LMFDB - Embedded newform 378.2.v.b.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			79.4
Character	$\chi$	$=$	378.79
Dual form			378.2.v.b.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-1.07856 + 1.35526i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.620533 + 3.51922i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-0.670349 + 2.55942i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.673434 - 2.92344i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-1.07856 + 1.35526i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.620533 + 3.51922i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-0.670349 + 2.55942i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.673434 - 2.92344i) q^{9} +(-1.78675 + 3.09475i) q^{10} +(0.735962 - 4.17385i) q^{11} +(-1.52196 - 0.826833i) q^{12} +(-0.585610 - 3.32116i) q^{13} +(-2.15868 + 1.52974i) q^{14} +(-5.43872 - 2.95469i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.28580 - 2.22707i) q^{17} +(1.36327 - 2.67236i) q^{18} +(3.01921 + 5.22942i) q^{19} +(-3.35800 + 1.22221i) q^{20} +(-2.74566 - 3.66897i) q^{21} +(3.24668 - 2.72429i) q^{22} +(-1.75410 + 1.47186i) q^{23} +(-0.634407 - 1.61168i) q^{24} +(-7.30136 + 2.65748i) q^{25} +(1.68620 - 2.92058i) q^{26} +(4.68834 + 2.24042i) q^{27} +(-2.63694 - 0.215726i) q^{28} +(-0.315874 + 1.79141i) q^{29} +(-2.26706 - 5.75936i) q^{30} +(1.79383 + 10.1733i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(4.86285 + 5.49914i) q^{33} +(2.41652 - 0.879540i) q^{34} +(-9.42313 - 0.770898i) q^{35} +(2.76208 - 1.17085i) q^{36} +7.16828 q^{37} +(-1.04856 + 5.94668i) q^{38} +(5.13263 + 2.78840i) q^{39} +(-3.35800 - 1.22221i) q^{40} +(-1.32145 - 7.49429i) q^{41} +(0.255073 - 4.57547i) q^{42} +(-2.13929 - 1.79507i) q^{43} +4.23824 q^{44} +(9.87032 - 4.18405i) q^{45} -2.28981 q^{46} +(-0.550684 + 3.12308i) q^{47} +(0.549987 - 1.64241i) q^{48} +(-6.10127 - 3.43141i) q^{49} +(-7.30136 - 2.65748i) q^{50} +(1.63144 + 4.14461i) q^{51} +(3.16901 - 1.15343i) q^{52} +(4.04351 + 7.00356i) q^{53} +(2.15136 + 4.72987i) q^{54} +15.1454 q^{55} +(-1.88135 - 1.86025i) q^{56} +(-10.3436 - 1.54843i) q^{57} +(-1.39347 + 1.16926i) q^{58} +(-5.98431 - 2.17811i) q^{59} +(1.96538 - 5.86917i) q^{60} +(0.904765 - 5.13118i) q^{61} +(-5.16512 + 8.94625i) q^{62} +(7.93374 + 0.236123i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(11.3245 - 4.12177i) q^{65} +(0.190379 + 7.33837i) q^{66} +(-1.43204 + 1.20163i) q^{67} +(2.41652 + 0.879540i) q^{68} +(-0.102857 - 3.96474i) q^{69} +(-6.72301 - 6.64761i) q^{70} +(-3.31293 - 5.73817i) q^{71} +(2.86849 + 0.878508i) q^{72} +12.1719 q^{73} +(5.49122 + 4.60768i) q^{74} +(4.27337 - 12.7614i) q^{75} +(-4.62570 + 3.88142i) q^{76} +(10.1893 + 4.68157i) q^{77} +(2.13947 + 5.43523i) q^{78} +(2.65034 + 2.22390i) q^{79} +(-1.78675 - 3.09475i) q^{80} +(-8.09297 + 3.93748i) q^{81} +(3.80495 - 6.59037i) q^{82} +(0.275388 - 1.56180i) q^{83} +(3.13645 - 3.34106i) q^{84} +(8.63544 + 3.14304i) q^{85} +(-0.484937 - 2.75021i) q^{86} +(-2.08713 - 2.36023i) q^{87} +(3.24668 + 2.72429i) q^{88} +(-2.58297 - 4.47383i) q^{89} +(10.2506 + 3.13935i) q^{90} +(8.89280 + 0.727513i) q^{91} +(-1.75410 - 1.47186i) q^{92} +(-15.7222 - 8.54138i) q^{93} +(-2.42933 + 2.03845i) q^{94} +(-16.5300 + 13.8703i) q^{95} +(1.47704 - 0.904635i) q^{96} +(14.6758 + 12.3145i) q^{97} +(-2.46817 - 6.55043i) q^{98} +(-12.6976 + 0.659271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−1.07856	+	1.35526i	−0.622705	+	0.782457i
$3$	−1.07856	+	1.35526i	−0.622705	+	0.782457i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.620533	+	3.51922i	0.277511	+	1.57384i	0.730872	+	0.682515i	$0.239114\pi$
$5$	0.620533	+	3.51922i	0.277511	+	1.57384i	−0.453361	+	0.891327i	$0.649775\pi$
$6$	−1.69736	+	0.344903i	−0.692946	+	0.140806i
$7$	−0.670349	+	2.55942i	−0.253368	+	0.967370i
$7$	−0.670349	+	2.55942i	−0.253368	+	0.967370i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.673434	−	2.92344i	−0.224478	−	0.974479i
$10$	−1.78675	+	3.09475i	−0.565021	+	0.978645i
$11$	0.735962	−	4.17385i	0.221901	−	1.25846i	−0.646621	−	0.762811i	$-0.723818\pi$
$11$	0.735962	−	4.17385i	0.221901	−	1.25846i	0.868522	−	0.495651i	$-0.165070\pi$
$12$	−1.52196	−	0.826833i	−0.439351	−	0.238686i
$13$	−0.585610	−	3.32116i	−0.162419	−	0.921123i	−0.951686	−	0.307073i	$-0.900650\pi$
$13$	−0.585610	−	3.32116i	−0.162419	−	0.921123i	0.789267	−	0.614050i	$-0.210461\pi$
$14$	−2.15868	+	1.52974i	−0.576932	+	0.408840i
$15$	−5.43872	−	2.95469i	−1.40427	−	0.762898i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.28580	−	2.22707i	0.311853	−	0.540145i	−0.666911	−	0.745138i	$-0.732384\pi$
$17$	1.28580	−	2.22707i	0.311853	−	0.540145i	0.978763	+	0.204993i	$0.0657171\pi$
$18$	1.36327	−	2.67236i	0.321326	−	0.629881i
$19$	3.01921	+	5.22942i	0.692654	+	1.19971i	0.970965	+	0.239221i	$0.0768920\pi$
$19$	3.01921	+	5.22942i	0.692654	+	1.19971i	−0.278311	+	0.960491i	$0.589775\pi$
$20$	−3.35800	+	1.22221i	−0.750871	+	0.273295i
$21$	−2.74566	−	3.66897i	−0.599152	−	0.800635i
$22$	3.24668	−	2.72429i	0.692194	−	0.580820i
$23$	−1.75410	+	1.47186i	−0.365755	+	0.306905i	−0.807079	−	0.590443i	$-0.798953\pi$
$23$	−1.75410	+	1.47186i	−0.365755	+	0.306905i	0.441325	+	0.897347i	$0.354509\pi$
$24$	−0.634407	−	1.61168i	−0.129498	−	0.328984i
$25$	−7.30136	+	2.65748i	−1.46027	+	0.531496i
$26$	1.68620	−	2.92058i	0.330690	−	0.572772i
$27$	4.68834	+	2.24042i	0.902271	+	0.431168i
$28$	−2.63694	−	0.215726i	−0.498335	−	0.0407684i
$29$	−0.315874	+	1.79141i	−0.0586563	+	0.332657i	−0.999988	−	0.00482527i	$-0.998464\pi$
$29$	−0.315874	+	1.79141i	−0.0586563	+	0.332657i	0.941332	+	0.337482i	$0.109575\pi$
$30$	−2.26706	−	5.75936i	−0.413906	−	1.05151i
$31$	1.79383	+	10.1733i	0.322181	+	1.82718i	0.528787	+	0.848755i	$0.322647\pi$
$31$	1.79383	+	10.1733i	0.322181	+	1.82718i	−0.206606	+	0.978424i	$0.566242\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	4.86285	+	5.49914i	0.846514	+	0.957278i
$34$	2.41652	−	0.879540i	0.414429	−	0.150840i
$35$	−9.42313	−	0.770898i	−1.59280	−	0.130306i
$36$	2.76208	−	1.17085i	0.460347	−	0.195142i
$37$	7.16828			1.17846			0.589229	−	0.807966i	$-0.299431\pi$
$37$	7.16828			1.17846			0.589229	+	0.807966i	$0.299431\pi$
$38$	−1.04856	+	5.94668i	−0.170099	+	0.964679i
$39$	5.13263	+	2.78840i	0.821879	+	0.446502i
$40$	−3.35800	−	1.22221i	−0.530946	−	0.193249i
$41$	−1.32145	−	7.49429i	−0.206375	−	1.17041i	−0.895261	−	0.445542i	$-0.853011\pi$
$41$	−1.32145	−	7.49429i	−0.206375	−	1.17041i	0.688886	−	0.724870i	$-0.258100\pi$
$42$	0.255073	−	4.57547i	0.0393586	−	0.706011i
$43$	−2.13929	−	1.79507i	−0.326238	−	0.273746i	0.464927	−	0.885349i	$-0.346081\pi$
$43$	−2.13929	−	1.79507i	−0.326238	−	0.273746i	−0.791165	+	0.611603i	$0.790525\pi$
$44$	4.23824			0.638938
$45$	9.87032	−	4.18405i	1.47138	−	0.623721i
$46$	−2.28981			−0.337614
$47$	−0.550684	+	3.12308i	−0.0803255	+	0.455549i	0.917942	+	0.396714i	$0.129850\pi$
$47$	−0.550684	+	3.12308i	−0.0803255	+	0.455549i	−0.998268	+	0.0588345i	$0.981262\pi$
$48$	0.549987	−	1.64241i	0.0793837	−	0.237062i
$49$	−6.10127	−	3.43141i	−0.871609	−	0.490201i
$50$	−7.30136	−	2.65748i	−1.03257	−	0.375824i
$51$	1.63144	+	4.14461i	0.228448	+	0.580362i
$52$	3.16901	−	1.15343i	0.439463	−	0.159951i
$53$	4.04351	+	7.00356i	0.555418	+	0.962012i	0.997871	+	0.0652206i	$0.0207751\pi$
$53$	4.04351	+	7.00356i	0.555418	+	0.962012i	−0.442453	+	0.896792i	$0.645892\pi$
$54$	2.15136	+	4.72987i	0.292764	+	0.643653i
$55$	15.1454			2.04220
$56$	−1.88135	−	1.86025i	−0.251406	−	0.248586i
$57$	−10.3436	−	1.54843i	−1.37004	−	0.205094i
$58$	−1.39347	+	1.16926i	−0.182972	+	0.153531i
$59$	−5.98431	−	2.17811i	−0.779091	−	0.283566i	−0.0782972	−	0.996930i	$-0.524948\pi$
$59$	−5.98431	−	2.17811i	−0.779091	−	0.283566i	−0.700793	+	0.713364i	$0.747171\pi$
$60$	1.96538	−	5.86917i	0.253730	−	0.757706i
$61$	0.904765	−	5.13118i	0.115843	−	0.656980i	−0.870486	−	0.492193i	$-0.836195\pi$
$61$	0.904765	−	5.13118i	0.115843	−	0.656980i	0.986329	−	0.164787i	$-0.0526936\pi$
$62$	−5.16512	+	8.94625i	−0.655971	+	1.13617i
$63$	7.93374	+	0.236123i	0.999557	+	0.0297487i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	11.3245	−	4.12177i	1.40463	−	0.511243i
$66$	0.190379	+	7.33837i	0.0234341	+	0.903291i
$67$	−1.43204	+	1.20163i	−0.174952	+	0.146802i	−0.726059	−	0.687633i	$-0.758650\pi$
$67$	−1.43204	+	1.20163i	−0.174952	+	0.146802i	0.551107	+	0.834435i	$0.314206\pi$
$68$	2.41652	+	0.879540i	0.293046	+	0.106660i
$69$	−0.102857	−	3.96474i	−0.0123825	−	0.477298i
$70$	−6.72301	−	6.64761i	−0.803553	−	0.794542i
$71$	−3.31293	−	5.73817i	−0.393173	−	0.680996i	0.599693	−	0.800230i	$-0.295289\pi$
$71$	−3.31293	−	5.73817i	−0.393173	−	0.680996i	−0.992866	+	0.119234i	$0.961956\pi$
$72$	2.86849	+	0.878508i	0.338055	+	0.103533i
$73$	12.1719			1.42462			0.712309	−	0.701866i	$-0.247649\pi$
$73$	12.1719			1.42462			0.712309	+	0.701866i	$0.247649\pi$
$74$	5.49122	+	4.60768i	0.638342	+	0.535632i
$75$	4.27337	−	12.7614i	0.493446	−	1.47356i
$76$	−4.62570	+	3.88142i	−0.530604	+	0.445229i
$77$	10.1893	+	4.68157i	1.16118	+	0.533514i
$78$	2.13947	+	5.43523i	0.242247	+	0.615419i
$79$	2.65034	+	2.22390i	0.298187	+	0.250208i	0.779589	−	0.626291i	$-0.215428\pi$
$79$	2.65034	+	2.22390i	0.298187	+	0.250208i	−0.481402	+	0.876500i	$0.659872\pi$
$80$	−1.78675	−	3.09475i	−0.199765	−	0.346003i
$81$	−8.09297	+	3.93748i	−0.899219	+	0.437498i
$82$	3.80495	−	6.59037i	0.420187	−	0.727785i
$83$	0.275388	−	1.56180i	0.0302278	−	0.171430i	−0.965957	−	0.258704i	$-0.916704\pi$
$83$	0.275388	−	1.56180i	0.0302278	−	0.171430i	0.996184	+	0.0872741i	$0.0278156\pi$
$84$	3.13645	−	3.34106i	0.342215	−	0.364539i
$85$	8.63544	+	3.14304i	0.936645	+	0.340911i
$86$	−0.484937	−	2.75021i	−0.0522921	−	0.296563i
$87$	−2.08713	−	2.36023i	−0.223764	−	0.253043i
$88$	3.24668	+	2.72429i	0.346097	+	0.290410i
$89$	−2.58297	−	4.47383i	−0.273794	−	0.474225i	0.696036	−	0.718007i	$-0.254945\pi$
$89$	−2.58297	−	4.47383i	−0.273794	−	0.474225i	−0.969830	+	0.243782i	$0.921612\pi$
$90$	10.2506	+	3.13935i	1.08050	+	0.330917i
$91$	8.89280	+	0.727513i	0.932219	+	0.0762640i
$92$	−1.75410	−	1.47186i	−0.182877	−	0.153452i
$93$	−15.7222	−	8.54138i	−1.63031	−	0.885700i
$94$	−2.42933	+	2.03845i	−0.250566	+	0.210250i
$95$	−16.5300	+	13.8703i	−1.69594	+	1.42306i
$96$	1.47704	−	0.904635i	0.150749	−	0.0923290i
$97$	14.6758	+	12.3145i	1.49010	+	1.25034i	0.894504	+	0.447060i	$0.147529\pi$
$97$	14.6758	+	12.3145i	1.49010	+	1.25034i	0.595597	+	0.803284i	$0.296916\pi$
$98$	−2.46817	−	6.55043i	−0.249323	−	0.661693i
$99$	−12.6976	+	0.659271i	−1.27616	+	0.0662592i
$100$	−3.88497	−	6.72897i	−0.388497	−	0.672897i
$101$	−6.46670	−	5.42621i	−0.643461	−	0.539928i	0.261618	−	0.965171i	$-0.415744\pi$
$101$	−6.46670	−	5.42621i	−0.643461	−	0.539928i	−0.905079	+	0.425244i	$0.860188\pi$
$102$	−1.41435	+	4.22363i	−0.140041	+	0.418202i
$103$	3.50065	+	19.8532i	0.344929	+	1.95619i	0.287250	+	0.957856i	$0.407259\pi$
$103$	3.50065	+	19.8532i	0.344929	+	1.95619i	0.0576796	+	0.998335i	$0.481630\pi$
$104$	3.16901	+	1.15343i	0.310747	+	0.113103i
$105$	11.2081	−	11.9393i	1.09380	−	1.16516i
$106$	−1.40429	+	7.96415i	−0.136397	+	0.773547i
$107$	3.04619	−	5.27616i	0.294487	−	0.510066i	−0.680379	−	0.732861i	$-0.738185\pi$
$107$	3.04619	−	5.27616i	0.294487	−	0.510066i	0.974865	+	0.222795i	$0.0715180\pi$
$108$	−1.39226	+	5.00616i	−0.133970	+	0.481718i
$109$	−5.46649	−	9.46824i	−0.523595	−	0.906893i	−0.999623	−	0.0274630i	$-0.991257\pi$
$109$	−5.46649	−	9.46824i	−0.523595	−	0.906893i	0.476028	−	0.879430i	$-0.342076\pi$
$110$	11.6020	+	9.73525i	1.10621	+	0.928220i
$111$	−7.73140	+	9.71485i	−0.733832	+	0.922093i
$112$	−0.245452	−	2.63434i	−0.0231930	−	0.248922i
$113$	3.76639	−	3.16038i	0.354312	−	0.297303i	−0.448207	−	0.893930i	$-0.647937\pi$
$113$	3.76639	−	3.16038i	0.354312	−	0.297303i	0.802519	+	0.596627i	$0.203493\pi$
$114$	−6.92834	−	7.83489i	−0.648898	−	0.733805i
$115$	−6.26828	−	5.25971i	−0.584520	−	0.490471i
$116$	−1.81905			−0.168894
$117$	−9.31483	+	3.94857i	−0.861156	+	0.365046i
$118$	−3.18418	−	5.51517i	−0.293128	−	0.507712i
$119$	4.83808	+	4.78382i	0.443506	+	0.438532i
$120$	5.27820	−	3.23272i	0.481831	−	0.295106i
$121$	−6.54274	−	2.38136i	−0.594795	−	0.216488i
$122$	3.99135	−	3.34914i	0.361360	−	0.303217i
$123$	11.5819	+	6.29212i	1.04431	+	0.567341i
$124$	−9.70725	+	3.53315i	−0.871737	+	0.317286i
$125$	−4.94921	−	8.57228i	−0.442671	−	0.766728i
$126$	5.92582	+	5.28059i	0.527914	+	0.470432i
$127$	2.75557	−	4.77279i	0.244517	−	0.423517i	−0.717478	−	0.696581i	$-0.754704\pi$
$127$	2.75557	−	4.77279i	0.244517	−	0.423517i	0.961996	+	0.273064i	$0.0880371\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	4.74012	−	0.963191i	0.417345	−	0.0848042i
$130$	11.3245	+	4.12177i	0.993223	+	0.361504i
$131$	2.24615	−	1.88474i	0.196247	−	0.164671i	−0.539369	−	0.842070i	$-0.681337\pi$
$131$	2.24615	−	1.88474i	0.196247	−	0.164671i	0.735616	+	0.677399i	$0.236893\pi$
$132$	−4.57117	+	5.74389i	−0.397870	+	0.499942i
$133$	−15.4082	+	4.22189i	−1.33606	+	0.366084i
$134$	−1.86940			−0.161491
$135$	−4.97524	+	17.8895i	−0.428201	+	1.53969i
$136$	1.28580	+	2.22707i	0.110257	+	0.190970i
$137$	15.2235	−	5.54091i	1.30063	−	0.473392i	0.403431	−	0.915010i	$-0.367818\pi$
$137$	15.2235	−	5.54091i	1.30063	−	0.473392i	0.897203	+	0.441618i	$0.145595\pi$
$138$	2.46969	−	3.10328i	0.210234	−	0.264169i
$139$	−13.9917	−	5.09257i	−1.18676	−	0.431946i	−0.328176	−	0.944617i	$-0.606434\pi$
$139$	−13.9917	−	5.09257i	−1.18676	−	0.431946i	−0.858585	+	0.512671i	$0.828656\pi$
$140$	−0.877122	−	9.41383i	−0.0741304	−	0.795614i
$141$	−3.63863	−	4.11474i	−0.306428	−	0.346523i
$142$	1.15057	−	6.52521i	0.0965537	−	0.547583i
$143$	−14.2930			−1.19524
$144$	1.63270	+	2.51680i	0.136058	+	0.209734i
$145$	−6.50037			−0.539827
$146$	9.32425	+	7.82397i	0.771680	+	0.647517i
$147$	11.2310	−	4.56781i	0.926317	−	0.376746i
$148$	1.24476	+	7.05938i	0.102319	+	0.580278i
$149$	−6.78584	−	2.46984i	−0.555918	−	0.202338i	0.0487561	−	0.998811i	$-0.484474\pi$
$149$	−6.78584	−	2.46984i	−0.555918	−	0.202338i	−0.604674	+	0.796473i	$0.706697\pi$
$150$	11.4765	−	7.02897i	0.937051	−	0.573913i
$151$	1.41821	−	8.04308i	0.115412	−	0.654536i	−0.871133	−	0.491048i	$-0.836614\pi$
$151$	1.41821	−	8.04308i	0.115412	−	0.654536i	0.986545	−	0.163489i	$-0.0522748\pi$
$152$	−6.03842			−0.489780
$153$	−7.37662	−	2.25917i	−0.596364	−	0.182643i
$154$	4.79619	+	10.1358i	0.386488	+	0.816769i
$155$	−34.6889	+	12.6257i	−2.78628	+	1.01412i
$156$	−1.85477	+	5.53885i	−0.148500	+	0.443463i
$157$	16.1435	+	5.87575i	1.28839	+	0.468936i	0.893198	−	0.449663i	$-0.148456\pi$
$157$	16.1435	+	5.87575i	1.28839	+	0.468936i	0.395192	+	0.918599i	$0.370678\pi$
$158$	0.600783	+	3.40721i	0.0477958	+	0.271063i
$159$	−13.8528	−	2.07375i	−1.09859	−	0.164459i
$160$	0.620533	−	3.51922i	0.0490574	−	0.278218i
$161$	−2.59126	−	5.47614i	−0.204220	−	0.431580i
$162$	−8.73054	−	2.18578i	−0.685936	−	0.171731i
$163$	5.52476	−	9.56917i	0.432733	−	0.749515i	−0.564375	−	0.825519i	$-0.690883\pi$
$163$	5.52476	−	9.56917i	0.432733	−	0.749515i	0.997108	+	0.0760035i	$0.0242160\pi$
$164$	7.15097	−	2.60274i	0.558397	−	0.203240i
$165$	−16.3351	+	20.5258i	−1.27169	+	1.59793i
$166$	1.21487	−	1.01940i	0.0942920	−	0.0791204i
$167$	15.1547	−	12.7163i	1.17270	−	0.984014i	0.172703	−	0.984974i	$-0.444750\pi$
$167$	15.1547	−	12.7163i	1.17270	−	0.984014i	1.00000		0.000959417i	$0.000305392\pi$
$168$	4.55025	−	0.543325i	0.351060	−	0.0419184i
$169$	1.52885	−	0.556457i	0.117604	−	0.0428044i
$170$	4.59482	+	7.95846i	0.352407	+	0.610386i
$171$	13.2547	−	12.3481i	1.01361	−	0.944286i
$172$	1.39632	−	2.41850i	0.106468	−	0.184409i
$173$	−18.2070	+	6.62682i	−1.38426	+	0.503828i	−0.923466	−	0.383681i	$-0.874656\pi$
$173$	−18.2070	+	6.62682i	−1.38426	+	0.503828i	−0.460790	+	0.887509i	$0.652434\pi$
$174$	−0.0817105	−	3.14962i	−0.00619446	−	0.238772i
$175$	−1.90714	−	20.4687i	−0.144167	−	1.54729i
$176$	0.735962	+	4.17385i	0.0554752	+	0.314616i
$177$	9.40631	−	5.76105i	0.707021	−	0.433027i
$178$	0.897055	−	5.08745i	0.0672371	−	0.381320i
$179$	10.9281	−	18.9280i	0.816805	−	1.41475i	−0.0912195	−	0.995831i	$-0.529076\pi$
$179$	10.9281	−	18.9280i	0.816805	−	1.41475i	0.908025	−	0.418917i	$-0.137590\pi$
$180$	5.83445	+	8.99382i	0.434874	+	0.670360i
$181$	2.48406	−	4.30251i	0.184638	−	0.319803i	−0.758816	−	0.651305i	$-0.774222\pi$
$181$	2.48406	−	4.30251i	0.184638	−	0.319803i	0.943455	+	0.331502i	$0.107555\pi$
$182$	6.34465	+	6.27349i	0.470296	+	0.465022i
$183$	5.97822	+	6.76045i	0.441923	+	0.499747i
$184$	−0.397622	−	2.25502i	−0.0293131	−	0.166243i
$185$	4.44816	+	25.2267i	0.327035	+	1.85471i
$186$	−6.55358	−	16.6491i	−0.480532	−	1.22077i
$187$	−8.34917	−	7.00578i	−0.610552	−	0.512314i
$188$	−3.17126			−0.231288
$189$	−8.87699	+	10.4976i	−0.645706	+	0.763586i
$190$	−21.5783			−1.56546
$191$	12.7309	+	10.6825i	0.921173	+	0.772956i	0.974212	−	0.225636i	$-0.0724461\pi$
$191$	12.7309	+	10.6825i	0.921173	+	0.772956i	−0.0530384	+	0.998592i	$0.516891\pi$
$192$	1.71296	+	0.256429i	0.123622	+	0.0185062i
$193$	−0.318916	−	1.80866i	−0.0229560	−	0.130190i	0.971176	−	0.238364i	$-0.0766110\pi$
$193$	−0.318916	−	1.80866i	−0.0229560	−	0.130190i	−0.994132	+	0.108173i	$0.965500\pi$
$194$	3.32673	+	18.8668i	0.238845	+	1.35456i
$195$	−6.62803	+	19.7931i	−0.474643	+	1.41742i
$196$	2.31980	−	6.60443i	0.165700	−	0.471745i
$197$	5.53938	−	9.59449i	0.394665	−	0.683579i	−0.598394	−	0.801202i	$-0.704194\pi$
$197$	5.53938	−	9.59449i	0.394665	−	0.683579i	0.993058	+	0.117623i	$0.0375274\pi$
$198$	−10.1507	−	7.65683i	−0.721379	−	0.544147i
$199$	4.99889	−	8.65832i	0.354362	−	0.613772i	−0.632647	−	0.774440i	$-0.718032\pi$
$199$	4.99889	−	8.65832i	0.354362	−	0.613772i	0.987008	+	0.160668i	$0.0513649\pi$
$200$	1.34924	−	7.65190i	0.0954055	−	0.541071i
$201$	−0.0839723	−	3.23680i	−0.00592295	−	0.228306i
$202$	−1.46588	−	8.31343i	−0.103139	−	0.584931i
$203$	−4.37323	−	2.00932i	−0.306940	−	0.141027i
$204$	−3.79835	+	2.32636i	−0.265938	+	0.162878i
$205$	25.5540	−	9.30091i	1.78477	−	0.649604i
$206$	−10.0797	+	17.4586i	−0.702287	+	1.21640i
$207$	5.48417	+	4.13679i	0.381176	+	0.287527i
$208$	1.68620	+	2.92058i	0.116917	+	0.202506i
$209$	24.0488	−	8.75306i	1.66349	−	0.605462i
$210$	16.2604	−	1.94157i	1.12207	−	0.133981i
$211$	−15.4658	+	12.9774i	−1.06471	+	0.893398i	−0.994563	−	0.104139i	$-0.966791\pi$
$211$	−15.4658	+	12.9774i	−1.06471	+	0.893398i	−0.0701473	+	0.997537i	$0.522347\pi$
$212$	−6.19501	+	5.19823i	−0.425475	+	0.357016i
$213$	11.3499	+	1.69907i	0.777680	+	0.116418i
$214$	5.72497	−	2.08372i	0.391351	−	0.142440i
$215$	4.98976	−	8.64251i	0.340299	−	0.589415i
$216$	−4.28443	+	2.94001i	−0.291518	+	0.200043i
$217$	−27.2402	−	2.22850i	−1.84919	−	0.151281i
$218$	1.89849	−	10.7669i	0.128582	−	0.729226i
$219$	−13.1281	+	16.4961i	−0.887116	+	1.11470i
$220$	2.62996	+	14.9153i	0.177312	+	1.00559i
$221$	−8.14944	−	2.96615i	−0.548191	−	0.199525i
$222$	−12.1672	+	2.47236i	−0.816608	+	0.165934i
$223$	−23.0056	+	8.37336i	−1.54057	+	0.560722i	−0.966182	−	0.257861i	$-0.916982\pi$
$223$	−23.0056	+	8.37336i	−1.54057	+	0.560722i	−0.574388	+	0.818583i	$0.694760\pi$
$224$	1.50530	−	2.17580i	0.100577	−	0.145376i
$225$	12.6860	+	19.5554i	0.845730	+	1.30370i
$226$	4.91667			0.327052
$227$	−2.47362	+	14.0286i	−0.164180	+	0.931111i	0.785726	+	0.618575i	$0.212290\pi$
$227$	−2.47362	+	14.0286i	−0.164180	+	0.931111i	−0.949906	+	0.312536i	$0.898821\pi$
$228$	−0.271242	−	10.4553i	−0.0179635	−	0.692421i
$229$	−18.1896	−	6.62047i	−1.20200	−	0.437493i	−0.338079	−	0.941118i	$-0.609777\pi$
$229$	−18.1896	−	6.62047i	−1.20200	−	0.437493i	−0.863922	+	0.503625i	$0.831999\pi$
$230$	−1.42090	−	8.05834i	−0.0936916	−	0.531352i
$231$	−17.3344	+	8.75974i	−1.14052	+	0.576348i
$232$	−1.39347	−	1.16926i	−0.0914858	−	0.0767657i
$233$	−14.4577			−0.947157			−0.473579	−	0.880752i	$-0.657038\pi$
$233$	−14.4577			−0.947157			−0.473579	+	0.880752i	$0.657038\pi$
$234$	−9.67367	−	2.96267i	−0.632387	−	0.193676i
$235$	−11.3325			−0.739252
$236$	1.10586	−	6.27162i	0.0719851	−	0.408248i
$237$	−5.87249	+	1.19329i	−0.381459	+	0.0775124i
$238$	0.631204	+	6.77448i	0.0409149	+	0.439124i
$239$	4.16230	+	1.51495i	0.269237	+	0.0979941i	0.473111	−	0.881003i	$-0.343131\pi$
$239$	4.16230	+	1.51495i	0.269237	+	0.0979941i	−0.203874	+	0.978997i	$0.565353\pi$
$240$	6.12129	+	0.916352i	0.395127	+	0.0591502i
$241$	−6.97073	+	2.53714i	−0.449024	+	0.163431i	−0.556627	−	0.830763i	$-0.687905\pi$
$241$	−6.97073	+	2.53714i	−0.449024	+	0.163431i	0.107603	+	0.994194i	$0.465683\pi$
$242$	−3.48132	−	6.02982i	−0.223788	−	0.387612i
$243$	3.39243	−	15.2148i	0.217625	−	0.976033i
$244$	5.21034			0.333558
$245$	8.28983	−	23.6010i	0.529618	−	1.50781i
$246$	4.82778	+	12.2648i	0.307808	+	0.781973i
$247$	15.5997	−	13.0897i	0.992582	−	0.832876i
$248$	−9.70725	−	3.53315i	−0.616411	−	0.224355i
$249$	1.81962	+	2.05771i	0.115314	+	0.130402i
$250$	1.71884	−	9.74804i	0.108709	−	0.616520i
$251$	7.82057	−	13.5456i	0.493630	−	0.854993i	−0.506343	−	0.862332i	$-0.669003\pi$
$251$	7.82057	−	13.5456i	0.493630	−	0.854993i	0.999973	+	0.00733960i	$0.00233629\pi$
$252$	1.14514	+	7.85421i	0.0721373	+	0.494769i
$253$	4.85238	+	8.40457i	0.305067	+	0.528391i
$254$	5.17878	−	1.88492i	0.324946	−	0.118270i
$255$	−13.5734	+	8.31328i	−0.850001	+	0.520598i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	3.23052	+	1.17581i	0.201514	+	0.0733452i	0.440805	−	0.897603i	$-0.354693\pi$
$257$	3.23052	+	1.17581i	0.201514	+	0.0733452i	−0.239291	+	0.970948i	$0.576915\pi$
$258$	4.25027	+	2.30905i	0.264610	+	0.143755i
$259$	−4.80525	+	18.3467i	−0.298584	+	1.14001i
$260$	6.02563	+	10.4367i	0.373694	+	0.647257i
$261$	5.44980	−	0.282958i	0.337334	−	0.0175147i
$262$	2.93214			0.181148
$263$	14.1176	+	11.8461i	0.870527	+	0.730459i	0.964209	−	0.265143i	$-0.0854192\pi$
$263$	14.1176	+	11.8461i	0.870527	+	0.730459i	−0.0936820	+	0.995602i	$0.529864\pi$
$264$	−7.19382	+	1.46178i	−0.442749	+	0.0899664i
$265$	−22.1379	+	18.5759i	−1.35992	+	1.14111i
$266$	−14.5172	−	6.67006i	−0.890104	−	0.408967i
$267$	8.84905	+	1.32470i	0.541553	+	0.0810701i
$268$	−1.43204	−	1.20163i	−0.0874759	−	0.0734010i
$269$	2.60573	+	4.51325i	0.158874	+	0.275178i	0.934463	−	0.356060i	$-0.115880\pi$
$269$	2.60573	+	4.51325i	0.158874	+	0.275178i	−0.775589	+	0.631238i	$0.782547\pi$
$270$	−15.3104	+	10.5062i	−0.931763	+	0.639384i
$271$	−7.42537	+	12.8611i	−0.451059	+	0.781257i	−0.998452	−	0.0556184i	$-0.982287\pi$
$271$	−7.42537	+	12.8611i	−0.451059	+	0.781257i	0.547393	+	0.836876i	$0.315620\pi$
$272$	−0.446554	+	2.53254i	−0.0270763	+	0.153558i
$273$	−10.5774	+	11.2674i	−0.640170	+	0.681931i
$274$	15.2235	+	5.54091i	0.919687	+	0.334739i
$275$	5.71838	+	32.4306i	0.344832	+	1.95564i
$276$	3.88664	−	0.789764i	0.233948	−	0.0475382i
$277$	−4.85881	−	4.07703i	−0.291938	−	0.244965i	0.485041	−	0.874491i	$-0.338805\pi$
$277$	−4.85881	−	4.07703i	−0.291938	−	0.244965i	−0.776979	+	0.629526i	$0.783249\pi$
$278$	−7.44483	−	12.8948i	−0.446511	−	0.773380i
$279$	28.5330	−	12.0952i	1.70823	−	0.724120i
$280$	5.37918	−	7.77522i	0.321468	−	0.464658i
$281$	6.51650	+	5.46799i	0.388742	+	0.326193i	0.816123	−	0.577879i	$-0.196119\pi$
$281$	6.51650	+	5.46799i	0.388742	+	0.326193i	−0.427381	+	0.904072i	$0.640564\pi$
$282$	−0.142451	−	5.49094i	−0.00848285	−	0.326981i
$283$	4.04102	−	3.39082i	0.240214	−	0.201563i	−0.514731	−	0.857352i	$-0.672108\pi$
$283$	4.04102	−	3.39082i	0.240214	−	0.201563i	0.754945	+	0.655789i	$0.227664\pi$
$284$	5.07571	−	4.25903i	0.301188	−	0.252727i
$285$	−0.969286	−	37.3622i	−0.0574155	−	2.21314i
$286$	−10.9491	−	9.18736i	−0.647432	−	0.543260i
$287$	20.0669	+	1.64165i	1.18451	+	0.0969038i
$288$	−0.367054	+	2.97746i	−0.0216289	+	0.175449i
$289$	5.19343	+	8.99528i	0.305496	+	0.529134i
$290$	−4.97957	−	4.17836i	−0.292411	−	0.245362i
$291$	−32.5179	+	6.60762i	−1.90623	+	0.387345i
$292$	2.11364	+	11.9870i	0.123691	+	0.701487i
$293$	−24.2167	−	8.81416i	−1.41476	−	0.514929i	−0.482234	−	0.876043i	$-0.660174\pi$
$293$	−24.2167	−	8.81416i	−1.41476	−	0.514929i	−0.932522	+	0.361114i	$0.882397\pi$
$294$	11.5396	+	3.72000i	0.673001	+	0.216955i
$295$	3.95178	−	22.4117i	0.230082	−	1.30486i
$296$	−3.58414	+	6.20792i	−0.208324	+	0.360828i
$297$	12.8016	−	17.9196i	0.742824	−	1.03980i
$298$	−3.61067	−	6.25386i	−0.209161	−	0.362277i
$299$	5.91551	+	4.96370i	0.342103	+	0.287058i
$300$	13.3096	+	1.99244i	0.768432	+	0.115034i
$301$	6.02842	−	4.27201i	0.347472	−	0.246234i
$302$	6.25640	−	5.24975i	0.360016	−	0.302089i
$303$	14.3286	−	2.91156i	0.823156	−	0.167265i
$304$	−4.62570	−	3.88142i	−0.265302	−	0.222615i
$305$	18.6192			1.06613
$306$	−4.19865	−	6.47223i	−0.240021	−	0.369992i
$307$	−12.7518	−	22.0867i	−0.727783	−	1.26056i	−0.957818	−	0.287374i	$-0.907218\pi$
$307$	−12.7518	−	22.0867i	−0.727783	−	1.26056i	0.230036	−	0.973182i	$-0.426116\pi$
$308$	−2.84110	+	10.8474i	−0.161886	+	0.618089i
$309$	−30.6818	−	16.6685i	−1.74542	−	0.948237i
$310$	−34.6889	−	12.6257i	−1.97020	−	0.717093i
$311$	5.05181	−	4.23898i	0.286462	−	0.240370i	−0.488221	−	0.872720i	$-0.662354\pi$
$311$	5.05181	−	4.23898i	0.286462	−	0.240370i	0.774683	+	0.632350i	$0.217909\pi$
$312$	−4.98114	+	3.05079i	−0.282002	+	0.172717i
$313$	−22.3439	+	8.13252i	−1.26295	+	0.459677i	−0.884759	−	0.466049i	$-0.845677\pi$
$313$	−22.3439	+	8.13252i	−1.26295	+	0.459677i	−0.378194	+	0.925726i	$0.623455\pi$
$314$	8.58977	+	14.8779i	0.484749	+	0.839609i
$315$	4.09218	+	28.0671i	0.230568	+	1.58140i
$316$	−1.72989	+	2.99625i	−0.0973138	+	0.168552i
$317$	4.58962	−	26.0290i	0.257779	−	1.46194i	−0.531060	−	0.847334i	$-0.678206\pi$
$317$	4.58962	−	26.0290i	0.257779	−	1.46194i	0.788838	−	0.614601i	$-0.210683\pi$
$318$	−9.27885	−	10.4930i	−0.520332	−	0.588416i
$319$	7.24460	+	2.63682i	0.405620	+	0.147634i
$320$	2.73746	−	2.29701i	0.153029	−	0.128407i
$321$	3.86506	+	9.81901i	0.215726	+	0.548044i
$322$	1.53497	−	5.86059i	0.0855407	−	0.326598i
$323$	15.5284			0.864024
$324$	−5.28299	−	7.28629i	−0.293500	−	0.404794i
$325$	13.1017	+	22.6927i	0.726749	+	1.25877i
$326$	10.3832	−	3.77916i	0.575070	−	0.209308i
$327$	18.7278	+	2.80354i	1.03565	+	0.155036i
$328$	7.15097	+	2.60274i	0.394846	+	0.143712i
$329$	−7.62413	−	3.50299i	−0.420332	−	0.193126i
$330$	−25.7072	+	5.22369i	−1.41513	+	0.287554i
$331$	1.36963	−	7.76758i	0.0752819	−	0.426945i	−0.923752	−	0.382992i	$-0.874894\pi$
$331$	1.36963	−	7.76758i	0.0752819	−	0.426945i	0.999034	−	0.0439529i	$-0.0139951\pi$
$332$	1.58590			0.0870374
$333$	−4.82736	−	20.9560i	−0.264538	−	1.14838i
$334$	19.7830			1.08248
$335$	−5.11741	−	4.29402i	−0.279594	−	0.234607i
$336$	3.83494	+	2.50864i	0.209213	+	0.136857i
$337$	−0.904111	−	5.12747i	−0.0492501	−	0.279311i	0.950230	−	0.311549i	$-0.100848\pi$
$337$	−0.904111	−	5.12747i	−0.0492501	−	0.279311i	−0.999480	+	0.0322377i	$0.989737\pi$
$338$	1.52885	+	0.556457i	0.0831587	+	0.0302673i
$339$	0.220854	+	8.51306i	0.0119952	+	0.462366i
$340$	−1.59576	+	9.05003i	−0.0865425	+	0.490807i
$341$	43.7820			2.37093
$342$	18.0909	−	0.939295i	0.978243	−	0.0507912i
$343$	12.8724	−	13.3155i	0.695044	−	0.718967i
$344$	2.62422	−	0.955139i	0.141489	−	0.0514976i
$345$	13.8889	−	2.82223i	0.747755	−	0.151944i
$346$	−18.2070	−	6.62682i	−0.978817	−	0.356260i
$347$	−0.607976	−	3.44800i	−0.0326379	−	0.185098i	0.964130	−	0.265429i	$-0.0855136\pi$
$347$	−0.607976	−	3.44800i	−0.0326379	−	0.185098i	−0.996768	+	0.0803304i	$0.974402\pi$
$348$	1.96194	−	2.46527i	0.105171	−	0.132152i
$349$	−0.112862	+	0.640070i	−0.00604134	+	0.0342622i	−0.987679	−	0.156491i	$-0.949982\pi$
$349$	−0.112862	+	0.640070i	−0.00604134	+	0.0342622i	0.981638	+	0.190753i	$0.0610929\pi$
$350$	11.6961	−	16.9058i	0.625181	−	0.903654i
$351$	4.69524	−	16.8827i	0.250613	−	0.901133i
$352$	−2.11912	+	3.67042i	−0.112949	+	0.195634i
$353$	−8.02159	+	2.91962i	−0.426946	+	0.155396i	−0.546551	−	0.837426i	$-0.684060\pi$
$353$	−8.02159	+	2.91962i	−0.426946	+	0.155396i	0.119605	+	0.992822i	$0.461837\pi$
$354$	10.9088	+	1.63304i	0.579795	+	0.0867949i
$355$	18.1381	−	15.2197i	0.962670	−	0.807776i
$356$	3.95733	−	3.32060i	0.209738	−	0.175991i
$357$	−11.7014	+	1.39722i	−0.619306	+	0.0739485i
$358$	20.5381	−	7.47527i	1.08547	−	0.395080i
$359$	9.31447	+	16.1331i	0.491599	+	0.851474i	0.999953	−	0.00967360i	$-0.00307925\pi$
$359$	9.31447	+	16.1331i	0.491599	+	0.851474i	−0.508354	+	0.861148i	$0.669746\pi$
$360$	−1.31167	+	10.6400i	−0.0691310	+	0.560776i
$361$	−8.73124	+	15.1229i	−0.459539	+	0.795944i
$362$	4.66850	−	1.69919i	0.245371	−	0.0893077i
$363$	10.2841	−	6.29865i	0.539774	−	0.330593i
$364$	0.827759	+	8.88403i	0.0433863	+	0.465650i
$365$	7.55309	+	42.8357i	0.395347	+	2.24212i
$366$	0.234045	+	9.02153i	0.0122337	+	0.471563i
$367$	−1.99519	+	11.3153i	−0.104148	+	0.590653i	0.887409	+	0.460983i	$0.152503\pi$
$367$	−1.99519	+	11.3153i	−0.104148	+	0.590653i	−0.991557	+	0.129670i	$0.958608\pi$
$368$	1.14491	−	1.98304i	0.0596824	−	0.103373i
$369$	−21.0192	+	8.91007i	−1.09422	+	0.463840i
$370$	−12.8080	+	22.1840i	−0.665854	+	1.15329i
$371$	−20.6356	+	5.65420i	−1.07135	+	0.293552i
$372$	5.68149	−	16.9665i	0.294572	−	0.879672i
$373$	−1.59415	−	9.04089i	−0.0825421	−	0.468119i	−0.997860	−	0.0653873i	$-0.979172\pi$
$373$	−1.59415	−	9.04089i	−0.0825421	−	0.468119i	0.915318	−	0.402732i	$-0.131939\pi$
$374$	−1.89260	−	10.7335i	−0.0978641	−	0.555015i
$375$	16.9556	+	2.53824i	0.875585	+	0.131074i
$376$	−2.42933	−	2.03845i	−0.125283	−	0.105125i
$377$	6.13454			0.315945
$378$	−13.5479	+	2.33559i	−0.696828	+	0.120130i
$379$	29.4786			1.51421			0.757107	−	0.653291i	$-0.226612\pi$
$379$	29.4786			1.51421			0.757107	+	0.653291i	$0.226612\pi$
$380$	−16.5300	−	13.8703i	−0.847969	−	0.711530i
$381$	3.49631	+	8.88222i	0.179121	+	0.455050i
$382$	2.88585	+	16.3665i	0.147653	+	0.837382i
$383$	1.43914	+	8.16177i	0.0735366	+	0.417047i	0.999247	+	0.0388125i	$0.0123575\pi$
$383$	1.43914	+	8.16177i	0.0735366	+	0.417047i	−0.925710	+	0.378234i	$0.876531\pi$
$384$	1.14738	+	1.29751i	0.0585518	+	0.0662132i
$385$	−10.1527	+	38.7633i	−0.517428	+	1.97556i
$386$	0.918281	−	1.59051i	0.0467393	−	0.0809548i
$387$	−3.80712	+	7.46293i	−0.193527	+	0.379362i
$388$	−9.57894	+	16.5912i	−0.486297	+	0.842291i
$389$	3.82567	−	21.6964i	0.193969	−	1.10005i	−0.719910	−	0.694067i	$-0.755817\pi$
$389$	3.82567	−	21.6964i	0.193969	−	1.10005i	0.913879	−	0.405986i	$-0.133072\pi$
$390$	−17.8001	+	10.9020i	−0.901345	+	0.552044i
$391$	1.02253	+	5.79903i	0.0517113	+	0.293270i
$392$	6.02232	−	3.56815i	0.304173	−	0.180219i
$393$	0.131710	+	5.07691i	0.00664390	+	0.256096i
$394$	10.4106	−	3.78916i	0.524480	−	0.190895i
$395$	−6.18176	+	10.7071i	−0.311038	+	0.538734i
$396$	−2.85417	−	12.3902i	−0.143427	−	0.622632i
$397$	9.27464	+	16.0642i	0.465481	+	0.806237i	0.999223	−	0.0394107i	$-0.0125481\pi$
$397$	9.27464	+	16.0642i	0.465481	+	0.806237i	−0.533742	+	0.845647i	$0.679215\pi$
$398$	9.39483	−	3.41944i	0.470920	−	0.171401i
$399$	10.8969	−	25.4356i	0.545527	−	1.27337i
$400$	5.95212	−	4.99442i	0.297606	−	0.249721i
$401$	0.307478	−	0.258005i	0.0153547	−	0.0128841i	−0.635078	−	0.772448i	$-0.719032\pi$
$401$	0.307478	−	0.258005i	0.0153547	−	0.0128841i	0.650433	+	0.759564i	$0.274588\pi$
$402$	2.01625	−	2.53351i	0.100561	−	0.126360i
$403$	32.7367	−	11.9152i	1.63073	−	0.593537i
$404$	4.22084	−	7.31071i	0.209995	−	0.363721i
$405$	−18.8788	−	26.0376i	−0.938096	−	1.29382i
$406$	−2.05852	−	4.35029i	−0.102163	−	0.215901i
$407$	5.27558	−	29.9193i	0.261501	−	1.48305i
$408$	−4.40506	−	0.659435i	−0.218083	−	0.0326469i
$409$	−3.11053	−	17.6407i	−0.153806	−	0.872277i	−0.959869	−	0.280448i	$-0.909517\pi$
$409$	−3.11053	−	17.6407i	−0.153806	−	0.872277i	0.806063	−	0.591829i	$-0.201594\pi$
$410$	25.5540	+	9.30091i	1.26202	+	0.459339i
$411$	−8.91008	+	26.6080i	−0.439502	+	1.31247i
$412$	−18.9437	+	6.89493i	−0.933288	+	0.339689i
$413$	9.58627	−	13.8563i	0.471710	−	0.681822i
$414$	1.54204	+	6.69412i	0.0757870	+	0.328998i
$415$	5.66721			0.278193
$416$	−0.585610	+	3.32116i	−0.0287119	+	0.162833i
$417$	21.9926	−	13.4697i	1.07698	−	0.659615i
$418$	24.0488	+	8.75306i	1.17627	+	0.428126i
$419$	−3.74670	−	21.2486i	−0.183038	−	1.03806i	−0.928450	−	0.371457i	$-0.878858\pi$
$419$	−3.74670	−	21.2486i	−0.183038	−	1.03806i	0.745412	−	0.666604i	$-0.232253\pi$
$420$	13.7042	+	8.96462i	0.668695	+	0.437429i
$421$	8.86652	+	7.43990i	0.432128	+	0.362598i	0.832754	−	0.553643i	$-0.186763\pi$
$421$	8.86652	+	7.43990i	0.432128	+	0.362598i	−0.400626	+	0.916242i	$0.631207\pi$
$422$	−20.1892			−0.982794
$423$	9.50099	−	0.493300i	0.461954	−	0.0239851i
$424$	−8.08701			−0.392740
$425$	−3.46970	+	19.6777i	−0.168305	+	0.954507i
$426$	7.60237	+	8.59712i	0.368336	+	0.416532i
$427$	12.5263	+	5.75536i	0.606192	+	0.278521i
$428$	5.72497	+	2.08372i	0.276727	+	0.100720i
$429$	15.4158	−	19.3707i	0.744281	−	0.935224i
$430$	9.37768	−	3.41320i	0.452232	−	0.164599i
$431$	−12.2662	−	21.2456i	−0.590840	−	1.02336i	−0.994120	−	0.108288i	$-0.965463\pi$
$431$	−12.2662	−	21.2456i	−0.590840	−	1.02336i	0.403280	−	0.915077i	$-0.367870\pi$
$432$	−5.17187	−	0.501796i	−0.248832	−	0.0241427i
$433$	16.3713			0.786753			0.393377	−	0.919377i	$-0.371307\pi$
$433$	16.3713			0.786753			0.393377	+	0.919377i	$0.371307\pi$
$434$	−19.4348	−	19.2168i	−0.932899	−	0.922437i
$435$	7.01102	−	8.80966i	0.336152	−	0.422391i
$436$	8.37515	−	7.02759i	0.401097	−	0.336560i
$437$	−12.9930	−	4.72906i	−0.621538	−	0.226222i
$438$	−20.6602	+	4.19814i	−0.987183	+	0.200595i
$439$	3.65877	−	20.7499i	0.174623	−	0.990338i	−0.763954	−	0.645270i	$-0.776745\pi$
$439$	3.65877	−	20.7499i	0.174623	−	0.990338i	0.938578	−	0.345068i	$-0.112144\pi$
$440$	−7.57268	+	13.1163i	−0.361013	+	0.625294i
$441$	−5.92271	+	20.1475i	−0.282034	+	0.959404i
$442$	−4.33623	−	7.51057i	−0.206253	−	0.357241i
$443$	−18.9032	+	6.88019i	−0.898117	+	0.326888i	−0.749498	−	0.662007i	$-0.769705\pi$
$443$	−18.9032	+	6.88019i	−0.898117	+	0.326888i	−0.148619	+	0.988895i	$0.547483\pi$
$444$	−10.9098	−	5.92697i	−0.517757	−	0.281282i
$445$	14.1416	−	11.8662i	0.670374	−	0.562511i
$446$	−23.0056	−	8.37336i	−1.08935	−	0.396490i
$447$	10.6662	−	6.53268i	0.504493	−	0.308985i
$448$	2.55170	−	0.699171i	0.120556	−	0.0330327i
$449$	6.10832	+	10.5799i	0.288270	+	0.499298i	0.973397	−	0.229126i	$-0.0735867\pi$
$449$	6.10832	+	10.5799i	0.288270	+	0.499298i	−0.685127	+	0.728423i	$0.740253\pi$
$450$	−2.85199	+	23.1347i	−0.134444	+	1.09058i
$451$	−32.2526			−1.51871
$452$	3.76639	+	3.16038i	0.177156	+	0.148652i
$453$	9.37080	+	10.5969i	0.440279	+	0.497888i
$454$	−10.9123	+	9.15652i	−0.512141	+	0.429737i
$455$	2.95800	+	31.7471i	0.138673	+	1.48833i
$456$	6.51277	−	8.18360i	0.304988	−	0.383232i
$457$	−14.7782	−	12.4004i	−0.691295	−	0.580065i	0.227988	−	0.973664i	$-0.426785\pi$
$457$	−14.7782	−	12.4004i	−0.691295	−	0.580065i	−0.919282	+	0.393599i	$0.871230\pi$
$458$	−9.67848	−	16.7636i	−0.452245	−	0.783312i
$459$	11.0179	−	7.56055i	0.514269	−	0.352896i
$460$	4.09133	−	7.08639i	0.190759	−	0.330405i
$461$	−2.70552	+	15.3438i	−0.126009	+	0.714630i	0.854695	+	0.519130i	$0.173744\pi$
$461$	−2.70552	+	15.3438i	−0.126009	+	0.714630i	−0.980704	+	0.195500i	$0.937367\pi$
$462$	−18.9096	−	4.43201i	−0.879754	−	0.206196i
$463$	11.9099	+	4.33484i	0.553499	+	0.201457i	0.603600	−	0.797287i	$-0.293732\pi$
$463$	11.9099	+	4.33484i	0.553499	+	0.201457i	−0.0501015	+	0.998744i	$0.515954\pi$
$464$	−0.315874	−	1.79141i	−0.0146641	−	0.0831642i
$465$	20.3029	−	60.6299i	0.941522	−	2.81164i
$466$	−11.0753	−	9.29325i	−0.513052	−	0.430501i
$467$	1.22127	+	2.11530i	0.0565135	+	0.0978842i	0.892898	−	0.450259i	$-0.148668\pi$
$467$	1.22127	+	2.11530i	0.0565135	+	0.0978842i	−0.836385	+	0.548143i	$0.815335\pi$
$468$	−5.50609	−	8.48765i	−0.254519	−	0.392342i
$469$	−2.11550	−	4.47071i	−0.0976846	−	0.206438i
$470$	−8.68122	−	7.28441i	−0.400435	−	0.336005i
$471$	−25.3748	+	15.5412i	−1.16921	+	0.716102i
$472$	4.87845	−	4.09351i	0.224549	−	0.188419i
$473$	−9.06680	+	7.60795i	−0.416892	+	0.349814i
$474$	−5.26562	−	2.86065i	−0.241858	−	0.131394i
$475$	−35.9414	−	30.1584i	−1.64910	−	1.38376i
$476$	−3.87102	+	5.59528i	−0.177428	+	0.256459i
$477$	17.7514	−	16.5374i	0.812782	−	0.757194i
$478$	2.21471	+	3.83599i	0.101299	+	0.175454i
$479$	−27.8263	−	23.3490i	−1.27142	−	1.06684i	−0.994367	−	0.105988i	$-0.966200\pi$
$479$	−27.8263	−	23.3490i	−1.27142	−	1.06684i	−0.277048	−	0.960856i	$-0.589356\pi$
$480$	4.10016	+	4.63665i	0.187146	+	0.211633i
$481$	−4.19782	−	23.8070i	−0.191404	−	1.08551i
$482$	−6.97073	−	2.53714i	−0.317508	−	0.115563i
$483$	10.2164	+	2.39450i	0.464861	+	0.108954i
$484$	1.20905	−	6.85686i	0.0549568	−	0.311676i
$485$	−34.2304	+	59.2888i	−1.55432	+	2.69217i
$486$	12.3787	−	9.47463i	0.561508	−	0.429778i
$487$	−14.0709	−	24.3714i	−0.637611	−	1.10437i	−0.985955	−	0.167008i	$-0.946589\pi$
$487$	−14.0709	−	24.3714i	−0.637611	−	1.10437i	0.348344	−	0.937367i	$-0.386744\pi$
$488$	3.99135	+	3.34914i	0.180680	+	0.151608i
$489$	7.00990	+	17.8083i	0.316999	+	0.805321i
$490$	21.5208	−	12.7508i	0.972210	−	0.576022i
$491$	−20.3127	+	17.0443i	−0.916698	+	0.769201i	−0.973381	−	0.229192i	$-0.926392\pi$
$491$	−20.3127	+	17.0443i	−0.916698	+	0.769201i	0.0566838	+	0.998392i	$0.481947\pi$
$492$	−4.18534	+	12.4986i	−0.188690	+	0.563480i
$493$	3.58345	+	3.00687i	0.161391	+	0.135423i
$494$	20.3639			0.916216
$495$	−10.1994	−	44.2765i	−0.458429	−	1.99008i
$496$	−5.16512	−	8.94625i	−0.231921	−	0.401698i
$497$	16.9072	−	4.63262i	0.758392	−	0.207801i
$498$	0.0712376	+	2.74593i	0.00319223	+	0.123048i
$499$	−15.2890	−	5.56474i	−0.684429	−	0.249112i	−0.0236811	−	0.999720i	$-0.507539\pi$
$499$	−15.2890	−	5.56474i	−0.684429	−	0.249112i	−0.660748	+	0.750608i	$0.729761\pi$
$500$	7.58263	−	6.36258i	0.339105	−	0.284543i
$501$	0.888641	+	34.2536i	0.0397016	+	1.53034i
$502$	14.6979	−	5.34959i	0.655998	−	0.238764i
$503$	12.7106	+	22.0155i	0.566739	+	0.981621i	0.996886	+	0.0788616i	$0.0251285\pi$
$503$	12.7106	+	22.0155i	0.566739	+	0.981621i	−0.430147	+	0.902759i	$0.641538\pi$
$504$	−4.17136	+	6.75276i	−0.185807	+	0.300792i
$505$	15.0832	−	26.1249i	0.671193	−	1.16254i
$506$	−1.68521	+	9.55733i	−0.0749169	+	0.424875i
$507$	−0.894813	+	2.67216i	−0.0397400	+	0.118675i
$508$	5.17878	+	1.88492i	0.229771	+	0.0836299i
$509$	22.4015	−	18.7971i	0.992928	−	0.833166i	0.00693932	−	0.999976i	$-0.497791\pi$
$509$	22.4015	−	18.7971i	0.992928	−	0.833166i	0.985989	+	0.166810i	$0.0533467\pi$
$510$	−15.7415	−	2.35649i	−0.697046	−	0.104347i
$511$	−8.15945	+	31.1531i	−0.360953	+	1.37813i
$512$	1.00000			0.0441942
$513$	2.43899	+	31.2816i	0.107684	+	1.38112i
$514$	1.71892	+	2.97726i	0.0758184	+	0.131321i
$515$	−67.6953	+	24.6391i	−2.98301	+	1.08573i
$516$	1.77167	+	4.50085i	0.0779935	+	0.198139i
$517$	12.6300	+	4.59694i	0.555466	+	0.202173i
$518$	−15.4740	+	10.9656i	−0.679890	+	0.481801i
$519$	10.6563	−	31.8226i	0.467759	−	1.39686i
$520$	−2.09268	+	11.8682i	−0.0917701	+	0.520454i
$521$	−32.0183			−1.40275			−0.701375	−	0.712793i	$-0.747430\pi$
$521$	−32.0183			−1.40275			−0.701375	+	0.712793i	$0.747430\pi$
$522$	4.35667	+	3.28630i	0.190686	+	0.143838i
$523$	−11.4164			−0.499203			−0.249602	−	0.968349i	$-0.580300\pi$
$523$	−11.4164			−0.499203			−0.249602	+	0.968349i	$0.580300\pi$
$524$	2.24615	+	1.88474i	0.0981236	+	0.0823354i
$525$	29.7973	+	19.4920i	1.30046	+	0.850699i
$526$	3.20019	+	18.1492i	0.139535	+	0.791343i
$527$	24.9632	+	9.08586i	1.08741	+	0.395786i
$528$	−6.45040	−	3.50431i	−0.280718	−	0.152506i
$529$	−3.08343	+	17.4870i	−0.134062	+	0.760304i
$530$	−28.8990			−1.25529
$531$	−2.33753	+	18.9616i	−0.101440	+	0.822862i
$532$	−6.83335	−	14.4410i	−0.296263	−	0.626097i
$533$	−24.1159	+	8.77746i	−1.04457	+	0.380194i
$534$	5.92727	+	6.70284i	0.256498	+	0.290060i
$535$	20.4582	+	7.44618i	0.884486	+	0.321927i
$536$	−0.324618	−	1.84100i	−0.0140213	−	0.0795190i
$537$	13.8657	+	35.2253i	0.598351	+	1.52008i
$538$	−0.904960	+	5.13228i	−0.0390156	+	0.221268i
$539$	−18.8125	+	22.9404i	−0.810311	+	0.988111i
$540$	−18.4817	−	1.79317i	−0.795326	−	0.0771658i
$541$	−8.61153	+	14.9156i	−0.370239	+	0.641272i	−0.989602	−	0.143832i	$-0.954057\pi$
$541$	−8.61153	+	14.9156i	−0.370239	+	0.641272i	0.619363	+	0.785104i	$0.287391\pi$
$542$	−13.9551	+	5.07925i	−0.599424	+	0.218173i
$543$	3.15181	+	8.00703i	0.135257	+	0.343615i
$544$	−1.96996	+	1.65300i	−0.0844615	+	0.0708716i
$545$	29.9287	−	25.1131i	1.28200	−	1.07573i
$546$	−15.3452	+	1.83230i	−0.656715	+	0.0784154i
$547$	17.2209	−	6.26790i	0.736313	−	0.267996i	0.0534785	−	0.998569i	$-0.482969\pi$
$547$	17.2209	−	6.26790i	0.736313	−	0.267996i	0.682835	+	0.730573i	$0.260747\pi$
$548$	8.10027	+	14.0301i	0.346026	+	0.599335i
$549$	−15.6100	+	0.810484i	−0.666218	+	0.0345906i
$550$	−16.4654	+	28.5190i	−0.702088	+	1.21605i
$551$	−10.3217	+	3.75680i	−0.439721	+	0.160045i
$552$	3.48499	+	1.89329i	0.148331	+	0.0805838i
$553$	−7.46855	+	5.29255i	−0.317595	+	0.225062i
$554$	−1.10140	−	6.24637i	−0.0467941	−	0.265383i
$555$	−38.9863	−	21.1801i	−1.65487	−	0.899044i
$556$	2.58556	−	14.6635i	0.109652	−	0.621869i
$557$	−16.4685	+	28.5242i	−0.697792	+	1.20861i	0.271438	+	0.962456i	$0.412501\pi$
$557$	−16.4685	+	28.5242i	−0.697792	+	1.20861i	−0.969230	+	0.246155i	$0.920833\pi$
$558$	29.6322	+	9.07520i	1.25443	+	0.384184i
$559$	−4.70894	+	8.15612i	−0.199167	+	0.344967i
$560$	9.11851	−	2.49849i	0.385327	−	0.105581i
$561$	18.4997	−	3.75912i	0.781057	−	0.158710i
$562$	1.47717	+	8.37745i	0.0623107	+	0.353381i
$563$	−2.82269	−	16.0083i	−0.118962	−	0.674668i	−0.984712	−	0.174191i	$-0.944269\pi$
$563$	−2.82269	−	16.0083i	−0.118962	−	0.674668i	0.865750	−	0.500477i	$-0.166842\pi$
$564$	3.42038	−	4.29787i	0.144024	−	0.180973i
$565$	13.4592	+	11.2936i	0.566234	+	0.475126i
$566$	5.27518			0.221732
$567$	−4.65256	−	23.3528i	−0.195389	−	0.980726i
$568$	6.62587			0.278015
$569$	−10.7885	−	9.05266i	−0.452279	−	0.379507i	0.388002	−	0.921659i	$-0.373165\pi$
$569$	−10.7885	−	9.05266i	−0.452279	−	0.379507i	−0.840281	+	0.542152i	$0.817610\pi$
$570$	23.2734	−	29.2441i	0.974817	−	1.22490i
$571$	−1.10444	−	6.26360i	−0.0462194	−	0.262124i	0.952938	−	0.303165i	$-0.0980434\pi$
$571$	−1.10444	−	6.26360i	−0.0462194	−	0.262124i	−0.999157	+	0.0410418i	$0.986932\pi$
$572$	−2.48195	−	14.0758i	−0.103776	−	0.588541i
$573$	−28.2084	+	5.73194i	−1.17842	+	0.239455i
$574$	14.3169	+	14.1563i	0.597575	+	0.590873i
$575$	8.89586	−	15.4081i	0.370983	−	0.642561i
$576$	−2.19505	+	2.04493i	−0.0914606	+	0.0852054i
$577$	−4.40925	+	7.63704i	−0.183559	+	0.317934i	−0.943090	−	0.332537i	$-0.892095\pi$
$577$	−4.40925	+	7.63704i	−0.183559	+	0.317934i	0.759531	+	0.650471i	$0.225429\pi$
$578$	−1.80366	+	10.2291i	−0.0750223	+	0.425473i
$579$	2.79517	+	1.51853i	0.116163	+	0.0631079i
$580$	−1.12878	−	6.40162i	−0.0468699	−	0.265813i
$581$	3.81271	+	1.75179i	0.158178	+	0.0726764i
$582$	−29.1574	−	15.8404i	−1.20861	−	0.656604i
$583$	32.2076	−	11.7226i	1.33390	−	0.485501i
$584$	−6.08597	+	10.5412i	−0.251839	+	0.436198i
$585$	−19.6760	−	30.3307i	−0.813504	−	1.25402i
$586$	−12.8854	−	22.3182i	−0.532293	−	0.921958i
$587$	−35.6777	+	12.9856i	−1.47258	+	0.535974i	−0.948799	−	0.315882i	$-0.897700\pi$
$587$	−35.6777	+	12.9856i	−1.47258	+	0.535974i	−0.523777	+	0.851855i	$0.675478\pi$
$588$	6.44865	+	10.2672i	0.265938	+	0.423411i
$589$	−47.7845	+	40.0960i	−1.96893	+	1.65213i
$590$	17.4332	−	14.6282i	0.717713	−	0.602233i
$591$	7.02845	+	17.8555i	0.289112	+	0.734476i
$592$	−6.73598	+	2.45170i	−0.276847	+	0.100764i
$593$	−10.9811	+	19.0198i	−0.450939	+	0.781049i	−0.998445	−	0.0557527i	$-0.982244\pi$
$593$	−10.9811	+	19.0198i	−0.450939	+	0.781049i	0.547506	+	0.836802i	$0.315578\pi$
$594$	21.3251	−	5.49847i	0.874978	−	0.225605i
$595$	−13.8331	+	19.9948i	−0.567103	+	0.819706i
$596$	1.25397	−	7.11163i	0.0513647	−	0.291304i
$597$	6.34266	+	16.1133i	0.259588	+	0.659472i
$598$	1.34094	+	7.60483i	0.0548350	+	0.310985i
$599$	−36.5041	−	13.2864i	−1.49152	−	0.542868i	−0.537669	−	0.843156i	$-0.680695\pi$
$599$	−36.5041	−	13.2864i	−1.49152	−	0.542868i	−0.953849	+	0.300288i	$0.902917\pi$
$600$	8.91505	+	10.0816i	0.363956	+	0.411578i
$601$	35.2616	−	12.8342i	1.43835	−	0.523516i	0.499037	−	0.866581i	$-0.333687\pi$
$601$	35.2616	−	12.8342i	1.43835	−	0.523516i	0.939312	+	0.343064i	$0.111465\pi$
$602$	7.36403	+	0.602445i	0.300135	+	0.0245538i
$603$	4.47726	+	3.37727i	0.182328	+	0.137533i
$604$	8.16716			0.332317
$605$	4.32055	−	24.5030i	0.175655	−	0.996190i
$606$	12.8479	+	6.97986i	0.521909	+	0.283537i
$607$	−7.93473	−	2.88800i	−0.322061	−	0.117220i	0.175931	−	0.984403i	$-0.443707\pi$
$607$	−7.93473	−	2.88800i	−0.322061	−	0.117220i	−0.497991	+	0.867182i	$0.665929\pi$
$608$	−1.04856	−	5.94668i	−0.0425247	−	0.241170i
$609$	7.43992	−	3.75967i	0.301481	−	0.152350i
$610$	14.2631	+	11.9682i	0.577497	+	0.484577i
$611$	10.6947			0.432663
$612$	0.943917	−	7.65685i	0.0381556	−	0.309510i
$613$	31.0659			1.25474			0.627370	−	0.778721i	$-0.284131\pi$
$613$	31.0659			1.25474			0.627370	+	0.778721i	$0.284131\pi$
$614$	4.42865	−	25.1161i	0.178726	−	1.01360i
$615$	−14.9564	+	44.6638i	−0.603098	+	1.80102i
$616$	−9.14900	+	6.48339i	−0.368624	+	0.261223i
$617$	−1.58599	−	0.577253i	−0.0638495	−	0.0232393i	0.309898	−	0.950770i	$-0.399705\pi$
$617$	−1.58599	−	0.577253i	−0.0638495	−	0.0232393i	−0.373747	+	0.927531i	$0.621927\pi$
$618$	−12.7893	−	32.4907i	−0.514461	−	1.30697i
$619$	−10.8615	+	3.95325i	−0.436560	+	0.158895i	−0.550945	−	0.834542i	$-0.685732\pi$
$619$	−10.8615	+	3.95325i	−0.436560	+	0.158895i	0.114385	+	0.993436i	$0.463510\pi$
$620$	−18.4576	−	31.9695i	−0.741275	−	1.28393i
$621$	−11.5214	+	2.97068i	−0.462338	+	0.119209i
$622$	6.59468			0.264422
$623$	13.1819	−	3.61187i	0.528121	−	0.144707i
$624$	−5.77678	−	0.864780i	−0.231256	−	0.0346189i
$625$	−2.66405	+	2.23540i	−0.106562	+	0.0894161i
$626$	−22.3439	−	8.13252i	−0.893042	−	0.325041i
$627$	−14.0754	+	42.0330i	−0.562117	+	1.67864i
$628$	−2.98320	+	16.9185i	−0.119042	+	0.675123i
$629$	9.21699	−	15.9643i	0.367506	−	0.636538i
$630$	−14.9064	+	24.1310i	−0.593884	+	0.961403i
$631$	−20.7060	−	35.8638i	−0.824291	−	1.42771i	−0.902460	−	0.430774i	$-0.858241\pi$
$631$	−20.7060	−	35.8638i	−0.824291	−	1.42771i	0.0781684	−	0.996940i	$-0.475093\pi$
$632$	−3.25112	+	1.18331i	−0.129323	+	0.0470696i
$633$	−0.906886	−	34.9569i	−0.0360455	−	1.38941i
$634$	20.2470	−	16.9892i	0.804110	−	0.674729i
$635$	18.5064	+	6.73578i	0.734404	+	0.267301i
$636$	−0.363264	−	14.0024i	−0.0144044	−	0.555231i
$637$	−7.82329	+	22.2727i	−0.309970	+	0.882478i
$638$	3.85477	+	6.67666i	0.152612	+	0.264332i
$639$	−14.5441	+	13.5494i	−0.575357	+	0.536007i
$640$	3.57351			0.141255
$641$	37.1288	+	31.1547i	1.46650	+	1.23054i	0.919314	+	0.393526i	$0.128745\pi$
$641$	37.1288	+	31.1547i	1.46650	+	1.23054i	0.547184	+	0.837012i	$0.315700\pi$
$642$	−3.35073	+	10.0062i	−0.132243	+	0.394914i
$643$	−14.2836	+	11.9854i	−0.563291	+	0.472658i	−0.879412	−	0.476061i	$-0.842064\pi$
$643$	−14.2836	+	11.9854i	−0.563291	+	0.472658i	0.316121	+	0.948719i	$0.397620\pi$
$644$	4.94297	−	3.50281i	0.194780	−	0.138030i
$645$	6.33108	+	16.0838i	0.249286	+	0.633300i
$646$	11.8955	+	9.98147i	0.468020	+	0.392716i
$647$	−7.77304	−	13.4633i	−0.305590	−	0.529297i	0.671803	−	0.740730i	$-0.265520\pi$
$647$	−7.77304	−	13.4633i	−0.305590	−	0.529297i	−0.977392	+	0.211433i	$0.932187\pi$
$648$	0.636527	−	8.97746i	0.0250051	−	0.352668i
$649$	−13.4953	+	23.3746i	−0.529738	+	0.917533i
$650$	−4.55016	+	25.8052i	−0.178472	+	1.01216i
$651$	32.4003	−	34.5139i	1.26987	−	1.35271i
$652$	10.3832	+	3.77916i	0.406636	+	0.148003i
$653$	−0.238128	−	1.35049i	−0.00931865	−	0.0528487i	0.979794	−	0.200010i	$-0.0640975\pi$
$653$	−0.238128	−	1.35049i	−0.00931865	−	0.0528487i	−0.989113	+	0.147161i	$0.952986\pi$
$654$	12.5443	+	14.1856i	0.490519	+	0.554702i
$655$	8.02663	+	6.73515i	0.313627	+	0.263164i
$656$	3.80495	+	6.59037i	0.148558	+	0.257311i
$657$	−8.19700	−	35.5839i	−0.319795	−	1.38826i
$658$	−3.58875	−	7.58414i	−0.139904	−	0.295661i
$659$	21.0943	+	17.7002i	0.821718	+	0.689503i	0.953374	−	0.301792i	$-0.0975850\pi$
$659$	21.0943	+	17.7002i	0.821718	+	0.689503i	−0.131656	+	0.991295i	$0.542029\pi$
$660$	−23.0506	−	12.5227i	−0.897242	−	0.487445i
$661$	−5.63017	+	4.72427i	−0.218988	+	0.183753i	−0.745682	−	0.666302i	$-0.767876\pi$
$661$	−5.63017	+	4.72427i	−0.218988	+	0.183753i	0.526693	+	0.850055i	$0.323432\pi$
$662$	6.04210	−	5.06993i	0.234833	−	0.197048i
$663$	12.8095	−	7.84541i	0.497481	−	0.304691i
$664$	1.21487	+	1.01940i	0.0471460	+	0.0395602i
$665$	−24.4190	−	51.6050i	−0.946929	−	2.00116i
$666$	9.77230	−	19.1562i	0.378669	−	0.742288i
$667$	−2.08264	−	3.60723i	−0.0806400	−	0.139673i
$668$	15.1547	+	12.7163i	0.586351	+	0.492007i
$669$	13.4648	−	40.2096i	0.520580	−	1.55459i
$670$	−1.16002	−	6.57882i	−0.0448156	−	0.254162i
$671$	−20.7509	−	7.55271i	−0.801079	−	0.291569i
$672$	1.32521	+	4.38678i	0.0511212	+	0.169224i
$673$	−3.58323	+	20.3215i	−0.138123	+	0.783336i	0.834510	+	0.550992i	$0.185751\pi$
$673$	−3.58323	+	20.3215i	−0.138123	+	0.783336i	−0.972634	+	0.232344i	$0.925361\pi$
$674$	2.60328	−	4.50902i	0.100275	−	0.173681i
$675$	−40.1851	−	3.89893i	−1.54673	−	0.150070i
$676$	0.813486	+	1.40900i	0.0312879	+	0.0541923i
$677$	24.7375	+	20.7572i	0.950739	+	0.797765i	0.979422	−	0.201823i	$-0.0646867\pi$
$677$	24.7375	+	20.7572i	0.950739	+	0.797765i	−0.0286825	+	0.999589i	$0.509131\pi$
$678$	−5.30291	+	6.66335i	−0.203657	+	0.255904i
$679$	−41.3558	+	29.3065i	−1.58709	+	1.12468i
$680$	−7.03967	+	5.90699i	−0.269959	+	0.226523i
$681$	−16.3444	−	18.4830i	−0.626319	−	0.708271i
$682$	33.5390	+	28.1425i	1.28427	+	1.07763i
$683$	−22.3000			−0.853286			−0.426643	−	0.904420i	$-0.640304\pi$
$683$	−22.3000			−0.853286			−0.426643	+	0.904420i	$0.640304\pi$
$684$	14.4622	+	10.9091i	0.552976	+	0.417118i
$685$	28.9464	+	50.1366i	1.10598	+	1.91562i
$686$	18.4198	−	1.92602i	0.703273	−	0.0735358i
$687$	28.5909	−	17.5110i	1.09081	−	0.668086i
$688$	2.62422	+	0.955139i	0.100048	+	0.0364143i
$689$	20.8920	−	17.5305i	0.795922	−	0.667858i
$690$	12.4536	+	6.76569i	0.474102	+	0.257565i
$691$	16.0011	−	5.82393i	0.608711	−	0.221553i	−0.0192281	−	0.999815i	$-0.506121\pi$
$691$	16.0011	−	5.82393i	0.608711	−	0.221553i	0.627939	+	0.778262i	$0.283899\pi$
$692$	−9.68777	−	16.7797i	−0.368274	−	0.637869i
$693$	6.82447	−	32.9404i	0.259240	−	1.25130i
$694$	1.75060	−	3.03212i	0.0664517	−	0.115098i
$695$	9.23953	−	52.4000i	0.350475	−	1.98764i
$696$	3.08758	−	0.627395i	0.117034	−	0.0237813i
$697$	−18.3895	−	6.69322i	−0.696551	−	0.253524i
$698$	−0.497886	+	0.417776i	−0.0188453	+	0.0158131i
$699$	15.5935	−	19.5939i	0.589799	−	0.741110i
$700$	19.8266	−	5.43252i	0.749373	−	0.205330i
$701$	−4.91861			−0.185773			−0.0928867	−	0.995677i	$-0.529609\pi$
$701$	−4.91861			−0.185773			−0.0928867	+	0.995677i	$0.529609\pi$
$702$	14.4488	−	9.91488i	0.545334	−	0.374213i
$703$	21.6425	+	37.4860i	0.816264	+	1.41381i
$704$	−3.98264	+	1.44956i	−0.150101	+	0.0546324i
$705$	12.2228	−	15.3585i	0.460336	−	0.578433i
$706$	−8.02159	−	2.91962i	−0.301897	−	0.109881i
$707$	18.2229	−	12.9136i	0.685342	−	0.485664i
$708$	7.30692	+	8.26301i	0.274611	+	0.310543i
$709$	−2.71149	+	15.3776i	−0.101832	+	0.577519i	0.890606	+	0.454775i	$0.150280\pi$
$709$	−2.71149	+	15.3776i	−0.101832	+	0.577519i	−0.992438	+	0.122744i	$0.960831\pi$
$710$	23.6776			0.888604
$711$	4.71660	−	9.24576i	0.176886	−	0.346743i
$712$	5.16593			0.193601
$713$	−18.1203	−	15.2047i	−0.678609	−	0.569420i
$714$	−9.86194	−	6.45122i	−0.369074	−	0.241431i
$715$	−8.86927	−	50.3001i	−0.331692	−	1.88112i
$716$	20.5381	+	7.47527i	0.767546	+	0.279364i
$717$	−6.54242	+	4.00701i	−0.244331	+	0.149645i
$718$	−3.23488	+	18.3459i	−0.120725	+	0.684664i
$719$	−19.9026			−0.742240			−0.371120	−	0.928585i	$-0.621026\pi$
$719$	−19.9026			−0.742240			−0.371120	+	0.928585i	$0.621026\pi$
$720$	−7.84404	+	7.30757i	−0.292330	+	0.272337i
$721$	−53.1593	−	4.34891i	−1.97975	−	0.161962i
$722$	−16.4094	+	5.97252i	−0.610693	+	0.222274i
$723$	4.07985	−	12.1836i	0.151731	−	0.453112i
$724$	4.66850	+	1.69919i	0.173503	+	0.0631501i
$725$	−2.45432	−	13.9192i	−0.0911513	−	0.516945i
$726$	11.9267	+	1.78543i	0.442643	+	0.0662633i
$727$	0.456609	−	2.58956i	0.0169347	−	0.0960414i	−0.975169	−	0.221462i	$-0.928917\pi$
$727$	0.456609	−	2.58956i	0.0169347	−	0.0960414i	0.992104	+	0.125421i	$0.0400281\pi$
$728$	−5.07645	+	7.33764i	−0.188146	+	0.271951i
$729$	16.9611	+	21.0077i	0.628188	+	0.778062i
$730$	−21.7483	+	37.6691i	−0.804939	+	1.39420i
$731$	−6.74846	+	2.45624i	−0.249601	+	0.0908473i
$732$	−5.61964	+	7.06134i	−0.207708	+	0.260995i
$733$	32.4848	−	27.2579i	1.19985	−	1.00680i	0.200218	−	0.979751i	$-0.435835\pi$
$733$	32.4848	−	27.2579i	1.19985	−	1.00680i	0.999634	−	0.0270437i	$-0.00860933\pi$
$734$	−8.80172	+	7.38552i	−0.324877	+	0.272605i
$735$	23.0443	+	36.6898i	0.850002	+	1.35332i
$736$	2.15172	−	0.783162i	0.0793134	−	0.0288677i
$737$	3.96147	+	6.86147i	0.145923	+	0.252746i
$738$	−21.8289	−	6.68536i	−0.803533	−	0.246092i
$739$	−0.211003	+	0.365468i	−0.00776186	+	0.0134439i	−0.869880	−	0.493263i	$-0.835804\pi$
$739$	−0.211003	+	0.365468i	−0.00776186	+	0.0134439i	0.862118	+	0.506707i	$0.169137\pi$
$740$	−24.0711	+	8.76116i	−0.884870	+	0.322067i
$741$	0.914735	+	35.2595i	0.0336036	+	1.29529i
$742$	−19.4422	−	8.93294i	−0.713747	−	0.327939i
$743$	−7.01750	−	39.7982i	−0.257447	−	1.46006i	−0.789712	−	0.613477i	$-0.789770\pi$
$743$	−7.01750	−	39.7982i	−0.257447	−	1.46006i	0.532265	−	0.846578i	$-0.321341\pi$
$744$	15.2581	−	9.34510i	0.559390	−	0.342608i
$745$	4.48108	−	25.4135i	0.164174	−	0.931077i
$746$	4.59018	−	7.95042i	0.168058	−	0.291086i
$747$	−4.75129	+	0.246691i	−0.173841	+	0.00902596i
$748$	5.44953	−	9.43887i	0.199255	−	0.345119i
$749$	11.4619	+	11.3334i	0.418809	+	0.414112i
$750$	11.3572	+	12.8433i	0.414707	+	0.468970i
$751$	−3.92766	−	22.2748i	−0.143322	−	0.812821i	−0.968699	−	0.248238i	$-0.920148\pi$
$751$	−3.92766	−	22.2748i	−0.143322	−	0.812821i	0.825377	−	0.564582i	$-0.190963\pi$
$752$	−0.550684	−	3.12308i	−0.0200814	−	0.113887i
$753$	9.92286	+	25.2086i	0.361609	+	0.918652i
$754$	4.69933	+	3.94320i	0.171139	+	0.143603i
$755$	29.1854			1.06216
$756$	−11.8796	−	6.91925i	−0.432056	−	0.251651i
$757$	−2.49660			−0.0907406			−0.0453703	−	0.998970i	$-0.514447\pi$
$757$	−2.49660			−0.0907406			−0.0453703	+	0.998970i	$0.514447\pi$
$758$	22.5819	+	18.9485i	0.820212	+	0.688240i
$759$	−16.6239	−	2.48859i	−0.603410	−	0.0903299i
$760$	−3.74704	−	21.2505i	−0.135919	−	0.770836i
$761$	0.837007	+	4.74690i	0.0303415	+	0.172075i	0.996213	−	0.0869467i	$-0.0277110\pi$
$761$	0.837007	+	4.74690i	0.0303415	+	0.172075i	−0.965871	+	0.259022i	$0.916600\pi$
$762$	−3.03105	+	9.05156i	−0.109803	+	0.327903i
$763$	27.8977	−	7.64403i	1.00996	−	0.276732i
$764$	−8.30948	+	14.3924i	−0.300627	+	0.520700i
$765$	3.37309	−	27.3618i	0.121954	−	0.989268i
$766$	−4.14384	+	7.17734i	−0.149723	+	0.259328i
$767$	−3.72938	+	21.1504i	−0.134660	+	0.763695i
$768$	0.0449194	+	1.73147i	0.00162089	+	0.0624790i
$769$	0.959984	+	5.44434i	0.0346179	+	0.196328i	0.997212	−

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.07856 + 1.35526i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.620533 + 3.51922i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-0.670349 + 2.55942i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.673434 - 2.92344i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.07856 + 1.35526i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.620533 + 3.51922i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-0.670349 + 2.55942i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.673434 - 2.92344i) q^{9} +(-1.78675 + 3.09475i) q^{10} +(0.735962 - 4.17385i) q^{11} +(-1.52196 - 0.826833i) q^{12} +(-0.585610 - 3.32116i) q^{13} +(-2.15868 + 1.52974i) q^{14} +(-5.43872 - 2.95469i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.28580 - 2.22707i) q^{17} +(1.36327 - 2.67236i) q^{18} +(3.01921 + 5.22942i) q^{19} +(-3.35800 + 1.22221i) q^{20} +(-2.74566 - 3.66897i) q^{21} +(3.24668 - 2.72429i) q^{22} +(-1.75410 + 1.47186i) q^{23} +(-0.634407 - 1.61168i) q^{24} +(-7.30136 + 2.65748i) q^{25} +(1.68620 - 2.92058i) q^{26} +(4.68834 + 2.24042i) q^{27} +(-2.63694 - 0.215726i) q^{28} +(-0.315874 + 1.79141i) q^{29} +(-2.26706 - 5.75936i) q^{30} +(1.79383 + 10.1733i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(4.86285 + 5.49914i) q^{33} +(2.41652 - 0.879540i) q^{34} +(-9.42313 - 0.770898i) q^{35} +(2.76208 - 1.17085i) q^{36} +7.16828 q^{37} +(-1.04856 + 5.94668i) q^{38} +(5.13263 + 2.78840i) q^{39} +(-3.35800 - 1.22221i) q^{40} +(-1.32145 - 7.49429i) q^{41} +(0.255073 - 4.57547i) q^{42} +(-2.13929 - 1.79507i) q^{43} +4.23824 q^{44} +(9.87032 - 4.18405i) q^{45} -2.28981 q^{46} +(-0.550684 + 3.12308i) q^{47} +(0.549987 - 1.64241i) q^{48} +(-6.10127 - 3.43141i) q^{49} +(-7.30136 - 2.65748i) q^{50} +(1.63144 + 4.14461i) q^{51} +(3.16901 - 1.15343i) q^{52} +(4.04351 + 7.00356i) q^{53} +(2.15136 + 4.72987i) q^{54} +15.1454 q^{55} +(-1.88135 - 1.86025i) q^{56} +(-10.3436 - 1.54843i) q^{57} +(-1.39347 + 1.16926i) q^{58} +(-5.98431 - 2.17811i) q^{59} +(1.96538 - 5.86917i) q^{60} +(0.904765 - 5.13118i) q^{61} +(-5.16512 + 8.94625i) q^{62} +(7.93374 + 0.236123i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(11.3245 - 4.12177i) q^{65} +(0.190379 + 7.33837i) q^{66} +(-1.43204 + 1.20163i) q^{67} +(2.41652 + 0.879540i) q^{68} +(-0.102857 - 3.96474i) q^{69} +(-6.72301 - 6.64761i) q^{70} +(-3.31293 - 5.73817i) q^{71} +(2.86849 + 0.878508i) q^{72} +12.1719 q^{73} +(5.49122 + 4.60768i) q^{74} +(4.27337 - 12.7614i) q^{75} +(-4.62570 + 3.88142i) q^{76} +(10.1893 + 4.68157i) q^{77} +(2.13947 + 5.43523i) q^{78} +(2.65034 + 2.22390i) q^{79} +(-1.78675 - 3.09475i) q^{80} +(-8.09297 + 3.93748i) q^{81} +(3.80495 - 6.59037i) q^{82} +(0.275388 - 1.56180i) q^{83} +(3.13645 - 3.34106i) q^{84} +(8.63544 + 3.14304i) q^{85} +(-0.484937 - 2.75021i) q^{86} +(-2.08713 - 2.36023i) q^{87} +(3.24668 + 2.72429i) q^{88} +(-2.58297 - 4.47383i) q^{89} +(10.2506 + 3.13935i) q^{90} +(8.89280 + 0.727513i) q^{91} +(-1.75410 - 1.47186i) q^{92} +(-15.7222 - 8.54138i) q^{93} +(-2.42933 + 2.03845i) q^{94} +(-16.5300 + 13.8703i) q^{95} +(1.47704 - 0.904635i) q^{96} +(14.6758 + 12.3145i) q^{97} +(-2.46817 - 6.55043i) q^{98} +(-12.6976 + 0.659271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

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