LMFDB - Embedded newform 54.3.f.a.47.4

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			47.4
Character	$\chi$	$=$	54.47
Dual form			54.3.f.a.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483690 + 1.32893i) q^{2} +(-1.47299 + 2.61348i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(-2.99623 + 0.528316i) q^{5} +(-4.18560 - 0.693383i) q^{6} +(6.30359 + 5.28934i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-4.66059 - 7.69928i) q^{9} +O(q^{10})$	\(q+(0.483690 + 1.32893i) q^{2} +(-1.47299 + 2.61348i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(-2.99623 + 0.528316i) q^{5} +(-4.18560 - 0.693383i) q^{6} +(6.30359 + 5.28934i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-4.66059 - 7.69928i) q^{9} +(-2.15134 - 3.72623i) q^{10} +(6.45500 + 1.13819i) q^{11} +(-1.10308 - 5.89773i) q^{12} +(17.4093 + 6.33646i) q^{13} +(-3.98016 + 10.9354i) q^{14} +(3.03268 - 8.60880i) q^{15} +(0.694593 - 3.93923i) q^{16} +(-11.4293 + 6.59870i) q^{17} +(7.97749 - 9.91764i) q^{18} +(17.4160 - 30.1654i) q^{19} +(3.91130 - 4.66131i) q^{20} +(-23.1087 + 8.68318i) q^{21} +(1.60964 + 9.12874i) q^{22} +(2.12998 + 2.53841i) q^{23} +(7.30410 - 4.31858i) q^{24} +(-14.7940 + 5.38459i) q^{25} +26.2005i q^{26} +(26.9869 - 0.839401i) q^{27} -16.4575 q^{28} +(-9.72486 - 26.7188i) q^{29} +(12.9073 - 0.133785i) q^{30} +(-10.6385 + 8.92675i) q^{31} +(5.57091 - 0.982302i) q^{32} +(-12.4828 + 15.1935i) q^{33} +(-14.2974 - 11.9970i) q^{34} +(-21.6815 - 12.5178i) q^{35} +(17.0384 + 5.80444i) q^{36} +(-3.33360 - 5.77397i) q^{37} +(48.5116 + 8.55390i) q^{38} +(-42.2040 + 36.1653i) q^{39} +(8.08639 + 2.94320i) q^{40} +(-19.4863 + 53.5382i) q^{41} +(-22.7168 - 26.5099i) q^{42} +(-5.68525 + 32.2426i) q^{43} +(-11.3529 + 6.55457i) q^{44} +(18.0319 + 20.6065i) q^{45} +(-2.34311 + 4.05838i) q^{46} +(34.5145 - 41.1328i) q^{47} +(9.27199 + 7.61776i) q^{48} +(3.24938 + 18.4281i) q^{49} +(-14.3114 - 17.0557i) q^{50} +(-0.410352 - 39.5901i) q^{51} +(-34.8186 + 12.6729i) q^{52} -98.5651i q^{53} +(14.1688 + 35.4576i) q^{54} -19.9420 q^{55} +(-7.96033 - 21.8708i) q^{56} +(53.1832 + 89.9499i) q^{57} +(30.8035 - 25.8472i) q^{58} +(101.204 - 17.8449i) q^{59} +(6.42093 + 17.0882i) q^{60} +(-5.50484 - 4.61911i) q^{61} +(-17.0087 - 9.81998i) q^{62} +(11.3457 - 73.1846i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-55.5099 - 9.78789i) q^{65} +(-26.2288 - 9.23979i) q^{66} +(-28.2566 - 10.2846i) q^{67} +(9.02755 - 24.8030i) q^{68} +(-9.77153 + 1.82761i) q^{69} +(6.14813 - 34.8678i) q^{70} +(8.46959 - 4.88992i) q^{71} +(0.527644 + 25.4504i) q^{72} +(64.7978 - 112.233i) q^{73} +(6.06075 - 7.22291i) q^{74} +(7.71896 - 46.5954i) q^{75} +(12.0970 + 68.6057i) q^{76} +(34.6694 + 41.3174i) q^{77} +(-68.4747 - 38.5932i) q^{78} +(-96.4782 + 35.1152i) q^{79} +12.1698i q^{80} +(-37.5578 + 71.7664i) q^{81} -80.5737 q^{82} +(37.0524 + 101.800i) q^{83} +(24.2418 - 43.0114i) q^{84} +(30.7586 - 25.8095i) q^{85} +(-45.5980 + 8.04015i) q^{86} +(84.1539 + 13.9409i) q^{87} +(-14.2018 - 11.9167i) q^{88} +(-20.1649 - 11.6422i) q^{89} +(-18.6628 + 33.9302i) q^{90} +(76.2254 + 132.026i) q^{91} +(-6.52663 - 1.15082i) q^{92} +(-7.65951 - 40.9525i) q^{93} +(71.3568 + 25.9718i) q^{94} +(-36.2455 + 99.5837i) q^{95} +(-5.63868 + 16.0064i) q^{96} +(-8.89809 + 50.4636i) q^{97} +(-22.9179 + 13.2317i) q^{98} +(-21.3209 - 55.0035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.483690	+	1.32893i	0.241845	+	0.664463i
$2$	0.483690	+	1.32893i	0.241845	+	0.664463i
$3$	−1.47299	+	2.61348i	−0.490997	+	0.871161i
$3$	−1.47299	+	2.61348i	−0.490997	+	0.871161i
$4$	−1.53209	+	1.28558i	−0.383022	+	0.321394i
$5$	−2.99623	+	0.528316i	−0.599246	+	0.105663i	−0.465039	−	0.885290i	$-0.653960\pi$
$5$	−2.99623	+	0.528316i	−0.599246	+	0.105663i	−0.134207	+	0.990953i	$0.542849\pi$
$6$	−4.18560	−	0.693383i	−0.697599	−	0.115564i
$7$	6.30359	+	5.28934i	0.900513	+	0.755620i	0.970291	−	0.241942i	$-0.0777845\pi$
$7$	6.30359	+	5.28934i	0.900513	+	0.755620i	−0.0697775	+	0.997563i	$0.522229\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$	−4.66059	−	7.69928i	−0.517843	−	0.855475i
$10$	−2.15134	−	3.72623i	−0.215134	−	0.372623i
$11$	6.45500	+	1.13819i	0.586818	+	0.103472i	0.459171	−	0.888348i	$-0.348147\pi$
$11$	6.45500	+	1.13819i	0.586818	+	0.103472i	0.127647	+	0.991820i	$0.459258\pi$
$12$	−1.10308	−	5.89773i	−0.0919229	−	0.491478i
$13$	17.4093	+	6.33646i	1.33918	+	0.487420i	0.909553	−	0.415588i	$-0.136424\pi$
$13$	17.4093	+	6.33646i	1.33918	+	0.487420i	0.429623	+	0.903008i	$0.358646\pi$
$14$	−3.98016	+	10.9354i	−0.284297	+	0.781101i
$15$	3.03268	−	8.60880i	0.202178	−	0.573920i
$16$	0.694593	−	3.93923i	0.0434120	−	0.246202i
$17$	−11.4293	+	6.59870i	−0.672311	+	0.388159i	−0.796952	−	0.604043i	$-0.793555\pi$
$17$	−11.4293	+	6.59870i	−0.672311	+	0.388159i	0.124641	+	0.992202i	$0.460222\pi$
$18$	7.97749	−	9.91764i	0.443194	−	0.550980i
$19$	17.4160	−	30.1654i	0.916632	−	1.58765i	0.112139	−	0.993693i	$-0.464230\pi$
$19$	17.4160	−	30.1654i	0.916632	−	1.58765i	0.804494	−	0.593961i	$-0.202437\pi$
$20$	3.91130	−	4.66131i	0.195565	−	0.233065i
$21$	−23.1087	+	8.68318i	−1.10042	+	0.413485i
$22$	1.60964	+	9.12874i	0.0731656	+	0.414943i
$23$	2.12998	+	2.53841i	0.0926077	+	0.110366i	0.810358	−	0.585935i	$-0.199273\pi$
$23$	2.12998	+	2.53841i	0.0926077	+	0.110366i	−0.717750	+	0.696300i	$0.754828\pi$
$24$	7.30410	−	4.31858i	0.304338	−	0.179941i
$25$	−14.7940	+	5.38459i	−0.591762	+	0.215384i
$26$			26.2005i			1.00771i
$27$	26.9869	−	0.839401i	0.999517	−	0.0310889i
$28$	−16.4575			−0.587768
$29$	−9.72486	−	26.7188i	−0.335340	−	0.921339i	−0.986697	−	0.162568i	$-0.948022\pi$
$29$	−9.72486	−	26.7188i	−0.335340	−	0.921339i	0.651357	−	0.758771i	$-0.274200\pi$
$30$	12.9073	−	0.133785i	0.430244	−	0.00445949i
$31$	−10.6385	+	8.92675i	−0.343177	+	0.287960i	−0.798043	−	0.602600i	$-0.794131\pi$
$31$	−10.6385	+	8.92675i	−0.343177	+	0.287960i	0.454866	+	0.890560i	$0.349687\pi$
$32$	5.57091	−	0.982302i	0.174091	−	0.0306970i
$33$	−12.4828	+	15.1935i	−0.378267	+	0.460408i
$34$	−14.2974	−	11.9970i	−0.420512	−	0.352851i
$35$	−21.6815	−	12.5178i	−0.619470	−	0.357651i
$36$	17.0384	+	5.80444i	0.473290	+	0.161234i
$37$	−3.33360	−	5.77397i	−0.0900973	−	0.156053i	0.817455	−	0.575993i	$-0.195384\pi$
$37$	−3.33360	−	5.77397i	−0.0900973	−	0.156053i	−0.907552	+	0.419940i	$0.862051\pi$
$38$	48.5116	+	8.55390i	1.27662	+	0.225103i
$39$	−42.2040	+	36.1653i	−1.08215	+	0.927316i
$40$	8.08639	+	2.94320i	0.202160	+	0.0735801i
$41$	−19.4863	+	53.5382i	−0.475276	+	1.30581i	0.438185	+	0.898885i	$0.355621\pi$
$41$	−19.4863	+	53.5382i	−0.475276	+	1.30581i	−0.913461	+	0.406926i	$0.866601\pi$
$42$	−22.7168	−	26.5099i	−0.540875	−	0.631187i
$43$	−5.68525	+	32.2426i	−0.132215	+	0.749829i	0.844544	+	0.535487i	$0.179872\pi$
$43$	−5.68525	+	32.2426i	−0.132215	+	0.749829i	−0.976759	+	0.214342i	$0.931239\pi$
$44$	−11.3529	+	6.55457i	−0.258019	+	0.148968i
$45$	18.0319	+	20.6065i	0.400708	+	0.457923i
$46$	−2.34311	+	4.05838i	−0.0509371	+	0.0882257i
$47$	34.5145	−	41.1328i	0.734352	−	0.875167i	−0.261589	−	0.965179i	$-0.584246\pi$
$47$	34.5145	−	41.1328i	0.734352	−	0.875167i	0.995941	+	0.0900128i	$0.0286908\pi$
$48$	9.27199	+	7.61776i	0.193166	+	0.158703i
$49$	3.24938	+	18.4281i	0.0663138	+	0.376084i
$50$	−14.3114	−	17.0557i	−0.286229	−	0.341114i
$51$	−0.410352	−	39.5901i	−0.00804611	−	0.776276i
$52$	−34.8186	+	12.6729i	−0.669588	+	0.243710i
$53$		−	98.5651i		−	1.85972i	−0.367914	−	0.929860i	$-0.619928\pi$
$53$		−	98.5651i		−	1.85972i	0.367914	−	0.929860i	$-0.380072\pi$
$54$	14.1688	+	35.4576i	0.262385	+	0.656623i
$55$	−19.9420			−0.362581
$56$	−7.96033	−	21.8708i	−0.142149	−	0.390550i
$57$	53.1832	+	89.9499i	0.933038	+	1.57807i
$58$	30.8035	−	25.8472i	0.531096	−	0.445642i
$59$	101.204	−	17.8449i	1.71532	−	0.302457i	0.772314	−	0.635241i	$-0.219099\pi$
$59$	101.204	−	17.8449i	1.71532	−	0.302457i	0.943003	+	0.332785i	$0.107988\pi$
$60$	6.42093	+	17.0882i	0.107016	+	0.284803i
$61$	−5.50484	−	4.61911i	−0.0902432	−	0.0757230i	0.596550	−	0.802576i	$-0.296538\pi$
$61$	−5.50484	−	4.61911i	−0.0902432	−	0.0757230i	−0.686793	+	0.726853i	$0.740982\pi$
$62$	−17.0087	−	9.81998i	−0.274334	−	0.158387i
$63$	11.3457	−	73.1846i	0.180090	−	1.16166i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−55.5099	−	9.78789i	−0.853998	−	0.150583i
$66$	−26.2288	−	9.23979i	−0.397406	−	0.139997i
$67$	−28.2566	−	10.2846i	−0.421740	−	0.153501i	0.122427	−	0.992477i	$-0.460932\pi$
$67$	−28.2566	−	10.2846i	−0.421740	−	0.153501i	−0.544167	+	0.838977i	$0.683154\pi$
$68$	9.02755	−	24.8030i	0.132758	−	0.364750i
$69$	−9.77153	+	1.82761i	−0.141616	+	0.0264870i
$70$	6.14813	−	34.8678i	0.0878304	−	0.498111i
$71$	8.46959	−	4.88992i	0.119290	−	0.0688721i	−0.439168	−	0.898405i	$-0.644727\pi$
$71$	8.46959	−	4.88992i	0.119290	−	0.0688721i	0.558458	+	0.829533i	$0.311393\pi$
$72$	0.527644	+	25.4504i	0.00732838	+	0.353477i
$73$	64.7978	−	112.233i	0.887642	−	1.53744i	0.0449857	−	0.998988i	$-0.485676\pi$
$73$	64.7978	−	112.233i	0.887642	−	1.53744i	0.842656	−	0.538453i	$-0.180991\pi$
$74$	6.06075	−	7.22291i	0.0819020	−	0.0976070i
$75$	7.71896	−	46.5954i	0.102920	−	0.621272i
$76$	12.0970	+	68.6057i	0.159172	+	0.902707i
$77$	34.6694	+	41.3174i	0.450252	+	0.536589i
$78$	−68.4747	−	38.5932i	−0.877881	−	0.494784i
$79$	−96.4782	+	35.1152i	−1.22124	+	0.444496i	−0.870590	−	0.492009i	$-0.836263\pi$
$79$	−96.4782	+	35.1152i	−1.22124	+	0.444496i	−0.350653	+	0.936505i	$0.614040\pi$
$80$			12.1698i			0.152123i
$81$	−37.5578	+	71.7664i	−0.463676	+	0.886005i
$82$	−80.5737			−0.982606
$83$	37.0524	+	101.800i	0.446414	+	1.22651i	0.935204	+	0.354110i	$0.115216\pi$
$83$	37.0524	+	101.800i	0.446414	+	1.22651i	−0.488790	+	0.872402i	$0.662561\pi$
$84$	24.2418	−	43.0114i	0.288593	−	0.512041i
$85$	30.7586	−	25.8095i	0.361865	−	0.303641i
$86$	−45.5980	+	8.04015i	−0.530209	+	0.0934902i
$87$	84.1539	+	13.9409i	0.967286	+	0.160240i
$88$	−14.2018	−	11.9167i	−0.161384	−	0.135417i
$89$	−20.1649	−	11.6422i	−0.226572	−	0.130811i	0.382418	−	0.923990i	$-0.375092\pi$
$89$	−20.1649	−	11.6422i	−0.226572	−	0.130811i	−0.608989	+	0.793178i	$0.708425\pi$
$90$	−18.6628	+	33.9302i	−0.207364	+	0.377002i
$91$	76.2254	+	132.026i	0.837641	+	1.45084i
$92$	−6.52663	−	1.15082i	−0.0709416	−	0.0125089i
$93$	−7.65951	−	40.9525i	−0.0823603	−	0.440350i
$94$	71.3568	+	25.9718i	0.759115	+	0.276295i
$95$	−36.2455	+	99.5837i	−0.381532	+	1.04825i
$96$	−5.63868	+	16.0064i	−0.0587362	+	0.166733i
$97$	−8.89809	+	50.4636i	−0.0917329	+	0.520243i	0.903967	+	0.427603i	$0.140642\pi$
$97$	−8.89809	+	50.4636i	−0.0917329	+	0.520243i	−0.995700	+	0.0926404i	$0.970469\pi$
$98$	−22.9179	+	13.2317i	−0.233856	+	0.135017i
$99$	−21.3209	−	55.0035i	−0.215362	−	0.555590i
$100$	15.7435	−	27.2685i	0.157435	−	0.272685i
$101$	−69.9824	+	83.4017i	−0.692895	+	0.825760i	−0.991703	−	0.128554i	$-0.958967\pi$
$101$	−69.9824	+	83.4017i	−0.692895	+	0.825760i	0.298808	+	0.954313i	$0.403411\pi$
$102$	52.4138	−	19.6946i	0.513861	−	0.193085i
$103$	−19.5497	−	110.872i	−0.189803	−	1.07643i	−0.919627	−	0.392792i	$-0.871509\pi$
$103$	−19.5497	−	110.872i	−0.189803	−	1.07643i	0.729824	−	0.683635i	$-0.239602\pi$
$104$	−33.6828	−	40.1416i	−0.323873	−	0.385977i
$105$	64.6517	−	38.2255i	0.615730	−	0.364053i
$106$	130.986	−	47.6749i	1.23571	−	0.449763i
$107$			125.974i			1.17733i	0.808378	+	0.588664i	$0.200346\pi$
$107$			125.974i			1.17733i	−0.808378	+	0.588664i	$0.799654\pi$
$108$	−40.2673	+	35.9798i	−0.372845	+	0.333146i
$109$	−71.2685			−0.653839			−0.326920	−	0.945052i	$-0.606011\pi$
$109$	−71.2685			−0.653839			−0.326920	+	0.945052i	$0.606011\pi$
$110$	−9.64572	−	26.5014i	−0.0876884	−	0.240922i
$111$	20.0005	−	0.207306i	0.180185	−	0.00186762i
$112$	25.2144	−	21.1574i	0.225128	−	0.188905i
$113$	−40.2664	+	7.10006i	−0.356340	+	0.0628324i	−0.348953	−	0.937140i	$-0.613463\pi$
$113$	−40.2664	+	7.10006i	−0.356340	+	0.0628324i	−0.00738746	+	0.999973i	$0.502352\pi$
$114$	−93.8126	+	114.184i	−0.822918	+	1.00162i
$115$	−7.72298	−	6.48035i	−0.0671564	−	0.0563509i
$116$	49.2484	+	28.4336i	0.424555	+	0.245117i
$117$	−32.3514	−	163.571i	−0.276508	−	1.39804i
$118$	72.6658	+	125.861i	0.615811	+	1.06662i
$119$	−106.948	−	18.8579i	−0.898725	−	0.158470i
$120$	−19.6032	+	16.7983i	−0.163360	+	0.139986i
$121$	−73.3313	−	26.6904i	−0.606044	−	0.220582i
$122$	3.47582	−	9.54973i	0.0284903	−	0.0782765i
$123$	−111.218	−	129.789i	−0.904212	−	1.05519i
$124$	4.82310	−	27.3531i	0.0388959	−	0.220590i
$125$	107.353	−	61.9800i	0.858821	−	0.495840i
$126$	102.745	−	20.3211i	0.815434	−	0.161278i
$127$	6.05212	−	10.4826i	0.0476545	−	0.0825399i	−0.841214	−	0.540702i	$-0.818159\pi$
$127$	6.05212	−	10.4826i	0.0476545	−	0.0825399i	0.888869	+	0.458162i	$0.151492\pi$
$128$	−7.27231	+	8.66680i	−0.0568149	+	0.0677094i
$129$	−75.8913	−	62.3514i	−0.588304	−	0.483345i
$130$	−13.8422	−	78.5029i	−0.106478	−	0.603868i
$131$	−47.7541	−	56.9111i	−0.364535	−	0.434436i	0.552335	−	0.833622i	$-0.313737\pi$
$131$	−47.7541	−	56.9111i	−0.364535	−	0.434436i	−0.916870	+	0.399187i	$0.869293\pi$
$132$	−0.407608	−	39.3253i	−0.00308794	−	0.297919i
$133$	269.339	−	98.0313i	2.02510	−	0.737077i
$134$		−	42.5255i		−	0.317354i
$135$	−80.4156	+	16.7727i	−0.595671	+	0.124242i
$136$	37.3279			0.274470
$137$	14.1317	+	38.8266i	0.103151	+	0.283406i	0.980523	−	0.196406i	$-0.0629270\pi$
$137$	14.1317	+	38.8266i	0.103151	+	0.283406i	−0.877371	+	0.479812i	$0.840705\pi$
$138$	−7.15514	−	12.1016i	−0.0518488	−	0.0876931i
$139$	−108.810	+	91.3026i	−0.782807	+	0.656853i	−0.943954	−	0.330077i	$-0.892925\pi$
$139$	−108.810	+	91.3026i	−0.782807	+	0.656853i	0.161147	+	0.986930i	$0.448481\pi$
$140$	49.3105	−	8.69477i	0.352218	−	0.0621055i
$141$	56.6603	+	150.792i	0.401846	+	1.06944i
$142$	10.5950	+	8.89025i	0.0746126	+	0.0626074i
$143$	105.165	+	60.7169i	0.735418	+	0.424594i
$144$	−33.5665	+	13.0113i	−0.233100	+	0.0903561i
$145$	43.2539	+	74.9180i	0.298303	+	0.516676i
$146$	180.492	+	31.8255i	1.23624	+	0.217983i
$147$	−52.9479	−	18.6523i	−0.360190	−	0.126886i
$148$	12.5302	+	4.56063i	0.0846638	+	0.0308151i
$149$	79.8207	−	219.306i	0.535709	−	1.47185i	−0.316471	−	0.948602i	$-0.602498\pi$
$149$	79.8207	−	219.306i	0.535709	−	1.47185i	0.852181	−	0.523247i	$-0.175280\pi$
$150$	65.6555	−	12.2798i	0.437703	−	0.0818653i
$151$	1.35424	−	7.68028i	0.00896848	−	0.0508628i	−0.979995	−	0.199022i	$-0.936224\pi$
$151$	1.35424	−	7.68028i	0.00896848	−	0.0508628i	0.988964	+	0.148159i	$0.0473347\pi$
$152$	−85.3207	+	49.2599i	−0.561320	+	0.324078i
$153$	104.072	+	57.2434i	0.680212	+	0.374140i
$154$	−38.1385	+	66.0578i	−0.247653	+	0.428947i
$155$	27.1592	−	32.3671i	0.175221	−	0.208820i
$156$	18.1670	−	109.665i	0.116455	−	0.702980i
$157$	−4.42811	−	25.1131i	−0.0282045	−	0.159956i	0.967453	−	0.253053i	$-0.0814345\pi$
$157$	−4.42811	−	25.1131i	−0.0282045	−	0.159956i	−0.995657	+	0.0930967i	$0.970323\pi$
$158$	−93.3310	−	111.228i	−0.590703	−	0.703972i
$159$	257.598	+	145.186i	1.62012	+	0.913117i
$160$	−16.1728	+	5.88641i	−0.101080	+	0.0367900i
$161$			27.2673i			0.169362i
$162$	−113.539	−	15.1989i	−0.700855	−	0.0938203i
$163$	−211.039			−1.29472			−0.647358	−	0.762186i	$-0.724126\pi$
$163$	−211.039			−1.29472			−0.647358	+	0.762186i	$0.724126\pi$
$164$	−38.9726	−	107.076i	−0.237638	−	0.652905i
$165$	29.3744	−	52.1180i	0.178026	−	0.315867i
$166$	−117.363	+	98.4797i	−0.707009	+	0.593251i
$167$	−11.3278	+	1.99740i	−0.0678311	+	0.0119605i	−0.207461	−	0.978243i	$-0.566520\pi$
$167$	−11.3278	+	1.99740i	−0.0678311	+	0.0119605i	0.139630	+	0.990204i	$0.455409\pi$
$168$	68.8845	+	11.4114i	0.410027	+	0.0679247i
$169$	133.471	+	111.996i	0.789771	+	0.662696i
$170$	49.1765	+	28.3921i	0.289274	+	0.167012i
$171$	−313.421	+	6.49792i	−1.83287	+	0.0379995i
$172$	−32.7400	−	56.7074i	−0.190349	−	0.329694i
$173$	−227.512	−	40.1166i	−1.31510	−	0.231888i	−0.528281	−	0.849070i	$-0.677163\pi$
$173$	−227.512	−	40.1166i	−1.31510	−	0.231888i	−0.786820	+	0.617182i	$0.788274\pi$
$174$	22.1780	+	118.577i	0.127460	+	0.681479i
$175$	−121.737	−	44.3085i	−0.695637	−	0.253191i
$176$	8.96719	−	24.6371i	0.0509499	−	0.139984i
$177$	−102.435	+	290.780i	−0.578727	+	1.64282i
$178$	5.71808	−	32.4288i	0.0321240	−	0.182185i
$179$	71.6862	−	41.3880i	0.400481	−	0.231218i	−0.286210	−	0.958167i	$-0.592396\pi$
$179$	71.6862	−	41.3880i	0.400481	−	0.231218i	0.686692	+	0.726949i	$0.259062\pi$
$180$	−54.1177	−	8.38975i	−0.300654	−	0.0466097i
$181$	83.1040	−	143.940i	0.459138	−	0.795250i	−0.539778	−	0.841808i	$-0.681492\pi$
$181$	83.1040	−	143.940i	0.459138	−	0.795250i	0.998916	+	0.0465572i	$0.0148250\pi$
$182$	−138.584	+	165.158i	−0.761449	+	0.907459i
$183$	20.1805	−	7.58289i	0.110276	−	0.0414366i
$184$	−1.62751	−	9.23005i	−0.00884514	−	0.0501633i
$185$	13.0387	+	15.5389i	0.0704795	+	0.0839942i
$186$	50.7181	−	29.9872i	0.272678	−	0.161222i
$187$	−81.2866	+	29.5859i	−0.434687	+	0.158213i
$188$			107.390i			0.571224i
$189$	174.555	+	137.452i	0.923569	+	0.727259i
$190$	−149.871			−0.788794
$191$	42.8208	+	117.649i	0.224192	+	0.615964i	0.999885	−	0.0151469i	$-0.00482159\pi$
$191$	42.8208	+	117.649i	0.224192	+	0.615964i	−0.775693	+	0.631111i	$0.782599\pi$
$192$	−23.9987	+	0.248747i	−0.124993	+	0.00129556i
$193$	−70.6839	+	59.3108i	−0.366238	+	0.307310i	−0.807271	−	0.590181i	$-0.799056\pi$
$193$	−70.6839	+	59.3108i	−0.366238	+	0.307310i	0.441033	+	0.897491i	$0.354612\pi$
$194$	−71.3663	+	12.5838i	−0.367867	+	0.0648650i
$195$	107.346	−	130.657i	0.550493	−	0.670034i
$196$	−28.6691	−	24.0562i	−0.146271	−	0.122736i
$197$	34.0836	+	19.6782i	0.173013	+	0.0998893i	0.584006	−	0.811749i	$-0.301484\pi$
$197$	34.0836	+	19.6782i	0.173013	+	0.0998893i	−0.410993	+	0.911639i	$0.634818\pi$
$198$	62.7828	−	54.9384i	0.317085	−	0.277467i
$199$	95.3069	+	165.076i	0.478929	+	0.829530i	0.999708	−	0.0241618i	$-0.00769168\pi$
$199$	95.3069	+	165.076i	0.478929	+	0.829530i	−0.520779	+	0.853692i	$0.674358\pi$
$200$	43.8528	+	7.73243i	0.219264	+	0.0386622i
$201$	68.5003	−	58.6991i	0.340797	−	0.292035i
$202$	−144.684	−	52.6608i	−0.716260	−	0.260697i
$203$	80.0235	−	219.863i	0.394204	−	1.08307i
$204$	51.5247	+	60.1280i	0.252572	+	0.294745i
$205$	30.1004	−	170.708i	0.146831	−	0.832721i
$206$	137.885	−	79.6077i	0.669343	−	0.386445i
$207$	9.61696	−	28.2298i	0.0464587	−	0.136376i
$208$	37.0532	−	64.1780i	0.178140	−	0.308548i
$209$	146.754	−	174.895i	0.702174	−	0.836818i
$210$	82.0702	+	67.4280i	0.390811	+	0.321086i
$211$	13.2835	+	75.3347i	0.0629551	+	0.357036i	0.999970	+	0.00774680i	$0.00246591\pi$
$211$	13.2835	+	75.3347i	0.0629551	+	0.357036i	−0.937015	+	0.349289i	$0.886423\pi$
$212$	126.713	+	151.011i	0.597702	+	0.712314i
$213$	0.304088	+	29.3379i	0.00142764	+	0.137737i
$214$	−167.410	+	60.9324i	−0.782291	+	0.284731i
$215$		−	99.6100i		−	0.463302i
$216$	−67.2913	−	36.1092i	−0.311534	−	0.167172i
$217$	−114.277			−0.526623
$218$	−34.4718	−	94.7105i	−0.158128	−	0.434452i
$219$	197.873	+	334.667i	0.903529	+	1.52816i
$220$	30.5529	−	25.6369i	0.138877	−	0.116531i
$221$	−240.788	+	42.4575i	−1.08954	+	0.192115i
$222$	9.94954	+	26.4790i	0.0448177	+	0.119275i
$223$	−38.1027	−	31.9720i	−0.170864	−	0.143372i	0.553346	−	0.832952i	$-0.313351\pi$
$223$	−38.1027	−	31.9720i	−0.170864	−	0.143372i	−0.724210	+	0.689580i	$0.757795\pi$
$224$	40.3125	+	23.2744i	0.179967	+	0.103904i
$225$	110.406	+	88.8081i	0.490695	+	0.394703i
$226$	−28.9119	−	50.0769i	−0.127929	−	0.221579i
$227$	298.583	+	52.6482i	1.31534	+	0.231930i	0.786922	−	0.617052i	$-0.211673\pi$
$227$	298.583	+	52.6482i	1.31534	+	0.231930i	0.528420	+	0.848983i	$0.322784\pi$
$228$	−197.119	−	69.4402i	−0.864556	−	0.304562i
$229$	−18.3111	−	6.66470i	−0.0799611	−	0.0291035i	0.301730	−	0.953393i	$-0.402436\pi$
$229$	−18.3111	−	6.66470i	−0.0799611	−	0.0291035i	−0.381691	+	0.924290i	$0.624658\pi$
$230$	4.87638	−	13.3978i	0.0212017	−	0.0582511i
$231$	−159.050	+	29.7477i	−0.688528	+	0.128778i
$232$	−13.9652	+	79.2005i	−0.0601948	+	0.341382i
$233$	−89.3347	+	51.5774i	−0.383411	+	0.221362i	−0.679301	−	0.733860i	$-0.737717\pi$
$233$	−89.3347	+	51.5774i	−0.383411	+	0.221362i	0.295890	+	0.955222i	$0.404384\pi$
$234$	201.725	−	122.110i	0.862074	−	0.521838i
$235$	−81.6824	+	141.478i	−0.347585	+	0.602034i
$236$	−132.112	+	157.445i	−0.559797	+	0.667140i
$237$	50.3386	−	303.869i	0.212399	−	1.28215i
$238$	−26.6691	−	151.248i	−0.112055	−	0.635495i
$239$	−135.523	−	161.510i	−0.567041	−	0.675773i	0.403980	−	0.914768i	$-0.367626\pi$
$239$	−135.523	−	161.510i	−0.567041	−	0.675773i	−0.971021	+	0.238995i	$0.923182\pi$
$240$	−31.8056	−	17.9260i	−0.132523	−	0.0746918i
$241$	58.1501	−	21.1649i	0.241287	−	0.0878211i	−0.218546	−	0.975827i	$-0.570132\pi$
$241$	58.1501	−	21.1649i	0.241287	−	0.0878211i	0.459833	+	0.888005i	$0.347909\pi$
$242$		−	110.362i		−	0.456040i
$243$	−132.238	−	203.868i	−0.544189	−	0.838963i
$244$	14.3721			0.0589021
$245$	−19.4718	−	53.4982i	−0.0794766	−	0.218360i
$246$	118.684	−	210.578i	0.482457	−	0.856008i
$247$	494.343	−	414.803i	2.00139	−	1.67936i
$248$	38.6832	−	6.82089i	0.155981	−	0.0275036i
$249$	−320.632	−	53.1156i	−1.28768	−	0.213316i
$250$	134.292	+	112.685i	0.537169	+	0.450738i
$251$	−99.2490	−	57.3014i	−0.395414	−	0.228293i	0.289089	−	0.957302i	$-0.406648\pi$
$251$	−99.2490	−	57.3014i	−0.395414	−	0.228293i	−0.684503	+	0.729010i	$0.739981\pi$
$252$	76.7017	+	126.711i	0.304372	+	0.502821i
$253$	10.8598	+	18.8097i	0.0429241	+	0.0743468i
$254$	16.8579	+	2.97250i	0.0663697	+	0.0117028i
$255$	22.1456	+	118.404i	0.0868454	+	0.464330i
$256$	−15.0351	−	5.47232i	−0.0587308	−	0.0213763i
$257$	−60.5933	+	166.479i	−0.235772	+	0.647777i	0.764224	+	0.644950i	$0.223122\pi$
$257$	−60.5933	+	166.479i	−0.235772	+	0.647777i	−0.999996	+	0.00282659i	$0.999100\pi$
$258$	46.1526	−	131.013i	0.178886	−	0.507801i
$259$	9.52682	−	54.0293i	0.0367831	−	0.208607i
$260$	97.6292	−	56.3662i	0.375497	−	0.216793i
$261$	−160.392	+	199.400i	−0.614529	+	0.763985i
$262$	52.5325	−	90.9889i	0.200506	−	0.347286i
$263$	44.5945	−	53.1457i	0.169561	−	0.202075i	−0.674572	−	0.738209i	$-0.735672\pi$
$263$	44.5945	−	53.1457i	0.169561	−	0.202075i	0.844133	+	0.536135i	$0.180116\pi$
$264$	52.0633	−	19.5629i	0.197210	−	0.0741020i
$265$	52.0735	+	295.324i	0.196504	+	1.11443i
$266$	260.553	+	310.515i	0.979521	+	1.16735i
$267$	60.1294	−	35.5517i	0.225204	−	0.133153i
$268$	56.5132	−	20.5691i	0.210870	−	0.0767504i
$269$		−	117.199i		−	0.435684i	−0.975984	−	0.217842i	$-0.930098\pi$
$269$		−	117.199i		−	0.435684i	0.975984	−	0.217842i	$-0.0699018\pi$
$270$	−61.1858	−	98.7537i	−0.226614	−	0.365754i
$271$	401.626			1.48201			0.741007	−	0.671497i	$-0.234349\pi$
$271$	401.626			1.48201			0.741007	+	0.671497i	$0.234349\pi$
$272$	18.0551	+	49.6060i	0.0663791	+	0.182375i
$273$	−457.328	+	4.74021i	−1.67519	+	0.0173634i
$274$	−44.7624	+	37.5601i	−0.163366	+	0.137081i
$275$	−101.624	+	17.9191i	−0.369542	+	0.0651603i
$276$	12.6213	−	15.3621i	0.0457294	−	0.0556597i
$277$	−165.256	−	138.666i	−0.596592	−	0.500600i	0.293756	−	0.955880i	$-0.405095\pi$
$277$	−165.256	−	138.666i	−0.596592	−	0.500600i	−0.890348	+	0.455280i	$0.849539\pi$
$278$	−173.965	−	100.439i	−0.625773	−	0.361290i
$279$	118.311	+	40.3047i	0.424054	+	0.144461i
$280$	35.4057	+	61.3244i	0.126449	+	0.219016i
$281$	−313.847	−	55.3398i	−1.11689	−	0.196939i	−0.415418	−	0.909631i	$-0.636365\pi$
$281$	−313.847	−	55.3398i	−1.11689	−	0.196939i	−0.701477	+	0.712692i	$0.747476\pi$
$282$	−172.985	+	148.234i	−0.613421	+	0.525651i
$283$	408.351	+	148.628i	1.44294	+	0.525186i	0.940609	−	0.339491i	$-0.110255\pi$
$283$	408.351	+	148.628i	1.44294	+	0.525186i	0.502328	+	0.864677i	$0.332477\pi$
$284$	−6.68980	+	18.3801i	−0.0235556	+	0.0647186i
$285$	−206.871	−	241.413i	−0.725863	−	0.847063i
$286$	−29.8212	+	169.124i	−0.104270	+	0.591344i
$287$	−406.016	+	234.413i	−1.41469	+	0.816771i
$288$	−33.5268	−	38.3139i	−0.116412	−	0.133034i
$289$	−57.4143	+	99.4445i	−0.198665	+	0.344099i
$290$	−78.6390	+	93.7183i	−0.271169	+	0.323167i
$291$	−118.779	−	97.5875i	−0.408175	−	0.335352i
$292$	45.0081	+	255.254i	0.154137	+	0.874156i
$293$	341.948	+	407.518i	1.16706	+	1.39085i	0.904793	+	0.425852i	$0.140026\pi$
$293$	341.948	+	407.518i	1.16706	+	1.39085i	0.262267	+	0.964995i	$0.415530\pi$
$294$	−0.822835	−	79.3858i	−0.00279876	−	0.270020i
$295$	−293.802	+	106.935i	−0.995938	+	0.362492i
$296$			18.8577i			0.0637084i
$297$	175.156	+	25.2979i	0.589751	+	0.0851783i
$298$	330.049			1.10755
$299$	20.9969	+	57.6884i	0.0702236	+	0.192938i
$300$	48.0758	+	81.3117i	0.160253	+	0.271039i
$301$	−206.380	+	173.173i	−0.685647	+	0.575326i
$302$	10.8616	−	1.91519i	0.0359654	−	0.00634167i
$303$	−114.886	−	305.748i	−0.379160	−	1.00907i
$304$	−106.732	−	89.5584i	−0.351091	−	0.294600i
$305$	18.9341	+	10.9316i	0.0620790	+	0.0358413i
$306$	−25.7335	+	165.993i	−0.0840964	+	0.542460i
$307$	−58.8902	−	102.001i	−0.191825	−	0.332250i	0.754030	−	0.656840i	$-0.228107\pi$
$307$	−58.8902	−	102.001i	−0.191825	−	0.332250i	−0.945855	+	0.324590i	$0.894774\pi$
$308$	−106.233	−	18.7318i	−0.344913	−	0.0608174i
$309$	318.558	+	112.221i	1.03093	+	0.363173i
$310$	56.1501	+	20.4370i	0.181129	+	0.0659256i
$311$	5.42440	−	14.9034i	0.0174418	−	0.0479210i	−0.930666	−	0.365869i	$-0.880772\pi$
$311$	5.42440	−	14.9034i	0.0174418	−	0.0479210i	0.948108	+	0.317948i	$0.102994\pi$
$312$	154.524	−	28.9012i	0.495268	−	0.0926320i
$313$	−15.1085	+	85.6847i	−0.0482700	+	0.273753i	−0.999384	−	0.0350863i	$-0.988829\pi$
$313$	−15.1085	+	85.6847i	−0.0482700	+	0.273753i	0.951114	+	0.308839i	$0.0999405\pi$
$314$	31.2316	−	18.0316i	0.0994636	−	0.0574254i
$315$	4.67039	+	225.272i	0.0148266	+	0.715149i
$316$	102.670	−	177.830i	0.324905	−	0.562752i
$317$	120.434	−	143.528i	0.379918	−	0.452769i	−0.541870	−	0.840462i	$-0.682284\pi$
$317$	120.434	−	143.528i	0.379918	−	0.452769i	0.921788	+	0.387693i	$0.126728\pi$
$318$	−68.3433	+	412.554i	−0.214916	+	1.29734i
$319$	−32.3628	−	183.539i	−0.101451	−	0.575357i
$320$	−15.6452	−	18.6452i	−0.0488913	−	0.0582663i
$321$	−329.231	−	185.559i	−1.02564	−	0.578065i
$322$	−36.2362	+	13.1889i	−0.112535	+	0.0409593i
$323$			459.692i			1.42320i
$324$	−34.7192	−	158.236i	−0.107158	−	0.488382i
$325$	−291.673			−0.897456
$326$	−102.077	−	280.455i	−0.313120	−	0.860291i
$327$	104.978	−	186.259i	0.321033	−	0.569599i
$328$	123.446	−	103.584i	0.376360	−	0.315803i
$329$	435.131	−	76.7254i	1.32259	−	0.233208i
$330$	83.4691	+	13.8274i	0.252937	+	0.0419013i
$331$	−14.7758	−	12.3984i	−0.0446400	−	0.0374574i	0.620195	−	0.784448i	$-0.287054\pi$
$331$	−14.7758	−	12.3984i	−0.0446400	−	0.0374574i	−0.664835	+	0.746990i	$0.731498\pi$
$332$	−187.640	−	108.334i	−0.565180	−	0.326307i
$333$	−28.9188	+	52.5764i	−0.0868433	+	0.157887i
$334$	−8.13353	−	14.0877i	−0.0243519	−	0.0421787i
$335$	90.0967	+	15.8865i	0.268946	+	0.0474223i
$336$	18.1539	+	97.0620i	0.0540294	+	0.288875i
$337$	389.139	+	141.635i	1.15472	+	0.420282i	0.847207	−	0.531263i	$-0.178282\pi$
$337$	389.139	+	141.635i	1.15472	+	0.420282i	0.307509	+	0.951545i	$0.400505\pi$
$338$	−84.2753	+	231.544i	−0.249335	+	0.685043i
$339$	40.7563	−	115.694i	0.120225	−	0.341280i
$340$	−13.9448	+	79.0849i	−0.0410141	+	0.232603i
$341$	−78.8317	+	45.5135i	−0.231178	+	0.133471i
$342$	−160.234	−	413.370i	−0.468520	−	1.20868i
$343$	124.615	−	215.839i	0.363308	−	0.629268i
$344$	59.5239	−	70.9379i	0.173035	−	0.206215i
$345$	28.3122	−	10.6384i	0.0820643	−	0.0308359i
$346$	−56.7334	−	321.751i	−0.163969	−	0.929917i
$347$	−72.6578	−	86.5902i	−0.209389	−	0.249540i	0.651121	−	0.758974i	$-0.274299\pi$
$347$	−72.6578	−	86.5902i	−0.209389	−	0.249540i	−0.860509	+	0.509434i	$0.829855\pi$
$348$	−146.853	+	86.8275i	−0.421992	+	0.249504i
$349$	−24.8178	+	9.03294i	−0.0711112	+	0.0258824i	−0.377331	−	0.926079i	$-0.623158\pi$
$349$	−24.8178	+	9.03294i	−0.0711112	+	0.0258824i	0.306220	+	0.951961i	$0.400936\pi$
$350$		−	183.210i		−	0.523458i
$351$	475.143	+	156.388i	1.35368	+	0.445551i
$352$	37.0783			0.105336
$353$	207.210	+	569.305i	0.586998	+	1.61276i	0.775962	+	0.630779i	$0.217265\pi$
$353$	207.210	+	569.305i	0.586998	+	1.61276i	−0.188964	+	0.981984i	$0.560513\pi$
$354$	−435.971	+	4.51885i	−1.23156	+	0.0127651i
$355$	−22.7934	+	19.1259i	−0.0642068	+	0.0538759i
$356$	45.8613	−	8.08659i	0.128824	−	0.0227151i
$357$	206.819	−	251.730i	0.579324	−	0.705127i
$358$	89.6755	+	75.2466i	0.250490	+	0.210186i
$359$	−387.446	−	223.692i	−1.07924	−	0.623097i	−0.148546	−	0.988906i	$-0.547459\pi$
$359$	−387.446	−	223.692i	−1.07924	−	0.623097i	−0.930690	+	0.365808i	$0.880793\pi$
$360$	−15.0268	−	75.9764i	−0.0417411	−	0.211046i
$361$	−426.135	−	738.088i	−1.18043	−	2.04456i
$362$	231.483	+	40.8166i	0.639455	+	0.112753i
$363$	177.771	−	152.335i	0.489728	−	0.419657i
$364$	−286.514	−	104.282i	−0.787125	−	0.286490i
$365$	−134.855	+	370.510i	−0.369465	+	1.01510i
$366$	19.8382	+	23.1507i	0.0542028	+	0.0632532i
$367$	25.2806	−	143.373i	0.0688844	−	0.390663i	−0.930800	−	0.365529i	$-0.880888\pi$
$367$	25.2806	−	143.373i	0.0688844	−	0.390663i	0.999684	−	0.0251331i	$-0.00800095\pi$
$368$	11.4788	−	6.62731i	0.0311925	−	0.0180090i
$369$	503.024	−	99.4891i	1.36321	−	0.269618i
$370$	−14.3434	+	24.8435i	−0.0387660	+	0.0671446i
$371$	521.345	−	621.314i	1.40524	−	1.67470i
$372$	64.3826	+	52.8960i	0.173071	+	0.142194i
$373$	37.2253	+	211.115i	0.0997998	+	0.565993i	0.993170	+	0.116672i	$0.0372227\pi$
$373$	37.2253	+	211.115i	0.0997998	+	0.565993i	−0.893371	+	0.449320i	$0.851666\pi$
$374$	−78.6349	−	93.7134i	−0.210254	−	0.250571i
$375$	3.85434	+	371.860i	0.0102782	+	0.991627i
$376$	−142.714	+	51.9435i	−0.379558	+	0.138148i
$377$		−	526.777i		−	1.39729i
$378$	−98.2333	+	298.454i	−0.259876	+	0.789561i
$379$	253.546			0.668988			0.334494	−	0.942398i	$-0.391435\pi$
$379$	253.546			0.668988			0.334494	+	0.942398i	$0.391435\pi$
$380$	−72.4910	−	199.167i	−0.190766	−	0.524125i
$381$	18.4813	+	31.2578i	0.0485074	+	0.0820416i
$382$	−135.635	+	113.811i	−0.355065	+	0.297935i
$383$	−552.793	+	97.4722i	−1.44332	+	0.254497i	−0.839820	−	0.542864i	$-0.817340\pi$
$383$	−552.793	+	97.4722i	−1.44332	+	0.254497i	−0.603502	+	0.797361i	$0.706229\pi$
$384$	−11.9385	−	31.7722i	−0.0310898	−	0.0827401i
$385$	−125.706	−	105.480i	−0.326509	−	0.273974i
$386$	−113.009	−	65.2456i	−0.292769	−	0.169030i
$387$	274.742	−	106.497i	0.709927	−	0.275187i
$388$	−51.2421	−	88.7539i	−0.132067	−	0.228747i
$389$	−37.4969	−	6.61172i	−0.0963931	−	0.0169967i	0.125244	−	0.992126i	$-0.460029\pi$
$389$	−37.4969	−	6.61172i	−0.0963931	−	0.0169967i	−0.221637	+	0.975129i	$0.571140\pi$
$390$	225.555	+	79.4578i	0.578347	+	0.203738i
$391$	−41.0943	−	14.9571i	−0.105101	−	0.0382535i
$392$	18.1020	−	49.7348i	0.0461786	−	0.126875i
$393$	219.078	−	40.9749i	0.557449	−	0.104262i
$394$	−9.66497	+	54.8128i	−0.0245304	+	0.139119i
$395$	270.519	−	156.184i	0.684858	−	0.395403i
$396$	103.377	+	56.8606i	0.261052	+	0.143587i
$397$	−382.127	+	661.864i	−0.962538	+	1.66716i	−0.246448	+	0.969156i	$0.579263\pi$
$397$	−382.127	+	661.864i	−0.962538	+	1.66716i	−0.716090	+	0.698008i	$0.754070\pi$
$398$	−173.275	+	206.502i	−0.435365	+	0.518848i
$399$	−140.531	+	848.311i	−0.352207	+	2.12609i
$400$	10.9353	+	62.0172i	0.0273383	+	0.155043i
$401$	10.0249	+	11.9472i	0.0249998	+	0.0297936i	0.778399	−	0.627769i	$-0.216032\pi$
$401$	10.0249	+	11.9472i	0.0249998	+	0.0297936i	−0.753400	+	0.657563i	$0.771587\pi$
$402$	111.140	+	62.6396i	0.276467	+	0.155820i
$403$	−241.773	+	87.9980i	−0.599932	+	0.218357i
$404$		−	217.746i		−	0.538976i
$405$	74.6164	−	234.871i	0.184238	−	0.579928i
$406$	330.888			0.814995
$407$	−14.9465	−	41.0652i	−0.0367236	−	0.100897i
$408$	−54.9837	+	97.5558i	−0.134764	+	0.239107i
$409$	−346.354	+	290.625i	−0.846830	+	0.710575i	−0.959089	−	0.283104i	$-0.908636\pi$
$409$	−346.354	+	290.625i	−0.846830	+	0.710575i	0.112259	+	0.993679i	$0.464191\pi$
$410$	241.417	−	42.5684i	0.588823	−	0.103825i
$411$	−122.289	−	20.2583i	−0.297539	−	0.0492901i
$412$	172.486	+	144.733i	0.418656	+	0.351294i
$413$	732.335	+	422.814i	1.77321	+	1.02376i
$414$	42.1669	−	0.874215i	0.101852	−	0.00211163i
$415$	−164.800	−	285.442i	−0.397109	−	0.687813i
$416$	103.210	+	18.1987i	0.248101	+	0.0437469i
$417$	−78.3413	−	418.862i	−0.187869	−	1.00446i
$418$	303.406	+	110.431i	0.725852	+	0.264188i
$419$	130.522	−	358.605i	0.311507	−	0.855859i	−0.680846	−	0.732427i	$-0.738388\pi$
$419$	130.522	−	358.605i	0.311507	−	0.855859i	0.992353	−	0.123432i	$-0.0393902\pi$
$420$	−49.9103	+	141.679i	−0.118834	+	0.337332i
$421$	−18.0874	+	102.579i	−0.0429629	+	0.243655i	−0.998725	−	0.0504869i	$-0.983923\pi$
$421$	−18.0874	+	102.579i	−0.0429629	+	0.243655i	0.955762	+	0.294142i	$0.0950338\pi$
$422$	−93.6891	+	54.0914i	−0.222012	+	0.128179i
$423$	−477.551	−	74.0338i	−1.12896	−	0.175021i
$424$	−139.392	+	241.434i	−0.328755	+	0.569420i
$425$	133.554	−	159.163i	0.314245	−	0.374502i
$426$	−38.8409	+	14.5946i	−0.0911757	+	0.0342595i
$427$	−10.2682	−	58.2339i	−0.0240473	−	0.136379i
$428$	−161.949	−	193.004i	−0.378386	−	0.450943i
$429$	−313.590	+	185.411i	−0.730978	+	0.432193i
$430$	132.374	−	48.1803i	0.307847	−	0.112047i
$431$			754.466i			1.75050i	0.483669	+	0.875251i	$0.339304\pi$
$431$			754.466i			1.75050i	−0.483669	+	0.875251i	$0.660696\pi$
$432$	15.4383	−	106.891i	0.0357369	−	0.247433i
$433$	−22.8890			−0.0528615			−0.0264308	−	0.999651i	$-0.508414\pi$
$433$	−22.8890			−0.0528615			−0.0264308	+	0.999651i	$0.508414\pi$
$434$	−55.2747	−	151.866i	−0.127361	−	0.349922i
$435$	−259.510	+	2.68982i	−0.596574	+	0.00618349i
$436$	109.190	−	91.6210i	0.250435	−	0.210140i
$437$	113.668	−	20.0427i	0.260110	−	0.0458643i
$438$	−349.038	+	424.833i	−0.796891	+	0.969938i
$439$	−345.329	−	289.765i	−0.786625	−	0.660057i	0.158282	−	0.987394i	$-0.449404\pi$
$439$	−345.329	−	289.765i	−0.786625	−	0.660057i	−0.944908	+	0.327337i	$0.893849\pi$
$440$	48.8477	+	28.2022i	0.111017	+	0.0640959i
$441$	126.739	−	110.904i	0.287391	−	0.251483i
$442$	−172.890	−	299.453i	−0.391153	−	0.677497i
$443$	382.296	+	67.4092i	0.862972	+	0.152165i	0.587579	−	0.809167i	$-0.300081\pi$
$443$	382.296	+	67.4092i	0.862972	+	0.152165i	0.275393	+	0.961332i	$0.411192\pi$
$444$	−30.3761	+	26.0298i	−0.0684146	+	0.0586257i
$445$	66.5694	+	24.2293i	0.149594	+	0.0544478i
$446$	24.0585	−	66.1002i	0.0539428	−	0.148207i
$447$	455.576	+	531.645i	1.01919	+	1.18936i
$448$	−11.4313	+	64.8299i	−0.0255162	+	0.144710i
$449$	−93.1858	+	53.8008i	−0.207541	+	0.119824i	−0.600168	−	0.799874i	$-0.704900\pi$
$449$	−93.1858	+	53.8008i	−0.207541	+	0.119824i	0.392627	+	0.919698i	$0.371566\pi$
$450$	−64.6169	+	189.678i	−0.143593	+	0.421506i
$451$	−186.721	+	323.410i	−0.414015	+	0.717095i
$452$	52.5641	−	62.6435i	0.116292	−	0.138592i
$453$	18.0775	+	14.8523i	0.0399062	+	0.0327865i
$454$	74.4558	+	422.260i	0.164000	+	0.930088i
$455$	−298.140	−	355.310i	−0.655253	−	0.780901i
$456$	−3.06331	−	295.544i	−0.00671779	−	0.648122i
$457$	170.310	−	61.9876i	0.372669	−	0.135640i	−0.148894	−	0.988853i	$-0.547571\pi$
$457$	170.310	−	61.9876i	0.372669	−	0.135640i	0.521563	+	0.853213i	$0.325349\pi$
$458$		−	27.5577i		−	0.0601697i
$459$	−302.903	+	187.673i	−0.659918	+	0.408873i
$460$	20.1633			0.0438332
$461$	−200.952	−	552.110i	−0.435904	−	1.19764i	−0.942134	−	0.335237i	$-0.891183\pi$
$461$	−200.952	−	552.110i	−0.435904	−	1.19764i	0.506230	−	0.862399i	$-0.331039\pi$
$462$	−116.463	−	196.977i	−0.252085	−	0.426357i
$463$	−37.7513	+	31.6771i	−0.0815363	+	0.0684170i	−0.682645	−	0.730750i	$-0.739170\pi$
$463$	−37.7513	+	31.6771i	−0.0815363	+	0.0684170i	0.601109	+	0.799167i	$0.294726\pi$
$464$	−112.006	+	19.7498i	−0.241393	+	0.0425642i
$465$	44.5855	+	118.657i	0.0958828	+	0.255175i
$466$	−111.753	−	93.7718i	−0.239813	−	0.201227i
$467$	−614.382	−	354.714i	−1.31559	−	0.759558i	−0.332577	−	0.943076i	$-0.607918\pi$
$467$	−614.382	−	354.714i	−1.31559	−	0.759558i	−0.983016	+	0.183518i	$0.941252\pi$
$468$	259.848	+	209.015i	0.555230	+	0.446613i
$469$	−123.719	−	214.288i	−0.263794	−	0.456905i
$470$	−227.523	−	40.1184i	−0.484091	−	0.0853583i
$471$	72.1552	+	25.4185i	0.153196	+	0.0539672i
$472$	−273.134	−	99.4126i	−0.578674	−	0.210620i
$473$	−73.3965	+	201.655i	−0.155172	+	0.426332i
$474$	428.167	−	80.0818i	0.903306	−	0.168949i
$475$	−95.2248	+	540.047i	−0.200473	+	1.13694i
$476$	188.098	−	108.598i	0.395163	−	0.228147i
$477$	−758.880	+	459.372i	−1.59094	+	0.963043i
$478$	149.084	−	258.220i	0.311890	−	0.540210i
$479$	−271.827	+	323.951i	−0.567489	+	0.676308i	−0.971114	−	0.238617i	$-0.923306\pi$
$479$	−271.827	+	323.951i	−0.567489	+	0.676308i	0.403624	+	0.914925i	$0.367750\pi$
$480$	8.43833	−	50.9379i	0.0175799	−	0.106121i
$481$	−21.4491	−	121.644i	−0.0445927	−	0.252898i
$482$	56.2531	+	67.0399i	0.116708	+	0.139087i
$483$	−71.2625	−	40.1645i	−0.147542	−	0.0831562i
$484$	146.663	−	53.3808i	0.303022	−	0.110291i
$485$		−	155.902i		−	0.321446i
$486$	206.963	−	274.343i	0.425850	−	0.564492i
$487$	444.129			0.911969			0.455985	−	0.889988i	$-0.349287\pi$
$487$	444.129			0.911969			0.455985	+	0.889988i	$0.349287\pi$
$488$	6.95164	+	19.0995i	0.0142452	+	0.0391382i
$489$	310.858	−	551.546i	0.635702	−	1.12791i
$490$	61.6769	−	51.7530i	0.125871	−	0.105618i
$491$	399.029	−	70.3596i	0.812686	−	0.143298i	0.248166	−	0.968718i	$-0.420172\pi$
$491$	399.029	−	70.3596i	0.812686	−	0.143298i	0.564520	+	0.825419i	$0.309061\pi$
$492$	337.249	+	55.8684i	0.685465	+	0.113554i
$493$	287.458	+	241.206i	0.583079	+	0.489261i
$494$	790.351	+	456.309i	1.59990	+	0.923703i
$495$	92.9414	+	153.539i	0.187760	+	0.310179i
$496$	27.7751	+	48.1079i	0.0559982	+	0.0969917i
$497$	79.2533	+	13.9745i	0.159463	+	0.0281177i
$498$	−84.4995	−	451.787i	−0.169678	−	0.907203i
$499$	−545.267	−	198.461i	−1.09272	−	0.397718i	−0.268092	−	0.963393i	$-0.586393\pi$
$499$	−545.267	−	198.461i	−1.09272	−	0.397718i	−0.824628	+	0.565676i	$0.808615\pi$
$500$	−84.7937	+	232.969i	−0.169587	+	0.465938i
$501$	11.4656	−	32.5472i	0.0228854	−	0.0649644i
$502$	28.1437	−	159.611i	0.0560631	−	0.317949i
$503$	−284.955	+	164.519i	−0.566510	+	0.327075i	−0.755754	−	0.654855i	$-0.772730\pi$
$503$	−284.955	+	164.519i	−0.566510	+	0.327075i	0.189244	+	0.981930i	$0.439396\pi$
$504$	−131.290	+	163.220i	−0.260495	+	0.323849i
$505$	165.621	−	286.864i	0.327962	−	0.568047i
$506$	−19.7440	+	23.5299i	−0.0390197	+	0.0465019i
$507$	−489.301	+	183.856i	−0.965090	+	0.362635i
$508$	4.20376	+	23.8407i	0.00827511	+	0.0469305i
$509$	−346.327	−	412.736i	−0.680406	−	0.810876i	0.309754	−	0.950817i	$-0.399753\pi$
$509$	−346.327	−	412.736i	−0.680406	−	0.810876i	−0.990160	+	0.139941i	$0.955309\pi$
$510$	−146.639	+	86.7007i	−0.287527	+	0.170001i
$511$	1002.10	−	364.734i	1.96105	−	0.713765i
$512$		−	22.6274i		−	0.0441942i
$513$	444.684	−	828.692i	0.866831	−	1.61538i
$514$	−250.546			−0.487444
$515$	117.151	+	321.869i	0.227477	+	0.624989i
$516$	196.430	−	2.03600i	0.380678	−	0.00394573i
$517$	269.608	−	226.228i	0.521486	−	0.437579i
$518$	76.4089	−	13.4730i	0.147508	−	0.0260096i
$519$	439.968	−	535.509i	0.847723	−	1.03181i
$520$	122.129	+	102.478i	0.234863	+	0.197073i
$521$	258.670	+	149.343i	0.496488	+	0.286647i	0.727262	−	0.686360i	$-0.240793\pi$
$521$	258.670	+	149.343i	0.496488	+	0.286647i	−0.230774	+	0.973007i	$0.574126\pi$
$522$	−342.568	−	116.702i	−0.656260	−	0.223566i
$523$	416.746	+	721.825i	0.796837	+	1.38016i	0.921666	+	0.387984i	$0.126828\pi$
$523$	416.746	+	721.825i	0.796837	+	1.38016i	−0.124829	+	0.992178i	$0.539838\pi$
$524$	146.327	+	25.8014i	0.279250	+	0.0492393i
$525$	295.116	−	252.890i	0.562126	−	0.481696i
$526$	92.1966	+	33.5568i	0.175279	+	0.0637962i
$527$	62.6853	−	172.226i	0.118947	−	0.326805i
$528$	51.1802	+	59.7259i	0.0969321	+	0.113117i
$529$	89.9532	−	510.150i	0.170044	−	0.964366i
$530$	−367.276	+	212.047i	−0.692974	+	0.400089i
$531$	−609.062	−	696.027i	−1.14701	−	1.31079i
$532$	−286.624	+	496.448i	−0.538767	+	0.933172i
$533$	−678.486	+	808.588i	−1.27296	+	1.51705i
$534$	76.3296	+	62.7115i	0.142939	+	0.117437i
$535$	−66.5542	−	377.448i	−0.124400	−	0.705509i
$536$	54.6697	+	65.1528i	0.101996	+	0.121554i
$537$	2.57379	+	248.315i	0.00479290	+	0.462411i
$538$	155.749	−	56.6880i	0.289496	−	0.105368i
$539$			122.652i			0.227555i
$540$	101.641	−	129.078i	0.188225	−	0.239033i
$541$	639.685			1.18241			0.591206	−	0.806521i	$-0.298652\pi$
$541$	639.685			1.18241			0.591206	+	0.806521i	$0.298652\pi$
$542$	194.262	+	533.731i	0.358417	+	0.984743i
$543$	253.774	+	429.214i	0.467356	+	0.790449i
$544$	−57.1896	+	47.9878i	−0.105128	+	0.0882129i
$545$	213.537	−	37.6523i	0.391811	−	0.0690868i
$546$	−227.504	−	605.462i	−0.416674	−	1.10890i
$547$	310.339	+	260.405i	0.567347	+	0.476060i	0.880764	−	0.473555i	$-0.157030\pi$
$547$	310.339	+	260.405i	0.567347	+	0.476060i	−0.313418	+	0.949615i	$0.601474\pi$
$548$	−71.5656	−	41.3184i	−0.130594	−	0.0753986i
$549$	−9.90800	+	63.9110i	−0.0180474	+	0.116414i
$550$	−72.9677	−	126.384i	−0.132669	−	0.229789i
$551$	−975.353	−	171.981i	−1.77015	−	0.312125i
$552$	26.5199	+	9.34232i	0.0480433	+	0.0169245i
$553$	−793.896	−	288.954i	−1.43562	−	0.522522i
$554$	104.345	−	286.685i	0.188348	−	0.517481i
$555$	−59.8167	+	11.1877i	−0.107778	+	0.0201581i
$556$	49.3305	−	279.767i	0.0887240	−	0.503179i
$557$	810.145	−	467.737i	1.45448	−	0.839744i	0.455748	−	0.890109i	$-0.349372\pi$
$557$	810.145	−	467.737i	1.45448	−	0.839744i	0.998731	+	0.0503648i	$0.0160384\pi$
$558$	3.66384	+	176.722i	0.00656602	+	0.316706i
$559$	−303.280	+	525.297i	−0.542541	+	0.939709i
$560$	−64.3703	+	76.7135i	−0.114947	+	0.136988i
$561$	42.4122	−	256.021i	0.0756011	−	0.456365i
$562$	−78.2623	−	443.847i	−0.139257	−	0.789764i
$563$	82.3153	+	98.0996i	0.146208	+	0.174244i	0.834178	−	0.551495i	$-0.185942\pi$
$563$	82.3153	+	98.0996i	0.146208	+	0.174244i	−0.687970	+	0.725739i	$0.741498\pi$
$564$	−280.663	−	158.185i	−0.497629	−	0.280470i
$565$	116.896	−	42.5468i	0.206896	−	0.0753041i
$566$			614.558i			1.08579i
$567$	−616.346	+	253.730i	−1.08703	+	0.447495i
$568$	−27.6616			−0.0486999
$569$	−10.7972	−	29.6651i	−0.0189758	−	0.0521355i	0.929843	−	0.367956i	$-0.119942\pi$
$569$	−10.7972	−	29.6651i	−0.0189758	−	0.0521355i	−0.948819	+	0.315821i	$0.897720\pi$
$570$	220.759	−	391.685i	0.387296	−	0.687167i
$571$	323.739	−	271.649i	0.566968	−	0.475743i	−0.313670	−	0.949532i	$-0.601559\pi$
$571$	323.739	−	271.649i	0.566968	−	0.475743i	0.880638	+	0.473789i	$0.157114\pi$
$572$	−239.178	+	42.1735i	−0.418143	+	0.0737300i
$573$	−370.549	−	61.3848i	−0.646682	−	0.107129i
$574$	−507.904	−	426.182i	−0.884849	−	0.742477i
$575$	−45.1793	−	26.0843i	−0.0785726	−	0.0453639i
$576$	34.6998	−	63.0866i	0.0602427	−	0.109525i
$577$	42.1505	+	73.0068i	0.0730511	+	0.126528i	0.900237	−	0.435400i	$-0.143393\pi$
$577$	42.1505	+	73.0068i	0.0730511	+	0.126528i	−0.827186	+	0.561928i	$0.810060\pi$
$578$	−159.925	−	28.1991i	−0.276687	−	0.0487874i
$579$	−50.8911	−	272.096i	−0.0878948	−	0.469941i
$580$	−162.582	−	59.1748i	−0.280313	−	0.102026i
$581$	−304.895	+	837.691i	−0.524776	+	1.44181i
$582$	72.2344	−	205.050i	0.124114	−	0.352320i
$583$	112.186	−	636.238i	0.192429	−	1.09132i
$584$	−317.443	+	183.276i	−0.543567	+	0.313829i
$585$	183.349	+	473.004i	0.313417	+	0.808553i
$586$	−376.165	+	651.537i	−0.641919	+	1.11184i
$587$	−474.170	+	565.094i	−0.807786	+	0.962682i	−0.999825	−	0.0187054i	$-0.994046\pi$
$587$	−474.170	+	565.094i	−0.807786	+	0.962682i	0.192039	+	0.981387i	$0.438490\pi$
$588$	105.100	−	39.4916i	0.178741	−	0.0671625i
$589$	83.9991	+	476.383i	0.142613	+	0.808799i
$590$	−284.218	−	338.717i	−0.481725	−	0.574097i
$591$	−101.634	+	60.0912i	−0.171969	+	0.101677i
$592$	−25.0605	+	9.12127i	−0.0423319	+	0.0154075i
$593$		−	361.460i		−	0.609545i	−0.952425	−	0.304773i	$-0.901420\pi$
$593$		−	361.460i		−	0.609545i	0.952425	−	0.304773i	$-0.0985804\pi$
$594$	51.1020	+	245.006i	0.0860304	+	0.412468i
$595$	330.405			0.555302
$596$	159.641	+	438.611i	0.267855	+	0.735925i
$597$	−571.811	+	5.92683i	−0.957807	+	0.00992768i
$598$	−66.5077	+	55.8066i	−0.111217	+	0.0933220i
$599$	201.974	−	35.6135i	0.337185	−	0.0594549i	−0.00249203	−	0.999997i	$-0.500793\pi$
$599$	201.974	−	35.6135i	0.337185	−	0.0594549i	0.339677	+	0.940542i	$0.389682\pi$
$600$	−84.8034	+	103.219i	−0.141339	+	0.172031i
$601$	726.408	+	609.528i	1.20866	+	1.01419i	0.999339	+	0.0363443i	$0.0115713\pi$
$601$	726.408	+	609.528i	1.20866	+	1.01419i	0.209326	+	0.977846i	$0.432873\pi$
$602$	−329.958	−	190.501i	−0.548103	−	0.316448i
$603$	52.5087	+	265.488i	0.0870791	+	0.440278i
$604$	7.79876	+	13.5079i	0.0129119	+	0.0223640i
$605$	233.818	+	41.2285i	0.386477	+	0.0681463i
$606$	350.747	−	300.561i	0.578791	−	0.495976i
$607$	382.467	+	139.207i	0.630094	+	0.229335i	0.637272	−	0.770639i	$-0.280063\pi$
$607$	382.467	+	139.207i	0.630094	+	0.229335i	−0.00717822	+	0.999974i	$0.502285\pi$
$608$	67.3916	−	185.157i	0.110841	−	0.304534i
$609$	456.734	+	532.996i	0.749973	+	0.875199i
$610$	−5.36907	+	30.4495i	−0.00880176	+	0.0499173i
$611$	861.511	−	497.393i	1.41000	−	0.814064i
$612$	−233.039	+	46.0910i	−0.380783	+	0.0753120i
$613$	−325.258	+	563.364i	−0.530601	+	0.919028i	0.468761	+	0.883325i	$0.344700\pi$
$613$	−325.258	+	563.364i	−0.530601	+	0.919028i	−0.999362	+	0.0357032i	$0.988633\pi$
$614$	107.067	−	127.597i	0.174376	−	0.207813i
$615$	401.804	+	330.118i	0.653340	+	0.536777i
$616$	−26.4907	−	150.236i	−0.0430044	−	0.243890i
$617$	−72.2760	−	86.1351i	−0.117141	−	0.139603i	0.704287	−	0.709915i	$-0.251267\pi$
$617$	−72.2760	−	86.1351i	−0.117141	−	0.139603i	−0.821428	+	0.570312i	$0.806822\pi$
$618$	4.95054	+	477.621i	0.00801059	+	0.772849i
$619$	−595.574	+	216.771i	−0.962155	+	0.350196i	−0.774878	−	0.632111i	$-0.782188\pi$
$619$	−595.574	+	216.771i	−0.962155	+	0.350196i	−0.187277	+	0.982307i	$0.559966\pi$
$620$			84.5044i			0.136297i
$621$	59.6123	+	66.7160i	0.0959941	+	0.107433i
$622$	22.4293			0.0360599
$623$	−65.5316	−	180.047i	−0.105187	−	0.288999i
$624$	113.149	+	191.371i	0.181329	+	0.306685i
$625$	12.5974	−	10.5704i	0.0201558	−	0.0169127i
$626$	−121.176	+	21.3667i	−0.193573	+	0.0341321i
$627$	240.917	+	641.159i	0.384238	+	1.02258i
$628$	39.0690	+	32.7828i	0.0622118	+	0.0522019i
$629$	76.2013	+	43.9949i	0.121147	+	0.0699441i
$630$	−297.111	+	115.168i	−0.471604	+	0.182807i
$631$	−320.988	−	555.967i	−0.508697	−	0.881089i	−0.999949	−	0.0100717i	$-0.996794\pi$
$631$	−320.988	−	555.967i	−0.508697	−	0.881089i	0.491252	−	0.871017i	$-0.336539\pi$
$632$	285.983	+	50.4265i	0.452504	+	0.0797887i
$633$	−216.452	−	76.2510i	−0.341947	−	0.120460i
$634$	248.991	+	90.6251i	0.392730	+	0.142942i
$635$	−12.5954	+	34.6056i	−0.0198353	+	0.0544970i
$636$	−581.311	+	108.725i	−0.914010	+	0.170951i
$637$	−60.1998	+	341.410i	−0.0945052	+	0.535966i
$638$	228.256	−	131.784i	0.357768	−	0.206557i
$639$	−77.1221	−	42.4198i	−0.120692	−	0.0663847i
$640$	17.2107	−	29.8098i	0.0268917	−	0.0465778i
$641$	114.585	−	136.557i	0.178759	−	0.213037i	−0.669223	−	0.743062i	$-0.733373\pi$
$641$	114.585	−	136.557i	0.178759	−	0.213037i	0.847982	+	0.530025i	$0.177817\pi$
$642$	87.3483	−	527.277i	0.136057	−	0.821304i
$643$	−98.7806	−	560.213i	−0.153625	−	0.871248i	−0.960032	−	0.279889i	$-0.909702\pi$
$643$	−98.7806	−	560.213i	−0.153625	−	0.871248i	0.806408	−	0.591360i	$-0.201409\pi$
$644$	−35.0541	−	41.7759i	−0.0544319	−	0.0648694i
$645$	260.329	+	146.725i	0.403611	+	0.227480i
$646$	−610.897	+	222.348i	−0.945661	+	0.344192i
$647$		−	331.991i		−	0.513124i	−0.966528	−	0.256562i	$-0.917410\pi$
$647$		−	331.991i		−	0.513124i	0.966528	−	0.256562i	$-0.0825898\pi$
$648$	193.490	−	122.676i	0.298596	−	0.189315i
$649$	673.580			1.03787
$650$	−141.079	−	387.612i	−0.217045	−	0.596326i
$651$	168.329	−	298.662i	0.258571	−	0.458774i
$652$	323.330	−	271.306i	0.495905	−	0.416114i
$653$	867.467	−	152.958i	1.32843	−	0.234239i	0.536011	−	0.844211i	$-0.319930\pi$
$653$	867.467	−	152.958i	1.32843	−	0.234239i	0.792423	+	0.609972i	$0.208819\pi$
$654$	298.301	+	49.4163i	0.456118	+	0.0755601i
$655$	173.149	+	145.289i	0.264350	+	0.221816i
$656$	197.364	+	113.948i	0.300860	+	0.173702i
$657$	−1166.11	+	24.1761i	−1.77490	+	0.0367977i
$658$	312.431	+	541.146i	0.474819	+	0.822410i
$659$	−956.120	−	168.590i	−1.45087	−	0.255827i	−0.607994	−	0.793942i	$-0.708025\pi$
$659$	−956.120	−	168.590i	−1.45087	−	0.255827i	−0.842871	+	0.538115i	$0.819137\pi$
$660$	21.9975	+	117.612i	0.0333295	+	0.178201i
$661$	207.696	+	75.5952i	0.314215	+	0.114365i	0.494313	−	0.869284i	$-0.335419\pi$
$661$	207.696	+	75.5952i	0.314215	+	0.114365i	−0.180099	+	0.983649i	$0.557642\pi$
$662$	9.32965	−	25.6330i	0.0140931	−	0.0387205i
$663$	243.717	−	691.835i	0.367598	−	1.04349i
$664$	53.2083	−	301.759i	0.0801330	−	0.454457i
$665$	−755.209	+	436.020i	−1.13565	+	0.655669i
$666$	−83.8579	−	13.0003i	−0.125913	−	0.0195200i
$667$	47.1096	−	81.5962i	0.0706291	−	0.122333i
$668$	14.7874	−	17.6229i	0.0221368	−	0.0263816i
$669$	139.683	−	52.4863i	0.208794	−	0.0784549i
$670$	22.4669	+	127.416i	0.0335327	+	0.190173i
$671$	−30.2763	−	36.0819i	−0.0451211	−	0.0537733i
$672$	−120.207	+	71.0730i	−0.178880	+	0.105763i
$673$	−484.870	+	176.478i	−0.720461	+	0.262226i	−0.676121	−	0.736790i	$-0.736340\pi$
$673$	−484.870	+	176.478i	−0.720461	+	0.262226i	−0.0443393	+	0.999017i	$0.514118\pi$
$674$			585.645i			0.868909i
$675$	−394.726	+	157.732i	−0.584780	+	0.233677i
$676$	−348.469			−0.515486
$677$	−11.8258	−	32.4910i	−0.0174679	−	0.0479927i	0.930652	−	0.365905i	$-0.119240\pi$
$677$	−11.8258	−	32.4910i	−0.0174679	−	0.0479927i	−0.948120	+	0.317912i	$0.897018\pi$
$678$	173.462	−	1.79794i	0.255844	−	0.00265183i
$679$	−323.009	+	271.037i	−0.475713	+	0.399171i
$680$	−111.843	+	19.7209i	−0.164475	+	0.0290014i
$681$	−577.405	+	702.791i	−0.847878	+	1.03200i
$682$	−98.6142	−	82.7471i	−0.144596	−	0.121330i
$683$	502.287	+	289.996i	0.735413	+	0.424591i	0.820399	−	0.571791i	$-0.193751\pi$
$683$	502.287	+	289.996i	0.735413	+	0.424591i	−0.0849858	+	0.996382i	$0.527085\pi$
$684$	471.835	−	412.882i	0.689817	−	0.603628i
$685$	−62.8547	−	108.868i	−0.0917587	−	0.158931i
$686$	347.109	+	61.2046i	0.505989	+	0.0892195i
$687$	44.3902	−	38.0387i	0.0646145	−	0.0553693i
$688$	123.062	+	44.7910i	0.178870	+	0.0651032i
$689$	624.554	−	1715.95i	0.906465	−	2.49049i
$690$	27.8319	+	32.4791i	0.0403361	+	0.0470712i
$691$	−67.3628	+	382.033i	−0.0974859	+	0.552870i	0.896471	+	0.443102i	$0.146122\pi$
$691$	−67.3628	+	382.033i	−0.0974859	+	0.552870i	−0.993957	+	0.109768i	$0.964989\pi$
$692$	400.142	−	231.022i	0.578240	−	0.333847i
$693$	156.534	−	459.493i	0.225879	−	0.663048i
$694$	79.9282	−	138.440i	0.115170	−	0.199481i
$695$	277.784	−	331.050i	0.399689	−	0.476331i
$696$	−186.419	−	153.160i	−0.267843	−	0.220057i
$697$	−130.568	−	740.488i	−0.187329	−	1.06239i
$698$	−24.0082	−	28.6119i	−0.0343957	−	0.0409912i
$699$	−3.20743	−	309.448i	−0.00458860	−	0.442701i
$700$	243.473	−	88.6170i	0.347819	−	0.126596i
$701$		−	1037.76i		−	1.48040i	−0.672387	−	0.740200i	$-0.734731\pi$
$701$		−	1037.76i		−	1.48040i	0.672387	−	0.740200i	$-0.265269\pi$
$702$	21.9928	+	707.073i	0.0313287	+	1.00723i
$703$	−232.232			−0.330344
$704$	17.9344	+	49.2743i	0.0254750	+	0.0699919i
$705$	−249.433	−	421.871i	−0.353806	−	0.598399i
$706$	−656.339	+	550.734i	−0.929659	+	0.780077i
$707$	−882.280	+	155.570i	−1.24792	+	0.220042i
$708$	−216.880	−	577.188i	−0.306328	−	0.815237i
$709$	−818.303	−	686.637i	−1.15416	−	0.968459i	−0.154356	−	0.988015i	$-0.549330\pi$
$709$	−818.303	−	686.637i	−1.15416	−	0.968459i	−0.999809	+	0.0195564i	$0.993775\pi$
$710$	−36.4419	−	21.0397i	−0.0513266	−	0.0296334i
$711$	720.007	+	579.155i	1.01267	+	0.814564i
$712$	32.9291	+	57.0349i	0.0462488	+	0.0801052i
$713$	−45.3195	−	7.99104i	−0.0635616	−	0.0112076i
$714$	434.567	+	153.088i	0.608637	+	0.214408i
$715$	−347.176	−	126.362i	−0.485560	−	0.176730i
$716$	−56.6221	+	155.568i	−0.0790812	+	0.217274i
$717$	621.727	−	116.284i	0.867122	−	0.162181i
$718$	109.867	−	623.084i	0.153017	−	0.867805i
$719$	642.439	−	370.913i	0.893518	−	0.515873i	0.0184263	−	0.999830i	$-0.494134\pi$
$719$	642.439	−	370.913i	0.893518	−	0.515873i	0.875092	+	0.483957i	$0.160801\pi$
$720$	93.6987	−	56.7185i	0.130137	−	0.0787757i
$721$	463.206	−	802.296i	0.642449	−	1.11276i
$722$	774.747	−	923.307i	1.07306	−	1.27882i
$723$	−30.3405	+	183.150i	−0.0419647	+	0.253319i
$724$	57.7234	+	327.366i	0.0797285	+	0.452163i
$725$	287.740	+	342.915i	0.396883	+	0.472986i
$726$	288.429	+	162.562i	0.397285	+	0.223915i
$727$	−148.771	+	54.1481i	−0.204637	+	0.0744816i	−0.442305	−	0.896865i	$-0.645839\pi$
$727$	−148.771	+	54.1481i	−0.204637	+	0.0744816i	0.237668	+	0.971346i	$0.423617\pi$
$728$		−	431.196i		−	0.592302i
$729$	727.591	−	45.3057i	0.998067	−	0.0621478i
$730$	−557.608			−0.763847
$731$	−147.781	−	406.026i	−0.202163	−	0.555438i
$732$	−21.1700	+	37.5613i	−0.0289208	+	0.0513132i
$733$	−419.711	+	352.179i	−0.572594	+	0.480463i	−0.882505	−	0.470302i	$-0.844145\pi$
$733$	−419.711	+	352.179i	−0.572594	+	0.480463i	0.309912	+	0.950765i	$0.399700\pi$
$734$	202.760	−	35.7521i	0.276240	−	0.0487086i
$735$	168.498	+	27.9133i	0.229250	+	0.0379773i
$736$	14.3594	+	12.0490i	0.0195101	+	0.0163709i
$737$	−170.690	−	98.5482i	−0.231602	−	0.133715i
$738$	375.521	+	620.359i	0.508836	+	0.840595i
$739$	264.592	+	458.286i	0.358040	+	0.620143i	0.987633	−	0.156781i	$-0.0501118\pi$
$739$	264.592	+	458.286i	0.358040	+	0.620143i	−0.629593	+	0.776925i	$0.716778\pi$
$740$	−39.9529	−	7.04478i	−0.0539904	−	0.00951997i
$741$	355.917	+	1902.96i	0.480320	+	2.56809i
$742$	1077.85	+	392.305i	1.45263	+	0.528713i
$743$	−75.5254	+	207.504i	−0.101649	+	0.279279i	−0.980084	−	0.198583i	$-0.936366\pi$
$743$	−75.5254	+	207.504i	−0.101649	+	0.279279i	0.878435	+	0.477862i	$0.158588\pi$
$744$	−39.1537	+	111.145i	−0.0526260	+	0.149388i
$745$	−123.298	+	699.260i	−0.165501	+	0.938605i
$746$	−262.551	+	151.584i	−0.351945	+	0.203196i
$747$	611.105	−	759.727i	0.818078	−	1.01704i
$748$	86.5033	−	149.828i	0.115646	−	0.200305i
$749$	−666.320	+	794.090i	−0.889613	+	1.06020i
$750$	−492.311	+	184.987i	−0.656414	+	0.246649i
$751$	62.2580	+	353.083i	0.0829001	+	0.470150i	0.997790	+	0.0664464i	$0.0211661\pi$
$751$	62.2580	+	353.083i	0.0829001	+	0.470150i	−0.914890	+	0.403703i	$0.867723\pi$
$752$	−138.058	−	164.531i	−0.183588	−	0.218792i
$753$	295.949	−	174.981i	0.393027	−	0.232379i
$754$	700.048	−	254.797i	0.928446	−	0.337927i
$755$			23.7274i			0.0314270i
$756$	−444.138	+	13.8144i	−0.587484	+	0.0182731i
$757$	−1279.40			−1.69009			−0.845044	−	0.534697i	$-0.820426\pi$
$757$	−1279.40			−1.69009			−0.845044	+	0.534697i	$0.820426\pi$
$758$	122.638	+	336.944i	0.161791	+	0.444518i
$759$	−65.1553	+	0.675336i	−0.0858436	+	0.000889770i
$760$	229.616	−	192.670i	0.302126	−	0.253514i
$761$	−1032.55	+	182.067i	−1.35684	+	0.239247i	−0.804292	−	0.594234i	$-0.797455\pi$
$761$	−1032.55	+	182.067i	−1.35684	+	0.239247i	−0.552547	+	0.833482i	$0.686344\pi$
$762$	−32.6001	+	39.6794i	−0.0427823	+	0.0520727i
$763$	−449.247	−	376.963i	−0.588791	−	0.494054i
$764$	−216.852	−	125.200i	−0.283838	−	0.163874i
$765$	−342.068	−	116.531i	−0.447147	−	0.152328i
$766$	−396.913	−	687.474i	−0.518164	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.483690 + 1.32893i) q^{2} +(-1.47299 + 2.61348i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(-2.99623 + 0.528316i) q^{5} +(-4.18560 - 0.693383i) q^{6} +(6.30359 + 5.28934i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-4.66059 - 7.69928i) q^{9} +O(q^{10})\)	\(q+(0.483690 + 1.32893i) q^{2} +(-1.47299 + 2.61348i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(-2.99623 + 0.528316i) q^{5} +(-4.18560 - 0.693383i) q^{6} +(6.30359 + 5.28934i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-4.66059 - 7.69928i) q^{9} +(-2.15134 - 3.72623i) q^{10} +(6.45500 + 1.13819i) q^{11} +(-1.10308 - 5.89773i) q^{12} +(17.4093 + 6.33646i) q^{13} +(-3.98016 + 10.9354i) q^{14} +(3.03268 - 8.60880i) q^{15} +(0.694593 - 3.93923i) q^{16} +(-11.4293 + 6.59870i) q^{17} +(7.97749 - 9.91764i) q^{18} +(17.4160 - 30.1654i) q^{19} +(3.91130 - 4.66131i) q^{20} +(-23.1087 + 8.68318i) q^{21} +(1.60964 + 9.12874i) q^{22} +(2.12998 + 2.53841i) q^{23} +(7.30410 - 4.31858i) q^{24} +(-14.7940 + 5.38459i) q^{25} +26.2005i q^{26} +(26.9869 - 0.839401i) q^{27} -16.4575 q^{28} +(-9.72486 - 26.7188i) q^{29} +(12.9073 - 0.133785i) q^{30} +(-10.6385 + 8.92675i) q^{31} +(5.57091 - 0.982302i) q^{32} +(-12.4828 + 15.1935i) q^{33} +(-14.2974 - 11.9970i) q^{34} +(-21.6815 - 12.5178i) q^{35} +(17.0384 + 5.80444i) q^{36} +(-3.33360 - 5.77397i) q^{37} +(48.5116 + 8.55390i) q^{38} +(-42.2040 + 36.1653i) q^{39} +(8.08639 + 2.94320i) q^{40} +(-19.4863 + 53.5382i) q^{41} +(-22.7168 - 26.5099i) q^{42} +(-5.68525 + 32.2426i) q^{43} +(-11.3529 + 6.55457i) q^{44} +(18.0319 + 20.6065i) q^{45} +(-2.34311 + 4.05838i) q^{46} +(34.5145 - 41.1328i) q^{47} +(9.27199 + 7.61776i) q^{48} +(3.24938 + 18.4281i) q^{49} +(-14.3114 - 17.0557i) q^{50} +(-0.410352 - 39.5901i) q^{51} +(-34.8186 + 12.6729i) q^{52} -98.5651i q^{53} +(14.1688 + 35.4576i) q^{54} -19.9420 q^{55} +(-7.96033 - 21.8708i) q^{56} +(53.1832 + 89.9499i) q^{57} +(30.8035 - 25.8472i) q^{58} +(101.204 - 17.8449i) q^{59} +(6.42093 + 17.0882i) q^{60} +(-5.50484 - 4.61911i) q^{61} +(-17.0087 - 9.81998i) q^{62} +(11.3457 - 73.1846i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-55.5099 - 9.78789i) q^{65} +(-26.2288 - 9.23979i) q^{66} +(-28.2566 - 10.2846i) q^{67} +(9.02755 - 24.8030i) q^{68} +(-9.77153 + 1.82761i) q^{69} +(6.14813 - 34.8678i) q^{70} +(8.46959 - 4.88992i) q^{71} +(0.527644 + 25.4504i) q^{72} +(64.7978 - 112.233i) q^{73} +(6.06075 - 7.22291i) q^{74} +(7.71896 - 46.5954i) q^{75} +(12.0970 + 68.6057i) q^{76} +(34.6694 + 41.3174i) q^{77} +(-68.4747 - 38.5932i) q^{78} +(-96.4782 + 35.1152i) q^{79} +12.1698i q^{80} +(-37.5578 + 71.7664i) q^{81} -80.5737 q^{82} +(37.0524 + 101.800i) q^{83} +(24.2418 - 43.0114i) q^{84} +(30.7586 - 25.8095i) q^{85} +(-45.5980 + 8.04015i) q^{86} +(84.1539 + 13.9409i) q^{87} +(-14.2018 - 11.9167i) q^{88} +(-20.1649 - 11.6422i) q^{89} +(-18.6628 + 33.9302i) q^{90} +(76.2254 + 132.026i) q^{91} +(-6.52663 - 1.15082i) q^{92} +(-7.65951 - 40.9525i) q^{93} +(71.3568 + 25.9718i) q^{94} +(-36.2455 + 99.5837i) q^{95} +(-5.63868 + 16.0064i) q^{96} +(-8.89809 + 50.4636i) q^{97} +(-22.9179 + 13.2317i) q^{98} +(-21.3209 - 55.0035i) 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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