LMFDB - Embedded newform 729.2.e.u.649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			649.1
Root			$-1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.u.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.135052 + 0.765917i) q^{2} +(1.31100 + 0.477163i) q^{4} +(-1.82039 + 1.52749i) q^{5} +(2.35052 - 0.855521i) q^{7} +(-1.32025 + 2.28674i) q^{8} +O(q^{10})$	\(q+(-0.135052 + 0.765917i) q^{2} +(1.31100 + 0.477163i) q^{4} +(-1.82039 + 1.52749i) q^{5} +(2.35052 - 0.855521i) q^{7} +(-1.32025 + 2.28674i) q^{8} +(-0.924081 - 1.60056i) q^{10} +(-2.40643 - 2.01923i) q^{11} +(0.232103 + 1.31632i) q^{13} +(0.337815 + 1.91585i) q^{14} +(0.564314 + 0.473515i) q^{16} +(3.13726 + 5.43389i) q^{17} +(-4.03234 + 6.98422i) q^{19} +(-3.11538 + 1.13391i) q^{20} +(1.87156 - 1.57042i) q^{22} +(3.81008 + 1.38675i) q^{23} +(0.112355 - 0.637198i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(1.61271 - 9.14613i) q^{29} +(-2.66104 - 0.968540i) q^{31} +(-4.48437 + 3.76284i) q^{32} +(-4.58560 + 1.66902i) q^{34} +(-2.97207 + 5.14778i) q^{35} +(-2.76596 - 4.79078i) q^{37} +(-4.80476 - 4.03167i) q^{38} +(-1.08960 - 6.17943i) q^{40} +(1.23390 + 6.99781i) q^{41} +(1.79017 + 1.50213i) q^{43} +(-2.19131 - 3.79547i) q^{44} +(-1.57670 + 2.73092i) q^{46} +(-4.33594 + 1.57815i) q^{47} +(-0.569260 + 0.477666i) q^{49} +(0.472867 + 0.172110i) q^{50} +(-0.323815 + 1.83645i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(-1.14693 + 6.50455i) q^{56} +(6.78738 + 2.47040i) q^{58} +(3.06321 - 2.57034i) q^{59} +(-0.321185 + 0.116902i) q^{61} +(1.10120 - 1.90733i) q^{62} +(-1.53974 - 2.66690i) q^{64} +(-2.43319 - 2.04168i) q^{65} +(1.75783 + 9.96913i) q^{67} +(1.52008 + 8.62079i) q^{68} +(-3.54139 - 2.97158i) q^{70} +(4.09540 + 7.09344i) q^{71} +(6.15722 - 10.6646i) q^{73} +(4.04288 - 1.47149i) q^{74} +(-8.61900 + 7.23220i) q^{76} +(-7.38387 - 2.68751i) q^{77} +(0.708606 - 4.01870i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(-0.158580 + 0.899354i) q^{83} +(-14.0112 - 5.09967i) q^{85} +(-1.39227 + 1.16826i) q^{86} +(7.79456 - 2.83699i) q^{88} +(-1.86437 + 3.22919i) q^{89} +(1.67171 + 2.89548i) q^{91} +(4.33328 + 3.63606i) q^{92} +(-0.623157 - 3.53410i) q^{94} +(-3.32788 - 18.8734i) q^{95} +(-4.59343 - 3.85434i) q^{97} +(-0.288973 - 0.500515i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 3 * q^13 - 15 * q^14 - 36 * q^16 + 9 * q^17 - 12 * q^19 - 42 * q^20 + 6 * q^22 - 6 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 54 * q^32 - 9 * q^34 - 30 * q^35 - 3 * q^37 - 42 * q^38 - 57 * q^40 - 24 * q^41 + 6 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 + 33 * q^49 - 21 * q^50 + 45 * q^52 - 18 * q^53 + 30 * q^55 - 3 * q^56 + 33 * q^58 - 15 * q^59 + 33 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 + 42 * q^67 + 18 * q^68 + 24 * q^70 - 12 * q^73 + 3 * q^74 - 87 * q^76 + 57 * q^77 - 48 * q^79 - 42 * q^80 - 42 * q^82 - 12 * q^83 - 36 * q^85 + 30 * q^86 + 30 * q^88 + 9 * q^89 - 18 * q^91 + 48 * q^92 + 33 * q^94 - 30 * q^95 - 3 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.135052	+	0.765917i	−0.0954961	+	0.541585i	0.899098	+	0.437747i	$0.144223\pi$
$2$	−0.135052	+	0.765917i	−0.0954961	+	0.541585i	−0.994594	+	0.103838i	$0.966888\pi$
$3$		0			0
$3$		0			0
$4$	1.31100	+	0.477163i	0.655498	+	0.238582i
$5$	−1.82039	+	1.52749i	−0.814102	+	0.683113i	−0.951583	−	0.307392i	$-0.900544\pi$
$5$	−1.82039	+	1.52749i	−0.814102	+	0.683113i	0.137481	+	0.990504i	$0.456099\pi$
$6$		0			0
$7$	2.35052	−	0.855521i	0.888415	−	0.323357i	0.142814	−	0.989750i	$-0.454385\pi$
$7$	2.35052	−	0.855521i	0.888415	−	0.323357i	0.745601	+	0.666393i	$0.232163\pi$
$8$	−1.32025	+	2.28674i	−0.466780	+	0.808486i
$9$		0			0
$10$	−0.924081	−	1.60056i	−0.292220	−	0.506140i
$11$	−2.40643	−	2.01923i	−0.725566	−	0.608822i	0.203353	−	0.979105i	$-0.434816\pi$
$11$	−2.40643	−	2.01923i	−0.725566	−	0.608822i	−0.928919	+	0.370284i	$0.879261\pi$
$12$		0			0
$13$	0.232103	+	1.31632i	0.0643739	+	0.365082i	0.999929	+	0.0119022i	$0.00378867\pi$
$13$	0.232103	+	1.31632i	0.0643739	+	0.365082i	−0.935555	+	0.353180i	$0.885100\pi$
$14$	0.337815	+	1.91585i	0.0902850	+	0.512031i
$15$		0			0
$16$	0.564314	+	0.473515i	0.141078	+	0.118379i
$17$	3.13726	+	5.43389i	0.760897	+	1.31791i	0.942389	+	0.334520i	$0.108574\pi$
$17$	3.13726	+	5.43389i	0.760897	+	1.31791i	−0.181492	+	0.983392i	$0.558093\pi$
$18$		0			0
$19$	−4.03234	+	6.98422i	−0.925083	+	1.60229i	−0.133656	+	0.991028i	$0.542672\pi$
$19$	−4.03234	+	6.98422i	−0.925083	+	1.60229i	−0.791427	+	0.611263i	$0.790662\pi$
$20$	−3.11538	+	1.13391i	−0.696620	+	0.253549i
$21$		0			0
$22$	1.87156	−	1.57042i	0.399018	−	0.334815i
$23$	3.81008	+	1.38675i	0.794456	+	0.289158i	0.707187	−	0.707027i	$-0.249964\pi$
$23$	3.81008	+	1.38675i	0.794456	+	0.289158i	0.0872688	+	0.996185i	$0.472186\pi$
$24$		0			0
$25$	0.112355	−	0.637198i	0.0224711	−	0.127440i
$26$	−1.03954			−0.203871
$27$		0			0
$28$	3.48975			0.659501
$29$	1.61271	−	9.14613i	0.299473	−	1.69839i	−0.348972	−	0.937133i	$-0.613469\pi$
$29$	1.61271	−	9.14613i	0.299473	−	1.69839i	0.648445	−	0.761261i	$-0.275420\pi$
$30$		0			0
$31$	−2.66104	−	0.968540i	−0.477937	−	0.173955i	0.0918074	−	0.995777i	$-0.470736\pi$
$31$	−2.66104	−	0.968540i	−0.477937	−	0.173955i	−0.569744	+	0.821822i	$0.692958\pi$
$32$	−4.48437	+	3.76284i	−0.792733	+	0.665182i
$33$		0			0
$34$	−4.58560	+	1.66902i	−0.786424	+	0.286235i
$35$	−2.97207	+	5.14778i	−0.502372	+	0.870133i
$36$		0			0
$37$	−2.76596	−	4.79078i	−0.454720	−	0.787599i	0.543952	−	0.839117i	$-0.316927\pi$
$37$	−2.76596	−	4.79078i	−0.454720	−	0.787599i	−0.998672	+	0.0515178i	$0.983594\pi$
$38$	−4.80476	−	4.03167i	−0.779435	−	0.654024i
$39$		0			0
$40$	−1.08960	−	6.17943i	−0.172281	−	0.977053i
$41$	1.23390	+	6.99781i	0.192703	+	1.09287i	0.915652	+	0.401972i	$0.131675\pi$
$41$	1.23390	+	6.99781i	0.192703	+	1.09287i	−0.722949	+	0.690902i	$0.757214\pi$
$42$		0			0
$43$	1.79017	+	1.50213i	0.272998	+	0.229073i	0.769000	−	0.639249i	$-0.220755\pi$
$43$	1.79017	+	1.50213i	0.272998	+	0.229073i	−0.496002	+	0.868322i	$0.665199\pi$
$44$	−2.19131	−	3.79547i	−0.330353	−	0.572188i
$45$		0			0
$46$	−1.57670	+	2.73092i	−0.232471	+	0.402652i
$47$	−4.33594	+	1.57815i	−0.632461	+	0.230197i	−0.638302	−	0.769786i	$-0.720363\pi$
$47$	−4.33594	+	1.57815i	−0.632461	+	0.230197i	0.00584102	+	0.999983i	$0.498141\pi$
$48$		0			0
$49$	−0.569260	+	0.477666i	−0.0813229	+	0.0682380i
$50$	0.472867	+	0.172110i	0.0668735	+	0.0243400i
$51$		0			0
$52$	−0.323815	+	1.83645i	−0.0449050	+	0.254669i
$53$	−0.135496			−0.0186118			−0.00930588	−	0.999957i	$-0.502962\pi$
$53$	−0.135496			−0.0186118			−0.00930588	+	0.999957i	$0.502962\pi$
$54$		0			0
$55$	7.46499			1.00658
$56$	−1.14693	+	6.50455i	−0.153265	+	0.869207i
$57$		0			0
$58$	6.78738	+	2.47040i	0.891226	+	0.324380i
$59$	3.06321	−	2.57034i	0.398796	−	0.334630i	−0.421232	−	0.906953i	$-0.638402\pi$
$59$	3.06321	−	2.57034i	0.398796	−	0.334630i	0.820028	+	0.572323i	$0.193958\pi$
$60$		0			0
$61$	−0.321185	+	0.116902i	−0.0411235	+	0.0149677i	−0.362500	−	0.931984i	$-0.618077\pi$
$61$	−0.321185	+	0.116902i	−0.0411235	+	0.0149677i	0.321376	+	0.946952i	$0.395855\pi$
$62$	1.10120	−	1.90733i	0.139852	−	0.242232i
$63$		0			0
$64$	−1.53974	−	2.66690i	−0.192467	−	0.333363i
$65$	−2.43319	−	2.04168i	−0.301799	−	0.253240i
$66$		0			0
$67$	1.75783	+	9.96913i	0.214753	+	1.21792i	0.881335	+	0.472492i	$0.156645\pi$
$67$	1.75783	+	9.96913i	0.214753	+	1.21792i	−0.666582	+	0.745431i	$0.732244\pi$
$68$	1.52008	+	8.62079i	0.184337	+	1.04542i
$69$		0			0
$70$	−3.54139	−	2.97158i	−0.423276	−	0.355171i
$71$	4.09540	+	7.09344i	0.486035	+	0.841837i	0.999871	−	0.0160515i	$-0.00510955\pi$
$71$	4.09540	+	7.09344i	0.486035	+	0.841837i	−0.513837	+	0.857888i	$0.671776\pi$
$72$		0			0
$73$	6.15722	−	10.6646i	0.720648	−	1.24820i	−0.240092	−	0.970750i	$-0.577178\pi$
$73$	6.15722	−	10.6646i	0.720648	−	1.24820i	0.960740	−	0.277449i	$-0.0894890\pi$
$74$	4.04288	−	1.47149i	0.469976	−	0.171057i
$75$		0			0
$76$	−8.61900	+	7.23220i	−0.988667	+	0.829590i
$77$	−7.38387	−	2.68751i	−0.841470	−	0.306270i
$78$		0			0
$79$	0.708606	−	4.01870i	0.0797244	−	0.452139i	−0.918646	−	0.395081i	$-0.870717\pi$
$79$	0.708606	−	4.01870i	0.0797244	−	0.452139i	0.998371	−	0.0570587i	$-0.0181722\pi$
$80$	−1.75056			−0.195718
$81$		0			0
$82$	−5.52638			−0.610287
$83$	−0.158580	+	0.899354i	−0.0174065	+	0.0987169i	−0.992273	−	0.124071i	$-0.960405\pi$
$83$	−0.158580	+	0.899354i	−0.0174065	+	0.0987169i	0.974867	+	0.222788i	$0.0715159\pi$
$84$		0			0
$85$	−14.0112	−	5.09967i	−1.51973	−	0.553137i
$86$	−1.39227	+	1.16826i	−0.150133	+	0.125976i
$87$		0			0
$88$	7.79456	−	2.83699i	0.830903	−	0.302424i
$89$	−1.86437	+	3.22919i	−0.197623	+	0.342293i	−0.947757	−	0.318992i	$-0.896656\pi$
$89$	−1.86437	+	3.22919i	−0.197623	+	0.342293i	0.750134	+	0.661286i	$0.229989\pi$
$90$		0			0
$91$	1.67171	+	2.89548i	0.175243	+	0.303529i
$92$	4.33328	+	3.63606i	0.451776	+	0.379085i
$93$		0			0
$94$	−0.623157	−	3.53410i	−0.0642737	−	0.364514i
$95$	−3.32788	−	18.8734i	−0.341433	−	1.93636i
$96$		0			0
$97$	−4.59343	−	3.85434i	−0.466392	−	0.391349i	0.379084	−	0.925362i	$-0.376239\pi$
$97$	−4.59343	−	3.85434i	−0.466392	−	0.391349i	−0.845476	+	0.534013i	$0.820683\pi$
$98$	−0.288973	−	0.500515i	−0.0291907	−	0.0505597i
$99$		0			0
$100$	0.451345	−	0.781752i	0.0451345	−	0.0781752i
$101$	9.60527	−	3.49603i	0.955760	−	0.347868i	0.183389	−	0.983040i	$-0.441293\pi$
$101$	9.60527	−	3.49603i	0.955760	−	0.347868i	0.772371	+	0.635172i	$0.219071\pi$
$102$		0			0
$103$	6.53747	−	5.48559i	0.644156	−	0.540511i	−0.261135	−	0.965302i	$-0.584097\pi$
$103$	6.53747	−	5.48559i	0.644156	−	0.540511i	0.905291	+	0.424791i	$0.139652\pi$
$104$	−3.31653	−	1.20712i	−0.325213	−	0.118368i
$105$		0			0
$106$	0.0182989	−	0.103778i	0.00177735	−	0.0100799i
$107$	7.74500			0.748738			0.374369	−	0.927280i	$-0.377859\pi$
$107$	7.74500			0.748738			0.374369	+	0.927280i	$0.377859\pi$
$108$		0			0
$109$	1.25438			0.120148			0.0600738	−	0.998194i	$-0.480866\pi$
$109$	1.25438			0.120148			0.0600738	+	0.998194i	$0.480866\pi$
$110$	−1.00816	+	5.71756i	−0.0961243	+	0.545148i
$111$		0			0
$112$	1.73154	+	0.630227i	0.163615	+	0.0595509i
$113$	13.6055	−	11.4164i	1.27990	−	1.07396i	0.286644	−	0.958037i	$-0.407460\pi$
$113$	13.6055	−	11.4164i	1.27990	−	1.07396i	0.993258	−	0.115928i	$-0.0369840\pi$
$114$		0			0
$115$	−9.05407	+	3.29541i	−0.844296	+	0.307299i
$116$	6.47846	−	11.2210i	0.601509	−	1.04185i
$117$		0			0
$118$	1.55497	+	2.69329i	0.143147	+	0.247938i
$119$	12.0230	+	10.0885i	1.10215	+	0.924812i
$120$		0			0
$121$	−0.196534	−	1.11460i	−0.0178667	−	0.101327i
$122$	−0.0461605	−	0.261789i	−0.00417917	−	0.0237013i
$123$		0			0
$124$	−3.02646	−	2.53950i	−0.271784	−	0.228054i
$125$	−5.17209	−	8.95832i	−0.462606	−	0.801256i
$126$		0			0
$127$	1.98279	−	3.43429i	0.175944	−	0.304744i	−0.764543	−	0.644572i	$-0.777036\pi$
$127$	1.98279	−	3.43429i	0.175944	−	0.304744i	0.940488	+	0.339828i	$0.110369\pi$
$128$	−8.75122	+	3.18518i	−0.773506	+	0.281533i
$129$		0			0
$130$	1.89237	−	1.58788i	0.165972	−	0.139267i
$131$	−0.0963170	−	0.0350565i	−0.00841525	−	0.00306290i	0.337809	−	0.941215i	$-0.390314\pi$
$131$	−0.0963170	−	0.0350565i	−0.00841525	−	0.00306290i	−0.346224	+	0.938152i	$0.612536\pi$
$132$		0			0
$133$	−3.50297	+	19.8663i	−0.303746	+	1.72263i
$134$	−7.87292			−0.680117
$135$		0			0
$136$	−16.5679			−1.42068
$137$	1.32312	−	7.50379i	0.113042	−	0.641092i	−0.874659	−	0.484738i	$-0.838915\pi$
$137$	1.32312	−	7.50379i	0.113042	−	0.641092i	0.987701	−	0.156354i	$-0.0499740\pi$
$138$		0			0
$139$	9.81108	+	3.57094i	0.832165	+	0.302883i	0.722747	−	0.691113i	$-0.242879\pi$
$139$	9.81108	+	3.57094i	0.832165	+	0.302883i	0.109418	+	0.993996i	$0.465101\pi$
$140$	−6.35270	+	5.33055i	−0.536901	+	0.450514i
$141$		0			0
$142$	−5.98608	+	2.17875i	−0.502341	+	0.182837i
$143$	2.09943	−	3.63631i	0.175563	−	0.304084i
$144$		0			0
$145$	11.0348	+	19.1129i	0.916394	+	1.58724i
$146$	7.33667	+	6.15619i	0.607187	+	0.509490i
$147$		0			0
$148$	−1.34017	−	7.60050i	−0.110162	−	0.624757i
$149$	−1.56849	−	8.89535i	−0.128496	−	0.728736i	−0.979170	−	0.203042i	$-0.934917\pi$
$149$	−1.56849	−	8.89535i	−0.128496	−	0.728736i	0.850674	−	0.525693i	$-0.176194\pi$
$150$		0			0
$151$	18.3011	+	15.3564i	1.48932	+	1.24969i	0.895475	+	0.445112i	$0.146836\pi$
$151$	18.3011	+	15.3564i	1.48932	+	1.24969i	0.593848	+	0.804578i	$0.297608\pi$
$152$	−10.6474	−	18.4419i	−0.863620	−	1.49583i
$153$		0			0
$154$	3.05561	−	5.29248i	0.246228	−	0.426480i
$155$	6.32356	−	2.30159i	0.507920	−	0.184868i
$156$		0			0
$157$	2.07750	−	1.74323i	0.165803	−	0.139125i	−0.556111	−	0.831108i	$-0.687707\pi$
$157$	2.07750	−	1.74323i	0.165803	−	0.139125i	0.721914	+	0.691983i	$0.243263\pi$
$158$	2.98229	+	1.08547i	0.237258	+	0.0863550i
$159$		0			0
$160$	2.41562	−	13.6996i	0.190971	−	1.08305i
$161$	10.1421			0.799308
$162$		0			0
$163$	−22.0489			−1.72701			−0.863504	−	0.504343i	$-0.831735\pi$
$163$	−22.0489			−1.72701			−0.863504	+	0.504343i	$0.831735\pi$
$164$	−1.72146	+	9.76287i	−0.134423	+	0.762352i
$165$		0			0
$166$	−0.667414	−	0.242919i	−0.0518014	−	0.0188542i
$167$	6.85671	−	5.75347i	0.530589	−	0.445217i	−0.337716	−	0.941248i	$-0.609654\pi$
$167$	6.85671	−	5.75347i	0.530589	−	0.445217i	0.868305	+	0.496031i	$0.165210\pi$
$168$		0			0
$169$	10.5372	−	3.83522i	0.810551	−	0.295017i
$170$	5.79816	−	10.0427i	0.444699	−	0.770241i
$171$		0			0
$172$	1.63014	+	2.82349i	0.124297	+	0.215289i
$173$	2.01795	+	1.69326i	0.153422	+	0.128736i	0.716268	−	0.697826i	$-0.245849\pi$
$173$	2.01795	+	1.69326i	0.153422	+	0.128736i	−0.562846	+	0.826562i	$0.690293\pi$
$174$		0			0
$175$	−0.281043	−	1.59387i	−0.0212448	−	0.120485i
$176$	−0.401843	−	2.27896i	−0.0302900	−	0.171783i
$177$		0			0
$178$	−2.22150	−	1.86406i	−0.166509	−	0.139717i
$179$	−1.84227	−	3.19090i	−0.137697	−	0.238499i	0.788927	−	0.614487i	$-0.210637\pi$
$179$	−1.84227	−	3.19090i	−0.137697	−	0.238499i	−0.926625	+	0.375988i	$0.877303\pi$
$180$		0			0
$181$	0.134255	−	0.232536i	0.00997906	−	0.0172842i	−0.860993	−	0.508617i	$-0.830157\pi$
$181$	0.134255	−	0.232536i	0.00997906	−	0.0172842i	0.870972	+	0.491333i	$0.163490\pi$
$182$	−2.44347	+	0.889349i	−0.181122	+	0.0659229i
$183$		0			0
$184$	−8.20141	+	6.88180i	−0.604616	+	0.507333i
$185$	12.3530	+	4.49611i	0.908208	+	0.330561i
$186$		0			0
$187$	3.42271	−	19.4111i	0.250293	−	1.41948i
$188$	−6.43743			−0.469498
$189$		0			0
$190$	14.9049			1.08131
$191$	−0.416406	+	2.36155i	−0.0301301	+	0.170876i	−0.996160	−	0.0875554i	$-0.972095\pi$
$191$	−0.416406	+	2.36155i	−0.0301301	+	0.170876i	0.966030	+	0.258432i	$0.0832056\pi$
$192$		0			0
$193$	−0.466278	−	0.169711i	−0.0335634	−	0.0122161i	0.325184	−	0.945651i	$-0.394574\pi$
$193$	−0.466278	−	0.169711i	−0.0335634	−	0.0122161i	−0.358747	+	0.933435i	$0.616796\pi$
$194$	3.57246	−	2.99765i	0.256488	−	0.215219i
$195$		0			0
$196$	−0.974222	+	0.354588i	−0.0695873	+	0.0253277i
$197$	11.0734	−	19.1797i	0.788946	−	1.36649i	−0.137667	−	0.990479i	$-0.543960\pi$
$197$	11.0734	−	19.1797i	0.788946	−	1.36649i	0.926613	−	0.376016i	$-0.122706\pi$
$198$		0			0
$199$	−1.06624	−	1.84677i	−0.0755834	−	0.130914i	0.825756	−	0.564027i	$-0.190749\pi$
$199$	−1.06624	−	1.84677i	−0.0755834	−	0.130914i	−0.901340	+	0.433113i	$0.857415\pi$
$200$	1.30877	+	1.09819i	0.0925442	+	0.0776538i
$201$		0			0
$202$	1.38046	+	7.82898i	0.0971289	+	0.550845i
$203$	−4.03399	−	22.8779i	−0.283131	−	1.60572i
$204$		0			0
$205$	−12.9352	−	10.8540i	−0.903437	−	0.758073i
$206$	3.31861	+	5.74800i	0.231218	+	0.400482i
$207$		0			0
$208$	−0.492320	+	0.852724i	−0.0341363	+	0.0591257i
$209$	23.8063	−	8.66480i	1.64672	−	0.599357i
$210$		0			0
$211$	15.3275	−	12.8613i	1.05519	−	0.885406i	0.0615569	−	0.998104i	$-0.480393\pi$
$211$	15.3275	−	12.8613i	1.05519	−	0.885406i	0.993629	+	0.112697i	$0.0359490\pi$
$212$	−0.177634	−	0.0646536i	−0.0122000	−	0.00444043i
$213$		0			0
$214$	−1.04598	+	5.93203i	−0.0715015	+	0.405505i
$215$	−5.55329			−0.378731
$216$		0			0
$217$	−7.08345			−0.480856
$218$	−0.169406	+	0.960749i	−0.0114736	+	0.0650701i
$219$		0			0
$220$	9.78657	+	3.56202i	0.659810	+	0.240151i
$221$	−6.42459	+	5.39087i	−0.432165	+	0.362629i
$222$		0			0
$223$	12.4777	−	4.54150i	0.835567	−	0.304122i	0.111425	−	0.993773i	$-0.464458\pi$
$223$	12.4777	−	4.54150i	0.835567	−	0.304122i	0.724142	+	0.689651i	$0.242236\pi$
$224$	−7.32144	+	12.6811i	−0.489185	+	0.847292i
$225$		0			0
$226$	6.90656	+	11.9625i	0.459418	+	0.795735i
$227$	−9.55329	−	8.01616i	−0.634074	−	0.532051i	0.268118	−	0.963386i	$-0.413598\pi$
$227$	−9.55329	−	8.01616i	−0.634074	−	0.532051i	−0.902192	+	0.431335i	$0.858043\pi$
$228$		0			0
$229$	4.45608	+	25.2717i	0.294466	+	1.67000i	0.669364	+	0.742935i	$0.266567\pi$
$229$	4.45608	+	25.2717i	0.294466	+	1.67000i	−0.374898	+	0.927066i	$0.622322\pi$
$230$	−1.30124	−	7.37971i	−0.0858014	−	0.486604i
$231$		0			0
$232$	18.7857	+	15.7631i	1.23334	+	1.03490i
$233$	2.69821	+	4.67344i	0.176766	+	0.306167i	0.940771	−	0.339043i	$-0.110103\pi$
$233$	2.69821	+	4.67344i	0.176766	+	0.306167i	−0.764005	+	0.645210i	$0.776770\pi$
$234$		0			0
$235$	5.48248	−	9.49593i	0.357637	−	0.619446i
$236$	5.24233	−	1.90805i	0.341247	−	0.124204i
$237$		0			0
$238$	−9.35069	+	7.84616i	−0.606115	+	0.508591i
$239$	−7.86621	−	2.86307i	−0.508823	−	0.185196i	0.0748353	−	0.997196i	$-0.476157\pi$
$239$	−7.86621	−	2.86307i	−0.508823	−	0.185196i	−0.583658	+	0.812000i	$0.698379\pi$
$240$		0			0
$241$	−0.0767854	+	0.435472i	−0.00494618	+	0.0280512i	−0.987181	−	0.159605i	$-0.948978\pi$
$241$	−0.0767854	+	0.435472i	−0.00494618	+	0.0280512i	0.982235	+	0.187656i	$0.0600891\pi$
$242$	0.880231			0.0565834
$243$		0			0
$244$	−0.476854			−0.0305274
$245$	0.306646	−	1.73907i	0.0195909	−	0.111105i
$246$		0			0
$247$	−10.1294	−	3.68681i	−0.644520	−	0.234586i
$248$	5.72805	−	4.80640i	0.363731	−	0.305207i
$249$		0			0
$250$	7.55983	−	2.75155i	0.478125	−	0.174023i
$251$	−8.51427	+	14.7471i	−0.537416	+	0.930832i	0.461626	+	0.887074i	$0.347266\pi$
$251$	−8.51427	+	14.7471i	−0.537416	+	0.930832i	−0.999042	+	0.0437571i	$0.986067\pi$
$252$		0			0
$253$	−6.36850	−	11.0306i	−0.400384	−	0.693486i
$254$	2.36260	+	1.98246i	0.148243	+	0.124391i
$255$		0			0
$256$	−2.32721	−	13.1983i	−0.145451	−	0.824891i
$257$	3.62520	+	20.5596i	0.226134	+	1.28247i	0.860505	+	0.509441i	$0.170148\pi$
$257$	3.62520	+	20.5596i	0.226134	+	1.28247i	−0.634371	+	0.773028i	$0.718741\pi$
$258$		0			0
$259$	−10.6001	−	8.89450i	−0.658656	−	0.552678i
$260$	−2.21568	−	3.83767i	−0.137411	−	0.238002i
$261$		0			0
$262$	0.0398582	−	0.0690364i	0.00246245	−	0.00426508i
$263$	−18.2221	+	6.63230i	−1.12362	+	0.408965i	−0.835973	−	0.548770i	$-0.815096\pi$
$263$	−18.2221	+	6.63230i	−1.12362	+	0.408965i	−0.287650	+	0.957736i	$0.592874\pi$
$264$		0			0
$265$	0.246655	−	0.206968i	0.0151519	−	0.0127139i
$266$	−14.7429	−	5.36597i	−0.903945	−	0.329009i
$267$		0			0
$268$	−2.45240	+	13.9083i	−0.149804	+	0.849582i
$269$	18.6791			1.13889			0.569443	−	0.822031i	$-0.307159\pi$
$269$	18.6791			1.13889			0.569443	+	0.822031i	$0.307159\pi$
$270$		0			0
$271$	12.9378			0.785917			0.392958	−	0.919556i	$-0.371452\pi$
$271$	12.9378			0.785917			0.392958	+	0.919556i	$0.371452\pi$
$272$	−0.802633	+	4.55196i	−0.0486668	+	0.276003i
$273$		0			0
$274$	5.56859	+	2.02680i	0.336411	+	0.122444i
$275$	−1.55703	+	1.30650i	−0.0938923	+	0.0787850i
$276$		0			0
$277$	−9.81164	+	3.57114i	−0.589524	+	0.214569i	−0.619520	−	0.784981i	$-0.712673\pi$
$277$	−9.81164	+	3.57114i	−0.589524	+	0.214569i	0.0299959	+	0.999550i	$0.490451\pi$
$278$	−4.06005	+	7.03221i	−0.243505	+	0.421764i
$279$		0			0
$280$	−7.84776	−	13.5927i	−0.468994	−	0.812321i
$281$	10.9895	+	9.22130i	0.655580	+	0.550097i	0.908758	−	0.417323i	$-0.137032\pi$
$281$	10.9895	+	9.22130i	0.655580	+	0.550097i	−0.253179	+	0.967420i	$0.581476\pi$
$282$		0			0
$283$	−3.24594	−	18.4086i	−0.192951	−	1.09428i	−0.915307	−	0.402758i	$-0.868052\pi$
$283$	−3.24594	−	18.4086i	−0.192951	−	1.09428i	0.722356	−	0.691522i	$-0.243059\pi$
$284$	1.98432	+	11.2536i	0.117748	+	0.667781i
$285$		0			0
$286$	2.50158	+	2.09908i	0.147922	+	0.124121i
$287$	8.88709	+	15.3929i	0.524588	+	0.908614i
$288$		0			0
$289$	−11.1848	+	19.3726i	−0.657929	+	1.13957i
$290$	−16.1292	+	5.87054i	−0.947138	+	0.344730i
$291$		0			0
$292$	13.1609	−	11.0433i	0.770181	−	0.646258i
$293$	10.1376	+	3.68978i	0.592243	+	0.215559i	0.620716	−	0.784036i	$-0.286842\pi$
$293$	10.1376	+	3.68978i	0.592243	+	0.215559i	−0.0284724	+	0.999595i	$0.509064\pi$
$294$		0			0
$295$	−1.65007	+	9.35803i	−0.0960710	+	0.544846i
$296$	14.6070			0.849017
$297$		0			0
$298$	7.02493			0.406943
$299$	−0.941086	+	5.33716i	−0.0544244	+	0.308656i
$300$		0			0
$301$	5.49295	+	1.99927i	0.316608	+	0.115236i
$302$	−14.2334	+	11.9432i	−0.819038	+	0.687254i
$303$		0			0
$304$	−5.58264	+	2.03192i	−0.320187	+	0.116538i
$305$	0.406116	−	0.703413i	0.0232541	−	0.0402773i
$306$		0			0
$307$	−0.0248747	−	0.0430843i	−0.00141967	−	0.00245895i	0.865315	−	0.501229i	$-0.167119\pi$
$307$	−0.0248747	−	0.0430843i	−0.00141967	−	0.00245895i	−0.866734	+	0.498770i	$0.833785\pi$
$308$	−8.39784	−	7.04662i	−0.478511	−	0.401519i
$309$		0			0
$310$	0.908816	+	5.15415i	0.0516173	+	0.292736i
$311$	2.29831	+	13.0344i	0.130325	+	0.739112i	0.978001	+	0.208598i	$0.0668900\pi$
$311$	2.29831	+	13.0344i	0.130325	+	0.739112i	−0.847676	+	0.530514i	$0.821999\pi$
$312$		0			0
$313$	−11.5542	−	9.69511i	−0.653081	−	0.548000i	0.254923	−	0.966961i	$-0.417950\pi$
$313$	−11.5542	−	9.69511i	−0.653081	−	0.548000i	−0.908004	+	0.418961i	$0.862394\pi$
$314$	1.05460	+	1.82662i	0.0595145	+	0.103082i
$315$		0			0
$316$	2.84656	−	4.93038i	0.160131	−	0.277356i
$317$	−8.11032	+	2.95192i	−0.455521	+	0.165796i	−0.559582	−	0.828775i	$-0.689038\pi$
$317$	−8.11032	+	2.95192i	−0.455521	+	0.165796i	0.104061	+	0.994571i	$0.466816\pi$
$318$		0			0
$319$	−22.3491	+	18.7531i	−1.25131	+	1.04997i
$320$	6.87658	+	2.50287i	0.384412	+	0.139915i
$321$		0			0
$322$	−1.36971	+	7.76799i	−0.0763307	+	0.432893i
$323$	−50.6020			−2.81557
$324$		0			0
$325$	0.864837			0.0479725
$326$	2.97775	−	16.8877i	0.164922	−	0.935321i
$327$		0			0
$328$	−17.6313	−	6.41725i	−0.973523	−	0.354334i
$329$	−8.84158	+	7.41897i	−0.487452	+	0.409021i
$330$		0			0
$331$	−29.1544	+	10.6113i	−1.60247	+	0.583252i	−0.979931	−	0.199336i	$-0.936121\pi$
$331$	−29.1544	+	10.6113i	−1.60247	+	0.583252i	−0.622540	+	0.782588i	$0.713899\pi$
$332$	−0.637037	+	1.10338i	−0.0349619	+	0.0605559i
$333$		0			0
$334$	3.48067	+	6.02869i	0.190454	+	0.329875i
$335$	−18.4276	−	15.4626i	−1.00681	−	0.844813i
$336$		0			0
$337$	−4.14452	−	23.5047i	−0.225766	−	1.28038i	−0.861215	−	0.508241i	$-0.830296\pi$
$337$	−4.14452	−	23.5047i	−0.225766	−	1.28038i	0.635449	−	0.772143i	$-0.280815\pi$
$338$	1.51439	+	8.58855i	0.0823721	+	0.467155i
$339$		0			0
$340$	−15.9353	−	13.3713i	−0.864212	−	0.725160i
$341$	4.44790	+	7.70399i	0.240867	+	0.417194i
$342$		0			0
$343$	−9.68422	+	16.7736i	−0.522899	+	0.905688i
$344$	−5.79847	+	2.11047i	−0.312632	+	0.113789i
$345$		0			0
$346$	−1.56943	+	1.31691i	−0.0843729	+	0.0707973i
$347$	−20.5898	−	7.49409i	−1.10532	−	0.402304i	−0.276045	−	0.961145i	$-0.589024\pi$
$347$	−20.5898	−	7.49409i	−1.10532	−	0.402304i	−0.829275	+	0.558841i	$0.811246\pi$
$348$		0			0
$349$	2.75178	−	15.6061i	0.147299	−	0.835376i	−0.818193	−	0.574944i	$-0.805024\pi$
$349$	2.75178	−	15.6061i	0.147299	−	0.835376i	0.965492	−	0.260432i	$-0.0838651\pi$
$350$	1.25873			0.0672819
$351$		0			0
$352$	18.3894			0.980157
$353$	2.24126	−	12.7108i	0.119290	−	0.676528i	−0.865246	−	0.501347i	$-0.832838\pi$
$353$	2.24126	−	12.7108i	0.119290	−	0.676528i	0.984536	−	0.175181i	$-0.0560509\pi$
$354$		0			0
$355$	−18.2904	−	6.65715i	−0.970751	−	0.353325i
$356$	−3.98503	+	3.34384i	−0.211206	+	0.177223i
$357$		0			0
$358$	2.69276	−	0.980086i	0.142317	−	0.0517991i
$359$	−12.9142	+	22.3681i	−0.681588	+	1.18054i	0.292909	+	0.956140i	$0.405377\pi$
$359$	−12.9142	+	22.3681i	−0.681588	+	1.18054i	−0.974496	+	0.224404i	$0.927956\pi$
$360$		0			0
$361$	−23.0196	−	39.8711i	−1.21156	−	2.09848i
$362$	0.159972	+	0.134232i	0.00840793	+	0.00705509i
$363$		0			0
$364$	0.809983	+	4.59364i	0.0424546	+	0.240772i
$365$	5.08153	+	28.8188i	0.265980	+	1.50845i
$366$		0			0
$367$	12.2372	+	10.2683i	0.638778	+	0.535999i	0.903643	−	0.428287i	$-0.140883\pi$
$367$	12.2372	+	10.2683i	0.638778	+	0.535999i	−0.264864	+	0.964286i	$0.585327\pi$
$368$	1.49343	+	2.58669i	0.0778503	+	0.134841i
$369$		0			0
$370$	−5.11194	+	8.85413i	−0.265757	+	0.460304i
$371$	−0.318486	+	0.115919i	−0.0165350	+	0.00601824i
$372$		0			0
$373$	1.39923	−	1.17409i	0.0724494	−	0.0607923i	−0.605844	−	0.795584i	$-0.707164\pi$
$373$	1.39923	−	1.17409i	0.0724494	−	0.0607923i	0.678293	+	0.734791i	$0.262720\pi$
$374$	14.4051	+	5.24302i	0.744869	+	0.271110i
$375$		0			0
$376$	2.11570	−	11.9987i	0.109109	−	0.618787i
$377$	12.4136			0.639332
$378$		0			0
$379$	1.14694			0.0589141			0.0294571	−	0.999566i	$-0.490622\pi$
$379$	1.14694			0.0589141			0.0294571	+	0.999566i	$0.490622\pi$
$380$	4.64283	−	26.3308i	0.238172	−	1.35074i
$381$		0			0
$382$	−1.75252	−	0.637865i	−0.0896666	−	0.0326360i
$383$	16.7209	−	14.0305i	0.854397	−	0.716924i	−0.106357	−	0.994328i	$-0.533919\pi$
$383$	16.7209	−	14.0305i	0.854397	−	0.716924i	0.960753	+	0.277404i	$0.0894741\pi$
$384$		0			0
$385$	17.5466	−	6.38646i	0.894260	−	0.325484i
$386$	0.192957	−	0.334210i	0.00982123	−	0.0170109i
$387$		0			0
$388$	−4.18281	−	7.24484i	−0.212350	−	0.367801i
$389$	−20.0674	−	16.8386i	−1.01746	−	0.853750i	−0.0281533	−	0.999604i	$-0.508963\pi$
$389$	−20.0674	−	16.8386i	−1.01746	−	0.853750i	−0.989306	+	0.145854i	$0.953407\pi$
$390$		0			0
$391$	4.41772	+	25.0541i	0.223414	+	1.26704i
$392$	−0.340733	−	1.93239i	−0.0172096	−	0.0976005i
$393$		0			0
$394$	13.1945	+	11.0715i	0.664732	+	0.557776i
$395$	4.84858	+	8.39798i	0.243958	+	0.422548i
$396$		0			0
$397$	−2.09915	+	3.63584i	−0.105353	+	0.182478i	−0.913883	−	0.405979i	$-0.866931\pi$
$397$	−2.09915	+	3.63584i	−0.105353	+	0.182478i	0.808529	+	0.588456i	$0.200264\pi$
$398$	1.55847	−	0.567237i	0.0781191	−	0.0284330i
$399$		0			0
$400$	0.365127	−	0.306378i	0.0182563	−	0.0153189i
$401$	7.35761	+	2.67795i	0.367422	+	0.133731i	0.519131	−	0.854695i	$-0.326256\pi$
$401$	7.35761	+	2.67795i	0.367422	+	0.133731i	−0.151709	+	0.988425i	$0.548478\pi$
$402$		0			0
$403$	0.657275	−	3.72759i	0.0327412	−	0.185685i
$404$	14.2606			0.709493
$405$		0			0
$406$	18.0674			0.896669
$407$	−3.01762	+	17.1138i	−0.149578	+	0.848298i
$408$		0			0
$409$	16.3779	+	5.96107i	0.809835	+	0.294756i	0.713556	−	0.700599i	$-0.247084\pi$
$409$	16.3779	+	5.96107i	0.809835	+	0.294756i	0.0962793	+	0.995354i	$0.469306\pi$
$410$	10.0602	−	8.44147i	0.496836	−	0.416895i
$411$		0			0
$412$	11.1881	−	4.07214i	0.551199	−	0.200620i
$413$	5.00118	−	8.66229i	0.246092	−	0.426243i
$414$		0			0
$415$	−1.08507	−	1.87940i	−0.0532642	−	0.0922563i
$416$	−5.99395	−	5.02952i	−0.293877	−	0.246592i
$417$		0			0
$418$	3.42143	+	19.4039i	0.167347	+	0.949074i
$419$	1.99403	+	11.3087i	0.0974148	+	0.552467i	0.993981	+	0.109556i	$0.0349430\pi$
$419$	1.99403	+	11.3087i	0.0974148	+	0.552467i	−0.896566	+	0.442911i	$0.853946\pi$
$420$		0			0
$421$	5.58540	+	4.68671i	0.272216	+	0.228416i	0.768668	−	0.639648i	$-0.220920\pi$
$421$	5.58540	+	4.68671i	0.272216	+	0.228416i	−0.496452	+	0.868064i	$0.665364\pi$
$422$	7.78066	+	13.4765i	0.378757	+	0.656026i
$423$		0			0
$424$	0.178889	−	0.309844i	0.00868759	−	0.0150474i
$425$	3.81495	−	1.38853i	0.185052	−	0.0673536i
$426$		0			0
$427$	−0.654942	+	0.549561i	−0.0316949	+	0.0265951i
$428$	10.1537	+	3.69563i	0.490796	+	0.178635i
$429$		0			0
$430$	0.749982	−	4.25336i	0.0361673	−	0.205115i
$431$	0.389084			0.0187415			0.00937075	−	0.999956i	$-0.497017\pi$
$431$	0.389084			0.0187415			0.00937075	+	0.999956i	$0.497017\pi$
$432$		0			0
$433$	24.1011			1.15822			0.579112	−	0.815248i	$-0.303400\pi$
$433$	24.1011			1.15822			0.579112	+	0.815248i	$0.303400\pi$
$434$	0.956633	−	5.42533i	0.0459198	−	0.260424i
$435$		0			0
$436$	1.64448	+	0.598543i	0.0787564	+	0.0286650i
$437$	−25.0489	+	21.0186i	−1.19825	+	1.00545i
$438$		0			0
$439$	−34.4544	+	12.5404i	−1.64442	+	0.598519i	−0.987803	−	0.155707i	$-0.950235\pi$
$439$	−34.4544	+	12.5404i	−1.64442	+	0.598519i	−0.656615	+	0.754226i	$0.728012\pi$
$440$	−9.85567	+	17.0705i	−0.469851	+	0.813805i
$441$		0			0
$442$	−3.26131	−	5.64875i	−0.155125	−	0.268684i
$443$	−28.9463	−	24.2888i	−1.37528	−	1.15400i	−0.970923	−	0.239394i	$-0.923051\pi$
$443$	−28.9463	−	24.2888i	−1.37528	−	1.15400i	−0.404356	−	0.914602i	$-0.632504\pi$
$444$		0			0
$445$	−1.53866	−	8.72618i	−0.0729395	−	0.413661i
$446$	1.79328	+	10.1702i	0.0849143	+	0.481573i
$447$		0			0
$448$	−5.90078	−	4.95134i	−0.278786	−	0.233929i
$449$	−5.89289	−	10.2068i	−0.278103	−	0.481688i	0.692811	−	0.721120i	$-0.256372\pi$
$449$	−5.89289	−	10.2068i	−0.278103	−	0.481688i	−0.970913	+	0.239432i	$0.923039\pi$
$450$		0			0
$451$	11.1609	−	19.3313i	0.525547	−	0.910274i
$452$	23.2843	−	8.47479i	1.09520	−	0.398621i
$453$		0			0
$454$	7.42990	−	6.23443i	0.348703	−	0.292596i
$455$	−7.46597	−	2.71739i	−0.350010	−	0.127393i
$456$		0			0
$457$	−3.44794	+	19.5542i	−0.161288	+	0.914709i	0.791522	+	0.611141i	$0.209289\pi$
$457$	−3.44794	+	19.5542i	−0.161288	+	0.914709i	−0.952810	+	0.303568i	$0.901822\pi$
$458$	−19.9578			−0.932568
$459$		0			0
$460$	−13.4423			−0.626750
$461$	−1.32699	+	7.52573i	−0.0618041	+	0.350508i	0.938186	+	0.346131i	$0.112505\pi$
$461$	−1.32699	+	7.52573i	−0.0618041	+	0.350508i	−0.999990	+	0.00437770i	$0.998607\pi$
$462$		0			0
$463$	14.9922	+	5.45673i	0.696749	+	0.253596i	0.666022	−	0.745932i	$-0.267996\pi$
$463$	14.9922	+	5.45673i	0.696749	+	0.253596i	0.0307267	+	0.999528i	$0.490218\pi$
$464$	5.24091	−	4.39764i	0.243303	−	0.204155i
$465$		0			0
$466$	−3.94387	+	1.43545i	−0.182696	+	0.0664959i
$467$	−13.0703	+	22.6385i	−0.604822	+	1.04758i	0.387257	+	0.921972i	$0.373423\pi$
$467$	−13.0703	+	22.6385i	−0.604822	+	1.04758i	−0.992080	+	0.125611i	$0.959911\pi$
$468$		0			0
$469$	12.6606	+	21.9288i	0.584613	+	1.01258i
$470$	6.53268	+	5.48157i	0.301330	+	0.252846i
$471$		0			0
$472$	1.83350	+	10.3983i	0.0843935	+	0.478619i
$473$	−1.27476	−	7.22955i	−0.0586137	−	0.332415i
$474$		0			0
$475$	3.99728	+	3.35412i	0.183408	+	0.153897i
$476$	10.9483	+	18.9629i	0.501812	+	0.869164i
$477$		0			0
$478$	3.25522	−	5.63820i	0.148890	−	0.257885i
$479$	−36.9772	+	13.4586i	−1.68953	+	0.614939i	−0.994566	−	0.104106i	$-0.966802\pi$
$479$	−36.9772	+	13.4586i	−1.68953	+	0.614939i	−0.694964	+	0.719045i	$0.744580\pi$
$480$		0			0
$481$	5.66422	−	4.75285i	0.258266	−	0.216711i
$482$	−0.323165	−	0.117622i	−0.0147198	−	0.00535756i
$483$		0			0
$484$	0.274190	−	1.55501i	0.0124632	−	0.0706823i
$485$	14.2493			0.647027
$486$		0			0
$487$	11.7133			0.530779			0.265389	−	0.964141i	$-0.414500\pi$
$487$	11.7133			0.530779			0.265389	+	0.964141i	$0.414500\pi$
$488$	0.156721	−	0.888808i	0.00709442	−	0.0402345i
$489$		0			0
$490$	1.29057	+	0.469730i	0.0583022	+	0.0212203i
$491$	−29.5309	+	24.7794i	−1.33271	+	1.11828i	−0.349275	+	0.937020i	$0.613572\pi$
$491$	−29.5309	+	24.7794i	−1.33271	+	1.11828i	−0.983436	+	0.181256i	$0.941984\pi$
$492$		0			0
$493$	54.7586	−	19.9305i	2.46620	−	0.897624i
$494$	4.19178	−	7.26038i	0.188597	−	0.326660i
$495$		0			0
$496$	−1.04304	−	1.80660i	−0.0468340	−	0.0811189i
$497$	15.6949	+	13.1696i	0.704014	+	0.590738i
$498$		0			0
$499$	−5.13332	−	29.1125i	−0.229799	−	1.30325i	−0.853295	−	0.521428i	$-0.825400\pi$
$499$	−5.13332	−	29.1125i	−0.229799	−	1.30325i	0.623497	−	0.781826i	$-0.285712\pi$
$500$	−2.50600	−	14.2122i	−0.112072	−	0.635591i
$501$		0			0
$502$	−10.1452	−	8.51285i	−0.452803	−	0.379947i
$503$	−17.7888	−	30.8110i	−0.793161	−	1.37380i	−0.924000	−	0.382392i	$-0.875100\pi$
$503$	−17.7888	−	30.8110i	−0.793161	−	1.37380i	0.130839	−	0.991404i	$-0.458233\pi$
$504$		0			0
$505$	−12.1452	+	21.0361i	−0.540453	+	0.936092i
$506$	9.30857	−	3.38804i	0.413816	−	0.150617i
$507$		0			0
$508$	4.23815	−	3.55623i	0.188037	−	0.157782i
$509$	26.6707	+	9.70733i	1.18216	+	0.430270i	0.856963	−	0.515377i	$-0.172348\pi$
$509$	26.6707	+	9.70733i	1.18216	+	0.430270i	0.325194	+	0.945647i	$0.394570\pi$
$510$		0			0
$511$	5.34889	−	30.3351i	0.236621	−	1.34195i
$512$	−8.20265			−0.362510
$513$		0			0
$514$	−16.2365			−0.716161
$515$	−3.52157	+	19.9718i	−0.155179	+	0.880062i
$516$		0			0
$517$	13.6208	+	4.95756i	0.599041	+	0.218033i
$518$	8.24401	−	6.91754i	0.362221	−	0.303939i
$519$		0			0
$520$	7.88123	−	2.86853i	0.345615	−	0.125793i
$521$	12.7176	−	22.0275i	0.557167	−	0.965041i	−0.440565	−	0.897721i	$-0.645222\pi$
$521$	12.7176	−	22.0275i	0.557167	−	0.965041i	0.997731	−	0.0673204i	$-0.0214450\pi$
$522$		0			0
$523$	−4.20395	−	7.28145i	−0.183826	−	0.318396i	0.759354	−	0.650677i	$-0.225515\pi$
$523$	−4.20395	−	7.28145i	−0.183826	−	0.318396i	−0.943180	+	0.332282i	$0.892182\pi$
$524$	−0.109543	−	0.0919179i	−0.00478543	−	0.00401545i
$525$		0			0
$526$	−2.61886	−	14.8523i	−0.114188	−	0.647592i
$527$	−3.08543	−	17.4984i	−0.134404	−	0.762241i
$528$		0			0
$529$	−5.02543	−	4.21683i	−0.218497	−	0.183341i
$530$	0.125209	+	0.216868i	0.00543873	+	0.00942016i
$531$		0			0
$532$	−14.0719	+	24.3732i	−0.610093	+	1.05671i
$533$	−8.92499	+	3.24843i	−0.386584	+	0.140705i
$534$		0			0
$535$	−14.0989	+	11.8304i	−0.609549	+	0.511472i
$536$	−25.1176	−	9.14207i	−1.08492	−	0.394877i
$537$		0			0
$538$	−2.52265	+	14.3067i	−0.108759	+	0.616804i
$539$	2.33440			0.100550
$540$		0			0
$541$	−12.8635			−0.553043			−0.276522	−	0.961008i	$-0.589182\pi$
$541$	−12.8635			−0.553043			−0.276522	+	0.961008i	$0.589182\pi$
$542$	−1.74728	+	9.90930i	−0.0750519	+	0.425641i
$543$		0			0
$544$	−34.5155	−	12.5626i	−1.47984	−	0.538617i
$545$	−2.28345	+	1.91604i	−0.0978124	+	0.0820743i
$546$		0			0
$547$	−12.3024	+	4.47771i	−0.526013	+	0.191453i	−0.591357	−	0.806410i	$-0.701408\pi$
$547$	−12.3024	+	4.47771i	−0.526013	+	0.191453i	0.0653440	+	0.997863i	$0.479186\pi$
$548$	5.31514	−	9.20609i	0.227051	−	0.393265i
$549$		0			0
$550$	−0.790392	−	1.36900i	−0.0337024	−	0.0583743i
$551$	57.3756	+	48.1439i	2.44428	+	2.05100i
$552$		0			0
$553$	−1.77249	−	10.0523i	−0.0753739	−	0.427467i
$554$	−1.41012	−	7.99719i	−0.0599103	−	0.339768i
$555$		0			0
$556$	11.1584	+	9.36297i	0.473220	+	0.397079i
$557$	−2.29110	−	3.96830i	−0.0970769	−	0.168142i	0.813397	−	0.581710i	$-0.197616\pi$
$557$	−2.29110	−	3.96830i	−0.0970769	−	0.168142i	−0.910474	+	0.413567i	$0.864283\pi$
$558$		0			0
$559$	−1.56179	+	2.70509i	−0.0660565	+	0.114413i
$560$	−4.11473	+	1.49764i	−0.173879	+	0.0632868i
$561$		0			0
$562$	−8.54690	+	7.17170i	−0.360529	+	0.302520i
$563$	−11.5431	−	4.20135i	−0.486484	−	0.177066i	0.0871210	−	0.996198i	$-0.472233\pi$
$563$	−11.5431	−	4.20135i	−0.486484	−	0.177066i	−0.573605	+	0.819132i	$0.694456\pi$
$564$		0			0
$565$	−7.32895	+	41.5646i	−0.308331	+	1.74863i
$566$	14.5378			0.611071
$567$		0			0
$568$	−21.6278			−0.907484
$569$	2.51680	−	14.2735i	0.105510	−	0.598375i	−0.885506	−	0.464628i	$-0.846188\pi$
$569$	2.51680	−	14.2735i	0.105510	−	0.598375i	0.991016	−	0.133747i	$-0.0427009\pi$
$570$		0			0
$571$	20.7159	+	7.53996i	0.866932	+	0.315537i	0.736924	−	0.675976i	$-0.236278\pi$
$571$	20.7159	+	7.53996i	0.866932	+	0.315537i	0.130008	+	0.991513i	$0.458500\pi$
$572$	4.48745	−	3.76542i	0.187630	−	0.157440i
$573$		0			0
$574$	−12.9899	+	4.72794i	−0.542188	+	0.197340i
$575$	1.31172	−	2.27197i	0.0547025	−	0.0947475i
$576$		0			0
$577$	15.7418	+	27.2655i	0.655338	+	1.13508i	0.981809	+	0.189872i	$0.0608072\pi$
$577$	15.7418	+	27.2655i	0.655338	+	1.13508i	−0.326471	+	0.945207i	$0.605859\pi$
$578$	−13.3273	−	11.1829i	−0.554342	−	0.465148i
$579$		0			0
$580$	5.34665	+	30.3224i	0.222008	+	1.25907i
$581$	0.396669	+	2.24962i	0.0164566	+	0.0933301i
$582$		0			0
$583$	0.326061	+	0.273598i	0.0135041	+	0.0113313i
$584$	16.2582	+	28.1600i	0.672768	+	1.16527i
$585$		0			0
$586$	−4.19516	+	7.26623i	−0.173300	+	0.300165i
$587$	13.5029	−	4.91464i	0.557323	−	0.202849i	−0.0479743	−	0.998849i	$-0.515277\pi$
$587$	13.5029	−	4.91464i	0.557323	−	0.202849i	0.605297	+	0.796000i	$0.293054\pi$
$588$		0			0
$589$	17.4947	−	14.6798i	0.720858	−	0.604872i
$590$	−6.94463	−	2.52764i	−0.285906	−	0.104061i
$591$		0			0
$592$	0.707639	−	4.01322i	0.0290838	−	0.164942i
$593$	−41.0988			−1.68772			−0.843862	−	0.536560i	$-0.819724\pi$
$593$	−41.0988			−1.68772			−0.843862	+	0.536560i	$0.819724\pi$
$594$		0			0
$595$	−37.2966			−1.52901
$596$	2.18825	−	12.4102i	0.0896343	−	0.508341i
$597$		0			0
$598$	−3.96073	−	1.44159i	−0.161966	−	0.0589509i
$599$	6.55899	−	5.50365i	0.267993	−	0.224873i	−0.498881	−	0.866671i	$-0.666255\pi$
$599$	6.55899	−	5.50365i	0.267993	−	0.224873i	0.766874	+	0.641798i	$0.221811\pi$
$600$		0			0
$601$	1.53660	−	0.559275i	0.0626790	−	0.0228133i	−0.310490	−	0.950577i	$-0.600493\pi$
$601$	1.53660	−	0.559275i	0.0626790	−	0.0228133i	0.373169	+	0.927763i	$0.378271\pi$
$602$	−2.27311	+	3.93713i	−0.0926449	+	0.160466i
$603$		0			0
$604$	16.6651	+	28.8648i	0.678094	+	1.17449i
$605$	2.06030	+	1.72880i	0.0837631	+	0.0702856i
$606$		0			0
$607$	1.14077	+	6.46963i	0.0463024	+	0.262594i	0.999167	−	0.0408009i	$-0.0129909\pi$
$607$	1.14077	+	6.46963i	0.0463024	+	0.262594i	−0.952865	+	0.303395i	$0.901880\pi$
$608$	−8.19795	−	46.4929i	−0.332471	−	1.88554i
$609$		0			0
$610$	0.483909	+	0.406048i	0.0195929	+	0.0164404i
$611$	−3.08374	−	5.34120i	−0.124755	−	0.216082i
$612$		0			0
$613$	13.1363	−	22.7527i	0.530569	−	0.918973i	−0.468795	−	0.883307i	$-0.655312\pi$
$613$	13.1363	−	22.7527i	0.530569	−	0.918973i	0.999364	−	0.0356656i	$-0.0113551\pi$
$614$	0.0363583	−	0.0132334i	0.00146730	−	0.000534055i
$615$		0			0
$616$	15.8942	−	13.3368i	0.640396	−	0.537356i
$617$	5.89472	+	2.14550i	0.237312	+	0.0863746i	0.457939	−	0.888984i	$-0.348588\pi$
$617$	5.89472	+	2.14550i	0.237312	+	0.0863746i	−0.220626	+	0.975358i	$0.570810\pi$
$618$		0			0
$619$	0.857974	−	4.86581i	0.0344849	−	0.195573i	−0.962698	−	0.270577i	$-0.912786\pi$
$619$	0.857974	−	4.86581i	0.0344849	−	0.195573i	0.997183	+	0.0750033i	$0.0238967\pi$
$620$	9.38839			0.377047
$621$		0			0
$622$	−10.2936			−0.412738
$623$	−1.61962	+	9.18530i	−0.0648885	+	0.368001i
$624$		0			0
$625$	26.1390	+	9.51380i	1.04556	+	0.380552i
$626$	8.98606	−	7.54020i	0.359155	−	0.301367i
$627$		0			0
$628$	3.55540	−	1.29406i	0.141876	−	0.0516387i
$629$	17.3550	−	30.0598i	0.691991	−	1.19856i
$630$		0			0
$631$	3.46210	+	5.99653i	0.137824	+	0.238718i	0.926673	−	0.375869i	$-0.122656\pi$
$631$	3.46210	+	5.99653i	0.137824	+	0.238718i	−0.788849	+	0.614587i	$0.789322\pi$
$632$	8.25420	+	6.92610i	0.328335	+	0.275505i
$633$		0			0
$634$	−1.16561	−	6.61049i	−0.0462922	−	0.262536i
$635$	1.63639	+	9.28043i	0.0649382	+	0.368283i
$636$		0			0
$637$	−0.760890	−	0.638463i	−0.0301476	−	0.0252968i
$638$	−11.3450	−	19.6502i	−0.449154	−	0.777957i
$639$		0			0
$640$	11.0653	−	19.1657i	0.437394	−	0.757589i
$641$	31.8733	−	11.6009i	1.25892	−	0.458210i	0.375514	−	0.926817i	$-0.377466\pi$
$641$	31.8733	−	11.6009i	1.25892	−	0.458210i	0.883407	+	0.468607i	$0.155244\pi$
$642$		0			0
$643$	5.91633	−	4.96439i	0.233317	−	0.195776i	−0.518632	−	0.854998i	$-0.673558\pi$
$643$	5.91633	−	4.96439i	0.233317	−	0.195776i	0.751949	+	0.659221i	$0.229114\pi$
$644$	13.2962	+	4.83943i	0.523944	+	0.190700i
$645$		0			0
$646$	6.83390	−	38.7569i	0.268876	−	1.52487i
$647$	35.1862			1.38331			0.691655	−	0.722228i	$-0.256882\pi$
$647$	35.1862			1.38331			0.691655	+	0.722228i	$0.256882\pi$
$648$		0			0
$649$	−12.5615			−0.493083
$650$	−0.116798	+	0.662393i	−0.00458119	+	0.0259812i
$651$		0			0
$652$	−28.9061	−	10.5210i	−1.13205	−	0.412032i
$653$	14.9470	−	12.5421i	0.584923	−	0.490808i	−0.301637	−	0.953423i	$-0.597533\pi$
$653$	14.9470	−	12.5421i	0.584923	−	0.490808i	0.886560	+	0.462614i	$0.153089\pi$
$654$		0			0
$655$	0.228883	−	0.0833065i	0.00894318	−	0.00325505i
$656$	−2.61726	+	4.53323i	−0.102187	+	0.176993i
$657$		0			0
$658$	−4.48824	−	7.77386i	−0.174970	−	0.303057i
$659$	17.6852	+	14.8397i	0.688919	+	0.578072i	0.918597	−	0.395195i	$-0.129323\pi$
$659$	17.6852	+	14.8397i	0.688919	+	0.578072i	−0.229678	+	0.973267i	$0.573767\pi$
$660$		0			0
$661$	−1.19407	−	6.77189i	−0.0464438	−	0.263396i	0.952740	−	0.303786i	$-0.0982509\pi$
$661$	−1.19407	−	6.77189i	−0.0464438	−	0.263396i	−0.999184	+	0.0403905i	$0.987140\pi$
$662$	−4.19005	−	23.7629i	−0.162851	−	0.923573i
$663$		0			0
$664$	−1.84723	−	1.55001i	−0.0716863	−	0.0601519i
$665$	−23.9688	−	41.5152i	−0.929471	−	1.60989i
$666$		0			0
$667$	18.8280	−	32.6110i	0.729023	−	1.26270i
$668$	11.7345	−	4.27100i	0.454020	−	0.165250i
$669$		0			0
$670$	14.3318	−	12.0258i	0.553685	−	0.464597i
$671$	1.00896	+	0.367232i	0.0389505	+	0.0141768i
$672$		0			0
$673$	−5.32619	+	30.2063i	−0.205310	+	1.16437i	0.691642	+	0.722240i	$0.256888\pi$
$673$	−5.32619	+	30.2063i	−0.205310	+	1.16437i	−0.896952	+	0.442128i	$0.854224\pi$
$674$	18.5624			0.714997
$675$		0			0
$676$	15.6442			0.601700
$677$	−2.35883	+	13.3776i	−0.0906572	+	0.514143i	0.905335	+	0.424699i	$0.139620\pi$
$677$	−2.35883	+	13.3776i	−0.0906572	+	0.514143i	−0.995992	+	0.0894438i	$0.971491\pi$
$678$		0			0
$679$	−14.0944	−	5.12996i	−0.540895	−	0.196870i
$680$	30.1600	−	25.3072i	1.15658	−	0.970488i
$681$		0			0
$682$	−6.50131	+	2.36628i	−0.248948	+	0.0906097i
$683$	3.03350	−	5.25418i	0.116074	−	0.201045i	−0.802135	−	0.597143i	$-0.796302\pi$
$683$	3.03350	−	5.25418i	0.116074	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$684$		0			0
$685$	9.05335	+	15.6809i	0.345911	+	0.599135i
$686$	−11.5393	−	9.68261i	−0.440572	−	0.369684i
$687$		0			0
$688$	0.298935	+	1.69535i	0.0113968	+	0.0646345i
$689$	−0.0314490	−	0.178356i	−0.00119811	−	0.00679483i
$690$		0			0
$691$	15.8304	+	13.2833i	0.602216	+	0.505319i	0.892157	−	0.451725i	$-0.149191\pi$
$691$	15.8304	+	13.2833i	0.602216	+	0.505319i	−0.289941	+	0.957044i	$0.593636\pi$
$692$	1.83756	+	3.18275i	0.0698537	+	0.120990i
$693$		0			0
$694$	8.52054	−	14.7580i	0.323435	−	0.560206i
$695$	−23.3145	+	8.48580i	−0.884371	+	0.321885i
$696$		0			0
$697$	−34.1543	+	28.6588i	−1.29368	+	1.08553i
$698$	11.5814	+	4.21527i	0.438361	+	0.159550i
$699$		0			0
$700$	0.392092	−	2.22366i	0.0148197	−	0.0840466i
$701$	11.0222			0.416303			0.208151	−	0.978097i	$-0.433255\pi$
$701$	11.0222			0.416303			0.208151	+	0.978097i	$0.433255\pi$
$702$		0			0
$703$	44.6131			1.68262
$704$	−1.67983	+	9.52680i	−0.0633111	+	0.359055i
$705$		0			0
$706$	9.43273	+	3.43323i	0.355006	+	0.129211i
$707$	19.5865	−	16.4350i	0.736626	−	0.618103i
$708$		0			0
$709$	10.3248	−	3.75793i	0.387757	−	0.141132i	−0.140783	−	0.990040i	$-0.544962\pi$
$709$	10.3248	−	3.75793i	0.387757	−	0.141132i	0.528540	+	0.848909i	$0.322740\pi$
$710$	7.56897	−	13.1098i	0.284058	−	0.492003i
$711$		0			0
$712$	−4.92288	−	8.52669i	−0.184493	−	0.319551i
$713$	−8.79564	−	7.38042i	−0.329399	−	0.276399i
$714$		0			0
$715$	1.73265	+	9.82634i	0.0647974	+	0.367484i
$716$	−0.892623	−	5.06231i	−0.0333589	−	0.189188i
$717$		0			0
$718$	−15.3880	−	12.9121i	−0.574276	−	0.481875i
$719$	−16.3529	−	28.3240i	−0.609859	−	1.05631i	−0.991263	−	0.131898i	$-0.957893\pi$
$719$	−16.3529	−	28.3240i	−0.609859	−	1.05631i	0.381404	−	0.924408i	$-0.375441\pi$
$720$		0			0
$721$	10.6734	−	18.4870i	0.397500	−	0.688490i
$722$	33.6468	−	12.2464i	1.25220	−	0.455765i
$723$		0			0
$724$	0.286965	−	0.240792i	0.0106650	−	0.00894896i
$725$	−5.64670	−	2.05523i	−0.209713	−	0.0763294i
$726$		0			0
$727$	6.67862	−	37.8763i	0.247696	−	1.40475i	−0.566451	−	0.824096i	$-0.691684\pi$
$727$	6.67862	−	37.8763i	0.247696	−	1.40475i	0.814147	−	0.580659i	$-0.197205\pi$
$728$	−8.82830			−0.327199
$729$		0			0
$730$	−22.7591			−0.842352
$731$	−2.54619	+	14.4402i	−0.0941743	+	0.534089i
$732$		0			0
$733$	−13.2569	−	4.82513i	−0.489656	−	0.178220i	0.0853795	−	0.996349i	$-0.472790\pi$
$733$	−13.2569	−	4.82513i	−0.489656	−	0.178220i	−0.575036	+	0.818128i	$0.695012\pi$
$734$	−9.51729	+	7.98596i	−0.351290	+	0.294767i
$735$		0			0
$736$	−22.3039	+	8.11797i	−0.822134	+	0.299232i
$737$	15.8999	−	27.5395i	0.585681	−	1.01443i
$738$		0			0
$739$	5.92286	+	10.2587i	0.217876	+	0.377372i	0.954158	−	0.299302i	$-0.0967539\pi$
$739$	5.92286	+	10.2587i	0.217876	+	0.377372i	−0.736283	+	0.676674i	$0.763421\pi$
$740$	14.0493	+	11.7888i	0.516462	+	0.433363i
$741$		0			0
$742$	−0.0457725	−	0.259589i	−0.00168036	−	0.00952981i
$743$	−3.77990	−	21.4369i	−0.138671	−	0.786442i	−0.972233	−	0.234016i	$-0.924813\pi$
$743$	−3.77990	−	21.4369i	−0.138671	−	0.786442i	0.833562	−	0.552426i	$-0.186298\pi$
$744$		0			0
$745$	16.4428	+	13.7971i	0.602417	+	0.505488i
$746$	0.710290	+	1.23026i	0.0260056	+	0.0450429i
$747$		0			0
$748$	13.7494	−	23.8147i	0.502729	−	0.870753i
$749$	18.2048	−	6.62601i	0.665190	−	0.242109i
$750$		0			0
$751$	−32.5944	+	27.3500i	−1.18939	+	0.998015i	−0.189518	+	0.981877i	$0.560693\pi$
$751$	−32.5944	+	27.3500i	−1.18939	+	0.998015i	−0.999870	+	0.0161380i	$0.994863\pi$
$752$	−3.19411	−	1.16256i	−0.116477	−	0.0423942i
$753$		0			0
$754$	−1.67648	+	9.50778i	−0.0610537	+	0.346253i
$755$	−56.7719			−2.06614
$756$		0			0
$757$	−20.6382			−0.750110			−0.375055	−	0.927003i	$-0.622376\pi$
$757$	−20.6382			−0.750110			−0.375055	+	0.927003i	$0.622376\pi$
$758$	−0.154896	+	0.878457i	−0.00562607	+	0.0319070i
$759$		0			0
$760$	47.5522	+	17.3076i	1.72490	+	0.627812i
$761$	−37.8771	+	31.7827i	−1.37304	+	1.15212i	−0.401336	+	0.915931i	$0.631454\pi$
$761$	−37.8771	+	31.7827i	−1.37304	+	1.15212i	−0.971707	+	0.236189i	$0.924101\pi$
$762$		0			0
$763$	2.94844	−	1.07315i	0.106741	−	0.0388505i
$764$	−1.67275	+	2.89729i	−0.0605181	+	0.104820i
$765$		0			0
$766$	8.48799	+	14.7016i	0.306684	+	0.531192i
$767$	4.09438	+	3.43559i	0.147840	+	0.124052i
$768$		0			0
$769$	3.84346	+	21.7973i	0.138599	+	0.786032i	0.972286	+	0.233795i	$0.0751145\pi$
$769$	3.84346	+	21.7973i	0.138599	+	0.786032i	−0.833687	+	0.552237i	$0.813774\pi$
$770$	2.52179	+	14.3018i	0.0908789	+	0.515400i
$771$		0			0
$772$	−0.530309	−	0.444982i	−0.0190862	−	0.0160152i
$773$	−10.9836	−	19.0241i	−0.395051	−	0.684248i	0.598057	−	0.801454i	$-0.295940\pi$
$773$	−10.9836	−	19.0241i	−0.395051	−	0.684248i	−0.993108	+	0.117206i	$0.962606\pi$
$774$		0			0
$775$	−0.916134	+	1.58679i	−0.0329085	+	0.0569992i
$776$	14.8784	−	5.41529i	0.534103	−	0.194398i
$777$		0			0
$778$	15.6071	−	13.0959i	0.559541	−	0.469511i
$779$	−53.8498	−	19.5997i	−1.92937	−	0.702233i

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.135052 + 0.765917i) q^{2} +(1.31100 + 0.477163i) q^{4} +(-1.82039 + 1.52749i) q^{5} +(2.35052 - 0.855521i) q^{7} +(-1.32025 + 2.28674i) q^{8} +O(q^{10})\)	\(q+(-0.135052 + 0.765917i) q^{2} +(1.31100 + 0.477163i) q^{4} +(-1.82039 + 1.52749i) q^{5} +(2.35052 - 0.855521i) q^{7} +(-1.32025 + 2.28674i) q^{8} +(-0.924081 - 1.60056i) q^{10} +(-2.40643 - 2.01923i) q^{11} +(0.232103 + 1.31632i) q^{13} +(0.337815 + 1.91585i) q^{14} +(0.564314 + 0.473515i) q^{16} +(3.13726 + 5.43389i) q^{17} +(-4.03234 + 6.98422i) q^{19} +(-3.11538 + 1.13391i) q^{20} +(1.87156 - 1.57042i) q^{22} +(3.81008 + 1.38675i) q^{23} +(0.112355 - 0.637198i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(1.61271 - 9.14613i) q^{29} +(-2.66104 - 0.968540i) q^{31} +(-4.48437 + 3.76284i) q^{32} +(-4.58560 + 1.66902i) q^{34} +(-2.97207 + 5.14778i) q^{35} +(-2.76596 - 4.79078i) q^{37} +(-4.80476 - 4.03167i) q^{38} +(-1.08960 - 6.17943i) q^{40} +(1.23390 + 6.99781i) q^{41} +(1.79017 + 1.50213i) q^{43} +(-2.19131 - 3.79547i) q^{44} +(-1.57670 + 2.73092i) q^{46} +(-4.33594 + 1.57815i) q^{47} +(-0.569260 + 0.477666i) q^{49} +(0.472867 + 0.172110i) q^{50} +(-0.323815 + 1.83645i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(-1.14693 + 6.50455i) q^{56} +(6.78738 + 2.47040i) q^{58} +(3.06321 - 2.57034i) q^{59} +(-0.321185 + 0.116902i) q^{61} +(1.10120 - 1.90733i) q^{62} +(-1.53974 - 2.66690i) q^{64} +(-2.43319 - 2.04168i) q^{65} +(1.75783 + 9.96913i) q^{67} +(1.52008 + 8.62079i) q^{68} +(-3.54139 - 2.97158i) q^{70} +(4.09540 + 7.09344i) q^{71} +(6.15722 - 10.6646i) q^{73} +(4.04288 - 1.47149i) q^{74} +(-8.61900 + 7.23220i) q^{76} +(-7.38387 - 2.68751i) q^{77} +(0.708606 - 4.01870i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(-0.158580 + 0.899354i) q^{83} +(-14.0112 - 5.09967i) q^{85} +(-1.39227 + 1.16826i) q^{86} +(7.79456 - 2.83699i) q^{88} +(-1.86437 + 3.22919i) q^{89} +(1.67171 + 2.89548i) q^{91} +(4.33328 + 3.63606i) q^{92} +(-0.623157 - 3.53410i) q^{94} +(-3.32788 - 18.8734i) q^{95} +(-4.59343 - 3.85434i) q^{97} +(-0.288973 - 0.500515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 3 * q^13 - 15 * q^14 - 36 * q^16 + 9 * q^17 - 12 * q^19 - 42 * q^20 + 6 * q^22 - 6 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 54 * q^32 - 9 * q^34 - 30 * q^35 - 3 * q^37 - 42 * q^38 - 57 * q^40 - 24 * q^41 + 6 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 + 33 * q^49 - 21 * q^50 + 45 * q^52 - 18 * q^53 + 30 * q^55 - 3 * q^56 + 33 * q^58 - 15 * q^59 + 33 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 + 42 * q^67 + 18 * q^68 + 24 * q^70 - 12 * q^73 + 3 * q^74 - 87 * q^76 + 57 * q^77 - 48 * q^79 - 42 * q^80 - 42 * q^82 - 12 * q^83 - 36 * q^85 + 30 * q^86 + 30 * q^88 + 9 * q^89 - 18 * q^91 + 48 * q^92 + 33 * q^94 - 30 * q^95 - 3 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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