LMFDB - Embedded newform 540.2.y.a.343.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("540.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			343.31
Character	$\chi$	$=$	540.343
Dual form			540.2.y.a.307.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38677 - 0.277260i) q^{2} +(1.84625 - 0.768990i) q^{4} +(-1.01645 + 1.99169i) q^{5} +(0.00373871 - 0.00100179i) q^{7} +(2.34712 - 1.57830i) q^{8} +O(q^{10})$	\(q+(1.38677 - 0.277260i) q^{2} +(1.84625 - 0.768990i) q^{4} +(-1.01645 + 1.99169i) q^{5} +(0.00373871 - 0.00100179i) q^{7} +(2.34712 - 1.57830i) q^{8} +(-0.857362 + 3.04383i) q^{10} +(3.58713 + 2.07103i) q^{11} +(-0.767553 + 2.86455i) q^{13} +(0.00490698 - 0.00242584i) q^{14} +(2.81731 - 2.83950i) q^{16} +(2.07784 - 2.07784i) q^{17} +7.31525 q^{19} +(-0.345029 + 4.45881i) q^{20} +(5.54873 + 1.87747i) q^{22} +(-3.73983 - 1.00208i) q^{23} +(-2.93367 - 4.04890i) q^{25} +(-0.270195 + 4.18528i) q^{26} +(0.00613225 - 0.00472458i) q^{28} +(-4.99228 - 2.88229i) q^{29} +(-1.77642 + 1.02562i) q^{31} +(3.11967 - 4.71886i) q^{32} +(2.30538 - 3.45758i) q^{34} +(-0.00180496 + 0.00846463i) q^{35} +(-6.09468 + 6.09468i) q^{37} +(10.1446 - 2.02822i) q^{38} +(0.757772 + 6.27900i) q^{40} +(-1.82477 - 3.16060i) q^{41} +(0.259538 + 0.968609i) q^{43} +(8.21535 + 1.06518i) q^{44} +(-5.46412 - 0.352755i) q^{46} +(4.55740 - 1.22115i) q^{47} +(-6.06216 + 3.49999i) q^{49} +(-5.19092 - 4.80150i) q^{50} +(0.785711 + 5.87892i) q^{52} +(-6.92974 - 6.92974i) q^{53} +(-7.77098 + 5.03936i) q^{55} +(0.00719408 - 0.00825213i) q^{56} +(-7.72228 - 2.61291i) q^{58} +(2.76056 + 4.78143i) q^{59} +(3.59007 - 6.21819i) q^{61} +(-2.17912 + 1.91482i) q^{62} +(3.01792 - 7.40893i) q^{64} +(-4.92512 - 4.44039i) q^{65} +(0.851369 - 3.17735i) q^{67} +(2.23838 - 5.43405i) q^{68} +(-0.000156161 + 0.0122389i) q^{70} -11.3127i q^{71} +(-6.50632 - 6.50632i) q^{73} +(-6.76210 + 10.1417i) q^{74} +(13.5058 - 5.62536i) q^{76} +(0.0154860 + 0.00414946i) q^{77} +(-2.99986 + 5.19591i) q^{79} +(2.79177 + 8.49741i) q^{80} +(-3.40684 - 3.87708i) q^{82} +(-0.756131 - 2.82192i) q^{83} +(2.02640 + 6.25042i) q^{85} +(0.628475 + 1.27128i) q^{86} +(11.6881 - 0.800629i) q^{88} +9.18764i q^{89} +0.0114786i q^{91} +(-7.67527 + 1.02579i) q^{92} +(5.98148 - 2.95704i) q^{94} +(-7.43557 + 14.5697i) q^{95} +(0.607478 + 2.26714i) q^{97} +(-7.43641 + 6.53447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$217$	$271$	$461$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.38677	−	0.277260i	0.980593	−	0.196052i
$2$	1.38677	−	0.277260i	0.980593	−	0.196052i
$3$		0			0
$3$		0			0
$4$	1.84625	−	0.768990i	0.923127	−	0.384495i
$5$	−1.01645	+	1.99169i	−0.454569	+	0.890711i
$5$	−1.01645	+	1.99169i	−0.454569	+	0.890711i
$6$		0			0
$7$	0.00373871	−	0.00100179i	0.00141310	−	0.000378639i	−0.258112	−	0.966115i	$-0.583100\pi$
$7$	0.00373871	−	0.00100179i	0.00141310	−	0.000378639i	0.259526	+	0.965736i	$0.416434\pi$
$8$	2.34712	−	1.57830i	0.829831	−	0.558015i
$9$		0			0
$10$	−0.857362	+	3.04383i	−0.271122	+	0.962545i
$11$	3.58713	+	2.07103i	1.08156	+	0.624439i	0.931317	−	0.364210i	$-0.118661\pi$
$11$	3.58713	+	2.07103i	1.08156	+	0.624439i	0.150243	+	0.988649i	$0.451994\pi$
$12$		0			0
$13$	−0.767553	+	2.86455i	−0.212881	+	0.794483i	0.774021	+	0.633160i	$0.218243\pi$
$13$	−0.767553	+	2.86455i	−0.212881	+	0.794483i	−0.986902	+	0.161322i	$0.948424\pi$
$14$	0.00490698	−	0.00242584i	0.00131144	−	0.000648333i
$15$		0			0
$16$	2.81731	−	2.83950i	0.704327	−	0.709876i
$17$	2.07784	−	2.07784i	0.503949	−	0.503949i	−0.408713	−	0.912663i	$-0.634022\pi$
$17$	2.07784	−	2.07784i	0.503949	−	0.503949i	0.912663	+	0.408713i	$0.134022\pi$
$18$		0			0
$19$	7.31525			1.67823			0.839117	−	0.543951i	$-0.183072\pi$
$19$	7.31525			1.67823			0.839117	+	0.543951i	$0.183072\pi$
$20$	−0.345029	+	4.45881i	−0.0771509	+	0.997019i
$21$		0			0
$22$	5.54873	+	1.87747i	1.18299	+	0.400279i
$23$	−3.73983	−	1.00208i	−0.779808	−	0.208949i	−0.153108	−	0.988209i	$-0.548928\pi$
$23$	−3.73983	−	1.00208i	−0.779808	−	0.208949i	−0.626700	+	0.779260i	$0.715595\pi$
$24$		0			0
$25$	−2.93367	−	4.04890i	−0.586734	−	0.809780i
$26$	−0.270195	+	4.18528i	−0.0529896	+	0.820800i
$27$		0			0
$28$	0.00613225	−	0.00472458i	0.00115889	−	0.000892863i
$29$	−4.99228	−	2.88229i	−0.927042	−	0.535228i	−0.0411674	−	0.999152i	$-0.513108\pi$
$29$	−4.99228	−	2.88229i	−0.927042	−	0.535228i	−0.885875	+	0.463924i	$0.846441\pi$
$30$		0			0
$31$	−1.77642	+	1.02562i	−0.319054	+	0.184206i	−0.650971	−	0.759103i	$-0.725638\pi$
$31$	−1.77642	+	1.02562i	−0.319054	+	0.184206i	0.331917	+	0.943309i	$0.392305\pi$
$32$	3.11967	−	4.71886i	0.551486	−	0.834184i
$33$		0			0
$34$	2.30538	−	3.45758i	0.395369	−	0.592970i
$35$	−0.00180496	+	0.00846463i	−0.000305094	+	0.00143078i
$36$		0			0
$37$	−6.09468	+	6.09468i	−1.00196	+	1.00196i	−0.00196150	+	0.999998i	$0.500624\pi$
$37$	−6.09468	+	6.09468i	−1.00196	+	1.00196i	−0.999998	+	0.00196150i	$0.999376\pi$
$38$	10.1446	−	2.02822i	1.64566	−	0.329021i
$39$		0			0
$40$	0.757772	+	6.27900i	0.119814	+	0.992796i
$41$	−1.82477	−	3.16060i	−0.284981	−	0.493602i	0.687623	−	0.726068i	$-0.258654\pi$
$41$	−1.82477	−	3.16060i	−0.284981	−	0.493602i	−0.972605	+	0.232465i	$0.925321\pi$
$42$		0			0
$43$	0.259538	+	0.968609i	0.0395792	+	0.147711i	0.982888	−	0.184206i	$-0.0589712\pi$
$43$	0.259538	+	0.968609i	0.0395792	+	0.147711i	−0.943309	+	0.331917i	$0.892305\pi$
$44$	8.21535	+	1.06518i	1.23851	+	0.160582i
$45$		0			0
$46$	−5.46412	−	0.352755i	−0.805640	−	0.0520108i
$47$	4.55740	−	1.22115i	0.664765	−	0.178123i	0.0893696	−	0.995999i	$-0.471515\pi$
$47$	4.55740	−	1.22115i	0.664765	−	0.178123i	0.575396	+	0.817875i	$0.304848\pi$
$48$		0			0
$49$	−6.06216	+	3.49999i	−0.866024	+	0.499999i
$50$	−5.19092	−	4.80150i	−0.734106	−	0.679034i
$51$		0			0
$52$	0.785711	+	5.87892i	0.108959	+	0.815260i
$53$	−6.92974	−	6.92974i	−0.951873	−	0.951873i	0.0470212	−	0.998894i	$-0.485027\pi$
$53$	−6.92974	−	6.92974i	−0.951873	−	0.951873i	−0.998894	+	0.0470212i	$0.985027\pi$
$54$		0			0
$55$	−7.77098	+	5.03936i	−1.04784	+	0.679507i
$56$	0.00719408	−	0.00825213i	0.000961349	−	0.00110274i
$57$		0			0
$58$	−7.72228	−	2.61291i	−1.01398	−	0.343092i
$59$	2.76056	+	4.78143i	0.359394	+	0.622489i	0.987860	−	0.155348i	$-0.0496499\pi$
$59$	2.76056	+	4.78143i	0.359394	+	0.622489i	−0.628465	+	0.777838i	$0.716317\pi$
$60$		0			0
$61$	3.59007	−	6.21819i	0.459662	−	0.796158i	−0.539281	−	0.842126i	$-0.681304\pi$
$61$	3.59007	−	6.21819i	0.459662	−	0.796158i	0.998943	+	0.0459683i	$0.0146373\pi$
$62$	−2.17912	+	1.91482i	−0.276748	+	0.243182i
$63$		0			0
$64$	3.01792	−	7.40893i	0.377239	−	0.926116i
$65$	−4.92512	−	4.44039i	−0.610886	−	0.550763i
$66$		0			0
$67$	0.851369	−	3.17735i	0.104011	−	0.388175i	−0.894220	−	0.447628i	$-0.852269\pi$
$67$	0.851369	−	3.17735i	0.104011	−	0.388175i	0.998231	+	0.0594528i	$0.0189356\pi$
$68$	2.23838	−	5.43405i	0.271443	−	0.658975i
$69$		0			0
$70$	−0.000156161		0.0122389i	−1.86648e−5		0.00146283i
$71$		−	11.3127i		−	1.34257i	−0.741200	−	0.671284i	$-0.765743\pi$
$71$		−	11.3127i		−	1.34257i	0.741200	−	0.671284i	$-0.234257\pi$
$72$		0			0
$73$	−6.50632	−	6.50632i	−0.761508	−	0.761508i	0.215087	−	0.976595i	$-0.430996\pi$
$73$	−6.50632	−	6.50632i	−0.761508	−	0.761508i	−0.976595	+	0.215087i	$0.930996\pi$
$74$	−6.76210	+	10.1417i	−0.786079	+	1.17895i
$75$		0			0
$76$	13.5058	−	5.62536i	1.54922	−	0.645273i
$77$	0.0154860	+	0.00414946i	0.00176479	+	0.000472874i
$78$		0			0
$79$	−2.99986	+	5.19591i	−0.337510	+	0.584585i	−0.983964	−	0.178368i	$-0.942918\pi$
$79$	−2.99986	+	5.19591i	−0.337510	+	0.584585i	0.646453	+	0.762953i	$0.276251\pi$
$80$	2.79177	+	8.49741i	0.312129	+	0.950040i
$81$		0			0
$82$	−3.40684	−	3.87708i	−0.376223	−	0.428152i
$83$	−0.756131	−	2.82192i	−0.0829962	−	0.309746i	0.911931	−	0.410344i	$-0.134591\pi$
$83$	−0.756131	−	2.82192i	−0.0829962	−	0.309746i	−0.994927	+	0.100598i	$0.967925\pi$
$84$		0			0
$85$	2.02640	+	6.25042i	0.219794	+	0.677953i
$86$	0.628475	+	1.27128i	0.0677702	+	0.137085i
$87$		0			0
$88$	11.6881	−	0.800629i	1.24596	−	0.0853474i
$89$			9.18764i			0.973888i	0.873433	+	0.486944i	$0.161888\pi$
$89$			9.18764i			0.973888i	−0.873433	+	0.486944i	$0.838112\pi$
$90$		0			0
$91$			0.0114786i			0.00120329i
$92$	−7.67527	+	1.02579i	−0.800202	+	0.106946i
$93$		0			0
$94$	5.98148	−	2.95704i	0.616943	−	0.304995i
$95$	−7.43557	+	14.5697i	−0.762873	+	1.49482i
$96$		0			0
$97$	0.607478	+	2.26714i	0.0616800	+	0.230193i	0.989884	−	0.141879i	$-0.0453143\pi$
$97$	0.607478	+	2.26714i	0.0616800	+	0.230193i	−0.928204	+	0.372072i	$0.878648\pi$
$98$	−7.43641	+	6.53447i	−0.751191	+	0.660082i
$99$		0			0
$100$	−8.52986	−	5.21933i	−0.852986	−	0.521933i
$101$	3.57015	−	6.18367i	0.355243	−	0.615299i	−0.631917	−	0.775036i	$-0.717732\pi$
$101$	3.57015	−	6.18367i	0.355243	−	0.615299i	0.987159	+	0.159738i	$0.0510649\pi$
$102$		0			0
$103$	4.03578	+	1.08138i	0.397657	+	0.106552i	0.452105	−	0.891965i	$-0.350673\pi$
$103$	4.03578	+	1.08138i	0.397657	+	0.106552i	−0.0544481	+	0.998517i	$0.517340\pi$
$104$	2.71959	+	7.93486i	0.266678	+	0.778077i
$105$		0			0
$106$	−11.5313	−	7.68860i	−1.12002	−	0.746783i
$107$	−8.23461	−	8.23461i	−0.796070	−	0.796070i	0.186403	−	0.982473i	$-0.440317\pi$
$107$	−8.23461	−	8.23461i	−0.796070	−	0.796070i	−0.982473	+	0.186403i	$0.940317\pi$
$108$		0			0
$109$			6.43234i			0.616106i	0.951369	+	0.308053i	$0.0996774\pi$
$109$			6.43234i			0.616106i	−0.951369	+	0.308053i	$0.900323\pi$
$110$	−9.37934	+	9.14301i	−0.894285	+	0.871752i
$111$		0			0
$112$	0.00768854	−	0.0134384i	0.000726498	−	0.00126981i
$113$	−4.02483	+	15.0209i	−0.378625	+	1.41305i	0.469351	+	0.883012i	$0.344488\pi$
$113$	−4.02483	+	15.0209i	−0.378625	+	1.41305i	−0.847976	+	0.530035i	$0.822179\pi$
$114$		0			0
$115$	5.79718	−	6.43002i	0.540590	−	0.599602i
$116$	−11.4335	−	1.48243i	−1.06157	−	0.137640i
$117$		0			0
$118$	5.15396	+	5.86535i	0.474460	+	0.539949i
$119$	0.00568689	−	0.00984998i	0.000521316	−	0.000902946i
$120$		0			0
$121$	3.07833	+	5.33183i	0.279848	+	0.484712i
$122$	3.25455	−	9.61857i	0.294653	−	0.870825i
$123$		0			0
$124$	−2.49103	+	3.25959i	−0.223701	+	0.292720i
$125$	11.0461	−	1.72747i	0.987991	−	0.154509i
$126$		0			0
$127$	−14.1298	−	14.1298i	−1.25381	−	1.25381i	−0.953996	−	0.299818i	$-0.903074\pi$
$127$	−14.1298	−	14.1298i	−1.25381	−	1.25381i	−0.299818	−	0.953996i	$-0.596926\pi$
$128$	2.13095	−	11.1112i	0.188351	−	0.982102i
$129$		0			0
$130$	−8.06114	−	4.79226i	−0.707009	−	0.420309i
$131$	7.13877	−	4.12157i	0.623717	−	0.360103i	−0.154598	−	0.987978i	$-0.549408\pi$
$131$	7.13877	−	4.12157i	0.623717	−	0.360103i	0.778315	+	0.627874i	$0.216075\pi$
$132$		0			0
$133$	0.0273496	−	0.00732831i	0.00237151	−	0.000635445i
$134$	0.299700	−	4.64230i	0.0258901	−	0.401034i
$135$		0			0
$136$	1.59747	−	8.15638i	0.136982	−	0.699404i
$137$	4.39479	+	16.4016i	0.375472	+	1.40128i	0.852654	+	0.522476i	$0.174992\pi$
$137$	4.39479	+	16.4016i	0.375472	+	1.40128i	−0.477182	+	0.878804i	$0.658342\pi$
$138$		0			0
$139$	0.575384	+	0.996595i	0.0488035	+	0.0845301i	0.889395	−	0.457139i	$-0.151126\pi$
$139$	0.575384	+	0.996595i	0.0488035	+	0.0845301i	−0.840592	+	0.541669i	$0.817793\pi$
$140$	0.00317680	+	0.0170158i	0.000268489	+	0.00143810i
$141$		0			0
$142$	−3.13655	−	15.6881i	−0.263214	−	1.31651i
$143$	−8.68588	+	8.68588i	−0.726350	+	0.726350i
$144$		0			0
$145$	10.8150	−	7.01337i	0.898139	−	0.582429i
$146$	−10.8267	−	7.21882i	−0.896025	−	0.597434i
$147$		0			0
$148$	−6.56558	+	15.9391i	−0.539687	+	1.31018i
$149$	15.4247	−	8.90547i	1.26364	−	0.729565i	0.289865	−	0.957067i	$-0.406389\pi$
$149$	15.4247	−	8.90547i	1.26364	−	0.729565i	0.973777	+	0.227503i	$0.0730561\pi$
$150$		0			0
$151$	−14.2092	−	8.20368i	−1.15633	−	0.667606i	−0.205906	−	0.978572i	$-0.566014\pi$
$151$	−14.2092	−	8.20368i	−1.15633	−	0.667606i	−0.950421	+	0.310966i	$0.899348\pi$
$152$	17.1697	−	11.5457i	1.39265	−	0.936479i
$153$		0			0
$154$	0.0226259	+	0.00146070i	0.00182325	+	0.000117706i
$155$	−0.237074	−	4.58056i	−0.0190422	−	0.367920i
$156$		0			0
$157$	−0.570890	−	0.152969i	−0.0455620	−	0.0122083i	0.235966	−	0.971761i	$-0.424175\pi$
$157$	−0.570890	−	0.152969i	−0.0455620	−	0.0122083i	−0.281528	+	0.959553i	$0.590841\pi$
$158$	−2.71949	+	8.03726i	−0.216351	+	0.639410i
$159$		0			0
$160$	6.22753	+	11.0099i	0.492329	+	0.870409i
$161$	−0.0149860			−0.00118106
$162$		0			0
$163$	−2.55591	+	2.55591i	−0.200194	+	0.200194i	−0.800083	−	0.599889i	$-0.795211\pi$
$163$	−2.55591	+	2.55591i	−0.200194	+	0.200194i	0.599889	+	0.800083i	$0.295211\pi$
$164$	−5.79946	−	4.43203i	−0.452862	−	0.346084i
$165$		0			0
$166$	−1.83098	−	3.70370i	−0.142112	−	0.287463i
$167$	−2.53503	+	9.46085i	−0.196166	+	0.732103i	0.795796	+	0.605565i	$0.207053\pi$
$167$	−2.53503	+	9.46085i	−0.196166	+	0.732103i	−0.991962	+	0.126537i	$0.959614\pi$
$168$		0			0
$169$	3.64184	+	2.10261i	0.280141	+	0.161740i
$170$	4.54313	+	8.10605i	0.348442	+	0.621706i
$171$		0			0
$172$	1.22402	+	1.58872i	0.0933309	+	0.121138i
$173$	−8.78942	+	2.35512i	−0.668247	+	0.179056i	−0.576965	−	0.816769i	$-0.695763\pi$
$173$	−8.78942	+	2.35512i	−0.668247	+	0.179056i	−0.0912819	+	0.995825i	$0.529096\pi$
$174$		0			0
$175$	−0.0150243	−	0.0121988i	−0.00113573	−	0.000922140i
$176$	15.9867	−	4.35093i	1.20505	−	0.327964i
$177$		0			0
$178$	2.54736	+	12.7411i	0.190933	+	0.954988i
$179$	−9.66859			−0.722664			−0.361332	−	0.932437i	$-0.617678\pi$
$179$	−9.66859			−0.722664			−0.361332	+	0.932437i	$0.617678\pi$
$180$		0			0
$181$	−0.725261			−0.0539082			−0.0269541	−	0.999637i	$-0.508581\pi$
$181$	−0.725261			−0.0539082			−0.0269541	+	0.999637i	$0.508581\pi$
$182$	0.00318257	+	0.0159182i	0.000235908	+	0.00117994i
$183$		0			0
$184$	−10.3594	+	3.55058i	−0.763706	+	0.261752i
$185$	−5.94380	−	18.3337i	−0.436997	−	1.34792i
$186$		0			0
$187$	11.7567	−	3.15021i	0.859737	−	0.230366i
$188$	7.47507	−	5.75915i	0.545175	−	0.420029i
$189$		0			0
$190$	−6.27181	+	22.2664i	−0.455005	+	1.61538i
$191$	4.39149	+	2.53543i	0.317757	+	0.183457i	0.650393	−	0.759598i	$-0.274604\pi$
$191$	4.39149	+	2.53543i	0.317757	+	0.183457i	−0.332635	+	0.943056i	$0.607938\pi$
$192$		0			0
$193$	6.65689	−	24.8439i	0.479174	−	1.78830i	−0.125801	−	0.992056i	$-0.540150\pi$
$193$	6.65689	−	24.8439i	0.479174	−	1.78830i	0.604975	−	0.796245i	$-0.293183\pi$
$194$	1.47102	+	2.97557i	0.105613	+	0.213633i
$195$		0			0
$196$	−8.50084	+	11.1236i	−0.607203	+	0.794544i
$197$	−7.34350	+	7.34350i	−0.523203	+	0.523203i	−0.918537	−	0.395334i	$-0.870629\pi$
$197$	−7.34350	+	7.34350i	−0.523203	+	0.523203i	0.395334	+	0.918537i	$0.370629\pi$
$198$		0			0
$199$	23.5313			1.66809			0.834046	−	0.551695i	$-0.186019\pi$
$199$	23.5313			1.66809			0.834046	+	0.551695i	$0.186019\pi$
$200$	−13.2761	−	4.87302i	−0.938759	−	0.344575i
$201$		0			0
$202$	3.23648	−	9.56518i	0.227718	−	0.673004i
$203$	−0.0215521	−	0.00577488i	−0.00151266	−	0.000405317i
$204$		0			0
$205$	8.14972	−	0.421800i	0.569201	−	0.0294598i
$206$	5.89651	+	0.380669i	0.410829	+	0.0265225i
$207$		0			0
$208$	5.97146	+	10.2498i	0.414046	+	0.710694i
$209$	26.2407	+	15.1501i	1.81511	+	1.04795i
$210$		0			0
$211$	11.4167	−	6.59145i	0.785960	−	0.453774i	−0.0525786	−	0.998617i	$-0.516744\pi$
$211$	11.4167	−	6.59145i	0.785960	−	0.453774i	0.838538	+	0.544843i	$0.183411\pi$
$212$	−18.1230	−	7.46516i	−1.24469	−	0.512709i
$213$		0			0
$214$	−13.7026	−	9.13638i	−0.936693	−	0.624550i
$215$	−2.19298	−	0.467621i	−0.149560	−	0.0318915i
$216$		0			0
$217$	−0.00561407	+	0.00561407i	−0.000381108	+	0.000381108i
$218$	1.78343	+	8.92016i	0.120789	+	0.604150i
$219$		0			0
$220$	−10.4720	+	15.2797i	−0.706021	+	1.03016i
$221$	4.35721	+	7.54691i	0.293098	+	0.507660i
$222$		0			0
$223$	1.78550	+	6.66356i	0.119566	+	0.446225i	0.999588	−	0.0287073i	$-0.00913908\pi$
$223$	1.78550	+	6.66356i	0.119566	+	0.446225i	−0.880022	+	0.474933i	$0.842472\pi$
$224$	0.00693628	−	0.0207677i	0.000463450	−	0.00138760i
$225$		0			0
$226$	−1.41683	+	21.9464i	−0.0942459	+	1.45985i
$227$	23.0916	−	6.18736i	1.53264	−	0.410670i	0.608761	−	0.793354i	$-0.291667\pi$
$227$	23.0916	−	6.18736i	1.53264	−	0.410670i	0.923879	+	0.382684i	$0.125000\pi$
$228$		0			0
$229$	10.8974	−	6.29160i	0.720118	−	0.415761i	−0.0946778	−	0.995508i	$-0.530182\pi$
$229$	10.8974	−	6.29160i	0.720118	−	0.415761i	0.814796	+	0.579747i	$0.196849\pi$
$230$	6.25657	−	10.5243i	0.412546	−	0.693950i
$231$		0			0
$232$	−16.2666	+	1.11425i	−1.06795	+	0.0731542i
$233$	−5.85463	−	5.85463i	−0.383550	−	0.383550i	0.488830	−	0.872379i	$-0.337424\pi$
$233$	−5.85463	−	5.85463i	−0.383550	−	0.383550i	−0.872379	+	0.488830i	$0.837424\pi$
$234$		0			0
$235$	−2.20020	+	10.3182i	−0.143525	+	0.673083i
$236$	8.77357	+	6.70489i	0.571111	+	0.436451i
$237$		0			0
$238$	0.00515540	−	0.0152364i	0.000334175	−	0.000987628i
$239$	8.52459	+	14.7650i	0.551410	+	0.955070i	0.998173	+	0.0604180i	$0.0192434\pi$
$239$	8.52459	+	14.7650i	0.551410	+	0.955070i	−0.446763	+	0.894652i	$0.647423\pi$
$240$		0			0
$241$	−6.97743	+	12.0853i	−0.449456	+	0.778481i	−0.998351	−	0.0574109i	$-0.981715\pi$
$241$	−6.97743	+	12.0853i	−0.449456	+	0.778481i	0.548895	+	0.835892i	$0.315049\pi$
$242$	5.74723	+	6.54051i	0.369446	+	0.420440i
$243$		0			0
$244$	1.84646	−	14.2411i	0.118207	−	0.911692i
$245$	−0.809032	−	15.6315i	−0.0516871	−	0.998661i
$246$		0			0
$247$	−5.61484	+	20.9549i	−0.357264	+	1.33333i
$248$	−2.55073	+	5.21097i	−0.161971	+	0.330897i
$249$		0			0
$250$	14.8394	−	5.45823i	0.938526	−	0.345209i
$251$			5.95154i			0.375658i	0.982202	+	0.187829i	$0.0601451\pi$
$251$			5.95154i			0.375658i	−0.982202	+	0.187829i	$0.939855\pi$
$252$		0			0
$253$	−11.3399	−	11.3399i	−0.712934	−	0.712934i
$254$	−23.5123	−	15.6771i	−1.47530	−	0.983669i
$255$		0			0
$256$	−0.125553	−	15.9995i	−0.00784707	−	0.999969i
$257$	−2.38369	−	0.638709i	−0.148691	−	0.0398416i	0.183706	−	0.982981i	$-0.441191\pi$
$257$	−2.38369	−	0.638709i	−0.148691	−	0.0398416i	−0.332397	+	0.943140i	$0.607857\pi$
$258$		0			0
$259$	−0.0166807	+	0.0288918i	−0.00103649	+	0.00179525i
$260$	−12.5076	−	4.41072i	−0.775691	−	0.273541i
$261$		0			0
$262$	8.75708	−	7.69496i	0.541014	−	0.475396i
$263$	−1.05558	−	3.93947i	−0.0650897	−	0.242918i	0.925714	−	0.378224i	$-0.123465\pi$
$263$	−1.05558	−	3.93947i	−0.0650897	−	0.242918i	−0.990804	+	0.135306i	$0.956798\pi$
$264$		0			0
$265$	20.8456	−	6.75818i	1.28054	−	0.415152i
$266$	0.0358958	−	0.0177456i	0.00220091	−	0.00108805i
$267$		0			0
$268$	−0.871509	−	6.52089i	−0.0532359	−	0.398327i
$269$			14.8292i			0.904151i	0.891980	+	0.452075i	$0.149316\pi$
$269$			14.8292i			0.904151i	−0.891980	+	0.452075i	$0.850684\pi$
$270$		0			0
$271$		−	2.28698i		−	0.138924i	−0.997585	−	0.0694621i	$-0.977872\pi$
$271$		−	2.28698i		−	0.138924i	0.997585	−	0.0694621i	$-0.0221283\pi$
$272$	−0.0461177	−	11.7539i	−0.00279629	−	0.712686i
$273$		0			0
$274$	10.6420	+	21.5267i	0.642909	+	1.30047i
$275$	−2.13806	−	20.5996i	−0.128930	−	1.24221i
$276$		0			0
$277$	0.240544	+	0.897723i	0.0144529	+	0.0539390i	0.972776	−	0.231749i	$-0.0744447\pi$
$277$	0.240544	+	0.897723i	0.0144529	+	0.0539390i	−0.958323	+	0.285688i	$0.907778\pi$
$278$	1.07424	+	1.22252i	0.0644287	+	0.0733216i
$279$		0			0
$280$	0.00912330	+	0.0227162i	0.000545221	+	0.00135756i
$281$	9.59486	−	16.6188i	0.572381	−	0.991394i	−0.423939	−	0.905691i	$-0.639353\pi$
$281$	9.59486	−	16.6188i	0.572381	−	0.991394i	0.996321	−	0.0857030i	$-0.0273136\pi$
$282$		0			0
$283$	−23.2929	−	6.24132i	−1.38462	−	0.371008i	−0.511823	−	0.859091i	$-0.671030\pi$
$283$	−23.2929	−	6.24132i	−1.38462	−	0.371008i	−0.872797	+	0.488083i	$0.837696\pi$
$284$	−8.69934	−	20.8861i	−0.516211	−	1.23936i
$285$		0			0
$286$	−9.63706	+	14.4535i	−0.569851	+	0.854656i
$287$	−0.00998854	−	0.00998854i	−0.000589605	−	0.000589605i
$288$		0			0
$289$			8.36519i			0.492070i
$290$	13.0534	−	12.7245i	0.766522	−	0.747208i
$291$		0			0
$292$	−17.0156	−	7.00903i	−0.995764	−	0.410172i
$293$	−0.547697	+	2.04403i	−0.0319968	+	0.119414i	−0.980077	−	0.198617i	$-0.936355\pi$
$293$	−0.547697	+	2.04403i	−0.0319968	+	0.119414i	0.948080	+	0.318031i	$0.103022\pi$
$294$		0			0
$295$	−12.3291	+	0.638110i	−0.717828	+	0.0371522i
$296$	−4.68567	+	23.9242i	−0.272349	+	1.39057i
$297$		0			0
$298$	18.9214	−	16.6265i	1.09609	−	0.963146i
$299$	5.74104	−	9.94377i	0.332013	−	0.575063i
$300$		0			0
$301$	0.00194068	+	0.00336135i	0.000111859	+	0.000193745i
$302$	−21.9794	−	7.43697i	−1.26477	−	0.427949i
$303$		0			0
$304$	20.6093	−	20.7717i	1.18202	−	1.19134i
$305$	8.73559	+	13.4708i	0.500199	+	0.771335i
$306$		0			0
$307$	10.6198	+	10.6198i	0.606102	+	0.606102i	0.941925	−	0.335823i	$-0.109015\pi$
$307$	10.6198	+	10.6198i	0.606102	+	0.606102i	−0.335823	+	0.941925i	$0.609015\pi$
$308$	0.0317819	−	0.00424762i	0.00181094	−	0.000242031i
$309$		0			0
$310$	−1.59877	−	6.28645i	−0.0908041	−	0.357046i
$311$	−16.3389	+	9.43325i	−0.926493	+	0.534911i	−0.885701	−	0.464257i	$-0.846321\pi$
$311$	−16.3389	+	9.43325i	−0.926493	+	0.534911i	−0.0407921	+	0.999168i	$0.512988\pi$
$312$		0			0
$313$	−16.1114	+	4.31704i	−0.910670	+	0.244013i	−0.683593	−	0.729863i	$-0.739584\pi$
$313$	−16.1114	+	4.31704i	−0.910670	+	0.244013i	−0.227077	+	0.973877i	$0.572917\pi$
$314$	−0.834104	−	0.0538484i	−0.0470712	−	0.00303884i
$315$		0			0
$316$	−1.54290	+	11.8998i	−0.0867948	+	0.669417i
$317$	4.68890	+	17.4992i	0.263355	+	0.982855i	0.963250	+	0.268608i	$0.0865637\pi$
$317$	4.68890	+	17.4992i	0.263355	+	0.982855i	−0.699894	+	0.714246i	$0.746770\pi$
$318$		0			0
$319$	−11.9386	−	20.6783i	−0.668435	−	1.15776i
$320$	11.6887	+	13.5415i	0.653420	+	0.756995i
$321$		0			0
$322$	−0.0207821	+	0.00415502i	−0.00115814	+	0.000231550i
$323$	15.1999	−	15.1999i	0.845745	−	0.845745i
$324$		0			0
$325$	13.8500	−	5.29589i	0.768260	−	0.293763i
$326$	−2.83580	+	4.25310i	−0.157060	+	0.235557i
$327$		0			0
$328$	−9.27133	−	4.53825i	−0.511924	−	0.250583i
$329$	0.0158155	−	0.00913108i	0.000871936	−	0.000503412i
$330$		0			0
$331$	30.9050	+	17.8430i	1.69869	+	0.980741i	0.947003	+	0.321225i	$0.104094\pi$
$331$	30.9050	+	17.8430i	1.69869	+	0.980741i	0.751690	+	0.659516i	$0.229239\pi$
$332$	−3.56604	−	4.62852i	−0.195712	−	0.254023i
$333$		0			0
$334$	−0.892383	+	13.8229i	−0.0488290	+	0.756354i
$335$	5.46293	+	4.92527i	0.298472	+	0.269096i
$336$		0			0
$337$	−20.2317	−	5.42108i	−1.10209	−	0.295305i	−0.338476	−	0.940975i	$-0.609911\pi$
$337$	−20.2317	−	5.42108i	−1.10209	−	0.295305i	−0.763616	+	0.645670i	$0.776578\pi$
$338$	5.63335	+	1.90611i	0.306414	+	0.103678i
$339$		0			0
$340$	8.54776	+	9.98158i	0.463567	+	0.541327i
$341$	−8.49632			−0.460102
$342$		0			0
$343$	−0.0383170	+	0.0383170i	−0.00206892	+	0.00206892i
$344$	2.13792	+	1.86381i	0.115269	+	0.100490i
$345$		0			0
$346$	−11.5359	+	5.70295i	−0.620174	+	0.306593i
$347$	2.65861	−	9.92205i	0.142721	−	0.532644i	−0.857125	−	0.515109i	$-0.827752\pi$
$347$	2.65861	−	9.92205i	0.142721	−	0.532644i	0.999846	−	0.0175348i	$-0.00558179\pi$
$348$		0			0
$349$	15.7613	+	9.09980i	0.843683	+	0.487101i	0.858515	−	0.512789i	$-0.171388\pi$
$349$	15.7613	+	9.09980i	0.843683	+	0.487101i	−0.0148311	+	0.999890i	$0.504721\pi$
$350$	−0.0242174	−	0.0127512i	−0.00129448	−	0.000681583i
$351$		0			0
$352$	20.9636	−	10.4662i	1.11736	−	0.557851i
$353$	−16.2917	+	4.36534i	−0.867119	+	0.232344i	−0.664842	−	0.746984i	$-0.731501\pi$
$353$	−16.2917	+	4.36534i	−0.867119	+	0.232344i	−0.202277	+	0.979328i	$0.564834\pi$
$354$		0			0
$355$	22.5314	+	11.4987i	1.19584	+	0.610290i
$356$	7.06521	+	16.9627i	0.374455	+	0.899023i
$357$		0			0
$358$	−13.4081	+	2.68071i	−0.708640	+	0.141680i
$359$	26.8572			1.41747			0.708736	−	0.705474i	$-0.249266\pi$
$359$	26.8572			1.41747			0.708736	+	0.705474i	$0.249266\pi$
$360$		0			0
$361$	34.5129			1.81647
$362$	−1.00577	+	0.201086i	−0.0528621	+	0.0105688i
$363$		0			0
$364$	0.00882697	+	0.0211925i	0.000462659	+	0.00111079i
$365$	19.5719	−	6.34525i	1.02444	−	0.332126i
$366$		0			0
$367$	−6.10468	+	1.63574i	−0.318662	+	0.0853851i	−0.414604	−	0.910002i	$-0.636080\pi$
$367$	−6.10468	+	1.63574i	−0.318662	+	0.0853851i	0.0959429	+	0.995387i	$0.469413\pi$
$368$	−13.3817	+	7.79608i	−0.697568	+	0.406399i
$369$		0			0
$370$	−13.3259	−	23.7766i	−0.692778	−	1.23608i
$371$	−0.0328504	−	0.0189662i	−0.00170551	−	0.000984676i
$372$		0			0
$373$	−3.25424	+	12.1450i	−0.168498	+	0.628843i	0.829070	+	0.559145i	$0.188870\pi$
$373$	−3.25424	+	12.1450i	−0.168498	+	0.628843i	−0.997568	+	0.0696984i	$0.977796\pi$
$374$	15.4304	−	7.62828i	0.797889	−	0.394449i
$375$		0			0
$376$	8.76940	−	10.0591i	0.452248	−	0.518761i
$377$	12.0883	−	12.0883i	0.622579	−	0.622579i
$378$		0			0
$379$	−13.2087			−0.678488			−0.339244	−	0.940698i	$-0.610171\pi$
$379$	−13.2087			−0.678488			−0.339244	+	0.940698i	$0.610171\pi$
$380$	−2.52397	+	32.6173i	−0.129477	+	1.67323i
$381$		0			0
$382$	6.79296	+	2.29847i	0.347558	+	0.117600i
$383$	18.1781	+	4.87081i	0.928858	+	0.248887i	0.691368	−	0.722503i	$-0.257009\pi$
$383$	18.1781	+	4.87081i	0.928858	+	0.248887i	0.237490	+	0.971390i	$0.423675\pi$
$384$		0			0
$385$	−0.0240051	+	0.0266256i	−0.00122341	+	0.00135697i
$386$	2.34337	−	36.2984i	0.119274	−	1.84754i
$387$		0			0
$388$	2.86497	+	3.71857i	0.145447	+	0.188782i
$389$	1.13890	+	0.657543i	0.0577444	+	0.0333388i	0.528594	−	0.848875i	$-0.322719\pi$
$389$	1.13890	+	0.657543i	0.0577444	+	0.0333388i	−0.470850	+	0.882213i	$0.656053\pi$
$390$		0			0
$391$	−9.85292	+	5.68859i	−0.498284	+	0.287684i
$392$	−8.70456	+	17.7828i	−0.439647	+	0.898168i
$393$		0			0
$394$	−8.14768	+	12.2198i	−0.410474	+	0.615624i
$395$	−7.29944	−	11.2562i	−0.367275	−	0.566359i
$396$		0			0
$397$	0.714896	−	0.714896i	0.0358796	−	0.0358796i	−0.688939	−	0.724819i	$-0.741923\pi$
$397$	0.714896	−	0.714896i	0.0358796	−	0.0358796i	0.724819	+	0.688939i	$0.241923\pi$
$398$	32.6325	−	6.52429i	1.63572	−	0.327033i
$399$		0			0
$400$	−19.7619	−	3.07684i	−0.988095	−	0.153842i
$401$	9.93987	+	17.2164i	0.496373	+	0.859744i	0.999991	−	0.00418285i	$-0.00133145\pi$
$401$	9.93987	+	17.2164i	0.496373	+	0.859744i	−0.503618	+	0.863926i	$0.667998\pi$
$402$		0			0
$403$	−1.57443	−	5.87585i	−0.0784279	−	0.292697i
$404$	1.83621	−	14.1620i	0.0913549	−	0.704588i
$405$		0			0
$406$	−0.0314890	−	0.00203288i	−0.00156277	−	0.000100890i
$407$	−34.4847	+	9.24014i	−1.70934	+	0.458017i
$408$		0			0
$409$	−21.4875	+	12.4058i	−1.06249	+	0.613428i	−0.926120	−	0.377230i	$-0.876877\pi$
$409$	−21.4875	+	12.4058i	−1.06249	+	0.613428i	−0.136369	+	0.990658i	$0.543543\pi$
$410$	11.1848	−	2.84453i	0.552379	−	0.140481i
$411$		0			0
$412$	8.28264	−	1.10696i	0.408056	−	0.0545362i
$413$	0.0151109	+	0.0151109i	0.000743560	+	0.000743560i
$414$		0			0
$415$	6.38896	+	1.36235i	0.313622	+	0.0668753i
$416$	11.1229	+	12.5584i	0.545344	+	0.615728i
$417$		0			0
$418$	40.5904	+	13.7342i	1.98534	+	0.671761i
$419$	−14.0411	−	24.3199i	−0.685953	−	1.18811i	−0.973136	−	0.230230i	$-0.926052\pi$
$419$	−14.0411	−	24.3199i	−0.685953	−	1.18811i	0.287183	−	0.957876i	$-0.407281\pi$
$420$		0			0
$421$	0.651510	−	1.12845i	0.0317527	−	0.0549972i	−0.849712	−	0.527246i	$-0.823224\pi$
$421$	0.651510	−	1.12845i	0.0317527	−	0.0549972i	0.881465	+	0.472249i	$0.156558\pi$
$422$	14.0048	−	12.3062i	0.681743	−	0.599057i
$423$		0			0
$424$	−27.2021	−	5.32768i	−1.32105	−	0.258735i
$425$	−14.5086	−	2.31727i	−0.703772	−	0.112404i
$426$		0			0
$427$	0.00719297	−	0.0268445i	0.000348092	−	0.00129910i
$428$	−21.5355	−	8.87085i	−1.04096	−	0.428789i
$429$		0			0
$430$	−3.17080	−	0.0404574i	−0.152910	−	0.00195103i
$431$			14.1271i			0.680479i	0.940339	+	0.340240i	$0.110508\pi$
$431$			14.1271i			0.680479i	−0.940339	+	0.340240i	$0.889492\pi$
$432$		0			0
$433$	−4.90201	−	4.90201i	−0.235576	−	0.235576i	0.579440	−	0.815015i	$-0.303271\pi$
$433$	−4.90201	−	4.90201i	−0.235576	−	0.235576i	−0.815015	+	0.579440i	$0.803271\pi$
$434$	−0.00622886	+	0.00934198i	−0.000298995	+	0.000448429i
$435$		0			0
$436$	4.94640	+	11.8757i	0.236890	+	0.568744i
$437$	−27.3578	−	7.33050i	−1.30870	−	0.350665i
$438$		0			0
$439$	−14.2344	+	24.6546i	−0.679369	+	1.17670i	0.295803	+	0.955249i	$0.404413\pi$
$439$	−14.2344	+	24.6546i	−0.679369	+	1.17670i	−0.975171	+	0.221452i	$0.928920\pi$
$440$	−10.2858	+	24.0929i	−0.490354	+	1.14859i
$441$		0			0
$442$	8.13490	+	9.25774i	0.386938	+	0.440346i
$443$	6.32386	+	23.6010i	0.300456	+	1.12132i	0.936787	+	0.349900i	$0.113784\pi$
$443$	6.32386	+	23.6010i	0.300456	+	1.12132i	−0.636332	+	0.771416i	$0.719549\pi$
$444$		0			0
$445$	−18.2989	−	9.33876i	−0.867453	−	0.442700i
$446$	4.32361	+	8.74578i	0.204729	+	0.414124i
$447$		0			0
$448$	0.00386097	−	0.0307232i	0.000182414	−	0.00145153i
$449$		−	32.1553i		−	1.51750i	−0.651382	−	0.758750i	$-0.725810\pi$
$449$		−	32.1553i		−	1.51750i	0.651382	−	0.758750i	$-0.274190\pi$
$450$		0			0
$451$		−	15.1166i		−	0.711814i
$452$	4.12005	+	30.8274i	0.193791	+	1.45000i
$453$		0			0
$454$	30.3071	−	14.9828i	1.42238	−	0.703178i
$455$	−0.0228619	−	0.0116674i	−0.00107178	−	0.000546978i
$456$		0			0
$457$	2.92218	+	10.9057i	0.136694	+	0.510149i	0.999985	+	0.00544282i	$0.00173251\pi$
$457$	2.92218	+	10.9057i	0.136694	+	0.510149i	−0.863291	+	0.504706i	$0.831601\pi$
$458$	13.3677	−	11.7464i	0.624633	−	0.548873i
$459$		0			0
$460$	5.75845	−	16.3294i	0.268489	−	0.761363i
$461$	1.41470	−	2.45032i	0.0658889	−	0.114123i	−0.831199	−	0.555975i	$-0.812345\pi$
$461$	1.41470	−	2.45032i	0.0658889	−	0.114123i	0.897088	+	0.441852i	$0.145678\pi$
$462$		0			0
$463$	20.7678	+	5.56471i	0.965161	+	0.258614i	0.706783	−	0.707430i	$-0.250146\pi$
$463$	20.7678	+	5.56471i	0.965161	+	0.258614i	0.258377	+	0.966044i	$0.416812\pi$
$464$	−22.2491	+	6.05528i	−1.03289	+	0.281109i
$465$		0			0
$466$	−9.74228	−	6.49577i	−0.451302	−	0.300911i
$467$	0.746518	+	0.746518i	0.0345447	+	0.0345447i	0.724168	−	0.689623i	$-0.242224\pi$
$467$	0.746518	+	0.746518i	0.0345447	+	0.0345447i	−0.689623	+	0.724168i	$0.742224\pi$
$468$		0			0
$469$		−	0.0127321i		−	0.000587914i
$470$	−0.190356	+	14.9189i	−0.00878047	+	0.688160i
$471$		0			0
$472$	14.0259	+	6.86558i	0.645595	+	0.316014i
$473$	−1.07502	+	4.01204i	−0.0494296	+	0.184474i
$474$		0			0
$475$	−21.4605	−	29.6187i	−0.984676	−	1.35900i
$476$	0.00292490	−	0.0225587i	0.000134063	−	0.00103398i
$477$		0			0
$478$	15.9154	+	18.1122i	0.727953	+	0.828430i
$479$	−8.68475	+	15.0424i	−0.396816	+	0.687306i	−0.993331	−	0.115296i	$-0.963218\pi$
$479$	−8.68475	+	15.0424i	−0.396816	+	0.687306i	0.596515	+	0.802602i	$0.296552\pi$
$480$		0			0
$481$	−12.7805	−	22.1365i	−0.582741	−	1.00934i
$482$	−6.32533	+	18.6940i	−0.288111	+	0.851490i
$483$		0			0
$484$	9.78351	+	7.47670i	0.444705	+	0.339850i
$485$	−5.13291	−	1.09452i	−0.233073	−	0.0496995i
$486$		0			0
$487$	−17.2233	−	17.2233i	−0.780462	−	0.780462i	0.199447	−	0.979909i	$-0.436086\pi$
$487$	−17.2233	−	17.2233i	−0.780462	−	0.780462i	−0.979909	+	0.199447i	$0.936086\pi$
$488$	−1.38787	−	20.2610i	−0.0628259	−	0.917174i
$489$		0			0
$490$	−5.45593	−	21.4530i	−0.246474	−	0.969147i
$491$	−13.8880	+	8.01824i	−0.626757	+	0.361858i	−0.779495	−	0.626409i	$-0.784524\pi$
$491$	−13.8880	+	8.01824i	−0.626757	+	0.361858i	0.152738	+	0.988267i	$0.451191\pi$
$492$		0			0
$493$	−16.3621	+	4.38420i	−0.736910	+	0.197455i
$494$	−1.97654	+	30.6163i	−0.0889288	+	1.37749i
$495$		0			0
$496$	−2.09248	+	7.93362i	−0.0939551	+	0.356230i
$497$	−0.0113329	−	0.0422949i	−0.000508349	−	0.00189718i
$498$		0			0
$499$	−18.9316	−	32.7905i	−0.847494	−	1.46790i	−0.883438	−	0.468548i	$-0.844777\pi$
$499$	−18.9316	−	32.7905i	−0.847494	−	1.46790i	0.0359441	−	0.999354i	$-0.488556\pi$
$500$	19.0655	−	11.6837i	0.852633	−	0.522510i
$501$		0			0
$502$	1.65012	+	8.25341i	0.0736486	+	0.368368i
$503$	1.97514	−	1.97514i	0.0880673	−	0.0880673i	−0.661701	−	0.749768i	$-0.730165\pi$
$503$	1.97514	−	1.97514i	0.0880673	−	0.0880673i	0.749768	+	0.661701i	$0.230165\pi$
$504$		0			0
$505$	8.68710	+	13.3960i	0.386571	+	0.596115i
$506$	−18.8699	−	12.5817i	−0.838870	−	0.559326i
$507$		0			0
$508$	−36.9528	−	15.2215i	−1.63952	−	0.675344i
$509$	−23.3128	+	13.4596i	−1.03332	+	0.596587i	−0.917934	−	0.396733i	$-0.870144\pi$
$509$	−23.3128	+	13.4596i	−1.03332	+	0.596587i	−0.115386	+	0.993321i	$0.536810\pi$
$510$		0			0
$511$	−0.0308432	−	0.0178073i	−0.00136442	−	0.000787750i
$512$	−4.61013	−	22.1528i	−0.203741	−	0.979025i
$513$		0			0
$514$	−3.48272	−	0.224839i	−0.153616	−	0.00991722i
$515$	−6.25594	+	6.93885i	−0.275669	+	0.305762i
$516$		0			0
$517$	18.8770	+	5.05809i	0.830211	+	0.222454i
$518$	−0.0151217	+	0.0446912i	−0.000664411	+	0.00196362i
$519$		0			0
$520$	−18.5681	−	2.64879i	−0.814266	−	0.116157i
$521$	−15.4522			−0.676975			−0.338487	−	0.940971i	$-0.609915\pi$
$521$	−15.4522			−0.676975			−0.338487	+	0.940971i	$0.609915\pi$
$522$		0			0
$523$	3.28250	−	3.28250i	0.143534	−	0.143534i	−0.631689	−	0.775222i	$-0.717638\pi$
$523$	3.28250	−	3.28250i	0.143534	−	0.143534i	0.775222	+	0.631689i	$0.217638\pi$
$524$	10.0105	−	13.0991i	0.437312	−	0.572237i
$525$		0			0
$526$	−2.55610	−	5.17046i	−0.111451	−	0.225443i
$527$	−1.56005	+	5.82217i	−0.0679566	+	0.253618i
$528$		0			0
$529$	−6.93643	−	4.00475i	−0.301584	−	0.174120i
$530$	27.0343	−	15.1517i	1.17429	−	0.658147i
$531$		0			0
$532$	0.0448590	−	0.0345615i	0.00194488	−	0.00149843i
$533$	10.4543	−	2.80122i	0.452826	−	0.121334i
$534$		0			0
$535$	24.7709	−	8.03076i	1.07094	−	0.347200i
$536$	−3.01656	−	8.80133i	−0.130296	−	0.380160i
$537$		0			0
$538$	4.11153	+	20.5646i	0.177261	+	0.886604i
$539$	−28.9944			−1.24888
$540$		0			0
$541$	−28.5369			−1.22690			−0.613448	−	0.789735i	$-0.710218\pi$
$541$	−28.5369			−1.22690			−0.613448	+	0.789735i	$0.710218\pi$
$542$	−0.634088	−	3.17152i	−0.0272364	−	0.136228i
$543$		0			0
$544$	−3.32285	−	16.2872i	−0.142466	−	0.698307i
$545$	−12.8112	−	6.53813i	−0.548773	−	0.280063i
$546$		0			0
$547$	34.8130	−	9.32812i	1.48850	−	0.398842i	0.579268	−	0.815137i	$-0.303338\pi$
$547$	34.8130	−	9.32812i	1.48850	−	0.398842i	0.909229	+	0.416295i	$0.136672\pi$
$548$	20.7265	+	26.9019i	0.885394	+	1.14919i
$549$		0			0
$550$	−8.67644	−	27.9741i	−0.369965	−	1.19282i
$551$	−36.5197	−	21.0847i	−1.55579	−	0.898238i
$552$		0			0
$553$	−0.00601043	+	0.0224312i	−0.000255589	+	0.000953872i
$554$	0.582482	+	1.17824i	0.0247473	+	0.0500587i
$555$		0			0
$556$	1.82868	+	1.39750i	0.0775532	+	0.0592673i
$557$	11.9128	−	11.9128i	0.504762	−	0.504762i	−0.408152	−	0.912914i	$-0.633827\pi$
$557$	11.9128	−	11.9128i	0.504762	−	0.504762i	0.912914	+	0.408152i	$0.133827\pi$
$558$		0			0
$559$	−2.97383			−0.125780
$560$	0.0189502	+	0.0289726i	0.000800792	+	0.00122432i
$561$		0			0
$562$	8.69813	−	25.7067i	0.366908	−	1.08437i
$563$	−6.87323	−	1.84168i	−0.289672	−	0.0776174i	0.111057	−	0.993814i	$-0.464576\pi$
$563$	−6.87323	−	1.84168i	−0.289672	−	0.0776174i	−0.400729	+	0.916197i	$0.631243\pi$
$564$		0			0
$565$	−25.8259	−	23.2842i	−1.08651	−	0.979573i
$566$	−34.0324	−	2.19708i	−1.43049	−	0.0923500i
$567$		0			0
$568$	−17.8548	−	26.5522i	−0.749173	−	1.11410i
$569$	−37.4538	−	21.6240i	−1.57015	−	0.906524i	−0.996150	−	0.0876662i	$-0.972059\pi$
$569$	−37.4538	−	21.6240i	−1.57015	−	0.906524i	−0.573996	−	0.818858i	$-0.694608\pi$
$570$		0			0
$571$	−15.2197	+	8.78710i	−0.636925	+	0.367729i	−0.783429	−	0.621481i	$-0.786531\pi$
$571$	−15.2197	+	8.78710i	−0.636925	+	0.367729i	0.146504	+	0.989210i	$0.453198\pi$
$572$	−9.35698	+	22.7157i	−0.391235	+	0.949791i
$573$		0			0
$574$	−0.0166212	−	0.0110824i	−0.000693756	−	0.000462569i
$575$	6.91408	+	18.0820i	0.288337	+	0.754071i
$576$		0			0
$577$	−14.1684	+	14.1684i	−0.589837	+	0.589837i	−0.937587	−	0.347750i	$-0.886946\pi$
$577$	−14.1684	+	14.1684i	−0.589837	+	0.589837i	0.347750	+	0.937587i	$0.386946\pi$
$578$	2.31933	+	11.6006i	0.0964715	+	0.482521i
$579$		0			0
$580$	14.5741	−	21.2651i	0.605155	−	0.882986i
$581$	−0.00565392	−	0.00979287i	−0.000234564	−	0.000406277i
$582$		0			0
$583$	−10.5062	−	39.2096i	−0.435121	−	1.62389i
$584$	−25.5401	−	5.00215i	−1.05685	−	0.206990i
$585$		0			0
$586$	−0.192801	+	2.98645i	−0.00796452	+	0.123369i
$587$	−1.37987	+	0.369735i	−0.0569533	+	0.0152606i	−0.287183	−	0.957876i	$-0.592719\pi$
$587$	−1.37987	+	0.369735i	−0.0569533	+	0.0152606i	0.230230	+	0.973136i	$0.426052\pi$
$588$		0			0
$589$	−12.9949	+	7.50263i	−0.535447	+	0.309141i
$590$	−16.9207	+	4.30328i	−0.696614	+	0.177163i
$591$		0			0
$592$	0.135272	+	34.4765i	0.00555963	+	1.41697i
$593$	−3.47274	−	3.47274i	−0.142608	−	0.142608i	0.632198	−	0.774807i	$-0.282153\pi$
$593$	−3.47274	−	3.47274i	−0.142608	−	0.142608i	−0.774807	+	0.632198i	$0.782153\pi$
$594$		0			0
$595$	0.0138377	+	0.0213385i	0.000567290	+	0.000874794i
$596$	21.6297	−	28.3032i	0.885989	−	1.15935i
$597$		0			0
$598$	5.20448	−	15.3815i	0.212827	−	0.628995i
$599$	−6.20251	−	10.7431i	−0.253428	−	0.438950i	0.711040	−	0.703152i	$-0.248225\pi$
$599$	−6.20251	−	10.7431i	−0.253428	−	0.438950i	−0.964467	+	0.264202i	$0.914891\pi$
$600$		0			0
$601$	1.54486	−	2.67578i	0.0630162	−	0.109147i	−0.832796	−	0.553580i	$-0.813261\pi$
$601$	1.54486	−	2.67578i	0.0630162	−	0.109147i	0.895812	+	0.444433i	$0.146595\pi$
$602$	0.00362324	+	0.00412334i	0.000147672	+	0.000168055i
$603$		0			0
$604$	−32.5423	−	4.21935i	−1.32413	−	0.171683i
$605$	−13.7483	+	0.711564i	−0.558949	+	0.0289292i
$606$		0			0
$607$	−9.90537	+	36.9673i	−0.402046	+	1.50046i	0.407392	+	0.913253i	$0.366438\pi$
$607$	−9.90537	+	36.9673i	−0.402046	+	1.50046i	−0.809439	+	0.587204i	$0.800228\pi$
$608$	22.8212	−	34.5196i	0.925522	−	1.39996i
$609$		0			0
$610$	15.8492	+	16.2588i	0.641713	+	0.658301i
$611$			13.9922i			0.566063i
$612$		0			0
$613$	14.5099	+	14.5099i	0.586049	+	0.586049i	0.936559	−	0.350510i	$-0.113992\pi$
$613$	14.5099	+	14.5099i	0.586049	+	0.586049i	−0.350510	+	0.936559i	$0.613992\pi$
$614$	17.6716	+	11.7827i	0.713167	+	0.475512i
$615$		0			0
$616$	0.0428965	−	0.0147023i	0.00172835	−	0.000592373i
$617$	0.139417	+	0.0373567i	0.00561272	+	0.00150392i	0.261624	−	0.965170i	$-0.415742\pi$
$617$	0.139417	+	0.0373567i	0.00561272	+	0.00150392i	−0.256012	+	0.966674i	$0.582409\pi$
$618$		0			0
$619$	−13.6832	+	23.7000i	−0.549975	+	0.952584i	0.448301	+	0.893883i	$0.352029\pi$
$619$	−13.6832	+	23.7000i	−0.549975	+	0.952584i	−0.998276	+	0.0587016i	$0.981304\pi$
$620$	−3.96010	−	8.27457i	−0.159042	−	0.332315i
$621$		0			0
$622$	−20.0428	+	17.6119i	−0.803642	+	0.706171i
$623$	0.00920405	+	0.0343500i	0.000368752	+	0.00137620i
$624$		0			0
$625$	−7.78718	+	23.7563i	−0.311487	+	0.950250i
$626$	−21.1458	+	10.4538i	−0.845158	+	0.417817i
$627$		0			0
$628$	−1.17164	+	0.156588i	−0.0467535	+	0.00624855i
$629$			25.3275i			1.00987i
$630$		0			0
$631$		−	26.4593i		−	1.05333i	−0.850074	−	0.526664i	$-0.823443\pi$
$631$		−	26.4593i		−	1.05333i	0.850074	−	0.526664i	$-0.176557\pi$
$632$	1.15970	+	16.9301i	0.0461304	+	0.673443i
$633$		0			0
$634$	11.3543	+	22.9673i	0.450935	+	0.912149i
$635$	42.5043	−	13.7800i	1.68673	−	0.546841i
$636$		0			0
$637$	−5.37286	−	20.0518i	−0.212880	−	0.794481i
$638$	−22.2894	−	25.3659i	−0.882445	−	1.00425i
$639$		0			0
$640$	19.9641	+	15.5382i	0.789150	+	0.614200i
$641$	2.73281	−	4.73337i	0.107940	−	0.186957i	−0.806996	−	0.590557i	$-0.798908\pi$
$641$	2.73281	−	4.73337i	0.107940	−	0.186957i	0.914935	+	0.403600i	$0.132241\pi$
$642$		0			0
$643$	40.3996	+	10.8251i	1.59321	+	0.426898i	0.942982	−	0.332844i	$-0.108008\pi$
$643$	40.3996	+	10.8251i	1.59321	+	0.426898i	0.650225	+	0.759742i	$0.274675\pi$
$644$	−0.0276680	+	0.0115241i	−0.00109027	+	0.000454113i
$645$		0			0
$646$	16.8644	−	25.2930i	0.663521	−	0.995142i
$647$	19.6463	+	19.6463i	0.772377	+	0.772377i	0.978522	−	0.206144i	$-0.0660917\pi$
$647$	19.6463	+	19.6463i	0.772377	+	0.772377i	−0.206144	+	0.978522i	$0.566092\pi$
$648$		0			0
$649$			22.8688i			0.897680i
$650$	17.7384	−	11.1842i	0.695758	−	0.438681i
$651$		0			0
$652$	−2.75339	+	6.68432i	−0.107831	+	0.261778i
$653$	3.22941	−	12.0523i	0.126376	−	0.471643i	−0.873509	−	0.486809i	$-0.838161\pi$
$653$	3.22941	−	12.0523i	0.126376	−	0.471643i	0.999885	+	0.0151655i	$0.00482752\pi$
$654$		0			0
$655$	0.952711	+	18.4076i	0.0372255	+	0.719244i
$656$	−14.1155	−	3.72293i	−0.551116	−	0.145356i
$657$		0			0
$658$	0.0194007	−	0.0170477i	0.000756320	−	0.000664588i
$659$	−2.60988	+	4.52045i	−0.101667	+	0.176092i	−0.912371	−	0.409363i	$-0.865751\pi$
$659$	−2.60988	+	4.52045i	−0.101667	+	0.176092i	0.810705	+	0.585455i	$0.199084\pi$
$660$		0			0
$661$	17.0620	+	29.5522i	0.663633	+	1.14945i	0.979654	+	0.200694i	$0.0643198\pi$
$661$	17.0620	+	29.5522i	0.663633	+	1.14945i	−0.316021	+	0.948752i	$0.602347\pi$
$662$	47.8053	+	16.1754i	1.85800	+	0.628676i
$663$		0			0
$664$	−6.22857	−	5.42997i	−0.241716	−	0.210724i
$665$	−0.0132037	+	0.0619209i	−0.000512019	+	0.00240119i
$666$		0			0
$667$	15.7820	+	15.7820i	0.611080	+	0.611080i
$668$	2.59500	+	19.4165i	0.100403	+	0.751249i
$669$		0			0
$670$	8.94140	+	5.31556i	0.345436	+	0.205358i
$671$	25.7561	−	14.8703i	0.994304	−	0.574062i
$672$		0			0
$673$	20.7053	−	5.54797i	0.798132	−	0.213859i	0.163368	−	0.986565i	$-0.447764\pi$
$673$	20.7053	−	5.54797i	0.798132	−	0.213859i	0.634763	+	0.772706i	$0.281098\pi$
$674$	−29.5598	−	1.90833i	−1.13860	−	0.0735062i
$675$		0			0
$676$	8.34064	+	1.08142i	0.320794	+	0.0415933i
$677$	−2.26411	−	8.44976i	−0.0870167	−	0.324751i	0.908672	−	0.417511i	$-0.137098\pi$
$677$	−2.26411	−	8.44976i	−0.0870167	−	0.324751i	−0.995688	+	0.0927605i	$0.970431\pi$
$678$		0			0
$679$	0.00454237	+	0.00786762i	0.000174320	+	0.000301931i
$680$	14.6213	+	11.4722i	0.560699	+	0.439939i
$681$		0			0
$682$	−11.7824	+	2.35569i	−0.451173	+	0.0902040i
$683$	−4.25385	+	4.25385i	−0.162769	+	0.162769i	−0.783792	−	0.621023i	$-0.786717\pi$
$683$	−4.25385	+	4.25385i	−0.162769	+	0.162769i	0.621023	+	0.783792i	$0.286717\pi$
$684$		0			0
$685$	−37.1339	−	7.91827i	−1.41881	−	0.302542i
$686$	−0.0425130	+	0.0637605i	−0.00162315	+	0.00243439i
$687$		0			0
$688$	3.48157	+	1.99191i	0.132733	+	0.0759409i
$689$	25.1695	−	14.5316i	0.958882	−	0.553611i
$690$		0			0
$691$	15.0306	+	8.67790i	0.571789	+	0.330123i	0.757864	−	0.652413i	$-0.226243\pi$
$691$	15.0306	+	8.67790i	0.571789	+	0.330123i	−0.186074	+	0.982536i	$0.559577\pi$
$692$	−14.4164	+	11.1071i	−0.548031	+	0.422229i
$693$		0			0
$694$	0.935885	−	14.4967i	0.0355257	−	0.550288i
$695$	−2.56976	+	0.133002i	−0.0974765	+	0.00504503i
$696$		0			0
$697$	−10.3588	−	2.77563i	−0.392367	−	0.105134i
$698$	24.3803	+	8.24933i	0.922808	+	0.312242i
$699$		0			0
$700$	−0.0371194	−	0.0109685i	−0.00140298	−	0.000414571i
$701$	23.2157			0.876846			0.438423	−	0.898769i	$-0.355537\pi$
$701$	23.2157			0.876846			0.438423	+	0.898769i	$0.355537\pi$
$702$		0			0
$703$	−44.5841	+	44.5841i	−1.68152	+	1.68152i
$704$	26.1698	−	20.3266i	0.986310	−	0.766087i
$705$		0			0
$706$	−21.3825	+	10.5708i	−0.804740	+	0.397836i
$707$	0.00715304	−	0.0266955i	0.000269018	−	0.00100399i
$708$		0			0
$709$	−22.8813	−	13.2105i	−0.859327	−	0.496133i	0.00446000	−	0.999990i	$-0.498580\pi$
$709$	−22.8813	−	13.2105i	−0.859327	−	0.496133i	−0.863787	+	0.503857i	$0.831914\pi$
$710$	34.4339	+	9.69906i	1.29228	+	0.363999i
$711$		0			0
$712$	14.5009	+	21.5645i	0.543444	+	0.808163i
$713$	7.67125	−	2.05551i	0.287291	−	0.0769793i
$714$		0			0
$715$	−8.47085	−	26.1283i	−0.316792	−	0.977144i
$716$	−17.8507	+	7.43505i	−0.667111	+	0.277861i
$717$		0			0
$718$	37.2448	−	7.44643i	1.38996	−	0.277898i
$719$	12.9840			0.484220			0.242110	−	0.970249i	$-0.422160\pi$
$719$	12.9840			0.484220			0.242110	+	0.970249i	$0.422160\pi$
$720$		0			0
$721$	0.0161719			0.000602274
$722$	47.8614	−	9.56903i	1.78122	−	0.356123i
$723$		0			0
$724$	−1.33902	+	0.557719i	−0.0497641	+	0.0207275i
$725$	2.97557	+	28.6689i	0.110510	+	1.06474i
$726$		0			0
$727$	1.64028	−	0.439513i	0.0608348	−	0.0163006i	−0.228273	−	0.973597i	$-0.573308\pi$
$727$	1.64028	−	0.439513i	0.0608348	−	0.0163006i	0.289108	+	0.957296i	$0.406641\pi$
$728$	0.0181168	+	0.0269417i	0.000671453	+	0.000998527i
$729$		0			0
$730$	25.3824	−	14.2259i	0.939446	−	0.526524i
$731$	2.55189	+	1.47333i	0.0943850	+	0.0544932i
$732$		0			0
$733$	−2.20422	+	8.22626i	−0.0814147	+	0.303844i	−0.994611	−	0.103676i	$-0.966940\pi$
$733$	−2.20422	+	8.22626i	−0.0814147	+	0.303844i	0.913196	+	0.407520i	$0.133606\pi$
$734$	−8.01225	+	3.96098i	−0.295737	+	0.146202i
$735$		0			0
$736$	−16.3957	+	14.5216i	−0.604355	+	0.535272i
$737$	9.63436	−	9.63436i	0.354886	−	0.354886i
$738$		0			0
$739$	19.1571			0.704704			0.352352	−	0.935867i	$-0.385382\pi$
$739$	19.1571			0.704704			0.352352	+	0.935867i	$0.385382\pi$
$740$	−25.0722	−	29.2779i	−0.921671	−	1.07628i
$741$		0			0
$742$	−0.0508145	−	0.0171936i	−0.00186546	−	0.000631198i
$743$	−6.78298	−	1.81749i	−0.248843	−	0.0666774i	0.132241	−	0.991218i	$-0.457783\pi$
$743$	−6.78298	−	1.81749i	−0.248843	−	0.0666774i	−0.381085	+	0.924540i	$0.624449\pi$
$744$		0			0
$745$	2.05852	+	39.7732i	0.0754184	+	1.45718i
$746$	−1.14556	+	17.7445i	−0.0419419	+	0.649674i
$747$		0			0
$748$	19.2834	−	14.8569i	0.705072	−	0.543222i
$749$	−0.0390362	−	0.0225375i	−0.00142635	−	0.000823504i
$750$		0			0
$751$	−26.5621	+	15.3357i	−0.969266	+	0.559606i	−0.899012	−	0.437923i	$-0.855714\pi$
$751$	−26.5621	+	15.3357i	−0.969266	+	0.559606i	−0.0702536	+	0.997529i	$0.522381\pi$
$752$	9.37214	−	16.3811i	0.341767	−	0.597358i
$753$		0			0
$754$	13.4121	−	20.1153i	0.488439	−	0.732555i
$755$	30.7821	−	19.9617i	1.12028	−	0.726481i
$756$		0			0
$757$	8.66077	−	8.66077i	0.314781	−	0.314781i	−0.531978	−	0.846758i	$-0.678551\pi$
$757$	8.66077	−	8.66077i	0.314781	−	0.314781i	0.846758	+	0.531978i	$0.178551\pi$
$758$	−18.3175	+	3.66225i	−0.665320	+	0.133019i
$759$		0			0
$760$	5.54329	+	45.9324i	0.201076	+	1.66614i
$761$	−12.3194	−	21.3379i	−0.446578	−	0.773497i	0.551582	−	0.834121i	$-0.314024\pi$
$761$	−12.3194	−	21.3379i	−0.446578	−	0.773497i	−0.998161	+	0.0606239i	$0.980691\pi$
$762$		0			0
$763$	0.00644382	+	0.0240487i	0.000233282	+	0.000870620i
$764$	10.0575	+	1.30403i	0.363869	+	0.0471782i
$765$		0			0
$766$	26.5593	+	1.71463i	0.959627	+	0.0619520i
$767$	−15.8155	+	4.23776i	−0.571065	+	0.153016i
$768$		0			0
$769$	16.9731	−	9.79945i	0.612067	−	0.353377i	−0.161707	−	0.986839i	$-0.551700\pi$
$769$	16.9731	−	9.79945i	0.612067	−	0.353377i	0.773774	+	0.633462i	$0.218367\pi$
$770$	−0.0259073	+	0.0435792i	−0.000933636	+	0.00157048i
$771$		0			0
$772$	−6.81437	−	50.9872i	−0.245255	−	1.83507i
$773$	−15.6893	−	15.6893i	−0.564306	−	0.564306i	0.366221	−	0.930528i	$-0.380651\pi$
$773$	−15.6893	−	15.6893i	−0.564306	−	0.564306i	−0.930528	+	0.366221i	$0.880651\pi$
$774$		0			0
$775$	9.36404	+	4.18372i	0.336366	+	0.150284i
$776$	5.00405	+	4.36245i	0.179635	+	0.156603i
$777$		0			0
$778$	1.76170	+	0.596090i	0.0631600	+	0.0213708i
$779$	−13.3487	−	23.1206i	−0.478265	−	0.828380i
$780$		0			0
$781$	23.4289	−	40.5800i	0.838352	−	1.45207i
$782$	−12.0865	+	10.6206i	−0.432213	+	0.379791i
$783$		0			0
$784$	−7.14075	+	27.0741i	−0.255027	+	0.966932i
$785$	0.884947	−	0.981551i	0.0315851	−	0.0350330i
$786$		0			0
$787$	4.71940	−	17.6130i	0.168228	−	0.627837i	−0.829378	−	0.558688i	$-0.811305\pi$
$787$	4.71940	−	17.6130i	0.168228	−	0.627837i	0.997606	−	0.0691489i	$-0.0220284\pi$
$788$	−7.91089	+	19.2050i	−0.281814	+	0.684152i
$789$		0			0
$790$	−13.2435	−	13.5858i	−0.471183	−	0.483363i
$791$			0.0601908i			0.00214014i
$792$		0			0
$793$	15.0567	+	15.0567i	0.534680	+	0.534680i
$794$	0.793183	−	1.18961i	0.0281490	−	0.0422176i
$795$		0			0
$796$	43.4448	−	18.0954i	1.53986	−	0.641373i
$797$	26.9560	+	7.22285i	0.954832	+	0.255846i	0.702411	−	0.711771i	$-0.252107\pi$
$797$	26.9560	+	7.22285i	0.954832	+	0.255846i	0.252420	+	0.967618i	$0.418773\pi$
$798$		0			0
$799$	6.93218	−	12.0069i	0.245243	−	0.424773i
$800$	−28.2583	+	1.21232i	−0.999081	+	0.0428621i
$801$		0			0
$802$	18.5577	+	21.1192i	0.655295	+	0.745744i
$803$	−9.86423	−	36.8138i	−0.348101	−	1.29913i
$804$		0			0
$805$	0.0152325	−	0.0298475i	0.000536875	−	0.00105199i
$806$	−3.81250	−	7.71192i	−0.134290	−	0.271641i
$807$		0			0
$808$	−1.38016	−	20.1486i	−0.0485540	−	0.708825i
$809$			10.0143i			0.352084i	0.984383	+	0.176042i	$0.0563294\pi$
$809$			10.0143i			0.352084i	−0.984383	+	0.176042i	$0.943671\pi$
$810$		0			0
$811$			40.6681i			1.42805i	0.700121	+	0.714024i	$0.253129\pi$
$811$			40.6681i			1.42805i	−0.700121	+	0.714024i	$0.746871\pi$
$812$	−0.0442315	+	0.00591149i	−0.00155222	+	0.000207453i
$813$		0			0
$814$	−45.2604	+	22.3752i	−1.58637	+	0.784249i
$815$	−2.49263	−	7.68852i	−0.0873131	−	0.269317i
$816$		0			0
$817$	1.89858	+	7.08561i	0.0664231	+	0.247894i
$818$	−26.3586	+	23.1616i	−0.921606	+	0.809827i
$819$		0			0
$820$	14.7221	−	7.04580i	0.514118	−	0.246050i
$821$	−14.4578	+	25.0416i	−0.504579	+	0.873957i	0.495407	+	0.868661i	$0.335019\pi$
$821$	−14.4578	+	25.0416i	−0.504579	+	0.873957i	−0.999986	+	0.00529574i	$0.998314\pi$
$822$		0			0
$823$	−2.66307	−	0.713567i	−0.0928287	−	0.0248734i	0.212106	−	0.977247i	$-0.431968\pi$
$823$	−2.66307	−	0.713567i	−0.0928287	−	0.0248734i	−0.304934	+	0.952373i	$0.598635\pi$
$824$	11.1792	−	3.83155i	0.389445	−	0.133478i
$825$		0			0
$826$	0.0251450	+	0.0167657i	0.000874906	+	0.000583353i
$827$	33.6286	+	33.6286i	1.16938	+	1.16938i	0.982355	+	0.187026i	$0.0598850\pi$
$827$	33.6286	+	33.6286i	1.16938	+	1.16938i	0.187026	+	0.982355i	$0.440115\pi$
$828$		0			0
$829$		−	52.3216i		−	1.81721i	−0.417662	−	0.908603i	$-0.637150\pi$
$829$		−	52.3216i		−	1.81721i	0.417662	−	0.908603i	$-0.362850\pi$
$830$	9.23773	+	0.117867i	0.320646	+	0.00409124i
$831$		0			0
$832$	18.9068	+	14.3317i	0.655476	+	0.496863i
$833$	−5.32377	+	19.8686i	−0.184458	+	0.688406i
$834$		0			0
$835$	−16.2664	−	14.6654i	−0.562921	−	0.507519i
$836$	60.0974	+	7.79206i	2.07851	+	0.269494i
$837$		0			0
$838$	−26.2147	−	29.8331i	−0.905572	−	1.03057i
$839$	17.7459	−	30.7367i	0.612655	−	1.06115i	−0.378136	−	0.925750i	$-0.623435\pi$
$839$	17.7459	−	30.7367i	0.612655	−	1.06115i	0.990791	−	0.135400i	$-0.0432319\pi$
$840$		0			0
$841$	2.11521	+	3.66366i	0.0729384	+	0.126333i
$842$	0.590620	−	1.74553i	0.0203541	−	0.0601551i
$843$		0			0
$844$	16.0094	−	20.9488i	0.551067	−	0.721089i
$845$	−7.88950	+	5.11621i	−0.271407	+	0.176003i
$846$		0			0
$847$	0.0168503	+	0.0168503i	0.000578985	+	0.000578985i
$848$	−39.2002	+	0.153806i	−1.34614	+	0.00528171i
$849$		0			0
$850$	−20.7626	+	0.809147i	−0.712151	+	0.0277535i
$851$	28.9005	−	16.6857i	0.990695	−	0.571978i
$852$		0			0
$853$	49.1748	−	13.1763i	1.68371	−	0.451149i	0.714957	−	0.699168i	$-0.246446\pi$
$853$	49.1748	−	13.1763i	1.68371	−	0.451149i	0.968755	+	0.248019i	$0.0797795\pi$
$854$	0.00253207	−	0.0392214i	8.66458e−5	−	0.00134213i
$855$		0			0
$856$	−32.3243	−	6.33088i	−1.10482	−	0.216385i
$857$	7.29593	+	27.2288i	0.249224	+	0.930117i	0.971213	+	0.238212i	$0.0765614\pi$
$857$	7.29593	+	27.2288i	0.249224	+	0.930117i	−0.721989	+	0.691904i	$0.756772\pi$
$858$		0			0
$859$	14.5156	+	25.1417i	0.495265	+	0.857824i	0.999985	−	0.00545874i	$-0.00173758\pi$
$859$	14.5156	+	25.1417i	0.495265	+	0.857824i	−0.504720	+	0.863283i	$0.668404\pi$
$860$	−4.40839	+	0.823031i	−0.150325	+	0.0280651i
$861$		0			0
$862$	3.91688	+	19.5910i	0.133410	+	0.667274i
$863$	−23.2326	+	23.2326i	−0.790845	+	0.790845i	−0.981632	−	0.190786i	$-0.938896\pi$
$863$	−23.2326	+	23.2326i	−0.790845	+	0.790845i	0.190786	+	0.981632i	$0.438896\pi$
$864$		0			0
$865$	4.24332	−	19.8997i	0.144277	−	0.676609i
$866$	−8.15708	−	5.43882i	−0.277189	−	0.184819i
$867$		0			0
$868$	−0.00604784	+	0.0146822i	−0.000205277	+	0.000498345i
$869$	−21.5218	+	12.4256i	−0.730076	+	0.421509i
$870$		0			0
$871$	8.44820	+	4.87757i	0.286256	+	0.165270i
$872$	10.1522	+	15.0974i	0.343796	+	0.511264i
$873$		0			0
$874$	−39.9714	−	2.58049i	−1.35205	−	0.0872863i
$875$	0.0395676	−	0.0175243i	0.00133763	−	0.000592430i
$876$		0			0
$877$	30.9645	+	8.29692i	1.04560	+	0.280167i	0.740431	−	0.672132i	$-0.234621\pi$
$877$	30.9645	+	8.29692i	1.04560	+	0.280167i	0.305166	+	0.952299i	$0.401288\pi$
$878$	−12.9040	+	38.1369i	−0.435489	+	1.28706i
$879$		0			0
$880$	−7.58397	+	36.2632i	−0.255656	+	1.22243i
$881$	−23.5070			−0.791970			−0.395985	−	0.918257i	$-0.629597\pi$
$881$	−23.5070			−0.791970			−0.395985	+	0.918257i	$0.629597\pi$
$882$		0			0
$883$	28.0638	−	28.0638i	0.944422	−	0.944422i	−0.0541127	−	0.998535i	$-0.517233\pi$
$883$	28.0638	−	28.0638i	0.944422	−	0.944422i	0.998535	+	0.0541127i	$0.0172330\pi$
$884$	13.8480	+	10.5829i	0.465759	+	0.355940i
$885$		0			0
$886$	15.3133	+	30.9757i	0.514461	+	1.04065i
$887$	5.86497	−	21.8884i	0.196927	−	0.734940i	−0.794833	−	0.606828i	$-0.792442\pi$
$887$	5.86497	−	21.8884i	0.196927	−	0.734940i	0.991760	−	0.128112i	$-0.0408916\pi$
$888$		0			0
$889$	−0.0669822	−	0.0386722i	−0.00224651	−	0.00129702i
$890$	−27.9657	−	7.87713i	−0.937411	−	0.264042i
$891$		0			0
$892$	8.42070	+	10.9296i	0.281946	+	0.365950i
$893$	33.3385	−	8.93303i	1.11563	−	0.298932i
$894$		0			0
$895$	9.82762	−	19.2568i	0.328501	−	0.643686i
$896$	−0.00316402	−	0.0436764i	−0.000105703	−	0.00145913i
$897$		0			0
$898$	−8.91536	−	44.5919i	−0.297509	−	1.48805i
$899$	11.8245			0.394369
$900$		0			0
$901$	−28.7977			−0.959391
$902$	−4.19123	−	20.9633i	−0.139553	−	0.698000i
$903$		0			0
$904$	14.2608	+	41.6082i	0.474306	+	1.38387i
$905$	0.737190	−	1.44450i	0.0245050	−	0.0480167i
$906$		0			0
$907$	10.5521	−	2.82743i	0.350377	−	0.0938833i	−0.0793379	−	0.996848i	$-0.525281\pi$
$907$	10.5521	−	2.82743i	0.350377	−	0.0938833i	0.429715	+	0.902964i	$0.358614\pi$
$908$	37.8748	−	29.1806i	1.25692	−	0.968393i
$909$		0			0
$910$	−0.0349391	−	0.00984135i	−0.00115822	−	0.000326238i
$911$	18.3234	+	10.5790i	0.607083	+	0.350499i	0.771823	−	0.635838i	$-0.219345\pi$
$911$	18.3234	+	10.5790i	0.607083	+	0.350499i	−0.164740	+	0.986337i	$0.552679\pi$
$912$		0			0
$913$	3.13194	−	11.6886i	0.103652	−	0.386835i
$914$	7.07612	+	14.3135i	0.234057	+	0.473450i
$915$		0			0
$916$	15.2811	−	19.9959i	0.504903	−	0.660682i
$917$	0.0225609	−	0.0225609i	0.000745026	−	0.000745026i
$918$		0			0
$919$	8.67860			0.286281			0.143140	−	0.989702i	$-0.454280\pi$
$919$	8.67860			0.286281			0.143140	+	0.989702i	$0.454280\pi$
$920$	3.45814	−	24.2417i	0.114012	−	0.799226i
$921$		0			0
$922$	1.28248	−	3.79027i	0.0422362	−	0.124826i
$923$	32.4057	+	8.68308i	1.06665	+	0.285807i
$924$		0			0
$925$	42.5565	+	6.79698i	1.39925	+	0.223483i
$926$	30.3430	+	1.95889i	0.997132	+	0.0643733i
$927$		0			0
$928$	−29.1754	+	14.5660i	−0.957730	+	0.478154i
$929$	−11.5252	−	6.65405i	−0.378128	−	0.218312i	0.298875	−	0.954292i	$-0.403389\pi$
$929$	−11.5252	−	6.65405i	−0.378128	−	0.218312i	−0.677004	+	0.735980i	$0.736722\pi$
$930$		0			0
$931$	−44.3462	+	25.6033i	−1.45339	+	0.839115i
$932$	−15.3113	−	6.30698i	−0.501538	−	0.206592i
$933$		0			0
$934$	1.24223	+	0.828268i	0.0406469	+	0.0271017i
$935$	−5.67586	+	26.6178i	−0.185621	+	0.870495i
$936$		0			0
$937$	16.8683	−	16.8683i	0.551063	−	0.551063i	−0.375685	−	0.926747i	$-0.622593\pi$
$937$	16.8683	−	16.8683i	0.551063	−	0.551063i	0.926747	+	0.375685i	$0.122593\pi$
$938$	−0.00353010	−	0.0176565i	−0.000115262	−	0.000576504i
$939$		0			0
$940$	3.87244	+	20.7419i	0.126305	+	0.676526i
$941$	−14.0053	−	24.2579i	−0.456560	−	0.790785i	0.542216	−	0.840239i	$-0.317585\pi$
$941$	−14.0053	−	24.2579i	−0.456560	−	0.790785i	−0.998776	+	0.0494537i	$0.984252\pi$
$942$		0			0
$943$	3.65715	+	13.6487i	0.119093	+	0.444462i
$944$	21.3542	+	5.63215i	0.695021	+	0.183311i
$945$		0			0
$946$	−0.378430	+	5.86183i	−0.0123038	+	0.190584i
$947$	−12.7811	+	3.42468i	−0.415329	+	0.111287i	−0.460431	−	0.887695i	$-0.652305\pi$
$947$	−12.7811	+	3.42468i	−0.415329	+	0.111287i	0.0451023	+	0.998982i	$0.485639\pi$
$948$		0			0
$949$	23.6316	−	13.6437i	0.767115	−	0.442894i
$950$	−37.9728	−	35.1242i	−1.23200	−	1.13958i
$951$		0			0
$952$	−0.00219847	−	0.0320947i	−7.12527e−5	−	0.00104020i
$953$	30.3998	+	30.3998i	0.984746	+	0.984746i	0.999885	−	0.0151397i	$-0.00481929\pi$
$953$	30.3998	+	30.3998i	0.984746	+	0.984746i	−0.0151397	+	0.999885i	$0.504819\pi$
$954$		0			0
$955$	−9.51352	+	6.16937i	−0.307850	+	0.199636i
$956$	27.0927	+	20.7047i	0.876241	+	0.669637i
$957$		0			0
$958$	−7.87307	+	23.2683i	−0.254367	+	0.751764i
$959$	0.0328617	+	0.0569181i	0.00106116	+	0.00183798i
$960$		0			0
$961$	−13.3962	+	23.2029i	−0.432136	+	0.748482i
$962$	−23.8612	−	27.1547i	−0.769315	−	0.875502i
$963$		0			0
$964$	−3.58866	+	27.6781i	−0.115583	+	0.891450i
$965$	42.7149	+	38.5110i	1.37504	+	1.23971i
$966$		0			0
$967$	2.41924	−	9.02872i	0.0777975	−	0.290344i	−0.916056	−	0.401051i	$-0.868645\pi$
$967$	2.41924	−	9.02872i	0.0777975	−	0.290344i	0.993853	+	0.110707i	$0.0353116\pi$
$968$	15.6404	+	7.65588i	0.502703	+	0.246069i
$969$		0			0
$970$	−7.42162	−	0.0946951i	−0.238294	−	0.00304048i
$971$		−	0.631006i		−	0.0202499i	−0.999949	−	0.0101250i	$-0.996777\pi$
$971$		−	0.631006i		−	0.0202499i	0.999949	−	0.0101250i	$-0.00322293\pi$
$972$		0			0
$973$	0.00314957	+	0.00314957i	0.000100971	+	0.000100971i
$974$	−28.6601	−	19.1094i	−0.918327	−	0.612305i
$975$		0			0
$976$	−7.54222	−	27.7126i	−0.241421	−	0.887058i
$977$	−0.224275	−	0.0600942i	−0.00717518	−	0.00192258i	0.255230	−	0.966880i	$-0.417849\pi$
$977$	−0.224275	−	0.0600942i	−0.00717518	−	0.00192258i	−0.262405	+	0.964958i	$0.584516\pi$
$978$		0			0
$979$	−19.0279	+	32.9573i	−0.608134	+	1.05332i
$980$	−13.5142	−	28.2376i	−0.431694	−	0.902018i
$981$		0			0
$982$	−17.0363	+	14.9700i	−0.543650	+	0.477713i
$983$	0.123617	+	0.461344i	0.00394276	+	0.0147146i	0.967869	−	0.251454i	$-0.0809088\pi$
$983$	0.123617	+	0.461344i	0.00394276	+	0.0147146i	−0.963926	+	0.266169i	$0.914242\pi$
$984$		0			0
$985$	−7.16170	−	22.0903i	−0.228191	−	0.703855i
$986$	−21.4748	+	10.6164i	−0.683898	+	0.338096i
$987$		0			0
$988$	5.74767	+	43.0058i	0.182858	+	1.36820i
$989$		−	3.88251i		−	0.123457i
$990$		0			0
$991$		−	16.8040i		−	0.533796i	−0.963725	−	0.266898i	$-0.914001\pi$
$991$		−	16.8040i		−	0.533796i	0.963725	−	0.266898i	$-0.0859986\pi$
$992$	−0.702110	+	11.5823i	−0.0222920	+	0.367737i
$993$		0			0
$994$	−0.0274427	−	0.0555110i	−0.000870431	−	0.00176070i
$995$	−23.9184	+	46.8672i	−0.758263	+	1.48579i
$996$		0			0
$997$	3.21617	+	12.0029i	0.101857	+	0.380135i	0.997970	−	0.0636912i	$-0.0202873\pi$
$997$	3.21617	+	12.0029i	0.101857	+	0.380135i	−0.896113	+	0.443827i	$0.853621\pi$
$998$	−35.3452	−	40.2238i	−1.11883	−	1.27326i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.y.a.343.31		128
3.2	odd	2		180.2.x.a.43.2	yes	128
4.3	odd	2	inner	540.2.y.a.343.4		128
5.2	odd	4	inner	540.2.y.a.127.19		128
9.4	even	3	inner	540.2.y.a.523.13		128
9.5	odd	6		180.2.x.a.103.20	yes	128
12.11	even	2		180.2.x.a.43.29	yes	128
15.2	even	4		180.2.x.a.7.14	✓	128
15.8	even	4		900.2.bf.e.7.19		128
15.14	odd	2		900.2.bf.e.43.31		128
20.7	even	4	inner	540.2.y.a.127.13		128
36.23	even	6		180.2.x.a.103.14	yes	128
36.31	odd	6	inner	540.2.y.a.523.19		128
45.14	odd	6		900.2.bf.e.643.13		128
45.22	odd	12	inner	540.2.y.a.307.4		128
45.23	even	12		900.2.bf.e.607.4		128
45.32	even	12		180.2.x.a.67.29	yes	128
60.23	odd	4		900.2.bf.e.7.13		128
60.47	odd	4		180.2.x.a.7.20	yes	128
60.59	even	2		900.2.bf.e.43.4		128
180.23	odd	12		900.2.bf.e.607.31		128
180.59	even	6		900.2.bf.e.643.19		128
180.67	even	12	inner	540.2.y.a.307.31		128
180.167	odd	12		180.2.x.a.67.2	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.14	✓	128	15.2	even	4
180.2.x.a.7.20	yes	128	60.47	odd	4
180.2.x.a.43.2	yes	128	3.2	odd	2
180.2.x.a.43.29	yes	128	12.11	even	2
180.2.x.a.67.2	yes	128	180.167	odd	12
180.2.x.a.67.29	yes	128	45.32	even	12
180.2.x.a.103.14	yes	128	36.23	even	6
180.2.x.a.103.20	yes	128	9.5	odd	6
540.2.y.a.127.13		128	20.7	even	4	inner
540.2.y.a.127.19		128	5.2	odd	4	inner
540.2.y.a.307.4		128	45.22	odd	12	inner
540.2.y.a.307.31		128	180.67	even	12	inner
540.2.y.a.343.4		128	4.3	odd	2	inner
540.2.y.a.343.31		128	1.1	even	1	trivial
540.2.y.a.523.13		128	9.4	even	3	inner
540.2.y.a.523.19		128	36.31	odd	6	inner
900.2.bf.e.7.13		128	60.23	odd	4
900.2.bf.e.7.19		128	15.8	even	4
900.2.bf.e.43.4		128	60.59	even	2
900.2.bf.e.43.31		128	15.14	odd	2
900.2.bf.e.607.4		128	45.23	even	12
900.2.bf.e.607.31		128	180.23	odd	12
900.2.bf.e.643.13		128	45.14	odd	6
900.2.bf.e.643.19		128	180.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.38677 - 0.277260i) q^{2} +(1.84625 - 0.768990i) q^{4} +(-1.01645 + 1.99169i) q^{5} +(0.00373871 - 0.00100179i) q^{7} +(2.34712 - 1.57830i) q^{8} +O(q^{10})\)	\(q+(1.38677 - 0.277260i) q^{2} +(1.84625 - 0.768990i) q^{4} +(-1.01645 + 1.99169i) q^{5} +(0.00373871 - 0.00100179i) q^{7} +(2.34712 - 1.57830i) q^{8} +(-0.857362 + 3.04383i) q^{10} +(3.58713 + 2.07103i) q^{11} +(-0.767553 + 2.86455i) q^{13} +(0.00490698 - 0.00242584i) q^{14} +(2.81731 - 2.83950i) q^{16} +(2.07784 - 2.07784i) q^{17} +7.31525 q^{19} +(-0.345029 + 4.45881i) q^{20} +(5.54873 + 1.87747i) q^{22} +(-3.73983 - 1.00208i) q^{23} +(-2.93367 - 4.04890i) q^{25} +(-0.270195 + 4.18528i) q^{26} +(0.00613225 - 0.00472458i) q^{28} +(-4.99228 - 2.88229i) q^{29} +(-1.77642 + 1.02562i) q^{31} +(3.11967 - 4.71886i) q^{32} +(2.30538 - 3.45758i) q^{34} +(-0.00180496 + 0.00846463i) q^{35} +(-6.09468 + 6.09468i) q^{37} +(10.1446 - 2.02822i) q^{38} +(0.757772 + 6.27900i) q^{40} +(-1.82477 - 3.16060i) q^{41} +(0.259538 + 0.968609i) q^{43} +(8.21535 + 1.06518i) q^{44} +(-5.46412 - 0.352755i) q^{46} +(4.55740 - 1.22115i) q^{47} +(-6.06216 + 3.49999i) q^{49} +(-5.19092 - 4.80150i) q^{50} +(0.785711 + 5.87892i) q^{52} +(-6.92974 - 6.92974i) q^{53} +(-7.77098 + 5.03936i) q^{55} +(0.00719408 - 0.00825213i) q^{56} +(-7.72228 - 2.61291i) q^{58} +(2.76056 + 4.78143i) q^{59} +(3.59007 - 6.21819i) q^{61} +(-2.17912 + 1.91482i) q^{62} +(3.01792 - 7.40893i) q^{64} +(-4.92512 - 4.44039i) q^{65} +(0.851369 - 3.17735i) q^{67} +(2.23838 - 5.43405i) q^{68} +(-0.000156161 + 0.0122389i) q^{70} -11.3127i q^{71} +(-6.50632 - 6.50632i) q^{73} +(-6.76210 + 10.1417i) q^{74} +(13.5058 - 5.62536i) q^{76} +(0.0154860 + 0.00414946i) q^{77} +(-2.99986 + 5.19591i) q^{79} +(2.79177 + 8.49741i) q^{80} +(-3.40684 - 3.87708i) q^{82} +(-0.756131 - 2.82192i) q^{83} +(2.02640 + 6.25042i) q^{85} +(0.628475 + 1.27128i) q^{86} +(11.6881 - 0.800629i) q^{88} +9.18764i q^{89} +0.0114786i q^{91} +(-7.67527 + 1.02579i) q^{92} +(5.98148 - 2.95704i) q^{94} +(-7.43557 + 14.5697i) q^{95} +(0.607478 + 2.26714i) q^{97} +(-7.43641 + 6.53447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

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