0.713340i
$761$	105.288	+	45.4169i	0.138355	+	0.0596805i	0.464132	−	0.885766i	$-0.346366\pi$
$761$	105.288	+	45.4169i	0.138355	+	0.0596805i	−0.325777	+	0.945447i	$0.605626\pi$
$762$	−386.540	+	952.876i	−0.507270	+	1.25049i
$763$	−2.45874	−	42.2149i	−0.00322246	−	0.0553276i
$764$	−61.4440	+	168.816i	−0.0804241	+	0.220963i
$765$	−39.6405	−	2.88350i	−0.0518177	−	0.00376928i
$766$	−464.005	+	168.884i	−0.605751	+	0.220475i
$767$	981.277	−	423.282i	1.27937	−	0.551867i
$768$

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.h (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.326140 - 1.37609i) q^{2} +(2.89210 + 0.797352i) q^{3} +(-1.78727 + 0.897598i) q^{4} +(-7.40578 + 5.51340i) q^{5} +(0.154002 - 4.23984i) q^{6} +(-1.07376 + 0.706223i) q^{7} +(1.81808 + 2.16670i) q^{8} +(7.72846 + 4.61204i) q^{9} +O(q^{10})\)	\(q+(-0.326140 - 1.37609i) q^{2} +(2.89210 + 0.797352i) q^{3} +(-1.78727 + 0.897598i) q^{4} +(-7.40578 + 5.51340i) q^{5} +(0.154002 - 4.23984i) q^{6} +(-1.07376 + 0.706223i) q^{7} +(1.81808 + 2.16670i) q^{8} +(7.72846 + 4.61204i) q^{9} +(10.0023 + 8.39290i) q^{10} +(-1.07678 + 9.21247i) q^{11} +(-5.88465 + 1.17086i) q^{12} +(4.35535 + 14.5479i) q^{13} +(1.32203 + 1.24727i) q^{14} +(-25.8144 + 10.0403i) q^{15} +(2.38863 - 3.20849i) q^{16} +(0.471048 + 0.0830584i) q^{17} +(3.82604 - 12.1393i) q^{18} +(-3.61111 - 20.4796i) q^{19} +(8.28728 - 16.5013i) q^{20} +(-3.66853 + 1.18630i) q^{21} +(13.0284 - 1.52280i) q^{22} +(-15.9635 + 24.2713i) q^{23} +(3.53043 + 7.71596i) q^{24} +(17.2779 - 57.7123i) q^{25} +(18.5988 - 10.7380i) q^{26} +(18.6740 + 19.5008i) q^{27} +(1.28519 - 2.22601i) q^{28} +(-7.55899 + 7.13154i) q^{29} +(22.2354 + 32.2484i) q^{30} +(-0.914886 + 15.7080i) q^{31} +(-5.19421 - 2.24057i) q^{32} +(-10.4597 + 25.7848i) q^{33} +(-0.0393314 - 0.675294i) q^{34} +(4.05834 - 11.1502i) q^{35} +(-17.9526 - 1.30589i) q^{36} +(61.2478 - 22.2924i) q^{37} +(-27.0042 + 11.6485i) q^{38} +(0.996308 + 45.5466i) q^{39} +(-25.4102 - 6.02232i) q^{40} +(8.54541 - 36.0559i) q^{41} +(2.82891 + 4.66134i) q^{42} +(-12.7320 - 29.5161i) q^{43} +(-6.34460 - 17.4316i) q^{44} +(-82.6633 + 8.45430i) q^{45} +(38.6059 + 14.0514i) q^{46} +(10.0825 - 0.587238i) q^{47} +(9.46646 - 7.37469i) q^{48} +(-18.7537 + 43.4760i) q^{49} +(-85.0525 - 4.95375i) q^{50} +(1.29609 + 0.615804i) q^{51} +(-20.8423 - 22.0915i) q^{52} +(14.3946 + 8.31072i) q^{53} +(20.7445 - 32.0572i) q^{54} +(-42.8176 - 74.1622i) q^{55} +(-3.48235 - 1.04255i) q^{56} +(5.88580 - 62.1084i) q^{57} +(12.2790 + 8.07600i) q^{58} +(-8.16985 - 69.8975i) q^{59} +(37.1250 - 41.1156i) q^{60} +(67.7959 + 34.0484i) q^{61} +(21.9140 - 3.86403i) q^{62} +(-11.5556 + 0.505789i) q^{63} +(-1.38919 + 7.87846i) q^{64} +(-112.463 - 83.7255i) q^{65} +(38.8936 + 5.98413i) q^{66} +(27.1526 - 28.7800i) q^{67} +(-0.916440 + 0.274364i) q^{68} +(-65.5207 + 57.4665i) q^{69} +(-16.6673 - 1.94813i) q^{70} +(-57.4122 + 68.4212i) q^{71} +(4.05802 + 25.1303i) q^{72} +(-97.8021 + 82.0657i) q^{73} +(-50.6518 - 77.0123i) q^{74} +(95.9865 - 153.133i) q^{75} +(24.8365 + 33.3612i) q^{76} +(-5.34985 - 10.6524i) q^{77} +(62.3514 - 16.2256i) q^{78} +(115.638 - 27.4066i) q^{79} +36.9309i q^{80} +(38.4581 + 71.2880i) q^{81} -52.4033 q^{82} +(9.97925 + 42.1058i) q^{83} +(5.49181 - 5.41310i) q^{84} +(-3.94641 + 1.98196i) q^{85} +(-36.4644 + 27.1468i) q^{86} +(-27.5477 + 14.5979i) q^{87} +(-21.9183 + 14.4159i) q^{88} +(52.4426 + 62.4987i) q^{89} +(38.5937 + 110.995i) q^{90} +(-14.9506 - 12.5451i) q^{91} +(6.74510 - 57.7081i) q^{92} +(-15.1707 + 44.6995i) q^{93} +(-4.09640 - 13.6829i) q^{94} +(139.655 + 131.758i) q^{95} +(-13.2357 - 10.6216i) q^{96} +(-83.7265 + 112.464i) q^{97} +(65.9433 + 11.6276i) q^{98} +(-50.8102 + 66.2320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q + 72 q^{18} + 108 q^{20} + 270 q^{21} + 162 q^{23} - 54 q^{27} - 162 q^{29} - 216 q^{30} - 378 q^{33} - 486 q^{35} - 180 q^{36} - 108 q^{38} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 1728 q^{65} - 1008 q^{66} + 702 q^{67} - 216 q^{68} - 1872 q^{69} + 540 q^{70} - 1296 q^{71} - 576 q^{72} - 864 q^{74} - 900 q^{75} + 108 q^{76} - 864 q^{77} - 288 q^{78} + 108 q^{79} + 144 q^{81} + 432 q^{83} + 144 q^{84} - 540 q^{85} + 864 q^{86} + 2016 q^{87} - 216 q^{88} + 1782 q^{89} + 1440 q^{90} + 864 q^{92} + 2124 q^{93} - 756 q^{94} + 2808 q^{95} + 288 q^{96} - 918 q^{97} + 1296 q^{98} + 1800 q^{99}+O(q^{100}) \) 324 * q + 72 * q^18 + 108 * q^20 + 270 * q^21 + 162 * q^23 - 54 * q^27 - 162 * q^29 - 216 * q^30 - 378 * q^33 - 486 * q^35 - 180 * q^36 - 108 * q^38 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 1728 * q^65 - 1008 * q^66 + 702 * q^67 - 216 * q^68 - 1872 * q^69 + 540 * q^70 - 1296 * q^71 - 576 * q^72 - 864 * q^74 - 900 * q^75 + 108 * q^76 - 864 * q^77 - 288 * q^78 + 108 * q^79 + 144 * q^81 + 432 * q^83 + 144 * q^84 - 540 * q^85 + 864 * q^86 + 2016 * q^87 - 216 * q^88 + 1782 * q^89 + 1440 * q^90 + 864 * q^92 + 2124 * q^93 - 756 * q^94 + 2808 * q^95 + 288 * q^96 - 918 * q^97 + 1296 * q^98 + 1800 * q^99

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