LMFDB - Embedded newform 540.2.y.a.523.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [540,2,Mod(127,540)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(540, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 3]))

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

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

chi := DirichletCharacter("540.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.y (of order $12$, degree $4$, not 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			523.13
Character	$\chi$	$=$	540.523
Dual form			540.2.y.a.127.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453270 + 1.33961i) q^{2} +(-1.58909 - 1.21441i) q^{4} +(2.23308 - 0.115576i) q^{5} +(-0.00100179 + 0.00373871i) q^{7} +(2.34712 - 1.57830i) q^{8} +O(q^{10})$	\(q+(-0.453270 + 1.33961i) q^{2} +(-1.58909 - 1.21441i) q^{4} +(2.23308 - 0.115576i) q^{5} +(-0.00100179 + 0.00373871i) q^{7} +(2.34712 - 1.57830i) q^{8} +(-0.857362 + 3.04383i) q^{10} +(-3.58713 + 2.07103i) q^{11} +(2.86455 - 0.767553i) q^{13} +(-0.00455433 - 0.00303665i) q^{14} +(1.05043 + 3.85961i) q^{16} +(2.07784 - 2.07784i) q^{17} +7.31525 q^{19} +(-3.68893 - 2.52821i) q^{20} +(-1.14843 - 5.74408i) q^{22} +(1.00208 + 3.73983i) q^{23} +(4.97328 - 0.516182i) q^{25} +(-0.270195 + 4.18528i) q^{26} +(0.00613225 - 0.00472458i) q^{28} +(4.99228 - 2.88229i) q^{29} +(1.77642 + 1.02562i) q^{31} +(-5.64649 - 0.342287i) q^{32} +(1.84166 + 3.72530i) q^{34} +(-0.00180496 + 0.00846463i) q^{35} +(-6.09468 + 6.09468i) q^{37} +(-3.31579 + 9.79956i) q^{38} +(5.05888 - 3.79575i) q^{40} +(-1.82477 + 3.16060i) q^{41} +(-0.968609 - 0.259538i) q^{43} +(8.21535 + 1.06518i) q^{44} +(-5.46412 - 0.352755i) q^{46} +(-1.22115 + 4.55740i) q^{47} +(6.06216 + 3.49999i) q^{49} +(-1.56276 + 6.89621i) q^{50} +(-5.48415 - 2.25902i) q^{52} +(-6.92974 - 6.92974i) q^{53} +(-7.77098 + 5.03936i) q^{55} +(0.00354952 + 0.0103563i) q^{56} +(1.59829 + 7.99414i) q^{58} +(2.76056 - 4.78143i) q^{59} +(3.59007 + 6.21819i) q^{61} +(-2.17912 + 1.91482i) q^{62} +(3.01792 - 7.40893i) q^{64} +(6.30805 - 2.04508i) q^{65} +(-3.17735 + 0.851369i) q^{67} +(-5.82521 + 0.778533i) q^{68} +(-0.0105211 - 0.00625470i) q^{70} -11.3127i q^{71} +(-6.50632 - 6.50632i) q^{73} +(-5.40194 - 10.9270i) q^{74} +(-11.6246 - 8.88370i) q^{76} +(-0.00414946 - 0.0154860i) q^{77} +(-2.99986 - 5.19591i) q^{79} +(2.79177 + 8.49741i) q^{80} +(-3.40684 - 3.87708i) q^{82} +(2.82192 + 0.756131i) q^{83} +(4.39982 - 4.88012i) q^{85} +(0.786720 - 1.17991i) q^{86} +(-5.15070 + 10.5225i) q^{88} +9.18764i q^{89} +0.0114786i q^{91} +(2.94927 - 7.15987i) q^{92} +(-5.55161 - 3.70160i) q^{94} +(16.3355 - 0.845469i) q^{95} +(-2.26714 - 0.607478i) q^{97} +(-7.43641 + 6.53447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.453270	+	1.33961i	−0.320510	+	0.947245i
$2$	−0.453270	+	1.33961i	−0.320510	+	0.947245i
$3$		0			0
$3$		0			0
$4$	−1.58909	−	1.21441i	−0.794546	−	0.607204i
$5$	2.23308	−	0.115576i	0.998663	−	0.0516873i
$5$	2.23308	−	0.115576i	0.998663	−	0.0516873i
$6$		0			0
$7$	−0.00100179	+	0.00373871i	−0.000378639	+	0.00141310i	−0.966115	−	0.258112i	$-0.916900\pi$
$7$	−0.00100179	+	0.00373871i	−0.000378639	+	0.00141310i	0.965736	+	0.259526i	$0.0835662\pi$
$8$	2.34712	−	1.57830i	0.829831	−	0.558015i
$9$		0			0
$10$	−0.857362	+	3.04383i	−0.271122	+	0.962545i
$11$	−3.58713	+	2.07103i	−1.08156	+	0.624439i	−0.931317	−	0.364210i	$-0.881339\pi$
$11$	−3.58713	+	2.07103i	−1.08156	+	0.624439i	−0.150243	+	0.988649i	$0.548006\pi$
$12$		0			0
$13$	2.86455	−	0.767553i	0.794483	−	0.212881i	0.161322	−	0.986902i	$-0.448424\pi$
$13$	2.86455	−	0.767553i	0.794483	−	0.212881i	0.633160	+	0.774021i	$0.281757\pi$
$14$	−0.00455433	−	0.00303665i	−0.00121719	−	0.000811578i
$15$		0			0
$16$	1.05043	+	3.85961i	0.262607	+	0.964903i
$17$	2.07784	−	2.07784i	0.503949	−	0.503949i	−0.408713	−	0.912663i	$-0.634022\pi$
$17$	2.07784	−	2.07784i	0.503949	−	0.503949i	0.912663	+	0.408713i	$0.134022\pi$
$18$		0			0
$19$	7.31525			1.67823			0.839117	−	0.543951i	$-0.183072\pi$
$19$	7.31525			1.67823			0.839117	+	0.543951i	$0.183072\pi$
$20$	−3.68893	−	2.52821i	−0.824869	−	0.565324i
$21$		0			0
$22$	−1.14843	−	5.74408i	−0.244845	−	1.22464i
$23$	1.00208	+	3.73983i	0.208949	+	0.779808i	0.988209	+	0.153108i	$0.0489283\pi$
$23$	1.00208	+	3.73983i	0.208949	+	0.779808i	−0.779260	+	0.626700i	$0.784405\pi$
$24$		0			0
$25$	4.97328	−	0.516182i	0.994657	−	0.103236i
$26$	−0.270195	+	4.18528i	−0.0529896	+	0.820800i
$27$		0			0
$28$	0.00613225	−	0.00472458i	0.00115889	−	0.000892863i
$29$	4.99228	−	2.88229i	0.927042	−	0.535228i	0.0411674	−	0.999152i	$-0.486892\pi$
$29$	4.99228	−	2.88229i	0.927042	−	0.535228i	0.885875	+	0.463924i	$0.153559\pi$
$30$		0			0
$31$	1.77642	+	1.02562i	0.319054	+	0.184206i	0.650971	−	0.759103i	$-0.274362\pi$
$31$	1.77642	+	1.02562i	0.319054	+	0.184206i	−0.331917	+	0.943309i	$0.607695\pi$
$32$	−5.64649	−	0.342287i	−0.998168	−	0.0605084i
$33$		0			0
$34$	1.84166	+	3.72530i	0.315842	+	0.638885i
$35$	−0.00180496	+	0.00846463i	−0.000305094	+	0.00143078i
$36$		0			0
$37$	−6.09468	+	6.09468i	−1.00196	+	1.00196i	−0.00196150	+	0.999998i	$0.500624\pi$
$37$	−6.09468	+	6.09468i	−1.00196	+	1.00196i	−0.999998	+	0.00196150i	$0.999376\pi$
$38$	−3.31579	+	9.79956i	−0.537891	+	1.58970i
$39$		0			0
$40$	5.05888	−	3.79575i	0.799880	−	0.600160i
$41$	−1.82477	+	3.16060i	−0.284981	+	0.493602i	−0.972605	−	0.232465i	$-0.925321\pi$
$41$	−1.82477	+	3.16060i	−0.284981	+	0.493602i	0.687623	+	0.726068i	$0.258654\pi$
$42$		0			0
$43$	−0.968609	−	0.259538i	−0.147711	−	0.0395792i	0.184206	−	0.982888i	$-0.441029\pi$
$43$	−0.968609	−	0.259538i	−0.147711	−	0.0395792i	−0.331917	+	0.943309i	$0.607695\pi$
$44$	8.21535	+	1.06518i	1.23851	+	0.160582i
$45$		0			0
$46$	−5.46412	−	0.352755i	−0.805640	−	0.0520108i
$47$	−1.22115	+	4.55740i	−0.178123	+	0.664765i	0.817875	+	0.575396i	$0.195152\pi$
$47$	−1.22115	+	4.55740i	−0.178123	+	0.664765i	−0.995999	+	0.0893696i	$0.971515\pi$
$48$		0			0
$49$	6.06216	+	3.49999i	0.866024	+	0.499999i
$50$	−1.56276	+	6.89621i	−0.221008	+	0.975272i
$51$		0			0
$52$	−5.48415	−	2.25902i	−0.760515	−	0.313269i
$53$	−6.92974	−	6.92974i	−0.951873	−	0.951873i	0.0470212	−	0.998894i	$-0.485027\pi$
$53$	−6.92974	−	6.92974i	−0.951873	−	0.951873i	−0.998894	+	0.0470212i	$0.985027\pi$
$54$		0			0
$55$	−7.77098	+	5.03936i	−1.04784	+	0.679507i
$56$	0.00354952	+	0.0103563i	0.000474324	+	0.00138392i
$57$		0			0
$58$	1.59829	+	7.99414i	0.209865	+	1.04968i
$59$	2.76056	−	4.78143i	0.359394	−	0.622489i	−0.628465	−	0.777838i	$-0.716317\pi$
$59$	2.76056	−	4.78143i	0.359394	−	0.622489i	0.987860	+	0.155348i	$0.0496499\pi$
$60$		0			0
$61$	3.59007	+	6.21819i	0.459662	+	0.796158i	0.998943	−	0.0459683i	$-0.0146373\pi$
$61$	3.59007	+	6.21819i	0.459662	+	0.796158i	−0.539281	+	0.842126i	$0.681304\pi$
$62$	−2.17912	+	1.91482i	−0.276748	+	0.243182i
$63$		0			0
$64$	3.01792	−	7.40893i	0.377239	−	0.926116i
$65$	6.30805	−	2.04508i	0.782417	−	0.253661i
$66$		0			0
$67$	−3.17735	+	0.851369i	−0.388175	+	0.104011i	−0.447628	−	0.894220i	$-0.647731\pi$
$67$	−3.17735	+	0.851369i	−0.388175	+	0.104011i	0.0594528	+	0.998231i	$0.481064\pi$
$68$	−5.82521	+	0.778533i	−0.706411	+	0.0944110i
$69$		0			0
$70$	−0.0105211	−	0.00625470i	−0.00125752	−	0.000747580i
$71$		−	11.3127i		−	1.34257i	−0.741200	−	0.671284i	$-0.765743\pi$
$71$		−	11.3127i		−	1.34257i	0.741200	−	0.671284i	$-0.234257\pi$
$72$		0			0
$73$	−6.50632	−	6.50632i	−0.761508	−	0.761508i	0.215087	−	0.976595i	$-0.430996\pi$
$73$	−6.50632	−	6.50632i	−0.761508	−	0.761508i	−0.976595	+	0.215087i	$0.930996\pi$
$74$	−5.40194	−	10.9270i	−0.627963	−	1.27024i
$75$		0			0
$76$	−11.6246	−	8.88370i	−1.33343	−	1.01903i
$77$	−0.00414946	−	0.0154860i	−0.000472874	−	0.00176479i
$78$		0			0
$79$	−2.99986	−	5.19591i	−0.337510	−	0.584585i	0.646453	−	0.762953i	$-0.276251\pi$
$79$	−2.99986	−	5.19591i	−0.337510	−	0.584585i	−0.983964	+	0.178368i	$0.942918\pi$
$80$	2.79177	+	8.49741i	0.312129	+	0.950040i
$81$		0			0
$82$	−3.40684	−	3.87708i	−0.376223	−	0.428152i
$83$	2.82192	+	0.756131i	0.309746	+	0.0829962i	0.410344	−	0.911931i	$-0.365409\pi$
$83$	2.82192	+	0.756131i	0.309746	+	0.0829962i	−0.100598	+	0.994927i	$0.532075\pi$
$84$		0			0
$85$	4.39982	−	4.88012i	0.477228	−	0.529323i
$86$	0.786720	−	1.17991i	0.0848342	−	0.127233i
$87$		0			0
$88$	−5.15070	+	10.5225i	−0.549066	+	1.12171i
$89$			9.18764i			0.973888i	0.873433	+	0.486944i	$0.161888\pi$
$89$			9.18764i			0.973888i	−0.873433	+	0.486944i	$0.838112\pi$
$90$		0			0
$91$			0.0114786i			0.00120329i
$92$	2.94927	−	7.15987i	0.307483	−	0.746468i
$93$		0			0
$94$	−5.55161	−	3.70160i	−0.572605	−	0.381791i
$95$	16.3355	−	0.845469i	1.67599	−	0.0867433i
$96$		0			0
$97$	−2.26714	−	0.607478i	−0.230193	−	0.0616800i	0.141879	−	0.989884i	$-0.454686\pi$
$97$	−2.26714	−	0.607478i	−0.230193	−	0.0616800i	−0.372072	+	0.928204i	$0.621352\pi$
$98$	−7.43641	+	6.53447i	−0.751191	+	0.660082i
$99$		0			0
$100$	−8.52986	−	5.21933i	−0.852986	−	0.521933i
$101$	3.57015	+	6.18367i	0.355243	+	0.615299i	0.987159	−	0.159738i	$-0.0510649\pi$
$101$	3.57015	+	6.18367i	0.355243	+	0.615299i	−0.631917	+	0.775036i	$0.717732\pi$
$102$		0			0
$103$	−1.08138	−	4.03578i	−0.106552	−	0.397657i	0.891965	−	0.452105i	$-0.149327\pi$
$103$	−1.08138	−	4.03578i	−0.106552	−	0.397657i	−0.998517	+	0.0544481i	$0.982660\pi$
$104$	5.51200	−	6.32266i	0.540496	−	0.619988i
$105$		0			0
$106$	12.4242	−	6.14208i	1.20674	−	0.596571i
$107$	−8.23461	−	8.23461i	−0.796070	−	0.796070i	0.186403	−	0.982473i	$-0.440317\pi$
$107$	−8.23461	−	8.23461i	−0.796070	−	0.796070i	−0.982473	+	0.186403i	$0.940317\pi$
$108$		0			0
$109$			6.43234i			0.616106i	0.951369	+	0.308053i	$0.0996774\pi$
$109$			6.43234i			0.616106i	−0.951369	+	0.308053i	$0.900323\pi$
$110$	−3.22841	−	12.6943i	−0.307816	−	1.21035i
$111$		0			0
$112$	−0.0154823		6.07462e-5i	−0.00146294		5.73998e-6i
$113$	15.0209	−	4.02483i	1.41305	−	0.378625i	0.530035	−	0.847976i	$-0.322179\pi$
$113$	15.0209	−	4.02483i	1.41305	−	0.378625i	0.883012	+	0.469351i	$0.155512\pi$
$114$		0			0
$115$	2.66997	+	8.23552i	0.248976	+	0.767966i
$116$	−11.4335	−	1.48243i	−1.06157	−	0.137640i
$117$		0			0
$118$	5.15396	+	5.86535i	0.474460	+	0.539949i
$119$	0.00568689	+	0.00984998i	0.000521316	+	0.000902946i
$120$		0			0
$121$	3.07833	−	5.33183i	0.279848	−	0.484712i
$122$	−9.95720	+	1.99077i	−0.901483	+	0.180235i
$123$		0			0
$124$	−1.57738	−	3.78709i	−0.141653	−	0.340091i
$125$	11.0461	−	1.72747i	0.987991	−	0.154509i
$126$		0			0
$127$	−14.1298	−	14.1298i	−1.25381	−	1.25381i	−0.953996	−	0.299818i	$-0.903074\pi$
$127$	−14.1298	−	14.1298i	−1.25381	−	1.25381i	−0.299818	−	0.953996i	$-0.596926\pi$
$128$	8.55712	+	7.40107i	0.756349	+	0.654168i
$129$		0			0
$130$	−0.119648	+	9.37728i	−0.0104938	+	0.822442i
$131$	−7.13877	−	4.12157i	−0.623717	−	0.360103i	0.154598	−	0.987978i	$-0.450592\pi$
$131$	−7.13877	−	4.12157i	−0.623717	−	0.360103i	−0.778315	+	0.627874i	$0.783925\pi$
$132$		0			0
$133$	−0.00732831	+	0.0273496i	−0.000635445	+	0.00237151i
$134$	0.299700	−	4.64230i	0.0258901	−	0.401034i
$135$		0			0
$136$	1.59747	−	8.15638i	0.136982	−	0.699404i
$137$	−16.4016	−	4.39479i	−1.40128	−	0.375472i	−0.522476	−	0.852654i	$-0.674992\pi$
$137$	−16.4016	−	4.39479i	−1.40128	−	0.375472i	−0.878804	+	0.477182i	$0.841658\pi$
$138$		0			0
$139$	0.575384	−	0.996595i	0.0488035	−	0.0845301i	−0.840592	−	0.541669i	$-0.817793\pi$
$139$	0.575384	−	0.996595i	0.0488035	−	0.0845301i	0.889395	+	0.457139i	$0.151126\pi$
$140$	0.0131478	−	0.0112591i	0.00111119	−	0.000951569i
$141$		0			0
$142$	15.1545	+	5.12770i	1.27174	+	0.430307i
$143$	−8.68588	+	8.68588i	−0.726350	+	0.726350i
$144$		0			0
$145$	10.8150	−	7.01337i	0.898139	−	0.582429i
$146$	11.6650	−	5.76679i	0.965405	−	0.477263i
$147$		0			0
$148$	17.0864	−	2.28358i	1.40450	−	0.187709i
$149$	−15.4247	−	8.90547i	−1.26364	−	0.729565i	−0.289865	−	0.957067i	$-0.593611\pi$
$149$	−15.4247	−	8.90547i	−1.26364	−	0.729565i	−0.973777	+	0.227503i	$0.926944\pi$
$150$		0			0
$151$	14.2092	−	8.20368i	1.15633	−	0.667606i	0.205906	−	0.978572i	$-0.433986\pi$
$151$	14.2092	−	8.20368i	1.15633	−	0.667606i	0.950421	+	0.310966i	$0.100652\pi$
$152$	17.1697	−	11.5457i	1.39265	−	0.936479i
$153$		0			0
$154$	0.0226259	+	0.00146070i	0.00182325	+	0.000117706i
$155$	4.08542	+	2.08497i	0.328149	+	0.167469i
$156$		0			0
$157$	0.152969	+	0.570890i	0.0122083	+	0.0455620i	0.971761	−	0.235966i	$-0.0758254\pi$
$157$	0.152969	+	0.570890i	0.0122083	+	0.0455620i	−0.959553	+	0.281528i	$0.909159\pi$
$158$	8.32022	−	1.66348i	0.661921	−	0.132339i
$159$		0			0
$160$	−12.6486	−	0.111754i	−0.999961	−	0.00883497i
$161$	−0.0149860			−0.00118106
$162$		0			0
$163$	−2.55591	+	2.55591i	−0.200194	+	0.200194i	−0.800083	−	0.599889i	$-0.795211\pi$
$163$	−2.55591	+	2.55591i	−0.200194	+	0.200194i	0.599889	+	0.800083i	$0.295211\pi$
$164$	6.73798	−	2.80646i	0.526148	−	0.219148i
$165$		0			0
$166$	−2.29201	+	3.43753i	−0.177895	+	0.266804i
$167$	9.46085	−	2.53503i	0.732103	−	0.196166i	0.126537	−	0.991962i	$-0.459614\pi$
$167$	9.46085	−	2.53503i	0.732103	−	0.196166i	0.605565	+	0.795796i	$0.292947\pi$
$168$		0			0
$169$	−3.64184	+	2.10261i	−0.280141	+	0.161740i
$170$	4.54313	+	8.10605i	0.348442	+	0.621706i
$171$		0			0
$172$	1.22402	+	1.58872i	0.0933309	+	0.121138i
$173$	2.35512	−	8.78942i	0.179056	−	0.668247i	−0.816769	−	0.576965i	$-0.804237\pi$
$173$	2.35512	−	8.78942i	0.179056	−	0.668247i	0.995825	−	0.0912819i	$-0.0290964\pi$
$174$		0			0
$175$	−0.00305231	+	0.0191108i	−0.000230733	+	0.00144464i
$176$	−11.7614	−	11.6695i	−0.886548	−	0.879619i
$177$		0			0
$178$	−12.3078	−	4.16449i	−0.922511	−	0.312141i
$179$	−9.66859			−0.722664			−0.361332	−	0.932437i	$-0.617678\pi$
$179$	−9.66859			−0.722664			−0.361332	+	0.932437i	$0.617678\pi$
$180$		0			0
$181$	−0.725261			−0.0539082			−0.0269541	−	0.999637i	$-0.508581\pi$
$181$	−0.725261			−0.0539082			−0.0269541	+	0.999637i	$0.508581\pi$
$182$	−0.0153769	−	0.00520293i	−0.00113981	−	0.000385667i
$183$		0			0
$184$	8.25460	+	7.19622i	0.608537	+	0.530513i
$185$	−12.9055	+	14.3143i	−0.948832	+	1.05241i
$186$		0			0
$187$	−3.15021	+	11.7567i	−0.230366	+	0.859737i
$188$	7.47507	−	5.75915i	0.545175	−	0.420029i
$189$		0			0
$190$	−6.27181	+	22.2664i	−0.455005	+	1.61538i
$191$	−4.39149	+	2.53543i	−0.317757	+	0.183457i	−0.650393	−	0.759598i	$-0.725396\pi$
$191$	−4.39149	+	2.53543i	−0.317757	+	0.183457i	0.332635	+	0.943056i	$0.392062\pi$
$192$		0			0
$193$	−24.8439	+	6.65689i	−1.78830	+	0.479174i	−0.992056	−	0.125801i	$-0.959850\pi$
$193$	−24.8439	+	6.65689i	−1.78830	+	0.479174i	−0.796245	+	0.604975i	$0.793183\pi$
$194$	1.84141	−	2.76172i	0.132205	−	0.198280i
$195$		0			0
$196$	−5.38292	−	12.9238i	−0.384494	−	0.923125i
$197$	−7.34350	+	7.34350i	−0.523203	+	0.523203i	−0.918537	−	0.395334i	$-0.870629\pi$
$197$	−7.34350	+	7.34350i	−0.523203	+	0.523203i	0.395334	+	0.918537i	$0.370629\pi$
$198$		0			0
$199$	23.5313			1.66809			0.834046	−	0.551695i	$-0.186019\pi$
$199$	23.5313			1.66809			0.834046	+	0.551695i	$0.186019\pi$
$200$	10.8582	−	9.06089i	0.767790	−	0.640702i
$201$		0			0
$202$	−9.90193	+	1.97972i	−0.696698	+	0.139292i
$203$	0.00577488	+	0.0215521i	0.000405317	+	0.00151266i
$204$		0			0
$205$	−3.70957	+	7.26876i	−0.259088	+	0.507672i
$206$	5.89651	+	0.380669i	0.410829	+	0.0265225i
$207$		0			0
$208$	5.97146	+	10.2498i	0.414046	+	0.710694i
$209$	−26.2407	+	15.1501i	−1.81511	+	1.04795i
$210$		0			0
$211$	−11.4167	−	6.59145i	−0.785960	−	0.453774i	0.0525786	−	0.998617i	$-0.483256\pi$
$211$	−11.4167	−	6.59145i	−0.785960	−	0.453774i	−0.838538	+	0.544843i	$0.816589\pi$
$212$	2.59646	+	19.4275i	0.178326	+	1.33429i
$213$		0			0
$214$	14.7636	−	7.29864i	1.00922	−	0.498925i
$215$	−2.19298	−	0.467621i	−0.149560	−	0.0318915i
$216$		0			0
$217$	−0.00561407	+	0.00561407i	−0.000381108	+	0.000381108i
$218$	−8.61680	−	2.91559i	−0.583603	−	0.197468i
$219$		0			0
$220$	18.4686	+	1.42913i	1.24516	+	0.0963520i
$221$	4.35721	−	7.54691i	0.293098	−	0.507660i
$222$		0			0
$223$	−6.66356	−	1.78550i	−0.446225	−	0.119566i	0.0287073	−	0.999588i	$-0.490861\pi$
$223$	−6.66356	−	1.78550i	−0.446225	−	0.119566i	−0.474933	+	0.880022i	$0.657528\pi$
$224$	0.00693628	−	0.0207677i	0.000463450	−	0.00138760i
$225$		0			0
$226$	−1.41683	+	21.9464i	−0.0942459	+	1.45985i
$227$	−6.18736	+	23.0916i	−0.410670	+	1.53264i	0.382684	+	0.923879i	$0.375000\pi$
$227$	−6.18736	+	23.0916i	−0.410670	+	1.53264i	−0.793354	+	0.608761i	$0.791667\pi$
$228$		0			0
$229$	−10.8974	−	6.29160i	−0.720118	−	0.415761i	0.0946778	−	0.995508i	$-0.469818\pi$
$229$	−10.8974	−	6.29160i	−0.720118	−	0.415761i	−0.814796	+	0.579747i	$0.803151\pi$
$230$	−12.2426	−	0.156207i	−0.807251	−	0.0103000i
$231$		0			0
$232$	7.16832	−	14.6444i	0.470624	−	0.961452i
$233$	−5.85463	−	5.85463i	−0.383550	−	0.383550i	0.488830	−	0.872379i	$-0.337424\pi$
$233$	−5.85463	−	5.85463i	−0.383550	−	0.383550i	−0.872379	+	0.488830i	$0.837424\pi$
$234$		0			0
$235$	−2.20020	+	10.3182i	−0.143525	+	0.673083i
$236$	−10.1934	+	4.24569i	−0.663533	+	0.276371i
$237$		0			0
$238$	−0.0157728	+	0.00315349i	−0.00102240	+	0.000204410i
$239$	8.52459	−	14.7650i	0.551410	−	0.955070i	−0.446763	−	0.894652i	$-0.647423\pi$
$239$	8.52459	−	14.7650i	0.551410	−	0.955070i	0.998173	−	0.0604180i	$-0.0192434\pi$
$240$		0			0
$241$	−6.97743	−	12.0853i	−0.449456	−	0.778481i	0.548895	−	0.835892i	$-0.315049\pi$
$241$	−6.97743	−	12.0853i	−0.449456	−	0.778481i	−0.998351	+	0.0574109i	$0.981715\pi$
$242$	5.74723	+	6.54051i	0.369446	+	0.420440i
$243$		0			0
$244$	1.84646	−	14.2411i	0.118207	−	0.911692i
$245$	13.9418	+	7.11512i	0.890710	+	0.454568i
$246$		0			0
$247$	20.9549	−	5.61484i	1.33333	−	0.357264i
$248$	5.78819	−	0.396488i	0.367551	−	0.0251770i
$249$		0			0
$250$	−2.69273	+	15.5804i	−0.170303	+	0.985392i
$251$			5.95154i			0.375658i	0.982202	+	0.187829i	$0.0601451\pi$
$251$			5.95154i			0.375658i	−0.982202	+	0.187829i	$0.939855\pi$
$252$		0			0
$253$	−11.3399	−	11.3399i	−0.712934	−	0.712934i
$254$	25.3329	−	12.5237i	1.58953	−	0.785809i
$255$		0			0
$256$	−13.7932	+	8.10849i	−0.862075	+	0.506780i
$257$	0.638709	+	2.38369i	0.0398416	+	0.148691i	0.982981	−	0.183706i	$-0.0588094\pi$
$257$	0.638709	+	2.38369i	0.0398416	+	0.148691i	−0.943140	+	0.332397i	$0.892143\pi$
$258$		0			0
$259$	−0.0166807	−	0.0288918i	−0.00103649	−	0.00179525i
$260$	−12.5076	−	4.41072i	−0.775691	−	0.273541i
$261$		0			0
$262$	8.75708	−	7.69496i	0.541014	−	0.475396i
$263$	3.93947	+	1.05558i	0.242918	+	0.0650897i	0.378224	−	0.925714i	$-0.376535\pi$
$263$	3.93947	+	1.05558i	0.242918	+	0.0650897i	−0.135306	+	0.990804i	$0.543202\pi$
$264$		0			0
$265$	−16.2756	−	14.6737i	−0.999800	−	0.901401i
$266$	−0.0333160	−	0.0222138i	−0.00204274	−	0.00136202i
$267$		0			0
$268$	6.08301	+	2.50570i	0.371579	+	0.153060i
$269$			14.8292i			0.904151i	0.891980	+	0.452075i	$0.149316\pi$
$269$			14.8292i			0.904151i	−0.891980	+	0.452075i	$0.850684\pi$
$270$		0			0
$271$		−	2.28698i		−	0.138924i	−0.997585	−	0.0694621i	$-0.977872\pi$
$271$		−	2.28698i		−	0.138924i	0.997585	−	0.0694621i	$-0.0221283\pi$
$272$	10.2023	+	5.83702i	0.618603	+	0.353922i
$273$		0			0
$274$	13.3216	−	19.9796i	0.804789	−	1.20701i
$275$	−16.7708	+	12.1514i	−1.01132	+	0.732759i
$276$		0			0
$277$	−0.897723	−	0.240544i	−0.0539390	−	0.0144529i	0.231749	−	0.972776i	$-0.425555\pi$
$277$	−0.897723	−	0.240544i	−0.0539390	−	0.0144529i	−0.285688	+	0.958323i	$0.592222\pi$
$278$	1.07424	+	1.22252i	0.0644287	+	0.0733216i
$279$		0			0
$280$	0.00912330	+	0.0227162i	0.000545221	+	0.00135756i
$281$	9.59486	+	16.6188i	0.572381	+	0.991394i	0.996321	+	0.0857030i	$0.0273136\pi$
$281$	9.59486	+	16.6188i	0.572381	+	0.991394i	−0.423939	+	0.905691i	$0.639353\pi$
$282$		0			0
$283$	6.24132	+	23.2929i	0.371008	+	1.38462i	0.859091	+	0.511823i	$0.171030\pi$
$283$	6.24132	+	23.2929i	0.371008	+	1.38462i	−0.488083	+	0.872797i	$0.662304\pi$
$284$	−13.7382	+	17.9769i	−0.815213	+	1.06673i
$285$		0			0
$286$	−7.69861	−	15.5727i	−0.455228	−	0.920834i
$287$	−0.00998854	−	0.00998854i	−0.000589605	−	0.000589605i
$288$		0			0
$289$			8.36519i			0.492070i
$290$	4.49303	+	17.6668i	0.263840	+	1.03743i
$291$		0			0
$292$	2.43782	+	18.2405i	0.142662	+	1.06744i
$293$	2.04403	−	0.547697i	0.119414	−	0.0319968i	−0.198617	−	0.980077i	$-0.563645\pi$
$293$	2.04403	−	0.547697i	0.119414	−	0.0319968i	0.318031	+	0.948080i	$0.396978\pi$
$294$		0			0
$295$	5.61193	−	10.9964i	0.326739	−	0.640234i
$296$	−4.68567	+	23.9242i	−0.272349	+	1.39057i
$297$		0			0
$298$	18.9214	−	16.6265i	1.09609	−	0.963146i
$299$	5.74104	+	9.94377i	0.332013	+	0.575063i
$300$		0			0
$301$	0.00194068	−	0.00336135i	0.000111859	−	0.000193745i
$302$	4.54910	+	22.7532i	0.261771	+	1.30930i
$303$		0			0
$304$	7.68414	+	28.2340i	0.440716	+	1.61933i
$305$	8.73559	+	13.4708i	0.500199	+	0.771335i
$306$		0			0
$307$	10.6198	+	10.6198i	0.606102	+	0.606102i	0.941925	−	0.335823i	$-0.109015\pi$
$307$	10.6198	+	10.6198i	0.606102	+	0.606102i	−0.335823	+	0.941925i	$0.609015\pi$
$308$	−0.0122124	+	0.0296478i	−0.000695867	+	0.00168934i
$309$		0			0
$310$	−4.64484	+	4.52780i	−0.263809	+	0.257162i
$311$	16.3389	+	9.43325i	0.926493	+	0.534911i	0.885701	−	0.464257i	$-0.153679\pi$
$311$	16.3389	+	9.43325i	0.926493	+	0.534911i	0.0407921	+	0.999168i	$0.487012\pi$
$312$		0			0
$313$	4.31704	−	16.1114i	0.244013	−	0.910670i	−0.729863	−	0.683593i	$-0.760416\pi$
$313$	4.31704	−	16.1114i	0.244013	−	0.910670i	0.973877	−	0.227077i	$-0.0729170\pi$
$314$	−0.834104	−	0.0538484i	−0.0470712	−	0.00303884i
$315$		0			0
$316$	−1.54290	+	11.8998i	−0.0867948	+	0.669417i
$317$	−17.4992	−	4.68890i	−0.982855	−	0.263355i	−0.268608	−	0.963250i	$-0.586564\pi$
$317$	−17.4992	−	4.68890i	−0.982855	−	0.263355i	−0.714246	+	0.699894i	$0.753230\pi$
$318$		0			0
$319$	−11.9386	+	20.6783i	−0.668435	+	1.15776i
$320$	5.88295	−	16.8935i	0.328867	−	0.944376i
$321$		0			0
$322$	0.00679272	−	0.0200754i	0.000378543	−	0.00111876i
$323$	15.1999	−	15.1999i	0.845745	−	0.845745i
$324$		0			0
$325$	13.8500	−	5.29589i	0.768260	−	0.293763i
$326$	−2.26539	−	4.58243i	−0.125469	−	0.253797i
$327$		0			0
$328$	0.705429	+	10.2983i	0.0389508	+	0.568630i
$329$	−0.0158155	−	0.00913108i	−0.000871936	−	0.000503412i
$330$		0			0
$331$	−30.9050	+	17.8430i	−1.69869	+	0.980741i	−0.751690	+	0.659516i	$0.770761\pi$
$331$	−30.9050	+	17.8430i	−1.69869	+	0.980741i	−0.947003	+	0.321225i	$0.895906\pi$
$332$	−3.56604	−	4.62852i	−0.195712	−	0.254023i
$333$		0			0
$334$	−0.892383	+	13.8229i	−0.0488290	+	0.756354i
$335$	−6.99688	+	2.26840i	−0.382280	+	0.123936i
$336$		0			0
$337$	5.42108	+	20.2317i	0.295305	+	1.10209i	0.940975	+	0.338476i	$0.109911\pi$
$337$	5.42108	+	20.2317i	0.295305	+	1.10209i	−0.645670	+	0.763616i	$0.723422\pi$
$338$	−1.16594	−	5.83168i	−0.0634188	−	0.317202i
$339$		0			0
$340$	−12.9182	+	2.41178i	−0.700587	+	0.130797i
$341$	−8.49632			−0.460102
$342$		0			0
$343$	−0.0383170	+	0.0383170i	−0.00206892	+	0.00206892i
$344$	−2.68307	+	0.919593i	−0.144661	+	0.0495811i
$345$		0			0
$346$	10.7069	+	7.13891i	0.575604	+	0.383790i
$347$	−9.92205	+	2.65861i	−0.532644	+	0.142721i	−0.515109	−	0.857125i	$-0.672248\pi$
$347$	−9.92205	+	2.65861i	−0.532644	+	0.142721i	−0.0175348	+	0.999846i	$0.505582\pi$
$348$		0			0
$349$	−15.7613	+	9.09980i	−0.843683	+	0.487101i	−0.858515	−	0.512789i	$-0.828612\pi$
$349$	−15.7613	+	9.09980i	−0.843683	+	0.487101i	0.0148311	+	0.999890i	$0.495279\pi$
$350$	−0.0242174	−	0.0127512i	−0.00129448	−	0.000681583i
$351$		0			0
$352$	20.9636	−	10.4662i	1.11736	−	0.557851i
$353$	4.36534	−	16.2917i	0.232344	−	0.867119i	−0.746984	−	0.664842i	$-0.768499\pi$
$353$	4.36534	−	16.2917i	0.232344	−	0.867119i	0.979328	−	0.202277i	$-0.0648343\pi$
$354$		0			0
$355$	−1.30748	−	25.2621i	−0.0693937	−	1.34077i
$356$	11.1575	−	14.6000i	0.591349	−	0.773799i
$357$		0			0
$358$	4.38249	−	12.9521i	0.231622	−	0.684540i
$359$	26.8572			1.41747			0.708736	−	0.705474i	$-0.249266\pi$
$359$	26.8572			1.41747			0.708736	+	0.705474i	$0.249266\pi$
$360$		0			0
$361$	34.5129			1.81647
$362$	0.328739	−	0.971564i	0.0172782	−	0.0510643i
$363$		0			0
$364$	0.0139398	−	0.0182406i	0.000730642	−	0.000956069i
$365$	−15.2811	−	13.7772i	−0.799850	−	0.721129i
$366$		0			0
$367$	1.63574	−	6.10468i	0.0853851	−	0.318662i	−0.910002	−	0.414604i	$-0.863920\pi$
$367$	1.63574	−	6.10468i	0.0853851	−	0.318662i	0.995387	+	0.0959429i	$0.0305866\pi$
$368$	−13.3817	+	7.79608i	−0.697568	+	0.406399i
$369$		0			0
$370$	−13.3259	−	23.7766i	−0.692778	−	1.23608i
$371$	0.0328504	−	0.0189662i	0.00170551	−	0.000984676i
$372$		0			0
$373$	12.1450	−	3.25424i	0.628843	−	0.168498i	0.0696984	−	0.997568i	$-0.477796\pi$
$373$	12.1450	−	3.25424i	0.628843	−	0.168498i	0.559145	+	0.829070i	$0.311130\pi$
$374$	−14.3215	−	9.54901i	−0.740547	−	0.493768i
$375$		0			0
$376$	4.32678	+	12.6241i	0.223136	+	0.651038i
$377$	12.0883	−	12.0883i	0.622579	−	0.622579i
$378$		0			0
$379$	−13.2087			−0.678488			−0.339244	−	0.940698i	$-0.610171\pi$
$379$	−13.2087			−0.678488			−0.339244	+	0.940698i	$0.610171\pi$
$380$	−26.9854	−	18.4945i	−1.38432	−	0.948746i
$381$		0			0
$382$	−1.40595	−	7.03211i	−0.0719345	−	0.359794i
$383$	−4.87081	−	18.1781i	−0.248887	−	0.928858i	−0.971390	−	0.237490i	$-0.923675\pi$
$383$	−4.87081	−	18.1781i	−0.248887	−	0.928858i	0.722503	−	0.691368i	$-0.242991\pi$
$384$		0			0
$385$	−0.0110559	−	0.0341018i	−0.000563459	−	0.00173799i
$386$	2.34337	−	36.2984i	0.119274	−	1.84754i
$387$		0			0
$388$	2.86497	+	3.71857i	0.145447	+	0.188782i
$389$	−1.13890	+	0.657543i	−0.0577444	+	0.0333388i	−0.528594	−	0.848875i	$-0.677281\pi$
$389$	−1.13890	+	0.657543i	−0.0577444	+	0.0333388i	0.470850	+	0.882213i	$0.343947\pi$
$390$		0			0
$391$	9.85292	+	5.68859i	0.498284	+	0.287684i
$392$	19.7527	−	1.35304i	0.997660	−	0.0683391i
$393$		0			0
$394$	−6.50881	−	13.1660i	−0.327909	−	0.663293i
$395$	−7.29944	−	11.2562i	−0.367275	−	0.566359i
$396$		0			0
$397$	0.714896	−	0.714896i	0.0358796	−	0.0358796i	−0.688939	−	0.724819i	$-0.741923\pi$
$397$	0.714896	−	0.714896i	0.0358796	−	0.0358796i	0.724819	+	0.688939i	$0.241923\pi$
$398$	−10.6661	+	31.5227i	−0.534641	+	1.58009i
$399$		0			0
$400$	7.21634	+	18.6527i	0.360817	+	0.932637i
$401$	9.93987	−	17.2164i	0.496373	−	0.859744i	−0.503618	−	0.863926i	$-0.667998\pi$
$401$	9.93987	−	17.2164i	0.496373	−	0.859744i	0.999991	+	0.00418285i	$0.00133145\pi$
$402$		0			0
$403$	5.87585	+	1.57443i	0.292697	+	0.0784279i
$404$	1.83621	−	14.1620i	0.0913549	−	0.704588i
$405$		0			0
$406$	−0.0314890	−	0.00203288i	−0.00156277	−	0.000100890i
$407$	9.24014	−	34.4847i	0.458017	−	1.70934i
$408$		0			0
$409$	21.4875	+	12.4058i	1.06249	+	0.613428i	0.926120	−	0.377230i	$-0.123123\pi$
$409$	21.4875	+	12.4058i	1.06249	+	0.613428i	0.136369	+	0.990658i	$0.456457\pi$
$410$	−8.05585	−	8.26408i	−0.397850	−	0.408134i
$411$		0			0
$412$	−3.18266	+	7.72646i	−0.156798	+	0.380655i
$413$	0.0151109	+	0.0151109i	0.000743560	+	0.000743560i
$414$		0			0
$415$	6.38896	+	1.36235i	0.313622	+	0.0668753i
$416$	−16.4374	+	3.35348i	−0.805908	+	0.164418i
$417$		0			0
$418$	−8.40103	−	42.0194i	−0.410908	−	2.05523i
$419$	−14.0411	+	24.3199i	−0.685953	+	1.18811i	0.287183	+	0.957876i	$0.407281\pi$
$419$	−14.0411	+	24.3199i	−0.685953	+	1.18811i	−0.973136	+	0.230230i	$0.926052\pi$
$420$		0			0
$421$	0.651510	+	1.12845i	0.0317527	+	0.0549972i	0.881465	−	0.472249i	$-0.156558\pi$
$421$	0.651510	+	1.12845i	0.0317527	+	0.0549972i	−0.849712	+	0.527246i	$0.823224\pi$
$422$	14.0048	−	12.3062i	0.681743	−	0.599057i
$423$		0			0
$424$	−27.2021	−	5.32768i	−1.32105	−	0.258735i
$425$	9.26113	−	11.4062i	0.449231	−	0.553283i
$426$		0			0
$427$	−0.0268445	+	0.00719297i	−0.00129910	+	0.000348092i
$428$	3.08538	+	23.0857i	0.149138	+	1.11589i
$429$		0			0
$430$	1.62044	−	2.72577i	0.0781445	−	0.131448i
$431$			14.1271i			0.680479i	0.940339	+	0.340240i	$0.110508\pi$
$431$			14.1271i			0.680479i	−0.940339	+	0.340240i	$0.889492\pi$
$432$		0			0
$433$	−4.90201	−	4.90201i	−0.235576	−	0.235576i	0.579440	−	0.815015i	$-0.303271\pi$
$433$	−4.90201	−	4.90201i	−0.235576	−	0.235576i	−0.815015	+	0.579440i	$0.803271\pi$
$434$	−0.00497596	−	0.0100653i	−0.000238854	−	0.000483152i
$435$		0			0
$436$	7.81148	−	10.2216i	0.374102	−	0.489525i
$437$	7.33050	+	27.3578i	0.350665	+	1.30870i
$438$		0			0
$439$	−14.2344	−	24.6546i	−0.679369	−	1.17670i	−0.975171	−	0.221452i	$-0.928920\pi$
$439$	−14.2344	−	24.6546i	−0.679369	−	1.17670i	0.295803	−	0.955249i	$-0.404413\pi$
$440$	−10.2858	+	24.0929i	−0.490354	+	1.14859i
$441$		0			0
$442$	8.13490	+	9.25774i	0.386938	+	0.440346i
$443$	−23.6010	−	6.32386i	−1.12132	−	0.300456i	−0.349900	−	0.936787i	$-0.613784\pi$
$443$	−23.6010	−	6.32386i	−1.12132	−	0.300456i	−0.771416	+	0.636332i	$0.780451\pi$
$444$		0			0
$445$	1.06187	+	20.5167i	0.0503376	+	0.972586i
$446$	5.41226	−	8.11724i	0.256278	−	0.384363i
$447$		0			0
$448$	0.0246766	+	0.0187053i	0.00116586	+	0.000883741i
$449$		−	32.1553i		−	1.51750i	−0.651382	−	0.758750i	$-0.725810\pi$
$449$		−	32.1553i		−	1.51750i	0.651382	−	0.758750i	$-0.274190\pi$
$450$		0			0
$451$		−	15.1166i		−	0.711814i
$452$	−28.7574	−	11.8456i	−1.35263	−	0.557172i
$453$		0			0
$454$	−28.1290	−	18.7553i	−1.32016	−	0.880232i
$455$	0.00132666	+	0.0256327i	6.21947e−5	+	0.00120168i
$456$		0			0
$457$	−10.9057	−	2.92218i	−0.510149	−	0.136694i	−0.00544282	−	0.999985i	$-0.501733\pi$
$457$	−10.9057	−	2.92218i	−0.510149	−	0.136694i	−0.504706	+	0.863291i	$0.668399\pi$
$458$	13.3677	−	11.7464i	0.624633	−	0.548873i
$459$		0			0
$460$	5.75845	−	16.3294i	0.268489	−	0.761363i
$461$	1.41470	+	2.45032i	0.0658889	+	0.114123i	0.897088	−	0.441852i	$-0.145678\pi$
$461$	1.41470	+	2.45032i	0.0658889	+	0.114123i	−0.831199	+	0.555975i	$0.812345\pi$
$462$		0			0
$463$	−5.56471	−	20.7678i	−0.258614	−	0.965161i	−0.966044	−	0.258377i	$-0.916812\pi$
$463$	−5.56471	−	20.7678i	−0.258614	−	0.965161i	0.707430	−	0.706783i	$-0.249854\pi$
$464$	16.3686	+	16.2406i	0.759891	+	0.753951i
$465$		0			0
$466$	10.4966	−	5.18917i	0.486247	−	0.240384i
$467$	0.746518	+	0.746518i	0.0345447	+	0.0345447i	0.724168	−	0.689623i	$-0.242224\pi$
$467$	0.746518	+	0.746518i	0.0345447	+	0.0345447i	−0.689623	+	0.724168i	$0.742224\pi$
$468$		0			0
$469$		−	0.0127321i		−	0.000587914i
$470$	−12.8250	−	7.62433i	−0.591574	−	0.351684i
$471$		0			0
$472$	−1.06719	−	15.5796i	−0.0491215	−	0.717108i
$473$	4.01204	−	1.07502i	0.184474	−	0.0494296i
$474$		0			0
$475$	36.3808	−	3.77600i	1.66927	−	0.173255i
$476$	0.00292490	−	0.0225587i	0.000134063	−	0.00103398i
$477$		0			0
$478$	15.9154	+	18.1122i	0.727953	+	0.828430i
$479$	−8.68475	−	15.0424i	−0.396816	−	0.687306i	0.596515	−	0.802602i	$-0.296552\pi$
$479$	−8.68475	−	15.0424i	−0.396816	−	0.687306i	−0.993331	+	0.115296i	$0.963218\pi$
$480$		0			0
$481$	−12.7805	+	22.1365i	−0.582741	+	1.00934i
$482$	19.3522	−	3.86912i	0.881467	−	0.176234i
$483$		0			0
$484$	−11.3668	+	4.73441i	−0.516671	+	0.215201i
$485$	−5.13291	−	1.09452i	−0.233073	−	0.0496995i
$486$		0			0
$487$	−17.2233	−	17.2233i	−0.780462	−	0.780462i	0.199447	−	0.979909i	$-0.436086\pi$
$487$	−17.2233	−	17.2233i	−0.780462	−	0.780462i	−0.979909	+	0.199447i	$0.936086\pi$
$488$	18.2405	+	8.92859i	0.825709	+	0.404178i
$489$		0			0
$490$	−15.8509	+	15.4515i	−0.716069	+	0.698026i
$491$	13.8880	+	8.01824i	0.626757	+	0.361858i	0.779495	−	0.626409i	$-0.215476\pi$
$491$	13.8880	+	8.01824i	0.626757	+	0.361858i	−0.152738	+	0.988267i	$0.548809\pi$
$492$		0			0
$493$	4.38420	−	16.3621i	0.197455	−	0.736910i
$494$	−1.97654	+	30.6163i	−0.0889288	+	1.37749i
$495$		0			0
$496$	−2.09248	+	7.93362i	−0.0939551	+	0.356230i
$497$	0.0422949	+	0.0113329i	0.00189718	+	0.000508349i
$498$		0			0
$499$	−18.9316	+	32.7905i	−0.847494	+	1.46790i	0.0359441	+	0.999354i	$0.488556\pi$
$499$	−18.9316	+	32.7905i	−0.847494	+	1.46790i	−0.883438	+	0.468548i	$0.844777\pi$
$500$	−19.6511	−	10.6693i	−0.878823	−	0.477147i
$501$		0			0
$502$	−7.97273	−	2.69766i	−0.355840	−	0.120402i
$503$	1.97514	−	1.97514i	0.0880673	−	0.0880673i	−0.661701	−	0.749768i	$-0.730165\pi$
$503$	1.97514	−	1.97514i	0.0880673	−	0.0880673i	0.749768	+	0.661701i	$0.230165\pi$
$504$		0			0
$505$	8.68710	+	13.3960i	0.386571	+	0.596115i
$506$	20.3311	−	10.0510i	0.903826	−	0.446820i
$507$		0			0
$508$	5.29421	+	39.6128i	0.234892	+	1.75753i
$509$	23.3128	+	13.4596i	1.03332	+	0.596587i	0.917934	−	0.396733i	$-0.129856\pi$
$509$	23.3128	+	13.4596i	1.03332	+	0.596587i	0.115386	+	0.993321i	$0.463190\pi$
$510$		0			0
$511$	0.0308432	−	0.0178073i	0.00136442	−	0.000787750i
$512$	−4.61013	−	22.1528i	−0.203741	−	0.979025i
$513$		0			0
$514$	−3.48272	−	0.224839i	−0.153616	−	0.00991722i
$515$	−2.88125	−	8.88722i	−0.126963	−	0.391618i
$516$		0			0
$517$	−5.05809	−	18.8770i	−0.222454	−	0.830211i
$518$	0.0462646	−	0.00924978i	0.00203275	−	0.000406412i
$519$		0			0
$520$	11.5780	−	14.7561i	0.507728	−	0.647096i
$521$	−15.4522			−0.676975			−0.338487	−	0.940971i	$-0.609915\pi$
$521$	−15.4522			−0.676975			−0.338487	+	0.940971i	$0.609915\pi$
$522$		0			0
$523$	3.28250	−	3.28250i	0.143534	−	0.143534i	−0.631689	−	0.775222i	$-0.717638\pi$
$523$	3.28250	−	3.28250i	0.143534	−	0.143534i	0.775222	+	0.631689i	$0.217638\pi$
$524$	6.33890	+	15.2189i	0.276916	+	0.664842i
$525$		0			0
$526$	−3.19970	+	4.79888i	−0.139514	+	0.209241i
$527$	5.82217	−	1.56005i	0.253618	−	0.0679566i
$528$		0			0
$529$	6.93643	−	4.00475i	0.301584	−	0.174120i
$530$	27.0343	−	15.1517i	1.17429	−	0.658147i
$531$		0			0
$532$	0.0448590	−	0.0345615i	0.00194488	−	0.00149843i
$533$	−2.80122	+	10.4543i	−0.121334	+	0.452826i
$534$		0			0
$535$	−19.3403	−	17.4368i	−0.836153	−	0.753859i
$536$	−6.11390	+	7.01309i	−0.264080	+	0.302919i
$537$		0			0
$538$	−19.8653	−	6.72163i	−0.856452	−	0.289790i
$539$	−28.9944			−1.24888
$540$		0			0
$541$	−28.5369			−1.22690			−0.613448	−	0.789735i	$-0.710218\pi$
$541$	−28.5369			−1.22690			−0.613448	+	0.789735i	$0.710218\pi$
$542$	3.06366	+	1.03662i	0.131595	+	0.0445267i
$543$		0			0
$544$	−12.4437	+	11.0213i	−0.533519	+	0.472533i
$545$	0.743425	+	14.3639i	0.0318448	+	0.615282i
$546$		0			0
$547$	−9.32812	+	34.8130i	−0.398842	+	1.48850i	0.416295	+	0.909229i	$0.363328\pi$
$547$	−9.32812	+	34.8130i	−0.398842	+	1.48850i	−0.815137	+	0.579268i	$0.803338\pi$
$548$	20.7265	+	26.9019i	0.885394	+	1.14919i
$549$		0			0
$550$	−8.67644	−	27.9741i	−0.369965	−	1.19282i
$551$	36.5197	−	21.0847i	1.55579	−	0.898238i
$552$		0			0
$553$	0.0224312	−	0.00601043i	0.000953872	−	0.000255589i
$554$	0.729146	−	1.09356i	0.0309784	−	0.0464611i
$555$		0			0
$556$	−2.12461	+	0.884930i	−0.0901036	+	0.0375294i
$557$	11.9128	−	11.9128i	0.504762	−	0.504762i	−0.408152	−	0.912914i	$-0.633827\pi$
$557$	11.9128	−	11.9128i	0.504762	−	0.504762i	0.912914	+	0.408152i	$0.133827\pi$
$558$		0			0
$559$	−2.97383			−0.125780
$560$	−0.0345661	+	0.00192504i	−0.00146069	+	8.13476e-5i
$561$		0			0
$562$	−26.6117	+	5.32054i	−1.12255	+	0.224433i
$563$	1.84168	+	6.87323i	0.0776174	+	0.289672i	0.993814	−	0.111057i	$-0.0354236\pi$
$563$	1.84168	+	6.87323i	0.0776174	+	0.289672i	−0.916197	+	0.400729i	$0.868757\pi$
$564$		0			0
$565$	33.0777	−	10.7238i	1.39159	−	0.451155i
$566$	−34.0324	−	2.19708i	−1.43049	−	0.0923500i
$567$		0			0
$568$	−17.8548	−	26.5522i	−0.749173	−	1.11410i
$569$	37.4538	−	21.6240i	1.57015	−	0.906524i	0.573996	−	0.818858i	$-0.305392\pi$
$569$	37.4538	−	21.6240i	1.57015	−	0.906524i	0.996150	−	0.0876662i	$-0.0279409\pi$
$570$		0			0
$571$	15.2197	+	8.78710i	0.636925	+	0.367729i	0.783429	−	0.621481i	$-0.213469\pi$
$571$	15.2197	+	8.78710i	0.636925	+	0.367729i	−0.146504	+	0.989210i	$0.546802\pi$
$572$	24.3509	−	3.25446i	1.01816	−	0.136076i
$573$		0			0
$574$	0.0179082	−	0.00885320i	0.000747475	−	0.000369526i
$575$	6.91408	+	18.0820i	0.288337	+	0.754071i
$576$		0			0
$577$	−14.1684	+	14.1684i	−0.589837	+	0.589837i	−0.937587	−	0.347750i	$-0.886946\pi$
$577$	−14.1684	+	14.1684i	−0.589837	+	0.589837i	0.347750	+	0.937587i	$0.386946\pi$
$578$	−11.2061	−	3.79169i	−0.466111	−	0.157714i
$579$		0			0
$580$	−25.7032	−	1.98895i	−1.06727	−	0.0825866i
$581$	−0.00565392	+	0.00979287i	−0.000234564	+	0.000406277i
$582$		0			0
$583$	39.2096	+	10.5062i	1.62389	+	0.435121i
$584$	−25.5401	−	5.00215i	−1.05685	−	0.206990i
$585$		0			0
$586$	−0.192801	+	2.98645i	−0.00796452	+	0.123369i
$587$	0.369735	−	1.37987i	0.0152606	−	0.0569533i	−0.957876	−	0.287183i	$-0.907281\pi$
$587$	0.369735	−	1.37987i	0.0152606	−	0.0569533i	0.973136	+	0.230230i	$0.0739478\pi$
$588$		0			0
$589$	12.9949	+	7.50263i	0.535447	+	0.309141i
$590$	12.1871	+	12.5021i	0.501735	+	0.514704i
$591$		0			0
$592$	−29.9251	−	17.1211i	−1.22992	−	0.703672i
$593$	−3.47274	−	3.47274i	−0.142608	−	0.142608i	0.632198	−	0.774807i	$-0.282153\pi$
$593$	−3.47274	−	3.47274i	−0.142608	−	0.142608i	−0.774807	+	0.632198i	$0.782153\pi$
$594$		0			0
$595$	0.0138377	+	0.0213385i	0.000567290	+	0.000874794i
$596$	13.6964	+	32.8835i	0.561028	+	1.34696i
$597$		0			0
$598$	−15.9230	+	3.18352i	−0.651139	+	0.130184i
$599$	−6.20251	+	10.7431i	−0.253428	+	0.438950i	−0.964467	−	0.264202i	$-0.914891\pi$
$599$	−6.20251	+	10.7431i	−0.253428	+	0.438950i	0.711040	+	0.703152i	$0.248225\pi$
$600$		0			0
$601$	1.54486	+	2.67578i	0.0630162	+	0.109147i	0.895812	−	0.444433i	$-0.146595\pi$
$601$	1.54486	+	2.67578i	0.0630162	+	0.109147i	−0.832796	+	0.553580i	$0.813261\pi$
$602$	0.00362324	+	0.00412334i	0.000147672	+	0.000168055i
$603$		0			0
$604$	−32.5423	−	4.21935i	−1.32413	−	0.171683i
$605$	6.25793	−	12.2622i	0.254421	−	0.498528i
$606$		0			0
$607$	36.9673	−	9.90537i	1.50046	−	0.402046i	0.587204	−	0.809439i	$-0.300228\pi$
$607$	36.9673	−	9.90537i	1.50046	−	0.402046i	0.913253	+	0.407392i	$0.133562\pi$
$608$	−41.3055	−	2.50392i	−1.67516	−	0.101547i
$609$		0			0
$610$	−22.0051	+	5.59635i	−0.890962	+	0.226590i
$611$			13.9922i			0.566063i
$612$		0			0
$613$	14.5099	+	14.5099i	0.586049	+	0.586049i	0.936559	−	0.350510i	$-0.113992\pi$
$613$	14.5099	+	14.5099i	0.586049	+	0.586049i	−0.350510	+	0.936559i	$0.613992\pi$
$614$	−19.0399	+	9.41268i	−0.768389	+	0.379865i
$615$		0			0
$616$	−0.0341808	−	0.0297983i	−0.00137718	−	0.00120061i
$617$	−0.0373567	−	0.139417i	−0.00150392	−	0.00561272i	0.965170	−	0.261624i	$-0.0842581\pi$
$617$	−0.0373567	−	0.139417i	−0.00150392	−	0.00561272i	−0.966674	+	0.256012i	$0.917591\pi$
$618$		0			0
$619$	−13.6832	−	23.7000i	−0.549975	−	0.952584i	−0.998276	−	0.0587016i	$-0.981304\pi$
$619$	−13.6832	−	23.7000i	−0.549975	−	0.952584i	0.448301	−	0.893883i	$-0.352029\pi$
$620$	−3.96010	−	8.27457i	−0.159042	−	0.332315i
$621$		0			0
$622$	−20.0428	+	17.6119i	−0.803642	+	0.706171i
$623$	−0.0343500	−	0.00920405i	−0.00137620	−	0.000368752i
$624$		0			0
$625$	24.4671	−	5.13424i	0.978685	−	0.205369i
$626$	19.6262	+	13.0859i	0.784419	+	0.523020i
$627$		0			0
$628$	0.450210	−	1.09296i	0.0179653	−	0.0436140i
$629$			25.3275i			1.00987i
$630$		0			0
$631$		−	26.4593i		−	1.05333i	−0.850074	−	0.526664i	$-0.823443\pi$
$631$		−	26.4593i		−	1.05333i	0.850074	−	0.526664i	$-0.176557\pi$
$632$	−15.2417	−	7.46071i	−0.606284	−	0.296771i
$633$		0			0
$634$	14.2132	−	21.3167i	0.564477	−	0.846596i
$635$	−33.1860	−	29.9198i	−1.31694	−	1.18733i
$636$		0			0
$637$	20.0518	+	5.37286i	0.794481	+	0.212880i
$638$	−22.2894	−	25.3659i	−0.882445	−	1.00425i
$639$		0			0
$640$	19.9641	+	15.5382i	0.789150	+	0.614200i
$641$	2.73281	+	4.73337i	0.107940	+	0.186957i	0.914935	−	0.403600i	$-0.132241\pi$
$641$	2.73281	+	4.73337i	0.107940	+	0.186957i	−0.806996	+	0.590557i	$0.798908\pi$
$642$		0			0
$643$	−10.8251	−	40.3996i	−0.426898	−	1.59321i	−0.759742	−	0.650225i	$-0.774675\pi$
$643$	−10.8251	−	40.3996i	−0.426898	−	1.59321i	0.332844	−	0.942982i	$-0.391992\pi$
$644$	0.0238142	+	0.0181991i	0.000938410	+	0.000717147i
$645$		0			0
$646$	13.4722	+	27.2515i	0.530057	+	1.07220i
$647$	19.6463	+	19.6463i	0.772377	+	0.772377i	0.978522	−	0.206144i	$-0.0660917\pi$
$647$	19.6463	+	19.6463i	0.772377	+	0.772377i	−0.206144	+	0.978522i	$0.566092\pi$
$648$		0			0
$649$			22.8688i			0.897680i
$650$	0.816607	+	20.9540i	0.0320300	+	0.821885i
$651$		0			0
$652$	7.16548	−	0.957658i	0.280622	−	0.0375048i
$653$	−12.0523	+	3.22941i	−0.471643	+	0.126376i	−0.486809	−	0.873509i	$-0.661839\pi$
$653$	−12.0523	+	3.22941i	−0.471643	+	0.126376i	0.0151655	+	0.999885i	$0.495172\pi$
$654$		0			0
$655$	−16.4178	−	8.37872i	−0.641496	−	0.327384i
$656$	−14.1155	−	3.72293i	−0.551116	−	0.145356i
$657$		0			0
$658$	0.0194007	−	0.0170477i	0.000756320	−	0.000664588i
$659$	−2.60988	−	4.52045i	−0.101667	−	0.176092i	0.810705	−	0.585455i	$-0.199084\pi$
$659$	−2.60988	−	4.52045i	−0.101667	−	0.176092i	−0.912371	+	0.409363i	$0.865751\pi$
$660$		0			0
$661$	17.0620	−	29.5522i	0.663633	−	1.14945i	−0.316021	−	0.948752i	$-0.602347\pi$
$661$	17.0620	−	29.5522i	0.663633	−	1.14945i	0.979654	−	0.200694i	$-0.0643198\pi$
$662$	−9.89430	−	49.4883i	−0.384553	−	1.92342i
$663$		0			0
$664$	7.81678	−	2.67912i	0.303350	−	0.103970i
$665$	−0.0132037	+	0.0619209i	−0.000512019	+	0.00240119i
$666$		0			0
$667$	15.7820	+	15.7820i	0.611080	+	0.611080i
$668$	−18.1127	−	7.46094i	−0.700802	−	0.288672i
$669$		0			0
$670$	0.132713	−	10.4013i	0.00512716	−	0.401836i
$671$	−25.7561	−	14.8703i	−0.994304	−	0.574062i
$672$		0			0
$673$	−5.54797	+	20.7053i	−0.213859	+	0.798132i	0.772706	+	0.634763i	$0.218902\pi$
$673$	−5.54797	+	20.7053i	−0.213859	+	0.798132i	−0.986565	+	0.163368i	$0.947764\pi$
$674$	−29.5598	−	1.90833i	−1.13860	−	0.0735062i
$675$		0			0
$676$	8.34064	+	1.08142i	0.320794	+	0.0415933i
$677$	8.44976	+	2.26411i	0.324751	+	0.0870167i	0.417511	−	0.908672i	$-0.362902\pi$
$677$	8.44976	+	2.26411i	0.324751	+	0.0870167i	−0.0927605	+	0.995688i	$0.529569\pi$
$678$		0			0
$679$	0.00454237	−	0.00786762i	0.000174320	−	0.000301931i
$680$	2.62459	−	18.3985i	0.100648	−	0.705549i
$681$		0			0
$682$	3.85113	−	11.3817i	0.147467	−	0.435829i
$683$	−4.25385	+	4.25385i	−0.162769	+	0.162769i	−0.783792	−	0.621023i	$-0.786717\pi$
$683$	−4.25385	+	4.25385i	−0.162769	+	0.162769i	0.621023	+	0.783792i	$0.286717\pi$
$684$		0			0
$685$	−37.1339	−	7.91827i	−1.41881	−	0.302542i
$686$	−0.0339617	−	0.0686976i	−0.00129666	−	0.00262289i
$687$		0			0
$688$	−0.0157379	−	4.01108i	−0.000600000	−	0.152921i
$689$	−25.1695	−	14.5316i	−0.958882	−	0.553611i
$690$		0			0
$691$	−15.0306	+	8.67790i	−0.571789	+	0.330123i	−0.757864	−	0.652413i	$-0.773757\pi$
$691$	−15.0306	+	8.67790i	−0.571789	+	0.330123i	0.186074	+	0.982536i	$0.440423\pi$
$692$	−14.4164	+	11.1071i	−0.548031	+	0.422229i
$693$		0			0
$694$	0.935885	−	14.4967i	0.0355257	−	0.550288i
$695$	1.16970	−	2.29198i	0.0443691	−	0.0869396i
$696$		0			0
$697$	2.77563	+	10.3588i	0.105134	+	0.392367i
$698$	−5.04601	−	25.2386i	−0.190994	−	0.955296i
$699$		0			0
$700$	0.0280587	−	0.0266621i	0.00106052	−	0.00100773i
$701$	23.2157			0.876846			0.438423	−	0.898769i	$-0.355537\pi$
$701$	23.2157			0.876846			0.438423	+	0.898769i	$0.355537\pi$
$702$		0			0
$703$	−44.5841	+	44.5841i	−1.68152	+	1.68152i
$704$	4.51845	+	32.8270i	0.170296	+	1.23721i
$705$		0			0
$706$	19.8458	+	13.2324i	0.746906	+	0.498007i
$707$	−0.0266955	+	0.00715304i	−0.00100399	+	0.000269018i
$708$		0			0
$709$	22.8813	−	13.2105i	0.859327	−	0.496133i	−0.00446000	−	0.999990i	$-0.501420\pi$
$709$	22.8813	−	13.2105i	0.859327	−	0.496133i	0.863787	+	0.503857i	$0.168086\pi$
$710$	34.4339	+	9.69906i	1.29228	+	0.363999i
$711$		0			0
$712$	14.5009	+	21.5645i	0.543444	+	0.808163i
$713$	−2.05551	+	7.67125i	−0.0769793	+	0.287291i
$714$		0			0
$715$	−18.3924	+	20.4001i	−0.687836	+	0.762922i
$716$	15.3643	+	11.7416i	0.574190	+	0.438805i
$717$		0			0
$718$	−12.1736	+	35.9781i	−0.454314	+	1.34269i
$719$	12.9840			0.484220			0.242110	−	0.970249i	$-0.422160\pi$
$719$	12.9840			0.484220			0.242110	+	0.970249i	$0.422160\pi$
$720$		0			0
$721$	0.0161719			0.000602274
$722$	−15.6437	+	46.2337i	−0.582197	+	1.72064i
$723$		0			0
$724$	1.15251	+	0.880763i	0.0428326	+	0.0327333i
$725$	23.3402	−	16.9114i	0.866834	−	0.628073i
$726$		0			0
$727$	−0.439513	+	1.64028i	−0.0163006	+	0.0608348i	−0.973597	−	0.228273i	$-0.926692\pi$
$727$	−0.439513	+	1.64028i	−0.0163006	+	0.0608348i	0.957296	+	0.289108i	$0.0933587\pi$
$728$	0.0181168	+	0.0269417i	0.000671453	+	0.000998527i
$729$		0			0
$730$	25.3824	−	14.2259i	0.939446	−	0.526524i
$731$	−2.55189	+	1.47333i	−0.0943850	+	0.0544932i
$732$		0			0
$733$	8.22626	−	2.20422i	0.303844	−	0.0814147i	−0.103676	−	0.994611i	$-0.533060\pi$
$733$	8.22626	−	2.20422i	0.303844	−	0.0814147i	0.407520	+	0.913196i	$0.366394\pi$
$734$	7.43643	+	4.95832i	0.274484	+	0.183015i
$735$		0			0
$736$	−4.37816	−	21.4599i	−0.161381	−	0.791023i
$737$	9.63436	−	9.63436i	0.354886	−	0.354886i
$738$		0			0
$739$	19.1571			0.704704			0.352352	−	0.935867i	$-0.385382\pi$
$739$	19.1571			0.704704			0.352352	+	0.935867i	$0.385382\pi$
$740$	37.8914	−	7.07421i	1.39292	−	0.260053i
$741$		0			0
$742$	0.0105171	+	0.0526034i	0.000386096	+	0.00193113i
$743$	1.81749	+	6.78298i	0.0666774	+	0.248843i	0.991218	−	0.132241i	$-0.0422173\pi$
$743$	1.81749	+	6.78298i	0.0666774	+	0.248843i	−0.924540	+	0.381085i	$0.875551\pi$
$744$		0			0
$745$	−35.4739	−	18.1039i	−1.29966	−	0.663275i
$746$	−1.14556	+	17.7445i	−0.0419419	+	0.649674i
$747$		0			0
$748$	19.2834	−	14.8569i	0.705072	−	0.543222i
$749$	0.0390362	−	0.0225375i	0.00142635	−	0.000823504i
$750$		0			0
$751$	26.5621	+	15.3357i	0.969266	+	0.559606i	0.899012	−	0.437923i	$-0.144286\pi$
$751$	26.5621	+	15.3357i	0.969266	+	0.559606i	0.0702536	+	0.997529i	$0.477619\pi$
$752$	−18.8725	+	0.0740482i	−0.688210	+	0.00270026i
$753$		0			0
$754$	10.7143	+	21.6728i	0.390192	+	0.789278i
$755$	30.7821	−	19.9617i	1.12028	−	0.726481i
$756$		0			0
$757$	8.66077	−	8.66077i	0.314781	−	0.314781i	−0.531978	−	0.846758i	$-0.678551\pi$
$757$	8.66077	−	8.66077i	0.314781	−	0.314781i	0.846758	+	0.531978i	$0.178551\pi$
$758$	5.98713	−	17.6945i	0.217462	−	0.642694i
$759$		0			0
$760$	37.0070	−	27.7668i	1.34238	−	1.00721i
$761$	−12.3194	+	21.3379i	−0.446578	+	0.773497i	−0.998161	−	0.0606239i	$-0.980691\pi$
$761$	−12.3194	+	21.3379i	−0.446578	+	0.773497i	0.551582	+	0.834121i	$0.314024\pi$
$762$		0			0
$763$	−0.0240487	−	0.00644382i	−0.000870620	−	0.000233282i
$764$	10.0575	+	1.30403i	0.363869	+	0.0471782i
$765$		0			0
$766$	26.5593	+	1.71463i	0.959627	+	0.0619520i
$767$	4.23776	−	15.8155i	0.153016	−	0.571065i
$768$		0			0
$769$	−16.9731	−	9.79945i	−0.612067	−	0.353377i	0.161707	−	0.986839i	$-0.448300\pi$
$769$	−16.9731	−	9.79945i	−0.612067	−	0.353377i	−0.773774	+	0.633462i	$0.781633\pi$
$770$	0.0506943		0.000646827i	0.00182690		2.33100e-5i
$771$		0			0
$772$	47.5634	+	19.5922i	1.71184	+	0.705137i
$773$	−15.6893	−	15.6893i	−0.564306	−	0.564306i	0.366221	−	0.930528i	$-0.380651\pi$
$773$	−15.6893	−	15.6893i	−0.564306	−	0.564306i	−0.930528	+	0.366221i	$0.880651\pi$
$774$		0			0
$775$	9.36404	+	4.18372i	0.336366	+	0.150284i
$776$	−6.28002	+	2.15241i	−0.225440	+	0.0772670i
$777$		0			0
$778$	−0.364621	−	1.82372i	−0.0130723	−	0.0653835i
$779$	−13.3487	+	23.1206i	−0.478265	+	0.828380i
$780$		0			0
$781$	23.4289	+	40.5800i	0.838352	+	1.45207i
$782$	−12.0865	+	10.6206i	−0.432213	+	0.379791i
$783$		0			0
$784$	−7.14075	+	27.0741i	−0.255027	+	0.966932i
$785$	0.407574	+	1.25716i	0.0145469	+	0.0448700i
$786$		0			0
$787$	−17.6130	+	4.71940i	−0.627837	+	0.168228i	−0.558688	−	0.829378i	$-0.688695\pi$
$787$	−17.6130	+	4.71940i	−0.627837	+	0.168228i	−0.0691489	+	0.997606i	$0.522028\pi$
$788$	20.5875	−	2.75150i	0.733399	−	0.0980180i
$789$		0			0
$790$	18.3874	−	4.67630i	0.654196	−	0.166375i
$791$			0.0601908i			0.00214014i
$792$		0			0
$793$	15.0567	+	15.0567i	0.534680	+	0.534680i
$794$	0.633638	+	1.28172i	0.0224870	+	0.0454866i
$795$		0			0
$796$	−37.3935	−	28.5766i	−1.32538	−	1.01287i
$797$	−7.22285	−	26.9560i	−0.255846	−	0.954832i	−0.967618	−	0.252420i	$-0.918773\pi$
$797$	−7.22285	−	26.9560i	−0.255846	−	0.954832i	0.711771	−	0.702411i	$-0.247893\pi$
$798$		0			0
$799$	6.93218	+	12.0069i	0.245243	+	0.424773i
$800$	−28.2583	+	1.21232i	−0.999081	+	0.0428621i
$801$		0			0
$802$	18.5577	+	21.1192i	0.655295	+	0.745744i
$803$	36.8138	+	9.86423i	1.29913	+	0.348101i
$804$		0			0
$805$	−0.0334650	+	0.00173203i	−0.00117949	+	6.10460e-5i
$806$	−4.77246	+	7.15768i	−0.168103	+	0.252119i
$807$		0			0
$808$	18.1393	+	8.87903i	0.638137	+	0.312363i
$809$			10.0143i			0.352084i	0.984383	+	0.176042i	$0.0563294\pi$
$809$			10.0143i			0.352084i	−0.984383	+	0.176042i	$0.943671\pi$
$810$		0			0
$811$			40.6681i			1.42805i	0.700121	+	0.714024i	$0.253129\pi$
$811$			40.6681i			1.42805i	−0.700121	+	0.714024i	$0.746871\pi$
$812$	0.0169963	−	0.0412614i	0.000596452	−	0.00144799i
$813$		0			0
$814$	42.0076	+	28.0090i	1.47237	+	0.981716i
$815$	−5.41214	+	6.00294i	−0.189579	+	0.210274i
$816$		0			0
$817$	−7.08561	−	1.89858i	−0.247894	−	0.0664231i
$818$	−26.3586	+	23.1616i	−0.921606	+	0.809827i
$819$		0			0
$820$	14.7221	−	7.04580i	0.514118	−	0.246050i
$821$	−14.4578	−	25.0416i	−0.504579	−	0.873957i	−0.999986	−	0.00529574i	$-0.998314\pi$
$821$	−14.4578	−	25.0416i	−0.504579	−	0.873957i	0.495407	−	0.868661i	$-0.335019\pi$
$822$		0			0
$823$	0.713567	+	2.66307i	0.0248734	+	0.0928287i	0.977247	−	0.212106i	$-0.0680321\pi$
$823$	0.713567	+	2.66307i	0.0248734	+	0.0928287i	−0.952373	+	0.304934i	$0.901365\pi$
$824$	−8.90781	−	7.76569i	−0.310318	−	0.270531i
$825$		0			0
$826$	−0.0270920	+	0.0133934i	−0.000942652	+	0.000466014i
$827$	33.6286	+	33.6286i	1.16938	+	1.16938i	0.982355	+	0.187026i	$0.0598850\pi$
$827$	33.6286	+	33.6286i	1.16938	+	1.16938i	0.187026	+	0.982355i	$0.440115\pi$
$828$		0			0
$829$		−	52.3216i		−	1.81721i	−0.417662	−	0.908603i	$-0.637150\pi$
$829$		−	52.3216i		−	1.81721i	0.417662	−	0.908603i	$-0.362850\pi$
$830$	−4.72094	+	7.94118i	−0.163866	+	0.275642i
$831$		0			0
$832$	2.95822	−	23.5396i	0.102558	−	0.816090i
$833$	19.8686	−	5.32377i	0.688406	−	0.184458i
$834$		0			0
$835$	20.8338	−	6.75436i	0.720985	−	0.233744i
$836$	60.0974	+	7.79206i	2.07851	+	0.269494i
$837$		0			0
$838$	−26.2147	−	29.8331i	−0.905572	−	1.03057i
$839$	17.7459	+	30.7367i	0.612655	+	1.06115i	0.990791	+	0.135400i	$0.0432319\pi$
$839$	17.7459	+	30.7367i	0.612655	+	1.06115i	−0.378136	+	0.925750i	$0.623435\pi$
$840$		0			0
$841$	2.11521	−	3.66366i	0.0729384	−	0.126333i
$842$	−1.80699	+	0.361275i	−0.0622729	+	0.0124504i
$843$		0			0
$844$	10.1375	+	24.3390i	0.348948	+	0.837782i
$845$	−7.88950	+	5.11621i	−0.271407	+	0.176003i
$846$		0			0
$847$	0.0168503	+	0.0168503i	0.000578985	+	0.000578985i
$848$	19.4669	−	34.0253i	0.668496	−	1.16843i
$849$		0			0
$850$	11.0820	+	17.5764i	0.380111	+	0.602864i
$851$	−28.9005	−	16.6857i	−0.990695	−	0.571978i
$852$		0			0
$853$	−13.1763	+	49.1748i	−0.451149	+	1.68371i	0.248019	+	0.968755i	$0.420221\pi$
$853$	−13.1763	+	49.1748i	−0.451149	+	1.68371i	−0.699168	+	0.714957i	$0.746446\pi$
$854$	0.00253207	−	0.0392214i	8.66458e−5	−	0.00134213i
$855$		0			0
$856$	−32.3243	−	6.33088i	−1.10482	−	0.216385i
$857$	−27.2288	−	7.29593i	−0.930117	−	0.249224i	−0.238212	−	0.971213i	$-0.576561\pi$
$857$	−27.2288	−	7.29593i	−0.930117	−	0.249224i	−0.691904	+	0.721989i	$0.743228\pi$
$858$		0			0
$859$	14.5156	−	25.1417i	0.495265	−	0.857824i	−0.504720	−	0.863283i	$-0.668404\pi$
$859$	14.5156	−	25.1417i	0.495265	−	0.857824i	0.999985	+	0.00545874i	$0.00173758\pi$
$860$	2.91696	+	3.40626i	0.0994675	+	0.116152i
$861$		0			0
$862$	−18.9248	−	6.40340i	−0.644581	−	0.218101i
$863$	−23.2326	+	23.2326i	−0.790845	+	0.790845i	−0.981632	−	0.190786i	$-0.938896\pi$
$863$	−23.2326	+	23.2326i	−0.790845	+	0.790845i	0.190786	+	0.981632i	$0.438896\pi$
$864$		0			0
$865$	4.24332	−	19.8997i	0.144277	−	0.676609i
$866$	8.78870	−	4.34483i	0.298652	−	0.147643i
$867$		0			0
$868$	0.0157391	−	0.00210351i	0.000534218	−	7.13976e-5i
$869$	21.5218	+	12.4256i	0.730076	+	0.421509i
$870$		0			0
$871$	−8.44820	+	4.87757i	−0.286256	+	0.165270i
$872$	10.1522	+	15.0974i	0.343796	+	0.511264i
$873$		0			0
$874$	−39.9714	−	2.58049i	−1.35205	−	0.0872863i
$875$	−0.00460729	+	0.0430287i	−0.000155755	+	0.00145463i
$876$		0			0
$877$	−8.29692	−	30.9645i	−0.280167	−	1.04560i	−0.952299	−	0.305166i	$-0.901288\pi$
$877$	−8.29692	−	30.9645i	−0.280167	−	1.04560i	0.672132	−	0.740431i	$-0.265379\pi$
$878$	39.4795	−	7.89323i	1.33237	−	0.266383i
$879$		0			0
$880$	−27.6128	−	24.6995i	−0.930828	−	0.832620i
$881$	−23.5070			−0.791970			−0.395985	−	0.918257i	$-0.629597\pi$
$881$	−23.5070			−0.791970			−0.395985	+	0.918257i	$0.629597\pi$
$882$		0			0
$883$	28.0638	−	28.0638i	0.944422	−	0.944422i	−0.0541127	−	0.998535i	$-0.517233\pi$
$883$	28.0638	−	28.0638i	0.944422	−	0.944422i	0.998535	+	0.0541127i	$0.0172330\pi$
$884$	−16.0890	+	6.70131i	−0.541133	+	0.225389i
$885$		0			0
$886$	19.1691	−	28.7496i	0.643998	−	0.965861i
$887$	−21.8884	+	5.86497i	−0.734940	+	0.196927i	−0.606828	−	0.794833i	$-0.707558\pi$
$887$	−21.8884	+	5.86497i	−0.734940	+	0.196927i	−0.128112	+	0.991760i	$0.540892\pi$
$888$		0			0
$889$	0.0669822	−	0.0386722i	0.00224651	−	0.00129702i
$890$	−27.9657	−	7.87713i	−0.937411	−	0.264042i
$891$		0			0
$892$	8.42070	+	10.9296i	0.281946	+	0.365950i
$893$	−8.93303	+	33.3385i	−0.298932	+	1.11563i
$894$		0			0
$895$	−21.5907	+	1.11746i	−0.721698	+	0.0373525i
$896$	−0.0362429	+	0.0245783i	−0.00121079	+	0.000821104i
$897$		0			0
$898$	43.0754	+	14.5750i	1.43744	+	0.486375i
$899$	11.8245			0.394369
$900$		0			0
$901$	−28.7977			−0.959391
$902$	20.2503	+	6.85192i	0.674262	+	0.228144i
$903$		0			0
$904$	28.9034	−	33.1543i	0.961312	−	1.10269i
$905$	−1.61957	+	0.0838229i	−0.0538362	+	0.00278637i
$906$		0			0
$907$	−2.82743	+	10.5521i	−0.0938833	+	0.350377i	−0.996848	−	0.0793379i	$-0.974719\pi$
$907$	−2.82743	+	10.5521i	−0.0938833	+	0.350377i	0.902964	+	0.429715i	$0.141386\pi$
$908$	37.8748	−	29.1806i	1.25692	−	0.968393i
$909$		0			0
$910$	−0.0349391	−	0.00984135i	−0.00115822	−	0.000326238i
$911$	−18.3234	+	10.5790i	−0.607083	+	0.350499i	−0.771823	−	0.635838i	$-0.780655\pi$
$911$	−18.3234	+	10.5790i	−0.607083	+	0.350499i	0.164740	+	0.986337i	$0.447321\pi$
$912$		0			0
$913$	−11.6886	+	3.13194i	−0.386835	+	0.103652i
$914$	8.85783	−	13.2849i	0.292991	−	0.439424i
$915$		0			0
$916$	9.67636	+	23.2318i	0.319716	+	0.767600i
$917$	0.0225609	−	0.0225609i	0.000745026	−	0.000745026i
$918$		0			0
$919$	8.67860			0.286281			0.143140	−	0.989702i	$-0.454280\pi$
$919$	8.67860			0.286281			0.143140	+	0.989702i	$0.454280\pi$
$920$	19.2649	+	15.1157i	0.635144	+	0.498350i
$921$		0			0
$922$	−3.92371	+	0.784476i	−0.129221	+	0.0258353i
$923$	−8.68308	−	32.4057i	−0.285807	−	1.06665i
$924$		0			0
$925$	−27.1646	+	33.4566i	−0.893167	+	1.10004i
$926$	30.3430	+	1.95889i	0.997132	+	0.0643733i
$927$		0			0
$928$	−29.1754	+	14.5660i	−0.957730	+	0.478154i
$929$	11.5252	−	6.65405i	0.378128	−	0.218312i	−0.298875	−	0.954292i	$-0.596611\pi$
$929$	11.5252	−	6.65405i	0.378128	−	0.218312i	0.677004	+	0.735980i	$0.263278\pi$
$930$		0			0
$931$	44.3462	+	25.6033i	1.45339	+	0.839115i
$932$	2.19364	+	16.4135i	0.0718551	+	0.537641i
$933$		0			0
$934$	−1.33841	+	0.661666i	−0.0437942	+	0.0216504i
$935$	−5.67586	+	26.6178i	−0.185621	+	0.870495i
$936$		0			0
$937$	16.8683	−	16.8683i	0.551063	−	0.551063i	−0.375685	−	0.926747i	$-0.622593\pi$
$937$	16.8683	−	16.8683i	0.551063	−	0.551063i	0.926747	+	0.375685i	$0.122593\pi$
$938$	0.0170560	+	0.00577108i	0.000556898	+	0.000188432i
$939$		0			0
$940$	16.0268	−	13.7246i	0.522736	−	0.447647i
$941$	−14.0053	+	24.2579i	−0.456560	+	0.790785i	−0.998776	−	0.0494537i	$-0.984252\pi$
$941$	−14.0053	+	24.2579i	−0.456560	+	0.790785i	0.542216	+	0.840239i	$0.317585\pi$
$942$		0			0
$943$	−13.6487	−	3.65715i	−0.444462	−	0.119093i
$944$	21.3542	+	5.63215i	0.695021	+	0.183311i
$945$		0			0
$946$	−0.378430	+	5.86183i	−0.0123038	+	0.190584i
$947$	3.42468	−	12.7811i	0.111287	−	0.415329i	−0.887695	−	0.460431i	$-0.847695\pi$
$947$	3.42468	−	12.7811i	0.111287	−	0.415329i	0.998982	+	0.0451023i	$0.0143614\pi$
$948$		0			0
$949$	−23.6316	−	13.6437i	−0.767115	−	0.442894i
$950$	−11.4320	+	50.4475i	−0.370903	+	1.63673i
$951$		0			0
$952$	0.0288941	+	0.0141434i	0.000936462	+	0.000458391i
$953$	30.3998	+	30.3998i	0.984746	+	0.984746i	0.999885	−	0.0151397i	$-0.00481929\pi$
$953$	30.3998	+	30.3998i	0.984746	+	0.984746i	−0.0151397	+	0.999885i	$0.504819\pi$
$954$		0			0
$955$	−9.51352	+	6.16937i	−0.307850	+	0.199636i
$956$	−31.4771	+	13.1107i	−1.01804	+	0.424029i
$957$		0			0
$958$	24.0875	−	4.81586i	0.778231	−	0.155593i
$959$	0.0328617	−	0.0569181i	0.00106116	−	0.00183798i
$960$		0			0
$961$	−13.3962	−	23.2029i	−0.432136	−	0.748482i
$962$	−23.8612	−	27.1547i	−0.769315	−	0.875502i
$963$		0			0
$964$	−3.58866	+	27.6781i	−0.115583	+	0.891450i
$965$	−54.7089	+	17.7367i	−1.76114	+	0.570965i
$966$		0			0
$967$	−9.02872	+	2.41924i	−0.290344	+	0.0777975i	−0.401051	−	0.916056i	$-0.631355\pi$
$967$	−9.02872	+	2.41924i	−0.290344	+	0.0777975i	0.110707	+	0.993853i	$0.464688\pi$
$968$	−1.19004	−	17.3730i	−0.0382492	−	0.558388i
$969$		0			0
$970$	3.79282	−	6.37997i	0.121780	−	0.204848i
$971$		−	0.631006i		−	0.0202499i	−0.999949	−	0.0101250i	$-0.996777\pi$
$971$		−	0.631006i		−	0.0202499i	0.999949	−	0.0101250i	$-0.00322293\pi$
$972$		0			0
$973$	0.00314957	+	0.00314957i	0.000100971	+	0.000100971i
$974$	30.8792	−	15.2656i	0.989435	−	0.489142i
$975$		0			0
$976$	−20.2287	+	20.3880i	−0.647504	+	0.652605i
$977$	0.0600942	+	0.224275i	0.00192258	+	0.00717518i	0.966880	−	0.255230i	$-0.0821511\pi$
$977$	0.0600942	+	0.224275i	0.00192258	+	0.00717518i	−0.964958	+	0.262405i	$0.915484\pi$
$978$		0			0
$979$	−19.0279	−	32.9573i	−0.608134	−	1.05332i
$980$	−13.5142	−	28.2376i	−0.431694	−	0.902018i
$981$		0			0
$982$	−17.0363	+	14.9700i	−0.543650	+	0.477713i
$983$	−0.461344	−	0.123617i	−0.0147146	−	0.00394276i	0.251454	−	0.967869i	$-0.419091\pi$
$983$	−0.461344	−	0.123617i	−0.0147146	−	0.00394276i	−0.266169	+	0.963926i	$0.585758\pi$
$984$		0			0
$985$	−15.5499	+	17.2474i	−0.495461	+	0.549546i
$986$	19.9315	+	13.2895i	0.634748	+	0.423225i
$987$		0			0
$988$	−40.1179	−	16.5253i	−1.27632	−	0.525739i
$989$		−	3.88251i		−	0.123457i
$990$		0			0
$991$		−	16.8040i		−	0.533796i	−0.963725	−	0.266898i	$-0.914001\pi$
$991$		−	16.8040i		−	0.533796i	0.963725	−	0.266898i	$-0.0859986\pi$
$992$	−9.67947	−	6.39917i	−0.307323	−	0.203174i
$993$		0			0
$994$	−0.0343526	+	0.0515216i	−0.00108960	+	0.00163417i
$995$	52.5473	−	2.71966i	1.66586	−	0.0862191i
$996$		0			0
$997$	−12.0029	−	3.21617i	−0.380135	−	0.101857i	0.0636912	−	0.997970i	$-0.479713\pi$
$997$	−12.0029	−	3.21617i	−0.380135	−	0.101857i	−0.443827	+	0.896113i	$0.646379\pi$
$998$	−35.3452	−	40.2238i	−1.11883	−	1.27326i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.y.a.523.13		128
3.2	odd	2		180.2.x.a.103.20	yes	128
4.3	odd	2	inner	540.2.y.a.523.19		128
5.2	odd	4	inner	540.2.y.a.307.4		128
9.2	odd	6		180.2.x.a.43.2	yes	128
9.7	even	3	inner	540.2.y.a.343.31		128
12.11	even	2		180.2.x.a.103.14	yes	128
15.2	even	4		180.2.x.a.67.29	yes	128
15.8	even	4		900.2.bf.e.607.4		128
15.14	odd	2		900.2.bf.e.643.13		128
20.7	even	4	inner	540.2.y.a.307.31		128
36.7	odd	6	inner	540.2.y.a.343.4		128
36.11	even	6		180.2.x.a.43.29	yes	128
45.2	even	12		180.2.x.a.7.14	✓	128
45.7	odd	12	inner	540.2.y.a.127.19		128
45.29	odd	6		900.2.bf.e.43.31		128
45.38	even	12		900.2.bf.e.7.19		128
60.23	odd	4		900.2.bf.e.607.31		128
60.47	odd	4		180.2.x.a.67.2	yes	128
60.59	even	2		900.2.bf.e.643.19		128
180.7	even	12	inner	540.2.y.a.127.13		128
180.47	odd	12		180.2.x.a.7.20	yes	128
180.83	odd	12		900.2.bf.e.7.13		128
180.119	even	6		900.2.bf.e.43.4		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.14	✓	128	45.2	even	12
180.2.x.a.7.20	yes	128	180.47	odd	12
180.2.x.a.43.2	yes	128	9.2	odd	6
180.2.x.a.43.29	yes	128	36.11	even	6
180.2.x.a.67.2	yes	128	60.47	odd	4
180.2.x.a.67.29	yes	128	15.2	even	4
180.2.x.a.103.14	yes	128	12.11	even	2
180.2.x.a.103.20	yes	128	3.2	odd	2
540.2.y.a.127.13		128	180.7	even	12	inner
540.2.y.a.127.19		128	45.7	odd	12	inner
540.2.y.a.307.4		128	5.2	odd	4	inner
540.2.y.a.307.31		128	20.7	even	4	inner
540.2.y.a.343.4		128	36.7	odd	6	inner
540.2.y.a.343.31		128	9.7	even	3	inner
540.2.y.a.523.13		128	1.1	even	1	trivial
540.2.y.a.523.19		128	4.3	odd	2	inner
900.2.bf.e.7.13		128	180.83	odd	12
900.2.bf.e.7.19		128	45.38	even	12
900.2.bf.e.43.4		128	180.119	even	6
900.2.bf.e.43.31		128	45.29	odd	6
900.2.bf.e.607.4		128	15.8	even	4
900.2.bf.e.607.31		128	60.23	odd	4
900.2.bf.e.643.13		128	15.14	odd	2
900.2.bf.e.643.19		128	60.59	even	2

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.453270 + 1.33961i) q^{2} +(-1.58909 - 1.21441i) q^{4} +(2.23308 - 0.115576i) q^{5} +(-0.00100179 + 0.00373871i) q^{7} +(2.34712 - 1.57830i) q^{8} +O(q^{10})\)	\(q+(-0.453270 + 1.33961i) q^{2} +(-1.58909 - 1.21441i) q^{4} +(2.23308 - 0.115576i) q^{5} +(-0.00100179 + 0.00373871i) q^{7} +(2.34712 - 1.57830i) q^{8} +(-0.857362 + 3.04383i) q^{10} +(-3.58713 + 2.07103i) q^{11} +(2.86455 - 0.767553i) q^{13} +(-0.00455433 - 0.00303665i) q^{14} +(1.05043 + 3.85961i) q^{16} +(2.07784 - 2.07784i) q^{17} +7.31525 q^{19} +(-3.68893 - 2.52821i) q^{20} +(-1.14843 - 5.74408i) q^{22} +(1.00208 + 3.73983i) q^{23} +(4.97328 - 0.516182i) q^{25} +(-0.270195 + 4.18528i) q^{26} +(0.00613225 - 0.00472458i) q^{28} +(4.99228 - 2.88229i) q^{29} +(1.77642 + 1.02562i) q^{31} +(-5.64649 - 0.342287i) q^{32} +(1.84166 + 3.72530i) q^{34} +(-0.00180496 + 0.00846463i) q^{35} +(-6.09468 + 6.09468i) q^{37} +(-3.31579 + 9.79956i) q^{38} +(5.05888 - 3.79575i) q^{40} +(-1.82477 + 3.16060i) q^{41} +(-0.968609 - 0.259538i) q^{43} +(8.21535 + 1.06518i) q^{44} +(-5.46412 - 0.352755i) q^{46} +(-1.22115 + 4.55740i) q^{47} +(6.06216 + 3.49999i) q^{49} +(-1.56276 + 6.89621i) q^{50} +(-5.48415 - 2.25902i) q^{52} +(-6.92974 - 6.92974i) q^{53} +(-7.77098 + 5.03936i) q^{55} +(0.00354952 + 0.0103563i) q^{56} +(1.59829 + 7.99414i) q^{58} +(2.76056 - 4.78143i) q^{59} +(3.59007 + 6.21819i) q^{61} +(-2.17912 + 1.91482i) q^{62} +(3.01792 - 7.40893i) q^{64} +(6.30805 - 2.04508i) q^{65} +(-3.17735 + 0.851369i) q^{67} +(-5.82521 + 0.778533i) q^{68} +(-0.0105211 - 0.00625470i) q^{70} -11.3127i q^{71} +(-6.50632 - 6.50632i) q^{73} +(-5.40194 - 10.9270i) q^{74} +(-11.6246 - 8.88370i) q^{76} +(-0.00414946 - 0.0154860i) q^{77} +(-2.99986 - 5.19591i) q^{79} +(2.79177 + 8.49741i) q^{80} +(-3.40684 - 3.87708i) q^{82} +(2.82192 + 0.756131i) q^{83} +(4.39982 - 4.88012i) q^{85} +(0.786720 - 1.17991i) q^{86} +(-5.15070 + 10.5225i) q^{88} +9.18764i q^{89} +0.0114786i q^{91} +(2.94927 - 7.15987i) q^{92} +(-5.55161 - 3.70160i) q^{94} +(16.3355 - 0.845469i) q^{95} +(-2.26714 - 0.607478i) q^{97} +(-7.43641 + 6.53447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

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