LMFDB - Embedded newform 162.2.g.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	162.43
Dual form			162.2.g.a.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.286803 + 0.957990i) q^{2} +(-0.524336 - 1.65078i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(-0.757906 - 1.75702i) q^{5} +(1.43105 - 0.975757i) q^{6} +(0.278553 - 4.78256i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.45014 + 1.73113i) q^{9} +O(q^{10})$	\(q+(0.286803 + 0.957990i) q^{2} +(-0.524336 - 1.65078i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(-0.757906 - 1.75702i) q^{5} +(1.43105 - 0.975757i) q^{6} +(0.278553 - 4.78256i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.45014 + 1.73113i) q^{9} +(1.46584 - 1.22999i) q^{10} +(0.564911 + 0.758806i) q^{11} +(1.34519 + 1.09108i) q^{12} +(3.51873 + 3.72964i) q^{13} +(4.66154 - 1.10480i) q^{14} +(-2.50306 + 2.17241i) q^{15} +(0.396080 - 0.918216i) q^{16} +(-0.189281 - 1.07347i) q^{17} +(-2.36111 - 1.85072i) q^{18} +(1.00260 - 5.68601i) q^{19} +(1.59872 + 1.05150i) q^{20} +(-8.04101 + 2.04784i) q^{21} +(-0.564911 + 0.758806i) q^{22} +(0.422979 + 7.26227i) q^{23} +(-0.659436 + 1.60161i) q^{24} +(0.918495 - 0.973548i) q^{25} +(-2.56377 + 4.44058i) q^{26} +(4.14241 + 3.13695i) q^{27} +(2.39533 + 4.14884i) q^{28} +(-4.08961 - 0.969255i) q^{29} +(-2.79903 - 1.77485i) q^{30} +(2.75494 + 1.38358i) q^{31} +(0.993238 + 0.116093i) q^{32} +(0.956419 - 1.33041i) q^{33} +(0.974085 - 0.489204i) q^{34} +(-8.61420 + 3.13531i) q^{35} +(1.09580 - 2.79271i) q^{36} +(-0.251178 - 0.0914213i) q^{37} +(5.73469 - 0.670289i) q^{38} +(4.31181 - 7.76423i) q^{39} +(-0.548804 + 1.83313i) q^{40} +(-2.66272 + 8.89409i) q^{41} +(-4.26800 - 7.11588i) q^{42} +(3.27638 - 0.382953i) q^{43} +(-0.888947 - 0.323550i) q^{44} +(4.89861 + 2.99293i) q^{45} +(-6.83586 + 2.48805i) q^{46} +(7.37949 - 3.70612i) q^{47} +(-1.72345 - 0.172386i) q^{48} +(-15.8427 - 1.85174i) q^{49} +(1.19608 + 0.600692i) q^{50} +(-1.67281 + 0.875320i) q^{51} +(-4.98932 - 1.18249i) q^{52} +(0.171014 + 0.296205i) q^{53} +(-1.81711 + 4.86807i) q^{54} +(0.905092 - 1.56767i) q^{55} +(-3.28756 + 3.48461i) q^{56} +(-9.91205 + 1.32631i) q^{57} +(-0.244377 - 4.19579i) q^{58} +(7.89735 - 10.6080i) q^{59} +(0.897520 - 3.19047i) q^{60} +(0.870559 + 0.572576i) q^{61} +(-0.535333 + 3.03602i) q^{62} +(7.59673 + 12.2002i) q^{63} +(0.173648 + 0.984808i) q^{64} +(3.88619 - 9.00921i) q^{65} +(1.54882 + 0.534673i) q^{66} +(-0.285565 + 0.0676801i) q^{67} +(0.748023 + 0.792858i) q^{68} +(11.7666 - 4.50611i) q^{69} +(-5.47418 - 7.35309i) q^{70} +(-1.69551 + 1.42271i) q^{71} +(2.98967 + 0.248802i) q^{72} +(10.8638 + 9.11577i) q^{73} +(0.0155420 - 0.266846i) q^{74} +(-2.08871 - 1.00577i) q^{75} +(2.28686 + 5.30153i) q^{76} +(3.78640 - 2.49035i) q^{77} +(8.67469 + 1.90386i) q^{78} +(0.645823 + 2.15720i) q^{79} -1.91352 q^{80} +(3.00641 - 8.48301i) q^{81} -9.28412 q^{82} +(-2.64436 - 8.83277i) q^{83} +(5.59286 - 6.12956i) q^{84} +(-1.74265 + 1.14616i) q^{85} +(1.30654 + 3.02890i) q^{86} +(0.544303 + 7.25926i) q^{87} +(0.0550049 - 0.944397i) q^{88} +(5.42459 + 4.55177i) q^{89} +(-1.46226 + 5.55120i) q^{90} +(18.8174 - 15.7897i) q^{91} +(-4.34407 - 5.83511i) q^{92} +(0.839476 - 5.27326i) q^{93} +(5.66689 + 6.00655i) q^{94} +(-10.7503 + 2.54788i) q^{95} +(-0.329147 - 1.70049i) q^{96} +(-4.51089 + 10.4574i) q^{97} +(-2.76978 - 15.7082i) q^{98} +(-2.69770 - 0.881253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{27}\right)$

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 $

$2$	0.286803	+	0.957990i	0.202801	+	0.677401i
$2$	0.286803	+	0.957990i	0.202801	+	0.677401i
$3$	−0.524336	−	1.65078i	−0.302726	−	0.953078i
$3$	−0.524336	−	1.65078i	−0.302726	−	0.953078i
$4$	−0.835488	+	0.549509i	−0.417744	+	0.274754i
$5$	−0.757906	−	1.75702i	−0.338946	−	0.785765i	−0.999391	−	0.0348909i	$-0.988892\pi$
$5$	−0.757906	−	1.75702i	−0.338946	−	0.785765i	0.660445	−	0.750874i	$-0.270368\pi$
$6$	1.43105	−	0.975757i	0.584223	−	0.398351i
$7$	0.278553	−	4.78256i	0.105283	−	1.80764i	−0.371303	−	0.928512i	$-0.621089\pi$
$7$	0.278553	−	4.78256i	0.105283	−	1.80764i	0.476586	−	0.879128i	$-0.341874\pi$
$8$	−0.766044	−	0.642788i	−0.270838	−	0.227260i
$9$	−2.45014	+	1.73113i	−0.816714	+	0.577042i
$10$	1.46584	−	1.22999i	0.463540	−	0.388956i
$11$	0.564911	+	0.758806i	0.170327	+	0.228789i	0.879088	−	0.476660i	$-0.158153\pi$
$11$	0.564911	+	0.758806i	0.170327	+	0.228789i	−0.708761	+	0.705449i	$0.750745\pi$
$12$	1.34519	+	1.09108i	0.388324	+	0.314967i
$13$	3.51873	+	3.72964i	0.975920	+	1.03441i	0.999398	+	0.0346906i	$0.0110446\pi$
$13$	3.51873	+	3.72964i	0.975920	+	1.03441i	−0.0234779	+	0.999724i	$0.507474\pi$
$14$	4.66154	−	1.10480i	1.24585	−	0.295271i
$15$	−2.50306	+	2.17241i	−0.646288	+	0.560913i
$16$	0.396080	−	0.918216i	0.0990199	−	0.229554i
$17$	−0.189281	−	1.07347i	−0.0459075	−	0.260354i	0.953212	−	0.302302i	$-0.0977550\pi$
$17$	−0.189281	−	1.07347i	−0.0459075	−	0.260354i	−0.999120	+	0.0419473i	$0.986644\pi$
$18$	−2.36111	−	1.85072i	−0.556519	−	0.436219i
$19$	1.00260	−	5.68601i	0.230012	−	1.30446i	−0.622857	−	0.782335i	$-0.714028\pi$
$19$	1.00260	−	5.68601i	0.230012	−	1.30446i	0.852869	−	0.522125i	$-0.174861\pi$
$20$	1.59872	+	1.05150i	0.357485	+	0.235122i
$21$	−8.04101	+	2.04784i	−1.75469	+	0.446876i
$22$	−0.564911	+	0.758806i	−0.120439	+	0.161778i
$23$	0.422979	+	7.26227i	0.0881972	+	1.51429i	0.694754	+	0.719247i	$0.255513\pi$
$23$	0.422979	+	7.26227i	0.0881972	+	1.51429i	−0.606557	+	0.795040i	$0.707450\pi$
$24$	−0.659436	+	1.60161i	−0.134607	+	0.326927i
$25$	0.918495	−	0.973548i	0.183699	−	0.194710i
$26$	−2.56377	+	4.44058i	−0.502796	+	0.870869i
$27$	4.14241	+	3.13695i	0.797206	+	0.603707i
$28$	2.39533	+	4.14884i	0.452676	+	0.784057i
$29$	−4.08961	−	0.969255i	−0.759421	−	0.179986i	−0.167379	−	0.985893i	$-0.553530\pi$
$29$	−4.08961	−	0.969255i	−0.759421	−	0.179986i	−0.592043	+	0.805907i	$0.701678\pi$
$30$	−2.79903	−	1.77485i	−0.511031	−	0.324042i
$31$	2.75494	+	1.38358i	0.494802	+	0.248499i	0.678658	−	0.734454i	$-0.262562\pi$
$31$	2.75494	+	1.38358i	0.494802	+	0.248499i	−0.183856	+	0.982953i	$0.558858\pi$
$32$	0.993238	+	0.116093i	0.175581	+	0.0205225i
$33$	0.956419	−	1.33041i	0.166491	−	0.231595i
$34$	0.974085	−	0.489204i	0.167054	−	0.0838977i
$35$	−8.61420	+	3.13531i	−1.45607	+	0.529964i
$36$	1.09580	−	2.79271i	0.182633	−	0.465452i
$37$	−0.251178	−	0.0914213i	−0.0412934	−	0.0150296i	0.321291	−	0.946981i	$-0.395883\pi$
$37$	−0.251178	−	0.0914213i	−0.0412934	−	0.0150296i	−0.362584	+	0.931951i	$0.618106\pi$
$38$	5.73469	−	0.670289i	0.930289	−	0.108735i
$39$	4.31181	−	7.76423i	0.690442	−	1.24327i
$40$	−0.548804	+	1.83313i	−0.0867735	+	0.289844i
$41$	−2.66272	+	8.89409i	−0.415846	+	1.38902i	0.451923	+	0.892057i	$0.350738\pi$
$41$	−2.66272	+	8.89409i	−0.415846	+	1.38902i	−0.867769	+	0.496967i	$0.834447\pi$
$42$	−4.26800	−	7.11588i	−0.658567	−	1.09800i
$43$	3.27638	−	0.382953i	0.499643	−	0.0583998i	0.137461	−	0.990507i	$-0.456106\pi$
$43$	3.27638	−	0.382953i	0.499643	−	0.0583998i	0.362182	+	0.932107i	$0.382032\pi$
$44$	−0.888947	−	0.323550i	−0.134014	−	0.0487770i
$45$	4.89861	+	2.99293i	0.730242	+	0.446160i
$46$	−6.83586	+	2.48805i	−1.00789	+	0.366843i
$47$	7.37949	−	3.70612i	1.07641	−	0.540593i	0.179930	−	0.983679i	$-0.442413\pi$
$47$	7.37949	−	3.70612i	1.07641	−	0.540593i	0.896479	+	0.443086i	$0.146116\pi$
$48$	−1.72345	−	0.172386i	−0.248759	−	0.0248818i
$49$	−15.8427	−	1.85174i	−2.26324	−	0.264534i
$50$	1.19608	+	0.600692i	0.169151	+	0.0849507i
$51$	−1.67281	+	0.875320i	−0.234240	+	0.122569i
$52$	−4.98932	−	1.18249i	−0.691895	−	0.163982i
$53$	0.171014	+	0.296205i	0.0234906	+	0.0406869i	0.877532	−	0.479519i	$-0.159189\pi$
$53$	0.171014	+	0.296205i	0.0234906	+	0.0406869i	−0.854041	+	0.520205i	$0.825855\pi$
$54$	−1.81711	+	4.86807i	−0.247278	+	0.662460i
$55$	0.905092	−	1.56767i	0.122043	−	0.211384i
$56$	−3.28756	+	3.48461i	−0.439318	+	0.465650i
$57$	−9.91205	+	1.32631i	−1.31288	+	0.175675i
$58$	−0.244377	−	4.19579i	−0.0320883	−	0.550934i
$59$	7.89735	−	10.6080i	1.02815	−	1.38104i	0.105929	−	0.994374i	$-0.466218\pi$
$59$	7.89735	−	10.6080i	1.02815	−	1.38104i	0.922219	−	0.386669i	$-0.126374\pi$
$60$	0.897520	−	3.19047i	0.115869	−	0.411889i
$61$	0.870559	+	0.572576i	0.111464	+	0.0733108i	0.604017	−	0.796972i	$-0.293566\pi$
$61$	0.870559	+	0.572576i	0.111464	+	0.0733108i	−0.492553	+	0.870282i	$0.663936\pi$
$62$	−0.535333	+	3.03602i	−0.0679873	+	0.385575i
$63$	7.59673	+	12.2002i	0.957098	+	1.53708i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	3.88619	−	9.00921i	0.482023	−	1.11746i
$66$	1.54882	+	0.534673i	0.190647	+	0.0658137i
$67$	−0.285565	+	0.0676801i	−0.0348873	+	0.00826844i	−0.248022	−	0.968754i	$-0.579781\pi$
$67$	−0.285565	+	0.0676801i	−0.0348873	+	0.00826844i	0.213135	+	0.977023i	$0.431633\pi$
$68$	0.748023	+	0.792858i	0.0907111	+	0.0961481i
$69$	11.7666	−	4.50611i	1.41653	−	0.542472i
$70$	−5.47418	−	7.35309i	−0.654289	−	0.878863i
$71$	−1.69551	+	1.42271i	−0.201221	+	0.168844i	−0.737830	−	0.674987i	$-0.764149\pi$
$71$	−1.69551	+	1.42271i	−0.201221	+	0.168844i	0.536609	+	0.843831i	$0.319705\pi$
$72$	2.98967	+	0.248802i	0.352335	+	0.0293216i
$73$	10.8638	+	9.11577i	1.27151	+	1.06692i	0.994356	+	0.106093i	$0.0338342\pi$
$73$	10.8638	+	9.11577i	1.27151	+	1.06692i	0.277150	+	0.960827i	$0.410610\pi$
$74$	0.0155420	−	0.266846i	0.00180672	−	0.0310202i
$75$	−2.08871	−	1.00577i	−0.241184	−	0.116136i
$76$	2.28686	+	5.30153i	0.262320	+	0.608127i
$77$	3.78640	−	2.49035i	0.431500	−	0.283802i
$78$	8.67469	+	1.90386i	0.982215	+	0.215570i
$79$	0.645823	+	2.15720i	0.0726607	+	0.242704i	0.986603	−	0.163141i	$-0.0521625\pi$
$79$	0.645823	+	2.15720i	0.0726607	+	0.242704i	−0.913942	+	0.405845i	$0.866977\pi$
$80$	−1.91352			−0.213938
$81$	3.00641	−	8.48301i	0.334045	−	0.942557i
$82$	−9.28412			−1.02526
$83$	−2.64436	−	8.83277i	−0.290256	−	0.969523i	−0.971415	−	0.237387i	$-0.923709\pi$
$83$	−2.64436	−	8.83277i	−0.290256	−	0.969523i	0.681159	−	0.732135i	$-0.261476\pi$
$84$	5.59286	−	6.12956i	0.610231	−	0.668789i
$85$	−1.74265	+	1.14616i	−0.189017	+	0.124319i
$86$	1.30654	+	3.02890i	0.140888	+	0.326615i
$87$	0.544303	+	7.25926i	0.0583554	+	0.778274i
$88$	0.0550049	−	0.944397i	0.00586354	−	0.100673i
$89$	5.42459	+	4.55177i	0.575005	+	0.482486i	0.883302	−	0.468804i	$-0.155315\pi$
$89$	5.42459	+	4.55177i	0.575005	+	0.482486i	−0.308297	+	0.951290i	$0.599759\pi$
$90$	−1.46226	+	5.55120i	−0.154136	+	0.585148i
$91$	18.8174	−	15.7897i	1.97260	−	1.65521i
$92$	−4.34407	−	5.83511i	−0.452901	−	0.608352i
$93$	0.839476	−	5.27326i	0.0870496	−	0.546812i
$94$	5.66689	+	6.00655i	0.584495	+	0.619528i
$95$	−10.7503	+	2.54788i	−1.10296	+	0.261407i
$96$	−0.329147	−	1.70049i	−0.0335934	−	0.173555i
$97$	−4.51089	+	10.4574i	−0.458012	+	1.06179i	0.520174	+	0.854060i	$0.325867\pi$
$97$	−4.51089	+	10.4574i	−0.458012	+	1.06179i	−0.978186	+	0.207731i	$0.933392\pi$
$98$	−2.76978	−	15.7082i	−0.279790	−	1.58677i
$99$	−2.69770	−	0.881253i	−0.271129	−	0.0885693i
$100$	−0.232418	+	1.31811i	−0.0232418	+	0.131811i
$101$	−6.69768	−	4.40513i	−0.666444	−	0.438327i	0.170690	−	0.985325i	$-0.445400\pi$
$101$	−6.69768	−	4.40513i	−0.666444	−	0.438327i	−0.837134	+	0.546998i	$0.815771\pi$
$102$	−1.31831	−	1.35149i	−0.130533	−	0.133818i
$103$	−10.4517	+	14.0390i	−1.02983	+	1.38330i	−0.108691	+	0.994076i	$0.534666\pi$
$103$	−10.4517	+	14.0390i	−1.02983	+	1.38330i	−0.921141	+	0.389229i	$0.872741\pi$
$104$	−0.298140	−	5.11886i	−0.0292350	−	0.501946i
$105$	9.69244	+	12.5762i	0.945886	+	1.22731i
$106$	−0.234714	+	0.248782i	−0.0227974	+	0.0241638i
$107$	0.230618	−	0.399443i	0.0222947	−	0.0386156i	−0.854663	−	0.519184i	$-0.826236\pi$
$107$	0.230618	−	0.399443i	0.0222947	−	0.0386156i	0.876958	+	0.480568i	$0.159569\pi$
$108$	−5.18471	−	0.344598i	−0.498899	−	0.0331589i
$109$	−1.15455	−	1.99973i	−0.110586	−	0.191540i	0.805421	−	0.592703i	$-0.201939\pi$
$109$	−1.15455	−	1.99973i	−0.110586	−	0.191540i	−0.916007	+	0.401163i	$0.868606\pi$
$110$	1.76139	+	0.417457i	0.167942	+	0.0398030i
$111$	−0.0192147	+	0.462575i	−0.00182378	+	0.0439057i
$112$	−4.28110	−	2.15005i	−0.404526	−	0.203160i
$113$	5.05324	+	0.590639i	0.475369	+	0.0555626i	0.350404	−	0.936599i	$-0.386044\pi$
$113$	5.05324	+	0.590639i	0.475369	+	0.0555626i	0.124964	+	0.992161i	$0.460118\pi$
$114$	−4.11340	−	9.11524i	−0.385255	−	0.853721i
$115$	12.4394	−	6.24730i	1.15998	−	0.582564i
$116$	3.94943	−	1.43748i	0.366696	−	0.133466i
$117$	−15.0779	−	3.04678i	−1.39395	−	0.281675i
$118$	12.4273	+	4.52318i	1.14403	+	0.416392i
$119$	−5.18665	+	0.606233i	−0.475460	+	0.0555733i
$120$	3.31385	−	0.0552235i	0.302512	−	0.00504119i
$121$	2.89817	−	9.68057i	0.263470	−	0.880052i
$122$	−0.298842	+	0.998203i	−0.0270559	+	0.0903730i
$123$	16.0783	−	0.267937i	1.44974	−	0.0241590i
$124$	−3.06201	+	0.357898i	−0.274977	+	0.0321402i
$125$	−11.3973	−	4.14827i	−1.01940	−	0.371033i
$126$	−9.50888	+	10.7766i	−0.847118	+	0.960059i
$127$	−16.3739	+	5.95962i	−1.45295	+	0.528830i	−0.943413	−	0.331619i	$-0.892405\pi$
$127$	−16.3739	+	5.95962i	−1.45295	+	0.528830i	−0.509536	+	0.860449i	$0.670183\pi$
$128$	−0.893633	+	0.448799i	−0.0789867	+	0.0396686i
$129$	−2.35009	−	5.20778i	−0.206914	−	0.458519i
$130$	9.74530	+	1.13906i	0.854720	+	0.0999024i
$131$	−12.5817	−	6.31877i	−1.09927	−	0.552073i	−0.195764	−	0.980651i	$-0.562719\pi$
$131$	−12.5817	−	6.31877i	−1.09927	−	0.552073i	−0.903505	+	0.428578i	$0.859015\pi$
$132$	−0.0680030	+	1.63710i	−0.00591890	+	0.142492i
$133$	−26.9144	−	6.37884i	−2.33378	−	0.553115i
$134$	−0.146738	−	0.254157i	−0.0126762	−	0.0219558i
$135$	2.37215	−	9.65582i	0.204162	−	0.831041i
$136$	−0.545014	+	0.943992i	−0.0467346	+	0.0809466i
$137$	−0.602329	+	0.638432i	−0.0514605	+	0.0545449i	−0.752592	−	0.658487i	$-0.771197\pi$
$137$	−0.602329	+	0.638432i	−0.0514605	+	0.0545449i	0.701132	+	0.713032i	$0.252678\pi$
$138$	7.69151	+	9.97993i	0.654745	+	0.849548i
$139$	0.362052	+	6.21619i	0.0307088	+	0.527250i	0.978226	+	0.207544i	$0.0665471\pi$
$139$	0.362052	+	6.21619i	0.0307088	+	0.527250i	−0.947517	+	0.319706i	$0.896416\pi$
$140$	5.47418	−	7.35309i	0.462652	−	0.621450i
$141$	−9.98732	−	10.2387i	−0.841084	−	0.862250i
$142$	−1.84922	−	1.21625i	−0.155183	−	0.102065i
$143$	−0.842304	+	4.77695i	−0.0704370	+	0.399468i
$144$	0.619096	+	2.93543i	0.0515913	+	0.244619i
$145$	1.39654	+	7.92015i	0.115976	+	0.657733i
$146$	−5.61705	+	13.0218i	−0.464871	+	1.07769i
$147$	5.25006	+	27.1237i	0.433018	+	2.23712i
$148$	0.260093	−	0.0616432i	0.0213795	−	0.00506704i
$149$	4.78905	+	5.07610i	0.392335	+	0.415850i	0.893189	−	0.449681i	$-0.148462\pi$
$149$	4.78905	+	5.07610i	0.392335	+	0.415850i	−0.500855	+	0.865531i	$0.666981\pi$
$150$	0.364464	−	2.28942i	0.0297584	−	0.186931i
$151$	1.36380	+	1.83191i	0.110985	+	0.149079i	0.854145	−	0.520035i	$-0.174081\pi$
$151$	1.36380	+	1.83191i	0.110985	+	0.149079i	−0.743160	+	0.669114i	$0.766674\pi$
$152$	−4.42293	+	3.71128i	−0.358747	+	0.301025i
$153$	2.32208	+	2.30248i	0.187729	+	0.186145i
$154$	3.47168	+	2.91309i	0.279756	+	0.234743i
$155$	0.343003	−	5.88913i	0.0275506	−	0.473026i
$156$	0.664050	+	8.85630i	0.0531666	+	0.709071i
$157$	−0.267278	−	0.619621i	−0.0213311	−	0.0494511i	0.907218	−	0.420662i	$-0.138202\pi$
$157$	−0.267278	−	0.619621i	−0.0213311	−	0.0494511i	−0.928549	+	0.371211i	$0.878943\pi$
$158$	−1.88135	+	1.23738i	−0.149672	+	0.0984409i
$159$	0.399300	−	0.437617i	0.0316665	−	0.0347053i
$160$	−0.548804	−	1.83313i	−0.0433867	−	0.144922i
$161$	34.8501			2.74657
$162$	8.98889	+	0.447149i	0.706234	+	0.0351313i
$163$	−2.04312			−0.160030			−0.0800149	−	0.996794i	$-0.525497\pi$
$163$	−2.04312			−0.160030			−0.0800149	+	0.996794i	$0.525497\pi$
$164$	−2.66272	−	8.89409i	−0.207923	−	0.694512i
$165$	−3.06244	−	0.672124i	−0.238411	−	0.0523248i
$166$	7.70329	−	5.06653i	0.597891	−	0.393239i
$167$	6.62121	+	15.3497i	0.512365	+	1.18779i	0.956473	+	0.291821i	$0.0942613\pi$
$167$	6.62121	+	15.3497i	0.512365	+	1.18779i	−0.444108	+	0.895973i	$0.646479\pi$
$168$	7.47610	+	3.59993i	0.576794	+	0.277740i
$169$	−0.772841	+	13.2692i	−0.0594493	+	1.02070i
$170$	−1.59781	−	1.34072i	−0.122546	−	0.102829i
$171$	7.38669	+	15.6672i	0.564875	+	1.19810i
$172$	−2.52694	+	2.12035i	−0.192677	+	0.161675i
$173$	4.28065	+	5.74991i	0.325452	+	0.437157i	0.934493	−	0.355981i	$-0.115853\pi$
$173$	4.28065	+	5.74991i	0.325452	+	0.437157i	−0.609042	+	0.793138i	$0.708446\pi$
$174$	−6.79818	+	2.60342i	−0.515369	+	0.197364i
$175$	−4.40021	−	4.66395i	−0.332624	−	0.352561i
$176$	0.920498	−	0.218162i	0.0693851	−	0.0164446i
$177$	−21.6523	−	7.47464i	−1.62749	−	0.561828i
$178$	−2.80476	+	6.50216i	−0.210225	+	0.487357i
$179$	−1.98676	−	11.2675i	−0.148497	−	0.842171i	−0.964492	−	0.264112i	$-0.914921\pi$
$179$	−1.98676	−	11.2675i	−0.148497	−	0.842171i	0.815995	−	0.578060i	$-0.196190\pi$
$180$	−5.73737	+	0.191273i	−0.427638	+	0.0142567i
$181$	−2.70185	+	15.3229i	−0.200827	+	1.13895i	0.703046	+	0.711144i	$0.251823\pi$
$181$	−2.70185	+	15.3229i	−0.200827	+	1.13895i	−0.903873	+	0.427801i	$0.859288\pi$
$182$	20.5232	+	13.4983i	1.52128	+	1.00056i
$183$	0.488730	−	1.73732i	0.0361280	−	0.128427i
$184$	4.34407	−	5.83511i	0.320249	−	0.430170i
$185$	0.0297399	+	0.510615i	0.00218652	+	0.0375411i
$186$	5.29250	−	0.708180i	0.388065	−	0.0519263i
$187$	0.707627	−	0.750041i	0.0517468	−	0.0548485i
$188$	−4.12893	+	7.15151i	−0.301133	+	0.521578i
$189$	16.1566	−	18.9375i	1.17522	−	1.37750i
$190$	−5.52407	−	9.56797i	−0.400758	−	0.694133i
$191$	−18.2685	−	4.32972i	−1.32186	−	0.313288i	−0.491680	−	0.870776i	$-0.663617\pi$
$191$	−18.2685	−	4.32972i	−1.32186	−	0.313288i	−0.830185	+	0.557489i	$0.811765\pi$
$192$	1.53465	−	0.803025i	0.110754	−	0.0579533i
$193$	−12.2341	−	6.14420i	−0.880630	−	0.442269i	−0.0497769	−	0.998760i	$-0.515851\pi$
$193$	−12.2341	−	6.14420i	−0.880630	−	0.442269i	−0.830854	+	0.556491i	$0.812147\pi$
$194$	−11.3118	−	1.32216i	−0.812143	−	0.0949259i
$195$	−16.9099	−	1.69139i	−1.21094	−	0.121123i
$196$	14.2539	−	7.15858i	1.01814	−	0.511327i
$197$	−3.57233	+	1.30022i	−0.254518	+	0.0926370i	−0.466128	−	0.884717i	$-0.654351\pi$
$197$	−3.57233	+	1.30022i	−0.254518	+	0.0926370i	0.211610	+	0.977354i	$0.432129\pi$
$198$	0.0705221	−	2.83712i	0.00501178	−	0.201625i
$199$	−3.09723	−	1.12730i	−0.219557	−	0.0799121i	0.229900	−	0.973214i	$-0.426160\pi$
$199$	−3.09723	−	1.12730i	−0.219557	−	0.0799121i	−0.449457	+	0.893302i	$0.648382\pi$
$200$	−1.32939	+	0.155384i	−0.0940023	+	0.0109873i
$201$	0.261457	+	0.435917i	0.0184417	+	0.0307472i
$202$	2.29915	−	7.67971i	0.161768	−	0.540343i
$203$	−5.77470	+	19.2888i	−0.405304	+	1.35381i
$204$	0.916618	−	1.65054i	0.0641761	−	0.115561i
$205$	17.6452	−	2.06243i	1.23240	−	0.144046i
$206$	−16.4468	−	5.98614i	−1.14590	−	0.417074i
$207$	−13.6083	−	17.0614i	−0.945839	−	1.18585i
$208$	4.81831	−	1.75372i	0.334090	−	0.121599i
$209$	4.88096	−	2.45131i	0.337623	−	0.169561i
$210$	−9.26803	+	12.8921i	−0.639555	+	0.889643i
$211$	−3.08746	−	0.360872i	−0.212550	−	0.0248435i	0.00915168	−	0.999958i	$-0.497087\pi$
$211$	−3.08746	−	0.360872i	−0.212550	−	0.0248435i	−0.221701	+	0.975115i	$0.571161\pi$
$212$	−0.305647	−	0.153502i	−0.0209919	−	0.0105425i
$213$	3.23759	+	2.05294i	0.221836	+	0.140665i
$214$	0.448804	+	0.106369i	0.0306796	+	0.00727120i
$215$	−3.15604	−	5.46643i	−0.215240	−	0.372807i
$216$	−1.15687	−	5.06573i	−0.0787151	−	0.344679i
$217$	7.38447	−	12.7903i	0.501291	−	0.868261i
$218$	1.58460	−	1.67957i	0.107322	−	0.113755i
$219$	9.35187	−	22.7134i	0.631940	−	1.53483i
$220$	0.105253	+	1.80712i	0.00709615	+	0.121836i
$221$	3.33762	−	4.48320i	0.224512	−	0.301572i
$222$	−0.448653	+	0.114260i	−0.0301116	+	0.00766866i
$223$	−0.124887	−	0.0821393i	−0.00836303	−	0.00550045i	0.545321	−	0.838228i	$-0.316408\pi$
$223$	−0.124887	−	0.0821393i	−0.00836303	−	0.00550045i	−0.553684	+	0.832727i	$0.686778\pi$
$224$	0.831891	−	4.71789i	0.0555831	−	0.315227i
$225$	−0.565111	+	3.97536i	−0.0376740	+	0.265024i
$226$	0.883459	+	5.01035i	0.0587668	+	0.333283i
$227$	8.80390	−	20.4097i	0.584335	−	1.35464i	−0.327798	−	0.944748i	$-0.606307\pi$
$227$	8.80390	−	20.4097i	0.584335	−	1.35464i	0.912134	−	0.409893i	$-0.134434\pi$
$228$	7.55257	−	6.55488i	0.500181	−	0.434107i
$229$	7.26364	−	1.72151i	0.479995	−	0.113761i	0.0165061	−	0.999864i	$-0.494746\pi$
$229$	7.26364	−	1.72151i	0.479995	−	0.113761i	0.463488	+	0.886103i	$0.346598\pi$
$230$	9.55251	+	10.1251i	0.629874	+	0.667627i
$231$	−6.09637	−	4.94472i	−0.401112	−	0.325339i
$232$	2.50980	+	3.37124i	0.164776	+	0.221333i
$233$	6.66557	−	5.59308i	0.436676	−	0.366415i	−0.397788	−	0.917478i	$-0.630222\pi$
$233$	6.66557	−	5.59308i	0.436676	−	0.366415i	0.834464	+	0.551063i	$0.185777\pi$
$234$	−1.40560	−	15.3183i	−0.0918869	−	1.00139i
$235$	−12.1047	−	10.1571i	−0.789624	−	0.662573i
$236$	−0.768959	+	13.2025i	−0.0500549	+	0.859410i
$237$	3.22243	−	2.19721i	0.209319	−	0.142724i
$238$	−2.06831	−	4.79489i	−0.134069	−	0.310807i
$239$	−18.9948	+	12.4931i	−1.22867	+	0.808110i	−0.986760	−	0.162188i	$-0.948145\pi$
$239$	−18.9948	+	12.4931i	−1.22867	+	0.808110i	−0.241912	+	0.970298i	$0.577774\pi$
$240$	1.00333	+	3.15880i	0.0647645	+	0.203900i
$241$	4.29763	+	14.3551i	0.276835	+	0.924692i	0.977453	+	0.211155i	$0.0677226\pi$
$241$	4.29763	+	14.3551i	0.276835	+	0.924692i	−0.700618	+	0.713537i	$0.747092\pi$
$242$	10.1051			0.649580
$243$	−15.5799	−	0.514961i	−0.999454	−	0.0330348i
$244$	−1.04198			−0.0667057
$245$	8.75370	+	29.2394i	0.559253	+	1.86804i
$246$	4.86800	+	15.3260i	0.310372	+	0.977152i
$247$	24.7346	−	16.2682i	1.57383	−	1.03512i
$248$	−1.22106	−	2.83073i	−0.0775372	−	0.179751i
$249$	−13.1944	+	8.99659i	−0.836162	+	0.570136i
$250$	0.705223	−	12.1082i	0.0446022	−	0.765791i
$251$	20.9029	+	17.5397i	1.31938	+	1.10709i	0.986436	+	0.164148i	$0.0524873\pi$
$251$	20.9029	+	17.5397i	1.31938	+	1.10709i	0.332947	+	0.942946i	$0.391957\pi$
$252$	−13.0511	−	6.01863i	−0.822141	−	0.379138i
$253$	−5.27171	+	4.42349i	−0.331430	+	0.278102i
$254$	−10.4053	−	13.9768i	−0.652889	−	0.876982i
$255$	2.80579	+	2.27576i	0.175706	+	0.142514i
$256$	−0.686242	−	0.727374i	−0.0428901	−	0.0454609i
$257$	11.8276	−	2.80319i	0.737784	−	0.174858i	0.155492	−	0.987837i	$-0.450304\pi$
$257$	11.8276	−	2.80319i	0.737784	−	0.174858i	0.582293	+	0.812979i	$0.302156\pi$
$258$	4.31498	−	3.74497i	0.268639	−	0.233152i
$259$	−0.507195	+	1.17581i	−0.0315155	+	0.0730612i
$260$	1.70377	+	9.66258i	0.105664	+	0.599248i
$261$	11.6980	−	4.70482i	0.724090	−	0.291221i
$262$	2.44484	−	13.8654i	0.151043	−	0.856606i
$263$	12.9433	+	8.51296i	0.798120	+	0.524932i	0.881835	−	0.471558i	$-0.156308\pi$
$263$	12.9433	+	8.51296i	0.798120	+	0.524932i	−0.0837150	+	0.996490i	$0.526679\pi$
$264$	−1.58783	+	0.404381i	−0.0977243	+	0.0248879i
$265$	0.390826	−	0.524971i	0.0240083	−	0.0322487i
$266$	−1.60829	−	27.6132i	−0.0986104	−	1.69308i
$267$	4.66966	−	11.3415i	0.285778	−	0.694085i
$268$	0.201395	−	0.213466i	0.0123022	−	0.0130395i
$269$	−3.60143	+	6.23787i	−0.219583	+	0.380329i	−0.954681	−	0.297632i	$-0.903803\pi$
$269$	−3.60143	+	6.23787i	−0.219583	+	0.380329i	0.735097	+	0.677962i	$0.237136\pi$
$270$	9.93052	−	0.496828i	0.604352	−	0.0302360i
$271$	−9.28051	−	16.0743i	−0.563751	−	0.976445i	−0.997165	−	0.0752497i	$-0.976025\pi$
$271$	−9.28051	−	16.0743i	−0.563751	−	0.976445i	0.433414	−	0.901195i	$-0.357309\pi$
$272$	−1.06065	−	0.251378i	−0.0643111	−	0.0152420i
$273$	−35.9319	−	22.7842i	−2.17469	−	1.37897i
$274$	−0.784361	−	0.393921i	−0.0473850	−	0.0237976i
$275$	1.25760	+	0.146993i	0.0758363	+	0.00886399i
$276$	−7.35471	+	10.2307i	−0.442702	+	0.615814i
$277$	−3.11738	+	1.56561i	−0.187305	+	0.0940683i	−0.539980	−	0.841678i	$-0.681568\pi$
$277$	−3.11738	+	1.56561i	−0.187305	+	0.0940683i	0.352675	+	0.935746i	$0.385272\pi$
$278$	−5.85120	+	2.12966i	−0.350932	+	0.127729i
$279$	−9.14516	+	1.37917i	−0.547506	+	0.0825689i
$280$	8.61420	+	3.13531i	0.514797	+	0.187371i
$281$	15.7652	−	1.84268i	0.940471	−	0.109925i	0.367978	−	0.929835i	$-0.380050\pi$
$281$	15.7652	−	1.84268i	0.940471	−	0.109925i	0.572493	+	0.819909i	$0.305976\pi$
$282$	6.94413	−	12.5042i	0.413517	−	0.744616i
$283$	−0.992578	+	3.31544i	−0.0590026	+	0.197083i	−0.982409	−	0.186741i	$-0.940208\pi$
$283$	−0.992578	+	3.31544i	−0.0590026	+	0.197083i	0.923407	+	0.383823i	$0.125393\pi$
$284$	0.634792	−	2.12035i	0.0376680	−	0.125820i
$285$	9.84277	+	16.4105i	0.583035	+	0.972073i
$286$	−4.81784	+	0.563125i	−0.284885	+	0.0332983i
$287$	41.7949	+	15.2121i	2.46707	+	0.897941i
$288$	−2.63455	+	1.43498i	−0.155242	+	0.0845568i
$289$	14.8583	−	5.40797i	0.874016	−	0.318116i
$290$	−7.18689	+	3.60939i	−0.422029	+	0.211951i
$291$	19.6281	+	1.96328i	1.15062	+	0.115090i
$292$	−14.0857	−	1.64639i	−0.824305	−	0.0963474i
$293$	3.06519	+	1.53940i	0.179070	+	0.0899326i	0.536076	−	0.844170i	$-0.319906\pi$
$293$	3.06519	+	1.53940i	0.179070	+	0.0899326i	−0.357006	+	0.934102i	$0.616202\pi$
$294$	−24.4785	+	12.8087i	−1.42761	+	0.747016i
$295$	−24.6239	−	5.83598i	−1.43366	−	0.339784i
$296$	0.133649	+	0.231487i	0.00776819	+	0.0134549i
$297$	−0.0402526	+	4.91538i	−0.00233569	+	0.285219i
$298$	−3.48933	+	6.04370i	−0.202132	+	0.350102i
$299$	−25.5973	+	27.1315i	−1.48033	+	1.56906i
$300$	2.29777	−	0.307461i	0.132662	−	0.0177513i
$301$	−0.918856	−	15.7761i	−0.0529620	−	0.909322i
$302$	−1.36380	+	1.83191i	−0.0784782	+	0.105414i
$303$	−3.76007	+	13.3662i	−0.216010	+	0.767866i
$304$	−4.82388	−	3.17271i	−0.276668	−	0.181968i
$305$	0.346227	−	1.96355i	0.0198249	−	0.112433i
$306$	−1.53977	+	2.88488i	−0.0880230	+	0.164918i
$307$	−3.71781	−	21.0847i	−0.212186	−	1.20337i	−0.885723	−	0.464215i	$-0.846337\pi$
$307$	−3.71781	−	21.0847i	−0.212186	−	1.20337i	0.673536	−	0.739154i	$-0.264774\pi$
$308$	−1.79502	+	4.16132i	−0.102281	+	0.237113i
$309$	28.6555	+	9.89221i	1.63015	+	0.562748i
$310$	5.74010	−	1.36043i	0.326016	−	0.0772671i
$311$	−23.4972	−	24.9056i	−1.33241	−	1.41227i	−0.840693	−	0.541511i	$-0.817852\pi$
$311$	−23.4972	−	24.9056i	−1.33241	−	1.41227i	−0.491713	−	0.870757i	$-0.663629\pi$
$312$	−8.29379	+	3.17617i	−0.469543	+	0.179815i
$313$	15.5585	+	20.8986i	0.879416	+	1.18126i	0.982440	+	0.186581i	$0.0597408\pi$
$313$	15.5585	+	20.8986i	0.879416	+	1.18126i	−0.103024	+	0.994679i	$0.532852\pi$
$314$	0.516934	−	0.433759i	0.0291723	−	0.0244784i
$315$	15.6784	−	22.5942i	0.883378	−	1.27304i
$316$	−1.72498	−	1.44743i	−0.0970375	−	0.0814242i
$317$	−1.95379	+	33.5453i	−0.109736	+	1.88409i	0.275540	+	0.961290i	$0.411143\pi$
$317$	−1.95379	+	33.5453i	−0.109736	+	1.88409i	−0.385276	+	0.922801i	$0.625894\pi$
$318$	0.533753	+	0.257015i	0.0299314	+	0.0144127i
$319$	−1.57479	−	3.65076i	−0.0881711	−	0.204404i
$320$	1.59872	−	1.05150i	0.0893713	−	0.0587804i
$321$	−0.780313	−	0.171258i	−0.0435528	−	0.00955868i
$322$	9.99512	+	33.3860i	0.557006	+	1.86053i
$323$	−6.29352			−0.350181
$324$	2.14968	+	8.73950i	0.119427	+	0.485528i
$325$	6.86292			0.380686
$326$	−0.585974	−	1.95729i	−0.0324541	−	0.108404i
$327$	−2.69575	+	2.95443i	−0.149075	+	0.163381i
$328$	7.75677	−	5.10171i	0.428296	−	0.281695i
$329$	−15.6692	−	36.3252i	−0.863870	−	2.00268i
$330$	−0.234431	−	3.12656i	−0.0129050	−	0.172111i
$331$	−0.490419	+	8.42018i	−0.0269559	+	0.462815i	0.957640	+	0.287969i	$0.0929799\pi$
$331$	−0.490419	+	8.42018i	−0.0269559	+	0.462815i	−0.984596	+	0.174846i	$0.944057\pi$
$332$	7.06302	+	5.92657i	0.387633	+	0.325263i
$333$	0.773684	−	0.210825i	0.0423976	−	0.0115532i
$334$	−12.8059	+	10.7454i	−0.700705	+	0.587962i
$335$	0.335347	+	0.450449i	0.0183220	+	0.0246107i
$336$	−1.30452	+	8.19450i	−0.0711674	+	0.447046i
$337$	20.0224	+	21.2225i	1.09069	+	1.15606i	0.986879	+	0.161464i	$0.0516215\pi$
$337$	20.0224	+	21.2225i	1.09069	+	1.15606i	0.103809	+	0.994597i	$0.466897\pi$
$338$	−12.9334	+	3.06527i	−0.703483	+	0.166728i
$339$	−1.67458	−	8.65147i	−0.0909507	−	0.469883i
$340$	0.826139	−	1.91521i	0.0448037	−	0.103867i
$341$	0.506423	+	2.87207i	0.0274244	+	0.155531i
$342$	−12.8905	+	11.5698i	−0.697036	+	0.625621i
$343$	−7.44585	+	42.2275i	−0.402038	+	2.28007i
$344$	−2.75601	−	1.81265i	−0.148594	−	0.0977318i
$345$	−16.8353	−	17.2590i	−0.906385	−	0.929194i
$346$	−4.28065	+	5.74991i	−0.230129	+	0.309117i
$347$	0.136808	+	2.34890i	0.00734422	+	0.126095i	0.999987	+	0.00501889i	$0.00159757\pi$
$347$	0.136808	+	2.34890i	0.00734422	+	0.126095i	−0.992643	+	0.121076i	$0.961365\pi$
$348$	−4.44379	−	5.76592i	−0.238212	−	0.309086i
$349$	20.9681	−	22.2249i	1.12240	−	1.18967i	0.142578	−	0.989784i	$-0.454461\pi$
$349$	20.9681	−	22.2249i	1.12240	−	1.18967i	0.979819	−	0.199887i	$-0.0640575\pi$
$350$	3.20602	−	5.55299i	0.171369	−	0.296820i
$351$	2.87631	+	26.4878i	0.153526	+	1.41381i
$352$	0.472999	+	0.819258i	0.0252109	+	0.0436666i
$353$	−11.4479	−	2.71321i	−0.609311	−	0.144409i	−0.0856347	−	0.996327i	$-0.527292\pi$
$353$	−11.4479	−	2.71321i	−0.609311	−	0.144409i	−0.523677	+	0.851917i	$0.675440\pi$
$354$	0.950671	−	22.8864i	0.0505276	−	1.21640i
$355$	3.78477	+	1.90078i	0.200875	+	0.100883i
$356$	−7.03341	−	0.822088i	−0.372770	−	0.0435706i
$357$	3.72031	+	8.24415i	0.196900	+	0.436327i
$358$	10.2243	−	5.13485i	0.540372	−	0.271385i
$359$	−11.0147	+	4.00902i	−0.581333	+	0.211588i	−0.615913	−	0.787814i	$-0.711213\pi$
$359$	−11.0147	+	4.00902i	−0.581333	+	0.211588i	0.0345802	+	0.999402i	$0.488991\pi$
$360$	−1.82873	−	5.44148i	−0.0963828	−	0.286791i
$361$	−13.4714	−	4.90317i	−0.709019	−	0.258062i
$362$	−15.4541	+	1.80633i	−0.812251	+	0.0949385i
$363$	−17.5001	+	0.291629i	−0.918517	+	0.0153066i
$364$	−7.04513	+	23.5324i	−0.369265	+	1.23343i
$365$	7.78292	−	25.9968i	0.407377	−	1.36073i
$366$	1.80451	−	0.0300711i	0.0943230	−	0.00157184i
$367$	32.9460	−	3.85084i	1.71977	−	0.201012i	0.801780	−	0.597619i	$-0.203886\pi$
$367$	32.9460	−	3.85084i	1.71977	−	0.201012i	0.917989	+	0.396607i	$0.129812\pi$
$368$	6.83586	+	2.48805i	0.356344	+	0.129699i
$369$	−8.87276	−	26.4013i	−0.461897	−	1.37440i
$370$	−0.480634	+	0.174936i	−0.0249870	+	0.00909451i
$371$	1.46425	−	0.735376i	0.0760203	−	0.0381788i
$372$	2.19633	+	4.86705i	0.113875	+	0.252345i
$373$	2.87819	+	0.336413i	0.149027	+	0.0174188i	0.190279	−	0.981730i	$-0.439061\pi$
$373$	2.87819	+	0.336413i	0.149027	+	0.0174188i	−0.0412522	+	0.999149i	$0.513135\pi$
$374$	0.921482	+	0.462785i	0.0476487	+	0.0239301i
$375$	−0.871874	+	20.9895i	−0.0450234	+	1.08389i
$376$	−8.03527	−	1.90439i	−0.414387	−	0.0982116i
$377$	−10.7753	−	18.6633i	−0.554954	−	0.961209i
$378$	22.7757	+	10.0465i	1.17146	+	0.516735i
$379$	−4.61620	+	7.99549i	−0.237118	+	0.410701i	−0.959886	−	0.280390i	$-0.909536\pi$
$379$	−4.61620	+	7.99549i	−0.237118	+	0.410701i	0.722768	+	0.691091i	$0.242869\pi$
$380$	7.58169	−	8.03613i	0.388933	−	0.412245i
$381$	18.4234	+	23.9049i	0.943861	+	1.22468i
$382$	−1.09165	−	18.7428i	−0.0558535	−	0.958967i
$383$	−5.88476	+	7.90460i	−0.300697	+	0.403906i	−0.926632	−	0.375969i	$-0.877310\pi$
$383$	−5.88476	+	7.90460i	−0.300697	+	0.403906i	0.625935	+	0.779875i	$0.284717\pi$
$384$	1.20943	+	1.23987i	0.0617186	+	0.0632718i
$385$	−7.24535	−	4.76534i	−0.369257	−	0.242864i
$386$	2.37730	−	13.4823i	0.121001	−	0.686232i
$387$	−7.36465	+	6.61011i	−0.374366	+	0.336011i
$388$	−1.97765	−	11.2158i	−0.100400	−	0.569397i
$389$	2.93073	−	6.79419i	0.148594	−	0.344479i	−0.827620	−	0.561289i	$-0.810306\pi$
$389$	2.93073	−	6.79419i	0.148594	−	0.344479i	0.976214	+	0.216809i	$0.0695650\pi$
$390$	−3.22947	−	16.6846i	−0.163531	−	0.844857i
$391$	7.71575	−	1.82867i	0.390202	−	0.0924796i
$392$	10.9459	+	11.6020i	0.552852	+	0.585989i
$393$	−3.83385	+	24.0828i	−0.193392	+	1.21482i
$394$	−2.27016	−	3.04935i	−0.114369	−	0.153624i
$395$	3.30078	−	2.76968i	0.166080	−	0.139358i
$396$	2.73815	−	0.746135i	0.137597	−	0.0374947i
$397$	−18.4893	−	15.5144i	−0.927951	−	0.778644i	0.0474970	−	0.998871i	$-0.484876\pi$
$397$	−18.4893	−	15.5144i	−0.927951	−	0.778644i	−0.975449	+	0.220228i	$0.929320\pi$
$398$	0.191646	−	3.29043i	0.00960632	−	0.164934i
$399$	3.58216	+	47.7744i	0.179332	+	2.39171i
$400$	−0.530130	−	1.22898i	−0.0265065	−	0.0614490i
$401$	11.5555	−	7.60019i	0.577055	−	0.379535i	−0.227174	−	0.973854i	$-0.572949\pi$
$401$	11.5555	−	7.60019i	0.577055	−	0.379535i	0.804230	+	0.594319i	$0.202578\pi$
$402$	−0.342618	+	0.375495i	−0.0170882	+	0.0187280i
$403$	4.53363	+	15.1434i	0.225836	+	0.754346i
$404$	8.01649			0.398835
$405$	−17.1834	+	1.14700i	−0.853852	+	0.0569950i
$406$	−20.1347			−0.999268
$407$	−0.0725220	−	0.242240i	−0.00359478	−	0.0120074i
$408$	1.84409	+	0.404729i	0.0912962	+	0.0200371i
$409$	−17.4230	+	11.4593i	−0.861510	+	0.566624i	−0.901599	−	0.432572i	$-0.857606\pi$
$409$	−17.4230	+	11.4593i	−0.861510	+	0.566624i	0.0400892	+	0.999196i	$0.487236\pi$
$410$	7.03650	+	16.3124i	0.347508	+	0.805614i
$411$	1.36973	+	0.659560i	0.0675639	+	0.0325337i
$412$	1.01767	−	17.4727i	0.0501369	−	0.860818i
$413$	−48.5336	−	40.7245i	−2.38818	−	2.00392i
$414$	12.4417	−	17.9298i	0.611477	−	0.881203i
$415$	−13.5152	+	11.3406i	−0.663436	+	0.556689i
$416$	3.06195	+	4.11292i	0.150125	+	0.201652i
$417$	10.0717	−	3.85704i	0.493214	−	0.188880i
$418$	3.74820	+	3.97286i	0.183331	+	0.194319i
$419$	12.4119	−	2.94168i	0.606363	−	0.143711i	0.0840458	−	0.996462i	$-0.473216\pi$
$419$	12.4119	−	2.94168i	0.606363	−	0.143711i	0.522317	+	0.852751i	$0.325068\pi$
$420$	−15.0086	−	5.18116i	−0.732347	−	0.252815i
$421$	−12.9626	+	30.0507i	−0.631759	+	1.46458i	0.238080	+	0.971245i	$0.423482\pi$
$421$	−12.9626	+	30.0507i	−0.631759	+	1.46458i	−0.869839	+	0.493336i	$0.835777\pi$
$422$	−0.539782	−	3.06125i	−0.0262762	−	0.149020i
$423$	−11.6651	+	21.8554i	−0.567174	+	1.06264i
$424$	0.0593925	−	0.336832i	0.00288435	−	0.0163580i
$425$	−1.21893	−	0.801701i	−0.0591266	−	0.0388882i
$426$	−1.03815	+	3.69037i	−0.0502984	+	0.178799i
$427$	2.98088	−	4.00401i	0.144255	−	0.193768i
$428$	0.0268185	+	0.460456i	0.00129632	+	0.0222570i
$429$	8.32733	−	1.11427i	0.402047	−	0.0537973i
$430$	4.33162	−	4.59125i	0.208889	−	0.221410i
$431$	0.498982	−	0.864263i	0.0240351	−	0.0416301i	−0.853758	−	0.520671i	$-0.825682\pi$
$431$	0.498982	−	0.864263i	0.0240351	−	0.0416301i	0.877793	+	0.479041i	$0.159015\pi$
$432$	4.52112	−	2.56114i	0.217523	−	0.123223i
$433$	−6.98746	−	12.1026i	−0.335796	−	0.581615i	0.647842	−	0.761775i	$-0.275672\pi$
$433$	−6.98746	−	12.1026i	−0.335796	−	0.581615i	−0.983637	+	0.180160i	$0.942339\pi$
$434$	14.3709	+	3.40595i	0.689823	+	0.163491i
$435$	12.3422	−	6.45819i	0.591761	−	0.309647i
$436$	2.06348	+	1.03632i	0.0988229	+	0.0496307i
$437$	41.7174	+	4.87607i	1.99561	+	0.233254i
$438$	24.4413	+	2.44472i	1.16785	+	0.116813i
$439$	−6.57693	+	3.30306i	−0.313900	+	0.157646i	−0.598773	−	0.800919i	$-0.704345\pi$
$439$	−6.57693	+	3.30306i	−0.313900	+	0.157646i	0.284873	+	0.958565i	$0.408049\pi$
$440$	−1.70102	+	0.619120i	−0.0810928	+	0.0295154i
$441$	42.0224	−	22.8886i	2.00107	−	1.08993i
$442$	5.25209	+	1.91161i	0.249817	+	0.0909258i
$443$	3.63480	−	0.424847i	0.172694	−	0.0201851i	−0.0293062	−	0.999570i	$-0.509330\pi$
$443$	3.63480	−	0.424847i	0.172694	−	0.0201851i	0.202001	+	0.979385i	$0.435256\pi$
$444$	−0.238135	−	0.397034i	−0.0113014	−	0.0188424i
$445$	3.88624	−	12.9809i	0.184225	−	0.615356i
$446$	0.0428706	−	0.143198i	0.00202998	−	0.00678062i
$447$	5.86845	−	10.5673i	0.277568	−	0.499814i
$448$	4.75828	−	0.556163i	0.224807	−	0.0262762i
$449$	−26.7642	−	9.74138i	−1.26308	−	0.459724i	−0.378280	−	0.925691i	$-0.623484\pi$
$449$	−26.7642	−	9.74138i	−1.26308	−	0.459724i	−0.884802	+	0.465967i	$0.845707\pi$
$450$	−3.97043	+	0.598777i	−0.187168	+	0.0282266i
$451$	−8.25309	+	3.00388i	−0.388623	+	0.141447i
$452$	−4.54648	+	2.28333i	−0.213848	+	0.107399i
$453$	2.30898	−	3.21188i	0.108485	−	0.150907i
$454$	22.0773	+	2.58046i	1.03614	+	0.121107i
$455$	−42.0046	−	21.0955i	−1.96921	−	0.988973i
$456$	8.44561	+	5.35532i	0.395502	+	0.250786i
$457$	−9.01991	−	2.13776i	−0.421934	−	0.100000i	0.0141635	−	0.999900i	$-0.495491\pi$
$457$	−9.01991	−	2.13776i	−0.421934	−	0.100000i	−0.436097	+	0.899900i	$0.643640\pi$
$458$	3.73243	+	6.46475i	0.174405	+	0.302078i
$459$	2.58334	−	5.04051i	0.120580	−	0.235271i
$460$	−6.96002	+	12.0551i	−0.324513	+	0.562072i
$461$	1.50084	−	1.59080i	0.0699011	−	0.0740908i	−0.691479	−	0.722396i	$-0.743041\pi$
$461$	1.50084	−	1.59080i	0.0699011	−	0.0740908i	0.761380	+	0.648306i	$0.224522\pi$
$462$	2.98854	−	7.25842i	0.139039	−	0.337692i
$463$	−0.225192	−	3.86639i	−0.0104655	−	0.179687i	−0.999490	−	0.0319344i	$-0.989833\pi$
$463$	−0.225192	−	3.86639i	−0.0104655	−	0.179687i	0.989024	−	0.147752i	$-0.0472038\pi$
$464$	−2.50980	+	3.37124i	−0.116514	+	0.156506i
$465$	−9.90150	+	2.52166i	−0.459171	+	0.116939i
$466$	7.26982	+	4.78144i	0.336768	+	0.221496i
$467$	−2.59162	+	14.6978i	−0.119926	+	0.680133i	0.864267	+	0.503033i	$0.167783\pi$
$467$	−2.59162	+	14.6978i	−0.119926	+	0.680133i	−0.984193	+	0.177100i	$0.943328\pi$
$468$	14.2716	−	5.73988i	0.659705	−	0.265326i
$469$	0.244140	+	1.38458i	0.0112733	+	0.0639342i
$470$	6.25868	−	14.5093i	0.288692	−	0.669262i
$471$	−0.882713	+	0.766107i	−0.0406733	+	0.0353003i
$472$	−12.8684	+	3.04987i	−0.592316	+	0.140382i
$473$	2.14145	+	2.26980i	0.0984638	+	0.104366i
$474$	3.02911	+	2.45689i	0.139131	+	0.112849i
$475$	−4.61472	−	6.19865i	−0.211738	−	0.284414i
$476$	4.00026	−	3.35661i	0.183351	−	0.153850i
$477$	−0.931776	−	0.429698i	−0.0426631	−	0.0196745i
$478$	−17.4160	−	14.6138i	−0.796590	−	0.668418i
$479$	2.05422	−	35.2696i	0.0938597	−	1.61151i	−0.542459	−	0.840083i	$-0.682506\pi$
$479$	2.05422	−	35.2696i	0.0938597	−	1.61151i	0.636318	−	0.771427i	$-0.280457\pi$
$480$	−2.73834	+	1.86713i	−0.124987	+	0.0852225i
$481$	−0.542859	−	1.25849i	−0.0247523	−	0.0573822i
$482$	−12.5194	+	8.23417i	−0.570245	+	0.375056i
$483$	−18.2732	−	57.5298i	−0.831457	−	2.61770i
$484$	2.89817	+	9.68057i	0.131735	+	0.440026i
$485$	21.7928			0.989559
$486$	−3.97505	−	15.0731i	−0.180312	−	0.683731i
$487$	12.0682			0.546860			0.273430	−	0.961892i	$-0.411842\pi$
$487$	12.0682			0.546860			0.273430	+	0.961892i	$0.411842\pi$
$488$	−0.298842	−	0.998203i	−0.0135280	−	0.0451865i
$489$	1.07128	+	3.37275i	0.0484451	+	0.152521i
$490$	−25.5004	+	16.7719i	−1.15199	+	0.757677i
$491$	−7.75178	−	17.9707i	−0.349833	−	0.811004i	−0.998742	−	0.0501384i	$-0.984034\pi$
$491$	−7.75178	−	17.9707i	−0.349833	−	0.811004i	0.648909	−	0.760866i	$-0.275225\pi$
$492$	−13.2860	+	9.05905i	−0.598980	+	0.408414i
$493$	−0.266378	+	4.57353i	−0.0119970	+	0.205981i
$494$	22.6787	+	19.0297i	1.02037	+	0.856188i
$495$	0.496221	+	5.40784i	0.0223035	+	0.243064i
$496$	2.36161	−	1.98162i	0.106039	−	0.0889775i
$497$	6.33189	+	8.50521i	0.284024	+	0.381511i
$498$	−12.4028	−	10.0599i	−0.555785	−	0.450793i
$499$	−8.43595	−	8.94159i	−0.377645	−	0.400280i	0.510474	−	0.859893i	$-0.329470\pi$
$499$	−8.43595	−	8.94159i	−0.377645	−	0.400280i	−0.888120	+	0.459613i	$0.847988\pi$
$500$	11.8018	−	2.79708i	0.527793	−	0.125089i
$501$	21.8672	−	18.9786i	0.976955	−	0.847899i
$502$	−10.8078	+	25.0552i	−0.482375	+	1.11827i
$503$	−1.34669	−	7.63745i	−0.0600459	−	0.340537i	0.939954	−	0.341302i	$-0.110868\pi$
$503$	−1.34669	−	7.63745i	−0.0600459	−	0.340537i	−1.00000		0.000764541i	$0.999757\pi$
$504$	2.02269	−	14.2290i	0.0900979	−	0.633808i
$505$	−2.66371	+	15.1067i	−0.118534	+	0.672238i
$506$	−5.74960	−	3.78157i	−0.255601	−	0.168111i
$507$	22.3097	−	5.68171i	0.990808	−	0.252334i
$508$	10.4053	−	13.9768i	0.461662	−	0.620120i
$509$	2.38159	+	40.8902i	0.105562	+	1.81243i	0.471583	+	0.881822i	$0.343683\pi$
$509$	2.38159	+	40.8902i	0.105562	+	1.81243i	−0.366021	+	0.930606i	$0.619280\pi$
$510$	−1.37544	+	3.34062i	−0.0609057	+	0.147925i
$511$	46.6229	−	49.4174i	2.06247	−	2.18610i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	21.9899	−	20.4087i	0.970879	−	0.901064i
$514$	6.07761	+	10.5267i	0.268072	+	0.464314i
$515$	32.5883	+	7.72356i	1.43601	+	0.340341i
$516$	4.82519	+	3.05964i	0.212417	+	0.134693i
$517$	6.98098	+	3.50598i	0.307023	+	0.154193i
$518$	−1.27188	−	0.148661i	−0.0558831	−	0.00653180i
$519$	7.24733	−	10.0813i	0.318122	−	0.442519i
$520$	−8.76801	+	4.40346i	−0.384503	+	0.193104i
$521$	−26.8524	+	9.77348i	−1.17643	+	0.428184i	−0.854938	−	0.518730i	$-0.826405\pi$
$521$	−26.8524	+	9.77348i	−1.17643	+	0.428184i	−0.321487	+	0.946914i	$0.604183\pi$
$522$	7.86220	+	9.85724i	0.344119	+	0.431440i
$523$	14.7081	+	5.35331i	0.643140	+	0.234084i	0.642940	−	0.765916i	$-0.277714\pi$
$523$	14.7081	+	5.35331i	0.643140	+	0.234084i	0.000199454		1.00000i	$0.499937\pi$
$524$	13.9841	−	1.63450i	0.610897	−	0.0714037i
$525$	−5.39196	+	9.70924i	−0.235324	+	0.423746i
$526$	−4.44314	+	14.8411i	−0.193730	+	0.647104i
$527$	0.963774	−	3.21923i	0.0419826	−	0.140232i
$528$	−0.842788	−	1.40515i	−0.0366776	−	0.0611512i
$529$	−29.7171	+	3.47343i	−1.29205	+	0.151019i
$530$	0.615007	+	0.223844i	0.0267142	+	0.00972317i
$531$	−0.985887	+	39.6624i	−0.0427838	+	1.72120i
$532$	25.9919	−	9.46028i	1.12689	−	0.410155i
$533$	−42.5411	+	21.3649i	−1.84266	+	0.925419i
$534$	12.2043	+	1.22072i	0.528130	+	0.0528257i
$535$	−0.876618	−	0.102462i	−0.0378995	−	0.00442982i
$536$	0.262259	+	0.131712i	0.0113279	+	0.00568907i
$537$	−17.5584	+	9.18765i	−0.757701	+	0.396476i
$538$	−7.00871	−	1.66110i	−0.302167	−	0.0716149i
$539$	−7.54457	−	13.0676i	−0.324968	−	0.562861i
$540$	3.32406	+	9.37084i	0.143045	+	0.403257i
$541$	−1.82058	+	3.15334i	−0.0782728	+	0.135573i	−0.902505	−	0.430680i	$-0.858274\pi$
$541$	−1.82058	+	3.15334i	−0.0782728	+	0.135573i	0.824232	+	0.566252i	$0.191607\pi$
$542$	12.7373	−	13.5008i	0.547116	−	0.579909i
$543$	26.7115	−	3.57422i	1.14630	−	0.153384i
$544$	−0.0633795	−	1.08818i	−0.00271737	−	0.0466555i
$545$	−2.63854	+	3.54418i	−0.113023	+	0.151816i
$546$	11.5217	−	40.9569i	0.493083	−	1.75280i
$547$	−31.8844	−	20.9707i	−1.36328	−	0.896642i	−0.363883	−	0.931445i	$-0.618549\pi$
$547$	−31.8844	−	20.9707i	−1.36328	−	0.896642i	−0.999394	+	0.0348031i	$0.988920\pi$
$548$	0.152415	−	0.864387i	0.00651084	−	0.0369248i
$549$	−3.12419	+	0.104155i	−0.133337	+	0.00444522i
$550$	0.219867	+	1.24693i	0.00937516	+	0.0531692i
$551$	−9.61143	+	22.2818i	−0.409461	+	0.949236i
$552$	−11.9102	−	4.11155i	−0.506933	−	0.174999i
$553$	10.4968	−	2.48780i	0.446371	−	0.105792i
$554$	−2.39391	−	2.53740i	−0.101708	−	0.107804i
$555$	0.827318	−	0.316828i	0.0351177	−	0.0134486i
$556$	−3.71834	−	4.99460i	−0.157693	−	0.211818i
$557$	−12.4902	+	10.4806i	−0.529229	+	0.444075i	−0.867835	−	0.496853i	$-0.834489\pi$
$557$	−12.4902	+	10.4806i	−0.529229	+	0.444075i	0.338606	+	0.940928i	$0.390045\pi$
$558$	−3.94409	−	8.36542i	−0.166967	−	0.354136i
$559$	12.9570	+	10.8722i	0.548021	+	0.459844i
$560$	−0.533016	+	9.15153i	−0.0225240	+	0.386723i
$561$	−1.60919	−	0.774863i	−0.0679399	−	0.0327147i
$562$	6.28677	+	14.5744i	0.265191	+	0.614783i
$563$	36.6052	−	24.0756i	1.54272	−	1.01466i	0.560236	−	0.828333i	$-0.310710\pi$
$563$	36.6052	−	24.0756i	1.54272	−	1.01466i	0.982487	−	0.186332i	$-0.0596601\pi$
$564$	13.9705	+	3.06615i	0.588265	+	0.129108i
$565$	−2.79211	−	9.32631i	−0.117465	−	0.392361i
$566$	−3.46083			−0.145470
$567$	−39.7331	−	16.7413i	−1.66863	−	0.703068i
$568$	2.21334			0.0928696
$569$	0.573948	+	1.91712i	0.0240611	+	0.0803698i	0.969177	−	0.246366i	$-0.0792365\pi$
$569$	0.573948	+	1.91712i	0.0240611	+	0.0803698i	−0.945116	+	0.326736i	$0.894051\pi$
$570$	−12.8981	+	14.1358i	−0.540243	+	0.592086i
$571$	−29.2742	+	19.2540i	−1.22509	+	0.805753i	−0.986243	−	0.165304i	$-0.947139\pi$
$571$	−29.2742	+	19.2540i	−1.22509	+	0.805753i	−0.238846	+	0.971057i	$0.576769\pi$
$572$	−1.92124	−	4.45393i	−0.0803311	−	0.186228i
$573$	2.43144	+	32.4275i	0.101575	+	1.35468i
$574$	−2.58612	+	44.4019i	−0.107942	+	1.85330i
$575$	7.45867	+	6.25857i	0.311048	+	0.261000i
$576$	−2.13029	−	2.11231i	−0.0887621	−	0.0880131i
$577$	−3.71605	+	3.11814i	−0.154701	+	0.129810i	−0.716853	−	0.697224i	$-0.754418\pi$
$577$	−3.71605	+	3.11814i	−0.154701	+	0.129810i	0.562152	+	0.827034i	$0.309974\pi$
$578$	9.44218	+	12.6830i	0.392743	+	0.527545i
$579$	−3.72793	+	23.4174i	−0.154928	+	0.973195i
$580$	−5.51898	−	5.84978i	−0.229163	−	0.242899i
$581$	−42.9799	+	10.1864i	−1.78311	+	0.422604i
$582$	3.74860	+	19.3666i	0.155385	+	0.802772i
$583$	−0.128155	+	0.297096i	−0.00530762	+	0.0123044i
$584$	−2.46261	−	13.9662i	−0.101904	−	0.577924i
$585$	6.07435	+	28.8013i	0.251143	+	1.19079i
$586$	−0.595620	+	3.37793i	−0.0246048	+	0.139541i
$587$	−24.7238	−	16.2611i	−1.02046	−	0.671166i	−0.0750924	−	0.997177i	$-0.523925\pi$
$587$	−24.7238	−	16.2611i	−1.02046	−	0.671166i	−0.945366	+	0.326010i	$0.894296\pi$
$588$	−19.2911	−	19.7765i	−0.795550	−	0.815571i
$589$	10.6292	−	14.2775i	0.437967	−	0.588292i
$590$	−1.47142	−	25.2633i	−0.0605773	−	1.04007i
$591$	4.01948	+	5.21538i	0.165339	+	0.214532i
$592$	−0.183431	+	0.194426i	−0.00753897	+	0.00799084i
$593$	10.4263	−	18.0589i	0.428157	−	0.741589i	−0.568553	−	0.822647i	$-0.692496\pi$
$593$	10.4263	−	18.0589i	0.428157	−	0.741589i	0.996709	+	0.0810575i	$0.0258298\pi$
$594$	−4.72043	+	1.37119i	−0.193682	+	0.0562604i
$595$	4.99616	+	8.65361i	0.204823	+	0.354763i
$596$	−6.79056	−	1.60939i	−0.278152	−	0.0659233i
$597$	−0.236933	+	5.70393i	−0.00969703	+	0.233446i
$598$	−33.3331	−	16.7405i	−1.36309	−	0.684570i
$599$	−4.24556	−	0.496235i	−0.173469	−	0.0202756i	0.0289150	−	0.999582i	$-0.490795\pi$
$599$	−4.24556	−	0.496235i	−0.173469	−	0.0202756i	−0.202384	+	0.979306i	$0.564869\pi$
$600$	0.953553	+	2.11306i	0.0389286	+	0.0862653i
$601$	8.12865	−	4.08236i	0.331575	−	0.166523i	−0.275221	−	0.961381i	$-0.588751\pi$
$601$	8.12865	−	4.08236i	0.331575	−	0.166523i	0.606796	+	0.794858i	$0.292455\pi$
$602$	14.8499	−	5.40490i	0.605235	−	0.220287i
$603$	0.582512	−	0.660175i	0.0237217	−	0.0268844i
$604$	−2.14609	−	0.781114i	−0.0873233	−	0.0317831i
$605$	−19.2055	+	2.24481i	−0.780816	+	0.0912643i
$606$	−13.8830	+	0.231353i	−0.563960	+	0.00939808i
$607$	−2.38453	+	7.96490i	−0.0967852	+	0.323285i	−0.992647	−	0.121049i	$-0.961374\pi$
$607$	−2.38453	+	7.96490i	−0.0967852	+	0.323285i	0.895861	+	0.444334i	$0.146560\pi$
$608$	1.65592	−	5.53117i	0.0671566	−	0.224319i
$609$	34.8695	−	0.581081i	1.41298	−	0.0235466i
$610$	1.98036	−	0.231471i	0.0801825	−	0.00937199i
$611$	39.7889	+	14.4820i	1.60969	+	0.585878i
$612$	−3.20530	−	0.647694i	−0.129567	−	0.0261815i
$613$	27.7883	−	10.1141i	1.12236	−	0.408505i	0.286846	−	0.957977i	$-0.407393\pi$
$613$	27.7883	−	10.1141i	1.12236	−	0.408505i	0.835512	+	0.549472i	$0.185171\pi$
$614$	19.1327	−	9.60879i	0.772132	−	0.387779i
$615$	−12.6566	−	28.0470i	−0.510365	−	1.13096i
$616$	−4.50132	−	0.526129i	−0.181363	−	0.0211983i
$617$	17.0393	+	8.55744i	0.685975	+	0.344509i	0.757413	−	0.652936i	$-0.226463\pi$
$617$	17.0393	+	8.55744i	0.685975	+	0.344509i	−0.0714387	+	0.997445i	$0.522759\pi$
$618$	−1.25815	+	30.2888i	−0.0506103	+	1.21839i
$619$	−1.51258	−	0.358487i	−0.0607955	−	0.0144088i	0.200106	−	0.979774i	$-0.435871\pi$
$619$	−1.51258	−	0.358487i	−0.0607955	−	0.0144088i	−0.260901	+	0.965366i	$0.584020\pi$
$620$	2.94955	+	5.10878i	0.118457	+	0.205173i
$621$	−21.0292	+	31.4101i	−0.843875	+	1.26044i
$622$	17.1202	−	29.6531i	0.686459	−	1.18898i
$623$	23.2802	−	24.6755i	0.932700	−	0.988604i
$624$	−5.42142	−	7.03443i	−0.217031	−	0.281602i
$625$	0.960341	+	16.4884i	0.0384136	+	0.659537i
$626$	−15.5585	+	20.8986i	−0.621841	+	0.835277i
$627$	−6.60583	−	6.77208i	−0.263812	−	0.270451i
$628$	0.563795	+	0.370814i	0.0224979	+	0.0147971i
$629$	−0.0505945	+	0.286936i	−0.00201734	+	0.0114409i
$630$	26.1417	+	8.53965i	1.04151	+	0.340228i
$631$	0.452253	+	2.56485i	0.0180039	+	0.102105i	0.992486	−	0.122362i	$-0.0390469\pi$
$631$	0.452253	+	2.56485i	0.0180039	+	0.102105i	−0.974482	+	0.224467i	$0.927936\pi$
$632$	0.891891	−	2.06764i	0.0354775	−	0.0822462i
$633$	1.02315	+	5.28593i	0.0406664	+	0.210097i
$634$	−32.6964	+	7.74919i	−1.29854	+	0.307759i
$635$	22.8811	+	24.2525i	0.908008	+	0.962432i
$636$	−0.0931357	+	0.585043i	−0.00369307	+	0.0231984i
$637$	−48.8397	−	65.6031i	−1.93510	−	2.59929i
$638$	3.04574	−	2.55568i	0.120582	−	0.101180i
$639$	1.69137	−	6.42098i	0.0669096	−	0.254010i
$640$	1.46584	+	1.22999i	0.0579425	+	0.0486195i
$641$	1.35300	−	23.2302i	0.0534404	−	0.917537i	−0.859931	−	0.510410i	$-0.829494\pi$
$641$	1.35300	−	23.2302i	0.0534404	−	0.917537i	0.913372	−	0.407127i	$-0.133469\pi$
$642$	−0.0597332	−	0.796649i	−0.00235748	−	0.0314412i
$643$	12.8599	+	29.8127i	0.507146	+	1.17570i	0.958949	+	0.283579i	$0.0915219\pi$
$643$	12.8599	+	29.8127i	0.507146	+	1.17570i	−0.451803	+	0.892118i	$0.649219\pi$
$644$	−29.1168	+	19.1504i	−1.14736	+	0.754633i
$645$	−7.36904	+	8.07618i	−0.290156	+	0.317999i
$646$	−1.80500	−	6.02913i	−0.0710169	−	0.237213i
$647$	−0.309516			−0.0121683			−0.00608417	−	0.999981i	$-0.501937\pi$
$647$	−0.309516			−0.0121683			−0.00608417	+	0.999981i	$0.501937\pi$
$648$	−7.75582	+	4.56589i	−0.304677	+	0.179365i
$649$	12.5107			0.491088
$650$	1.96831	+	6.57460i	0.0772033	+	0.257877i
$651$	−24.9859	−	5.48373i	−0.979274	−	0.214924i
$652$	1.70700	−	1.12271i	0.0668515	−	0.0439689i
$653$	4.90331	+	11.3671i	0.191881	+	0.444831i	0.986812	−	0.161869i	$-0.0517523\pi$
$653$	4.90331	+	11.3671i	0.191881	+	0.444831i	−0.794931	+	0.606700i	$0.792493\pi$
$654$	−3.60347	−	1.73516i	−0.140907	−	0.0678500i
$655$	−1.56648	+	26.8954i	−0.0612074	+	1.05089i
$656$	7.11205	+	5.96772i	0.277679	+	0.233000i
$657$	−42.3983	−	3.52842i	−1.65411	−	0.137657i
$658$	30.3052	−	25.4291i	1.18142	−	0.991330i
$659$	−21.3400	−	28.6645i	−0.831287	−	1.11661i	−0.991574	−	0.129542i	$-0.958649\pi$
$659$	−21.3400	−	28.6645i	−0.831287	−	1.11661i	0.160287	−	0.987070i	$-0.448758\pi$
$660$	2.92797	−	1.12129i	0.113971	−	0.0436461i
$661$	−18.4925	−	19.6009i	−0.719276	−	0.762388i	0.259849	−	0.965649i	$-0.416327\pi$
$661$	−18.4925	−	19.6009i	−0.719276	−	0.762388i	−0.979124	+	0.203262i	$0.934846\pi$
$662$	−8.20710	+	1.94512i	−0.318978	+	0.0755991i
$663$	−9.15080	−	3.15896i	−0.355388	−	0.122684i
$664$	−3.65190	+	8.46606i	−0.141721	+	0.328547i
$665$	9.19085	+	52.1239i	0.356406	+	2.02128i
$666$	0.423864	+	0.680716i	0.0164244	+	0.0263772i
$667$	5.30917	−	30.1098i	0.205572	−	1.16586i
$668$	−13.9667	−	9.18606i	−0.540389	−	0.355419i
$669$	−0.0701112	+	0.249229i	−0.00271065	+	0.00963575i
$670$	−0.335347	+	0.450449i	−0.0129556	+	0.0174024i
$671$	0.0573138	+	0.984040i	0.00221257	+	0.0379884i
$672$	−8.22438	+	1.10049i	−0.317262	+	0.0424523i
$673$	−8.89653	+	9.42977i	−0.342936	+	0.363491i	−0.875770	−	0.482729i	$-0.839646\pi$
$673$	−8.89653	+	9.42977i	−0.342936	+	0.363491i	0.532834	+	0.846220i	$0.321127\pi$
$674$	−14.5884	+	25.2679i	−0.561925	+	0.973282i
$675$	6.85875	−	1.15155i	0.263994	−	0.0443233i
$676$	−6.64582	−	11.5109i	−0.255609	−	0.442727i
$677$	27.8084	+	6.59070i	1.06876	+	0.253301i	0.727107	−	0.686524i	$-0.240864\pi$
$677$	27.8084	+	6.59070i	1.06876	+	0.253301i	0.341655	+	0.939825i	$0.389013\pi$
$678$	7.80774	−	4.08550i	0.299855	−	0.156903i
$679$	48.7568	+	24.4866i	1.87111	+	0.939709i
$680$	2.07169	+	0.242145i	0.0794456	+	0.00928585i
$681$	−38.3081	−	3.83173i	−1.46797	−	0.146832i
$682$	−2.60617	+	1.30887i	−0.0997953	+	0.0501191i
$683$	0.280624	−	0.102139i	0.0107378	−	0.00390823i	−0.336646	−	0.941631i	$-0.609292\pi$
$683$	0.280624	−	0.102139i	0.0107378	−	0.00390823i	0.347383	+	0.937723i	$0.387070\pi$
$684$	−14.7807	−	9.03067i	−0.565156	−	0.345296i
$685$	1.57825	+	0.574436i	0.0603018	+	0.0219481i
$686$	−42.5890	+	4.97794i	−1.62606	+	0.190059i
$687$	−6.65042	−	11.0880i	−0.253729	−	0.423034i
$688$	0.946072	−	3.16010i	0.0360687	−	0.120478i
$689$	−0.502984	+	1.68008i	−0.0191622	+	0.0640061i
$690$	11.7055	−	21.0780i	0.445622	−	0.802427i
$691$	40.1830	−	4.69672i	1.52863	−	0.178672i	0.690177	−	0.723641i	$-0.257533\pi$
$691$	40.1830	−	4.69672i	1.52863	−	0.178672i	0.838456	+	0.544969i	$0.183459\pi$
$692$	−6.73605	−	2.45172i	−0.256066	−	0.0932005i
$693$	−4.96610	+	12.6565i	−0.188647	+	0.480779i
$694$	−2.21098	+	0.804731i	−0.0839277	+	0.0305472i
$695$	10.6476	−	5.34742i	0.403886	−	0.202839i
$696$	4.24920	−	5.91079i	0.161066	−	0.224048i
$697$	10.0515	+	1.17486i	0.380729	+	0.0445008i
$698$	27.3049	+	13.7130i	1.03351	+	0.519047i
$699$	−12.7279	−	8.07074i	−0.481415	−	0.305263i
$700$	6.23920	+	1.47872i	0.235820	+	0.0558903i
$701$	−13.0877	−	22.6685i	−0.494315	−	0.856179i	0.505663	−	0.862731i	$-0.331248\pi$
$701$	−13.0877	−	22.6685i	−0.494315	−	0.856179i	−0.999979	+	0.00655186i	$0.997914\pi$
$702$	−24.5501	+	10.3523i	−0.926582	+	0.390721i
$703$	−0.771653	+	1.33654i	−0.0291034	+	0.0504086i
$704$	−0.649183	+	0.688094i	−0.0244670	+	0.0259335i
$705$	−10.4201	+	25.3079i	−0.392444	+	0.953151i
$706$	−0.684077	−	11.7451i	−0.0257456	−	0.442034i
$707$	−22.9335	+	30.8050i	−0.862502	+	1.15854i
$708$	22.1976	−	5.65317i	0.834238	−	0.212459i
$709$	−5.65372	−	3.71851i	−0.212330	−	0.139652i	0.438890	−	0.898541i	$-0.355372\pi$
$709$	−5.65372	−	3.71851i	−0.212330	−	0.139652i	−0.651219	+	0.758889i	$0.725742\pi$
$710$	−0.735446	+	4.17092i	−0.0276008	+	0.156532i
$711$	−5.31674	−	4.16745i	−0.199393	−	0.156291i
$712$	−1.22965	−	6.97371i	−0.0460832	−	0.261351i
$713$	−8.88267	+	20.5924i	−0.332659	+	0.771190i
$714$	−6.83081	+	5.92846i	−0.255637	+	0.221867i
$715$	9.03160	−	2.14053i	0.337763	−	0.0800512i
$716$	7.85150	+	8.32210i	0.293424	+	0.311012i
$717$	30.5830	+	24.8057i	1.14214	+	0.926384i
$718$	−6.99965	−	9.40216i	−0.261224	−	0.350885i
$719$	−37.0066	+	31.0522i	−1.38011	+	1.15805i	−0.410943	+	0.911661i	$0.634801\pi$
$719$	−37.0066	+	31.0522i	−1.38011	+	1.15805i	−0.969170	+	0.246392i	$0.920755\pi$
$720$	4.68840	−	3.31254i	0.174726	−	0.123451i
$721$	64.2311	+	53.8963i	2.39209	+	2.00720i
$722$	0.833560	−	14.3117i	0.0310219	−	0.532625i
$723$	21.4437	−	14.6213i	0.797499	−	0.543773i
$724$	−6.16274	−	14.2868i	−0.229036	−	0.530966i
$725$	−4.69990	+	3.09117i	−0.174550	+	0.114803i
$726$	−5.29846	−	16.6813i	−0.196644	−	0.619100i
$727$	−1.66021	−	5.54547i	−0.0615736	−	0.205670i	0.921667	−	0.387981i	$-0.126827\pi$
$727$	−1.66021	−	5.54547i	−0.0615736	−	0.205670i	−0.983241	+	0.182311i	$0.941642\pi$
$728$	−24.5643			−0.910415
$729$	7.31904	+	25.9891i	0.271076	+	0.962558i
$730$	27.1368			1.00438
$731$	−1.03125	−	3.44460i	−0.0381420	−	0.127403i
$732$	0.546346	+	1.72007i	0.0201935	+	0.0635757i
$733$	31.1186	−	20.4671i	1.14939	−	0.755968i	0.175838	−	0.984419i	$-0.443737\pi$
$733$	31.1186	−	20.4671i	1.14939	−	0.755968i	0.973555	+	0.228451i	$0.0733661\pi$
$734$	13.1381	+	30.4575i	0.484936	+	1.12421i
$735$	43.6779	−	29.7817i	1.61108	−	1.09851i
$736$	−0.422979	+	7.26227i	−0.0155912	+	0.267691i
$737$	−0.212675	−	0.178455i	−0.00783397	−	0.00657348i
$738$	22.7474	−	16.0720i	0.837345	−	0.591618i
$739$	−18.3154	+	15.3685i	−0.673744	+	0.565339i	−0.914171	−	0.405329i	$-0.867157\pi$
$739$	−18.3154	+	15.3685i	−0.673744	+	0.565339i	0.240427	+	0.970667i	$0.422713\pi$
$740$	−0.305435	−	0.410270i	−0.0112280	−	0.0150818i
$741$	−39.8245	−	32.3014i	−1.46299	−	1.18662i
$742$	1.12444	+	1.19183i	0.0412793	+	0.0437535i
$743$	30.3305	−	7.18847i	1.11272	−	0.263719i	0.367159	−	0.930158i	$-0.380330\pi$
$743$	30.3305	−	7.18847i	1.11272	−	0.263719i	0.745560	+	0.666439i	$0.232182\pi$
$744$	−4.03266	+	3.49995i	−0.147845	+	0.128314i
$745$	5.28918	−	12.2617i	0.193780	−	0.449234i
$746$	0.503195	+	2.85376i	0.0184233	+	0.104484i
$747$	21.7697	+	17.0638i	0.796511	+	0.624333i
$748$	−0.179060	+	1.01550i	−0.00654707	+	0.0371303i
$749$	−1.84612	−	1.21421i	−0.0674558	−	0.0443664i
$750$	−20.3578	+	5.18461i	−0.743360	+	0.189315i
$751$	−16.0006	+	21.4926i	−0.583871	+	0.784274i	−0.991671	−	0.128797i	$-0.958889\pi$
$751$	−16.0006	+	21.4926i	−0.583871	+	0.784274i	0.407800	+	0.913071i	$0.366296\pi$
$752$	−0.480152	−	8.24389i	−0.0175093	−	0.300624i
$753$	17.9939	−	43.7028i	0.655735	−	1.59262i
$754$	14.7889	−	15.6753i	0.538579	−	0.570860i
$755$	2.18507	−	3.78465i	0.0795229	−	0.137738i
$756$	−3.09228	+	24.7002i	−0.112465	+	0.898339i
$757$	12.3413	+	21.3757i	0.448552	+	0.776914i	0.998292	−	0.0584212i	$-0.0186066\pi$
$757$	12.3413	+	21.3757i	0.448552	+	0.776914i	−0.549740	+	0.835336i	$0.685273\pi$
$758$	−8.98353	−	2.12914i	−0.326297	−	0.0773337i
$759$	10.0664	+	6.38303i	0.365385	+	0.231689i
$760$	9.87298	+	4.95840i	0.358131	+	0.179860i
$761$	22.4590	+	2.62508i	0.814139	+	0.0951592i	0.512965	−	0.858410i	$-0.328547\pi$
$761$	22.4590	+	2.62508i	0.814139	+	0.0951592i	0.301175	+	0.953569i	$0.402621\pi$
$762$	−17.6167	+	24.5055i	−0.638186	+	0.887739i
$763$	−9.88546	+	4.96466i	−0.357878	+	0.179733i
$764$	17.6423	−	6.42129i	0.638278	−	0.232314i
$765$	2.28560	−	5.82501i	0.0826360	−	0.210604i
$766$	−9.26030	−	3.37047i	−0.334588	−	0.121780i
$767$	67.3526	−

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.286803 + 0.957990i) q^{2} +(-0.524336 - 1.65078i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(-0.757906 - 1.75702i) q^{5} +(1.43105 - 0.975757i) q^{6} +(0.278553 - 4.78256i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.45014 + 1.73113i) q^{9} +O(q^{10})\)	\(q+(0.286803 + 0.957990i) q^{2} +(-0.524336 - 1.65078i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(-0.757906 - 1.75702i) q^{5} +(1.43105 - 0.975757i) q^{6} +(0.278553 - 4.78256i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.45014 + 1.73113i) q^{9} +(1.46584 - 1.22999i) q^{10} +(0.564911 + 0.758806i) q^{11} +(1.34519 + 1.09108i) q^{12} +(3.51873 + 3.72964i) q^{13} +(4.66154 - 1.10480i) q^{14} +(-2.50306 + 2.17241i) q^{15} +(0.396080 - 0.918216i) q^{16} +(-0.189281 - 1.07347i) q^{17} +(-2.36111 - 1.85072i) q^{18} +(1.00260 - 5.68601i) q^{19} +(1.59872 + 1.05150i) q^{20} +(-8.04101 + 2.04784i) q^{21} +(-0.564911 + 0.758806i) q^{22} +(0.422979 + 7.26227i) q^{23} +(-0.659436 + 1.60161i) q^{24} +(0.918495 - 0.973548i) q^{25} +(-2.56377 + 4.44058i) q^{26} +(4.14241 + 3.13695i) q^{27} +(2.39533 + 4.14884i) q^{28} +(-4.08961 - 0.969255i) q^{29} +(-2.79903 - 1.77485i) q^{30} +(2.75494 + 1.38358i) q^{31} +(0.993238 + 0.116093i) q^{32} +(0.956419 - 1.33041i) q^{33} +(0.974085 - 0.489204i) q^{34} +(-8.61420 + 3.13531i) q^{35} +(1.09580 - 2.79271i) q^{36} +(-0.251178 - 0.0914213i) q^{37} +(5.73469 - 0.670289i) q^{38} +(4.31181 - 7.76423i) q^{39} +(-0.548804 + 1.83313i) q^{40} +(-2.66272 + 8.89409i) q^{41} +(-4.26800 - 7.11588i) q^{42} +(3.27638 - 0.382953i) q^{43} +(-0.888947 - 0.323550i) q^{44} +(4.89861 + 2.99293i) q^{45} +(-6.83586 + 2.48805i) q^{46} +(7.37949 - 3.70612i) q^{47} +(-1.72345 - 0.172386i) q^{48} +(-15.8427 - 1.85174i) q^{49} +(1.19608 + 0.600692i) q^{50} +(-1.67281 + 0.875320i) q^{51} +(-4.98932 - 1.18249i) q^{52} +(0.171014 + 0.296205i) q^{53} +(-1.81711 + 4.86807i) q^{54} +(0.905092 - 1.56767i) q^{55} +(-3.28756 + 3.48461i) q^{56} +(-9.91205 + 1.32631i) q^{57} +(-0.244377 - 4.19579i) q^{58} +(7.89735 - 10.6080i) q^{59} +(0.897520 - 3.19047i) q^{60} +(0.870559 + 0.572576i) q^{61} +(-0.535333 + 3.03602i) q^{62} +(7.59673 + 12.2002i) q^{63} +(0.173648 + 0.984808i) q^{64} +(3.88619 - 9.00921i) q^{65} +(1.54882 + 0.534673i) q^{66} +(-0.285565 + 0.0676801i) q^{67} +(0.748023 + 0.792858i) q^{68} +(11.7666 - 4.50611i) q^{69} +(-5.47418 - 7.35309i) q^{70} +(-1.69551 + 1.42271i) q^{71} +(2.98967 + 0.248802i) q^{72} +(10.8638 + 9.11577i) q^{73} +(0.0155420 - 0.266846i) q^{74} +(-2.08871 - 1.00577i) q^{75} +(2.28686 + 5.30153i) q^{76} +(3.78640 - 2.49035i) q^{77} +(8.67469 + 1.90386i) q^{78} +(0.645823 + 2.15720i) q^{79} -1.91352 q^{80} +(3.00641 - 8.48301i) q^{81} -9.28412 q^{82} +(-2.64436 - 8.83277i) q^{83} +(5.59286 - 6.12956i) q^{84} +(-1.74265 + 1.14616i) q^{85} +(1.30654 + 3.02890i) q^{86} +(0.544303 + 7.25926i) q^{87} +(0.0550049 - 0.944397i) q^{88} +(5.42459 + 4.55177i) q^{89} +(-1.46226 + 5.55120i) q^{90} +(18.8174 - 15.7897i) q^{91} +(-4.34407 - 5.83511i) q^{92} +(0.839476 - 5.27326i) q^{93} +(5.66689 + 6.00655i) q^{94} +(-10.7503 + 2.54788i) q^{95} +(-0.329147 - 1.70049i) q^{96} +(-4.51089 + 10.4574i) q^{97} +(-2.76978 - 15.7082i) q^{98} +(-2.69770 - 0.881253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more