LMFDB - Embedded newform 378.2.v.b.67.2

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			67.2
Character	$\chi$	$=$	378.67
Dual form			378.2.v.b.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-1.69832 - 0.340165i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.294026 + 1.66751i) q^{5} +(-1.51964 + 0.831077i) q^{6} +(1.80729 - 1.93228i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.76858 + 1.15542i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-1.69832 - 0.340165i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.294026 + 1.66751i) q^{5} +(-1.51964 + 0.831077i) q^{6} +(1.80729 - 1.93228i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.76858 + 1.15542i) q^{9} +(0.846615 + 1.46638i) q^{10} +(-0.980775 - 5.56225i) q^{11} +(-0.629907 + 1.61345i) q^{12} +(0.0358158 - 0.203122i) q^{13} +(0.142417 - 2.64192i) q^{14} +(1.06658 - 2.73194i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.17767 - 2.03979i) q^{17} +(2.86354 - 0.894506i) q^{18} +(1.71011 - 2.96199i) q^{19} +(1.59112 + 0.579119i) q^{20} +(-3.72665 + 2.66685i) q^{21} +(-4.32666 - 3.63050i) q^{22} +(-0.344834 - 0.289350i) q^{23} +(0.554568 + 1.64087i) q^{24} +(2.00434 + 0.729519i) q^{25} +(-0.103128 - 0.178622i) q^{26} +(-4.30889 - 2.90404i) q^{27} +(-1.58909 - 2.11537i) q^{28} +(-1.32033 - 7.48794i) q^{29} +(-0.939012 - 2.77837i) q^{30} +(-0.450105 + 2.55267i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.226412 + 9.78010i) q^{33} +(-2.21330 - 0.805575i) q^{34} +(2.69070 + 3.58181i) q^{35} +(1.61862 - 2.52588i) q^{36} +2.20094 q^{37} +(-0.593913 - 3.36825i) q^{38} +(-0.129922 + 0.332782i) q^{39} +(1.59112 - 0.579119i) q^{40} +(-1.67524 + 9.50074i) q^{41} +(-1.14056 + 4.43837i) q^{42} +(5.43420 - 4.55984i) q^{43} -5.64806 q^{44} +(-2.74070 + 4.27689i) q^{45} -0.450149 q^{46} +(1.59157 + 9.02625i) q^{47} +(1.47955 + 0.900510i) q^{48} +(-0.467419 - 6.98438i) q^{49} +(2.00434 - 0.729519i) q^{50} +(1.30620 + 3.86481i) q^{51} +(-0.193816 - 0.0705434i) q^{52} +(-5.33897 + 9.24737i) q^{53} +(-5.16748 + 0.545083i) q^{54} +9.56346 q^{55} +(-2.57705 - 0.599017i) q^{56} +(-3.91187 + 4.44869i) q^{57} +(-5.82458 - 4.88741i) q^{58} +(6.10176 - 2.22086i) q^{59} +(-2.50523 - 1.52477i) q^{60} +(-0.548842 - 3.11264i) q^{61} +(1.29602 + 2.24478i) q^{62} +(7.23620 - 3.26150i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.328176 + 0.119446i) q^{65} +(6.11309 + 7.63753i) q^{66} +(8.65223 + 7.26008i) q^{67} +(-2.21330 + 0.805575i) q^{68} +(0.487212 + 0.608709i) q^{69} +(4.36354 + 1.01427i) q^{70} +(-0.0841130 + 0.145688i) q^{71} +(-0.383668 - 2.97537i) q^{72} +13.4099 q^{73} +(1.68602 - 1.41474i) q^{74} +(-3.15585 - 1.92076i) q^{75} +(-2.62003 - 2.19847i) q^{76} +(-12.5204 - 8.15746i) q^{77} +(0.114383 + 0.338438i) q^{78} +(-11.5036 + 9.65270i) q^{79} +(0.846615 - 1.46638i) q^{80} +(6.33003 + 6.39771i) q^{81} +(4.82365 + 8.35481i) q^{82} +(-0.953373 - 5.40684i) q^{83} +(1.97921 + 4.13312i) q^{84} +(3.74762 - 1.36402i) q^{85} +(1.23183 - 6.98607i) q^{86} +(-0.304797 + 13.1660i) q^{87} +(-4.32666 + 3.63050i) q^{88} +(-1.50855 + 2.61288i) q^{89} +(0.649639 + 5.03798i) q^{90} +(-0.327759 - 0.436306i) q^{91} +(-0.344834 + 0.289350i) q^{92} +(1.63275 - 4.18214i) q^{93} +(7.02118 + 5.89147i) q^{94} +(4.43632 + 3.72251i) q^{95} +(1.71224 - 0.261209i) q^{96} +(-12.0491 + 10.1104i) q^{97} +(-4.84753 - 5.04989i) q^{98} +(3.71136 - 16.5327i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.69832	−	0.340165i	−0.980525	−	0.196394i
$3$	−1.69832	−	0.340165i	−0.980525	−	0.196394i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.294026	+	1.66751i	−0.131493	+	0.745731i	0.845746	+	0.533586i	$0.179156\pi$
$5$	−0.294026	+	1.66751i	−0.131493	+	0.745731i	−0.977238	+	0.212145i	$0.931955\pi$
$6$	−1.51964	+	0.831077i	−0.620391	+	0.339286i
$7$	1.80729	−	1.93228i	0.683091	−	0.730334i
$7$	1.80729	−	1.93228i	0.683091	−	0.730334i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.76858	+	1.15542i	0.922859	+	0.385139i
$10$	0.846615	+	1.46638i	0.267723	+	0.463710i
$11$	−0.980775	−	5.56225i	−0.295715	−	1.67708i	−0.664283	−	0.747481i	$-0.731263\pi$
$11$	−0.980775	−	5.56225i	−0.295715	−	1.67708i	0.368568	−	0.929601i	$-0.379848\pi$
$12$	−0.629907	+	1.61345i	−0.181838	+	0.465763i
$13$	0.0358158	−	0.203122i	0.00993352	−	0.0563358i	−0.979438	−	0.201745i	$-0.935339\pi$
$13$	0.0358158	−	0.203122i	0.00993352	−	0.0563358i	0.989372	+	0.145409i	$0.0464499\pi$
$14$	0.142417	−	2.64192i	0.0380625	−	0.706082i
$15$	1.06658	−	2.73194i	0.275389	−	0.705384i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.17767	−	2.03979i	−0.285627	−	0.494721i	0.687134	−	0.726531i	$-0.258869\pi$
$17$	−1.17767	−	2.03979i	−0.285627	−	0.494721i	−0.972761	+	0.231810i	$0.925535\pi$
$18$	2.86354	−	0.894506i	0.674943	−	0.210837i
$19$	1.71011	−	2.96199i	0.392325	−	0.679527i	−0.600431	−	0.799677i	$-0.705004\pi$
$19$	1.71011	−	2.96199i	0.392325	−	0.679527i	0.992756	+	0.120150i	$0.0383375\pi$
$20$	1.59112	+	0.579119i	0.355784	+	0.129495i
$21$	−3.72665	+	2.66685i	−0.813221	+	0.581955i
$22$	−4.32666	−	3.63050i	−0.922448	−	0.774026i
$23$	−0.344834	−	0.289350i	−0.0719029	−	0.0603337i	0.606128	−	0.795367i	$-0.292722\pi$
$23$	−0.344834	−	0.289350i	−0.0719029	−	0.0603337i	−0.678031	+	0.735034i	$0.737166\pi$
$24$	0.554568	+	1.64087i	0.113201	+	0.334941i
$25$	2.00434	+	0.729519i	0.400868	+	0.145904i
$26$	−0.103128	−	0.178622i	−0.0202250	−	0.0350307i
$27$	−4.30889	−	2.90404i	−0.829247	−	0.558882i
$28$	−1.58909	−	2.11537i	−0.300310	−	0.399767i
$29$	−1.32033	−	7.48794i	−0.245178	−	1.39048i	−0.820078	−	0.572252i	$-0.806070\pi$
$29$	−1.32033	−	7.48794i	−0.245178	−	1.39048i	0.574900	−	0.818224i	$-0.305041\pi$
$30$	−0.939012	−	2.77837i	−0.171439	−	0.507259i
$31$	−0.450105	+	2.55267i	−0.0808412	+	0.458473i	0.917336	+	0.398115i	$0.130335\pi$
$31$	−0.450105	+	2.55267i	−0.0808412	+	0.458473i	−0.998177	+	0.0603584i	$0.980776\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−0.226412	+	9.78010i	−0.0394133	+	1.70250i
$34$	−2.21330	−	0.805575i	−0.379577	−	0.138155i
$35$	2.69070	+	3.58181i	0.454811	+	0.605436i
$36$	1.61862	−	2.52588i	0.269770	−	0.420980i
$37$	2.20094			0.361832			0.180916	−	0.983499i	$-0.442094\pi$
$37$	2.20094			0.361832			0.180916	+	0.983499i	$0.442094\pi$
$38$	−0.593913	−	3.36825i	−0.0963455	−	0.546402i
$39$	−0.129922	+	0.332782i	−0.0208041	+	0.0532878i
$40$	1.59112	−	0.579119i	0.251578	−	0.0915667i
$41$	−1.67524	+	9.50074i	−0.261628	+	1.48377i	0.516840	+	0.856082i	$0.327108\pi$
$41$	−1.67524	+	9.50074i	−0.261628	+	1.48377i	−0.778468	+	0.627684i	$0.784003\pi$
$42$	−1.14056	+	4.43837i	−0.175992	+	0.684855i
$43$	5.43420	−	4.55984i	0.828708	−	0.695368i	−0.126286	−	0.991994i	$-0.540306\pi$
$43$	5.43420	−	4.55984i	0.828708	−	0.695368i	0.954994	+	0.296625i	$0.0958613\pi$
$44$	−5.64806			−0.851477
$45$	−2.74070	+	4.27689i	−0.408559	+	0.637562i
$46$	−0.450149			−0.0663709
$47$	1.59157	+	9.02625i	0.232155	+	1.31661i	0.848524	+	0.529157i	$0.177492\pi$
$47$	1.59157	+	9.02625i	0.232155	+	1.31661i	−0.616369	+	0.787457i	$0.711397\pi$
$48$	1.47955	+	0.900510i	0.213555	+	0.129977i
$49$	−0.467419	−	6.98438i	−0.0667741	−	0.997768i
$50$	2.00434	−	0.729519i	0.283456	−	0.103170i
$51$	1.30620	+	3.86481i	0.182904	+	0.541182i
$52$	−0.193816	−	0.0705434i	−0.0268775	−	0.00978261i
$53$	−5.33897	+	9.24737i	−0.733364	+	1.27022i	0.222073	+	0.975030i	$0.428718\pi$
$53$	−5.33897	+	9.24737i	−0.733364	+	1.27022i	−0.955437	+	0.295194i	$0.904616\pi$
$54$	−5.16748	+	0.545083i	−0.703205	+	0.0741764i
$55$	9.56346			1.28954
$56$	−2.57705	−	0.599017i	−0.344373	−	0.0800470i
$57$	−3.91187	+	4.44869i	−0.518140	+	0.589243i
$58$	−5.82458	−	4.88741i	−0.764805	−	0.641748i
$59$	6.10176	−	2.22086i	0.794382	−	0.289131i	0.0872256	−	0.996189i	$-0.472200\pi$
$59$	6.10176	−	2.22086i	0.794382	−	0.289131i	0.707156	+	0.707057i	$0.249978\pi$
$60$	−2.50523	−	1.52477i	−0.323423	−	0.196847i
$61$	−0.548842	−	3.11264i	−0.0702720	−	0.398532i	−0.999573	−	0.0292098i	$-0.990701\pi$
$61$	−0.548842	−	3.11264i	−0.0702720	−	0.398532i	0.929301	−	0.369322i	$-0.120410\pi$
$62$	1.29602	+	2.24478i	0.164595	+	0.285087i
$63$	7.23620	−	3.26150i	0.911676	−	0.410910i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.328176	+	0.119446i	0.0407052	+	0.0148155i
$66$	6.11309	+	7.63753i	0.752469	+	0.940115i
$67$	8.65223	+	7.26008i	1.05704	+	0.886960i	0.993816	−	0.111039i	$-0.0354180\pi$
$67$	8.65223	+	7.26008i	1.05704	+	0.886960i	0.0632219	+	0.997999i	$0.479862\pi$
$68$	−2.21330	+	0.805575i	−0.268402	+	0.0976903i
$69$	0.487212	+	0.608709i	0.0586534	+	0.0732800i
$70$	4.36354	+	1.01427i	0.521542	+	0.121229i
$71$	−0.0841130	+	0.145688i	−0.00998238	+	0.0172900i	−0.870973	−	0.491330i	$-0.836511\pi$
$71$	−0.0841130	+	0.145688i	−0.00998238	+	0.0172900i	0.860991	+	0.508620i	$0.169844\pi$
$72$	−0.383668	−	2.97537i	−0.0452158	−	0.350650i
$73$	13.4099			1.56950			0.784752	−	0.619810i	$-0.212790\pi$
$73$	13.4099			1.56950			0.784752	+	0.619810i	$0.212790\pi$
$74$	1.68602	−	1.41474i	0.195995	−	0.164460i
$75$	−3.15585	−	1.92076i	−0.364406	−	0.221790i
$76$	−2.62003	−	2.19847i	−0.300538	−	0.252182i
$77$	−12.5204	−	8.15746i	−1.42683	−	0.929629i
$78$	0.114383	+	0.338438i	0.0129513	+	0.0383205i
$79$	−11.5036	+	9.65270i	−1.29426	+	1.08601i	−0.303154	+	0.952942i	$0.598040\pi$
$79$	−11.5036	+	9.65270i	−1.29426	+	1.08601i	−0.991106	+	0.133072i	$0.957516\pi$
$80$	0.846615	−	1.46638i	0.0946544	−	0.163946i
$81$	6.33003	+	6.39771i	0.703336	+	0.710857i
$82$	4.82365	+	8.35481i	0.532683	+	0.922634i
$83$	−0.953373	−	5.40684i	−0.104646	−	0.593478i	−0.991361	−	0.131161i	$-0.958129\pi$
$83$	−0.953373	−	5.40684i	−0.104646	−	0.593478i	0.886715	−	0.462317i	$-0.152982\pi$
$84$	1.97921	+	4.13312i	0.215950	+	0.450961i
$85$	3.74762	−	1.36402i	0.406487	−	0.147949i
$86$	1.23183	−	6.98607i	0.132832	−	0.753328i
$87$	−0.304797	+	13.1660i	−0.0326777	+	1.41155i
$88$	−4.32666	+	3.63050i	−0.461224	+	0.387013i
$89$	−1.50855	+	2.61288i	−0.159906	+	0.276965i	−0.934834	−	0.355084i	$-0.884452\pi$
$89$	−1.50855	+	2.61288i	−0.159906	+	0.276965i	0.774929	+	0.632048i	$0.217786\pi$
$90$	0.649639	+	5.03798i	0.0684780	+	0.531050i
$91$	−0.327759	−	0.436306i	−0.0343584	−	0.0457373i
$92$	−0.344834	+	0.289350i	−0.0359514	+	0.0301668i
$93$	1.63275	−	4.18214i	0.169308	−	0.433668i
$94$	7.02118	+	5.89147i	0.724179	+	0.607659i
$95$	4.43632	+	3.72251i	0.455157	+	0.381922i
$96$	1.71224	−	0.261209i	0.174755	−	0.0266596i
$97$	−12.0491	+	10.1104i	−1.22340	+	1.02656i	−0.224761	+	0.974414i	$0.572160\pi$
$97$	−12.0491	+	10.1104i	−1.22340	+	1.02656i	−0.998640	+	0.0521411i	$0.983395\pi$
$98$	−4.84753	−	5.04989i	−0.489675	−	0.510116i
$99$	3.71136	−	16.5327i	0.373006	−	1.66160i
$100$	1.06649	−	1.84721i	0.106649	−	0.184721i
$101$	−2.15337	+	1.80689i	−0.214269	+	0.179793i	−0.743605	−	0.668620i	$-0.766885\pi$
$101$	−2.15337	+	1.80689i	−0.214269	+	0.179793i	0.529336	+	0.848412i	$0.322441\pi$
$102$	3.48486	+	2.12101i	0.345052	+	0.210011i
$103$	1.49078	−	8.45461i	0.146891	−	0.833058i	−0.818939	−	0.573880i	$-0.805437\pi$
$103$	1.49078	−	8.45461i	0.146891	−	0.833058i	0.965830	−	0.259177i	$-0.0834515\pi$
$104$	−0.193816	+	0.0705434i	−0.0190053	+	0.00691735i
$105$	−3.35126	−	6.99833i	−0.327050	−	0.682967i
$106$	1.85421	+	10.5157i	0.180096	+	1.02138i
$107$	0.814926	+	1.41149i	0.0787819	+	0.136454i	0.902725	−	0.430219i	$-0.141564\pi$
$107$	0.814926	+	1.41149i	0.0787819	+	0.136454i	−0.823943	+	0.566673i	$0.808230\pi$
$108$	−3.60815	+	3.73915i	−0.347194	+	0.359800i
$109$	4.07509	−	7.05825i	0.390322	−	0.676058i	−0.602170	−	0.798368i	$-0.705697\pi$
$109$	4.07509	−	7.05825i	0.390322	−	0.676058i	0.992492	+	0.122310i	$0.0390302\pi$
$110$	7.32604	−	6.14728i	0.698510	−	0.586120i
$111$	−3.73790	−	0.748681i	−0.354785	−	0.0710617i
$112$	−2.35917	+	1.19762i	−0.222921	+	0.113165i
$113$	−7.05517	−	5.91999i	−0.663695	−	0.556906i	0.247497	−	0.968889i	$-0.420392\pi$
$113$	−7.05517	−	5.91999i	−0.663695	−	0.556906i	−0.911192	+	0.411983i	$0.864836\pi$
$114$	−0.137105	+	5.92239i	−0.0128410	+	0.554683i
$115$	0.583884	−	0.489936i	0.0544474	−	0.0456868i
$116$	−7.60345			−0.705963
$117$	0.333849	−	0.520976i	0.0308643	−	0.0481642i
$118$	3.24668	−	5.62342i	0.298881	−	0.517677i
$119$	−6.06983	−	1.41089i	−0.556421	−	0.129336i
$120$	−2.89922	+	0.442287i	−0.264661	+	0.0403751i
$121$	−19.6401	+	7.14841i	−1.78546	+	0.649856i
$122$	−2.42120	−	2.03163i	−0.219205	−	0.183935i
$123$	6.07690	−	15.5654i	0.547936	−	1.40349i
$124$	2.43573	+	0.886533i	0.218735	+	0.0796130i
$125$	−6.03888	+	10.4596i	−0.540134	+	0.935539i
$126$	3.44680	−	7.14979i	0.307066	−	0.636954i
$127$	4.22298	+	7.31441i	0.374729	+	0.649049i	0.990286	−	0.139043i	$-0.0444025\pi$
$127$	4.22298	+	7.31441i	0.374729	+	0.649049i	−0.615558	+	0.788092i	$0.711069\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−10.7801	+	5.89553i	−0.949135	+	0.519073i
$130$	0.328176	−	0.119446i	0.0287829	−	0.0104761i
$131$	−10.8204	−	9.07941i	−0.945384	−	0.793271i	0.0331300	−	0.999451i	$-0.489452\pi$
$131$	−10.8204	−	9.07941i	−0.945384	−	0.793271i	−0.978514	+	0.206180i	$0.933897\pi$
$132$	9.59221	+	1.92127i	0.834894	+	0.167225i
$133$	−2.63274	−	8.65757i	−0.228288	−	0.750707i
$134$	11.2947			0.975712
$135$	6.10943	−	6.33124i	0.525816	−	0.544907i
$136$	−1.17767	+	2.03979i	−0.100984	+	0.174910i
$137$	16.0821	+	5.85341i	1.37399	+	0.500091i	0.920350	−	0.391095i	$-0.127904\pi$
$137$	16.0821	+	5.85341i	1.37399	+	0.500091i	0.453638	+	0.891186i	$0.350126\pi$
$138$	0.764497	+	0.153125i	0.0650783	+	0.0130348i
$139$	4.30835	−	1.56811i	0.365429	−	0.133005i	−0.152778	−	0.988261i	$-0.548822\pi$
$139$	4.30835	−	1.56811i	0.365429	−	0.133005i	0.518207	+	0.855255i	$0.326600\pi$
$140$	3.99463	−	2.02785i	0.337607	−	0.171384i
$141$	0.367414	−	15.8709i	0.0309419	−	1.33657i
$142$	0.0292121	+	0.165670i	0.00245143	+	0.0139027i
$143$	−1.16494			−0.0974173
$144$	−2.20643	−	2.03264i	−0.183870	−	0.169387i
$145$	12.8744			1.06916
$146$	10.2725	−	8.61969i	0.850162	−	0.713370i
$147$	−1.58201	+	12.0207i	−0.130482	+	0.991451i
$148$	0.382189	−	2.16750i	0.0314157	−	0.178168i
$149$	−2.63059	+	0.957455i	−0.215506	+	0.0784378i	−0.447517	−	0.894275i	$-0.647692\pi$
$149$	−2.63059	+	0.957455i	−0.215506	+	0.0784378i	0.232011	+	0.972713i	$0.425469\pi$
$150$	−3.65216	+	0.557152i	−0.298198	+	0.0454913i
$151$	−1.79690	−	10.1907i	−0.146229	−	0.829308i	−0.966372	−	0.257149i	$-0.917217\pi$
$151$	−1.79690	−	10.1907i	−0.146229	−	0.829308i	0.820143	−	0.572159i	$-0.193894\pi$
$152$	−3.42021			−0.277416
$153$	−0.903670	−	7.00800i	−0.0730574	−	0.566564i
$154$	−14.8347	+	1.79897i	−1.19541	+	0.144965i
$155$	−4.12425	−	1.50110i	−0.331268	−	0.120572i
$156$	0.305166	+	0.185735i	0.0244328	+	0.0148707i
$157$	−16.1176	+	5.86633i	−1.28633	+	0.468184i	−0.892519	−	0.451009i	$-0.851064\pi$
$157$	−16.1176	+	5.86633i	−1.28633	+	0.468184i	−0.393806	+	0.919193i	$0.628842\pi$
$158$	−2.60766	+	14.7888i	−0.207455	+	1.17653i
$159$	12.2129	−	13.8889i	0.968547	−	1.10146i
$160$	−0.294026	−	1.66751i	−0.0232448	−	0.131828i
$161$	−1.18232	+	0.143377i	−0.0931799	+	0.0112997i
$162$	8.96145	+	0.832070i	0.704078	+	0.0653736i
$163$	9.99264	+	17.3078i	0.782684	+	1.35565i	0.930373	+	0.366615i	$0.119483\pi$
$163$	9.99264	+	17.3078i	0.782684	+	1.35565i	−0.147689	+	0.989034i	$0.547183\pi$
$164$	9.06550	+	3.29957i	0.707897	+	0.257653i
$165$	−16.2418	−	3.25315i	−1.26442	−	0.253257i
$166$	−4.20578	−	3.52907i	−0.326432	−	0.273909i
$167$	−9.33758	−	7.83516i	−0.722564	−	0.606303i	0.205529	−	0.978651i	$-0.434108\pi$
$167$	−9.33758	−	7.83516i	−0.722564	−	0.606303i	−0.928093	+	0.372348i	$0.878553\pi$
$168$	4.17289	+	1.89394i	0.321945	+	0.146121i
$169$	12.1760	+	4.43171i	0.936618	+	0.340901i
$170$	1.99407	−	3.45383i	0.152938	−	0.264896i
$171$	8.15689	−	6.22461i	0.623773	−	0.476008i
$172$	−3.54692	−	6.14345i	−0.270450	−	0.468434i
$173$	23.9535	+	8.71837i	1.82115	+	0.662845i	0.995056	+	0.0993161i	$0.0316655\pi$
$173$	23.9535	+	8.71837i	1.82115	+	0.662845i	0.826096	+	0.563529i	$0.190557\pi$
$174$	8.22948	+	10.2817i	0.623875	+	0.779453i
$175$	5.03205	−	2.55449i	0.380387	−	0.193101i
$176$	−0.980775	+	5.56225i	−0.0739287	+	0.419271i
$177$	−11.1182	+	1.69613i	−0.835695	+	0.127489i
$178$	0.523913	+	2.97126i	0.0392689	+	0.222705i
$179$	−0.433233	−	0.750381i	−0.0323813	−	0.0560861i	0.849381	−	0.527781i	$-0.176976\pi$
$179$	−0.433233	−	0.750381i	−0.0323813	−	0.0560861i	−0.881762	+	0.471695i	$0.843642\pi$
$180$	3.73600	+	3.44174i	0.278465	+	0.256532i
$181$	−4.37148	−	7.57162i	−0.324929	−	0.562794i	0.656569	−	0.754266i	$-0.272007\pi$
$181$	−4.37148	−	7.57162i	−0.324929	−	0.562794i	−0.981498	+	0.191472i	$0.938674\pi$
$182$	−0.531529	−	0.123550i	−0.0393996	−	0.00915816i
$183$	−0.126700	+	5.47295i	−0.00936594	+	0.404572i
$184$	−0.0781676	+	0.443310i	−0.00576259	+	0.0326813i
$185$	−0.647134	+	3.67008i	−0.0475782	+	0.269830i
$186$	−1.43747	−	4.25322i	−0.105400	−	0.311861i
$187$	−10.1908	+	8.55108i	−0.745223	+	0.625317i
$188$	9.16550			0.668463
$189$	−13.3988	+	3.07756i	−0.974621	+	0.223860i
$190$	5.79120			0.420138
$191$	−3.51614	+	2.95039i	−0.254419	+	0.213483i	−0.761072	−	0.648667i	$-0.775327\pi$
$191$	−3.51614	+	2.95039i	−0.254419	+	0.213483i	0.506653	+	0.862150i	$0.330882\pi$
$192$	1.14375	−	1.30071i	0.0825431	−	0.0938703i
$193$	−0.0183890	+	0.104289i	−0.00132367	+	0.00750691i	−0.985462	−	0.169893i	$-0.945658\pi$
$193$	−0.0183890	+	0.104289i	−0.00132367	+	0.00750691i	0.984139	+	0.177400i	$0.0567688\pi$
$194$	−2.73131	+	15.4900i	−0.196097	+	1.11212i
$195$	−0.516716	−	0.314492i	−0.0370028	−	0.0225212i
$196$	−6.95943	−	0.752507i	−0.497102	−	0.0537505i
$197$	7.20342	+	12.4767i	0.513222	+	0.888927i	0.999882	+	0.0153354i	$0.00488161\pi$
$197$	7.20342	+	12.4767i	0.513222	+	0.888927i	−0.486660	+	0.873591i	$0.661785\pi$
$198$	−7.78396	−	15.0504i	−0.553182	−	1.06959i
$199$	−0.904328	−	1.56634i	−0.0641061	−	0.111035i	0.832191	−	0.554489i	$-0.187086\pi$
$199$	−0.904328	−	1.56634i	−0.0641061	−	0.111035i	−0.896297	+	0.443454i	$0.853753\pi$
$200$	−0.370387	−	2.10057i	−0.0261903	−	0.148533i
$201$	−12.2246	−	15.2731i	−0.862258	−	1.07728i
$202$	−0.488130	+	2.76832i	−0.0343447	+	0.194778i
$203$	−16.8550	−	10.9816i	−1.18299	−	0.770759i
$204$	4.03291	−	0.615237i	0.282360	−	0.0430752i
$205$	−15.3500	−	5.58693i	−1.07209	−	0.390208i
$206$	−4.29252	−	7.43486i	−0.299074	−	0.518011i
$207$	−0.620380	−	1.19952i	−0.0431194	−	0.0833721i
$208$	−0.103128	+	0.178622i	−0.00715061	+	0.0123852i
$209$	−18.1526	−	6.60699i	−1.25564	−	0.457015i
$210$	−7.06566	−	3.20688i	−0.487577	−	0.221296i
$211$	−7.31410	−	6.13726i	−0.503524	−	0.422507i	0.355320	−	0.934745i	$-0.384372\pi$
$211$	−7.31410	−	6.13726i	−0.503524	−	0.422507i	−0.858843	+	0.512238i	$0.828816\pi$
$212$	8.17978	+	6.86365i	0.561790	+	0.471397i
$213$	0.192409	−	0.218812i	0.0131836	−	0.0149928i
$214$	1.53156	+	0.557442i	0.104695	+	0.0381060i
$215$	6.00576	+	10.4023i	0.409589	+	0.709429i
$216$	−0.360522	+	5.18363i	−0.0245304	+	0.352701i
$217$	4.11901	+	5.48314i	0.279616	+	0.372220i
$218$	−1.41526	−	8.02635i	−0.0958537	−	0.543613i
$219$	−22.7742	−	4.56156i	−1.53894	−	0.308241i
$220$	1.66068	−	9.41817i	0.111963	−	0.634973i
$221$	−0.456504	+	0.166154i	−0.0307078	+	0.0111767i
$222$	−3.34464	+	1.82915i	−0.224477	+	0.122765i
$223$	−0.823249	−	0.299638i	−0.0551288	−	0.0200653i	0.314309	−	0.949321i	$-0.398227\pi$
$223$	−0.823249	−	0.299638i	−0.0551288	−	0.0200653i	−0.369437	+	0.929256i	$0.620450\pi$
$224$	−1.03742	+	2.43388i	−0.0693153	+	0.162620i
$225$	4.70626	+	4.33557i	0.313751	+	0.289038i
$226$	−9.20987			−0.612632
$227$	−2.42132	−	13.7320i	−0.160709	−	0.911426i	−0.953379	−	0.301775i	$-0.902421\pi$
$227$	−2.42132	−	13.7320i	−0.160709	−	0.911426i	0.792670	−	0.609651i	$-0.208690\pi$
$228$	3.70181	+	4.62494i	0.245158	+	0.306294i
$229$	19.2072	−	6.99086i	1.26925	−	0.461969i	0.382386	−	0.924002i	$-0.375102\pi$
$229$	19.2072	−	6.99086i	1.26925	−	0.461969i	0.886862	+	0.462034i	$0.152880\pi$
$230$	0.132356	−	0.750626i	0.00872727	−	0.0494948i
$231$	18.4887	+	18.1130i	1.21647	+	1.19175i
$232$	−5.82458	+	4.88741i	−0.382403	+	0.320874i
$233$	24.3488			1.59515			0.797573	−	0.603223i	$-0.206117\pi$
$233$	24.3488			1.59515			0.797573	+	0.603223i	$0.206117\pi$
$234$	−0.0791336	−	0.613684i	−0.00517312	−	0.0401178i
$235$	−15.5193			−1.01237
$236$	−1.12756	−	6.39471i	−0.0733979	−	0.416260i
$237$	22.8204	−	12.4802i	1.48234	−	0.810678i
$238$	−5.55666	+	2.82081i	−0.360185	+	0.182846i
$239$	16.4753	−	5.99650i	1.06570	−	0.387882i	0.251130	−	0.967953i	$-0.419198\pi$
$239$	16.4753	−	5.99650i	1.06570	−	0.387882i	0.814565	+	0.580072i	$0.196975\pi$
$240$	−1.93663	+	2.20239i	−0.125009	+	0.142164i
$241$	−2.52171	−	0.917829i	−0.162438	−	0.0591226i	0.259521	−	0.965737i	$-0.416435\pi$
$241$	−2.52171	−	0.917829i	−0.162438	−	0.0591226i	−0.421959	+	0.906615i	$0.638657\pi$
$242$	−10.4503	+	18.1004i	−0.671770	+	1.16354i
$243$	−8.57413	−	13.0186i	−0.550031	−	0.835144i
$244$	−3.16065			−0.202340
$245$	11.7839	+	1.27417i	0.752847	+	0.0814035i
$246$	−5.35009	−	15.8300i	−0.341109	−	1.00928i
$247$	−0.540395	−	0.453445i	−0.0343845	−	0.0288520i
$248$	2.43573	−	0.886533i	0.154669	−	0.0562949i
$249$	−0.220086	+	9.50685i	−0.0139474	+	0.602472i
$250$	2.09728	+	11.8943i	0.132644	+	0.752260i
$251$	6.29044	+	10.8954i	0.397049	+	0.687709i	0.993360	−	0.115044i	$-0.0367010\pi$
$251$	6.29044	+	10.8954i	0.397049	+	0.687709i	−0.596311	+	0.802753i	$0.703368\pi$
$252$	−1.95539	−	7.69262i	−0.123178	−	0.484590i
$253$	−1.27123	+	2.20184i	−0.0799218	+	0.138429i
$254$	7.93660	+	2.88869i	0.497987	+	0.181252i
$255$	−6.82865	+	1.04174i	−0.427627	+	0.0652362i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	27.8426	−	10.1339i	1.73678	−	0.632134i	0.737700	−	0.675129i	$-0.235912\pi$
$257$	27.8426	−	10.1339i	1.73678	−	0.632134i	0.999075	+	0.0429945i	$0.0136898\pi$
$258$	−4.46846	+	11.4456i	−0.278194	+	0.712569i
$259$	3.97773	−	4.25283i	0.247164	−	0.264258i
$260$	0.174619	−	0.302448i	0.0108294	−	0.0187571i
$261$	4.99626	−	22.2565i	0.309261	−	1.37764i
$262$	−14.1250			−0.872648
$263$	−5.27725	+	4.42814i	−0.325409	+	0.273051i	−0.790826	−	0.612041i	$-0.790349\pi$
$263$	−5.27725	+	4.42814i	−0.325409	+	0.273051i	0.465417	+	0.885092i	$0.345904\pi$
$264$	8.58302	−	4.69397i	0.528249	−	0.288894i
$265$	−13.8502	−	11.6217i	−0.850814	−	0.713918i
$266$	−7.58178	−	4.93979i	−0.464869	−	0.302878i
$267$	3.45080	−	3.92435i	0.211186	−	0.240166i
$268$	8.65223	−	7.26008i	0.528519	−	0.443480i
$269$	8.04559	−	13.9354i	0.490549	−	0.849655i	−0.509392	−	0.860534i	$-0.670130\pi$
$269$	8.04559	−	13.9354i	0.490549	−	0.849655i	0.999941	+	0.0108795i	$0.00346311\pi$
$270$	0.610447	−	8.77708i	0.0371507	−	0.534156i
$271$	−6.24998	−	10.8253i	−0.379659	−	0.657589i	0.611353	−	0.791358i	$-0.290625\pi$
$271$	−6.24998	−	10.8253i	−0.379659	−	0.657589i	−0.991013	+	0.133769i	$0.957292\pi$
$272$	0.409001	+	2.31956i	0.0247993	+	0.140644i
$273$	0.408223	+	0.852478i	0.0247068	+	0.0515943i
$274$	16.0821	−	5.85341i	0.971556	−	0.353618i
$275$	2.09197	−	11.8641i	0.126150	−	0.715434i
$276$	0.684065	−	0.374109i	0.0411759	−	0.0225187i
$277$	3.55626	−	2.98406i	0.213675	−	0.179295i	−0.529668	−	0.848205i	$-0.677683\pi$
$277$	3.55626	−	2.98406i	0.213675	−	0.179295i	0.743343	+	0.668910i	$0.233239\pi$
$278$	2.29242	−	3.97059i	0.137490	−	0.238140i
$279$	−4.19555	+	6.54721i	−0.251181	+	0.391971i
$280$	1.75658	−	4.12112i	0.104976	−	0.246284i
$281$	9.87096	−	8.28272i	0.588852	−	0.494106i	−0.298989	−	0.954257i	$-0.596649\pi$
$281$	9.87096	−	8.28272i	0.588852	−	0.494106i	0.887841	+	0.460151i	$0.152205\pi$
$282$	−9.92013	−	12.3940i	−0.590735	−	0.738049i
$283$	15.9002	+	13.3419i	0.945171	+	0.793092i	0.978478	−	0.206353i	$-0.0661595\pi$
$283$	15.9002	+	13.3419i	0.945171	+	0.793092i	−0.0333071	+	0.999445i	$0.510604\pi$
$284$	0.128869	+	0.108134i	0.00764694	+	0.00641655i
$285$	−6.26802	−	7.83109i	−0.371285	−	0.463874i
$286$	−0.892397	+	0.748810i	−0.0527685	+	0.0442780i
$287$	15.3305	+	20.4076i	0.904928	+	1.20462i
$288$	−2.99679	−	0.138827i	−0.176587	−	0.00818047i
$289$	5.72618	−	9.91804i	0.336834	−	0.583414i
$290$	9.86236	−	8.27550i	0.579138	−	0.485954i
$291$	23.9024	−	13.0720i	1.40118	−	0.766294i
$292$	2.32860	−	13.2061i	0.136271	−	0.772830i
$293$	−30.4718	+	11.0908i	−1.78018	+	0.647934i	−0.780441	+	0.625230i	$0.785005\pi$
$293$	−30.4718	+	11.0908i	−1.78018	+	0.647934i	−0.999742	+	0.0227038i	$0.992773\pi$
$294$	6.51487	+	10.2253i	0.379955	+	0.596351i
$295$	1.90922	+	10.8277i	0.111159	+	0.630414i
$296$	−1.10047	−	1.90607i	−0.0639635	−	0.110788i
$297$	−11.9269	+	26.8154i	−0.692071	+	1.55599i
$298$	−1.39971	+	2.42436i	−0.0810827	+	0.140439i
$299$	−0.0711238	+	0.0596800i	−0.00411320	+	0.00345138i
$300$	−2.43959	+	2.77437i	−0.140850	+	0.160178i
$301$	1.01028	−	18.7413i	0.0582317	−	1.08023i
$302$	−7.92696	−	6.65151i	−0.456145	−	0.382751i
$303$	4.27175	−	2.33618i	0.245406	−	0.134210i
$304$	−2.62003	+	2.19847i	−0.150269	+	0.126091i
$305$	5.35171			0.306438
$306$	−5.19691	−	4.78757i	−0.297088	−	0.273687i
$307$	1.01574	−	1.75932i	0.0579714	−	0.100409i	−0.835583	−	0.549364i	$-0.814870\pi$
$307$	1.01574	−	1.75932i	0.0579714	−	0.100409i	0.893555	+	0.448954i	$0.148203\pi$
$308$	−10.2077	+	10.9136i	−0.581636	+	0.621862i
$309$	−5.40777	+	13.8515i	−0.307638	+	0.787986i
$310$	−4.12425	+	1.50110i	−0.234242	+	0.0852570i
$311$	0.763636	+	0.640767i	0.0433018	+	0.0363346i	0.664182	−	0.747571i	$-0.268780\pi$
$311$	0.763636	+	0.640767i	0.0433018	+	0.0363346i	−0.620880	+	0.783906i	$0.713225\pi$
$312$	0.353159	−	0.0538757i	0.0199937	−	0.00305011i
$313$	−24.4115	−	8.88506i	−1.37982	−	0.502213i	−0.457696	−	0.889109i	$-0.651325\pi$
$313$	−24.4115	−	8.88506i	−1.37982	−	0.502213i	−0.922124	+	0.386895i	$0.873547\pi$
$314$	−8.57600	+	14.8541i	−0.483972	+	0.838264i
$315$	3.31093	+	13.0254i	0.186550	+	0.733897i
$316$	7.50847	+	13.0050i	0.422384	+	0.731591i
$317$	5.99279	+	33.9868i	0.336589	+	1.90889i	0.410951	+	0.911658i	$0.365197\pi$
$317$	5.99279	+	33.9868i	0.336589	+	1.90889i	−0.0743621	+	0.997231i	$0.523692\pi$
$318$	0.428043	−	18.4898i	0.0240035	−	1.03686i
$319$	−40.3549	+	14.6880i	−2.25944	+	0.822368i
$320$	−1.29709	−	1.08839i	−0.0725095	−	0.0608427i
$321$	−0.903864	−	2.67437i	−0.0504488	−	0.149269i
$322$	−0.813549	+	0.869814i	−0.0453373	+	0.0484729i
$323$	−8.05577			−0.448235
$324$	7.39972	−	5.12291i	0.411095	−	0.284606i
$325$	0.219968	−	0.380996i	0.0122016	−	0.0211339i
$326$	18.7800	+	6.83537i	1.04013	+	0.378576i
$327$	−9.32176	+	10.6010i	−0.515495	+	0.586235i
$328$	9.06550	−	3.29957i	0.500558	−	0.182188i
$329$	20.3177	+	13.2377i	1.12015	+	0.729817i
$330$	−14.5330	+	7.94798i	−0.800017	+	0.437522i
$331$	4.41274	+	25.0259i	0.242546	+	1.37555i	0.826123	+	0.563490i	$0.190542\pi$
$331$	4.41274	+	25.0259i	0.242546	+	1.37555i	−0.583577	+	0.812058i	$0.698347\pi$
$332$	−5.49025			−0.301317
$333$	6.09347	+	2.54300i	0.333920	+	0.139356i
$334$	−12.1893			−0.666972
$335$	−14.6502	+	12.2930i	−0.800427	+	0.671638i
$336$	4.41402	−	1.23144i	0.240804	−	0.0671803i
$337$	−2.70420	+	15.3363i	−0.147307	+	0.835420i	0.818179	+	0.574964i	$0.194984\pi$
$337$	−2.70420	+	15.3363i	−0.147307	+	0.835420i	−0.965486	+	0.260456i	$0.916127\pi$
$338$	12.1760	−	4.43171i	0.662289	−	0.241053i
$339$	9.96816	+	12.4540i	0.541396	+	0.676406i
$340$	−0.692533	−	3.92755i	−0.0375579	−	0.213001i
$341$	14.6401			0.792803
$342$	2.24744	−	10.0115i	0.121527	−	0.541358i
$343$	−14.3405	−	11.7196i	−0.774316	−	0.632799i
$344$	−6.66603	−	2.42624i	−0.359408	−	0.130814i
$345$	−1.15828	+	0.633452i	−0.0623597	+	0.0341039i
$346$	23.9535	−	8.71837i	1.28775	−	0.468702i
$347$	4.42760	−	25.1102i	0.237686	−	1.34798i	−0.599197	−	0.800602i	$-0.704513\pi$
$347$	4.42760	−	25.1102i	0.237686	−	1.34798i	0.836883	−	0.547382i	$-0.184376\pi$
$348$	12.9131	+	2.58643i	0.692214	+	0.138647i
$349$	−0.194379	−	1.10238i	−0.0104049	−	0.0590090i	0.979163	−	0.203075i	$-0.0650934\pi$
$349$	−0.194379	−	1.10238i	−0.0104049	−	0.0590090i	−0.989568	+	0.144066i	$0.953982\pi$
$350$	2.21278	−	5.19140i	0.118278	−	0.277492i
$351$	−0.744199	+	0.771219i	−0.0397224	+	0.0411646i
$352$	2.82403	+	4.89136i	0.150521	+	0.260710i
$353$	−18.2649	−	6.64788i	−0.972142	−	0.353831i	−0.193362	−	0.981128i	$-0.561939\pi$
$353$	−18.2649	−	6.64788i	−0.972142	−	0.353831i	−0.778780	+	0.627297i	$0.784161\pi$
$354$	−7.42679	+	8.44595i	−0.394729	+	0.448897i
$355$	−0.218204	−	0.183095i	−0.0115811	−	0.00971767i
$356$	2.31123	+	1.93935i	0.122495	+	0.102785i
$357$	9.82858	+	4.46088i	0.520183	+	0.236095i
$358$	−0.814211	−	0.296349i	−0.0430324	−	0.0156625i
$359$	−3.35513	+	5.81126i	−0.177077	+	0.306707i	−0.940878	−	0.338745i	$-0.889998\pi$
$359$	−3.35513	+	5.81126i	−0.177077	+	0.306707i	0.763801	+	0.645452i	$0.223331\pi$
$360$	5.07425	+	0.235066i	0.267436	+	0.0123891i
$361$	3.65108	+	6.32386i	0.192162	+	0.332835i
$362$	−8.21569	−	2.99027i	−0.431807	−	0.157165i
$363$	35.7868	−	5.45942i	1.87832	−	0.286545i
$364$	−0.486592	+	0.247016i	−0.0255043	+	0.0129471i
$365$	−3.94285	+	22.3610i	−0.206378	+	1.17043i
$366$	3.42088	+	4.27396i	0.178812	+	0.223404i
$367$	4.54295	+	25.7644i	0.237140	+	1.34489i	0.838059	+	0.545579i	$0.183690\pi$
$367$	4.54295	+	25.7644i	0.237140	+	1.34489i	−0.600919	+	0.799310i	$0.705199\pi$
$368$	0.225075	+	0.389840i	0.0117328	+	0.0203218i
$369$	−15.6153	+	24.3679i	−0.812901	+	1.26854i
$370$	1.86335	+	3.22741i	0.0968708	+	0.167785i
$371$	8.21946	+	27.0291i	0.426733	+	1.40328i
$372$	−3.83508	−	2.33417i	−0.198840	−	0.121021i
$373$	−4.35921	+	24.7223i	−0.225711	+	1.28007i	0.635609	+	0.772011i	$0.280749\pi$
$373$	−4.35921	+	24.7223i	−0.225711	+	1.28007i	−0.861321	+	0.508062i	$0.830362\pi$
$374$	−2.31006	+	13.1010i	−0.119450	+	0.677437i
$375$	13.8140	−	15.7096i	0.713349	−	0.811241i
$376$	7.02118	−	5.89147i	0.362090	−	0.303829i
$377$	−1.56825			−0.0807690
$378$	−8.28588	+	10.9702i	−0.426180	+	0.564244i
$379$	−37.7778			−1.94051			−0.970257	−	0.242076i	$-0.922172\pi$
$379$	−37.7778			−1.94051			−0.970257	+	0.242076i	$0.922172\pi$
$380$	4.43632	−	3.72251i	0.227578	−	0.190961i
$381$	−4.68386	−	13.8587i	−0.239961	−	0.710003i
$382$	−0.797045	+	4.52026i	−0.0407803	+	0.231277i
$383$	1.05156	−	5.96369i	0.0537321	−	0.304730i	−0.946084	−	0.323922i	$-0.894998\pi$
$383$	1.05156	−	5.96369i	0.0537321	−	0.304730i	0.999816	+	0.0191922i	$0.00610945\pi$
$384$	0.0400867	−	1.73159i	0.00204566	−	0.0883647i
$385$	17.2839	−	18.4793i	0.880871	−	0.941792i
$386$	0.0529491	+	0.0917105i	0.00269504	+	0.00466794i
$387$	20.3135	−	6.34549i	1.03259	−	0.322559i
$388$	7.86449	+	13.6217i	0.399259	+	0.691537i
$389$	1.11311	+	6.31277i	0.0564370	+	0.320070i	0.999936	−	0.0113049i	$-0.00359853\pi$
$389$	1.11311	+	6.31277i	0.0564370	+	0.320070i	−0.943499	+	0.331375i	$0.892487\pi$
$390$	−0.597979	+	0.0912240i	−0.0302798	+	0.00461931i
$391$	−0.184111	+	1.04415i	−0.00931091	+	0.0528048i
$392$	−5.81494	+	3.89699i	−0.293699	+	0.196827i
$393$	15.2880	+	19.1005i	0.771179	+	0.963490i
$394$	13.5380	+	4.92743i	0.682034	+	0.248240i
$395$	−12.7136	−	22.0205i	−0.639689	−	1.10797i
$396$	−15.6371	−	6.52586i	−0.785793	−	0.327937i
$397$	−9.98132	+	17.2882i	−0.500948	+	0.867668i	0.499051	+	0.866572i	$0.333682\pi$
$397$	−9.98132	+	17.2882i	−0.500948	+	0.867668i	−0.999999	+	0.00109513i	$0.999651\pi$
$398$	−1.69958	−	0.618597i	−0.0851923	−	0.0310075i
$399$	1.52624	+	15.5989i	0.0764074	+	0.780921i
$400$	−1.63395	−	1.37105i	−0.0816976	−	0.0685524i
$401$	22.5210	+	18.8974i	1.12464	+	0.943689i	0.998830	−	0.0483650i	$-0.0154011\pi$
$401$	22.5210	+	18.8974i	1.12464	+	0.943689i	0.125815	+	0.992054i	$0.459846\pi$
$402$	−19.1820	−	3.84205i	−0.956710	−	0.191624i
$403$	0.502382	+	0.182852i	0.0250254	+	0.00910851i
$404$	1.40551	+	2.43442i	0.0699269	+	0.121117i
$405$	−12.5294	+	8.67426i	−0.622592	+	0.431028i
$406$	−19.9705	+	2.42178i	−0.991121	+	0.120191i
$407$	−2.15863	−	12.2422i	−0.106999	−	0.606822i
$408$	2.69392	−	3.06361i	0.133369	−	0.151671i
$409$	2.68041	−	15.2014i	0.132538	−	0.751660i	−0.844005	−	0.536336i	$-0.819808\pi$
$409$	2.68041	−	15.2014i	0.132538	−	0.751660i	0.976543	−	0.215324i	$-0.0690808\pi$
$410$	−15.3500	+	5.58693i	−0.758081	+	0.275919i
$411$	−25.3214	−	15.4115i	−1.24901	−	0.760195i
$412$	−8.06730	−	2.93626i	−0.397447	−	0.144659i
$413$	6.73632	−	15.8041i	0.331473	−	0.777667i
$414$	−1.24627	−	0.520109i	−0.0612509	−	0.0255620i
$415$	9.29626			0.456336
$416$	0.0358158	+	0.203122i	0.00175602	+	0.00995886i
$417$	−7.85036	+	1.19760i	−0.384434	+	0.0586469i
$418$	−18.1526	+	6.60699i	−0.887871	+	0.323158i
$419$	2.20925	−	12.5293i	0.107929	−	0.612095i	−0.882081	−	0.471098i	$-0.843858\pi$
$419$	2.20925	−	12.5293i	0.107929	−	0.612095i	0.990010	−	0.140997i	$-0.0450309\pi$
$420$	−7.47395	+	2.08510i	−0.364691	+	0.101743i
$421$	−9.53540	+	8.00115i	−0.464727	+	0.389952i	−0.844867	−	0.534977i	$-0.820320\pi$
$421$	−9.53540	+	8.00115i	−0.464727	+	0.389952i	0.380140	+	0.924929i	$0.375876\pi$
$422$	−9.54788			−0.464784
$423$	−6.02269	+	26.8288i	−0.292833	+	1.30446i
$424$	10.6779			0.518567
$425$	−0.872387	−	4.94755i	−0.0423170	−	0.239992i
$426$	0.00674362	−	0.291298i	0.000326730	−	0.0141134i
$427$	−7.00640	−	4.56491i	−0.339064	−	0.220912i
$428$	1.53156	−	0.557442i	0.0740307	−	0.0269450i
$429$	1.97844	+	0.396272i	0.0955201	+	0.0191322i
$430$	11.2871	+	4.10818i	0.544314	+	0.198114i
$431$	12.2003	−	21.1315i	0.587668	−	1.01787i	−0.406869	−	0.913487i	$-0.633379\pi$
$431$	12.2003	−	21.1315i	0.587668	−	1.01787i	0.994537	−	0.104384i	$-0.0332872\pi$
$432$	3.05580	+	4.20263i	0.147022	+	0.202199i
$433$	25.7332			1.23666			0.618329	−	0.785920i	$-0.287810\pi$
$433$	25.7332			1.23666			0.618329	+	0.785920i	$0.287810\pi$
$434$	6.67984	+	1.55268i	0.320642	+	0.0745311i
$435$	−21.8648	−	4.37941i	−1.04834	−	0.209977i
$436$	−6.24339	−	5.23883i	−0.299004	−	0.250894i
$437$	−1.44675	+	0.526576i	−0.0692077	+	0.0251895i
$438$	−20.3782	+	11.1446i	−0.973707	+	0.532511i
$439$	1.74422	+	9.89197i	0.0832472	+	0.472118i	0.997721	+	0.0674732i	$0.0214937\pi$
$439$	1.74422	+	9.89197i	0.0832472	+	0.472118i	−0.914474	+	0.404645i	$0.867395\pi$
$440$	−4.78173	−	8.28220i	−0.227960	−	0.394838i
$441$	6.77578	−	19.8768i	0.322656	−	0.946516i
$442$	−0.242901	+	0.420716i	−0.0115536	+	0.0200114i
$443$	−20.7285	−	7.54455i	−0.984840	−	0.358453i	−0.201120	−	0.979567i	$-0.564458\pi$
$443$	−20.7285	−	7.54455i	−0.984840	−	0.358453i	−0.783720	+	0.621114i	$0.786680\pi$
$444$	−1.38639	+	3.55110i	−0.0657950	+	0.168528i
$445$	−3.91344	−	3.28377i	−0.185515	−	0.155665i
$446$	−0.823249	+	0.299638i	−0.0389820	+	0.0141883i
$447$	4.79327	−	0.731232i	0.226714	−	0.0345861i
$448$	0.769760	+	2.53130i	0.0363678	+	0.119593i
$449$	8.71834	−	15.1006i	0.411444	−	0.712642i	−0.583604	−	0.812038i	$-0.698358\pi$
$449$	8.71834	−	15.1006i	0.411444	−	0.712642i	0.995048	+	0.0993966i	$0.0316912\pi$
$450$	6.39206	+	0.296114i	0.301325	+	0.0139590i
$451$	54.4885			2.56576
$452$	−7.05517	+	5.91999i	−0.331847	+	0.278453i
$453$	−0.414813	+	17.9183i	−0.0194896	+	0.841876i
$454$	−10.6816	−	8.96294i	−0.501313	−	0.420651i
$455$	0.823912	−	0.418254i	0.0386256	−	0.0196081i
$456$	5.80861	+	1.16343i	0.272013	+	0.0544828i
$457$	−0.683861	+	0.573827i	−0.0319897	+	0.0268425i	−0.658642	−	0.752456i	$-0.728869\pi$
$457$	−0.683861	+	0.573827i	−0.0319897	+	0.0268425i	0.626653	+	0.779299i	$0.284424\pi$
$458$	10.2199	−	17.7015i	0.477547	−	0.827135i
$459$	−0.849154	+	12.2092i	−0.0396351	+	0.569878i
$460$	−0.381103	−	0.660090i	−0.0177690	−	0.0307768i
$461$	−0.0821216	−	0.465735i	−0.00382479	−	0.0216914i	0.982836	−	0.184483i	$-0.0590612\pi$
$461$	−0.0821216	−	0.465735i	−0.00382479	−	0.0216914i	−0.986660	+	0.162792i	$0.947950\pi$
$462$	25.8060	+	1.99101i	1.20060	+	0.0926303i
$463$	20.4265	−	7.43464i	0.949300	−	0.345517i	0.179468	−	0.983764i	$-0.442562\pi$
$463$	20.4265	−	7.43464i	0.949300	−	0.345517i	0.769832	+	0.638247i	$0.220340\pi$
$464$	−1.32033	+	7.48794i	−0.0612946	+	0.347619i
$465$	6.49367	+	3.95228i	0.301137	+	0.183283i
$466$	18.6523	−	15.6511i	0.864051	−	0.725025i
$467$	−17.0881	+	29.5974i	−0.790741	+	1.36960i	0.134767	+	0.990877i	$0.456971\pi$
$467$	−17.0881	+	29.5974i	−0.790741	+	1.36960i	−0.925508	+	0.378727i	$0.876362\pi$
$468$	−0.455089	−	0.419243i	−0.0210365	−	0.0193795i
$469$	29.6656	−	3.59748i	1.36983	−	0.166116i
$470$	−11.8885	+	9.97561i	−0.548374	+	0.460141i
$471$	29.3684	−	4.48026i	1.35322	−	0.206440i
$472$	−4.97420	−	4.17385i	−0.228956	−	0.192117i
$473$	−30.6927	−	25.7542i	−1.41125	−	1.18418i
$474$	9.45927	−	24.2291i	0.434478	−	1.11288i
$475$	5.58846	−	4.68927i	0.256416	−	0.215159i
$476$	−2.44347	+	5.73262i	−0.111996	+	0.262754i
$477$	−25.4659	+	19.4333i	−1.16600	+	0.889790i
$478$	8.76630	−	15.1837i	0.400961	−	0.694485i
$479$	14.6503	−	12.2931i	0.669391	−	0.561686i	−0.243494	−	0.969902i	$-0.578294\pi$
$479$	14.6503	−	12.2931i	0.669391	−	0.561686i	0.912885	+	0.408217i	$0.133849\pi$
$480$	−0.0678760	+	2.93198i	−0.00309810	+	0.133826i
$481$	0.0788284	−	0.447058i	0.00359427	−	0.0203841i
$482$	−2.52171	+	0.917829i	−0.114861	+	0.0418060i
$483$	2.05673	+	0.158683i	0.0935844	+	0.00722034i
$484$	3.62935	+	20.5830i	0.164970	+	0.935593i
$485$	−13.3164	−	23.0647i	−0.604666	−	1.04731i
$486$	−14.9364	−	4.46149i	−0.677527	−	0.202377i
$487$	−17.6386	+	30.5510i	−0.799283	+	1.38440i	0.120801	+	0.992677i	$0.461454\pi$
$487$	−17.6386	+	30.5510i	−0.799283	+	1.38440i	−0.920084	+	0.391722i	$0.871880\pi$
$488$	−2.42120	+	2.03163i	−0.109603	+	0.0919675i
$489$	−11.0832	−	32.7933i	−0.501200	−	1.48296i
$490$	9.84603	−	6.59849i	0.444798	−	0.298090i
$491$	−2.53088	−	2.12366i	−0.114217	−	0.0958393i	0.583891	−	0.811832i	$-0.301530\pi$
$491$	−2.53088	−	2.12366i	−0.114217	−	0.0958393i	−0.698107	+	0.715993i	$0.745974\pi$
$492$	−14.2737	−	8.68749i	−0.643509	−	0.391662i
$493$	−13.7189	+	11.5115i	−0.617868	+	0.518452i
$494$	−0.705436			−0.0317391
$495$	26.4772	+	11.0498i	1.19006	+	0.496651i
$496$	1.29602	−	2.24478i	0.0581932	−	0.100794i
$497$	0.129494	+	0.425830i	0.00580859	+	0.0191011i
$498$	5.94229	+	7.42414i	0.266280	+	0.332684i
$499$	−22.6597	+	8.24747i	−1.01439	+	0.369207i	−0.795117	−	0.606456i	$-0.792591\pi$
$499$	−22.6597	+	8.24747i	−1.01439	+	0.369207i	−0.219272	+	0.975664i	$0.570368\pi$
$500$	9.25210	+	7.76344i	0.413767	+	0.347191i
$501$	13.1930	+	16.4829i	0.589418	+	0.736403i
$502$	11.8222	+	4.30291i	0.527649	+	0.192048i
$503$	10.4388	−	18.0806i	0.465444	−	0.806172i	−0.533778	−	0.845625i	$-0.679228\pi$
$503$	10.4388	−	18.0806i	0.465444	−	0.806172i	0.999221	+	0.0394528i	$0.0125615\pi$
$504$	−6.44264	−	4.63599i	−0.286978	−	0.206503i
$505$	−2.37986	−	4.12204i	−0.105902	−	0.183428i
$506$	0.441495	+	2.50384i	0.0196268	+	0.111309i
$507$	−19.1713	−	11.6683i	−0.851426	−	0.518208i
$508$	7.93660	−	2.88869i	0.352130	−	0.128165i
$509$	5.24518	+	4.40123i	0.232489	+	0.195081i	0.751588	−	0.659633i	$-0.229288\pi$
$509$	5.24518	+	4.40123i	0.232489	+	0.195081i	−0.519100	+	0.854714i	$0.673733\pi$
$510$	−4.56143	+	5.18739i	−0.201984	+	0.229701i
$511$	24.2355	−	25.9116i	1.07211	−	1.14626i
$512$	1.00000			0.0441942
$513$	−15.9704	+	7.79669i	−0.705110	+	0.344232i
$514$	14.8147	−	25.6599i	0.653451	−	1.13181i
$515$	13.6598	+	4.97176i	0.601922	+	0.219082i
$516$	3.93402	+	11.6401i	0.173186	+	0.512426i
$517$	48.6453	−	17.7054i	2.13942	−	0.778685i
$518$	0.313451	−	5.81469i	0.0137722	−	0.255483i
$519$	−37.7150	−	22.9547i	−1.65551	−	1.00760i
$520$	−0.0606444	−	0.343932i	−0.00265943	−	0.0150824i
$521$	−6.49997			−0.284769			−0.142384	−	0.989811i	$-0.545477\pi$
$521$	−6.49997			−0.284769			−0.142384	+	0.989811i	$0.545477\pi$
$522$	−10.4788	−	20.2610i	−0.458645	−	0.886799i
$523$	−14.4698			−0.632722			−0.316361	−	0.948639i	$-0.602461\pi$
$523$	−14.4698			−0.632722			−0.316361	+	0.948639i	$0.602461\pi$
$524$	−10.8204	+	9.07941i	−0.472692	+	0.396636i
$525$	−9.41498	+	2.62662i	−0.410903	+	0.114635i
$526$	−1.19626	+	6.78430i	−0.0521592	+	0.295810i
$527$	5.73698	−	2.08809i	0.249907	−	0.0909586i
$528$	3.55775	−	9.11285i	0.154831	−	0.396586i
$529$	−3.95872	−	22.4510i	−0.172118	−	0.976131i
$530$	−18.0802			−0.785354
$531$	19.4592	+	0.901455i	0.844458	+	0.0391198i
$532$	−8.98321	+	1.08937i	−0.389472	+	0.0472303i
$533$	1.86981	+	0.680554i	0.0809903	+	0.0294781i
$534$	0.120945	−	5.22436i	0.00523381	−	0.226080i
$535$	−2.59328	+	0.943878i	−0.112117	+	0.0408074i
$536$	1.96130	−	11.1231i	0.0847153	−	0.480444i
$537$	0.480515	+	1.42176i	0.0207357	+	0.0613534i
$538$	−2.79421	−	15.8467i	−0.120467	−	0.683201i
$539$	−38.3904	+	9.45000i	−1.65359	+	0.407041i
$540$	−5.17417	−	7.11602i	−0.222661	−	0.306225i
$541$	−21.6356	−	37.4739i	−0.930186	−	1.61113i	−0.783001	−	0.622020i	$-0.786312\pi$
$541$	−21.6356	−	37.4739i	−0.930186	−	1.61113i	−0.147184	−	0.989109i	$-0.547021\pi$
$542$	−11.7461	−	4.27524i	−0.504539	−	0.183637i
$543$	4.84856	+	14.3460i	0.208072	+	0.615648i
$544$	1.80430	+	1.51398i	0.0773586	+	0.0649116i
$545$	10.5715	+	8.87054i	0.452833	+	0.379972i
$546$	0.860679	+	0.390635i	0.0368337	+	0.0167177i
$547$	−28.6878	−	10.4415i	−1.22660	−	0.446446i	−0.354169	−	0.935182i	$-0.615236\pi$
$547$	−28.6878	−	10.4415i	−1.22660	−	0.446446i	−0.872432	+	0.488736i	$0.837458\pi$
$548$	8.55712	−	14.8214i	0.365542	−	0.633137i
$549$	2.07688	−	9.25171i	0.0886391	−	0.394853i
$550$	−6.02357	−	10.4331i	−0.256846	−	0.444870i
$551$	−24.4371	−	8.89437i	−1.04105	−	0.378913i
$552$	0.283552	−	0.726292i	0.0120688	−	0.0309131i
$553$	−2.13866	+	39.6735i	−0.0909452	+	1.68709i
$554$	0.806140	−	4.57184i	0.0342496	−	0.194239i
$555$	2.34747	−	6.01283i	0.0996446	−	0.255231i
$556$	−0.796150	−	4.51519i	−0.0337643	−	0.191487i
$557$	3.09137	+	5.35442i	0.130986	+	0.226874i	0.924057	−	0.382255i	$-0.124852\pi$
$557$	3.09137	+	5.35442i	0.130986	+	0.226874i	−0.793071	+	0.609129i	$0.791519\pi$
$558$	0.994488	+	7.71230i	0.0421000	+	0.326488i
$559$	−0.731571	−	1.26712i	−0.0309422	−	0.0535934i
$560$	−1.30338	−	4.28607i	−0.0550779	−	0.181120i
$561$	20.2160	−	11.0559i	0.853519	−	0.466781i
$562$	2.23756	−	12.6899i	0.0943860	−	0.535289i
$563$	3.56982	−	20.2454i	0.150450	−	0.853244i	−0.812379	−	0.583130i	$-0.801828\pi$
$563$	3.56982	−	20.2454i	0.150450	−	0.853244i	0.962829	−	0.270113i	$-0.0870612\pi$
$564$	−15.5659	−	3.11778i	−0.655444	−	0.131282i
$565$	11.9460	−	10.0239i	0.502573	−	0.421709i
$566$	20.7563			0.872451
$567$	23.8024	−	0.668877i	0.999605	−	0.0280902i
$568$	0.168226			0.00705861
$569$	−17.4434	+	14.6367i	−0.731263	+	0.613603i	−0.930476	−	0.366354i	$-0.880606\pi$
$569$	−17.4434	+	14.6367i	−0.731263	+	0.613603i	0.199212	+	0.979956i	$0.436162\pi$
$570$	−9.83531	−	1.96996i	−0.411956	−	0.0825126i
$571$	0.635659	−	3.60500i	0.0266015	−	0.150865i	−0.968614	−	0.248570i	$-0.920039\pi$
$571$	0.635659	−	3.60500i	0.0266015	−	0.150865i	0.995215	+	0.0977057i	$0.0311504\pi$
$572$	−0.202290	+	1.14724i	−0.00845817	+	0.0479686i
$573$	6.97515	−	3.81464i	0.291391	−	0.159359i
$574$	24.8616	+	5.77890i	1.03770	+	0.241207i
$575$	−0.480078	−	0.831519i	−0.0200206	−	0.0346767i
$576$	−2.38491	+	1.81995i	−0.0993712	+	0.0758312i
$577$	−7.65418	−	13.2574i	−0.318648	−	0.551914i	0.661558	−	0.749894i	$-0.269895\pi$
$577$	−7.65418	−	13.2574i	−0.318648	−	0.551914i	−0.980206	+	0.197980i	$0.936562\pi$
$578$	−1.98868	−	11.2784i	−0.0827183	−	0.469119i
$579$	0.0667060	−	0.170861i	0.00277221	−	0.00710075i
$580$	2.23562	−	12.6788i	0.0928289	−	0.526459i
$581$	−12.1706	−	7.92954i	−0.504920	−	0.328973i
$582$	9.90779	−	25.3779i	0.410691	−	1.05195i
$583$	56.6725	+	20.6271i	2.34714	+	0.854288i
$584$	−6.70493	−	11.6133i	−0.277452	−	0.480561i
$585$	0.770570	+	0.709876i	0.0318591	+	0.0293497i
$586$	−16.2137	+	28.0830i	−0.669783	+	1.16010i
$587$	−16.2195	−	5.90342i	−0.669451	−	0.243660i	−0.0151398	−	0.999885i	$-0.504819\pi$
$587$	−16.2195	−	5.90342i	−0.669451	−	0.243660i	−0.654312	+	0.756225i	$0.727042\pi$
$588$	11.5634	+	3.64535i	0.476865	+	0.150332i
$589$	6.79126	+	5.69854i	0.279829	+	0.234804i
$590$	8.42247	+	7.06729i	0.346748	+	0.290956i
$591$	−7.98957	−	23.6397i	−0.328647	−	0.972409i
$592$	−2.06821	−	0.752765i	−0.0850027	−	0.0309385i
$593$	−13.1849	−	22.8369i	−0.541438	−	0.937798i	−0.998822	−	0.0485288i	$-0.984547\pi$
$593$	−13.1849	−	22.8369i	−0.541438	−	0.937798i	0.457384	−	0.889269i	$-0.348787\pi$
$594$	8.10003	+	28.2082i	0.332348	+	1.15740i
$595$	4.13736	−	9.70664i	0.169615	−	0.397934i
$596$	0.486113	+	2.75688i	0.0199119	+	0.112926i
$597$	1.00302	+	2.96777i	0.0410510	+	0.121463i
$598$	−0.0161225	+	0.0914350i	−0.000659296	+	0.00373906i
$599$	−10.8417	+	3.94606i	−0.442981	+	0.161232i	−0.553874	−	0.832601i	$-0.686851\pi$
$599$	−10.8417	+	3.94606i	−0.442981	+	0.161232i	0.110893	+	0.993832i	$0.464629\pi$
$600$	−0.0855038	+	3.69343i	−0.00349068	+	0.150783i
$601$	−40.3357	−	14.6810i	−1.64533	−	0.598850i	−0.657369	−	0.753569i	$-0.728331\pi$
$601$	−40.3357	−	14.6810i	−1.64533	−	0.598850i	−0.987959	+	0.154718i	$0.950553\pi$
$602$	−11.2728	−	15.0061i	−0.459444	−	0.611603i
$603$	15.5659	+	30.0970i	0.633894	+	1.22565i
$604$	−10.3479			−0.421051
$605$	−6.14532	−	34.8518i	−0.249843	−	1.41693i
$606$	1.77069	−	4.53545i	0.0719292	−	0.184240i
$607$	14.3124	−	5.20929i	0.580922	−	0.211438i	−0.0348098	−	0.999394i	$-0.511083\pi$
$607$	14.3124	−	5.20929i	0.580922	−	0.211438i	0.615732	+	0.787955i	$0.288860\pi$
$608$	−0.593913	+	3.36825i	−0.0240864	+	0.136601i
$609$	24.8896	+	24.3838i	1.00858	+	0.988081i
$610$	4.09965	−	3.44001i	0.165990	−	0.139282i
$611$	1.89043			0.0764787
$612$	−7.05846	−	0.326985i	−0.285321	−	0.0132176i
$613$	−6.12589			−0.247422			−0.123711	−	0.992318i	$-0.539480\pi$
$613$	−6.12589			−0.247422			−0.123711	+	0.992318i	$0.539480\pi$
$614$	−0.352763	−	2.00062i	−0.0142364	−	0.0807385i
$615$	24.1687	+	14.7099i	0.974575	+	0.593161i
$616$	−0.804379	+	14.9217i	−0.0324093	+	0.601212i
$617$	31.7447	−	11.5541i	1.27799	−	0.465151i	0.388225	−	0.921565i	$-0.373089\pi$
$617$	31.7447	−	11.5541i	1.27799	−	0.465151i	0.889768	+	0.456414i	$0.150866\pi$
$618$	4.76099	+	14.0869i	0.191515	+	0.566660i
$619$	−26.1402	−	9.51425i	−1.05066	−	0.382410i	−0.241750	−	0.970339i	$-0.577721\pi$
$619$	−26.1402	−	9.51425i	−1.05066	−	0.382410i	−0.808913	+	0.587929i	$0.799944\pi$
$620$	−2.19447	+	3.80093i	−0.0881320	+	0.152649i
$621$	0.645570	+	2.24819i	0.0259058	+	0.0902168i
$622$	0.996856			0.0399703
$623$	2.32244	+	7.63716i	0.0930465	+	0.305976i
$624$	0.235904	−	0.268277i	0.00944374	−	0.0107397i
$625$	−7.49618	−	6.29004i	−0.299847	−	0.251602i
$626$	−24.4115	+	8.88506i	−0.975680	+	0.355118i
$627$	28.5814	+	17.3956i	1.14143	+	0.694715i
$628$	2.97841	+	16.8914i	0.118852	+	0.674041i
$629$	−2.59198	−	4.48944i	−0.103349	−	0.179006i
$630$	10.9089	+	7.84979i	0.434620	+	0.312743i
$631$	−15.4352	+	26.7346i	−0.614467	+	1.06429i	0.376011	+	0.926615i	$0.377295\pi$
$631$	−15.4352	+	26.7346i	−0.614467	+	1.06429i	−0.990478	+	0.137672i	$0.956038\pi$
$632$	14.1113	+	5.13609i	0.561317	+	0.204303i
$633$	10.3340	+	12.9110i	0.410740	+	0.513167i
$634$	26.4370	+	22.1833i	1.04995	+	0.881012i
$635$	−13.4385	+	4.89121i	−0.533290	+	0.194102i
$636$	−11.5571	−	14.4391i	−0.458269	−	0.572549i
$637$	−1.43542	−	0.155208i	−0.0568734	−	0.00614958i
$638$	−21.4724	+	37.1912i	−0.850099	+	1.47242i
$639$	−0.401203	+	0.306163i	−0.0158714	+	0.0121116i
$640$	−1.69323			−0.0669308
$641$	11.7763	−	9.88146i	0.465134	−	0.390294i	−0.379882	−	0.925035i	$-0.624035\pi$
$641$	11.7763	−	9.88146i	0.465134	−	0.390294i	0.845016	+	0.534741i	$0.179591\pi$
$642$	−2.41145	−	1.46770i	−0.0951725	−	0.0579254i
$643$	−13.4996	−	11.3275i	−0.532373	−	0.446714i	0.336547	−	0.941667i	$-0.390741\pi$
$643$	−13.4996	−	11.3275i	−0.532373	−	0.446714i	−0.868920	+	0.494953i	$0.835185\pi$
$644$	−0.0641088	+	1.18926i	−0.00252624	+	0.0468632i
$645$	−6.66121	−	19.7093i	−0.262285	−	0.776054i
$646$	−6.17107	+	5.17815i	−0.242798	+	0.203731i
$647$	3.41059	−	5.90731i	0.134084	−	0.232240i	−0.791163	−	0.611605i	$-0.790524\pi$
$647$	3.41059	−	5.90731i	0.134084	−	0.232240i	0.925247	+	0.379365i	$0.123857\pi$
$648$	2.37557	−	8.68082i	0.0933212	−	0.341015i
$649$	−18.3374	−	31.7614i	−0.719808	−	1.24674i
$650$	−0.0763942	−	0.433253i	−0.00299643	−	0.0169936i
$651$	−5.13022	−	10.7133i	−0.201069	−	0.419886i
$652$	18.7800	−	6.83537i	0.735483	−	0.267694i
$653$	3.61832	−	20.5205i	0.141596	−	0.803030i	−0.828442	−	0.560075i	$-0.810772\pi$
$653$	3.61832	−	20.5205i	0.141596	−	0.803030i	0.970038	−	0.242955i	$-0.0781166\pi$
$654$	−0.326713	+	14.1127i	−0.0127755	+	0.551851i
$655$	18.3215	−	15.3735i	0.715878	−	0.600693i
$656$	4.82365	−	8.35481i	0.188332	−	0.326201i
$657$	37.1262	+	15.4940i	1.44843	+	0.604477i
$658$	24.0733	−	2.91931i	0.938474	−	0.113806i
$659$	−21.5752	+	18.1037i	−0.840449	+	0.705220i	−0.957665	−	0.287886i	$-0.907048\pi$
$659$	−21.5752	+	18.1037i	−0.840449	+	0.705220i	0.117216	+	0.993106i	$0.462603\pi$
$660$	−6.02409	+	15.4302i	−0.234487	+	0.600618i
$661$	31.4180	+	26.3628i	1.22202	+	1.02539i	0.998717	+	0.0506451i	$0.0161277\pi$
$661$	31.4180	+	26.3628i	1.22202	+	1.02539i	0.223301	+	0.974750i	$0.428317\pi$
$662$	19.4667	+	16.3345i	0.756595	+	0.634858i
$663$	0.831809	−	0.126896i	0.0323048	−	0.00492823i
$664$	−4.20578	+	3.52907i	−0.163216	+	0.136954i
$665$	15.2106	−	1.84456i	0.589844	−	0.0715289i
$666$	6.30247	−	1.96875i	0.244216	−	0.0762877i
$667$	−1.71134	+	2.96413i	−0.0662635	+	0.114772i
$668$	−9.33758	+	7.83516i	−0.361282	+	0.303152i
$669$	1.29621	+	0.788921i	0.0501145	+	0.0305015i
$670$	−3.32093	+	18.8340i	−0.128299	+	0.727619i
$671$	−16.7750	+	6.10559i	−0.647591	+	0.235704i
$672$	2.58978	−	3.78061i	0.0999031	−	0.145840i
$673$	−1.27652	−	7.23951i	−0.0492063	−	0.279063i	0.950270	−	0.311428i	$-0.100807\pi$
$673$	−1.27652	−	7.23951i	−0.0492063	−	0.279063i	−0.999476	+	0.0323651i	$0.989696\pi$
$674$	7.78643	+	13.4865i	0.299922	+	0.519480i
$675$	−6.51793	−	8.96409i	−0.250875	−	0.345028i
$676$	6.47873	−	11.2215i	0.249182	−	0.431596i
$677$	−32.5714	+	27.3307i	−1.25182	+	1.05040i	−0.255317	+	0.966857i	$0.582180\pi$
$677$	−32.5714	+	27.3307i	−1.25182	+	1.05040i	−0.996504	+	0.0835456i	$0.973376\pi$
$678$	15.6413	+	3.13287i	0.600701	+	0.120317i
$679$	−2.24007	+	41.5546i	−0.0859661	+	1.59472i
$680$	−3.05509	−	2.56352i	−0.117157	−	0.0983067i
$681$	−0.558963	+	24.1450i	−0.0214195	+	0.925238i
$682$	11.2149	−	9.41044i	0.429442	−	0.360344i
$683$	−11.8099			−0.451895			−0.225947	−	0.974139i	$-0.572548\pi$
$683$	−11.8099			−0.451895			−0.225947	+	0.974139i	$0.572548\pi$
$684$	−4.71361	−	9.11386i	−0.180230	−	0.348477i
$685$	−14.4892	+	25.0960i	−0.553603	+	0.958868i
$686$	−18.5187	+	0.240188i	−0.707047	+	0.00917044i
$687$	−34.9980	+	5.33909i	−1.33526	+	0.203699i
$688$	−6.66603	+	2.42624i	−0.254140	+	0.0924995i
$689$	1.68712	+	1.41566i	0.0642742	+	0.0539325i
$690$	−0.480119	+	1.22978i	−0.0182778	+	0.0468169i
$691$	−12.8891	−	4.69125i	−0.490325	−	0.178464i	0.0850124	−	0.996380i	$-0.472907\pi$
$691$	−12.8891	−	4.69125i	−0.490325	−	0.178464i	−0.575337	+	0.817916i	$0.695129\pi$
$692$	12.7454	−	22.0757i	0.484507	−	0.839191i
$693$	−25.2384	−	37.0508i	−0.958726	−	1.40744i
$694$	−12.7488	−	22.0815i	−0.483936	−	0.838202i
$695$	1.34807	+	7.64526i	0.0511351	+	0.290001i
$696$	11.5545	−	6.31906i	0.437973	−	0.239523i
$697$	21.3524	−	7.77162i	0.808778	−	0.294371i
$698$	−0.857498	−	0.719526i	−0.0324568	−	0.0272345i
$699$	−41.3521	−	8.28261i	−1.56408	−	0.313277i
$700$	−1.64188	−	5.39919i	−0.0620571	−	0.204070i
$701$	3.51937			0.132925			0.0664624	−	0.997789i	$-0.478829\pi$
$701$	3.51937			0.132925			0.0664624	+	0.997789i	$0.478829\pi$
$702$	−0.0743596	+	1.06915i	−0.00280652	+	0.0403525i
$703$	3.76384	−	6.51916i	0.141956	−	0.245875i
$704$	5.30744	+	1.93175i	0.200032	+	0.0728056i
$705$	26.3567	+	5.27912i	0.992652	+	0.198823i
$706$	−18.2649	+	6.64788i	−0.687408	+	0.250196i
$707$	−0.400338	+	7.42650i	−0.0150562	+	0.279302i
$708$	−0.260297	+	11.2438i	−0.00978257	+	0.422569i
$709$	−2.83688	−	16.0888i	−0.106541	−	0.604226i	−0.990593	−	0.136838i	$-0.956306\pi$
$709$	−2.83688	−	16.0888i	−0.106541	−	0.604226i	0.884052	−	0.467388i	$-0.154805\pi$
$710$	−0.284845			−0.0106901
$711$	−43.0016	+	13.4327i	−1.61269	+	0.503767i
$712$	3.01709			0.113070
$713$	0.893827	−	0.750010i	0.0334741	−	0.0280881i
$714$	10.3965	−	2.90045i	0.389080	−	0.108547i
$715$	0.342523	−	1.94255i	0.0128096	−	0.0726471i
$716$	−0.814211	+	0.296349i	−0.0304285	+	0.0110751i
$717$	−30.0200	+	4.57968i	−1.12112	+	0.171031i
$718$	1.16523	+	6.60832i	0.0434858	+	0.246620i
$719$	17.9244			0.668469			0.334234	−	0.942490i	$-0.391522\pi$
$719$	17.9244			0.668469			0.334234	+	0.942490i	$0.391522\pi$
$720$	4.03820	−	3.08159i	0.150495	−	0.114844i
$721$	−13.6424	−	18.1605i	−0.508071	−	0.676333i
$722$	6.86179	+	2.49749i	0.255369	+	0.0929468i
$723$	3.97046	+	2.41656i	0.147663	+	0.0898730i
$724$	−8.21569	+	2.99027i	−0.305334	+	0.111132i
$725$	2.81622	−	15.9716i	0.104592	−	0.593169i
$726$	23.9050	−	27.1855i	0.887199	−	1.00895i
$727$	2.59174	+	14.6985i	0.0961224	+	0.545137i	0.994398	+	0.105704i	$0.0337096\pi$
$727$	2.59174	+	14.6985i	0.0961224	+	0.545137i	−0.898275	+	0.439433i	$0.855179\pi$
$728$	−0.213972	+	0.502000i	−0.00793035	+	0.0186054i
$729$	10.1331	+	25.0264i	0.375302	+	0.926903i
$730$	11.3530	+	19.6639i	0.420193	+	0.727795i
$731$	−15.7008	−	5.71462i	−0.580715	−	0.211363i
$732$	5.36780	+	1.07514i	0.198400	+	0.0397384i
$733$	32.7380	+	27.4705i	1.20921	+	1.01464i	0.999318	+	0.0369194i	$0.0117545\pi$
$733$	32.7380	+	27.4705i	1.20921	+	1.01464i	0.209888	+	0.977725i	$0.432690\pi$
$734$	20.0411	+	16.8165i	0.739731	+	0.620708i
$735$	−19.5794	−	6.17242i	−0.722198	−	0.227673i
$736$	0.423002	+	0.153960i	0.0155920	+	0.00567504i
$737$	31.8965	−	55.2464i	1.17492	−	2.03503i
$738$	3.70137	+	28.7042i	0.136249	+	1.05662i
$739$	−24.0485	−	41.6532i	−0.884637	−	1.53224i	−0.846129	−	0.532978i	$-0.821073\pi$
$739$	−24.0485	−	41.6532i	−0.884637	−	1.53224i	−0.0385081	−	0.999258i	$-0.512261\pi$
$740$	3.50195	+	1.27460i	0.128734	+	0.0468554i
$741$	0.763518	+	0.953918i	0.0280485	+	0.0350431i
$742$	23.6704	+	15.4221i	0.868968	+	0.566163i
$743$	−0.0795008	+	0.450871i	−0.00291660	+	0.0165409i	−0.986231	−	0.165372i	$-0.947118\pi$
$743$	−0.0795008	+	0.450871i	−0.00291660	+	0.0165409i	0.983315	+	0.181912i	$0.0582288\pi$
$744$	−4.43821	+	0.677067i	−0.162713	+	0.0248225i
$745$	−0.823100	−	4.66803i	−0.0301561	−	0.171024i
$746$	12.5518	+	21.7404i	0.459556	+	0.795974i
$747$	3.60767	−	16.0708i	0.131998	−	0.588000i
$748$	6.65156	+	11.5208i	0.243205	+	0.421243i
$749$	4.20021	+	0.976309i	0.153472	+	0.0356736i
$750$	0.484157	−	20.9137i	0.0176789	−	0.763660i
$751$	−3.25424	+	18.4557i	−0.118749	+	0.673458i	0.866077	+	0.499911i	$0.166634\pi$
$751$	−3.25424	+	18.4557i	−0.118749	+	0.673458i	−0.984826	+	0.173547i	$0.944477\pi$
$752$	1.59157	−	9.02625i	0.0580387	−	0.329154i
$753$	−6.97696	−	20.6436i	−0.254254	−	0.752294i
$754$	−1.20135	+	1.00805i	−0.0437506	+	0.0367111i
$755$	17.5214			0.637669
$756$	0.704126	+	13.7297i	0.0256088	+	0.499344i
$757$	1.36049			0.0494477			0.0247239	−	0.999694i	$-0.492129\pi$
$757$	1.36049			0.0494477			0.0247239	+	0.999694i	$0.492129\pi$
$758$	−28.9395	+	24.2831i	−1.05113	+	0.882002i
$759$	2.90795	−	3.30700i	0.105552	−	0.120037i
$760$	1.00563	−	5.70322i	0.0364781	−	0.206878i
$761$	0.254885	−	1.44553i	0.00923959	−	0.0524003i	−0.979839	−	0.199787i	$-0.935975\pi$
$761$	0.254885	−	1.44553i	0.00923959	−	0.0524003i	0.989079	+	0.147387i	$0.0470861\pi$
$762$	−12.4963	−	7.60566i	−0.452692	−	0.275524i
$763$	−6.27368	−	20.6305i	−0.227122	−	0.746875i
$764$	2.29500	+	3.97505i	0.0830301	+	0.143812i
$765$	11.9516	+	0.553662i	0.432111	+	0.0200177i
$766$	−3.02784	−	5.24438i	−0.109400	−	0.189487i
$767$	−0.232565	−	1.31894i	−0.00839744	−	0.0476242i
$768$	−1.08233	−	1.35224i	−0.0390554	−	0.0487947i
$769$	−0.415270

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)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.69832 - 0.340165i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.294026 + 1.66751i) q^{5} +(-1.51964 + 0.831077i) q^{6} +(1.80729 - 1.93228i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.76858 + 1.15542i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.69832 - 0.340165i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.294026 + 1.66751i) q^{5} +(-1.51964 + 0.831077i) q^{6} +(1.80729 - 1.93228i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.76858 + 1.15542i) q^{9} +(0.846615 + 1.46638i) q^{10} +(-0.980775 - 5.56225i) q^{11} +(-0.629907 + 1.61345i) q^{12} +(0.0358158 - 0.203122i) q^{13} +(0.142417 - 2.64192i) q^{14} +(1.06658 - 2.73194i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.17767 - 2.03979i) q^{17} +(2.86354 - 0.894506i) q^{18} +(1.71011 - 2.96199i) q^{19} +(1.59112 + 0.579119i) q^{20} +(-3.72665 + 2.66685i) q^{21} +(-4.32666 - 3.63050i) q^{22} +(-0.344834 - 0.289350i) q^{23} +(0.554568 + 1.64087i) q^{24} +(2.00434 + 0.729519i) q^{25} +(-0.103128 - 0.178622i) q^{26} +(-4.30889 - 2.90404i) q^{27} +(-1.58909 - 2.11537i) q^{28} +(-1.32033 - 7.48794i) q^{29} +(-0.939012 - 2.77837i) q^{30} +(-0.450105 + 2.55267i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.226412 + 9.78010i) q^{33} +(-2.21330 - 0.805575i) q^{34} +(2.69070 + 3.58181i) q^{35} +(1.61862 - 2.52588i) q^{36} +2.20094 q^{37} +(-0.593913 - 3.36825i) q^{38} +(-0.129922 + 0.332782i) q^{39} +(1.59112 - 0.579119i) q^{40} +(-1.67524 + 9.50074i) q^{41} +(-1.14056 + 4.43837i) q^{42} +(5.43420 - 4.55984i) q^{43} -5.64806 q^{44} +(-2.74070 + 4.27689i) q^{45} -0.450149 q^{46} +(1.59157 + 9.02625i) q^{47} +(1.47955 + 0.900510i) q^{48} +(-0.467419 - 6.98438i) q^{49} +(2.00434 - 0.729519i) q^{50} +(1.30620 + 3.86481i) q^{51} +(-0.193816 - 0.0705434i) q^{52} +(-5.33897 + 9.24737i) q^{53} +(-5.16748 + 0.545083i) q^{54} +9.56346 q^{55} +(-2.57705 - 0.599017i) q^{56} +(-3.91187 + 4.44869i) q^{57} +(-5.82458 - 4.88741i) q^{58} +(6.10176 - 2.22086i) q^{59} +(-2.50523 - 1.52477i) q^{60} +(-0.548842 - 3.11264i) q^{61} +(1.29602 + 2.24478i) q^{62} +(7.23620 - 3.26150i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.328176 + 0.119446i) q^{65} +(6.11309 + 7.63753i) q^{66} +(8.65223 + 7.26008i) q^{67} +(-2.21330 + 0.805575i) q^{68} +(0.487212 + 0.608709i) q^{69} +(4.36354 + 1.01427i) q^{70} +(-0.0841130 + 0.145688i) q^{71} +(-0.383668 - 2.97537i) q^{72} +13.4099 q^{73} +(1.68602 - 1.41474i) q^{74} +(-3.15585 - 1.92076i) q^{75} +(-2.62003 - 2.19847i) q^{76} +(-12.5204 - 8.15746i) q^{77} +(0.114383 + 0.338438i) q^{78} +(-11.5036 + 9.65270i) q^{79} +(0.846615 - 1.46638i) q^{80} +(6.33003 + 6.39771i) q^{81} +(4.82365 + 8.35481i) q^{82} +(-0.953373 - 5.40684i) q^{83} +(1.97921 + 4.13312i) q^{84} +(3.74762 - 1.36402i) q^{85} +(1.23183 - 6.98607i) q^{86} +(-0.304797 + 13.1660i) q^{87} +(-4.32666 + 3.63050i) q^{88} +(-1.50855 + 2.61288i) q^{89} +(0.649639 + 5.03798i) q^{90} +(-0.327759 - 0.436306i) q^{91} +(-0.344834 + 0.289350i) q^{92} +(1.63275 - 4.18214i) q^{93} +(7.02118 + 5.89147i) q^{94} +(4.43632 + 3.72251i) q^{95} +(1.71224 - 0.261209i) q^{96} +(-12.0491 + 10.1104i) q^{97} +(-4.84753 - 5.04989i) q^{98} +(3.71136 - 16.5327i) 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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