LMFDB - Embedded newform 54.3.f.a.41.6

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			41.6
Character	$\chi$	$=$	54.41
Dual form			54.3.f.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39273 - 0.245576i) q^{2} +(2.89593 - 0.783318i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-3.55779 + 4.24001i) q^{5} +(3.84088 - 1.80212i) q^{6} +(-10.2625 - 3.73526i) q^{7} +(2.44949 - 1.41421i) q^{8} +(7.77283 - 4.53687i) q^{9} +O(q^{10})$	\(q+(1.39273 - 0.245576i) q^{2} +(2.89593 - 0.783318i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-3.55779 + 4.24001i) q^{5} +(3.84088 - 1.80212i) q^{6} +(-10.2625 - 3.73526i) q^{7} +(2.44949 - 1.41421i) q^{8} +(7.77283 - 4.53687i) q^{9} +(-3.91380 + 6.77890i) q^{10} +(2.64446 + 3.15155i) q^{11} +(4.90675 - 3.45309i) q^{12} +(-0.953621 + 5.40825i) q^{13} +(-15.2102 - 2.68197i) q^{14} +(-6.98185 + 15.0657i) q^{15} +(3.06418 - 2.57115i) q^{16} +(4.10708 + 2.37123i) q^{17} +(9.71129 - 8.22744i) q^{18} +(-17.1665 - 29.7332i) q^{19} +(-3.78613 + 10.4023i) q^{20} +(-32.6455 - 2.77822i) q^{21} +(4.45696 + 3.73984i) q^{22} +(12.6292 + 34.6986i) q^{23} +(5.98577 - 6.01419i) q^{24} +(-0.978615 - 5.55000i) q^{25} +7.76642i q^{26} +(18.9558 - 19.2270i) q^{27} -21.8423 q^{28} +(-5.18449 + 0.914165i) q^{29} +(-6.02406 + 22.6970i) q^{30} +(34.9235 - 12.7111i) q^{31} +(3.63616 - 4.33340i) q^{32} +(10.1269 + 7.05521i) q^{33} +(6.30237 + 2.29387i) q^{34} +(52.3496 - 30.2240i) q^{35} +(11.5047 - 13.8434i) q^{36} +(-12.1981 + 21.1278i) q^{37} +(-31.2100 - 37.1946i) q^{38} +(1.47476 + 16.4089i) q^{39} +(-2.71850 + 15.4174i) q^{40} +(-22.6189 - 3.98833i) q^{41} +(-46.1486 + 4.14763i) q^{42} +(39.1915 - 32.8855i) q^{43} +(7.12575 + 4.11406i) q^{44} +(-8.41774 + 49.0981i) q^{45} +(26.1102 + 45.2243i) q^{46} +(28.3436 - 77.8733i) q^{47} +(6.85962 - 9.84610i) q^{48} +(53.8315 + 45.1700i) q^{49} +(-2.72589 - 7.48932i) q^{50} +(13.7513 + 3.64975i) q^{51} +(1.90724 + 10.8165i) q^{52} +16.2927i q^{53} +(21.6785 - 31.4331i) q^{54} -22.7711 q^{55} +(-30.4205 + 5.36395i) q^{56} +(-73.0035 - 72.6585i) q^{57} +(-6.99608 + 2.54637i) q^{58} +(-45.6558 + 54.4105i) q^{59} +(-2.81606 + 33.0901i) q^{60} +(-74.1675 - 26.9948i) q^{61} +(45.5174 - 26.2795i) q^{62} +(-96.7154 + 17.5263i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-19.5383 - 23.2848i) q^{65} +(15.8365 + 7.33909i) q^{66} +(-12.1162 + 68.7145i) q^{67} +(9.34081 + 1.64704i) q^{68} +(63.7534 + 90.5919i) q^{69} +(65.4865 - 54.9497i) q^{70} +(-65.9072 - 38.0516i) q^{71} +(12.6234 - 22.1054i) q^{72} +(25.5063 + 44.1783i) q^{73} +(-11.8002 + 32.4208i) q^{74} +(-7.18141 - 15.3058i) q^{75} +(-52.6012 - 44.1376i) q^{76} +(-15.3671 - 42.2207i) q^{77} +(6.08357 + 22.4910i) q^{78} +(5.51385 + 31.2706i) q^{79} +22.1398i q^{80} +(39.8337 - 70.5286i) q^{81} -32.4815 q^{82} +(28.7447 - 5.06847i) q^{83} +(-63.2539 + 17.1095i) q^{84} +(-24.6662 + 8.97776i) q^{85} +(46.5072 - 55.4251i) q^{86} +(-14.2978 + 6.70846i) q^{87} +(10.9346 + 3.97985i) q^{88} +(-69.2878 + 40.0033i) q^{89} +(0.333680 + 70.4476i) q^{90} +(29.9878 - 51.9404i) q^{91} +(47.4704 + 56.5731i) q^{92} +(91.1791 - 64.1666i) q^{93} +(20.3511 - 115.417i) q^{94} +(187.144 + 32.9986i) q^{95} +(7.13562 - 15.3975i) q^{96} +(36.3741 - 30.5215i) q^{97} +(86.0653 + 49.6898i) q^{98} +(34.8531 + 12.4989i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	1.39273	−	0.245576i	0.696364	−	0.122788i
$2$	1.39273	−	0.245576i	0.696364	−	0.122788i
$3$	2.89593	−	0.783318i	0.965310	−	0.261106i
$3$	2.89593	−	0.783318i	0.965310	−	0.261106i
$4$	1.87939	−	0.684040i	0.469846	−	0.171010i
$5$	−3.55779	+	4.24001i	−0.711559	+	0.848003i	−0.993782	−	0.111346i	$-0.964484\pi$
$5$	−3.55779	+	4.24001i	−0.711559	+	0.848003i	0.282223	+	0.959349i	$0.408928\pi$
$6$	3.84088	−	1.80212i	0.640147	−	0.300353i
$7$	−10.2625	−	3.73526i	−1.46608	−	0.533609i	−0.519045	−	0.854747i	$-0.673712\pi$
$7$	−10.2625	−	3.73526i	−1.46608	−	0.533609i	−0.947032	+	0.321138i	$0.895935\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$	7.77283	−	4.53687i	0.863647	−	0.504096i
$10$	−3.91380	+	6.77890i	−0.391380	+	0.677890i
$11$	2.64446	+	3.15155i	0.240406	+	0.286505i	0.872734	−	0.488196i	$-0.162345\pi$
$11$	2.64446	+	3.15155i	0.240406	+	0.286505i	−0.632328	+	0.774701i	$0.717901\pi$
$12$	4.90675	−	3.45309i	0.408896	−	0.287757i
$13$	−0.953621	+	5.40825i	−0.0733555	+	0.416020i	0.925912	+	0.377740i	$0.123299\pi$
$13$	−0.953621	+	5.40825i	−0.0733555	+	0.416020i	−0.999267	+	0.0382793i	$0.987812\pi$
$14$	−15.2102	−	2.68197i	−1.08644	−	0.191570i
$15$	−6.98185	+	15.0657i	−0.465456	+	1.00438i
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$	4.10708	+	2.37123i	0.241593	+	0.139484i	0.615909	−	0.787817i	$-0.288789\pi$
$17$	4.10708	+	2.37123i	0.241593	+	0.139484i	−0.374316	+	0.927301i	$0.622122\pi$
$18$	9.71129	−	8.22744i	0.539516	−	0.457080i
$19$	−17.1665	−	29.7332i	−0.903499	−	1.56491i	−0.822919	−	0.568158i	$-0.807656\pi$
$19$	−17.1665	−	29.7332i	−0.903499	−	1.56491i	−0.0805801	−	0.996748i	$-0.525677\pi$
$20$	−3.78613	+	10.4023i	−0.189306	+	0.520115i
$21$	−32.6455	−	2.77822i	−1.55455	−	0.132296i
$22$	4.45696	+	3.73984i	0.202589	+	0.169993i
$23$	12.6292	+	34.6986i	0.549098	+	1.50863i	0.834931	+	0.550354i	$0.185507\pi$
$23$	12.6292	+	34.6986i	0.549098	+	1.50863i	−0.285833	+	0.958279i	$0.592270\pi$
$24$	5.98577	−	6.01419i	0.249407	−	0.250591i
$25$	−0.978615	−	5.55000i	−0.0391446	−	0.222000i
$26$			7.76642i			0.298708i
$27$	18.9558	−	19.2270i	0.702065	−	0.712113i
$28$	−21.8423			−0.780084
$29$	−5.18449	+	0.914165i	−0.178775	+	0.0315229i	−0.262319	−	0.964981i	$-0.584487\pi$
$29$	−5.18449	+	0.914165i	−0.178775	+	0.0315229i	0.0835437	+	0.996504i	$0.473376\pi$
$30$	−6.02406	+	22.6970i	−0.200802	+	0.756565i
$31$	34.9235	−	12.7111i	1.12656	−	0.410036i	0.289520	−	0.957172i	$-0.406504\pi$
$31$	34.9235	−	12.7111i	1.12656	−	0.410036i	0.837044	+	0.547136i	$0.184282\pi$
$32$	3.63616	−	4.33340i	0.113630	−	0.135419i
$33$	10.1269	+	7.05521i	0.306874	+	0.213794i
$34$	6.30237	+	2.29387i	0.185364	+	0.0674669i
$35$	52.3496	−	30.2240i	1.49570	−	0.863544i
$36$	11.5047	−	13.8434i	0.319576	−	0.384540i
$37$	−12.1981	+	21.1278i	−0.329679	+	0.571021i	−0.982448	−	0.186536i	$-0.940274\pi$
$37$	−12.1981	+	21.1278i	−0.329679	+	0.571021i	0.652769	+	0.757557i	$0.273607\pi$
$38$	−31.2100	−	37.1946i	−0.821316	−	0.978806i
$39$	1.47476	+	16.4089i	0.0378144	+	0.420741i
$40$	−2.71850	+	15.4174i	−0.0679624	+	0.385434i
$41$	−22.6189	−	3.98833i	−0.551681	−	0.0972763i	−0.109143	−	0.994026i	$-0.534811\pi$
$41$	−22.6189	−	3.98833i	−0.551681	−	0.0972763i	−0.442538	+	0.896750i	$0.645922\pi$
$42$	−46.1486	+	4.14763i	−1.09878	+	0.0987531i
$43$	39.1915	−	32.8855i	0.911430	−	0.764780i	−0.0609609	−	0.998140i	$-0.519416\pi$
$43$	39.1915	−	32.8855i	0.911430	−	0.764780i	0.972390	+	0.233360i	$0.0749720\pi$
$44$	7.12575	+	4.11406i	0.161949	+	0.0935013i
$45$	−8.41774	+	49.0981i	−0.187061	+	1.09107i
$46$	26.1102	+	45.2243i	0.567614	+	0.983136i
$47$	28.3436	−	77.8733i	0.603055	−	1.65688i	−0.141992	−	0.989868i	$-0.545351\pi$
$47$	28.3436	−	77.8733i	0.603055	−	1.65688i	0.745047	−	0.667012i	$-0.232427\pi$
$48$	6.85962	−	9.84610i	0.142909	−	0.205127i
$49$	53.8315	+	45.1700i	1.09860	+	0.921836i
$50$	−2.72589	−	7.48932i	−0.0545178	−	0.149786i
$51$	13.7513	+	3.64975i	0.269632	+	0.0715638i
$52$	1.90724	+	10.8165i	0.0366777	+	0.208010i
$53$			16.2927i			0.307409i	0.988117	+	0.153704i	$0.0491204\pi$
$53$			16.2927i			0.307409i	−0.988117	+	0.153704i	$0.950880\pi$
$54$	21.6785	−	31.4331i	0.401454	−	0.582095i
$55$	−22.7711			−0.414020
$56$	−30.4205	+	5.36395i	−0.543222	+	0.0957848i
$57$	−73.0035	−	72.6585i	−1.28076	−	1.27471i
$58$	−6.99608	+	2.54637i	−0.120622	+	0.0439029i
$59$	−45.6558	+	54.4105i	−0.773827	+	0.922212i	−0.998637	−	0.0521911i	$-0.983380\pi$
$59$	−45.6558	+	54.4105i	−0.773827	+	0.922212i	0.224810	+	0.974403i	$0.427824\pi$
$60$	−2.81606	+	33.0901i	−0.0469343	+	0.551501i
$61$	−74.1675	−	26.9948i	−1.21586	−	0.442537i	−0.347128	−	0.937818i	$-0.612843\pi$
$61$	−74.1675	−	26.9948i	−1.21586	−	0.442537i	−0.868733	+	0.495281i	$0.835065\pi$
$62$	45.5174	−	26.2795i	0.734151	−	0.423862i
$63$	−96.7154	+	17.5263i	−1.53516	+	0.278195i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	−19.5383	−	23.2848i	−0.300589	−	0.358228i
$66$	15.8365	+	7.33909i	0.239948	+	0.111198i
$67$	−12.1162	+	68.7145i	−0.180839	+	1.02559i	0.750347	+	0.661045i	$0.229887\pi$
$67$	−12.1162	+	68.7145i	−0.180839	+	1.02559i	−0.931186	+	0.364545i	$0.881224\pi$
$68$	9.34081	+	1.64704i	0.137365	+	0.0242211i
$69$	63.7534	+	90.5919i	0.923963	+	1.31293i
$70$	65.4865	−	54.9497i	0.935521	−	0.784995i
$71$	−65.9072	−	38.0516i	−0.928271	−	0.535937i	−0.0420065	−	0.999117i	$-0.513375\pi$
$71$	−65.9072	−	38.0516i	−0.928271	−	0.535937i	−0.886264	+	0.463180i	$0.846708\pi$
$72$	12.6234	−	22.1054i	0.175324	−	0.307020i
$73$	25.5063	+	44.1783i	0.349402	+	0.605182i	0.986143	−	0.165896i	$-0.0530515\pi$
$73$	25.5063	+	44.1783i	0.349402	+	0.605182i	−0.636741	+	0.771077i	$0.719718\pi$
$74$	−11.8002	+	32.4208i	−0.159462	+	0.438119i
$75$	−7.18141	−	15.3058i	−0.0957522	−	0.204078i
$76$	−52.6012	−	44.1376i	−0.692121	−	0.580758i
$77$	−15.3671	−	42.2207i	−0.199572	−	0.548321i
$78$	6.08357	+	22.4910i	0.0779945	+	0.288346i
$79$	5.51385	+	31.2706i	0.0697956	+	0.395830i	0.999613	+	0.0278099i	$0.00885329\pi$
$79$	5.51385	+	31.2706i	0.0697956	+	0.395830i	−0.929818	+	0.368021i	$0.880036\pi$
$80$			22.1398i			0.276747i
$81$	39.8337	−	70.5286i	0.491774	−	0.870723i
$82$	−32.4815			−0.396115
$83$	28.7447	−	5.06847i	0.346322	−	0.0610659i	0.00221805	−	0.999998i	$-0.499294\pi$
$83$	28.7447	−	5.06847i	0.346322	−	0.0610659i	0.344104	+	0.938932i	$0.388183\pi$
$84$	−63.2539	+	17.1095i	−0.753023	+	0.203684i
$85$	−24.6662	+	8.97776i	−0.290190	+	0.105621i
$86$	46.5072	−	55.4251i	0.540781	−	0.644478i
$87$	−14.2978	+	6.70846i	−0.164343	+	0.0771087i
$88$	10.9346	+	3.97985i	0.124256	+	0.0452256i
$89$	−69.2878	+	40.0033i	−0.778514	+	0.449475i	−0.835903	−	0.548877i	$-0.815056\pi$
$89$	−69.2878	+	40.0033i	−0.778514	+	0.449475i	0.0573893	+	0.998352i	$0.481722\pi$
$90$	0.333680	+	70.4476i	0.00370755	+	0.782751i
$91$	29.9878	−	51.9404i	0.329536	−	0.570774i
$92$	47.4704	+	56.5731i	0.515983	+	0.614925i
$93$	91.1791	−	64.1666i	0.980421	−	0.689964i
$94$	20.3511	−	115.417i	0.216501	−	1.22784i
$95$	187.144	+	32.9986i	1.96994	+	0.347353i
$96$	7.13562	−	15.3975i	0.0743294	−	0.160391i
$97$	36.3741	−	30.5215i	0.374991	−	0.314655i	−0.435741	−	0.900072i	$-0.643514\pi$
$97$	36.3741	−	30.5215i	0.374991	−	0.314655i	0.810732	+	0.585417i	$0.199069\pi$
$98$	86.0653	+	49.6898i	0.878217	+	0.507039i
$99$	34.8531	+	12.4989i	0.352052	+	0.126251i
$100$	−5.63562	−	9.76118i	−0.0563562	−	0.0976118i
$101$	−15.6059	+	42.8769i	−0.154514	+	0.424524i	−0.992662	−	0.120918i	$-0.961416\pi$
$101$	−15.6059	+	42.8769i	−0.154514	+	0.424524i	0.838148	+	0.545442i	$0.183638\pi$
$102$	20.0481	+	1.70614i	0.196550	+	0.0167269i
$103$	−10.9188	−	9.16192i	−0.106007	−	0.0889507i	0.588243	−	0.808684i	$-0.299820\pi$
$103$	−10.9188	−	9.16192i	−0.106007	−	0.0889507i	−0.694251	+	0.719733i	$0.744264\pi$
$104$	5.31254	+	14.5961i	0.0510821	+	0.140347i
$105$	127.926	−	128.533i	1.21834	−	1.22412i
$106$	4.00108	+	22.6913i	0.0377461	+	0.214069i
$107$			105.487i			0.985863i	0.870068	+	0.492931i	$0.164075\pi$
$107$			105.487i			0.985863i	−0.870068	+	0.492931i	$0.835925\pi$
$108$	22.4731	−	49.1015i	0.208084	−	0.454644i
$109$	57.5260			0.527762			0.263881	−	0.964555i	$-0.414997\pi$
$109$	57.5260			0.527762			0.263881	+	0.964555i	$0.414997\pi$
$110$	−31.7139	+	5.59202i	−0.288308	+	0.0508366i
$111$	−18.7752	+	70.7396i	−0.169146	+	0.637293i
$112$	−41.0502	+	14.9410i	−0.366519	+	0.133402i
$113$	−76.8178	+	91.5479i	−0.679803	+	0.810158i	−0.990082	−	0.140487i	$-0.955133\pi$
$113$	−76.8178	+	91.5479i	−0.679803	+	0.810158i	0.310279	+	0.950646i	$0.399577\pi$
$114$	−119.517	−	83.2657i	−1.04840	−	0.730401i
$115$	−192.055	−	69.9022i	−1.67004	−	0.607845i
$116$	−9.11832	+	5.26446i	−0.0786062	+	0.0453833i
$117$	17.1242	+	46.3639i	0.146361	+	0.396272i
$118$	−50.2243	+	86.9910i	−0.425629	+	0.737212i
$119$	−33.2920	−	39.6758i	−0.279765	−	0.333410i
$120$	4.20411	+	46.7770i	0.0350343	+	0.389809i
$121$	18.0724	−	102.493i	0.149358	−	0.847053i
$122$	−109.924	−	19.3826i	−0.901020	−	0.158874i
$123$	−68.6270	+	6.16789i	−0.557943	+	0.0501454i
$124$	56.9397	−	47.7781i	0.459192	−	0.385307i
$125$	−92.8213	−	53.5904i	−0.742570	−	0.428723i
$126$	−130.394	+	48.1603i	−1.03487	+	0.382224i
$127$	−68.8561	−	119.262i	−0.542174	−	0.939072i	−0.998779	−	0.0494029i	$-0.984268\pi$
$127$	−68.8561	−	119.262i	−0.542174	−	0.939072i	0.456605	−	0.889669i	$-0.349065\pi$
$128$	3.86952	−	10.6314i	0.0302306	−	0.0830579i
$129$	87.7359	−	125.934i	0.680124	−	0.976230i
$130$	−32.9297	−	27.6313i	−0.253305	−	0.212549i
$131$	−21.9189	−	60.2217i	−0.167320	−	0.459708i	0.827487	−	0.561484i	$-0.189769\pi$
$131$	−21.9189	−	60.2217i	−0.167320	−	0.459708i	−0.994807	+	0.101777i	$0.967547\pi$
$132$	23.8583	+	6.33229i	0.180745	+	0.0479719i
$133$	65.1105	+	369.260i	0.489552	+	2.77639i
$134$			98.6761i			0.736389i
$135$	14.0822	+	148.779i	0.104313	+	1.10206i
$136$	13.4137			0.0986300
$137$	75.1710	−	13.2547i	0.548694	−	0.0967495i	0.107573	−	0.994197i	$-0.465692\pi$
$137$	75.1710	−	13.2547i	0.548694	−	0.0967495i	0.441121	+	0.897448i	$0.354581\pi$
$138$	111.038	+	110.514i	0.804626	+	0.800824i
$139$	−100.055	+	36.4171i	−0.719821	+	0.261993i	−0.675850	−	0.737039i	$-0.736223\pi$
$139$	−100.055	+	36.4171i	−0.719821	+	0.261993i	−0.0439712	+	0.999033i	$0.514001\pi$
$140$	77.7106	−	92.6118i	0.555075	−	0.661513i
$141$	21.0815	−	247.718i	0.149514	−	1.75686i
$142$	−101.135	−	36.8103i	−0.712221	−	0.259227i
$143$	−19.5662	+	11.2966i	−0.136827	+	0.0789969i
$144$	12.1524	−	33.8869i	0.0843914	−	0.235326i
$145$	14.5693	−	25.2347i	0.100478	−	0.174032i
$146$	46.3725	+	55.2646i	0.317620	+	0.378525i
$147$	191.275	+	88.6419i	1.30119	+	0.603006i
$148$	−8.47273	+	48.0512i	−0.0572482	+	0.324670i
$149$	−84.0145	−	14.8140i	−0.563856	−	0.0994230i	−0.115547	−	0.993302i	$-0.536862\pi$
$149$	−84.0145	−	14.8140i	−0.563856	−	0.0994230i	−0.448308	+	0.893879i	$0.647973\pi$
$150$	−13.7605	−	19.5533i	−0.0917367	−	0.130355i
$151$	−42.4996	+	35.6614i	−0.281454	+	0.236168i	−0.772575	−	0.634923i	$-0.781032\pi$
$151$	−42.4996	+	35.6614i	−0.281454	+	0.236168i	0.491121	+	0.871091i	$0.336587\pi$
$152$	−84.0983	−	48.5542i	−0.553278	−	0.319435i
$153$	42.6816	−	0.202164i	0.278965	−	0.00132133i
$154$	−31.7705	−	55.0282i	−0.206302	−	0.357326i
$155$	−70.3553	+	193.299i	−0.453905	+	1.24709i
$156$	13.9960	+	29.8299i	0.0897180	+	0.191217i
$157$	−12.9857	−	10.8963i	−0.0827115	−	0.0694032i	0.600494	−	0.799629i	$-0.294970\pi$
$157$	−12.9857	−	10.8963i	−0.0827115	−	0.0694032i	−0.683206	+	0.730226i	$0.739415\pi$
$158$	15.3586	+	42.1974i	0.0972063	+	0.267072i
$159$	12.7623	+	47.1825i	0.0802663	+	0.296745i
$160$	5.43699	+	30.8347i	0.0339812	+	0.192717i
$161$		−	403.269i		−	2.50478i
$162$	38.1574	−	108.009i	0.235540	−	0.666724i
$163$	230.772			1.41578			0.707890	−	0.706322i	$-0.249647\pi$
$163$	230.772			1.41578			0.707890	+	0.706322i	$0.249647\pi$
$164$	−45.2379	+	7.97666i	−0.275841	+	0.0486382i
$165$	−65.9435	+	17.8370i	−0.399657	+	0.108103i
$166$	38.7889	−	14.1180i	0.233668	−	0.0850481i
$167$	103.061	−	122.823i	0.617132	−	0.735469i	−0.363442	−	0.931617i	$-0.618399\pi$
$167$	103.061	−	122.823i	0.617132	−	0.735469i	0.980574	+	0.196147i	$0.0628431\pi$
$168$	−83.8938	+	39.3625i	−0.499368	+	0.234301i
$169$	130.468	+	47.4866i	0.772001	+	0.280986i
$170$	−32.1486	+	18.5610i	−0.189109	+	0.109182i
$171$	−268.328	−	153.229i	−1.56917	−	0.896077i
$172$	51.1608	−	88.6132i	0.297447	−	0.515193i
$173$	204.014	+	243.135i	1.17927	+	1.40540i	0.894653	+	0.446762i	$0.147423\pi$
$173$	204.014	+	243.135i	1.17927	+	1.40540i	0.284620	+	0.958640i	$0.408133\pi$
$174$	−18.2656	+	12.8543i	−0.104974	+	0.0738750i
$175$	−10.6876	+	60.6125i	−0.0610721	+	0.346357i
$176$	16.2062	+	2.85759i	0.0920808	+	0.0162363i
$177$	−89.5954	+	193.332i	−0.506189	+	1.09227i
$178$	−86.6752	+	72.7291i	−0.486939	+	0.408591i
$179$	−38.5365	−	22.2490i	−0.215287	−	0.124296i	0.388479	−	0.921458i	$-0.373001\pi$
$179$	−38.5365	−	22.2490i	−0.215287	−	0.124296i	−0.603766	+	0.797161i	$0.706334\pi$
$180$	17.7649	+	98.0324i	0.0986940	+	0.544624i
$181$	19.0288	+	32.9588i	0.105131	+	0.182093i	0.913792	−	0.406183i	$-0.133140\pi$
$181$	19.0288	+	32.9588i	0.105131	+	0.182093i	−0.808661	+	0.588276i	$0.799807\pi$
$182$	29.0096	−	79.7032i	0.159393	−	0.437930i
$183$	−235.929	−	20.0782i	−1.28923	−	0.109717i
$184$	80.0064	+	67.1333i	0.434817	+	0.364855i
$185$	−46.1836	−	126.888i	−0.249641	−	0.685884i
$186$	111.230	−	111.758i	0.598011	−	0.600850i
$187$	3.38800	+	19.2143i	0.0181176	+	0.102750i
$188$		−	165.742i		−	0.881607i
$189$	−266.352	+	126.514i	−1.40927	+	0.669385i
$190$	268.745			1.41445
$191$	201.386	−	35.5097i	1.05438	−	0.185915i	0.380516	−	0.924774i	$-0.375746\pi$
$191$	201.386	−	35.5097i	1.05438	−	0.185915i	0.673859	+	0.738860i	$0.264635\pi$
$192$	6.15674	−	23.1969i	0.0320663	−	0.120817i
$193$	108.871	−	39.6259i	0.564100	−	0.205316i	−0.0442003	−	0.999023i	$-0.514074\pi$
$193$	108.871	−	39.6259i	0.564100	−	0.205316i	0.608300	+	0.793707i	$0.291852\pi$
$194$	43.1639	−	51.4408i	0.222495	−	0.265159i
$195$	−74.8209	−	52.1265i	−0.383697	−	0.267316i
$196$	132.068	+	48.0689i	0.673817	+	0.245249i
$197$	−76.7079	+	44.2873i	−0.389380	+	0.224809i	−0.681892	−	0.731453i	$-0.738842\pi$
$197$	−76.7079	+	44.2873i	−0.389380	+	0.224809i	0.292511	+	0.956262i	$0.405509\pi$
$198$	51.6104	+	8.84845i	0.260658	+	0.0446892i
$199$	134.773	−	233.434i	0.677253	−	1.17304i	−0.298551	−	0.954394i	$-0.596503\pi$
$199$	134.773	−	233.434i	0.677253	−	1.17304i	0.975805	−	0.218644i	$-0.0701632\pi$
$200$	−10.2460	−	12.2107i	−0.0512300	−	0.0610535i
$201$	18.7376	+	208.483i	0.0932217	+	1.03723i
$202$	−11.2053	+	63.5483i	−0.0554717	+	0.314596i
$203$	56.6207	+	9.98375i	0.278920	+	0.0491810i
$204$	28.3405	−	2.54712i	0.138924	−	0.0124859i
$205$	97.3841	−	81.7149i	0.475044	−	0.398609i
$206$	−17.4568	−	10.0787i	−0.0847418	−	0.0489257i
$207$	255.588	+	212.409i	1.23472	+	1.02613i
$208$	10.9834	+	19.0238i	0.0528047	+	0.0914604i
$209$	48.3096	−	132.729i	0.231146	−	0.635069i
$210$	146.601	−	210.427i	0.698101	−	1.00203i
$211$	−107.762	−	90.4231i	−0.510721	−	0.428546i	0.350662	−	0.936502i	$-0.385957\pi$
$211$	−107.762	−	90.4231i	−0.510721	−	0.428546i	−0.861383	+	0.507957i	$0.830401\pi$
$212$	11.1448	+	30.6202i	0.0525700	+	0.144435i
$213$	−220.669	−	58.5684i	−1.03601	−	0.274969i
$214$	25.9051	+	146.915i	0.121052	+	0.686520i
$215$			283.172i			1.31708i
$216$	19.2408	−	73.9039i	0.0890777	−	0.342148i
$217$	−405.883			−1.87043
$218$	80.1181	−	14.1270i	0.367514	−	0.0648027i
$219$	108.470	+	107.958i	0.495298	+	0.492957i
$220$	−42.7956	+	15.5763i	−0.194526	+	0.0708015i
$221$	−16.7408	+	19.9509i	−0.0757502	+	0.0902756i
$222$	−8.77679	+	103.132i	−0.0395351	+	0.464557i
$223$	−324.808	−	118.221i	−1.45654	−	0.530137i	−0.512130	−	0.858908i	$-0.671144\pi$
$223$	−324.808	−	118.221i	−1.45654	−	0.530137i	−0.944410	+	0.328770i	$0.893366\pi$
$224$	−53.5026	+	30.8897i	−0.238851	+	0.137901i
$225$	−32.7862	−	38.6993i	−0.145717	−	0.171997i
$226$	−84.5044	+	146.366i	−0.373913	+	0.647637i
$227$	−118.546	−	141.278i	−0.522230	−	0.622369i	0.438877	−	0.898547i	$-0.355376\pi$
$227$	−118.546	−	141.278i	−0.522230	−	0.622369i	−0.961106	+	0.276178i	$0.910932\pi$
$228$	−186.903	−	86.6161i	−0.819750	−	0.379895i
$229$	38.3747	−	217.634i	0.167575	−	0.950365i	−0.778794	−	0.627279i	$-0.784168\pi$
$229$	38.3747	−	217.634i	0.167575	−	0.950365i	0.946370	−	0.323086i	$-0.104720\pi$
$230$	−284.646	−	50.1908i	−1.23759	−	0.218221i
$231$	−77.5742	−	110.231i	−0.335819	−	0.477190i
$232$	−11.4065	+	9.57121i	−0.0491660	+	0.0412552i
$233$	364.370	+	210.369i	1.56382	+	0.902872i	0.996865	+	0.0791236i	$0.0252122\pi$
$233$	364.370	+	210.369i	1.56382	+	0.902872i	0.566955	+	0.823748i	$0.308121\pi$
$234$	35.2352	+	60.3670i	0.150578	+	0.257979i
$235$	229.343	+	397.234i	0.975929	+	1.69036i
$236$	−48.5859	+	133.489i	−0.205872	+	0.565630i
$237$	40.4625	+	86.2384i	0.170728	+	0.363875i
$238$	−56.1101	−	47.0820i	−0.235757	−	0.197823i
$239$	−27.2416	−	74.8456i	−0.113981	−	0.313162i	0.869565	−	0.493819i	$-0.164400\pi$
$239$	−27.2416	−	74.8456i	−0.113981	−	0.313162i	−0.983546	+	0.180658i	$0.942177\pi$
$240$	17.3425	+	64.1153i	0.0722603	+	0.267147i
$241$	−9.36196	−	53.0943i	−0.0388463	−	0.220308i	0.959205	−	0.282713i	$-0.0912343\pi$
$241$	−9.36196	−	53.0943i	−0.0388463	−	0.220308i	−0.998051	+	0.0624044i	$0.980123\pi$
$242$		−	147.184i		−	0.608197i
$243$	60.1093	−	235.448i	0.247363	−	0.968923i
$244$	−157.855			−0.646946
$245$	−383.043	+	67.5407i	−1.56344	+	0.275677i
$246$	−94.0641	+	25.4433i	−0.382374	+	0.103428i
$247$	177.175	−	64.4865i	0.717308	−	0.261079i
$248$	67.5685	−	80.5250i	0.272453	−	0.324697i
$249$	79.2724	−	37.1942i	0.318363	−	0.149374i
$250$	−142.435	−	51.8422i	−0.569741	−	0.207369i
$251$	−179.256	+	103.494i	−0.714167	+	0.412325i	−0.812602	−	0.582819i	$-0.801950\pi$
$251$	−179.256	+	103.494i	−0.714167	+	0.412325i	0.0984348	+	0.995144i	$0.468616\pi$
$252$	−169.777	+	99.0958i	−0.673717	+	0.393237i
$253$	−75.9567	+	131.561i	−0.300224	+	0.520003i
$254$	−125.186	−	149.190i	−0.492857	−	0.587364i
$255$	−64.3991	+	45.3204i	−0.252546	+	0.177727i
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	201.153	+	35.4686i	0.782695	+	0.138010i	0.550696	−	0.834706i	$-0.314362\pi$
$257$	201.153	+	35.4686i	0.782695	+	0.138010i	0.231999	+	0.972716i	$0.425473\pi$
$258$	91.2661	−	196.937i	0.353745	−	0.763322i
$259$	204.102	−	171.262i	0.788037	−	0.661241i
$260$	−52.6477	−	30.3962i	−0.202491	−	0.116908i
$261$	−36.1507	+	30.6270i	−0.138508	+	0.117345i
$262$	−45.3161	−	78.4897i	−0.172962	−	0.299579i
$263$	65.2110	−	179.166i	0.247951	−	0.681239i	−0.751810	−	0.659379i	$-0.770819\pi$
$263$	65.2110	−	179.166i	0.247951	−	0.681239i	0.999761	−	0.0218596i	$-0.00695867\pi$
$264$	34.7832	+	2.96015i	0.131755	+	0.0112127i
$265$	−69.0812	−	57.9660i	−0.260684	−	0.218740i
$266$	181.362	+	498.289i	0.681814	+	1.87327i
$267$	−169.317	+	170.121i	−0.634147	+	0.637158i
$268$	24.2324	+	137.429i	0.0904196	+	0.512795i
$269$			70.9150i			0.263624i	0.991275	+	0.131812i	$0.0420796\pi$
$269$			70.9150i			0.263624i	−0.991275	+	0.131812i	$0.957920\pi$
$270$	56.1491	+	203.750i	0.207960	+	0.754629i
$271$	−117.923			−0.435141			−0.217570	−	0.976045i	$-0.569813\pi$
$271$	−117.923			−0.435141			−0.217570	+	0.976045i	$0.569813\pi$
$272$	18.6816	−	3.29407i	0.0686824	−	0.0121106i
$273$	46.1568	−	173.906i	0.169072	−	0.637018i
$274$	101.438	−	36.9203i	0.370211	−	0.134746i
$275$	14.9032	−	17.7609i	0.0541934	−	0.0645852i
$276$	181.786	+	126.647i	0.658644	+	0.458867i
$277$	232.933	+	84.7808i	0.840915	+	0.306068i	0.726331	−	0.687346i	$-0.241224\pi$
$277$	232.933	+	84.7808i	0.840915	+	0.306068i	0.114584	+	0.993414i	$0.463446\pi$
$278$	−130.406	+	75.2902i	−0.469088	+	0.270828i
$279$	213.786	−	257.244i	0.766256	−	0.922023i
$280$	85.4865	−	148.067i	0.305309	−	0.528811i
$281$	46.1416	+	54.9895i	0.164205	+	0.195692i	0.841872	−	0.539677i	$-0.181453\pi$
$281$	46.1416	+	54.9895i	0.164205	+	0.195692i	−0.677667	+	0.735369i	$0.737009\pi$
$282$	−31.4727	−	350.181i	−0.111605	−	1.24178i
$283$	−52.2646	+	296.407i	−0.184681	+	1.04738i	0.741685	+	0.670749i	$0.234027\pi$
$283$	−52.2646	+	296.407i	−0.184681	+	1.04738i	−0.926365	+	0.376627i	$0.877084\pi$
$284$	−149.894	−	26.4303i	−0.527795	−	0.0930646i
$285$	567.805	−	51.0318i	1.99230	−	0.179059i
$286$	−24.4762	+	20.5380i	−0.0855813	+	0.0718112i
$287$	217.230	+	125.418i	0.756900	+	0.436997i
$288$	8.60314	−	50.1795i	0.0298720	−	0.174235i
$289$	−133.255	−	230.804i	−0.461088	−	0.798629i
$290$	14.0940	−	38.7229i	0.0486000	−	0.133527i
$291$	81.4289	−	116.881i	0.279824	−	0.401652i
$292$	78.1560	+	65.5806i	0.267657	+	0.224591i
$293$	−34.3361	−	94.3376i	−0.117188	−	0.321971i	0.867206	−	0.497949i	$-0.165913\pi$
$293$	−34.3361	−	94.3376i	−0.117188	−	0.321971i	−0.984394	+	0.175978i	$0.943691\pi$
$294$	288.162	+	76.4818i	0.980143	+	0.260142i
$295$	−68.2672	−	387.163i	−0.231414	−	1.31242i
$296$			69.0030i			0.233118i
$297$	110.723	+	8.89479i	0.372804	+	0.0299488i
$298$	−120.647			−0.404857
$299$	−199.702	+	35.2129i	−0.667900	+	0.117769i
$300$	−23.9665	−	23.8532i	−0.0798882	−	0.0795107i
$301$	−525.040	+	191.099i	−1.74432	+	0.634881i
$302$	−50.4328	+	60.1035i	−0.166996	+	0.199018i
$303$	−11.6074	+	136.393i	−0.0383083	+	0.450142i
$304$	−129.050	−	46.9703i	−0.424506	−	0.154507i
$305$	378.331	−	218.429i	1.24043	−	0.716162i
$306$	59.3942	−	10.7631i	0.194099	−	0.0351736i
$307$	−136.003	+	235.565i	−0.443008	+	0.767312i	−0.997911	−	0.0646029i	$-0.979422\pi$
$307$	−136.003	+	235.565i	−0.443008	+	0.767312i	0.554903	+	0.831915i	$0.312755\pi$
$308$	−57.7613	−	68.8372i	−0.187537	−	0.223498i
$309$	−38.7967	−	17.9794i	−0.125556	−	0.0581859i
$310$	−50.5161	+	286.491i	−0.162955	+	0.924165i
$311$	402.304	+	70.9371i	1.29358	+	0.228094i	0.777738	−	0.628588i	$-0.216367\pi$
$311$	402.304	+	70.9371i	1.29358	+	0.228094i	0.515845	+	0.856682i	$0.327478\pi$
$312$	26.8181	+	38.1078i	0.0859555	+	0.122141i
$313$	186.473	−	156.470i	0.595761	−	0.499903i	−0.294319	−	0.955707i	$-0.595093\pi$
$313$	186.473	−	156.470i	0.595761	−	0.499903i	0.890080	+	0.455805i	$0.150648\pi$
$314$	−20.7614	−	11.9866i	−0.0661192	−	0.0381739i
$315$	269.782	−	472.429i	0.856450	−	1.49978i
$316$	31.7530	+	54.9978i	0.100484	+	0.174044i
$317$	−92.9426	+	255.358i	−0.293194	+	0.805545i	0.702400	+	0.711782i	$0.252112\pi$
$317$	−92.9426	+	255.358i	−0.293194	+	0.805545i	−0.995595	+	0.0937628i	$0.970110\pi$
$318$	29.3613	+	62.5782i	0.0923313	+	0.196787i
$319$	−16.5912	−	13.9217i	−0.0520101	−	0.0436417i
$320$	15.1445	+	41.6092i	0.0473266	+	0.130029i
$321$	82.6301	+	305.484i	0.257415	+	0.951663i
$322$	−99.0331	−	561.644i	−0.307556	−	1.74424i
$323$		−	162.822i		−	0.504094i
$324$	26.6184	−	159.798i	0.0821557	−	0.493204i
$325$	30.9490			0.0952278
$326$	321.403	−	56.6720i	0.985899	−	0.173841i
$327$	166.591	−	45.0612i	0.509454	−	0.137802i
$328$	−61.0452	+	22.2186i	−0.186113	+	0.0677397i
$329$	−581.754	+	693.308i	−1.76825	+	2.10732i
$330$	−87.4610	+	41.0362i	−0.265033	+	0.124352i
$331$	416.626	+	151.639i	1.25869	+	0.458125i	0.883329	−	0.468754i	$-0.155297\pi$
$331$	416.626	+	151.639i	1.25869	+	0.458125i	0.375360	+	0.926879i	$0.377519\pi$
$332$	50.5553	−	29.1881i	0.152275	−	0.0879161i
$333$	1.03998	+	219.564i	0.00312306	+	0.659351i
$334$	113.374	−	196.369i	0.339442	−	0.587931i
$335$	−248.243	−	295.845i	−0.741025	−	0.883120i
$336$	−107.175	+	75.4236i	−0.318973	+	0.224475i
$337$	26.8736	−	152.408i	0.0797435	−	0.452248i	−0.918624	−	0.395133i	$-0.870699\pi$
$337$	26.8736	−	152.408i	0.0797435	−	0.452248i	0.998368	−	0.0571153i	$-0.0181903\pi$
$338$	193.368	+	34.0961i	0.572096	+	0.100876i
$339$	−150.748	+	325.289i	−0.444684	+	0.959554i
$340$	−40.2161	+	33.7453i	−0.118283	+	0.0992510i
$341$	132.414	+	76.4490i	0.388310	+	0.224191i
$342$	−411.337	−	147.512i	−1.20274	−	0.431321i
$343$	−116.158	−	201.191i	−0.338652	−	0.586562i
$344$	49.4919	−	135.978i	0.143872	−	0.395285i
$345$	−610.933	−	51.9921i	−1.77082	−	0.150702i
$346$	343.844	+	288.520i	0.993770	+	0.833872i
$347$	−71.9673	−	197.728i	−0.207398	−	0.569823i	0.791760	−	0.610832i	$-0.209165\pi$
$347$	−71.9673	−	197.728i	−0.207398	−	0.569823i	−0.999159	+	0.0410093i	$0.986943\pi$
$348$	−22.2823	+	22.3881i	−0.0640295	+	0.0643335i
$349$	−74.8630	−	424.569i	−0.214507	−	1.21653i	−0.881760	−	0.471699i	$-0.843641\pi$
$349$	−74.8630	−	424.569i	−0.214507	−	1.21653i	0.667252	−	0.744832i	$-0.267470\pi$
$350$			87.0414i			0.248690i
$351$	85.9081	+	120.853i	0.244752	+	0.344310i
$352$	23.2726			0.0661154
$353$	−269.966	+	47.6023i	−0.764777	+	0.134851i	−0.542412	−	0.840113i	$-0.682489\pi$
$353$	−269.966	+	47.6023i	−0.764777	+	0.134851i	−0.222365	+	0.974964i	$0.571378\pi$
$354$	−77.3044	+	291.261i	−0.218374	+	0.822772i
$355$	395.823	−	144.068i	1.11500	−	0.405825i
$356$	−102.855	+	122.577i	−0.288917	+	0.344318i
$357$	−127.490	−	88.8203i	−0.357115	−	0.248796i
$358$	−59.1346	−	21.5233i	−0.165181	−	0.0601208i
$359$	−40.2168	+	23.2192i	−0.112025	+	0.0646774i	−0.554965	−	0.831873i	$-0.687269\pi$
$359$	−40.2168	+	23.2192i	−0.112025	+	0.0646774i	0.442941	+	0.896551i	$0.353935\pi$
$360$	48.8161	+	132.170i	0.135600	+	0.367138i
$361$	−408.876	+	708.195i	−1.13262	+	1.96176i
$362$	34.5958	+	41.2296i	0.0955685	+	0.113894i
$363$	−27.9486	−	310.970i	−0.0769934	−	0.856667i
$364$	20.8293	−	118.129i	0.0572234	−	0.324530i
$365$	−278.063	−	49.0300i	−0.761816	−	0.134329i
$366$	−333.516	+	29.9750i	−0.911247	+	0.0818988i
$367$	−490.518	+	411.594i	−1.33656	+	1.12151i	−0.354067	+	0.935220i	$0.615201\pi$
$367$	−490.518	+	411.594i	−1.33656	+	1.12151i	−0.982495	+	0.186288i	$0.940354\pi$
$368$	127.914	+	73.8509i	0.347591	+	0.200682i
$369$	−193.908	+	71.6185i	−0.525495	+	0.194088i
$370$	−95.4820	−	165.380i	−0.258059	−	0.446972i
$371$	60.8574	−	167.204i	0.164036	−	0.450686i
$372$	127.468	−	182.964i	0.342656	−	0.491839i
$373$	−3.55616	−	2.98397i	−0.00953393	−	0.00799992i	0.638008	−	0.770030i	$-0.279759\pi$
$373$	−3.55616	−	2.98397i	−0.00953393	−	0.00799992i	−0.647542	+	0.762030i	$0.724203\pi$
$374$	9.43713	+	25.9283i	0.0252330	+	0.0693270i
$375$	−310.782	−	82.4855i	−0.828753	−	0.219961i
$376$	−40.7022	−	230.834i	−0.108251	−	0.613920i
$377$		−	28.9108i		−	0.0766864i
$378$	−339.888	+	241.609i	−0.899174	+	0.639177i
$379$	259.991			0.685992			0.342996	−	0.939337i	$-0.388558\pi$
$379$	259.991			0.685992			0.342996	+	0.939337i	$0.388558\pi$
$380$	374.288	−	65.9971i	0.984969	−	0.173677i
$381$	−292.823	−	291.439i	−0.768563	−	0.764931i
$382$	271.755	−	98.9108i	0.711401	−	0.258929i
$383$	−171.274	+	204.117i	−0.447191	+	0.532942i	−0.941800	−	0.336174i	$-0.890867\pi$
$383$	−171.274	+	204.117i	−0.447191	+	0.532942i	0.494609	+	0.869116i	$0.335311\pi$
$384$	2.87808	−	33.8189i	0.00749500	−	0.0880700i
$385$	233.689	+	85.0559i	0.606985	+	0.220924i
$386$	141.897	−	81.9242i	0.367609	−	0.212239i
$387$	155.431	−	433.420i	0.401631	−	1.11995i
$388$	47.4830	−	82.2430i	0.122379	−	0.211967i
$389$	15.2282	+	18.1483i	0.0391471	+	0.0466538i	0.785263	−	0.619163i	$-0.212528\pi$
$389$	15.2282	+	18.1483i	0.0391471	+	0.0466538i	−0.746116	+	0.665816i	$0.768083\pi$
$390$	−117.006	−	54.2239i	−0.300016	−	0.139036i
$391$	−30.4088	+	172.457i	−0.0777718	+	0.441066i
$392$	195.740	+	34.5142i	0.499336	+	0.0880464i
$393$	−110.648	−	157.228i	−0.281548	−	0.400072i
$394$	−95.9574	+	80.5178i	−0.243547	+	0.204360i
$395$	−152.205	−	87.8756i	−0.385329	−	0.222470i
$396$	74.0522	−	0.350753i	0.187000	−	0.000885740i
$397$	113.459	+	196.518i	0.285792	+	0.495006i	0.972801	−	0.231643i	$-0.0744100\pi$
$397$	113.459	+	196.518i	0.285792	+	0.495006i	−0.687009	+	0.726649i	$0.741077\pi$
$398$	130.377	−	358.208i	0.327580	−	0.900020i
$399$	477.803	+	1018.35i	1.19750	+	2.55225i
$400$	−17.2685	−	14.4900i	−0.0431713	−	0.0362251i
$401$	−175.968	−	483.469i	−0.438824	−	1.20566i	−0.940258	−	0.340463i	$-0.889416\pi$
$401$	−175.968	−	483.469i	−0.438824	−	1.20566i	0.501434	−	0.865196i	$-0.332806\pi$
$402$	77.2947	+	285.759i	0.192275	+	0.710844i
$403$	35.4411	+	200.997i	0.0879432	+	0.498751i
$404$			91.2573i			0.225884i
$405$	157.322	+	419.821i	0.388450	+	1.03660i
$406$	81.3090			0.200268
$407$	−98.8427	+	17.4286i	−0.242857	+	0.0428222i
$408$	38.8451	−	10.5072i	0.0952085	−	0.0257529i
$409$	260.800	−	94.9234i	0.637653	−	0.232087i	−0.00290599	−	0.999996i	$-0.500925\pi$
$409$	260.800	−	94.9234i	0.637653	−	0.232087i	0.640559	+	0.767909i	$0.278703\pi$
$410$	115.562	−	137.722i	0.281859	−	0.335907i
$411$	207.307	−	97.2674i	0.504398	−	0.236660i
$412$	−26.7877	−	9.74992i	−0.0650186	−	0.0236648i
$413$	671.782	−	387.854i	1.62659	−	0.939113i
$414$	408.127	+	233.062i	0.985813	+	0.562951i
$415$	−80.7773	+	139.910i	−0.194644	+	0.337134i
$416$	19.9686	+	23.7977i	0.0480015	+	0.0572060i
$417$	−261.227	+	183.836i	−0.626442	+	0.440854i
$418$	34.6870	−	196.720i	0.0829833	−	0.470622i
$419$	−316.326	−	55.7768i	−0.754955	−	0.133119i	−0.217092	−	0.976151i	$-0.569657\pi$
$419$	−316.326	−	55.7768i	−0.754955	−	0.133119i	−0.537863	+	0.843032i	$0.680768\pi$
$420$	152.500	−	329.070i	0.363095	−	0.783499i
$421$	−101.935	+	85.5332i	−0.242125	+	0.203167i	−0.755772	−	0.654834i	$-0.772738\pi$
$421$	−101.935	+	85.5332i	−0.242125	+	0.203167i	0.513648	+	0.858001i	$0.328294\pi$
$422$	−172.289	−	99.4711i	−0.408268	−	0.235714i
$423$	−132.991	−	733.887i	−0.314400	−	1.73496i
$424$	23.0413	+	39.9087i	0.0543427	+	0.0941244i
$425$	9.14105	−	25.1148i	0.0215084	−	0.0590937i
$426$	−321.715	−	27.3789i	−0.755200	−	0.0642696i
$427$	660.315	+	554.070i	1.54640	+	1.29759i
$428$	72.1576	+	198.251i	0.168592	+	0.463204i
$429$	−47.8136	+	48.0406i	−0.111454	+	0.111983i
$430$	69.5402	+	394.382i	0.161721	+	0.917168i
$431$			24.4994i			0.0568432i	0.999596	+	0.0284216i	$0.00904810\pi$
$431$			24.4994i			0.0568432i	−0.999596	+	0.0284216i	$0.990952\pi$
$432$	8.64819	−	107.653i	0.0200190	−	0.249197i
$433$	−25.7694			−0.0595137			−0.0297568	−	0.999557i	$-0.509473\pi$
$433$	−25.7694			−0.0595137			−0.0297568	+	0.999557i	$0.509473\pi$
$434$	−565.285	+	99.6750i	−1.30250	+	0.229666i
$435$	22.4248	−	84.4903i	0.0515512	−	0.194231i
$436$	108.114	−	39.3501i	0.247967	−	0.0902526i
$437$	814.901	−	971.161i	1.86476	−	2.22234i
$438$	177.581	+	123.718i	0.405437	+	0.282461i
$439$	425.746	+	154.959i	0.969809	+	0.352981i	0.777870	−	0.628425i	$-0.216300\pi$
$439$	425.746	+	154.959i	0.969809	+	0.352981i	0.191939	+	0.981407i	$0.438522\pi$
$440$	−55.7775	+	32.2032i	−0.126767	+	0.0731890i
$441$	623.353	+	106.872i	1.41350	+	0.242340i
$442$	−18.4159	+	31.8973i	−0.0416650	+	0.0721659i
$443$	−320.772	−	382.281i	−0.724090	−	0.862937i	0.270931	−	0.962599i	$-0.412668\pi$
$443$	−320.772	−	382.281i	−0.724090	−	0.862937i	−0.995021	+	0.0996616i	$0.968224\pi$
$444$	13.1029	+	145.790i	0.0295111	+	0.328356i
$445$	76.8970	−	436.105i	0.172802	−	0.980010i
$446$	−481.402	−	84.8842i	−1.07938	−	0.190323i
$447$	−254.904	+	22.9097i	−0.570256	+	0.0512520i
$448$	−66.9288	+	56.1600i	−0.149395	+	0.125357i
$449$	−172.434	−	99.5548i	−0.384040	−	0.221726i	0.295534	−	0.955332i	$-0.404502\pi$
$449$	−172.434	−	99.5548i	−0.384040	−	0.221726i	−0.679575	+	0.733606i	$0.737836\pi$
$450$	−55.1659	−	45.8462i	−0.122591	−	0.101880i
$451$	−47.2456	−	81.8317i	−0.104757	−	0.181445i
$452$	−81.7478	+	224.600i	−0.180858	+	0.496903i
$453$	−95.1417	+	136.564i	−0.210026	+	0.301465i
$454$	−199.797	−	167.650i	−0.440081	−	0.369272i
$455$	113.538	+	311.942i	0.249533	+	0.685587i
$456$	−281.576	−	74.7338i	−0.617491	−	0.163890i
$457$	1.65470	+	9.38428i	0.00362079	+	0.0205345i	0.986565	−	0.163371i	$-0.0522369\pi$
$457$	1.65470	+	9.38428i	0.00362079	+	0.0205345i	−0.982944	+	0.183906i	$0.941126\pi$
$458$		−	312.529i		−	0.682377i
$459$	123.445	−	34.0187i	0.268942	−	0.0741148i
$460$	−408.761			−0.888610
$461$	746.412	−	131.612i	1.61911	−	0.285493i	0.710678	−	0.703517i	$-0.248388\pi$
$461$	746.412	−	131.612i	1.61911	−	0.285493i	0.908436	+	0.418024i	$0.137277\pi$
$462$	−135.110	−	134.471i	−0.292445	−	0.291064i
$463$	−598.493	+	217.833i	−1.29264	+	0.470483i	−0.894593	−	0.446882i	$-0.852534\pi$
$463$	−598.493	+	217.833i	−1.29264	+	0.470483i	−0.398048	+	0.917365i	$0.630312\pi$
$464$	−13.5357	+	16.1313i	−0.0291718	+	0.0347656i
$465$	−52.3290	+	614.892i	−0.112536	+	1.32235i
$466$	559.130	+	203.507i	1.19985	+	0.436710i
$467$	−632.615	+	365.241i	−1.35464	+	0.782100i	−0.988895	−	0.148617i	$-0.952518\pi$
$467$	−632.615	+	365.241i	−1.35464	+	0.782100i	−0.365742	+	0.930716i	$0.619185\pi$
$468$	63.8977	+	75.4219i	0.136534	+	0.161158i
$469$	381.010	−	659.929i	0.812388	−	1.40710i
$470$	416.964	+	496.919i	0.887158	+	1.05727i
$471$	−46.1410	−	21.3830i	−0.0979639	−	0.0453992i
$472$	−34.8854	+	197.845i	−0.0739098	+	0.419163i
$473$	207.281	+	36.5492i	0.438226	+	0.0772711i
$474$	77.5314	+	110.170i	0.163568	+	0.232426i
$475$	−148.220	+	124.371i	−0.312042	+	0.261834i
$476$	−89.7083	−	51.7931i	−0.188463	−	0.108809i
$477$	73.9177	+	126.640i	0.154964	+	0.265493i
$478$	−56.3204	−	97.5497i	−0.117825	−	0.204079i
$479$	−119.189	+	327.468i	−0.248828	+	0.683650i	0.750902	+	0.660414i	$0.229619\pi$
$479$	−119.189	+	327.468i	−0.248828	+	0.683650i	−0.999730	+	0.0232359i	$0.992603\pi$
$480$	39.8985	+	85.0363i	0.0831219	+	0.177159i
$481$	−102.632	−	86.1184i	−0.213372	−	0.179040i
$482$	−26.0773	−	71.6469i	−0.0541023	−	0.148645i
$483$	−315.888	−	1167.84i	−0.654012	−	2.41789i
$484$	−36.1447	−	204.987i	−0.0746791	−	0.423527i
$485$			262.816i			0.541889i
$486$	25.8956	−	342.677i	0.0532831	−	0.705096i
$487$	−24.8144			−0.0509535			−0.0254768	−	0.999675i	$-0.508110\pi$
$487$	−24.8144			−0.0509535			−0.0254768	+	0.999675i	$0.508110\pi$
$488$	−219.849	+	38.7653i	−0.450510	+	0.0794371i
$489$	668.301	−	180.768i	1.36667	−	0.369669i
$490$	−516.888	+	188.132i	−1.05487	+	0.383943i
$491$	−357.910	+	426.541i	−0.728941	+	0.868719i	−0.995467	−	0.0951093i	$-0.969680\pi$
$491$	−357.910	+	426.541i	−0.728941	+	0.868719i	0.266525	+	0.963828i	$0.414124\pi$
$492$	−124.757	+	58.5355i	−0.253572	+	0.118975i
$493$	−23.4608	−	8.53904i	−0.0475879	−	0.0173206i
$494$	230.921	−	133.322i	0.467451	−	0.269883i
$495$	−176.996	+	103.309i	−0.357567	+	0.208706i
$496$	74.3296	−	128.743i	0.149858	−	0.259562i
$497$	534.243	+	636.686i	1.07494	+	1.28106i
$498$	101.271	−	71.2687i	0.203355	−	0.143110i
$499$	−71.2311	+	403.972i	−0.142748	+	0.809562i	0.826400	+	0.563083i	$0.190385\pi$
$499$	−71.2311	+	403.972i	−0.142748	+	0.809562i	−0.969148	+	0.246479i	$0.920726\pi$
$500$	−211.105	−	37.2235i	−0.422210	−	0.0744470i
$501$	202.248	−	436.418i	0.403688	−	0.871093i
$502$	−224.239	+	188.159i	−0.446692	+	0.374819i
$503$	−435.156	−	251.237i	−0.865121	−	0.499478i	0.000603145	−	1.00000i	$-0.499808\pi$
$503$	−435.156	−	251.237i	−0.865121	−	0.499478i	−0.865724	+	0.500522i	$0.833141\pi$
$504$	−212.117	+	179.707i	−0.420868	+	0.356561i
$505$	−126.276	−	218.717i	−0.250052	−	0.433102i
$506$	−73.4789	+	201.882i	−0.145215	+	0.398976i
$507$	415.024	+	35.3197i	0.818588	+	0.0696641i
$508$	−210.987	−	177.039i	−0.415329	−	0.348503i
$509$	40.2964	+	110.713i	0.0791678	+	0.217512i	0.972962	−	0.230966i	$-0.0741886\pi$
$509$	40.2964	+	110.713i	0.0791678	+	0.217512i	−0.893794	+	0.448478i	$0.851966\pi$
$510$	−78.5609	+	78.9339i	−0.154041	+	0.154772i
$511$	−96.7426	−	548.654i	−0.189320	−	1.07369i
$512$		−	22.6274i		−	0.0441942i
$513$	−897.086	−	233.555i	−1.74871	−	0.455273i
$514$	288.861			0.561987
$515$	77.6934	−	13.6994i	0.150861	−	0.0266008i
$516$	78.7460	−	296.693i	0.152608	−	0.574986i
$517$	320.375	−	116.607i	0.619681	−	0.225546i
$518$	242.200	−	288.643i	0.467568	−	0.557226i
$519$	781.263	+	544.293i	1.50532	+	1.04873i
$520$	−80.7885	−	29.4046i	−0.155363	−	0.0565474i
$521$	0.627494	−	0.362284i	0.00120440	−	0.000695363i	−0.499398	−	0.866373i	$-0.666445\pi$
$521$	0.627494	−	0.362284i	0.00120440	−	0.000695363i	0.500602	+	0.865678i	$0.333112\pi$
$522$	−42.8268	+	51.5328i	−0.0820437	+	0.0987218i
$523$	290.424	−	503.029i	0.555304	−	0.961814i	−0.442576	−	0.896731i	$-0.645935\pi$
$523$	290.424	−	503.029i	0.555304	−	0.961814i	0.997880	−	0.0650834i	$-0.0207313\pi$
$524$	−82.3881	−	98.1863i	−0.157229	−	0.187379i
$525$	16.5282	+	183.901i	0.0314824	+	0.350288i
$526$	46.8225	−	265.544i	0.0890162	−	0.504836i
$527$	173.575	+	30.6059i	0.329363	+	0.0580757i
$528$	49.1705	−	4.41922i	0.0931259	−	0.00836974i
$529$	−639.256	+	536.399i	−1.20842	+	1.01399i
$530$	−110.446	−	63.7662i	−0.208389	−	0.120314i
$531$	−108.022	+	630.058i	−0.203431	+	1.18655i
$532$	374.956	+	649.443i	0.704805	+	1.22076i
$533$	43.1398	−	118.526i	0.0809377	−	0.222374i
$534$	−194.035	+	278.513i	−0.363362	+	0.521559i
$535$	−447.268	−	375.302i	−0.836014	−	0.701499i
$536$	67.4984	+	185.450i	0.125930	+	0.345990i
$537$	−129.027	−	34.2454i	−0.240274	−	0.0637716i
$538$	17.4150	+	98.7653i	0.0323699	+	0.183579i
$539$			289.103i			0.536369i
$540$	128.236	+	269.979i	0.237475	+	0.499962i
$541$	15.2361			0.0281629			0.0140815	−	0.999901i	$-0.495518\pi$
$541$	15.2361			0.0281629			0.0140815	+	0.999901i	$0.495518\pi$
$542$	−164.235	+	28.9590i	−0.303016	+	0.0534300i
$543$	80.9232	+	80.5408i	0.149030	+	0.148326i
$544$	25.2095	−	9.17550i	0.0463409	−	0.0168667i
$545$	−204.666	+	243.911i	−0.375534	+	0.447543i
$546$	21.5768	−	253.539i	0.0395180	−	0.464356i
$547$	−539.917	−	196.514i	−0.987051	−	0.359257i	−0.202473	−	0.979288i	$-0.564898\pi$
$547$	−539.917	−	196.514i	−0.987051	−	0.359257i	−0.784578	+	0.620031i	$0.787120\pi$
$548$	132.209	−	76.3307i	0.241257	−	0.139290i
$549$	−698.963	+	126.662i	−1.27316	+	0.230715i
$550$	16.3944	−	28.3960i	0.0298081	−	0.0516291i
$551$	116.180	+	138.458i	0.210854	+	0.251286i
$552$	284.280	+	131.743i	0.514999	+	0.238665i
$553$	60.2177	−	341.512i	0.108893	−	0.617562i
$554$	345.233	+	60.8739i	0.623164	+	0.109881i
$555$	−233.139	−	331.284i	−0.420069	−	0.596908i
$556$	−163.131	+	136.883i	−0.293402	+	0.246193i
$557$	−276.094	−	159.403i	−0.495680	−	0.286181i	0.231248	−	0.972895i	$-0.425719\pi$
$557$	−276.094	−	159.403i	−0.495680	−	0.286181i	−0.726928	+	0.686714i	$0.759052\pi$
$558$	234.572	−	410.772i	0.420380	−	0.736151i
$559$	140.480	+	243.318i	0.251305	+	0.435273i
$560$	82.6979	−	227.210i	0.147675	−	0.405733i
$561$	24.8623	+	52.9894i	0.0443179	+	0.0944553i
$562$	77.7668	+	65.2541i	0.138375	+	0.116111i
$563$	84.4286	+	231.966i	0.149962	+	0.412017i	0.991814	−	0.127691i	$-0.0407567\pi$
$563$	84.4286	+	231.966i	0.149962	+	0.412017i	−0.841852	+	0.539708i	$0.818534\pi$
$564$	−129.829	−	479.978i	−0.230193	−	0.851024i
$565$	−114.862	−	651.417i	−0.203296	−	1.15295i
$566$			425.650i			0.752031i
$567$	−672.237	+	575.013i	−1.18560	+	1.01413i
$568$	−215.252			−0.378965
$569$	165.837	−	29.2415i	0.291454	−	0.0513911i	−0.0260097	−	0.999662i	$-0.508280\pi$
$569$	165.837	−	29.2415i	0.291454	−	0.0513911i	0.317463	+	0.948271i	$0.397169\pi$
$570$	778.266	−	210.512i	1.36538	−	0.369320i
$571$	−605.483	+	220.378i	−1.06039	+	0.385951i	−0.812575	−	0.582856i	$-0.801935\pi$
$571$	−605.483	+	220.378i	−1.06039	+	0.385951i	−0.247816	+	0.968807i	$0.579713\pi$
$572$	−29.0451	+	34.6146i	−0.0507782	+	0.0605151i
$573$	555.383	−	260.583i	0.969256	−	0.454769i
$574$	333.343	+	121.327i	0.580736	+	0.211371i
$575$	180.218	−	104.049i	0.313422	−	0.180955i
$576$	−0.341029	−	71.9992i	−0.000592064	−	0.124999i
$577$	63.2482	−	109.549i	0.109616	−	0.189860i	−0.805999	−	0.591917i	$-0.798371\pi$
$577$	63.2482	−	109.549i	0.109616	−	0.189860i	0.915615	+	0.402057i	$0.131705\pi$
$578$	−242.267	−	288.723i	−0.419147	−	0.499520i
$579$	284.244	−	200.035i	0.490922	−	0.345483i
$580$	10.1197	−	57.3917i	0.0174478	−	0.0989512i
$581$	−313.926	−	55.3536i	−0.540320	−	0.0952730i
$582$	84.7053	−	182.780i	0.145542	−	0.314055i
$583$	−51.3472	+	43.0854i	−0.0880741	+	0.0739029i
$584$	124.955	+	72.1428i	0.213964	+	0.123532i
$585$	−257.508	−	92.3463i	−0.440184	−	0.157857i
$586$	−70.9878	−	122.955i	−0.121140	−	0.209820i
$587$	−327.703	+	900.357i	−0.558268	+	1.53383i	0.263881	+	0.964555i	$0.414997\pi$
$587$	−327.703	+	900.357i	−0.558268	+	1.53383i	−0.822149	+	0.569273i	$0.807225\pi$
$588$	420.113	+	35.7528i	0.714479	+	0.0608041i
$589$	−977.455	−	820.182i	−1.65952	−	1.39250i
$590$	−190.155	−	522.448i	−0.322297	−	0.885504i
$591$	−187.450	+	188.340i	−0.317174	+	0.318680i
$592$	16.9455	+	96.1025i	0.0286241	+	0.162335i
$593$			733.805i			1.23745i	0.785609	+	0.618723i	$0.212350\pi$
$593$			733.805i			1.23745i	−0.785609	+	0.618723i	$0.787650\pi$
$594$	156.391	−	14.8028i	0.263285	−	0.0249205i
$595$	286.672			0.481802
$596$	−168.029	+	29.6280i	−0.281928	+	0.0497115i
$597$	207.441	−	781.580i	0.347473	−	1.30918i
$598$	−269.484	+	98.0840i	−0.450641	+	0.164020i
$599$	727.241	−	866.692i	1.21409	−	1.44690i	0.355162	−	0.934805i	$-0.384426\pi$
$599$	727.241	−	866.692i	1.21409	−	1.44690i	0.858930	−	0.512094i	$-0.171130\pi$
$600$	−39.2365	−	27.3355i	−0.0653942	−	0.0455591i
$601$	713.313	+	259.625i	1.18688	+	0.431988i	0.858626	−	0.512602i	$-0.171318\pi$
$601$	713.313	+	259.625i	1.18688	+	0.431988i	0.328251	+	0.944590i	$0.393541\pi$
$602$	−684.309	+	395.086i	−1.13673	+	0.656289i
$603$	217.571	+	589.076i	0.360815	+	0.976908i
$604$	−55.4793	+	96.0929i	−0.0918531	+	0.159094i
$605$	370.276	+	441.278i	0.612026	+	0.729384i
$606$	17.3288	+	192.809i	0.0285954	+	0.318166i
$607$	79.5776	−	451.307i	0.131100	−	0.743504i	−0.846397	−	0.532553i	$-0.821233\pi$
$607$	79.5776	−	451.307i	0.131100	−	0.743504i	0.977497	−	0.210951i	$-0.0676561\pi$
$608$	−191.266	−	33.7254i	−0.314582	−	0.0554693i
$609$	171.790	−	15.4397i	0.282085	−	0.0253526i
$610$	473.271	−	397.122i	0.775855	−	0.651019i
$611$	394.130	+	227.551i	0.645057	+	0.372424i
$612$	80.0769	−	29.5759i	0.130845	−	0.0483266i
$613$	44.6060	+	77.2599i	0.0727667	+	0.126036i	0.900113	−	0.435657i	$-0.143484\pi$
$613$	44.6060	+	77.2599i	0.0727667	+	0.126036i	−0.827346	+	0.561692i	$0.810150\pi$
$614$	−131.567	+	361.477i	−0.214278	+	0.588725i
$615$	218.009	−	312.923i	0.354486	−	0.508819i
$616$	−97.3506	−	81.6868i	−0.158037	−	0.132608i
$617$	185.560	+	509.821i	0.300745	+	0.826290i	0.994371	+	0.105955i	$0.0337899\pi$
$617$	185.560	+	509.821i	0.300745	+	0.826290i	−0.693626	+	0.720335i	$0.743988\pi$
$618$	−58.4485	−	15.5130i	−0.0945769	−	0.0251019i
$619$	89.2899	+	506.388i	0.144249	+	0.818075i	0.967967	+	0.251076i	$0.0807844\pi$
$619$	89.2899	+	506.388i	0.144249	+	0.818075i	−0.823719	+	0.566999i	$0.808104\pi$
$620$			411.410i			0.663565i
$621$	906.548	+	414.915i	1.45982	+	0.668140i
$622$	577.721			0.928812
$623$	860.491	−	151.728i	1.38121	−	0.243544i
$624$	46.7087	+	46.4880i	0.0748537	+	0.0745000i
$625$	689.857	−	251.087i	1.10377	−	0.401740i
$626$	221.281	−	263.713i	0.353485	−	0.421266i
$627$	35.9318	−	422.217i	0.0573076	−	0.673393i
$628$	−31.8587	−	11.5956i	−0.0507304	−	0.0184643i
$629$	−100.197	+	57.8490i	−0.159296	+	0.0919698i
$630$	259.716	−	724.218i	0.412247	−	1.14955i
$631$	317.732	−	550.327i	0.503537	−	0.872151i	−0.496455	−	0.868062i	$-0.665365\pi$
$631$	317.732	−	550.327i	0.503537	−	0.872151i	0.999992	−	0.00408856i	$-0.00130143\pi$
$632$	57.7294	+	68.7993i	0.0913440	+	0.108860i
$633$	−382.902	−	177.447i	−0.604900	−	0.280327i
$634$	−66.7342	+	378.469i	−0.105259	+	0.596954i
$635$	750.649	+	132.360i	1.18212	+	0.208440i
$636$	56.2601	+	79.9441i	0.0884592	+	0.125698i
$637$	−295.625	+	248.059i	−0.464090	+	0.389418i
$638$	−26.5259	−	15.3147i	−0.0415766	−	0.0240043i
$639$	−684.920	+	3.24417i	−1.07186	+	0.00507695i
$640$	31.3104	+	54.2312i	0.0489225	+	0.0847362i
$641$	219.882	−	604.121i	0.343030	−	0.942466i	−0.641481	−	0.767139i	$-0.721680\pi$
$641$	219.882	−	604.121i	0.343030	−	0.942466i	0.984510	−	0.175327i	$-0.0560982\pi$
$642$	190.101	+	405.164i	0.296107	+	0.631097i
$643$	499.083	+	418.781i	0.776179	+	0.651292i	0.942283	−	0.334816i	$-0.108674\pi$
$643$	499.083	+	418.781i	0.776179	+	0.651292i	−0.166104	+	0.986108i	$0.553119\pi$
$644$	−275.852	−	757.898i	−0.428342	−	1.17686i
$645$	221.814	+	820.048i	0.343898	+	1.27139i
$646$	−39.9852	−	226.768i	−0.0618966	−	0.351033i
$647$		−	736.107i		−	1.13772i	−0.822433	−	0.568862i	$-0.807384\pi$
$647$		−	736.107i		−	1.13772i	0.822433	−	0.568862i	$-0.192616\pi$
$648$	−2.17027	−	229.092i	−0.00334918	−	0.353538i
$649$	−292.213			−0.450250
$650$	43.1036	−	7.60033i	0.0663132	−	0.0116928i
$651$	−1175.41	+	317.935i	−1.80554	+	0.488380i
$652$	433.710	−	157.858i	0.665199	−	0.242113i
$653$	102.032	−	121.597i	0.156251	−	0.186213i	−0.682240	−	0.731129i	$-0.738994\pi$
$653$	102.032	−	121.597i	0.156251	−	0.186213i	0.838491	+	0.544916i	$0.183438\pi$
$654$	220.951	−	103.669i	0.337845	−	0.158515i
$655$	333.324	+	121.320i	0.508891	+	0.185221i
$656$	−79.5630	+	45.9357i	−0.121285	+	0.0700240i
$657$	398.687	+	227.671i	0.606830	+	0.346532i
$658$	−639.966	+	1108.45i	−0.972593	+	1.68458i
$659$	−813.429	−	969.407i	−1.23434	−	1.47103i	−0.831281	−	0.555852i	$-0.812392\pi$
$659$	−813.429	−	969.407i	−1.23434	−	1.47103i	−0.403057	−	0.915175i	$-0.632052\pi$
$660$	−111.732	+	78.6305i	−0.169291	+	0.119137i
$661$	−155.505	+	881.911i	−0.235257	+	1.33421i	0.606816	+	0.794842i	$0.292447\pi$
$661$	−155.505	+	881.911i	−0.235257	+	1.33421i	−0.842073	+	0.539364i	$0.818665\pi$
$662$	617.486	+	108.879i	0.932758	+	0.164470i
$663$	−32.8523	+	70.8898i	−0.0495510	+	0.106923i
$664$	63.2419	−	53.0663i	0.0952439	−	0.0799191i
$665$	−1797.32	−	1037.68i	−2.70273	−	1.56042i
$666$	55.3679	+	305.537i	0.0831350	+	0.458765i
$667$	−97.1964	−	168.349i	−0.145722	−	0.252397i
$668$	109.675	−	301.330i	0.164185	−	0.451093i
$669$	−1033.23	−	87.9305i	−1.54444	−	0.131436i
$670$	−418.388	−	351.069i	−0.624460	−	0.523984i
$671$	−111.058	−	305.129i	−0.165511	−	0.454738i
$672$	−130.743	+	131.364i	−0.194559	+	0.195482i
$673$	198.279	+	1124.50i	0.294620	+	1.67087i	0.668742	+	0.743495i	$0.266833\pi$
$673$	198.279	+	1124.50i	0.294620	+	1.67087i	−0.374122	+	0.927380i	$0.622056\pi$
$674$		−	218.862i		−	0.324721i
$675$	−125.260	−	86.3886i	−0.185571	−	0.127983i
$676$	277.683			0.410773
$677$	−1228.42	+	216.603i	−1.81450	+	0.319945i	−0.974795	−	0.223101i	$-0.928382\pi$
$677$	−1228.42	+	216.603i	−1.81450	+	0.319945i	−0.839703	+	0.543046i	$0.817271\pi$
$678$	−130.068	+	490.059i	−0.191840	+	0.722801i
$679$	−487.297	+	177.362i	−0.717668	+	0.261210i
$680$	−47.7231	+	56.8742i	−0.0701811	+	0.0836385i
$681$	−453.967	−	316.271i	−0.666618	−	0.464422i
$682$	203.190	+	73.9552i	0.297933	+	0.108439i
$683$	−779.418	+	449.997i	−1.14117	+	0.658854i	−0.946720	−	0.322059i	$-0.895625\pi$
$683$	−779.418	+	449.997i	−1.14117	+	0.658854i	−0.194449	+	0.980913i	$0.562292\pi$
$684$	−609.106	−	104.430i	−0.890506	−	0.152675i
$685$	−211.243	+	365.884i	−0.308384	+	0.534137i
$686$	−211.184	−	251.679i	−0.307848	−	0.366879i
$687$	−59.3459	−	660.312i	−0.0863841	−	0.961152i
$688$	35.5359	−	201.534i	0.0516511	−	0.292928i
$689$	−88.1149	−	15.5370i	−0.127888	−	0.0225501i
$690$	−863.631	+	77.6193i	−1.25164	+	0.112492i
$691$	−286.646	+	240.525i	−0.414828	+	0.348082i	−0.826192	−	0.563389i	$-0.809497\pi$
$691$	−286.646	+	240.525i	−0.414828	+	0.348082i	0.411363	+	0.911471i	$0.365053\pi$
$692$	549.735	+	317.390i	0.794415	+	0.458656i
$693$	−310.995	−	258.456i	−0.448767	−	0.372952i
$694$	−148.788	−	257.709i	−0.214392	−	0.371338i
$695$	201.567	−	553.800i	0.290024	−	0.796834i
$696$	−25.5352	+	36.6525i	−0.0366885	+	0.0526616i
$697$	−83.4406	−	70.0150i	−0.119714	−	0.100452i
$698$	−208.528	−	572.925i	−0.298750	−	0.820810i
$699$	1219.98	+	323.797i	1.74532	+	0.463229i
$700$	21.3752	+	121.225i	0.0305361	+	0.173179i
$701$		−	574.292i		−	0.819247i	−0.912255	−	0.409624i	$-0.865660\pi$
$701$		−	574.292i		−	0.819247i	0.912255	−	0.409624i	$-0.134340\pi$
$702$	149.325	+	147.218i	0.212714	+	0.209713i
$703$	837.596			1.19146
$704$	32.4124	−	5.71519i	0.0460404	−	0.00811816i
$705$	975.323	+	970.715i	1.38344	+	1.37690i
$706$	−364.300	+	132.594i	−0.516005	+	0.187811i
$707$	320.313	−	381.734i	0.453059	−	0.539935i
$708$	−36.1374	+	424.632i	−0.0510415	+	0.599763i
$709$	−98.2153	−	35.7475i	−0.138527	−	0.0504195i	0.271827	−	0.962346i	$-0.412372\pi$
$709$	−98.2153	−	35.7475i	−0.138527	−	0.0504195i	−0.410353	+	0.911927i	$0.634595\pi$
$710$	515.895	−	297.852i	0.726613	−	0.419510i
$711$	184.729	+	218.045i	0.259815	+	0.306674i
$712$	−113.146	+	195.975i	−0.158914	+	0.275246i
$713$	882.114	+	1051.26i	1.23719	+	1.47442i
$714$	−199.371	−	92.3941i	−0.279231	−	0.129403i
$715$	21.7150	−	123.152i	0.0303706	−	0.172240i
$716$	−87.6441	−	15.4540i	−0.122408	−	0.0215838i
$717$	−137.518	−	195.409i	−0.191796	−	0.272537i
$718$	−50.3091	+	42.2143i	−0.0700683	+	0.0587943i
$719$	960.194	+	554.368i	1.33546	+	0.771027i	0.986130	−	0.165974i	$-0.0530766\pi$
$719$	960.194	+	554.368i	1.33546	+	0.771027i	0.349328	+	0.937001i	$0.386410\pi$
$720$	100.445	+	172.089i	0.139507	+	0.239012i
$721$	77.8320	+	134.809i	0.107950	+	0.186975i
$722$	−395.539	+	1086.73i	−0.547837	+	1.50517i
$723$	−68.7013	−	146.424i	−0.0950225	−	0.202523i
$724$	58.3075	+	48.9258i	0.0805353	+	0.0675771i
$725$	10.1472	+	27.8793i	0.0139962	+	0.0384542i
$726$	−115.292	−	426.234i	−0.158804	−	0.587099i
$727$	−178.676	−	1013.32i	−0.245772	−	1.39384i	−0.818693	−	0.574232i	$-0.805301\pi$
$727$	−178.676	−	1013.32i	−0.245772	−	1.39384i	0.572921	−	0.819611i	$-0.305810\pi$
$728$		−	169.637i		−	0.233017i
$729$	−10.3584	−	728.926i	−0.0142091	−	0.999899i
$730$	−399.307			−0.546995
$731$	238.942	−	42.1319i	0.326870	−	0.0576359i
$732$	−457.137	+	123.650i	−0.624504	+	0.168921i
$733$	315.178	−	114.715i	0.429984	−	0.156501i	−0.117956	−	0.993019i	$-0.537634\pi$
$733$	315.178	−	114.715i	0.429984	−	0.156501i	0.547940	+	0.836517i	$0.315412\pi$
$734$	−582.081	+	693.697i	−0.793026	+	0.945092i
$735$	−1056.36	+	495.637i	−1.43722	+	0.674337i
$736$	196.285	+	71.4418i	0.266691	+	0.0970677i
$737$	−248.598	+	143.528i	−0.337311	+	0.194747i
$738$	−252.473	+	147.364i	−0.342104	+	0.199680i
$739$	130.983	−	226.869i	0.177244	−	0.306995i	−0.763692	−	0.645581i	$-0.776615\pi$
$739$	130.983	−	226.869i	0.177244	−	0.306995i	0.940935	+	0.338586i	$0.109949\pi$
$740$	−173.594	−	206.881i	−0.234586	−	0.279569i
$741$	462.574	−	325.533i	0.624256	−	0.439316i
$742$	43.6965	−	247.815i	0.0588902	−	0.333983i
$743$	−477.341	−	84.1680i	−0.642450	−	0.113281i	−0.157074	−	0.987587i	$-0.550206\pi$
$743$	−477.341	−	84.1680i	−0.642450	−	0.113281i	−0.485376	+	0.874305i	$0.661317\pi$
$744$	132.597	−	286.122i	0.178222	−	0.384573i
$745$	361.718	−	303.517i	0.485527	−	0.407406i
$746$	−5.68555	−	3.28255i	−0.00762138	−	0.00440021i
$747$	200.433	−	169.807i	0.268317	−	0.227319i
$748$	19.5107	+	33.7936i	0.0260838	+	0.0451785i
$749$	394.023	−	1082.57i	0.526065	−	1.44535i
$750$	−453.092	−	38.5594i	−0.604122	−	0.0514125i
$751$	668.630	+	561.047i	0.890320	+	0.747067i	0.968274	−	0.249890i	$-0.0803944\pi$
$751$	668.630	+	561.047i	0.890320	+	0.747067i	−0.0779544	+	0.996957i	$0.524839\pi$
$752$	−113.374	−	311.493i	−0.150764	−	0.414220i
$753$	−438.045	+	440.124i	−0.581733	+	0.584495i
$754$	−7.09978	−	40.2649i	−0.00941616	−	0.0534017i
$755$		−	307.075i		−	0.406722i
$756$	−414.038	+	419.964i	−0.547670	+	0.555508i
$757$	599.418			0.791834			0.395917	−	0.918286i	$-0.370427\pi$
$757$	599.418			0.791834			0.395917	+	0.918286i	$0.370427\pi$
$758$	362.097	−	63.8474i	0.477700	−	0.0842314i
$759$	−116.911	+	440.489i	−0.154033	+	0.580355i
$760$	505.075	−	183.832i	0.664572	−	0.241884i
$761$	−754.984	+	899.755i	−0.992094	+	1.18233i	−0.00886470	+	0.999961i	$0.502822\pi$
$761$	−754.984	+	899.755i	−0.992094	+	1.18233i	−0.983230	+	0.182371i	$0.941623\pi$
$762$	−479.393	−	333.985i	−0.629124	−	0.438301i
$763$	−590.364	−	214.875i	−0.773740	−	0.281618i
$764$	354.191	−	204.492i	0.463601	−	0.267660i
$765$	−150.995	+	181.690i	−0.197379	+	0.237503i
$766$	−188.412	+	326.340i	−0.245969	+	0.426031i

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)

\(f(q)\)	\(=\)	\(q+(1.39273 - 0.245576i) q^{2} +(2.89593 - 0.783318i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-3.55779 + 4.24001i) q^{5} +(3.84088 - 1.80212i) q^{6} +(-10.2625 - 3.73526i) q^{7} +(2.44949 - 1.41421i) q^{8} +(7.77283 - 4.53687i) q^{9} +O(q^{10})\)	\(q+(1.39273 - 0.245576i) q^{2} +(2.89593 - 0.783318i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-3.55779 + 4.24001i) q^{5} +(3.84088 - 1.80212i) q^{6} +(-10.2625 - 3.73526i) q^{7} +(2.44949 - 1.41421i) q^{8} +(7.77283 - 4.53687i) q^{9} +(-3.91380 + 6.77890i) q^{10} +(2.64446 + 3.15155i) q^{11} +(4.90675 - 3.45309i) q^{12} +(-0.953621 + 5.40825i) q^{13} +(-15.2102 - 2.68197i) q^{14} +(-6.98185 + 15.0657i) q^{15} +(3.06418 - 2.57115i) q^{16} +(4.10708 + 2.37123i) q^{17} +(9.71129 - 8.22744i) q^{18} +(-17.1665 - 29.7332i) q^{19} +(-3.78613 + 10.4023i) q^{20} +(-32.6455 - 2.77822i) q^{21} +(4.45696 + 3.73984i) q^{22} +(12.6292 + 34.6986i) q^{23} +(5.98577 - 6.01419i) q^{24} +(-0.978615 - 5.55000i) q^{25} +7.76642i q^{26} +(18.9558 - 19.2270i) q^{27} -21.8423 q^{28} +(-5.18449 + 0.914165i) q^{29} +(-6.02406 + 22.6970i) q^{30} +(34.9235 - 12.7111i) q^{31} +(3.63616 - 4.33340i) q^{32} +(10.1269 + 7.05521i) q^{33} +(6.30237 + 2.29387i) q^{34} +(52.3496 - 30.2240i) q^{35} +(11.5047 - 13.8434i) q^{36} +(-12.1981 + 21.1278i) q^{37} +(-31.2100 - 37.1946i) q^{38} +(1.47476 + 16.4089i) q^{39} +(-2.71850 + 15.4174i) q^{40} +(-22.6189 - 3.98833i) q^{41} +(-46.1486 + 4.14763i) q^{42} +(39.1915 - 32.8855i) q^{43} +(7.12575 + 4.11406i) q^{44} +(-8.41774 + 49.0981i) q^{45} +(26.1102 + 45.2243i) q^{46} +(28.3436 - 77.8733i) q^{47} +(6.85962 - 9.84610i) q^{48} +(53.8315 + 45.1700i) q^{49} +(-2.72589 - 7.48932i) q^{50} +(13.7513 + 3.64975i) q^{51} +(1.90724 + 10.8165i) q^{52} +16.2927i q^{53} +(21.6785 - 31.4331i) q^{54} -22.7711 q^{55} +(-30.4205 + 5.36395i) q^{56} +(-73.0035 - 72.6585i) q^{57} +(-6.99608 + 2.54637i) q^{58} +(-45.6558 + 54.4105i) q^{59} +(-2.81606 + 33.0901i) q^{60} +(-74.1675 - 26.9948i) q^{61} +(45.5174 - 26.2795i) q^{62} +(-96.7154 + 17.5263i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-19.5383 - 23.2848i) q^{65} +(15.8365 + 7.33909i) q^{66} +(-12.1162 + 68.7145i) q^{67} +(9.34081 + 1.64704i) q^{68} +(63.7534 + 90.5919i) q^{69} +(65.4865 - 54.9497i) q^{70} +(-65.9072 - 38.0516i) q^{71} +(12.6234 - 22.1054i) q^{72} +(25.5063 + 44.1783i) q^{73} +(-11.8002 + 32.4208i) q^{74} +(-7.18141 - 15.3058i) q^{75} +(-52.6012 - 44.1376i) q^{76} +(-15.3671 - 42.2207i) q^{77} +(6.08357 + 22.4910i) q^{78} +(5.51385 + 31.2706i) q^{79} +22.1398i q^{80} +(39.8337 - 70.5286i) q^{81} -32.4815 q^{82} +(28.7447 - 5.06847i) q^{83} +(-63.2539 + 17.1095i) q^{84} +(-24.6662 + 8.97776i) q^{85} +(46.5072 - 55.4251i) q^{86} +(-14.2978 + 6.70846i) q^{87} +(10.9346 + 3.97985i) q^{88} +(-69.2878 + 40.0033i) q^{89} +(0.333680 + 70.4476i) q^{90} +(29.9878 - 51.9404i) q^{91} +(47.4704 + 56.5731i) q^{92} +(91.1791 - 64.1666i) q^{93} +(20.3511 - 115.417i) q^{94} +(187.144 + 32.9986i) q^{95} +(7.13562 - 15.3975i) q^{96} +(36.3741 - 30.5215i) q^{97} +(86.0653 + 49.6898i) q^{98} +(34.8531 + 12.4989i) 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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