LMFDB - Embedded newform 1458.2.c.e.973.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1458,2,Mod(487,1458)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1458, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("1458.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1458 = 2 \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1458.c (of order $3$, degree $2$, 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:	$11.6421886147$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			973.5
Root			$0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	1458.973
Dual form			1458.2.c.e.487.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.192377 - 0.333207i) q^{5} +(-0.474416 - 0.821712i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.192377 - 0.333207i) q^{5} +(-0.474416 - 0.821712i) q^{7} +1.00000 q^{8} -0.384754 q^{10} +(-0.805242 - 1.39472i) q^{11} +(2.16727 - 3.75382i) q^{13} +(-0.474416 + 0.821712i) q^{14} +(-0.500000 - 0.866025i) q^{16} +1.49642 q^{17} +6.66356 q^{19} +(0.192377 + 0.333207i) q^{20} +(-0.805242 + 1.39472i) q^{22} +(-3.29283 + 5.70336i) q^{23} +(2.42598 + 4.20192i) q^{25} -4.33454 q^{26} +0.948831 q^{28} +(-5.06018 - 8.76449i) q^{29} +(-2.10265 + 3.64190i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.748210 - 1.29594i) q^{34} -0.365067 q^{35} -3.40088 q^{37} +(-3.33178 - 5.77081i) q^{38} +(0.192377 - 0.333207i) q^{40} +(1.92125 - 3.32771i) q^{41} +(-0.913284 - 1.58185i) q^{43} +1.61048 q^{44} +6.58567 q^{46} +(-4.74230 - 8.21391i) q^{47} +(3.04986 - 5.28251i) q^{49} +(2.42598 - 4.20192i) q^{50} +(2.16727 + 3.75382i) q^{52} -2.01268 q^{53} -0.619641 q^{55} +(-0.474416 - 0.821712i) q^{56} +(-5.06018 + 8.76449i) q^{58} +(4.50435 - 7.80176i) q^{59} +(-4.30089 - 7.44936i) q^{61} +4.20530 q^{62} +1.00000 q^{64} +(-0.833866 - 1.44430i) q^{65} +(5.84514 - 10.1241i) q^{67} +(-0.748210 + 1.29594i) q^{68} +(0.182534 + 0.316157i) q^{70} +0.440680 q^{71} +10.5525 q^{73} +(1.70044 + 2.94525i) q^{74} +(-3.33178 + 5.77081i) q^{76} +(-0.764039 + 1.32335i) q^{77} +(6.67514 + 11.5617i) q^{79} -0.384754 q^{80} -3.84251 q^{82} +(-3.99117 - 6.91291i) q^{83} +(0.287877 - 0.498618i) q^{85} +(-0.913284 + 1.58185i) q^{86} +(-0.805242 - 1.39472i) q^{88} -10.3213 q^{89} -4.11275 q^{91} +(-3.29283 - 5.70336i) q^{92} +(-4.74230 + 8.21391i) q^{94} +(1.28192 - 2.22034i) q^{95} +(-6.57408 - 11.3866i) q^{97} -6.09972 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 - 6 * q^5 + 12 * q^8	$ 12 q - 6 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} - 6 q^{16} + 24 q^{17} + 12 q^{19} - 6 q^{20} - 6 q^{22} - 12 q^{23} - 6 q^{25} + 12 q^{26} - 6 q^{29} + 6 q^{31} - 6 q^{32} - 12 q^{34} + 24 q^{35} - 6 q^{38} - 6 q^{40} - 24 q^{41} + 6 q^{43} + 12 q^{44} + 24 q^{46} - 18 q^{47} - 6 q^{49} - 6 q^{50} - 6 q^{52} + 48 q^{53} - 36 q^{55} - 6 q^{58} - 12 q^{59} + 6 q^{61} - 12 q^{62} + 12 q^{64} - 12 q^{65} + 24 q^{67} - 12 q^{68} - 12 q^{70} - 12 q^{71} - 48 q^{73} - 6 q^{76} - 12 q^{77} + 12 q^{79} + 12 q^{80} + 48 q^{82} - 18 q^{83} + 6 q^{86} - 6 q^{88} + 24 q^{89} - 60 q^{91} - 12 q^{92} - 18 q^{94} + 6 q^{95} - 6 q^{97} + 12 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 6 * q^5 + 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 - 6 * q^16 + 24 * q^17 + 12 * q^19 - 6 * q^20 - 6 * q^22 - 12 * q^23 - 6 * q^25 + 12 * q^26 - 6 * q^29 + 6 * q^31 - 6 * q^32 - 12 * q^34 + 24 * q^35 - 6 * q^38 - 6 * q^40 - 24 * q^41 + 6 * q^43 + 12 * q^44 + 24 * q^46 - 18 * q^47 - 6 * q^49 - 6 * q^50 - 6 * q^52 + 48 * q^53 - 36 * q^55 - 6 * q^58 - 12 * q^59 + 6 * q^61 - 12 * q^62 + 12 * q^64 - 12 * q^65 + 24 * q^67 - 12 * q^68 - 12 * q^70 - 12 * q^71 - 48 * q^73 - 6 * q^76 - 12 * q^77 + 12 * q^79 + 12 * q^80 + 48 * q^82 - 18 * q^83 + 6 * q^86 - 6 * q^88 + 24 * q^89 - 60 * q^91 - 12 * q^92 - 18 * q^94 + 6 * q^95 - 6 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1458\mathbb{Z}\right)^\times$.

$n$	$731$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.192377	−	0.333207i	0.0860337	−	0.149015i	−0.819798	−	0.572653i	$-0.805914\pi$
$5$	0.192377	−	0.333207i	0.0860337	−	0.149015i	0.905831	+	0.423639i	$0.139247\pi$
$6$		0			0
$7$	−0.474416	−	0.821712i	−0.179312	−	0.310578i	0.762333	−	0.647185i	$-0.224054\pi$
$7$	−0.474416	−	0.821712i	−0.179312	−	0.310578i	−0.941645	+	0.336607i	$0.890721\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.384754			−0.121670
$11$	−0.805242	−	1.39472i	−0.242790	−	0.420524i	0.718718	−	0.695301i	$-0.244729\pi$
$11$	−0.805242	−	1.39472i	−0.242790	−	0.420524i	−0.961508	+	0.274778i	$0.911396\pi$
$12$		0			0
$13$	2.16727	−	3.75382i	0.601092	−	1.04112i	−0.391564	−	0.920151i	$-0.628066\pi$
$13$	2.16727	−	3.75382i	0.601092	−	1.04112i	0.992656	−	0.120971i	$-0.0386009\pi$
$14$	−0.474416	+	0.821712i	−0.126793	+	0.219612i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.49642			0.362935			0.181468	−	0.983397i	$-0.441915\pi$
$17$	1.49642			0.362935			0.181468	+	0.983397i	$0.441915\pi$
$18$		0			0
$19$	6.66356			1.52872			0.764362	−	0.644787i	$-0.223054\pi$
$19$	6.66356			1.52872			0.764362	+	0.644787i	$0.223054\pi$
$20$	0.192377	+	0.333207i	0.0430169	+	0.0745074i
$21$		0			0
$22$	−0.805242	+	1.39472i	−0.171678	+	0.297355i
$23$	−3.29283	+	5.70336i	−0.686603	+	1.18923i	0.286327	+	0.958132i	$0.407566\pi$
$23$	−3.29283	+	5.70336i	−0.686603	+	1.18923i	−0.972930	+	0.231100i	$0.925768\pi$
$24$		0			0
$25$	2.42598	+	4.20192i	0.485196	+	0.840385i
$26$	−4.33454			−0.850073
$27$		0			0
$28$	0.948831			0.179312
$29$	−5.06018	−	8.76449i	−0.939652	−	1.62752i	−0.766121	−	0.642696i	$-0.777816\pi$
$29$	−5.06018	−	8.76449i	−0.939652	−	1.62752i	−0.173530	−	0.984829i	$-0.555517\pi$
$30$		0			0
$31$	−2.10265	+	3.64190i	−0.377648	+	0.654105i	−0.990719	−	0.135922i	$-0.956600\pi$
$31$	−2.10265	+	3.64190i	−0.377648	+	0.654105i	0.613072	+	0.790027i	$0.289934\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−0.748210	−	1.29594i	−0.128317	−	0.222252i
$35$	−0.365067			−0.0617076
$36$		0			0
$37$	−3.40088			−0.559101			−0.279550	−	0.960131i	$-0.590185\pi$
$37$	−3.40088			−0.559101			−0.279550	+	0.960131i	$0.590185\pi$
$38$	−3.33178	−	5.77081i	−0.540486	−	0.936149i
$39$		0			0
$40$	0.192377	−	0.333207i	0.0304175	−	0.0526847i
$41$	1.92125	−	3.32771i	0.300049	−	0.519701i	−0.676097	−	0.736812i	$-0.736330\pi$
$41$	1.92125	−	3.32771i	0.300049	−	0.519701i	0.976147	+	0.217111i	$0.0696635\pi$
$42$		0			0
$43$	−0.913284	−	1.58185i	−0.139274	−	0.241230i	0.787948	−	0.615742i	$-0.211144\pi$
$43$	−0.913284	−	1.58185i	−0.139274	−	0.241230i	−0.927222	+	0.374512i	$0.877810\pi$
$44$	1.61048			0.242790
$45$		0			0
$46$	6.58567			0.971004
$47$	−4.74230	−	8.21391i	−0.691736	−	1.19812i	−0.971269	−	0.237985i	$-0.923513\pi$
$47$	−4.74230	−	8.21391i	−0.691736	−	1.19812i	0.279533	−	0.960136i	$-0.409820\pi$
$48$		0			0
$49$	3.04986	−	5.28251i	0.435694	−	0.754645i
$50$	2.42598	−	4.20192i	0.343086	−	0.594242i
$51$		0			0
$52$	2.16727	+	3.75382i	0.300546	+	0.520561i
$53$	−2.01268			−0.276463			−0.138231	−	0.990400i	$-0.544142\pi$
$53$	−2.01268			−0.276463			−0.138231	+	0.990400i	$0.544142\pi$
$54$		0			0
$55$	−0.619641			−0.0835524
$56$	−0.474416	−	0.821712i	−0.0633965	−	0.109806i
$57$		0			0
$58$	−5.06018	+	8.76449i	−0.664434	+	1.15083i
$59$	4.50435	−	7.80176i	0.586416	−	1.01570i	−0.408281	−	0.912856i	$-0.633872\pi$
$59$	4.50435	−	7.80176i	0.586416	−	1.01570i	0.994697	−	0.102846i	$-0.0327949\pi$
$60$		0			0
$61$	−4.30089	−	7.44936i	−0.550673	−	0.953793i	−0.998226	−	0.0595361i	$-0.981038\pi$
$61$	−4.30089	−	7.44936i	−0.550673	−	0.953793i	0.447553	−	0.894257i	$-0.352295\pi$
$62$	4.20530			0.534074
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.833866	−	1.44430i	−0.103428	−	0.179143i
$66$		0			0
$67$	5.84514	−	10.1241i	0.714097	−	1.23685i	−0.249209	−	0.968450i	$-0.580171\pi$
$67$	5.84514	−	10.1241i	0.714097	−	1.23685i	0.963307	−	0.268403i	$-0.0864959\pi$
$68$	−0.748210	+	1.29594i	−0.0907338	+	0.157156i
$69$		0			0
$70$	0.182534	+	0.316157i	0.0218169	+	0.0377880i
$71$	0.440680			0.0522991			0.0261496	−	0.999658i	$-0.491675\pi$
$71$	0.440680			0.0522991			0.0261496	+	0.999658i	$0.491675\pi$
$72$		0			0
$73$	10.5525			1.23507			0.617537	−	0.786542i	$-0.288131\pi$
$73$	10.5525			1.23507			0.617537	+	0.786542i	$0.288131\pi$
$74$	1.70044	+	2.94525i	0.197672	+	0.342378i
$75$		0			0
$76$	−3.33178	+	5.77081i	−0.382181	+	0.661957i
$77$	−0.764039	+	1.32335i	−0.0870703	+	0.150810i
$78$		0			0
$79$	6.67514	+	11.5617i	0.751012	+	1.30079i	0.947332	+	0.320252i	$0.103768\pi$
$79$	6.67514	+	11.5617i	0.751012	+	1.30079i	−0.196320	+	0.980540i	$0.562899\pi$
$80$	−0.384754			−0.0430169
$81$		0			0
$82$	−3.84251			−0.424334
$83$	−3.99117	−	6.91291i	−0.438088	−	0.758791i	0.559454	−	0.828861i	$-0.311011\pi$
$83$	−3.99117	−	6.91291i	−0.438088	−	0.758791i	−0.997542	+	0.0700707i	$0.977678\pi$
$84$		0			0
$85$	0.287877	−	0.498618i	0.0312247	−	0.0540827i
$86$	−0.913284	+	1.58185i	−0.0984819	+	0.170576i
$87$		0			0
$88$	−0.805242	−	1.39472i	−0.0858391	−	0.148678i
$89$	−10.3213			−1.09405			−0.547026	−	0.837115i	$-0.684240\pi$
$89$	−10.3213			−1.09405			−0.547026	+	0.837115i	$0.684240\pi$
$90$		0			0
$91$	−4.11275			−0.431133
$92$	−3.29283	−	5.70336i	−0.343302	−	0.594616i
$93$		0			0
$94$	−4.74230	+	8.21391i	−0.489131	+	0.847200i
$95$	1.28192	−	2.22034i	0.131522	−	0.227803i
$96$		0			0
$97$	−6.57408	−	11.3866i	−0.667497	−	1.15614i	−0.978602	−	0.205763i	$-0.934033\pi$
$97$	−6.57408	−	11.3866i	−0.667497	−	1.15614i	0.311105	−	0.950375i	$-0.399301\pi$
$98$	−6.09972			−0.616165
$99$		0			0
$100$	−4.85196			−0.485196
$101$	−7.20725	−	12.4833i	−0.717149	−	1.24214i	−0.962125	−	0.272609i	$-0.912114\pi$
$101$	−7.20725	−	12.4833i	−0.717149	−	1.24214i	0.244977	−	0.969529i	$-0.421220\pi$
$102$		0			0
$103$	3.06095	−	5.30172i	0.301604	−	0.522394i	−0.674895	−	0.737914i	$-0.735811\pi$
$103$	3.06095	−	5.30172i	0.301604	−	0.522394i	0.976500	+	0.215520i	$0.0691445\pi$
$104$	2.16727	−	3.75382i	0.212518	−	0.368092i
$105$		0			0
$106$	1.00634	+	1.74303i	0.0977443	+	0.169298i
$107$	17.4187			1.68392			0.841962	−	0.539536i	$-0.181400\pi$
$107$	17.4187			1.68392			0.841962	+	0.539536i	$0.181400\pi$
$108$		0			0
$109$	−9.94273			−0.952340			−0.476170	−	0.879353i	$-0.657975\pi$
$109$	−9.94273			−0.952340			−0.476170	+	0.879353i	$0.657975\pi$
$110$	0.309820	+	0.536625i	0.0295402	+	0.0511652i
$111$		0			0
$112$	−0.474416	+	0.821712i	−0.0448281	+	0.0776445i
$113$	−4.52939	+	7.84514i	−0.426089	+	0.738008i	−0.996521	−	0.0833364i	$-0.973442\pi$
$113$	−4.52939	+	7.84514i	−0.426089	+	0.738008i	0.570432	+	0.821345i	$0.306776\pi$
$114$		0			0
$115$	1.26693	+	2.19439i	0.118142	+	0.204628i
$116$	10.1204			0.939652
$117$		0			0
$118$	−9.00869			−0.829317
$119$	−0.709925	−	1.22963i	−0.0650787	−	0.112720i
$120$		0			0
$121$	4.20317	−	7.28011i	0.382106	−	0.661828i
$122$	−4.30089	+	7.44936i	−0.389385	+	0.674434i
$123$		0			0
$124$	−2.10265	−	3.64190i	−0.188824	−	0.327052i
$125$	3.79059			0.339040
$126$		0			0
$127$	−5.08866			−0.451546			−0.225773	−	0.974180i	$-0.572491\pi$
$127$	−5.08866			−0.451546			−0.225773	+	0.974180i	$0.572491\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.833866	+	1.44430i	−0.0731349	+	0.126673i
$131$	−0.396342	+	0.686484i	−0.0346285	+	0.0599784i	−0.882820	−	0.469711i	$-0.844358\pi$
$131$	−0.396342	+	0.686484i	−0.0346285	+	0.0599784i	0.848192	+	0.529689i	$0.177691\pi$
$132$		0			0
$133$	−3.16130	−	5.47552i	−0.274119	−	0.474788i
$134$	−11.6903			−1.00989
$135$		0			0
$136$	1.49642			0.128317
$137$	3.38637	+	5.86536i	0.289317	+	0.501111i	0.973647	−	0.228061i	$-0.0732386\pi$
$137$	3.38637	+	5.86536i	0.289317	+	0.501111i	−0.684330	+	0.729172i	$0.739905\pi$
$138$		0			0
$139$	1.73533	−	3.00567i	0.147188	−	0.254938i	−0.782999	−	0.622023i	$-0.786311\pi$
$139$	1.73533	−	3.00567i	0.147188	−	0.254938i	0.930187	+	0.367085i	$0.119644\pi$
$140$	0.182534	−	0.316157i	0.0154269	−	0.0267202i
$141$		0			0
$142$	−0.220340	−	0.381640i	−0.0184905	−	0.0320265i
$143$	−6.98070			−0.583756
$144$		0			0
$145$	−3.89385			−0.323367
$146$	−5.27624	−	9.13871i	−0.436664	−	0.756325i
$147$		0			0
$148$	1.70044	−	2.94525i	0.139775	−	0.242098i
$149$	3.66435	−	6.34684i	0.300195	−	0.519953i	−0.675985	−	0.736916i	$-0.736282\pi$
$149$	3.66435	−	6.34684i	0.300195	−	0.519953i	0.976180	+	0.216962i	$0.0696149\pi$
$150$		0			0
$151$	8.57068	+	14.8449i	0.697472	+	1.20806i	0.969340	+	0.245723i	$0.0790254\pi$
$151$	8.57068	+	14.8449i	0.697472	+	1.20806i	−0.271868	+	0.962335i	$0.587641\pi$
$152$	6.66356			0.540486
$153$		0			0
$154$	1.52808			0.123136
$155$	0.809005	+	1.40124i	0.0649808	+	0.112550i
$156$		0			0
$157$	−0.666793	+	1.15492i	−0.0532159	+	0.0921726i	−0.891406	−	0.453205i	$-0.850280\pi$
$157$	−0.666793	+	1.15492i	−0.0532159	+	0.0921726i	0.838190	+	0.545378i	$0.183614\pi$
$158$	6.67514	−	11.5617i	0.531046	−	0.919799i
$159$		0			0
$160$	0.192377	+	0.333207i	0.0152088	+	0.0263423i
$161$	6.24869			0.492466
$162$		0			0
$163$	1.68576			0.132039			0.0660194	−	0.997818i	$-0.478970\pi$
$163$	1.68576			0.132039			0.0660194	+	0.997818i	$0.478970\pi$
$164$	1.92125	+	3.32771i	0.150025	+	0.259850i
$165$		0			0
$166$	−3.99117	+	6.91291i	−0.309775	+	0.536546i
$167$	−1.55769	+	2.69800i	−0.120538	+	0.208778i	−0.919980	−	0.391965i	$-0.871795\pi$
$167$	−1.55769	+	2.69800i	−0.120538	+	0.208778i	0.799442	+	0.600743i	$0.205129\pi$
$168$		0			0
$169$	−2.89411	−	5.01274i	−0.222624	−	0.385596i
$170$	−0.575754			−0.0441583
$171$		0			0
$172$	1.82657			0.139274
$173$	11.4906	+	19.9023i	0.873614	+	1.51314i	0.858232	+	0.513262i	$0.171563\pi$
$173$	11.4906	+	19.9023i	0.873614	+	1.51314i	0.0153821	+	0.999882i	$0.495104\pi$
$174$		0			0
$175$	2.30185	−	3.98692i	0.174003	−	0.301383i
$176$	−0.805242	+	1.39472i	−0.0606974	+	0.105131i
$177$		0			0
$178$	5.16064	+	8.93848i	0.386806	+	0.669968i
$179$	−25.7661			−1.92585			−0.962923	−	0.269776i	$-0.913050\pi$
$179$	−25.7661			−1.92585			−0.962923	+	0.269776i	$0.913050\pi$
$180$		0			0
$181$	−16.1080			−1.19730			−0.598651	−	0.801010i	$-0.704296\pi$
$181$	−16.1080			−1.19730			−0.598651	+	0.801010i	$0.704296\pi$
$182$	2.05637	+	3.56174i	0.152428	+	0.264014i
$183$		0			0
$184$	−3.29283	+	5.70336i	−0.242751	+	0.420457i
$185$	−0.654251	+	1.13320i	−0.0481015	+	0.0833142i
$186$		0			0
$187$	−1.20498	−	2.08709i	−0.0881169	−	0.152623i
$188$	9.48460			0.691736
$189$		0			0
$190$	−2.56383			−0.186000
$191$	5.81076	+	10.0645i	0.420452	+	0.728244i	0.995984	−	0.0895354i	$-0.0285382\pi$
$191$	5.81076	+	10.0645i	0.420452	+	0.728244i	−0.575532	+	0.817779i	$0.695205\pi$
$192$		0			0
$193$	2.93074	−	5.07620i	0.210960	−	0.365393i	−0.741056	−	0.671444i	$-0.765675\pi$
$193$	2.93074	−	5.07620i	0.210960	−	0.365393i	0.952015	+	0.306051i	$0.0990078\pi$
$194$	−6.57408	+	11.3866i	−0.471991	+	0.817513i
$195$		0			0
$196$	3.04986	+	5.28251i	0.217847	+	0.377322i
$197$	−1.84952			−0.131773			−0.0658863	−	0.997827i	$-0.520987\pi$
$197$	−1.84952			−0.131773			−0.0658863	+	0.997827i	$0.520987\pi$
$198$		0			0
$199$	−6.83609			−0.484597			−0.242299	−	0.970202i	$-0.577901\pi$
$199$	−6.83609			−0.484597			−0.242299	+	0.970202i	$0.577901\pi$
$200$	2.42598	+	4.20192i	0.171543	+	0.297121i
$201$		0			0
$202$	−7.20725	+	12.4833i	−0.507101	+	0.878324i
$203$	−4.80126	+	8.31602i	−0.336982	+	0.583670i
$204$		0			0
$205$	−0.739211	−	1.28035i	−0.0516287	−	0.0894236i
$206$	−6.12190			−0.426533
$207$		0			0
$208$	−4.33454			−0.300546
$209$	−5.36578	−	9.29380i	−0.371158	−	0.642865i
$210$		0			0
$211$	5.06905	−	8.77985i	0.348968	−	0.604430i	−0.637099	−	0.770782i	$-0.719866\pi$
$211$	5.06905	−	8.77985i	0.348968	−	0.604430i	0.986066	+	0.166352i	$0.0531989\pi$
$212$	1.00634	−	1.74303i	0.0691157	−	0.119712i
$213$		0			0
$214$	−8.70933	−	15.0850i	−0.595357	−	1.03119i
$215$	−0.702780			−0.0479292
$216$		0			0
$217$	3.99012			0.270867
$218$	4.97136	+	8.61065i	0.336703	+	0.583187i
$219$		0			0
$220$	0.309820	−	0.536625i	0.0208881	−	0.0361792i
$221$	3.24315	−	5.61729i	0.218158	−	0.377860i
$222$		0			0
$223$	11.9793	+	20.7487i	0.802191	+	1.38944i	0.918171	+	0.396184i	$0.129666\pi$
$223$	11.9793	+	20.7487i	0.802191	+	1.38944i	−0.115981	+	0.993251i	$0.537001\pi$
$224$	0.948831			0.0633965
$225$		0			0
$226$	9.05878			0.602581
$227$	−3.58227	−	6.20468i	−0.237764	−	0.411819i	0.722309	−	0.691571i	$-0.243081\pi$
$227$	−3.58227	−	6.20468i	−0.237764	−	0.411819i	−0.960072	+	0.279752i	$0.909748\pi$
$228$		0			0
$229$	−4.42354	+	7.66180i	−0.292316	+	0.506306i	−0.974357	−	0.225008i	$-0.927759\pi$
$229$	−4.42354	+	7.66180i	−0.292316	+	0.506306i	0.682041	+	0.731314i	$0.261092\pi$
$230$	1.26693	−	2.19439i	0.0835391	−	0.144694i
$231$		0			0
$232$	−5.06018	−	8.76449i	−0.332217	−	0.575417i
$233$	23.7835			1.55811			0.779053	−	0.626958i	$-0.215700\pi$
$233$	23.7835			1.55811			0.779053	+	0.626958i	$0.215700\pi$
$234$		0			0
$235$	−3.64924			−0.238050
$236$	4.50435	+	7.80176i	0.293208	+	0.507851i
$237$		0			0
$238$	−0.709925	+	1.22963i	−0.0460176	+	0.0797048i
$239$	−8.04881	+	13.9410i	−0.520634	+	0.901765i	0.479078	+	0.877772i	$0.340971\pi$
$239$	−8.04881	+	13.9410i	−0.520634	+	0.901765i	−0.999712	+	0.0239927i	$0.992362\pi$
$240$		0			0
$241$	−11.6250	−	20.1351i	−0.748832	−	1.29701i	−0.948383	−	0.317127i	$-0.897282\pi$
$241$	−11.6250	−	20.1351i	−0.748832	−	1.29701i	0.199552	−	0.979887i	$-0.436051\pi$
$242$	−8.40634			−0.540380
$243$		0			0
$244$	8.60179			0.550673
$245$	−1.17345	−	2.03247i	−0.0749688	−	0.129850i
$246$		0			0
$247$	14.4417	−	25.0138i	0.918905	−	1.59159i
$248$	−2.10265	+	3.64190i	−0.133519	+	0.231261i
$249$		0			0
$250$	−1.89529	−	3.28274i	−0.119869	−	0.207619i
$251$	−0.0740798			−0.00467588			−0.00233794	−	0.999997i	$-0.500744\pi$
$251$	−0.0740798			−0.00467588			−0.00233794	+	0.999997i	$0.500744\pi$
$252$		0			0
$253$	10.6061			0.666801
$254$	2.54433	+	4.40691i	0.159646	+	0.276514i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.70503	+	9.88140i	−0.355870	+	0.616385i	−0.987266	−	0.159075i	$-0.949149\pi$
$257$	−5.70503	+	9.88140i	−0.355870	+	0.616385i	0.631396	+	0.775460i	$0.282482\pi$
$258$		0			0
$259$	1.61343	+	2.79454i	0.100254	+	0.173644i
$260$	1.66773			0.103428
$261$		0			0
$262$	0.792684			0.0489722
$263$	13.0996	+	22.6892i	0.807757	+	1.39908i	0.914414	+	0.404780i	$0.132652\pi$
$263$	13.0996	+	22.6892i	0.807757	+	1.39908i	−0.106658	+	0.994296i	$0.534015\pi$
$264$		0			0
$265$	−0.387193	+	0.670639i	−0.0237851	+	0.0411970i
$266$	−3.16130	+	5.47552i	−0.193831	+	0.335726i
$267$		0			0
$268$	5.84514	+	10.1241i	0.357049	+	0.618426i
$269$	0.668509			0.0407597			0.0203799	−	0.999792i	$-0.493512\pi$
$269$	0.668509			0.0407597			0.0203799	+	0.999792i	$0.493512\pi$
$270$		0			0
$271$	−2.97592			−0.180774			−0.0903871	−	0.995907i	$-0.528810\pi$
$271$	−2.97592			−0.180774			−0.0903871	+	0.995907i	$0.528810\pi$
$272$	−0.748210	−	1.29594i	−0.0453669	−	0.0785778i
$273$		0			0
$274$	3.38637	−	5.86536i	0.204578	−	0.354339i
$275$	3.90700	−	6.76713i	0.235601	−	0.408073i
$276$		0			0
$277$	0.855405	+	1.48160i	0.0513963	+	0.0890210i	0.890579	−	0.454829i	$-0.150300\pi$
$277$	0.855405	+	1.48160i	0.0513963	+	0.0890210i	−0.839183	+	0.543850i	$0.816966\pi$
$278$	−3.47065			−0.208156
$279$		0			0
$280$	−0.365067			−0.0218169
$281$	14.8691	+	25.7540i	0.887017	+	1.53636i	0.843385	+	0.537310i	$0.180559\pi$
$281$	14.8691	+	25.7540i	0.887017	+	1.53636i	0.0436317	+	0.999048i	$0.486107\pi$
$282$		0			0
$283$	−10.5787	+	18.3229i	−0.628840	+	1.08918i	0.358945	+	0.933359i	$0.383137\pi$
$283$	−10.5787	+	18.3229i	−0.628840	+	1.08918i	−0.987785	+	0.155824i	$0.950197\pi$
$284$	−0.220340	+	0.381640i	−0.0130748	+	0.0226462i
$285$		0			0
$286$	3.49035	+	6.04547i	0.206389	+	0.357476i
$287$	−3.64589			−0.215210
$288$		0			0
$289$	−14.7607			−0.868278
$290$	1.94693	+	3.37218i	0.114327	+	0.198021i
$291$		0			0
$292$	−5.27624	+	9.13871i	−0.308768	+	0.534803i
$293$	10.2509	−	17.7550i	0.598862	−	1.03726i	−0.394128	−	0.919056i	$-0.628953\pi$
$293$	10.2509	−	17.7550i	0.598862	−	1.03726i	0.992989	−	0.118203i	$-0.0377134\pi$
$294$		0			0
$295$	−1.73307	−	3.00176i	−0.100903	−	0.174769i
$296$	−3.40088			−0.197672
$297$		0			0
$298$	−7.32870			−0.424540
$299$	14.2729	+	24.7214i	0.825424	+	1.42968i
$300$		0			0
$301$	−0.866552	+	1.50091i	−0.0499472	+	0.0865111i
$302$	8.57068	−	14.8449i	0.493187	−	0.854226i
$303$		0			0
$304$	−3.33178	−	5.77081i	−0.191091	−	0.330979i
$305$	−3.30958			−0.189506
$306$		0			0
$307$	28.6098			1.63285			0.816425	−	0.577452i	$-0.195953\pi$
$307$	28.6098			1.63285			0.816425	+	0.577452i	$0.195953\pi$
$308$	−0.764039	−	1.32335i	−0.0435351	−	0.0754051i
$309$		0			0
$310$	0.809005	−	1.40124i	0.0459484	−	0.0795849i
$311$	16.8235	−	29.1391i	0.953972	−	1.65233i	0.217270	−	0.976112i	$-0.430285\pi$
$311$	16.8235	−	29.1391i	0.953972	−	1.65233i	0.736702	−	0.676217i	$-0.236382\pi$
$312$		0			0
$313$	2.95914	+	5.12538i	0.167260	+	0.289703i	0.937456	−	0.348105i	$-0.113175\pi$
$313$	2.95914	+	5.12538i	0.167260	+	0.289703i	−0.770195	+	0.637808i	$0.779841\pi$
$314$	1.33359			0.0752586
$315$		0			0
$316$	−13.3503			−0.751012
$317$	14.3413	+	24.8398i	0.805485	+	1.39514i	0.915963	+	0.401262i	$0.131428\pi$
$317$	14.3413	+	24.8398i	0.805485	+	1.39514i	−0.110478	+	0.993879i	$0.535238\pi$
$318$		0			0
$319$	−8.14934	+	14.1151i	−0.456275	+	0.790292i
$320$	0.192377	−	0.333207i	0.0107542	−	0.0186268i
$321$		0			0
$322$	−3.12434	−	5.41152i	−0.174113	−	0.301572i
$323$	9.97148			0.554828
$324$		0			0
$325$	21.0310			1.16659
$326$	−0.842879	−	1.45991i	−0.0466828	−	0.0808569i
$327$		0			0
$328$	1.92125	−	3.32771i	0.106084	−	0.183742i
$329$	−4.49964	+	7.79361i	−0.248073	+	0.429676i
$330$		0			0
$331$	−0.791396	−	1.37074i	−0.0434990	−	0.0753425i	0.843456	−	0.537198i	$-0.180517\pi$
$331$	−0.791396	−	1.37074i	−0.0434990	−	0.0753425i	−0.886955	+	0.461855i	$0.847184\pi$
$332$	7.98234			0.438088
$333$		0			0
$334$	3.11539			0.170466
$335$	−2.24894	−	3.89528i	−0.122873	−	0.212822i
$336$		0			0
$337$	−8.66359	+	15.0058i	−0.471936	+	0.817417i	−0.999484	−	0.0321079i	$-0.989778\pi$
$337$	−8.66359	+	15.0058i	−0.471936	+	0.817417i	0.527548	+	0.849525i	$0.323111\pi$
$338$	−2.89411	+	5.01274i	−0.157419	+	0.272657i
$339$		0			0
$340$	0.287877	+	0.498618i	0.0156123	+	0.0270414i
$341$	6.77258			0.366756
$342$		0			0
$343$	−12.4294			−0.671126
$344$	−0.913284	−	1.58185i	−0.0492410	−	0.0852878i
$345$		0			0
$346$	11.4906	−	19.9023i	0.617738	−	1.06995i
$347$	−13.5130	+	23.4053i	−0.725418	+	1.25646i	0.233384	+	0.972385i	$0.425020\pi$
$347$	−13.5130	+	23.4053i	−0.725418	+	1.25646i	−0.958802	+	0.284076i	$0.908313\pi$
$348$		0			0
$349$	−9.14403	−	15.8379i	−0.489469	−	0.847785i	0.510458	−	0.859903i	$-0.329476\pi$
$349$	−9.14403	−	15.8379i	−0.489469	−	0.847785i	−0.999927	+	0.0121181i	$0.996143\pi$
$350$	−4.60370			−0.246078
$351$		0			0
$352$	1.61048			0.0858391
$353$	−8.05813	−	13.9571i	−0.428891	−	0.742861i	0.567884	−	0.823108i	$-0.307762\pi$
$353$	−8.05813	−	13.9571i	−0.428891	−	0.742861i	−0.996775	+	0.0802479i	$0.974429\pi$
$354$		0			0
$355$	0.0847768	−	0.146838i	0.00449949	−	0.00779334i
$356$	5.16064	−	8.93848i	0.273513	−	0.473739i
$357$		0			0
$358$	12.8830	+	22.3141i	0.680889	+	1.17934i
$359$	22.3287			1.17846			0.589231	−	0.807964i	$-0.299431\pi$
$359$	22.3287			1.17846			0.589231	+	0.807964i	$0.299431\pi$
$360$		0			0
$361$	25.4030			1.33700
$362$	8.05402	+	13.9500i	0.423310	+	0.733195i
$363$		0			0
$364$	2.05637	−	3.56174i	0.107783	−	0.186686i
$365$	2.03006	−	3.51616i	0.106258	−	0.184044i
$366$		0			0
$367$	2.75113	+	4.76509i	0.143608	+	0.248736i	0.928853	−	0.370449i	$-0.120796\pi$
$367$	2.75113	+	4.76509i	0.143608	+	0.248736i	−0.785245	+	0.619185i	$0.787463\pi$
$368$	6.58567			0.343302
$369$		0			0
$370$	1.30850			0.0680258
$371$	0.954846	+	1.65384i	0.0495731	+	0.0858632i
$372$		0			0
$373$	5.95181	−	10.3088i	0.308173	−	0.533772i	−0.669790	−	0.742551i	$-0.733616\pi$
$373$	5.95181	−	10.3088i	0.308173	−	0.533772i	0.977963	+	0.208779i	$0.0669490\pi$
$374$	−1.20498	+	2.08709i	−0.0623081	+	0.107921i
$375$		0			0
$376$	−4.74230	−	8.21391i	−0.244565	−	0.423600i
$377$	−43.8671			−2.25927
$378$		0			0
$379$	18.3389			0.942006			0.471003	−	0.882131i	$-0.343892\pi$
$379$	18.3389			0.942006			0.471003	+	0.882131i	$0.343892\pi$
$380$	1.28192	+	2.22034i	0.0657609	+	0.113901i
$381$		0			0
$382$	5.81076	−	10.0645i	0.297304	−	0.514946i
$383$	14.7248	−	25.5040i	0.752400	−	1.30320i	−0.194256	−	0.980951i	$-0.562229\pi$
$383$	14.7248	−	25.5040i	0.752400	−	1.30320i	0.946656	−	0.322245i	$-0.104437\pi$
$384$		0			0
$385$	0.293967	+	0.509166i	0.0149820	+	0.0259495i
$386$	−5.86149			−0.298342
$387$		0			0
$388$	13.1482			0.667497
$389$	2.45458	+	4.25146i	0.124452	+	0.215557i	0.921519	−	0.388334i	$-0.126949\pi$
$389$	2.45458	+	4.25146i	0.124452	+	0.215557i	−0.797067	+	0.603892i	$0.793616\pi$
$390$		0			0
$391$	−4.92746	+	8.53462i	−0.249193	+	0.431614i
$392$	3.04986	−	5.28251i	0.154041	−	0.266807i
$393$		0			0
$394$	0.924759	+	1.60173i	0.0465887	+	0.0806939i
$395$	5.13658			0.258450
$396$		0			0
$397$	25.6473			1.28720			0.643601	−	0.765361i	$-0.277440\pi$
$397$	25.6473			1.28720			0.643601	+	0.765361i	$0.277440\pi$
$398$	3.41804	+	5.92022i	0.171331	+	0.296754i
$399$		0			0
$400$	2.42598	−	4.20192i	0.121299	−	0.210096i
$401$	12.5165	−	21.6793i	0.625047	−	1.08261i	−0.363485	−	0.931600i	$-0.618413\pi$
$401$	12.5165	−	21.6793i	0.625047	−	1.08261i	0.988532	−	0.151012i	$-0.0482533\pi$
$402$		0			0
$403$	9.11403	+	15.7860i	0.454002	+	0.786355i
$404$	14.4145			0.717149
$405$		0			0
$406$	9.60251			0.476565
$407$	2.73853	+	4.74327i	0.135744	+	0.235115i
$408$		0			0
$409$	13.4041	−	23.2166i	0.662789	−	1.14798i	−0.317090	−	0.948395i	$-0.602706\pi$
$409$	13.4041	−	23.2166i	0.662789	−	1.14798i	0.979880	−	0.199589i	$-0.0639608\pi$
$410$	−0.739211	+	1.28035i	−0.0365070	+	0.0632320i
$411$		0			0
$412$	3.06095	+	5.30172i	0.150802	+	0.261197i
$413$	−8.54773			−0.420606
$414$		0			0
$415$	−3.07124			−0.150761
$416$	2.16727	+	3.75382i	0.106259	+	0.184046i
$417$		0			0
$418$	−5.36578	+	9.29380i	−0.262449	+	0.454574i
$419$	−14.8586	+	25.7358i	−0.725889	+	1.25728i	0.232718	+	0.972544i	$0.425238\pi$
$419$	−14.8586	+	25.7358i	−0.725889	+	1.25728i	−0.958607	+	0.284733i	$0.908095\pi$
$420$		0			0
$421$	−8.73540	−	15.1302i	−0.425737	−	0.737398i	0.570752	−	0.821123i	$-0.306652\pi$
$421$	−8.73540	−	15.1302i	−0.425737	−	0.737398i	−0.996489	+	0.0837242i	$0.973319\pi$
$422$	−10.1381			−0.493515
$423$		0			0
$424$	−2.01268			−0.0977443
$425$	3.63029	+	6.28784i	0.176095	+	0.305005i
$426$		0			0
$427$	−4.08082	+	7.06819i	−0.197485	+	0.342054i
$428$	−8.70933	+	15.0850i	−0.420981	+	0.729161i
$429$		0			0
$430$	0.351390	+	0.608625i	0.0169455	+	0.0293505i
$431$	−4.27087			−0.205721			−0.102860	−	0.994696i	$-0.532799\pi$
$431$	−4.27087			−0.205721			−0.102860	+	0.994696i	$0.532799\pi$
$432$		0			0
$433$	−15.3582			−0.738066			−0.369033	−	0.929416i	$-0.620311\pi$
$433$	−15.3582			−0.738066			−0.369033	+	0.929416i	$0.620311\pi$
$434$	−1.99506	−	3.45555i	−0.0957661	−	0.165872i
$435$		0			0
$436$	4.97136	−	8.61065i	0.238085	−	0.412375i
$437$	−21.9420	+	38.0046i	−1.04963	+	1.81801i
$438$		0			0
$439$	7.30751	+	12.6570i	0.348769	+	0.604085i	0.986031	−	0.166562i	$-0.0532666\pi$
$439$	7.30751	+	12.6570i	0.348769	+	0.604085i	−0.637262	+	0.770647i	$0.719933\pi$
$440$	−0.619641			−0.0295402
$441$		0			0
$442$	−6.48629			−0.308521
$443$	2.86520	+	4.96267i	0.136130	+	0.235784i	0.926028	−	0.377454i	$-0.123200\pi$
$443$	2.86520	+	4.96267i	0.136130	+	0.235784i	−0.789899	+	0.613237i	$0.789867\pi$
$444$		0			0
$445$	−1.98558	+	3.43912i	−0.0941254	+	0.163030i
$446$	11.9793	−	20.7487i	0.567235	−	0.982479i
$447$		0			0
$448$	−0.474416	−	0.821712i	−0.0224140	−	0.0388222i
$449$	−2.38888			−0.112738			−0.0563690	−	0.998410i	$-0.517952\pi$
$449$	−2.38888			−0.112738			−0.0563690	+	0.998410i	$0.517952\pi$
$450$		0			0
$451$	−6.18830			−0.291396
$452$	−4.52939	−	7.84514i	−0.213045	−	0.369004i
$453$		0			0
$454$	−3.58227	+	6.20468i	−0.168124	+	0.291200i
$455$	−0.791199	+	1.37040i	−0.0370920	+	0.0642452i
$456$		0			0
$457$	−9.83789	−	17.0397i	−0.460197	−	0.797085i	0.538773	−	0.842451i	$-0.318888\pi$
$457$	−9.83789	−	17.0397i	−0.460197	−	0.797085i	−0.998970	+	0.0453661i	$0.985555\pi$
$458$	8.84708			0.413397
$459$		0			0
$460$	−2.53387			−0.118142
$461$	4.01181	+	6.94866i	0.186849	+	0.323631i	0.944198	−	0.329379i	$-0.106839\pi$
$461$	4.01181	+	6.94866i	0.186849	+	0.323631i	−0.757349	+	0.653010i	$0.773506\pi$
$462$		0			0
$463$	−11.9741	+	20.7397i	−0.556484	+	0.963858i	0.441303	+	0.897358i	$0.354516\pi$
$463$	−11.9741	+	20.7397i	−0.556484	+	0.963858i	−0.997786	+	0.0664995i	$0.978817\pi$
$464$	−5.06018	+	8.76449i	−0.234913	+	0.406881i
$465$		0			0
$466$	−11.8917	−	20.5971i	−0.550874	−	0.954141i
$467$	11.3484			0.525141			0.262571	−	0.964913i	$-0.415430\pi$
$467$	11.3484			0.525141			0.262571	+	0.964913i	$0.415430\pi$
$468$		0			0
$469$	−11.0921			−0.512186
$470$	1.82462	+	3.16034i	0.0841635	+	0.145775i
$471$		0			0
$472$	4.50435	−	7.80176i	0.207329	−	0.359105i
$473$	−1.47083	+	2.54755i	−0.0676288	+	0.117136i
$474$		0			0
$475$	16.1657	+	27.9998i	0.741732	+	1.28472i
$476$	1.41985			0.0650787
$477$		0			0
$478$	16.0976			0.736288
$479$	17.7905	+	30.8141i	0.812869	+	1.40793i	0.910848	+	0.412742i	$0.135429\pi$
$479$	17.7905	+	30.8141i	0.812869	+	1.40793i	−0.0979785	+	0.995189i	$0.531238\pi$
$480$		0			0
$481$	−7.37061	+	12.7663i	−0.336071	+	0.582092i
$482$	−11.6250	+	20.1351i	−0.529504	+	0.917128i
$483$		0			0
$484$	4.20317	+	7.28011i	0.191053	+	0.330914i
$485$	−5.05881			−0.229709
$486$		0			0
$487$	−19.0377			−0.862679			−0.431339	−	0.902190i	$-0.641959\pi$
$487$	−19.0377			−0.862679			−0.431339	+	0.902190i	$0.641959\pi$
$488$	−4.30089	−	7.44936i	−0.194692	−	0.337217i
$489$		0			0
$490$	−1.17345	+	2.03247i	−0.0530109	+	0.0918176i
$491$	13.5007	−	23.3839i	0.609279	−	1.05530i	−0.382080	−	0.924129i	$-0.624792\pi$
$491$	13.5007	−	23.3839i	0.609279	−	1.05530i	0.991359	−	0.131173i	$-0.0418744\pi$
$492$		0			0
$493$	−7.57215	−	13.1154i	−0.341033	−	0.590686i
$494$	−28.8834			−1.29953
$495$		0			0
$496$	4.20530			0.188824
$497$	−0.209066	−	0.362112i	−0.00937787	−	0.0162430i
$498$		0			0
$499$	0.831452	−	1.44012i	0.0372209	−	0.0644685i	−0.846815	−	0.531888i	$-0.821483\pi$
$499$	0.831452	−	1.44012i	0.0372209	−	0.0644685i	0.884036	+	0.467419i	$0.154816\pi$
$500$	−1.89529	+	3.28274i	−0.0847601	+	0.146809i
$501$		0			0
$502$	0.0370399	+	0.0641550i	0.00165317	+	0.00286338i
$503$	−3.71565			−0.165673			−0.0828364	−	0.996563i	$-0.526398\pi$
$503$	−3.71565			−0.165673			−0.0828364	+	0.996563i	$0.526398\pi$
$504$		0			0
$505$	−5.54605			−0.246796
$506$	−5.30306	−	9.18516i	−0.235750	−	0.408330i
$507$		0			0
$508$	2.54433	−	4.40691i	0.112886	−	0.195525i
$509$	−4.30589	+	7.45802i	−0.190855	+	0.330571i	−0.945534	−	0.325524i	$-0.894459\pi$
$509$	−4.30589	+	7.45802i	−0.190855	+	0.330571i	0.754679	+	0.656095i	$0.227793\pi$
$510$		0			0
$511$	−5.00626	−	8.67109i	−0.221464	−	0.383587i
$512$	1.00000			0.0441942
$513$		0			0
$514$	11.4101			0.503276
$515$	−1.17771	−	2.03986i	−0.0518963	−	0.0898870i
$516$		0			0
$517$	−7.63740	+	13.2284i	−0.335892	+	0.581783i
$518$	1.61343	−	2.79454i	0.0708900	−	0.122785i
$519$		0			0
$520$	−0.833866	−	1.44430i	−0.0365675	−	0.0633367i
$521$	39.5039			1.73070			0.865348	−	0.501171i	$-0.167097\pi$
$521$	39.5039			1.73070			0.865348	+	0.501171i	$0.167097\pi$
$522$		0			0
$523$	−1.18762			−0.0519310			−0.0259655	−	0.999663i	$-0.508266\pi$
$523$	−1.18762			−0.0519310			−0.0259655	+	0.999663i	$0.508266\pi$
$524$	−0.396342	−	0.686484i	−0.0173143	−	0.0299892i
$525$		0			0
$526$	13.0996	−	22.6892i	0.571170	−	0.989296i
$527$	−3.14645	+	5.44981i	−0.137062	+	0.237398i
$528$		0			0
$529$	−10.1855	−	17.6418i	−0.442848	−	0.767036i
$530$	0.774387			0.0336372
$531$		0			0
$532$	6.32259			0.274119
$533$	−8.32775	−	14.4241i	−0.360715	−	0.624776i
$534$		0			0
$535$	3.35095	−	5.80402i	0.144874	−	0.250930i
$536$	5.84514	−	10.1241i	0.252472	−	0.437294i
$537$		0			0
$538$	−0.334254	−	0.578946i	−0.0144107	−	0.0249601i
$539$	−9.82350			−0.423128
$540$		0			0
$541$	25.2367			1.08501			0.542506	−	0.840052i	$-0.317476\pi$
$541$	25.2367			1.08501			0.542506	+	0.840052i	$0.317476\pi$
$542$	1.48796	+	2.57722i	0.0639133	+	0.110701i
$543$		0			0
$544$	−0.748210	+	1.29594i	−0.0320792	+	0.0555629i
$545$	−1.91275	+	3.31299i	−0.0819334	+	0.141913i
$546$		0			0
$547$	13.1129	+	22.7123i	0.560668	+	0.971106i	0.997438	+	0.0715326i	$0.0227890\pi$
$547$	13.1129	+	22.7123i	0.560668	+	0.971106i	−0.436770	+	0.899573i	$0.643878\pi$
$548$	−6.77273			−0.289317
$549$		0			0
$550$	−7.81401			−0.333191
$551$	−33.7188	−	58.4027i	−1.43647	−	2.48804i
$552$		0			0
$553$	6.33359	−	10.9701i	0.269331	−	0.466496i
$554$	0.855405	−	1.48160i	0.0363427	−	0.0629474i
$555$		0			0
$556$	1.73533	+	3.00567i	0.0735942	+	0.127469i
$557$	11.5277			0.488444			0.244222	−	0.969719i	$-0.421467\pi$
$557$	11.5277			0.488444			0.244222	+	0.969719i	$0.421467\pi$
$558$		0			0
$559$	−7.91733			−0.334867
$560$	0.182534	+	0.316157i	0.00771345	+	0.0133601i
$561$		0			0
$562$	14.8691	−	25.7540i	0.627215	−	1.08637i
$563$	15.9212	−	27.5764i	0.671000	−	1.16221i	−0.306621	−	0.951832i	$-0.599198\pi$
$563$	15.9212	−	27.5764i	0.671000	−	1.16221i	0.977621	−	0.210375i	$-0.0674684\pi$
$564$		0			0
$565$	1.74270	+	3.01845i	0.0733161	+	0.126987i
$566$	21.1575			0.889314
$567$		0			0
$568$	0.440680			0.0184905
$569$	−12.1928	−	21.1186i	−0.511150	−	0.885338i	−0.999916	−	0.0129232i	$-0.995886\pi$
$569$	−12.1928	−	21.1186i	−0.511150	−	0.885338i	0.488766	−	0.872415i	$-0.337447\pi$
$570$		0			0
$571$	−17.3922	+	30.1243i	−0.727843	+	1.26066i	0.229950	+	0.973202i	$0.426144\pi$
$571$	−17.3922	+	30.1243i	−0.727843	+	1.26066i	−0.957793	+	0.287459i	$0.907190\pi$
$572$	3.49035	−	6.04547i	0.145939	−	0.252774i
$573$		0			0
$574$	1.82295	+	3.15744i	0.0760883	+	0.131789i
$575$	−31.9534			−1.33255
$576$		0			0
$577$	−26.1469			−1.08851			−0.544255	−	0.838920i	$-0.683188\pi$
$577$	−26.1469			−1.08851			−0.544255	+	0.838920i	$0.683188\pi$
$578$	7.38036	+	12.7832i	0.306983	+	0.531710i
$579$		0			0
$580$	1.94693	−	3.37218i	0.0808417	−	0.140022i
$581$	−3.78695	+	6.55919i	−0.157109	+	0.272121i
$582$		0			0
$583$	1.62069	+	2.80712i	0.0671222	+	0.116259i
$584$	10.5525			0.436664
$585$		0			0
$586$	−20.5017			−0.846918
$587$	−16.2780	−	28.1943i	−0.671864	−	1.16370i	−0.977375	−	0.211514i	$-0.932161\pi$
$587$	−16.2780	−	28.1943i	−0.671864	−	1.16370i	0.305511	−	0.952189i	$-0.401173\pi$
$588$		0			0
$589$	−14.0111	+	24.2680i	−0.577319	+	0.999946i
$590$	−1.73307	+	3.00176i	−0.0713493	+	0.123581i
$591$		0			0
$592$	1.70044	+	2.94525i	0.0698876	+	0.121049i
$593$	6.75797			0.277517			0.138758	−	0.990326i	$-0.455689\pi$
$593$	6.75797			0.277517			0.138758	+	0.990326i	$0.455689\pi$
$594$		0			0
$595$	−0.546294			−0.0223959
$596$	3.66435	+	6.34684i	0.150098	+	0.259977i
$597$		0			0
$598$	14.2729	−	24.7214i	0.583663	−	1.01093i
$599$	−8.26901	+	14.3224i	−0.337863	+	0.585195i	−0.984030	−	0.178000i	$-0.943037\pi$
$599$	−8.26901	+	14.3224i	−0.337863	+	0.585195i	0.646168	+	0.763195i	$0.276371\pi$
$600$		0			0
$601$	−21.1718	−	36.6706i	−0.863614	−	1.49582i	−0.868417	−	0.495835i	$-0.834862\pi$
$601$	−21.1718	−	36.6706i	−0.863614	−	1.49582i	0.00480228	−	0.999988i	$-0.498471\pi$
$602$	1.73310			0.0706361
$603$		0			0
$604$	−17.1414			−0.697472
$605$	−1.61719	−	2.80105i	−0.0657481	−	0.113879i
$606$		0			0
$607$	−5.36665	+	9.29531i	−0.217826	+	0.377285i	−0.954143	−	0.299351i	$-0.903230\pi$
$607$	−5.36665	+	9.29531i	−0.217826	+	0.377285i	0.736317	+	0.676636i	$0.236563\pi$
$608$	−3.33178	+	5.77081i	−0.135121	+	0.234037i
$609$		0			0
$610$	1.65479	+	2.86618i	0.0670004	+	0.116048i
$611$	−41.1114			−1.66319
$612$		0			0
$613$	−5.67291			−0.229127			−0.114563	−	0.993416i	$-0.536547\pi$
$613$	−5.67291			−0.229127			−0.114563	+	0.993416i	$0.536547\pi$
$614$	−14.3049	−	24.7768i	−0.577299	−	0.999912i
$615$		0			0
$616$	−0.764039	+	1.32335i	−0.0307840	+	0.0533194i
$617$	8.26427	−	14.3141i	0.332707	−	0.576266i	−0.650335	−	0.759648i	$-0.725371\pi$
$617$	8.26427	−	14.3141i	0.332707	−	0.576266i	0.983042	+	0.183382i	$0.0587046\pi$
$618$		0			0
$619$	23.1332	+	40.0678i	0.929801	+	1.61046i	0.783652	+	0.621200i	$0.213354\pi$
$619$	23.1332	+	40.0678i	0.929801	+	1.61046i	0.146149	+	0.989263i	$0.453312\pi$
$620$	−1.61801			−0.0649808
$621$		0			0
$622$	−33.6470			−1.34912
$623$	4.89657	+	8.48111i	0.196177	+	0.339789i
$624$		0			0
$625$	−11.4007	+	19.7466i	−0.456027	+	0.789863i
$626$	2.95914	−	5.12538i	0.118271	−	0.204851i
$627$		0			0
$628$	−0.666793	−	1.15492i	−0.0266079	−	0.0460863i
$629$	−5.08914			−0.202917
$630$		0			0
$631$	−26.2601			−1.04540			−0.522699	−	0.852518i	$-0.675075\pi$
$631$	−26.2601			−1.04540			−0.522699	+	0.852518i	$0.675075\pi$
$632$	6.67514	+	11.5617i	0.265523	+	0.459899i
$633$		0			0
$634$	14.3413	−	24.8398i	0.569564	−	0.986514i
$635$	−0.978943	+	1.69558i	−0.0388482	+	0.0672870i
$636$		0			0
$637$	−13.2197	−	22.8972i	−0.523785	−	0.907222i
$638$	16.2987			0.645271
$639$		0			0
$640$	−0.384754			−0.0152088
$641$	−9.46936	−	16.4014i	−0.374017	−	0.647817i	0.616162	−	0.787619i	$-0.288687\pi$
$641$	−9.46936	−	16.4014i	−0.374017	−	0.647817i	−0.990179	+	0.139803i	$0.955353\pi$
$642$		0			0
$643$	−11.4636	+	19.8556i	−0.452081	+	0.783028i	−0.998515	−	0.0544744i	$-0.982652\pi$
$643$	−11.4636	+	19.8556i	−0.452081	+	0.783028i	0.546434	+	0.837502i	$0.315985\pi$
$644$	−3.12434	+	5.41152i	−0.123116	+	0.213244i
$645$		0			0
$646$	−4.98574	−	8.63556i	−0.196161	−	0.339761i
$647$	33.3928			1.31281			0.656403	−	0.754410i	$-0.272077\pi$
$647$	33.3928			1.31281			0.656403	+	0.754410i	$0.272077\pi$
$648$		0			0
$649$	−14.5084			−0.569503
$650$	−10.5155	−	18.2134i	−0.412452	−	0.714388i
$651$		0			0
$652$	−0.842879	+	1.45991i	−0.0330097	+	0.0571745i
$653$	−16.2333	+	28.1169i	−0.635258	+	1.10030i	0.351203	+	0.936299i	$0.385773\pi$
$653$	−16.2333	+	28.1169i	−0.635258	+	1.10030i	−0.986461	+	0.163999i	$0.947561\pi$
$654$		0			0
$655$	0.152494	+	0.264128i	0.00595844	+	0.0103203i
$656$	−3.84251			−0.150025
$657$		0			0
$658$	8.99929			0.350829
$659$	−5.85604	−	10.1430i	−0.228119	−	0.395114i	0.729132	−	0.684373i	$-0.239924\pi$
$659$	−5.85604	−	10.1430i	−0.228119	−	0.395114i	−0.957251	+	0.289260i	$0.906591\pi$
$660$		0			0
$661$	7.80613	−	13.5206i	0.303623	−	0.525891i	−0.673331	−	0.739341i	$-0.735137\pi$
$661$	7.80613	−	13.5206i	0.303623	−	0.525891i	0.976954	+	0.213451i	$0.0684703\pi$
$662$	−0.791396	+	1.37074i	−0.0307585	+	0.0532752i
$663$		0			0
$664$	−3.99117	−	6.91291i	−0.154888	−	0.268273i
$665$	−2.43265			−0.0943339
$666$		0			0
$667$	66.6493			2.58067
$668$	−1.55769	−	2.69800i	−0.0602690	−	0.104389i
$669$		0			0
$670$	−2.24894	+	3.89528i	−0.0868842	+	0.150488i
$671$	−6.92652	+	11.9971i	−0.267395	+	0.463142i
$672$		0			0
$673$	8.74255	+	15.1425i	0.337000	+	0.583702i	0.983867	−	0.178901i	$-0.0572543\pi$
$673$	8.74255	+	15.1425i	0.337000	+	0.583702i	−0.646867	+	0.762603i	$0.723921\pi$
$674$	17.3272			0.667418
$675$		0			0
$676$	5.78822			0.222624
$677$	5.83323	+	10.1035i	0.224189	+	0.388307i	0.956076	−	0.293119i	$-0.0946933\pi$
$677$	5.83323	+	10.1035i	0.224189	+	0.388307i	−0.731887	+	0.681426i	$0.761360\pi$
$678$		0			0
$679$	−6.23769	+	10.8040i	−0.239381	+	0.414619i
$680$	0.287877	−	0.498618i	0.0110396	−	0.0191211i
$681$		0			0
$682$	−3.38629	−	5.86522i	−0.129668	−	0.224591i
$683$	35.9229			1.37455			0.687276	−	0.726396i	$-0.258806\pi$
$683$	35.9229			1.37455			0.687276	+	0.726396i	$0.258806\pi$
$684$		0			0
$685$	2.60584			0.0995640
$686$	6.21471	+	10.7642i	0.237279	+	0.410979i
$687$		0			0
$688$	−0.913284	+	1.58185i	−0.0348186	+	0.0603076i
$689$	−4.36202	+	7.55523i	−0.166180	+	0.287831i
$690$		0			0
$691$	3.82811	+	6.63048i	0.145628	+	0.252235i	0.929607	−	0.368552i	$-0.120146\pi$
$691$	3.82811	+	6.63048i	0.145628	+	0.252235i	−0.783979	+	0.620787i	$0.786813\pi$
$692$	−22.9812			−0.873614
$693$		0			0
$694$	27.0261			1.02590
$695$	−0.667675	−	1.15645i	−0.0253263	−	0.0438665i
$696$		0			0
$697$	2.87500	−	4.97965i	0.108899	−	0.188618i
$698$	−9.14403	+	15.8379i	−0.346107	+	0.599474i
$699$		0			0
$700$	2.30185	+	3.98692i	0.0870017	+	0.150691i
$701$	−24.9479			−0.942268			−0.471134	−	0.882062i	$-0.656155\pi$
$701$	−24.9479			−0.942268			−0.471134	+	0.882062i	$0.656155\pi$
$702$		0			0
$703$	−22.6619			−0.854711
$704$	−0.805242	−	1.39472i	−0.0303487	−	0.0525655i
$705$		0			0
$706$	−8.05813	+	13.9571i	−0.303272	+	0.525282i
$707$	−6.83847	+	11.8446i	−0.257187	+	0.445461i
$708$		0			0
$709$	−4.85146	−	8.40297i	−0.182200	−	0.315580i	0.760429	−	0.649421i	$-0.224989\pi$
$709$	−4.85146	−	8.40297i	−0.182200	−	0.315580i	−0.942630	+	0.333841i	$0.891655\pi$
$710$	−0.169554			−0.00636324
$711$		0			0
$712$	−10.3213			−0.386806
$713$	−13.8474	−	23.9844i	−0.518588	−	0.898221i
$714$		0			0
$715$	−1.34293	+	2.32602i	−0.0502227	+	0.0869882i
$716$	12.8830	−	22.3141i	0.481462	−	0.833916i
$717$		0			0
$718$	−11.1643	−	19.3372i	−0.416649	−	0.721658i
$719$	18.7209			0.698171			0.349085	−	0.937091i	$-0.386492\pi$
$719$	18.7209			0.698171			0.349085	+	0.937091i	$0.386492\pi$
$720$		0			0
$721$	−5.80865			−0.216325
$722$	−12.7015	−	21.9996i	−0.472701	−	0.818742i
$723$		0			0
$724$	8.05402	−	13.9500i	0.299325	−	0.518447i
$725$	24.5518	−	42.5250i	0.911831	−	1.57934i
$726$		0			0
$727$	16.6566	+	28.8501i	0.617760	+	1.06999i	0.989894	+	0.141812i	$0.0452930\pi$
$727$	16.6566	+	28.8501i	0.617760	+	1.06999i	−0.372134	+	0.928179i	$0.621374\pi$
$728$	−4.11275			−0.152428
$729$		0			0
$730$	−4.06011			−0.150271
$731$	−1.36666	−	2.36712i	−0.0505476	−	0.0875510i
$732$		0			0
$733$	−10.5826	+	18.3297i	−0.390878	+	0.677021i	−0.992566	−	0.121711i	$-0.961162\pi$
$733$	−10.5826	+	18.3297i	−0.390878	+	0.677021i	0.601687	+	0.798732i	$0.294495\pi$
$734$	2.75113	−	4.76509i	0.101546	−	0.175883i
$735$		0			0
$736$	−3.29283	−	5.70336i	−0.121375	−	0.210229i
$737$	−18.8270			−0.693502
$738$		0			0
$739$	−0.358645			−0.0131930			−0.00659648	−	0.999978i	$-0.502100\pi$
$739$	−0.358645			−0.0131930			−0.00659648	+	0.999978i	$0.502100\pi$
$740$	−0.654251	−	1.13320i	−0.0240507	−	0.0416571i
$741$		0			0
$742$	0.954846	−	1.65384i	0.0350535	−	0.0607144i
$743$	−11.9620	+	20.7188i	−0.438844	+	0.760100i	−0.997601	−	0.0692317i	$-0.977945\pi$
$743$	−11.9620	+	20.7188i	−0.438844	+	0.760100i	0.558757	+	0.829332i	$0.311279\pi$
$744$		0			0
$745$	−1.40987	−	2.44197i	−0.0516538	−	0.0894670i
$746$	−11.9036			−0.435823
$747$		0			0
$748$	2.40996			0.0881169
$749$	−8.26368	−	14.3131i	−0.301948	−	0.522990i
$750$		0			0
$751$	10.0106	−	17.3389i	0.365293	−	0.632706i	−0.623530	−	0.781799i	$-0.714302\pi$
$751$	10.0106	−	17.3389i	0.365293	−	0.632706i	0.988823	+	0.149093i	$0.0476355\pi$
$752$	−4.74230	+	8.21391i	−0.172934	+	0.299530i
$753$		0			0
$754$	21.9335	+	37.9900i	0.798772	+	1.38351i
$755$	6.59522			0.240025
$756$		0			0
$757$	−44.8127			−1.62874			−0.814372	−	0.580343i	$-0.802919\pi$
$757$	−44.8127			−1.62874			−0.814372	+	0.580343i	$0.802919\pi$
$758$	−9.16945	−	15.8820i	−0.333050	−	0.576859i
$759$		0			0
$760$	1.28192	−	2.22034i	0.0465000	−	0.0805404i
$761$	12.2073	−	21.1437i	0.442516	−	0.766460i	−0.555360	−	0.831610i	$-0.687419\pi$
$761$	12.2073	−	21.1437i	0.442516	−	0.766460i	0.997875	+	0.0651506i	$0.0207528\pi$
$762$		0			0
$763$	4.71698	+	8.17006i	0.170766	+	0.295776i
$764$	−11.6215			−0.420452
$765$		0			0
$766$	−29.4495			−1.06405
$767$	−19.5243	−	33.8170i	−0.704980	−	1.22106i
$768$		0			0
$769$	1.00827	−	1.74637i	0.0363590	−	0.0629756i	−0.847273	−	0.531157i	$-0.821757\pi$
$769$	1.00827	−	1.74637i	0.0363590	−	0.0629756i	0.883632	+	0.468182i	$0.155091\pi$
$770$	0.293967	−	0.509166i	0.0105938	−	0.0183491i
$771$		0			0
$772$	2.93074	+	5.07620i	0.105480	+	0.182696i
$773$	24.8601			0.894156			0.447078	−	0.894495i	$-0.352465\pi$
$773$	24.8601			0.894156			0.447078	+	0.894495i	$0.352465\pi$
$774$		0			0
$775$	−20.4040			−0.732933
$776$	−6.57408	−	11.3866i	−0.235996	−	0.408757i
$777$		0			0
$778$	2.45458	−	4.25146i	0.0880010	−	0.152422i
$779$	12.8024	−	22.1744i	0.458693	−	0.794480i
$780$		0			0
$781$	−0.354854	−	0.614626i	−0.0126977	−	0.0219930i
$782$	9.85493			0.352411
$783$		0			0
$784$	−6.09972			−0.217847
$785$	0.256552	+	0.444360i	0.00915672	+	0.0158599i
$786$		0			0
$787$	11.0354	−	19.1139i	0.393369	−	0.681335i	−0.599522	−	0.800358i	$-0.704643\pi$
$787$	11.0354	−	19.1139i	0.393369	−	0.681335i	0.992892	+	0.119023i	$0.0379761\pi$
$788$	0.924759	−	1.60173i	0.0329432	−	0.0570592i
$789$		0			0
$790$	−2.56829	−	4.44841i	−0.0913757	−	0.158267i
$791$	8.59526			0.305612
$792$		0			0
$793$	−37.2848			−1.32402
$794$	−12.8237	−	22.2112i	−0.455094	−	0.788247i
$795$		0			0
$796$	3.41804	−	5.92022i	0.121149	−	0.209837i
$797$	7.99061	−	13.8401i	0.283042	−	0.490243i	−0.689090	−	0.724675i	$-0.741990\pi$
$797$	7.99061	−	13.8401i	0.283042	−	0.490243i	0.972132	+	0.234432i	$0.0753231\pi$
$798$		0			0
$799$	−7.09647	−	12.2915i	−0.251055	−	0.434840i
$800$	−4.85196			−0.171543
$801$		0			0
$802$	−25.0331			−0.883949
$803$	−8.49729	−	14.7177i	−0.299863	−	0.519378i
$804$		0			0
$805$	1.20211	−	2.08211i	0.0423686	−	0.0733846i
$806$	9.11403	−	15.7860i	0.321028	−	0.556037i
$807$		0			0
$808$	−7.20725	−	12.4833i	−0.253550	−	0.439162i
$809$	−20.8047			−0.731455			−0.365728	−	0.930722i	$-0.619180\pi$
$809$	−20.8047			−0.731455			−0.365728	+	0.930722i	$0.619180\pi$
$810$		0			0
$811$	14.5757			0.511823			0.255912	−	0.966700i	$-0.417624\pi$
$811$	14.5757			0.511823			0.255912	+	0.966700i	$0.417624\pi$
$812$	−4.80126	−	8.31602i	−0.168491	−	0.291835i
$813$		0			0
$814$	2.73853	−	4.74327i	0.0959854	−	0.166252i
$815$	0.324302	−	0.561707i	0.0113598	−	0.0196757i
$816$		0			0
$817$	−6.08572	−	10.5408i	−0.212912	−	0.368775i
$818$	−26.8082			−0.937326
$819$		0			0
$820$	1.47842			0.0516287
$821$	−3.05919	−	5.29868i	−0.106767	−	0.184925i	0.807692	−	0.589605i	$-0.200716\pi$
$821$	−3.05919	−	5.29868i	−0.106767	−	0.184925i	−0.914459	+	0.404679i	$0.867383\pi$
$822$		0			0
$823$	15.2663	−	26.4420i	0.532150	−	0.921710i	−0.467146	−	0.884180i	$-0.654718\pi$
$823$	15.2663	−	26.4420i	0.532150	−	0.921710i	0.999296	−	0.0375298i	$-0.0119489\pi$
$824$	3.06095	−	5.30172i	0.106633	−	0.184694i
$825$		0			0
$826$	4.27386	+	7.40255i	0.148707	+	0.257568i
$827$	−54.3079			−1.88847			−0.944235	−	0.329272i	$-0.893197\pi$
$827$	−54.3079			−1.88847			−0.944235	+	0.329272i	$0.893197\pi$
$828$		0			0
$829$	26.2193			0.910633			0.455316	−	0.890330i	$-0.349526\pi$
$829$	26.2193			0.910633			0.455316	+	0.890330i	$0.349526\pi$
$830$	1.53562	+	2.65977i	0.0533022	+	0.0923221i
$831$		0			0
$832$	2.16727	−	3.75382i	0.0751365	−	0.130140i
$833$	4.56387	−	7.90486i	0.158129	−	0.273887i
$834$		0			0
$835$	0.599329	+	1.03807i	0.0207407	+	0.0359239i
$836$	10.7316			0.371158
$837$		0			0
$838$	29.7172			1.02656
$839$	−9.25046	−	16.0223i	−0.319361	−	0.553150i	0.660994	−	0.750392i	$-0.270135\pi$
$839$	−9.25046	−	16.0223i	−0.319361	−	0.553150i	−0.980355	+	0.197241i	$0.936802\pi$
$840$		0			0
$841$	−36.7108	+	63.5850i	−1.26589	+	2.19259i
$842$	−8.73540	+	15.1302i	−0.301042	+	0.521419i
$843$		0			0
$844$	5.06905	+	8.77985i	0.174484	+	0.302215i
$845$	−2.22704			−0.0766126
$846$		0			0
$847$	−7.97620			−0.274065
$848$	1.00634	+	1.74303i	0.0345578	+	0.0598559i
$849$		0			0
$850$	3.63029	−	6.28784i	0.124518	−	0.215671i
$851$	11.1985	−	19.3964i	0.383880	−	0.664900i
$852$		0			0
$853$	5.09210	+	8.81978i	0.174350	+	0.301984i	0.939936	−	0.341350i	$-0.110884\pi$
$853$	5.09210	+	8.81978i	0.174350	+	0.301984i	−0.765586	+	0.643334i	$0.777551\pi$
$854$	8.16164			0.279286
$855$		0			0
$856$	17.4187			0.595357
$857$	−5.23626	−	9.06947i	−0.178867	−	0.309807i	0.762626	−	0.646840i	$-0.223910\pi$
$857$	−5.23626	−	9.06947i	−0.178867	−	0.309807i	−0.941493	+	0.337033i	$0.890577\pi$
$858$		0			0
$859$	0.806961	−	1.39770i	0.0275331	−	0.0476888i	−0.851931	−	0.523655i	$-0.824568\pi$
$859$	0.806961	−	1.39770i	0.0275331	−	0.0476888i	0.879464	+	0.475966i	$0.157901\pi$
$860$	0.351390	−	0.608625i	0.0119823	−	0.0207539i
$861$		0			0
$862$	2.13544	+	3.69868i	0.0727332	+	0.125978i
$863$	−3.73210			−0.127042			−0.0635211	−	0.997980i	$-0.520233\pi$
$863$	−3.73210			−0.127042			−0.0635211	+	0.997980i	$0.520233\pi$
$864$		0			0
$865$	8.84212			0.300641
$866$	7.67908	+	13.3006i	0.260946	+	0.451971i
$867$		0			0
$868$	−1.99506	+	3.45555i	−0.0677168	+	0.117289i
$869$	10.7502	−	18.6199i	0.364676	−	0.631637i
$870$		0			0
$871$	−25.3360	−	43.8832i	−0.858477	−	1.48693i
$872$	−9.94273			−0.336703
$873$		0			0
$874$	43.8840			1.48440
$875$	−1.79831	−	3.11477i	−0.0607941	−	0.105298i
$876$		0			0
$877$	−17.8061	+	30.8411i	−0.601270	+	1.04143i	0.391359	+	0.920238i	$0.372005\pi$
$877$	−17.8061	+	30.8411i	−0.601270	+	1.04143i	−0.992629	+	0.121193i	$0.961328\pi$
$878$	7.30751	−	12.6570i	0.246617	−	0.427153i
$879$		0			0
$880$	0.309820	+	0.536625i	0.0104440	+	0.0180896i
$881$	20.6136			0.694489			0.347244	−	0.937775i	$-0.387117\pi$
$881$	20.6136			0.694489			0.347244	+	0.937775i	$0.387117\pi$
$882$		0			0
$883$	20.9067			0.703568			0.351784	−	0.936081i	$-0.385575\pi$
$883$	20.9067			0.703568			0.351784	+	0.936081i	$0.385575\pi$
$884$	3.24315	+	5.61729i	0.109079	+	0.188930i
$885$		0			0
$886$	2.86520	−	4.96267i	0.0962583	−	0.166724i
$887$	−17.9082	+	31.0180i	−0.601300	+	1.04148i	0.391325	+	0.920253i	$0.372017\pi$
$887$	−17.9082	+	31.0180i	−0.601300	+	1.04148i	−0.992625	+	0.121229i	$0.961316\pi$
$888$		0			0
$889$	2.41414	+	4.18142i	0.0809677	+	0.140240i
$890$	3.97116			0.133113
$891$		0			0
$892$	−23.9585			−0.802191
$893$	−31.6006	−	54.7338i	−1.05747	−	1.83160i
$894$		0			0
$895$	−4.95680	+	8.58544i	−0.165688	+	0.286979i
$896$	−0.474416	+	0.821712i	−0.0158491	+	0.0274515i
$897$		0			0
$898$	1.19444	+	2.06883i	0.0398589	+	0.0690377i
$899$	42.5592			1.41943
$900$		0			0
$901$	−3.01181			−0.100338
$902$	3.09415	+	5.35922i	0.103024	+	0.178443i
$903$		0			0
$904$	−4.52939	+	7.84514i	−0.150645	+	0.260925i
$905$	−3.09882	+	5.36732i	−0.103008	+	0.178416i
$906$		0			0
$907$	−16.3897	−	28.3878i	−0.544210	−	0.942600i	−0.998656	−	0.0518256i	$-0.983496\pi$
$907$	−16.3897	−	28.3878i	−0.544210	−	0.942600i	0.454446	−	0.890774i	$-0.349837\pi$
$908$	7.16454			0.237764
$909$		0			0
$910$	1.58240			0.0524560
$911$	17.2837	+	29.9362i	0.572634	+	0.991831i	0.996294	+	0.0860099i	$0.0274117\pi$
$911$	17.2837	+	29.9362i	0.572634	+	0.991831i	−0.423660	+	0.905821i	$0.639255\pi$
$912$		0			0
$913$	−6.42772	+	11.1331i	−0.212726	+	0.368453i
$914$	−9.83789	+	17.0397i	−0.325408	+	0.563624i
$915$		0			0
$916$	−4.42354	−	7.66180i	−0.146158	−	0.253153i
$917$	0.752123			0.0248373
$918$		0			0
$919$	−19.9647			−0.658574			−0.329287	−	0.944230i	$-0.606808\pi$
$919$	−19.9647			−0.658574			−0.329287	+	0.944230i	$0.606808\pi$
$920$	1.26693	+	2.19439i	0.0417695	+	0.0723470i
$921$		0			0
$922$	4.01181	−	6.94866i	0.132122	−	0.228842i
$923$	0.955073	−	1.65423i	0.0314366	−	0.0544498i
$924$		0			0
$925$	−8.25046	−	14.2902i	−0.271274	−	0.469860i
$926$	23.9482			0.786987
$927$		0			0
$928$	10.1204			0.332217
$929$	16.2402	+	28.1288i	0.532823	+	0.922877i	0.999265	+	0.0383249i	$0.0122022\pi$
$929$	16.2402	+	28.1288i	0.532823	+	0.922877i	−0.466442	+	0.884552i	$0.654464\pi$
$930$		0			0
$931$	20.3229	−	35.2003i	0.666057	−	1.15364i
$932$	−11.8917	+	20.5971i	−0.389527	+	0.674680i
$933$		0			0
$934$	−5.67420	−	9.82801i	−0.185666	−	0.321582i
$935$	−0.927243			−0.0303241
$936$		0			0
$937$	27.5689			0.900637			0.450318	−	0.892868i	$-0.351310\pi$
$937$	27.5689			0.900637			0.450318	+	0.892868i	$0.351310\pi$
$938$	5.54605	+	9.60604i	0.181085	+	0.313648i
$939$		0			0
$940$	1.82462	−	3.16034i	0.0595126	−	0.103079i
$941$	−1.92868	+	3.34056i	−0.0628730	+	0.108899i	−0.895749	−	0.444561i	$-0.853360\pi$
$941$	−1.92868	+	3.34056i	−0.0628730	+	0.108899i	0.832875	+	0.553460i	$0.186693\pi$
$942$		0			0
$943$	12.6527	+	21.9152i	0.412030	+	0.713657i
$944$	−9.00869			−0.293208
$945$		0			0
$946$	2.94166			0.0956415
$947$	4.07077	+	7.05079i	0.132282	+	0.229120i	0.924556	−	0.381046i	$-0.124436\pi$
$947$	4.07077	+	7.05079i	0.132282	+	0.229120i	−0.792274	+	0.610166i	$0.791103\pi$
$948$		0			0
$949$	22.8700	−	39.6121i	0.742393	−	1.28586i
$950$	16.1657	−	27.9998i	0.524484	−	0.908432i
$951$		0			0
$952$	−0.709925	−	1.22963i	−0.0230088	−	0.0398524i
$953$	−24.1615			−0.782668			−0.391334	−	0.920249i	$-0.627986\pi$
$953$	−24.1615			−0.782668			−0.391334	+	0.920249i	$0.627986\pi$
$954$		0			0
$955$	4.47143			0.144692
$956$	−8.04881	−	13.9410i	−0.260317	−	0.450883i
$957$		0			0
$958$	17.7905	−	30.8141i	0.574785	−	0.995558i
$959$	3.21309	−	5.56523i	0.103756	−	0.179711i
$960$		0			0
$961$	6.65771	+	11.5315i	0.214765	+	0.371983i
$962$	14.7412			0.475276
$963$		0			0
$964$	23.2500			0.748832
$965$	−1.12762	−	1.95309i	−0.0362993	−	0.0628722i
$966$		0			0
$967$	−11.0094	+	19.0688i	−0.354038	+	0.613211i	−0.986953	−	0.161010i	$-0.948525\pi$
$967$	−11.0094	+	19.0688i	−0.354038	+	0.613211i	0.632915	+	0.774221i	$0.281858\pi$
$968$	4.20317	−	7.28011i	0.135095	−	0.233991i
$969$		0			0
$970$	2.52941	+	4.38106i	0.0812143	+	0.140667i
$971$	−3.05626			−0.0980800			−0.0490400	−	0.998797i	$-0.515616\pi$
$971$	−3.05626			−0.0980800			−0.0490400	+	0.998797i	$0.515616\pi$
$972$		0			0
$973$	−3.29306			−0.105571
$974$	9.51883	+	16.4871i	0.305003	+	0.528281i
$975$		0			0
$976$	−4.30089	+	7.44936i	−0.137668	+	0.238448i
$977$	−25.2672	+	43.7642i	−0.808371	+	1.40014i	0.105621	+	0.994406i	$0.466317\pi$
$977$	−25.2672	+	43.7642i	−0.808371	+	1.40014i	−0.913992	+	0.405733i	$0.867016\pi$
$978$		0			0
$979$	8.31112	+	14.3953i	0.265625	+	0.460075i
$980$	2.34689			0.0749688
$981$		0			0
$982$	−27.0014			−0.861651
$983$	−4.31652	−	7.47643i	−0.137675	−	0.238461i	0.788941	−	0.614469i	$-0.210630\pi$
$983$	−4.31652	−	7.47643i	−0.137675	−	0.238461i	−0.926616	+	0.376008i	$0.877296\pi$
$984$		0			0
$985$	−0.355805	+	0.616272i	−0.0113369	+	0.0196361i
$986$	−7.57215	+	13.1154i	−0.241147	+	0.417678i
$987$		0			0
$988$	14.4417	+	25.0138i	0.459452	+	0.795795i
$989$	12.0292			0.382505
$990$		0			0
$991$	−24.1555			−0.767325			−0.383662	−	0.923473i	$-0.625337\pi$
$991$	−24.1555			−0.767325			−0.383662	+	0.923473i	$0.625337\pi$
$992$	−2.10265	−	3.64190i	−0.0667593	−	0.115630i
$993$		0			0
$994$	−0.209066	+	0.362112i	−0.00663116	+	0.0114855i
$995$	−1.31511	+	2.27783i	−0.0416917	+	0.0722121i
$996$		0			0
$997$	−6.27186	−	10.8632i	−0.198632	−	0.344041i	0.749453	−	0.662057i	$-0.230316\pi$
$997$	−6.27186	−	10.8632i	−0.198632	−	0.344041i	−0.948085	+	0.318017i	$0.896983\pi$
$998$	−1.66290			−0.0526383
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1458.2.c.e.973.5		12
3.2	odd	2		1458.2.c.h.973.2		12
9.2	odd	6		1458.2.c.h.487.2		12
9.4	even	3		1458.2.a.h.1.2	yes	6
9.5	odd	6		1458.2.a.e.1.5	✓	6
9.7	even	3	inner	1458.2.c.e.487.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1458.2.a.e.1.5	✓	6	9.5	odd	6
1458.2.a.h.1.2	yes	6	9.4	even	3
1458.2.c.e.487.5		12	9.7	even	3	inner
1458.2.c.e.973.5		12	1.1	even	1	trivial
1458.2.c.h.487.2		12	9.2	odd	6
1458.2.c.h.973.2		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1458 = 2 \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1458.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.192377 - 0.333207i) q^{5} +(-0.474416 - 0.821712i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.192377 - 0.333207i) q^{5} +(-0.474416 - 0.821712i) q^{7} +1.00000 q^{8} -0.384754 q^{10} +(-0.805242 - 1.39472i) q^{11} +(2.16727 - 3.75382i) q^{13} +(-0.474416 + 0.821712i) q^{14} +(-0.500000 - 0.866025i) q^{16} +1.49642 q^{17} +6.66356 q^{19} +(0.192377 + 0.333207i) q^{20} +(-0.805242 + 1.39472i) q^{22} +(-3.29283 + 5.70336i) q^{23} +(2.42598 + 4.20192i) q^{25} -4.33454 q^{26} +0.948831 q^{28} +(-5.06018 - 8.76449i) q^{29} +(-2.10265 + 3.64190i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.748210 - 1.29594i) q^{34} -0.365067 q^{35} -3.40088 q^{37} +(-3.33178 - 5.77081i) q^{38} +(0.192377 - 0.333207i) q^{40} +(1.92125 - 3.32771i) q^{41} +(-0.913284 - 1.58185i) q^{43} +1.61048 q^{44} +6.58567 q^{46} +(-4.74230 - 8.21391i) q^{47} +(3.04986 - 5.28251i) q^{49} +(2.42598 - 4.20192i) q^{50} +(2.16727 + 3.75382i) q^{52} -2.01268 q^{53} -0.619641 q^{55} +(-0.474416 - 0.821712i) q^{56} +(-5.06018 + 8.76449i) q^{58} +(4.50435 - 7.80176i) q^{59} +(-4.30089 - 7.44936i) q^{61} +4.20530 q^{62} +1.00000 q^{64} +(-0.833866 - 1.44430i) q^{65} +(5.84514 - 10.1241i) q^{67} +(-0.748210 + 1.29594i) q^{68} +(0.182534 + 0.316157i) q^{70} +0.440680 q^{71} +10.5525 q^{73} +(1.70044 + 2.94525i) q^{74} +(-3.33178 + 5.77081i) q^{76} +(-0.764039 + 1.32335i) q^{77} +(6.67514 + 11.5617i) q^{79} -0.384754 q^{80} -3.84251 q^{82} +(-3.99117 - 6.91291i) q^{83} +(0.287877 - 0.498618i) q^{85} +(-0.913284 + 1.58185i) q^{86} +(-0.805242 - 1.39472i) q^{88} -10.3213 q^{89} -4.11275 q^{91} +(-3.29283 - 5.70336i) q^{92} +(-4.74230 + 8.21391i) q^{94} +(1.28192 - 2.22034i) q^{95} +(-6.57408 - 11.3866i) q^{97} -6.09972 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 - 6 * q^5 + 12 * q^8	\( 12 q - 6 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} - 6 q^{16} + 24 q^{17} + 12 q^{19} - 6 q^{20} - 6 q^{22} - 12 q^{23} - 6 q^{25} + 12 q^{26} - 6 q^{29} + 6 q^{31} - 6 q^{32} - 12 q^{34} + 24 q^{35} - 6 q^{38} - 6 q^{40} - 24 q^{41} + 6 q^{43} + 12 q^{44} + 24 q^{46} - 18 q^{47} - 6 q^{49} - 6 q^{50} - 6 q^{52} + 48 q^{53} - 36 q^{55} - 6 q^{58} - 12 q^{59} + 6 q^{61} - 12 q^{62} + 12 q^{64} - 12 q^{65} + 24 q^{67} - 12 q^{68} - 12 q^{70} - 12 q^{71} - 48 q^{73} - 6 q^{76} - 12 q^{77} + 12 q^{79} + 12 q^{80} + 48 q^{82} - 18 q^{83} + 6 q^{86} - 6 q^{88} + 24 q^{89} - 60 q^{91} - 12 q^{92} - 18 q^{94} + 6 q^{95} - 6 q^{97} + 12 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 6 * q^5 + 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 - 6 * q^16 + 24 * q^17 + 12 * q^19 - 6 * q^20 - 6 * q^22 - 12 * q^23 - 6 * q^25 + 12 * q^26 - 6 * q^29 + 6 * q^31 - 6 * q^32 - 12 * q^34 + 24 * q^35 - 6 * q^38 - 6 * q^40 - 24 * q^41 + 6 * q^43 + 12 * q^44 + 24 * q^46 - 18 * q^47 - 6 * q^49 - 6 * q^50 - 6 * q^52 + 48 * q^53 - 36 * q^55 - 6 * q^58 - 12 * q^59 + 6 * q^61 - 12 * q^62 + 12 * q^64 - 12 * q^65 + 24 * q^67 - 12 * q^68 - 12 * q^70 - 12 * q^71 - 48 * q^73 - 6 * q^76 - 12 * q^77 + 12 * q^79 + 12 * q^80 + 48 * q^82 - 18 * q^83 + 6 * q^86 - 6 * q^88 + 24 * q^89 - 60 * q^91 - 12 * q^92 - 18 * q^94 + 6 * q^95 - 6 * q^97 + 12 * q^98

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