LMFDB - Embedded newform 243.2.c.e.163.3

Error: no document with id 239787888 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(82,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,0,-3,-6,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	243.163
Dual form			243.2.c.e.82.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.439693 - 0.761570i) q^{2} +(0.613341 + 1.06234i) q^{4} +(-1.93969 - 3.35965i) q^{5} +(1.09240 - 1.89209i) q^{7} +2.83750 q^{8} -3.41147 q^{10} +(-0.0812519 + 0.140732i) q^{11} +(-1.20574 - 2.08840i) q^{13} +(-0.960637 - 1.66387i) q^{14} +(0.0209445 - 0.0362770i) q^{16} +3.00000 q^{17} +3.59627 q^{19} +(2.37939 - 4.12122i) q^{20} +(0.0714517 + 0.123758i) q^{22} +(-1.41875 - 2.45734i) q^{23} +(-5.02481 + 8.70323i) q^{25} -2.12061 q^{26} +2.68004 q^{28} +(-3.35844 + 5.81699i) q^{29} +(2.59240 + 4.49016i) q^{31} +(2.81908 + 4.88279i) q^{32} +(1.31908 - 2.28471i) q^{34} -8.47565 q^{35} -6.63816 q^{37} +(1.58125 - 2.73881i) q^{38} +(-5.50387 - 9.53298i) q^{40} +(2.90033 + 5.02352i) q^{41} +(3.11334 - 5.39246i) q^{43} -0.199340 q^{44} -2.49525 q^{46} +(-3.69846 + 6.40593i) q^{47} +(1.11334 + 1.92836i) q^{49} +(4.41875 + 7.65350i) q^{50} +(1.47906 - 2.56180i) q^{52} +1.40373 q^{53} +0.630415 q^{55} +(3.09967 - 5.36879i) q^{56} +(2.95336 + 5.11538i) q^{58} +(2.56031 + 4.43458i) q^{59} +(1.89053 - 3.27449i) q^{61} +4.55943 q^{62} +5.04189 q^{64} +(-4.67752 + 8.10170i) q^{65} +(2.93242 + 5.07910i) q^{67} +(1.84002 + 3.18701i) q^{68} +(-3.72668 + 6.45480i) q^{70} -15.3182 q^{71} +8.68004 q^{73} +(-2.91875 + 5.05542i) q^{74} +(2.20574 + 3.82045i) q^{76} +(0.177519 + 0.307471i) q^{77} +(0.634285 - 1.09861i) q^{79} -0.162504 q^{80} +5.10101 q^{82} +(4.23783 - 7.34013i) q^{83} +(-5.81908 - 10.0789i) q^{85} +(-2.73783 - 4.74205i) q^{86} +(-0.230552 + 0.399328i) q^{88} +7.72193 q^{89} -5.26857 q^{91} +(1.74035 - 3.01438i) q^{92} +(3.25237 + 5.63328i) q^{94} +(-6.97565 - 12.0822i) q^{95} +(1.95336 - 3.38332i) q^{97} +1.95811 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 3 q^{7} + 12 q^{8} - 3 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} + 18 q^{17} - 6 q^{19} + 3 q^{20} - 6 q^{23} - 3 q^{25} - 24 q^{26} - 24 q^{28} - 12 q^{29} + 12 q^{31}+ \cdots + 18 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 3 * q^7 + 12 * q^8 - 3 * q^11 + 3 * q^13 + 3 * q^14 - 3 * q^16 + 18 * q^17 - 6 * q^19 + 3 * q^20 - 6 * q^23 - 3 * q^25 - 24 * q^26 - 24 * q^28 - 12 * q^29 + 12 * q^31 - 9 * q^34 - 12 * q^35 - 6 * q^37 + 12 * q^38 - 9 * q^40 + 3 * q^41 + 12 * q^43 - 30 * q^44 + 18 * q^46 + 6 * q^47 + 24 * q^50 + 12 * q^52 + 36 * q^53 + 18 * q^55 + 33 * q^56 - 9 * q^58 + 21 * q^59 - 6 * q^61 - 24 * q^62 + 24 * q^64 - 3 * q^65 - 6 * q^67 - 9 * q^68 - 9 * q^70 - 18 * q^71 + 12 * q^73 - 15 * q^74 + 3 * q^76 - 24 * q^77 - 6 * q^79 - 6 * q^80 + 36 * q^82 + 6 * q^83 - 18 * q^85 + 3 * q^86 + 36 * q^88 - 12 * q^91 - 24 * q^92 + 36 * q^94 - 3 * q^95 - 15 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.439693	−	0.761570i	0.310910	−	0.538511i	−0.667650	−	0.744475i	$-0.732700\pi$
$2$	0.439693	−	0.761570i	0.310910	−	0.538511i	0.978560	+	0.205964i	$0.0660330\pi$
$3$		0			0
$3$		0			0
$4$	0.613341	+	1.06234i	0.306670	+	0.531169i
$5$	−1.93969	−	3.35965i	−0.867457	−	1.50248i	−0.864587	−	0.502484i	$-0.832420\pi$
$5$	−1.93969	−	3.35965i	−0.867457	−	1.50248i	−0.00287015	−	0.999996i	$-0.500914\pi$
$6$		0			0
$7$	1.09240	−	1.89209i	0.412887	−	0.715141i	−0.582317	−	0.812962i	$-0.697854\pi$
$7$	1.09240	−	1.89209i	0.412887	−	0.715141i	0.995204	+	0.0978205i	$0.0311871\pi$
$8$	2.83750			1.00321
$9$		0			0
$10$	−3.41147			−1.07880
$11$	−0.0812519	+	0.140732i	−0.0244984	+	0.0424324i	−0.878015	−	0.478634i	$-0.841132\pi$
$11$	−0.0812519	+	0.140732i	−0.0244984	+	0.0424324i	0.853516	+	0.521066i	$0.174466\pi$
$12$		0			0
$13$	−1.20574	−	2.08840i	−0.334411	−	0.579217i	0.648960	−	0.760822i	$-0.275204\pi$
$13$	−1.20574	−	2.08840i	−0.334411	−	0.579217i	−0.983372	+	0.181605i	$0.941871\pi$
$14$	−0.960637	−	1.66387i	−0.256741	−	0.444689i
$15$		0			0
$16$	0.0209445	−	0.0362770i	0.00523613	−	0.00906925i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$	3.59627			0.825040			0.412520	−	0.910949i	$-0.364649\pi$
$19$	3.59627			0.825040			0.412520	+	0.910949i	$0.364649\pi$
$20$	2.37939	−	4.12122i	0.532047	−	0.921532i
$21$		0			0
$22$	0.0714517	+	0.123758i	0.0152336	+	0.0263853i
$23$	−1.41875	−	2.45734i	−0.295829	−	0.512392i	0.679348	−	0.733816i	$-0.262263\pi$
$23$	−1.41875	−	2.45734i	−0.295829	−	0.512392i	−0.975177	+	0.221425i	$0.928929\pi$
$24$		0			0
$25$	−5.02481	+	8.70323i	−1.00496	+	1.74065i
$26$	−2.12061			−0.415887
$27$		0			0
$28$	2.68004			0.506481
$29$	−3.35844	+	5.81699i	−0.623647	+	1.08019i	0.365154	+	0.930947i	$0.381016\pi$
$29$	−3.35844	+	5.81699i	−0.623647	+	1.08019i	−0.988801	+	0.149241i	$0.952317\pi$
$30$		0			0
$31$	2.59240	+	4.49016i	0.465608	+	0.806457i	0.999229	−	0.0392670i	$-0.0125023\pi$
$31$	2.59240	+	4.49016i	0.465608	+	0.806457i	−0.533621	+	0.845724i	$0.679169\pi$
$32$	2.81908	+	4.88279i	0.498347	+	0.863163i
$33$		0			0
$34$	1.31908	−	2.28471i	0.226220	−	0.391825i
$35$	−8.47565			−1.43265
$36$		0			0
$37$	−6.63816			−1.09131			−0.545653	−	0.838011i	$-0.683718\pi$
$37$	−6.63816			−1.09131			−0.545653	+	0.838011i	$0.683718\pi$
$38$	1.58125	−	2.73881i	0.256513	−	0.444293i
$39$		0			0
$40$	−5.50387	−	9.53298i	−0.870238	−	1.50730i
$41$	2.90033	+	5.02352i	0.452955	+	0.784542i	0.998568	−	0.0534957i	$-0.0170363\pi$
$41$	2.90033	+	5.02352i	0.452955	+	0.784542i	−0.545613	+	0.838037i	$0.683703\pi$
$42$		0			0
$43$	3.11334	−	5.39246i	0.474780	−	0.822343i	−0.524803	−	0.851224i	$-0.675861\pi$
$43$	3.11334	−	5.39246i	0.474780	−	0.822343i	0.999583	+	0.0288807i	$0.00919429\pi$
$44$	−0.199340			−0.0300517
$45$		0			0
$46$	−2.49525			−0.367905
$47$	−3.69846	+	6.40593i	−0.539476	+	0.934400i	0.459456	+	0.888201i	$0.348044\pi$
$47$	−3.69846	+	6.40593i	−0.539476	+	0.934400i	−0.998932	+	0.0461998i	$0.985289\pi$
$48$		0			0
$49$	1.11334	+	1.92836i	0.159049	+	0.275480i
$50$	4.41875	+	7.65350i	0.624905	+	1.08237i
$51$		0			0
$52$	1.47906	−	2.56180i	0.205108	−	0.355258i
$53$	1.40373			0.192818			0.0964088	−	0.995342i	$-0.469264\pi$
$53$	1.40373			0.192818			0.0964088	+	0.995342i	$0.469264\pi$
$54$		0			0
$55$	0.630415			0.0850051
$56$	3.09967	−	5.36879i	0.414211	−	0.717434i
$57$		0			0
$58$	2.95336	+	5.11538i	0.387796	+	0.671682i
$59$	2.56031	+	4.43458i	0.333324	+	0.577333i	0.983161	−	0.182740i	$-0.0584965\pi$
$59$	2.56031	+	4.43458i	0.333324	+	0.577333i	−0.649838	+	0.760073i	$0.725163\pi$
$60$		0			0
$61$	1.89053	−	3.27449i	0.242058	−	0.419256i	−0.719243	−	0.694759i	$-0.755511\pi$
$61$	1.89053	−	3.27449i	0.242058	−	0.419256i	0.961300	+	0.275503i	$0.0888444\pi$
$62$	4.55943			0.579048
$63$		0			0
$64$	5.04189			0.630236
$65$	−4.67752	+	8.10170i	−0.580175	+	1.00489i
$66$		0			0
$67$	2.93242	+	5.07910i	0.358252	+	0.620511i	0.987669	−	0.156557i	$-0.0500395\pi$
$67$	2.93242	+	5.07910i	0.358252	+	0.620511i	−0.629417	+	0.777068i	$0.716706\pi$
$68$	1.84002	+	3.18701i	0.223135	+	0.386482i
$69$		0			0
$70$	−3.72668	+	6.45480i	−0.445424	+	0.771496i
$71$	−15.3182			−1.81794			−0.908968	−	0.416866i	$-0.863128\pi$
$71$	−15.3182			−1.81794			−0.908968	+	0.416866i	$0.863128\pi$
$72$		0			0
$73$	8.68004			1.01592			0.507961	−	0.861380i	$-0.330399\pi$
$73$	8.68004			1.01592			0.507961	+	0.861380i	$0.330399\pi$
$74$	−2.91875	+	5.05542i	−0.339298	+	0.587681i
$75$		0			0
$76$	2.20574	+	3.82045i	0.253015	+	0.438236i
$77$	0.177519	+	0.307471i	0.0202301	+	0.0350396i
$78$		0			0
$79$	0.634285	−	1.09861i	0.0713627	−	0.123604i	−0.828136	−	0.560527i	$-0.810599\pi$
$79$	0.634285	−	1.09861i	0.0713627	−	0.123604i	0.899499	+	0.436923i	$0.143932\pi$
$80$	−0.162504			−0.0181685
$81$		0			0
$82$	5.10101			0.563313
$83$	4.23783	−	7.34013i	0.465162	−	0.805684i	−0.534047	−	0.845455i	$-0.679329\pi$
$83$	4.23783	−	7.34013i	0.465162	−	0.805684i	0.999209	+	0.0397709i	$0.0126628\pi$
$84$		0			0
$85$	−5.81908	−	10.0789i	−0.631168	−	1.09321i
$86$	−2.73783	−	4.74205i	−0.295227	−	0.511349i
$87$		0			0
$88$	−0.230552	+	0.399328i	−0.0245769	+	0.0425685i
$89$	7.72193			0.818523			0.409262	−	0.912417i	$-0.365786\pi$
$89$	7.72193			0.818523			0.409262	+	0.912417i	$0.365786\pi$
$90$		0			0
$91$	−5.26857			−0.552296
$92$	1.74035	−	3.01438i	0.181444	−	0.314271i
$93$		0			0
$94$	3.25237	+	5.63328i	0.335457	+	0.581028i
$95$	−6.97565	−	12.0822i	−0.715687	−	1.23961i
$96$		0			0
$97$	1.95336	−	3.38332i	0.198334	−	0.343525i	−0.749654	−	0.661830i	$-0.769780\pi$
$97$	1.95336	−	3.38332i	0.198334	−	0.343525i	0.947988	+	0.318305i	$0.103114\pi$
$98$	1.95811			0.197799
$99$		0			0
$100$	−12.3277			−1.23277
$101$	4.05690	−	7.02676i	0.403677	−	0.699189i	−0.590489	−	0.807045i	$-0.701065\pi$
$101$	4.05690	−	7.02676i	0.403677	−	0.699189i	0.994167	+	0.107856i	$0.0343986\pi$
$102$		0			0
$103$	−9.32295	−	16.1478i	−0.918617	−	1.59109i	−0.801517	−	0.597972i	$-0.795973\pi$
$103$	−9.32295	−	16.1478i	−0.918617	−	1.59109i	−0.117100	−	0.993120i	$-0.537360\pi$
$104$	−3.42127	−	5.92582i	−0.335484	−	0.581075i
$105$		0			0
$106$	0.617211	−	1.06904i	0.0599489	−	0.103834i
$107$	7.59627			0.734359			0.367179	−	0.930150i	$-0.380324\pi$
$107$	7.59627			0.734359			0.367179	+	0.930150i	$0.380324\pi$
$108$		0			0
$109$	−15.6382			−1.49786			−0.748932	−	0.662647i	$-0.769433\pi$
$109$	−15.6382			−1.49786			−0.748932	+	0.662647i	$0.769433\pi$
$110$	0.277189	−	0.480105i	0.0264289	−	0.0457762i
$111$		0			0
$112$	−0.0457595	−	0.0792577i	−0.00432386	−	0.00748915i
$113$	1.15657	+	2.00324i	0.108801	+	0.188449i	0.915285	−	0.402807i	$-0.131965\pi$
$113$	1.15657	+	2.00324i	0.108801	+	0.188449i	−0.806484	+	0.591256i	$0.798632\pi$
$114$		0			0
$115$	−5.50387	+	9.53298i	−0.513239	+	0.888955i
$116$	−8.23947			−0.765016
$117$		0			0
$118$	4.50299			0.414534
$119$	3.27719	−	5.67626i	0.300419	−	0.520342i
$120$		0			0
$121$	5.48680	+	9.50341i	0.498800	+	0.863946i
$122$	−1.66250	−	2.87954i	−0.150516	−	0.260701i
$123$		0			0
$124$	−3.18004	+	5.50800i	−0.285576	+	0.494633i
$125$	19.5895			1.75213
$126$		0			0
$127$	0.0418891			0.00371705			0.00185853	−	0.999998i	$-0.499408\pi$
$127$	0.0418891			0.00371705			0.00185853	+	0.999998i	$0.499408\pi$
$128$	−3.42127	+	5.92582i	−0.302401	+	0.523774i
$129$		0			0
$130$	4.11334	+	7.12452i	0.360764	+	0.624861i
$131$	−9.17412	−	15.8900i	−0.801546	−	1.38832i	−0.918598	−	0.395193i	$-0.870678\pi$
$131$	−9.17412	−	15.8900i	−0.801546	−	1.38832i	0.117052	−	0.993126i	$-0.462656\pi$
$132$		0			0
$133$	3.92855	−	6.80445i	0.340648	−	0.590020i
$134$	5.15745			0.445536
$135$		0			0
$136$	8.51249			0.729940
$137$	−7.15657	+	12.3955i	−0.611427	+	1.05902i	0.379573	+	0.925162i	$0.376071\pi$
$137$	−7.15657	+	12.3955i	−0.611427	+	1.05902i	−0.991000	+	0.133861i	$0.957262\pi$
$138$		0			0
$139$	−5.24763	−	9.08916i	−0.445098	−	0.770932i	0.552961	−	0.833207i	$-0.313498\pi$
$139$	−5.24763	−	9.08916i	−0.445098	−	0.770932i	−0.998059	+	0.0622749i	$0.980164\pi$
$140$	−5.19846	−	9.00400i	−0.439350	−	0.760977i
$141$		0			0
$142$	−6.73530	+	11.6659i	−0.565214	+	0.978979i
$143$	0.391874			0.0327701
$144$		0			0
$145$	26.0574			2.16395
$146$	3.81655	−	6.61046i	0.315860	−	0.547086i
$147$		0			0
$148$	−4.07145	−	7.05196i	−0.334671	−	0.579668i
$149$	0.635630	+	1.10094i	0.0520728	+	0.0901927i	0.890887	−	0.454225i	$-0.150084\pi$
$149$	0.635630	+	1.10094i	0.0520728	+	0.0901927i	−0.838814	+	0.544418i	$0.816751\pi$
$150$		0			0
$151$	−3.92855	+	6.80445i	−0.319701	+	0.553738i	−0.980426	−	0.196890i	$-0.936916\pi$
$151$	−3.92855	+	6.80445i	−0.319701	+	0.553738i	0.660725	+	0.750628i	$0.270249\pi$
$152$	10.2044			0.827686
$153$		0			0
$154$	0.312214			0.0251590
$155$	10.0569	−	17.4191i	0.807790	−	1.39913i
$156$		0			0
$157$	6.17617	+	10.6974i	0.492912	+	0.853749i	0.999967	−	0.00816484i	$-0.00259898\pi$
$157$	6.17617	+	10.6974i	0.492912	+	0.853749i	−0.507054	+	0.861914i	$0.669266\pi$
$158$	−0.557781	−	0.966105i	−0.0443747	−	0.0768592i
$159$		0			0
$160$	10.9363	−	18.9422i	0.864590	−	1.49751i
$161$	−6.19934			−0.488576
$162$		0			0
$163$	−13.7469			−1.07674			−0.538371	−	0.842708i	$-0.680960\pi$
$163$	−13.7469			−1.07674			−0.538371	+	0.842708i	$0.680960\pi$
$164$	−3.55778	+	6.16226i	−0.277816	+	0.481191i
$165$		0			0
$166$	−3.72668	−	6.45480i	−0.289247	−	0.500990i
$167$	1.85844	+	3.21891i	0.143810	+	0.249087i	0.928929	−	0.370259i	$-0.120731\pi$
$167$	1.85844	+	3.21891i	0.143810	+	0.249087i	−0.785118	+	0.619346i	$0.787398\pi$
$168$		0			0
$169$	3.59240	−	6.22221i	0.276338	−	0.478632i
$170$	−10.2344			−0.784944
$171$		0			0
$172$	7.63816			0.582404
$173$	0.779715	−	1.35051i	0.0592806	−	0.102677i	−0.834862	−	0.550459i	$-0.814453\pi$
$173$	0.779715	−	1.35051i	0.0592806	−	0.102677i	0.894143	+	0.447782i	$0.147786\pi$
$174$		0			0
$175$	10.9782	+	19.0148i	0.829872	+	1.43738i
$176$	0.00340357	+	0.00589515i	0.000256553	+	0.000444364i
$177$		0			0
$178$	3.39528	−	5.88079i	0.254487	−	0.440784i
$179$	−12.1925			−0.911313			−0.455656	−	0.890156i	$-0.650595\pi$
$179$	−12.1925			−0.911313			−0.455656	+	0.890156i	$0.650595\pi$
$180$		0			0
$181$	−16.8726			−1.25413			−0.627064	−	0.778967i	$-0.715744\pi$
$181$	−16.8726			−1.25413			−0.627064	+	0.778967i	$0.715744\pi$
$182$	−2.31655	+	4.01239i	−0.171714	+	0.297418i
$183$		0			0
$184$	−4.02569	−	6.97270i	−0.296778	−	0.514035i
$185$	12.8760	+	22.3019i	0.946661	+	1.63966i
$186$		0			0
$187$	−0.243756	+	0.422197i	−0.0178252	+	0.0308741i
$188$	−9.07367			−0.661766
$189$		0			0
$190$	−12.2686			−0.890056
$191$	8.73783	−	15.1344i	0.632247	−	1.09508i	−0.354844	−	0.934925i	$-0.615466\pi$
$191$	8.73783	−	15.1344i	0.632247	−	1.09508i	0.987091	−	0.160158i	$-0.0512005\pi$
$192$		0			0
$193$	0.996130	+	1.72535i	0.0717030	+	0.124193i	0.899648	−	0.436616i	$-0.143823\pi$
$193$	0.996130	+	1.72535i	0.0717030	+	0.124193i	−0.827945	+	0.560810i	$0.810490\pi$
$194$	−1.71776	−	2.97525i	−0.123328	−	0.213610i
$195$		0			0
$196$	−1.36571	+	2.36549i	−0.0975510	+	0.168963i
$197$	21.1925			1.50991			0.754953	−	0.655779i	$-0.227660\pi$
$197$	21.1925			1.50991			0.754953	+	0.655779i	$0.227660\pi$
$198$		0			0
$199$	−3.08378			−0.218603			−0.109302	−	0.994009i	$-0.534861\pi$
$199$	−3.08378			−0.218603			−0.109302	+	0.994009i	$0.534861\pi$
$200$	−14.2579	+	24.6954i	−1.00819	+	1.74623i
$201$		0			0
$202$	−3.56758	−	6.17923i	−0.251014	−	0.434769i
$203$	7.33750	+	12.7089i	0.514991	+	0.891991i
$204$		0			0
$205$	11.2515	−	19.4882i	0.785839	−	1.36111i
$206$	−16.3969			−1.14243
$207$		0			0
$208$	−0.101014			−0.00700409
$209$	−0.292204	+	0.506111i	−0.0202121	+	0.0350085i
$210$		0			0
$211$	−0.503870	−	0.872729i	−0.0346879	−	0.0600812i	0.848160	−	0.529740i	$-0.177710\pi$
$211$	−0.503870	−	0.872729i	−0.0346879	−	0.0600812i	−0.882848	+	0.469659i	$0.844377\pi$
$212$	0.860967	+	1.49124i	0.0591315	+	0.102419i
$213$		0			0
$214$	3.34002	−	5.78509i	0.228319	−	0.395461i
$215$	−24.1557			−1.64740
$216$		0			0
$217$	11.3277			0.768974
$218$	−6.87598	+	11.9095i	−0.465700	+	0.806616i
$219$		0			0
$220$	0.386659	+	0.669713i	0.0260686	+	0.0451521i
$221$	−3.61721	−	6.26519i	−0.243320	−	0.421443i
$222$		0			0
$223$	−9.14203	+	15.8345i	−0.612195	+	1.06035i	0.378674	+	0.925530i	$0.376380\pi$
$223$	−9.14203	+	15.8345i	−0.612195	+	1.06035i	−0.990870	+	0.134823i	$0.956953\pi$
$224$	12.3182			0.823044
$225$		0			0
$226$	2.03415			0.135310
$227$	1.32248	−	2.29061i	0.0877762	−	0.152033i	−0.818795	−	0.574087i	$-0.805357\pi$
$227$	1.32248	−	2.29061i	0.0877762	−	0.152033i	0.906571	+	0.422054i	$0.138691\pi$
$228$		0			0
$229$	1.73143	+	2.99892i	0.114416	+	0.198174i	0.917546	−	0.397629i	$-0.130167\pi$
$229$	1.73143	+	2.99892i	0.114416	+	0.198174i	−0.803130	+	0.595804i	$0.796834\pi$
$230$	4.84002	+	8.38316i	0.319142	+	0.552770i
$231$		0			0
$232$	−9.52956	+	16.5057i	−0.625646	+	1.08365i
$233$	6.12567			0.401306			0.200653	−	0.979662i	$-0.435694\pi$
$233$	6.12567			0.401306			0.200653	+	0.979662i	$0.435694\pi$
$234$		0			0
$235$	28.6955			1.87189
$236$	−3.14068	+	5.43982i	−0.204441	+	0.354102i
$237$		0			0
$238$	−2.88191	−	4.99162i	−0.186807	−	0.323558i
$239$	14.4757	+	25.0726i	0.936352	+	1.62181i	0.772205	+	0.635374i	$0.219154\pi$
$239$	14.4757	+	25.0726i	0.936352	+	1.62181i	0.164147	+	0.986436i	$0.447513\pi$
$240$		0			0
$241$	−11.1630	+	19.3348i	−0.719070	+	1.24547i	0.242298	+	0.970202i	$0.422099\pi$
$241$	−11.1630	+	19.3348i	−0.719070	+	1.24547i	−0.961369	+	0.275264i	$0.911235\pi$
$242$	9.65002			0.620326
$243$		0			0
$244$	4.63816			0.296927
$245$	4.31908	−	7.48086i	0.275936	−	0.477935i
$246$		0			0
$247$	−4.33615	−	7.51044i	−0.275903	−	0.477878i
$248$	7.35591	+	12.7408i	0.467101	+	0.809043i
$249$		0			0
$250$	8.61334	−	14.9187i	0.544756	−	0.943544i
$251$	−22.7219			−1.43420			−0.717098	−	0.696972i	$-0.754530\pi$
$251$	−22.7219			−1.43420			−0.717098	+	0.696972i	$0.754530\pi$
$252$		0			0
$253$	0.461104			0.0289894
$254$	0.0184183	−	0.0319015i	0.00115567	−	0.00200168i
$255$		0			0
$256$	8.05051	+	13.9439i	0.503157	+	0.871493i
$257$	9.79473	+	16.9650i	0.610978	+	1.05825i	0.991076	+	0.133299i	$0.0425571\pi$
$257$	9.79473	+	16.9650i	0.610978	+	1.05825i	−0.380097	+	0.924946i	$0.624110\pi$
$258$		0			0
$259$	−7.25150	+	12.5600i	−0.450586	+	0.780438i
$260$	−11.4757			−0.711690
$261$		0			0
$262$	−16.1352			−0.996834
$263$	−8.90033	+	15.4158i	−0.548818	+	0.950580i	0.449538	+	0.893261i	$0.351589\pi$
$263$	−8.90033	+	15.4158i	−0.548818	+	0.950580i	−0.998356	+	0.0573192i	$0.981745\pi$
$264$		0			0
$265$	−2.72281	−	4.71605i	−0.167261	−	0.289704i
$266$	−3.45471	−	5.98373i	−0.211822	−	0.366886i
$267$		0			0
$268$	−3.59714	+	6.23044i	−0.219731	+	0.380584i
$269$	22.7888			1.38946			0.694729	−	0.719272i	$-0.255524\pi$
$269$	22.7888			1.38946			0.694729	+	0.719272i	$0.255524\pi$
$270$		0			0
$271$	−3.44562			−0.209307			−0.104653	−	0.994509i	$-0.533373\pi$
$271$	−3.44562			−0.209307			−0.104653	+	0.994509i	$0.533373\pi$
$272$	0.0628336	−	0.108831i	0.00380985	−	0.00659885i
$273$		0			0
$274$	6.29339	+	10.9005i	0.380197	+	0.658521i
$275$	−0.816552	−	1.41431i	−0.0492399	−	0.0852860i
$276$		0			0
$277$	1.30675	−	2.26336i	0.0785151	−	0.135992i	−0.824094	−	0.566453i	$-0.808315\pi$
$277$	1.30675	−	2.26336i	0.0785151	−	0.135992i	0.902609	+	0.430460i	$0.141649\pi$
$278$	−9.22937			−0.553541
$279$		0			0
$280$	−24.0496			−1.43724
$281$	6.84255	−	11.8516i	0.408192	−	0.707010i	−0.586495	−	0.809953i	$-0.699493\pi$
$281$	6.84255	−	11.8516i	0.408192	−	0.707010i	0.994687	+	0.102943i	$0.0328260\pi$
$282$		0			0
$283$	−11.4402	−	19.8149i	−0.680047	−	1.17788i	−0.974966	−	0.222354i	$-0.928626\pi$
$283$	−11.4402	−	19.8149i	−0.680047	−	1.17788i	0.294919	−	0.955522i	$-0.404707\pi$
$284$	−9.39528	−	16.2731i	−0.557507	−	0.965631i
$285$		0			0
$286$	0.172304	−	0.298439i	0.0101885	−	0.0176471i
$287$	12.6732			0.748078
$288$		0			0
$289$	−8.00000			−0.470588
$290$	11.4572	−	19.8445i	0.672792	−	1.16531i
$291$		0			0
$292$	5.32383	+	9.22114i	0.311553	+	0.539626i
$293$	−12.1407	−	21.0283i	−0.709266	−	1.22849i	−0.965130	−	0.261772i	$-0.915693\pi$
$293$	−12.1407	−	21.0283i	−0.709266	−	1.22849i	0.255863	−	0.966713i	$-0.417640\pi$
$294$		0			0
$295$	9.93242	−	17.2035i	0.578288	−	1.00162i
$296$	−18.8357			−1.09481
$297$		0			0
$298$	1.11793			0.0647597
$299$	−3.42127	+	5.92582i	−0.197857	+	0.342699i
$300$		0			0
$301$	−6.80200	−	11.7814i	−0.392061	−	0.679070i
$302$	3.45471	+	5.98373i	0.198796	+	0.344325i
$303$		0			0
$304$	0.0753221	−	0.130462i	0.00432002	−	0.00748249i
$305$	−14.6682			−0.839898
$306$		0			0
$307$	−16.1489			−0.921666			−0.460833	−	0.887487i	$-0.652449\pi$
$307$	−16.1489			−0.921666			−0.460833	+	0.887487i	$0.652449\pi$
$308$	−0.217759	+	0.377169i	−0.0124080	+	0.0214912i
$309$		0			0
$310$	−8.84389	−	15.3181i	−0.502299	−	0.870008i
$311$	−9.35504	−	16.2034i	−0.530475	−	0.918810i	−0.999368	−	0.0355551i	$-0.988680\pi$
$311$	−9.35504	−	16.2034i	−0.530475	−	0.918810i	0.468892	−	0.883255i	$-0.344653\pi$
$312$		0			0
$313$	−1.38666	+	2.40176i	−0.0783786	+	0.135756i	−0.902551	−	0.430584i	$-0.858308\pi$
$313$	−1.38666	+	2.40176i	−0.0783786	+	0.135756i	0.824172	+	0.566340i	$0.191641\pi$
$314$	10.8625			0.613005
$315$		0			0
$316$	1.55613			0.0875393
$317$	−8.74123	+	15.1403i	−0.490956	+	0.850361i	−0.999946	−	0.0104114i	$-0.996686\pi$
$317$	−8.74123	+	15.1403i	−0.490956	+	0.850361i	0.508989	+	0.860773i	$0.330019\pi$
$318$		0			0
$319$	−0.545759	−	0.945283i	−0.0305567	−	0.0529257i
$320$	−9.77972	−	16.9390i	−0.546703	−	0.946917i
$321$		0			0
$322$	−2.72580	+	4.72123i	−0.151903	+	0.263104i
$323$	10.7888			0.600305
$324$		0			0
$325$	24.2344			1.34428
$326$	−6.04442	+	10.4692i	−0.334769	+	0.579837i
$327$		0			0
$328$	8.22967	+	14.2542i	0.454408	+	0.787057i
$329$	8.08037	+	13.9956i	0.445485	+	0.771603i
$330$		0			0
$331$	16.2297	−	28.1106i	0.892064	−	1.54510i	0.0546664	−	0.998505i	$-0.482590\pi$
$331$	16.2297	−	28.1106i	0.892064	−	1.54510i	0.837397	−	0.546595i	$-0.184076\pi$
$332$	10.3969			0.570605
$333$		0			0
$334$	3.26857			0.178848
$335$	11.3760	−	19.7038i	0.621536	−	1.07653i
$336$		0			0
$337$	−4.14290	−	7.17572i	−0.225678	−	0.390886i	0.730844	−	0.682544i	$-0.239126\pi$
$337$	−4.14290	−	7.17572i	−0.225678	−	0.390886i	−0.956523	+	0.291658i	$0.905793\pi$
$338$	−3.15910	−	5.47172i	−0.171832	−	0.297622i
$339$		0			0
$340$	7.13816	−	12.3636i	0.387121	−	0.670513i
$341$	−0.842549			−0.0456266
$342$		0			0
$343$	20.1584			1.08845
$344$	8.83409	−	15.3011i	0.476302	−	0.824980i
$345$		0			0
$346$	−0.685670	−	1.18762i	−0.0368618	−	0.0638466i
$347$	−7.48158	−	12.9585i	−0.401632	−	0.695648i	0.592291	−	0.805724i	$-0.298224\pi$
$347$	−7.48158	−	12.9585i	−0.401632	−	0.695648i	−0.993923	+	0.110077i	$0.964890\pi$
$348$		0			0
$349$	−16.8229	+	29.1382i	−0.900512	+	1.55973i	−0.0736807	+	0.997282i	$0.523475\pi$
$349$	−16.8229	+	29.1382i	−0.900512	+	1.55973i	−0.826831	+	0.562450i	$0.809859\pi$
$350$	19.3081			1.03206
$351$		0			0
$352$	−0.916222			−0.0488348
$353$	7.87686	−	13.6431i	0.419243	−	0.726150i	−0.576621	−	0.817012i	$-0.695629\pi$
$353$	7.87686	−	13.6431i	0.419243	−	0.726150i	0.995863	+	0.0908620i	$0.0289622\pi$
$354$		0			0
$355$	29.7126	+	51.4637i	1.57698	+	2.73141i
$356$	4.73618	+	8.20330i	0.251017	+	0.434774i
$357$		0			0
$358$	−5.36097	+	9.28547i	−0.283336	+	0.490752i
$359$	18.1257			0.956636			0.478318	−	0.878187i	$-0.341247\pi$
$359$	18.1257			0.956636			0.478318	+	0.878187i	$0.341247\pi$
$360$		0			0
$361$	−6.06687			−0.319309
$362$	−7.41875	+	12.8496i	−0.389921	+	0.675363i
$363$		0			0
$364$	−3.23143	−	5.59700i	−0.169373	−	0.293363i
$365$	−16.8366	−	29.1619i	−0.881269	−	1.52640i
$366$		0			0
$367$	9.57145	−	16.5782i	0.499626	−	0.865377i	−0.500374	−	0.865809i	$-0.666804\pi$
$367$	9.57145	−	16.5782i	0.499626	−	0.865377i	1.00000		0.000432135i	$0.000137553\pi$
$368$	−0.118860			−0.00619601
$369$		0			0
$370$	22.6459			1.17730
$371$	1.53343	−	2.65598i	0.0796119	−	0.137892i
$372$		0			0
$373$	7.62495	+	13.2068i	0.394805	+	0.683822i	0.993076	−	0.117471i	$-0.0374788\pi$
$373$	7.62495	+	13.2068i	0.394805	+	0.683822i	−0.598271	+	0.801294i	$0.704145\pi$
$374$	0.214355	+	0.371274i	0.0110840	+	0.0191981i
$375$		0			0
$376$	−10.4944	+	18.1768i	−0.541206	+	0.937396i
$377$	16.1976			0.834218
$378$		0			0
$379$	9.84760			0.505837			0.252919	−	0.967488i	$-0.418610\pi$
$379$	9.84760			0.505837			0.252919	+	0.967488i	$0.418610\pi$
$380$	8.55690	−	14.8210i	0.438960	−	0.760301i
$381$		0			0
$382$	−7.68392	−	13.3089i	−0.393143	−	0.680944i
$383$	−14.1951	−	24.5866i	−0.725334	−	1.25631i	−0.958837	−	0.283959i	$-0.908352\pi$
$383$	−14.1951	−	24.5866i	−0.725334	−	1.25631i	0.233503	−	0.972356i	$-0.424981\pi$
$384$		0			0
$385$	0.688663	−	1.19280i	0.0350975	−	0.0607907i
$386$	1.75196			0.0891726
$387$		0			0
$388$	4.79231			0.243293
$389$	−5.44222	+	9.42620i	−0.275931	+	0.477927i	−0.970370	−	0.241625i	$-0.922320\pi$
$389$	−5.44222	+	9.42620i	−0.275931	+	0.477927i	0.694438	+	0.719552i	$0.255653\pi$
$390$		0			0
$391$	−4.25624	−	7.37203i	−0.215248	−	0.372820i
$392$	3.15910	+	5.47172i	0.159559	+	0.276364i
$393$		0			0
$394$	9.31820	−	16.1396i	0.469444	−	0.813101i
$395$	−4.92127			−0.247616
$396$		0			0
$397$	−18.1070			−0.908764			−0.454382	−	0.890807i	$-0.650140\pi$
$397$	−18.1070			−0.908764			−0.454382	+	0.890807i	$0.650140\pi$
$398$	−1.35591	+	2.34851i	−0.0679659	+	0.117720i
$399$		0			0
$400$	0.210485	+	0.364570i	0.0105242	+	0.0182285i
$401$	−0.716881	−	1.24168i	−0.0357993	−	0.0620063i	0.847571	−	0.530683i	$-0.178064\pi$
$401$	−0.716881	−	1.24168i	−0.0357993	−	0.0620063i	−0.883370	+	0.468676i	$0.844731\pi$
$402$		0			0
$403$	6.25150	−	10.8279i	0.311409	−	0.539377i
$404$	9.95306			0.495183
$405$		0			0
$406$	12.9050			0.640463
$407$	0.539363	−	0.934204i	0.0267352	−	0.0463068i
$408$		0			0
$409$	−4.30200	−	7.45129i	−0.212720	−	0.368443i	0.739845	−	0.672778i	$-0.234899\pi$
$409$	−4.30200	−	7.45129i	−0.212720	−	0.368443i	−0.952565	+	0.304335i	$0.901566\pi$
$410$	−9.89440	−	17.1376i	−0.488650	−	0.846366i
$411$		0			0
$412$	11.4363	−	19.8082i	0.563426	−	0.975882i
$413$	11.1875			0.550500
$414$		0			0
$415$	−32.8803			−1.61403
$416$	6.79813	−	11.7747i	0.333306	−	0.577303i
$417$		0			0
$418$	0.256959	+	0.445067i	0.0125683	+	0.0217689i
$419$	6.15570	+	10.6620i	0.300725	+	0.520872i	0.976300	−	0.216419i	$-0.0694379\pi$
$419$	6.15570	+	10.6620i	0.300725	+	0.520872i	−0.675575	+	0.737291i	$0.736105\pi$
$420$		0			0
$421$	−5.55825	+	9.62717i	−0.270892	+	0.469199i	−0.969091	−	0.246705i	$-0.920652\pi$
$421$	−5.55825	+	9.62717i	−0.270892	+	0.469199i	0.698198	+	0.715905i	$0.253985\pi$
$422$	−0.886192			−0.0431392
$423$		0			0
$424$	3.98309			0.193436
$425$	−15.0744	+	26.1097i	−0.731218	+	1.26651i
$426$		0			0
$427$	−4.13041	−	7.15409i	−0.199885	−	0.346211i
$428$	4.65910	+	8.06980i	0.225206	+	0.390068i
$429$		0			0
$430$	−10.6211	+	18.3963i	−0.512194	+	0.887146i
$431$	−36.8958			−1.77721			−0.888604	−	0.458675i	$-0.848324\pi$
$431$	−36.8958			−1.77721			−0.888604	+	0.458675i	$0.848324\pi$
$432$		0			0
$433$	−37.9982			−1.82608			−0.913040	−	0.407871i	$-0.866271\pi$
$433$	−37.9982			−1.82608			−0.913040	+	0.407871i	$0.866271\pi$
$434$	4.98070	−	8.62683i	0.239081	−	0.414101i
$435$		0			0
$436$	−9.59152	−	16.6130i	−0.459350	−	0.795618i
$437$	−5.10220	−	8.83726i	−0.244071	−	0.422744i
$438$		0			0
$439$	−0.101014	+	0.174962i	−0.00482115	+	0.00835048i	−0.868426	−	0.495819i	$-0.834868\pi$
$439$	−0.101014	+	0.174962i	−0.00482115	+	0.00835048i	0.863605	+	0.504169i	$0.168201\pi$
$440$	1.78880			0.0852777
$441$		0			0
$442$	−6.36184			−0.302602
$443$	−10.6147	+	18.3852i	−0.504319	+	0.873506i	0.495669	+	0.868512i	$0.334923\pi$
$443$	−10.6147	+	18.3852i	−0.504319	+	0.873506i	−0.999988	+	0.00499424i	$0.998410\pi$
$444$		0			0
$445$	−14.9782	−	25.9430i	−0.710034	−	1.22981i
$446$	8.03936	+	13.9246i	0.380675	+	0.659348i
$447$		0			0
$448$	5.50774	−	9.53969i	0.260216	−	0.450708i
$449$	−33.2594			−1.56961			−0.784804	−	0.619744i	$-0.787236\pi$
$449$	−33.2594			−1.56961			−0.784804	+	0.619744i	$0.787236\pi$
$450$		0			0
$451$	−0.942629			−0.0443867
$452$	−1.41875	+	2.45734i	−0.0667323	+	0.115584i
$453$		0			0
$454$	−1.16297	−	2.01432i	−0.0545809	−	0.0945369i
$455$	10.2194	+	17.7005i	0.479093	+	0.829814i
$456$		0			0
$457$	0.0170741	−	0.0295733i	0.000798695	−	0.00138338i	−0.865626	−	0.500692i	$-0.833079\pi$
$457$	0.0170741	−	0.0295733i	0.000798695	−	0.00138338i	0.866424	+	0.499308i	$0.166412\pi$
$458$	3.04519			0.142292
$459$		0			0
$460$	−13.5030			−0.629580
$461$	7.49319	−	12.9786i	0.348993	−	0.604473i	−0.637078	−	0.770799i	$-0.719857\pi$
$461$	7.49319	−	12.9786i	0.348993	−	0.604473i	0.986071	+	0.166326i	$0.0531904\pi$
$462$		0			0
$463$	15.2212	+	26.3639i	0.707390	+	1.22524i	0.965822	+	0.259206i	$0.0834609\pi$
$463$	15.2212	+	26.3639i	0.707390	+	1.22524i	−0.258432	+	0.966029i	$0.583206\pi$
$464$	0.140682	+	0.243668i	0.00653100	+	0.0113120i
$465$		0			0
$466$	2.69341	−	4.66512i	0.124770	−	0.216108i
$467$	−0.510734			−0.0236339			−0.0118170	−	0.999930i	$-0.503762\pi$
$467$	−0.510734			−0.0236339			−0.0118170	+	0.999930i	$0.503762\pi$
$468$		0			0
$469$	12.8135			0.591670
$470$	12.6172	−	21.8537i	0.581989	−	1.00803i
$471$		0			0
$472$	7.26486	+	12.5831i	0.334392	+	0.579185i
$473$	0.505930	+	0.876296i	0.0232627	+	0.0402921i
$474$		0			0
$475$	−18.0706	+	31.2992i	−0.829135	+	1.43610i
$476$	8.04013			0.368519
$477$		0			0
$478$	25.4593			1.16448
$479$	7.72534	−	13.3807i	0.352980	−	0.611379i	−0.633790	−	0.773505i	$-0.718502\pi$
$479$	7.72534	−	13.3807i	0.352980	−	0.611379i	0.986770	+	0.162126i	$0.0518351\pi$
$480$		0			0
$481$	8.00387	+	13.8631i	0.364945	+	0.632103i
$482$	9.81655	+	17.0028i	0.447132	+	0.774455i
$483$		0			0
$484$	−6.73055	+	11.6577i	−0.305934	+	0.529894i
$485$	−15.1557			−0.688185
$486$		0			0
$487$	29.5107			1.33726			0.668629	−	0.743596i	$-0.266881\pi$
$487$	29.5107			1.33726			0.668629	+	0.743596i	$0.266881\pi$
$488$	5.36437	−	9.29136i	0.242834	−	0.420600i
$489$		0			0
$490$	−3.79813	−	6.57856i	−0.171582	−	0.297189i
$491$	−1.07873	−	1.86841i	−0.0486822	−	0.0843201i	0.840657	−	0.541567i	$-0.182169\pi$
$491$	−1.07873	−	1.86841i	−0.0486822	−	0.0843201i	−0.889340	+	0.457247i	$0.848835\pi$
$492$		0			0
$493$	−10.0753	+	17.4510i	−0.453770	+	0.785952i
$494$	−7.62630			−0.343123
$495$		0			0
$496$	0.217186			0.00975194
$497$	−16.7335	+	28.9834i	−0.750602	+	1.30008i
$498$		0			0
$499$	−3.74763	−	6.49108i	−0.167767	−	0.290581i	0.769868	−	0.638204i	$-0.220322\pi$
$499$	−3.74763	−	6.49108i	−0.167767	−	0.290581i	−0.937634	+	0.347623i	$0.886989\pi$
$500$	12.0150	+	20.8106i	0.537328	+	0.930679i
$501$		0			0
$502$	−9.99067	+	17.3043i	−0.445905	+	0.772331i
$503$	28.5963			1.27504			0.637522	−	0.770432i	$-0.279959\pi$
$503$	28.5963			1.27504			0.637522	+	0.770432i	$0.279959\pi$
$504$		0			0
$505$	−31.4766			−1.40069
$506$	0.202744	−	0.351163i	0.00901307	−	0.0156111i
$507$		0			0
$508$	0.0256923	+	0.0445003i	0.00113991	+	0.00197438i
$509$	0.845952	+	1.46523i	0.0374962	+	0.0649453i	0.884164	−	0.467176i	$-0.154728\pi$
$509$	0.845952	+	1.46523i	0.0374962	+	0.0649453i	−0.846668	+	0.532121i	$0.821395\pi$
$510$		0			0
$511$	9.48205	−	16.4234i	0.419461	−	0.726528i
$512$	0.473897			0.0209435
$513$		0			0
$514$	17.2267			0.759836
$515$	−36.1673	+	62.6436i	−1.59372	+	2.76041i
$516$		0			0
$517$	−0.601014	−	1.04099i	−0.0264326	−	0.0457826i
$518$	6.37686	+	11.0450i	0.280183	+	0.485291i
$519$		0			0
$520$	−13.2724	+	22.9885i	−0.582035	+	1.00811i
$521$	−22.4037			−0.981525			−0.490763	−	0.871293i	$-0.663282\pi$
$521$	−22.4037			−0.981525			−0.490763	+	0.871293i	$0.663282\pi$
$522$		0			0
$523$	2.42871			0.106200			0.0531000	−	0.998589i	$-0.483090\pi$
$523$	2.42871			0.106200			0.0531000	+	0.998589i	$0.483090\pi$
$524$	11.2537	−	19.4920i	0.491621	−	0.851512i
$525$		0			0
$526$	7.82682	+	13.5564i	0.341266	+	0.591089i
$527$	7.77719	+	13.4705i	0.338780	+	0.586784i
$528$		0			0
$529$	7.47431	−	12.9459i	0.324970	−	0.562864i
$530$	−4.78880			−0.208012
$531$		0			0
$532$	9.63816			0.417867
$533$	6.99407	−	12.1141i	0.302947	−	0.524719i
$534$		0			0
$535$	−14.7344	−	25.5208i	−0.637025	−	1.10336i
$536$	8.32073	+	14.4119i	0.359401	+	0.622500i
$537$		0			0
$538$	10.0201	−	17.3553i	0.431996	−	0.748239i
$539$	−0.361844			−0.0155857
$540$		0			0
$541$	38.9394			1.67414			0.837069	−	0.547098i	$-0.184267\pi$
$541$	38.9394			1.67414			0.837069	+	0.547098i	$0.184267\pi$
$542$	−1.51501	+	2.62408i	−0.0650755	+	0.112714i
$543$		0			0
$544$	8.45723	+	14.6484i	0.362601	+	0.628043i
$545$	30.3332	+	52.5387i	1.29933	+	2.25051i
$546$		0			0
$547$	7.33615	−	12.7066i	0.313671	−	0.543294i	−0.665483	−	0.746413i	$-0.731774\pi$
$547$	7.33615	−	12.7066i	0.313671	−	0.543294i	0.979154	+	0.203119i	$0.0651077\pi$
$548$	−17.5577			−0.750027
$549$		0			0
$550$	−1.43613			−0.0612367
$551$	−12.0778	+	20.9194i	−0.514534	+	0.891198i
$552$		0			0
$553$	−1.38578	−	2.40024i	−0.0589294	−	0.102069i
$554$	−1.14914	−	1.99037i	−0.0488222	−	0.0845625i
$555$		0			0
$556$	6.43717	−	11.1495i	0.272997	−	0.472844i
$557$	−11.1070			−0.470619			−0.235309	−	0.971921i	$-0.575610\pi$
$557$	−11.1070			−0.470619			−0.235309	+	0.971921i	$0.575610\pi$
$558$		0			0
$559$	−15.0155			−0.635087
$560$	−0.177519	+	0.307471i	−0.00750153	+	0.0129930i
$561$		0			0
$562$	−6.01724	−	10.4222i	−0.253822	−	0.439632i
$563$	−8.15405	−	14.1232i	−0.343652	−	0.595223i	0.641456	−	0.767160i	$-0.278331\pi$
$563$	−8.15405	−	14.1232i	−0.343652	−	0.595223i	−0.985108	+	0.171937i	$0.944997\pi$
$564$		0			0
$565$	4.48680	−	7.77136i	0.188761	−	0.326944i
$566$	−20.1206			−0.845733
$567$		0			0
$568$	−43.4653			−1.82376
$569$	−18.0082	+	31.1911i	−0.754943	+	1.30760i	0.190459	+	0.981695i	$0.439002\pi$
$569$	−18.0082	+	31.1911i	−0.754943	+	1.30760i	−0.945402	+	0.325905i	$0.894331\pi$
$570$		0			0
$571$	−19.5792	−	33.9122i	−0.819364	−	1.41918i	−0.906152	−	0.422953i	$-0.860994\pi$
$571$	−19.5792	−	33.9122i	−0.819364	−	1.41918i	0.0867880	−	0.996227i	$-0.472340\pi$
$572$	0.240352	+	0.416302i	0.0100496	+	0.0174065i
$573$		0			0
$574$	5.57233	−	9.65156i	0.232585	−	0.402848i
$575$	28.5158			1.18919
$576$		0			0
$577$	11.8057			0.491478			0.245739	−	0.969336i	$-0.420969\pi$
$577$	11.8057			0.491478			0.245739	+	0.969336i	$0.420969\pi$
$578$	−3.51754	+	6.09256i	−0.146310	+	0.253417i
$579$		0			0
$580$	15.9820	+	27.6817i	0.663618	+	1.14942i
$581$	−9.25877	−	16.0367i	−0.384119	−	0.665313i
$582$		0			0
$583$	−0.114056	+	0.197551i	−0.00472372	+	0.00818172i
$584$	24.6296			1.01918
$585$		0			0
$586$	−21.3527			−0.882071
$587$	19.9807	−	34.6076i	0.824692	−	1.42841i	−0.0774626	−	0.996995i	$-0.524682\pi$
$587$	19.9807	−	34.6076i	0.824692	−	1.42841i	0.902155	−	0.431413i	$-0.141985\pi$
$588$		0			0
$589$	9.32295	+	16.1478i	0.384145	+	0.665359i
$590$	−8.73442	−	15.1285i	−0.359590	−	0.622829i
$591$		0			0
$592$	−0.139033	+	0.240812i	−0.00571422	+	0.00989733i
$593$	−29.2995			−1.20319			−0.601594	−	0.798802i	$-0.705467\pi$
$593$	−29.2995			−1.20319			−0.601594	+	0.798802i	$0.705467\pi$
$594$		0			0
$595$	−25.4270			−1.04240
$596$	−0.779715	+	1.35051i	−0.0319384	+	0.0553189i
$597$		0			0
$598$	3.00862	+	5.21108i	0.123032	+	0.213097i
$599$	−5.03596	−	8.72254i	−0.205764	−	0.356393i	0.744612	−	0.667497i	$-0.232635\pi$
$599$	−5.03596	−	8.72254i	−0.205764	−	0.356393i	−0.950376	+	0.311104i	$0.899301\pi$
$600$		0			0
$601$	15.2096	−	26.3438i	0.620413	−	1.07459i	−0.368996	−	0.929431i	$-0.620298\pi$
$601$	15.2096	−	26.3438i	0.620413	−	1.07459i	0.989409	−	0.145156i	$-0.0463683\pi$
$602$	−11.9632			−0.487582
$603$		0			0
$604$	−9.63816			−0.392171
$605$	21.2854	−	36.8674i	0.865374	−	1.49887i
$606$		0			0
$607$	11.5371	+	19.9829i	0.468278	+	0.811081i	0.999343	−	0.0362498i	$-0.0115412\pi$
$607$	11.5371	+	19.9829i	0.468278	+	0.811081i	−0.531065	+	0.847331i	$0.678208\pi$
$608$	10.1382	+	17.5598i	0.411157	+	0.712144i
$609$		0			0
$610$	−6.44949	+	11.1708i	−0.261132	+	0.452294i
$611$	17.8375			0.721628
$612$		0			0
$613$	0.765578			0.0309214			0.0154607	−	0.999880i	$-0.495079\pi$
$613$	0.765578			0.0309214			0.0154607	+	0.999880i	$0.495079\pi$
$614$	−7.10055	+	12.2985i	−0.286555	+	0.496327i
$615$		0			0
$616$	0.503708	+	0.872448i	0.0202950	+	0.0351519i
$617$	4.64409	+	8.04379i	0.186964	+	0.323831i	0.944237	−	0.329268i	$-0.106802\pi$
$617$	4.64409	+	8.04379i	0.186964	+	0.323831i	−0.757273	+	0.653099i	$0.773469\pi$
$618$		0			0
$619$	17.5412	−	30.3822i	0.705039	−	1.22116i	−0.261638	−	0.965166i	$-0.584263\pi$
$619$	17.5412	−	30.3822i	0.705039	−	1.22116i	0.966677	−	0.255998i	$-0.0824040\pi$
$620$	24.6732			0.990901
$621$		0			0
$622$	−16.4534			−0.659720
$623$	8.43541	−	14.6106i	0.337958	−	0.585360i
$624$		0			0
$625$	−12.8735	−	22.2975i	−0.514938	−	0.891899i
$626$	1.21941	+	2.11208i	0.0487373	+	0.0844155i
$627$		0			0
$628$	−7.57620	+	13.1224i	−0.302323	+	0.523639i
$629$	−19.9145			−0.794042
$630$		0			0
$631$	35.7621			1.42367			0.711833	−	0.702349i	$-0.247865\pi$
$631$	35.7621			1.42367			0.711833	+	0.702349i	$0.247865\pi$
$632$	1.79978	−	3.11731i	0.0715915	−	0.124000i
$633$		0			0
$634$	7.68691	+	13.3141i	0.305286	+	0.528771i
$635$	−0.0812519	−	0.140732i	−0.00322438	−	0.00558480i
$636$		0			0
$637$	2.68479	−	4.65020i	0.106375	−	0.184248i
$638$	−0.959866			−0.0380014
$639$		0			0
$640$	26.5449			1.04928
$641$	−1.46316	+	2.53427i	−0.0577915	+	0.100098i	−0.893474	−	0.449115i	$-0.851739\pi$
$641$	−1.46316	+	2.53427i	−0.0577915	+	0.100098i	0.835682	+	0.549213i	$0.185073\pi$
$642$		0			0
$643$	10.1258	+	17.5385i	0.399324	+	0.691649i	0.993643	−	0.112581i	$-0.0359116\pi$
$643$	10.1258	+	17.5385i	0.399324	+	0.691649i	−0.594319	+	0.804229i	$0.702578\pi$
$644$	−3.80231	−	6.58579i	−0.149832	−	0.259517i
$645$		0			0
$646$	4.74376	−	8.21643i	0.186641	−	0.323271i
$647$	10.7219			0.421523			0.210761	−	0.977538i	$-0.432406\pi$
$647$	10.7219			0.421523			0.210761	+	0.977538i	$0.432406\pi$
$648$		0			0
$649$	−0.832119			−0.0326635
$650$	10.6557	−	18.4562i	0.417951	−	0.723912i
$651$		0			0
$652$	−8.43154	−	14.6039i	−0.330205	−	0.571931i
$653$	−17.8635	−	30.9405i	−0.699053	−	1.21079i	−0.968795	−	0.247862i	$-0.920272\pi$
$653$	−17.8635	−	30.9405i	−0.699053	−	1.21079i	0.269743	−	0.962932i	$-0.413061\pi$
$654$		0			0
$655$	−35.5899	+	61.6436i	−1.39061	+	2.40861i
$656$	0.242984			0.00948694
$657$		0			0
$658$	14.2115			0.554023
$659$	−15.4329	+	26.7305i	−0.601180	+	1.04127i	0.391463	+	0.920194i	$0.371969\pi$
$659$	−15.4329	+	26.7305i	−0.601180	+	1.04127i	−0.992643	+	0.121080i	$0.961364\pi$
$660$		0			0
$661$	4.92396	+	8.52855i	0.191520	+	0.331722i	0.945754	−	0.324883i	$-0.105325\pi$
$661$	4.92396	+	8.52855i	0.191520	+	0.331722i	−0.754234	+	0.656606i	$0.771992\pi$
$662$	−14.2721	−	24.7201i	−0.554702	−	0.960773i
$663$		0			0
$664$	12.0248	−	20.8276i	0.466653	−	0.808267i
$665$	−30.4807			−1.18199
$666$		0			0
$667$	19.0591			0.737972
$668$	−2.27972	+	3.94858i	−0.0882048	+	0.152775i
$669$		0			0
$670$	−10.0039	−	17.3272i	−0.386483	−	0.669409i
$671$	0.307218	+	0.532118i	0.0118600	+	0.0205422i
$672$		0			0
$673$	9.84864	−	17.0583i	0.379637	−	0.657551i	−0.611372	−	0.791343i	$-0.709382\pi$
$673$	9.84864	−	17.0583i	0.379637	−	0.657551i	0.991009	+	0.133792i	$0.0427155\pi$
$674$	−7.28642			−0.280662
$675$		0			0
$676$	8.81345			0.338979
$677$	14.2285	−	24.6445i	0.546845	−	0.947164i	−0.451643	−	0.892199i	$-0.649162\pi$
$677$	14.2285	−	24.6445i	0.546845	−	0.947164i	0.998488	−	0.0549652i	$-0.0175048\pi$
$678$		0			0
$679$	−4.26769	−	7.39186i	−0.163779	−	0.283674i
$680$	−16.5116	−	28.5989i	−0.633191	−	1.09672i
$681$		0			0
$682$	−0.370462	+	0.641660i	−0.0141857	+	0.0245704i
$683$	12.5107			0.478710			0.239355	−	0.970932i	$-0.423064\pi$
$683$	12.5107			0.478710			0.239355	+	0.970932i	$0.423064\pi$
$684$		0			0
$685$	55.5262			2.12155
$686$	8.86349	−	15.3520i	0.338410	−	0.586143i
$687$		0			0
$688$	−0.130415	−	0.225885i	−0.00497202	−	0.00861180i
$689$	−1.69253	−	2.93155i	−0.0644804	−	0.111683i
$690$		0			0
$691$	−21.3127	+	36.9147i	−0.810775	+	1.40430i	0.101548	+	0.994831i	$0.467621\pi$
$691$	−21.3127	+	36.9147i	−0.810775	+	1.40430i	−0.912323	+	0.409472i	$0.865713\pi$
$692$	1.91292			0.0727185
$693$		0			0
$694$	−13.1584			−0.499485
$695$	−20.3576	+	35.2603i	−0.772206	+	1.33750i
$696$		0			0
$697$	8.70099	+	15.0706i	0.329573	+	0.570838i
$698$	14.7939	+	25.6237i	0.559956	+	0.969872i
$699$		0			0
$700$	−13.4667	+	23.3251i	−0.508995	+	0.881604i
$701$	51.7701			1.95533			0.977665	−	0.210167i	$-0.0674008\pi$
$701$	51.7701			1.95533			0.977665	+	0.210167i	$0.0674008\pi$
$702$		0			0
$703$	−23.8726			−0.900371
$704$	−0.409663	+	0.709557i	−0.0154398	+	0.0267424i
$705$		0			0
$706$	−6.92679	−	11.9976i	−0.260693	−	0.451534i
$707$	−8.86349	−	15.3520i	−0.333346	−	0.577372i
$708$		0			0
$709$	−7.57919	+	13.1275i	−0.284643	+	0.493015i	−0.972522	−	0.232809i	$-0.925208\pi$
$709$	−7.57919	+	13.1275i	−0.284643	+	0.493015i	0.687880	+	0.725825i	$0.258542\pi$
$710$	52.2576			1.96119
$711$		0			0
$712$	21.9110			0.821148
$713$	7.35591	−	12.7408i	0.275481	−	0.477147i
$714$		0			0
$715$	−0.760115	−	1.31656i	−0.0284267	−	0.0492364i
$716$	−7.47818	−	12.9526i	−0.279473	−	0.484061i
$717$		0			0
$718$	7.96972	−	13.8040i	0.297427	−	0.515159i
$719$	−2.61493			−0.0975206			−0.0487603	−	0.998811i	$-0.515527\pi$
$719$	−2.61493			−0.0975206			−0.0487603	+	0.998811i	$0.515527\pi$
$720$		0			0
$721$	−40.7374			−1.51714
$722$	−2.66756	+	4.62034i	−0.0992762	+	0.171951i
$723$		0			0
$724$	−10.3486	−	17.9244i	−0.384604	−	0.666154i
$725$	−33.7511	−	58.4586i	−1.25348	−	2.17110i
$726$		0			0
$727$	2.04963	−	3.55006i	0.0760166	−	0.131665i	−0.825511	−	0.564386i	$-0.809113\pi$
$727$	2.04963	−	3.55006i	0.0760166	−	0.131665i	0.901528	+	0.432721i	$0.142446\pi$
$728$	−14.9495			−0.554067
$729$		0			0
$730$	−29.6117			−1.09598
$731$	9.34002	−	16.1774i	0.345453	−	0.598343i
$732$		0			0
$733$	19.1040	+	33.0891i	0.705623	+	1.22217i	0.966466	+	0.256793i	$0.0826659\pi$
$733$	19.1040	+	33.0891i	0.705623	+	1.22217i	−0.260844	+	0.965381i	$0.584001\pi$
$734$	−8.41699	−	14.5787i	−0.310677	−	0.538108i
$735$		0			0
$736$	7.99912	−	13.8549i	0.294852	−	0.510698i
$737$	−0.953058			−0.0351064
$738$		0			0
$739$	−24.2094			−0.890559			−0.445279	−	0.895392i	$-0.646896\pi$
$739$	−24.2094			−0.890559			−0.445279	+	0.895392i	$0.646896\pi$
$740$	−15.7947	+	27.3573i	−0.580626	+	1.00567i
$741$		0			0
$742$	−1.34848	−	2.33563i	−0.0495042	−	0.0857438i
$743$	1.65570	+	2.86775i	0.0607416	+	0.105208i	0.894797	−	0.446473i	$-0.147320\pi$
$743$	1.65570	+	2.86775i	0.0607416	+	0.105208i	−0.834055	+	0.551681i	$0.813987\pi$
$744$		0			0
$745$	2.46585	−	4.27098i	0.0903418	−	0.156477i
$746$	13.4105			0.490995
$747$		0			0
$748$	−0.598021			−0.0218658
$749$	8.29813	−	14.3728i	0.303207	−	0.525170i
$750$		0			0
$751$	−6.85550	−	11.8741i	−0.250161	−	0.433291i	0.713409	−	0.700748i	$-0.247150\pi$
$751$	−6.85550	−	11.8741i	−0.250161	−	0.433291i	−0.963570	+	0.267456i	$0.913817\pi$
$752$	0.154925	+	0.268338i	0.00564954	+	0.00978529i
$753$		0			0
$754$	7.12196	−	12.3356i	0.259366	−	0.449236i
$755$	30.4807			1.10931
$756$		0			0
$757$	12.3833			0.450079			0.225040	−	0.974350i	$-0.427749\pi$
$757$	12.3833			0.450079			0.225040	+	0.974350i	$0.427749\pi$
$758$	4.32992	−	7.49964i	0.157270	−	0.272399i
$759$		0			0
$760$	−19.7934	−	34.2831i	−0.717982	−	1.24358i
$761$	−3.79133	−	6.56677i	−0.137435	−	0.238045i	0.789090	−	0.614278i	$-0.210553\pi$
$761$	−3.79133	−	6.56677i	−0.137435	−	0.238045i	−0.926525	+	0.376233i	$0.877219\pi$
$762$		0			0
$763$	−17.0831	+	29.5887i	−0.618448	+	1.07118i
$764$	21.4371			0.775566
$765$		0			0
$766$	−24.9659			−0.902053
$767$	6.17412	−	10.6939i	0.222934	−	0.386134i
$768$		0			0
$769$	−1.60859	−	2.78616i	−0.0580073	−	0.100472i	0.835563	−	0.549394i	$-0.185141\pi$
$769$	−1.60859	−	2.78616i	−0.0580073	−	0.100472i	−0.893571	+	0.448922i	$0.851808\pi$
$770$	−0.605600	−	1.04893i	−0.0218243	−	0.0378008i
$771$		0			0
$772$	−1.22193	+	2.11645i	−0.0439784	+	0.0761728i
$773$	−0.184468			−0.00663486			−0.00331743	−	0.999994i	$-0.501056\pi$
$773$	−0.184468			−0.00663486			−0.00331743	+	0.999994i	$0.501056\pi$
$774$		0			0
$775$	−52.1052			−1.87168
$776$	5.54266	−	9.60017i	0.198970	−	0.344626i
$777$		0			0
$778$	4.78581	+	8.28926i	0.171579	+	0.297184i
$779$	10.4304	+	18.0659i	0.373706	+	0.647278i
$780$		0			0
$781$	1.24463	−	2.15577i	0.0445365	−	0.0771394i
$782$	−7.48576			−0.267690
$783$		0			0
$784$	0.0932736			0.00333120
$785$	23.9598	−	41.4995i	0.855160	−	1.48118i
$786$		0			0
$787$	0.239008	+	0.413974i	0.00851971	+	0.0147566i	0.870254	−	0.492604i	$-0.163955\pi$
$787$	0.239008	+	0.413974i	0.00851971	+	0.0147566i	−0.861734	+	0.507360i	$0.830621\pi$
$788$	12.9982	+	22.5136i	0.463043	+	0.802015i
$789$		0			0
$790$	−2.16385	+	3.74789i	−0.0769863	+	0.133344i
$791$	5.05375			0.179691
$792$		0			0
$793$	−9.11793			−0.323787
$794$	−7.96151	+	13.7897i	−0.282544	+	0.489380i
$795$		0			0
$796$	−1.89141	−	3.27601i	−0.0670391	−	0.116115i
$797$	−7.24944	−	12.5564i	−0.256788	−	0.444770i	0.708591	−	0.705619i	$-0.249331\pi$
$797$	−7.24944	−	12.5564i	−0.256788	−	0.444770i	−0.965380	+	0.260849i	$0.915998\pi$
$798$		0			0
$799$	−11.0954	+	19.2178i	−0.392527	+	0.679876i
$800$	−56.6614			−2.00328
$801$		0			0
$802$	−1.26083			−0.0445215
$803$	−0.705270	+	1.22156i	−0.0248884	+	0.0431081i
$804$		0			0
$805$	12.0248	+	20.8276i	0.423819	+	0.734076i
$806$	−5.49747	−	9.52190i	−0.193640	−	0.335395i
$807$		0			0
$808$	11.5114	−	19.9384i	0.404971	−	0.701431i
$809$	−14.8743			−0.522954			−0.261477	−	0.965210i	$-0.584210\pi$
$809$	−14.8743			−0.522954			−0.261477	+	0.965210i	$0.584210\pi$
$810$		0			0
$811$	21.5963			0.758347			0.379174	−	0.925325i	$-0.376208\pi$
$811$	21.5963			0.758347			0.379174	+	0.925325i	$0.376208\pi$
$812$	−9.00077	+	15.5898i	−0.315865	+	0.547095i
$813$		0			0
$814$	−0.474308	−	0.821525i	−0.0166245	−	0.0287944i
$815$	26.6648	+	46.1848i	0.934027	+	1.61778i
$816$		0			0
$817$	11.1964	−	19.3927i	0.391713	−	0.678466i
$818$	−7.56624			−0.264547
$819$		0			0
$820$	27.6040			0.963974
$821$	1.64068	−	2.84174i	0.0572602	−	0.0991776i	−0.835974	−	0.548768i	$-0.815097\pi$
$821$	1.64068	−	2.84174i	0.0572602	−	0.0991776i	0.893235	+	0.449591i	$0.148430\pi$
$822$		0			0
$823$	−6.86571	−	11.8918i	−0.239324	−	0.414521i	0.721197	−	0.692730i	$-0.243592\pi$
$823$	−6.86571	−	11.8918i	−0.239324	−	0.414521i	−0.960520	+	0.278209i	$0.910259\pi$
$824$	−26.4538	−	45.8194i	−0.921563	−	1.59619i
$825$		0			0
$826$	4.91905	−	8.52005i	0.171156	−	0.296450i
$827$	20.2327			0.703559			0.351779	−	0.936083i	$-0.385577\pi$
$827$	20.2327			0.703559			0.351779	+	0.936083i	$0.385577\pi$
$828$		0			0
$829$	25.5276			0.886612			0.443306	−	0.896370i	$-0.353806\pi$
$829$	25.5276			0.886612			0.443306	+	0.896370i	$0.353806\pi$
$830$	−14.4572	+	25.0407i	−0.501818	+	0.869174i
$831$		0			0
$832$	−6.07919	−	10.5295i	−0.210758	−	0.365044i
$833$	3.34002	+	5.78509i	0.115725	+	0.200441i
$834$		0			0
$835$	7.20961	−	12.4874i	0.249499	−	0.432145i
$836$	−0.716881			−0.0247939
$837$		0			0
$838$	10.8265			0.373994
$839$	−8.69001	+	15.0515i	−0.300012	+	0.519637i	−0.976138	−	0.217149i	$-0.930324\pi$
$839$	−8.69001	+	15.0515i	−0.300012	+	0.519637i	0.676126	+	0.736786i	$0.263657\pi$
$840$		0			0
$841$	−8.05825	−	13.9573i	−0.277871	−	0.481286i
$842$	4.88784	+	8.46599i	0.168446	+	0.291757i
$843$		0			0
$844$	0.618089	−	1.07056i	0.0212755	−	0.0368502i
$845$	−27.8726			−0.958846
$846$		0			0
$847$	23.9750			0.823792
$848$	0.0294005	−	0.0509232i	0.00100962	−	0.00174871i
$849$		0			0
$850$	13.2562	+	22.9605i	0.454685	+	0.787538i
$851$	9.41787	+	16.3122i	0.322840	+	0.559176i
$852$		0			0
$853$	−6.65136	+	11.5205i	−0.227738	+	0.394454i	−0.957137	−	0.289634i	$-0.906466\pi$
$853$	−6.65136	+	11.5205i	−0.227738	+	0.394454i	0.729399	+	0.684088i	$0.239800\pi$
$854$	−7.26445			−0.248584
$855$		0			0
$856$	21.5544			0.736713
$857$	9.96064	−	17.2523i	0.340249	−	0.589328i	−0.644230	−	0.764832i	$-0.722822\pi$
$857$	9.96064	−	17.2523i	0.340249	−	0.589328i	0.984479	+	0.175504i	$0.0561553\pi$
$858$		0			0
$859$	−13.1723	−	22.8151i	−0.449433	−	0.778441i	0.548916	−	0.835878i	$-0.315041\pi$
$859$	−13.1723	−	22.8151i	−0.449433	−	0.778441i	−0.998349	+	0.0574364i	$0.981707\pi$
$860$	−14.8157	−	25.6615i	−0.505210	−	0.875050i
$861$		0			0
$862$	−16.2228	+	28.0987i	−0.552551	+	0.957047i
$863$	38.2995			1.30373			0.651866	−	0.758334i	$-0.273987\pi$
$863$	38.2995			1.30373			0.651866	+	0.758334i	$0.273987\pi$
$864$		0			0
$865$	−6.04963			−0.205694
$866$	−16.7075	+	28.9383i	−0.567746	+	0.983364i
$867$		0			0
$868$	6.94774	+	12.0338i	0.235822	+	0.408455i
$869$	0.103074	+	0.178529i	0.00349654	+	0.00605618i
$870$		0			0
$871$	7.07145	−	12.2481i	0.239607	−	0.415012i
$872$	−44.3732			−1.50267
$873$		0			0
$874$	−8.97359			−0.303536
$875$	21.3995	−	37.0649i	0.723434	−	1.25302i
$876$		0			0
$877$	13.5287	+	23.4324i	0.456831	+	0.791255i	0.998791	−	0.0491492i	$-0.0156510\pi$
$877$	13.5287	+	23.4324i	0.456831	+	0.791255i	−0.541960	+	0.840404i	$0.682318\pi$
$878$	0.0888306	+	0.153859i	0.00299789	+	0.00519249i
$879$		0			0
$880$	0.0132037	−	0.0228696i	0.000445098	−	0.000770933i
$881$	30.5776			1.03019			0.515093	−	0.857134i	$-0.327757\pi$
$881$	30.5776			1.03019			0.515093	+	0.857134i	$0.327757\pi$
$882$		0			0
$883$	44.1052			1.48426			0.742130	−	0.670256i	$-0.233816\pi$
$883$	44.1052			1.48426			0.742130	+	0.670256i	$0.233816\pi$
$884$	4.43717	−	7.68540i	0.149238	−	0.258488i
$885$		0			0
$886$	9.33440	+	16.1677i	0.313595	+	0.543163i
$887$	3.94222	+	6.82812i	0.132367	+	0.229266i	0.924588	−	0.380967i	$-0.124409\pi$
$887$	3.94222	+	6.82812i	0.132367	+	0.229266i	−0.792222	+	0.610233i	$0.791076\pi$
$888$		0			0
$889$	0.0457595	−	0.0792577i	0.00153472	−	0.00265822i
$890$	−26.3432			−0.883025
$891$		0			0
$892$	−22.4287			−0.750969
$893$	−13.3007	+	23.0374i	−0.445090	+	0.770918i
$894$		0			0
$895$	23.6498	+	40.9626i	0.790525	+	1.36923i
$896$	7.47477	+	12.9467i	0.249715	+	0.432519i
$897$		0			0
$898$	−14.6239	+	25.3294i	−0.488006	+	0.845252i
$899$	−34.8256			−1.16150
$900$		0			0
$901$	4.21120			0.140295
$902$	−0.414467	+	0.717878i	−0.0138002	+	0.0239027i
$903$		0			0
$904$	3.28177	+	5.68420i	0.109150	+	0.189054i
$905$	32.7276	+	56.6859i	1.08790	+	1.88430i
$906$		0			0
$907$	6.45336	−	11.1776i	0.214280	−	0.371145i	−0.738769	−	0.673958i	$-0.764593\pi$
$907$	6.45336	−	11.1776i	0.214280	−	0.371145i	0.953050	+	0.302814i	$0.0979260\pi$
$908$	3.24453			0.107673
$909$		0			0
$910$	17.9736			0.595819
$911$	−10.5929	+	18.3474i	−0.350957	+	0.607876i	−0.986417	−	0.164258i	$-0.947477\pi$
$911$	−10.5929	+	18.3474i	−0.350957	+	0.607876i	0.635460	+	0.772134i	$0.280810\pi$
$912$		0			0
$913$	0.688663	+	1.19280i	0.0227914	+	0.0394759i
$914$	−0.0150147	−	0.0260063i	−0.000496644	−	0.000860212i
$915$		0			0
$916$	−2.12391	+	3.67872i	−0.0701760	+	0.121548i
$917$	−40.0871			−1.32379
$918$		0			0
$919$	31.4688			1.03806			0.519031	−	0.854756i	$-0.326293\pi$
$919$	31.4688			1.03806			0.519031	+	0.854756i	$0.326293\pi$
$920$	−15.6172	+	27.0498i	−0.514884	+	0.891806i
$921$		0			0
$922$	−6.58940	−	11.4132i	−0.217010	−	0.375873i
$923$	18.4697	+	31.9905i	0.607938	+	1.05298i
$924$		0			0
$925$	33.3555	−	57.7734i	1.09672	−	1.89958i
$926$	26.7706			0.879737
$927$		0			0
$928$	−37.8708			−1.24317
$929$	1.16338	−	2.01504i	0.0381693	−	0.0661112i	−0.846310	−	0.532691i	$-0.821181\pi$
$929$	1.16338	−	2.01504i	0.0381693	−	0.0661112i	0.884479	+	0.466580i	$0.154514\pi$
$930$		0			0
$931$	4.00387	+	6.93491i	0.131222	+	0.227282i
$932$	3.75712	+	6.50753i	0.123069	+	0.213161i
$933$		0			0
$934$	−0.224566	+	0.388960i	−0.00734802	+	0.0127271i
$935$	1.89124			0.0618503
$936$		0			0
$937$	−10.9982			−0.359297			−0.179649	−	0.983731i	$-0.557496\pi$
$937$	−10.9982			−0.359297			−0.179649	+	0.983731i	$0.557496\pi$
$938$	5.63398	−	9.75834i	0.183956	−	0.318621i
$939$		0			0
$940$	17.6001	+	30.4843i	0.574053	+	0.994289i
$941$	12.0519	+	20.8744i	0.392879	+	0.680487i	0.992828	−	0.119552i	$-0.0381457\pi$
$941$	12.0519	+	20.8744i	0.392879	+	0.680487i	−0.599949	+	0.800038i	$0.704812\pi$
$942$		0			0
$943$	8.22967	−	14.2542i	0.267995	−	0.464181i
$944$	0.214498			0.00698131
$945$		0			0
$946$	0.889814			0.0289304
$947$	5.95976	−	10.3226i	0.193666	−	0.335440i	−0.752796	−	0.658254i	$-0.771295\pi$
$947$	5.95976	−	10.3226i	0.193666	−	0.335440i	0.946462	+	0.322814i	$0.104629\pi$
$948$		0			0
$949$	−10.4659	−	18.1274i	−0.339736	−	0.588440i
$950$	15.8910	+	27.5240i	0.515572	+	0.892997i
$951$		0			0
$952$	9.29901	−	16.1064i	0.301383	−	0.522010i
$953$	−36.8289			−1.19301			−0.596503	−	0.802611i	$-0.703444\pi$
$953$	−36.8289			−1.19301			−0.596503	+	0.802611i	$0.703444\pi$
$954$		0			0
$955$	−67.7948			−2.19379
$956$	−17.7570	+	30.7561i	−0.574303	+	0.994722i
$957$		0			0
$958$	−6.79355	−	11.7668i	−0.219490	−	0.380167i
$959$	15.6356	+	27.0817i	0.504901	+	0.874514i
$960$		0			0
$961$	2.05896	−	3.56623i	0.0664182	−	0.115040i
$962$	14.0770			0.453860
$963$		0			0
$964$	−27.3868			−0.882070
$965$	3.86437	−	6.69329i	0.124398	−	0.215465i
$966$		0			0
$967$	−26.7802	−	46.3846i	−0.861193	−	1.49163i	−0.870779	−	0.491675i	$-0.836385\pi$
$967$	−26.7802	−	46.3846i	−0.861193	−	1.49163i	0.00958604	−	0.999954i	$-0.496949\pi$
$968$	15.5688	+	26.9659i	0.500399	+	0.866717i
$969$		0			0
$970$	−6.66385	+	11.5421i	−0.213963	+	0.370595i
$971$	53.2327			1.70832			0.854159	−	0.520012i	$-0.174073\pi$
$971$	53.2327			1.70832			0.854159	+	0.520012i	$0.174073\pi$
$972$		0			0
$973$	−22.9299			−0.735100
$974$	12.9757	−	22.4745i	0.415767	−	0.720129i
$975$		0			0
$976$	−0.0791925	−	0.137165i	−0.00253489	−	0.00439056i
$977$	−6.72849	−	11.6541i	−0.215264	−	0.372847i	0.738091	−	0.674702i	$-0.235728\pi$
$977$	−6.72849	−	11.6541i	−0.215264	−	0.372847i	−0.953354	+	0.301854i	$0.902394\pi$
$978$		0			0
$979$	−0.627422	+	1.08673i	−0.0200525	+	0.0347319i
$980$	10.5963			0.338485
$981$		0			0
$982$	−1.89723			−0.0605431
$983$	5.12061	−	8.86916i	0.163322	−	0.282882i	−0.772736	−	0.634728i	$-0.781112\pi$
$983$	5.12061	−	8.86916i	0.163322	−	0.282882i	0.936058	+	0.351845i	$0.114446\pi$
$984$		0			0
$985$	−41.1070	−	71.1994i	−1.30978	−	2.26860i
$986$	8.86009	+	15.3461i	0.282163	+	0.488720i
$987$		0			0
$988$	5.31908	−	9.21291i	0.169222	−	0.293102i
$989$	−17.6682			−0.561816
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	−14.6163	+	25.3162i	−0.464069	+	0.803791i
$993$		0			0
$994$	14.7152	+	25.4875i	0.466739	+	0.808415i
$995$	5.98158	+	10.3604i	0.189629	+	0.328447i
$996$		0			0
$997$	−19.2508	+	33.3433i	−0.609678	+	1.05599i	0.381615	+	0.924321i	$0.375368\pi$
$997$	−19.2508	+	33.3433i	−0.609678	+	1.05599i	−0.991293	+	0.131672i	$0.957965\pi$
$998$	−6.59121			−0.208641
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.c.e.163.3		6
3.2	odd	2		243.2.c.f.163.1		6
9.2	odd	6		243.2.a.e.1.3	✓	3
9.4	even	3	inner	243.2.c.e.82.3		6
9.5	odd	6		243.2.c.f.82.1		6
9.7	even	3		243.2.a.f.1.1	yes	3
27.2	odd	18		729.2.e.g.325.1		6
27.4	even	9		729.2.e.i.163.1		6
27.5	odd	18		729.2.e.g.406.1		6
27.7	even	9		729.2.e.c.82.1		6
27.11	odd	18		729.2.e.a.568.1		6
27.13	even	9		729.2.e.c.649.1		6
27.14	odd	18		729.2.e.h.649.1		6
27.16	even	9		729.2.e.i.568.1		6
27.20	odd	18		729.2.e.h.82.1		6
27.22	even	9		729.2.e.b.406.1		6
27.23	odd	18		729.2.e.a.163.1		6
27.25	even	9		729.2.e.b.325.1		6
36.7	odd	6		3888.2.a.bk.1.3		3
36.11	even	6		3888.2.a.bd.1.1		3
45.29	odd	6		6075.2.a.bv.1.1		3
45.34	even	6		6075.2.a.bq.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.3	✓	3	9.2	odd	6
243.2.a.f.1.1	yes	3	9.7	even	3
243.2.c.e.82.3		6	9.4	even	3	inner
243.2.c.e.163.3		6	1.1	even	1	trivial
243.2.c.f.82.1		6	9.5	odd	6
243.2.c.f.163.1		6	3.2	odd	2
729.2.e.a.163.1		6	27.23	odd	18
729.2.e.a.568.1		6	27.11	odd	18
729.2.e.b.325.1		6	27.25	even	9
729.2.e.b.406.1		6	27.22	even	9
729.2.e.c.82.1		6	27.7	even	9
729.2.e.c.649.1		6	27.13	even	9
729.2.e.g.325.1		6	27.2	odd	18
729.2.e.g.406.1		6	27.5	odd	18
729.2.e.h.82.1		6	27.20	odd	18
729.2.e.h.649.1		6	27.14	odd	18
729.2.e.i.163.1		6	27.4	even	9
729.2.e.i.568.1		6	27.16	even	9
3888.2.a.bd.1.1		3	36.11	even	6
3888.2.a.bk.1.3		3	36.7	odd	6
6075.2.a.bq.1.3		3	45.34	even	6
6075.2.a.bv.1.1		3	45.29	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.439693 - 0.761570i) q^{2} +(0.613341 + 1.06234i) q^{4} +(-1.93969 - 3.35965i) q^{5} +(1.09240 - 1.89209i) q^{7} +2.83750 q^{8} -3.41147 q^{10} +(-0.0812519 + 0.140732i) q^{11} +(-1.20574 - 2.08840i) q^{13} +(-0.960637 - 1.66387i) q^{14} +(0.0209445 - 0.0362770i) q^{16} +3.00000 q^{17} +3.59627 q^{19} +(2.37939 - 4.12122i) q^{20} +(0.0714517 + 0.123758i) q^{22} +(-1.41875 - 2.45734i) q^{23} +(-5.02481 + 8.70323i) q^{25} -2.12061 q^{26} +2.68004 q^{28} +(-3.35844 + 5.81699i) q^{29} +(2.59240 + 4.49016i) q^{31} +(2.81908 + 4.88279i) q^{32} +(1.31908 - 2.28471i) q^{34} -8.47565 q^{35} -6.63816 q^{37} +(1.58125 - 2.73881i) q^{38} +(-5.50387 - 9.53298i) q^{40} +(2.90033 + 5.02352i) q^{41} +(3.11334 - 5.39246i) q^{43} -0.199340 q^{44} -2.49525 q^{46} +(-3.69846 + 6.40593i) q^{47} +(1.11334 + 1.92836i) q^{49} +(4.41875 + 7.65350i) q^{50} +(1.47906 - 2.56180i) q^{52} +1.40373 q^{53} +0.630415 q^{55} +(3.09967 - 5.36879i) q^{56} +(2.95336 + 5.11538i) q^{58} +(2.56031 + 4.43458i) q^{59} +(1.89053 - 3.27449i) q^{61} +4.55943 q^{62} +5.04189 q^{64} +(-4.67752 + 8.10170i) q^{65} +(2.93242 + 5.07910i) q^{67} +(1.84002 + 3.18701i) q^{68} +(-3.72668 + 6.45480i) q^{70} -15.3182 q^{71} +8.68004 q^{73} +(-2.91875 + 5.05542i) q^{74} +(2.20574 + 3.82045i) q^{76} +(0.177519 + 0.307471i) q^{77} +(0.634285 - 1.09861i) q^{79} -0.162504 q^{80} +5.10101 q^{82} +(4.23783 - 7.34013i) q^{83} +(-5.81908 - 10.0789i) q^{85} +(-2.73783 - 4.74205i) q^{86} +(-0.230552 + 0.399328i) q^{88} +7.72193 q^{89} -5.26857 q^{91} +(1.74035 - 3.01438i) q^{92} +(3.25237 + 5.63328i) q^{94} +(-6.97565 - 12.0822i) q^{95} +(1.95336 - 3.38332i) q^{97} +1.95811 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 3 q^{7} + 12 q^{8} - 3 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} + 18 q^{17} - 6 q^{19} + 3 q^{20} - 6 q^{23} - 3 q^{25} - 24 q^{26} - 24 q^{28} - 12 q^{29} + 12 q^{31}+ \cdots + 18 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 3 * q^7 + 12 * q^8 - 3 * q^11 + 3 * q^13 + 3 * q^14 - 3 * q^16 + 18 * q^17 - 6 * q^19 + 3 * q^20 - 6 * q^23 - 3 * q^25 - 24 * q^26 - 24 * q^28 - 12 * q^29 + 12 * q^31 - 9 * q^34 - 12 * q^35 - 6 * q^37 + 12 * q^38 - 9 * q^40 + 3 * q^41 + 12 * q^43 - 30 * q^44 + 18 * q^46 + 6 * q^47 + 24 * q^50 + 12 * q^52 + 36 * q^53 + 18 * q^55 + 33 * q^56 - 9 * q^58 + 21 * q^59 - 6 * q^61 - 24 * q^62 + 24 * q^64 - 3 * q^65 - 6 * q^67 - 9 * q^68 - 9 * q^70 - 18 * q^71 + 12 * q^73 - 15 * q^74 + 3 * q^76 - 24 * q^77 - 6 * q^79 - 6 * q^80 + 36 * q^82 + 6 * q^83 - 18 * q^85 + 3 * q^86 + 36 * q^88 - 12 * q^91 - 24 * q^92 + 36 * q^94 - 3 * q^95 - 15 * q^97 + 18 * q^98

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