LMFDB - Embedded newform 729.2.e.j.649.2

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			649.2
Root			$1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.j.82.2

$q$-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	$-0.855777\pi$
$2$	0.135052	−	0.765917i	0.0954961	−	0.541585i	0.994594	−	0.103838i	$-0.0331123\pi$
$3$		0			0
$3$		0			0
$4$	1.31100	+	0.477163i	0.655498	+	0.238582i
$5$	1.82039	−	1.52749i	0.814102	−	0.683113i	−0.137481	−	0.990504i	$-0.543901\pi$
$5$	1.82039	−	1.52749i	0.814102	−	0.683113i	0.951583	+	0.307392i	$0.0994561\pi$
$6$		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	0.928919	−	0.370284i	$-0.120739\pi$
$11$	2.40643	+	2.01923i	0.725566	+	0.608822i	−0.203353	+	0.979105i	$0.565184\pi$
$12$		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	$-0.891426\pi$
$17$	−3.13726	−	5.43389i	−0.760897	−	1.31791i	0.181492	−	0.983392i	$-0.441907\pi$
$18$		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	−0.0872688	−	0.996185i	$-0.527814\pi$
$23$	−3.81008	−	1.38675i	−0.794456	−	0.289158i	−0.707187	+	0.707027i	$0.750036\pi$
$24$		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	$0.386531\pi$
$29$	−1.61271	+	9.14613i	−0.299473	+	1.69839i	−0.648445	+	0.761261i	$0.724580\pi$
$30$		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	$-0.868325\pi$
$41$	−1.23390	−	6.99781i	−0.192703	−	1.09287i	0.722949	−	0.690902i	$-0.242786\pi$
$42$		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	−0.00584102	−	0.999983i	$-0.501859\pi$
$47$	4.33594	−	1.57815i	0.632461	−	0.230197i	0.638302	+	0.769786i	$0.279637\pi$
$48$		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	$-0.497038\pi$
$53$	0.135496			0.0186118			0.00930588	+	0.999957i	$0.497038\pi$
$54$		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	−0.820028	−	0.572323i	$-0.806042\pi$
$59$	−3.06321	+	2.57034i	−0.398796	+	0.334630i	0.421232	+	0.906953i	$0.361598\pi$
$60$		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	0.513837	−	0.857888i	$-0.328224\pi$
$71$	−4.09540	−	7.09344i	−0.486035	−	0.841837i	−0.999871	+	0.0160515i	$0.994890\pi$
$72$		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	−0.974867	−	0.222788i	$-0.928484\pi$
$83$	0.158580	−	0.899354i	0.0174065	−	0.0987169i	0.992273	+	0.124071i	$0.0395952\pi$
$84$		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	−0.750134	−	0.661286i	$-0.770011\pi$
$89$	1.86437	−	3.22919i	0.197623	−	0.342293i	0.947757	+	0.318992i	$0.103344\pi$
$90$		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	−0.772371	−	0.635172i	$-0.780929\pi$
$101$	−9.60527	+	3.49603i	−0.955760	+	0.347868i	−0.183389	+	0.983040i	$0.558707\pi$
$102$		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	$-0.622141\pi$
$107$	−7.74500			−0.748738			−0.374369	+	0.927280i	$0.622141\pi$
$108$		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	$0.592540\pi$
$113$	−13.6055	+	11.4164i	−1.27990	+	1.07396i	−0.993258	+	0.115928i	$0.963016\pi$
$114$		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	0.346224	−	0.938152i	$-0.387464\pi$
$131$	0.0963170	+	0.0350565i	0.00841525	+	0.00306290i	−0.337809	+	0.941215i	$0.609686\pi$
$132$		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	$0.161085\pi$
$137$	−1.32312	+	7.50379i	−0.113042	+	0.641092i	−0.987701	+	0.156354i	$0.950026\pi$
$138$		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	$0.0650829\pi$
$149$	1.56849	+	8.89535i	0.128496	+	0.728736i	−0.850674	+	0.525693i	$0.823806\pi$
$150$		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	−0.868305	−	0.496031i	$-0.834790\pi$
$167$	−6.85671	+	5.75347i	−0.530589	+	0.445217i	0.337716	+	0.941248i	$0.390346\pi$
$168$		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	0.562846	−	0.826562i	$-0.309707\pi$
$173$	−2.01795	−	1.69326i	−0.153422	−	0.128736i	−0.716268	+	0.697826i	$0.754151\pi$
$174$		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	0.926625	−	0.375988i	$-0.122697\pi$
$179$	1.84227	+	3.19090i	0.137697	+	0.238499i	−0.788927	+	0.614487i	$0.789363\pi$
$180$		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	−0.966030	−	0.258432i	$-0.916794\pi$
$191$	0.416406	−	2.36155i	0.0301301	−	0.170876i	0.996160	+	0.0875554i	$0.0279055\pi$
$192$		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	$0.456040\pi$
$197$	−11.0734	+	19.1797i	−0.788946	+	1.36649i	−0.926613	+	0.376016i	$0.877294\pi$
$198$		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	0.902192	−	0.431335i	$-0.141957\pi$
$227$	9.55329	+	8.01616i	0.634074	+	0.532051i	−0.268118	+	0.963386i	$0.586402\pi$
$228$		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	0.764005	−	0.645210i	$-0.223230\pi$
$233$	−2.69821	−	4.67344i	−0.176766	−	0.306167i	−0.940771	+	0.339043i	$0.889897\pi$
$234$		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	0.583658	−	0.812000i	$-0.301621\pi$
$239$	7.86621	+	2.86307i	0.508823	+	0.185196i	−0.0748353	+	0.997196i	$0.523843\pi$
$240$		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	$-0.652734\pi$
$251$	8.51427	−	14.7471i	0.537416	−	0.930832i	0.999042	−	0.0437571i	$-0.0139328\pi$
$252$		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	$-0.829852\pi$
$257$	−3.62520	−	20.5596i	−0.226134	−	1.28247i	0.634371	−	0.773028i	$-0.281259\pi$
$258$		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	0.287650	−	0.957736i	$-0.407126\pi$
$263$	18.2221	−	6.63230i	1.12362	−	0.408965i	0.835973	+	0.548770i	$0.184904\pi$
$264$		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	$-0.692841\pi$
$269$	−18.6791			−1.13889			−0.569443	+	0.822031i	$0.692841\pi$
$270$		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	0.253179	−	0.967420i	$-0.418524\pi$
$281$	−10.9895	−	9.22130i	−0.655580	−	0.550097i	−0.908758	+	0.417323i	$0.862968\pi$
$282$		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	0.0284724	−	0.999595i	$-0.490936\pi$
$293$	−10.1376	−	3.68978i	−0.592243	−	0.215559i	−0.620716	+	0.784036i	$0.713158\pi$
$294$		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	$-0.933110\pi$
$311$	−2.29831	−	13.0344i	−0.130325	−	0.739112i	0.847676	−	0.530514i	$-0.178001\pi$
$312$		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	−0.104061	−	0.994571i	$-0.533184\pi$
$317$	8.11032	−	2.95192i	0.455521	−	0.165796i	0.559582	+	0.828775i	$0.310962\pi$
$318$		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	0.829275	−	0.558841i	$-0.188754\pi$
$347$	20.5898	+	7.49409i	1.10532	+	0.402304i	0.276045	+	0.961145i	$0.410976\pi$
$348$		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	$0.167162\pi$
$353$	−2.24126	+	12.7108i	−0.119290	+	0.676528i	−0.984536	+	0.175181i	$0.943949\pi$
$354$		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	$-0.594623\pi$
$359$	12.9142	−	22.3681i	0.681588	−	1.18054i	0.974496	−	0.224404i	$-0.0720435\pi$
$360$		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	−0.960753	−	0.277404i	$-0.910526\pi$
$383$	−16.7209	+	14.0305i	−0.854397	+	0.716924i	0.106357	+	0.994328i	$0.466081\pi$
$384$		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	0.989306	−	0.145854i	$-0.0465929\pi$
$389$	20.0674	+	16.8386i	1.01746	+	0.853750i	0.0281533	+	0.999604i	$0.491037\pi$
$390$		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	0.151709	−	0.988425i	$-0.451522\pi$
$401$	−7.35761	−	2.67795i	−0.367422	−	0.133731i	−0.519131	+	0.854695i	$0.673744\pi$
$402$		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	$-0.965057\pi$
$419$	−1.99403	−	11.3087i	−0.0974148	−	0.552467i	0.896566	−	0.442911i	$-0.146054\pi$
$420$		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	$-0.502983\pi$
$431$	−0.389084			−0.0187415			−0.00937075	+	0.999956i	$0.502983\pi$
$432$		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	$0.0769487\pi$
$443$	28.9463	+	24.2888i	1.37528	+	1.15400i	0.404356	+	0.914602i	$0.367496\pi$
$444$		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	0.970913	−	0.239432i	$-0.0769611\pi$
$449$	5.89289	+	10.2068i	0.278103	+	0.481688i	−0.692811	+	0.721120i	$0.743628\pi$
$450$		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	$-0.887495\pi$
$461$	1.32699	−	7.52573i	0.0618041	−	0.350508i	0.999990	−	0.00437770i	$-0.00139347\pi$
$462$		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	$-0.626577\pi$
$467$	13.0703	−	22.6385i	0.604822	−	1.04758i	0.992080	−	0.125611i	$-0.0400892\pi$
$468$		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	0.694964	−	0.719045i	$-0.255420\pi$
$479$	36.9772	−	13.4586i	1.68953	−	0.614939i	0.994566	+	0.104106i	$0.0331982\pi$
$480$		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	$-0.386428\pi$
$491$	29.5309	−	24.7794i	1.33271	−	1.11828i	0.983436	−	0.181256i	$-0.0580164\pi$
$492$		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	$0.124900\pi$
$503$	17.7888	+	30.8110i	0.793161	+	1.37380i	−0.130839	+	0.991404i	$0.541767\pi$
$504$		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	−0.325194	−	0.945647i	$-0.605430\pi$
$509$	−26.6707	−	9.70733i	−1.18216	−	0.430270i	−0.856963	+	0.515377i	$0.827652\pi$
$510$		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	$0.354778\pi$
$521$	−12.7176	+	22.0275i	−0.557167	+	0.965041i	−0.997731	+	0.0673204i	$0.978555\pi$
$522$		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	0.910474	−	0.413567i	$-0.135717\pi$
$557$	2.29110	+	3.96830i	0.0970769	+	0.168142i	−0.813397	+	0.581710i	$0.802384\pi$
$558$		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	0.573605	−	0.819132i	$-0.305544\pi$
$563$	11.5431	+	4.20135i	0.486484	+	0.177066i	−0.0871210	+	0.996198i	$0.527767\pi$
$564$		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	$0.153812\pi$
$569$	−2.51680	+	14.2735i	−0.105510	+	0.598375i	−0.991016	+	0.133747i	$0.957299\pi$
$570$		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	−0.605297	−	0.796000i	$-0.706946\pi$
$587$	−13.5029	+	4.91464i	−0.557323	+	0.202849i	0.0479743	+	0.998849i	$0.484723\pi$
$588$		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	$-0.180276\pi$
$593$	41.0988			1.68772			0.843862	+	0.536560i	$0.180276\pi$
$594$		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	−0.766874	−	0.641798i	$-0.778189\pi$
$599$	−6.55899	+	5.50365i	−0.267993	+	0.224873i	0.498881	+	0.866671i	$0.333745\pi$
$600$		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	0.220626	−	0.975358i	$-0.429190\pi$
$617$	−5.89472	−	2.14550i	−0.237312	−	0.0863746i	−0.457939	+	0.888984i	$0.651412\pi$
$618$		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	−0.883407	−	0.468607i	$-0.844756\pi$
$641$	−31.8733	+	11.6009i	−1.25892	+	0.458210i	−0.375514	+	0.926817i	$0.622534\pi$
$642$		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	$-0.743118\pi$
$647$	−35.1862			−1.38331			−0.691655	+	0.722228i	$0.743118\pi$
$648$		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	−0.886560	−	0.462614i	$-0.846911\pi$
$653$	−14.9470	+	12.5421i	−0.584923	+	0.490808i	0.301637	+	0.953423i	$0.402467\pi$
$654$		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	0.229678	−	0.973267i	$-0.426233\pi$
$659$	−17.6852	−	14.8397i	−0.688919	−	0.578072i	−0.918597	+	0.395195i	$0.870677\pi$
$660$		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	$-0.860380\pi$
$677$	2.35883	−	13.3776i	0.0906572	−	0.514143i	0.995992	−	0.0894438i	$-0.0285090\pi$
$678$		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	−0.918208	−	0.396098i	$-0.870364\pi$
$683$	−3.03350	+	5.25418i	−0.116074	+	0.201045i	0.802135	+	0.597143i	$0.203698\pi$
$684$		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	$-0.566745\pi$
$701$	−11.0222			−0.416303			−0.208151	+	0.978097i	$0.566745\pi$
$702$		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	$0.0421072\pi$
$719$	16.3529	+	28.3240i	0.609859	+	1.05631i	−0.381404	+	0.924408i	$0.624559\pi$
$720$		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	$0.0751868\pi$
$743$	3.77990	+	21.4369i	0.138671	+	0.786442i	−0.833562	+	0.552426i	$0.813702\pi$
$744$		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	$-0.368546\pi$
$761$	37.8771	−	31.7827i	1.37304	−	1.15212i	0.971707	−	0.236189i	$-0.0758986\pi$
$762$		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	0.993108	−	0.117206i	$-0.0373936\pi$
$773$	10.9836	+	19.0241i	0.395051	+	0.684248i	−0.598057	+	0.801454i	$0.704060\pi$
$774$		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
$780$		0			0
$781$	4.46803	−	25.3394i	0.159879	−	0.906716i
$782$	19.7860			0.707547
$783$		0			0
$784$	−0.547423			−0.0195508
$785$	1.11910	−	6.34672i	0.0399423	−	0.226524i
$786$		0			0
$787$	−0.503234	−	0.183162i	−0.0179384	−	0.00652903i	0.333035	−	0.942914i	$-0.391927\pi$
$787$	−0.503234	−	0.183162i	−0.0179384	−	0.00652903i	−0.350974	+	0.936385i	$0.614149\pi$
$788$	−23.6690	+	19.8606i	−0.843173	+	0.707506i
$789$		0			0
$790$	−7.08697	+	2.57944i	−0.252143	+	0.0917725i
$791$	−22.2132	+	38.4744i	−0.789810	+	1.36799i
$792$		0			0
$793$	−0.228429	−	0.395650i	−0.00811174	−	0.0140500i
$794$	2.50126	+	2.09880i	0.0887663	+	0.0744837i
$795$		0			0
$796$	−0.516617	−	2.92988i	−0.0183110	−	0.103847i
$797$	−6.96311	−	39.4898i	−0.246646	−	1.39880i	−0.816639	−	0.577149i	$-0.804165\pi$
$797$	−6.96311	−	39.4898i	−0.246646	−	1.39880i	0.569992	−	0.821650i	$-0.306946\pi$
$798$		0			0
$799$	−22.1785	−	18.6099i	−0.784617	−	0.658372i
$800$	−1.89383	−	3.28021i	−0.0669570	−	0.115973i
$801$		0			0
$802$	−3.04475	+	5.27366i	−0.107514	+	0.186219i
$803$	36.3513	−	13.2308i	1.28281	−	0.466904i
$804$		0			0
$805$	−18.4625	+	15.4919i	−0.650718	+	0.546017i
$806$	−2.76626	−	1.00684i	−0.0974373	−	0.0354643i
$807$		0			0
$808$	−4.68685	+	26.5804i	−0.164883	+	0.935096i
$809$	−17.1826			−0.604110			−0.302055	−	0.953291i	$-0.597673\pi$
$809$	−17.1826			−0.604110			−0.302055	+	0.953291i	$0.597673\pi$
$810$		0			0
$811$	−19.6169			−0.688842			−0.344421	−	0.938815i	$-0.611925\pi$
$811$	−19.6169			−0.688842			−0.344421	+	0.938815i	$0.611925\pi$
$812$	−5.62796	+	31.9177i	−0.197503	+	1.12009i
$813$		0			0
$814$	−12.7002	−	4.62249i	−0.445142	−	0.162018i
$815$	−40.1376	+	33.6795i	−1.40596	+	1.17974i
$816$		0			0
$817$	−17.7098	+	6.44584i	−0.619588	+	0.225511i
$818$	6.77755	−	11.7391i	0.236971	−	0.410446i
$819$		0			0
$820$	−11.7789	−	20.4017i	−0.411338	−	0.712459i
$821$	−27.5055	−	23.0799i	−0.959950	−	0.805494i	0.0209950	−	0.999780i	$-0.493317\pi$
$821$	−27.5055	−	23.0799i	−0.959950	−	0.805494i	−0.980945	+	0.194286i	$0.937761\pi$
$822$		0			0
$823$	−4.48326	−	25.4258i	−0.156277	−	0.886288i	−0.957609	−	0.288070i	$-0.906986\pi$
$823$	−4.48326	−	25.4258i	−0.156277	−	0.886288i	0.801333	−	0.598219i	$-0.204125\pi$
$824$	−3.91303	−	22.1919i	−0.136317	−	0.773091i
$825$		0			0
$826$	5.95918	+	5.00034i	0.207346	+	0.173984i
$827$	−12.4793	−	21.6148i	−0.433948	−	0.751619i	0.563261	−	0.826279i	$-0.309546\pi$
$827$	−12.4793	−	21.6148i	−0.433948	−	0.751619i	−0.997209	+	0.0746593i	$0.976213\pi$
$828$		0			0
$829$	−1.39964	+	2.42424i	−0.0486114	+	0.0841974i	−0.889307	−	0.457310i	$-0.848813\pi$
$829$	−1.39964	+	2.42424i	−0.0486114	+	0.0841974i	0.840696	+	0.541508i	$0.182146\pi$
$830$	−1.58601	+	0.577260i	−0.0550511	+	0.0200370i
$831$		0			0
$832$	3.15313	−	2.64579i	0.109315	−	0.0917263i
$833$	4.38150	+	1.59474i	0.151810	+	0.0552543i
$834$		0			0
$835$	−3.69354	+	20.9471i	−0.127820	+	0.724904i
$836$	−35.3445			−1.22242
$837$		0			0
$838$	−8.93083			−0.308511
$839$	7.76344	−	44.0287i	0.268024	−	1.52004i	−0.492261	−	0.870448i	$-0.663829\pi$
$839$	7.76344	−	44.0287i	0.268024	−	1.52004i	0.760284	−	0.649590i	$-0.225060\pi$
$840$		0			0
$841$	−53.7998	−	19.5815i	−1.85517	−	0.675225i
$842$	4.34395	−	3.64501i	0.149702	−	0.125615i
$843$		0			0
$844$	26.2312	−	9.54736i	0.902914	−	0.328634i
$845$	13.3235	−	23.0770i	0.458342	−	0.793872i
$846$		0			0
$847$	−1.41552	−	2.45175i	−0.0486378	−	0.0842431i
$848$	0.0764621	+	0.0641593i	0.00262572	+	0.00220324i
$849$		0			0
$850$	0.548282	+	3.10946i	0.0188059	+	0.106654i
$851$	3.89487	+	22.0889i	0.133515	+	0.757199i
$852$		0			0
$853$	−33.3344	−	27.9709i	−1.14135	−	0.957704i	−0.141866	−	0.989886i	$-0.545310\pi$
$853$	−33.3344	−	27.9709i	−1.14135	−	0.957704i	−0.999482	+	0.0321814i	$0.989755\pi$
$854$	0.332467	+	0.575850i	0.0113768	+	0.0197052i
$855$		0			0
$856$	−10.2254	+	17.7108i	−0.349496	+	0.605344i
$857$	6.86962	−	2.50034i	0.234662	−	0.0854099i	−0.222013	−	0.975044i	$-0.571263\pi$
$857$	6.86962	−	2.50034i	0.234662	−	0.0854099i	0.456674	+	0.889634i	$0.349040\pi$
$858$		0			0
$859$	−7.40236	+	6.21132i	−0.252565	+	0.211928i	−0.760276	−	0.649600i	$-0.774936\pi$
$859$	−7.40236	+	6.21132i	−0.252565	+	0.211928i	0.507711	+	0.861528i	$0.330492\pi$
$860$	7.28034	+	2.64983i	0.248258	+	0.0903583i
$861$		0			0
$862$	−0.0525465	+	0.298006i	−0.00178974	+	0.0101501i
$863$	−3.15525			−0.107406			−0.0537030	−	0.998557i	$-0.517102\pi$
$863$	−3.15525			−0.107406			−0.0537030	+	0.998557i	$0.517102\pi$
$864$		0			0
$865$	−6.25989			−0.212843
$866$	3.25489	−	18.4594i	0.110606	−	0.627276i
$867$		0			0
$868$	−9.28637	−	3.37996i	−0.315200	−	0.114723i
$869$	9.81991	−	8.23988i	0.333118	−	0.279519i
$870$		0			0
$871$	−12.7146	+	4.62774i	−0.430818	+	0.156805i
$872$	1.65609	−	2.86844i	0.0560824	−	0.0971376i
$873$		0			0
$874$	−12.7156	−	22.0240i	−0.430110	−	0.744973i
$875$	19.8211	+	16.6319i	0.670077	+	0.562262i
$876$		0			0
$877$	−9.18996	−	52.1188i	−0.310323	−	1.75993i	−0.597326	−	0.801999i	$-0.703770\pi$
$877$	−9.18996	−	52.1188i	−0.310323	−	1.75993i	0.287003	−	0.957930i	$-0.407341\pi$
$878$	4.95176	+	28.0828i	0.167114	+	0.947749i
$879$		0			0
$880$	4.21259	+	3.53479i	0.142007	+	0.119158i
$881$	−18.3507	−	31.7843i	−0.618250	−	1.07084i	−0.989805	−	0.142430i	$-0.954508\pi$
$881$	−18.3507	−	31.7843i	−0.618250	−	1.07084i	0.371555	−	0.928411i	$-0.378825\pi$
$882$		0			0
$883$	−14.9551	+	25.9031i	−0.503280	+	0.871707i	0.496712	+	0.867915i	$0.334540\pi$
$883$	−14.9551	+	25.9031i	−0.503280	+	0.871707i	−0.999993	+	0.00379204i	$0.998793\pi$
$884$	10.9949	−	4.00183i	0.369800	−	0.134596i
$885$		0			0
$886$	22.5124	−	18.8902i	0.756320	−	0.634628i
$887$	−52.3893	−	19.0681i	−1.75906	−	0.640245i	−0.759116	−	0.650955i	$-0.774369\pi$
$887$	−52.3893	−	19.0681i	−1.75906	−	0.640245i	−0.999943	+	0.0107097i	$0.996591\pi$
$888$		0			0
$889$	1.72249	−	9.76871i	0.0577704	−	0.327632i
$890$	−6.89133			−0.230998
$891$		0			0
$892$	18.5252			0.620270
$893$	−6.46182	+	36.6468i	−0.216237	+	1.22634i
$894$		0			0
$895$	8.22769	+	2.99463i	0.275021	+	0.100100i
$896$	17.8450	−	14.9737i	0.596159	−	0.500237i
$897$		0			0
$898$	8.61340	−	3.13502i	0.287433	−	0.104617i
$899$	13.1499	−	22.7763i	0.438573	−	0.759631i
$900$		0			0
$901$	−0.425085	−	0.736269i	−0.0141616	−	0.0245287i
$902$	−13.2988	−	11.1591i	−0.442803	−	0.371556i
$903$		0			0
$904$	8.14365	+	46.1849i	0.270854	+	1.53609i
$905$	−0.110800	−	0.628377i	−0.00368311	−	0.0208880i
$906$		0			0
$907$	27.5789	+	23.1414i	0.915741	+	0.768398i	0.973203	−	0.229950i	$-0.0738561\pi$
$907$	27.5789	+	23.1414i	0.915741	+	0.768398i	−0.0574613	+	0.998348i	$0.518301\pi$
$908$	8.69930	+	15.0676i	0.288696	+	0.500037i
$909$		0			0
$910$	3.08959	−	5.35132i	0.102419	−	0.177395i
$911$	15.3892	−	5.60121i	0.509866	−	0.185576i	−0.0742599	−	0.997239i	$-0.523659\pi$
$911$	15.3892	−	5.60121i	0.509866	−	0.185576i	0.584126	+	0.811663i	$0.301437\pi$
$912$		0			0
$913$	2.19762	−	1.84402i	0.0727306	−	0.0610282i
$914$	14.5113	+	5.28167i	0.479990	+	0.174702i
$915$		0			0
$916$	−6.21683	+	35.2574i	−0.205410	+	1.16494i
$917$	0.256387			0.00846665
$918$		0			0
$919$	19.5368			0.644461			0.322231	−	0.946661i	$-0.395567\pi$
$919$	19.5368			0.644461			0.322231	+	0.946661i	$0.395567\pi$
$920$	−4.41789	+	25.0551i	−0.145654	+	0.826042i
$921$		0			0
$922$	−5.58487	−	2.03273i	−0.183928	−	0.0669443i
$923$	8.38671	−	7.03728i	0.276052	−	0.231635i
$924$		0			0
$925$	−3.36344	+	1.22419i	−0.110589	+	0.0402512i
$926$	6.20413	−	10.7459i	0.203880	−	0.353131i
$927$		0			0
$928$	27.1834	+	47.0830i	0.892339	+	1.54558i
$929$	−8.23584	−	6.91069i	−0.270209	−	0.226732i	0.497607	−	0.867403i	$-0.334212\pi$
$929$	−8.23584	−	6.91069i	−0.270209	−	0.226732i	−0.767816	+	0.640670i	$0.778657\pi$
$930$		0			0
$931$	−1.04067	−	5.90195i	−0.0341067	−	0.193429i
$932$	−1.30735	−	7.41435i	−0.0428237	−	0.242865i
$933$		0			0
$934$	−15.5740	−	13.0681i	−0.509597	−	0.427603i
$935$	−23.4196	−	40.5639i	−0.765903	−	1.32658i
$936$		0			0
$937$	14.2219	−	24.6330i	0.464609	−	0.804727i	−0.534575	−	0.845121i	$-0.679528\pi$
$937$	14.2219	−	24.6330i	0.464609	−	0.804727i	0.999184	+	0.0403947i	$0.0128615\pi$
$938$	18.5055	−	6.73545i	0.604226	−	0.219920i
$939$		0			0
$940$	11.7186	−	9.83309i	0.382219	−	0.320720i
$941$	26.0864	+	9.49466i	0.850391	+	0.309517i	0.730200	−	0.683234i	$-0.239427\pi$
$941$	26.0864	+	9.49466i	0.850391	+	0.309517i	0.120191	+	0.992751i	$0.461649\pi$
$942$		0			0
$943$	−5.00298	+	28.3733i	−0.162919	+	0.923962i
$944$	−2.94571			−0.0958746
$945$		0			0
$946$	5.70939			0.185628
$947$	−7.37580	+	41.8302i	−0.239681	+	1.35930i	0.592846	+	0.805316i	$0.298004\pi$
$947$	−7.37580	+	41.8302i	−0.239681	+	1.35930i	−0.832527	+	0.553984i	$0.813107\pi$
$948$		0			0
$949$	15.4672	+	5.62960i	0.502087	+	0.182745i
$950$	3.10882	−	2.60861i	0.100863	−	0.0846343i
$951$		0			0
$952$	−38.9432	+	14.1742i	−1.26216	+	0.459388i
$953$	24.5758	−	42.5665i	0.796088	−	1.37886i	−0.126058	−	0.992023i	$-0.540233\pi$
$953$	24.5758	−	42.5665i	0.796088	−	1.37886i	0.922146	−	0.386842i	$-0.126434\pi$
$954$		0			0
$955$	−2.84922	−	4.93500i	−0.0921987	−	0.159693i
$956$	8.94641	+	7.50693i	0.289348	+	0.242792i
$957$		0			0
$958$	−5.31433	−	30.1390i	−0.171698	−	0.973748i
$959$	3.30962	+	18.7698i	0.106873	+	0.606109i
$960$		0			0
$961$	−17.6043	−	14.7718i	−0.567881	−	0.476509i
$962$	−2.87532	−	4.98021i	−0.0927041	−	0.160568i
$963$		0			0
$964$	−0.308456	+	0.534262i	−0.00993471	+	0.0172074i
$965$	−1.10804	+	0.403293i	−0.0356690	+	0.0129825i
$966$		0			0
$967$	36.7602	−	30.8454i	1.18213	−	0.991923i	0.182165	−	0.983268i	$-0.441690\pi$
$967$	36.7602	−	30.8454i	1.18213	−	0.991923i	0.999963	−	0.00865458i	$-0.00275487\pi$
$968$	−2.80827	−	1.02213i	−0.0902613	−	0.0328524i
$969$		0			0
$970$	−1.92439	+	10.9138i	−0.0617885	+	0.350420i
$971$	28.9682			0.929633			0.464817	−	0.885407i	$-0.346120\pi$
$971$	28.9682			0.929633			0.464817	+	0.885407i	$0.346120\pi$
$972$		0			0
$973$	26.1162			0.837247
$974$	1.58190	−	8.97139i	0.0506873	−	0.287462i
$975$		0			0
$976$	−0.236604	−	0.0861168i	−0.00757351	−	0.00275653i
$977$	11.6417	−	9.76855i	0.372451	−	0.312524i	−0.437279	−	0.899326i	$-0.644058\pi$
$977$	11.6417	−	9.76855i	0.372451	−	0.312524i	0.809730	+	0.586802i	$0.199613\pi$
$978$		0			0
$979$	11.0070	−	4.00621i	0.351784	−	0.128039i
$980$	−1.23183	+	2.13360i	−0.0393495	+	0.0681553i
$981$		0			0
$982$	−14.9907	−	25.9647i	−0.478373	−	0.828567i
$983$	29.5480	+	24.7937i	0.942435	+	0.790797i	0.978007	−	0.208570i	$-0.0668810\pi$
$983$	29.5480	+	24.7937i	0.942435	+	0.790797i	−0.0355724	+	0.999367i	$0.511325\pi$
$984$		0			0
$985$	9.13883	+	51.8289i	0.291187	+	1.65141i
$986$	−7.86986	−	44.6322i	−0.250627	−	1.42138i
$987$		0			0
$988$	−11.5204	−	9.66678i	−0.366513	−	0.307541i
$989$	−4.73760	−	8.20576i	−0.150647	−	0.260928i
$990$		0			0
$991$	−25.5171	+	44.1968i	−0.810576	+	1.40396i	0.101885	+	0.994796i	$0.467512\pi$
$991$	−25.5171	+	44.1968i	−0.810576	+	1.40396i	−0.912461	+	0.409163i	$0.865821\pi$
$992$	−15.5776	+	5.66977i	−0.494588	+	0.180015i
$993$		0			0
$994$	−12.2065	+	10.2424i	−0.387165	+	0.324870i
$995$	−4.76188	−	1.73318i	−0.150962	−	0.0549456i
$996$		0			0
$997$	5.52154	−	31.3142i	0.174869	−	0.991730i	−0.763426	−	0.645895i	$-0.776484\pi$
$997$	5.52154	−	31.3142i	0.174869	−	0.991730i	0.938295	−	0.345835i	$-0.112404\pi$
$998$	−22.9910			−0.727768
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.j.649.2		12
3.2	odd	2		729.2.e.u.649.1		12
9.2	odd	6		729.2.e.l.163.2		12
9.4	even	3		729.2.e.t.406.2		12
9.5	odd	6		729.2.e.k.406.1		12
9.7	even	3		729.2.e.s.163.1		12
27.2	odd	18		729.2.c.a.487.5		12
27.4	even	9		729.2.e.t.325.2		12
27.5	odd	18		729.2.e.l.568.2		12
27.7	even	9		729.2.c.d.244.2		12
27.11	odd	18		729.2.a.e.1.2	yes	6
27.13	even	9	inner	729.2.e.j.82.2		12
27.14	odd	18		729.2.e.u.82.1		12
27.16	even	9		729.2.a.b.1.5	✓	6
27.20	odd	18		729.2.c.a.244.5		12
27.22	even	9		729.2.e.s.568.1		12
27.23	odd	18		729.2.e.k.325.1		12
27.25	even	9		729.2.c.d.487.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.5	✓	6	27.16	even	9
729.2.a.e.1.2	yes	6	27.11	odd	18
729.2.c.a.244.5		12	27.20	odd	18
729.2.c.a.487.5		12	27.2	odd	18
729.2.c.d.244.2		12	27.7	even	9
729.2.c.d.487.2		12	27.25	even	9
729.2.e.j.82.2		12	27.13	even	9	inner
729.2.e.j.649.2		12	1.1	even	1	trivial
729.2.e.k.325.1		12	27.23	odd	18
729.2.e.k.406.1		12	9.5	odd	6
729.2.e.l.163.2		12	9.2	odd	6
729.2.e.l.568.2		12	27.5	odd	18
729.2.e.s.163.1		12	9.7	even	3
729.2.e.s.568.1		12	27.22	even	9
729.2.e.t.325.2		12	27.4	even	9
729.2.e.t.406.2		12	9.4	even	3
729.2.e.u.82.1		12	27.14	odd	18
729.2.e.u.649.1		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
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

Properties

Related objects

Downloads

Learn more