LMFDB - Embedded newform 162.2.g.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	162.7
Dual form			162.2.g.a.139.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.597159 - 0.802123i) q^{2} +(1.64484 - 0.542681i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-1.45045 + 0.953973i) q^{5} +(-1.41753 - 0.995298i) q^{6} +(2.66288 - 2.82248i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.41100 - 1.78525i) q^{9} +O(q^{10})$	\(q+(-0.597159 - 0.802123i) q^{2} +(1.64484 - 0.542681i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-1.45045 + 0.953973i) q^{5} +(-1.41753 - 0.995298i) q^{6} +(2.66288 - 2.82248i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.41100 - 1.78525i) q^{9} +(1.63135 + 0.593763i) q^{10} +(1.28498 - 0.645340i) q^{11} +(0.0481371 + 1.73138i) q^{12} +(-0.271082 - 0.628438i) q^{13} +(-3.85414 - 0.450484i) q^{14} +(-1.86805 + 2.35626i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(-4.76609 + 3.99923i) q^{17} +(-2.87173 - 0.867840i) q^{18} +(1.04702 + 0.878553i) q^{19} +(-0.497904 - 1.66311i) q^{20} +(2.84830 - 6.08763i) q^{21} +(-1.28498 - 0.645340i) q^{22} +(0.559525 + 0.593062i) q^{23} +(1.36004 - 1.07252i) q^{24} +(-0.786670 + 1.82371i) q^{25} +(-0.342206 + 0.592718i) q^{26} +(2.99688 - 4.24484i) q^{27} +(1.94019 + 3.36051i) q^{28} +(-2.07235 + 0.242223i) q^{29} +(3.00553 + 0.0913425i) q^{30} +(-4.68397 + 1.11012i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(1.76337 - 1.75881i) q^{33} +(6.05398 + 1.43482i) q^{34} +(-1.16978 + 6.63418i) q^{35} +(1.01877 + 2.82172i) q^{36} +(1.22447 + 6.94432i) q^{37} +(0.0794716 - 1.36447i) q^{38} +(-0.786927 - 0.886569i) q^{39} +(-1.03670 + 1.39252i) q^{40} +(3.89565 - 5.23277i) q^{41} +(-6.58391 + 1.35059i) q^{42} +(-0.738710 + 12.6832i) q^{43} +(0.249693 + 1.41608i) q^{44} +(-1.79394 + 4.88943i) q^{45} +(0.141583 - 0.802960i) q^{46} +(-11.7680 - 2.78906i) q^{47} +(-1.67245 - 0.450451i) q^{48} +(-0.468492 - 8.04370i) q^{49} +(1.93260 - 0.458036i) q^{50} +(-5.66915 + 9.16455i) q^{51} +(0.679784 - 0.0794554i) q^{52} +(0.343696 + 0.595300i) q^{53} +(-5.19450 + 0.130976i) q^{54} +(-1.24815 + 2.16186i) q^{55} +(1.53694 - 3.56303i) q^{56} +(2.19895 + 0.876882i) q^{57} +(1.43181 + 1.51763i) q^{58} +(13.5557 + 6.80793i) q^{59} +(-1.72151 - 2.46535i) q^{60} +(-4.19072 - 13.9980i) q^{61} +(3.68753 + 3.09420i) q^{62} +(1.38136 - 11.5589i) q^{63} +(0.766044 - 0.642788i) q^{64} +(0.992703 + 0.652911i) q^{65} +(-2.46380 - 0.364148i) q^{66} +(-8.84227 - 1.03351i) q^{67} +(-2.46429 - 5.71286i) q^{68} +(1.24217 + 0.671848i) q^{69} +(6.01997 - 3.02334i) q^{70} +(4.58515 + 1.66886i) q^{71} +(1.65500 - 2.50219i) q^{72} +(9.38954 - 3.41751i) q^{73} +(4.83899 - 5.12903i) q^{74} +(-0.304256 + 3.42662i) q^{75} +(-1.14193 + 0.751061i) q^{76} +(1.60027 - 5.34529i) q^{77} +(-0.241217 + 1.16064i) q^{78} +(-3.68901 - 4.95520i) q^{79} +1.73605 q^{80} +(2.62580 - 8.60844i) q^{81} -6.52365 q^{82} +(4.45274 + 5.98107i) q^{83} +(5.01498 + 4.47459i) q^{84} +(3.09780 - 10.3474i) q^{85} +(10.6146 - 6.98132i) q^{86} +(-3.27723 + 1.52304i) q^{87} +(0.986764 - 1.04591i) q^{88} +(-6.11142 + 2.22437i) q^{89} +(4.99319 - 1.48080i) q^{90} +(-2.49562 - 0.908330i) q^{91} +(-0.728620 + 0.365927i) q^{92} +(-7.10194 + 4.36787i) q^{93} +(4.79017 + 11.1049i) q^{94} +(-2.35676 - 0.275466i) q^{95} +(0.637402 + 1.61050i) q^{96} +(-7.98430 - 5.25136i) q^{97} +(-6.17228 + 5.17916i) q^{98} +(1.94598 - 3.84991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	−0.597159	−	0.802123i	−0.422255	−	0.567187i
$2$	−0.597159	−	0.802123i	−0.422255	−	0.567187i
$3$	1.64484	−	0.542681i	0.949649	−	0.313317i
$3$	1.64484	−	0.542681i	0.949649	−	0.313317i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	−1.45045	+	0.953973i	−0.648659	+	0.426630i	−0.830745	−	0.556653i	$-0.812085\pi$
$5$	−1.45045	+	0.953973i	−0.648659	+	0.426630i	0.182086	+	0.983283i	$0.441715\pi$
$6$	−1.41753	−	0.995298i	−0.578703	−	0.406329i
$7$	2.66288	−	2.82248i	1.00647	−	1.06680i	0.00870908	−	0.999962i	$-0.497228\pi$
$7$	2.66288	−	2.82248i	1.00647	−	1.06680i	0.997764	−	0.0668370i	$-0.0212907\pi$
$8$	0.939693	−	0.342020i	0.332232	−	0.120922i
$9$	2.41100	−	1.78525i	0.803665	−	0.595082i
$10$	1.63135	+	0.593763i	0.515878	+	0.187764i
$11$	1.28498	−	0.645340i	0.387435	−	0.194577i	−0.244410	−	0.969672i	$-0.578594\pi$
$11$	1.28498	−	0.645340i	0.387435	−	0.194577i	0.631845	+	0.775095i	$0.282298\pi$
$12$	0.0481371	+	1.73138i	0.0138960	+	0.499807i
$13$	−0.271082	−	0.628438i	−0.0751846	−	0.174297i	0.876479	−	0.481440i	$-0.159886\pi$
$13$	−0.271082	−	0.628438i	−0.0751846	−	0.174297i	−0.951663	+	0.307143i	$0.900627\pi$
$14$	−3.85414	−	0.450484i	−1.03006	−	0.120397i
$15$	−1.86805	+	2.35626i	−0.482328	+	0.608384i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	−4.76609	+	3.99923i	−1.15595	+	0.969955i	−0.999842	−	0.0177857i	$-0.994338\pi$
$17$	−4.76609	+	3.99923i	−1.15595	+	0.969955i	−0.156105	+	0.987740i	$0.549894\pi$
$18$	−2.87173	−	0.867840i	−0.676874	−	0.204552i
$19$	1.04702	+	0.878553i	0.240203	+	0.201554i	0.754940	−	0.655794i	$-0.227666\pi$
$19$	1.04702	+	0.878553i	0.240203	+	0.201554i	−0.514737	+	0.857348i	$0.672110\pi$
$20$	−0.497904	−	1.66311i	−0.111335	−	0.371884i
$21$	2.84830	−	6.08763i	0.621550	−	1.32843i
$22$	−1.28498	−	0.645340i	−0.273958	−	0.137587i
$23$	0.559525	+	0.593062i	0.116669	+	0.123662i	0.783075	−	0.621927i	$-0.213650\pi$
$23$	0.559525	+	0.593062i	0.116669	+	0.123662i	−0.666406	+	0.745589i	$0.732168\pi$
$24$	1.36004	−	1.07252i	0.277616	−	0.218928i
$25$	−0.786670	+	1.82371i	−0.157334	+	0.364741i
$26$	−0.342206	+	0.592718i	−0.0671121	+	0.116242i
$27$	2.99688	−	4.24484i	0.576750	−	0.816921i
$28$	1.94019	+	3.36051i	0.366661	+	0.635076i
$29$	−2.07235	+	0.242223i	−0.384826	+	0.0449797i	−0.306307	−	0.951933i	$-0.599093\pi$
$29$	−2.07235	+	0.242223i	−0.384826	+	0.0449797i	−0.0785192	+	0.996913i	$0.525019\pi$
$30$	3.00553	+	0.0913425i	0.548733	+	0.0166768i
$31$	−4.68397	+	1.11012i	−0.841266	+	0.199384i	−0.628588	−	0.777739i	$-0.716367\pi$
$31$	−4.68397	+	1.11012i	−0.841266	+	0.199384i	−0.212678	+	0.977122i	$0.568219\pi$
$32$	0.0581448	+	0.998308i	0.0102787	+	0.176478i
$33$	1.76337	−	1.75881i	0.306963	−	0.306170i
$34$	6.05398	+	1.43482i	1.03825	+	0.246070i
$35$	−1.16978	+	6.63418i	−0.197730	+	1.12138i
$36$	1.01877	+	2.82172i	0.169794	+	0.470287i
$37$	1.22447	+	6.94432i	0.201302	+	1.14164i	0.903154	+	0.429316i	$0.141245\pi$
$37$	1.22447	+	6.94432i	0.201302	+	1.14164i	−0.701853	+	0.712322i	$0.747643\pi$
$38$	0.0794716	−	1.36447i	0.0128920	−	0.221347i
$39$	−0.786927	−	0.886569i	−0.126009	−	0.141965i
$40$	−1.03670	+	1.39252i	−0.163916	+	0.220177i
$41$	3.89565	−	5.23277i	0.608399	−	0.817222i	−0.386046	−	0.922480i	$-0.626159\pi$
$41$	3.89565	−	5.23277i	0.608399	−	0.817222i	0.994445	+	0.105258i	$0.0335668\pi$
$42$	−6.58391	+	1.35059i	−1.01592	+	0.208401i
$43$	−0.738710	+	12.6832i	−0.112652	+	1.93416i	0.191408	+	0.981511i	$0.438695\pi$
$43$	−0.738710	+	12.6832i	−0.112652	+	1.93416i	−0.304060	+	0.952653i	$0.598342\pi$
$44$	0.249693	+	1.41608i	0.0376427	+	0.213482i
$45$	−1.79394	+	4.88943i	−0.267425	+	0.728873i
$46$	0.141583	−	0.802960i	0.0208753	−	0.118390i
$47$	−11.7680	−	2.78906i	−1.71653	−	0.406826i	−0.749607	−	0.661883i	$-0.769758\pi$
$47$	−11.7680	−	2.78906i	−1.71653	−	0.406826i	−0.966926	+	0.255057i	$0.917906\pi$
$48$	−1.67245	−	0.450451i	−0.241398	−	0.0650170i
$49$	−0.468492	−	8.04370i	−0.0669275	−	1.14910i
$50$	1.93260	−	0.458036i	0.273312	−	0.0647760i
$51$	−5.66915	+	9.16455i	−0.793840	+	1.28329i
$52$	0.679784	−	0.0794554i	0.0942691	−	0.0110185i
$53$	0.343696	+	0.595300i	0.0472103	+	0.0817707i	0.888665	−	0.458557i	$-0.151634\pi$
$53$	0.343696	+	0.595300i	0.0472103	+	0.0817707i	−0.841455	+	0.540328i	$0.818300\pi$
$54$	−5.19450	+	0.130976i	−0.706882	+	0.0178236i
$55$	−1.24815	+	2.16186i	−0.168301	+	0.291506i
$56$	1.53694	−	3.56303i	0.205382	−	0.476129i
$57$	2.19895	+	0.876882i	0.291258	+	0.116146i
$58$	1.43181	+	1.51763i	0.188006	+	0.199275i
$59$	13.5557	+	6.80793i	1.76480	+	0.886316i	0.953334	+	0.301918i	$0.0976270\pi$
$59$	13.5557	+	6.80793i	1.76480	+	0.886316i	0.811467	+	0.584398i	$0.198669\pi$
$60$	−1.72151	−	2.46535i	−0.222246	−	0.318276i
$61$	−4.19072	−	13.9980i	−0.536566	−	1.79226i	−0.606955	−	0.794736i	$-0.707609\pi$
$61$	−4.19072	−	13.9980i	−0.536566	−	1.79226i	0.0703885	−	0.997520i	$-0.477576\pi$
$62$	3.68753	+	3.09420i	0.468316	+	0.392964i
$63$	1.38136	−	11.5589i	0.174034	−	1.45628i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	0.992703	+	0.652911i	0.123130	+	0.0809836i
$66$	−2.46380	−	0.364148i	−0.303272	−	0.0448235i
$67$	−8.84227	−	1.03351i	−1.08026	−	0.126264i	−0.442701	−	0.896669i	$-0.645980\pi$
$67$	−8.84227	−	1.03351i	−1.08026	−	0.126264i	−0.637554	+	0.770406i	$0.720054\pi$
$68$	−2.46429	−	5.71286i	−0.298839	−	0.692786i
$69$	1.24217	+	0.671848i	0.149540	+	0.0808810i
$70$	6.01997	−	3.02334i	0.719524	−	0.361359i
$71$	4.58515	+	1.66886i	0.544157	+	0.198057i	0.599449	−	0.800413i	$-0.295387\pi$
$71$	4.58515	+	1.66886i	0.544157	+	0.198057i	−0.0552913	+	0.998470i	$0.517609\pi$
$72$	1.65500	−	2.50219i	0.195044	−	0.294886i
$73$	9.38954	−	3.41751i	1.09896	−	0.399990i	0.272029	−	0.962289i	$-0.412305\pi$
$73$	9.38954	−	3.41751i	1.09896	−	0.399990i	0.826934	+	0.562300i	$0.190083\pi$
$74$	4.83899	−	5.12903i	0.562522	−	0.596238i
$75$	−0.304256	+	3.42662i	−0.0351325	+	0.395672i
$76$	−1.14193	+	0.751061i	−0.130989	+	0.0861526i
$77$	1.60027	−	5.34529i	0.182368	−	0.609152i
$78$	−0.241217	+	1.16064i	−0.0273125	+	0.131416i
$79$	−3.68901	−	4.95520i	−0.415046	−	0.557504i	0.544607	−	0.838692i	$-0.316679\pi$
$79$	−3.68901	−	4.95520i	−0.415046	−	0.557504i	−0.959653	+	0.281188i	$0.909272\pi$
$80$	1.73605			0.194096
$81$	2.62580	−	8.60844i	0.291755	−	0.956493i
$82$	−6.52365			−0.720417
$83$	4.45274	+	5.98107i	0.488752	+	0.656508i	0.976258	−	0.216612i	$-0.0695006\pi$
$83$	4.45274	+	5.98107i	0.488752	+	0.656508i	−0.487506	+	0.873120i	$0.662093\pi$
$84$	5.01498	+	4.47459i	0.547179	+	0.488218i
$85$	3.09780	−	10.3474i	0.336004	−	1.12233i
$86$	10.6146	−	6.98132i	1.14460	−	0.752815i
$87$	−3.27723	+	1.52304i	−0.351356	+	0.163287i
$88$	0.986764	−	1.04591i	0.105189	−	0.111494i
$89$	−6.11142	+	2.22437i	−0.647809	+	0.235783i	−0.644964	−	0.764213i	$-0.723128\pi$
$89$	−6.11142	+	2.22437i	−0.647809	+	0.235783i	−0.00284473	+	0.999996i	$0.500906\pi$
$90$	4.99319	−	1.48080i	0.526329	−	0.156090i
$91$	−2.49562	−	0.908330i	−0.261612	−	0.0952188i
$92$	−0.728620	+	0.365927i	−0.0759639	+	0.0381505i
$93$	−7.10194	+	4.36787i	−0.736437	+	0.452927i
$94$	4.79017	+	11.1049i	0.494068	+	1.14538i
$95$	−2.35676	−	0.275466i	−0.241799	−	0.0282622i
$96$	0.637402	+	1.61050i	0.0650545	+	0.164371i
$97$	−7.98430	−	5.25136i	−0.810683	−	0.533195i	0.0751643	−	0.997171i	$-0.476052\pi$
$97$	−7.98430	−	5.25136i	−0.810683	−	0.533195i	−0.885848	+	0.463976i	$0.846422\pi$
$98$	−6.17228	+	5.17916i	−0.623494	+	0.523174i
$99$	1.94598	−	3.84991i	0.195579	−	0.386931i
$100$	−1.52147	−	1.27667i	−0.152147	−	0.127667i
$101$	−4.47597	−	14.9508i	−0.445376	−	1.48766i	−0.826394	−	0.563092i	$-0.809612\pi$
$101$	−4.47597	−	14.9508i	−0.445376	−	1.48766i	0.381019	−	0.924567i	$-0.375573\pi$
$102$	10.7365	−	0.925331i	1.06307	−	0.0916214i
$103$	−11.8658	−	5.95922i	−1.16917	−	0.587179i	−0.245135	−	0.969489i	$-0.578832\pi$
$103$	−11.8658	−	5.95922i	−1.16917	−	0.587179i	−0.924034	+	0.382310i	$0.875129\pi$
$104$	−0.469672	−	0.497823i	−0.0460551	−	0.0488156i
$105$	1.67613	+	11.5470i	0.163574	+	1.12687i
$106$	0.272262	−	0.631175i	0.0264445	−	0.0613051i
$107$	6.61983	−	11.4659i	0.639963	−	1.10845i	−0.345477	−	0.938427i	$-0.612283\pi$
$107$	6.61983	−	11.4659i	0.639963	−	1.10845i	0.985440	−	0.170022i	$-0.0543838\pi$
$108$	3.20700	+	4.08842i	0.308594	+	0.393408i
$109$	7.05417	+	12.2182i	0.675667	+	1.17029i	0.976273	+	0.216541i	$0.0694777\pi$
$109$	7.05417	+	12.2182i	0.675667	+	1.17029i	−0.300606	+	0.953748i	$0.597189\pi$
$110$	2.47943	−	0.289803i	0.236404	−	0.0276317i
$111$	5.78260	+	10.7578i	0.548860	+	1.02108i
$112$	−3.77578	+	0.894877i	−0.356778	+	0.0845579i
$113$	0.105133	+	1.80506i	0.00989007	+	0.169806i	0.999636	+	0.0269688i	$0.00858548\pi$
$113$	0.105133	+	1.80506i	0.00989007	+	0.169806i	−0.989746	+	0.142837i	$0.954377\pi$
$114$	−0.609756	−	2.28747i	−0.0571089	−	0.214241i
$115$	−1.37733	−	0.326432i	−0.128436	−	0.0304400i
$116$	0.362310	−	2.05476i	0.0336396	−	0.190780i
$117$	−1.77549	−	1.03121i	−0.164144	−	0.0953358i
$118$	−2.63410	−	14.9387i	−0.242489	−	1.37522i
$119$	−1.40376	+	24.1017i	−0.128683	+	2.20940i
$120$	−0.949502	+	2.85307i	−0.0866773	+	0.260449i
$121$	−5.33404	+	7.16486i	−0.484913	+	0.651351i
$122$	−8.72557	+	11.7205i	−0.789976	+	1.06112i
$123$	3.56800	−	10.7212i	0.321716	−	0.966695i
$124$	0.279893	−	4.80558i	0.0251351	−	0.431554i
$125$	−2.10605	−	11.9440i	−0.188371	−	1.06831i
$126$	−10.0965	+	5.79447i	−0.899471	+	0.516213i
$127$	0.00211844	−	0.0120143i	0.000187981	−	0.00106609i	−0.984714	−	0.174181i	$-0.944272\pi$
$127$	0.00211844	−	0.0120143i	0.000187981	−	0.00106609i	0.984902	+	0.173115i	$0.0553833\pi$
$128$	−0.973045	−	0.230616i	−0.0860058	−	0.0203838i
$129$	5.66785	+	21.2626i	0.499026	+	1.87207i
$130$	−0.0690860	−	1.18616i	−0.00605925	−	0.104033i
$131$	6.59557	−	1.56318i	0.576257	−	0.136575i	0.0678550	−	0.997695i	$-0.478384\pi$
$131$	6.59557	−	1.56318i	0.576257	−	0.136575i	0.508402	+	0.861120i	$0.330236\pi$
$132$	1.17918	+	2.19372i	0.102635	+	0.190939i
$133$	5.26779	−	0.615716i	0.456775	−	0.0533893i
$134$	4.45123	+	7.70976i	0.384528	+	0.666022i
$135$	−0.297348	+	9.01586i	−0.0255916	+	0.775962i
$136$	−3.11085	+	5.38814i	−0.266753	+	0.462029i
$137$	2.53261	−	5.87124i	0.216375	−	0.501614i	−0.775111	−	0.631825i	$-0.782306\pi$
$137$	2.53261	−	5.87124i	0.216375	−	0.501614i	0.991486	+	0.130211i	$0.0415654\pi$
$138$	−0.202869	−	1.39757i	−0.0172693	−	0.118969i
$139$	12.0078	+	12.7276i	1.01849	+	1.07954i	0.996813	+	0.0797718i	$0.0254192\pi$
$139$	12.0078	+	12.7276i	1.01849	+	1.07954i	0.0216773	+	0.999765i	$0.493099\pi$
$140$	−6.01997	−	3.02334i	−0.508781	−	0.255519i
$141$	−20.8700	+	1.79869i	−1.75757	+	0.151477i
$142$	−1.39943	−	4.67443i	−0.117438	−	0.392269i
$143$	−0.753890	−	0.632589i	−0.0630435	−	0.0528998i
$144$	−2.99537	+	0.166688i	−0.249614	+	0.0138906i
$145$	2.77476	−	2.32830i	0.230431	−	0.193355i
$146$	−8.34831	−	5.49077i	−0.690911	−	0.454419i
$147$	−5.13576	−	12.9764i	−0.423590	−	1.07027i
$148$	−7.00376	−	0.818623i	−0.575706	−	0.0672904i
$149$	4.44323	+	10.3006i	0.364003	+	0.843854i	0.997537	+	0.0701394i	$0.0223444\pi$
$149$	4.44323	+	10.3006i	0.364003	+	0.843854i	−0.633534	+	0.773715i	$0.718396\pi$
$150$	2.93026	−	1.80218i	0.239255	−	0.147148i
$151$	4.65881	−	2.33974i	0.379129	−	0.190406i	−0.249021	−	0.968498i	$-0.580109\pi$
$151$	4.65881	−	2.33974i	0.379129	−	0.190406i	0.628150	+	0.778092i	$0.283812\pi$
$152$	1.28436	+	0.467468i	0.104175	+	0.0379167i
$153$	−4.35142	+	18.1508i	−0.351792	+	1.46740i
$154$	−5.24320	+	1.90837i	−0.422509	+	0.153781i
$155$	5.73482	−	6.07855i	0.460632	−	0.488241i
$156$	1.07502	−	0.499597i	0.0860703	−	0.0399998i
$157$	14.1684	−	9.31868i	1.13076	−	0.743712i	0.160801	−	0.986987i	$-0.448592\pi$
$157$	14.1684	−	9.31868i	1.13076	−	0.743712i	0.969957	+	0.243275i	$0.0782218\pi$
$158$	−1.77176	+	5.91808i	−0.140953	+	0.470817i
$159$	0.888383	+	0.792655i	0.0704534	+	0.0628616i
$160$	−1.03670	−	1.39252i	−0.0819580	−	0.110089i
$161$	3.16385			0.249347
$162$	−8.47304	+	3.03439i	−0.665705	+	0.238404i
$163$	−16.5418			−1.29565			−0.647825	−	0.761789i	$-0.724321\pi$
$163$	−16.5418			−1.29565			−0.647825	+	0.761789i	$0.724321\pi$
$164$	3.89565	+	5.23277i	0.304200	+	0.408611i
$165$	−0.879809	+	4.23327i	−0.0684931	+	0.329560i
$166$	2.13856	−	7.14330i	0.165985	−	0.554427i
$167$	11.8653	−	7.80391i	0.918162	−	0.603884i	−3.90682e−5	−	1.00000i	$-0.500012\pi$
$167$	11.8653	−	7.80391i	0.918162	−	0.603884i	0.918201	+	0.396116i	$0.129642\pi$
$168$	0.594433	−	6.69467i	0.0458615	−	0.516505i
$169$	8.59969	−	9.11514i	0.661515	−	0.701165i
$170$	−10.1498	+	3.69421i	−0.778451	+	0.283333i
$171$	4.09279	+	0.249002i	0.312984	+	0.0190416i
$172$	−11.9385	−	4.34525i	−0.910300	−	0.331322i
$173$	−8.24942	+	4.14301i	−0.627191	+	0.314987i	−0.733853	−	0.679308i	$-0.762280\pi$
$173$	−8.24942	+	4.14301i	−0.627191	+	0.314987i	0.106662	+	0.994295i	$0.465984\pi$
$174$	3.17870	+	1.71925i	0.240976	+	0.130336i
$175$	3.05258	+	7.07667i	0.230753	+	0.534946i
$176$	−1.42820	−	0.166933i	−0.107655	−	0.0125830i
$177$	25.9915	+	3.84153i	1.95364	+	0.288747i
$178$	5.43371	+	3.57381i	0.407274	+	0.267868i
$179$	0.945576	−	0.793432i	0.0706756	−	0.0593039i	−0.606765	−	0.794881i	$-0.707533\pi$
$179$	0.945576	−	0.793432i	0.0706756	−	0.0593039i	0.677441	+	0.735577i	$0.263089\pi$
$180$	−4.16951	−	3.12088i	−0.310777	−	0.232617i
$181$	2.84970	+	2.39118i	0.211816	+	0.177735i	0.742523	−	0.669821i	$-0.233629\pi$
$181$	2.84970	+	2.39118i	0.211816	+	0.177735i	−0.530707	+	0.847556i	$0.678073\pi$
$182$	0.761686	+	2.54421i	0.0564599	+	0.188589i
$183$	−14.4895	−	20.7502i	−1.07109	−	1.53390i
$184$	0.728620	+	0.365927i	0.0537146	+	0.0269765i
$185$	−8.40072	−	8.90424i	−0.617633	−	0.654653i
$186$	7.74455	+	3.08832i	0.567858	+	0.226446i
$187$	−3.54346	+	8.21466i	−0.259123	+	0.600716i
$188$	6.04698	−	10.4737i	0.441021	−	0.763871i
$189$	−4.00068	−	19.7622i	−0.291007	−	1.43749i
$190$	1.18640	+	2.05491i	0.0860707	+	0.149079i
$191$	−9.12896	+	1.06702i	−0.660548	+	0.0772070i	−0.439761	−	0.898115i	$-0.644937\pi$
$191$	−9.12896	+	1.06702i	−0.660548	+	0.0772070i	−0.220787	+	0.975322i	$0.570863\pi$
$192$	0.911192	−	1.47300i	0.0657596	−	0.106305i
$193$	2.86602	−	0.679258i	0.206300	−	0.0488941i	−0.126166	−	0.992009i	$-0.540267\pi$
$193$	2.86602	−	0.679258i	0.206300	−	0.0488941i	0.332467	+	0.943115i	$0.392119\pi$
$194$	0.555659	+	9.54029i	0.0398940	+	0.684953i
$195$	1.98716	+	0.535213i	0.142303	+	0.0383274i
$196$	7.84015	+	1.85815i	0.560011	+	0.132725i
$197$	−1.30527	+	7.40253i	−0.0929963	+	0.527408i	0.902347	+	0.431011i	$0.141843\pi$
$197$	−1.30527	+	7.40253i	−0.0929963	+	0.527408i	−0.995343	+	0.0963973i	$0.969268\pi$
$198$	−4.25016	+	0.738089i	−0.302046	+	0.0524537i
$199$	−1.01029	−	5.72961i	−0.0716172	−	0.406162i	−0.999450	−	0.0331648i	$-0.989441\pi$
$199$	−1.01029	−	5.72961i	−0.0716172	−	0.406162i	0.927833	−	0.372997i	$-0.121670\pi$
$200$	−0.115484	+	1.98278i	−0.00816594	+	0.140204i
$201$	−15.1050	+	3.09857i	−1.06542	+	0.218556i
$202$	−9.31951	+	12.5183i	−0.655718	+	0.880783i
$203$	−4.83474	+	6.49419i	−0.339333	+	0.455803i
$204$	−7.15361	−	8.05941i	−0.500853	−	0.564272i
$205$	−0.658511	+	11.3062i	−0.0459924	+	0.789660i
$206$	2.30572	+	13.0764i	0.160647	+	0.911077i
$207$	2.40777	+	0.430979i	0.167352	+	0.0299551i
$208$	−0.118847	+	0.674014i	−0.00824055	+	0.0467345i
$209$	1.91236	+	0.453238i	0.132281	+	0.0313511i
$210$	8.26118	−	8.23984i	0.570076	−	0.568603i
$211$	0.384871	+	6.60798i	0.0264956	+	0.454912i	0.985299	+	0.170840i	$0.0546482\pi$
$211$	0.384871	+	6.60798i	0.0264956	+	0.454912i	−0.958803	+	0.284071i	$0.908315\pi$
$212$	−0.668864	+	0.158524i	−0.0459378	+	0.0108875i
$213$	8.44750	+	0.256732i	0.578813	+	0.0175910i
$214$	−13.1501	+	1.53703i	−0.898925	+	0.105069i
$215$	−11.0279	−	19.1009i	−0.752099	−	1.30267i
$216$	1.36433	−	5.01384i	0.0928306	−	0.341149i
$217$	−9.33954	+	16.1766i	−0.634009	+	1.09814i
$218$	5.58803	−	12.9545i	0.378469	−	0.877390i
$219$	13.5897	−	10.7168i	0.918305	−	0.724173i
$220$	−1.71307	−	1.81575i	−0.115495	−	0.122418i
$221$	3.80527	+	1.91108i	0.255970	+	0.128553i
$222$	5.17594	−	11.0625i	0.347386	−	0.742464i
$223$	2.53058	+	8.45273i	0.169460	+	0.566036i	0.999959	+	0.00901651i	$0.00287008\pi$
$223$	2.53058	+	8.45273i	0.169460	+	0.566036i	−0.830499	+	0.557020i	$0.811945\pi$
$224$	2.97254	+	2.49426i	0.198611	+	0.166655i
$225$	1.35911	+	5.80135i	0.0906071	+	0.386757i
$226$	1.38510	−	1.16224i	0.0921356	−	0.0773109i
$227$	6.17545	+	4.06165i	0.409879	+	0.269581i	0.737660	−	0.675172i	$-0.235931\pi$
$227$	6.17545	+	4.06165i	0.409879	+	0.269581i	−0.327782	+	0.944754i	$0.606301\pi$
$228$	−1.47071	+	1.85508i	−0.0974002	+	0.122856i
$229$	2.57921	+	0.301467i	0.170439	+	0.0199215i	0.200884	−	0.979615i	$-0.435618\pi$
$229$	2.57921	+	0.301467i	0.170439	+	0.0199215i	−0.0304453	+	0.999536i	$0.509693\pi$
$230$	0.560643	+	1.29972i	0.0369677	+	0.0857008i
$231$	−0.268591	−	9.66058i	−0.0176720	−	0.635620i
$232$	−1.86453	+	0.936401i	−0.122412	+	0.0614777i
$233$	−16.7191	−	6.08524i	−1.09530	−	0.398657i	−0.269719	−	0.962939i	$-0.586931\pi$
$233$	−16.7191	−	6.08524i	−1.09530	−	0.398657i	−0.825582	+	0.564282i	$0.809153\pi$
$234$	0.233091	+	2.03996i	0.0152376	+	0.133357i
$235$	19.7295	−	7.18094i	1.28701	−	0.468433i
$236$	−10.4097	+	11.0337i	−0.677616	+	0.718231i
$237$	−8.75692	−	6.14856i	−0.568823	−	0.399392i
$238$	20.1708	−	13.2665i	1.30748	−	0.859941i
$239$	4.64030	−	15.4997i	0.300156	−	1.00259i	−0.666284	−	0.745698i	$-0.732116\pi$
$239$	4.64030	−	15.4997i	0.300156	−	1.00259i	0.966440	−	0.256893i	$-0.0826987\pi$
$240$	2.85552	−	0.942119i	0.184323	−	0.0608135i
$241$	2.54961	+	3.42473i	0.164235	+	0.220606i	0.876620	−	0.481182i	$-0.159793\pi$
$241$	2.54961	+	3.42473i	0.164235	+	0.220606i	−0.712385	+	0.701789i	$0.752385\pi$
$242$	8.93237			0.574194
$243$	−0.352620	−	15.5845i	−0.0226206	−	0.999744i
$244$	14.6118			0.935426
$245$	8.35300	+	11.2200i	0.533654	+	0.716821i
$246$	−10.7304	+	3.54026i	−0.684143	+	0.225719i
$247$	0.268289	−	0.896147i	0.0170708	−	0.0570204i
$248$	−4.02181	+	2.64518i	−0.255385	+	0.167969i
$249$	10.5699	+	7.42149i	0.669838	+	0.470318i
$250$	−8.32292	+	8.82178i	−0.526388	+	0.557939i
$251$	0.929843	−	0.338435i	0.0586912	−	0.0213618i	−0.312508	−	0.949915i	$-0.601169\pi$
$251$	0.929843	−	0.338435i	0.0586912	−	0.0213618i	0.371199	+	0.928553i	$0.378947\pi$
$252$	10.6771	+	4.63845i	0.672595	+	0.292195i
$253$	1.10170	+	0.400987i	0.0692635	+	0.0252098i
$254$	−0.0109020	+	0.00547517i	−0.000684050	+	0.000343543i
$255$	−0.519936	−	18.7009i	−0.0325597	−	1.17110i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	−6.73625	−	0.787355i	−0.420196	−	0.0491139i	−0.0966320	−	0.995320i	$-0.530807\pi$
$257$	−6.73625	−	0.787355i	−0.420196	−	0.0491139i	−0.323564	+	0.946206i	$0.604881\pi$
$258$	13.6707	−	17.2435i	0.851098	−	1.07353i
$259$	22.8608	+	15.0358i	1.42050	+	0.934280i
$260$	−0.910192	+	0.763742i	−0.0564477	+	0.0473653i
$261$	−4.56400	+	4.28365i	−0.282505	+	0.265152i
$262$	−5.19246	−	4.35699i	−0.320791	−	0.269176i
$263$	2.72961	+	9.11754i	0.168315	+	0.562212i	0.999976	+	0.00692776i	$0.00220519\pi$
$263$	2.72961	+	9.11754i	0.168315	+	0.562212i	−0.831661	+	0.555284i	$0.812610\pi$
$264$	1.05547	−	2.25585i	0.0649600	−	0.138838i
$265$	−1.06641	−	0.535573i	−0.0655092	−	0.0329000i
$266$	−3.63958	−	3.85773i	−0.223157	−	0.236533i
$267$	−8.84518	+	6.97529i	−0.541316	+	0.426881i
$268$	3.52609	−	8.17439i	0.215390	−	0.499330i
$269$	5.97364	−	10.3467i	0.364220	−	0.630847i	−0.624431	−	0.781080i	$-0.714669\pi$
$269$	5.97364	−	10.3467i	0.364220	−	0.630847i	0.988651	+	0.150233i	$0.0480024\pi$
$270$	7.40940	−	5.14539i	0.450921	−	0.313138i
$271$	2.73992	+	4.74568i	0.166438	+	0.288279i	0.937165	−	0.348886i	$-0.113440\pi$
$271$	2.73992	+	4.74568i	0.166438	+	0.288279i	−0.770727	+	0.637166i	$0.780107\pi$
$272$	6.17962	−	0.722294i	0.374695	−	0.0437955i
$273$	−4.59782	−	0.139734i	−0.278273	−	0.00845711i
$274$	−6.22183	+	1.47460i	−0.375874	+	0.0890839i
$275$	0.166057	+	2.85109i	0.0100136	+	0.171927i
$276$	−0.999882	+	0.997299i	−0.0601858	+	0.0600304i
$277$	−11.1125	−	2.63371i	−0.667685	−	0.158244i	−0.117225	−	0.993105i	$-0.537400\pi$
$277$	−11.1125	−	2.63371i	−0.667685	−	0.158244i	−0.550461	+	0.834861i	$0.685548\pi$
$278$	3.03849	−	17.2321i	0.182236	−	1.03351i
$279$	−9.31119	+	11.0385i	−0.557446	+	0.660860i
$280$	1.16978	+	6.63418i	0.0699080	+	0.396468i
$281$	−0.219442	+	3.76767i	−0.0130908	+	0.224760i	0.985417	+	0.170155i	$0.0544270\pi$
$281$	−0.219442	+	3.76767i	−0.0130908	+	0.224760i	−0.998508	+	0.0546050i	$0.982610\pi$
$282$	13.9055	+	15.6662i	0.828058	+	0.932908i
$283$	17.2575	−	23.1809i	1.02585	−	1.37796i	0.102184	−	0.994765i	$-0.467417\pi$
$283$	17.2575	−	23.1809i	1.02585	−	1.37796i	0.923668	−	0.383194i	$-0.125176\pi$
$284$	−2.91379	+	3.91389i	−0.172901	+	0.232247i
$285$	−4.02598	+	0.825872i	−0.238479	+	0.0489204i
$286$	−0.0572223	+	0.982469i	−0.00338363	+	0.0580946i
$287$	−4.39577	−	24.9297i	−0.259474	−	1.47155i
$288$	1.92241	+	2.30311i	0.113279	+	0.135712i
$289$	3.76980	−	21.3796i	0.221753	−	1.25762i
$290$	−3.52455	−	0.835334i	−0.206969	−	0.0490525i
$291$	−15.9827	−	4.30472i	−0.936923	−	0.252347i
$292$	0.580991	+	9.97523i	0.0339999	+	0.583756i
$293$	−19.6389	+	4.65452i	−1.14732	+	0.271920i	−0.759935	−	0.649999i	$-0.774769\pi$
$293$	−19.6389	+	4.65452i	−1.14732	+	0.271920i	−0.387384	+	0.921918i	$0.626621\pi$
$294$	−7.34178	+	11.8685i	−0.428181	+	0.692183i
$295$	−26.1564	+	3.05724i	−1.52288	+	0.178000i
$296$	3.52572	+	6.10673i	0.204928	+	0.354946i
$297$	1.11156	−	7.38854i	0.0644992	−	0.428726i
$298$	5.60900	−	9.71508i	0.324921	−	0.562779i
$299$	0.221026	−	0.512395i	0.0127822	−	0.0296326i
$300$	−3.19540	−	1.27424i	−0.184487	−	0.0735682i
$301$	33.8309	+	35.8587i	1.94998	+	2.06686i
$302$	−4.65881	−	2.33974i	−0.268085	−	0.134637i
$303$	−15.4758	−	22.1626i	−0.889059	−	1.27321i
$304$	−0.391999	−	1.30937i	−0.0224827	−	0.0750973i
$305$	19.4321	+	16.3055i	1.11268	+	0.933648i
$306$	17.1576	−	7.34850i	0.980837	−	0.420086i
$307$	−5.43014	+	4.55643i	−0.309915	+	0.260049i	−0.784457	−	0.620183i	$-0.787058\pi$
$307$	−5.43014	+	4.55643i	−0.309915	+	0.260049i	0.474542	+	0.880233i	$0.342614\pi$
$308$	4.66177	+	3.06609i	0.265629	+	0.174707i
$309$	−22.7512	−	3.36263i	−1.29427	−	0.191293i
$310$	−8.30035	−	0.970171i	−0.471428	−	0.0551020i
$311$	−5.49630	−	12.7418i	−0.311666	−	0.722524i	0.688330	−	0.725398i	$-0.258344\pi$
$311$	−5.49630	−	12.7418i	−0.311666	−	0.722524i	−0.999996	+	0.00287432i	$0.999085\pi$
$312$	−1.04269	−	0.563958i	−0.0590310	−	0.0319278i
$313$	−27.7117	+	13.9174i	−1.56636	+	0.786656i	−0.999314	−	0.0370299i	$-0.988210\pi$
$313$	−27.7117	+	13.9174i	−1.56636	+	0.786656i	−0.567046	+	0.823686i	$0.691914\pi$
$314$	−15.9355	−	5.80004i	−0.899292	−	0.327315i
$315$	9.02329	+	18.0833i	0.508405	+	1.01888i
$316$	5.80505	−	2.11287i	0.326560	−	0.118858i
$317$	7.57842	−	8.03265i	0.425646	−	0.451159i	−0.478687	−	0.877986i	$-0.658887\pi$
$317$	7.57842	−	8.03265i	0.425646	−	0.451159i	0.904333	+	0.426827i	$0.140369\pi$
$318$	0.105301	−	1.18593i	0.00590501	−	0.0665038i
$319$	−2.50661	+	1.64862i	−0.140343	+	0.0923051i
$320$	−0.497904	+	1.66311i	−0.0278337	+	0.0929709i
$321$	4.66625	−	22.4520i	0.260444	−	1.25315i
$322$	−1.88932	−	2.53780i	−0.105288	−	0.141426i
$323$	−8.50372			−0.473160
$324$	7.49371	+	4.98441i	0.416317	+	0.276912i
$325$	1.35934			0.0754026
$326$	9.87805	+	13.2685i	0.547095	+	0.734876i
$327$	18.2336	+	16.2688i	1.00832	+	0.899666i
$328$	1.87100	−	6.24959i	0.103309	−	0.345076i
$329$	−39.2087	+	25.7880i	−2.16165	+	1.42174i
$330$	3.92099	−	1.82222i	0.215843	−	0.100310i
$331$	2.83698	−	3.00702i	0.155934	−	0.165281i	−0.644697	−	0.764439i	$-0.723016\pi$
$331$	2.83698	−	3.00702i	0.155934	−	0.165281i	0.800631	+	0.599158i	$0.204498\pi$
$332$	−7.00687	+	2.55029i	−0.384552	+	0.139965i
$333$	15.3495	+	14.5567i	0.841148	+	0.797704i
$334$	−13.3451	−	4.85723i	−0.730213	−	0.265776i
$335$	13.8112	−	6.93623i	0.754585	−	0.378967i
$336$	−5.72492	+	3.52097i	−0.312320	+	0.192085i
$337$	−6.54309	−	15.1686i	−0.356425	−	0.826286i	−0.998233	−	0.0594206i	$-0.981075\pi$
$337$	−6.54309	−	15.1686i	−0.356425	−	0.826286i	0.641808	−	0.766865i	$-0.278185\pi$
$338$	−12.4468	−	1.45483i	−0.677019	−	0.0791322i
$339$	1.15250	+	2.91198i	0.0625952	+	0.158157i
$340$	9.02423	+	5.93533i	0.489407	+	0.321888i
$341$	−5.30239	+	4.44923i	−0.287140	+	0.240939i
$342$	−2.24432	−	3.43162i	−0.121359	−	0.185561i
$343$	−3.14298	−	2.63727i	−0.169705	−	0.142399i
$344$	3.64374	+	12.1709i	0.196457	+	0.656212i
$345$	−2.44263	+	0.210519i	−0.131507	+	0.0113340i
$346$	8.24942	+	4.14301i	0.443491	+	0.222730i
$347$	0.860506	+	0.912083i	0.0461944	+	0.0489632i	0.750059	−	0.661371i	$-0.230025\pi$
$347$	0.860506	+	0.912083i	0.0461944	+	0.0489632i	−0.703864	+	0.710334i	$0.748544\pi$
$348$	−0.519138	−	3.57637i	−0.0278287	−	0.191714i
$349$	−5.91657	+	13.7162i	−0.316707	+	0.734209i	0.683285	+	0.730152i	$0.260551\pi$
$349$	−5.91657	+	13.7162i	−0.316707	+	0.734209i	−0.999992	+	0.00405704i	$0.998709\pi$
$350$	3.85349	−	6.67444i	0.205978	−	0.356764i
$351$	−3.48002	−	0.732656i	−0.185750	−	0.0391063i
$352$	0.718963	+	1.24528i	0.0383208	+	0.0663737i
$353$	−19.3462	+	2.26125i	−1.02969	+	0.120354i	−0.614126	−	0.789208i	$-0.710491\pi$
$353$	−19.3462	+	2.26125i	−1.02969	+	0.120354i	−0.415569	+	0.909562i	$0.636417\pi$
$354$	−12.4396	−	23.1424i	−0.661160	−	1.23000i
$355$	−8.24256	+	1.95352i	−0.437470	+	0.103682i
$356$	−0.378153	−	6.49263i	−0.0200421	−	0.344109i
$357$	10.7705	+	40.4052i	0.570038	+	2.13847i
$358$	−1.20109	−	0.284663i	−0.0634795	−	0.0150449i
$359$	−4.07481	+	23.1094i	−0.215060	+	1.21967i	0.665742	+	0.746182i	$0.268115\pi$
$359$	−4.07481	+	23.1094i	−0.215060	+	1.21967i	−0.880802	+	0.473484i	$0.842996\pi$
$360$	−0.0134709	+	5.20812i	−0.000709979	+	0.274492i
$361$	−2.97492	−	16.8716i	−0.156575	−	0.887980i
$362$	0.216300	−	3.71372i	0.0113685	−	0.195189i
$363$	−4.88541	+	14.6797i	−0.256418	+	0.770486i
$364$	1.58592	−	2.13026i	0.0831248	−	0.111656i
$365$	−10.3588	+	13.9143i	−0.542204	+	0.728307i
$366$	−7.99169	+	24.0135i	−0.417732	+	1.25521i
$367$	0.195855	−	3.36271i	0.0102236	−	0.175532i	−0.989331	−	0.145686i	$-0.953461\pi$
$367$	0.195855	−	3.36271i	0.0102236	−	0.175532i	0.999555	−	0.0298463i	$-0.00950177\pi$
$368$	−0.141583	−	0.802960i	−0.00738055	−	0.0418572i
$369$	0.0506205	−	19.5709i	0.00263520	−	1.01882i
$370$	−2.12574	+	12.0557i	−0.110512	+	0.626744i
$371$	2.59545	+	0.615132i	0.134749	+	0.0319361i
$372$	−2.14752	−	8.05630i	−0.111344	−	0.417700i
$373$	0.545964	+	9.37385i	0.0282690	+	0.485359i	0.982497	+	0.186279i	$0.0596428\pi$
$373$	0.545964	+	9.37385i	0.0282690	+	0.485359i	−0.954228	+	0.299080i	$0.903320\pi$
$374$	8.70518	−	2.06317i	0.450134	−	0.106684i
$375$	−9.94590	−	18.5031i	−0.513604	−	0.955495i
$376$	−12.0122	+	1.40402i	−0.619481	+	0.0724069i
$377$	0.713999	+	1.23668i	0.0367728	+	0.0636924i
$378$	−13.4626	+	15.0102i	−0.692444	+	0.772040i
$379$	13.6284	−	23.6051i	0.700046	−	1.21252i	−0.268404	−	0.963306i	$-0.586496\pi$
$379$	13.6284	−	23.6051i	0.700046	−	1.21252i	0.968450	−	0.249209i	$-0.0801705\pi$
$380$	0.939820	−	2.17875i	0.0482117	−	0.111767i
$381$	−0.00303542	−	0.0209112i	−0.000155509	−	0.00107131i
$382$	6.30732	+	6.68537i	0.322710	+	0.342053i
$383$	14.7824	+	7.42400i	0.755346	+	0.379349i	0.784421	−	0.620228i	$-0.212960\pi$
$383$	14.7824	+	7.42400i	0.755346	+	0.379349i	−0.0290757	+	0.999577i	$0.509256\pi$
$384$	−1.72565	+	0.148727i	−0.0880619	+	0.00758967i
$385$	2.77815	+	9.27967i	0.141588	+	0.472936i
$386$	−2.25631	−	1.89327i	−0.114843	−	0.0963650i
$387$	20.8615	+	31.8978i	1.06045	+	1.62146i
$388$	7.32067	−	6.14277i	0.371651	−	0.311852i
$389$	−2.64143	−	1.73729i	−0.133926	−	0.0880843i	0.480778	−	0.876842i	$-0.340354\pi$
$389$	−2.64143	−	1.73729i	−0.133926	−	0.0880843i	−0.614704	+	0.788758i	$0.710725\pi$
$390$	−0.757342	−	1.91355i	−0.0383495	−	0.0968966i
$391$	−5.03853	−	0.588920i	−0.254810	−	0.0297830i
$392$	−3.19135	−	7.39838i	−0.161187	−	0.373674i
$393$	10.0003	−	6.15046i	0.504451	−	0.310250i
$394$	6.71719	−	3.37350i	0.338407	−	0.169954i
$395$	10.0778	+	3.66803i	0.507071	+	0.184559i
$396$	3.13006	+	2.96840i	0.157291	+	0.149168i
$397$	−3.59675	+	1.30911i	−0.180516	+	0.0657024i	−0.430697	−	0.902497i	$-0.641732\pi$
$397$	−3.59675	+	1.30911i	−0.180516	+	0.0657024i	0.250181	+	0.968199i	$0.419510\pi$
$398$	−3.99256	+	4.23186i	−0.200129	+	0.212124i
$399$	8.33053	−	3.87148i	0.417048	−	0.193816i
$400$	1.65940	−	1.09140i	0.0829698	−	0.0545701i
$401$	5.53963	−	18.5036i	0.276636	−	0.924028i	−0.700900	−	0.713259i	$-0.747218\pi$
$401$	5.53963	−	18.5036i	0.276636	−	0.924028i	0.977536	−	0.210769i	$-0.0675967\pi$
$402$	11.5055	+	10.2657i	0.573842	+	0.512008i
$403$	1.96738	+	2.64265i	0.0980023	+	0.131640i
$404$	15.6064			0.776449
$405$	4.40365	+	14.9910i	0.218819	+	0.744909i
$406$	8.09625			0.401810
$407$	6.05486	+	8.13309i	0.300128	+	0.403142i
$408$	−2.19280	+	10.5508i	−0.108560	+	0.522344i
$409$	9.84234	−	32.8757i	0.486672	−	1.62560i	−0.263716	−	0.964600i	$-0.584948\pi$
$409$	9.84234	−	32.8757i	0.486672	−	1.62560i	0.750388	−	0.660998i	$-0.229867\pi$
$410$	9.46220	−	6.22339i	0.467305	−	0.307351i
$411$	0.979522	−	11.0317i	0.0483163	−	0.544151i
$412$	9.11201	−	9.65816i	0.448916	−	0.475824i
$413$	55.3124	−	20.1321i	2.72175	−	0.990635i
$414$	−1.09212	−	2.18869i	−0.0536749	−	0.107568i
$415$	−12.1642	−	4.42742i	−0.597119	−	0.217334i
$416$	0.611613	−	0.307164i	0.0299868	−	0.0150599i
$417$	26.6579	+	14.4184i	1.30545	+	0.706070i
$418$	−0.778430	−	1.80460i	−0.0380743	−	0.0882661i
$419$	−5.62863	−	0.657892i	−0.274976	−	0.0321401i	−0.0225129	−	0.999747i	$-0.507167\pi$
$419$	−5.62863	−	0.657892i	−0.274976	−	0.0321401i	−0.252464	+	0.967606i	$0.581241\pi$
$420$	−11.5426	−	1.70599i	−0.563221	−	0.0832439i
$421$	1.40613	+	0.924823i	0.0685303	+	0.0450731i	0.583312	−	0.812248i	$-0.301757\pi$
$421$	1.40613	+	0.924823i	0.0685303	+	0.0450731i	−0.514781	+	0.857321i	$0.672127\pi$
$422$	5.07058	−	4.25472i	0.246832	−	0.207117i
$423$	−33.3516	+	14.2843i	−1.62161	+	0.694526i
$424$	0.526573	+	0.441848i	0.0255727	+	0.0214580i
$425$	−3.54407	−	11.8380i	−0.171913	−	0.574229i
$426$	−4.83857	−	6.92924i	−0.234429	−	0.335723i
$427$	−50.6684	−	25.4466i	−2.45202	−	1.23145i
$428$	9.08561	+	9.63018i	0.439169	+	0.465492i
$429$	−1.58332	−	0.631386i	−0.0764435	−	0.0304836i
$430$	−8.73588	+	20.2521i	−0.421282	+	0.976641i
$431$	−18.2224	+	31.5621i	−0.877741	+	1.52029i	−0.0239268	+	0.999714i	$0.507617\pi$
$431$	−18.2224	+	31.5621i	−0.877741	+	1.52029i	−0.853814	+	0.520578i	$0.825716\pi$
$432$	−4.83644	+	1.89970i	−0.232693	+	0.0913994i
$433$	−14.6370	−	25.3520i	−0.703410	−	1.21834i	−0.967262	−	0.253778i	$-0.918327\pi$
$433$	−14.6370	−	25.3520i	−0.703410	−	1.21834i	0.263853	−	0.964563i	$-0.415007\pi$
$434$	18.5528	−	2.16851i	0.890561	−	0.104092i
$435$	3.30051	−	5.33549i	0.158247	−	0.255817i
$436$	−13.7281	+	3.25361i	−0.657454	+	0.155820i
$437$	0.0647969	+	1.11252i	0.00309965	+	0.0532190i
$438$	−16.7114	−	4.50097i	−0.798500	−	0.215065i
$439$	−14.0869	−	3.33866i	−0.672333	−	0.159346i	−0.119750	−	0.992804i	$-0.538209\pi$
$439$	−14.0869	−	3.33866i	−0.672333	−	0.159346i	−0.552582	+	0.833458i	$0.686358\pi$
$440$	−0.433479	+	2.45838i	−0.0206653	+	0.117199i
$441$	−15.4895	−	18.5570i	−0.737596	−	0.883665i
$442$	−0.739429	−	4.19351i	−0.0351710	−	0.199465i
$443$	−0.357549	+	6.13887i	−0.0169877	+	0.291667i	0.979105	+	0.203354i	$0.0651844\pi$
$443$	−0.357549	+	6.13887i	−0.0169877	+	0.291667i	−0.996093	+	0.0883123i	$0.971853\pi$
$444$	−11.9643	+	2.45431i	−0.567801	+	0.116476i
$445$	6.74229	−	9.05646i	0.319615	−	0.429318i
$446$	5.26897	−	7.07745i	0.249493	−	0.335127i
$447$	12.8983	+	14.5315i	0.610069	+	0.687317i
$448$	0.225624	−	3.87381i	0.0106597	−	0.183020i
$449$	1.36368	+	7.73382i	0.0643561	+	0.364982i	0.999930	+	0.0118501i	$0.00377209\pi$
$449$	1.36368	+	7.73382i	0.0643561	+	0.364982i	−0.935574	+	0.353132i	$0.885117\pi$
$450$	3.84179	−	4.55450i	0.181104	−	0.214701i
$451$	1.62891	−	9.23802i	0.0767024	−	0.435001i
$452$	−1.75938	−	0.416981i	−0.0827544	−	0.0196132i
$453$	6.39327	−	6.37675i	0.300382	−	0.299606i
$454$	−0.429773	−	7.37892i	−0.0201703	−	0.346310i
$455$	4.48628	−	1.06327i	0.210320	−	0.0498467i
$456$	2.36625	+	0.0719137i	0.110810	+	0.00336767i
$457$	16.9415	−	1.98018i	0.792491	−	0.0926289i	0.289791	−	0.957090i	$-0.406414\pi$
$457$	16.9415	−	1.98018i	0.792491	−	0.0926289i	0.502700	+	0.864461i	$0.332340\pi$
$458$	−1.29839	−	2.24887i	−0.0606696	−	0.105083i
$459$	2.69267	+	32.2165i	0.125683	+	1.50374i
$460$	0.707740	−	1.22584i	0.0329985	−	0.0571552i
$461$	12.8960	−	29.8963i	0.600627	−	1.39241i	−0.298368	−	0.954451i	$-0.596442\pi$
$461$	12.8960	−	29.8963i	0.600627	−	1.39241i	0.898995	−	0.437959i	$-0.144299\pi$
$462$	−7.58859	+	5.98434i	−0.353053	+	0.278417i
$463$	14.6679	+	15.5471i	0.681676	+	0.722534i	0.972153	−	0.234348i	$-0.0752955\pi$
$463$	14.6679	+	15.5471i	0.681676	+	0.722534i	−0.290477	+	0.956882i	$0.593814\pi$
$464$	1.86453	+	0.936401i	0.0865585	+	0.0434713i
$465$	6.13414	−	13.1104i	0.284464	−	0.607981i
$466$	5.10282	+	17.0446i	0.236383	+	0.789576i
$467$	−14.7122	−	12.3450i	−0.680798	−	0.571258i	0.235441	−	0.971889i	$-0.424346\pi$
$467$	−14.7122	−	12.3450i	−0.680798	−	0.571258i	−0.916239	+	0.400631i	$0.868791\pi$
$468$	1.49711	−	1.40515i	0.0692039	−	0.0649530i
$469$	−26.4630	+	22.2051i	−1.22195	+	1.02533i
$470$	−17.5416	−	11.5373i	−0.809135	−	0.532176i
$471$	18.2476	−	23.0166i	0.840806	−	1.06055i
$472$	15.0666	+	1.76104i	0.693498	+	0.0810583i
$473$	7.23572	+	16.7743i	0.332699	+	0.771283i
$474$	0.297372	+	10.6958i	0.0136588	+	0.491274i
$475$	−2.42588	+	1.21832i	−0.111307	+	0.0559005i
$476$	−22.6865	−	8.25723i	−1.03984	−	0.378469i
$477$	1.89141	+	0.821682i	0.0866015	+	0.0376222i
$478$	−15.2036	+	5.53367i	−0.695399	+	0.253104i
$479$	6.09926	−	6.46484i	0.278682	−	0.295386i	−0.572880	−	0.819639i	$-0.694174\pi$
$479$	6.09926	−	6.46484i	0.278682	−	0.295386i	0.851562	+	0.524253i	$0.175655\pi$
$480$	−2.46089	−	1.72788i	−0.112324	−	0.0788667i
$481$	4.03214	−	2.65198i	0.183850	−	0.120920i
$482$	1.22453	−	4.09021i	0.0557757	−	0.186304i
$483$	5.20403	−	1.71696i	0.236792	−	0.0781245i
$484$	−5.33404	−	7.16486i	−0.242456	−	0.325676i
$485$	16.5905			0.753334
$486$	−12.2901	+	9.58924i	−0.557490	+	0.434977i
$487$	−16.6394			−0.754001			−0.377001	−	0.926213i	$-0.623045\pi$
$487$	−16.6394			−0.754001			−0.377001	+	0.926213i	$0.623045\pi$
$488$	−8.72557	−	11.7205i	−0.394988	−	0.530561i
$489$	−27.2085	+	8.97689i	−1.23041	+	0.405949i
$490$	4.01178	−	13.4003i	0.181234	−	0.605363i
$491$	−1.20852	+	0.794853i	−0.0545395	+	0.0358712i	−0.576486	−	0.817107i	$-0.695576\pi$
$491$	−1.20852	+	0.794853i	−0.0545395	+	0.0358712i	0.521946	+	0.852978i	$0.325206\pi$
$492$	9.24745	+	6.49298i	0.416907	+	0.292726i
$493$	8.90831	−	9.44226i	0.401210	−	0.425258i
$494$	−0.879031	+	0.319941i	−0.0395495	+	0.0143948i
$495$	0.850168	+	7.44051i	0.0382122	+	0.334426i
$496$	4.52342	+	1.64639i	0.203108	+	0.0739251i
$497$	16.9200	−	8.49756i	0.758967	−	0.381167i
$498$	−0.358937	−	12.9101i	−0.0160843	−	0.578517i
$499$	11.0945	+	25.7199i	0.496658	+	1.15138i	0.963661	+	0.267127i	$0.0860744\pi$
$499$	11.0945	+	25.7199i	0.496658	+	1.15138i	−0.467003	+	0.884256i	$0.654666\pi$
$500$	12.0463	+	1.40801i	0.538725	+	0.0629679i
$501$	15.2814	−	19.2752i	0.682724	−	0.861153i
$502$	−0.826731	−	0.543749i	−0.0368988	−	0.0242687i
$503$	24.3836	−	20.4603i	1.08721	−	0.912278i	0.0907113	−	0.995877i	$-0.471086\pi$
$503$	24.3836	−	20.4603i	1.08721	−	0.912278i	0.996499	+	0.0835990i	$0.0266415\pi$
$504$	−2.65532	−	11.3343i	−0.118277	−	0.504868i
$505$	20.7548	+	17.4154i	0.923577	+	0.774973i
$506$	−0.336250	−	1.12315i	−0.0149482	−	0.0499303i
$507$	9.19850	−	19.6598i	0.408520	−	0.873124i
$508$	0.0109020	+	0.00547517i	0.000483697	+	0.000242922i
$509$	−17.1496	−	18.1775i	−0.760140	−	0.805702i	0.225556	−	0.974230i	$-0.427580\pi$
$509$	−17.1496	−	18.1775i	−0.760140	−	0.805702i	−0.985697	+	0.168528i	$0.946099\pi$
$510$	−14.6899	+	11.5845i	−0.650482	+	0.512969i
$511$	15.3573	−	35.6022i	0.679367	−	1.57495i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	6.86711	−	1.81151i	0.303190	−	0.0799802i
$514$	3.39106	+	5.87348i	0.149573	+	0.259068i
$515$	22.8956	−	2.67611i	1.00890	−	0.117924i
$516$	−21.9949	−	0.668458i	−0.968274	−	0.0294272i
$517$	−16.9214	+	4.01046i	−0.744204	+	0.176380i
$518$	−1.59097	−	27.3160i	−0.0699034	−	1.20020i
$519$	−11.3206	+	11.2914i	−0.496921	+	0.495637i
$520$	1.15614	+	0.274011i	0.0507003	+	0.0120162i
$521$	−3.55429	+	20.1574i	−0.155716	+	0.883111i	0.802412	+	0.596771i	$0.203550\pi$
$521$	−3.55429	+	20.1574i	−0.155716	+	0.883111i	−0.958128	+	0.286340i	$0.907561\pi$
$522$	6.16145	+	1.10287i	0.269679	+	0.0482713i
$523$	2.95674	+	16.7685i	0.129289	+	0.733236i	0.978667	+	0.205451i	$0.0658662\pi$
$523$	2.95674	+	16.7685i	0.129289	+	0.733236i	−0.849378	+	0.527785i	$0.823023\pi$
$524$	−0.394122	+	6.76681i	−0.0172173	+	0.295609i
$525$	8.86138	+	9.98342i	0.386742	+	0.435712i
$526$	5.68338	−	7.63410i	0.247807	−	0.332863i
$527$	17.8846	−	24.0232i	0.779066	−	1.04647i
$528$	−2.43976	+	0.500480i	−0.106177	+	0.0217806i
$529$	1.29868	−	22.2974i	0.0564642	−	0.969453i
$530$	0.207222	+	1.17522i	0.00900116	+	0.0510481i
$531$	44.8365	−	7.78637i	1.94574	−	0.337900i
$532$	−0.920969	+	5.22307i	−0.0399291	+	0.226449i
$533$	−4.34452	−	1.02967i	−0.188182	−	0.0445999i
$534$	10.8770	+	2.92957i	0.470694	+	0.126775i
$535$	1.33644	+	22.9458i	0.0577793	+	0.992033i
$536$	−8.66250	+	2.05305i	−0.374163	+	0.0886782i
$537$	1.12474	−	1.81821i	0.0485361	−	0.0784617i
$538$	−11.8665	+	1.38700i	−0.511601	+	0.0597976i
$539$	−5.79293	−	10.0336i	−0.249519	−	0.432180i
$540$	−8.55182	−	2.87063i	−0.368012	−	0.123532i
$541$	−2.10201	+	3.64079i	−0.0903726	+	0.156530i	−0.907668	−	0.419689i	$-0.862139\pi$
$541$	−2.10201	+	3.64079i	−0.0903726	+	0.156530i	0.817295	+	0.576219i	$0.195472\pi$
$542$	2.17045	−	5.03167i	0.0932289	−	0.216129i
$543$	5.98494	+	2.38663i	0.256838	+	0.102420i
$544$	−4.26958	−	4.52549i	−0.183057	−	0.194029i
$545$	−21.8875	−	10.9923i	−0.937558	−	0.470859i
$546$	2.63354	+	3.77146i	0.112705	+	0.161404i
$547$	−0.308554	−	1.03064i	−0.0131928	−	0.0440671i	0.951140	−	0.308761i	$-0.0999143\pi$
$547$	−0.308554	−	1.03064i	−0.0131928	−	0.0440671i	−0.964333	+	0.264694i	$0.914729\pi$
$548$	4.89823	+	4.11010i	0.209242	+	0.175575i
$549$	−35.0936	−	26.2676i	−1.49776	−	1.12107i
$550$	2.18776	−	1.83575i	0.0932866	−	0.0782767i
$551$	−2.38260	−	1.56706i	−0.101502	−	0.0667589i
$552$	1.39705	+	0.206483i	0.0594622	+	0.00878849i
$553$	−23.8094	−	2.78291i	−1.01248	−	0.118342i
$554$	4.52336	+	10.4863i	0.192179	+	0.445522i
$555$	−18.6500	−	10.0871i	−0.791648	−	0.428175i
$556$	−15.6367	+	7.85307i	−0.663146	+	0.333044i
$557$	28.0851	+	10.2222i	1.19001	+	0.433126i	0.859725	−	0.510757i	$-0.170635\pi$
$557$	28.0851	+	10.2222i	1.19001	+	0.433126i	0.330280	+	0.943883i	$0.392857\pi$
$558$	14.4145	+	0.876966i	0.610215	+	0.0371249i
$559$	8.17083	−	2.97394i	0.345589	−	0.125784i
$560$	4.62288	−	4.89997i	0.195352	−	0.207061i
$561$	−1.37048	+	15.4348i	−0.0578619	+	0.651657i
$562$	3.15318	−	2.07388i	0.133009	−	0.0874813i
$563$	−8.81589	+	29.4471i	−0.371546	+	1.24105i	0.544086	+	0.839030i	$0.316877\pi$
$563$	−8.81589	+	29.4471i	−0.371546	+	1.24105i	−0.915631	+	0.402019i	$0.868308\pi$
$564$	4.26245	−	20.5091i	0.179481	−	0.863588i
$565$	−1.87447	−	2.51785i	−0.0788596	−	0.105927i
$566$	−28.8994			−1.21473
$567$	−17.3050	−	30.3345i	−0.726742	−	1.27393i
$568$	4.87942			0.204736
$569$	18.0560	+	24.2534i	0.756948	+	1.01676i	0.998920	+	0.0464740i	$0.0147985\pi$
$569$	18.0560	+	24.2534i	0.756948	+	1.01676i	−0.241972	+	0.970283i	$0.577794\pi$
$570$	3.06660	+	2.73616i	0.128446	+	0.114605i
$571$	1.23675	−	4.13105i	0.0517566	−	0.172879i	−0.928204	−	0.372073i	$-0.878647\pi$
$571$	1.23675	−	4.13105i	0.0517566	−	0.172879i	0.979960	+	0.199194i	$0.0638323\pi$
$572$	0.822232	−	0.540790i	0.0343792	−	0.0226116i
$573$	−14.4366	+	6.70919i	−0.603098	+	0.280280i
$574$	−17.3717	+	18.4129i	−0.725080	+	0.768540i
$575$	−1.52173	+	0.553865i	−0.0634606	+	0.0230978i
$576$	0.699396	−	2.91734i	0.0291415	−	0.121556i
$577$	−3.88959	−	1.41570i	−0.161926	−	0.0589362i	0.259785	−	0.965666i	$-0.416348\pi$
$577$	−3.88959	−	1.41570i	−0.161926	−	0.0589362i	−0.421711	+	0.906730i	$0.638570\pi$
$578$	−19.4003	+	9.74318i	−0.806945	+	0.405263i
$579$	4.34551	−	2.67260i	0.180593	−	0.111070i
$580$	1.43468	+	3.32595i	0.0595717	+	0.138103i
$581$	28.7386	+	3.35906i	1.19228	+	0.139357i
$582$	6.09130	+	15.3907i	0.252493	+	0.637965i
$583$	0.825813	+	0.543145i	0.0342017	+	0.0224948i
$584$	7.65442	−	6.42282i	0.316742	−	0.265778i
$585$	3.55901	−	0.198053i	0.147147	−	0.00818850i
$586$	15.4611	+	12.9734i	0.638691	+	0.535925i
$587$	8.90846	+	29.7563i	0.367692	+	1.22818i	0.919128	+	0.393959i	$0.128895\pi$
$587$	8.90846	+	29.7563i	0.367692	+	1.22818i	−0.551437	+	0.834217i	$0.685920\pi$
$588$	13.9042	−	1.19834i	0.573398	−	0.0494187i
$589$	−5.87951	−	2.95280i	−0.242261	−	0.121668i
$590$	18.0718	+	19.1550i	0.744004	+	0.788598i
$591$	1.87026	+	12.8843i	0.0769321	+	0.529990i
$592$	2.79293	−	6.47475i	0.114789	−	0.266111i
$593$	−19.3213	+	33.4654i	−0.793430	+	1.37426i	0.130402	+	0.991461i	$0.458373\pi$
$593$	−19.3213	+	33.4654i	−0.793430	+	1.37426i	−0.923831	+	0.382800i	$0.874960\pi$
$594$	−6.59029	+	3.52052i	−0.270403	+	0.144449i
$595$	−20.9563	−	36.2973i	−0.859123	−	1.48805i
$596$	−11.1422	+	1.30233i	−0.456400	+	0.0533456i
$597$	−4.77111	−	8.87603i	−0.195268	−	0.363272i
$598$	−0.542991	+	0.128691i	−0.0222046	+	0.00526258i
$599$	2.48803	+	42.7177i	0.101658	+	1.74540i	0.535612	+	0.844464i	$0.320081\pi$
$599$	2.48803	+	42.7177i	0.101658	+	1.74540i	−0.433954	+	0.900935i	$0.642882\pi$
$600$	0.886065	+	3.32403i	0.0361734	+	0.135703i
$601$	−10.4936	−	2.48702i	−0.428041	−	0.101448i	0.0109480	−	0.999940i	$-0.496515\pi$
$601$	−10.4936	−	2.48702i	−0.428041	−	0.101448i	−0.438989	+	0.898493i	$0.644663\pi$
$602$	8.56066	−	48.5499i	0.348906	−	1.97875i
$603$	−23.1637	+	13.2938i	−0.943301	+	0.541367i
$604$	0.905288	+	5.13414i	0.0368356	+	0.208905i
$605$	0.901653	−	15.4808i	0.0366574	−	0.629383i
$606$	−8.53567	+	25.6481i	−0.346738	+	1.04188i
$607$	−8.63415	+	11.5977i	−0.350449	+	0.470735i	−0.942039	−	0.335504i	$-0.891093\pi$
$607$	−8.63415	+	11.5977i	−0.350449	+	0.470735i	0.591589	+	0.806239i	$0.298501\pi$
$608$	−0.816188	+	1.09633i	−0.0331008	+	0.0444621i
$609$	−4.42811	+	13.3056i	−0.179436	+	0.539171i
$610$	1.47495	−	25.3239i	0.0597189	−	1.02533i
$611$	1.43733	+	8.15150i	0.0581481	+	0.329774i
$612$	−16.1402	−	9.37431i	−0.652430	−	0.378934i
$613$	−6.30861	+	35.7779i	−0.254802	+	1.44506i	0.541777	+	0.840522i	$0.317752\pi$
$613$	−6.30861	+	35.7779i	−0.254802	+	1.44506i	−0.796579	+	0.604534i	$0.793359\pi$
$614$	6.89748	+	1.63473i	0.278360	+	0.0659724i
$615$	5.05251	+	18.9543i	0.203737	+	0.764309i
$616$	−0.324430	−	5.57026i	−0.0130717	−	0.224432i
$617$	1.74226	−	0.412922i	0.0701406	−	0.0166236i	−0.195396	−	0.980724i	$-0.562599\pi$
$617$	1.74226	−	0.412922i	0.0701406	−	0.0166236i	0.265536	+	0.964101i	$0.414451\pi$
$618$	10.8889	+	20.2573i	0.438014	+	0.814869i
$619$	41.8691	−	4.89380i	1.68286	−	0.196698i	0.779746	−	0.626096i	$-0.215348\pi$
$619$	41.8691	−	4.89380i	1.68286	−	0.196698i	0.903116	+	0.429397i	$0.141274\pi$
$620$	4.17843	+	7.23725i	0.167810	+	0.290655i
$621$	4.19428	−	0.597759i	0.168311	−	0.0239873i
$622$	−6.93837	+	12.0176i	−0.278203	+	0.481862i
$623$	−9.99569	+	23.1726i	−0.400469	+	0.928391i
$624$	0.170291	+	1.17314i	0.00681708	+	0.0469632i
$625$	7.63412	+	8.09169i	0.305365	+	0.323668i
$626$	27.7117	+	13.9174i	1.10758	+	0.556250i
$627$	3.39149	−	0.292298i	0.135443	−	0.0116733i
$628$	4.86367	+	16.2458i	0.194081	+	0.648277i
$629$	−33.6078	−	28.2003i	−1.34003	−	1.12442i
$630$	9.11671	−	18.0364i	0.363219	−	0.718587i
$631$	19.8479	−	16.6544i	0.790134	−	0.663001i	−0.155644	−	0.987813i	$-0.549745\pi$
$631$	19.8479	−	16.6544i	0.790134	−	0.663001i	0.945779	+	0.324812i	$0.105301\pi$
$632$	−5.16131	−	3.39465i	−0.205306	−	0.135032i
$633$	4.21907	+	10.6602i	0.167693	+	0.423705i
$634$	−10.9687	−	1.28206i	−0.435623	−	0.0509170i
$635$	0.00838861	+	0.0194470i	0.000332892	+	0.000771730i
$636$	−1.01415	+	0.623726i	−0.0402135	+	0.0247323i
$637$	−4.92797	+	2.47492i	−0.195253	+	0.0980599i
$638$	2.81924	+	1.02612i	0.111615	+	0.0406245i
$639$	14.0341	−	4.16201i	0.555180	−	0.164647i
$640$	1.63135	−	0.593763i	0.0644848	−	0.0234705i
$641$	−11.0581	+	11.7209i	−0.436770	+	0.462950i	−0.907944	−	0.419091i	$-0.862349\pi$
$641$	−11.0581	+	11.7209i	−0.436770	+	0.462950i	0.471174	+	0.882040i	$0.343830\pi$
$642$	−20.7958	+	9.66450i	−0.820743	+	0.381427i
$643$	−21.8971	+	14.4019i	−0.863537	+	0.567957i	−0.902211	−	0.431295i	$-0.858057\pi$
$643$	−21.8971	+	14.4019i	−0.863537	+	0.567957i	0.0386740	+	0.999252i	$0.487687\pi$
$644$	−0.907403	+	3.03094i	−0.0357567	+	0.119436i
$645$	−28.5049	−	25.4333i	−1.12238	−	1.00144i
$646$	5.07807	+	6.82103i	0.199794	+	0.268370i
$647$	−32.7231			−1.28648			−0.643240	−	0.765665i	$-0.722410\pi$
$647$	−32.7231			−1.28648			−0.643240	+	0.765665i	$0.722410\pi$
$648$	−0.476818	−	8.98736i	−0.0187312	−	0.353057i
$649$	21.8122			0.856203
$650$	−0.811741	−	1.09036i	−0.0318391	−	0.0427673i
$651$	−6.58334	+	31.6762i	−0.258021	+	1.24149i
$652$	4.74423	−	15.8468i	0.185798	−	0.620610i
$653$	17.7128	−	11.6499i	0.693157	−	0.455897i	−0.153421	−	0.988161i	$-0.549029\pi$
$653$	17.7128	−	11.6499i	0.693157	−	0.455897i	0.846578	+	0.532264i	$0.178659\pi$
$654$	2.16125	−	24.3406i	0.0845116	−	0.951793i
$655$	−8.07528	+	8.55930i	−0.315527	+	0.334440i
$656$	−6.13023	+	2.23122i	−0.239345	+	0.0871145i
$657$	16.5370	−	25.0022i	0.645171	−	0.975430i
$658$	44.0989	+	16.0507i	1.71916	+	0.625721i
$659$	−29.8595	+	14.9960i	−1.16316	+	0.584161i	−0.922329	−	0.386406i	$-0.873716\pi$
$659$	−29.8595	+	14.9960i	−1.16316	+	0.584161i	−0.240831	+	0.970567i	$0.577420\pi$
$660$	−3.80310	−	2.05696i	−0.148035	−	0.0800672i
$661$	2.48510	+	5.76110i	0.0966591	+	0.224081i	0.959684	−	0.281080i	$-0.0906925\pi$
$661$	2.48510	+	5.76110i	0.0966591	+	0.224081i	−0.863025	+	0.505161i	$0.831433\pi$
$662$	−4.10613	−	0.479938i	−0.159589	−	0.0186533i
$663$	7.29616	+	1.07837i	0.283359	+	0.0418804i
$664$	6.22986	+	4.09744i	0.241765	+	0.159012i
$665$	−7.05326	+	5.91839i	−0.273514	+	0.229505i
$666$	2.51021	−	21.0049i	0.0972685	−	0.813922i
$667$	−1.30318	−	1.09350i	−0.0504595	−	0.0423406i
$668$	4.07306	+	13.6050i	0.157592	+	0.526393i
$669$	8.74953	+	12.5301i	0.338276	+	0.484441i
$670$	−13.8112	−	6.93623i	−0.533572	−	0.267970i
$671$	−14.4184	−	15.2826i	−0.556617	−	0.589980i
$672$	6.24294	+	2.48951i	0.240827	+	0.0960351i
$673$	13.6963	−	31.7515i	0.527952	−	1.22393i	−0.420582	−	0.907255i	$-0.638174\pi$
$673$	13.6963	−	31.7515i	0.527952	−	1.22393i	0.948534	−	0.316676i	$-0.102567\pi$
$674$	−8.25982	+	14.3064i	−0.318156	+	0.551063i
$675$	5.38379	+	8.80473i	0.207222	+	0.338894i
$676$	6.26579	+	10.8527i	0.240992	+	0.417410i
$677$	−17.7455	+	2.07415i	−0.682015	+	0.0797161i	−0.450044	−	0.893007i	$-0.648592\pi$
$677$	−17.7455	+	2.07415i	−0.682015	+	0.0797161i	−0.231971	+	0.972723i	$0.574518\pi$
$678$	1.64755	−	2.66336i	0.0632736	−	0.102286i
$679$	−36.0831	+	8.55185i	−1.38474	+	0.328190i
$680$	−0.628031	−	10.7829i	−0.0240839	−	0.413504i
$681$	12.3618	+	3.32947i	0.473705	+	0.127586i
$682$	6.73520	+	1.59627i	0.257904	+	0.0611244i
$683$	−1.39814	+	7.92922i	−0.0534982	+	0.303403i	−0.999802	−	0.0198739i	$-0.993674\pi$
$683$	−1.39814	+	7.92922i	−0.0534982	+	0.303403i	0.946304	+	0.323277i	$0.104785\pi$
$684$	−1.41237	+	3.84944i	−0.0540032	+	0.147187i
$685$	1.92760	+	10.9320i	0.0736498	+	0.417689i
$686$	−0.238560	+	4.09592i	−0.00910828	+	0.156383i
$687$	4.40599	−	0.903824i	0.168099	−	0.0344830i
$688$	7.58669	−	10.1907i	0.289240	−	0.388517i
$689$	0.280939	−	0.377367i	0.0107029	−	0.0143765i
$690$	1.62750	+	1.83357i	0.0619578	+	0.0698030i
$691$	0.464483	−	7.97486i	0.0176697	−	0.303378i	−0.977882	−	0.209159i	$-0.932927\pi$
$691$	0.464483	−	7.97486i	0.0176697	−	0.303378i	0.995551	−	0.0942192i	$-0.0300355\pi$
$692$	−1.60300	−	9.09108i	−0.0609370	−	0.345591i
$693$	−5.68440	−	15.7444i	−0.215933	−	0.598078i
$694$	0.217744	−	1.23489i	0.00826547	−	0.0468758i
$695$	−29.5584	−	7.00548i	−1.12122	−	0.265733i
$696$	−2.55868	+	2.55207i	−0.0969866	+	0.0967361i
$697$	2.35999	+	40.5195i	0.0893910	+	1.53478i
$698$	14.5352	−	3.44490i	0.550164	−	0.130391i
$699$	−30.8025	−	0.936132i	−1.16506	−	0.0354078i
$700$	−7.65487	+	0.894726i	−0.289327	+	0.0338175i
$701$	7.74009	+	13.4062i	0.292339	+	0.506347i	0.974362	−	0.224984i	$-0.0722330\pi$
$701$	7.74009	+	13.4062i	0.292339	+	0.506347i	−0.682023	+	0.731331i	$0.738900\pi$
$702$	1.49045	+	3.22892i	0.0562532	+	0.121868i
$703$	−4.81891	+	8.34659i	−0.181749	+	0.314798i
$704$	0.569533	−	1.32033i	0.0214651	−	0.0497617i
$705$	28.5549	−	22.5183i	1.07544	−	0.848088i
$706$	13.3666	+	14.1677i	0.503057	+	0.533209i
$707$	−54.1173	−	27.1788i	−2.03529	−	1.02216i
$708$	−11.1346	+	23.7978i	−0.418463	+	0.894376i
$709$	−6.26078	−	20.9125i	−0.235129	−	0.785384i	−0.991370	−	0.131092i	$-0.958152\pi$
$709$	−6.26078	−	20.9125i	−0.235129	−	0.785384i	0.756242	−	0.654292i	$-0.227033\pi$
$710$	6.48908	+	5.44499i	0.243531	+	0.204347i
$711$	−17.7404	−	5.36118i	−0.665318	−	0.201060i
$712$	−4.98207	+	4.18046i	−0.186711	+	0.156669i
$713$	−3.27917	−	2.15674i	−0.122806	−	0.0807706i
$714$	25.9782	−	32.7676i	0.972210	−	1.22630i
$715$	1.69695	+	0.198345i	0.0634623	+	0.00741768i
$716$	0.488906	+	1.13341i	0.0182713	+	0.0423575i
$717$	−0.778829	−	28.0127i	−0.0290859	−	1.04615i
$718$	20.9699	−	10.5315i	0.782588	−	0.393031i
$719$	−26.1007	−	9.49987i	−0.973391	−	0.354285i	−0.194123	−	0.980977i	$-0.562186\pi$
$719$	−26.1007	−	9.49987i	−0.973391	−	0.354285i	−0.779267	+	0.626692i	$0.784408\pi$
$720$	4.18560	−	3.09927i	0.155988	−	0.115503i
$721$	−48.4169	+	17.6223i	−1.80314	+	0.656289i
$722$	−11.7566	+	12.4613i	−0.437536	+	0.463761i
$723$	6.05224	+	4.24950i	0.225085	+	0.158041i
$724$	−3.10803	+	2.04418i	−0.115509	+	0.0759714i
$725$	1.18851	−	3.96991i	0.0441403	−	0.147439i
$726$	14.6923	−	4.84743i	0.545283	−	0.179905i
$727$	10.8559	+	14.5820i	0.402622	+	0.540815i	0.956481	−	0.291795i	$-0.0942526\pi$
$727$	10.8559	+	14.5820i	0.402622	+	0.540815i	−0.553859	+	0.832611i	$0.686845\pi$
$728$	−2.65578			−0.0984297
$729$	−9.03740	−	25.4426i	−0.334718	−	0.942318i
$730$	17.3468			0.642035
$731$	−47.2021	−	63.4034i	−1.74583	−	2.34506i
$732$	24.0341	−	7.92955i	0.888326	−	0.293085i
$733$	6.10800	−	20.4022i	0.225604	−	0.753571i	−0.767980	−	0.640474i	$-0.778738\pi$
$733$	6.10800	−	20.4022i	0.225604	−	0.753571i	0.993584	−	0.113097i	$-0.0360770\pi$
$734$	−2.81426	+	1.85097i	−0.103876	+	0.0683205i
$735$	19.8282	+	13.9221i	0.731376	+	0.513526i
$736$	−0.559525	+	0.593062i	−0.0206244	+	0.0218605i
$737$	−12.0291	+	4.37823i	−0.443097	+	0.161274i
$738$	−15.7285	+	11.6463i	−0.578974	+	0.428707i
$739$	28.5799	+	10.4022i	1.05133	+	0.382652i	0.809164	−	0.587583i	$-0.199920\pi$
$739$	28.5799	+	10.4022i	1.05133	+	0.382652i	0.242164	+	0.970235i	$0.422143\pi$
$740$	10.9395	−	5.49404i	0.402145	−	0.201965i
$741$	−0.0450296	−	1.61961i	−0.00165421	−	0.0594980i
$742$	−1.05648	−	2.44920i	−0.0387846	−	0.0899129i
$743$	51.4783	+	6.01695i	1.88856	+	0.220741i	0.980278	−	0.197625i	$-0.0633229\pi$
$743$	51.4783	+	6.01695i	1.88856	+	0.220741i	0.908279	+	0.418366i	$0.137397\pi$
$744$	−5.17974	+	6.53346i	−0.189898	+	0.239528i
$745$	−16.2711	−	10.7017i	−0.596127	−	0.392079i
$746$	7.19295	−	6.03560i	0.263353	−	0.220979i
$747$	21.4132	+	6.47110i	0.783469	+	0.236765i
$748$	−6.85329	−	5.75059i	−0.250581	−	0.210262i
$749$	−14.7345	−	49.2166i	−0.538386	−	1.79834i
$750$	−8.90246	+	19.0271i	−0.325072	+	0.694772i
$751$	43.5227	+	21.8579i	1.58816	+	0.797606i	0.999938	−	0.0110908i	$-0.00353037\pi$
$751$	43.5227	+	21.8579i	1.58816	+	0.797606i	0.588226	+	0.808697i	$0.299827\pi$
$752$	8.29937	+	8.79682i	0.302647	+	0.320787i
$753$	1.34578	−	1.06128i	0.0490430	−	0.0386752i
$754$	0.565601	−	1.31121i	0.0205980	−	0.0477515i
$755$	−4.52530	+	7.83806i	−0.164693	+	0.285256i
$756$	20.0793	+	1.83524i	0.730279	+	0.0667471i
$757$	5.42011	+	9.38791i	0.196997	+	0.341209i	0.947553	−	0.319597i	$-0.103548\pi$
$757$	5.42011	+	9.38791i	0.196997	+	0.341209i	−0.750556	+	0.660807i	$0.770214\pi$
$758$	−27.0726	+	3.16433i	−0.983320	+	0.114934i
$759$	2.02973	+	0.0616865i	0.0736746	+	0.00223908i
$760$	−2.30885	+	0.547206i	−0.0837506	+	0.0198493i
$761$	−0.813760	−	13.9717i	−0.0294988	−	0.506474i	−0.980405	−	0.196994i	$-0.936882\pi$
$761$	−0.813760	−	13.9717i	−0.0294988	−	0.506474i	0.950906	−	0.309480i	$-0.100155\pi$
$762$	−0.0149607	+	0.0149221i	−0.000541970	+	0.000540570i
$763$	53.2700	+	12.6252i	1.92850	+	0.457064i
$764$	1.59602	−	9.05147i	0.0577419	−	0.327471i
$765$	−11.0038	−	30.4778i	−0.397845	−	1.10193i
$766$	−2.87248	−	16.2906i	−0.103787	−	0.588604i
$767$	0.603659	−	10.3644i	0.0217969	−	0.374238i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.597159 - 0.802123i) q^{2} +(1.64484 - 0.542681i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-1.45045 + 0.953973i) q^{5} +(-1.41753 - 0.995298i) q^{6} +(2.66288 - 2.82248i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.41100 - 1.78525i) q^{9} +O(q^{10})\)	\(q+(-0.597159 - 0.802123i) q^{2} +(1.64484 - 0.542681i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-1.45045 + 0.953973i) q^{5} +(-1.41753 - 0.995298i) q^{6} +(2.66288 - 2.82248i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.41100 - 1.78525i) q^{9} +(1.63135 + 0.593763i) q^{10} +(1.28498 - 0.645340i) q^{11} +(0.0481371 + 1.73138i) q^{12} +(-0.271082 - 0.628438i) q^{13} +(-3.85414 - 0.450484i) q^{14} +(-1.86805 + 2.35626i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(-4.76609 + 3.99923i) q^{17} +(-2.87173 - 0.867840i) q^{18} +(1.04702 + 0.878553i) q^{19} +(-0.497904 - 1.66311i) q^{20} +(2.84830 - 6.08763i) q^{21} +(-1.28498 - 0.645340i) q^{22} +(0.559525 + 0.593062i) q^{23} +(1.36004 - 1.07252i) q^{24} +(-0.786670 + 1.82371i) q^{25} +(-0.342206 + 0.592718i) q^{26} +(2.99688 - 4.24484i) q^{27} +(1.94019 + 3.36051i) q^{28} +(-2.07235 + 0.242223i) q^{29} +(3.00553 + 0.0913425i) q^{30} +(-4.68397 + 1.11012i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(1.76337 - 1.75881i) q^{33} +(6.05398 + 1.43482i) q^{34} +(-1.16978 + 6.63418i) q^{35} +(1.01877 + 2.82172i) q^{36} +(1.22447 + 6.94432i) q^{37} +(0.0794716 - 1.36447i) q^{38} +(-0.786927 - 0.886569i) q^{39} +(-1.03670 + 1.39252i) q^{40} +(3.89565 - 5.23277i) q^{41} +(-6.58391 + 1.35059i) q^{42} +(-0.738710 + 12.6832i) q^{43} +(0.249693 + 1.41608i) q^{44} +(-1.79394 + 4.88943i) q^{45} +(0.141583 - 0.802960i) q^{46} +(-11.7680 - 2.78906i) q^{47} +(-1.67245 - 0.450451i) q^{48} +(-0.468492 - 8.04370i) q^{49} +(1.93260 - 0.458036i) q^{50} +(-5.66915 + 9.16455i) q^{51} +(0.679784 - 0.0794554i) q^{52} +(0.343696 + 0.595300i) q^{53} +(-5.19450 + 0.130976i) q^{54} +(-1.24815 + 2.16186i) q^{55} +(1.53694 - 3.56303i) q^{56} +(2.19895 + 0.876882i) q^{57} +(1.43181 + 1.51763i) q^{58} +(13.5557 + 6.80793i) q^{59} +(-1.72151 - 2.46535i) q^{60} +(-4.19072 - 13.9980i) q^{61} +(3.68753 + 3.09420i) q^{62} +(1.38136 - 11.5589i) q^{63} +(0.766044 - 0.642788i) q^{64} +(0.992703 + 0.652911i) q^{65} +(-2.46380 - 0.364148i) q^{66} +(-8.84227 - 1.03351i) q^{67} +(-2.46429 - 5.71286i) q^{68} +(1.24217 + 0.671848i) q^{69} +(6.01997 - 3.02334i) q^{70} +(4.58515 + 1.66886i) q^{71} +(1.65500 - 2.50219i) q^{72} +(9.38954 - 3.41751i) q^{73} +(4.83899 - 5.12903i) q^{74} +(-0.304256 + 3.42662i) q^{75} +(-1.14193 + 0.751061i) q^{76} +(1.60027 - 5.34529i) q^{77} +(-0.241217 + 1.16064i) q^{78} +(-3.68901 - 4.95520i) q^{79} +1.73605 q^{80} +(2.62580 - 8.60844i) q^{81} -6.52365 q^{82} +(4.45274 + 5.98107i) q^{83} +(5.01498 + 4.47459i) q^{84} +(3.09780 - 10.3474i) q^{85} +(10.6146 - 6.98132i) q^{86} +(-3.27723 + 1.52304i) q^{87} +(0.986764 - 1.04591i) q^{88} +(-6.11142 + 2.22437i) q^{89} +(4.99319 - 1.48080i) q^{90} +(-2.49562 - 0.908330i) q^{91} +(-0.728620 + 0.365927i) q^{92} +(-7.10194 + 4.36787i) q^{93} +(4.79017 + 11.1049i) q^{94} +(-2.35676 - 0.275466i) q^{95} +(0.637402 + 1.61050i) q^{96} +(-7.98430 - 5.25136i) q^{97} +(-6.17228 + 5.17916i) q^{98} +(1.94598 - 3.84991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

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