LMFDB - Embedded newform 54.3.f.a.29.6

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			29.6
Character	$\chi$	$=$	54.29
Dual form			54.3.f.a.41.6

$q$-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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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	0.282223	−	0.959349i	$-0.408928\pi$
$5$	−3.55779	−	4.24001i	−0.711559	−	0.848003i	−0.993782	+	0.111346i	$0.964484\pi$
$6$	3.84088	+	1.80212i	0.640147	+	0.300353i
$7$	−10.2625	+	3.73526i	−1.46608	+	0.533609i	−0.947032	−	0.321138i	$-0.895935\pi$
$7$	−10.2625	+	3.73526i	−1.46608	+	0.533609i	−0.519045	+	0.854747i	$0.673712\pi$
$8$	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	−0.632328	−	0.774701i	$-0.717901\pi$
$11$	2.64446	−	3.15155i	0.240406	−	0.286505i	0.872734	+	0.488196i	$0.162345\pi$
$12$	4.90675	+	3.45309i	0.408896	+	0.287757i
$13$	−0.953621	−	5.40825i	−0.0733555	−	0.416020i	−0.999267	−	0.0382793i	$-0.987812\pi$
$13$	−0.953621	−	5.40825i	−0.0733555	−	0.416020i	0.925912	−	0.377740i	$-0.123299\pi$
$14$	−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	−0.374316	−	0.927301i	$-0.622122\pi$
$17$	4.10708	−	2.37123i	0.241593	−	0.139484i	0.615909	+	0.787817i	$0.288789\pi$
$18$	9.71129	+	8.22744i	0.539516	+	0.457080i
$19$	−17.1665	+	29.7332i	−0.903499	+	1.56491i	−0.0805801	+	0.996748i	$0.525677\pi$
$19$	−17.1665	+	29.7332i	−0.903499	+	1.56491i	−0.822919	+	0.568158i	$0.807656\pi$
$20$	−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	−0.285833	−	0.958279i	$-0.592270\pi$
$23$	12.6292	−	34.6986i	0.549098	−	1.50863i	0.834931	−	0.550354i	$-0.185507\pi$
$24$	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	0.0835437	−	0.996504i	$-0.473376\pi$
$29$	−5.18449	−	0.914165i	−0.178775	−	0.0315229i	−0.262319	+	0.964981i	$0.584487\pi$
$30$	−6.02406	−	22.6970i	−0.200802	−	0.756565i
$31$	34.9235	+	12.7111i	1.12656	+	0.410036i	0.837044	−	0.547136i	$-0.184282\pi$
$31$	34.9235	+	12.7111i	1.12656	+	0.410036i	0.289520	+	0.957172i	$0.406504\pi$
$32$	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	0.652769	−	0.757557i	$-0.273607\pi$
$37$	−12.1981	−	21.1278i	−0.329679	−	0.571021i	−0.982448	+	0.186536i	$0.940274\pi$
$38$	−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	−0.442538	−	0.896750i	$-0.645922\pi$
$41$	−22.6189	+	3.98833i	−0.551681	+	0.0972763i	−0.109143	+	0.994026i	$0.534811\pi$
$42$	−46.1486	−	4.14763i	−1.09878	−	0.0987531i
$43$	39.1915	+	32.8855i	0.911430	+	0.764780i	0.972390	−	0.233360i	$-0.0749720\pi$
$43$	39.1915	+	32.8855i	0.911430	+	0.764780i	−0.0609609	+	0.998140i	$0.519416\pi$
$44$	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	0.745047	+	0.667012i	$0.232427\pi$
$47$	28.3436	+	77.8733i	0.603055	+	1.65688i	−0.141992	+	0.989868i	$0.545351\pi$
$48$	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	$-0.950880\pi$
$53$		−	16.2927i		−	0.307409i	0.988117	−	0.153704i	$-0.0491204\pi$
$54$	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	0.224810	−	0.974403i	$-0.427824\pi$
$59$	−45.6558	−	54.4105i	−0.773827	−	0.922212i	−0.998637	+	0.0521911i	$0.983380\pi$
$60$	−2.81606	−	33.0901i	−0.0469343	−	0.551501i
$61$	−74.1675	+	26.9948i	−1.21586	+	0.442537i	−0.868733	−	0.495281i	$-0.835065\pi$
$61$	−74.1675	+	26.9948i	−1.21586	+	0.442537i	−0.347128	+	0.937818i	$0.612843\pi$
$62$	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	−0.931186	−	0.364545i	$-0.881224\pi$
$67$	−12.1162	−	68.7145i	−0.180839	−	1.02559i	0.750347	−	0.661045i	$-0.229887\pi$
$68$	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	−0.886264	−	0.463180i	$-0.846708\pi$
$71$	−65.9072	+	38.0516i	−0.928271	+	0.535937i	−0.0420065	+	0.999117i	$0.513375\pi$
$72$	12.6234	+	22.1054i	0.175324	+	0.307020i
$73$	25.5063	−	44.1783i	0.349402	−	0.605182i	−0.636741	−	0.771077i	$-0.719718\pi$
$73$	25.5063	−	44.1783i	0.349402	−	0.605182i	0.986143	+	0.165896i	$0.0530515\pi$
$74$	−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	−0.929818	−	0.368021i	$-0.880036\pi$
$79$	5.51385	−	31.2706i	0.0697956	−	0.395830i	0.999613	−	0.0278099i	$-0.00885329\pi$
$80$		−	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	0.344104	−	0.938932i	$-0.388183\pi$
$83$	28.7447	+	5.06847i	0.346322	+	0.0610659i	0.00221805	+	0.999998i	$0.499294\pi$
$84$	−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	0.0573893	−	0.998352i	$-0.481722\pi$
$89$	−69.2878	−	40.0033i	−0.778514	−	0.449475i	−0.835903	+	0.548877i	$0.815056\pi$
$90$	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	0.810732	−	0.585417i	$-0.199069\pi$
$97$	36.3741	+	30.5215i	0.374991	+	0.314655i	−0.435741	+	0.900072i	$0.643514\pi$
$98$	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	0.838148	−	0.545442i	$-0.183638\pi$
$101$	−15.6059	−	42.8769i	−0.154514	−	0.424524i	−0.992662	+	0.120918i	$0.961416\pi$
$102$	20.0481	−	1.70614i	0.196550	−	0.0167269i
$103$	−10.9188	+	9.16192i	−0.106007	+	0.0889507i	−0.694251	−	0.719733i	$-0.744264\pi$
$103$	−10.9188	+	9.16192i	−0.106007	+	0.0889507i	0.588243	+	0.808684i	$0.299820\pi$
$104$	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	$-0.835925\pi$
$107$		−	105.487i		−	0.985863i	0.870068	−	0.492931i	$-0.164075\pi$
$108$	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	0.310279	−	0.950646i	$-0.399577\pi$
$113$	−76.8178	−	91.5479i	−0.679803	−	0.810158i	−0.990082	+	0.140487i	$0.955133\pi$
$114$	−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	0.456605	+	0.889669i	$0.349065\pi$
$127$	−68.8561	+	119.262i	−0.542174	+	0.939072i	−0.998779	+	0.0494029i	$0.984268\pi$
$128$	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	−0.994807	−	0.101777i	$-0.967547\pi$
$131$	−21.9189	+	60.2217i	−0.167320	+	0.459708i	0.827487	+	0.561484i	$0.189769\pi$
$132$	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	0.441121	−	0.897448i	$-0.354581\pi$
$137$	75.1710	+	13.2547i	0.548694	+	0.0967495i	0.107573	+	0.994197i	$0.465692\pi$
$138$	111.038	−	110.514i	0.804626	−	0.800824i
$139$	−100.055	−	36.4171i	−0.719821	−	0.261993i	−0.0439712	−	0.999033i	$-0.514001\pi$
$139$	−100.055	−	36.4171i	−0.719821	−	0.261993i	−0.675850	+	0.737039i	$0.736223\pi$
$140$	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	−0.448308	−	0.893879i	$-0.647973\pi$
$149$	−84.0145	+	14.8140i	−0.563856	+	0.0994230i	−0.115547	+	0.993302i	$0.536862\pi$
$150$	−13.7605	+	19.5533i	−0.0917367	+	0.130355i
$151$	−42.4996	−	35.6614i	−0.281454	−	0.236168i	0.491121	−	0.871091i	$-0.336587\pi$
$151$	−42.4996	−	35.6614i	−0.281454	−	0.236168i	−0.772575	+	0.634923i	$0.781032\pi$
$152$	−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	−0.683206	−	0.730226i	$-0.739415\pi$
$157$	−12.9857	+	10.8963i	−0.0827115	+	0.0694032i	0.600494	+	0.799629i	$0.294970\pi$
$158$	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	0.980574	−	0.196147i	$-0.0628431\pi$
$167$	103.061	+	122.823i	0.617132	+	0.735469i	−0.363442	+	0.931617i	$0.618399\pi$
$168$	−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	0.284620	−	0.958640i	$-0.408133\pi$
$173$	204.014	−	243.135i	1.17927	−	1.40540i	0.894653	−	0.446762i	$-0.147423\pi$
$174$	−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	−0.603766	−	0.797161i	$-0.706334\pi$
$179$	−38.5365	+	22.2490i	−0.215287	+	0.124296i	0.388479	+	0.921458i	$0.373001\pi$
$180$	17.7649	−	98.0324i	0.0986940	−	0.544624i
$181$	19.0288	−	32.9588i	0.105131	−	0.182093i	−0.808661	−	0.588276i	$-0.799807\pi$
$181$	19.0288	−	32.9588i	0.105131	−	0.182093i	0.913792	+	0.406183i	$0.133140\pi$
$182$	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	0.673859	−	0.738860i	$-0.264635\pi$
$191$	201.386	+	35.5097i	1.05438	+	0.185915i	0.380516	+	0.924774i	$0.375746\pi$
$192$	6.15674	+	23.1969i	0.0320663	+	0.120817i
$193$	108.871	+	39.6259i	0.564100	+	0.205316i	0.608300	−	0.793707i	$-0.291852\pi$
$193$	108.871	+	39.6259i	0.564100	+	0.205316i	−0.0442003	+	0.999023i	$0.514074\pi$
$194$	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	0.292511	−	0.956262i	$-0.405509\pi$
$197$	−76.7079	−	44.2873i	−0.389380	−	0.224809i	−0.681892	+	0.731453i	$0.738842\pi$
$198$	51.6104	−	8.84845i	0.260658	−	0.0446892i
$199$	134.773	+	233.434i	0.677253	+	1.17304i	0.975805	+	0.218644i	$0.0701632\pi$
$199$	134.773	+	233.434i	0.677253	+	1.17304i	−0.298551	+	0.954394i	$0.596503\pi$
$200$	−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	−0.861383	−	0.507957i	$-0.830401\pi$
$211$	−107.762	+	90.4231i	−0.510721	+	0.428546i	0.350662	+	0.936502i	$0.385957\pi$
$212$	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	−0.944410	−	0.328770i	$-0.893366\pi$
$223$	−324.808	+	118.221i	−1.45654	+	0.530137i	−0.512130	+	0.858908i	$0.671144\pi$
$224$	−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	−0.961106	−	0.276178i	$-0.910932\pi$
$227$	−118.546	+	141.278i	−0.522230	+	0.622369i	0.438877	+	0.898547i	$0.355376\pi$
$228$	−186.903	+	86.6161i	−0.819750	+	0.379895i
$229$	38.3747	+	217.634i	0.167575	+	0.950365i	0.946370	+	0.323086i	$0.104720\pi$
$229$	38.3747	+	217.634i	0.167575	+	0.950365i	−0.778794	+	0.627279i	$0.784168\pi$
$230$	−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	0.566955	−	0.823748i	$-0.308121\pi$
$233$	364.370	−	210.369i	1.56382	−	0.902872i	0.996865	−	0.0791236i	$-0.0252122\pi$
$234$	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	−0.983546	−	0.180658i	$-0.942177\pi$
$239$	−27.2416	+	74.8456i	−0.113981	+	0.313162i	0.869565	+	0.493819i	$0.164400\pi$
$240$	17.3425	−	64.1153i	0.0722603	−	0.267147i
$241$	−9.36196	+	53.0943i	−0.0388463	+	0.220308i	−0.998051	−	0.0624044i	$-0.980123\pi$
$241$	−9.36196	+	53.0943i	−0.0388463	+	0.220308i	0.959205	+	0.282713i	$0.0912343\pi$
$242$			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	0.0984348	−	0.995144i	$-0.468616\pi$
$251$	−179.256	−	103.494i	−0.714167	−	0.412325i	−0.812602	+	0.582819i	$0.801950\pi$
$252$	−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	0.231999	−	0.972716i	$-0.425473\pi$
$257$	201.153	−	35.4686i	0.782695	−	0.138010i	0.550696	+	0.834706i	$0.314362\pi$
$258$	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	0.999761	+	0.0218596i	$0.00695867\pi$
$263$	65.2110	+	179.166i	0.247951	+	0.681239i	−0.751810	+	0.659379i	$0.770819\pi$
$264$	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	$-0.957920\pi$
$269$		−	70.9150i		−	0.263624i	0.991275	−	0.131812i	$-0.0420796\pi$
$270$	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	0.114584	−	0.993414i	$-0.463446\pi$
$277$	232.933	−	84.7808i	0.840915	−	0.306068i	0.726331	+	0.687346i	$0.241224\pi$
$278$	−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	−0.677667	−	0.735369i	$-0.737009\pi$
$281$	46.1416	−	54.9895i	0.164205	−	0.195692i	0.841872	+	0.539677i	$0.181453\pi$
$282$	−31.4727	+	350.181i	−0.111605	+	1.24178i
$283$	−52.2646	−	296.407i	−0.184681	−	1.04738i	−0.926365	−	0.376627i	$-0.877084\pi$
$283$	−52.2646	−	296.407i	−0.184681	−	1.04738i	0.741685	−	0.670749i	$-0.234027\pi$
$284$	−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	−0.984394	−	0.175978i	$-0.943691\pi$
$293$	−34.3361	+	94.3376i	−0.117188	+	0.321971i	0.867206	+	0.497949i	$0.165913\pi$
$294$	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	0.554903	−	0.831915i	$-0.312755\pi$
$307$	−136.003	−	235.565i	−0.443008	−	0.767312i	−0.997911	+	0.0646029i	$0.979422\pi$
$308$	−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	0.515845	−	0.856682i	$-0.327478\pi$
$311$	402.304	−	70.9371i	1.29358	−	0.228094i	0.777738	+	0.628588i	$0.216367\pi$
$312$	26.8181	−	38.1078i	0.0859555	−	0.122141i
$313$	186.473	+	156.470i	0.595761	+	0.499903i	0.890080	−	0.455805i	$-0.150648\pi$
$313$	186.473	+	156.470i	0.595761	+	0.499903i	−0.294319	+	0.955707i	$0.595093\pi$
$314$	−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	−0.995595	−	0.0937628i	$-0.970110\pi$
$317$	−92.9426	−	255.358i	−0.293194	−	0.805545i	0.702400	−	0.711782i	$-0.252112\pi$
$318$	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	0.375360	−	0.926879i	$-0.377519\pi$
$331$	416.626	−	151.639i	1.25869	−	0.458125i	0.883329	+	0.468754i	$0.155297\pi$
$332$	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	0.998368	+	0.0571153i	$0.0181903\pi$
$337$	26.8736	+	152.408i	0.0797435	+	0.452248i	−0.918624	+	0.395133i	$0.870699\pi$
$338$	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	−0.999159	−	0.0410093i	$-0.986943\pi$
$347$	−71.9673	+	197.728i	−0.207398	+	0.569823i	0.791760	+	0.610832i	$0.209165\pi$
$348$	−22.2823	−	22.3881i	−0.0640295	−	0.0643335i
$349$	−74.8630	+	424.569i	−0.214507	+	1.21653i	0.667252	+	0.744832i	$0.267470\pi$
$349$	−74.8630	+	424.569i	−0.214507	+	1.21653i	−0.881760	+	0.471699i	$0.843641\pi$
$350$		−	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	−0.222365	−	0.974964i	$-0.571378\pi$
$353$	−269.966	−	47.6023i	−0.764777	−	0.134851i	−0.542412	+	0.840113i	$0.682489\pi$
$354$	−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	0.442941	−	0.896551i	$-0.353935\pi$
$359$	−40.2168	−	23.2192i	−0.112025	−	0.0646774i	−0.554965	+	0.831873i	$0.687269\pi$
$360$	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	−0.982495	−	0.186288i	$-0.940354\pi$
$367$	−490.518	−	411.594i	−1.33656	−	1.12151i	−0.354067	−	0.935220i	$-0.615201\pi$
$368$	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	−0.647542	−	0.762030i	$-0.724203\pi$
$373$	−3.55616	+	2.98397i	−0.00953393	+	0.00799992i	0.638008	+	0.770030i	$0.279759\pi$
$374$	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	0.494609	−	0.869116i	$-0.335311\pi$
$383$	−171.274	−	204.117i	−0.447191	−	0.532942i	−0.941800	+	0.336174i	$0.890867\pi$
$384$	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	−0.746116	−	0.665816i	$-0.768083\pi$
$389$	15.2282	−	18.1483i	0.0391471	−	0.0466538i	0.785263	+	0.619163i	$0.212528\pi$
$390$	−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	−0.687009	−	0.726649i	$-0.741077\pi$
$397$	113.459	−	196.518i	0.285792	−	0.495006i	0.972801	+	0.231643i	$0.0744100\pi$
$398$	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	0.501434	+	0.865196i	$0.332806\pi$
$401$	−175.968	+	483.469i	−0.438824	+	1.20566i	−0.940258	+	0.340463i	$0.889416\pi$
$402$	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	0.640559	−	0.767909i	$-0.278703\pi$
$409$	260.800	+	94.9234i	0.637653	+	0.232087i	−0.00290599	+	0.999996i	$0.500925\pi$
$410$	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	−0.537863	−	0.843032i	$-0.680768\pi$
$419$	−316.326	+	55.7768i	−0.754955	+	0.133119i	−0.217092	+	0.976151i	$0.569657\pi$
$420$	152.500	+	329.070i	0.363095	+	0.783499i
$421$	−101.935	−	85.5332i	−0.242125	−	0.203167i	0.513648	−	0.858001i	$-0.328294\pi$
$421$	−101.935	−	85.5332i	−0.242125	−	0.203167i	−0.755772	+	0.654834i	$0.772738\pi$
$422$	−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	$-0.990952\pi$
$431$		−	24.4994i		−	0.0568432i	0.999596	−	0.0284216i	$-0.00904810\pi$
$432$	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	0.191939	−	0.981407i	$-0.438522\pi$
$439$	425.746	−	154.959i	0.969809	−	0.352981i	0.777870	+	0.628425i	$0.216300\pi$
$440$	−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	−0.995021	−	0.0996616i	$-0.968224\pi$
$443$	−320.772	+	382.281i	−0.724090	+	0.862937i	0.270931	+	0.962599i	$0.412668\pi$
$444$	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	−0.679575	−	0.733606i	$-0.737836\pi$
$449$	−172.434	+	99.5548i	−0.384040	+	0.221726i	0.295534	+	0.955332i	$0.404502\pi$
$450$	−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	−0.982944	−	0.183906i	$-0.941126\pi$
$457$	1.65470	−	9.38428i	0.00362079	−	0.0205345i	0.986565	+	0.163371i	$0.0522369\pi$
$458$			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	0.908436	−	0.418024i	$-0.137277\pi$
$461$	746.412	+	131.612i	1.61911	+	0.285493i	0.710678	+	0.703517i	$0.248388\pi$
$462$	−135.110	+	134.471i	−0.292445	+	0.291064i
$463$	−598.493	−	217.833i	−1.29264	−	0.470483i	−0.398048	−	0.917365i	$-0.630312\pi$
$463$	−598.493	−	217.833i	−1.29264	−	0.470483i	−0.894593	+	0.446882i	$0.852534\pi$
$464$	−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	−0.365742	−	0.930716i	$-0.619185\pi$
$467$	−632.615	−	365.241i	−1.35464	−	0.782100i	−0.988895	+	0.148617i	$0.952518\pi$
$468$	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	−0.999730	−	0.0232359i	$-0.992603\pi$
$479$	−119.189	−	327.468i	−0.248828	−	0.683650i	0.750902	−	0.660414i	$-0.229619\pi$
$480$	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	0.266525	−	0.963828i	$-0.414124\pi$
$491$	−357.910	−	426.541i	−0.728941	−	0.868719i	−0.995467	+	0.0951093i	$0.969680\pi$
$492$	−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	−0.969148	−	0.246479i	$-0.920726\pi$
$499$	−71.2311	−	403.972i	−0.142748	−	0.809562i	0.826400	−	0.563083i	$-0.190385\pi$
$500$	−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	−0.865724	−	0.500522i	$-0.833141\pi$
$503$	−435.156	+	251.237i	−0.865121	+	0.499478i	0.000603145		1.00000i	$0.499808\pi$
$504$	−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	−0.893794	−	0.448478i	$-0.851966\pi$
$509$	40.2964	−	110.713i	0.0791678	−	0.217512i	0.972962	+	0.230966i	$0.0741886\pi$
$510$	−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	0.500602	−	0.865678i	$-0.333112\pi$
$521$	0.627494	+	0.362284i	0.00120440	+	0.000695363i	−0.499398	+	0.866373i	$0.666445\pi$
$522$	−42.8268	−	51.5328i	−0.0820437	−	0.0987218i
$523$	290.424	+	503.029i	0.555304	+	0.961814i	0.997880	+	0.0650834i	$0.0207313\pi$
$523$	290.424	+	503.029i	0.555304	+	0.961814i	−0.442576	+	0.896731i	$0.645935\pi$
$524$	−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	−0.784578	−	0.620031i	$-0.787120\pi$
$547$	−539.917	+	196.514i	−0.987051	+	0.359257i	−0.202473	+	0.979288i	$0.564898\pi$
$548$	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	−0.726928	−	0.686714i	$-0.759052\pi$
$557$	−276.094	+	159.403i	−0.495680	+	0.286181i	0.231248	+	0.972895i	$0.425719\pi$
$558$	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	−0.841852	−	0.539708i	$-0.818534\pi$
$563$	84.4286	−	231.966i	0.149962	−	0.412017i	0.991814	+	0.127691i	$0.0407567\pi$
$564$	−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	0.317463	−	0.948271i	$-0.397169\pi$
$569$	165.837	+	29.2415i	0.291454	+	0.0513911i	−0.0260097	+	0.999662i	$0.508280\pi$
$570$	778.266	+	210.512i	1.36538	+	0.369320i
$571$	−605.483	−	220.378i	−1.06039	−	0.385951i	−0.247816	−	0.968807i	$-0.579713\pi$
$571$	−605.483	−	220.378i	−1.06039	−	0.385951i	−0.812575	+	0.582856i	$0.801935\pi$
$572$	−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	0.915615	−	0.402057i	$-0.131705\pi$
$577$	63.2482	+	109.549i	0.109616	+	0.189860i	−0.805999	+	0.591917i	$0.798371\pi$
$578$	−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	−0.822149	−	0.569273i	$-0.807225\pi$
$587$	−327.703	−	900.357i	−0.558268	−	1.53383i	0.263881	−	0.964555i	$-0.414997\pi$
$588$	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	$-0.787650\pi$
$593$		−	733.805i		−	1.23745i	0.785609	−	0.618723i	$-0.212350\pi$
$594$	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	0.858930	+	0.512094i	$0.171130\pi$
$599$	727.241	+	866.692i	1.21409	+	1.44690i	0.355162	+	0.934805i	$0.384426\pi$
$600$	−39.2365	+	27.3355i	−0.0653942	+	0.0455591i
$601$	713.313	−	259.625i	1.18688	−	0.431988i	0.328251	−	0.944590i	$-0.393541\pi$
$601$	713.313	−	259.625i	1.18688	−	0.431988i	0.858626	+	0.512602i	$0.171318\pi$
$602$	−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	0.977497	+	0.210951i	$0.0676561\pi$
$607$	79.5776	+	451.307i	0.131100	+	0.743504i	−0.846397	+	0.532553i	$0.821233\pi$
$608$	−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	−0.827346	−	0.561692i	$-0.810150\pi$
$613$	44.6060	−	77.2599i	0.0727667	−	0.126036i	0.900113	+	0.435657i	$0.143484\pi$
$614$	−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	−0.693626	−	0.720335i	$-0.743988\pi$
$617$	185.560	−	509.821i	0.300745	−	0.826290i	0.994371	−	0.105955i	$-0.0337899\pi$
$618$	−58.4485	+	15.5130i	−0.0945769	+	0.0251019i
$619$	89.2899	−	506.388i	0.144249	−	0.818075i	−0.823719	−	0.566999i	$-0.808104\pi$
$619$	89.2899	−	506.388i	0.144249	−	0.818075i	0.967967	−	0.251076i	$-0.0807844\pi$
$620$		−	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	0.999992	+	0.00408856i	$0.00130143\pi$
$631$	317.732	+	550.327i	0.503537	+	0.872151i	−0.496455	+	0.868062i	$0.665365\pi$
$632$	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	0.984510	+	0.175327i	$0.0560982\pi$
$641$	219.882	+	604.121i	0.343030	+	0.942466i	−0.641481	+	0.767139i	$0.721680\pi$
$642$	190.101	−	405.164i	0.296107	−	0.631097i
$643$	499.083	−	418.781i	0.776179	−	0.651292i	−0.166104	−	0.986108i	$-0.553119\pi$
$643$	499.083	−	418.781i	0.776179	−	0.651292i	0.942283	+	0.334816i	$0.108674\pi$
$644$	−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	$0.192616\pi$
$647$			736.107i			1.13772i	−0.822433	+	0.568862i	$0.807384\pi$
$648$	−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	0.838491	−	0.544916i	$-0.183438\pi$
$653$	102.032	+	121.597i	0.156251	+	0.186213i	−0.682240	+	0.731129i	$0.738994\pi$
$654$	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	−0.403057	+	0.915175i	$0.632052\pi$
$659$	−813.429	+	969.407i	−1.23434	+	1.47103i	−0.831281	+	0.555852i	$0.812392\pi$
$660$	−111.732	−	78.6305i	−0.169291	−	0.119137i
$661$	−155.505	−	881.911i	−0.235257	−	1.33421i	−0.842073	−	0.539364i	$-0.818665\pi$
$661$	−155.505	−	881.911i	−0.235257	−	1.33421i	0.606816	−	0.794842i	$-0.292447\pi$
$662$	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	−0.374122	−	0.927380i	$-0.622056\pi$
$673$	198.279	−	1124.50i	0.294620	−	1.67087i	0.668742	−	0.743495i	$-0.266833\pi$
$674$			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	−0.839703	−	0.543046i	$-0.817271\pi$
$677$	−1228.42	−	216.603i	−1.81450	−	0.319945i	−0.974795	+	0.223101i	$0.928382\pi$
$678$	−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	−0.194449	−	0.980913i	$-0.562292\pi$
$683$	−779.418	−	449.997i	−1.14117	−	0.658854i	−0.946720	+	0.322059i	$0.895625\pi$
$684$	−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	0.411363	−	0.911471i	$-0.365053\pi$
$691$	−286.646	−	240.525i	−0.414828	−	0.348082i	−0.826192	+	0.563389i	$0.809497\pi$
$692$	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	$0.134340\pi$
$701$			574.292i			0.819247i	−0.912255	+	0.409624i	$0.865660\pi$
$702$	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	−0.410353	−	0.911927i	$-0.634595\pi$
$709$	−98.2153	+	35.7475i	−0.138527	+	0.0504195i	0.271827	+	0.962346i	$0.412372\pi$
$710$	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	0.349328	−	0.937001i	$-0.386410\pi$
$719$	960.194	−	554.368i	1.33546	−	0.771027i	0.986130	+	0.165974i	$0.0530766\pi$
$720$	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	0.572921	+	0.819611i	$0.305810\pi$
$727$	−178.676	+	1013.32i	−0.245772	+	1.39384i	−0.818693	+	0.574232i	$0.805301\pi$
$728$			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	0.547940	−	0.836517i	$-0.315412\pi$
$733$	315.178	+	114.715i	0.429984	+	0.156501i	−0.117956	+	0.993019i	$0.537634\pi$
$734$	−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	0.940935	−	0.338586i	$-0.109949\pi$
$739$	130.983	+	226.869i	0.177244	+	0.306995i	−0.763692	+	0.645581i	$0.776615\pi$
$740$	−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	−0.485376	−	0.874305i	$-0.661317\pi$
$743$	−477.341	+	84.1680i	−0.642450	+	0.113281i	−0.157074	+	0.987587i	$0.550206\pi$
$744$	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	−0.0779544	−	0.996957i	$-0.524839\pi$
$751$	668.630	−	561.047i	0.890320	−	0.747067i	0.968274	+	0.249890i	$0.0803944\pi$
$752$	−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	−0.983230	−	0.182371i	$-0.941623\pi$
$761$	−754.984	−	899.755i	−0.992094	−	1.18233i	−0.00886470	−	0.999961i	$-0.502822\pi$
$762$	−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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