LMFDB - Embedded newform 486.2.g.a.253.4

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			253.4
Character	$\chi$	$=$	486.253
Dual form			486.2.g.a.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$245$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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	0.944732	+	0.327845i	$0.106322\pi$
$5$	0.750365	+	2.50640i	0.335574	+	1.12089i	−0.609158	+	0.793049i	$0.708492\pi$
$6$		0			0
$7$	0.318489	+	0.738341i	0.120378	+	0.279067i	0.967741	−	0.251947i	$-0.0810707\pi$
$7$	0.318489	+	0.738341i	0.120378	+	0.279067i	−0.847364	+	0.531013i	$0.821811\pi$
$8$	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	−0.253370	−	0.967370i	$-0.581539\pi$
$11$	−0.151352	+	0.0358710i	−0.0456342	+	0.0108155i	0.207735	+	0.978185i	$0.433391\pi$
$12$		0			0
$13$	−0.574171	−	0.377638i	−0.159246	−	0.104738i	0.467385	−	0.884054i	$-0.345196\pi$
$13$	−0.574171	−	0.377638i	−0.159246	−	0.104738i	−0.626631	+	0.779316i	$0.715567\pi$
$14$	−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	−0.349610	−	0.936895i	$-0.613686\pi$
$17$	−0.0626772	+	0.0228126i	−0.0152015	+	0.00553288i	0.334408	+	0.942428i	$0.391464\pi$
$18$		0			0
$19$	−0.221311	−	0.0805504i	−0.0507721	−	0.0184795i	0.316509	−	0.948589i	$-0.397489\pi$
$19$	−0.221311	−	0.0805504i	−0.0507721	−	0.0184795i	−0.367281	+	0.930110i	$0.619711\pi$
$20$	−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	0.0236702	+	0.999720i	$0.492465\pi$
$23$	−3.45177	+	8.00209i	−0.719743	+	1.66855i	−0.743413	+	0.668832i	$0.766794\pi$
$24$		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	−0.409622	−	0.912255i	$-0.634339\pi$
$29$	−0.585239	−	10.0482i	−0.108676	−	1.86590i	0.300946	−	0.953641i	$-0.402698\pi$
$30$		0			0
$31$	7.28783	−	0.851825i	1.30893	−	0.152992i	0.567140	−	0.823621i	$-0.308050\pi$
$31$	7.28783	−	0.851825i	1.30893	−	0.152992i	0.741793	+	0.670629i	$0.233976\pi$
$32$	−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	0.988040	−	0.154195i	$-0.0492783\pi$
$37$	6.12996	+	5.14365i	1.00776	+	0.845611i	0.0197193	+	0.999806i	$0.493723\pi$
$38$	−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	−0.0619553	−	0.998079i	$-0.519734\pi$
$41$	4.49262	−	2.25628i	0.701630	−	0.352372i	0.763585	+	0.645707i	$0.223437\pi$
$42$		0			0
$43$	2.28836	+	2.42552i	0.348971	+	0.369888i	0.877954	−	0.478744i	$-0.158908\pi$
$43$	2.28836	+	2.42552i	0.348971	+	0.369888i	−0.528983	+	0.848632i	$0.677426\pi$
$44$	−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	−0.864968	−	0.501827i	$-0.832662\pi$
$47$	−12.4934	−	1.46027i	−1.82235	−	0.213002i	−0.957382	+	0.288824i	$0.906736\pi$
$48$		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	−0.549075	−	0.835773i	$-0.685020\pi$
$53$	3.27068	−	5.66499i	0.449263	−	0.778146i	0.998338	+	0.0576268i	$0.0183533\pi$
$54$		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	0.662450	−	0.749106i	$-0.269517\pi$
$59$	7.05313	+	1.67162i	0.918239	+	0.217627i	0.255789	+	0.966733i	$0.417665\pi$
$60$		0			0
$61$	−3.70223	+	4.97296i	−0.474023	+	0.636723i	−0.973250	−	0.229748i	$-0.926210\pi$
$61$	−3.70223	+	4.97296i	−0.474023	+	0.636723i	0.499228	+	0.866471i	$0.333617\pi$
$62$	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	−0.829959	−	0.557824i	$-0.811636\pi$
$67$	0.484143	−	8.31242i	0.0591475	−	1.01552i	0.889107	−	0.457700i	$-0.151326\pi$
$68$	−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	−0.917022	−	0.398836i	$-0.869414\pi$
$71$	0.683417	−	3.87585i	0.0811066	−	0.459979i	0.998129	−	0.0611428i	$-0.0194745\pi$
$72$		0			0
$73$	−1.74184	−	9.87849i	−0.203867	−	1.15619i	−0.899212	−	0.437513i	$-0.855859\pi$
$73$	−1.74184	−	9.87849i	−0.203867	−	1.15619i	0.695344	−	0.718677i	$-0.255252\pi$
$74$	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	−0.990058	−	0.140661i	$-0.955077\pi$
$79$	−15.0576	−	7.56219i	−1.69411	−	0.850812i	−0.704049	−	0.710151i	$-0.748627\pi$
$80$	−2.61631			−0.292512
$81$		0			0
$82$	5.02737			0.555180
$83$	−1.94848	−	0.978564i	−0.213874	−	0.107411i	0.338637	−	0.940917i	$-0.390034\pi$
$83$	−1.94848	−	0.978564i	−0.213874	−	0.107411i	−0.552511	+	0.833506i	$0.686330\pi$
$84$		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	0.999983	+	0.00582641i	$0.00185461\pi$
$89$	0.587729	+	3.33317i	0.0622991	+	0.353316i	−0.937684	+	0.347489i	$0.887034\pi$
$90$		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	−0.785717	−	0.618586i	$-0.787706\pi$
$97$	2.07475	−	6.93014i	0.210659	−	0.703649i	0.996376	−	0.0850629i	$-0.0271091\pi$
$98$	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	−0.547653	−	0.836706i	$-0.684478\pi$
$101$	4.13021	−	5.54784i	0.410971	−	0.552030i	0.958624	+	0.284676i	$0.0918858\pi$
$102$		0			0
$103$	12.1774	+	2.88610i	1.19988	+	0.284376i	0.781504	−	0.623900i	$-0.214453\pi$
$103$	12.1774	+	2.88610i	1.19988	+	0.284376i	0.418372	+	0.908276i	$0.362601\pi$
$104$	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	0.567213	−	0.823571i	$-0.308022\pi$
$107$	−4.44410	−	7.69740i	−0.429627	−	0.744136i	−0.996840	+	0.0794354i	$0.974688\pi$
$108$		0			0
$109$	−5.81125	+	10.0654i	−0.556617	+	0.964089i	0.441158	+	0.897429i	$0.354568\pi$
$109$	−5.81125	+	10.0654i	−0.556617	+	0.964089i	−0.997776	+	0.0666601i	$0.978766\pi$
$110$	−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	−0.189420	−	0.981896i	$-0.560661\pi$
$113$	8.52356	−	9.03445i	0.801829	−	0.849889i	0.991249	+	0.132007i	$0.0421422\pi$
$114$		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	−0.867528	−	0.497388i	$-0.834293\pi$
$127$	−5.95411	+	4.99609i	−0.528342	+	0.443331i	0.339187	+	0.940719i	$0.389848\pi$
$128$	−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	−0.513152	−	0.858298i	$-0.671522\pi$
$131$	−9.32278	+	1.08968i	−0.814535	+	0.0952055i	−0.301383	+	0.953503i	$0.597448\pi$
$132$		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	0.131721	−	0.991287i	$-0.457950\pi$
$137$	12.8062	−	8.42278i	1.09411	−	0.719606i	0.962388	+	0.271680i	$0.0875793\pi$
$138$		0			0
$139$	−1.56019	+	3.61692i	−0.132333	+	0.306783i	−0.971480	−	0.237122i	$-0.923796\pi$
$139$	−1.56019	+	3.61692i	−0.132333	+	0.306783i	0.839146	+	0.543906i	$0.183055\pi$
$140$	−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	0.599937	−	0.800047i	$-0.295192\pi$
$149$	1.25658	+	0.826467i	0.102943	+	0.0677068i	−0.496994	+	0.867754i	$0.665563\pi$
$150$		0			0
$151$	12.7162	−	3.01380i	1.03483	−	0.245259i	0.322106	−	0.946704i	$-0.395609\pi$
$151$	12.7162	−	3.01380i	1.03483	−	0.245259i	0.712724	+	0.701444i	$0.247461\pi$
$152$	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	0.795869	+	0.605469i	$0.207014\pi$
$157$	5.80940	+	19.4048i	0.463641	+	1.54867i	−0.332228	+	0.943199i	$0.607800\pi$
$158$	−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	0.976688	+	0.214662i	$0.0688650\pi$
$167$	3.60077	+	12.0274i	0.278636	+	0.930709i	−0.698053	+	0.716047i	$0.745950\pi$
$168$		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	−0.613643	−	0.789584i	$-0.710297\pi$
$173$	−10.6230	+	2.51769i	−0.807650	+	0.191416i	−0.194007	+	0.981000i	$0.562148\pi$
$174$		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	0.00583785	−	0.999983i	$-0.498142\pi$
$179$	8.73770	−	3.18026i	0.653087	−	0.237704i	0.647249	+	0.762279i	$0.275920\pi$
$180$		0			0
$181$	14.1384	+	5.14597i	1.05090	+	0.382497i	0.809003	−	0.587804i	$-0.200007\pi$
$181$	14.1384	+	5.14597i	1.05090	+	0.382497i	0.241899	+	0.970301i	$0.422230\pi$
$182$	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	−0.976901	−	0.213694i	$-0.931450\pi$
$191$	−0.434148	−	7.45404i	−0.0314139	−	0.539355i	0.945487	−	0.325661i	$-0.105587\pi$
$192$		0			0
$193$	−12.3408	+	1.44244i	−0.888313	+	0.103829i	−0.547995	−	0.836481i	$-0.684609\pi$
$193$	−12.3408	+	1.44244i	−0.888313	+	0.103829i	−0.340318	+	0.940310i	$0.610535\pi$
$194$	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	−0.998034	−	0.0626719i	$-0.980038\pi$
$197$	−15.5743	+	13.0684i	−1.10962	+	0.931083i	−0.111587	+	0.993755i	$0.535593\pi$
$198$		0			0
$199$	−17.7742	−	14.9143i	−1.25998	−	1.05725i	−0.995684	−	0.0928038i	$-0.970417\pi$
$199$	−17.7742	−	14.9143i	−1.25998	−	1.05725i	−0.264293	−	0.964443i	$-0.585139\pi$
$200$	−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	−0.998380	−	0.0569065i	$-0.981876\pi$
$211$	−12.8338	+	13.6031i	−0.883519	+	0.936475i	0.114861	+	0.993382i	$0.463358\pi$
$212$	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	−0.948566	−	0.316581i	$-0.897465\pi$
$223$	−5.57356	+	7.48658i	−0.373233	+	0.501339i	0.575333	+	0.817919i	$0.304873\pi$
$224$	−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	0.485851	+	0.874042i	$0.338510\pi$
$227$	−6.03211	+	20.1487i	−0.400365	+	1.33731i	−0.886216	+	0.463272i	$0.846675\pi$
$228$		0			0
$229$	0.524687	−	9.00853i	0.0346723	−	0.595301i	−0.935566	−	0.353151i	$-0.885110\pi$
$229$	0.524687	−	9.00853i	0.0346723	−	0.595301i	0.970239	−	0.242150i	$-0.0778526\pi$
$230$	−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	0.894333	+	0.447403i	$0.147651\pi$
$233$	−1.51248	+	8.57770i	−0.0990858	+	0.561944i	−0.993419	+	0.114541i	$0.963460\pi$
$234$		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	−0.955703	−	0.294332i	$-0.904903\pi$
$239$	−14.8965	−	20.0094i	−0.963572	−	1.29430i	−0.00786849	−	0.999969i	$-0.502505\pi$
$240$		0			0
$241$	17.6807	+	8.87956i	1.13891	+	0.571983i	0.915331	−	0.402703i	$-0.131929\pi$
$241$	17.6807	+	8.87956i	1.13891	+	0.571983i	0.223581	+	0.974685i	$0.428225\pi$
$242$	−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	0.934068	+	0.357096i	$0.116233\pi$
$251$	2.82742	+	16.0351i	0.178465	+	1.01213i	−0.755602	+	0.655031i	$0.772656\pi$
$252$		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	−0.992341	−	0.123529i	$-0.960579\pi$
$257$	0.122334	−	2.10039i	0.00763099	−	0.131019i	0.999972	−	0.00748998i	$-0.00238416\pi$
$258$		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	−0.897689	−	0.440629i	$-0.854755\pi$
$263$	−3.53716	+	4.75123i	−0.218111	+	0.292973i	0.679579	+	0.733603i	$0.262163\pi$
$264$		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	0.803735	−	0.594987i	$-0.202843\pi$
$269$	−1.86000	−	3.22161i	−0.113406	−	0.196425i	−0.917141	+	0.398562i	$0.869509\pi$
$270$		0			0
$271$	−9.85402	+	17.0677i	−0.598589	+	1.03679i	0.394441	+	0.918921i	$0.370938\pi$
$271$	−9.85402	+	17.0677i	−0.598589	+	1.03679i	−0.993030	+	0.117865i	$0.962395\pi$
$272$	−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	0.0216257	−	0.999766i	$-0.493116\pi$
$277$	−3.12717	−	0.365514i	−0.187893	−	0.0219616i	−0.209519	+	0.977805i	$0.567190\pi$
$278$	−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	0.122533	−	0.992464i	$-0.460898\pi$
$281$	−14.6740	−	15.5535i	−0.875377	−	0.927845i	−0.997910	+	0.0646194i	$0.979417\pi$
$282$		0			0
$283$	−9.73365	+	4.88842i	−0.578606	+	0.290587i	−0.713933	−	0.700214i	$-0.753088\pi$
$283$	−9.73365	+	4.88842i	−0.578606	+	0.290587i	0.135327	+	0.990801i	$0.456791\pi$
$284$	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	0.494888	−	0.868957i	$-0.335209\pi$
$293$	20.1441	−	2.35451i	1.17683	−	0.137552i	0.681943	+	0.731405i	$0.261135\pi$
$294$		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	−0.195877	−	0.980629i	$-0.562755\pi$
$307$	4.98325	−	1.81375i	0.284409	−	0.103516i	0.480286	+	0.877112i	$0.340533\pi$
$308$	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	0.445055	−	0.895503i	$-0.353184\pi$
$311$	−3.54349	−	2.33059i	−0.200933	−	0.132156i	−0.645988	+	0.763347i	$0.723554\pi$
$312$		0			0
$313$	4.47705	−	1.06108i	0.253058	−	0.0599758i	−0.102129	−	0.994771i	$-0.532565\pi$
$313$	4.47705	−	1.06108i	0.253058	−	0.0599758i	0.355187	+	0.934795i	$0.384417\pi$
$314$	−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	0.973930	−	0.226850i	$-0.0728427\pi$
$317$	2.50285	+	5.80226i	0.140574	+	0.325887i	−0.833356	+	0.552737i	$0.813583\pi$
$318$		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	0.998775	+	0.0494782i	$0.0157558\pi$
$331$	6.35611	+	14.7351i	0.349363	+	0.809915i	−0.649412	+	0.760437i	$0.724985\pi$
$332$	−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	0.609566	−	0.792735i	$-0.291344\pi$
$337$	2.25984	+	1.48632i	0.123101	+	0.0809650i	−0.486465	+	0.873700i	$0.661714\pi$
$338$	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	−0.988413	−	0.151786i	$-0.951498\pi$
$347$	−3.72033	+	8.62470i	−0.199718	+	0.462998i	0.788696	+	0.614784i	$0.210757\pi$
$348$		0			0
$349$	17.9125	−	11.7812i	0.958834	−	0.630635i	0.0293780	−	0.999568i	$-0.490647\pi$
$349$	17.9125	−	11.7812i	0.958834	−	0.630635i	0.929456	+	0.368933i	$0.120277\pi$
$350$	−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	−0.989786	−	0.142558i	$-0.954467\pi$
$353$	−0.436688	−	7.49765i	−0.0232426	−	0.399060i	0.966544	−	0.256501i	$-0.0825698\pi$
$354$		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	−0.955425	−	0.295234i	$-0.904602\pi$
$359$	−15.7373	+	13.2052i	−0.830584	+	0.696943i	0.124841	+	0.992177i	$0.460158\pi$
$360$		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	0.943055	−	0.332636i	$-0.107938\pi$
$367$	10.6543	+	11.2929i	0.556149	+	0.589483i	−0.386907	+	0.922119i	$0.626456\pi$
$368$	−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	−0.962539	−	0.271144i	$-0.912598\pi$
$373$	−12.2810	+	13.0171i	−0.635887	+	0.674001i	0.326652	+	0.945145i	$0.394080\pi$
$374$	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	0.800891	−	0.598810i	$-0.204360\pi$
$379$	−2.29993	−	3.98360i	−0.118140	−	0.204624i	−0.919030	+	0.394187i	$0.871026\pi$
$380$	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	−0.466298	−	0.884627i	$-0.654413\pi$
$383$	−25.0504	−	5.93707i	−1.28002	−	0.303370i	−0.813720	+	0.581258i	$0.802561\pi$
$384$		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	−0.995513	−	0.0946293i	$-0.969833\pi$
$389$	−2.20453	+	7.36366i	−0.111774	+	0.373352i	0.883738	+	0.467981i	$0.155019\pi$
$390$		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	−0.990514	−	0.137412i	$-0.956122\pi$
$397$	−2.12664	−	12.0608i	−0.106733	−	0.605312i	0.883781	−	0.467900i	$-0.154989\pi$
$398$	−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	0.999994	−	0.00331841i	$-0.00105629\pi$
$401$	14.2180	+	19.0981i	0.710014	+	0.953714i	−0.289981	+	0.957033i	$0.593649\pi$
$402$		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	−0.975916	−	0.218146i	$-0.929999\pi$
$409$	−18.3025	−	24.5846i	−0.905002	−	1.21563i	0.0709147	−	0.997482i	$-0.477408\pi$
$410$	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	−0.852557	−	0.522634i	$-0.824949\pi$
$419$	1.12397	−	19.2978i	0.0549094	−	0.942759i	0.907466	−	0.420125i	$-0.138014\pi$
$420$		0			0
$421$	3.40157	−	11.3620i	0.165782	−	0.553752i	−0.834215	−	0.551440i	$-0.814079\pi$
$421$	3.40157	−	11.3620i	0.165782	−	0.553752i	0.999997	−	0.00231247i	$-0.000736082\pi$
$422$	−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	0.999347	−	0.0361326i	$-0.0115039\pi$
$431$	9.72386	+	16.8422i	0.468382	+	0.811261i	−0.530965	+	0.847394i	$0.678171\pi$
$432$		0			0
$433$	−2.82936	+	4.90059i	−0.135970	+	0.235507i	−0.925968	−	0.377603i	$-0.876748\pi$
$433$	−2.82936	+	4.90059i	−0.135970	+	0.235507i	0.789997	+	0.613110i	$0.210082\pi$
$434$	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	0.402519	−	0.915412i	$-0.368135\pi$
$439$	12.2169	+	1.42795i	0.583079	+	0.0681521i	0.180560	+	0.983564i	$0.442209\pi$
$440$	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	0.876351	−	0.481674i	$-0.159971\pi$
$443$	7.25165	+	7.68630i	0.344536	+	0.365187i	−0.531814	+	0.846861i	$0.678490\pi$
$444$		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	−0.928952	−	0.370201i	$-0.879289\pi$
$449$	−30.8275	−	25.8673i	−1.45484	−	1.22075i	−0.525887	−	0.850554i	$-0.676267\pi$
$450$		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	−0.535924	−	0.844266i	$-0.680037\pi$
$457$	−2.17275	−	37.3047i	−0.101637	−	1.74504i	0.434287	−	0.900774i	$-0.357000\pi$
$458$	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	0.455983	−	0.889988i	$-0.349288\pi$
$461$	31.2142	−	20.5299i	1.45379	−	0.956173i	0.997807	−	0.0661850i	$-0.0210828\pi$
$462$		0			0
$463$	9.18807	−	21.3003i	0.427006	−	0.989911i	−0.559892	−	0.828566i	$-0.689157\pi$
$463$	9.18807	−	21.3003i	0.427006	−	0.989911i	0.986898	−	0.161345i	$-0.0515833\pi$
$464$	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	0.332595	−	0.943070i	$-0.392076\pi$
$467$	−0.406622	−	0.147998i	−0.0188162	−	0.00684855i	−0.351411	+	0.936221i	$0.614298\pi$
$468$		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	0.761425	−	0.648253i	$-0.224500\pi$
$479$	−5.09110	−	11.8025i	−0.232618	−	0.539270i	−0.994044	+	0.108983i	$0.965241\pi$
$480$		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	−0.998648	−	0.0519904i	$-0.983443\pi$
$491$	−4.27347	−	14.2744i	−0.192859	−	0.644194i	0.805789	−	0.592203i	$-0.201742\pi$
$492$		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	0.343002	−	0.939335i	$-0.388556\pi$
$499$	−8.57019	−	5.63670i	−0.383654	−	0.252333i	−0.726656	+	0.687001i	$0.758927\pi$
$500$	−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	0.0260494	−	0.999661i	$-0.491707\pi$
$503$	15.4431	−	5.62083i	0.688574	−	0.250620i	0.662524	+	0.749040i	$0.269485\pi$
$504$		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	−0.962184	−	0.272400i	$-0.912183\pi$
$509$	−2.34085	+	5.42671i	−0.103757	+	0.240535i	0.858428	+	0.512935i	$0.171442\pi$
$510$		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	−0.339191	−	0.940717i	$-0.610153\pi$
$521$	12.0595	−	10.1191i	0.528335	−	0.443325i	0.867526	+	0.497392i	$0.165709\pi$
$522$		0			0
$523$	−32.0731	−	26.9125i	−1.40246	−	1.17680i	−0.959996	−	0.280015i	$-0.909661\pi$
$523$	−32.0731	−	26.9125i	−1.40246	−	1.17680i	−0.442462	−	0.896787i	$-0.645895\pi$
$524$	−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	0.828450	−	0.560063i	$-0.189223\pi$
$541$	−1.64686	−	2.85244i	−0.0708039	−	0.122636i	−0.899254	+	0.437427i	$0.855890\pi$
$542$	−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	−0.683848	−	0.729625i	$-0.739695\pi$
$547$	4.94084	−	6.63669i	0.211255	−	0.283765i	0.895103	+	0.445860i	$0.147102\pi$
$548$	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	−0.999900	−	0.0141167i	$-0.995506\pi$
$557$	−1.30921	+	7.42492i	−0.0554732	+	0.314604i	0.944427	+	0.328721i	$0.106617\pi$
$558$		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	−0.998885	−	0.0472070i	$-0.984968\pi$
$563$	−17.9766	−	24.1468i	−0.757625	−	1.01767i	0.241260	−	0.970461i	$-0.422439\pi$
$564$		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	−0.345827	−	0.938298i	$-0.612402\pi$
$569$	−31.1284	−	15.6333i	−1.30497	−	0.655381i	−0.959144	+	0.282917i	$0.908698\pi$
$570$		0			0
$571$	3.98459	+	5.35223i	0.166750	+	0.223984i	0.877642	−	0.479318i	$-0.159116\pi$
$571$	3.98459	+	5.35223i	0.166750	+	0.223984i	−0.710892	+	0.703302i	$0.751708\pi$
$572$	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	0.516875	+	0.856061i	$0.327095\pi$
$577$	−6.28429	+	35.6400i	−0.261619	+	1.48371i	−0.778494	+	0.627652i	$0.784016\pi$
$578$	−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	0.281957	+	0.959427i	$0.409016\pi$
$587$	−17.3965	+	23.3675i	−0.718030	+	0.964482i	−0.999987	+	0.00505460i	$0.998391\pi$
$588$		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	0.945092	−	0.326803i	$-0.105971\pi$
$593$	4.61527	+	7.99387i	0.189526	+	0.328269i	−0.755566	+	0.655072i	$0.772638\pi$
$594$		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	−0.710662	−	0.703533i	$-0.751605\pi$
$599$	0.807714	−	0.856127i	0.0330023	−	0.0349804i	0.743664	+	0.668553i	$0.233086\pi$
$600$		0			0
$601$	16.3686	+	1.91321i	0.667688	+	0.0780416i	0.443183	−	0.896431i	$-0.353849\pi$
$601$	16.3686	+	1.91321i	0.667688	+	0.0780416i	0.224506	+	0.974473i	$0.427923\pi$
$602$	−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	0.346261	−	0.938138i	$-0.387451\pi$
$607$	32.1650	−	16.1539i	1.30554	−	0.655665i	0.959275	+	0.282473i	$0.0911548\pi$
$608$	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	−0.974628	−	0.223830i	$-0.928144\pi$
$613$	−22.8633	+	19.1846i	−0.923441	+	0.774859i	0.0511868	+	0.998689i	$0.483700\pi$
$614$	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	−0.0148690	−	0.999889i	$-0.504733\pi$
$617$	4.99903	−	0.584303i	0.201253	−	0.0235231i	0.216122	+	0.976366i	$0.430659\pi$
$618$		0			0
$619$	1.28092	+	21.9925i	0.0514844	+	0.883954i	0.920882	+	0.389841i	$0.127470\pi$
$619$	1.28092	+	21.9925i	0.0514844	+	0.883954i	−0.869398	+	0.494113i	$0.835493\pi$
$620$	−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	−0.836743	−	0.547595i	$-0.815543\pi$
$631$	−28.2782	+	10.2924i	−1.12574	+	0.409735i	−0.288995	+	0.957331i	$0.593321\pi$
$632$	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	−0.976846	−	0.213942i	$-0.931370\pi$
$641$	−11.6997	−	27.1229i	−0.462109	−	1.07129i	0.514737	−	0.857348i	$-0.327890\pi$
$642$		0			0
$643$	1.81855	+	6.07439i	0.0717167	+	0.239550i	0.986331	−	0.164778i	$-0.0526906\pi$
$643$	1.81855	+	6.07439i	0.0717167	+	0.239550i	−0.914614	+	0.404328i	$0.867505\pi$
$644$	−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	0.998692	+	0.0511212i	$0.0162795\pi$
$653$	4.91627	+	16.4215i	0.192389	+	0.642623i	−0.806304	+	0.591502i	$0.798535\pi$
$654$		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	0.272305	−	0.962211i	$-0.412214\pi$
$659$	24.3229	−	5.76463i	0.947484	−	0.224558i	0.675180	+	0.737653i	$0.264066\pi$
$660$		0			0
$661$	−0.607381	−	0.399481i	−0.0236244	−	0.0155380i	0.537642	−	0.843173i	$-0.319315\pi$
$661$	−0.607381	−	0.399481i	−0.0236244	−	0.0155380i	−0.561266	+	0.827635i	$0.689686\pi$
$662$	−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	−0.431861	+	0.901940i	$0.642143\pi$
$673$	−37.1257	+	24.4179i	−1.43109	+	0.941242i	−0.999227	+	0.0393018i	$0.987487\pi$
$674$	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	0.554703	+	0.832048i	$0.312832\pi$
$677$	2.61091	+	44.8277i	0.100346	+	1.72287i	−0.454358	+	0.890819i	$0.650131\pi$
$678$		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	−0.270235	−	0.962795i	$-0.587101\pi$
$683$	16.4909	−	13.8375i	0.631007	−	0.529478i	0.901242	+	0.433317i	$0.142657\pi$
$684$		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	0.994137	−	0.108124i	$-0.0344842\pi$
$691$	21.7759	+	23.0811i	0.828393	+	0.878045i	−0.165745	+	0.986169i	$0.553003\pi$
$692$	−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	−0.573611	−	0.819128i	$-0.694458\pi$
$701$	11.1884	−	19.3789i	0.422580	−	0.731929i	0.996191	+	0.0871983i	$0.0277914\pi$
$702$		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	−0.755347	−	0.655324i	$-0.772532\pi$
$709$	2.37201	−	3.18616i	0.0890826	−	0.119659i	0.844430	+	0.535666i	$0.179939\pi$
$710$	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	−0.849051	−	0.528310i	$-0.822826\pi$
$719$	3.47213	−	19.6915i	0.129489	−	0.734367i	0.978540	−	0.206057i	$-0.0660632\pi$
$720$		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	0.455663	−	0.890152i	$-0.349402\pi$
$727$	0.370860	+	0.186253i	0.0137545	+	0.00690774i	−0.441909	+	0.897060i	$0.645698\pi$
$728$	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	0.712328	−	0.701846i	$-0.247641\pi$
$733$	−4.44910	−	5.97617i	−0.164331	−	0.220735i	−0.876660	+	0.481111i	$0.840233\pi$
$734$	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	−0.998518	−	0.0544304i	$-0.982666\pi$
$739$	−1.13092	+	6.41379i	−0.0416017	+	0.235935i	0.956916	+	0.290365i	$0.0937768\pi$
$740$	−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	0.827408	+	0.561602i	$0.189815\pi$
$743$	−1.62467	+	27.8945i	−0.0596033	+	1.02335i	−0.887011	+	0.461748i	$0.847222\pi$
$744$		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	−0.322233	−	0.946660i	$-0.604433\pi$
$751$	−28.3649	−	6.72261i	−1.03505	−	0.245312i	−0.712818	+	0.701349i	$0.752581\pi$
$752$	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	−0.316511	+	0.948589i	$0.602512\pi$
$757$	−26.9567	+	46.6904i	−0.979758	+	1.69699i	−0.663246	+	0.748401i	$0.730822\pi$
$758$	−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	−0.929025	−	0.370018i	$-0.879351\pi$
$761$	−13.9480	+	14.7840i	−0.505614	+	0.535920i	0.423410	+	0.905938i	$0.360833\pi$
$762$		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	0.334801	−	0.942289i	$-0.391331\pi$
$769$	35.7884	−	17.9736i	1.29056	−	0.648145i	0.955761	+	0.294144i	$0.0950346\pi$
$770$	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	0.878292	−	0.478124i	$-0.158683\pi$
$773$	15.5681	+	13.0632i	0.559945	+	0.469850i	−0.318347	+	0.947974i	$0.603128\pi$
$774$		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	−0.963820	−	0.266554i	$-0.914115\pi$
$787$	−3.04443	+	7.05779i	−0.108522	+	0.251583i	0.855298	+	0.518137i	$0.173374\pi$
$788$	−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	0.960391	−	0.278656i	$-0.0898891\pi$
$797$	30.6284	+	20.1446i	1.08492	+	0.713560i	0.124525	+	0.992217i	$0.460259\pi$
$798$		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	0.298657	−	0.954361i	$-0.403461\pi$
$821$	28.4772	−	6.74923i	0.993862	−	0.235550i	0.695206	+	0.718811i	$0.255313\pi$
$822$		0			0
$823$	25.8934	+	17.0304i	0.902588	+	0.593642i	0.913741	−	0.406296i	$-0.133180\pi$
$823$	25.8934	+	17.0304i	0.902588	+	0.593642i	−0.0111532	+	0.999938i	$0.503550\pi$
$824$	−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	−0.209551	−	0.977798i	$-0.567200\pi$
$827$	7.43214	−	2.70508i	0.258441	−	0.0940647i	0.467991	+	0.883733i	$0.344978\pi$
$828$		0			0
$829$	44.4988	+	16.1962i	1.54551	+	0.562518i	0.967358	−	0.253413i	$-0.0815532\pi$
$829$	44.4988	+	16.1962i	1.54551	+	0.562518i	0.578148	+	0.815932i	$0.303775\pi$
$830$	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	−0.958573	−	0.284846i	$-0.908057\pi$
$839$	−1.14559	−	19.6690i	−0.0395502	−	0.679050i	0.919023	−	0.394204i	$-0.128980\pi$
$840$		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	−0.858221	−	0.513280i	$-0.828430\pi$
$853$	−38.5735	−	40.8855i	−1.32073	−	1.39989i	−0.462510	−	0.886614i	$-0.653051\pi$
$854$	−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	−0.0839765	−	0.996468i	$-0.526762\pi$
$857$	−11.5778	−	1.35325i	−0.395491	−	0.0462262i	−0.311514	+	0.950242i	$0.600836\pi$
$858$		0			0
$859$	28.7098	−	30.4306i	0.979567	−	1.03828i	−0.0196927	−	0.999806i	$-0.506269\pi$
$859$	28.7098	−	30.4306i	0.979567	−	1.03828i	0.999260	−	0.0384741i	$-0.0122497\pi$
$860$	−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	−0.806111	−	0.591765i	$-0.798432\pi$
$863$	3.21464	−	5.56792i	0.109428	−	0.189534i	0.915539	+	0.402230i	$0.131765\pi$
$864$		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	0.968531	+	0.248892i	$0.0800665\pi$
$877$	−0.661751	+	11.3618i	−0.0223457	+	0.383662i	−0.990877	+	0.134770i	$0.956971\pi$
$878$	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	0.290148	+	0.956982i	$0.406295\pi$
$881$	−9.19564	+	52.1511i	−0.309809	+	1.75701i	−0.599957	+	0.800032i	$0.704816\pi$
$882$		0			0
$883$	−5.69410	−	32.2928i	−0.191622	−	1.08674i	−0.917148	−	0.398546i	$-0.869515\pi$
$883$	−5.69410	−	32.2928i	−0.191622	−	1.08674i	0.725526	−	0.688194i	$-0.241596\pi$
$884$	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	0.996901	−	0.0786686i	$-0.0250669\pi$
$887$	18.9305	+	25.4280i	0.635623	+	0.853789i	−0.361278	+	0.932458i	$0.617659\pi$
$888$		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	−0.490179	−	0.871622i	$-0.663069\pi$
$907$	11.9961	−	40.0697i	0.398324	−	1.33049i	0.888503	−	0.458872i	$-0.151746\pi$
$908$	−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	−0.409911	−	0.912126i	$-0.634440\pi$
$911$	17.5501	−	23.5738i	0.581460	−	0.781036i	0.991370	+	0.131090i	$0.0418476\pi$
$912$		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	−0.940999	−	0.338410i	$-0.890111\pi$
$919$	−5.37872	+	9.31622i	−0.177428	+	0.307314i	0.763571	+	0.645724i	$0.223444\pi$
$920$	−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	0.748716	−	0.662891i	$-0.230671\pi$
$929$	1.32318	+	1.40249i	0.0434121	+	0.0460141i	−0.705304	+	0.708905i	$0.749189\pi$
$930$		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	−0.948988	−	0.315313i	$-0.897891\pi$
$937$	−24.5880	+	20.6318i	−0.803255	+	0.674011i	0.145732	+	0.989324i	$0.453446\pi$
$938$	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	−0.611147	−	0.791517i	$-0.709292\pi$
$941$	−31.3900	+	3.66897i	−1.02328	+	0.119605i	−0.412137	+	0.911122i	$0.635218\pi$
$942$		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	−0.869467	−	0.493990i	$-0.835538\pi$
$947$	−23.3956	+	15.3875i	−0.760256	+	0.500028i	0.109211	+	0.994019i	$0.465167\pi$
$948$		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	0.647573	−	0.762004i	$-0.275784\pi$
$953$	20.1844	+	7.34651i	0.653836	+	0.237977i	0.00626309	+	0.999980i	$0.498006\pi$
$954$		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	−0.919464	−	0.393174i	$-0.871377\pi$
$967$	−11.4223	−	38.1531i	−0.367316	−	1.22692i	0.552148	−	0.833746i	$-0.313808\pi$
$968$	−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	−0.715898	−	0.698204i	$-0.753983\pi$
$977$	−15.6736	−	52.3535i	−0.501444	−	1.67494i	0.214455	−	0.976734i	$-0.431203\pi$
$978$		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	0.123023	−	0.992404i	$-0.460741\pi$
$983$	21.2682	−	5.04066i	0.678351	−	0.160772i	0.555328	+	0.831632i	$0.312593\pi$
$984$		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	−0.395550	−	0.918444i	$-0.629446\pi$
$991$	−40.5755	−	14.7683i	−1.28892	−	0.469130i	−0.893374	+	0.449315i	$0.851668\pi$
$992$	−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	−0.483562	−	0.875310i	$-0.660657\pi$
$997$	4.06161	−	2.67136i	0.128633	−	0.0846029i	0.612195	+	0.790707i	$0.290287\pi$
$998$	−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.253.4		72
3.2	odd	2		162.2.g.a.13.3	✓	72
81.25	even	27	inner	486.2.g.a.73.4		72
81.56	odd	54		162.2.g.a.25.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.13.3	✓	72	3.2	odd	2
162.2.g.a.25.3	yes	72	81.56	odd	54
486.2.g.a.73.4		72	81.25	even	27	inner
486.2.g.a.253.4		72	1.1	even	1	trivial

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)

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

Introduction

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