LMFDB - Embedded newform 54.3.f.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,3,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.47139342755$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	54.11
Dual form			54.3.f.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909039 + 1.08335i) q^{2} +(2.80846 - 1.05478i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.86430 - 7.86960i) q^{5} +(-1.41030 + 4.00138i) q^{6} +(-1.95208 + 11.0708i) q^{7} +(2.44949 + 1.41421i) q^{8} +(6.77487 - 5.92462i) q^{9} +O(q^{10})$	\(q+(-0.909039 + 1.08335i) q^{2} +(2.80846 - 1.05478i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.86430 - 7.86960i) q^{5} +(-1.41030 + 4.00138i) q^{6} +(-1.95208 + 11.0708i) q^{7} +(2.44949 + 1.41421i) q^{8} +(6.77487 - 5.92462i) q^{9} +(5.92177 + 10.2568i) q^{10} +(0.538121 + 1.47848i) q^{11} +(-3.05288 - 5.16526i) q^{12} +(-6.82419 + 5.72617i) q^{13} +(-10.2191 - 12.1786i) q^{14} +(-0.256445 - 25.1227i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-16.9870 + 9.80744i) q^{17} +(0.259819 + 12.7253i) q^{18} +(4.86486 - 8.42619i) q^{19} +(-16.4948 - 2.90849i) q^{20} +(6.19496 + 33.1510i) q^{21} +(-2.09088 - 0.761018i) q^{22} +(-13.8255 + 2.43781i) q^{23} +(8.37098 + 1.38808i) q^{24} +(-34.5753 - 29.0121i) q^{25} -12.5983i q^{26} +(12.7778 - 23.7851i) q^{27} +22.4832 q^{28} +(7.05122 - 8.40331i) q^{29} +(27.4498 + 22.5597i) q^{30} +(8.04854 + 45.6456i) q^{31} +(1.93476 - 5.31570i) q^{32} +(3.07076 + 3.58464i) q^{33} +(4.81694 - 27.3182i) q^{34} +(81.5316 + 47.0723i) q^{35} +(-14.0221 - 11.2863i) q^{36} +(7.89337 + 13.6717i) q^{37} +(4.70617 + 12.9301i) q^{38} +(-13.1256 + 23.2797i) q^{39} +(18.1454 - 15.2258i) q^{40} +(-6.59742 - 7.86250i) q^{41} +(-41.5456 - 23.4242i) q^{42} +(24.6205 - 8.96112i) q^{43} +(2.72514 - 1.57336i) q^{44} +(-27.2191 - 70.2854i) q^{45} +(9.92691 - 17.1939i) q^{46} +(-42.2938 - 7.45754i) q^{47} +(-9.11332 + 7.80688i) q^{48} +(-72.7075 - 26.4634i) q^{49} +(62.8606 - 11.0840i) q^{50} +(-37.3625 + 45.4614i) q^{51} +(13.6484 + 11.4523i) q^{52} +41.5395i q^{53} +(14.1521 + 35.4643i) q^{54} +13.1764 q^{55} +(-20.4381 + 24.3572i) q^{56} +(4.77497 - 28.7960i) q^{57} +(2.69390 + 15.2779i) q^{58} +(20.6989 - 56.8698i) q^{59} +(-49.3929 + 9.23010i) q^{60} +(13.2934 - 75.3906i) q^{61} +(-56.7666 - 32.7742i) q^{62} +(52.3653 + 86.5688i) q^{63} +(4.00000 + 6.92820i) q^{64} +(25.5162 + 70.1051i) q^{65} +(-6.67486 + 0.0681351i) q^{66} +(2.09011 - 1.75381i) q^{67} +(25.2164 + 30.0518i) q^{68} +(-36.2569 + 21.4293i) q^{69} +(-125.111 + 45.5367i) q^{70} +(65.1324 - 37.6042i) q^{71} +(24.9737 - 4.93118i) q^{72} +(33.0777 - 57.2922i) q^{73} +(-21.9866 - 3.87684i) q^{74} +(-127.705 - 45.0099i) q^{75} +(-18.2859 - 6.65552i) q^{76} +(-17.4184 + 3.07133i) q^{77} +(-13.2885 - 35.3818i) q^{78} +(38.8113 + 32.5666i) q^{79} +33.4986i q^{80} +(10.7977 - 80.2771i) q^{81} +14.5152 q^{82} +(21.4712 - 25.5884i) q^{83} +(63.1432 - 23.7149i) q^{84} +(28.5248 + 161.772i) q^{85} +(-12.6729 + 34.8186i) q^{86} +(10.9394 - 31.0378i) q^{87} +(-0.772758 + 4.38253i) q^{88} +(-75.2876 - 43.4673i) q^{89} +(100.887 + 34.4043i) q^{90} +(-50.0720 - 86.7273i) q^{91} +(9.60308 + 26.3842i) q^{92} +(70.7501 + 119.704i) q^{93} +(46.5258 - 39.0398i) q^{94} +(-52.3763 - 62.4197i) q^{95} +(-0.173222 - 16.9697i) q^{96} +(132.434 - 48.2019i) q^{97} +(94.7631 - 54.7115i) q^{98} +(12.4051 + 6.82832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.909039	+	1.08335i	−0.454519	+	0.541675i
$2$	−0.909039	+	1.08335i	−0.454519	+	0.541675i
$3$	2.80846	−	1.05478i	0.936153	−	0.351594i
$3$	2.80846	−	1.05478i	0.936153	−	0.351594i
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	2.86430	−	7.86960i	0.572860	−	1.57392i	−0.227103	−	0.973871i	$-0.572925\pi$
$5$	2.86430	−	7.86960i	0.572860	−	1.57392i	0.799963	−	0.600049i	$-0.204852\pi$
$6$	−1.41030	+	4.00138i	−0.235050	+	0.666897i
$7$	−1.95208	+	11.0708i	−0.278869	+	1.58155i	0.447527	+	0.894270i	$0.352305\pi$
$7$	−1.95208	+	11.0708i	−0.278869	+	1.58155i	−0.726397	+	0.687276i	$0.758806\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$	6.77487	−	5.92462i	0.752763	−	0.658291i
$10$	5.92177	+	10.2568i	0.592177	+	1.02568i
$11$	0.538121	+	1.47848i	0.0489201	+	0.134407i	0.961747	−	0.273941i	$-0.0883273\pi$
$11$	0.538121	+	1.47848i	0.0489201	+	0.134407i	−0.912826	+	0.408348i	$0.866105\pi$
$12$	−3.05288	−	5.16526i	−0.254407	−	0.430438i
$13$	−6.82419	+	5.72617i	−0.524937	+	0.440475i	−0.866349	−	0.499439i	$-0.833539\pi$
$13$	−6.82419	+	5.72617i	−0.524937	+	0.440475i	0.341412	+	0.939914i	$0.389095\pi$
$14$	−10.2191	−	12.1786i	−0.729933	−	0.869900i
$15$	−0.256445	−	25.1227i	−0.0170963	−	1.67484i
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	−16.9870	+	9.80744i	−0.999235	+	0.576909i	−0.908022	−	0.418923i	$-0.862408\pi$
$17$	−16.9870	+	9.80744i	−0.999235	+	0.576909i	−0.0912130	+	0.995831i	$0.529074\pi$
$18$	0.259819	+	12.7253i	0.0144344	+	0.706959i
$19$	4.86486	−	8.42619i	0.256045	−	0.443484i	−0.709134	−	0.705074i	$-0.750914\pi$
$19$	4.86486	−	8.42619i	0.256045	−	0.443484i	0.965179	+	0.261591i	$0.0842470\pi$
$20$	−16.4948	−	2.90849i	−0.824742	−	0.145424i
$21$	6.19496	+	33.1510i	0.294998	+	1.57862i
$22$	−2.09088	−	0.761018i	−0.0950400	−	0.0345917i
$23$	−13.8255	+	2.43781i	−0.601108	+	0.105992i	−0.465918	−	0.884828i	$-0.654276\pi$
$23$	−13.8255	+	2.43781i	−0.601108	+	0.105992i	−0.135190	+	0.990820i	$0.543165\pi$
$24$	8.37098	+	1.38808i	0.348791	+	0.0578367i
$25$	−34.5753	−	29.0121i	−1.38301	−	1.16048i
$26$		−	12.5983i		−	0.484550i
$27$	12.7778	−	23.7851i	0.473250	−	0.880928i
$28$	22.4832			0.802972
$29$	7.05122	−	8.40331i	0.243145	−	0.289769i	−0.630646	−	0.776071i	$-0.717210\pi$
$29$	7.05122	−	8.40331i	0.243145	−	0.289769i	0.873791	+	0.486301i	$0.161654\pi$
$30$	27.4498	+	22.5597i	0.914992	+	0.751988i
$31$	8.04854	+	45.6456i	0.259630	+	1.47244i	0.783901	+	0.620886i	$0.213227\pi$
$31$	8.04854	+	45.6456i	0.259630	+	1.47244i	−0.524271	+	0.851552i	$0.675662\pi$
$32$	1.93476	−	5.31570i	0.0604612	−	0.166116i
$33$	3.07076	+	3.58464i	0.0930534	+	0.108625i
$34$	4.81694	−	27.3182i	0.141675	−	0.803477i
$35$	81.5316	+	47.0723i	2.32947	+	1.34492i
$36$	−14.0221	−	11.2863i	−0.389503	−	0.313508i
$37$	7.89337	+	13.6717i	0.213334	+	0.369506i	0.952756	−	0.303737i	$-0.0982343\pi$
$37$	7.89337	+	13.6717i	0.213334	+	0.369506i	−0.739422	+	0.673243i	$0.764901\pi$
$38$	4.70617	+	12.9301i	0.123846	+	0.340265i
$39$	−13.1256	+	23.2797i	−0.336553	+	0.596916i
$40$	18.1454	−	15.2258i	0.453634	−	0.380644i
$41$	−6.59742	−	7.86250i	−0.160913	−	0.191768i	0.679564	−	0.733617i	$-0.262169\pi$
$41$	−6.59742	−	7.86250i	−0.160913	−	0.191768i	−0.840476	+	0.541848i	$0.817725\pi$
$42$	−41.5456	−	23.4242i	−0.989180	−	0.557719i
$43$	24.6205	−	8.96112i	0.572569	−	0.208398i	−0.0394765	−	0.999220i	$-0.512569\pi$
$43$	24.6205	−	8.96112i	0.572569	−	0.208398i	0.612046	+	0.790822i	$0.290347\pi$
$44$	2.72514	−	1.57336i	0.0619350	−	0.0357582i
$45$	−27.2191	−	70.2854i	−0.604870	−	1.56190i
$46$	9.92691	−	17.1939i	0.215802	−	0.373781i
$47$	−42.2938	−	7.45754i	−0.899868	−	0.158671i	−0.295468	−	0.955352i	$-0.595476\pi$
$47$	−42.2938	−	7.45754i	−0.899868	−	0.158671i	−0.604399	+	0.796682i	$0.706587\pi$
$48$	−9.11332	+	7.80688i	−0.189861	+	0.162643i
$49$	−72.7075	−	26.4634i	−1.48383	−	0.540069i
$50$	62.8606	−	11.0840i	1.25721	−	0.221680i
$51$	−37.3625	+	45.4614i	−0.732599	+	0.891399i
$52$	13.6484	+	11.4523i	0.262469	+	0.220237i
$53$			41.5395i			0.783764i	0.920016	+	0.391882i	$0.128176\pi$
$53$			41.5395i			0.783764i	−0.920016	+	0.391882i	$0.871824\pi$
$54$	14.1521	+	35.4643i	0.262075	+	0.656747i
$55$	13.1764			0.239570
$56$	−20.4381	+	24.3572i	−0.364966	+	0.434950i
$57$	4.77497	−	28.7960i	0.0837714	−	0.505192i
$58$	2.69390	+	15.2779i	0.0464466	+	0.263412i
$59$	20.6989	−	56.8698i	0.350829	−	0.963895i	−0.631275	−	0.775559i	$-0.717468\pi$
$59$	20.6989	−	56.8698i	0.350829	−	0.963895i	0.982105	−	0.188336i	$-0.0603095\pi$
$60$	−49.3929	+	9.23010i	−0.823215	+	0.153835i
$61$	13.2934	−	75.3906i	0.217924	−	1.23591i	−0.657835	−	0.753162i	$-0.728527\pi$
$61$	13.2934	−	75.3906i	0.217924	−	1.23591i	0.875759	−	0.482748i	$-0.160361\pi$
$62$	−56.7666	−	32.7742i	−0.915590	−	0.528616i
$63$	52.3653	+	86.5688i	0.831195	+	1.37411i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	25.5162	+	70.1051i	0.392556	+	1.07854i
$66$	−6.67486	+	0.0681351i	−0.101134	+	0.00103235i
$67$	2.09011	−	1.75381i	0.0311956	−	0.0261762i	−0.627057	−	0.778974i	$-0.715741\pi$
$67$	2.09011	−	1.75381i	0.0311956	−	0.0261762i	0.658252	+	0.752798i	$0.271296\pi$
$68$	25.2164	+	30.0518i	0.370830	+	0.441938i
$69$	−36.2569	+	21.4293i	−0.525463	+	0.310570i
$70$	−125.111	+	45.5367i	−1.78730	+	0.650525i
$71$	65.1324	−	37.6042i	0.917358	−	0.529637i	0.0345668	−	0.999402i	$-0.488995\pi$
$71$	65.1324	−	37.6042i	0.917358	−	0.529637i	0.882791	+	0.469765i	$0.155662\pi$
$72$	24.9737	−	4.93118i	0.346856	−	0.0684887i
$73$	33.0777	−	57.2922i	0.453119	−	0.784825i	−0.545459	−	0.838138i	$-0.683645\pi$
$73$	33.0777	−	57.2922i	0.453119	−	0.784825i	0.998578	+	0.0533125i	$0.0169779\pi$
$74$	−21.9866	−	3.87684i	−0.297117	−	0.0523897i
$75$	−127.705	−	45.0099i	−1.70273	−	0.600132i
$76$	−18.2859	−	6.65552i	−0.240604	−	0.0875727i
$77$	−17.4184	+	3.07133i	−0.226213	+	0.0398875i
$78$	−13.2885	−	35.3818i	−0.170365	−	0.453613i
$79$	38.8113	+	32.5666i	0.491283	+	0.412235i	0.854486	−	0.519475i	$-0.173872\pi$
$79$	38.8113	+	32.5666i	0.491283	+	0.412235i	−0.363203	+	0.931710i	$0.618317\pi$
$80$			33.4986i			0.418733i
$81$	10.7977	−	80.2771i	0.133305	−	0.991075i
$82$	14.5152			0.177014
$83$	21.4712	−	25.5884i	0.258689	−	0.308294i	−0.621030	−	0.783787i	$-0.713286\pi$
$83$	21.4712	−	25.5884i	0.258689	−	0.308294i	0.879720	+	0.475492i	$0.157730\pi$
$84$	63.1432	−	23.7149i	0.751704	−	0.282320i
$85$	28.5248	+	161.772i	0.335586	+	1.90320i
$86$	−12.6729	+	34.8186i	−0.147360	+	0.404868i
$87$	10.9394	−	31.0378i	0.125740	−	0.356757i
$88$	−0.772758	+	4.38253i	−0.00878135	+	0.0498015i
$89$	−75.2876	−	43.4673i	−0.845928	−	0.488397i	0.0133471	−	0.999911i	$-0.495751\pi$
$89$	−75.2876	−	43.4673i	−0.845928	−	0.488397i	−0.859275	+	0.511514i	$0.829085\pi$
$90$	100.887	+	34.4043i	1.12097	+	0.382270i
$91$	−50.0720	−	86.7273i	−0.550242	−	0.953047i
$92$	9.60308	+	26.3842i	0.104381	+	0.286785i
$93$	70.7501	+	119.704i	0.760754	+	1.28714i
$94$	46.5258	−	39.0398i	0.494956	−	0.415317i
$95$	−52.3763	−	62.4197i	−0.551330	−	0.657049i
$96$	−0.173222	−	16.9697i	−0.00180439	−	0.176767i
$97$	132.434	−	48.2019i	1.36530	−	0.496927i	0.447608	−	0.894230i	$-0.352276\pi$
$97$	132.434	−	48.2019i	1.36530	−	0.496927i	0.917688	+	0.397303i	$0.130054\pi$
$98$	94.7631	−	54.7115i	0.966970	−	0.558281i
$99$	12.4051	+	6.82832i	0.125304	+	0.0689729i
$100$	−45.1348	+	78.1758i	−0.451348	+	0.781758i
$101$	−88.8791	−	15.6718i	−0.879991	−	0.155166i	−0.284642	−	0.958634i	$-0.591875\pi$
$101$	−88.8791	−	15.6718i	−0.879991	−	0.155166i	−0.595348	+	0.803468i	$0.702986\pi$
$102$	−15.2866	−	81.8029i	−0.149869	−	0.801989i
$103$	19.7299	+	7.18111i	0.191553	+	0.0697195i	0.436015	−	0.899939i	$-0.356389\pi$
$103$	19.7299	+	7.18111i	0.191553	+	0.0697195i	−0.244463	+	0.969659i	$0.578612\pi$
$104$	−24.8138	+	4.37534i	−0.238594	+	0.0420706i
$105$	278.629	+	46.2025i	2.65361	+	0.440024i
$106$	−45.0018	−	37.7610i	−0.424545	−	0.356236i
$107$		−	21.8959i		−	0.204635i	−0.994752	−	0.102317i	$-0.967374\pi$
$107$		−	21.8959i		−	0.204635i	0.994752	−	0.102317i	$-0.0326257\pi$
$108$	−51.2851	−	16.9068i	−0.474862	−	0.156544i
$109$	−92.6448			−0.849953			−0.424976	−	0.905204i	$-0.639718\pi$
$109$	−92.6448			−0.849953			−0.424976	+	0.905204i	$0.639718\pi$
$110$	−11.9778	+	14.2746i	−0.108889	+	0.129769i
$111$	36.5889	+	30.0707i	0.329629	+	0.270907i
$112$	−7.80834	−	44.2833i	−0.0697173	−	0.395387i
$113$	−52.9813	+	145.565i	−0.468861	+	1.28819i	0.449796	+	0.893131i	$0.351497\pi$
$113$	−52.9813	+	145.565i	−0.468861	+	1.28819i	−0.918657	+	0.395055i	$0.870726\pi$
$114$	26.8555	+	31.3496i	0.235574	+	0.274997i
$115$	−20.4158	+	115.784i	−0.177529	+	1.00681i
$116$	−19.0002	−	10.9697i	−0.163794	−	0.0945668i
$117$	−12.3076	+	79.2248i	−0.105193	+	0.677135i
$118$	42.7938	+	74.1211i	0.362659	+	0.628145i
$119$	−75.4164	−	207.205i	−0.633752	−	1.74122i
$120$	34.9006	−	61.9004i	0.290839	−	0.515836i
$121$	90.7951	−	76.1861i	0.750372	−	0.629637i
$122$	69.5902	+	82.9344i	0.570411	+	0.679790i
$123$	−26.8218	−	15.1227i	−0.218063	−	0.122948i
$124$	87.1090	−	31.7051i	0.702492	−	0.255686i
$125$	−146.031	+	84.3111i	−1.16825	+	0.674489i
$126$	−141.386	−	21.9644i	−1.12211	−	0.174321i
$127$	−115.693	+	200.387i	−0.910971	+	1.57785i	−0.0982763	+	0.995159i	$0.531333\pi$
$127$	−115.693	+	200.387i	−0.910971	+	1.57785i	−0.812695	+	0.582689i	$0.802000\pi$
$128$	−11.1418	−	1.96460i	−0.0870455	−	0.0153485i
$129$	59.6935	−	51.1362i	0.462741	−	0.396404i
$130$	−99.1436	−	36.0853i	−0.762643	−	0.277579i
$131$	−69.0825	+	12.1811i	−0.527347	+	0.0929856i	−0.430982	−	0.902360i	$-0.641833\pi$
$131$	−69.0825	+	12.1811i	−0.527347	+	0.0929856i	−0.0963653	+	0.995346i	$0.530722\pi$
$132$	5.99389	−	7.29315i	0.0454083	−	0.0552511i
$133$	83.7882	+	70.3067i	0.629987	+	0.528621i
$134$			3.85860i			0.0287955i
$135$	−150.580	−	168.683i	−1.11540	−	1.24951i
$136$	−55.4793			−0.407936
$137$	136.898	−	163.149i	0.999257	−	1.19087i	0.0176713	−	0.999844i	$-0.494375\pi$
$137$	136.898	−	163.149i	0.999257	−	1.19087i	0.981585	−	0.191024i	$-0.0611808\pi$
$138$	9.74348	−	58.7591i	0.0706049	−	0.425790i
$139$	9.79795	+	55.5669i	0.0704888	+	0.399762i	0.999554	+	0.0298471i	$0.00950205\pi$
$139$	9.79795	+	55.5669i	0.0704888	+	0.399762i	−0.929066	+	0.369915i	$0.879387\pi$
$140$	64.3987	−	176.934i	0.459991	−	1.26381i
$141$	−126.646	+	23.6665i	−0.898201	+	0.167848i
$142$	−18.4694	+	104.745i	−0.130066	+	0.737640i
$143$	−12.1382	−	7.00802i	−0.0848829	−	0.0490071i
$144$	−17.3598	+	31.5379i	−0.120554	+	0.219013i
$145$	−45.9339	−	79.5599i	−0.316786	−	0.548689i
$146$	31.9987	+	87.9156i	0.219169	+	0.602162i
$147$	−232.109	+	2.36931i	−1.57897	+	0.0161177i
$148$	24.1867	−	20.2950i	0.163424	−	0.137129i
$149$	18.5161	+	22.0666i	0.124269	+	0.148098i	0.824592	−	0.565728i	$-0.191405\pi$
$149$	18.5161	+	22.0666i	0.124269	+	0.148098i	−0.700323	+	0.713826i	$0.746961\pi$
$150$	164.850	−	97.4332i	1.09900	−	0.649554i
$151$	−145.452	+	52.9400i	−0.963255	+	0.350596i	−0.775308	−	0.631583i	$-0.782405\pi$
$151$	−145.452	+	52.9400i	−0.963255	+	0.350596i	−0.187947	+	0.982179i	$0.560183\pi$
$152$	23.8329	−	13.7599i	0.156795	−	0.0905257i
$153$	−56.9793	+	167.086i	−0.372414	+	1.09206i
$154$	12.5067	−	21.6622i	0.0812122	−	0.140664i
$155$	382.266	+	67.4038i	2.46623	+	0.434863i
$156$	50.4106	+	17.7674i	0.323145	+	0.113893i
$157$	−200.915	−	73.1270i	−1.27971	−	0.465777i	−0.389375	−	0.921080i	$-0.627309\pi$
$157$	−200.915	−	73.1270i	−1.27971	−	0.465777i	−0.890337	+	0.455303i	$0.849531\pi$
$158$	−70.5620	+	12.4420i	−0.446595	+	0.0787467i
$159$	43.8151	+	116.662i	0.275567	+	0.733722i
$160$	−36.2907	−	30.4515i	−0.226817	−	0.190322i
$161$		−	157.818i		−	0.980238i
$162$	77.1526	+	84.6727i	0.476251	+	0.522671i
$163$	147.201			0.903076			0.451538	−	0.892252i	$-0.350876\pi$
$163$	147.201			0.903076			0.451538	+	0.892252i	$0.350876\pi$
$164$	−13.1948	+	15.7250i	−0.0804564	+	0.0958842i
$165$	37.0052	−	13.8982i	0.224274	−	0.0842314i
$166$	8.20304	+	46.5217i	0.0494159	+	0.280251i
$167$	−50.5448	+	138.871i	−0.302664	+	0.831561i	0.691371	+	0.722500i	$0.257007\pi$
$167$	−50.5448	+	138.871i	−0.302664	+	0.831561i	−0.994035	+	0.109062i	$0.965215\pi$
$168$	−31.7081	+	89.9639i	−0.188738	+	0.535500i
$169$	−15.5661	+	88.2796i	−0.0921070	+	0.522364i
$170$	−201.186	−	116.155i	−1.18345	−	0.683264i
$171$	−16.9632	−	85.9088i	−0.0991997	−	0.502391i
$172$	−26.2006	−	45.3807i	−0.152329	−	0.263841i
$173$	72.2331	+	198.459i	0.417532	+	1.14716i	0.953097	+	0.302666i	$0.0978766\pi$
$173$	72.2331	+	198.459i	0.417532	+	1.14716i	−0.535565	+	0.844494i	$0.679901\pi$
$174$	23.6805	+	40.0658i	0.136095	+	0.230263i
$175$	388.682	−	326.143i	2.22104	−	1.86367i
$176$	−4.04535	−	4.82106i	−0.0229849	−	0.0273924i
$177$	−1.85320	−	181.549i	−0.0104701	−	1.02570i
$178$	115.530	−	42.0493i	0.649043	−	0.236232i
$179$	−225.133	+	129.980i	−1.25772	+	0.726147i	−0.972632	−	0.232353i	$-0.925358\pi$
$179$	−225.133	+	129.980i	−1.25772	+	0.726147i	−0.285092	+	0.958500i	$0.592024\pi$
$180$	−128.982	+	78.0211i	−0.716567	+	0.433451i
$181$	159.698	−	276.606i	0.882311	−	1.52821i	0.0335470	−	0.999437i	$-0.489320\pi$
$181$	159.698	−	276.606i	0.882311	−	1.52821i	0.848764	−	0.528771i	$-0.177347\pi$
$182$	139.474	+	24.5929i	0.766338	+	0.135126i
$183$	−42.1867	−	225.753i	−0.230528	−	1.23362i
$184$	−37.3130	−	13.5808i	−0.202788	−	0.0738087i
$185$	130.200	−	22.9578i	0.703783	−	0.124096i
$186$	−193.996	−	32.1686i	−1.04299	−	0.172949i
$187$	−23.6411	−	19.8373i	−0.126423	−	0.106082i
$188$			85.8925i			0.456875i
$189$	238.377	+	187.891i	1.26125	+	0.994131i
$190$	115.234			0.606497
$191$	−25.0422	+	29.8442i	−0.131111	+	0.156252i	−0.827606	−	0.561310i	$-0.810298\pi$
$191$	−25.0422	+	29.8442i	−0.131111	+	0.156252i	0.696495	+	0.717562i	$0.254742\pi$
$192$	18.5416	+	15.2384i	0.0965707	+	0.0793669i
$193$	−28.3760	−	160.928i	−0.147026	−	0.833825i	−0.965718	−	0.259593i	$-0.916412\pi$
$193$	−28.3760	−	160.928i	−0.147026	−	0.833825i	0.818692	−	0.574233i	$-0.194699\pi$
$194$	−68.1678	+	187.289i	−0.351380	+	0.965410i
$195$	145.607	+	169.973i	0.746701	+	0.871657i
$196$	−26.8716	+	152.397i	−0.137100	+	0.777533i
$197$	296.815	+	171.366i	1.50668	+	0.869880i	0.999970	+	0.00776089i	$0.00247039\pi$
$197$	296.815	+	171.366i	1.50668	+	0.869880i	0.506706	+	0.862119i	$0.330863\pi$
$198$	−18.6742	+	7.23188i	−0.0943141	+	0.0365246i
$199$	98.8611	+	171.232i	0.496789	+	0.860464i	0.999993	−	0.00370331i	$-0.00117880\pi$
$199$	98.8611	+	171.232i	0.496789	+	0.860464i	−0.503204	+	0.864168i	$0.667845\pi$
$200$	−43.6625	−	119.962i	−0.218312	−	0.599809i
$201$	4.02009	−	7.13010i	0.0200005	−	0.0354731i
$202$	97.7725	−	82.0409i	0.484022	−	0.406143i
$203$	79.2670	+	94.4668i	0.390478	+	0.465353i
$204$	102.517	+	57.8013i	0.502536	+	0.283340i
$205$	−80.7718	+	29.3985i	−0.394009	+	0.143407i
$206$	−25.7149	+	14.8465i	−0.124830	+	0.0720705i
$207$	−79.2228	+	98.4266i	−0.382719	+	0.475491i
$208$	17.8167	−	30.8594i	0.0856571	−	0.148363i
$209$	15.0758	+	2.65827i	0.0721330	+	0.0127190i
$210$	−303.338	+	259.853i	−1.44447	+	1.23740i
$211$	−214.619	−	78.1150i	−1.01715	−	0.370213i	−0.220977	−	0.975279i	$-0.570925\pi$
$211$	−214.619	−	78.1150i	−1.01715	−	0.370213i	−0.796176	+	0.605066i	$0.793147\pi$
$212$	81.8168	−	14.4265i	0.385928	−	0.0680496i
$213$	143.257	−	174.310i	0.672570	−	0.818359i
$214$	23.7210	+	19.9042i	0.110846	+	0.0930105i
$215$		−	219.421i		−	1.02056i
$216$	64.9361	−	40.1908i	0.300630	−	0.186068i
$217$	−521.045			−2.40113
$218$	84.2178	−	100.367i	0.386320	−	0.460398i
$219$	32.4665	−	195.793i	0.148249	−	0.894030i
$220$	−4.57610	−	25.9524i	−0.0208005	−	0.117965i
$221$	59.7633	−	164.198i	0.270422	−	0.742979i
$222$	−65.8378	+	12.3032i	−0.296566	+	0.0554197i
$223$	67.0596	−	380.314i	0.300716	−	1.70544i	−0.342301	−	0.939590i	$-0.611206\pi$
$223$	67.0596	−	380.314i	0.300716	−	1.70544i	0.643016	−	0.765852i	$-0.277683\pi$
$224$	55.0724	+	31.7961i	0.245859	+	0.141947i
$225$	−406.129	+	8.29216i	−1.80502	+	0.0368541i
$226$	−109.536	−	189.722i	−0.484672	−	0.839476i
$227$	−63.6795	−	174.958i	−0.280527	−	0.770740i	−0.997300	−	0.0734342i	$-0.976604\pi$
$227$	−63.6795	−	174.958i	−0.280527	−	0.770740i	0.716774	−	0.697306i	$-0.245618\pi$
$228$	−58.3753	+	0.595879i	−0.256032	+	0.00261350i
$229$	−236.706	+	198.620i	−1.03365	+	0.867336i	−0.991281	−	0.131766i	$-0.957935\pi$
$229$	−236.706	+	198.620i	−1.03365	+	0.867336i	−0.0423704	+	0.999102i	$0.513491\pi$
$230$	−106.876	−	127.369i	−0.464676	−	0.553780i
$231$	−45.6793	+	26.9983i	−0.197746	+	0.116876i
$232$	29.1560	−	10.6119i	0.125672	−	0.0457410i
$233$	−17.8085	+	10.2818i	−0.0764315	+	0.0441277i	−0.537729	−	0.843118i	$-0.680718\pi$
$233$	−17.8085	+	10.2818i	−0.0764315	+	0.0441277i	0.461297	+	0.887246i	$0.347384\pi$
$234$	−74.6401	−	85.3518i	−0.318975	−	0.364751i
$235$	−179.830	+	311.475i	−0.765234	+	1.32542i
$236$	−119.200	−	21.0182i	−0.505086	−	0.0890603i
$237$	143.351	+	50.5243i	0.604855	+	0.213183i
$238$	293.032	+	106.655i	1.23123	+	0.448130i
$239$	−101.144	+	17.8344i	−0.423197	+	0.0746211i	−0.381191	−	0.924496i	$-0.624486\pi$
$239$	−101.144	+	17.8344i	−0.423197	+	0.0746211i	−0.0420061	+	0.999117i	$0.513375\pi$
$240$	35.3337	+	94.0795i	0.147224	+	0.391998i
$241$	294.337	+	246.978i	1.22131	+	1.02480i	0.998755	+	0.0498853i	$0.0158856\pi$
$241$	294.337	+	246.978i	1.22131	+	1.02480i	0.222559	+	0.974919i	$0.428559\pi$
$242$			167.619i			0.692641i
$243$	−54.3498	−	236.844i	−0.223662	−	0.974667i
$244$	−153.107			−0.627488
$245$	−416.512	+	496.380i	−1.70005	+	2.02604i
$246$	40.7652	−	15.3103i	0.165712	−	0.0622371i
$247$	15.0511	+	85.3589i	0.0609355	+	0.345583i
$248$	−44.8377	+	123.191i	−0.180797	+	0.496737i
$249$	33.3108	−	94.5114i	0.133778	−	0.379564i
$250$	41.4095	−	234.845i	0.165638	−	0.939380i
$251$	281.668	+	162.621i	1.12218	+	0.647893i	0.941958	−	0.335732i	$-0.108984\pi$
$251$	281.668	+	162.621i	1.12218	+	0.647893i	0.180227	+	0.983625i	$0.442317\pi$
$252$	152.321	−	133.205i	0.604448	−	0.528589i
$253$	−11.0440	−	19.1288i	−0.0436523	−	0.0756080i
$254$	−111.919	−	307.496i	−0.440627	−	1.21061i
$255$	250.745	+	424.243i	0.983315	+	1.66370i
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	−21.5034	−	25.6267i	−0.0836708	−	0.0997150i	0.722585	−	0.691282i	$-0.242954\pi$
$257$	−21.5034	−	25.6267i	−0.0836708	−	0.0997150i	−0.806256	+	0.591567i	$0.798509\pi$
$258$	1.13463	+	111.154i	0.00439778	+	0.430829i
$259$	−166.766	+	60.6977i	−0.643883	+	0.234354i
$260$	129.218	−	74.6043i	0.496994	−	0.286940i
$261$	−2.01536	−	98.7072i	−0.00772169	−	0.378188i
$262$	49.6023	−	85.9137i	0.189322	−	0.327915i
$263$	−154.814	−	27.2979i	−0.588646	−	0.103794i	−0.128611	−	0.991695i	$-0.541052\pi$
$263$	−154.814	−	27.2979i	−0.588646	−	0.103794i	−0.460035	+	0.887901i	$0.652163\pi$
$264$	2.45235	+	13.1232i	0.00928922	+	0.0497093i
$265$	326.899	+	118.982i	1.23358	+	0.448987i
$266$	−152.333	+	26.8605i	−0.572682	+	0.100979i
$267$	−257.290	−	42.6641i	−0.963635	−	0.159791i
$268$	−4.18021	−	3.50762i	−0.0155978	−	0.0130881i
$269$		−	289.194i		−	1.07507i	−0.843241	−	0.537536i	$-0.819355\pi$
$269$		−	289.194i		−	1.07507i	0.843241	−	0.537536i	$-0.180645\pi$
$270$	319.626	−	9.79068i	1.18380	−	0.0362618i
$271$	438.046			1.61641			0.808204	−	0.588903i	$-0.200440\pi$
$271$	438.046			1.61641			0.808204	+	0.588903i	$0.200440\pi$
$272$	50.4328	−	60.1035i	0.185415	−	0.220969i
$273$	−232.104	−	190.755i	−0.850196	−	0.698736i
$274$	52.3016	+	296.617i	0.190882	+	1.08255i
$275$	24.2880	−	66.7308i	0.0883201	−	0.242657i
$276$	54.7995	+	63.9699i	0.198549	+	0.231775i
$277$	2.95396	−	16.7527i	0.0106641	−	0.0604791i	−0.979011	−	0.203806i	$-0.934669\pi$
$277$	2.95396	−	16.7527i	0.0106641	−	0.0604791i	0.989675	+	0.143327i	$0.0457800\pi$
$278$	−69.1052	−	39.8979i	−0.248580	−	0.143518i
$279$	324.960	+	261.558i	1.16473	+	0.937484i
$280$	133.141	+	230.606i	0.475502	+	0.823594i
$281$	31.3851	+	86.2298i	0.111691	+	0.306867i	0.982927	−	0.183996i	$-0.0589035\pi$
$281$	31.3851	+	86.2298i	0.111691	+	0.306867i	−0.871236	+	0.490864i	$0.836681\pi$
$282$	89.4873	−	158.716i	0.317331	−	0.562824i
$283$	−335.404	+	281.438i	−1.18517	+	0.994479i	−0.185243	+	0.982693i	$0.559307\pi$
$283$	−335.404	+	281.438i	−1.18517	+	0.994479i	−0.999931	+	0.0117863i	$0.996248\pi$
$284$	−96.6861	−	115.226i	−0.340444	−	0.405725i
$285$	−212.936	−	120.057i	−0.747143	−	0.421254i
$286$	18.6263	−	6.77941i	0.0651269	−	0.0237042i
$287$	99.9231	−	57.6906i	0.348164	−	0.201013i
$288$	−18.3858	−	47.4759i	−0.0638396	−	0.164847i
$289$	47.8719	−	82.9166i	0.165647	−	0.286909i
$290$	127.947	+	22.5605i	0.441196	+	0.0777948i
$291$	321.092	−	275.062i	1.10341	−	0.945229i
$292$	−124.331	−	45.2529i	−0.425793	−	0.154976i
$293$	254.746	−	44.9185i	0.869439	−	0.153305i	0.278905	−	0.960319i	$-0.410028\pi$
$293$	254.746	−	44.9185i	0.869439	−	0.153305i	0.590533	+	0.807013i	$0.298917\pi$
$294$	208.429	−	253.609i	0.708944	−	0.862617i
$295$	−388.255	−	325.784i	−1.31612	−	1.10435i
$296$			44.6516i			0.150850i
$297$	42.0416	+	6.09236i	0.141554	+	0.0205130i
$298$	−40.7377			−0.136704
$299$	80.3884	−	95.8031i	0.268857	−	0.320412i
$300$	−44.3008	+	267.161i	−0.147669	+	0.890536i
$301$	51.1457	+	290.062i	0.169919	+	0.963661i
$302$	74.8685	−	205.700i	0.247909	−	0.681124i
$303$	−266.143	+	49.7345i	−0.878361	+	0.164140i
$304$	−6.75819	+	38.3276i	−0.0222309	+	0.126078i
$305$	−555.217	−	320.555i	−1.82038	−	1.05100i
$306$	−129.216	−	213.616i	−0.422274	−	0.698091i
$307$	106.596	+	184.630i	0.347219	+	0.601401i	0.985754	−	0.168192i	$-0.0537927\pi$
$307$	106.596	+	184.630i	0.347219	+	0.601401i	−0.638535	+	0.769592i	$0.720459\pi$
$308$	12.0987	+	33.2409i	0.0392815	+	0.107925i
$309$	62.9852	−	0.642935i	0.203835	−	0.00208070i
$310$	−420.516	+	352.855i	−1.35650	+	1.13824i
$311$	299.915	+	357.425i	0.964358	+	1.14928i	0.988750	+	0.149575i	$0.0477904\pi$
$311$	299.915	+	357.425i	0.964358	+	1.14928i	−0.0243925	+	0.999702i	$0.507765\pi$
$312$	−65.0735	+	38.4611i	−0.208569	+	0.123273i
$313$	−88.7107	+	32.2881i	−0.283421	+	0.103157i	−0.479819	−	0.877367i	$-0.659298\pi$
$313$	−88.7107	+	32.2881i	−0.283421	+	0.103157i	0.196398	+	0.980524i	$0.437075\pi$
$314$	261.861	−	151.186i	0.833953	−	0.481483i
$315$	831.251	−	164.135i	2.63889	−	0.521064i
$316$	50.6646	−	87.7536i	0.160331	−	0.277701i
$317$	−250.991	−	44.2565i	−0.791769	−	0.139610i	−0.236885	−	0.971538i	$-0.576126\pi$
$317$	−250.991	−	44.2565i	−0.791769	−	0.139610i	−0.554884	+	0.831927i	$0.687238\pi$
$318$	−166.215	−	58.5831i	−0.522690	−	0.184224i
$319$	16.2185	+	5.90305i	0.0508417	+	0.0185049i
$320$	65.9794	−	11.6339i	0.206186	−	0.0363561i
$321$	−23.0954	−	61.4938i	−0.0719484	−	0.191569i
$322$	170.973	+	143.463i	0.530971	+	0.445537i
$323$			190.847i			0.590859i
$324$	−161.865	+	6.61254i	−0.499583	+	0.0204091i
$325$	402.076			1.23716
$326$	−133.812	+	159.471i	−0.410466	+	0.489174i
$327$	−260.189	+	97.7201i	−0.795685	+	0.298838i
$328$	−5.04106	−	28.5893i	−0.0153691	−	0.0871625i
$329$	165.122	−	453.669i	0.501891	−	1.37893i
$330$	−18.5826	+	52.7236i	−0.0563109	+	0.159769i
$331$	−63.9844	+	362.874i	−0.193306	+	1.09629i	0.721504	+	0.692410i	$0.243451\pi$
$331$	−63.9844	+	362.874i	−0.193306	+	1.09629i	−0.914810	+	0.403884i	$0.867660\pi$
$332$	−57.8562	−	33.4033i	−0.174266	−	0.100612i
$333$	134.476	+	45.8589i	0.403833	+	0.137714i
$334$	−104.498	−	180.997i	−0.312870	−	0.541906i
$335$	−7.81507	−	21.4717i	−0.0233286	−	0.0640947i
$336$	−68.6386	−	116.132i	−0.204282	−	0.345630i
$337$	150.868	−	126.593i	0.447679	−	0.375647i	−0.390895	−	0.920435i	$-0.627834\pi$
$337$	150.868	−	126.593i	0.447679	−	0.375647i	0.838574	+	0.544788i	$0.183390\pi$
$338$	−81.4876	−	97.1131i	−0.241087	−	0.287317i
$339$	4.74350	+	464.697i	0.0139926	+	1.37079i
$340$	308.723	−	112.366i	0.908008	−	0.330488i
$341$	−63.1548	+	36.4624i	−0.185205	+	0.106928i
$342$	108.489	+	59.7174i	0.317221	+	0.174612i
$343$	159.483	−	276.233i	0.464966	−	0.805344i
$344$	72.9805	+	12.8684i	0.212153	+	0.0374083i
$345$	64.7896	+	346.708i	0.187796	+	1.00495i
$346$	−280.663	−	102.153i	−0.811165	−	0.295240i
$347$	−263.673	+	46.4927i	−0.759864	+	0.133985i	−0.540137	−	0.841577i	$-0.681628\pi$
$347$	−263.673	+	46.4927i	−0.759864	+	0.133985i	−0.219727	+	0.975561i	$0.570517\pi$
$348$	−64.9318	−	10.7670i	−0.186586	−	0.0309398i
$349$	−395.788	−	332.105i	−1.13406	−	0.951591i	−0.134834	−	0.990868i	$-0.543050\pi$
$349$	−395.788	−	332.105i	−1.13406	−	0.951591i	−0.999228	+	0.0392770i	$0.987495\pi$
$350$			717.555i			2.05016i
$351$	48.9995	+	235.481i	0.139600	+	0.670887i
$352$	8.90028			0.0252849
$353$	−186.396	+	222.139i	−0.528035	+	0.629288i	−0.962461	−	0.271420i	$-0.912507\pi$
$353$	−186.396	+	222.139i	−0.528035	+	0.629288i	0.434426	+	0.900708i	$0.356951\pi$
$354$	198.366	+	163.028i	0.560356	+	0.460530i
$355$	−109.371	−	620.276i	−0.308088	−	1.74726i
$356$	−59.4668	+	163.384i	−0.167041	+	0.458943i
$357$	−430.360	−	502.378i	−1.20549	−	1.40722i
$358$	63.8400	−	362.055i	0.178324	−	1.01133i
$359$	35.8110	+	20.6755i	0.0997520	+	0.0575918i	0.549046	−	0.835792i	$-0.314991\pi$
$359$	35.8110	+	20.6755i	0.0997520	+	0.0575918i	−0.449294	+	0.893384i	$0.648324\pi$
$360$	32.7256	−	210.657i	0.0909045	−	0.585159i
$361$	133.166	+	230.651i	0.368882	+	0.638922i
$362$	154.489	+	424.455i	0.426765	+	1.17253i
$363$	174.634	−	309.734i	0.481086	−	0.853263i
$364$	−153.430	+	128.743i	−0.421510	+	0.353689i
$365$	−356.123	−	424.410i	−0.975678	−	1.16277i
$366$	282.919	+	159.515i	0.773002	+	0.435834i
$367$	152.544	−	55.5215i	0.415651	−	0.151285i	−0.125725	−	0.992065i	$-0.540126\pi$
$367$	152.544	−	55.5215i	0.415651	−	0.151285i	0.541376	+	0.840780i	$0.317903\pi$
$368$	48.6317	−	28.0775i	0.132151	−	0.0762976i
$369$	−91.2790	−	14.1802i	−0.247369	−	0.0384287i
$370$	−93.4855	+	161.922i	−0.252663	+	0.437626i
$371$	−459.876	−	81.0886i	−1.23956	−	0.218568i
$372$	211.200	−	180.923i	0.567742	−	0.486353i
$373$	63.6401	+	23.1631i	0.170617	+	0.0620995i	0.425916	−	0.904763i	$-0.359952\pi$
$373$	63.6401	+	23.1631i	0.170617	+	0.0620995i	−0.255299	+	0.966862i	$0.582174\pi$
$374$	42.9814	−	7.57879i	0.114924	−	0.0202641i
$375$	−321.193	+	390.815i	−0.856513	+	1.04217i
$376$	−93.0516	−	78.0796i	−0.247478	−	0.207659i
$377$			97.7223i			0.259210i
$378$	−420.245	+	87.4457i	−1.11176	+	0.231338i
$379$	122.431			0.323038			0.161519	−	0.986870i	$-0.448361\pi$
$379$	122.431			0.323038			0.161519	+	0.986870i	$0.448361\pi$
$380$	−104.753	+	124.839i	−0.275665	+	0.328524i
$381$	−113.556	+	684.809i	−0.298046	+	1.79740i
$382$	−9.56733	−	54.2590i	−0.0250454	−	0.142039i
$383$	−20.6906	+	56.8471i	−0.0540226	+	0.148426i	−0.963769	−	0.266739i	$-0.914054\pi$
$383$	−20.6906	+	56.8471i	−0.0540226	+	0.148426i	0.909746	+	0.415165i	$0.136276\pi$
$384$	−33.3636	+	6.23469i	−0.0868843	+	0.0162362i
$385$	−25.7214	+	145.873i	−0.0668087	+	0.378891i
$386$	200.137	+	115.549i	0.518489	+	0.299350i
$387$	113.709	−	206.577i	0.293823	−	0.533792i
$388$	−140.933	−	244.103i	−0.363229	−	0.629132i
$389$	−82.3102	−	226.145i	−0.211594	−	0.581350i	0.787808	−	0.615921i	$-0.211216\pi$
$389$	−82.3102	−	226.145i	−0.211594	−	0.581350i	−0.999402	+	0.0345705i	$0.988994\pi$
$390$	−316.503	+	3.23077i	−0.811545	+	0.00828403i
$391$	210.945	−	177.004i	0.539501	−	0.452695i
$392$	−140.672	−	167.646i	−0.358856	−	0.427668i
$393$	−181.167	+	107.077i	−0.460984	+	0.272461i
$394$	−455.466	+	165.776i	−1.15601	+	0.420752i
$395$	367.453	−	212.149i	0.930261	−	0.537087i
$396$	9.14091	−	26.8048i	0.0230831	−	0.0676888i
$397$	14.3451	−	24.8464i	0.0361337	−	0.0625854i	−0.847393	−	0.530966i	$-0.821829\pi$
$397$	14.3451	−	24.8464i	0.0361337	−	0.0625854i	0.883527	+	0.468381i	$0.155162\pi$
$398$	−275.373	−	48.5557i	−0.691893	−	0.121999i
$399$	309.474	+	109.075i	0.775624	+	0.273371i
$400$	169.651	+	61.7481i	0.424129	+	0.154370i
$401$	697.035	−	122.906i	1.73824	−	0.306499i	0.787461	−	0.616365i	$-0.211395\pi$
$401$	697.035	−	122.906i	1.73824	−	0.306499i	0.950780	+	0.309866i	$0.100284\pi$
$402$	4.06998	+	10.8367i	0.0101243	+	0.0269570i
$403$	−316.299	−	265.406i	−0.784861	−	0.658577i
$404$			180.500i			0.446783i
$405$	−600.821	−	314.912i	−1.48351	−	0.777559i
$406$	−174.397			−0.429550
$407$	−15.9657	+	19.0272i	−0.0392278	+	0.0467499i
$408$	−155.811	+	58.5185i	−0.381890	+	0.143428i
$409$	−13.6664	−	77.5062i	−0.0334143	−	0.189502i	0.963532	−	0.267593i	$-0.0862284\pi$
$409$	−13.6664	−	77.5062i	−0.0334143	−	0.189502i	−0.996946	+	0.0780917i	$0.975117\pi$
$410$	41.5758	−	114.229i	0.101404	−	0.278606i
$411$	212.386	−	602.594i	0.516755	−	1.46617i
$412$	7.29189	−	41.3543i	0.0176988	−	0.100375i
$413$	589.190	+	340.169i	1.42661	+	0.823653i
$414$	−34.6139	−	175.300i	−0.0836084	−	0.423429i
$415$	−139.871	−	242.263i	−0.337037	−	0.583766i
$416$	17.2355	+	47.3541i	0.0414315	+	0.113832i
$417$	86.1281	+	145.723i	0.206542	+	0.349455i
$418$	−16.5843	+	13.9159i	−0.0396754	+	0.0332916i
$419$	33.8949	+	40.3944i	0.0808948	+	0.0964067i	0.804974	−	0.593310i	$-0.202179\pi$
$419$	33.8949	+	40.3944i	0.0808948	+	0.0964067i	−0.724079	+	0.689717i	$0.757735\pi$
$420$	−5.76571	−	564.838i	−0.0137279	−	1.34485i
$421$	664.624	−	241.903i	1.57868	−	0.574592i	0.603763	−	0.797164i	$-0.293667\pi$
$421$	664.624	−	241.903i	1.57868	−	0.574592i	0.974916	+	0.222572i	$0.0714452\pi$
$422$	279.723	−	161.498i	0.662851	−	0.382697i
$423$	−330.718	+	200.051i	−0.781839	+	0.472933i
$424$	−58.7457	+	101.751i	−0.138551	+	0.239978i
$425$	871.865	+	153.733i	2.05145	+	0.361725i
$426$	58.6126	+	313.653i	0.137588	+	0.736274i
$427$	808.686	+	294.338i	1.89388	+	0.689315i
$428$	−43.1265	+	7.60437i	−0.100763	+	0.0177672i
$429$	−41.4817	−	6.87853i	−0.0966939	−	0.0160339i
$430$	237.709	+	199.462i	0.552813	+	0.463865i
$431$			279.279i			0.647978i	0.946061	+	0.323989i	$0.105024\pi$
$431$			279.279i			0.647978i	−0.946061	+	0.323989i	$0.894976\pi$
$432$	−15.4888	+	106.884i	−0.0358536	+	0.247416i
$433$	100.836			0.232877			0.116439	−	0.993198i	$-0.462852\pi$
$433$	100.836			0.232877			0.116439	+	0.993198i	$0.462852\pi$
$434$	473.650	−	564.475i	1.09136	−	1.30063i
$435$	−212.922	−	174.990i	−0.489475	−	0.402277i
$436$	32.1752	+	182.475i	0.0737964	+	0.418520i
$437$	−46.7177	+	128.356i	−0.106905	+	0.293720i
$438$	182.599	+	213.156i	0.416892	+	0.486657i
$439$	17.2883	−	98.0470i	0.0393812	−	0.223342i	−0.958765	−	0.284199i	$-0.908272\pi$
$439$	17.2883	−	98.0470i	0.0393812	−	0.223342i	0.998146	+	0.0608574i	$0.0193835\pi$
$440$	32.2754	+	18.6342i	0.0733531	+	0.0423504i
$441$	−649.370	+	251.479i	−1.47249	+	0.570246i
$442$	123.557	+	214.007i	0.279541	+	0.484179i
$443$	117.281	+	322.226i	0.264742	+	0.727373i	0.998832	+	0.0483203i	$0.0153868\pi$
$443$	117.281	+	322.226i	0.264742	+	0.727373i	−0.734090	+	0.679052i	$0.762391\pi$
$444$	46.5204	−	82.5094i	0.104776	−	0.185832i
$445$	−557.716	+	467.980i	−1.25330	+	1.05164i
$446$	351.053	+	418.369i	0.787115	+	0.938047i
$447$	75.2771	+	42.4427i	0.168405	+	0.0949501i
$448$	−84.5092	+	30.7589i	−0.188637	+	0.0686581i
$449$	−433.309	+	250.171i	−0.965053	+	0.557174i	−0.897725	−	0.440557i	$-0.854781\pi$
$449$	−433.309	+	250.171i	−0.965053	+	0.557174i	−0.0673285	+	0.997731i	$0.521448\pi$
$450$	360.204	−	447.518i	0.800452	−	0.994484i
$451$	8.07431	−	13.9851i	0.0179031	−	0.0310091i
$452$	305.107	+	53.7987i	0.675016	+	0.119024i
$453$	−352.654	+	302.099i	−0.778486	+	0.666886i
$454$	247.428	+	90.0564i	0.544996	+	0.198362i
$455$	−825.931	+	145.634i	−1.81523	+	0.320074i
$456$	52.4199	−	63.7826i	0.114956	−	0.139874i
$457$	88.1631	+	73.9776i	0.192917	+	0.161877i	0.734130	−	0.679009i	$-0.237590\pi$
$457$	88.1631	+	73.9776i	0.192917	+	0.161877i	−0.541213	+	0.840886i	$0.682035\pi$
$458$		−	436.989i		−	0.954125i
$459$	16.2150	+	529.354i	0.0353268	+	1.15328i
$460$	235.140			0.511173
$461$	371.972	−	443.299i	0.806880	−	0.961602i	−0.192928	−	0.981213i	$-0.561798\pi$
$461$	371.972	−	443.299i	0.806880	−	0.961602i	0.999808	+	0.0196109i	$0.00624274\pi$
$462$	12.2756	−	74.0292i	0.0265705	−	0.160236i
$463$	−138.386	−	784.826i	−0.298890	−	1.69509i	−0.650957	−	0.759114i	$-0.725632\pi$
$463$	−138.386	−	784.826i	−0.298890	−	1.69509i	0.352067	−	0.935975i	$-0.385479\pi$
$464$	−15.0075	+	41.2328i	−0.0323437	+	0.0888637i
$465$	1144.67	−	213.906i	2.46166	−	0.460014i
$466$	5.04990	−	28.6394i	0.0108367	−	0.0614579i
$467$	234.565	+	135.426i	0.502281	+	0.289992i	0.729655	−	0.683816i	$-0.239681\pi$
$467$	234.565	+	135.426i	0.502281	+	0.289992i	−0.227374	+	0.973807i	$0.573014\pi$
$468$	160.317	−	3.27328i	0.342557	−	0.00699418i
$469$	15.3360	+	26.5628i	0.0326994	+	0.0566371i
$470$	−173.964	−	477.961i	−0.370136	−	1.01694i
$471$	−641.393	+	6.54716i	−1.36177	+	0.0139006i
$472$	131.128	−	110.029i	0.277813	−	0.233113i
$473$	26.4976	+	31.5786i	0.0560203	+	0.0667624i
$474$	−185.047	+	109.370i	−0.390394	+	0.230739i
$475$	−412.665	+	150.198i	−0.868769	+	0.316206i
$476$	−381.922	+	220.503i	−0.802358	+	0.463241i
$477$	246.106	+	281.425i	0.515945	+	0.589989i
$478$	72.6230	−	125.787i	0.151931	−	0.263152i
$479$	−785.792	−	138.556i	−1.64048	−	0.289262i	−0.724140	−	0.689653i	$-0.757763\pi$
$479$	−785.792	−	138.556i	−1.64048	−	0.289262i	−0.916344	+	0.400391i	$0.868874\pi$
$480$	−134.041	−	47.2431i	−0.279252	−	0.0984231i
$481$	−132.152	−	48.0995i	−0.274745	−	0.0999990i
$482$	−535.127	+	94.3574i	−1.11022	+	0.195762i
$483$	−166.464	−	443.226i	−0.344646	−	0.917652i
$484$	−181.590	−	152.372i	−0.375186	−	0.314819i
$485$		−	1180.26i		−	2.43354i
$486$	305.991	+	156.421i	0.629611	+	0.321853i
$487$	−139.213			−0.285859			−0.142929	−	0.989733i	$-0.545652\pi$
$487$	−139.213			−0.285859			−0.142929	+	0.989733i	$0.545652\pi$
$488$	139.180	−	165.869i	0.285206	−	0.339895i
$489$	413.409	−	155.265i	0.845417	−	0.317516i
$490$	−159.128	−	902.458i	−0.324750	−	1.84175i
$491$	−73.6069	+	202.233i	−0.149912	+	0.411881i	−0.991804	−	0.127765i	$-0.959220\pi$
$491$	−73.6069	+	202.233i	−0.149912	+	0.411881i	0.841892	+	0.539646i	$0.181442\pi$
$492$	−20.4707	+	58.0807i	−0.0416072	+	0.118050i
$493$	−37.3639	+	211.901i	−0.0757889	+	0.429820i
$494$	−106.156	−	61.2890i	−0.214890	−	0.124067i
$495$	89.2681	−	78.0649i	0.180340	−	0.157707i
$496$	−92.6994	−	160.560i	−0.186894	−	0.323710i
$497$	289.166	+	794.476i	0.581822	+	1.59854i
$498$	72.1082	+	122.002i	0.144795	+	0.244984i
$499$	−363.724	+	305.201i	−0.728906	+	0.611624i	−0.929833	−	0.367982i	$-0.880049\pi$
$499$	−363.724	+	305.201i	−0.728906	+	0.611624i	0.200927	+	0.979606i	$0.435604\pi$
$500$	216.777	+	258.344i	0.433553	+	0.516689i
$501$	4.52535	+	443.326i	0.00903264	+	0.884883i
$502$	−432.223	+	157.316i	−0.861002	+	0.313379i
$503$	−696.911	+	402.362i	−1.38551	+	0.799924i	−0.992805	−	0.119740i	$-0.961794\pi$
$503$	−696.911	+	402.362i	−1.38551	+	0.799924i	−0.392704	+	0.919665i	$0.628460\pi$
$504$	5.84157	+	286.105i	0.0115904	+	0.567669i
$505$	−377.907	+	654.554i	−0.748331	+	1.29615i
$506$	30.7627	+	5.42429i	0.0607958	+	0.0107199i
$507$	49.3991	+	264.348i	0.0974340	+	0.521397i
$508$	434.865	+	158.278i	0.856033	+	0.311571i
$509$	924.707	−	163.051i	1.81671	−	0.320336i	0.841275	−	0.540607i	$-0.181806\pi$
$509$	924.707	−	163.051i	1.81671	−	0.320336i	0.975439	+	0.220272i	$0.0706945\pi$
$510$	−687.541	−	114.009i	−1.34812	−	0.223546i
$511$	569.702	+	478.036i	1.11488	+	0.935492i
$512$			22.6274i			0.0441942i
$513$	−138.255	−	223.379i	−0.269504	−	0.435436i
$514$	47.3102			0.0920431
$515$	113.025	−	134.698i	0.219466	−	0.261549i
$516$	−121.450	−	99.8139i	−0.235368	−	0.193438i
$517$	−11.7334	−	66.5434i	−0.0226952	−	0.128711i
$518$	85.8396	−	235.842i	0.165713	−	0.455294i
$519$	412.194	+	481.173i	0.794208	+	0.927115i
$520$	−36.6420	+	207.807i	−0.0704654	+	0.399629i
$521$	−832.809	−	480.823i	−1.59848	−	0.922884i	−0.991780	−	0.127955i	$-0.959159\pi$
$521$	−832.809	−	480.823i	−1.59848	−	0.922884i	−0.606703	−	0.794929i	$-0.707508\pi$
$522$	108.766	+	87.5453i	0.208365	+	0.167711i
$523$	−19.2517	−	33.3450i	−0.0368102	−	0.0637572i	0.847033	−	0.531540i	$-0.178386\pi$
$523$	−19.2517	−	33.3450i	−0.0368102	−	0.0637572i	−0.883844	+	0.467783i	$0.845053\pi$
$524$	47.9842	+	131.836i	0.0915729	+	0.251595i
$525$	747.587	−	1325.93i	1.42398	−	2.52559i
$526$	170.305	−	142.903i	0.323774	−	0.271679i
$527$	−584.387	−	696.445i	−1.10889	−	1.32153i
$528$	−16.4464	−	9.27278i	−0.0311484	−	0.0175621i
$529$	−311.896	+	113.521i	−0.589596	+	0.214595i
$530$	−426.063	+	245.987i	−0.803892	+	0.464127i
$531$	−196.700	−	507.919i	−0.370432	−	0.956533i
$532$	109.378	−	189.448i	0.205597	−	0.356105i
$533$	90.0441	+	15.8772i	0.168938	+	0.0297884i
$534$	280.107	−	239.952i	0.524545	−	0.449349i
$535$	−172.312	−	62.7165i	−0.322079	−	0.117227i
$536$	7.59995	−	1.34008i	0.0141790	−	0.00250014i
$537$	−495.174	+	602.510i	−0.922112	+	1.12199i
$538$	313.299	+	262.889i	0.582340	+	0.488641i
$539$		−	121.737i		−	0.225857i
$540$	−279.946	+	355.167i	−0.518418	+	0.657717i
$541$	−16.4860			−0.0304731			−0.0152366	−	0.999884i	$-0.504850\pi$
$541$	−16.4860			−0.0304731			−0.0152366	+	0.999884i	$0.504850\pi$
$542$	−398.201	+	474.558i	−0.734689	+	0.875568i
$543$	156.747	−	945.282i	0.288669	−	1.74085i
$544$	19.2678	+	109.273i	0.0354187	+	0.200869i
$545$	−265.363	+	729.078i	−0.486904	+	1.33776i
$546$	417.646	−	78.0459i	0.764919	−	0.142941i
$547$	8.02809	−	45.5295i	0.0146766	−	0.0832350i	−0.976590	−	0.215111i	$-0.930989\pi$
$547$	8.02809	−	45.5295i	0.0146766	−	0.0832350i	0.991266	+	0.131876i	$0.0420999\pi$
$548$	−368.885	−	212.976i	−0.673147	−	0.388642i
$549$	−356.599	−	589.520i	−0.649544	−	1.07381i
$550$	50.2141	+	86.9733i	0.0912983	+	0.158133i
$551$	−36.5047	−	100.296i	−0.0662517	−	0.182025i
$552$	−119.117	+	1.21591i	−0.215791	+	0.00220274i
$553$	−436.302	+	366.101i	−0.788972	+	0.662026i
$554$	15.4638	+	18.4290i	0.0279130	+	0.0332654i
$555$	341.446	−	201.808i	0.615217	−	0.363619i
$556$	106.043	−	38.5964i	0.190724	−	0.0694179i
$557$	62.2086	−	35.9161i	0.111685	−	0.0644814i	−0.443117	−	0.896464i	$-0.646127\pi$
$557$	62.2086	−	35.9161i	0.111685	−	0.0644814i	0.554802	+	0.831982i	$0.312794\pi$
$558$	−578.761	+	114.279i	−1.03721	+	0.204802i
$559$	−116.702	+	202.133i	−0.208769	+	0.361598i
$560$	−370.857	−	65.3921i	−0.662245	−	0.116772i
$561$	−87.3191	−	30.7759i	−0.155649	−	0.0548590i
$562$	−121.947	−	44.3852i	−0.216988	−	0.0789772i
$563$	−342.983	+	60.4772i	−0.609206	+	0.107420i	−0.469736	−	0.882807i	$-0.655651\pi$
$563$	−342.983	+	60.4772i	−0.609206	+	0.107420i	−0.139470	+	0.990226i	$0.544540\pi$
$564$	90.5978	+	241.225i	0.160634	+	0.427705i
$565$	993.784	+	833.884i	1.75891	+	1.47590i
$566$		−	619.198i		−	1.09399i
$567$	867.655	+	276.248i	1.53026	+	0.487209i
$568$	212.722			0.374510
$569$	218.985	−	260.976i	0.384859	−	0.458657i	−0.538483	−	0.842637i	$-0.681002\pi$
$569$	218.985	−	260.976i	0.384859	−	0.458657i	0.923342	+	0.383980i	$0.125447\pi$
$570$	323.631	−	121.547i	0.567774	−	0.213241i
$571$	−93.4096	−	529.752i	−0.163589	−	0.927762i	−0.950507	−	0.310704i	$-0.899435\pi$
$571$	−93.4096	−	529.752i	−0.163589	−	0.927762i	0.786917	−	0.617058i	$-0.211676\pi$
$572$	−9.58754	+	26.3415i	−0.0167614	+	0.0460516i
$573$	−38.8510	+	110.230i	−0.0678027	+	0.192374i
$574$	−28.3348	+	160.695i	−0.0493638	+	0.279956i
$575$	548.746	+	316.819i	0.954341	+	0.550989i
$576$	68.1465	+	23.2392i	0.118310	+	0.0403458i
$577$	−146.659	−	254.021i	−0.254175	−	0.440244i	0.710496	−	0.703701i	$-0.248471\pi$
$577$	−146.659	−	254.021i	−0.254175	−	0.440244i	−0.964671	+	0.263457i	$0.915137\pi$
$578$	46.3103	+	127.237i	0.0801216	+	0.220132i
$579$	−249.437	−	422.030i	−0.430807	−	0.728894i
$580$	−140.750	+	118.103i	−0.242672	+	0.203626i
$581$	241.371	+	287.655i	0.415441	+	0.495103i
$582$	6.10316	+	597.897i	0.0104865	+	1.02731i
$583$	−61.4151	+	22.3533i	−0.105343	+	0.0383418i
$584$	162.047	−	93.5578i	0.277478	−	0.160202i
$585$	588.215	+	323.779i	1.00550	+	0.553469i
$586$	−182.911	+	316.811i	−0.312135	+	0.540634i
$587$	462.413	+	81.5359i	0.787757	+	0.138903i	0.553033	−	0.833159i	$-0.313470\pi$
$587$	462.413	+	81.5359i	0.787757	+	0.138903i	0.234724	+	0.972062i	$0.424581\pi$
$588$	85.2773	+	456.343i	0.145029	+	0.776093i
$589$	423.773	+	154.241i	0.719479	+	0.261869i
$590$	705.877	−	124.465i	1.19640	−	0.210958i
$591$	1014.35	+	168.200i	1.71632	+	0.284602i
$592$	−48.3734	−	40.5901i	−0.0817118	−	0.0685643i
$593$			880.585i			1.48497i	0.669864	+	0.742483i	$0.266352\pi$
$593$			880.585i			1.48497i	−0.669864	+	0.742483i	$0.733648\pi$
$594$	−44.8176	+	40.0076i	−0.0754506	+	0.0673529i
$595$	−1846.64			−3.10359
$596$	37.0322	−	44.1332i	0.0621345	−	0.0740490i
$597$	458.260	+	376.622i	0.767605	+	0.630858i
$598$	30.7122	+	174.178i	0.0513582	+	0.291267i
$599$	117.916	−	323.972i	0.196855	−	0.540855i	−0.801512	−	0.597979i	$-0.795971\pi$
$599$	117.916	−	323.972i	0.196855	−	0.540855i	0.998367	+	0.0571238i	$0.0181930\pi$
$600$	−249.158	−	290.853i	−0.415263	−	0.484755i
$601$	108.241	−	613.865i	0.180102	−	1.02141i	−0.751987	−	0.659177i	$-0.770905\pi$
$601$	108.241	−	613.865i	0.180102	−	1.02141i	0.932089	−	0.362229i	$-0.117984\pi$
$602$	−360.732	−	208.269i	−0.599223	−	0.345961i
$603$	3.76956	−	24.2649i	0.00625134	−	0.0402403i
$604$	154.786	+	268.098i	0.256269	+	0.443870i
$605$	−339.490	−	932.741i	−0.561140	−	1.54172i
$606$	188.055	−	333.537i	0.310321	−	0.550391i
$607$	725.795	−	609.015i	1.19571	−	1.00332i	0.195967	−	0.980610i	$-0.437215\pi$
$607$	725.795	−	609.015i	1.19571	−	1.00332i	0.999742	−	0.0227086i	$-0.00722899\pi$
$608$	−35.3788	−	42.1628i	−0.0581888	−	0.0693467i
$609$	322.260	+	181.696i	0.529162	+	0.298352i
$610$	851.987	−	310.098i	1.39670	−	0.508358i
$611$	331.324	−	191.290i	0.542265	−	0.313077i
$612$	348.883	+	54.1990i	0.570071	+	0.0885605i
$613$	352.677	−	610.854i	0.575329	−	0.996499i	−0.420677	−	0.907211i	$-0.638207\pi$
$613$	352.677	−	610.854i	0.575329	−	0.996499i	0.996006	−	0.0892887i	$-0.0284594\pi$
$614$	−296.919	−	52.3549i	−0.483582	−	0.0852685i
$615$	−195.835	+	167.761i	−0.318431	+	0.272782i
$616$	−47.0097	−	17.1101i	−0.0763145	−	0.0277762i
$617$	−876.465	+	154.544i	−1.42053	+	0.250477i	−0.830550	−	0.556943i	$-0.811974\pi$
$617$	−876.465	+	154.544i	−1.42053	+	0.250477i	−0.589976	+	0.807421i	$0.700863\pi$
$618$	−56.5594	+	68.8195i	−0.0915201	+	0.111358i
$619$	−376.539	−	315.954i	−0.608303	−	0.510426i	0.285800	−	0.958289i	$-0.407741\pi$
$619$	−376.539	−	315.954i	−0.608303	−	0.510426i	−0.894102	+	0.447863i	$0.852185\pi$
$620$		−	776.326i		−	1.25214i
$621$	−118.675	+	359.990i	−0.191104	+	0.579693i
$622$	−659.851			−1.06085
$623$	628.186	−	748.643i	1.00832	−	1.20167i
$624$	17.4875	−	105.460i	0.0280248	−	0.169006i
$625$	49.2783	+	279.471i	0.0788452	+	0.447154i
$626$	45.6622	−	125.456i	0.0729428	−	0.200409i
$627$	45.1437	−	8.43604i	0.0719994	−	0.0134546i
$628$	−74.2551	+	421.121i	−0.118241	+	0.670575i
$629$	−268.169	−	154.828i	−0.426342	−	0.246149i
$630$	−577.824	+	1049.74i	−0.917181	+	1.66626i
$631$	14.7611	+	25.5670i	0.0233932	+	0.0405183i	0.877485	−	0.479604i	$-0.159220\pi$
$631$	14.7611	+	25.5670i	0.0233932	+	0.0405183i	−0.854092	+	0.520122i	$0.825886\pi$
$632$	49.0119	+	134.659i	0.0775504	+	0.213068i
$633$	−685.143	+	6.99375i	−1.08238	+	0.0110486i
$634$	276.106	−	231.680i	0.435498	−	0.365426i
$635$	1245.58	+	1484.43i	1.96155	+	2.33768i
$636$	214.562	−	126.815i	0.337362	−	0.199395i
$637$	647.704	−	235.745i	1.01680	−	0.370086i
$638$	−21.1383	+	12.2042i	−0.0331322	+	0.0191289i
$639$	218.473	−	640.649i	0.341898	−	1.00258i
$640$	−47.3742	+	82.0545i	−0.0740222	+	0.128210i
$641$	−94.3541	−	16.6372i	−0.147198	−	0.0259550i	0.0995634	−	0.995031i	$-0.468255\pi$
$641$	−94.3541	−	16.6372i	−0.147198	−	0.0259550i	−0.246762	+	0.969076i	$0.579366\pi$
$642$	87.6139	+	30.8798i	0.136470	+	0.0480994i
$643$	537.766	+	195.731i	0.836339	+	0.304402i	0.724458	−	0.689319i	$-0.242090\pi$
$643$	537.766	+	195.731i	0.836339	+	0.304402i	0.111881	+	0.993722i	$0.464313\pi$
$644$	−310.841	+	54.8097i	−0.482673	+	0.0851083i
$645$	−231.441	−	616.234i	−0.358823	−	0.955401i
$646$	−206.755	−	173.488i	−0.320054	−	0.268557i
$647$		−	419.943i		−	0.649061i	−0.945875	−	0.324531i	$-0.894794\pi$
$647$		−	419.943i		−	0.649061i	0.945875	−	0.324531i	$-0.105206\pi$
$648$	139.978	−	181.368i	0.216015	−	0.279888i
$649$	95.2192			0.146717
$650$	−365.503	+	435.590i	−0.562313	+	0.670138i
$651$	−1463.33	+	549.589i	−2.24782	+	0.844223i
$652$	−51.1225	−	289.930i	−0.0784087	−	0.444678i
$653$	−425.980	+	1170.37i	−0.652343	+	1.79230i	−0.0434334	+	0.999056i	$0.513830\pi$
$653$	−425.980	+	1170.37i	−0.652343	+	1.79230i	−0.608909	+	0.793240i	$0.708393\pi$
$654$	130.657	−	370.707i	0.199781	−	0.566831i
$655$	−102.013	+	578.542i	−0.155744	+	0.883270i
$656$	35.5547	+	20.5275i	0.0541993	+	0.0312920i
$657$	−115.338	−	584.120i	−0.175552	−	0.889072i
$658$	341.380	+	591.288i	0.518815	+	0.898614i
$659$	159.051	+	436.990i	0.241353	+	0.663111i	0.999934	+	0.0115322i	$0.00367091\pi$
$659$	159.051	+	436.990i	0.241353	+	0.663111i	−0.758581	+	0.651579i	$0.774107\pi$
$660$	−40.2259	−	68.0593i	−0.0609483	−	0.103120i
$661$	−250.507	+	210.201i	−0.378982	+	0.318004i	−0.812303	−	0.583236i	$-0.801786\pi$
$661$	−250.507	+	210.201i	−0.378982	+	0.318004i	0.433320	+	0.901240i	$0.357342\pi$
$662$	−334.955	−	399.184i	−0.505974	−	0.602996i
$663$	−5.35069	−	524.181i	−0.00807043	−	0.790620i
$664$	88.7810	−	32.3137i	0.133706	−	0.0486651i
$665$	793.280	−	458.000i	1.19290	−	0.688722i
$666$	−171.925	+	103.997i	−0.258146	+	0.156152i
$667$	−77.0009	+	133.369i	−0.115444	+	0.199954i
$668$	291.076	+	51.3245i	0.435742	+	0.0768332i
$669$	−212.814	−	1138.83i	−0.318108	−	1.70228i
$670$	30.3656	+	11.0522i	0.0453218	+	0.0164958i
$671$	118.617	−	20.9153i	0.176776	−	0.0311704i
$672$	188.206	+	31.2085i	0.280069	+	0.0464413i
$673$	−221.219	−	185.625i	−0.328706	−	0.275817i	0.463466	−	0.886115i	$-0.346605\pi$
$673$	−221.219	−	185.625i	−0.328706	−	0.275817i	−0.792172	+	0.610297i	$0.791050\pi$
$674$			278.521i			0.413235i
$675$	−1131.85	+	451.666i	−1.67681	+	0.669134i
$676$	179.283			0.265211
$677$	110.656	−	131.875i	0.163450	−	0.194793i	−0.678102	−	0.734967i	$-0.737197\pi$
$677$	110.656	−	131.875i	0.163450	−	0.194793i	0.841553	+	0.540175i	$0.181642\pi$
$678$	−507.742	−	417.289i	−0.748882	−	0.615470i
$679$	275.113	+	1560.24i	0.405174	+	2.29786i
$680$	−158.909	+	436.600i	−0.233690	+	0.642059i
$681$	−363.384	−	424.194i	−0.533603	−	0.622899i
$682$	17.9086	−	101.565i	0.0262589	−	0.148922i
$683$	−113.042	−	65.2651i	−0.165509	−	0.0955565i	0.414958	−	0.909841i	$-0.363796\pi$
$683$	−113.042	−	65.2651i	−0.165509	−	0.0955565i	−0.580466	+	0.814284i	$0.697130\pi$
$684$	−163.316	+	63.2467i	−0.238766	+	0.0924659i
$685$	−891.799	−	1544.64i	−1.30190	−	2.25495i
$686$	154.281	+	423.883i	0.224899	+	0.617905i
$687$	−455.278	+	807.489i	−0.662705	+	1.17538i
$688$	−80.2832	+	67.3656i	−0.116691	+	0.0979151i
$689$	−237.862	−	283.473i	−0.345228	−	0.411427i
$690$	−434.502	−	244.981i	−0.629713	−	0.355045i
$691$	−259.558	+	94.4713i	−0.375626	+	0.136717i	−0.522932	−	0.852374i	$-0.675162\pi$
$691$	−259.558	+	94.4713i	−0.375626	+	0.136717i	0.147306	+	0.989091i	$0.452940\pi$
$692$	365.801	−	211.195i	0.528614	−	0.305196i
$693$	−99.8110	+	124.005i	−0.144027	+	0.178940i
$694$	189.321	−	327.914i	0.272797	−	0.472498i
$695$	465.354	+	82.0544i	0.669574	+	0.118064i
$696$	70.6901	−	60.5563i	0.101566	−	0.0870061i
$697$	189.181	+	68.8564i	0.271422	+	0.0987897i
$698$	719.573	−	126.880i	1.03091	−	0.181777i
$699$	−39.1695	+	47.6600i	−0.0560365	+	0.0681831i
$700$	−777.364	−	652.286i	−1.11052	−	0.931837i
$701$			865.652i			1.23488i	0.786617	+	0.617441i	$0.211830\pi$
$701$			865.652i			1.23488i	−0.786617	+	0.617441i	$0.788170\pi$
$702$	−299.651	−	160.978i	−0.426854	−	0.229313i
$703$	153.601			0.218493
$704$	−8.09070	+	9.64212i	−0.0114925	+	0.0136962i
$705$	−176.507	+	1064.44i	−0.250365	+	1.50985i
$706$	−71.2123	−	403.865i	−0.100867	−	0.572047i
$707$	346.999	−	953.372i	0.490805	−	1.34847i
$708$	−356.939	+	66.7015i	−0.504151	+	0.0942112i
$709$	−19.7944	+	112.259i	−0.0279187	+	0.158335i	−0.995580	−	0.0939188i	$-0.970061\pi$
$709$	−19.7944	+	112.259i	−0.0279187	+	0.158335i	0.967661	+	0.252254i	$0.0811717\pi$
$710$	771.399	+	445.367i	1.08648	+	0.627278i
$711$	455.886	−	9.30809i	0.641190	−	0.0130915i
$712$	−122.944	−	212.945i	−0.172674	−	0.299081i
$713$	−222.550	−	611.451i	−0.312132	−	0.857575i
$714$	935.466	−	9.54897i	1.31018	−	0.0133739i
$715$	−89.9179	+	75.4501i	−0.125759	+	0.105525i
$716$	334.199	+	398.283i	0.466758	+	0.556261i
$717$	−265.248	+	156.772i	−0.369941	+	0.218650i
$718$	−54.9523	+	20.0010i	−0.0765353	+	0.0278566i
$719$	−117.571	+	67.8798i	−0.163521	+	0.0944086i	−0.579527	−	0.814953i	$-0.696763\pi$
$719$	−117.571	+	67.8798i	−0.163521	+	0.0944086i	0.416006	+	0.909362i	$0.363429\pi$
$720$	198.467	+	226.949i	0.275648	+	0.315207i
$721$	−118.015	+	204.408i	−0.163683	+	0.283507i
$722$	−370.929	−	65.4048i	−0.513752	−	0.0905883i
$723$	1087.14	+	383.166i	1.50365	+	0.529967i
$724$	−600.270	−	218.480i	−0.829102	−	0.301768i
$725$	−487.596	+	85.9763i	−0.672546	+	0.118588i
$726$	176.801	+	470.751i	0.243528	+	0.648417i
$727$	76.0522	+	63.8154i	0.104611	+	0.0877790i	0.693593	−	0.720367i	$-0.256027\pi$
$727$	76.0522	+	63.8154i	0.104611	+	0.0877790i	−0.588982	+	0.808146i	$0.700471\pi$
$728$		−	283.250i		−	0.389080i
$729$	−402.458	−	607.839i	−0.552068	−	0.833799i
$730$	783.514			1.07331
$731$	−330.342	+	393.686i	−0.451904	+	0.538559i
$732$	−429.995	+	161.495i	−0.587425	+	0.220621i
$733$	−132.435	−	751.078i	−0.180676	−	1.02466i	−0.931387	−	0.364032i	$-0.881400\pi$
$733$	−132.435	−	751.078i	−0.180676	−	1.02466i	0.750711	−	0.660631i	$-0.229711\pi$
$734$	−78.5192	+	215.730i	−0.106974	+	0.293910i
$735$	−646.185	+	1833.39i	−0.879163	+	2.49441i
$736$	−13.7903	+	78.2088i	−0.0187368	+	0.106262i
$737$	3.71769	+	2.14641i	0.00504436	+	0.00291236i
$738$	98.3383	−	85.9968i	0.133250	−	0.116527i
$739$	436.285	+	755.668i	0.590373	+	1.02256i	0.994182	+	0.107712i	$0.0343525\pi$
$739$	436.285	+	755.668i	0.590373	+	1.02256i	−0.403810	+	0.914843i	$0.632314\pi$
$740$	−90.4359	−	248.471i	−0.122211	−	0.335771i
$741$	132.305	+	223.851i	0.178550	+	0.302093i
$742$	505.893	−	424.494i	0.681796	−	0.572095i
$743$	−515.245	−	614.045i	−0.693466	−	0.826441i	0.298304	−	0.954471i	$-0.403579\pi$
$743$	−515.245	−	614.045i	−0.693466	−	0.826441i	−0.991770	+	0.128030i	$0.959135\pi$
$744$	4.01439	+	393.270i	0.00539568	+	0.528589i
$745$	226.691	−	82.5088i	0.304283	−	0.110750i
$746$	−82.9451	+	47.8884i	−0.111186	+	0.0641935i
$747$	−6.13685	−	300.567i	−0.00821533	−	0.402366i
$748$	−30.8613	+	53.4534i	−0.0412584	+	0.0714617i
$749$	242.406	+	42.7427i	0.323639	+	0.0570663i
$750$	−131.413	−	703.230i	−0.175218	−	0.937640i
$751$	−814.474	−	296.444i	−1.08452	−	0.394733i	−0.262931	−	0.964815i	$-0.584689\pi$
$751$	−814.474	−	296.444i	−1.08452	−	0.394733i	−0.821588	+	0.570082i	$0.806911\pi$
$752$	169.175	−	29.8301i	0.224967	−	0.0396677i
$753$	962.583	+	159.616i	1.27833	+	0.211974i
$754$	−105.867	−	88.8333i	−0.140408	−	0.117816i
$755$			1296.28i			1.71693i
$756$	287.285	−	534.765i	0.380007	−	0.707361i
$757$	−305.290			−0.403289			−0.201644	−	0.979459i	$-0.564629\pi$
$757$	−305.290			−0.403289			−0.201644	+	0.979459i	$0.564629\pi$
$758$	−111.295	+	132.636i	−0.146827	+	0.174981i
$759$	−51.1934	−	42.0734i	−0.0674485	−	0.0554327i
$760$	−40.0205	−	226.968i	−0.0526586	−	0.298642i
$761$	210.316	−	577.838i	0.276367	−	0.759313i	−0.721399	−	0.692519i	$-0.756501\pi$
$761$	210.316	−	577.838i	0.276367	−	0.759313i	0.997767	−	0.0667941i	$-0.0212771\pi$
$762$	−638.662	−	745.539i	−0.838139	−	0.978397i
$763$	180.851	−	1025.65i	0.237026	−	1.34424i
$764$	67.4786	+	38.9588i	0.0883228	+	0.0509932i
$765$	1151.69	+	926.988i	1.50548	+	1.21175i
$766$	−42.7767	−	74.0914i	−0.0558443	−	0.0967251i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.909039 + 1.08335i) q^{2} +(2.80846 - 1.05478i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.86430 - 7.86960i) q^{5} +(-1.41030 + 4.00138i) q^{6} +(-1.95208 + 11.0708i) q^{7} +(2.44949 + 1.41421i) q^{8} +(6.77487 - 5.92462i) q^{9} +O(q^{10})\)	\(q+(-0.909039 + 1.08335i) q^{2} +(2.80846 - 1.05478i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.86430 - 7.86960i) q^{5} +(-1.41030 + 4.00138i) q^{6} +(-1.95208 + 11.0708i) q^{7} +(2.44949 + 1.41421i) q^{8} +(6.77487 - 5.92462i) q^{9} +(5.92177 + 10.2568i) q^{10} +(0.538121 + 1.47848i) q^{11} +(-3.05288 - 5.16526i) q^{12} +(-6.82419 + 5.72617i) q^{13} +(-10.2191 - 12.1786i) q^{14} +(-0.256445 - 25.1227i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-16.9870 + 9.80744i) q^{17} +(0.259819 + 12.7253i) q^{18} +(4.86486 - 8.42619i) q^{19} +(-16.4948 - 2.90849i) q^{20} +(6.19496 + 33.1510i) q^{21} +(-2.09088 - 0.761018i) q^{22} +(-13.8255 + 2.43781i) q^{23} +(8.37098 + 1.38808i) q^{24} +(-34.5753 - 29.0121i) q^{25} -12.5983i q^{26} +(12.7778 - 23.7851i) q^{27} +22.4832 q^{28} +(7.05122 - 8.40331i) q^{29} +(27.4498 + 22.5597i) q^{30} +(8.04854 + 45.6456i) q^{31} +(1.93476 - 5.31570i) q^{32} +(3.07076 + 3.58464i) q^{33} +(4.81694 - 27.3182i) q^{34} +(81.5316 + 47.0723i) q^{35} +(-14.0221 - 11.2863i) q^{36} +(7.89337 + 13.6717i) q^{37} +(4.70617 + 12.9301i) q^{38} +(-13.1256 + 23.2797i) q^{39} +(18.1454 - 15.2258i) q^{40} +(-6.59742 - 7.86250i) q^{41} +(-41.5456 - 23.4242i) q^{42} +(24.6205 - 8.96112i) q^{43} +(2.72514 - 1.57336i) q^{44} +(-27.2191 - 70.2854i) q^{45} +(9.92691 - 17.1939i) q^{46} +(-42.2938 - 7.45754i) q^{47} +(-9.11332 + 7.80688i) q^{48} +(-72.7075 - 26.4634i) q^{49} +(62.8606 - 11.0840i) q^{50} +(-37.3625 + 45.4614i) q^{51} +(13.6484 + 11.4523i) q^{52} +41.5395i q^{53} +(14.1521 + 35.4643i) q^{54} +13.1764 q^{55} +(-20.4381 + 24.3572i) q^{56} +(4.77497 - 28.7960i) q^{57} +(2.69390 + 15.2779i) q^{58} +(20.6989 - 56.8698i) q^{59} +(-49.3929 + 9.23010i) q^{60} +(13.2934 - 75.3906i) q^{61} +(-56.7666 - 32.7742i) q^{62} +(52.3653 + 86.5688i) q^{63} +(4.00000 + 6.92820i) q^{64} +(25.5162 + 70.1051i) q^{65} +(-6.67486 + 0.0681351i) q^{66} +(2.09011 - 1.75381i) q^{67} +(25.2164 + 30.0518i) q^{68} +(-36.2569 + 21.4293i) q^{69} +(-125.111 + 45.5367i) q^{70} +(65.1324 - 37.6042i) q^{71} +(24.9737 - 4.93118i) q^{72} +(33.0777 - 57.2922i) q^{73} +(-21.9866 - 3.87684i) q^{74} +(-127.705 - 45.0099i) q^{75} +(-18.2859 - 6.65552i) q^{76} +(-17.4184 + 3.07133i) q^{77} +(-13.2885 - 35.3818i) q^{78} +(38.8113 + 32.5666i) q^{79} +33.4986i q^{80} +(10.7977 - 80.2771i) q^{81} +14.5152 q^{82} +(21.4712 - 25.5884i) q^{83} +(63.1432 - 23.7149i) q^{84} +(28.5248 + 161.772i) q^{85} +(-12.6729 + 34.8186i) q^{86} +(10.9394 - 31.0378i) q^{87} +(-0.772758 + 4.38253i) q^{88} +(-75.2876 - 43.4673i) q^{89} +(100.887 + 34.4043i) q^{90} +(-50.0720 - 86.7273i) q^{91} +(9.60308 + 26.3842i) q^{92} +(70.7501 + 119.704i) q^{93} +(46.5258 - 39.0398i) q^{94} +(-52.3763 - 62.4197i) q^{95} +(-0.173222 - 16.9697i) q^{96} +(132.434 - 48.2019i) q^{97} +(94.7631 - 54.7115i) q^{98} +(12.4051 + 6.82832i) 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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