LMFDB - Embedded newform 486.2.g.a.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [486,2,Mod(19,486)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(486, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([52]))

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

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

chi := DirichletCharacter("486.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.g (of order $27$, degree $18$, 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:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 162)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	486.73
Dual form			486.2.g.a.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893633 - 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(0.750365 - 2.50640i) q^{5} +(0.318489 - 0.738341i) q^{7} +(0.173648 - 0.984808i) q^{8} +O(q^{10})$	\(q+(0.893633 - 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(0.750365 - 2.50640i) q^{5} +(0.318489 - 0.738341i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-0.454317 - 2.57656i) q^{10} +(-0.151352 - 0.0358710i) q^{11} +(-0.574171 + 0.377638i) q^{13} +(-0.0467545 - 0.802743i) q^{14} +(-0.286803 - 0.957990i) q^{16} +(-0.0626772 - 0.0228126i) q^{17} +(-0.221311 + 0.0805504i) q^{19} +(-1.56235 - 2.09860i) q^{20} +(-0.151352 + 0.0358710i) q^{22} +(-3.45177 - 8.00209i) q^{23} +(-1.54153 - 1.01388i) q^{25} +(-0.343614 + 0.595158i) q^{26} +(-0.402052 - 0.696374i) q^{28} +(-0.585239 + 10.0482i) q^{29} +(7.28783 + 0.851825i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-0.0662487 + 0.00774336i) q^{34} +(-1.61159 - 1.35229i) q^{35} +(6.12996 - 5.14365i) q^{37} +(-0.161619 + 0.171306i) q^{38} +(-2.33802 - 1.17420i) q^{40} +(4.49262 + 2.25628i) q^{41} +(2.28836 - 2.42552i) q^{43} +(-0.119154 + 0.0999819i) q^{44} +(-6.67595 - 5.60178i) q^{46} +(-12.4934 + 1.46027i) q^{47} +(4.35998 + 4.62131i) q^{49} +(-1.83259 - 0.214199i) q^{50} +(-0.0399588 + 0.686066i) q^{52} +(3.27068 + 5.66499i) q^{53} +(-0.203476 + 0.352430i) q^{55} +(-0.671819 - 0.441862i) q^{56} +(3.98662 + 9.24202i) q^{58} +(7.05313 - 1.67162i) q^{59} +(-3.70223 - 4.97296i) q^{61} +(6.89494 - 2.50955i) q^{62} +(-0.939693 - 0.342020i) q^{64} +(0.515673 + 1.72247i) q^{65} +(0.484143 + 8.31242i) q^{67} +(-0.0557268 + 0.0366521i) q^{68} +(-2.04708 - 0.485166i) q^{70} +(0.683417 + 3.87585i) q^{71} +(-1.74184 + 9.87849i) q^{73} +(3.16947 - 7.34766i) q^{74} +(-0.0675461 + 0.225620i) q^{76} +(-0.0746888 + 0.100325i) q^{77} +(-15.0576 + 7.56219i) q^{79} -2.61631 q^{80} +5.02737 q^{82} +(-1.94848 + 0.978564i) q^{83} +(-0.104208 + 0.139976i) q^{85} +(0.956381 - 3.19454i) q^{86} +(-0.0616079 + 0.142823i) q^{88} +(0.587729 - 3.33317i) q^{89} +(0.0959586 + 0.544208i) q^{91} +(-8.47992 - 2.00978i) q^{92} +(-10.5091 + 6.91197i) q^{94} +(0.0358275 + 0.615134i) q^{95} +(2.07475 + 6.93014i) q^{97} +(5.97026 + 2.17300i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 18 q^{13} + 9 q^{20} + 81 q^{23} + 18 q^{25} + 27 q^{26} + 18 q^{28} + 27 q^{29} - 54 q^{31} + 27 q^{35} - 9 q^{38} + 9 q^{41} + 36 q^{43} - 18 q^{46} + 27 q^{47} - 36 q^{52} + 27 q^{53} + 54 q^{55} + 9 q^{58} + 18 q^{59} - 9 q^{65} - 135 q^{67} + 18 q^{68} + 18 q^{70} - 72 q^{71} + 36 q^{73} - 99 q^{74} - 9 q^{76} - 144 q^{77} - 9 q^{79} - 18 q^{80} - 72 q^{82} - 99 q^{83} + 9 q^{85} - 72 q^{86} - 9 q^{88} - 126 q^{89} + 63 q^{91} - 36 q^{92} + 18 q^{94} - 45 q^{95} - 171 q^{97} - 36 q^{98}+O(q^{100}) $ 72 * q + 18 * q^13 + 9 * q^20 + 81 * q^23 + 18 * q^25 + 27 * q^26 + 18 * q^28 + 27 * q^29 - 54 * q^31 + 27 * q^35 - 9 * q^38 + 9 * q^41 + 36 * q^43 - 18 * q^46 + 27 * q^47 - 36 * q^52 + 27 * q^53 + 54 * q^55 + 9 * q^58 + 18 * q^59 - 9 * q^65 - 135 * q^67 + 18 * q^68 + 18 * q^70 - 72 * q^71 + 36 * q^73 - 99 * q^74 - 9 * q^76 - 144 * q^77 - 9 * q^79 - 18 * q^80 - 72 * q^82 - 99 * q^83 + 9 * q^85 - 72 * q^86 - 9 * q^88 - 126 * q^89 + 63 * q^91 - 36 * q^92 + 18 * q^94 - 45 * q^95 - 171 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$3$		0			0
$3$		0			0
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	0.750365	−	2.50640i	0.335574	−	1.12089i	−0.609158	−	0.793049i	$-0.708492\pi$
$5$	0.750365	−	2.50640i	0.335574	−	1.12089i	0.944732	−	0.327845i	$-0.106322\pi$
$6$		0			0
$7$	0.318489	−	0.738341i	0.120378	−	0.279067i	−0.847364	−	0.531013i	$-0.821811\pi$
$7$	0.318489	−	0.738341i	0.120378	−	0.279067i	0.967741	+	0.251947i	$0.0810707\pi$
$8$	0.173648	−	0.984808i	0.0613939	−	0.348182i
$9$		0			0
$10$	−0.454317	−	2.57656i	−0.143668	−	0.814780i
$11$	−0.151352	−	0.0358710i	−0.0456342	−	0.0108155i	0.207735	−	0.978185i	$-0.433391\pi$
$11$	−0.151352	−	0.0358710i	−0.0456342	−	0.0108155i	−0.253370	+	0.967370i	$0.581539\pi$
$12$		0			0
$13$	−0.574171	+	0.377638i	−0.159246	+	0.104738i	−0.626631	−	0.779316i	$-0.715567\pi$
$13$	−0.574171	+	0.377638i	−0.159246	+	0.104738i	0.467385	+	0.884054i	$0.345196\pi$
$14$	−0.0467545	−	0.802743i	−0.0124957	−	0.214542i
$15$		0			0
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	−0.0626772	−	0.0228126i	−0.0152015	−	0.00553288i	0.334408	−	0.942428i	$-0.391464\pi$
$17$	−0.0626772	−	0.0228126i	−0.0152015	−	0.00553288i	−0.349610	+	0.936895i	$0.613686\pi$
$18$		0			0
$19$	−0.221311	+	0.0805504i	−0.0507721	+	0.0184795i	−0.367281	−	0.930110i	$-0.619711\pi$
$19$	−0.221311	+	0.0805504i	−0.0507721	+	0.0184795i	0.316509	+	0.948589i	$0.397489\pi$
$20$	−1.56235	−	2.09860i	−0.349352	−	0.469261i
$21$		0			0
$22$	−0.151352	+	0.0358710i	−0.0322683	+	0.00764772i
$23$	−3.45177	−	8.00209i	−0.719743	−	1.66855i	−0.743413	−	0.668832i	$-0.766794\pi$
$23$	−3.45177	−	8.00209i	−0.719743	−	1.66855i	0.0236702	−	0.999720i	$-0.492465\pi$
$24$		0			0
$25$	−1.54153	−	1.01388i	−0.308306	−	0.202776i
$26$	−0.343614	+	0.595158i	−0.0673883	+	0.116720i
$27$		0			0
$28$	−0.402052	−	0.696374i	−0.0759807	−	0.131602i
$29$	−0.585239	+	10.0482i	−0.108676	+	1.86590i	0.300946	+	0.953641i	$0.402698\pi$
$29$	−0.585239	+	10.0482i	−0.108676	+	1.86590i	−0.409622	+	0.912255i	$0.634339\pi$
$30$		0			0
$31$	7.28783	+	0.851825i	1.30893	+	0.152992i	0.741793	−	0.670629i	$-0.233976\pi$
$31$	7.28783	+	0.851825i	1.30893	+	0.152992i	0.567140	+	0.823621i	$0.308050\pi$
$32$	−0.686242	−	0.727374i	−0.121312	−	0.128583i
$33$		0			0
$34$	−0.0662487	+	0.00774336i	−0.0113616	+	0.00132798i
$35$	−1.61159	−	1.35229i	−0.272409	−	0.228578i
$36$		0			0
$37$	6.12996	−	5.14365i	1.00776	−	0.845611i	0.0197193	−	0.999806i	$-0.493723\pi$
$37$	6.12996	−	5.14365i	1.00776	−	0.845611i	0.988040	+	0.154195i	$0.0492783\pi$
$38$	−0.161619	+	0.171306i	−0.0262181	+	0.0277896i
$39$		0			0
$40$	−2.33802	−	1.17420i	−0.369673	−	0.185657i
$41$	4.49262	+	2.25628i	0.701630	+	0.352372i	0.763585	−	0.645707i	$-0.223437\pi$
$41$	4.49262	+	2.25628i	0.701630	+	0.352372i	−0.0619553	+	0.998079i	$0.519734\pi$
$42$		0			0
$43$	2.28836	−	2.42552i	0.348971	−	0.369888i	−0.528983	−	0.848632i	$-0.677426\pi$
$43$	2.28836	−	2.42552i	0.348971	−	0.369888i	0.877954	+	0.478744i	$0.158908\pi$
$44$	−0.119154	+	0.0999819i	−0.0179631	+	0.0150728i
$45$		0			0
$46$	−6.67595	−	5.60178i	−0.984314	−	0.825938i
$47$	−12.4934	+	1.46027i	−1.82235	+	0.213002i	−0.957382	−	0.288824i	$-0.906736\pi$
$47$	−12.4934	+	1.46027i	−1.82235	+	0.213002i	−0.864968	+	0.501827i	$0.832662\pi$
$48$		0			0
$49$	4.35998	+	4.62131i	0.622854	+	0.660187i
$50$	−1.83259	−	0.214199i	−0.259167	−	0.0302923i
$51$		0			0
$52$	−0.0399588	+	0.686066i	−0.00554129	+	0.0951403i
$53$	3.27068	+	5.66499i	0.449263	+	0.778146i	0.998338	−	0.0576268i	$-0.0183533\pi$
$53$	3.27068	+	5.66499i	0.449263	+	0.778146i	−0.549075	+	0.835773i	$0.685020\pi$
$54$		0			0
$55$	−0.203476	+	0.352430i	−0.0274367	+	0.0475217i
$56$	−0.671819	−	0.441862i	−0.0897756	−	0.0590463i
$57$		0			0
$58$	3.98662	+	9.24202i	0.523469	+	1.21354i
$59$	7.05313	−	1.67162i	0.918239	−	0.217627i	0.255789	−	0.966733i	$-0.417665\pi$
$59$	7.05313	−	1.67162i	0.918239	−	0.217627i	0.662450	+	0.749106i	$0.269517\pi$
$60$		0			0
$61$	−3.70223	−	4.97296i	−0.474023	−	0.636723i	0.499228	−	0.866471i	$-0.333617\pi$
$61$	−3.70223	−	4.97296i	−0.474023	−	0.636723i	−0.973250	+	0.229748i	$0.926210\pi$
$62$	6.89494	−	2.50955i	0.875658	−	0.318714i
$63$		0			0
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	0.515673	+	1.72247i	0.0639613	+	0.213646i
$66$		0			0
$67$	0.484143	+	8.31242i	0.0591475	+	1.01552i	0.889107	+	0.457700i	$0.151326\pi$
$67$	0.484143	+	8.31242i	0.0591475	+	1.01552i	−0.829959	+	0.557824i	$0.811636\pi$
$68$	−0.0557268	+	0.0366521i	−0.00675787	+	0.00444472i
$69$		0			0
$70$	−2.04708	−	0.485166i	−0.244672	−	0.0579884i
$71$	0.683417	+	3.87585i	0.0811066	+	0.459979i	0.998129	+	0.0611428i	$0.0194745\pi$
$71$	0.683417	+	3.87585i	0.0811066	+	0.459979i	−0.917022	+	0.398836i	$0.869414\pi$
$72$		0			0
$73$	−1.74184	+	9.87849i	−0.203867	+	1.15619i	0.695344	+	0.718677i	$0.255252\pi$
$73$	−1.74184	+	9.87849i	−0.203867	+	1.15619i	−0.899212	+	0.437513i	$0.855859\pi$
$74$	3.16947	−	7.34766i	0.368443	−	0.854148i
$75$		0			0
$76$	−0.0675461	+	0.225620i	−0.00774807	+	0.0258804i
$77$	−0.0746888	+	0.100325i	−0.00851158	+	0.0114330i
$78$		0			0
$79$	−15.0576	+	7.56219i	−1.69411	+	0.850812i	−0.704049	+	0.710151i	$0.748627\pi$
$79$	−15.0576	+	7.56219i	−1.69411	+	0.850812i	−0.990058	+	0.140661i	$0.955077\pi$
$80$	−2.61631			−0.292512
$81$		0			0
$82$	5.02737			0.555180
$83$	−1.94848	+	0.978564i	−0.213874	+	0.107411i	−0.552511	−	0.833506i	$-0.686330\pi$
$83$	−1.94848	+	0.978564i	−0.213874	+	0.107411i	0.338637	+	0.940917i	$0.390034\pi$
$84$		0			0
$85$	−0.104208	+	0.139976i	−0.0113030	+	0.0151825i
$86$	0.956381	−	3.19454i	0.103129	−	0.344476i
$87$		0			0
$88$	−0.0616079	+	0.142823i	−0.00656743	+	0.0152250i
$89$	0.587729	−	3.33317i	0.0622991	−	0.353316i	−0.937684	−	0.347489i	$-0.887034\pi$
$89$	0.587729	−	3.33317i	0.0622991	−	0.353316i	0.999983	−	0.00582641i	$-0.00185461\pi$
$90$		0			0
$91$	0.0959586	+	0.544208i	0.0100592	+	0.0570485i
$92$	−8.47992	−	2.00978i	−0.884093	−	0.209534i
$93$		0			0
$94$	−10.5091	+	6.91197i	−1.08394	+	0.712916i
$95$	0.0358275	+	0.615134i	0.00367582	+	0.0631114i
$96$		0			0
$97$	2.07475	+	6.93014i	0.210659	+	0.703649i	0.996376	+	0.0850629i	$0.0271091\pi$
$97$	2.07475	+	6.93014i	0.210659	+	0.703649i	−0.785717	+	0.618586i	$0.787706\pi$
$98$	5.97026	+	2.17300i	0.603087	+	0.219506i
$99$		0			0
$100$	−1.73379	+	0.631050i	−0.173379	+	0.0631050i
$101$	4.13021	+	5.54784i	0.410971	+	0.552030i	0.958624	−	0.284676i	$-0.0918858\pi$
$101$	4.13021	+	5.54784i	0.410971	+	0.552030i	−0.547653	+	0.836706i	$0.684478\pi$
$102$		0			0
$103$	12.1774	−	2.88610i	1.19988	−	0.284376i	0.418372	−	0.908276i	$-0.362601\pi$
$103$	12.1774	−	2.88610i	1.19988	−	0.284376i	0.781504	+	0.623900i	$0.214453\pi$
$104$	0.272197	+	0.631025i	0.0266912	+	0.0618771i
$105$		0			0
$106$	5.46523	+	3.59454i	0.530830	+	0.349133i
$107$	−4.44410	+	7.69740i	−0.429627	+	0.744136i	−0.996840	−	0.0794354i	$-0.974688\pi$
$107$	−4.44410	+	7.69740i	−0.429627	+	0.744136i	0.567213	+	0.823571i	$0.308022\pi$
$108$		0			0
$109$	−5.81125	−	10.0654i	−0.556617	−	0.964089i	−0.997776	−	0.0666601i	$-0.978766\pi$
$109$	−5.81125	−	10.0654i	−0.556617	−	0.964089i	0.441158	−	0.897429i	$-0.354568\pi$
$110$	−0.0236621	+	0.406263i	−0.00225610	+	0.0387357i
$111$		0			0
$112$	−0.798667	−	0.0933508i	−0.0754669	−	0.00882082i
$113$	8.52356	+	9.03445i	0.801829	+	0.849889i	0.991249	−	0.132007i	$-0.0421422\pi$
$113$	8.52356	+	9.03445i	0.801829	+	0.849889i	−0.189420	+	0.981896i	$0.560661\pi$
$114$		0			0
$115$	−22.6465	+	2.64700i	−2.11180	+	0.246834i
$116$	7.71038	+	6.46978i	0.715891	+	0.600704i
$117$		0			0
$118$	5.55268	−	4.65925i	0.511166	−	0.428919i
$119$	−0.0368055	+	0.0390116i	−0.00337396	+	0.00357619i
$120$		0			0
$121$	−9.80834	−	4.92593i	−0.891667	−	0.447812i
$122$	−5.54030	−	2.78244i	−0.501595	−	0.251911i
$123$		0			0
$124$	5.03526	−	5.33706i	0.452180	−	0.479282i
$125$	6.32314	−	5.30575i	0.565559	−	0.474561i
$126$		0			0
$127$	−5.95411	−	4.99609i	−0.528342	−	0.443331i	0.339187	−	0.940719i	$-0.389848\pi$
$127$	−5.95411	−	4.99609i	−0.528342	−	0.443331i	−0.867528	+	0.497388i	$0.834293\pi$
$128$	−0.993238	+	0.116093i	−0.0877907	+	0.0102613i
$129$		0			0
$130$	1.23386	+	1.30782i	0.108217	+	0.114703i
$131$	−9.32278	−	1.08968i	−0.814535	−	0.0952055i	−0.301383	−	0.953503i	$-0.597448\pi$
$131$	−9.32278	−	1.08968i	−0.814535	−	0.0952055i	−0.513152	+	0.858298i	$0.671522\pi$
$132$		0			0
$133$	−0.0110113	+	0.189057i	−0.000954803	+	0.0163933i
$134$	4.16325	+	7.21096i	0.359650	+	0.622932i
$135$		0			0
$136$	−0.0333499	+	0.0577636i	−0.00285973	+	0.00495319i
$137$	12.8062	+	8.42278i	1.09411	+	0.719606i	0.962388	−	0.271680i	$-0.0875793\pi$
$137$	12.8062	+	8.42278i	1.09411	+	0.719606i	0.131721	+	0.991287i	$0.457950\pi$
$138$		0			0
$139$	−1.56019	−	3.61692i	−0.132333	−	0.306783i	0.839146	−	0.543906i	$-0.183055\pi$
$139$	−1.56019	−	3.61692i	−0.132333	−	0.306783i	−0.971480	+	0.237122i	$0.923796\pi$
$140$	−2.04708	+	0.485166i	−0.173009	+	0.0410040i
$141$		0			0
$142$	2.35020	+	3.15687i	0.197224	+	0.264918i
$143$	0.100448	−	0.0365601i	0.00839988	−	0.00305731i
$144$		0			0
$145$	24.7455	+	9.00663i	2.05500	+	0.747960i
$146$	2.87689	+	9.60948i	0.238093	+	0.795286i
$147$		0			0
$148$	−0.465281	−	7.98856i	−0.0382458	−	0.656656i
$149$	1.25658	−	0.826467i	0.102943	−	0.0677068i	−0.496994	−	0.867754i	$-0.665563\pi$
$149$	1.25658	−	0.826467i	0.102943	−	0.0677068i	0.599937	+	0.800047i	$0.295192\pi$
$150$		0			0
$151$	12.7162	+	3.01380i	1.03483	+	0.245259i	0.712724	−	0.701444i	$-0.247461\pi$
$151$	12.7162	+	3.01380i	1.03483	+	0.245259i	0.322106	+	0.946704i	$0.395609\pi$
$152$	0.0408965	+	0.231936i	0.00331715	+	0.0188125i
$153$		0			0
$154$	−0.0217188	+	0.123174i	−0.00175015	+	0.00992561i
$155$	7.60355	−	17.6270i	0.610732	−	1.41583i
$156$		0			0
$157$	5.80940	−	19.4048i	0.463641	−	1.54867i	−0.332228	−	0.943199i	$-0.607800\pi$
$157$	5.80940	−	19.4048i	0.463641	−	1.54867i	0.795869	−	0.605469i	$-0.207014\pi$
$158$	−10.0620	+	13.5156i	−0.800491	+	1.07525i
$159$		0			0
$160$	−2.33802	+	1.17420i	−0.184837	+	0.0928284i
$161$	−7.00763			−0.552278
$162$		0			0
$163$	−1.85361			−0.145186			−0.0725930	−	0.997362i	$-0.523127\pi$
$163$	−1.85361			−0.145186			−0.0725930	+	0.997362i	$0.523127\pi$
$164$	4.49262	−	2.25628i	0.350815	−	0.176186i
$165$		0			0
$166$	−1.30205	+	1.74895i	−0.101058	+	0.135745i
$167$	3.60077	−	12.0274i	0.278636	−	0.930709i	−0.698053	−	0.716047i	$-0.745950\pi$
$167$	3.60077	−	12.0274i	0.278636	−	0.930709i	0.976688	−	0.214662i	$-0.0688650\pi$
$168$		0			0
$169$	−4.96198	+	11.5032i	−0.381690	+	0.884858i
$170$	−0.0303028	+	0.171856i	−0.00232412	+	0.0131807i
$171$		0			0
$172$	−0.579051	−	3.28396i	−0.0441523	−	0.250400i
$173$	−10.6230	−	2.51769i	−0.807650	−	0.191416i	−0.194007	−	0.981000i	$-0.562148\pi$
$173$	−10.6230	−	2.51769i	−0.807650	−	0.191416i	−0.613643	+	0.789584i	$0.710297\pi$
$174$		0			0
$175$	−1.23955	+	0.815265i	−0.0937012	+	0.0616282i
$176$	0.00904409	+	0.155281i	0.000681724	+	0.0117048i
$177$		0			0
$178$	−0.970712	−	3.24241i	−0.0727580	−	0.243029i
$179$	8.73770	+	3.18026i	0.653087	+	0.237704i	0.647249	−	0.762279i	$-0.275920\pi$
$179$	8.73770	+	3.18026i	0.653087	+	0.237704i	0.00583785	+	0.999983i	$0.498142\pi$
$180$		0			0
$181$	14.1384	−	5.14597i	1.05090	−	0.382497i	0.241899	−	0.970301i	$-0.422230\pi$
$181$	14.1384	−	5.14597i	1.05090	−	0.382497i	0.809003	+	0.587804i	$0.200007\pi$
$182$	0.329992	+	0.443256i	0.0244606	+	0.0328563i
$183$		0			0
$184$	−8.47992	+	2.00978i	−0.625148	+	0.148163i
$185$	−8.29231	−	19.2237i	−0.609663	−	1.41336i
$186$		0			0
$187$	0.00866798	+	0.00570102i	0.000633866	+	0.000416900i
$188$	−6.28923	+	10.8933i	−0.458689	+	0.794473i
$189$		0			0
$190$	0.308088	+	0.533624i	0.0223511	+	0.0387132i
$191$	−0.434148	+	7.45404i	−0.0314139	+	0.539355i	0.945487	+	0.325661i	$0.105587\pi$
$191$	−0.434148	+	7.45404i	−0.0314139	+	0.539355i	−0.976901	+	0.213694i	$0.931450\pi$
$192$		0			0
$193$	−12.3408	−	1.44244i	−0.888313	−	0.103829i	−0.340318	−	0.940310i	$-0.610535\pi$
$193$	−12.3408	−	1.44244i	−0.888313	−	0.103829i	−0.547995	+	0.836481i	$0.684609\pi$
$194$	4.96430	+	5.26186i	0.356416	+	0.377779i
$195$		0			0
$196$	6.31046	−	0.737587i	0.450747	−	0.0526848i
$197$	−15.5743	−	13.0684i	−1.10962	−	0.931083i	−0.111587	−	0.993755i	$-0.535593\pi$
$197$	−15.5743	−	13.0684i	−1.10962	−	0.931083i	−0.998034	+	0.0626719i	$0.980038\pi$
$198$		0			0
$199$	−17.7742	+	14.9143i	−1.25998	+	1.05725i	−0.264293	+	0.964443i	$0.585139\pi$
$199$	−17.7742	+	14.9143i	−1.25998	+	1.05725i	−0.995684	+	0.0928038i	$0.970417\pi$
$200$	−1.26616	+	1.34205i	−0.0895311	+	0.0948974i
$201$		0			0
$202$	6.18076	+	3.10409i	0.434876	+	0.218403i
$203$	7.23258	+	3.63234i	0.507627	+	0.254940i
$204$		0			0
$205$	9.02624	−	9.56725i	0.630420	−	0.668206i
$206$	9.58685	−	8.04433i	0.667948	−	0.560475i
$207$		0			0
$208$	0.526448	+	0.441742i	0.0365026	+	0.0306293i
$209$	0.0363851	−	0.00425281i	0.00251681	−	0.000294173i
$210$		0			0
$211$	−12.8338	−	13.6031i	−0.883519	−	0.936475i	0.114861	−	0.993382i	$-0.463358\pi$
$211$	−12.8338	−	13.6031i	−0.883519	−	0.936475i	−0.998380	+	0.0569065i	$0.981876\pi$
$212$	6.49714	+	0.759406i	0.446225	+	0.0521562i
$213$		0			0
$214$	−0.516802	+	8.87315i	−0.0353279	+	0.606556i
$215$	−4.36220	−	7.55556i	−0.297500	−	0.515285i
$216$		0			0
$217$	2.95003	−	5.10961i	0.200261	−	0.346863i
$218$	−9.71046	−	6.38667i	−0.657676	−	0.432560i
$219$		0			0
$220$	0.161185	+	0.373670i	0.0108671	+	0.0251928i
$221$	0.0446024	−	0.0105710i	0.00300028	−	0.000711080i
$222$		0			0
$223$	−5.57356	−	7.48658i	−0.373233	−	0.501339i	0.575333	−	0.817919i	$-0.304873\pi$
$223$	−5.57356	−	7.48658i	−0.373233	−	0.501339i	−0.948566	+	0.316581i	$0.897465\pi$
$224$	−0.755610	+	0.275020i	−0.0504863	+	0.0183755i
$225$		0			0
$226$	11.6716	+	4.24811i	0.776382	+	0.282580i
$227$	−6.03211	−	20.1487i	−0.400365	−	1.33731i	−0.886216	−	0.463272i	$-0.846675\pi$
$227$	−6.03211	−	20.1487i	−0.400365	−	1.33731i	0.485851	−	0.874042i	$-0.338510\pi$
$228$		0			0
$229$	0.524687	+	9.00853i	0.0346723	+	0.595301i	0.970239	+	0.242150i	$0.0778526\pi$
$229$	0.524687	+	9.00853i	0.0346723	+	0.595301i	−0.935566	+	0.353151i	$0.885110\pi$
$230$	−19.0497	+	12.5292i	−1.25610	+	0.826149i
$231$		0			0
$232$	9.79388	+	2.32119i	0.643000	+	0.152394i
$233$	−1.51248	−	8.57770i	−0.0990858	−	0.561944i	−0.993419	−	0.114541i	$-0.963460\pi$
$233$	−1.51248	−	8.57770i	−0.0990858	−	0.561944i	0.894333	−	0.447403i	$-0.147651\pi$
$234$		0			0
$235$	−5.71461	+	32.4091i	−0.372780	+	2.11414i
$236$	2.87099	−	6.65570i	0.186885	−	0.433249i
$237$		0			0
$238$	−0.0153823	+	0.0513803i	−0.000997084	+	0.00333049i
$239$	−14.8965	+	20.0094i	−0.963572	+	1.29430i	−0.00786849	+	0.999969i	$0.502505\pi$
$239$	−14.8965	+	20.0094i	−0.963572	+	1.29430i	−0.955703	+	0.294332i	$0.904903\pi$
$240$		0			0
$241$	17.6807	−	8.87956i	1.13891	−	0.571983i	0.223581	−	0.974685i	$-0.428225\pi$
$241$	17.6807	−	8.87956i	1.13891	−	0.571983i	0.915331	+	0.402703i	$0.131929\pi$
$242$	−10.9758			−0.705552
$243$		0			0
$244$	−6.19975			−0.396898
$245$	14.8544	−	7.46016i	0.949013	−	0.476612i
$246$		0			0
$247$	0.0966512	−	0.129825i	0.00614977	−	0.00826057i
$248$	2.10440	−	7.02919i	0.133630	−	0.446354i
$249$		0			0
$250$	3.26935	−	7.57921i	0.206772	−	0.479351i
$251$	2.82742	−	16.0351i	0.178465	−	1.01213i	−0.755602	−	0.655031i	$-0.772656\pi$
$251$	2.82742	−	16.0351i	0.178465	−	1.01213i	0.934068	−	0.357096i	$-0.116233\pi$
$252$		0			0
$253$	0.235387	+	1.33495i	0.0147987	+	0.0839274i
$254$	−7.56303	−	1.79247i	−0.474546	−	0.112470i
$255$		0			0
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	0.122334	+	2.10039i	0.00763099	+	0.131019i	0.999972	+	0.00748998i	$0.00238416\pi$
$257$	0.122334	+	2.10039i	0.00763099	+	0.131019i	−0.992341	+	0.123529i	$0.960579\pi$
$258$		0			0
$259$	−1.84544	−	6.16420i	−0.114670	−	0.383025i
$260$	1.68957	+	0.614953i	0.104783	+	0.0381378i
$261$		0			0
$262$	−8.82019	+	3.21029i	−0.544913	+	0.198332i
$263$	−3.53716	−	4.75123i	−0.218111	−	0.292973i	0.679579	−	0.733603i	$-0.262163\pi$
$263$	−3.53716	−	4.75123i	−0.218111	−	0.292973i	−0.897689	+	0.440629i	$0.854755\pi$
$264$		0			0
$265$	16.6529	−	3.94681i	1.02298	−	0.242451i
$266$	0.0750086	+	0.173889i	0.00459907	+	0.0106618i
$267$		0			0
$268$	6.95669	+	4.57549i	0.424948	+	0.279492i
$269$	−1.86000	+	3.22161i	−0.113406	+	0.196425i	−0.917141	−	0.398562i	$-0.869509\pi$
$269$	−1.86000	+	3.22161i	−0.113406	+	0.196425i	0.803735	+	0.594987i	$0.202843\pi$
$270$		0			0
$271$	−9.85402	−	17.0677i	−0.598589	−	1.03679i	−0.993030	−	0.117865i	$-0.962395\pi$
$271$	−9.85402	−	17.0677i	−0.598589	−	1.03679i	0.394441	−	0.918921i	$-0.370938\pi$
$272$	−0.00387824	+	0.0665869i	−0.000235153	+	0.00403742i
$273$		0			0
$274$	15.2242	+	1.77945i	0.919727	+	0.107501i
$275$	0.196944	+	0.208748i	0.0118762	+	0.0125880i
$276$		0			0
$277$	−3.12717	+	0.365514i	−0.187893	+	0.0219616i	−0.209519	−	0.977805i	$-0.567190\pi$
$277$	−3.12717	+	0.365514i	−0.187893	+	0.0219616i	0.0216257	+	0.999766i	$0.493116\pi$
$278$	−3.01751	−	2.53199i	−0.180978	−	0.151859i
$279$		0			0
$280$	−1.61159	+	1.35229i	−0.0963110	+	0.0808145i
$281$	−14.6740	+	15.5535i	−0.875377	+	0.927845i	−0.997910	−	0.0646194i	$-0.979417\pi$
$281$	−14.6740	+	15.5535i	−0.875377	+	0.927845i	0.122533	+	0.992464i	$0.460898\pi$
$282$		0			0
$283$	−9.73365	−	4.88842i	−0.578606	−	0.290587i	0.135327	−	0.990801i	$-0.456791\pi$
$283$	−9.73365	−	4.88842i	−0.578606	−	0.290587i	−0.713933	+	0.700214i	$0.753088\pi$
$284$	3.51702	+	1.76631i	0.208696	+	0.104811i
$285$		0			0
$286$	0.0733555	−	0.0777522i	0.00433760	−	0.00459759i
$287$	3.09676	−	2.59849i	0.182796	−	0.153384i
$288$		0			0
$289$	−13.0193	−	10.9245i	−0.765844	−	0.642619i
$290$	26.1556	−	3.05715i	1.53591	−	0.179522i
$291$		0			0
$292$	6.88361	+	7.29620i	0.402833	+	0.426978i
$293$	20.1441	+	2.35451i	1.17683	+	0.137552i	0.681943	−	0.731405i	$-0.261135\pi$
$293$	20.1441	+	2.35451i	1.17683	+	0.137552i	0.494888	+	0.868957i	$0.335209\pi$
$294$		0			0
$295$	1.10268	−	18.9322i	0.0642004	−	1.10228i
$296$	−4.00105	−	6.93002i	−0.232556	−	0.402799i
$297$		0			0
$298$	0.752005	−	1.30251i	0.0435625	−	0.0754524i
$299$	5.00380	+	3.29105i	0.289377	+	0.190327i
$300$		0			0
$301$	−1.06204	−	2.46209i	−0.0612151	−	0.141913i
$302$	12.7162	−	3.01380i	0.731735	−	0.173424i
$303$		0			0
$304$	0.140639	+	0.188911i	0.00806620	+	0.0108348i
$305$	−15.2422	+	5.54772i	−0.872768	+	0.317662i
$306$		0			0
$307$	4.98325	+	1.81375i	0.284409	+	0.103516i	0.480286	−	0.877112i	$-0.340533\pi$
$307$	4.98325	+	1.81375i	0.284409	+	0.103516i	−0.195877	+	0.980629i	$0.562755\pi$
$308$	0.0358715	+	0.119819i	0.00204397	+	0.00682734i
$309$		0			0
$310$	−1.11621	−	19.1645i	−0.0633963	−	1.08847i
$311$	−3.54349	+	2.33059i	−0.200933	+	0.132156i	−0.645988	−	0.763347i	$-0.723554\pi$
$311$	−3.54349	+	2.33059i	−0.200933	+	0.132156i	0.445055	+	0.895503i	$0.353184\pi$
$312$		0			0
$313$	4.47705	+	1.06108i	0.253058	+	0.0599758i	0.355187	−	0.934795i	$-0.384417\pi$
$313$	4.47705	+	1.06108i	0.253058	+	0.0599758i	−0.102129	+	0.994771i	$0.532565\pi$
$314$	−3.51737	−	19.9480i	−0.198496	−	1.12573i
$315$		0			0
$316$	−2.92594	+	16.5938i	−0.164597	+	0.933476i
$317$	2.50285	−	5.80226i	0.140574	−	0.325887i	−0.833356	−	0.552737i	$-0.813583\pi$
$317$	2.50285	−	5.80226i	0.140574	−	0.325887i	0.973930	+	0.226850i	$0.0728427\pi$
$318$		0			0
$319$	0.449014	−	1.49981i	0.0251400	−	0.0839733i
$320$	−1.56235	+	2.09860i	−0.0873381	+	0.117315i
$321$		0			0
$322$	−6.26224	+	3.14502i	−0.348981	+	0.175265i
$323$	0.0157087			0.000874055
$324$		0			0
$325$	1.26798			0.0703350
$326$	−1.65645	+	0.831899i	−0.0917421	+	0.0460746i
$327$		0			0
$328$	3.00214	−	4.03257i	0.165765	−	0.222661i
$329$	−2.90084	+	9.68947i	−0.159928	+	0.534198i
$330$		0			0
$331$	6.35611	−	14.7351i	0.349363	−	0.809915i	−0.649412	−	0.760437i	$-0.724985\pi$
$331$	6.35611	−	14.7351i	0.349363	−	0.809915i	0.998775	−	0.0494782i	$-0.0157558\pi$
$332$	−0.378623	+	2.14728i	−0.0207797	+	0.117847i
$333$		0			0
$334$	−2.18013	−	12.3641i	−0.119291	−	0.676534i
$335$	21.1975	+	5.02390i	1.15814	+	0.274485i
$336$		0			0
$337$	2.25984	−	1.48632i	0.123101	−	0.0809650i	−0.486465	−	0.873700i	$-0.661714\pi$
$337$	2.25984	−	1.48632i	0.123101	−	0.0809650i	0.609566	+	0.792735i	$0.291344\pi$
$338$	0.728422	+	12.5065i	0.0396209	+	0.680265i
$339$		0			0
$340$	0.0500492	+	0.167176i	0.00271430	+	0.00906638i
$341$	−1.07247	−	0.390347i	−0.0580774	−	0.0211385i
$342$		0			0
$343$	10.0900	−	3.67245i	0.544808	−	0.198294i
$344$	−1.99130	−	2.67478i	−0.107364	−	0.144214i
$345$		0			0
$346$	−10.6230	+	2.51769i	−0.571095	+	0.135352i
$347$	−3.72033	−	8.62470i	−0.199718	−	0.462998i	0.788696	−	0.614784i	$-0.210757\pi$
$347$	−3.72033	−	8.62470i	−0.199718	−	0.462998i	−0.988413	+	0.151786i	$0.951498\pi$
$348$		0			0
$349$	17.9125	+	11.7812i	0.958834	+	0.630635i	0.929456	−	0.368933i	$-0.120277\pi$
$349$	17.9125	+	11.7812i	0.958834	+	0.630635i	0.0293780	+	0.999568i	$0.490647\pi$
$350$	−0.741812	+	1.28486i	−0.0396515	+	0.0686785i
$351$		0			0
$352$	0.0777721	+	0.134705i	0.00414527	+	0.00717981i
$353$	−0.436688	+	7.49765i	−0.0232426	+	0.399060i	0.966544	+	0.256501i	$0.0825698\pi$
$353$	−0.436688	+	7.49765i	−0.0232426	+	0.399060i	−0.989786	+	0.142558i	$0.954467\pi$
$354$		0			0
$355$	10.2272	+	1.19539i	0.542804	+	0.0634447i
$356$	−2.32265	−	2.46186i	−0.123100	−	0.130479i
$357$		0			0
$358$	9.23560	−	1.07949i	0.488116	−	0.0570526i
$359$	−15.7373	−	13.2052i	−0.830584	−	0.696943i	0.124841	−	0.992177i	$-0.460158\pi$
$359$	−15.7373	−	13.2052i	−0.830584	−	0.696943i	−0.955425	+	0.295234i	$0.904602\pi$
$360$		0			0
$361$	−14.5124	+	12.1773i	−0.763808	+	0.640911i
$362$	10.3251	−	10.9439i	0.542673	−	0.575200i
$363$		0			0
$364$	0.493824	+	0.248008i	0.0258834	+	0.0129991i
$365$	23.4524	+	11.7782i	1.22755	+	0.616501i
$366$		0			0
$367$	10.6543	−	11.2929i	0.556149	−	0.589483i	−0.386907	−	0.922119i	$-0.626456\pi$
$367$	10.6543	−	11.2929i	0.556149	−	0.589483i	0.943055	+	0.332636i	$0.107938\pi$
$368$	−6.67595	+	5.60178i	−0.348008	+	0.292013i
$369$		0			0
$370$	−16.0379	−	13.4574i	−0.833769	−	0.699615i
$371$	5.22437	−	0.610641i	0.271236	−	0.0317029i
$372$		0			0
$373$	−12.2810	−	13.0171i	−0.635887	−	0.674001i	0.326652	−	0.945145i	$-0.394080\pi$
$373$	−12.2810	−	13.0171i	−0.635887	−	0.674001i	−0.962539	+	0.271144i	$0.912598\pi$
$374$	0.0103046	+	0.00120444i	0.000532839	+	6.22799e-5i
$375$		0			0
$376$	−0.731372	+	12.5572i	−0.0377176	+	0.647587i
$377$	−3.45854	−	5.99038i	−0.178124	−	0.308520i
$378$		0			0
$379$	−2.29993	+	3.98360i	−0.118140	+	0.204624i	−0.919030	−	0.394187i	$-0.871026\pi$
$379$	−2.29993	+	3.98360i	−0.118140	+	0.204624i	0.800891	+	0.598810i	$0.204360\pi$
$380$	0.514808	+	0.338594i	0.0264091	+	0.0173695i
$381$		0			0
$382$	2.95740	+	6.85601i	0.151314	+	0.350784i
$383$	−25.0504	+	5.93707i	−1.28002	+	0.303370i	−0.813720	−	0.581258i	$-0.802561\pi$
$383$	−25.0504	+	5.93707i	−1.28002	+	0.303370i	−0.466298	+	0.884627i	$0.654413\pi$
$384$		0			0
$385$	0.195409	+	0.262480i	0.00995896	+	0.0133772i
$386$	−11.6755	+	4.24955i	−0.594270	+	0.216296i
$387$		0			0
$388$	6.79778	+	2.47419i	0.345105	+	0.125608i
$389$	−2.20453	−	7.36366i	−0.111774	−	0.373352i	0.883738	−	0.467981i	$-0.155019\pi$
$389$	−2.20453	−	7.36366i	−0.111774	−	0.373352i	−0.995513	+	0.0946293i	$0.969833\pi$
$390$		0			0
$391$	0.0337982	+	0.580293i	0.00170925	+	0.0293467i
$392$	5.30820	−	3.49126i	0.268105	−	0.176335i
$393$		0			0
$394$	−19.7828	−	4.68860i	−0.996641	−	0.236208i
$395$	7.65516	+	43.4146i	0.385173	+	2.18442i
$396$		0			0
$397$	−2.12664	+	12.0608i	−0.106733	+	0.605312i	0.883781	+	0.467900i	$0.154989\pi$
$397$	−2.12664	+	12.0608i	−0.106733	+	0.605312i	−0.990514	+	0.137412i	$0.956122\pi$
$398$	−9.19005	+	21.3049i	−0.460656	+	1.06792i
$399$		0			0
$400$	−0.529171	+	1.76755i	−0.0264585	+	0.0883777i
$401$	14.2180	−	19.0981i	0.710014	−	0.953714i	−0.289981	−	0.957033i	$-0.593649\pi$
$401$	14.2180	−	19.0981i	0.710014	−	0.953714i	0.999994	+	0.00331841i	$0.00105629\pi$
$402$		0			0
$403$	−4.50615	+	2.26307i	−0.224467	+	0.112732i
$404$	6.91644			0.344106
$405$		0			0
$406$	8.09346			0.401672
$407$	−1.11229	+	0.558612i	−0.0551340	+	0.0276893i
$408$		0			0
$409$	−18.3025	+	24.5846i	−0.905002	+	1.21563i	0.0709147	+	0.997482i	$0.477408\pi$
$409$	−18.3025	+	24.5846i	−0.905002	+	1.21563i	−0.975916	+	0.218146i	$0.929999\pi$
$410$	3.77237	−	12.6006i	0.186304	−	0.622298i
$411$		0			0
$412$	4.95684	−	11.4912i	0.244206	−	0.566133i
$413$	1.01212	−	5.74001i	0.0498031	−	0.282447i
$414$		0			0
$415$	0.990595	+	5.61794i	0.0486264	+	0.275774i
$416$	0.668705	+	0.158486i	0.0327859	+	0.00777041i
$417$		0			0
$418$	0.0306063	−	0.0201301i	0.00149700	−	0.000984593i
$419$	1.12397	+	19.2978i	0.0549094	+	0.942759i	0.907466	+	0.420125i	$0.138014\pi$
$419$	1.12397	+	19.2978i	0.0549094	+	0.942759i	−0.852557	+	0.522634i	$0.824949\pi$
$420$		0			0
$421$	3.40157	+	11.3620i	0.165782	+	0.553752i	0.999997	+	0.00231247i	$0.000736082\pi$
$421$	3.40157	+	11.3620i	0.165782	+	0.553752i	−0.834215	+	0.551440i	$0.814079\pi$
$422$	−17.5738	−	6.39634i	−0.855479	−	0.311369i
$423$		0			0
$424$	6.14687	−	2.23728i	0.298519	−	0.108652i
$425$	0.0734895	+	0.0987136i	0.00356477	+	0.00478831i
$426$		0			0
$427$	−4.85087	+	1.14968i	−0.234750	+	0.0556367i
$428$	3.52043	+	8.16128i	0.170167	+	0.394490i
$429$		0			0
$430$	−7.28913	−	4.79414i	−0.351513	−	0.231194i
$431$	9.72386	−	16.8422i	0.468382	−	0.811261i	−0.530965	−	0.847394i	$-0.678171\pi$
$431$	9.72386	−	16.8422i	0.468382	−	0.811261i	0.999347	+	0.0361326i	$0.0115039\pi$
$432$		0			0
$433$	−2.82936	−	4.90059i	−0.135970	−	0.235507i	0.789997	−	0.613110i	$-0.210082\pi$
$433$	−2.82936	−	4.90059i	−0.135970	−	0.235507i	−0.925968	+	0.377603i	$0.876748\pi$
$434$	0.343058	−	5.89008i	0.0164673	−	0.282733i
$435$		0			0
$436$	−11.5439	−	1.34929i	−0.552854	−	0.0646193i
$437$	1.40848	+	1.49291i	0.0673770	+	0.0714154i
$438$		0			0
$439$	12.2169	−	1.42795i	0.583079	−	0.0681521i	0.180560	−	0.983564i	$-0.442209\pi$
$439$	12.2169	−	1.42795i	0.583079	−	0.0681521i	0.402519	+	0.915412i	$0.368135\pi$
$440$	0.311743	+	0.261583i	0.0148618	+	0.0124705i
$441$		0			0
$442$	0.0351139	−	0.0294641i	0.00167020	−	0.00140146i
$443$	7.25165	−	7.68630i	0.344536	−	0.365187i	−0.531814	−	0.846861i	$-0.678490\pi$
$443$	7.25165	−	7.68630i	0.344536	−	0.365187i	0.876351	+	0.481674i	$0.159971\pi$
$444$		0			0
$445$	−7.91324	−	3.97418i	−0.375124	−	0.188394i
$446$	−8.34068	−	4.18885i	−0.394943	−	0.198348i
$447$		0			0
$448$	−0.551810	+	0.584884i	−0.0260705	+	0.0276332i
$449$	−30.8275	+	25.8673i	−1.45484	+	1.22075i	−0.525887	+	0.850554i	$0.676267\pi$
$449$	−30.8275	+	25.8673i	−1.45484	+	1.22075i	−0.928952	+	0.370201i	$0.879289\pi$
$450$		0			0
$451$	−0.599030	−	0.502646i	−0.0282072	−	0.0236687i
$452$	12.3367	−	1.44195i	0.580267	−	0.0678235i
$453$		0			0
$454$	−14.4332	−	15.2983i	−0.677384	−	0.717985i
$455$	1.43600	+	0.167845i	0.0673209	+	0.00786869i
$456$		0			0
$457$	−2.17275	+	37.3047i	−0.101637	+	1.74504i	0.434287	+	0.900774i	$0.357000\pi$
$457$	−2.17275	+	37.3047i	−0.101637	+	1.74504i	−0.535924	+	0.844266i	$0.680037\pi$
$458$	4.51190	+	7.81484i	0.210827	+	0.365164i
$459$		0			0
$460$	−11.4003	+	19.7460i	−0.531543	+	0.920660i
$461$	31.2142	+	20.5299i	1.45379	+	0.956173i	0.997807	+	0.0661850i	$0.0210828\pi$
$461$	31.2142	+	20.5299i	1.45379	+	0.956173i	0.455983	+	0.889988i	$0.349288\pi$
$462$		0			0
$463$	9.18807	+	21.3003i	0.427006	+	0.989911i	0.986898	+	0.161345i	$0.0515833\pi$
$463$	9.18807	+	21.3003i	0.427006	+	0.989911i	−0.559892	+	0.828566i	$0.689157\pi$
$464$	9.79388	−	2.32119i	0.454670	−	0.107759i
$465$		0			0
$466$	−5.20127	−	6.98651i	−0.240944	−	0.323644i
$467$	−0.406622	+	0.147998i	−0.0188162	+	0.00684855i	−0.351411	−	0.936221i	$-0.614298\pi$
$467$	−0.406622	+	0.147998i	−0.0188162	+	0.00684855i	0.332595	+	0.943070i	$0.392076\pi$
$468$		0			0
$469$	6.29159	+	2.28995i	0.290519	+	0.105740i
$470$	9.43844	+	31.5266i	0.435363	+	1.45421i
$471$		0			0
$472$	−0.421463	−	7.23625i	−0.0193994	−	0.333075i
$473$	−0.433352	+	0.285020i	−0.0199256	+	0.0131052i
$474$		0			0
$475$	0.422825	+	0.100211i	0.0194006	+	0.00459802i
$476$	0.00931336	+	0.0528187i	0.000426877	+	0.00242094i
$477$		0			0
$478$	−4.33175	+	24.5666i	−0.198130	+	1.12365i
$479$	−5.09110	+	11.8025i	−0.232618	+	0.539270i	−0.994044	−	0.108983i	$-0.965241\pi$
$479$	−5.09110	+	11.8025i	−0.232618	+	0.539270i	0.761425	+	0.648253i	$0.224500\pi$
$480$		0			0
$481$	−1.57721	+	5.26825i	−0.0719146	+	0.240211i
$482$	11.8149	−	15.8701i	0.538153	−	0.722865i
$483$		0			0
$484$	−9.80834	+	4.92593i	−0.445834	+	0.223906i
$485$	18.9265			0.859408
$486$		0			0
$487$	8.21477			0.372247			0.186123	−	0.982526i	$-0.440408\pi$
$487$	8.21477			0.372247			0.186123	+	0.982526i	$0.440408\pi$
$488$	−5.54030	+	2.78244i	−0.250798	+	0.125955i
$489$		0			0
$490$	9.92626	−	13.3333i	0.448423	−	0.602337i
$491$	−4.27347	+	14.2744i	−0.192859	+	0.644194i	0.805789	+	0.592203i	$0.201742\pi$
$491$	−4.27347	+	14.2744i	−0.192859	+	0.644194i	−0.998648	+	0.0519904i	$0.983443\pi$
$492$		0			0
$493$	0.265906	−	0.616440i	0.0119758	−	0.0277631i
$494$	0.0281053	−	0.159393i	0.00126452	−	0.00717143i
$495$		0			0
$496$	−1.27413	−	7.22597i	−0.0572103	−	0.324456i
$497$	3.07936	+	0.729821i	0.138128	+	0.0327370i
$498$		0			0
$499$	−8.57019	+	5.63670i	−0.383654	+	0.252333i	−0.726656	−	0.687001i	$-0.758927\pi$
$499$	−8.57019	+	5.63670i	−0.383654	+	0.252333i	0.343002	+	0.939335i	$0.388556\pi$
$500$	−0.479944	−	8.24031i	−0.0214637	−	0.368518i
$501$		0			0
$502$	−4.66987	−	15.5984i	−0.208426	−	0.696192i
$503$	15.4431	+	5.62083i	0.688574	+	0.250620i	0.662524	−	0.749040i	$-0.269485\pi$
$503$	15.4431	+	5.62083i	0.688574	+	0.250620i	0.0260494	+	0.999661i	$0.491707\pi$
$504$		0			0
$505$	17.0042	−	6.18904i	0.756679	−	0.275409i
$506$	0.809473	+	1.08731i	0.0359855	+	0.0483369i
$507$		0			0
$508$	−7.56303	+	1.79247i	−0.335555	+	0.0795280i
$509$	−2.34085	−	5.42671i	−0.103757	−	0.240535i	0.858428	−	0.512935i	$-0.171442\pi$
$509$	−2.34085	−	5.42671i	−0.103757	−	0.240535i	−0.962184	+	0.272400i	$0.912183\pi$
$510$		0			0
$511$	6.73894	+	4.43227i	0.298113	+	0.196072i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$		0			0
$514$	1.05198	+	1.82208i	0.0464007	+	0.0803684i
$515$	1.90380	−	32.6870i	0.0838916	−	1.44036i
$516$		0			0
$517$	1.94328	+	0.227137i	0.0854652	+	0.00998945i
$518$	−4.41563	−	4.68030i	−0.194012	−	0.205641i
$519$		0			0
$520$	1.78584	−	0.208735i	0.0783145	−	0.00915365i
$521$	12.0595	+	10.1191i	0.528335	+	0.443325i	0.867526	−	0.497392i	$-0.165709\pi$
$521$	12.0595	+	10.1191i	0.528335	+	0.443325i	−0.339191	+	0.940717i	$0.610153\pi$
$522$		0			0
$523$	−32.0731	+	26.9125i	−1.40246	+	1.17680i	−0.442462	+	0.896787i	$0.645895\pi$
$523$	−32.0731	+	26.9125i	−1.40246	+	1.17680i	−0.959996	+	0.280015i	$0.909661\pi$
$524$	−6.44123	+	6.82731i	−0.281387	+	0.298252i
$525$		0			0
$526$	−5.29327	−	2.65838i	−0.230797	−	0.115911i
$527$	−0.437349	−	0.219645i	−0.0190512	−	0.00956787i
$528$		0			0
$529$	−36.3353	+	38.5131i	−1.57979	+	1.67448i
$530$	13.1103	−	11.0008i	0.569473	−	0.477845i
$531$		0			0
$532$	0.145072	+	0.121730i	0.00628965	+	0.00527764i
$533$	−3.43159	+	0.401096i	−0.148639	+	0.0173734i
$534$		0			0
$535$	15.9580	+	16.9145i	0.689926	+	0.731279i
$536$	8.27020	+	0.966648i	0.357218	+	0.0417528i
$537$		0			0
$538$	−0.216298	+	3.71370i	−0.00932528	+	0.160109i
$539$	−0.494119	−	0.855839i	−0.0212832	−	0.0368636i
$540$		0			0
$541$	−1.64686	+	2.85244i	−0.0708039	+	0.122636i	−0.899254	−	0.437427i	$-0.855890\pi$
$541$	−1.64686	+	2.85244i	−0.0708039	+	0.122636i	0.828450	+	0.560063i	$0.189223\pi$
$542$	−16.4658	−	10.8297i	−0.707268	−	0.465177i
$543$		0			0
$544$	0.0264184	+	0.0612448i	0.00113268	+	0.00262585i
$545$	−29.5884	+	7.01258i	−1.26743	+	0.300386i
$546$		0			0
$547$	4.94084	+	6.63669i	0.211255	+	0.283765i	0.895103	−	0.445860i	$-0.147102\pi$
$547$	4.94084	+	6.63669i	0.211255	+	0.283765i	−0.683848	+	0.729625i	$0.739695\pi$
$548$	14.4034	−	5.24243i	0.615285	−	0.223945i
$549$		0			0
$550$	0.269682	+	0.0981561i	0.0114993	+	0.00418539i
$551$	−0.679864	−	2.27091i	−0.0289632	−	0.0967438i
$552$		0			0
$553$	0.787805	+	13.5261i	0.0335009	+	0.575188i
$554$	−2.63050	+	1.73011i	−0.111759	+	0.0735052i
$555$		0			0
$556$	−3.83290	−	0.908413i	−0.162551	−	0.0385253i
$557$	−1.30921	−	7.42492i	−0.0554732	−	0.314604i	0.944427	−	0.328721i	$-0.106617\pi$
$557$	−1.30921	−	7.42492i	−0.0554732	−	0.314604i	−0.999900	+	0.0141167i	$0.995506\pi$
$558$		0			0
$559$	−0.397941	+	2.25683i	−0.0168311	+	0.0954539i
$560$	−0.833266	+	1.93173i	−0.0352119	+	0.0816304i
$561$		0			0
$562$	−6.13275	+	20.4848i	−0.258694	+	0.864099i
$563$	−17.9766	+	24.1468i	−0.757625	+	1.01767i	0.241260	+	0.970461i	$0.422439\pi$
$563$	−17.9766	+	24.1468i	−0.757625	+	1.01767i	−0.998885	+	0.0472070i	$0.984968\pi$
$564$		0			0
$565$	29.0397	−	14.5843i	1.22171	−	0.613565i
$566$	−10.8922			−0.457835
$567$		0			0
$568$	3.93564			0.165136
$569$	−31.1284	+	15.6333i	−1.30497	+	0.655381i	−0.959144	−	0.282917i	$-0.908698\pi$
$569$	−31.1284	+	15.6333i	−1.30497	+	0.655381i	−0.345827	+	0.938298i	$0.612402\pi$
$570$		0			0
$571$	3.98459	−	5.35223i	0.166750	−	0.223984i	−0.710892	−	0.703302i	$-0.751708\pi$
$571$	3.98459	−	5.35223i	0.166750	−	0.223984i	0.877642	+	0.479318i	$0.159116\pi$
$572$	0.0306577	−	0.102404i	0.00128186	−	0.00428172i
$573$		0			0
$574$	1.60116	−	3.71191i	0.0668313	−	0.154932i
$575$	−2.79216	+	15.8351i	−0.116441	+	0.660371i
$576$		0			0
$577$	−6.28429	−	35.6400i	−0.261619	−	1.48371i	−0.778494	−	0.627652i	$-0.784016\pi$
$577$	−6.28429	−	35.6400i	−0.261619	−	1.48371i	0.516875	−	0.856061i	$-0.327095\pi$
$578$	−16.5374	−	3.91944i	−0.687867	−	0.163027i
$579$		0			0
$580$	22.0014	−	14.4706i	0.913560	−	0.600858i
$581$	0.101944	+	1.75031i	0.00422934	+	0.0726149i
$582$		0			0
$583$	−0.291814	−	0.974727i	−0.0120857	−	0.0403691i
$584$	9.42595	+	3.43076i	0.390048	+	0.141966i
$585$		0			0
$586$	19.0581	−	6.93659i	0.787284	−	0.286548i
$587$	−17.3965	−	23.3675i	−0.718030	−	0.964482i	−0.999987	−	0.00505460i	$-0.998391\pi$
$587$	−17.3965	−	23.3675i	−0.718030	−	0.964482i	0.281957	−	0.959427i	$-0.409016\pi$
$588$		0			0
$589$	−1.68149	+	0.398520i	−0.0692845	+	0.0164207i
$590$	−7.51139	−	17.4134i	−0.309239	−	0.716897i
$591$		0			0
$592$	−6.68566	−	4.39723i	−0.274779	−	0.180725i
$593$	4.61527	−	7.99387i	0.189526	−	0.328269i	−0.755566	−	0.655072i	$-0.772638\pi$
$593$	4.61527	−	7.99387i	0.189526	−	0.328269i	0.945092	+	0.326803i	$0.105971\pi$
$594$		0			0
$595$	0.0701609	+	0.121522i	0.00287631	+	0.00498192i
$596$	0.0874504	−	1.50147i	0.00358211	−	0.0615024i
$597$		0			0
$598$	5.94859	+	0.695290i	0.243256	+	0.0284325i
$599$	0.807714	+	0.856127i	0.0330023	+	0.0349804i	0.743664	−	0.668553i	$-0.233086\pi$
$599$	0.807714	+	0.856127i	0.0330023	+	0.0349804i	−0.710662	+	0.703533i	$0.751605\pi$
$600$		0			0
$601$	16.3686	−	1.91321i	0.667688	−	0.0780416i	0.224506	−	0.974473i	$-0.427923\pi$
$601$	16.3686	−	1.91321i	0.667688	−	0.0780416i	0.443183	+	0.896431i	$0.353849\pi$
$602$	−2.05406	−	1.72356i	−0.0837172	−	0.0702471i
$603$		0			0
$604$	10.0110	−	8.40025i	0.407343	−	0.341801i
$605$	−19.7062	+	20.8873i	−0.801170	+	0.849190i
$606$		0			0
$607$	32.1650	+	16.1539i	1.30554	+	0.655665i	0.959275	−	0.282473i	$-0.0911548\pi$
$607$	32.1650	+	16.1539i	1.30554	+	0.655665i	0.346261	+	0.938138i	$0.387451\pi$
$608$	0.210463	+	0.105698i	0.00853539	+	0.00428664i
$609$		0			0
$610$	−11.1312	+	11.7983i	−0.450687	+	0.477700i
$611$	6.62190	−	5.55643i	0.267893	−	0.224789i
$612$		0			0
$613$	−22.8633	−	19.1846i	−0.923441	−	0.774859i	0.0511868	−	0.998689i	$-0.483700\pi$
$613$	−22.8633	−	19.1846i	−0.923441	−	0.774859i	−0.974628	+	0.223830i	$0.928144\pi$
$614$	5.26721	−	0.615648i	0.212567	−	0.0248455i
$615$		0			0
$616$	0.0858308	+	0.0909753i	0.00345822	+	0.00366550i
$617$	4.99903	+	0.584303i	0.201253	+	0.0235231i	0.216122	−	0.976366i	$-0.430659\pi$
$617$	4.99903	+	0.584303i	0.201253	+	0.0235231i	−0.0148690	+	0.999889i	$0.504733\pi$
$618$		0			0
$619$	1.28092	−	21.9925i	0.0514844	−	0.883954i	−0.869398	−	0.494113i	$-0.835493\pi$
$619$	1.28092	−	21.9925i	0.0514844	−	0.883954i	0.920882	−	0.389841i	$-0.127470\pi$
$620$	−9.59850	−	16.6251i	−0.385485	−	0.667680i
$621$		0			0
$622$	−2.12061	+	3.67301i	−0.0850288	+	0.147274i
$623$	−2.27383	−	1.49552i	−0.0910992	−	0.0599169i
$624$		0			0
$625$	−12.2076	−	28.3004i	−0.488304	−	1.13202i
$626$	4.47705	−	1.06108i	0.178939	−	0.0424093i
$627$		0			0
$628$	−12.0959	−	16.2476i	−0.482678	−	0.648349i
$629$	−0.501549	+	0.182549i	−0.0199981	+	0.00727871i
$630$		0			0
$631$	−28.2782	−	10.2924i	−1.12574	−	0.409735i	−0.288995	−	0.957331i	$-0.593321\pi$
$631$	−28.2782	−	10.2924i	−1.12574	−	0.409735i	−0.836743	+	0.547595i	$0.815543\pi$
$632$	4.83258	+	16.1420i	0.192230	+	0.642092i
$633$		0			0
$634$	−0.367420	−	6.30836i	−0.0145921	−	0.250537i
$635$	−16.9899	+	11.1745i	−0.674225	+	0.443445i
$636$		0			0
$637$	−4.24856	−	1.00693i	−0.168334	−	0.0398959i
$638$	−0.271861	−	1.54180i	−0.0107631	−	0.0610404i
$639$		0			0
$640$	−0.454317	+	2.57656i	−0.0179585	+	0.101847i
$641$	−11.6997	+	27.1229i	−0.462109	+	1.07129i	0.514737	+	0.857348i	$0.327890\pi$
$641$	−11.6997	+	27.1229i	−0.462109	+	1.07129i	−0.976846	+	0.213942i	$0.931370\pi$
$642$		0			0
$643$	1.81855	−	6.07439i	0.0717167	−	0.239550i	−0.914614	−	0.404328i	$-0.867505\pi$
$643$	1.81855	−	6.07439i	0.0717167	−	0.239550i	0.986331	+	0.164778i	$0.0526906\pi$
$644$	−4.18466	+	5.62098i	−0.164899	+	0.221498i
$645$		0			0
$646$	0.0140378	−	0.00705005i	0.000552310	−	0.000277381i
$647$	34.8610			1.37053			0.685264	−	0.728295i	$-0.259687\pi$
$647$	34.8610			1.37053			0.685264	+	0.728295i	$0.259687\pi$
$648$		0			0
$649$	−1.12746			−0.0442568
$650$	1.13311	−	0.569069i	0.0444443	−	0.0223207i
$651$		0			0
$652$	−1.10690	+	1.48682i	−0.0433495	+	0.0582285i
$653$	4.91627	−	16.4215i	0.192389	−	0.642623i	−0.806304	−	0.591502i	$-0.798535\pi$
$653$	4.91627	−	16.4215i	0.192389	−	0.642623i	0.998692	−	0.0511212i	$-0.0162795\pi$
$654$		0			0
$655$	−9.72665	+	22.5489i	−0.380052	+	0.881059i
$656$	0.872994	−	4.95099i	0.0340847	−	0.193304i
$657$		0			0
$658$	1.75634	+	9.96072i	0.0684694	+	0.388309i
$659$	24.3229	+	5.76463i	0.947484	+	0.224558i	0.675180	−	0.737653i	$-0.264066\pi$
$659$	24.3229	+	5.76463i	0.947484	+	0.224558i	0.272305	+	0.962211i	$0.412214\pi$
$660$		0			0
$661$	−0.607381	+	0.399481i	−0.0236244	+	0.0155380i	−0.561266	−	0.827635i	$-0.689686\pi$
$661$	−0.607381	+	0.399481i	−0.0236244	+	0.0155380i	0.537642	+	0.843173i	$0.319315\pi$
$662$	−0.933082	−	16.0204i	−0.0362652	−	0.622650i
$663$		0			0
$664$	0.625347	+	2.08880i	0.0242682	+	0.0810613i
$665$	0.465589	+	0.169461i	0.0180548	+	0.00657140i
$666$		0			0
$667$	82.4265	−	30.0008i	3.19156	−	1.16163i
$668$	−7.49723	−	10.0705i	−0.290077	−	0.389640i
$669$		0			0
$670$	21.1975	−	5.02390i	0.818930	−	0.194090i
$671$	0.381954	+	0.885468i	0.0147452	+	0.0341831i
$672$		0			0
$673$	−37.1257	−	24.4179i	−1.43109	−	0.941242i	−0.999227	−	0.0393018i	$-0.987487\pi$
$673$	−37.1257	−	24.4179i	−1.43109	−	0.941242i	−0.431861	−	0.901940i	$-0.642143\pi$
$674$	1.35241	−	2.34244i	0.0520928	−	0.0902274i
$675$		0			0
$676$	6.26386	+	10.8493i	0.240918	+	0.417282i
$677$	2.61091	−	44.8277i	0.100346	−	1.72287i	−0.454358	−	0.890819i	$-0.650131\pi$
$677$	2.61091	−	44.8277i	0.100346	−	1.72287i	0.554703	−	0.832048i	$-0.312832\pi$
$678$		0			0
$679$	5.77759	+	0.675304i	0.221724	+	0.0259158i
$680$	0.119754	+	0.126932i	0.00459235	+	0.00486761i
$681$		0			0
$682$	−1.13358	+	0.132497i	−0.0434070	+	0.00507355i
$683$	16.4909	+	13.8375i	0.631007	+	0.529478i	0.901242	−	0.433317i	$-0.142657\pi$
$683$	16.4909	+	13.8375i	0.631007	+	0.529478i	−0.270235	+	0.962795i	$0.587101\pi$
$684$		0			0
$685$	30.7201	−	25.7773i	1.17376	−	0.984899i
$686$	7.36854	−	7.81020i	0.281332	−	0.298195i
$687$		0			0
$688$	−2.97993	−	1.49658i	−0.113609	−	0.0570565i
$689$	−4.01725	−	2.01754i	−0.153045	−	0.0768621i
$690$		0			0
$691$	21.7759	−	23.0811i	0.828393	−	0.878045i	−0.165745	−	0.986169i	$-0.553003\pi$
$691$	21.7759	−	23.0811i	0.828393	−	0.878045i	0.994137	+	0.108124i	$0.0344842\pi$
$692$	−8.36310	+	7.01747i	−0.317917	+	0.266764i
$693$		0			0
$694$	−7.19537	−	6.03763i	−0.273132	−	0.229185i
$695$	−10.2361	+	1.19643i	−0.388279	+	0.0453833i
$696$		0			0
$697$	−0.230113	−	0.243906i	−0.00871617	−	0.00923860i
$698$	21.2946	+	2.48898i	0.806012	+	0.0942093i
$699$		0			0
$700$	−0.0862651	+	1.48111i	−0.00326051	+	0.0559809i
$701$	11.1884	+	19.3789i	0.422580	+	0.731929i	0.996191	−	0.0871983i	$-0.0277914\pi$
$701$	11.1884	+	19.3789i	0.422580	+	0.731929i	−0.573611	+	0.819128i	$0.694458\pi$
$702$		0			0
$703$	−0.942302	+	1.63212i	−0.0355396	+	0.0615564i
$704$	0.129955	+	0.0854730i	0.00489788	+	0.00322138i
$705$		0			0
$706$	2.97470	+	6.89613i	0.111954	+	0.259539i
$707$	5.41162	−	1.28258i	0.203525	−	0.0482363i
$708$		0			0
$709$	2.37201	+	3.18616i	0.0890826	+	0.119659i	0.844430	−	0.535666i	$-0.179939\pi$
$709$	2.37201	+	3.18616i	0.0890826	+	0.119659i	−0.755347	+	0.655324i	$0.772532\pi$
$710$	9.67587	−	3.52173i	0.363129	−	0.132168i
$711$		0			0
$712$	−3.18048	−	1.15760i	−0.119193	−	0.0433829i
$713$	−18.3395	−	61.2582i	−0.686820	−	2.29414i
$714$		0			0
$715$	−0.0162613	−	0.279196i	−0.000608138	−	0.0104413i
$716$	7.76876	−	5.10959i	0.290332	−	0.190954i
$717$		0			0
$718$	−19.9899	−	4.73769i	−0.746015	−	0.176809i
$719$	3.47213	+	19.6915i	0.129489	+	0.734367i	0.978540	+	0.206057i	$0.0660632\pi$
$719$	3.47213	+	19.6915i	0.129489	+	0.734367i	−0.849051	+	0.528310i	$0.822826\pi$
$720$		0			0
$721$	1.74745	−	9.91028i	0.0650784	−	0.369078i
$722$	−7.50355	+	17.3952i	−0.279253	+	0.647381i
$723$		0			0
$724$	4.31519	−	14.4137i	0.160373	−	0.535682i
$725$	11.0898	−	14.8962i	0.411865	−	0.553230i
$726$		0			0
$727$	0.370860	−	0.186253i	0.0137545	−	0.00690774i	−0.441909	−	0.897060i	$-0.645698\pi$
$727$	0.370860	−	0.186253i	0.0137545	−	0.00690774i	0.455663	+	0.890152i	$0.349402\pi$
$728$	0.552603			0.0204808
$729$		0			0
$730$	26.2439			0.971329
$731$	−0.198760	+	0.0998212i	−0.00735142	+	0.00369202i
$732$		0			0
$733$	−4.44910	+	5.97617i	−0.164331	+	0.220735i	−0.876660	−	0.481111i	$-0.840233\pi$
$733$	−4.44910	+	5.97617i	−0.164331	+	0.220735i	0.712328	+	0.701846i	$0.247641\pi$
$734$	4.45278	−	14.8733i	0.164355	−	0.548984i
$735$		0			0
$736$	−3.45177	+	8.00209i	−0.127234	+	0.294961i
$737$	0.224899	−	1.27546i	0.00828425	−	0.0469823i
$738$		0			0
$739$	−1.13092	−	6.41379i	−0.0416017	−	0.235935i	0.956916	−	0.290365i	$-0.0937768\pi$
$739$	−1.13092	−	6.41379i	−0.0416017	−	0.235935i	−0.998518	+	0.0544304i	$0.982666\pi$
$740$	−20.3716	−	4.82816i	−0.748876	−	0.177487i
$741$		0			0
$742$	4.39461	−	2.89038i	0.161331	−	0.106109i
$743$	−1.62467	−	27.8945i	−0.0596033	−	1.02335i	−0.887011	−	0.461748i	$-0.847222\pi$
$743$	−1.62467	−	27.8945i	−0.0596033	−	1.02335i	0.827408	−	0.561602i	$-0.189815\pi$
$744$		0			0
$745$	−1.12856	−	3.76964i	−0.0413471	−	0.138109i
$746$	−16.8168	−	6.12081i	−0.615706	−	0.224099i
$747$		0			0
$748$	0.00974908	−	0.00354838i	0.000356462	−	0.000129741i
$749$	4.26791	+	5.73280i	0.155946	+	0.209472i
$750$		0			0
$751$	−28.3649	+	6.72261i	−1.03505	+	0.245312i	−0.712818	−	0.701349i	$-0.752581\pi$
$751$	−28.3649	+	6.72261i	−1.03505	+	0.245312i	−0.322233	+	0.946660i	$0.604433\pi$
$752$	4.98207	+	11.5497i	0.181677	+	0.421176i
$753$		0			0
$754$	−5.77914	−	3.80100i	−0.210464	−	0.138424i
$755$	17.0956	−	29.6104i	0.622171	−	1.07763i
$756$		0			0
$757$	−26.9567	−	46.6904i	−0.979758	−	1.69699i	−0.663246	−	0.748401i	$-0.730822\pi$
$757$	−26.9567	−	46.6904i	−0.979758	−	1.69699i	−0.316511	−	0.948589i	$-0.602512\pi$
$758$	−0.267458	+	4.59208i	−0.00971453	+	0.166792i
$759$		0			0
$760$	0.612010	+	0.0715337i	0.0221999	+	0.00259480i
$761$	−13.9480	−	14.7840i	−0.505614	−	0.535920i	0.423410	−	0.905938i	$-0.360833\pi$
$761$	−13.9480	−	14.7840i	−0.505614	−	0.535920i	−0.929025	+	0.370018i	$0.879351\pi$
$762$		0			0
$763$	−9.28251	+	1.08497i	−0.336049	+	0.0392786i
$764$	5.71980	+	4.79948i	0.206935	+	0.173639i
$765$		0			0
$766$	−19.7213	+	16.5482i	−0.712561	+	0.597910i
$767$	−3.41843	+	3.62333i	−0.123433	+	0.130831i
$768$		0			0
$769$	35.7884	+	17.9736i	1.29056	+	0.648145i	0.955761	−	0.294144i	$-0.0950346\pi$
$769$	35.7884	+	17.9736i	1.29056	+	0.648145i	0.334801	+	0.942289i	$0.391331\pi$
$770$	0.292425	+	0.146861i	0.0105383	+	0.00529251i
$771$		0			0
$772$	−8.52645	+	9.03751i	−0.306874	+	0.325267i
$773$	15.5681	−	13.0632i	0.559945	−	0.469850i	−0.318347	−	0.947974i	$-0.603128\pi$
$773$	15.5681	−	13.0632i	0.559945	−	0.469850i	0.878292	+	0.478124i	$0.158683\pi$
$774$		0			0
$775$	−10.3708	−	8.70210i	−0.372529	−	0.312589i
$776$	7.18513	−	0.839822i	0.257931	−	0.0301478i
$777$		0			0
$778$	−5.27485	−	5.59101i	−0.189112	−	0.200447i
$779$	−1.17601	−	0.137456i	−0.0421349	−	0.00492486i
$780$		0			0
$781$	0.0355943	−	0.611130i	0.00127366	−	0.0218680i
$782$	0.290638	+	0.503400i	0.0103932	+	0.0180016i
$783$		0			0
$784$	3.17671	−	5.50222i	0.113454	−	0.196508i
$785$	−44.2768	−	29.1213i	−1.58031	−	1.03938i
$786$		0			0
$787$	−3.04443	−	7.05779i	−0.108522	−	0.251583i	0.855298	−	0.518137i	$-0.173374\pi$
$787$	−3.04443	−	7.05779i	−0.108522	−	0.251583i	−0.963820	+	0.266554i	$0.914115\pi$
$788$	−19.7828	+	4.68860i	−0.704731	+	0.167024i
$789$		0			0
$790$	26.3253	+	35.3611i	0.936613	+	1.25809i
$791$	9.38516	−	3.41592i	0.333698	−	0.121456i
$792$		0			0
$793$	4.00370	+	1.45723i	0.142176	+	0.0517477i
$794$	3.51243	+	11.7323i	0.124651	+	0.416365i
$795$		0			0
$796$	1.34911	+	23.1633i	0.0478178	+	0.821000i
$797$	30.6284	−	20.1446i	1.08492	−	0.713560i	0.124525	−	0.992217i	$-0.460259\pi$
$797$	30.6284	−	20.1446i	1.08492	−	0.713560i	0.960391	+	0.278656i	$0.0898891\pi$
$798$		0			0
$799$	0.816365	+	0.193482i	0.0288809	+	0.00684490i
$800$	0.320392	+	1.81703i	0.0113276	+	0.0642419i
$801$		0			0
$802$	4.13447	−	23.4477i	0.145993	−	0.827968i
$803$	0.617982	−	1.43264i	0.0218081	−	0.0505569i
$804$		0			0
$805$	−5.25828	+	17.5639i	−0.185330	+	0.619045i
$806$	−3.01117	+	4.04471i	−0.106064	+	0.142469i
$807$		0			0
$808$	6.18076	−	3.10409i	0.217438	−	0.109202i
$809$	−32.5645			−1.14491			−0.572454	−	0.819937i	$-0.694008\pi$
$809$	−32.5645			−1.14491			−0.572454	+	0.819937i	$0.694008\pi$
$810$		0			0
$811$	36.0860			1.26715			0.633575	−	0.773681i	$-0.281587\pi$
$811$	36.0860			1.26715			0.633575	+	0.773681i	$0.281587\pi$
$812$	7.23258	−	3.63234i	0.253814	−	0.127470i
$813$		0			0
$814$	−0.743272	+	0.998387i	−0.0260517	+	0.0349934i
$815$	−1.39089	+	4.64588i	−0.0487206	+	0.162738i
$816$		0			0
$817$	−0.311061	+	0.721121i	−0.0108827	+	0.0252288i
$818$	−5.32220	+	30.1837i	−0.186086	+	1.05535i
$819$		0			0
$820$	−2.28402	−	12.9533i	−0.0797614	−	0.452350i
$821$	28.4772	+	6.74923i	0.993862	+	0.235550i	0.695206	−	0.718811i	$-0.255313\pi$
$821$	28.4772	+	6.74923i	0.993862	+	0.235550i	0.298657	+	0.954361i	$0.403461\pi$
$822$		0			0
$823$	25.8934	−	17.0304i	0.902588	−	0.593642i	−0.0111532	−	0.999938i	$-0.503550\pi$
$823$	25.8934	−	17.0304i	0.902588	−	0.593642i	0.913741	+	0.406296i	$0.133180\pi$
$824$	−0.727668	−	12.4936i	−0.0253495	−	0.435234i
$825$		0			0
$826$	−1.67165	−	5.58369i	−0.0581641	−	0.194282i
$827$	7.43214	+	2.70508i	0.258441	+	0.0940647i	0.467991	−	0.883733i	$-0.344978\pi$
$827$	7.43214	+	2.70508i	0.258441	+	0.0940647i	−0.209551	+	0.977798i	$0.567200\pi$
$828$		0			0
$829$	44.4988	−	16.1962i	1.54551	−	0.562518i	0.578148	−	0.815932i	$-0.303775\pi$
$829$	44.4988	−	16.1962i	1.54551	−	0.562518i	0.967358	+	0.253413i	$0.0815532\pi$
$830$	3.40656	+	4.57580i	0.118243	+	0.158828i
$831$		0			0
$832$	0.668705	−	0.158486i	0.0231832	−	0.00549451i
$833$	−0.167847	−	0.389113i	−0.00581556	−	0.0134820i
$834$		0			0
$835$	−27.4435	−	18.0499i	−0.949723	−	0.624643i
$836$	0.0183164	−	0.0317249i	0.000633486	−	0.00109723i
$837$		0			0
$838$	9.66525	+	16.7407i	0.333880	+	0.578298i
$839$	−1.14559	+	19.6690i	−0.0395502	+	0.679050i	0.919023	+	0.394204i	$0.128980\pi$
$839$	−1.14559	+	19.6690i	−0.0395502	+	0.679050i	−0.958573	+	0.284846i	$0.908057\pi$
$840$		0			0
$841$	−71.8191	−	8.39445i	−2.47652	−	0.289464i
$842$	8.13903	+	8.62687i	0.280490	+	0.297302i
$843$		0			0
$844$	−18.5752	+	2.17113i	−0.639385	+	0.0747333i
$845$	25.1081	+	21.0682i	0.863747	+	0.724769i
$846$		0			0
$847$	−6.76087	+	5.67304i	−0.232306	+	0.194928i
$848$	4.48896	−	4.75802i	0.154151	−	0.163391i
$849$		0			0
$850$	0.109975	+	0.0552316i	0.00377212	+	0.00189443i
$851$	−62.3192	−	31.2979i	−2.13627	−	1.07288i
$852$		0			0
$853$	−38.5735	+	40.8855i	−1.32073	+	1.39989i	−0.462510	+	0.886614i	$0.653051\pi$
$853$	−38.5735	+	40.8855i	−1.32073	+	1.39989i	−0.858221	+	0.513280i	$0.828430\pi$
$854$	−3.81892	+	3.20445i	−0.130681	+	0.109654i
$855$		0			0
$856$	6.80875	+	5.71322i	0.232718	+	0.195274i
$857$	−11.5778	+	1.35325i	−0.395491	+	0.0462262i	−0.311514	−	0.950242i	$-0.600836\pi$
$857$	−11.5778	+	1.35325i	−0.395491	+	0.0462262i	−0.0839765	+	0.996468i	$0.526762\pi$
$858$		0			0
$859$	28.7098	+	30.4306i	0.979567	+	1.03828i	0.999260	+	0.0384741i	$0.0122497\pi$
$859$	28.7098	+	30.4306i	0.979567	+	1.03828i	−0.0196927	+	0.999806i	$0.506269\pi$
$860$	−8.66541	−	1.01284i	−0.295488	−	0.0345376i
$861$		0			0
$862$	1.13078	−	19.4148i	0.0385147	−	0.661271i
$863$	3.21464	+	5.56792i	0.109428	+	0.189534i	0.915539	−	0.402230i	$-0.131765\pi$
$863$	3.21464	+	5.56792i	0.109428	+	0.189534i	−0.806111	+	0.591765i	$0.798432\pi$
$864$		0			0
$865$	−14.2814	+	24.7362i	−0.485584	+	0.841055i
$866$	−4.72779	−	3.10951i	−0.160657	−	0.105666i
$867$		0			0
$868$	−2.33690	−	5.41754i	−0.0793194	−	0.183883i
$869$	2.55025	−	0.604420i	0.0865112	−	0.0205035i
$870$		0			0
$871$	−3.41707	−	4.58992i	−0.115783	−	0.155524i
$872$	−10.9216	+	3.97513i	−0.369852	+	0.134615i
$873$		0			0
$874$	1.92868	+	0.701983i	0.0652387	+	0.0237449i
$875$	−1.90360	−	6.35846i	−0.0643534	−	0.214955i
$876$		0			0
$877$	−0.661751	−	11.3618i	−0.0223457	−	0.383662i	−0.990877	−	0.134770i	$-0.956971\pi$
$877$	−0.661751	−	11.3618i	−0.0223457	−	0.383662i	0.968531	−	0.248892i	$-0.0800665\pi$
$878$	10.2765	−	6.75897i	0.346816	−	0.228104i
$879$		0			0
$880$	0.395982	+	0.0938495i	0.0133486	+	0.00316367i
$881$	−9.19564	−	52.1511i	−0.309809	−	1.75701i	−0.599957	−	0.800032i	$-0.704816\pi$
$881$	−9.19564	−	52.1511i	−0.309809	−	1.75701i	0.290148	−	0.956982i	$-0.406295\pi$
$882$		0			0
$883$	−5.69410	+	32.2928i	−0.191622	+	1.08674i	0.725526	+	0.688194i	$0.241596\pi$
$883$	−5.69410	+	32.2928i	−0.191622	+	1.08674i	−0.917148	+	0.398546i	$0.869515\pi$
$884$	0.0181555	−	0.0420892i	0.000610635	−	0.00141561i
$885$		0			0
$886$	3.03071	−	10.1233i	0.101819	−	0.340098i
$887$	18.9305	−	25.4280i	0.635623	−	0.853789i	−0.361278	−	0.932458i	$-0.617659\pi$
$887$	18.9305	−	25.4280i	0.635623	−	0.853789i	0.996901	+	0.0786686i	$0.0250669\pi$
$888$		0			0
$889$	−5.58514	+	2.80496i	−0.187320	+	0.0940754i
$890$	−8.85514			−0.296825
$891$		0			0
$892$	−9.33346			−0.312507
$893$	2.64730	−	1.32952i	0.0885884	−	0.0444908i
$894$		0			0
$895$	14.5275	−	19.5138i	0.485600	−	0.652274i
$896$	−0.230620	+	0.770323i	−0.00770446	+	0.0257347i
$897$		0			0
$898$	−15.9392	+	36.9512i	−0.531898	+	1.23308i
$899$	−12.8244	+	72.7308i	−0.427718	+	2.42571i
$900$		0			0
$901$	−0.0757640	−	0.429679i	−0.00252406	−	0.0143147i
$902$	−0.760900	−	0.180337i	−0.0253352	−	0.00600455i
$903$		0			0
$904$	10.3773	−	6.82525i	0.345144	−	0.227005i
$905$	−2.28884	−	39.2979i	−0.0760837	−	1.30631i
$906$		0			0
$907$	11.9961	+	40.0697i	0.398324	+	1.33049i	0.888503	+	0.458872i	$0.151746\pi$
$907$	11.9961	+	40.0697i	0.398324	+	1.33049i	−0.490179	+	0.871622i	$0.663069\pi$
$908$	−19.7638	−	7.19345i	−0.655886	−	0.238723i
$909$		0			0
$910$	1.35859	−	0.494486i	0.0450368	−	0.0163921i
$911$	17.5501	+	23.5738i	0.581460	+	0.781036i	0.991370	−	0.131090i	$-0.0418476\pi$
$911$	17.5501	+	23.5738i	0.581460	+	0.781036i	−0.409911	+	0.912126i	$0.634440\pi$
$912$		0			0
$913$	0.330008	−	0.0782132i	0.0109217	−	0.00258848i
$914$	14.8007	+	34.3118i	0.489563	+	1.13493i
$915$		0			0
$916$	7.53928	+	4.95866i	0.249105	+	0.163839i
$917$	−3.77376	+	6.53634i	−0.124620	+	0.215849i
$918$		0			0
$919$	−5.37872	−	9.31622i	−0.177428	−	0.307314i	0.763571	−	0.645724i	$-0.223444\pi$
$919$	−5.37872	−	9.31622i	−0.177428	−	0.307314i	−0.940999	+	0.338410i	$0.890111\pi$
$920$	−1.32574	+	22.7621i	−0.0437084	+	0.750444i
$921$		0			0
$922$	37.1078	+	4.33729i	1.22208	+	0.142841i
$923$	−1.85607	−	1.96732i	−0.0610932	−	0.0647550i
$924$		0			0
$925$	−14.6646	+	1.71404i	−0.482168	+	0.0563574i
$926$	17.7703	+	14.9111i	0.583970	+	0.490009i
$927$		0			0
$928$	7.71038	−	6.46978i	0.253106	−	0.212381i
$929$	1.32318	−	1.40249i	0.0434121	−	0.0460141i	−0.705304	−	0.708905i	$-0.749189\pi$
$929$	1.32318	−	1.40249i	0.0434121	−	0.0460141i	0.748716	+	0.662891i	$0.230671\pi$
$930$		0			0
$931$	−1.33716	−	0.671546i	−0.0438236	−	0.0220090i
$932$	−7.78356	−	3.90905i	−0.254959	−	0.128045i
$933$		0			0
$934$	−0.296949	+	0.314748i	−0.00971647	+	0.0102989i
$935$	0.0207932	−	0.0174475i	0.000680009	−	0.000570596i
$936$		0			0
$937$	−24.5880	−	20.6318i	−0.803255	−	0.674011i	0.145732	−	0.989324i	$-0.453446\pi$
$937$	−24.5880	−	20.6318i	−0.803255	−	0.674011i	−0.948988	+	0.315313i	$0.897891\pi$
$938$	6.65010	−	0.777286i	0.217134	−	0.0253793i
$939$		0			0
$940$	22.5836	+	23.9372i	0.736596	+	0.780746i
$941$	−31.3900	−	3.66897i	−1.02328	−	0.119605i	−0.412137	−	0.911122i	$-0.635218\pi$
$941$	−31.3900	−	3.66897i	−1.02328	−	0.119605i	−0.611147	+	0.791517i	$0.709292\pi$
$942$		0			0
$943$	2.54748	−	43.7385i	0.0829574	−	1.42432i
$944$	−3.62426	−	6.27739i	−0.117959	−	0.204312i
$945$		0			0
$946$	−0.259341	+	0.449191i	−0.00843190	+	0.0146045i
$947$	−23.3956	−	15.3875i	−0.760256	−	0.500028i	0.109211	−	0.994019i	$-0.465167\pi$
$947$	−23.3956	−	15.3875i	−0.760256	−	0.500028i	−0.869467	+	0.493990i	$0.835538\pi$
$948$		0			0
$949$	−2.73038	−	6.32973i	−0.0886319	−	0.205472i
$950$	0.422825	−	0.100211i	0.0137183	−	0.00325129i
$951$		0			0
$952$	0.0320277	+	0.0430207i	0.00103802	+	0.00139431i
$953$	20.1844	−	7.34651i	0.653836	−	0.237977i	0.00626309	−	0.999980i	$-0.498006\pi$
$953$	20.1844	−	7.34651i	0.653836	−	0.237977i	0.647573	+	0.762004i	$0.275784\pi$
$954$		0			0
$955$	18.3570	+	6.68140i	0.594018	+	0.216205i
$956$	7.15447	+	23.8976i	0.231392	+	0.772903i
$957$		0			0
$958$	0.747378	+	12.8320i	0.0241467	+	0.414583i
$959$	10.2975	−	6.77279i	0.332524	−	0.218705i
$960$		0			0
$961$	22.2225	+	5.26682i	0.716854	+	0.169897i
$962$	0.954939	+	5.41573i	0.0307885	+	0.174610i
$963$		0			0
$964$	3.43566	−	19.4846i	0.110655	−	0.627556i
$965$	−12.8755	+	29.8487i	−0.414476	+	0.960863i
$966$		0			0
$967$	−11.4223	+	38.1531i	−0.367316	+	1.22692i	0.552148	+	0.833746i	$0.313808\pi$
$967$	−11.4223	+	38.1531i	−0.367316	+	1.22692i	−0.919464	+	0.393174i	$0.871377\pi$
$968$	−6.55430	+	8.80395i	−0.210663	+	0.282970i
$969$		0			0
$970$	16.9133	−	8.49419i	0.543054	−	0.272732i
$971$	33.1226			1.06295			0.531477	−	0.847073i	$-0.321637\pi$
$971$	33.1226			1.06295			0.531477	+	0.847073i	$0.321637\pi$
$972$		0			0
$973$	−3.16743			−0.101543
$974$	7.34099	−	3.68678i	0.235220	−	0.118132i
$975$		0			0
$976$	−3.70223	+	4.97296i	−0.118506	+	0.159181i
$977$	−15.6736	+	52.3535i	−0.501444	+	1.67494i	0.214455	+	0.976734i	$0.431203\pi$
$977$	−15.6736	+	52.3535i	−0.501444	+	1.67494i	−0.715898	+	0.698204i	$0.753983\pi$
$978$		0			0
$979$	−0.208518	+	0.483399i	−0.00666426	+	0.0154495i
$980$	2.88647	−	16.3700i	0.0922048	−	0.522919i
$981$		0			0
$982$	2.58742	+	14.6740i	0.0825678	+	0.468265i
$983$	21.2682	+	5.04066i	0.678351	+	0.160772i	0.555328	−	0.831632i	$-0.312593\pi$
$983$	21.2682	+	5.04066i	0.678351	+	0.160772i	0.123023	+	0.992404i	$0.460741\pi$
$984$		0			0
$985$	−44.4409	+	29.2292i	−1.41600	+	0.931321i
$986$	−0.0390353	−	0.670210i	−0.00124314	−	0.0213438i
$987$		0			0
$988$	−0.0464196	−	0.155052i	−0.00147681	−	0.00493287i
$989$	−27.3081	−	9.93934i	−0.868347	−	0.316053i
$990$		0			0
$991$	−40.5755	+	14.7683i	−1.28892	+	0.469130i	−0.893374	−	0.449315i	$-0.851668\pi$
$991$	−40.5755	+	14.7683i	−1.28892	+	0.469130i	−0.395550	+	0.918444i	$0.629446\pi$
$992$	−4.38162	−	5.88553i	−0.139116	−	0.186866i
$993$		0			0
$994$	3.07936	−	0.729821i	0.0976713	−	0.0231485i
$995$	24.0440	+	55.7403i	0.762246	+	1.76708i
$996$		0			0
$997$	4.06161	+	2.67136i	0.128633	+	0.0846029i	0.612195	−	0.790707i	$-0.290287\pi$
$997$	4.06161	+	2.67136i	0.128633	+	0.0846029i	−0.483562	+	0.875310i	$0.660657\pi$
$998$	−5.12885	+	8.88343i	−0.162351	+	0.281200i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.g.a.73.4		72
3.2	odd	2		162.2.g.a.25.3	yes	72
81.13	even	27	inner	486.2.g.a.253.4		72
81.68	odd	54		162.2.g.a.13.3	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.13.3	✓	72	81.68	odd	54
162.2.g.a.25.3	yes	72	3.2	odd	2
486.2.g.a.73.4		72	1.1	even	1	trivial
486.2.g.a.253.4		72	81.13	even	27	inner

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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.893633 - 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(0.750365 - 2.50640i) q^{5} +(0.318489 - 0.738341i) q^{7} +(0.173648 - 0.984808i) q^{8} +O(q^{10})\)	\(q+(0.893633 - 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(0.750365 - 2.50640i) q^{5} +(0.318489 - 0.738341i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-0.454317 - 2.57656i) q^{10} +(-0.151352 - 0.0358710i) q^{11} +(-0.574171 + 0.377638i) q^{13} +(-0.0467545 - 0.802743i) q^{14} +(-0.286803 - 0.957990i) q^{16} +(-0.0626772 - 0.0228126i) q^{17} +(-0.221311 + 0.0805504i) q^{19} +(-1.56235 - 2.09860i) q^{20} +(-0.151352 + 0.0358710i) q^{22} +(-3.45177 - 8.00209i) q^{23} +(-1.54153 - 1.01388i) q^{25} +(-0.343614 + 0.595158i) q^{26} +(-0.402052 - 0.696374i) q^{28} +(-0.585239 + 10.0482i) q^{29} +(7.28783 + 0.851825i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-0.0662487 + 0.00774336i) q^{34} +(-1.61159 - 1.35229i) q^{35} +(6.12996 - 5.14365i) q^{37} +(-0.161619 + 0.171306i) q^{38} +(-2.33802 - 1.17420i) q^{40} +(4.49262 + 2.25628i) q^{41} +(2.28836 - 2.42552i) q^{43} +(-0.119154 + 0.0999819i) q^{44} +(-6.67595 - 5.60178i) q^{46} +(-12.4934 + 1.46027i) q^{47} +(4.35998 + 4.62131i) q^{49} +(-1.83259 - 0.214199i) q^{50} +(-0.0399588 + 0.686066i) q^{52} +(3.27068 + 5.66499i) q^{53} +(-0.203476 + 0.352430i) q^{55} +(-0.671819 - 0.441862i) q^{56} +(3.98662 + 9.24202i) q^{58} +(7.05313 - 1.67162i) q^{59} +(-3.70223 - 4.97296i) q^{61} +(6.89494 - 2.50955i) q^{62} +(-0.939693 - 0.342020i) q^{64} +(0.515673 + 1.72247i) q^{65} +(0.484143 + 8.31242i) q^{67} +(-0.0557268 + 0.0366521i) q^{68} +(-2.04708 - 0.485166i) q^{70} +(0.683417 + 3.87585i) q^{71} +(-1.74184 + 9.87849i) q^{73} +(3.16947 - 7.34766i) q^{74} +(-0.0675461 + 0.225620i) q^{76} +(-0.0746888 + 0.100325i) q^{77} +(-15.0576 + 7.56219i) q^{79} -2.61631 q^{80} +5.02737 q^{82} +(-1.94848 + 0.978564i) q^{83} +(-0.104208 + 0.139976i) q^{85} +(0.956381 - 3.19454i) q^{86} +(-0.0616079 + 0.142823i) q^{88} +(0.587729 - 3.33317i) q^{89} +(0.0959586 + 0.544208i) q^{91} +(-8.47992 - 2.00978i) q^{92} +(-10.5091 + 6.91197i) q^{94} +(0.0358275 + 0.615134i) q^{95} +(2.07475 + 6.93014i) q^{97} +(5.97026 + 2.17300i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 18 q^{13} + 9 q^{20} + 81 q^{23} + 18 q^{25} + 27 q^{26} + 18 q^{28} + 27 q^{29} - 54 q^{31} + 27 q^{35} - 9 q^{38} + 9 q^{41} + 36 q^{43} - 18 q^{46} + 27 q^{47} - 36 q^{52} + 27 q^{53} + 54 q^{55} + 9 q^{58} + 18 q^{59} - 9 q^{65} - 135 q^{67} + 18 q^{68} + 18 q^{70} - 72 q^{71} + 36 q^{73} - 99 q^{74} - 9 q^{76} - 144 q^{77} - 9 q^{79} - 18 q^{80} - 72 q^{82} - 99 q^{83} + 9 q^{85} - 72 q^{86} - 9 q^{88} - 126 q^{89} + 63 q^{91} - 36 q^{92} + 18 q^{94} - 45 q^{95} - 171 q^{97} - 36 q^{98}+O(q^{100}) \) 72 * q + 18 * q^13 + 9 * q^20 + 81 * q^23 + 18 * q^25 + 27 * q^26 + 18 * q^28 + 27 * q^29 - 54 * q^31 + 27 * q^35 - 9 * q^38 + 9 * q^41 + 36 * q^43 - 18 * q^46 + 27 * q^47 - 36 * q^52 + 27 * q^53 + 54 * q^55 + 9 * q^58 + 18 * q^59 - 9 * q^65 - 135 * q^67 + 18 * q^68 + 18 * q^70 - 72 * q^71 + 36 * q^73 - 99 * q^74 - 9 * q^76 - 144 * q^77 - 9 * q^79 - 18 * q^80 - 72 * q^82 - 99 * q^83 + 9 * q^85 - 72 * q^86 - 9 * q^88 - 126 * q^89 + 63 * q^91 - 36 * q^92 + 18 * q^94 - 45 * q^95 - 171 * q^97 - 36 * q^98

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