LMFDB - Embedded newform 729.2.g.b.55.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			55.5
Character	$\chi$	$=$	729.55
Dual form			729.2.g.b.676.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.314515 - 0.729128i) q^{2} +(0.939775 + 0.996103i) q^{4} +(-0.127484 - 2.18881i) q^{5} +(-3.45959 - 0.819939i) q^{7} +(2.51422 - 0.915103i) q^{8} +O(q^{10})$	\(q+(0.314515 - 0.729128i) q^{2} +(0.939775 + 0.996103i) q^{4} +(-0.127484 - 2.18881i) q^{5} +(-3.45959 - 0.819939i) q^{7} +(2.51422 - 0.915103i) q^{8} +(-1.63602 - 0.595462i) q^{10} +(-3.62940 - 2.38710i) q^{11} +(-6.02225 - 0.703900i) q^{13} +(-1.68594 + 2.26460i) q^{14} +(-0.0357186 + 0.613264i) q^{16} +(-1.52297 + 1.27793i) q^{17} +(-2.70233 - 2.26753i) q^{19} +(2.06047 - 2.18397i) q^{20} +(-2.88200 + 1.89552i) q^{22} +(5.36375 - 1.27123i) q^{23} +(0.191560 - 0.0223902i) q^{25} +(-2.40732 + 4.16961i) q^{26} +(-2.43450 - 4.21667i) q^{28} +(-0.388529 - 0.521885i) q^{29} +(0.732013 - 2.44509i) q^{31} +(5.21789 + 2.62052i) q^{32} +(0.452774 + 1.51237i) q^{34} +(-1.35365 + 7.67692i) q^{35} +(0.702191 + 3.98232i) q^{37} +(-2.50324 + 1.25718i) q^{38} +(-2.32351 - 5.38650i) q^{40} +(-3.24228 - 7.51644i) q^{41} +(2.08047 - 1.04485i) q^{43} +(-1.03303 - 5.85859i) q^{44} +(0.760089 - 4.31068i) q^{46} +(-0.837341 - 2.79691i) q^{47} +(5.04106 + 2.53172i) q^{49} +(0.0439233 - 0.146714i) q^{50} +(-4.95840 - 6.66029i) q^{52} +(1.34845 + 2.33558i) q^{53} +(-4.76221 + 8.24838i) q^{55} +(-9.44853 + 1.10437i) q^{56} +(-0.502720 + 0.119147i) q^{58} +(6.21681 - 4.08886i) q^{59} +(-1.80586 + 1.91410i) q^{61} +(-1.55256 - 1.30275i) q^{62} +(2.61064 - 2.19058i) q^{64} +(-0.772965 + 13.2713i) q^{65} +(2.18642 - 2.93688i) q^{67} +(-2.70420 - 0.316075i) q^{68} +(5.17172 + 3.40149i) q^{70} +(-1.04338 - 0.379759i) q^{71} +(-8.97377 + 3.26619i) q^{73} +(3.12448 + 0.740514i) q^{74} +(-0.280894 - 4.82277i) q^{76} +(10.5990 + 11.2343i) q^{77} +(1.09986 - 2.54976i) q^{79} +1.34687 q^{80} -6.50019 q^{82} +(4.95776 - 11.4934i) q^{83} +(2.99129 + 3.17058i) q^{85} +(-0.107491 - 1.84555i) q^{86} +(-11.3096 - 2.68042i) q^{88} +(3.58032 - 1.30313i) q^{89} +(20.2574 + 7.37309i) q^{91} +(6.30699 + 4.14817i) q^{92} +(-2.30267 - 0.269143i) q^{94} +(-4.61868 + 6.20396i) q^{95} +(-0.611885 + 10.5057i) q^{97} +(3.43144 - 2.87932i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	0.314515	−	0.729128i	0.222396	−	0.515572i	−0.770089	−	0.637936i	$-0.779788\pi$
$2$	0.314515	−	0.729128i	0.222396	−	0.515572i	0.992485	+	0.122364i	$0.0390477\pi$
$3$		0			0
$3$		0			0
$4$	0.939775	+	0.996103i	0.469888	+	0.498052i
$5$	−0.127484	−	2.18881i	−0.0570124	−	0.978865i	−0.898607	−	0.438755i	$-0.855420\pi$
$5$	−0.127484	−	2.18881i	−0.0570124	−	0.978865i	0.841594	−	0.540110i	$-0.181617\pi$
$6$		0			0
$7$	−3.45959	−	0.819939i	−1.30760	−	0.309908i	−0.483001	−	0.875620i	$-0.660453\pi$
$7$	−3.45959	−	0.819939i	−1.30760	−	0.309908i	−0.824603	+	0.565712i	$0.808601\pi$
$8$	2.51422	−	0.915103i	0.888913	−	0.323538i
$9$		0			0
$10$	−1.63602	−	0.595462i	−0.517354	−	0.188302i
$11$	−3.62940	−	2.38710i	−1.09431	−	0.719736i	−0.131876	−	0.991266i	$-0.542100\pi$
$11$	−3.62940	−	2.38710i	−1.09431	−	0.719736i	−0.962430	+	0.271530i	$0.912470\pi$
$12$		0			0
$13$	−6.02225	−	0.703900i	−1.67027	−	0.195227i	−0.772293	−	0.635266i	$-0.780890\pi$
$13$	−6.02225	−	0.703900i	−1.67027	−	0.195227i	−0.897979	+	0.440039i	$0.854965\pi$
$14$	−1.68594	+	2.26460i	−0.450585	+	0.605241i
$15$		0			0
$16$	−0.0357186	+	0.613264i	−0.00892964	+	0.153316i
$17$	−1.52297	+	1.27793i	−0.369375	+	0.309942i	−0.808514	−	0.588477i	$-0.799728\pi$
$17$	−1.52297	+	1.27793i	−0.369375	+	0.309942i	0.439139	+	0.898419i	$0.355283\pi$
$18$		0			0
$19$	−2.70233	−	2.26753i	−0.619958	−	0.520206i	0.277832	−	0.960630i	$-0.410384\pi$
$19$	−2.70233	−	2.26753i	−0.619958	−	0.520206i	−0.897790	+	0.440423i	$0.854828\pi$
$20$	2.06047	−	2.18397i	0.460736	−	0.488352i
$21$		0			0
$22$	−2.88200	+	1.89552i	−0.614445	+	0.404127i
$23$	5.36375	−	1.27123i	1.11842	−	0.265070i	0.370481	−	0.928840i	$-0.379193\pi$
$23$	5.36375	−	1.27123i	1.11842	−	0.265070i	0.747937	+	0.663770i	$0.231045\pi$
$24$		0			0
$25$	0.191560	−	0.0223902i	0.0383120	−	0.00447804i
$26$	−2.40732	+	4.16961i	−0.472115	+	0.817727i
$27$		0			0
$28$	−2.43450	−	4.21667i	−0.460077	−	0.796876i
$29$	−0.388529	−	0.521885i	−0.0721480	−	0.0969116i	0.764584	−	0.644524i	$-0.222944\pi$
$29$	−0.388529	−	0.521885i	−0.0721480	−	0.0969116i	−0.836732	+	0.547612i	$0.815537\pi$
$30$		0			0
$31$	0.732013	−	2.44509i	0.131473	−	0.439152i	−0.866749	−	0.498744i	$-0.833795\pi$
$31$	0.732013	−	2.44509i	0.131473	−	0.439152i	0.998223	+	0.0595921i	$0.0189800\pi$
$32$	5.21789	+	2.62052i	0.922401	+	0.463247i
$33$		0			0
$34$	0.452774	+	1.51237i	0.0776500	+	0.259369i
$35$	−1.35365	+	7.67692i	−0.228808	+	1.29764i
$36$		0			0
$37$	0.702191	+	3.98232i	0.115440	+	0.654690i	0.986532	+	0.163570i	$0.0523011\pi$
$37$	0.702191	+	3.98232i	0.115440	+	0.654690i	−0.871092	+	0.491120i	$0.836588\pi$
$38$	−2.50324	+	1.25718i	−0.406080	+	0.203941i
$39$		0			0
$40$	−2.32351	−	5.38650i	−0.367379	−	0.851680i
$41$	−3.24228	−	7.51644i	−0.506358	−	1.17387i	−0.959315	−	0.282338i	$-0.908890\pi$
$41$	−3.24228	−	7.51644i	−0.506358	−	1.17387i	0.452957	−	0.891533i	$-0.350369\pi$
$42$		0			0
$43$	2.08047	−	1.04485i	0.317269	−	0.159338i	−0.283037	−	0.959109i	$-0.591342\pi$
$43$	2.08047	−	1.04485i	0.317269	−	0.159338i	0.600306	+	0.799771i	$0.295046\pi$
$44$	−1.03303	−	5.85859i	−0.155735	−	0.883216i
$45$		0			0
$46$	0.760089	−	4.31068i	0.112069	−	0.635575i
$47$	−0.837341	−	2.79691i	−0.122139	−	0.407972i	0.874951	−	0.484212i	$-0.160894\pi$
$47$	−0.837341	−	2.79691i	−0.122139	−	0.407972i	−0.997089	+	0.0762401i	$0.975708\pi$
$48$		0			0
$49$	5.04106	+	2.53172i	0.720152	+	0.361674i
$50$	0.0439233	−	0.146714i	0.00621169	−	0.0207485i
$51$		0			0
$52$	−4.95840	−	6.66029i	−0.687607	−	0.923616i
$53$	1.34845	+	2.33558i	0.185224	+	0.320817i	0.943652	−	0.330940i	$-0.107366\pi$
$53$	1.34845	+	2.33558i	0.185224	+	0.320817i	−0.758428	+	0.651757i	$0.774032\pi$
$54$		0			0
$55$	−4.76221	+	8.24838i	−0.642136	+	1.11221i
$56$	−9.44853	+	1.10437i	−1.26261	+	0.147578i
$57$		0			0
$58$	−0.502720	+	0.119147i	−0.0660103	+	0.0156447i
$59$	6.21681	−	4.08886i	0.809360	−	0.532324i	−0.0760672	−	0.997103i	$-0.524236\pi$
$59$	6.21681	−	4.08886i	0.809360	−	0.532324i	0.885427	+	0.464778i	$0.153866\pi$
$60$		0			0
$61$	−1.80586	+	1.91410i	−0.231217	+	0.245076i	−0.832586	−	0.553895i	$-0.813141\pi$
$61$	−1.80586	+	1.91410i	−0.231217	+	0.245076i	0.601369	+	0.798971i	$0.294622\pi$
$62$	−1.55256	−	1.30275i	−0.197175	−	0.165450i
$63$		0			0
$64$	2.61064	−	2.19058i	0.326329	−	0.273823i
$65$	−0.772965	+	13.2713i	−0.0958745	+	1.64610i
$66$		0			0
$67$	2.18642	−	2.93688i	0.267114	−	0.358797i	−0.648247	−	0.761430i	$-0.724498\pi$
$67$	2.18642	−	2.93688i	0.267114	−	0.358797i	0.915361	+	0.402633i	$0.131905\pi$
$68$	−2.70420	−	0.316075i	−0.327932	−	0.0383298i
$69$		0			0
$70$	5.17172	+	3.40149i	0.618138	+	0.406556i
$71$	−1.04338	−	0.379759i	−0.123826	−	0.0450691i	0.279364	−	0.960185i	$-0.409876\pi$
$71$	−1.04338	−	0.379759i	−0.123826	−	0.0450691i	−0.403190	+	0.915116i	$0.632099\pi$
$72$		0			0
$73$	−8.97377	+	3.26619i	−1.05030	+	0.382278i	−0.808776	−	0.588117i	$-0.799870\pi$
$73$	−8.97377	+	3.26619i	−1.05030	+	0.382278i	−0.241525	+	0.970395i	$0.577647\pi$
$74$	3.12448	+	0.740514i	0.363213	+	0.0860830i
$75$		0			0
$76$	−0.280894	−	4.82277i	−0.0322208	−	0.553210i
$77$	10.5990	+	11.2343i	1.20787	+	1.28026i
$78$		0			0
$79$	1.09986	−	2.54976i	0.123744	−	0.286871i	−0.845072	−	0.534653i	$-0.820442\pi$
$79$	1.09986	−	2.54976i	0.123744	−	0.286871i	0.968816	+	0.247782i	$0.0797017\pi$
$80$	1.34687			0.150585
$81$		0			0
$82$	−6.50019			−0.717826
$83$	4.95776	−	11.4934i	0.544185	−	1.26156i	−0.395168	−	0.918609i	$-0.629313\pi$
$83$	4.95776	−	11.4934i	0.544185	−	1.26156i	0.939352	−	0.342953i	$-0.111427\pi$
$84$		0			0
$85$	2.99129	+	3.17058i	0.324451	+	0.343898i
$86$	−0.107491	−	1.84555i	−0.0115911	−	0.199011i
$87$		0			0
$88$	−11.3096	−	2.68042i	−1.20560	−	0.285734i
$89$	3.58032	−	1.30313i	0.379514	−	0.138132i	−0.145217	−	0.989400i	$-0.546388\pi$
$89$	3.58032	−	1.30313i	0.379514	−	0.138132i	0.524731	+	0.851268i	$0.324166\pi$
$90$		0			0
$91$	20.2574	+	7.37309i	2.12355	+	0.772909i
$92$	6.30699	+	4.14817i	0.657549	+	0.432477i
$93$		0			0
$94$	−2.30267	−	0.269143i	−0.237502	−	0.0277600i
$95$	−4.61868	+	6.20396i	−0.473867	+	0.636513i
$96$		0			0
$97$	−0.611885	+	10.5057i	−0.0621275	+	1.06669i	0.812834	+	0.582495i	$0.197923\pi$
$97$	−0.611885	+	10.5057i	−0.0621275	+	1.06669i	−0.874962	+	0.484192i	$0.839114\pi$
$98$	3.43144	−	2.87932i	0.346628	−	0.290855i
$99$		0			0
$100$	0.202326	+	0.169772i	0.0202326	+	0.0169772i
$101$	6.34862	−	6.72914i	0.631711	−	0.669575i	−0.329892	−	0.944019i	$-0.607012\pi$
$101$	6.34862	−	6.72914i	0.631711	−	0.669575i	0.961603	+	0.274444i	$0.0884938\pi$
$102$		0			0
$103$	−8.61167	+	5.66398i	−0.848533	+	0.558089i	−0.897653	−	0.440704i	$-0.854729\pi$
$103$	−8.61167	+	5.66398i	−0.848533	+	0.558089i	0.0491194	+	0.998793i	$0.484359\pi$
$104$	−15.7854	+	3.74122i	−1.54789	+	0.366856i
$105$		0			0
$106$	2.12705	−	0.248616i	0.206597	−	0.0241477i
$107$	−1.36475	+	2.36382i	−0.131936	+	0.228519i	−0.924423	−	0.381370i	$-0.875453\pi$
$107$	−1.36475	+	2.36382i	−0.131936	+	0.228519i	0.792487	+	0.609889i	$0.208786\pi$
$108$		0			0
$109$	0.572236	+	0.991142i	0.0548103	+	0.0949342i	0.892129	−	0.451781i	$-0.149211\pi$
$109$	0.572236	+	0.991142i	0.0548103	+	0.0949342i	−0.837318	+	0.546715i	$0.815878\pi$
$110$	4.51634	+	6.06650i	0.430616	+	0.578418i
$111$		0			0
$112$	0.626411	−	2.09236i	0.0591903	−	0.197709i
$113$	−10.8348	−	5.44144i	−1.01925	−	0.511887i	−0.140961	−	0.990015i	$-0.545019\pi$
$113$	−10.8348	−	5.44144i	−1.01925	−	0.511887i	−0.878290	+	0.478128i	$0.841316\pi$
$114$		0			0
$115$	−3.46627	−	11.5782i	−0.323231	−	1.07967i
$116$	0.154722	−	0.877470i	0.0143655	−	0.0814710i
$117$		0			0
$118$	−1.02602	−	5.81886i	−0.0944530	−	0.535670i
$119$	6.31669	−	3.17236i	0.579050	−	0.290810i
$120$		0			0
$121$	3.11746	+	7.22709i	0.283406	+	0.657008i
$122$	0.827656	+	1.91872i	0.0749324	+	0.173713i
$123$		0			0
$124$	3.12349	−	1.56868i	0.280498	−	0.140871i
$125$	−1.97706	−	11.2125i	−0.176834	−	1.00287i
$126$		0			0
$127$	1.90657	−	10.8127i	0.169181	−	0.959471i	−0.775468	−	0.631387i	$-0.782486\pi$
$127$	1.90657	−	10.8127i	0.169181	−	0.959471i	0.944648	−	0.328084i	$-0.106403\pi$
$128$	2.57314	+	8.59487i	0.227435	+	0.759687i
$129$		0			0
$130$	9.43336	+	4.73761i	0.827361	+	0.415516i
$131$	−0.126951	+	0.424045i	−0.0110917	+	0.0370490i	−0.963356	−	0.268225i	$-0.913563\pi$
$131$	−0.126951	+	0.424045i	−0.0110917	+	0.0370490i	0.952265	+	0.305274i	$0.0987481\pi$
$132$		0			0
$133$	7.48974	+	10.0605i	0.649443	+	0.872354i
$134$	−1.45370	−	2.51788i	−0.125580	−	0.217511i
$135$		0			0
$136$	−2.65966	+	4.60667i	−0.228064	+	0.395019i
$137$	−18.3072	+	2.13981i	−1.56409	+	0.182816i	−0.853615	−	0.520905i	$-0.825595\pi$
$137$	−18.3072	+	2.13981i	−1.56409	+	0.182816i	−0.710476	+	0.703721i	$0.751521\pi$
$138$		0			0
$139$	19.5674	−	4.63757i	1.65969	−	0.393353i	0.709420	−	0.704786i	$-0.248957\pi$
$139$	19.5674	−	4.63757i	1.65969	−	0.393353i	0.950268	+	0.311433i	$0.100809\pi$
$140$	−8.91913	+	5.86620i	−0.753804	+	0.495785i
$141$		0			0
$142$	−0.605052	+	0.641317i	−0.0507748	+	0.0538181i
$143$	20.1769	+	16.9304i	1.68728	+	1.41579i
$144$		0			0
$145$	−1.09278	+	0.916948i	−0.0907501	+	0.0761484i
$146$	−0.440920	+	7.57030i	−0.0364908	+	0.626522i
$147$		0			0
$148$	−3.30691	+	4.44194i	−0.271826	+	0.365126i
$149$	−2.02579	−	0.236781i	−0.165959	−	0.0193979i	0.0327074	−	0.999465i	$-0.489587\pi$
$149$	−2.02579	−	0.236781i	−0.165959	−	0.0193979i	−0.198667	+	0.980067i	$0.563661\pi$
$150$		0			0
$151$	7.70340	+	5.06660i	0.626894	+	0.412314i	0.822818	−	0.568305i	$-0.192400\pi$
$151$	7.70340	+	5.06660i	0.626894	+	0.412314i	−0.195925	+	0.980619i	$0.562771\pi$
$152$	−8.86930	−	3.22816i	−0.719395	−	0.261838i
$153$		0			0
$154$	11.5248	−	4.19467i	0.928692	−	0.338016i
$155$	−5.44516	−	1.29053i	−0.437366	−	0.103658i
$156$		0			0
$157$	1.29436	+	22.2233i	0.103301	+	1.77362i	0.510116	+	0.860106i	$0.329602\pi$
$157$	1.29436	+	22.2233i	0.103301	+	1.77362i	−0.406815	+	0.913511i	$0.633360\pi$
$158$	−1.51318	−	1.60388i	−0.120382	−	0.127598i
$159$		0			0
$160$	5.07063	−	11.7550i	0.400868	−	0.929317i
$161$	−19.5987			−1.54460
$162$		0			0
$163$	18.7475			1.46842			0.734210	−	0.678922i	$-0.237553\pi$
$163$	18.7475			1.46842			0.734210	+	0.678922i	$0.237553\pi$
$164$	4.44014	−	10.2934i	0.346717	−	0.803780i
$165$		0			0
$166$	−6.82086	−	7.22969i	−0.529401	−	0.561132i
$167$	−0.251837	−	4.32388i	−0.0194878	−	0.334592i	−0.993935	−	0.109973i	$-0.964923\pi$
$167$	−0.251837	−	4.32388i	−0.0194878	−	0.334592i	0.974447	−	0.224619i	$-0.0721136\pi$
$168$		0			0
$169$	23.1224	+	5.48012i	1.77865	+	0.421548i
$170$	3.25257	−	1.18384i	0.249460	−	0.0907962i
$171$		0			0
$172$	2.99595	+	1.09044i	0.228439	+	0.0831451i
$173$	−7.94546	−	5.22581i	−0.604082	−	0.397311i	0.210303	−	0.977636i	$-0.432555\pi$
$173$	−7.94546	−	5.22581i	−0.604082	−	0.397311i	−0.814385	+	0.580325i	$0.802925\pi$
$174$		0			0
$175$	−0.681079	−	0.0796068i	−0.0514848	−	0.00601770i
$176$	1.59356	−	2.14052i	0.120119	−	0.161348i
$177$		0			0
$178$	0.175917	−	3.02037i	0.0131855	−	0.226386i
$179$	14.6883	−	12.3250i	1.09786	−	0.921212i	0.100579	−	0.994929i	$-0.467930\pi$
$179$	14.6883	−	12.3250i	1.09786	−	0.921212i	0.997279	+	0.0737166i	$0.0234860\pi$
$180$		0			0
$181$	5.16508	+	4.33401i	0.383917	+	0.322145i	0.814238	−	0.580531i	$-0.197155\pi$
$181$	5.16508	+	4.33401i	0.383917	+	0.322145i	−0.430321	+	0.902676i	$0.641600\pi$
$182$	11.7472	−	12.4513i	0.870759	−	0.922951i
$183$		0			0
$184$	12.3224	−	8.10454i	0.908416	−	0.597475i
$185$	8.62703	−	2.04464i	0.634272	−	0.150325i
$186$		0			0
$187$	8.57801	−	1.00263i	0.627286	−	0.0733193i
$188$	1.99910	−	3.46255i	0.145800	−	0.252532i
$189$		0			0
$190$	3.07084	+	5.31885i	0.222782	+	0.385870i
$191$	10.9826	+	14.7521i	0.794671	+	1.06743i	0.996127	+	0.0879303i	$0.0280253\pi$
$191$	10.9826	+	14.7521i	0.794671	+	1.06743i	−0.201456	+	0.979498i	$0.564567\pi$
$192$		0			0
$193$	2.65584	−	8.87112i	0.191171	−	0.638557i	−0.807634	−	0.589685i	$-0.799252\pi$
$193$	2.65584	−	8.87112i	0.191171	−	0.638557i	0.998805	−	0.0488723i	$-0.0155627\pi$
$194$	7.46752	+	3.75033i	0.536137	+	0.269258i
$195$		0			0
$196$	2.21561	+	7.40067i	0.158258	+	0.528619i
$197$	4.14143	−	23.4872i	0.295065	−	1.67340i	−0.371874	−	0.928283i	$-0.621285\pi$
$197$	4.14143	−	23.4872i	0.295065	−	1.67340i	0.666939	−	0.745112i	$-0.267604\pi$
$198$		0			0
$199$	−1.69676	−	9.62282i	−0.120280	−	0.682144i	−0.984000	−	0.178170i	$-0.942982\pi$
$199$	−1.69676	−	9.62282i	−0.120280	−	0.682144i	0.863719	−	0.503973i	$-0.168129\pi$
$200$	0.461136	−	0.231591i	0.0326073	−	0.0163760i
$201$		0			0
$202$	−2.90967	−	6.74537i	−0.204724	−	0.474603i
$203$	0.916239	+	2.12408i	0.0643074	+	0.149081i
$204$		0			0
$205$	−16.0387	+	8.05494i	−1.12019	+	0.562582i
$206$	1.42127	+	8.06042i	0.0990246	+	0.561596i
$207$		0			0
$208$	0.646783	−	3.66809i	0.0448463	−	0.254336i
$209$	4.39505	+	14.6805i	0.304012	+	1.01547i
$210$		0			0
$211$	−15.3073	−	7.68759i	−1.05380	−	0.529236i	−0.164409	−	0.986392i	$-0.552572\pi$
$211$	−15.3073	−	7.68759i	−1.05380	−	0.529236i	−0.889386	+	0.457156i	$0.848868\pi$
$212$	−1.05924	+	3.53812i	−0.0727491	+	0.242999i
$213$		0			0
$214$	1.29429	+	1.73854i	0.0884760	+	0.118844i
$215$	−2.55220	−	4.42055i	−0.174059	−	0.301479i
$216$		0			0
$217$	−4.53730	+	7.85883i	−0.308012	+	0.533492i
$218$	0.902647	−	0.105504i	0.0611349	−	0.00714565i
$219$		0			0
$220$	−12.6916	+	3.00798i	−0.855671	+	0.202798i
$221$	10.0713	−	6.62397i	0.677466	−	0.445576i
$222$		0			0
$223$	−10.9437	+	11.5997i	−0.732845	+	0.776770i	−0.981426	−	0.191841i	$-0.938554\pi$
$223$	−10.9437	+	11.5997i	−0.732845	+	0.776770i	0.248581	+	0.968611i	$0.420036\pi$
$224$	−15.9031	−	13.3443i	−1.06257	−	0.891603i
$225$		0			0
$226$	−7.37521	+	6.18854i	−0.490592	+	0.411656i
$227$	0.180528	−	3.09955i	0.0119821	−	0.205724i	−0.987004	−	0.160697i	$-0.948626\pi$
$227$	0.180528	−	3.09955i	0.0119821	−	0.205724i	0.998986	−	0.0450268i	$-0.0143373\pi$
$228$		0			0
$229$	1.68303	−	2.26070i	0.111218	−	0.149391i	−0.743029	−	0.669259i	$-0.766611\pi$
$229$	1.68303	−	2.26070i	0.111218	−	0.149391i	0.854247	+	0.519868i	$0.174019\pi$
$230$	−9.53215	−	1.11415i	−0.628532	−	0.0734648i
$231$		0			0
$232$	−1.45443	−	0.956593i	−0.0954879	−	0.0628034i
$233$	0.753290	+	0.274175i	0.0493497	+	0.0179618i	0.366577	−	0.930388i	$-0.380530\pi$
$233$	0.753290	+	0.274175i	0.0493497	+	0.0179618i	−0.317227	+	0.948350i	$0.602752\pi$
$234$		0			0
$235$	−6.01516	+	2.18934i	−0.392386	+	0.142817i
$236$	9.91533	+	2.34998i	0.645433	+	0.152970i
$237$		0			0
$238$	−0.326363	−	5.60343i	−0.0211550	−	0.363216i
$239$	−11.6903	−	12.3910i	−0.756186	−	0.801510i	0.228923	−	0.973445i	$-0.426480\pi$
$239$	−11.6903	−	12.3910i	−0.756186	−	0.801510i	−0.985108	+	0.171935i	$0.944998\pi$
$240$		0			0
$241$	1.35982	−	3.15243i	0.0875940	−	0.203066i	−0.868788	−	0.495184i	$-0.835101\pi$
$241$	1.35982	−	3.15243i	0.0875940	−	0.203066i	0.956382	+	0.292118i	$0.0943600\pi$
$242$	6.24996			0.401763
$243$		0			0
$244$	−3.60375			−0.230707
$245$	4.89879	−	11.3567i	0.312972	−	0.725551i
$246$		0			0
$247$	14.6780	+	15.5578i	0.933940	+	0.989919i
$248$	−0.397067	−	6.81738i	−0.0252138	−	0.432904i
$249$		0			0
$250$	−8.79715	−	2.08496i	−0.556381	−	0.131865i
$251$	−18.8184	+	6.84933i	−1.18781	+	0.432326i	−0.858953	−	0.512055i	$-0.828884\pi$
$251$	−18.8184	+	6.84933i	−1.18781	+	0.432326i	−0.328853	+	0.944381i	$0.606662\pi$
$252$		0			0
$253$	−22.5017	−	8.18996i	−1.41467	−	0.514899i
$254$	−7.28419	−	4.79089i	−0.457051	−	0.300607i
$255$		0			0
$256$	13.8459	+	1.61835i	0.865366	+	0.101147i
$257$	−4.34011	+	5.82977i	−0.270728	+	0.363651i	−0.916607	−	0.399788i	$-0.869084\pi$
$257$	−4.34011	+	5.82977i	−0.270728	+	0.363651i	0.645879	+	0.763440i	$0.276491\pi$
$258$		0			0
$259$	0.835966	−	14.3530i	0.0519444	−	0.891851i
$260$	−13.9460	+	11.7021i	−0.864894	+	0.725732i
$261$		0			0
$262$	0.269255	+	0.225932i	0.0166346	+	0.0139581i
$263$	−16.9390	+	17.9542i	−1.04450	+	1.10711i	−0.0503907	+	0.998730i	$0.516047\pi$
$263$	−16.9390	+	17.9542i	−1.04450	+	1.10711i	−0.994110	+	0.108376i	$0.965435\pi$
$264$		0			0
$265$	4.94024	−	3.24925i	0.303476	−	0.199600i
$266$	9.69101	−	2.29681i	0.594194	−	0.140827i
$267$		0			0
$268$	4.98018	−	0.582100i	0.304213	−	0.0355574i
$269$	0.710882	−	1.23128i	0.0433432	−	0.0750727i	−0.843540	−	0.537066i	$-0.819532\pi$
$269$	0.710882	−	1.23128i	0.0433432	−	0.0750727i	0.886883	+	0.461994i	$0.152866\pi$
$270$		0			0
$271$	−5.71617	−	9.90069i	−0.347232	−	0.601424i	0.638524	−	0.769602i	$-0.279545\pi$
$271$	−5.71617	−	9.90069i	−0.347232	−	0.601424i	−0.985757	+	0.168177i	$0.946212\pi$
$272$	−0.729308	−	0.979630i	−0.0442208	−	0.0593988i
$273$		0			0
$274$	−4.19771	+	14.0213i	−0.253593	+	0.847058i
$275$	−0.748697	−	0.376010i	−0.0451481	−	0.0226742i
$276$		0			0
$277$	5.74367	+	19.1852i	0.345104	+	1.15273i	0.937764	+	0.347274i	$0.112893\pi$
$277$	5.74367	+	19.1852i	0.345104	+	1.15273i	−0.592660	+	0.805453i	$0.701922\pi$
$278$	2.77287	−	15.7258i	0.166306	−	0.943168i
$279$		0			0
$280$	3.62180	+	20.5402i	0.216444	+	1.22751i
$281$	24.9957	−	12.5533i	1.49112	−	0.748867i	0.498132	−	0.867101i	$-0.334020\pi$
$281$	24.9957	−	12.5533i	1.49112	−	0.748867i	0.992986	+	0.118234i	$0.0377232\pi$
$282$		0			0
$283$	−6.34849	−	14.7175i	−0.377379	−	0.874862i	−0.996015	−	0.0891846i	$-0.971574\pi$
$283$	−6.34849	−	14.7175i	−0.377379	−	0.874862i	0.618636	−	0.785677i	$-0.287685\pi$
$284$	−0.602262	−	1.39620i	−0.0357377	−	0.0828493i
$285$		0			0
$286$	18.6904	−	9.38667i	1.10519	−	0.555045i
$287$	5.05394	+	28.6623i	0.298324	+	1.69188i
$288$		0			0
$289$	−2.26567	+	12.8492i	−0.133275	+	0.755838i
$290$	0.324878	+	1.08517i	0.0190775	+	0.0637232i
$291$		0			0
$292$	−11.6868	−	5.86933i	−0.683918	−	0.343476i
$293$	−6.62381	+	22.1251i	−0.386967	+	1.29256i	0.513670	+	0.857988i	$0.328286\pi$
$293$	−6.62381	+	22.1251i	−0.386967	+	1.29256i	−0.900637	+	0.434572i	$0.856900\pi$
$294$		0			0
$295$	−9.74228	−	13.0861i	−0.567217	−	0.761905i
$296$	5.40970	+	9.36988i	0.314433	+	0.544613i
$297$		0			0
$298$	−0.809786	+	1.40259i	−0.0469097	+	0.0812499i
$299$	−33.1966	+	3.88013i	−1.91981	+	0.224394i
$300$		0			0
$301$	−8.05429	+	1.90890i	−0.464242	+	0.110027i
$302$	6.11704	−	4.02324i	0.351996	−	0.231511i
$303$		0			0
$304$	1.48712	−	1.57625i	0.0852920	−	0.0904042i
$305$	4.41983	+	3.70868i	0.253079	+	0.212358i
$306$		0			0
$307$	13.6869	−	11.4846i	0.781150	−	0.655463i	−0.162388	−	0.986727i	$-0.551920\pi$
$307$	13.6869	−	11.4846i	0.781150	−	0.655463i	0.943538	+	0.331264i	$0.107475\pi$
$308$	−1.22983	+	21.1154i	−0.0700761	+	1.20316i
$309$		0			0
$310$	−2.65355	+	3.56433i	−0.150711	+	0.202440i
$311$	11.5637	+	1.35160i	0.655718	+	0.0766424i	0.437445	−	0.899245i	$-0.355884\pi$
$311$	11.5637	+	1.35160i	0.655718	+	0.0766424i	0.218273	+	0.975888i	$0.429958\pi$
$312$		0			0
$313$	−17.3722	−	11.4259i	−0.981938	−	0.645831i	−0.0463500	−	0.998925i	$-0.514759\pi$
$313$	−17.3722	−	11.4259i	−0.981938	−	0.645831i	−0.935588	+	0.353095i	$0.885129\pi$
$314$	16.6108	+	6.04583i	0.937400	+	0.341186i
$315$		0			0
$316$	3.57345	−	1.30063i	0.201022	−	0.0731661i
$317$	−27.0983	−	6.42242i	−1.52199	−	0.360719i	−0.617282	−	0.786742i	$-0.711766\pi$
$317$	−27.0983	−	6.42242i	−1.52199	−	0.360719i	−0.904712	+	0.426023i	$0.859914\pi$
$318$		0			0
$319$	0.164339	+	2.82159i	0.00920120	+	0.157979i
$320$	−5.12758	−	5.43492i	−0.286640	−	0.303821i
$321$		0			0
$322$	−6.16409	+	14.2900i	−0.343512	+	0.796349i
$323$	7.01331			0.390231
$324$		0			0
$325$	−1.16938			−0.0648658
$326$	5.89638	−	13.6694i	0.326570	−	0.757076i
$327$		0			0
$328$	−15.0301	−	15.9310i	−0.829900	−	0.879643i
$329$	0.603562	+	10.3628i	0.0332754	+	0.571317i
$330$		0			0
$331$	5.51555	+	1.30721i	0.303162	+	0.0718507i	0.379382	−	0.925240i	$-0.376137\pi$
$331$	5.51555	+	1.30721i	0.303162	+	0.0718507i	−0.0762194	+	0.997091i	$0.524285\pi$
$332$	16.1078	−	5.86275i	0.884029	−	0.321760i
$333$		0			0
$334$	−3.23187	−	1.17630i	−0.176840	−	0.0643645i
$335$	−6.70700	−	4.41126i	−0.366442	−	0.241013i
$336$		0			0
$337$	3.22663	+	0.377139i	0.175766	+	0.0205441i	0.203520	−	0.979071i	$-0.434762\pi$
$337$	3.22663	+	0.377139i	0.175766	+	0.0205441i	−0.0277547	+	0.999615i	$0.508836\pi$
$338$	11.2681	−	15.1356i	0.612902	−	0.823271i
$339$		0			0
$340$	−0.347088	+	5.95927i	−0.0188235	+	0.323187i
$341$	−8.49344	+	7.12685i	−0.459946	+	0.385940i
$342$		0			0
$343$	3.70115	+	3.10563i	0.199843	+	0.167688i
$344$	4.27462	−	4.53083i	0.230472	−	0.244286i
$345$		0			0
$346$	−6.30925	+	4.14966i	−0.339187	+	0.223087i
$347$	0.624696	−	0.148056i	0.0335354	−	0.00794804i	−0.213814	−	0.976874i	$-0.568589\pi$
$347$	0.624696	−	0.148056i	0.0335354	−	0.00794804i	0.247349	+	0.968926i	$0.420440\pi$
$348$		0			0
$349$	−35.7089	+	4.17377i	−1.91145	+	0.223417i	−0.987330	−	0.158682i	$-0.949275\pi$
$349$	−35.7089	+	4.17377i	−1.91145	+	0.223417i	−0.924121	+	0.382099i	$0.875201\pi$
$350$	−0.272253	+	0.471557i	−0.0145526	+	0.0252058i
$351$		0			0
$352$	−12.6824	−	21.9665i	−0.675973	−	1.17082i
$353$	19.3357	+	25.9723i	1.02913	+	1.38237i	0.921590	+	0.388165i	$0.126891\pi$
$353$	19.3357	+	25.9723i	1.02913	+	1.38237i	0.107543	+	0.994200i	$0.465702\pi$
$354$		0			0
$355$	−0.698206	+	2.33217i	−0.0370569	+	0.123779i
$356$	4.66275	+	2.34172i	0.247125	+	0.124111i
$357$		0			0
$358$	−4.36679	−	14.5861i	−0.230792	−	0.770898i
$359$	−6.49719	+	36.8474i	−0.342908	+	1.94473i	−0.0154001	+	0.999881i	$0.504902\pi$
$359$	−6.49719	+	36.8474i	−0.342908	+	1.94473i	−0.327508	+	0.944848i	$0.606209\pi$
$360$		0			0
$361$	−1.13839	−	6.45612i	−0.0599151	−	0.339796i
$362$	4.78455	−	2.40289i	0.251470	−	0.126293i
$363$		0			0
$364$	11.6930	+	27.1075i	0.612881	+	1.42082i
$365$	8.29307	+	19.2255i	0.434079	+	1.00631i
$366$		0			0
$367$	−8.18006	+	4.10818i	−0.426996	+	0.214445i	−0.649301	−	0.760532i	$-0.724938\pi$
$367$	−8.18006	+	4.10818i	−0.426996	+	0.214445i	0.222305	+	0.974977i	$0.428642\pi$
$368$	0.588015	+	3.33480i	0.0306524	+	0.173838i
$369$		0			0
$370$	1.22252	−	6.93328i	0.0635560	−	0.360444i
$371$	−2.75005	−	9.18581i	−0.142776	−	0.476904i
$372$		0			0
$373$	−9.00646	−	4.52321i	−0.466337	−	0.234203i	0.200084	−	0.979779i	$-0.435878\pi$
$373$	−9.00646	−	4.52321i	−0.466337	−	0.234203i	−0.666421	+	0.745576i	$0.732175\pi$
$374$	1.96687	−	6.56981i	0.101705	−	0.339717i
$375$		0			0
$376$	−4.66473	−	6.26582i	−0.240565	−	0.323135i
$377$	1.97246	+	3.41641i	0.101587	+	0.175954i
$378$		0			0
$379$	7.02304	−	12.1643i	0.360749	−	0.624836i	−0.627335	−	0.778750i	$-0.715854\pi$
$379$	7.02304	−	12.1643i	0.360749	−	0.624836i	0.988084	+	0.153913i	$0.0491876\pi$
$380$	−10.5203	+	1.22965i	−0.539681	+	0.0630796i
$381$		0			0
$382$	14.2104	−	3.36792i	0.727067	−	0.172318i
$383$	−18.5585	+	12.2061i	−0.948293	+	0.623702i	−0.926594	−	0.376063i	$-0.877278\pi$
$383$	−18.5585	+	12.2061i	−0.948293	+	0.623702i	−0.0216984	+	0.999765i	$0.506907\pi$
$384$		0			0
$385$	23.2385	−	24.6313i	1.18434	−	1.25533i
$386$	−5.63288	−	4.72655i	−0.286706	−	0.240575i
$387$		0			0
$388$	−11.0397	+	9.26345i	−0.560458	+	0.470280i
$389$	1.47416	−	25.3103i	0.0747428	−	1.28328i	−0.727425	−	0.686187i	$-0.759283\pi$
$389$	1.47416	−	25.3103i	0.0747428	−	1.28328i	0.802168	−	0.597098i	$-0.203680\pi$
$390$		0			0
$391$	−6.54430	+	8.79052i	−0.330959	+	0.444556i
$392$	14.9912	+	1.75221i	0.757167	+	0.0885002i
$393$		0			0
$394$	−15.8227	−	10.4067i	−0.797134	−	0.524283i
$395$	−5.72116	−	2.08233i	−0.287863	−	0.104773i
$396$		0			0
$397$	0.810757	−	0.295091i	0.0406907	−	0.0148102i	−0.321595	−	0.946877i	$-0.604219\pi$
$397$	0.810757	−	0.295091i	0.0406907	−	0.0148102i	0.362285	+	0.932067i	$0.381997\pi$
$398$	−7.54993	−	1.78937i	−0.378444	−	0.0896928i
$399$		0			0
$400$	0.00688884	+	0.118277i	0.000344442	+	0.00591384i
$401$	6.03889	+	6.40085i	0.301568	+	0.319643i	0.860382	−	0.509650i	$-0.170225\pi$
$401$	6.03889	+	6.40085i	0.301568	+	0.319643i	−0.558814	+	0.829293i	$0.688743\pi$
$402$		0			0
$403$	−6.12947	+	14.2097i	−0.305331	+	0.707836i
$404$	12.6692			0.630316
$405$		0			0
$406$	1.83690			0.0911638
$407$	6.95765	−	16.1297i	0.344878	−	0.799517i
$408$		0			0
$409$	−14.5025	−	15.3718i	−0.717102	−	0.760084i	0.261643	−	0.965165i	$-0.415736\pi$
$409$	−14.5025	−	15.3718i	−0.717102	−	0.760084i	−0.978745	+	0.205081i	$0.934254\pi$
$410$	0.828668	+	14.2277i	0.0409250	+	0.702655i
$411$		0			0
$412$	−13.7349	−	3.25524i	−0.676672	−	0.160374i
$413$	−24.8603	+	9.04839i	−1.22329	+	0.445242i
$414$		0			0
$415$	−25.7888	−	9.38637i	−1.26592	−	0.460759i
$416$	−29.5789	−	19.4543i	−1.45022	−	0.953826i
$417$		0			0
$418$	12.0863	+	1.41268i	0.591159	+	0.0690966i
$419$	21.9968	−	29.5469i	1.07462	−	1.44346i	0.187296	−	0.982304i	$-0.440028\pi$
$419$	21.9968	−	29.5469i	1.07462	−	1.44346i	0.887320	−	0.461155i	$-0.152565\pi$
$420$		0			0
$421$	0.586747	−	10.0741i	0.0285963	−	0.490979i	−0.953356	−	0.301849i	$-0.902396\pi$
$421$	0.586747	−	10.0741i	0.0285963	−	0.490979i	0.981952	−	0.189130i	$-0.0605668\pi$
$422$	−10.4196	+	8.74309i	−0.507219	+	0.425607i
$423$		0			0
$424$	5.52760	+	4.63821i	0.268444	+	0.225251i
$425$	−0.263128	+	0.278899i	−0.0127636	+	0.0135286i
$426$		0			0
$427$	7.81701	−	5.14133i	0.378292	−	0.248806i
$428$	−3.63717	+	0.862025i	−0.175809	+	0.0416675i
$429$		0			0
$430$	−4.02585	+	0.470555i	−0.194144	+	0.0226922i
$431$	4.93273	−	8.54374i	0.237601	−	0.411537i	−0.722424	−	0.691450i	$-0.756972\pi$
$431$	4.93273	−	8.54374i	0.237601	−	0.411537i	0.960025	+	0.279913i	$0.0903055\pi$
$432$		0			0
$433$	13.7845	+	23.8755i	0.662441	+	1.14738i	0.979972	+	0.199133i	$0.0638127\pi$
$433$	13.7845	+	23.8755i	0.662441	+	1.14738i	−0.317532	+	0.948248i	$0.602854\pi$
$434$	4.30304	+	5.77999i	0.206553	+	0.277448i
$435$		0			0
$436$	−0.449507	+	1.50146i	−0.0215275	+	0.0719067i
$437$	−17.3772	−	8.72715i	−0.831263	−	0.417476i
$438$		0			0
$439$	−5.32810	−	17.7971i	−0.254296	−	0.849408i	−0.985851	−	0.167626i	$-0.946390\pi$
$439$	−5.32810	−	17.7971i	−0.254296	−	0.849408i	0.731555	−	0.681783i	$-0.238795\pi$
$440$	−4.42514	+	25.0962i	−0.210960	+	1.19641i
$441$		0			0
$442$	−1.66216	−	9.42657i	−0.0790609	−	0.448376i
$443$	−0.318644	+	0.160029i	−0.0151392	+	0.00760322i	−0.456353	−	0.889799i	$-0.650844\pi$
$443$	−0.318644	+	0.160029i	−0.0151392	+	0.00760322i	0.441213	+	0.897402i	$0.354548\pi$
$444$		0			0
$445$	−3.30874	−	7.67052i	−0.156849	−	0.363617i
$446$	5.01567	+	11.6276i	0.237499	+	0.550584i
$447$		0			0
$448$	−10.8279	+	5.43797i	−0.511569	+	0.256920i
$449$	−4.01408	−	22.7650i	−0.189436	−	1.07435i	−0.920122	−	0.391632i	$-0.871911\pi$
$449$	−4.01408	−	22.7650i	−0.189436	−	1.07435i	0.730686	−	0.682714i	$-0.239201\pi$
$450$		0			0
$451$	−6.17494	+	35.0198i	−0.290766	+	1.64902i
$452$	−4.76203	−	15.9063i	−0.223987	−	0.748170i
$453$		0			0
$454$	−2.20319	−	1.10648i	−0.103401	−	0.0519298i
$455$	13.5558	−	45.2795i	0.635505	−	2.12274i
$456$		0			0
$457$	14.3589	+	19.2874i	0.671683	+	0.902227i	0.999090	−	0.0426563i	$-0.0135820\pi$
$457$	14.3589	+	19.2874i	0.671683	+	0.902227i	−0.327406	+	0.944884i	$0.606175\pi$
$458$	−1.11900	−	1.93817i	−0.0522876	−	0.0905648i
$459$		0			0
$460$	8.27552	−	14.3336i	0.385848	−	0.668309i
$461$	35.9966	−	4.20740i	1.67653	−	0.195958i	0.775994	−	0.630741i	$-0.217249\pi$
$461$	35.9966	−	4.20740i	1.67653	−	0.195958i	0.900535	+	0.434783i	$0.143175\pi$
$462$		0			0
$463$	−27.5609	+	6.53205i	−1.28086	+	0.303570i	−0.814055	−	0.580788i	$-0.802745\pi$
$463$	−27.5609	+	6.53205i	−1.28086	+	0.303570i	−0.466809	+	0.884358i	$0.654596\pi$
$464$	0.333931	−	0.219630i	0.0155024	−	0.0101961i
$465$		0			0
$466$	0.436830	−	0.463013i	0.0202358	−	0.0214487i
$467$	−14.1681	−	11.8885i	−0.655622	−	0.550132i	0.253149	−	0.967427i	$-0.418534\pi$
$467$	−14.1681	−	11.8885i	−0.655622	−	0.550132i	−0.908771	+	0.417295i	$0.862978\pi$
$468$		0			0
$469$	−9.97220	+	8.36767i	−0.460473	+	0.386383i
$470$	−0.295550	+	5.07441i	−0.0136327	+	0.234065i
$471$		0			0
$472$	11.8887	−	15.9693i	0.547223	−	0.735048i
$473$	−10.0450	−	1.17409i	−0.461871	−	0.0539849i
$474$		0			0
$475$	−0.568430	−	0.373862i	−0.0260814	−	0.0171540i
$476$	9.09626	+	3.31077i	0.416927	+	0.151749i
$477$		0			0
$478$	−12.7115	+	4.62659i	−0.581408	+	0.211615i
$479$	−23.0375	−	5.45998i	−1.05261	−	0.249473i	−0.332334	−	0.943162i	$-0.607836\pi$
$479$	−23.0375	−	5.45998i	−1.05261	−	0.249473i	−0.720275	+	0.693689i	$0.755984\pi$
$480$		0			0
$481$	−1.42561	−	24.4768i	−0.0650024	−	1.11605i
$482$	−1.87084	−	1.98297i	−0.0852144	−	0.0903219i
$483$		0			0
$484$	−4.26921	+	9.89715i	−0.194055	+	0.449870i
$485$	23.0729			1.04768
$486$		0			0
$487$	3.88368			0.175986			0.0879932	−	0.996121i	$-0.471955\pi$
$487$	3.88368			0.175986			0.0879932	+	0.996121i	$0.471955\pi$
$488$	−2.78875	+	6.46504i	−0.126241	+	0.292659i
$489$		0			0
$490$	−6.73973	−	7.14370i	−0.304470	−	0.322719i
$491$	0.253301	+	4.34902i	0.0114313	+	0.196268i	0.999189	+	0.0402710i	$0.0128221\pi$
$491$	0.253301	+	4.34902i	0.0114313	+	0.196268i	−0.987757	+	0.155997i	$0.950141\pi$
$492$		0			0
$493$	1.25865	+	0.298305i	0.0566867	+	0.0134350i
$494$	15.9601	−	5.80900i	0.718078	−	0.261359i
$495$		0			0
$496$	1.47334	+	0.536253i	0.0661550	+	0.0240785i
$497$	3.29829	+	2.16932i	0.147948	+	0.0973073i
$498$		0			0
$499$	−9.49505	−	1.10981i	−0.425057	−	0.0496820i	−0.0991244	−	0.995075i	$-0.531604\pi$
$499$	−9.49505	−	1.10981i	−0.425057	−	0.0496820i	−0.325933	+	0.945393i	$0.605678\pi$
$500$	9.31079	−	12.5066i	0.416391	−	0.559311i
$501$		0			0
$502$	−0.924627	+	15.8752i	−0.0412681	+	0.708546i
$503$	13.3954	−	11.2401i	0.597271	−	0.501170i	−0.293296	−	0.956022i	$-0.594752\pi$
$503$	13.3954	−	11.2401i	0.597271	−	0.501170i	0.890567	+	0.454852i	$0.150308\pi$
$504$		0			0
$505$	−15.5381	−	13.0381i	−0.691439	−	0.580186i
$506$	−13.0487	+	13.8308i	−0.580084	+	0.614854i
$507$		0			0
$508$	12.5623	−	8.26236i	0.557362	−	0.366583i
$509$	−4.67625	+	1.10829i	−0.207271	+	0.0491242i	−0.332940	−	0.942948i	$-0.608041\pi$
$509$	−4.67625	+	1.10829i	−0.207271	+	0.0491242i	0.125669	+	0.992072i	$0.459892\pi$
$510$		0			0
$511$	33.7237	−	3.94173i	1.49185	−	0.174372i
$512$	−3.43707	+	5.95318i	−0.151898	+	0.263096i
$513$		0			0
$514$	2.88562	+	4.99805i	0.127279	+	0.220454i
$515$	13.4952	+	18.1272i	0.594671	+	0.798781i
$516$		0			0
$517$	−3.63745	+	12.1499i	−0.159975	+	0.534354i
$518$	−10.2022	−	5.12376i	−0.448261	−	0.225125i
$519$		0			0
$520$	10.2012	+	34.0744i	0.447352	+	1.49426i
$521$	1.19409	−	6.77202i	0.0523140	−	0.296688i	−0.947414	−	0.320011i	$-0.896314\pi$
$521$	1.19409	−	6.77202i	0.0523140	−	0.296688i	0.999728	+	0.0233231i	$0.00742464\pi$
$522$		0			0
$523$	−4.96810	−	28.1755i	−0.217240	−	1.23203i	−0.876977	−	0.480532i	$-0.840444\pi$
$523$	−4.96810	−	28.1755i	−0.217240	−	1.23203i	0.659738	−	0.751496i	$-0.270667\pi$
$524$	−0.541697	+	0.272051i	−0.0236642	+	0.0118846i
$525$		0			0
$526$	7.76339	+	17.9976i	0.338500	+	0.784731i
$527$	2.00981	+	4.65927i	0.0875488	+	0.202961i
$528$		0			0
$529$	6.60019	−	3.31474i	0.286965	−	0.144119i
$530$	−0.815337	−	4.62400i	−0.0354160	−	0.200854i
$531$		0			0
$532$	−2.98260	+	16.9151i	−0.129312	+	0.733364i
$533$	14.2350	+	47.5481i	0.616585	+	2.05954i
$534$		0			0
$535$	5.34793	+	2.68583i	0.231211	+	0.116119i
$536$	2.80962	−	9.38477i	0.121357	−	0.405361i
$537$		0			0
$538$	−0.674180	−	0.905581i	−0.0290660	−	0.0390424i
$539$	−12.2526	−	21.2221i	−0.527757	−	0.914102i
$540$		0			0
$541$	16.4141	−	28.4300i	0.705695	−	1.22230i	−0.260745	−	0.965408i	$-0.583968\pi$
$541$	16.4141	−	28.4300i	0.705695	−	1.22230i	0.966440	−	0.256892i	$-0.0826985\pi$
$542$	−9.01670	+	1.05390i	−0.387300	+	0.0452689i
$543$		0			0
$544$	−11.2955	+	2.67709i	−0.484292	+	0.114779i
$545$	2.09647	−	1.37887i	0.0898029	−	0.0590643i
$546$		0			0
$547$	24.9358	−	26.4304i	1.06618	−	1.13008i	0.0750494	−	0.997180i	$-0.476089\pi$
$547$	24.9358	−	26.4304i	1.06618	−	1.13008i	0.991129	−	0.132903i	$-0.0424300\pi$
$548$	−19.3361	−	16.2249i	−0.825999	−	0.693095i
$549$		0			0
$550$	−0.509636	+	0.427635i	−0.0217309	+	0.0182344i
$551$	−0.133454	+	2.29131i	−0.00568531	+	0.0976130i
$552$		0			0
$553$	−5.89572	+	7.91933i	−0.250712	+	0.336764i
$554$	15.7950	+	1.84617i	0.671063	+	0.0784360i
$555$		0			0
$556$	23.0085	+	15.1329i	0.975777	+	0.641779i
$557$	7.83290	+	2.85094i	0.331891	+	0.120798i	0.502590	−	0.864525i	$-0.332380\pi$
$557$	7.83290	+	2.85094i	0.331891	+	0.120798i	−0.170699	+	0.985323i	$0.554603\pi$
$558$		0			0
$559$	−13.2646	+	4.82791i	−0.561032	+	0.204199i
$560$	−4.65963	−	1.10435i	−0.196905	−	0.0466674i
$561$		0			0
$562$	−1.29145	−	22.1733i	−0.0544764	−	0.935323i
$563$	−9.75835	−	10.3432i	−0.411266	−	0.435916i	0.488317	−	0.872666i	$-0.337611\pi$
$563$	−9.75835	−	10.3432i	−0.411266	−	0.435916i	−0.899583	+	0.436750i	$0.856129\pi$
$564$		0			0
$565$	−10.5290	+	24.4090i	−0.442959	+	1.02689i
$566$	−12.7276			−0.534981
$567$		0			0
$568$	−2.97081			−0.124652
$569$	−3.72797	+	8.64240i	−0.156285	+	0.362308i	−0.978311	−	0.207141i	$-0.933584\pi$
$569$	−3.72797	+	8.64240i	−0.156285	+	0.362308i	0.822027	+	0.569449i	$0.192843\pi$
$570$		0			0
$571$	18.5168	+	19.6267i	0.774905	+	0.821351i	0.987801	−	0.155724i	$-0.0497710\pi$
$571$	18.5168	+	19.6267i	0.774905	+	0.821351i	−0.212896	+	0.977075i	$0.568290\pi$
$572$	2.09729	+	36.0091i	0.0876921	+	1.50561i
$573$		0			0
$574$	22.4880	+	5.32976i	0.938632	+	0.222460i
$575$	0.999017	−	0.363613i	0.0416619	−	0.0151637i
$576$		0			0
$577$	35.2517	+	12.8306i	1.46755	+	0.534143i	0.947433	−	0.319954i	$-0.103667\pi$
$577$	35.2517	+	12.8306i	1.46755	+	0.534143i	0.520113	+	0.854097i	$0.325890\pi$
$578$	8.65616	+	5.69324i	0.360049	+	0.236808i
$579$		0			0
$580$	−1.94034	−	0.226793i	−0.0805682	−	0.00941707i
$581$	−26.5757	+	35.6974i	−1.10255	+	1.48098i
$582$		0			0
$583$	0.681194	−	11.6956i	0.0282122	−	0.484384i
$584$	−19.5732	+	16.4239i	−0.809944	+	0.679624i
$585$		0			0
$586$	14.0487	+	11.7883i	0.580347	+	0.486969i
$587$	17.8340	−	18.9029i	0.736087	−	0.780206i	−0.245872	−	0.969302i	$-0.579074\pi$
$587$	17.8340	−	18.9029i	0.736087	−	0.780206i	0.981959	+	0.189096i	$0.0605557\pi$
$588$		0			0
$589$	−7.52246	+	4.94760i	−0.309958	+	0.203862i
$590$	−12.6056	+	2.98758i	−0.518963	+	0.122997i
$591$		0			0
$592$	−2.46730	+	0.288386i	−0.101405	+	0.0118526i
$593$	11.0981	−	19.2224i	0.455744	−	0.789371i	−0.542987	−	0.839741i	$-0.682707\pi$
$593$	11.0981	−	19.2224i	0.455744	−	0.789371i	0.998731	+	0.0503700i	$0.0160401\pi$
$594$		0			0
$595$	−7.74896	−	13.4216i	−0.317676	−	0.550232i
$596$	−1.66793	−	2.24042i	−0.0683211	−	0.0917711i
$597$		0			0
$598$	−7.61174	+	25.4250i	−0.311267	+	1.03970i
$599$	24.7245	+	12.4171i	1.01022	+	0.507349i	0.875337	−	0.483513i	$-0.160639\pi$
$599$	24.7245	+	12.4171i	1.01022	+	0.507349i	0.134878	+	0.990862i	$0.456936\pi$
$600$		0			0
$601$	−5.28556	−	17.6550i	−0.215603	−	0.720163i	−0.995543	−	0.0943089i	$-0.969936\pi$
$601$	−5.28556	−	17.6550i	−0.215603	−	0.720163i	0.779940	−	0.625854i	$-0.215249\pi$
$602$	−1.14136	+	6.47299i	−0.0465185	+	0.263819i
$603$		0			0
$604$	2.19260	+	12.4348i	0.0892156	+	0.505967i
$605$	15.4213	−	7.74486i	0.626964	−	0.314873i
$606$		0			0
$607$	−2.32395	−	5.38752i	−0.0943262	−	0.218673i	0.864520	−	0.502598i	$-0.167622\pi$
$607$	−2.32395	−	5.38752i	−0.0943262	−	0.218673i	−0.958846	+	0.283925i	$0.908363\pi$
$608$	−8.15837	−	18.9132i	−0.330866	−	0.767033i
$609$		0			0
$610$	4.09420	−	2.05619i	0.165769	−	0.0832525i
$611$	3.07393	+	17.4331i	0.124358	+	0.705269i
$612$		0			0
$613$	4.27094	−	24.2217i	0.172502	−	0.978305i	−0.768487	−	0.639866i	$-0.778990\pi$
$613$	4.27094	−	24.2217i	0.172502	−	0.978305i	0.940988	−	0.338439i	$-0.109899\pi$
$614$	−4.06905	−	13.5916i	−0.164213	−	0.548511i
$615$		0			0
$616$	36.9288	+	18.5463i	1.48790	+	0.747252i
$617$	1.10523	−	3.69173i	0.0444949	−	0.148623i	−0.932856	−	0.360251i	$-0.882691\pi$
$617$	1.10523	−	3.69173i	0.0444949	−	0.148623i	0.977350	+	0.211627i	$0.0678763\pi$
$618$		0			0
$619$	11.9740	+	16.0839i	0.481277	+	0.646467i	0.974751	−	0.223294i	$-0.0716808\pi$
$619$	11.9740	+	16.0839i	0.481277	+	0.646467i	−0.493475	+	0.869760i	$0.664273\pi$
$620$	−3.83173	−	6.63675i	−0.153886	−	0.266538i
$621$		0			0
$622$	4.62246	−	8.00633i	0.185344	−	0.321024i
$623$	−13.4550	+	1.57266i	−0.539061	+	0.0630072i
$624$		0			0
$625$	−23.3516	+	5.53443i	−0.934064	+	0.221377i
$626$	−13.7948	+	9.07298i	−0.551351	+	0.362629i
$627$		0			0
$628$	−20.9203	+	22.1743i	−0.834813	+	0.884850i
$629$	−6.15853	−	5.16762i	−0.245557	−	0.206047i
$630$		0			0
$631$	−1.61408	+	1.35437i	−0.0642554	+	0.0539167i	−0.674350	−	0.738412i	$-0.735576\pi$
$631$	−1.61408	+	1.35437i	−0.0642554	+	0.0539167i	0.610094	+	0.792329i	$0.291132\pi$
$632$	0.432001	−	7.41716i	0.0171841	−	0.295039i
$633$		0			0
$634$	−13.2056	+	17.7382i	−0.524462	+	0.704474i
$635$	−23.9100	−	2.79467i	−0.948838	−	0.110903i
$636$		0			0
$637$	−28.5765	−	18.7950i	−1.13224	−	0.744687i
$638$	2.10899	+	0.767608i	0.0834956	+	0.0303899i
$639$		0			0
$640$	18.4845	−	6.72781i	0.730664	−	0.265940i
$641$	17.1457	+	4.06360i	0.677214	+	0.160503i	0.554809	−	0.831978i	$-0.312791\pi$
$641$	17.1457	+	4.06360i	0.677214	+	0.160503i	0.122405	+	0.992480i	$0.460939\pi$
$642$		0			0
$643$	−1.98349	−	34.0553i	−0.0782213	−	1.34301i	−0.777827	−	0.628479i	$-0.783678\pi$
$643$	−1.98349	−	34.0553i	−0.0782213	−	1.34301i	0.699605	−	0.714529i	$-0.253359\pi$
$644$	−18.4184	−	19.5223i	−0.725786	−	0.769288i
$645$		0			0
$646$	2.20579	−	5.11360i	0.0867858	−	0.201192i
$647$	−14.3650			−0.564747			−0.282374	−	0.959305i	$-0.591122\pi$
$647$	−14.3650			−0.564747			−0.282374	+	0.959305i	$0.591122\pi$
$648$		0			0
$649$	−32.3238			−1.26882
$650$	−0.367789	+	0.852631i	−0.0144259	+	0.0334429i
$651$		0			0
$652$	17.6185	+	18.6745i	0.689992	+	0.731349i
$653$	−0.705096	−	12.1060i	−0.0275925	−	0.473745i	−0.983595	−	0.180388i	$-0.942265\pi$
$653$	−0.705096	−	12.1060i	−0.0275925	−	0.473745i	0.956003	−	0.293357i	$-0.0947725\pi$
$654$		0			0
$655$	0.944337	+	0.223812i	0.0368983	+	0.00874506i
$656$	4.72537	−	1.71989i	0.184495	−	0.0671506i
$657$		0			0
$658$	7.74561	+	2.81917i	0.301955	+	0.109903i
$659$	16.7459	+	11.0140i	0.652328	+	0.429043i	0.832070	−	0.554671i	$-0.187156\pi$
$659$	16.7459	+	11.0140i	0.652328	+	0.429043i	−0.179742	+	0.983714i	$0.557526\pi$
$660$		0			0
$661$	3.52498	+	0.412011i	0.137106	+	0.0160254i	0.184369	−	0.982857i	$-0.440976\pi$
$661$	3.52498	+	0.412011i	0.137106	+	0.0160254i	−0.0472632	+	0.998882i	$0.515050\pi$
$662$	2.68785	−	3.61041i	0.104466	−	0.140322i
$663$		0			0
$664$	1.94730	−	33.4338i	0.0755698	−	1.29748i
$665$	21.0656	−	17.6762i	0.816890	−	0.685452i
$666$		0			0
$667$	−2.74741	−	2.30535i	−0.106380	−	0.0892635i
$668$	4.07036	−	4.31433i	0.157487	−	0.166926i
$669$		0			0
$670$	−5.32583	+	3.50285i	−0.205755	+	0.135327i
$671$	11.1234	−	2.63628i	0.429413	−	0.101773i
$672$		0			0
$673$	−26.5108	+	3.09867i	−1.02192	+	0.119445i	−0.610511	−	0.792008i	$-0.709036\pi$
$673$	−26.5108	+	3.09867i	−1.02192	+	0.119445i	−0.411405	+	0.911453i	$0.634962\pi$
$674$	1.28981	−	2.23401i	0.0496815	−	0.0860509i
$675$		0			0
$676$	16.2711	+	28.1824i	0.625813	+	1.08394i
$677$	21.2644	+	28.5631i	0.817258	+	1.09777i	0.993546	+	0.113430i	$0.0361837\pi$
$677$	21.2644	+	28.5631i	0.817258	+	1.09777i	−0.176288	+	0.984339i	$0.556409\pi$
$678$		0			0
$679$	10.7309	−	35.8436i	0.411813	−	1.37555i
$680$	10.4222	+	5.23422i	0.399672	+	0.200723i
$681$		0			0
$682$	2.52507	+	8.43431i	0.0966898	+	0.322966i
$683$	8.25887	−	46.8384i	0.316017	−	1.79222i	−0.250442	−	0.968132i	$-0.580576\pi$
$683$	8.25887	−	46.8384i	0.316017	−	1.79222i	0.566459	−	0.824090i	$-0.308313\pi$
$684$		0			0
$685$	7.01750	+	39.7982i	0.268125	+	1.52061i
$686$	3.42847	−	1.72184i	0.130900	−	0.0657403i
$687$		0			0
$688$	0.566458	+	1.31320i	0.0215960	+	0.0500652i
$689$	−6.47668	−	15.0146i	−0.246742	−	0.572012i
$690$		0			0
$691$	2.78462	−	1.39849i	0.105932	−	0.0532011i	−0.395044	−	0.918662i	$-0.629271\pi$
$691$	2.78462	−	1.39849i	0.105932	−	0.0532011i	0.500976	+	0.865461i	$0.332974\pi$
$692$	−2.26150	−	12.8256i	−0.0859692	−	0.487555i
$693$		0			0
$694$	0.0885248	−	0.502049i	0.00336035	−	0.0190575i
$695$	−12.6453	−	42.2382i	−0.479663	−	1.60218i
$696$		0			0
$697$	14.5433	+	7.30394i	0.550869	+	0.276657i
$698$	−8.18777	+	27.3490i	−0.309912	+	1.03518i
$699$		0			0
$700$	−0.560765	−	0.753238i	−0.0211949	−	0.0284697i
$701$	7.89786	+	13.6795i	0.298298	+	0.516667i	0.975747	−	0.218903i	$-0.0702477\pi$
$701$	7.89786	+	13.6795i	0.298298	+	0.516667i	−0.677449	+	0.735570i	$0.736914\pi$
$702$		0			0
$703$	7.13247	−	12.3538i	0.269006	−	0.465933i
$704$	−14.7042	+	1.71867i	−0.554185	+	0.0647749i
$705$		0			0
$706$	25.0185	−	5.92949i	0.941583	−	0.223159i
$707$	−27.4811	+	18.0746i	−1.03353	+	0.679766i
$708$		0			0
$709$	−11.7116	+	12.4135i	−0.439837	+	0.466200i	−0.908930	−	0.416949i	$-0.863099\pi$
$709$	−11.7116	+	12.4135i	−0.439837	+	0.466200i	0.469093	+	0.883149i	$0.344581\pi$
$710$	1.48085	+	1.24258i	0.0555755	+	0.0466334i
$711$		0			0
$712$	7.80924	−	6.55273i	0.292664	−	0.245574i
$713$	0.818052	−	14.0454i	0.0306363	−	0.526005i
$714$		0			0
$715$	34.4852	−	46.3217i	1.28967	−	1.73233i
$716$	26.0807	+	3.04840i	0.974681	+	0.113924i
$717$		0			0
$718$	24.8230	+	16.3263i	0.926386	+	0.609294i
$719$	−9.60505	−	3.49595i	−0.358208	−	0.130377i	0.156646	−	0.987655i	$-0.449932\pi$
$719$	−9.60505	−	3.49595i	−0.358208	−	0.130377i	−0.514854	+	0.857278i	$0.672154\pi$
$720$		0			0
$721$	34.4370	−	12.5340i	1.28250	−	0.466792i
$722$	−5.06538	−	1.20052i	−0.188514	−	0.0446786i
$723$		0			0
$724$	0.536884	+	9.21795i	0.0199531	+	0.342582i
$725$	−0.0861118	−	0.0912732i	−0.00319811	−	0.00338980i
$726$		0			0
$727$	14.7266	−	34.1401i	0.546179	−	1.26619i	−0.391977	−	0.919975i	$-0.628209\pi$
$727$	14.7266	−	34.1401i	0.546179	−	1.26619i	0.938157	−	0.346211i	$-0.112532\pi$
$728$	57.6788			2.13772
$729$		0			0
$730$	16.6261			0.615361
$731$	−1.83326	+	4.24996i	−0.0678054	+	0.157191i
$732$		0			0
$733$	24.2509	+	25.7045i	0.895728	+	0.949416i	0.998976	−	0.0452398i	$-0.0144052\pi$
$733$	24.2509	+	25.7045i	0.895728	+	0.949416i	−0.103249	+	0.994656i	$0.532924\pi$
$734$	0.422637	+	7.25640i	0.0155998	+	0.267839i
$735$		0			0
$736$	31.3187	+	7.42267i	1.15442	+	0.273603i
$737$	−14.9460	+	5.43991i	−0.550544	+	0.200382i
$738$		0			0
$739$	−23.2146	−	8.44943i	−0.853964	−	0.310817i	−0.122308	−	0.992492i	$-0.539030\pi$
$739$	−23.2146	−	8.44943i	−0.853964	−	0.310817i	−0.731655	+	0.681675i	$0.761252\pi$
$740$	10.1441	+	6.67191i	0.372906	+	0.245264i
$741$		0			0
$742$	−7.56257	−	0.883938i	−0.277631	−	0.0324504i
$743$	−18.6294	+	25.0236i	−0.683447	+	0.918028i	−0.999529	−	0.0307037i	$-0.990225\pi$
$743$	−18.6294	+	25.0236i	−0.683447	+	0.918028i	0.316082	+	0.948732i	$0.397633\pi$
$744$		0			0
$745$	−0.260013	+	4.46426i	−0.00952615	+	0.163558i
$746$	−6.13067	+	5.14424i	−0.224460	+	0.188344i
$747$		0			0
$748$	9.06012	+	7.60234i	0.331271	+	0.277969i
$749$	6.65968	−	7.05885i	0.243339	−	0.257925i
$750$		0			0
$751$	18.1119	−	11.9124i	0.660911	−	0.434688i	−0.174244	−	0.984703i	$-0.555748\pi$
$751$	18.1119	−	11.9124i	0.660911	−	0.434688i	0.835155	+	0.550014i	$0.185378\pi$
$752$	1.74516	−	0.413609i	0.0636393	−	0.0150828i
$753$		0			0
$754$	3.11137	−	0.363667i	0.113309	−	0.0132440i
$755$	10.1078	−	17.5072i	0.367859	−	0.637151i
$756$		0			0
$757$	20.8452	+	36.1050i	0.757632	+	1.31226i	0.944055	+	0.329788i	$0.106977\pi$
$757$	20.8452	+	36.1050i	0.757632	+	1.31226i	−0.186422	+	0.982470i	$0.559689\pi$
$758$	−6.66046	−	8.94655i	−0.241919	−	0.324953i
$759$		0			0
$760$	−5.93513	+	19.8247i	−0.215290	+	0.719119i
$761$	−2.14236	−	1.07593i	−0.0776604	−	0.0390025i	0.409545	−	0.912290i	$-0.365687\pi$
$761$	−2.14236	−	1.07593i	−0.0776604	−	0.0390025i	−0.487206	+	0.873287i	$0.661984\pi$
$762$		0			0
$763$	−1.16703	−	3.89815i	−0.0422493	−	0.141122i
$764$	−4.37352	+	24.8035i	−0.158228	+	0.897358i
$765$		0			0
$766$	3.06289	+	17.3705i	0.110667	+	0.627621i
$767$	−40.3173	+	20.2481i	−1.45577	+	0.731118i
$768$		0			0
$769$	11.1782	+	25.9140i	0.403096	+	0.934481i	0.991995	+	0.126275i	$0.0403021\pi$
$769$	11.1782	+	25.9140i	0.403096	+	0.934481i	−0.588899	+	0.808206i	$0.700439\pi$
$770$	−10.6506	−	24.6908i	−0.383819	−	0.889793i
$771$		0			0
$772$	11.3324	−	5.69136i	0.407863	−	0.204837i
$773$	5.35215	+	30.3536i	0.192504	+	1.09174i	0.915929	+	0.401340i	$0.131455\pi$
$773$	5.35215	+	30.3536i	0.192504	+	1.09174i	−0.723426	+	0.690402i	$0.757434\pi$
$774$		0			0
$775$	0.0854785	−	0.484773i	0.00307048	−	0.0174135i
$776$	8.07534	+	26.9735i	0.289888	+	0.968293i
$777$		0			0
$778$	−17.9908	−	9.03534i	−0.645003	−	0.323933i
$779$	−8.28202	+	27.6639i	−0.296734	+	0.991161i
$780$		0			0
$781$	2.88032	+	3.86894i	0.103066	+	0.138442i
$782$	4.35113	+	7.53638i	0.155596	+	0.269501i
$783$

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.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.314515 - 0.729128i) q^{2} +(0.939775 + 0.996103i) q^{4} +(-0.127484 - 2.18881i) q^{5} +(-3.45959 - 0.819939i) q^{7} +(2.51422 - 0.915103i) q^{8} +O(q^{10})\)	\(q+(0.314515 - 0.729128i) q^{2} +(0.939775 + 0.996103i) q^{4} +(-0.127484 - 2.18881i) q^{5} +(-3.45959 - 0.819939i) q^{7} +(2.51422 - 0.915103i) q^{8} +(-1.63602 - 0.595462i) q^{10} +(-3.62940 - 2.38710i) q^{11} +(-6.02225 - 0.703900i) q^{13} +(-1.68594 + 2.26460i) q^{14} +(-0.0357186 + 0.613264i) q^{16} +(-1.52297 + 1.27793i) q^{17} +(-2.70233 - 2.26753i) q^{19} +(2.06047 - 2.18397i) q^{20} +(-2.88200 + 1.89552i) q^{22} +(5.36375 - 1.27123i) q^{23} +(0.191560 - 0.0223902i) q^{25} +(-2.40732 + 4.16961i) q^{26} +(-2.43450 - 4.21667i) q^{28} +(-0.388529 - 0.521885i) q^{29} +(0.732013 - 2.44509i) q^{31} +(5.21789 + 2.62052i) q^{32} +(0.452774 + 1.51237i) q^{34} +(-1.35365 + 7.67692i) q^{35} +(0.702191 + 3.98232i) q^{37} +(-2.50324 + 1.25718i) q^{38} +(-2.32351 - 5.38650i) q^{40} +(-3.24228 - 7.51644i) q^{41} +(2.08047 - 1.04485i) q^{43} +(-1.03303 - 5.85859i) q^{44} +(0.760089 - 4.31068i) q^{46} +(-0.837341 - 2.79691i) q^{47} +(5.04106 + 2.53172i) q^{49} +(0.0439233 - 0.146714i) q^{50} +(-4.95840 - 6.66029i) q^{52} +(1.34845 + 2.33558i) q^{53} +(-4.76221 + 8.24838i) q^{55} +(-9.44853 + 1.10437i) q^{56} +(-0.502720 + 0.119147i) q^{58} +(6.21681 - 4.08886i) q^{59} +(-1.80586 + 1.91410i) q^{61} +(-1.55256 - 1.30275i) q^{62} +(2.61064 - 2.19058i) q^{64} +(-0.772965 + 13.2713i) q^{65} +(2.18642 - 2.93688i) q^{67} +(-2.70420 - 0.316075i) q^{68} +(5.17172 + 3.40149i) q^{70} +(-1.04338 - 0.379759i) q^{71} +(-8.97377 + 3.26619i) q^{73} +(3.12448 + 0.740514i) q^{74} +(-0.280894 - 4.82277i) q^{76} +(10.5990 + 11.2343i) q^{77} +(1.09986 - 2.54976i) q^{79} +1.34687 q^{80} -6.50019 q^{82} +(4.95776 - 11.4934i) q^{83} +(2.99129 + 3.17058i) q^{85} +(-0.107491 - 1.84555i) q^{86} +(-11.3096 - 2.68042i) q^{88} +(3.58032 - 1.30313i) q^{89} +(20.2574 + 7.37309i) q^{91} +(6.30699 + 4.14817i) q^{92} +(-2.30267 - 0.269143i) q^{94} +(-4.61868 + 6.20396i) q^{95} +(-0.611885 + 10.5057i) q^{97} +(3.43144 - 2.87932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

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