LMFDB - Embedded newform 162.2.g.a.103.4

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			103.4
Character	$\chi$	$=$	162.103
Dual form			162.2.g.a.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.686242 + 0.727374i) q^{2} +(1.65061 + 0.524883i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-1.97104 + 0.230382i) q^{5} +(0.750928 + 1.56080i) q^{6} +(0.868864 + 0.436360i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(2.44900 + 1.73275i) q^{9} +O(q^{10})$	\(q+(0.686242 + 0.727374i) q^{2} +(1.65061 + 0.524883i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-1.97104 + 0.230382i) q^{5} +(0.750928 + 1.56080i) q^{6} +(0.868864 + 0.436360i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(2.44900 + 1.73275i) q^{9} +(-1.52019 - 1.27559i) q^{10} +(-1.12994 - 2.61950i) q^{11} +(-0.619969 + 1.61729i) q^{12} +(1.19896 + 0.284159i) q^{13} +(0.278854 + 0.931437i) q^{14} +(-3.37434 - 0.654298i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(0.944814 - 5.35831i) q^{17} +(0.420246 + 2.97042i) q^{18} +(-0.724393 - 4.10824i) q^{19} +(-0.115386 - 1.98110i) q^{20} +(1.20511 + 1.17631i) q^{21} +(1.12994 - 2.61950i) q^{22} +(-5.83149 + 2.92869i) q^{23} +(-1.60183 + 0.658905i) q^{24} +(-1.03329 + 0.244894i) q^{25} +(0.616088 + 1.06710i) q^{26} +(3.13283 + 4.14552i) q^{27} +(-0.486141 + 0.842022i) q^{28} +(1.00971 - 3.37266i) q^{29} +(-1.83969 - 2.90341i) q^{30} +(7.08842 + 4.66213i) q^{31} +(-0.597159 - 0.802123i) q^{32} +(-0.490156 - 4.91685i) q^{33} +(4.54586 - 2.98986i) q^{34} +(-1.81310 - 0.659913i) q^{35} +(-1.87221 + 2.34410i) q^{36} +(-3.74261 + 1.36220i) q^{37} +(2.49111 - 3.34615i) q^{38} +(1.82986 + 1.09835i) q^{39} +(1.36182 - 1.44344i) q^{40} +(-6.52714 + 6.91836i) q^{41} +(-0.0286179 + 1.68380i) q^{42} +(6.25458 - 8.40136i) q^{43} +(2.68077 - 0.975719i) q^{44} +(-5.22627 - 2.85112i) q^{45} +(-6.13206 - 2.23189i) q^{46} +(-3.54890 + 2.33415i) q^{47} +(-1.57851 - 0.712958i) q^{48} +(-3.61560 - 4.85659i) q^{49} +(-0.887215 - 0.583531i) q^{50} +(4.37200 - 8.34854i) q^{51} +(-0.353392 + 1.18041i) q^{52} +(0.380960 - 0.659842i) q^{53} +(-0.865464 + 5.12357i) q^{54} +(2.83065 + 4.90283i) q^{55} +(-0.946075 + 0.224224i) q^{56} +(0.960658 - 7.16130i) q^{57} +(3.14608 - 1.58002i) q^{58} +(-0.0874810 + 0.202804i) q^{59} +(0.849391 - 3.33058i) q^{60} +(0.258923 + 4.44553i) q^{61} +(1.47326 + 8.35528i) q^{62} +(1.37174 + 2.57417i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-2.42867 - 0.283871i) q^{65} +(3.24002 - 3.73067i) q^{66} +(2.08086 + 6.95054i) q^{67} +(5.29431 + 1.25477i) q^{68} +(-11.1627 + 1.77325i) q^{69} +(-0.764219 - 1.77166i) q^{70} +(11.3942 + 9.56084i) q^{71} +(-2.98983 + 0.246820i) q^{72} +(-5.51892 + 4.63093i) q^{73} +(-3.55916 - 1.78748i) q^{74} +(-1.83409 - 0.138133i) q^{75} +(4.14341 - 0.484295i) q^{76} +(0.161279 - 2.76905i) q^{77} +(0.456817 + 2.08473i) q^{78} +(-1.53350 - 1.62541i) q^{79} +1.98446 q^{80} +(2.99515 + 8.48699i) q^{81} -9.51143 q^{82} +(8.03965 + 8.52153i) q^{83} +(-1.24439 + 1.13468i) q^{84} +(-0.627813 + 10.7791i) q^{85} +(10.4031 - 1.21595i) q^{86} +(3.43688 - 5.03695i) q^{87} +(2.54937 + 1.28034i) q^{88} +(0.108478 - 0.0910242i) q^{89} +(-1.51265 - 5.75801i) q^{90} +(0.917739 + 0.770075i) q^{91} +(-2.58466 - 5.99192i) q^{92} +(9.25311 + 11.4159i) q^{93} +(-4.13320 - 0.979586i) q^{94} +(2.37427 + 7.93063i) q^{95} +(-0.564652 - 1.63743i) q^{96} +(-10.5566 - 1.23389i) q^{97} +(1.05138 - 5.96268i) q^{98} +(1.77172 - 8.37304i) 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	0.686242	+	0.727374i	0.485246	+	0.514331i
$2$	0.686242	+	0.727374i	0.485246	+	0.514331i
$3$	1.65061	+	0.524883i	0.952977	+	0.303041i
$3$	1.65061	+	0.524883i	0.952977	+	0.303041i
$4$	−0.0581448	+	0.998308i	−0.0290724	+	0.499154i
$5$	−1.97104	+	0.230382i	−0.881477	+	0.103030i	−0.544776	−	0.838582i	$-0.683385\pi$
$5$	−1.97104	+	0.230382i	−0.881477	+	0.103030i	−0.336701	+	0.941612i	$0.609311\pi$
$6$	0.750928	+	1.56080i	0.306565	+	0.637195i
$7$	0.868864	+	0.436360i	0.328400	+	0.164928i	0.605358	−	0.795954i	$-0.293030\pi$
$7$	0.868864	+	0.436360i	0.328400	+	0.164928i	−0.276958	+	0.960882i	$0.589326\pi$
$8$	−0.766044	+	0.642788i	−0.270838	+	0.227260i
$9$	2.44900	+	1.73275i	0.816332	+	0.577583i
$10$	−1.52019	−	1.27559i	−0.480725	−	0.403376i
$11$	−1.12994	−	2.61950i	−0.340690	−	0.789809i	−0.999303	−	0.0373267i	$-0.988116\pi$
$11$	−1.12994	−	2.61950i	−0.340690	−	0.789809i	0.658613	−	0.752482i	$-0.271143\pi$
$12$	−0.619969	+	1.61729i	−0.178970	+	0.466872i
$13$	1.19896	+	0.284159i	0.332532	+	0.0788116i	0.393490	−	0.919329i	$-0.371267\pi$
$13$	1.19896	+	0.284159i	0.332532	+	0.0788116i	−0.0609580	+	0.998140i	$0.519416\pi$
$14$	0.278854	+	0.931437i	0.0745268	+	0.248937i
$15$	−3.37434	−	0.654298i	−0.871250	−	0.168939i
$16$	−0.993238	−	0.116093i	−0.248310	−	0.0290232i
$17$	0.944814	−	5.35831i	0.229151	−	1.29958i	−0.625437	−	0.780275i	$-0.715079\pi$
$17$	0.944814	−	5.35831i	0.229151	−	1.29958i	0.854588	−	0.519306i	$-0.173810\pi$
$18$	0.420246	+	2.97042i	0.0990529	+	0.700135i
$19$	−0.724393	−	4.10824i	−0.166187	−	0.942494i	−0.947832	−	0.318770i	$-0.896730\pi$
$19$	−0.724393	−	4.10824i	−0.166187	−	0.942494i	0.781645	−	0.623724i	$-0.214381\pi$
$20$	−0.115386	−	1.98110i	−0.0258011	−	0.442988i
$21$	1.20511	+	1.17631i	0.262977	+	0.256692i
$22$	1.12994	−	2.61950i	0.240904	−	0.558479i
$23$	−5.83149	+	2.92869i	−1.21595	+	0.610673i	−0.936898	−	0.349603i	$-0.886317\pi$
$23$	−5.83149	+	2.92869i	−1.21595	+	0.610673i	−0.279052	+	0.960276i	$0.590020\pi$
$24$	−1.60183	+	0.658905i	−0.326971	+	0.134498i
$25$	−1.03329	+	0.244894i	−0.206658	+	0.0489788i
$26$	0.616088	+	1.06710i	0.120825	+	0.209275i
$27$	3.13283	+	4.14552i	0.602914	+	0.797806i
$28$	−0.486141	+	0.842022i	−0.0918721	+	0.159127i
$29$	1.00971	−	3.37266i	0.187498	−	0.626287i	−0.811616	−	0.584192i	$-0.801412\pi$
$29$	1.00971	−	3.37266i	0.187498	−	0.626287i	0.999114	−	0.0420949i	$-0.0134032\pi$
$30$	−1.83969	−	2.90341i	−0.335880	−	0.530088i
$31$	7.08842	+	4.66213i	1.27312	+	0.837343i	0.992472	−	0.122469i	$-0.0390811\pi$
$31$	7.08842	+	4.66213i	1.27312	+	0.837343i	0.280645	+	0.959812i	$0.409452\pi$
$32$	−0.597159	−	0.802123i	−0.105564	−	0.141797i
$33$	−0.490156	−	4.91685i	−0.0853252	−	0.855913i
$34$	4.54586	−	2.98986i	0.779609	−	0.512757i
$35$	−1.81310	−	0.659913i	−0.306469	−	0.111546i
$36$	−1.87221	+	2.34410i	−0.312036	+	0.390684i
$37$	−3.74261	+	1.36220i	−0.615281	+	0.223944i	−0.630812	−	0.775935i	$-0.717278\pi$
$37$	−3.74261	+	1.36220i	−0.615281	+	0.223944i	0.0155313	+	0.999879i	$0.495056\pi$
$38$	2.49111	−	3.34615i	0.404112	−	0.542817i
$39$	1.82986	+	1.09835i	0.293013	+	0.175877i
$40$	1.36182	−	1.44344i	0.215323	−	0.228229i
$41$	−6.52714	+	6.91836i	−1.01937	+	1.08047i	−0.0226309	+	0.999744i	$0.507204\pi$
$41$	−6.52714	+	6.91836i	−1.01937	+	1.08047i	−0.996737	+	0.0807225i	$0.974277\pi$
$42$	−0.0286179	+	1.68380i	−0.00441584	+	0.259816i
$43$	6.25458	−	8.40136i	0.953815	−	1.28120i	−0.00583023	−	0.999983i	$-0.501856\pi$
$43$	6.25458	−	8.40136i	0.953815	−	1.28120i	0.959645	−	0.281213i	$-0.0907368\pi$
$44$	2.68077	−	0.975719i	0.404141	−	0.147095i
$45$	−5.22627	−	2.85112i	−0.779086	−	0.425020i
$46$	−6.13206	−	2.23189i	−0.904123	−	0.329074i
$47$	−3.54890	+	2.33415i	−0.517660	+	0.340470i	−0.781305	−	0.624149i	$-0.785446\pi$
$47$	−3.54890	+	2.33415i	−0.517660	+	0.340470i	0.263645	+	0.964620i	$0.415075\pi$
$48$	−1.57851	−	0.712958i	−0.227838	−	0.102907i
$49$	−3.61560	−	4.85659i	−0.516514	−	0.693798i
$50$	−0.887215	−	0.583531i	−0.125471	−	0.0825237i
$51$	4.37200	−	8.34854i	0.612203	−	1.16903i
$52$	−0.353392	+	1.18041i	−0.0490067	+	0.163694i
$53$	0.380960	−	0.659842i	0.0523288	−	0.0906362i	−0.838674	−	0.544633i	$-0.816669\pi$
$53$	0.380960	−	0.659842i	0.0523288	−	0.0906362i	0.891003	+	0.453997i	$0.150002\pi$
$54$	−0.865464	+	5.12357i	−0.117775	+	0.697230i
$55$	2.83065	+	4.90283i	0.381685	+	0.661097i
$56$	−0.946075	+	0.224224i	−0.126425	+	0.0299632i
$57$	0.960658	−	7.16130i	0.127242	−	0.948537i
$58$	3.14608	−	1.58002i	0.413101	−	0.207467i
$59$	−0.0874810	+	0.202804i	−0.0113891	+	0.0264028i	−0.923816	−	0.382837i	$-0.874947\pi$
$59$	−0.0874810	+	0.202804i	−0.0113891	+	0.0264028i	0.912427	+	0.409240i	$0.134206\pi$
$60$	0.849391	−	3.33058i	0.109656	−	0.429977i
$61$	0.258923	+	4.44553i	0.0331517	+	0.569192i	0.973458	+	0.228864i	$0.0735011\pi$
$61$	0.258923	+	4.44553i	0.0331517	+	0.569192i	−0.940307	+	0.340328i	$0.889462\pi$
$62$	1.47326	+	8.35528i	0.187104	+	1.06112i
$63$	1.37174	+	2.57417i	0.172823	+	0.324314i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	−2.42867	−	0.283871i	−0.301240	−	0.0352099i
$66$	3.24002	−	3.73067i	0.398819	−	0.459214i
$67$	2.08086	+	6.95054i	0.254217	+	0.849144i	0.985877	+	0.167474i	$0.0535610\pi$
$67$	2.08086	+	6.95054i	0.254217	+	0.849144i	−0.731659	+	0.681670i	$0.761254\pi$
$68$	5.29431	+	1.25477i	0.642029	+	0.152164i
$69$	−11.1627	+	1.77325i	−1.34383	+	0.213474i
$70$	−0.764219	−	1.77166i	−0.0913417	−	0.211754i
$71$	11.3942	+	9.56084i	1.35224	+	1.13466i	0.978296	+	0.207212i	$0.0664389\pi$
$71$	11.3942	+	9.56084i	1.35224	+	1.13466i	0.373943	+	0.927452i	$0.378006\pi$
$72$	−2.98983	+	0.246820i	−0.352355	+	0.0290880i
$73$	−5.51892	+	4.63093i	−0.645941	+	0.542009i	−0.905836	−	0.423628i	$-0.860756\pi$
$73$	−5.51892	+	4.63093i	−0.645941	+	0.542009i	0.259895	+	0.965637i	$0.416312\pi$
$74$	−3.55916	−	1.78748i	−0.413744	−	0.207790i
$75$	−1.83409	−	0.138133i	−0.211783	−	0.0159502i
$76$	4.14341	−	0.484295i	0.475281	−	0.0555524i
$77$	0.161279	−	2.76905i	0.0183794	−	0.315562i
$78$	0.456817	+	2.08473i	0.0517244	+	0.236049i
$79$	−1.53350	−	1.62541i	−0.172532	−	0.182873i	0.635338	−	0.772234i	$-0.280861\pi$
$79$	−1.53350	−	1.62541i	−0.172532	−	0.182873i	−0.807870	+	0.589361i	$0.799379\pi$
$80$	1.98446			0.221870
$81$	2.99515	+	8.48699i	0.332795	+	0.942999i
$82$	−9.51143			−1.05036
$83$	8.03965	+	8.52153i	0.882466	+	0.935360i	0.998322	−	0.0579063i	$-0.0184425\pi$
$83$	8.03965	+	8.52153i	0.882466	+	0.935360i	−0.115856	+	0.993266i	$0.536961\pi$
$84$	−1.24439	+	1.13468i	−0.135774	+	0.123803i
$85$	−0.627813	+	10.7791i	−0.0680958	+	1.16916i
$86$	10.4031	−	1.21595i	1.12179	−	0.131119i
$87$	3.43688	−	5.03695i	0.368472	−	0.540017i
$88$	2.54937	+	1.28034i	0.271763	+	0.136485i
$89$	0.108478	−	0.0910242i	0.0114987	−	0.00964855i	−0.637020	−	0.770847i	$-0.719833\pi$
$89$	0.108478	−	0.0910242i	0.0114987	−	0.00964855i	0.648519	+	0.761199i	$0.275389\pi$
$90$	−1.51265	−	5.75801i	−0.159448	−	0.606947i
$91$	0.917739	+	0.770075i	0.0962052	+	0.0807258i
$92$	−2.58466	−	5.99192i	−0.269469	−	0.624700i
$93$	9.25311	+	11.4159i	0.959503	+	1.18378i
$94$	−4.13320	−	0.979586i	−0.426307	−	0.101037i
$95$	2.37427	+	7.93063i	0.243595	+	0.813665i
$96$	−0.564652	−	1.63743i	−0.0576296	−	0.167119i
$97$	−10.5566	−	1.23389i	−1.07186	−	0.125283i	−0.438188	−	0.898883i	$-0.644380\pi$
$97$	−10.5566	−	1.23389i	−1.07186	−	0.125283i	−0.633674	+	0.773601i	$0.718454\pi$
$98$	1.05138	−	5.96268i	0.106206	−	0.602322i
$99$	1.77172	−	8.37304i	0.178064	−	0.841523i
$100$	−0.184399	−	1.04578i	−0.0184399	−	0.104578i
$101$	−0.296004	−	5.08219i	−0.0294535	−	0.505697i	−0.980484	−	0.196599i	$-0.937010\pi$
$101$	−0.296004	−	5.08219i	−0.0294535	−	0.505697i	0.951030	−	0.309097i	$-0.100027\pi$
$102$	9.07275	−	2.54903i	0.898337	−	0.252392i
$103$	−6.19951	+	14.3721i	−0.610856	+	1.41612i	0.279183	+	0.960238i	$0.409936\pi$
$103$	−6.19951	+	14.3721i	−0.610856	+	1.41612i	−0.890039	+	0.455885i	$0.849323\pi$
$104$	−1.10111	+	0.553000i	−0.107973	+	0.0542261i
$105$	−2.64633	−	2.04092i	−0.258255	−	0.199173i
$106$	0.741382	−	0.175711i	0.0720094	−	0.0170665i
$107$	−2.98808	−	5.17551i	−0.288869	−	0.500336i	0.684671	−	0.728852i	$-0.259946\pi$
$107$	−2.98808	−	5.17551i	−0.288869	−	0.500336i	−0.973540	+	0.228516i	$0.926613\pi$
$108$	−4.32067	+	2.88649i	−0.415756	+	0.277753i
$109$	−1.48611	+	2.57401i	−0.142343	+	0.246546i	−0.928379	−	0.371636i	$-0.878797\pi$
$109$	−1.48611	+	2.57401i	−0.142343	+	0.246546i	0.786035	+	0.618182i	$0.212130\pi$
$110$	−1.62368	+	5.42346i	−0.154812	+	0.517107i
$111$	−6.89256	+	0.284019i	−0.654213	+	0.0269579i
$112$	−0.812330	−	0.534278i	−0.0767580	−	0.0504845i
$113$	−9.71400	−	13.0482i	−0.913816	−	1.22747i	−0.973369	−	0.229243i	$-0.926375\pi$
$113$	−9.71400	−	13.0482i	−0.913816	−	1.22747i	0.0595531	−	0.998225i	$-0.481032\pi$
$114$	5.86818	−	4.21562i	0.549606	−	0.394829i
$115$	10.8194	−	7.11604i	1.00892	−	0.663574i
$116$	3.30824	+	1.20410i	0.307163	+	0.111798i
$117$	2.44388	+	2.77341i	0.225936	+	0.256402i
$118$	−0.207547	+	0.0755410i	−0.0191063	+	0.00695412i
$119$	3.15907	−	4.24336i	0.289591	−	0.388988i
$120$	3.00547	−	1.66776i	0.274360	−	0.152245i
$121$	1.96365	−	2.08135i	0.178514	−	0.189214i
$122$	−3.05588	+	3.23904i	−0.276666	+	0.293249i
$123$	−14.4051	+	7.99350i	−1.29886	+	0.720749i
$124$	−5.06639	+	6.80535i	−0.454976	+	0.611138i
$125$	11.3042	−	4.11438i	1.01107	−	0.368001i
$126$	−0.931035	+	2.76427i	−0.0829432	+	0.246261i
$127$	−6.20947	−	2.26006i	−0.551002	−	0.200548i	0.0514898	−	0.998674i	$-0.483603\pi$
$127$	−6.20947	−	2.26006i	−0.551002	−	0.200548i	−0.602492	+	0.798125i	$0.705825\pi$
$128$	0.835488	−	0.549509i	0.0738474	−	0.0485702i
$129$	14.7336	−	10.5844i	1.29722	−	0.931905i
$130$	−1.46018	−	1.96136i	−0.128066	−	0.172022i
$131$	17.9758	+	11.8229i	1.57055	+	1.03297i	0.972904	+	0.231208i	$0.0742677\pi$
$131$	17.9758	+	11.8229i	1.57055	+	1.03297i	0.597646	+	0.801760i	$0.296103\pi$
$132$	4.93703	−	0.203438i	0.429713	−	0.0177070i
$133$	1.16327	−	3.88559i	0.100868	−	0.336924i
$134$	−3.62767	+	6.28331i	−0.313383	+	0.542796i
$135$	−7.13000	−	7.44926i	−0.613653	−	0.641130i
$136$	2.72048	+	4.71202i	0.233280	+	0.404052i
$137$	19.7062	−	4.67046i	1.68362	−	0.399024i	0.726142	−	0.687545i	$-0.241311\pi$
$137$	19.7062	−	4.67046i	1.68362	−	0.399024i	0.957474	+	0.288520i	$0.0931633\pi$
$138$	−8.95013	−	6.90258i	−0.761886	−	0.587587i
$139$	0.844890	−	0.424320i	0.0716626	−	0.0359903i	−0.412607	−	0.910909i	$-0.635382\pi$
$139$	0.844890	−	0.424320i	0.0716626	−	0.0359903i	0.484270	+	0.874919i	$0.339085\pi$
$140$	0.764219	−	1.77166i	0.0645883	−	0.149733i
$141$	−7.08299	+	1.99000i	−0.596495	+	0.167588i
$142$	0.864848	+	14.8489i	0.0725764	+	1.24609i
$143$	−0.610402	−	3.46176i	−0.0510444	−	0.289487i
$144$	−2.23128	−	2.00534i	−0.185940	−	0.167112i
$145$	−1.21318	+	6.88027i	−0.100749	+	0.571375i
$146$	−7.15573	−	0.836385i	−0.592212	−	0.0692197i
$147$	−3.41878	−	9.91408i	−0.281976	−	0.817699i
$148$	−1.14228	−	3.81548i	−0.0938949	−	0.313631i
$149$	−13.5047	−	3.20067i	−1.10635	−	0.262209i	−0.363450	−	0.931614i	$-0.618401\pi$
$149$	−13.5047	−	3.20067i	−1.10635	−	0.262209i	−0.742898	+	0.669404i	$0.766549\pi$
$150$	−1.15816	−	1.42886i	−0.0945631	−	0.116666i
$151$	−8.89594	−	20.6231i	−0.723942	−	1.67829i	−0.734745	−	0.678344i	$-0.762698\pi$
$151$	−8.89594	−	20.6231i	−0.723942	−	1.67829i	0.0108032	−	0.999942i	$-0.496561\pi$
$152$	3.19564	+	2.68146i	0.259201	+	0.217495i
$153$	11.5985	−	11.4853i	0.937680	−	0.928535i
$154$	2.12481	−	1.78293i	0.171222	−	0.143672i
$155$	−15.0457	−	7.55621i	−1.20850	−	0.606929i
$156$	−1.20289	+	1.76290i	−0.0963082	+	0.141145i
$157$	−13.9173	+	1.62669i	−1.11072	+	0.129824i	−0.651609	−	0.758555i	$-0.725906\pi$
$157$	−13.9173	+	1.62669i	−1.11072	+	0.129824i	−0.459110	+	0.888380i	$0.651832\pi$
$158$	0.129932	−	2.23085i	0.0103369	−	0.177477i
$159$	0.975154	−	0.889179i	0.0773347	−	0.0705164i
$160$	1.36182	+	1.44344i	0.107661	+	0.114114i
$161$	−6.34473			−0.500035
$162$	−4.11782	+	8.00272i	−0.323526	+	0.628753i
$163$	13.5318			1.05990			0.529948	−	0.848030i	$-0.322211\pi$
$163$	13.5318			1.05990			0.529948	+	0.848030i	$0.322211\pi$
$164$	−6.52714	−	6.91836i	−0.509684	−	0.540233i
$165$	2.09887	+	9.57839i	0.163397	+	0.745677i
$166$	−0.681195	+	11.6957i	−0.0528710	+	0.907759i
$167$	−6.19397	+	0.723971i	−0.479304	+	0.0560226i	−0.352315	−	0.935882i	$-0.614605\pi$
$167$	−6.19397	+	0.723971i	−0.479304	+	0.0560226i	−0.126989	+	0.991904i	$0.540531\pi$
$168$	−1.67929	−	0.126474i	−0.129560	−	0.00975766i
$169$	−10.2605	−	5.15300i	−0.789266	−	0.396384i
$170$	−8.27128	+	6.94043i	−0.634378	+	0.532307i
$171$	5.34451	−	11.3162i	0.408705	−	0.865375i
$172$	8.02348	+	6.73250i	0.611785	+	0.513348i
$173$	4.76907	+	11.0560i	0.362586	+	0.840569i	0.997676	+	0.0681309i	$0.0217035\pi$
$173$	4.76907	+	11.0560i	0.362586	+	0.840569i	−0.635090	+	0.772438i	$0.719037\pi$
$174$	6.02227	−	0.956667i	0.456547	−	0.0725248i
$175$	−1.00465	−	0.238106i	−0.0759443	−	0.0179991i
$176$	0.818196	+	2.73296i	0.0616738	+	0.206005i
$177$	−0.250845	+	0.288832i	−0.0188547	+	0.0217099i
$178$	0.140651	+	0.0164397i	0.0105422	+	0.00123221i
$179$	1.82508	−	10.3506i	0.136413	−	0.773637i	−0.837452	−	0.546510i	$-0.815956\pi$
$179$	1.82508	−	10.3506i	0.136413	−	0.773637i	0.973865	−	0.227126i	$-0.0729330\pi$
$180$	3.15018	−	5.05165i	0.234800	−	0.376528i
$181$	−3.69405	−	20.9500i	−0.274577	−	1.55720i	−0.740303	−	0.672273i	$-0.765318\pi$
$181$	−3.69405	−	20.9500i	−0.274577	−	1.55720i	0.465727	−	0.884929i	$-0.345793\pi$
$182$	0.0696589	+	1.19600i	0.00516346	+	0.0886532i
$183$	−1.90601	+	7.47372i	−0.140896	+	0.552473i
$184$	2.58466	−	5.99192i	0.190544	−	0.441730i
$185$	7.06302	−	3.54718i	0.519283	−	0.260794i
$186$	−1.95377	+	14.5646i	−0.143258	+	1.06792i
$187$	−15.1037	+	3.57963i	−1.10449	+	0.261769i
$188$	−2.12385	−	3.67861i	−0.154898	−	0.268290i
$189$	0.913065	+	4.96894i	0.0664157	+	0.361437i
$190$	−4.13920	+	7.16931i	−0.300289	+	0.520116i
$191$	−1.54218	+	5.15125i	−0.111589	+	0.372732i	−0.995481	−	0.0949580i	$-0.969728\pi$
$191$	−1.54218	+	5.15125i	−0.111589	+	0.372732i	0.883893	+	0.467690i	$0.154914\pi$
$192$	0.803534	−	1.53438i	0.0579900	−	0.110735i
$193$	1.48697	+	0.977995i	0.107034	+	0.0703977i	0.601898	−	0.798573i	$-0.294411\pi$
$193$	1.48697	+	0.977995i	0.107034	+	0.0703977i	−0.494863	+	0.868971i	$0.664782\pi$
$194$	−6.34689	−	8.52535i	−0.455680	−	0.612085i
$195$	−3.85978	−	1.74333i	−0.276405	−	0.124842i
$196$	5.05860	−	3.32709i	0.361329	−	0.237650i
$197$	13.2546	+	4.82428i	0.944352	+	0.343716i	0.767883	−	0.640590i	$-0.221310\pi$
$197$	13.2546	+	4.82428i	0.944352	+	0.343716i	0.176469	+	0.984306i	$0.443532\pi$
$198$	7.30616	−	4.45723i	0.519226	−	0.316762i
$199$	26.4129	−	9.61351i	1.87236	−	0.681484i	0.906639	−	0.421906i	$-0.138639\pi$
$199$	26.4129	−	9.61351i	1.87236	−	0.681484i	0.965722	−	0.259578i	$-0.0835833\pi$
$200$	0.634130	−	0.851785i	0.0448398	−	0.0602303i
$201$	−0.213552	+	12.5648i	−0.0150628	+	0.886254i
$202$	3.49352	−	3.70291i	0.245803	−	0.260536i
$203$	2.34899	−	2.48978i	0.164867	−	0.174749i
$204$	8.08020	+	4.85003i	0.565727	+	0.339570i
$205$	11.2714	−	15.1401i	0.787229	−	1.05743i
$206$	−14.7082	+	5.35336i	−1.02477	+	0.372986i
$207$	−19.3560	−	2.93218i	−1.34533	−	0.203801i
$208$	−1.15787	−	0.421429i	−0.0802836	−	0.0292208i
$209$	−9.94300	+	6.53961i	−0.687772	+	0.452355i
$210$	−0.331510	−	3.32544i	−0.0228764	−	0.229477i
$211$	−4.64579	−	6.24038i	−0.319830	−	0.429606i	0.612912	−	0.790151i	$-0.289998\pi$
$211$	−4.64579	−	6.24038i	−0.319830	−	0.429606i	−0.932742	+	0.360545i	$0.882591\pi$
$212$	0.636574	+	0.418682i	0.0437201	+	0.0287552i
$213$	13.7890	+	21.7618i	0.944803	+	1.49109i
$214$	1.71398	−	5.72511i	0.117166	−	0.391360i
$215$	−10.3925	+	18.0004i	−0.708765	+	1.22762i
$216$	−5.06458	−	1.16191i	−0.344601	−	0.0790579i
$217$	4.12451	+	7.14385i	0.279990	+	0.484956i
$218$	−2.89210	+	0.685440i	−0.195878	+	0.0464239i
$219$	−11.5403	+	4.74704i	−0.779818	+	0.320775i
$220$	−5.05912	+	2.54079i	−0.341086	+	0.171300i
$221$	2.65541	−	6.15593i	0.178622	−	0.414093i
$222$	−4.93655	−	4.81856i	−0.331320	−	0.323401i
$223$	1.33370	+	22.8987i	0.0893110	+	1.53341i	0.684016	+	0.729467i	$0.260232\pi$
$223$	1.33370	+	22.8987i	0.0893110	+	1.53341i	−0.594705	+	0.803944i	$0.702731\pi$
$224$	−0.168835	−	0.957512i	−0.0112808	−	0.0639764i
$225$	−2.95486	−	1.19069i	−0.196991	−	0.0793792i
$226$	2.82474	−	16.0199i	0.187899	−	1.06563i
$227$	8.01258	+	0.936536i	0.531813	+	0.0621601i	0.377762	−	0.925903i	$-0.376694\pi$
$227$	8.01258	+	0.936536i	0.531813	+	0.0621601i	0.154052	+	0.988063i	$0.450768\pi$
$228$	7.09333	+	1.37543i	0.469767	+	0.0910898i
$229$	−7.42196	−	24.7911i	−0.490457	−	1.63824i	−0.742004	−	0.670395i	$-0.766125\pi$
$229$	−7.42196	−	24.7911i	−0.490457	−	1.63824i	0.251547	−	0.967845i	$-0.419061\pi$
$230$	12.6007	+	2.98643i	0.830869	+	0.196920i
$231$	1.71963	−	4.48595i	0.113144	−	0.295154i
$232$	1.39442	+	3.23263i	0.0915483	+	0.212233i
$233$	5.02217	+	4.21410i	0.329013	+	0.276075i	0.792298	−	0.610135i	$-0.208885\pi$
$233$	5.02217	+	4.21410i	0.329013	+	0.276075i	−0.463284	+	0.886210i	$0.653329\pi$
$234$	−0.340214	+	3.68084i	−0.0222405	+	0.240624i
$235$	6.45729	−	5.41831i	0.421227	−	0.353451i
$236$	−0.197374	−	0.0991250i	−0.0128480	−	0.00645249i
$237$	−1.67805	−	3.48782i	−0.109001	−	0.226558i
$238$	5.25439	−	0.614150i	0.340592	−	0.0398094i
$239$	0.437409	−	7.51002i	0.0282936	−	0.485783i	−0.954163	−	0.299289i	$-0.903251\pi$
$239$	0.437409	−	7.51002i	0.0282936	−	0.485783i	0.982456	−	0.186494i	$-0.0597124\pi$
$240$	3.27556	+	1.04161i	0.211437	+	0.0672357i
$241$	19.2683	+	20.4232i	1.24118	+	1.31557i	0.931055	+	0.364879i	$0.118890\pi$
$241$	19.2683	+	20.4232i	1.24118	+	1.31557i	0.310126	+	0.950696i	$0.399629\pi$
$242$	2.86146			0.183942
$243$	0.489137	+	15.5808i	0.0313781	+	0.999508i
$244$	−4.45306			−0.285078
$245$	8.24537	+	8.73958i	0.526777	+	0.558351i
$246$	−15.6996	−	4.99239i	−1.00097	−	0.318303i
$247$	0.298874	−	5.13147i	0.0190169	−	0.326507i
$248$	−8.42680	+	0.984952i	−0.535102	+	0.0625445i
$249$	8.79748	+	18.2856i	0.557518	+	1.15880i
$250$	10.7501	+	5.39889i	0.679894	+	0.341456i
$251$	−6.61197	+	5.54810i	−0.417344	+	0.350193i	−0.827152	−	0.561979i	$-0.810040\pi$
$251$	−6.61197	+	5.54810i	−0.417344	+	0.350193i	0.409808	+	0.912172i	$0.365596\pi$
$252$	−2.64957	+	1.21975i	−0.166907	+	0.0768367i
$253$	14.2609	+	11.9663i	0.896577	+	0.752318i
$254$	−2.61729	−	6.06756i	−0.164223	−	0.380712i
$255$	−6.69405	+	17.4626i	−0.419198	+	1.09355i
$256$	0.973045	+	0.230616i	0.0608153	+	0.0144135i
$257$	−1.84364	−	6.15819i	−0.115003	−	0.384138i	0.881036	−	0.473049i	$-0.156846\pi$
$257$	−1.84364	−	6.15819i	−0.115003	−	0.384138i	−0.996040	+	0.0889110i	$0.971661\pi$
$258$	17.8096	+	3.45336i	1.10878	+	0.214997i
$259$	−3.84623	−	0.449559i	−0.238993	−	0.0279343i
$260$	0.424606	−	2.40806i	0.0263329	−	0.149341i
$261$	8.31674	−	6.51005i	0.514793	−	0.402962i
$262$	3.73609	+	21.1884i	0.230817	+	1.30903i
$263$	0.326352	+	5.60324i	0.0201237	+	0.345511i	0.993309	+	0.115488i	$0.0368431\pi$
$263$	0.326352	+	5.60324i	0.0201237	+	0.345511i	−0.973185	+	0.230023i	$0.926120\pi$
$264$	3.53597	+	3.45146i	0.217624	+	0.212422i
$265$	−0.598872	+	1.38834i	−0.0367884	+	0.0852852i
$266$	3.62456	−	1.82032i	0.222236	−	0.111611i
$267$	0.226832	−	0.0933065i	0.0138819	−	0.00571027i
$268$	−7.05978	+	1.67320i	−0.431244	+	0.102207i
$269$	−13.8587	−	24.0039i	−0.844978	−	1.46354i	−0.885641	−	0.464372i	$-0.846280\pi$
$269$	−13.8587	−	24.0039i	−0.844978	−	1.46354i	0.0406627	−	0.999173i	$-0.487053\pi$
$270$	0.525489	−	10.2982i	0.0319802	−	0.626726i
$271$	0.898149	−	1.55564i	0.0545587	−	0.0944984i	−0.837456	−	0.546504i	$-0.815958\pi$
$271$	0.898149	−	1.55564i	0.0545587	−	0.0944984i	0.892015	+	0.452006i	$0.149291\pi$
$272$	−1.56049	+	5.21239i	−0.0946185	+	0.316048i
$273$	1.11063	+	1.75280i	0.0672181	+	0.106084i
$274$	16.9204	+	11.1287i	1.02220	+	0.672311i
$275$	1.80906	+	2.42998i	0.109090	+	0.146533i
$276$	−1.12120	−	11.2469i	−0.0674881	−	0.676986i
$277$	6.99361	−	4.59977i	0.420205	−	0.276373i	−0.321747	−	0.946826i	$-0.604270\pi$
$277$	6.99361	−	4.59977i	0.420205	−	0.276373i	0.741953	+	0.670452i	$0.233900\pi$
$278$	0.888438	+	0.323365i	0.0532850	+	0.0193941i
$279$	9.28120	+	23.7000i	0.555651	+	1.41888i
$280$	1.81310	−	0.659913i	0.108353	−	0.0394374i
$281$	−8.75814	+	11.7642i	−0.522467	+	0.701795i	−0.982533	−	0.186090i	$-0.940418\pi$
$281$	−8.75814	+	11.7642i	−0.522467	+	0.701795i	0.460066	+	0.887885i	$0.347826\pi$
$282$	−6.30811	−	3.78636i	−0.375643	−	0.225474i
$283$	14.6425	−	15.5202i	0.870407	−	0.922578i	−0.127188	−	0.991879i	$-0.540595\pi$
$283$	14.6425	−	15.5202i	0.870407	−	0.922578i	0.997596	+	0.0693007i	$0.0220768\pi$
$284$	−10.2072	+	10.8190i	−0.605685	+	0.641988i
$285$	−0.243665	+	14.3365i	−0.0144334	+	0.849224i
$286$	2.09911	−	2.81960i	0.124123	−	0.166726i
$287$	−8.69009	+	3.16293i	−0.512960	+	0.186702i
$288$	−0.0725594	−	2.99912i	−0.00427561	−	0.176725i
$289$	−11.8440	−	4.31087i	−0.696707	−	0.253581i
$290$	−5.83706	+	3.83909i	−0.342764	+	0.225439i
$291$	−16.7772	−	7.57766i	−0.983494	−	0.444210i
$292$	−4.30219	−	5.77885i	−0.251767	−	0.338182i
$293$	12.9636	+	8.52628i	0.757341	+	0.498111i	0.868498	−	0.495692i	$-0.165085\pi$
$293$	12.9636	+	8.52628i	0.757341	+	0.498111i	−0.111158	+	0.993803i	$0.535456\pi$
$294$	4.86513	−	9.29018i	0.283740	−	0.541814i
$295$	0.125707	−	0.419889i	0.00731892	−	0.0244469i
$296$	1.99140	−	3.44921i	0.115748	−	0.200481i
$297$	7.31927	−	12.8906i	0.424707	−	0.747991i
$298$	−6.93940	−	12.0194i	−0.401989	−	0.696265i
$299$	−7.82396	+	1.85431i	−0.452471	+	0.107238i
$300$	0.244542	−	1.82296i	0.0141186	−	0.105249i
$301$	9.10040	−	4.57039i	0.524538	−	0.263433i
$302$	8.89594	−	20.6231i	0.511904	−	1.18673i
$303$	2.17897	−	8.54405i	0.125179	−	0.490843i
$304$	0.242558	+	4.16456i	0.0139116	+	0.238854i
$305$	−1.53452	−	8.70268i	−0.0878662	−	0.498314i
$306$	16.3135	+	0.554689i	0.932580	+	0.0317095i
$307$	−0.146163	+	0.828930i	−0.00834195	+	0.0473096i	−0.988695	−	0.149943i	$-0.952091\pi$
$307$	−0.146163	+	0.828930i	−0.00834195	+	0.0473096i	0.980353	+	0.197253i	$0.0632020\pi$
$308$	2.75499	+	0.322012i	0.156980	+	0.0183483i
$309$	−17.7766	+	20.4686i	−1.01128	+	1.16442i
$310$	−4.82876	−	16.1292i	−0.274255	−	0.916077i
$311$	−7.29384	−	1.72867i	−0.413596	−	0.0980239i	0.0185498	−	0.999828i	$-0.494095\pi$
$311$	−7.29384	−	1.72867i	−0.413596	−	0.0980239i	−0.432145	+	0.901804i	$0.642243\pi$
$312$	−2.10776	+	0.334828i	−0.119329	+	0.0189559i
$313$	11.2311	+	26.0367i	0.634821	+	1.47168i	0.866646	+	0.498923i	$0.166271\pi$
$313$	11.2311	+	26.0367i	0.634821	+	1.47168i	−0.231826	+	0.972757i	$0.574470\pi$
$314$	−10.7338	−	9.00674i	−0.605745	−	0.508280i
$315$	−3.29680	−	4.75777i	−0.185754	−	0.268070i
$316$	1.71183	−	1.43639i	0.0962978	−	0.0808034i
$317$	−0.263419	−	0.132294i	−0.0147951	−	0.00743037i	0.441386	−	0.897317i	$-0.354487\pi$
$317$	−0.263419	−	0.132294i	−0.0147951	−	0.00743037i	−0.456181	+	0.889887i	$0.650783\pi$
$318$	1.31596	+	0.0991099i	0.0737952	+	0.00555781i
$319$	−9.97558	+	1.16598i	−0.558525	+	0.0652822i
$320$	−0.115386	+	1.98110i	−0.00645028	+	0.110747i
$321$	−2.21561	−	10.1111i	−0.123663	−	0.564348i
$322$	−4.35402	−	4.61499i	−0.242640	−	0.257183i
$323$	−22.6976			−1.26293
$324$	−8.64679	+	2.49661i	−0.480377	+	0.138701i
$325$	−1.30846			−0.0725805
$326$	9.28611	+	9.84271i	0.514310	+	0.545137i
$327$	−3.80403	+	3.46865i	−0.210364	+	0.191817i
$328$	0.553040	−	9.49533i	0.0305365	−	0.524292i
$329$	−4.10204	+	0.479459i	−0.226153	+	0.0264334i
$330$	−5.52674	+	8.09975i	−0.304237	+	0.445877i
$331$	−23.2599	−	11.6816i	−1.27848	−	0.642076i	−0.325623	−	0.945500i	$-0.605574\pi$
$331$	−23.2599	−	11.6816i	−1.27848	−	0.642076i	−0.952856	+	0.303423i	$0.901870\pi$
$332$	−8.97458	+	7.53057i	−0.492544	+	0.413294i
$333$	−11.5260	−	3.14899i	−0.631620	−	0.172564i
$334$	−4.77716	−	4.00851i	−0.261394	−	0.219336i
$335$	−5.70274	−	13.2204i	−0.311574	−	0.722309i
$336$	−1.06040	−	1.30826i	−0.0578497	−	0.0713715i
$337$	5.69426	+	1.34956i	0.310186	+	0.0735154i	0.382761	−	0.923848i	$-0.374973\pi$
$337$	5.69426	+	1.34956i	0.310186	+	0.0735154i	−0.0725746	+	0.997363i	$0.523122\pi$
$338$	−3.29300	−	10.9994i	−0.179116	−	0.598288i
$339$	−9.18521	−	26.6361i	−0.498872	−	1.44667i
$340$	−10.7244	−	1.25350i	−0.581611	−	0.0679806i
$341$	4.20294	−	23.8360i	0.227602	−	1.29079i
$342$	11.8988	−	3.87822i	0.643412	−	0.209710i
$343$	−2.20409	−	12.5000i	−0.119009	−	0.674936i
$344$	0.609004	+	10.4562i	0.0328353	+	0.563760i
$345$	21.5937	−	6.06684i	1.16256	−	0.326628i
$346$	−4.76907	+	11.0560i	−0.256387	+	0.594372i
$347$	20.1631	−	10.1263i	1.08241	−	0.543609i	0.184076	−	0.982912i	$-0.441071\pi$
$347$	20.1631	−	10.1263i	1.08241	−	0.543609i	0.898339	+	0.439303i	$0.144775\pi$
$348$	4.82859	+	3.72394i	0.258839	+	0.199624i
$349$	−31.3627	+	7.43310i	−1.67881	+	0.397885i	−0.956047	−	0.293214i	$-0.905275\pi$
$349$	−31.3627	+	7.43310i	−1.67881	+	0.397885i	−0.722760	+	0.691099i	$0.757127\pi$
$350$	−0.516240	−	0.894154i	−0.0275942	−	0.0477945i
$351$	2.57816	+	5.86055i	0.137612	+	0.312813i
$352$	−1.42641	+	2.47061i	−0.0760277	+	0.131684i
$353$	−2.61760	+	8.74338i	−0.139321	+	0.465363i	−0.998963	−	0.0455332i	$-0.985501\pi$
$353$	−2.61760	+	8.74338i	−0.139321	+	0.465363i	0.859642	+	0.510897i	$0.170686\pi$
$354$	−0.382229	+	0.0157503i	−0.0203152	+	0.000837121i
$355$	−24.6610	−	16.2198i	−1.30887	−	0.860859i
$356$	0.0845627	+	0.113587i	0.00448182	+	0.00602012i
$357$	7.44164	−	5.34597i	0.393853	−	0.282939i
$358$	8.78117	−	5.77546i	0.464099	−	0.305243i
$359$	−1.25255	−	0.455890i	−0.0661069	−	0.0240609i	0.308755	−	0.951142i	$-0.400088\pi$
$359$	−1.25255	−	0.455890i	−0.0661069	−	0.0240609i	−0.374862	+	0.927081i	$0.622310\pi$
$360$	5.83622	−	1.17530i	0.307596	−	0.0619435i
$361$	1.50129	−	0.546425i	0.0790153	−	0.0287592i
$362$	12.7035	−	17.0637i	0.667680	−	0.896849i
$363$	4.33368	−	2.40480i	0.227459	−	0.126219i
$364$	−0.822134	+	0.871411i	−0.0430915	+	0.0456743i
$365$	9.81115	−	10.3992i	0.513539	−	0.544320i
$366$	−6.74417	+	3.74240i	−0.352523	+	0.195618i
$367$	−6.53198	+	8.77397i	−0.340966	+	0.457997i	−0.939223	−	0.343307i	$-0.888453\pi$
$367$	−6.53198	+	8.77397i	−0.340966	+	0.457997i	0.598257	+	0.801304i	$0.295860\pi$
$368$	6.13206	−	2.23189i	0.319656	−	0.116345i
$369$	−27.9727	+	5.63313i	−1.45620	+	0.293249i
$370$	7.42706	+	2.70323i	0.386115	+	0.140534i
$371$	0.618930	−	0.407077i	0.0321333	−	0.0211344i
$372$	−11.9346	+	8.57368i	−0.618782	+	0.444525i
$373$	−5.02841	−	6.75432i	−0.260361	−	0.349726i	0.652651	−	0.757659i	$-0.273657\pi$
$373$	−5.02841	−	6.75432i	−0.260361	−	0.349726i	−0.913012	+	0.407933i	$0.866250\pi$
$374$	−12.9685	−	8.52951i	−0.670585	−	0.441051i
$375$	20.8183	−	0.857849i	1.07505	−	0.0442991i
$376$	1.21825	−	4.06925i	0.0628266	−	0.209855i
$377$	2.16897	−	3.75677i	0.111708	−	0.193484i
$378$	−2.98769	+	4.07403i	−0.153670	+	0.209546i
$379$	5.48813	+	9.50572i	0.281906	+	0.488276i	0.971854	−	0.235583i	$-0.0756999\pi$
$379$	5.48813	+	9.50572i	0.281906	+	0.488276i	−0.689948	+	0.723859i	$0.742367\pi$
$380$	−8.05526	+	1.90913i	−0.413226	+	0.0979364i
$381$	−9.06312	−	6.98972i	−0.464318	−	0.358094i
$382$	−4.80520	+	2.41326i	−0.245855	+	0.123473i
$383$	−6.04204	+	14.0070i	−0.308734	+	0.715725i	−0.999976	−	0.00689765i	$-0.997804\pi$
$383$	−6.04204	+	14.0070i	−0.308734	+	0.715725i	0.691242	+	0.722623i	$0.257064\pi$
$384$	1.66749	−	0.468489i	0.0850937	−	0.0239075i
$385$	0.320051	+	5.49507i	0.0163113	+	0.280055i
$386$	0.309052	+	1.75272i	0.0157304	+	0.0892113i
$387$	29.8749	−	9.73727i	1.51863	−	0.494973i
$388$	1.84562	−	10.4670i	0.0936970	−	0.531382i
$389$	25.7573	+	3.01059i	1.30595	+	0.152643i	0.740452	−	0.672109i	$-0.234611\pi$
$389$	25.7573	+	3.01059i	1.30595	+	0.152643i	0.565494	+	0.824752i	$0.308686\pi$
$390$	−1.38069	−	4.00385i	−0.0699140	−	0.202743i
$391$	10.1831	+	34.0140i	0.514983	+	1.72016i
$392$	5.89146	+	1.39630i	0.297564	+	0.0705239i
$393$	23.4653	+	28.9500i	1.18367	+	1.46034i
$394$	5.58681	+	12.9517i	0.281459	+	0.652496i
$395$	3.39705	+	2.85047i	0.170924	+	0.143423i
$396$	8.25586	+	2.25557i	0.414873	+	0.113347i
$397$	−10.2452	+	8.59675i	−0.514192	+	0.431458i	−0.862601	−	0.505884i	$-0.831166\pi$
$397$	−10.2452	+	8.59675i	−0.514192	+	0.431458i	0.348409	+	0.937342i	$0.386722\pi$
$398$	25.1183	+	12.6149i	1.25906	+	0.632326i
$399$	3.95958	−	5.80300i	0.198227	−	0.290513i
$400$	1.05473	−	0.123281i	0.0527366	−	0.00616403i
$401$	0.216108	−	3.71042i	0.0107919	−	0.185290i	−0.988604	−	0.150539i	$-0.951899\pi$
$401$	0.216108	−	3.71042i	0.0107919	−	0.185290i	0.999396	−	0.0347509i	$-0.0110638\pi$
$402$	−9.28586	+	8.46717i	−0.463137	+	0.422304i
$403$	7.17396	+	7.60396i	0.357361	+	0.378780i
$404$	5.09080			0.253277
$405$	−7.85883	−	16.0382i	−0.390508	−	0.796945i
$406$	3.42298			0.169879
$407$	7.79720	+	8.26455i	0.386493	+	0.409659i
$408$	2.01719	+	9.20562i	0.0998656	+	0.455746i
$409$	0.553163	−	9.49745i	0.0273522	−	0.469618i	−0.956625	−	0.291323i	$-0.905905\pi$
$409$	0.553163	−	9.49745i	0.0273522	−	0.469618i	0.983977	−	0.178296i	$-0.0570583\pi$
$410$	18.7474	−	2.19126i	0.925870	−	0.108219i
$411$	34.9786	+	2.63438i	1.72537	+	0.129944i
$412$	−13.9873	−	7.02468i	−0.689104	−	0.346081i
$413$	−0.164505	+	0.138036i	−0.00809474	+	0.00679229i
$414$	−11.1501	−	16.0912i	−0.547997	−	0.790840i
$415$	−17.8097	−	14.9441i	−0.874244	−	0.733578i
$416$	−0.488040	−	1.13140i	−0.0239281	−	0.0554716i
$417$	1.61730	−	0.256916i	0.0791994	−	0.0125812i
$418$	−11.5800	−	2.74452i	−0.566398	−	0.134239i
$419$	2.87324	+	9.59729i	0.140367	+	0.468859i	0.999047	−	0.0436541i	$-0.0139000\pi$
$419$	2.87324	+	9.59729i	0.140367	+	0.468859i	−0.858680	+	0.512513i	$0.828715\pi$
$420$	2.19134	−	2.52318i	0.106926	−	0.123119i
$421$	13.8333	+	1.61688i	0.674195	+	0.0788021i	0.446300	−	0.894884i	$-0.352742\pi$
$421$	13.8333	+	1.61688i	0.674195	+	0.0788021i	0.227895	+	0.973686i	$0.426816\pi$
$422$	1.35095	−	7.66164i	0.0657634	−	0.372963i
$423$	−12.7357	−	0.433039i	−0.619232	−	0.0210551i
$424$	0.132306	+	0.750344i	0.00642534	+	0.0364399i
$425$	0.335951	+	5.76806i	0.0162960	+	0.279792i
$426$	−6.36640	+	24.9636i	−0.308453	+	1.20949i
$427$	−1.71488	+	3.97554i	−0.0829890	+	0.192390i
$428$	5.34050	−	2.68210i	0.258143	−	0.129644i
$429$	0.809489	−	6.03440i	0.0390825	−	0.291343i
$430$	−20.2248	+	4.79337i	−0.975327	+	0.231157i
$431$	−2.88041	−	4.98901i	−0.138744	−	0.240312i	0.788277	−	0.615320i	$-0.210973\pi$
$431$	−2.88041	−	4.98901i	−0.138744	−	0.240312i	−0.927022	+	0.375008i	$0.877640\pi$
$432$	−2.63038	−	4.48119i	−0.126554	−	0.215601i
$433$	−8.41428	+	14.5740i	−0.404364	+	0.700380i	−0.994247	−	0.107109i	$-0.965841\pi$
$433$	−8.41428	+	14.5740i	−0.404364	+	0.700380i	0.589883	+	0.807489i	$0.299174\pi$
$434$	−2.36584	+	7.90247i	−0.113564	+	0.379331i
$435$	−5.61382	+	10.7198i	−0.269162	+	0.513977i
$436$	−2.48325	−	1.63326i	−0.118926	−	0.0782189i
$437$	16.2560	+	21.8356i	0.777631	+	1.04454i
$438$	−11.3723	−	5.13646i	−0.543388	−	0.245430i
$439$	14.5175	−	9.54834i	0.692884	−	0.455717i	−0.153598	−	0.988133i	$-0.549086\pi$
$439$	14.5175	−	9.54834i	0.692884	−	0.455717i	0.846483	+	0.532416i	$0.178716\pi$
$440$	−5.31988	−	1.93628i	−0.253615	−	0.0923084i
$441$	−0.439323	−	18.1587i	−0.0209202	−	0.864699i
$442$	6.29992	−	2.29298i	0.299657	−	0.109066i
$443$	9.72557	−	13.0637i	0.462076	−	0.620675i	−0.508619	−	0.860992i	$-0.669844\pi$
$443$	9.72557	−	13.0637i	0.462076	−	0.620675i	0.970695	+	0.240316i	$0.0772512\pi$
$444$	0.117229	−	6.89742i	0.00556343	−	0.327337i
$445$	−0.192845	+	0.204404i	−0.00914175	+	0.00968968i
$446$	−15.7407	+	16.6841i	−0.745343	+	0.790017i
$447$	−20.6109	−	12.3714i	−0.974864	−	0.585149i
$448$	0.580607	−	0.779891i	0.0274311	−	0.0368464i
$449$	−25.5331	+	9.29330i	−1.20498	+	0.438578i	−0.864961	−	0.501840i	$-0.832657\pi$
$449$	−25.5331	+	9.29330i	−1.20498	+	0.438578i	−0.340022	+	0.940417i	$0.610435\pi$
$450$	−1.16167	−	2.96639i	−0.0547618	−	0.139837i
$451$	25.4979	+	9.28048i	1.20065	+	0.437001i
$452$	13.5909	−	8.93888i	0.639263	−	0.420450i
$453$	−3.85896	−	38.7100i	−0.181310	−	1.81875i
$454$	4.81735	+	6.47083i	0.226090	+	0.303691i
$455$	−1.98632	−	1.30642i	−0.0931199	−	0.0612459i
$456$	3.86729	+	6.10337i	0.181102	+	0.285817i
$457$	−9.69386	+	32.3798i	−0.453460	+	1.51466i	0.359951	+	0.932971i	$0.382794\pi$
$457$	−9.69386	+	32.3798i	−0.453460	+	1.51466i	−0.813411	+	0.581690i	$0.802392\pi$
$458$	12.9391	−	22.4112i	0.604605	−	1.04721i
$459$	25.1729	−	12.8699i	1.17497	−	0.600717i
$460$	6.47491	+	11.2149i	0.301894	+	0.522896i
$461$	−7.38299	+	1.74980i	−0.343860	+	0.0814963i	−0.398917	−	0.916987i	$-0.630614\pi$
$461$	−7.38299	+	1.74980i	−0.343860	+	0.0814963i	0.0550573	+	0.998483i	$0.482466\pi$
$462$	4.44305	−	1.82763i	0.206709	−	0.0850291i
$463$	3.86605	−	1.94161i	0.179671	−	0.0902341i	−0.356690	−	0.934223i	$-0.616095\pi$
$463$	3.86605	−	1.94161i	0.179671	−	0.0902341i	0.536361	+	0.843989i	$0.319799\pi$
$464$	−1.39442	+	3.23263i	−0.0647344	+	0.150071i
$465$	−20.8683	−	20.3695i	−0.967744	−	0.944614i
$466$	0.381196	+	6.54489i	0.0176586	+	0.303186i
$467$	0.567766	+	3.21996i	0.0262731	+	0.149002i	0.995122	−	0.0986496i	$-0.0314523\pi$
$467$	0.567766	+	3.21996i	0.0262731	+	0.149002i	−0.968849	+	0.247652i	$0.920341\pi$
$468$	−2.91081	+	2.27848i	−0.134552	+	0.105323i
$469$	−1.22496	+	6.94708i	−0.0565633	+	0.320786i
$470$	8.37239	+	0.978592i	0.386190	+	0.0451391i
$471$	−23.8257	−	4.61991i	−1.09783	−	0.212874i
$472$	−0.0633454	−	0.211588i	−0.00291571	−	0.00973915i
$473$	−29.0747	−	6.89082i	−1.33685	−	0.316840i
$474$	1.38540	−	3.61405i	0.0636337	−	0.165999i
$475$	1.75459	+	4.06760i	0.0805061	+	0.186634i
$476$	4.05250	+	3.40045i	0.185746	+	0.155859i
$477$	2.07631	−	0.955841i	0.0950677	−	0.0437649i
$478$	5.76276	−	4.83553i	0.263582	−	0.221172i
$479$	6.32528	+	3.17667i	0.289009	+	0.145146i	0.587397	−	0.809299i	$-0.300153\pi$
$479$	6.32528	+	3.17667i	0.289009	+	0.145146i	−0.298388	+	0.954445i	$0.596449\pi$
$480$	1.49019	+	3.09735i	0.0680174	+	0.141374i
$481$	−4.87433	+	0.569727i	−0.222250	+	0.0259773i
$482$	−1.63259	+	28.0305i	−0.0743625	+	1.27675i
$483$	−10.4727	−	3.33024i	−0.476522	−	0.151531i
$484$	1.96365	+	2.08135i	0.0892570	+	0.0946069i
$485$	21.0918			0.957730
$486$	−10.9974	+	11.0480i	−0.498851	+	0.501146i
$487$	4.59607			0.208268			0.104134	−	0.994563i	$-0.466793\pi$
$487$	4.59607			0.208268			0.104134	+	0.994563i	$0.466793\pi$
$488$	−3.05588	−	3.23904i	−0.138333	−	0.146625i
$489$	22.3357	+	7.10264i	1.01006	+	0.321192i
$490$	−0.698625	+	11.9949i	−0.0315606	+	0.541875i
$491$	−8.61591	+	1.00706i	−0.388831	+	0.0454478i	−0.308263	−	0.951301i	$-0.599748\pi$
$491$	−8.61591	+	1.00706i	−0.388831	+	0.0454478i	−0.0805682	+	0.996749i	$0.525673\pi$
$492$	−7.14239	−	14.8455i	−0.322004	−	0.669285i
$493$	−17.1178	−	8.59686i	−0.770945	−	0.387183i
$494$	3.93759	−	3.30403i	0.177161	−	0.148655i
$495$	−1.56313	+	16.9118i	−0.0702574	+	0.760129i
$496$	−6.49925	−	5.45352i	−0.291825	−	0.244870i
$497$	5.72801	+	13.2790i	0.256937	+	0.595646i
$498$	−7.26324	+	18.9474i	−0.325474	+	0.849052i
$499$	23.1673	+	5.49075i	1.03711	+	0.245800i	0.713694	−	0.700457i	$-0.247021\pi$
$499$	23.1673	+	5.49075i	1.03711	+	0.245800i	0.323416	+	0.946257i	$0.395169\pi$
$500$	3.45014	+	11.5243i	0.154295	+	0.515381i
$501$	−10.6038	−	2.05612i	−0.473743	−	0.0918607i
$502$	−8.57295	−	1.00203i	−0.382629	−	0.0447230i
$503$	−5.01805	+	28.4588i	−0.223744	+	1.26891i	0.641329	+	0.767266i	$0.278384\pi$
$503$	−5.01805	+	28.4588i	−0.223744	+	1.26891i	−0.865072	+	0.501647i	$0.832728\pi$
$504$	−2.70546	−	1.09019i	−0.120511	−	0.0485608i
$505$	1.75428	+	9.94902i	0.0780644	+	0.442725i
$506$	1.08244	+	18.5848i	0.0481205	+	0.826197i
$507$	−14.2312	−	13.8911i	−0.632032	−	0.616926i
$508$	2.61729	−	6.06756i	0.116123	−	0.269204i
$509$	−3.09062	+	1.55217i	−0.136989	+	0.0687986i	−0.515974	−	0.856604i	$-0.672570\pi$
$509$	−3.09062	+	1.55217i	−0.136989	+	0.0687986i	0.378984	+	0.925403i	$0.376273\pi$
$510$	−17.2955	+	7.11445i	−0.765859	+	0.315033i
$511$	−6.81594	+	1.61541i	−0.301519	+	0.0714614i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	14.7614	−	15.8734i	0.651731	−	0.700828i
$514$	3.21412	−	5.56703i	0.141769	−	0.245551i
$515$	8.90843	−	29.7562i	0.392552	−	1.31122i
$516$	9.70982	+	15.3241i	0.427451	+	0.674605i
$517$	10.1243	+	6.65889i	0.445268	+	0.292857i
$518$	−2.31244	−	3.10615i	−0.101603	−	0.136476i
$519$	2.06877	+	20.7522i	0.0908090	+	0.910921i
$520$	2.04294	−	1.34366i	0.0895888	−	0.0589235i
$521$	16.4823	+	5.99907i	0.722103	+	0.262824i	0.676818	−	0.736150i	$-0.263358\pi$
$521$	16.4823	+	5.99907i	0.722103	+	0.262824i	0.0452845	+	0.998974i	$0.485581\pi$
$522$	10.4425	+	1.58191i	0.457057	+	0.0692383i
$523$	−19.7671	+	7.19463i	−0.864354	+	0.314599i	−0.735879	−	0.677113i	$-0.763231\pi$
$523$	−19.7671	+	7.19463i	−0.864354	+	0.314599i	−0.128476	+	0.991713i	$0.541008\pi$
$524$	−12.8481	+	17.2579i	−0.561270	+	0.753916i
$525$	−1.53330	−	0.920343i	−0.0669187	−	0.0401671i
$526$	−3.85169	+	4.08256i	−0.167942	+	0.178008i
$527$	31.6784	−	33.5771i	1.37993	−	1.46264i
$528$	−0.0839690	+	4.94050i	−0.00365428	+	0.215008i
$529$	11.6945	−	15.7084i	0.508455	−	0.682974i
$530$	−1.42081	+	0.517134i	−0.0617163	+	0.0224629i
$531$	−0.565649	+	0.345083i	−0.0245471	+	0.0149753i
$532$	3.81138	+	1.38723i	0.165244	+	0.0601440i
$533$	−9.79171	+	6.44011i	−0.424126	+	0.278952i
$534$	0.223530	+	0.100961i	0.00967310	+	0.00436901i
$535$	7.08199	+	9.51276i	0.306181	+	0.411272i
$536$	−6.06175	−	3.98688i	−0.261828	−	0.172207i
$537$	8.44532	−	16.1267i	0.364443	−	0.695919i
$538$	7.94942	−	26.5529i	0.342724	−	1.14478i
$539$	−8.63641	+	14.9587i	−0.371997	+	0.644317i
$540$	7.85123	−	6.68480i	0.337863	−	0.287668i
$541$	−20.1667	−	34.9297i	−0.867033	−	1.50174i	−0.865015	−	0.501746i	$-0.832691\pi$
$541$	−20.1667	−	34.9297i	−0.867033	−	1.50174i	−0.00201779	−	0.999998i	$-0.500642\pi$
$542$	1.74788	−	0.414255i	0.0750778	−	0.0177938i
$543$	4.89889	−	36.5191i	0.210231	−	1.56719i
$544$	−4.86223	+	2.44190i	−0.208466	+	0.104696i
$545$	2.33618	−	5.41587i	0.100071	−	0.231990i
$546$	−0.512779	+	2.01068i	−0.0219449	+	0.0860492i
$547$	1.80071	+	30.9170i	0.0769927	+	1.32191i	0.786664	+	0.617381i	$0.211806\pi$
$547$	1.80071	+	30.9170i	0.0769927	+	1.32191i	−0.709672	+	0.704533i	$0.751157\pi$
$548$	3.51674	+	19.9444i	0.150228	+	0.851984i
$549$	−7.06889	+	11.3357i	−0.301693	+	0.483797i
$550$	−0.526057	+	2.98341i	−0.0224311	+	0.127213i
$551$	−14.5871	−	1.70499i	−0.621431	−	0.0726349i
$552$	7.41131	−	8.53364i	0.315446	−	0.363216i
$553$	−0.623135	−	2.08142i	−0.0264984	−	0.0885109i
$554$	8.14506	+	1.93041i	0.346050	+	0.0820154i
$555$	13.5201	−	2.14774i	0.573897	−	0.0911663i
$556$	0.374476	+	0.868133i	0.0158813	+	0.0368170i
$557$	10.3130	+	8.65366i	0.436977	+	0.366667i	0.834577	−	0.550892i	$-0.185712\pi$
$557$	10.3130	+	8.65366i	0.436977	+	0.366667i	−0.397600	+	0.917559i	$0.630157\pi$
$558$	−10.8696	+	23.0148i	−0.460147	+	0.974295i
$559$	9.88634	−	8.29562i	0.418148	−	0.350867i
$560$	1.72423	+	0.865939i	0.0728619	+	0.0365926i
$561$	−26.8091	−	2.01910i	−1.13188	−	0.0852464i
$562$	−14.5672	+	1.70266i	−0.614480	+	0.0718224i
$563$	−0.458868	+	7.87846i	−0.0193390	+	0.332037i	0.974737	+	0.223354i	$0.0717006\pi$
$563$	−0.458868	+	7.87846i	−0.0193390	+	0.332037i	−0.994076	+	0.108684i	$0.965336\pi$
$564$	−1.57479	−	7.18671i	−0.0663107	−	0.302615i
$565$	22.1528	+	23.4806i	0.931974	+	0.987835i
$566$	21.3373			0.896872
$567$	−1.10100	+	8.68100i	−0.0462377	+	0.364568i
$568$	−14.8740			−0.624101
$569$	−25.8894	−	27.4412i	−1.08534	−	1.15039i	−0.987890	−	0.155155i	$-0.950412\pi$
$569$	−25.8894	−	27.4412i	−1.08534	−	1.15039i	−0.0974514	−	0.995240i	$-0.531069\pi$
$570$	−10.5952	+	9.66110i	−0.443786	+	0.404659i
$571$	0.919070	−	15.7798i	0.0384619	−	0.660365i	−0.922894	−	0.385055i	$-0.874182\pi$
$571$	0.919070	−	15.7798i	0.0384619	−	0.660365i	0.961355	−	0.275310i	$-0.0887805\pi$
$572$	3.49140	−	0.408086i	0.145983	−	0.0170629i
$573$	−5.24934	+	7.69322i	−0.219294	+	0.321389i
$574$	−8.26413	−	4.15040i	−0.344938	−	0.173234i
$575$	5.30840	−	4.45428i	0.221376	−	0.185756i
$576$	2.13169	−	2.11090i	0.0888204	−	0.0879542i
$577$	5.24576	+	4.40171i	0.218384	+	0.183246i	0.745416	−	0.666600i	$-0.232251\pi$
$577$	5.24576	+	4.40171i	0.218384	+	0.183246i	−0.527032	+	0.849845i	$0.676695\pi$
$578$	−4.99225	−	11.5733i	−0.207650	−	0.481387i
$579$	1.94107	+	2.39477i	0.0806680	+	0.0995232i
$580$	−6.79809	−	1.61118i	−0.282275	−	0.0669005i
$581$	3.26691	+	10.9122i	0.135534	+	0.452716i
$582$	−6.00139	−	17.4034i	−0.248766	−	0.721393i
$583$	−2.15892	−	0.252341i	−0.0894132	−	0.0104509i
$584$	1.25104	−	7.09499i	0.0517683	−	0.293593i
$585$	−5.45593	−	4.90348i	−0.225575	−	0.202734i
$586$	2.69436	+	15.2805i	0.111303	+	0.631230i
$587$	−0.563435	−	9.67381i	−0.0232555	−	0.399281i	−0.989770	−	0.142670i	$-0.954431\pi$
$587$	−0.563435	−	9.67381i	−0.0232555	−	0.399281i	0.966515	−	0.256611i	$-0.0826058\pi$
$588$	10.0961	−	2.83654i	0.416356	−	0.116977i
$589$	14.0183	−	32.4981i	0.577615	−	1.33906i
$590$	0.391681	−	0.196710i	0.0161253	−	0.00809841i
$591$	19.3459	+	14.9201i	0.795786	+	0.613731i
$592$	3.87544	−	0.918497i	0.159280	−	0.0377500i
$593$	0.957963	+	1.65924i	0.0393388	+	0.0681368i	0.885024	−	0.465545i	$-0.154142\pi$
$593$	0.957963	+	1.65924i	0.0393388	+	0.0681368i	−0.845686	+	0.533681i	$0.820808\pi$
$594$	14.3991	−	3.52225i	0.590803	−	0.144520i
$595$	−5.24906	+	9.09164i	−0.215190	+	0.372721i
$596$	3.98049	−	13.2958i	0.163047	−	0.544615i
$597$	48.6433	−	2.00442i	1.99084	−	0.0820355i
$598$	−6.71790	−	4.41843i	−0.274715	−	0.180683i
$599$	−0.862763	−	1.15889i	−0.0352515	−	0.0473510i	0.784148	−	0.620574i	$-0.213100\pi$
$599$	−0.862763	−	1.15889i	−0.0352515	−	0.0473510i	−0.819399	+	0.573223i	$0.805693\pi$
$600$	1.49379	−	1.07312i	0.0609836	−	0.0438098i
$601$	39.7954	−	26.1738i	1.62329	−	1.06765i	0.681301	−	0.732003i	$-0.261414\pi$
$601$	39.7954	−	26.1738i	1.62329	−	1.06765i	0.941987	−	0.335650i	$-0.108956\pi$
$602$	9.56945	+	3.48300i	0.390022	+	0.141956i
$603$	−6.94755	+	20.6275i	−0.282926	+	0.840015i
$604$	21.1055	−	7.68177i	0.858770	−	0.312567i
$605$	−3.39094	+	4.55482i	−0.137861	+	0.185180i
$606$	7.71002	−	4.27836i	0.313198	−	0.173796i
$607$	−15.2794	+	16.1952i	−0.620171	+	0.657343i	−0.958967	−	0.283517i	$-0.908499\pi$
$607$	−15.2794	+	16.1952i	−0.620171	+	0.657343i	0.338796	+	0.940860i	$0.389980\pi$
$608$	−2.86273	+	3.03432i	−0.116099	+	0.123058i
$609$	5.18410	−	2.87670i	0.210070	−	0.116570i
$610$	5.27705	−	7.08831i	0.213662	−	0.286997i
$611$	−4.91827	+	1.79010i	−0.198972	+	0.0724198i
$612$	10.7915	+	12.2466i	0.436221	+	0.495041i
$613$	−25.2994	−	9.20823i	−1.02183	−	0.371917i	−0.223868	−	0.974620i	$-0.571868\pi$
$613$	−25.2994	−	9.20823i	−1.02183	−	0.371917i	−0.797966	+	0.602703i	$0.794091\pi$
$614$	−0.703245	+	0.462532i	−0.0283807	+	0.0186663i
$615$	26.5514	−	19.0742i	1.07066	−	0.769146i
$616$	1.65636	+	2.22488i	0.0667368	+	0.0896430i
$617$	−29.6392	−	19.4940i	−1.19323	−	0.784800i	−0.211930	−	0.977285i	$-0.567975\pi$
$617$	−29.6392	−	19.4940i	−1.19323	−	0.784800i	−0.981300	+	0.192485i	$0.938345\pi$
$618$	−27.0874	+	1.11618i	−1.08961	+	0.0448992i
$619$	5.62648	−	18.7937i	0.226147	−	0.755384i	−0.767320	−	0.641265i	$-0.778410\pi$
$619$	5.62648	−	18.7937i	0.226147	−	0.755384i	0.993467	−	0.114120i	$-0.0364047\pi$
$620$	8.41825	−	14.5808i	0.338085	−	0.585581i
$621$	−30.4100	−	14.9995i	−1.22031	−	0.601910i
$622$	−3.74794	−	6.49163i	−0.150279	−	0.260291i
$623$	0.133972	−	0.0317520i	0.00536748	−	0.00127212i
$624$	−1.68998	−	1.30336i	−0.0676533	−	0.0521761i
$625$	−16.5883	+	8.33096i	−0.663532	+	0.333238i
$626$	−11.2311	+	26.0367i	−0.448886	+	1.04063i
$627$	−19.8445	+	5.57541i	−0.792513	+	0.222660i
$628$	−0.814726	−	13.9883i	−0.0325111	−	0.558194i
$629$	3.76301	+	21.3411i	0.150041	+	0.850925i
$630$	1.19827	−	5.66299i	0.0477404	−	0.225619i
$631$	0.517896	−	2.93714i	0.0206171	−	0.116926i	−0.972762	−	0.231805i	$-0.925537\pi$
$631$	0.517896	−	2.93714i	0.0206171	−	0.116926i	0.993379	+	0.114879i	$0.0366481\pi$
$632$	2.21952	+	0.259425i	0.0882878	+	0.0103194i
$633$	−4.39290	−	12.7389i	−0.174602	−	0.506326i
$634$	−0.0845419	−	0.282390i	−0.00335759	−	0.0112151i
$635$	12.7598	+	3.02413i	0.506358	+	0.120009i
$636$	0.830974	+	1.02521i	0.0329503	+	0.0406520i
$637$	−2.95492	−	6.85027i	−0.117078	−	0.271418i
$638$	−7.69376	−	6.45583i	−0.304599	−	0.255589i
$639$	11.3377	+	43.1577i	0.448513	+	1.70729i
$640$	−1.52019	+	1.27559i	−0.0600906	+	0.0504220i
$641$	−28.3678	−	14.2469i	−1.12046	−	0.562717i	−0.210577	−	0.977577i	$-0.567534\pi$
$641$	−28.3678	−	14.2469i	−1.12046	−	0.562717i	−0.909885	+	0.414860i	$0.863830\pi$
$642$	5.83412	−	8.55025i	0.230254	−	0.337451i
$643$	−0.206843	+	0.0241765i	−0.00815709	+	0.000953427i	−0.120170	−	0.992753i	$-0.538344\pi$
$643$	−0.206843	+	0.0241765i	−0.00815709	+	0.000953427i	0.112013	+	0.993707i	$0.464270\pi$
$644$	0.368913	−	6.33400i	0.0145372	−	0.249595i
$645$	−26.6021	+	24.2567i	−1.04746	+	0.955106i
$646$	−15.5761	−	16.5097i	−0.612832	−	0.649564i
$647$	6.27460			0.246680			0.123340	−	0.992364i	$-0.460639\pi$
$647$	6.27460			0.246680			0.123340	+	0.992364i	$0.460639\pi$
$648$	−7.74976	−	4.57617i	−0.304439	−	0.179769i
$649$	0.630093			0.0247333
$650$	−0.897922	−	0.951742i	−0.0352194	−	0.0373304i
$651$	3.05824	+	13.9566i	0.119862	+	0.547001i
$652$	−0.786807	+	13.5090i	−0.0308137	+	0.529051i
$653$	−13.8519	+	1.61905i	−0.542066	+	0.0633584i	−0.382720	−	0.923864i	$-0.625013\pi$
$653$	−13.8519	+	1.61905i	−0.542066	+	0.0633584i	−0.159346	+	0.987223i	$0.550939\pi$
$654$	−5.13349	−	0.386623i	−0.200735	−	0.0151182i
$655$	−38.1548	−	19.1621i	−1.49083	−	0.748724i
$656$	7.28618	−	6.11383i	0.284477	−	0.238705i
$657$	−21.5400	+	1.77820i	−0.840357	+	0.0693742i
$658$	−3.16373	−	2.65469i	−0.123335	−	0.103491i
$659$	−6.52478	−	15.1261i	−0.254169	−	0.589231i	0.742583	−	0.669754i	$-0.233600\pi$
$659$	−6.52478	−	15.1261i	−0.254169	−	0.589231i	−0.996753	+	0.0805227i	$0.974341\pi$
$660$	−9.68422	+	1.53839i	−0.376958	+	0.0598816i
$661$	7.39619	+	1.75293i	0.287679	+	0.0681811i	0.371922	−	0.928264i	$-0.378699\pi$
$661$	7.39619	+	1.75293i	0.287679	+	0.0681811i	−0.0842429	+	0.996445i	$0.526847\pi$
$662$	−7.46505	−	24.9350i	−0.290137	−	0.969126i
$663$	7.61418	−	8.76724i	0.295710	−	0.340491i
$664$	−11.6363	−	1.36008i	−0.451575	−	0.0527815i
$665$	−1.39769	+	7.92667i	−0.0541999	+	0.307383i
$666$	−5.61912	−	10.5447i	−0.217736	−	0.408597i
$667$	3.98935	+	22.6247i	0.154468	+	0.876034i
$668$	−0.362599	−	6.22559i	−0.0140294	−	0.240875i
$669$	−9.81774	+	38.4968i	−0.379576	+	1.48837i
$670$	5.70274	−	13.2204i	0.220316	−	0.510750i
$671$	11.3525	−	5.70144i	0.438258	−	0.220102i
$672$	0.223902	−	1.66909i	0.00863719	−	0.0643866i
$673$	35.8100	−	8.48713i	1.38037	−	0.327155i	0.527626	−	0.849477i	$-0.323082\pi$
$673$	35.8100	−	8.48713i	1.38037	−	0.327155i	0.852749	+	0.522322i	$0.174934\pi$
$674$	2.92600	+	5.06798i	0.112705	+	0.195211i
$675$	−4.25234	−	3.51631i	−0.163672	−	0.135343i
$676$	5.74087	−	9.94348i	0.220803	−	0.382442i
$677$	−3.60674	+	12.0473i	−0.138618	+	0.463017i	−0.998905	−	0.0467941i	$-0.985100\pi$
$677$	−3.60674	+	12.0473i	−0.138618	+	0.463017i	0.860286	+	0.509811i	$0.170285\pi$
$678$	13.0711	−	24.9599i	0.501993	−	0.958578i
$679$	−8.63384	−	5.67857i	−0.331336	−	0.217923i
$680$	−6.44776	−	8.66084i	−0.247260	−	0.332128i
$681$	12.7340	+	5.75152i	0.487969	+	0.220399i
$682$	20.2219	−	13.3002i	0.774338	−	0.509290i
$683$	−39.4063	−	14.3427i	−1.50784	−	0.548809i	−0.549765	−	0.835320i	$-0.685283\pi$
$683$	−39.4063	−	14.3427i	−1.50784	−	0.548809i	−0.958077	+	0.286510i	$0.907505\pi$
$684$	10.9863	+	5.99345i	0.420073	+	0.229165i
$685$	−37.7658	+	13.7456i	−1.44296	+	0.525194i
$686$	7.57963	−	10.1812i	0.289392	−	0.388720i
$687$	0.761693	−	44.8159i	0.0290604	−	1.70983i
$688$	−7.18763	+	7.61844i	−0.274026	+	0.290450i
$689$	0.644257	−	0.682872i	0.0245442	−	0.0260154i
$690$	19.2313	+	11.5433i	0.732124	+	0.439448i
$691$	8.96528	−	12.0425i	0.341055	−	0.458117i	−0.598194	−	0.801351i	$-0.704115\pi$
$691$	8.96528	−	12.0425i	0.341055	−	0.458117i	0.939250	+	0.343234i	$0.111522\pi$
$692$	−11.3145	+	4.11816i	−0.430114	+	0.156549i
$693$	5.19304	−	6.50193i	0.197267	−	0.246988i
$694$	21.2024	+	7.71704i	0.804832	+	0.292935i
$695$	−1.56756	+	1.03100i	−0.0594609	+	0.0391081i
$696$	0.604885	+	6.06771i	0.0229281	+	0.229996i
$697$	30.9038	+	41.5110i	1.17056	+	1.57234i
$698$	−26.9290	−	17.7115i	−1.01928	−	0.670390i
$699$	6.07771	+	9.59187i	0.229880	+	0.362798i
$700$	0.296119	−	0.989105i	0.0111922	−	0.0373846i
$701$	−0.796766	+	1.38004i	−0.0300934	+	0.0521234i	−0.880680	−	0.473712i	$-0.842914\pi$
$701$	−0.796766	+	1.38004i	−0.0300934	+	0.0521234i	0.850586	+	0.525835i	$0.176247\pi$
$702$	−2.49357	+	5.89704i	−0.0941137	+	0.222569i
$703$	8.30735	+	14.3888i	0.313318	+	0.542682i
$704$	−2.77591	+	0.657904i	−0.104621	+	0.0247957i
$705$	13.5024	−	5.55416i	0.508530	−	0.209182i
$706$	−8.15601	+	4.09610i	−0.306956	+	0.154159i
$707$	1.96048	−	4.54489i	0.0737313	−	0.170928i
$708$	−0.273758	−	0.267215i	−0.0102884	−	0.0100425i
$709$	0.669472	+	11.4944i	0.0251426	+	0.431681i	0.987267	+	0.159071i	$0.0508499\pi$
$709$	0.669472	+	11.4944i	0.0251426	+	0.431681i	−0.962125	+	0.272610i	$0.912113\pi$
$710$	−5.12556	−	29.0685i	−0.192359	−	1.09092i
$711$	−0.939094	−	6.63779i	−0.0352188	−	0.248937i
$712$	−0.0245901	+	0.139457i	−0.000921552	+	0.00522638i
$713$	−54.9900	−	6.42741i	−2.05939	−	0.240708i
$714$	8.99528	+	1.74422i	0.336640	+	0.0652759i
$715$	2.00066	+	6.68266i	0.0748203	+	0.249917i
$716$	10.2269	+	2.42383i	0.382198	+	0.0905826i
$717$	4.66387	−	12.1665i	0.174175	−	0.454366i
$718$	−0.527948	−	1.22392i	−0.0197028	−	0.0456763i
$719$	28.3871	+	23.8196i	1.05866	+	0.888321i	0.993977	−	0.109584i	$-0.0349520\pi$
$719$	28.3871	+	23.8196i	1.05866	+	0.888321i	0.0646828	+	0.997906i	$0.479396\pi$
$720$	4.85994	+	3.43858i	0.181119	+	0.128148i
$721$	−11.6579	+	9.78216i	−0.434164	+	0.364307i
$722$	1.42770	+	0.717020i	0.0531336	+	0.0266847i
$723$	21.0846	+	43.8243i	0.784143	+	1.62984i
$724$	21.1293	−	2.46967i	0.785266	−	0.0917844i
$725$	−0.217376	+	3.73220i	−0.00807314	+	0.138610i
$726$	4.72314	+	1.50193i	0.175292	+	0.0557419i
$727$	−11.2689	−	11.9444i	−0.417941	−	0.442992i	0.483858	−	0.875146i	$-0.339235\pi$
$727$	−11.2689	−	11.9444i	−0.417941	−	0.442992i	−0.901800	+	0.432154i	$0.857754\pi$
$728$	−1.19802			−0.0444017
$729$	−7.37072	+	25.9745i	−0.272990	+	0.962017i
$730$	14.2969			0.529153
$731$	−39.1077	−	41.4517i	−1.44645	−	1.53315i
$732$	−7.35025	−	2.33734i	−0.271673	−	0.0863905i
$733$	2.18643	−	37.5395i	0.0807575	−	1.38655i	−0.677944	−	0.735114i	$-0.737129\pi$
$733$	2.18643	−	37.5395i	0.0807575	−	1.38655i	0.758701	−	0.651439i	$-0.225834\pi$
$734$	−10.8645	+	1.26987i	−0.401015	+	0.0468719i
$735$	9.02259	+	18.7534i	0.332803	+	0.691731i
$736$	5.83149	+	2.92869i	0.214952	+	0.107953i
$737$	15.8557	−	13.3045i	0.584052	−	0.490078i
$738$	−23.2934	−	16.4809i	−0.857443	−	0.606671i
$739$	−5.93639	−	4.98123i	−0.218374	−	0.183237i	0.527038	−	0.849842i	$-0.323303\pi$
$739$	−5.93639	−	4.98123i	−0.218374	−	0.183237i	−0.745412	+	0.666604i	$0.767747\pi$
$740$	3.13050	+	7.25732i	0.115080	+	0.266784i
$741$	3.18674	−	8.31315i	0.117068	−	0.305391i
$742$	0.720833	+	0.170840i	0.0264626	+	0.00627175i
$743$	−7.94369	−	26.5338i	−0.291426	−	0.973430i	−0.970851	−	0.239685i	$-0.922956\pi$
$743$	−7.94369	−	26.5338i	−0.291426	−	0.973430i	0.679425	−	0.733745i	$-0.262229\pi$
$744$	−14.4263	−	2.79732i	−0.528894	−	0.102555i
$745$	27.3557	+	3.19743i	1.00224	+	0.117145i
$746$	1.46221	−	8.29263i	0.0535355	−	0.303615i
$747$	4.92338	+	34.7999i	0.180137	+	1.27326i
$748$	−2.69538	−	15.2863i	−0.0985528	−	0.558921i
$749$	−0.337852	−	5.80069i	−0.0123448	−	0.211953i
$750$	14.9103	+	14.5540i	0.544449	+	0.531436i
$751$	−16.7919	+	38.9280i	−0.612745	+	1.42050i	0.275576	+	0.961279i	$0.411131\pi$
$751$	−16.7919	+	38.9280i	−0.612745	+	1.42050i	−0.888321	+	0.459223i	$0.848128\pi$
$752$	3.79588	−	1.90636i	0.138422	−	0.0695179i
$753$	−13.8259	+	5.68721i	−0.503842	+	0.207254i
$754$	4.22102	−	1.00040i	0.153720	−	0.0364324i
$755$	22.2855	+	38.5996i	0.811052	+	1.40478i
$756$	−5.01362	+	0.622602i	−0.182344	+	0.0226438i
$757$	18.8633	−	32.6722i	0.685598	−	1.18749i	−0.287651	−	0.957735i	$-0.592874\pi$
$757$	18.8633	−	32.6722i	0.685598	−	1.18749i	0.973249	−	0.229755i	$-0.0737924\pi$
$758$	−3.14803	+	10.5151i	−0.114341	+	0.381927i
$759$	17.2582	+	27.2370i	0.626434	+	0.988642i
$760$	−6.91651	−	4.54906i	−0.250888	−	0.165012i
$761$	29.8042	+	40.0340i	1.08040	+	1.45123i	0.882084	+	0.471092i	$0.156140\pi$
$761$	29.8042	+	40.0340i	1.08040	+	1.45123i	0.198316	+	0.980138i	$0.436453\pi$
$762$	−1.13535	−	11.3889i	−0.0411294	−	0.412577i
$763$	−2.41442	+	1.58799i	−0.0874079	+	0.0574891i
$764$	−5.05287	−	1.83909i	−0.182806	−	0.0665361i
$765$	−20.2150	+	25.3102i	−0.730876	+	0.915092i
$766$	−14.3346	+	5.21738i	−0.517931	+	0.188512i
$767$	−0.162515	+

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)

\(f(q)\)	\(=\)	\(q+(0.686242 + 0.727374i) q^{2} +(1.65061 + 0.524883i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-1.97104 + 0.230382i) q^{5} +(0.750928 + 1.56080i) q^{6} +(0.868864 + 0.436360i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(2.44900 + 1.73275i) q^{9} +O(q^{10})\)	\(q+(0.686242 + 0.727374i) q^{2} +(1.65061 + 0.524883i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-1.97104 + 0.230382i) q^{5} +(0.750928 + 1.56080i) q^{6} +(0.868864 + 0.436360i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(2.44900 + 1.73275i) q^{9} +(-1.52019 - 1.27559i) q^{10} +(-1.12994 - 2.61950i) q^{11} +(-0.619969 + 1.61729i) q^{12} +(1.19896 + 0.284159i) q^{13} +(0.278854 + 0.931437i) q^{14} +(-3.37434 - 0.654298i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(0.944814 - 5.35831i) q^{17} +(0.420246 + 2.97042i) q^{18} +(-0.724393 - 4.10824i) q^{19} +(-0.115386 - 1.98110i) q^{20} +(1.20511 + 1.17631i) q^{21} +(1.12994 - 2.61950i) q^{22} +(-5.83149 + 2.92869i) q^{23} +(-1.60183 + 0.658905i) q^{24} +(-1.03329 + 0.244894i) q^{25} +(0.616088 + 1.06710i) q^{26} +(3.13283 + 4.14552i) q^{27} +(-0.486141 + 0.842022i) q^{28} +(1.00971 - 3.37266i) q^{29} +(-1.83969 - 2.90341i) q^{30} +(7.08842 + 4.66213i) q^{31} +(-0.597159 - 0.802123i) q^{32} +(-0.490156 - 4.91685i) q^{33} +(4.54586 - 2.98986i) q^{34} +(-1.81310 - 0.659913i) q^{35} +(-1.87221 + 2.34410i) q^{36} +(-3.74261 + 1.36220i) q^{37} +(2.49111 - 3.34615i) q^{38} +(1.82986 + 1.09835i) q^{39} +(1.36182 - 1.44344i) q^{40} +(-6.52714 + 6.91836i) q^{41} +(-0.0286179 + 1.68380i) q^{42} +(6.25458 - 8.40136i) q^{43} +(2.68077 - 0.975719i) q^{44} +(-5.22627 - 2.85112i) q^{45} +(-6.13206 - 2.23189i) q^{46} +(-3.54890 + 2.33415i) q^{47} +(-1.57851 - 0.712958i) q^{48} +(-3.61560 - 4.85659i) q^{49} +(-0.887215 - 0.583531i) q^{50} +(4.37200 - 8.34854i) q^{51} +(-0.353392 + 1.18041i) q^{52} +(0.380960 - 0.659842i) q^{53} +(-0.865464 + 5.12357i) q^{54} +(2.83065 + 4.90283i) q^{55} +(-0.946075 + 0.224224i) q^{56} +(0.960658 - 7.16130i) q^{57} +(3.14608 - 1.58002i) q^{58} +(-0.0874810 + 0.202804i) q^{59} +(0.849391 - 3.33058i) q^{60} +(0.258923 + 4.44553i) q^{61} +(1.47326 + 8.35528i) q^{62} +(1.37174 + 2.57417i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-2.42867 - 0.283871i) q^{65} +(3.24002 - 3.73067i) q^{66} +(2.08086 + 6.95054i) q^{67} +(5.29431 + 1.25477i) q^{68} +(-11.1627 + 1.77325i) q^{69} +(-0.764219 - 1.77166i) q^{70} +(11.3942 + 9.56084i) q^{71} +(-2.98983 + 0.246820i) q^{72} +(-5.51892 + 4.63093i) q^{73} +(-3.55916 - 1.78748i) q^{74} +(-1.83409 - 0.138133i) q^{75} +(4.14341 - 0.484295i) q^{76} +(0.161279 - 2.76905i) q^{77} +(0.456817 + 2.08473i) q^{78} +(-1.53350 - 1.62541i) q^{79} +1.98446 q^{80} +(2.99515 + 8.48699i) q^{81} -9.51143 q^{82} +(8.03965 + 8.52153i) q^{83} +(-1.24439 + 1.13468i) q^{84} +(-0.627813 + 10.7791i) q^{85} +(10.4031 - 1.21595i) q^{86} +(3.43688 - 5.03695i) q^{87} +(2.54937 + 1.28034i) q^{88} +(0.108478 - 0.0910242i) q^{89} +(-1.51265 - 5.75801i) q^{90} +(0.917739 + 0.770075i) q^{91} +(-2.58466 - 5.99192i) q^{92} +(9.25311 + 11.4159i) q^{93} +(-4.13320 - 0.979586i) q^{94} +(2.37427 + 7.93063i) q^{95} +(-0.564652 - 1.63743i) q^{96} +(-10.5566 - 1.23389i) q^{97} +(1.05138 - 5.96268i) q^{98} +(1.77172 - 8.37304i) 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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