LMFDB - Embedded newform 729.2.g.b.541.1

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			541.1
Character	$\chi$	$=$	729.541
Dual form			729.2.g.b.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35812 - 1.82427i) q^{2} +(-0.909876 + 3.03920i) q^{4} +(-0.490328 + 0.322494i) q^{5} +(-2.61431 + 2.77101i) q^{7} +(2.50575 - 0.912019i) q^{8} +O(q^{10})$	\(q+(-1.35812 - 1.82427i) q^{2} +(-0.909876 + 3.03920i) q^{4} +(-0.490328 + 0.322494i) q^{5} +(-2.61431 + 2.77101i) q^{7} +(2.50575 - 0.912019i) q^{8} +(1.25424 + 0.456507i) q^{10} +(4.45885 - 2.23932i) q^{11} +(-0.984610 - 2.28258i) q^{13} +(8.60563 + 1.00585i) q^{14} +(0.234238 + 0.154061i) q^{16} +(2.18854 - 1.83640i) q^{17} +(0.319901 + 0.268429i) q^{19} +(-0.533984 - 1.78363i) q^{20} +(-10.1408 - 5.09290i) q^{22} +(-5.04828 - 5.35087i) q^{23} +(-1.84398 + 4.27482i) q^{25} +(-2.82684 + 4.89622i) q^{26} +(-6.04293 - 10.4667i) q^{28} +(-5.24696 + 0.613281i) q^{29} +(2.85906 - 0.677609i) q^{31} +(-0.347168 - 5.96065i) q^{32} +(-6.32240 - 1.49844i) q^{34} +(0.388237 - 2.20180i) q^{35} +(-1.09265 - 6.19675i) q^{37} +(0.0552232 - 0.948146i) q^{38} +(-0.934519 + 1.25528i) q^{40} +(2.17987 - 2.92807i) q^{41} +(0.349862 - 6.00689i) q^{43} +(2.74873 + 15.5888i) q^{44} +(-2.90527 + 16.4766i) q^{46} +(-6.40659 - 1.51839i) q^{47} +(-0.436847 - 7.50038i) q^{49} +(10.3028 - 2.44181i) q^{50} +(7.83309 - 0.915557i) q^{52} +(-1.23882 - 2.14569i) q^{53} +(-1.46413 + 2.53595i) q^{55} +(-4.02360 + 9.32775i) q^{56} +(8.24480 + 8.73898i) q^{58} +(-4.14106 - 2.07972i) q^{59} +(-3.26814 - 10.9163i) q^{61} +(-5.11909 - 4.29543i) q^{62} +(-9.97283 + 8.36820i) q^{64} +(1.21890 + 0.801684i) q^{65} +(-5.90700 - 0.690429i) q^{67} +(3.58989 + 8.32230i) q^{68} +(-4.54396 + 2.28206i) q^{70} +(-2.65492 - 0.966311i) q^{71} +(12.9084 - 4.69828i) q^{73} +(-9.82061 + 10.4092i) q^{74} +(-1.10688 + 0.728005i) q^{76} +(-5.45165 + 18.2098i) q^{77} +(7.50465 + 10.0805i) q^{79} -0.164537 q^{80} -8.30214 q^{82} +(-1.25294 - 1.68299i) q^{83} +(-0.480874 + 1.60623i) q^{85} +(-11.4334 + 7.51985i) q^{86} +(9.13046 - 9.67772i) q^{88} +(0.324629 - 0.118155i) q^{89} +(8.89913 + 3.23902i) q^{91} +(20.8556 - 10.4741i) q^{92} +(5.93097 + 13.7495i) q^{94} +(-0.243423 - 0.0284521i) q^{95} +(-9.16575 - 6.02841i) q^{97} +(-13.0895 + 10.9834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	−1.35812	−	1.82427i	−0.960337	−	1.28996i	−0.957038	−	0.289962i	$-0.906357\pi$
$2$	−1.35812	−	1.82427i	−0.960337	−	1.28996i	−0.00329926	−	0.999995i	$-0.501050\pi$
$3$		0			0
$3$		0			0
$4$	−0.909876	+	3.03920i	−0.454938	+	1.51960i
$5$	−0.490328	+	0.322494i	−0.219281	+	0.144224i	−0.654398	−	0.756151i	$-0.727078\pi$
$5$	−0.490328	+	0.322494i	−0.219281	+	0.144224i	0.435116	+	0.900374i	$0.356707\pi$
$6$		0			0
$7$	−2.61431	+	2.77101i	−0.988116	+	1.04734i	0.0107598	+	0.999942i	$0.496575\pi$
$7$	−2.61431	+	2.77101i	−0.988116	+	1.04734i	−0.998876	+	0.0473999i	$0.984907\pi$
$8$	2.50575	−	0.912019i	0.885917	−	0.322447i
$9$		0			0
$10$	1.25424	+	0.456507i	0.396626	+	0.144360i
$11$	4.45885	−	2.23932i	1.34439	−	0.675180i	0.376471	−	0.926429i	$-0.377138\pi$
$11$	4.45885	−	2.23932i	1.34439	−	0.675180i	0.967923	+	0.251249i	$0.0808413\pi$
$12$		0			0
$13$	−0.984610	−	2.28258i	−0.273082	−	0.633075i	0.725390	−	0.688338i	$-0.241659\pi$
$13$	−0.984610	−	2.28258i	−0.273082	−	0.633075i	−0.998472	+	0.0552635i	$0.982400\pi$
$14$	8.60563	+	1.00585i	2.29995	+	0.268826i
$15$		0			0
$16$	0.234238	+	0.154061i	0.0585595	+	0.0385152i
$17$	2.18854	−	1.83640i	0.530799	−	0.445393i	−0.337578	−	0.941297i	$-0.609608\pi$
$17$	2.18854	−	1.83640i	0.530799	−	0.445393i	0.868377	+	0.495904i	$0.165163\pi$
$18$		0			0
$19$	0.319901	+	0.268429i	0.0733903	+	0.0615818i	0.678745	−	0.734374i	$-0.262524\pi$
$19$	0.319901	+	0.268429i	0.0733903	+	0.0615818i	−0.605355	+	0.795956i	$0.706969\pi$
$20$	−0.533984	−	1.78363i	−0.119403	−	0.398832i
$21$		0			0
$22$	−10.1408	−	5.09290i	−2.16202	−	1.08581i
$23$	−5.04828	−	5.35087i	−1.05264	−	1.11573i	−0.993072	−	0.117509i	$-0.962509\pi$
$23$	−5.04828	−	5.35087i	−1.05264	−	1.11573i	−0.0595677	−	0.998224i	$-0.518972\pi$
$24$		0			0
$25$	−1.84398	+	4.27482i	−0.368796	+	0.854965i
$26$	−2.82684	+	4.89622i	−0.554388	+	0.960229i
$27$		0			0
$28$	−6.04293	−	10.4667i	−1.14201	−	1.97801i
$29$	−5.24696	+	0.613281i	−0.974335	+	0.113883i	−0.588337	−	0.808616i	$-0.700217\pi$
$29$	−5.24696	+	0.613281i	−0.974335	+	0.113883i	−0.385998	+	0.922499i	$0.626143\pi$
$30$		0			0
$31$	2.85906	−	0.677609i	0.513502	−	0.121702i	0.0343079	−	0.999411i	$-0.489077\pi$
$31$	2.85906	−	0.677609i	0.513502	−	0.121702i	0.479194	+	0.877709i	$0.340929\pi$
$32$	−0.347168	−	5.96065i	−0.0613713	−	1.05370i
$33$		0			0
$34$	−6.32240	−	1.49844i	−1.08428	−	0.256980i
$35$	0.388237	−	2.20180i	0.0656240	−	0.372172i
$36$		0			0
$37$	−1.09265	−	6.19675i	−0.179631	−	1.01874i	−0.932661	−	0.360753i	$-0.882520\pi$
$37$	−1.09265	−	6.19675i	−0.179631	−	1.01874i	0.753030	−	0.657986i	$-0.228591\pi$
$38$	0.0552232	−	0.948146i	0.00895839	−	0.153810i
$39$		0			0
$40$	−0.934519	+	1.25528i	−0.147760	+	0.198477i
$41$	2.17987	−	2.92807i	0.340439	−	0.457288i	−0.598626	−	0.801028i	$-0.704287\pi$
$41$	2.17987	−	2.92807i	0.340439	−	0.457288i	0.939065	+	0.343740i	$0.111694\pi$
$42$		0			0
$43$	0.349862	−	6.00689i	0.0533534	−	0.916042i	−0.860361	−	0.509685i	$-0.829762\pi$
$43$	0.349862	−	6.00689i	0.0533534	−	0.916042i	0.913714	−	0.406357i	$-0.133201\pi$
$44$	2.74873	+	15.5888i	0.414386	+	2.35010i
$45$		0			0
$46$	−2.90527	+	16.4766i	−0.428358	+	2.42934i
$47$	−6.40659	−	1.51839i	−0.934497	−	0.221480i	−0.264961	−	0.964259i	$-0.585359\pi$
$47$	−6.40659	−	1.51839i	−0.934497	−	0.221480i	−0.669536	+	0.742779i	$0.733507\pi$
$48$		0			0
$49$	−0.436847	−	7.50038i	−0.0624068	−	1.07148i
$50$	10.3028	−	2.44181i	1.45704	−	0.345324i
$51$		0			0
$52$	7.83309	−	0.915557i	1.08625	−	0.126965i
$53$	−1.23882	−	2.14569i	−0.170165	−	0.294734i	0.768313	−	0.640075i	$-0.221097\pi$
$53$	−1.23882	−	2.14569i	−0.170165	−	0.294734i	−0.938477	+	0.345341i	$0.887763\pi$
$54$		0			0
$55$	−1.46413	+	2.53595i	−0.197424	+	0.341948i
$56$	−4.02360	+	9.32775i	−0.537676	+	1.24647i
$57$		0			0
$58$	8.24480	+	8.73898i	1.08260	+	1.14748i
$59$	−4.14106	−	2.07972i	−0.539120	−	0.270756i	0.158334	−	0.987386i	$-0.449388\pi$
$59$	−4.14106	−	2.07972i	−0.539120	−	0.270756i	−0.697454	+	0.716629i	$0.745684\pi$
$60$		0			0
$61$	−3.26814	−	10.9163i	−0.418442	−	1.39769i	−0.864474	−	0.502677i	$-0.832349\pi$
$61$	−3.26814	−	10.9163i	−0.418442	−	1.39769i	0.446032	−	0.895017i	$-0.352837\pi$
$62$	−5.11909	−	4.29543i	−0.650125	−	0.545520i
$63$		0			0
$64$	−9.97283	+	8.36820i	−1.24660	+	1.04602i
$65$	1.21890	+	0.801684i	0.151186	+	0.0994366i
$66$		0			0
$67$	−5.90700	−	0.690429i	−0.721655	−	0.0843494i	−0.252666	−	0.967554i	$-0.581307\pi$
$67$	−5.90700	−	0.690429i	−0.721655	−	0.0843494i	−0.468989	+	0.883204i	$0.655382\pi$
$68$	3.58989	+	8.32230i	0.435338	+	1.00923i
$69$		0			0
$70$	−4.54396	+	2.28206i	−0.543107	+	0.272759i
$71$	−2.65492	−	0.966311i	−0.315081	−	0.114680i	0.179639	−	0.983733i	$-0.442507\pi$
$71$	−2.65492	−	0.966311i	−0.315081	−	0.114680i	−0.494720	+	0.869053i	$0.664729\pi$
$72$		0			0
$73$	12.9084	−	4.69828i	1.51082	−	0.549892i	0.551981	−	0.833857i	$-0.313872\pi$
$73$	12.9084	−	4.69828i	1.51082	−	0.549892i	0.958835	+	0.283965i	$0.0916499\pi$
$74$	−9.82061	+	10.4092i	−1.14162	+	1.21005i
$75$		0			0
$76$	−1.10688	+	0.728005i	−0.126968	+	0.0835079i
$77$	−5.45165	+	18.2098i	−0.621273	+	2.07520i
$78$		0			0
$79$	7.50465	+	10.0805i	0.844339	+	1.13414i	0.989471	+	0.144732i	$0.0462319\pi$
$79$	7.50465	+	10.0805i	0.844339	+	1.13414i	−0.145132	+	0.989412i	$0.546361\pi$
$80$	−0.164537			−0.0183958
$81$		0			0
$82$	−8.30214			−0.916818
$83$	−1.25294	−	1.68299i	−0.137528	−	0.184733i	0.728023	−	0.685553i	$-0.240439\pi$
$83$	−1.25294	−	1.68299i	−0.137528	−	0.184733i	−0.865552	+	0.500820i	$0.833032\pi$
$84$		0			0
$85$	−0.480874	+	1.60623i	−0.0521581	+	0.174220i
$86$	−11.4334	+	7.51985i	−1.23289	+	0.810886i
$87$		0			0
$88$	9.13046	−	9.67772i	0.973310	−	1.03165i
$89$	0.324629	−	0.118155i	0.0344106	−	0.0125244i	−0.324758	−	0.945797i	$-0.605283\pi$
$89$	0.324629	−	0.118155i	0.0344106	−	0.0125244i	0.359168	+	0.933273i	$0.383060\pi$
$90$		0			0
$91$	8.89913	+	3.23902i	0.932882	+	0.339541i
$92$	20.8556	−	10.4741i	2.17435	−	1.09200i
$93$		0			0
$94$	5.93097	+	13.7495i	0.611733	+	1.41816i
$95$	−0.243423	−	0.0284521i	−0.0249747	−	0.00291912i
$96$		0			0
$97$	−9.16575	−	6.02841i	−0.930640	−	0.612092i	−0.00892563	−	0.999960i	$-0.502841\pi$
$97$	−9.16575	−	6.02841i	−0.930640	−	0.612092i	−0.921715	+	0.387868i	$0.873212\pi$
$98$	−13.0895	+	10.9834i	−1.32224	+	1.10949i
$99$		0			0
$100$	−11.3142	−	9.49377i	−1.13142	−	0.949377i
$101$	−0.508708	−	1.69920i	−0.0506184	−	0.169077i	0.928943	−	0.370223i	$-0.120719\pi$
$101$	−0.508708	−	1.69920i	−0.0506184	−	0.169077i	−0.979561	+	0.201146i	$0.935534\pi$
$102$		0			0
$103$	15.7258	+	7.89781i	1.54951	+	0.778194i	0.998417	−	0.0562479i	$-0.0179137\pi$
$103$	15.7258	+	7.89781i	1.54951	+	0.778194i	0.551095	+	0.834442i	$0.314210\pi$
$104$	−4.54894	−	4.82160i	−0.446061	−	0.472797i
$105$		0			0
$106$	−2.23187	+	5.17405i	−0.216778	+	0.502549i
$107$	2.26990	−	3.93158i	0.219439	−	0.380080i	−0.735197	−	0.677853i	$-0.762911\pi$
$107$	2.26990	−	3.93158i	0.219439	−	0.380080i	0.954637	+	0.297773i	$0.0962439\pi$
$108$		0			0
$109$	−1.95094	−	3.37913i	−0.186866	−	0.323662i	0.757337	−	0.653024i	$-0.226500\pi$
$109$	−1.95094	−	3.37913i	−0.186866	−	0.323662i	−0.944204	+	0.329362i	$0.893166\pi$
$110$	6.61474	−	0.773152i	0.630691	−	0.0737172i
$111$		0			0
$112$	−1.03927	+	0.246313i	−0.0982022	+	0.0232744i
$113$	−0.758067	−	13.0155i	−0.0713129	−	1.22440i	−0.824220	−	0.566269i	$-0.808386\pi$
$113$	−0.758067	−	13.0155i	−0.0713129	−	1.22440i	0.752908	−	0.658126i	$-0.228651\pi$
$114$		0			0
$115$	4.20094	+	0.995640i	0.391739	+	0.0928439i
$116$	2.91019	−	16.5045i	0.270205	−	1.53241i
$117$		0			0
$118$	1.83009	+	10.3789i	0.168473	+	0.955459i
$119$	−0.632836	+	10.8654i	−0.0580120	+	0.996028i
$120$		0			0
$121$	8.29804	−	11.1462i	0.754367	−	1.01329i
$122$	−15.4759	+	20.7877i	−1.40112	+	1.88203i
$123$		0			0
$124$	−0.541999	+	9.30577i	−0.0486730	+	0.835683i
$125$	−0.984000	−	5.58054i	−0.0880116	−	0.499139i
$126$		0			0
$127$	−1.42278	+	8.06900i	−0.126252	+	0.716008i	0.854305	+	0.519772i	$0.173983\pi$
$127$	−1.42278	+	8.06900i	−0.126252	+	0.716008i	−0.980557	+	0.196236i	$0.937128\pi$
$128$	17.1906	+	4.07425i	1.51945	+	0.360116i
$129$		0			0
$130$	−0.192925	−	3.31239i	−0.0169206	−	0.290516i
$131$	1.68890	−	0.400277i	0.147560	−	0.0349723i	−0.156172	−	0.987730i	$-0.549915\pi$
$131$	1.68890	−	0.400277i	0.147560	−	0.0349723i	0.303732	+	0.952758i	$0.401767\pi$
$132$		0			0
$133$	−1.58014	+	0.184692i	−0.137015	+	0.0160148i
$134$	6.76289	+	11.7137i	0.584225	+	1.01191i
$135$		0			0
$136$	3.80910	−	6.59755i	0.326628	−	0.565736i
$137$	1.08844	−	2.52328i	0.0929914	−	0.215578i	−0.865372	−	0.501130i	$-0.832918\pi$
$137$	1.08844	−	2.52328i	0.0929914	−	0.215578i	0.958363	+	0.285552i	$0.0921769\pi$
$138$		0			0
$139$	−5.93877	−	6.29473i	−0.503720	−	0.533912i	0.424755	−	0.905309i	$-0.360360\pi$
$139$	−5.93877	−	6.29473i	−0.503720	−	0.533912i	−0.928474	+	0.371397i	$0.878879\pi$
$140$	6.33846	+	3.18329i	0.535697	+	0.269037i
$141$		0			0
$142$	1.84289	+	6.15567i	0.154652	+	0.516572i
$143$	−9.50165	−	7.97283i	−0.794568	−	0.666722i
$144$		0			0
$145$	2.37495	−	1.99282i	0.197229	−	0.165495i
$146$	−26.1021	−	17.1677i	−2.16023	−	1.42081i
$147$		0			0
$148$	19.8273	+	2.31748i	1.62979	+	0.190496i
$149$	−2.27082	−	5.26435i	−0.186033	−	0.431272i	0.799520	−	0.600639i	$-0.205087\pi$
$149$	−2.27082	−	5.26435i	−0.186033	−	0.431272i	−0.985553	+	0.169367i	$0.945828\pi$
$150$		0			0
$151$	1.58586	−	0.796449i	0.129055	−	0.0648141i	−0.383100	−	0.923707i	$-0.625143\pi$
$151$	1.58586	−	0.796449i	0.129055	−	0.0648141i	0.512155	+	0.858893i	$0.328847\pi$
$152$	1.04640	+	0.380860i	0.0848746	+	0.0308918i
$153$		0			0
$154$	40.6236	−	14.7858i	3.27354	−	1.19147i
$155$	−1.18335	+	1.25428i	−0.0950490	+	0.100746i
$156$		0			0
$157$	−7.94471	+	5.22532i	−0.634057	+	0.417026i	−0.825440	−	0.564489i	$-0.809073\pi$
$157$	−7.94471	+	5.22532i	−0.634057	+	0.417026i	0.191383	+	0.981515i	$0.438703\pi$
$158$	8.19736	−	27.3811i	0.652147	−	2.17832i
$159$		0			0
$160$	2.09250	+	2.81072i	0.165427	+	0.222207i
$161$	28.0251			2.20868
$162$		0			0
$163$	7.38623			0.578534			0.289267	−	0.957248i	$-0.406588\pi$
$163$	7.38623			0.578534			0.289267	+	0.957248i	$0.406588\pi$
$164$	6.91558	+	9.28923i	0.540016	+	0.725367i
$165$		0			0
$166$	−1.36859	+	4.57142i	−0.106224	+	0.354811i
$167$	−3.80430	+	2.50213i	−0.294386	+	0.193621i	−0.688107	−	0.725609i	$-0.741558\pi$
$167$	−3.80430	+	2.50213i	−0.294386	+	0.193621i	0.393721	+	0.919230i	$0.371188\pi$
$168$		0			0
$169$	4.68041	−	4.96095i	0.360032	−	0.381612i
$170$	3.58329	−	1.30421i	0.274826	−	0.100028i
$171$		0			0
$172$	17.9378	+	6.52882i	1.36774	+	0.497818i
$173$	−4.15925	+	2.08885i	−0.316222	+	0.158813i	−0.599830	−	0.800128i	$-0.704765\pi$
$173$	−4.15925	+	2.08885i	−0.316222	+	0.158813i	0.283608	+	0.958940i	$0.408469\pi$
$174$		0			0
$175$	−7.02483	−	16.2854i	−0.531028	−	1.23106i
$176$	1.38942	+	0.162400i	0.104732	+	0.0122414i
$177$		0			0
$178$	−0.656433	−	0.431743i	−0.0492017	−	0.0323605i
$179$	2.66027	−	2.23223i	0.198838	−	0.166845i	−0.537932	−	0.842988i	$-0.680794\pi$
$179$	2.66027	−	2.23223i	0.198838	−	0.166845i	0.736770	+	0.676143i	$0.236350\pi$
$180$		0			0
$181$	−11.7147	−	9.82983i	−0.870749	−	0.730645i	0.0935067	−	0.995619i	$-0.470192\pi$
$181$	−11.7147	−	9.82983i	−0.870749	−	0.730645i	−0.964256	+	0.264973i	$0.914637\pi$
$182$	−6.17724	−	20.6334i	−0.457888	−	1.52945i
$183$		0			0
$184$	−17.5298	−	8.80381i	−1.29232	−	0.649025i
$185$	2.53417	+	2.68606i	0.186316	+	0.197483i
$186$		0			0
$187$	5.64607	−	13.0891i	0.412882	−	0.957168i
$188$	10.4439	−	18.0893i	0.761699	−	1.31930i
$189$		0			0
$190$	0.278694	+	0.482712i	0.0202186	+	0.0350196i
$191$	22.2359	−	2.59901i	1.60894	−	0.188058i	0.736379	−	0.676569i	$-0.236534\pi$
$191$	22.2359	−	2.59901i	1.60894	−	0.188058i	0.872557	+	0.488512i	$0.162460\pi$
$192$		0			0
$193$	−6.29843	+	1.49275i	−0.453371	+	0.107451i	−0.450956	−	0.892546i	$-0.648917\pi$
$193$	−6.29843	+	1.49275i	−0.453371	+	0.107451i	−0.00241481	+	0.999997i	$0.500769\pi$
$194$	1.45073	+	24.9081i	0.104157	+	1.78830i
$195$		0			0
$196$	23.1926	+	5.49675i	1.65661	+	0.392625i
$197$	−0.961298	+	5.45179i	−0.0684897	+	0.388424i	0.931223	+	0.364450i	$0.118743\pi$
$197$	−0.961298	+	5.45179i	−0.0684897	+	0.388424i	−0.999713	+	0.0239741i	$0.992368\pi$
$198$		0			0
$199$	−2.91762	−	16.5467i	−0.206825	−	1.17296i	−0.894542	−	0.446984i	$-0.852498\pi$
$199$	−2.91762	−	16.5467i	−0.206825	−	1.17296i	0.687717	−	0.725979i	$-0.258613\pi$
$200$	−0.721833	+	12.3934i	−0.0510413	+	0.876345i
$201$		0			0
$202$	−2.40893	+	3.23575i	−0.169492	+	0.227667i
$203$	12.0178	−	16.1427i	0.843481	−	1.13299i
$204$		0			0
$205$	−0.124566	+	2.13871i	−0.00870005	+	0.149374i
$206$	−6.94983	−	39.4144i	−0.484217	−	2.74613i
$207$		0			0
$208$	0.121023	−	0.686358i	0.00839146	−	0.0475903i
$209$	2.02749	+	0.480523i	0.140244	+	0.0332385i
$210$		0			0
$211$	0.444815	+	7.63718i	0.0306223	+	0.525765i	0.978385	+	0.206790i	$0.0663017\pi$
$211$	0.444815	+	7.63718i	0.0306223	+	0.525765i	−0.947763	+	0.318975i	$0.896661\pi$
$212$	7.64835	−	1.81269i	0.525291	−	0.124496i
$213$		0			0
$214$	−10.2551	+	1.19865i	−0.701023	+	0.0819378i
$215$	1.76564	+	3.05818i	0.120416	+	0.208566i
$216$		0			0
$217$	−5.59680	+	9.69394i	−0.379935	+	0.658068i
$218$	−3.51485	+	8.14833i	−0.238055	+	0.551874i
$219$		0			0
$220$	−6.37507	−	6.75718i	−0.429807	−	0.455569i
$221$	−6.34660	−	3.18738i	−0.426918	−	0.214406i
$222$		0			0
$223$	2.42568	+	8.10235i	0.162436	+	0.542573i	0.999993	−	0.00377653i	$-0.00120211\pi$
$223$	2.42568	+	8.10235i	0.162436	+	0.542573i	−0.837557	+	0.546350i	$0.816017\pi$
$224$	17.4246	+	14.6210i	1.16423	+	0.976906i
$225$		0			0
$226$	−22.7143	+	19.0596i	−1.51093	+	1.26782i
$227$	22.3403	+	14.6935i	1.48278	+	0.975239i	0.994742	+	0.102416i	$0.0326572\pi$
$227$	22.3403	+	14.6935i	1.48278	+	0.975239i	0.488037	+	0.872823i	$0.337713\pi$
$228$		0			0
$229$	3.05784	+	0.357410i	0.202068	+	0.0236183i	0.216525	−	0.976277i	$-0.430528\pi$
$229$	3.05784	+	0.357410i	0.202068	+	0.0236183i	−0.0144569	+	0.999895i	$0.504602\pi$
$230$	−3.88906	−	9.01586i	−0.256437	−	0.594488i
$231$		0			0
$232$	−12.5882	+	6.32205i	−0.826458	+	0.415063i
$233$	−6.67642	−	2.43002i	−0.437387	−	0.159196i	0.113936	−	0.993488i	$-0.463654\pi$
$233$	−6.67642	−	2.43002i	−0.437387	−	0.159196i	−0.551322	+	0.834292i	$0.685876\pi$
$234$		0			0
$235$	3.63100	−	1.32158i	0.236860	−	0.0862102i
$236$	10.0885	−	10.6932i	0.656706	−	0.696068i
$237$		0			0
$238$	20.6809	−	13.6020i	1.34054	−	0.881690i
$239$	1.31529	−	4.39336i	0.0850787	−	0.284183i	−0.904854	−	0.425722i	$-0.860020\pi$
$239$	1.31529	−	4.39336i	0.0850787	−	0.284183i	0.989933	+	0.141540i	$0.0452052\pi$
$240$		0			0
$241$	3.67688	+	4.93891i	0.236849	+	0.318143i	0.904616	−	0.426227i	$-0.140157\pi$
$241$	3.67688	+	4.93891i	0.236849	+	0.318143i	−0.667768	+	0.744370i	$0.732750\pi$
$242$	−31.6035			−2.03155
$243$		0			0
$244$	36.1505			2.31430
$245$	2.63303	+	3.53677i	0.168218	+	0.225956i
$246$		0			0
$247$	0.297733	−	0.994498i	0.0189443	−	0.0632784i
$248$	6.54609	−	4.30543i	0.415677	−	0.273395i
$249$		0			0
$250$	−8.84405	+	9.37414i	−0.559347	+	0.592873i
$251$	−27.6062	+	10.0478i	−1.74249	+	0.634213i	−0.999388	−	0.0349710i	$-0.988866\pi$
$251$	−27.6062	+	10.0478i	−1.74249	+	0.634213i	−0.743097	+	0.669184i	$0.766644\pi$
$252$		0			0
$253$	−34.4918	−	12.5540i	−2.16848	−	0.789263i
$254$	16.6524	−	8.36314i	1.04486	−	0.524750i
$255$		0			0
$256$	−5.60157	−	12.9859i	−0.350098	−	0.811618i
$257$	−18.7791	−	2.19496i	−1.17141	−	0.136918i	−0.491945	−	0.870627i	$-0.663714\pi$
$257$	−18.7791	−	2.19496i	−1.17141	−	0.136918i	−0.679464	+	0.733708i	$0.737788\pi$
$258$		0			0
$259$	20.0278	+	13.1725i	1.24446	+	0.818497i
$260$	−3.54552	+	2.97505i	−0.219884	+	0.184505i
$261$		0			0
$262$	−3.02395	−	2.53739i	−0.186820	−	0.156761i
$263$	−4.20169	−	14.0346i	−0.259087	−	0.865411i	−0.984242	−	0.176826i	$-0.943417\pi$
$263$	−4.20169	−	14.0346i	−0.259087	−	0.865411i	0.725155	−	0.688586i	$-0.241768\pi$
$264$		0			0
$265$	1.29940	+	0.652583i	0.0798215	+	0.0400878i
$266$	2.48295	+	2.63177i	0.152239	+	0.161364i
$267$		0			0
$268$	7.47299	−	17.3243i	0.456485	−	1.05825i
$269$	2.94518	−	5.10121i	0.179571	−	0.311026i	−0.762163	−	0.647386i	$-0.775862\pi$
$269$	2.94518	−	5.10121i	0.179571	−	0.311026i	0.941734	+	0.336360i	$0.109196\pi$
$270$		0			0
$271$	11.5965	+	20.0857i	0.704435	+	1.22012i	0.966895	+	0.255175i	$0.0821330\pi$
$271$	11.5965	+	20.0857i	0.704435	+	1.22012i	−0.262460	+	0.964943i	$0.584534\pi$
$272$	0.795557	−	0.0929873i	0.0482377	−	0.00563818i
$273$		0			0
$274$	−6.08139	+	1.44131i	−0.367390	+	0.0870730i
$275$	1.35067	+	23.1900i	0.0814483	+	1.39841i
$276$		0			0
$277$	−16.9688	−	4.02167i	−1.01955	−	0.241639i	−0.313343	−	0.949640i	$-0.601449\pi$
$277$	−16.9688	−	4.02167i	−1.01955	−	0.241639i	−0.706211	+	0.708001i	$0.749597\pi$
$278$	−3.41774	+	19.3829i	−0.204982	+	1.16251i
$279$		0			0
$280$	−1.03526	−	5.87124i	−0.0618685	−	0.350874i
$281$	−1.66215	+	28.5380i	−0.0991555	+	1.70243i	0.472006	+	0.881595i	$0.343530\pi$
$281$	−1.66215	+	28.5380i	−0.0991555	+	1.70243i	−0.571161	+	0.820838i	$0.693507\pi$
$282$		0			0
$283$	10.6352	−	14.2856i	0.632199	−	0.849191i	−0.364430	−	0.931231i	$-0.618736\pi$
$283$	10.6352	−	14.2856i	0.632199	−	0.849191i	0.996629	+	0.0820397i	$0.0261434\pi$
$284$	5.35246	−	7.18959i	0.317610	−	0.426624i
$285$		0			0
$286$	−1.64023	+	28.1617i	−0.0969890	+	1.66524i
$287$	2.41486	+	13.6953i	0.142544	+	0.808410i
$288$		0			0
$289$	−1.53469	+	8.70366i	−0.0902758	+	0.511980i
$290$	−6.86092	−	1.62607i	−0.402887	−	0.0954860i
$291$		0			0
$292$	2.53394	+	43.5060i	0.148288	+	2.54600i
$293$	−16.1869	+	3.83637i	−0.945649	+	0.224123i	−0.674383	−	0.738381i	$-0.735590\pi$
$293$	−16.1869	+	3.83637i	−0.945649	+	0.224123i	−0.271266	+	0.962504i	$0.587442\pi$
$294$		0			0
$295$	2.70117	−	0.315722i	0.157268	−	0.0183820i
$296$	−8.38946	−	14.5310i	−0.487628	−	0.844596i
$297$		0			0
$298$	−6.51957	+	11.2922i	−0.377668	+	0.654141i
$299$	−7.24321	+	16.7916i	−0.418885	+	0.971086i
$300$		0			0
$301$	15.7305	+	16.6733i	0.906690	+	0.961035i
$302$	−3.60673	−	1.81137i	−0.207544	−	0.104233i
$303$		0			0
$304$	0.0335786	+	0.112160i	0.00192587	+	0.00643284i
$305$	5.12291	+	4.29863i	0.293337	+	0.246139i
$306$		0			0
$307$	−10.8094	+	9.07013i	−0.616923	+	0.517660i	−0.896835	−	0.442366i	$-0.854139\pi$
$307$	−10.8094	+	9.07013i	−0.616923	+	0.517660i	0.279912	+	0.960026i	$0.409695\pi$
$308$	−50.3827	−	33.1372i	−2.87082	−	1.88817i
$309$		0			0
$310$	3.89528	+	0.455293i	0.221237	+	0.0258589i
$311$	9.36652	+	21.7140i	0.531127	+	1.23129i	0.946814	+	0.321782i	$0.104282\pi$
$311$	9.36652	+	21.7140i	0.531127	+	1.23129i	−0.415687	+	0.909508i	$0.636459\pi$
$312$		0			0
$313$	7.31342	−	3.67294i	0.413379	−	0.207607i	−0.229940	−	0.973205i	$-0.573853\pi$
$313$	7.31342	−	3.67294i	0.413379	−	0.207607i	0.643319	+	0.765598i	$0.277557\pi$
$314$	20.3223	+	7.39671i	1.14685	+	0.417421i
$315$		0			0
$316$	−37.4649	+	13.6361i	−2.10756	+	0.767091i
$317$	−2.81258	+	2.98116i	−0.157970	+	0.167439i	−0.801525	−	0.597962i	$-0.795978\pi$
$317$	−2.81258	+	2.98116i	−0.157970	+	0.167439i	0.643554	+	0.765400i	$0.277459\pi$
$318$		0			0
$319$	−22.0220	+	14.4841i	−1.23300	+	0.810955i
$320$	2.19127	−	7.31934i	0.122496	−	0.409164i
$321$		0			0
$322$	−38.0614	−	51.1254i	−2.12108	−	2.84911i
$323$	1.19306			0.0663836
$324$		0			0
$325$	11.5732			0.641968
$326$	−10.0314	−	13.4745i	−0.555588	−	0.746284i
$327$		0			0
$328$	2.79175	−	9.32510i	0.154149	−	0.514893i
$329$	20.9563	−	13.7832i	1.15536	−	0.759890i
$330$		0			0
$331$	17.0161	−	18.0360i	0.935290	−	0.991349i	−0.0646885	−	0.997906i	$-0.520605\pi$
$331$	17.0161	−	18.0360i	0.935290	−	0.991349i	0.999979	+	0.00655602i	$0.00208686\pi$
$332$	6.25497	−	2.27662i	0.343286	−	0.124946i
$333$		0			0
$334$	9.73128	+	3.54190i	0.532472	+	0.193804i
$335$	3.11903	−	1.56643i	0.170411	−	0.0855835i
$336$		0			0
$337$	6.00510	+	13.9214i	0.327118	+	0.758346i	0.999830	+	0.0184408i	$0.00587023\pi$
$337$	6.00510	+	13.9214i	0.327118	+	0.758346i	−0.672712	+	0.739905i	$0.734871\pi$
$338$	−15.4067	−	1.80079i	−0.838014	−	0.0979498i
$339$		0			0
$340$	−4.44411	−	2.92294i	−0.241016	−	0.158519i
$341$	11.2307	−	9.42369i	0.608177	−	0.510321i
$342$		0			0
$343$	1.49737	+	1.25644i	0.0808503	+	0.0678415i
$344$	−4.60173	−	15.3708i	−0.248109	−	0.828741i
$345$		0			0
$346$	9.45941	+	4.75069i	0.508541	+	0.255399i
$347$	17.2399	+	18.2732i	0.925487	+	0.980959i	0.999868	−	0.0162707i	$-0.00517934\pi$
$347$	17.2399	+	18.2732i	0.925487	+	0.980959i	−0.0743803	+	0.997230i	$0.523698\pi$
$348$		0			0
$349$	−6.87027	+	15.9271i	−0.367757	+	0.852557i	0.629391	+	0.777089i	$0.283304\pi$
$349$	−6.87027	+	15.9271i	−0.367757	+	0.852557i	−0.997148	+	0.0754680i	$0.975955\pi$
$350$	−20.1684	+	34.9328i	−1.07805	+	1.86724i
$351$		0			0
$352$	−14.8958	−	25.8002i	−0.793947	−	1.37516i
$353$	−21.5756	+	2.52183i	−1.14835	+	0.134223i	−0.668906	−	0.743347i	$-0.733237\pi$
$353$	−21.5756	+	2.52183i	−1.14835	+	0.134223i	−0.479448	+	0.877570i	$0.659163\pi$
$354$		0			0
$355$	1.61341	−	0.382385i	0.0856309	−	0.0202949i
$356$	0.0637250	+	1.09412i	0.00337742	+	0.0579881i
$357$		0			0
$358$	−7.68517	−	1.82142i	−0.406174	−	0.0962650i
$359$	−4.78039	+	27.1110i	−0.252299	+	1.43086i	0.550611	+	0.834762i	$0.314395\pi$
$359$	−4.78039	+	27.1110i	−0.252299	+	1.43086i	−0.802911	+	0.596100i	$0.796716\pi$
$360$		0			0
$361$	−3.26903	−	18.5396i	−0.172054	−	0.975769i
$362$	−2.02227	+	34.7210i	−0.106288	+	1.82489i
$363$		0			0
$364$	−17.9411	+	24.0991i	−0.940369	+	1.26314i
$365$	−4.81419	+	6.46658i	−0.251986	+	0.338476i
$366$		0			0
$367$	1.41611	−	24.3136i	0.0739202	−	1.26916i	−0.733706	−	0.679467i	$-0.762211\pi$
$367$	1.41611	−	24.3136i	0.0739202	−	1.26916i	0.807626	−	0.589694i	$-0.200752\pi$
$368$	−0.358141	−	2.03112i	−0.0186694	−	0.105879i
$369$		0			0
$370$	1.45841	−	8.27103i	0.0758189	−	0.429990i
$371$	9.18438	+	2.17674i	0.476829	+	0.113011i
$372$		0			0
$373$	−0.969427	−	16.6444i	−0.0501950	−	0.861815i	−0.925618	−	0.378458i	$-0.876454\pi$
$373$	−0.969427	−	16.6444i	−0.0501950	−	0.861815i	0.875423	−	0.483357i	$-0.160583\pi$
$374$	−31.5461	+	7.47657i	−1.63121	+	0.386604i
$375$		0			0
$376$	−17.4381	+	2.03822i	−0.899302	+	0.105113i
$377$	6.56607	+	11.3728i	0.338170	+	0.585727i
$378$		0			0
$379$	1.03268	−	1.78866i	0.0530454	−	0.0918773i	−0.838283	−	0.545235i	$-0.816441\pi$
$379$	1.03268	−	1.78866i	0.0530454	−	0.0918773i	0.891329	+	0.453357i	$0.149774\pi$
$380$	0.307956	−	0.713922i	0.0157978	−	0.0366234i
$381$		0			0
$382$	−34.9404	−	37.0347i	−1.78771	−	1.89486i
$383$	12.8776	+	6.46739i	0.658017	+	0.330468i	0.746283	−	0.665628i	$-0.231836\pi$
$383$	12.8776	+	6.46739i	0.658017	+	0.330468i	−0.0882665	+	0.996097i	$0.528133\pi$
$384$		0			0
$385$	−3.19944	−	10.6869i	−0.163059	−	0.544654i
$386$	11.2772	+	9.46272i	0.573996	+	0.481640i
$387$		0			0
$388$	26.6612	−	22.3714i	1.35352	−	1.13574i
$389$	−10.3118	−	6.78220i	−0.522831	−	0.343871i	0.260502	−	0.965473i	$-0.416112\pi$
$389$	−10.3118	−	6.78220i	−0.522831	−	0.343871i	−0.783333	+	0.621602i	$0.786482\pi$
$390$		0			0
$391$	−20.8747	−	2.43990i	−1.05568	−	0.123391i
$392$	−7.93512	−	18.3957i	−0.400784	−	0.929122i
$393$		0			0
$394$	11.2511	−	5.65053i	0.566824	−	0.284669i
$395$	−6.93064	−	2.52255i	−0.348718	−	0.126923i
$396$		0			0
$397$	−18.0123	+	6.55594i	−0.904011	+	0.329033i	−0.751859	−	0.659324i	$-0.770843\pi$
$397$	−18.0123	+	6.55594i	−0.904011	+	0.329033i	−0.152152	+	0.988357i	$0.548620\pi$
$398$	−26.2232	+	27.7949i	−1.31445	+	1.39323i
$399$		0			0
$400$	−1.09051	+	0.717242i	−0.0545257	+	0.0358621i
$401$	2.89211	−	9.66032i	0.144425	−	0.482414i	−0.854914	−	0.518770i	$-0.826390\pi$
$401$	2.89211	−	9.66032i	0.144425	−	0.482414i	0.999339	+	0.0363566i	$0.0115752\pi$
$402$		0			0
$403$	−4.36175	−	5.85885i	−0.217274	−	0.291850i
$404$	5.62708			0.279957
$405$		0			0
$406$	−45.7702			−2.27154
$407$	−18.7485	−	25.1836i	−0.929327	−	1.24830i
$408$		0			0
$409$	0.992437	−	3.31497i	0.0490728	−	0.163915i	−0.929941	−	0.367709i	$-0.880142\pi$
$409$	0.992437	−	3.31497i	0.0490728	−	0.163915i	0.979014	+	0.203794i	$0.0653274\pi$
$410$	4.07077	−	2.67739i	0.201041	−	0.132227i
$411$		0			0
$412$	−38.3115	+	40.6079i	−1.88747	+	2.00061i
$413$	16.5889	−	6.03787i	0.816287	−	0.297104i
$414$		0			0
$415$	1.15711	+	0.421153i	0.0568002	+	0.0206736i
$416$	−13.2639	+	6.66136i	−0.650314	+	0.326600i
$417$		0			0
$418$	−1.87697	−	4.35130i	−0.0918055	−	0.212829i
$419$	5.79048	+	0.676810i	0.282884	+	0.0330644i	0.256352	−	0.966584i	$-0.417480\pi$
$419$	5.79048	+	0.676810i	0.282884	+	0.0330644i	0.0265321	+	0.999648i	$0.491554\pi$
$420$		0			0
$421$	−32.2127	−	21.1866i	−1.56995	−	1.03257i	−0.973147	−	0.230185i	$-0.926067\pi$
$421$	−32.2127	−	21.1866i	−1.56995	−	1.03257i	−0.596803	−	0.802388i	$-0.703563\pi$
$422$	13.3282	−	11.1837i	0.648807	−	0.544414i
$423$		0			0
$424$	−5.06108	−	4.24675i	−0.245788	−	0.206240i
$425$	3.81468	+	12.7419i	0.185039	+	0.618073i
$426$		0			0
$427$	38.7932	+	19.4827i	1.87733	+	0.942832i
$428$	9.88352	+	10.4759i	0.477738	+	0.506372i
$429$		0			0
$430$	3.18100	−	7.37438i	0.153401	−	0.355624i
$431$	0.101111	−	0.175130i	0.00487036	−	0.00843570i	−0.863580	−	0.504212i	$-0.831783\pi$
$431$	0.101111	−	0.175130i	0.00487036	−	0.00843570i	0.868450	+	0.495776i	$0.165116\pi$
$432$		0			0
$433$	4.03061	+	6.98122i	0.193699	+	0.335496i	0.946473	−	0.322782i	$-0.104618\pi$
$433$	4.03061	+	6.98122i	0.193699	+	0.335496i	−0.752774	+	0.658279i	$0.771285\pi$
$434$	25.2855	−	2.95546i	1.21375	−	0.141866i
$435$		0			0
$436$	12.0450	−	2.85471i	0.576849	−	0.136716i
$437$	−0.178624	−	3.06685i	−0.00854473	−	0.146707i
$438$		0			0
$439$	−2.12701	−	0.504111i	−0.101517	−	0.0240599i	0.179544	−	0.983750i	$-0.442538\pi$
$439$	−2.12701	−	0.504111i	−0.101517	−	0.0240599i	−0.281060	+	0.959690i	$0.590686\pi$
$440$	−1.35591	+	7.68978i	−0.0646407	+	0.366596i
$441$		0			0
$442$	2.80480	+	15.9068i	0.133411	+	0.756609i
$443$	1.88147	−	32.3036i	0.0893913	−	1.53479i	−0.593838	−	0.804585i	$-0.702388\pi$
$443$	1.88147	−	32.3036i	0.0893913	−	1.53479i	0.683229	−	0.730204i	$-0.260575\pi$
$444$		0			0
$445$	−0.121070	+	0.162626i	−0.00573928	+	0.00770919i
$446$	11.4865	−	15.4291i	0.543903	−	0.730589i
$447$		0			0
$448$	2.88374	−	49.5118i	0.136244	−	2.33921i
$449$	6.74854	+	38.2728i	0.318483	+	1.80621i	0.551988	+	0.833852i	$0.313869\pi$
$449$	6.74854	+	38.2728i	0.318483	+	1.80621i	−0.233505	+	0.972356i	$0.575020\pi$
$450$		0			0
$451$	3.16282	−	17.9373i	0.148931	−	0.844632i
$452$	40.2464	+	9.53857i	1.89303	+	0.448657i
$453$		0			0
$454$	−3.53598	−	60.7104i	−0.165952	−	2.84928i
$455$	−5.40805	+	1.28173i	−0.253534	+	0.0600885i
$456$		0			0
$457$	29.3258	−	3.42769i	1.37180	−	0.160341i	0.601935	−	0.798545i	$-0.294396\pi$
$457$	29.3258	−	3.42769i	1.37180	−	0.160341i	0.769867	+	0.638204i	$0.220322\pi$
$458$	−3.50090	−	6.06374i	−0.163586	−	0.283340i
$459$		0			0
$460$	−6.84827	+	11.8616i	−0.319302	+	0.553048i
$461$	8.52535	−	19.7640i	0.397065	−	0.920500i	−0.596006	−	0.802980i	$-0.703246\pi$
$461$	8.52535	−	19.7640i	0.397065	−	0.920500i	0.993071	−	0.117520i	$-0.0374943\pi$
$462$		0			0
$463$	23.9773	+	25.4145i	1.11432	+	1.18111i	0.981798	+	0.189931i	$0.0608263\pi$
$463$	23.9773	+	25.4145i	1.11432	+	1.18111i	0.132523	+	0.991180i	$0.457692\pi$
$464$	−1.32352	−	0.664697i	−0.0614429	−	0.0308578i
$465$		0			0
$466$	4.63437	+	15.4799i	0.214683	+	0.717092i
$467$	−19.2365	−	16.1414i	−0.890161	−	0.746933i	0.0780818	−	0.996947i	$-0.475120\pi$
$467$	−19.2365	−	16.1414i	−0.890161	−	0.746933i	−0.968242	+	0.250014i	$0.919565\pi$
$468$		0			0
$469$	17.3559	−	14.5633i	0.801422	−	0.672473i
$470$	−7.34226	−	4.82908i	−0.338673	−	0.222749i
$471$		0			0
$472$	−12.2732	−	1.43453i	−0.564920	−	0.0660297i
$473$	−11.8914	−	27.5673i	−0.546765	−	1.26754i
$474$		0			0
$475$	−1.73738	+	0.872543i	−0.0797163	+	0.0400350i
$476$	−32.4462	−	11.8095i	−1.48717	−	0.541286i
$477$		0			0
$478$	−9.80101	+	3.56728i	−0.448288	+	0.163163i
$479$	6.73335	−	7.13693i	0.307655	−	0.326095i	−0.555037	−	0.831826i	$-0.687296\pi$
$479$	6.73335	−	7.13693i	0.307655	−	0.326095i	0.862691	+	0.505731i	$0.168777\pi$
$480$		0			0
$481$	−13.0687	+	8.59545i	−0.595884	+	0.391919i
$482$	4.01627	−	13.4153i	0.182936	−	0.611049i
$483$		0			0
$484$	26.3253	+	35.3610i	1.19660	+	1.60732i
$485$	6.43835			0.292350
$486$		0			0
$487$	−17.0318			−0.771785			−0.385892	−	0.922544i	$-0.626106\pi$
$487$	−17.0318			−0.771785			−0.385892	+	0.922544i	$0.626106\pi$
$488$	−18.1450	−	24.3730i	−0.821387	−	1.10331i
$489$		0			0
$490$	2.87606	−	9.60672i	0.129927	−	0.433987i
$491$	7.02593	−	4.62103i	0.317076	−	0.208544i	−0.380987	−	0.924580i	$-0.624416\pi$
$491$	7.02593	−	4.62103i	0.317076	−	0.208544i	0.698063	+	0.716036i	$0.254045\pi$
$492$		0			0
$493$	−10.3569	+	10.9777i	−0.466453	+	0.494411i
$494$	−2.21860	+	0.807503i	−0.0998193	+	0.0363313i
$495$		0			0
$496$	0.774093	+	0.281747i	0.0347578	+	0.0126508i
$497$	9.61843	−	4.83056i	0.431446	−	0.216680i
$498$		0			0
$499$	9.57041	+	22.1867i	0.428430	+	0.993213i	0.986551	+	0.163453i	$0.0522633\pi$
$499$	9.57041	+	22.1867i	0.428430	+	0.993213i	−0.558121	+	0.829760i	$0.688477\pi$
$500$	17.8557	+	2.08703i	0.798530	+	0.0933348i
$501$		0			0
$502$	55.8225	+	36.7150i	2.49148	+	1.63867i
$503$	−2.81544	+	2.36243i	−0.125534	+	0.105336i	−0.703393	−	0.710801i	$-0.748333\pi$
$503$	−2.81544	+	2.36243i	−0.125534	+	0.105336i	0.577859	+	0.816136i	$0.303888\pi$
$504$		0			0
$505$	0.797417	+	0.669112i	0.0354846	+	0.0297751i
$506$	23.9422	+	79.9724i	1.06436	+	3.55521i
$507$		0			0
$508$	−23.2287	−	11.6659i	−1.03061	−	0.517591i
$509$	20.1561	+	21.3642i	0.893403	+	0.946952i	0.998873	−	0.0474702i	$-0.0151159\pi$
$509$	20.1561	+	21.3642i	0.893403	+	0.946952i	−0.105469	+	0.994423i	$0.533634\pi$
$510$		0			0
$511$	−20.7276	+	48.0520i	−0.916936	+	2.12570i
$512$	1.58458	−	2.74458i	0.0700293	−	0.121294i
$513$		0			0
$514$	21.5001	+	37.2393i	0.948329	+	1.64255i
$515$	−10.2578	+	1.19897i	−0.452013	+	0.0528328i
$516$		0			0
$517$	−31.9662	+	7.57612i	−1.40587	+	0.333197i
$518$	−3.16995	−	54.4259i	−0.139280	−	2.39134i
$519$		0			0
$520$	3.78541	+	0.897159i	0.166001	+	0.0393430i
$521$	6.02463	−	34.1674i	0.263944	−	1.49690i	−0.508083	−	0.861308i	$-0.669646\pi$
$521$	6.02463	−	34.1674i	0.263944	−	1.49690i	0.772026	−	0.635591i	$-0.219243\pi$
$522$		0			0
$523$	5.01556	+	28.4447i	0.219315	+	1.24380i	0.873259	+	0.487256i	$0.162002\pi$
$523$	5.01556	+	28.4447i	0.219315	+	1.24380i	−0.653944	+	0.756543i	$0.726887\pi$
$524$	−0.320170	+	5.49710i	−0.0139867	+	0.240142i
$525$		0			0
$526$	−19.8966	+	26.7257i	−0.867532	+	1.16530i
$527$	5.01279	−	6.73335i	0.218361	−	0.293309i
$528$		0			0
$529$	−1.80929	+	31.0643i	−0.0786647	+	1.35062i
$530$	−0.574252	−	3.25675i	−0.0249439	−	0.141464i
$531$		0			0
$532$	0.876415	−	4.97039i	0.0379974	−	0.215494i
$533$	−8.82989	−	2.09272i	−0.382465	−	0.0906459i
$534$		0			0
$535$	0.154915	+	2.65979i	0.00669757	+	0.114993i
$536$	−15.4312	+	3.65725i	−0.666524	+	0.157969i
$537$		0			0
$538$	−13.3059	+	1.55524i	−0.573659	+	0.0670511i
$539$	−18.7436	−	32.4648i	−0.807343	−	1.39836i
$540$		0			0
$541$	4.28774	−	7.42658i	0.184344	−	0.319294i	−0.759011	−	0.651078i	$-0.774317\pi$
$541$	4.28774	−	7.42658i	0.184344	−	0.319294i	0.943355	+	0.331784i	$0.107650\pi$
$542$	20.8924	−	48.4339i	0.897404	−	2.08042i
$543$		0			0
$544$	−11.7059	−	12.4076i	−0.501888	−	0.531971i
$545$	2.04635	+	1.02772i	0.0876560	+	0.0440225i
$546$		0			0
$547$	7.22232	+	24.1242i	0.308804	+	1.03148i	0.961717	+	0.274044i	$0.0883614\pi$
$547$	7.22232	+	24.1242i	0.308804	+	1.03148i	−0.652913	+	0.757433i	$0.726453\pi$
$548$	6.67840	+	5.60384i	0.285287	+	0.239384i
$549$		0			0
$550$	40.4706	−	33.9589i	1.72567	−	1.44801i
$551$	−1.84313	−	1.21224i	−0.0785199	−	0.0516434i
$552$		0			0
$553$	−47.5526	−	5.55810i	−2.02214	−	0.236354i
$554$	15.7090	+	36.4176i	0.667412	+	1.54724i
$555$		0			0
$556$	24.5344	−	12.3217i	1.04049	−	0.522555i
$557$	15.3188	+	5.57558i	0.649077	+	0.236245i	0.645514	−	0.763749i	$-0.276643\pi$
$557$	15.3188	+	5.57558i	0.649077	+	0.236245i	0.00356379	+	0.999994i	$0.498866\pi$
$558$		0			0
$559$	−14.0557	+	5.11586i	−0.594493	+	0.216378i
$560$	0.430151	−	0.455934i	0.0181772	−	0.0192667i
$561$		0			0
$562$	54.3185	−	35.7258i	2.29129	−	1.50700i
$563$	−12.5471	+	41.9103i	−0.528798	+	1.76631i	0.106790	+	0.994282i	$0.465943\pi$
$563$	−12.5471	+	41.9103i	−0.528798	+	1.76631i	−0.635588	+	0.772028i	$0.719242\pi$
$564$		0			0
$565$	4.56912	+	6.13739i	0.192224	+	0.258202i
$566$	−40.5048			−1.70254
$567$		0			0
$568$	−7.53386			−0.316114
$569$	20.4417	+	27.4580i	0.856962	+	1.15110i	0.987179	+	0.159615i	$0.0510252\pi$
$569$	20.4417	+	27.4580i	0.856962	+	1.15110i	−0.130217	+	0.991486i	$0.541567\pi$
$570$		0			0
$571$	9.28681	−	31.0201i	0.388641	−	1.29815i	−0.510268	−	0.860016i	$-0.670454\pi$
$571$	9.28681	−	31.0201i	0.388641	−	1.29815i	0.898909	−	0.438136i	$-0.144361\pi$
$572$	32.8763	−	21.6231i	1.37463	−	0.904107i
$573$		0			0
$574$	21.7044	−	23.0053i	0.905923	−	0.960222i
$575$	32.1829	−	11.7136i	1.34212	−	0.488492i
$576$		0			0
$577$	43.0486	+	15.6684i	1.79214	+	0.652285i	0.999068	+	0.0431527i	$0.0137402\pi$
$577$	43.0486	+	15.6684i	1.79214	+	0.652285i	0.793069	+	0.609132i	$0.208482\pi$
$578$	17.9622	−	9.02093i	0.747127	−	0.375221i
$579$		0			0
$580$	3.89566	+	9.03116i	0.161759	+	0.374998i
$581$	7.93917	+	0.927956i	0.329372	+	0.0384981i
$582$		0			0
$583$	−10.3286	−	6.79321i	−0.427766	−	0.281346i
$584$	28.0603	−	23.5454i	1.16115	−	0.974317i
$585$		0			0
$586$	28.9824	+	24.3191i	1.19725	+	1.00461i
$587$	−12.3442	−	41.2325i	−0.509500	−	1.70185i	−0.694831	−	0.719173i	$-0.744521\pi$
$587$	−12.3442	−	41.2325i	−0.509500	−	1.70185i	0.185331	−	0.982676i	$-0.440664\pi$
$588$		0			0
$589$	1.09650	+	0.550685i	0.0451807	+	0.0226906i
$590$	−4.24449	−	4.49889i	−0.174743	−	0.185216i
$591$		0			0
$592$	0.698735	−	1.61985i	0.0287178	−	0.0665754i
$593$	−13.5379	+	23.4484i	−0.555935	+	0.962909i	0.441895	+	0.897067i	$0.354307\pi$
$593$	−13.5379	+	23.4484i	−0.555935	+	0.962909i	−0.997830	+	0.0658415i	$0.979027\pi$
$594$		0			0
$595$	−3.19372	−	5.53169i	−0.130930	−	0.226777i
$596$	18.0655	−	2.11156i	0.739993	−	0.0864928i
$597$		0			0
$598$	40.4697	−	9.59150i	1.65493	−	0.392226i
$599$	−0.117944	−	2.02502i	−0.00481906	−	0.0827400i	0.995041	−	0.0994649i	$-0.0317131\pi$
$599$	−0.117944	−	2.02502i	−0.00481906	−	0.0827400i	−0.999860	+	0.0167249i	$0.994676\pi$
$600$		0			0
$601$	7.63366	+	1.80921i	0.311383	+	0.0737992i	0.383336	−	0.923609i	$-0.374775\pi$
$601$	7.63366	+	1.80921i	0.311383	+	0.0737992i	−0.0719530	+	0.997408i	$0.522923\pi$
$602$	9.05283	−	51.3412i	0.368966	−	2.09251i
$603$		0			0
$604$	0.977629	+	5.54441i	0.0397792	+	0.225599i
$605$	−0.474180	+	8.14136i	−0.0192782	+	0.330993i
$606$		0			0
$607$	−12.2952	+	16.5154i	−0.499048	+	0.670338i	−0.978265	−	0.207359i	$-0.933513\pi$
$607$	−12.2952	+	16.5154i	−0.499048	+	0.670338i	0.479217	+	0.877696i	$0.340921\pi$
$608$	1.48895	−	2.00001i	0.0603849	−	0.0811110i
$609$		0			0
$610$	0.884348	−	15.1837i	0.0358062	−	0.614769i
$611$	2.84214	+	16.1186i	0.114981	+	0.652089i
$612$		0			0
$613$	−0.250445	+	1.42034i	−0.0101154	+	0.0573671i	−0.989448	−	0.144891i	$-0.953717\pi$
$613$	−0.250445	+	1.42034i	−0.0101154	+	0.0573671i	0.979332	+	0.202258i	$0.0648280\pi$
$614$	31.2268	+	7.40090i	1.26021	+	0.298676i
$615$		0			0
$616$	2.94718	+	50.6011i	0.118745	+	2.03878i
$617$	−3.30216	+	0.782627i	−0.132940	+	0.0315074i	−0.296547	−	0.955018i	$-0.595835\pi$
$617$	−3.30216	+	0.782627i	−0.132940	+	0.0315074i	0.163607	+	0.986526i	$0.447687\pi$
$618$		0			0
$619$	−30.7290	+	3.59170i	−1.23510	+	0.144363i	−0.708476	−	0.705735i	$-0.750617\pi$
$619$	−30.7290	+	3.59170i	−1.23510	+	0.144363i	−0.526626	+	0.850097i	$0.676543\pi$
$620$	−2.73530	−	4.73767i	−0.109852	−	0.190269i
$621$		0			0
$622$	26.8915	−	46.5774i	1.07825	−	1.86758i
$623$	−0.521271	+	1.20844i	−0.0208843	+	0.0484152i
$624$		0			0
$625$	−13.6921	−	14.5128i	−0.547683	−	0.580510i
$626$	−16.6330	−	8.35339i	−0.664787	−	0.333869i
$627$		0			0
$628$	−8.65207	−	28.8999i	−0.345255	−	1.15323i
$629$	−13.7710	−	11.5553i	−0.549087	−	0.460739i
$630$		0			0
$631$	25.7219	−	21.5833i	1.02397	−	0.859217i	0.0338527	−	0.999427i	$-0.489222\pi$
$631$	25.7219	−	21.5833i	1.02397	−	0.859217i	0.990122	+	0.140210i	$0.0447778\pi$
$632$	27.9984	+	18.4148i	1.11372	+	0.732502i
$633$		0			0
$634$	9.25829	+	1.08214i	0.367694	+	0.0429772i
$635$	−1.90457	−	4.41530i	−0.0755807	−	0.175216i
$636$		0			0
$637$	−16.6901	+	8.38209i	−0.661286	+	0.332111i
$638$	56.3316	+	20.5030i	2.23019	+	0.811723i
$639$		0			0
$640$	−9.74295	+	3.54614i	−0.385124	+	0.140174i
$641$	−11.0620	+	11.7250i	−0.436921	+	0.463109i	−0.907993	−	0.418986i	$-0.862386\pi$
$641$	−11.0620	+	11.7250i	−0.436921	+	0.463109i	0.471072	+	0.882095i	$0.343867\pi$
$642$		0			0
$643$	−6.27416	+	4.12658i	−0.247429	+	0.162736i	−0.667166	−	0.744909i	$-0.732493\pi$
$643$	−6.27416	+	4.12658i	−0.247429	+	0.162736i	0.419737	+	0.907646i	$0.362122\pi$
$644$	−25.4993	+	85.1736i	−1.00481	+	3.35631i
$645$		0			0
$646$	−1.62032	−	2.17647i	−0.0637506	−	0.0856319i
$647$	−18.2475			−0.717384			−0.358692	−	0.933456i	$-0.616777\pi$
$647$	−18.2475			−0.717384			−0.358692	+	0.933456i	$0.616777\pi$
$648$		0			0
$649$	−23.1215			−0.907598
$650$	−15.7179	−	21.1128i	−0.616506	−	0.828111i
$651$		0			0
$652$	−6.72055	+	22.4482i	−0.263197	+	0.879139i
$653$	−7.11035	+	4.67655i	−0.278250	+	0.183008i	−0.680962	−	0.732319i	$-0.738438\pi$
$653$	−7.11035	+	4.67655i	−0.278250	+	0.183008i	0.402712	+	0.915327i	$0.368068\pi$
$654$		0			0
$655$	−0.699028	+	0.740927i	−0.0273133	+	0.0289504i
$656$	0.961710	−	0.350034i	0.0375485	−	0.0136665i
$657$		0			0
$658$	−53.6055	−	19.5108i	−2.08976	−	0.760610i
$659$	11.7605	−	5.90633i	0.458123	−	0.230078i	−0.204743	−	0.978816i	$-0.565636\pi$
$659$	11.7605	−	5.90633i	0.458123	−	0.230078i	0.662866	+	0.748738i	$0.269340\pi$
$660$		0			0
$661$	−4.59814	−	10.6597i	−0.178847	−	0.414613i	0.805085	−	0.593160i	$-0.202120\pi$
$661$	−4.59814	−	10.6597i	−0.178847	−	0.414613i	−0.983931	+	0.178546i	$0.942861\pi$
$662$	−56.0126	−	6.54694i	−2.17699	−	0.254454i
$663$		0			0
$664$	−4.67448	−	3.07446i	−0.181405	−	0.119312i
$665$	0.715224	−	0.600144i	0.0277352	−	0.0232726i
$666$		0			0
$667$	29.7697	+	24.9797i	1.15269	+	0.967219i
$668$	−4.14302	−	13.8387i	−0.160298	−	0.535434i
$669$		0			0
$670$	−7.09363	−	3.56255i	−0.274051	−	0.137633i
$671$	−39.0173	−	41.3559i	−1.50624	−	1.59653i
$672$		0			0
$673$	15.9128	−	36.8901i	0.613395	−	1.42201i	−0.274330	−	0.961636i	$-0.588456\pi$
$673$	15.9128	−	36.8901i	0.613395	−	1.42201i	0.887725	−	0.460374i	$-0.152285\pi$
$674$	17.2408	−	29.8619i	0.664089	−	1.15024i
$675$		0			0
$676$	10.8187	+	18.7385i	0.416104	+	0.720713i
$677$	−13.6063	+	1.59034i	−0.522931	+	0.0611219i	−0.373464	−	0.927645i	$-0.621830\pi$
$677$	−13.6063	+	1.59034i	−0.522931	+	0.0611219i	−0.149467	+	0.988767i	$0.547756\pi$
$678$		0			0
$679$	40.6668	−	9.63822i	1.56065	−	0.369881i
$680$	0.259962	+	4.46338i	0.00996909	+	0.171163i
$681$		0			0
$682$	−32.4441	−	7.68939i	−1.24235	−	0.294442i
$683$	−3.43677	+	19.4909i	−0.131504	+	0.745798i	0.845726	+	0.533617i	$0.179168\pi$
$683$	−3.43677	+	19.4909i	−0.131504	+	0.745798i	−0.977230	+	0.212181i	$0.931943\pi$
$684$		0			0
$685$	0.280051	+	1.58825i	0.0107002	+	0.0606839i
$686$	0.258485	−	4.43801i	0.00986899	−	0.169444i
$687$		0			0
$688$	1.00738	−	1.35314i	0.0384059	−	0.0515881i
$689$	−3.67797	+	4.94037i	−0.140120	+	0.188213i
$690$		0			0
$691$	−0.546536	+	9.38367i	−0.0207912	+	0.356972i	0.971827	+	0.235694i	$0.0757362\pi$
$691$	−0.546536	+	9.38367i	−0.0207912	+	0.356972i	−0.992619	+	0.121278i	$0.961301\pi$
$692$	−2.56404	−	14.5414i	−0.0974700	−	0.552780i
$693$		0			0
$694$	9.92150	−	56.2676i	0.376615	−	2.13589i
$695$	4.94195	+	1.17126i	0.187459	+	0.0444286i
$696$		0			0
$697$	−0.606390	−	10.4113i	−0.0229687	−	0.394357i
$698$	38.3860	−	9.09765i	1.45293	−	0.344351i
$699$		0			0
$700$	55.8862	−	6.53216i	2.11230	−	0.246893i
$701$	−9.65096	−	16.7160i	−0.364512	−	0.631353i	0.624186	−	0.781276i	$-0.285431\pi$
$701$	−9.65096	−	16.7160i	−0.364512	−	0.631353i	−0.988698	+	0.149923i	$0.952097\pi$
$702$		0			0
$703$	1.31384	−	2.27564i	0.0495526	−	0.0858276i
$704$	−25.7283	+	59.6449i	−0.969671	+	2.24795i
$705$		0			0
$706$	33.9028	+	35.9349i	1.27595	+	1.35243i
$707$	6.03843	+	3.03261i	0.227098	+	0.114053i
$708$		0			0
$709$	−2.85166	−	9.52520i	−0.107096	−	0.357726i	0.887596	−	0.460623i	$-0.152374\pi$
$709$	−2.85166	−	9.52520i	−0.107096	−	0.357726i	−0.994692	+	0.102897i	$0.967189\pi$
$710$	−2.88878	−	2.42398i	−0.108414	−	0.0909703i
$711$		0			0
$712$	0.705679	−	0.592135i	0.0264464	−	0.0221912i
$713$	−18.0591	−	11.8777i	−0.676319	−	0.444822i
$714$		0			0
$715$	7.23012	+	0.845079i	0.270391	+	0.0316042i
$716$	4.36367	+	10.1161i	0.163078	+	0.378058i
$717$		0			0
$718$	55.9502	−	28.0992i	2.08804	−	1.04865i
$719$	−35.9855	−	13.0976i	−1.34203	−	0.488459i	−0.431580	−	0.902075i	$-0.642044\pi$
$719$	−35.9855	−	13.0976i	−1.34203	−	0.488459i	−0.910452	+	0.413615i	$0.864266\pi$
$720$		0			0
$721$	−62.9971	+	22.9291i	−2.34613	+	0.853923i
$722$	−29.3816	+	31.1427i	−1.09347	+	1.15901i
$723$		0			0
$724$	40.5337	−	26.6594i	1.50642	−	0.990790i
$725$	7.05361	−	23.5607i	0.261964	−	0.875022i
$726$		0			0
$727$	14.0176	+	18.8289i	0.519884	+	0.698326i	0.982083	−	0.188451i	$-0.0603466\pi$
$727$	14.0176	+	18.8289i	0.519884	+	0.698326i	−0.462198	+	0.886777i	$0.652939\pi$
$728$	25.2530			0.935940
$729$		0			0
$730$	18.3351			0.678612
$731$	−10.2654	−	13.7888i	−0.379679	−	0.509997i
$732$		0			0
$733$	5.94536	−	19.8589i	0.219597	−	0.733504i	−0.775208	−	0.631706i	$-0.782355\pi$
$733$	5.94536	−	19.8589i	0.219597	−	0.733504i	0.994805	−	0.101799i	$-0.0324597\pi$
$734$	−46.2780	+	30.4375i	−1.70815	+	1.12347i
$735$		0			0
$736$	−30.1421	+	31.9487i	−1.11105	+	1.17765i
$737$	−27.8845	+	10.1491i	−1.02714	+	0.373848i
$738$		0			0
$739$	−17.6513	−	6.42454i	−0.649313	−	0.236331i	−0.00369738	−	0.999993i	$-0.501177\pi$
$739$	−17.6513	−	6.42454i	−0.649313	−	0.236331i	−0.645616	+	0.763663i	$0.723399\pi$
$740$	−10.4693	+	5.25786i	−0.384858	+	0.193283i
$741$		0			0
$742$	−8.50254	−	19.7111i	−0.312138	−	0.723617i
$743$	30.8677	+	3.60792i	1.13243	+	0.132362i	0.661595	−	0.749861i	$-0.269880\pi$
$743$	30.8677	+	3.60792i	1.13243	+	0.132362i	0.470832	+	0.882223i	$0.343954\pi$
$744$		0			0
$745$	2.81116	+	1.84893i	0.102993	+	0.0677396i
$746$	−29.0474	+	24.3736i	−1.06350	+	0.892382i
$747$		0			0
$748$	34.6430	+	29.0690i	1.26667	+	1.06287i
$749$	4.96021	+	16.5683i	0.181242	+	0.605391i
$750$		0			0
$751$	−21.5859	−	10.8408i	−0.787679	−	0.395587i	0.00902310	−	0.999959i	$-0.497128\pi$
$751$	−21.5859	−	10.8408i	−0.787679	−	0.395587i	−0.796702	+	0.604372i	$0.793424\pi$
$752$	−1.26674	−	1.34267i	−0.0461934	−	0.0489621i
$753$		0			0
$754$	11.8295	−	27.4239i	0.430806	−	0.998720i
$755$	−0.520742	+	0.901951i	−0.0189517	+	0.0328254i
$756$		0			0
$757$	0.457633	+	0.792644i	0.0166330	+	0.0288091i	0.874222	−	0.485526i	$-0.161372\pi$
$757$	0.457633	+	0.792644i	0.0166330	+	0.0288091i	−0.857589	+	0.514335i	$0.828039\pi$
$758$	−4.66552	+	0.545321i	−0.169459	+	0.0198070i
$759$		0			0
$760$	−0.635906	+	0.150713i	−0.0230667	+	0.00546692i
$761$	−1.18527	−	20.3503i	−0.0429659	−	0.737696i	−0.949152	−	0.314818i	$-0.898057\pi$
$761$	−1.18527	−	20.3503i	−0.0429659	−	0.737696i	0.906186	−	0.422879i	$-0.138980\pi$
$762$		0			0
$763$	14.4640	+	3.42802i	0.523631	+	0.124103i
$764$	−12.3330	+	69.9441i	−0.446194	+	2.53049i
$765$		0			0
$766$	−5.69111	−	32.2759i	−0.205628	−	1.16617i
$767$	−0.669800	+	11.5000i	−0.0241851	+	0.415242i
$768$		0			0
$769$	13.4894	−	18.1194i	0.486439	−	0.653401i	−0.489357	−	0.872083i	$-0.662769\pi$
$769$	13.4894	−	18.1194i	0.486439	−	0.653401i	0.975796	+	0.218683i	$0.0701760\pi$
$770$	−15.1506	+	20.3507i	−0.545989	+	0.733390i
$771$		0			0
$772$	1.19401	−	20.5004i	0.0429734	−	0.737825i
$773$	0.291023	+	1.65048i	0.0104674	+	0.0593635i	0.989594	−	0.143888i	$-0.0459604\pi$
$773$	0.291023	+	1.65048i	0.0104674	+	0.0593635i	−0.979127	+	0.203251i	$0.934849\pi$
$774$		0			0
$775$	−2.37538	+	13.4715i	−0.0853262	+	0.483909i
$776$	−28.4651	−	6.74635i	−1.02184	−	0.242180i
$777$		0			0
$778$	1.63214	+	28.0227i	0.0585149	+	1.00466i
$779$	1.48332	−	0.351554i	0.0531455	−	0.0125957i
$780$		0			0
$781$	−14.0018	+	1.63657i	−0.501022	+	0.0585611i
$782$	23.8993	+	41.3949i	0.854639	+	1.48028i
$783$		0			0
$784$	1.05319	−	1.82418i	0.0376139	−	0.0651491i
$785$	2.21038	−	5.12424i	0.0788919	−	0.182892i
$786$		0			0
$787$	21.5274	+	22.8177i	0.767368	+	0.813363i	0.986745	−	0.162277i	$-0.0518839\pi$
$787$	21.5274	+	22.8177i	0.767368	+	0.813363i	−0.219377	+	0.975640i	$0.570402\pi$
$788$	−15.6944	−	7.88203i	−0.559090	−	0.280786i
$789$		0			0
$790$	4.81084	+	16.0693i	0.171162	+	0.571720i
$791$	38.0479	+	31.9259i	1.35283	+	1.13516i
$792$		0			0
$793$	−21.6996	+	18.2081i	−0.770575	+	0.646590i
$794$	36.4227	+	23.9556i	1.29259	+	0.850153i
$795$		0			0
$796$	52.9432	+	6.18818i	1.87652	+	0.219334i
$797$	−18.7033	−	43.3591i	−0.662504	−	1.53586i	−0.834647	−	0.550785i	$-0.814328\pi$
$797$	−18.7033	−	43.3591i	−0.662504	−	1.53586i	0.172143	−	0.985072i	$-0.444931\pi$
$798$		0			0
$799$	−16.8094	+	8.44202i	−0.594676	+	0.298657i
$800$	26.1209	+	9.50724i	0.923514	+	0.336132i
$801$		0			0
$802$	−21.5509	+	7.84389i	−0.760990	+	0.276978i
$803$	47.0357	−	49.8549i	1.65985	−	1.75934i
$804$		0			0
$805$	−13.7415	+	9.03791i	−0.484323	+	0.318544i
$806$	−4.76436	+	15.9141i	−0.167817	+	0.560549i
$807$		0			0
$808$	−2.82440	−	3.79383i	−0.0993621	−	0.133466i
$809$	−15.1675			−0.533260			−0.266630	−	0.963799i	$-0.585910\pi$
$809$	−15.1675			−0.533260			−0.266630	+	0.963799i	$0.585910\pi$
$810$		0			0
$811$	35.5509			1.24836			0.624181	−	0.781280i	$-0.285433\pi$
$811$	35.5509			1.24836			0.624181	+	0.781280i	$0.285433\pi$
$812$	38.1260	+	51.2121i	1.33796	+	1.79719i
$813$		0			0
$814$	−20.4790	+	68.4047i	−0.717789	+	2.39758i
$815$	−3.62167	+	2.38201i	−0.126862	+	0.0834382i
$816$		0			0
$817$	1.72434	−	1.82770i	0.0603271	−	0.0639430i
$818$	−7.39526	+	2.69166i	−0.258569	+	0.0941115i
$819$		0			0
$820$	−6.38662	−	2.32454i	−0.223031	−	0.0811765i
$821$	10.7700	−	5.40891i	0.375876	−	0.188772i	−0.250824	−	0.968033i	$-0.580701\pi$
$821$	10.7700	−	5.40891i	0.375876	−	0.188772i	0.626700	+	0.779261i	$0.284405\pi$
$822$		0			0
$823$	14.5254	+	33.6736i	0.506322	+	1.17379i	0.959332	+	0.282281i	$0.0910911\pi$
$823$	14.5254	+	33.6736i	0.506322	+	1.17379i	−0.453010	+	0.891506i	$0.649650\pi$
$824$	46.6080	+	5.44769i	1.62367	+	0.189779i
$825$		0			0
$826$	−33.5445	−	22.0626i	−1.16716	−	0.767655i
$827$	35.8302	−	30.0651i	1.24594	−	1.04547i	0.248901	−	0.968529i	$-0.419931\pi$
$827$	35.8302	−	30.0651i	1.24594	−	1.04547i	0.997036	−	0.0769360i	$-0.0245137\pi$
$828$		0			0
$829$	0.460070	+	0.386045i	0.0159789	+	0.0134079i	0.650742	−	0.759299i	$-0.274458\pi$
$829$	0.460070	+	0.386045i	0.0159789	+	0.0134079i	−0.634763	+	0.772707i	$0.718902\pi$
$830$	−0.803196	−	2.68286i	−0.0278793	−	0.0931235i
$831$		0			0
$832$	28.9205	+	14.5244i	1.00264	+	0.503543i
$833$	−14.7298	−	15.6126i	−0.510356	−	0.540946i
$834$		0			0
$835$	1.05844	−	2.45373i	0.0366287	−	0.0849148i
$836$	−3.30516	+	5.72471i	−0.114312	+	0.197993i
$837$		0			0
$838$	−6.62950	−	11.4826i	−0.229012	−	0.396661i
$839$	−43.0393	+	5.03057i	−1.48588	+	0.173675i	−0.819992	−	0.572376i	$-0.806022\pi$
$839$	−43.0393	+	5.03057i	−1.48588	+	0.173675i	−0.665890	+	0.746050i	$0.731948\pi$
$840$		0			0
$841$	−1.06387	+	0.252142i	−0.0366852	+	0.00869456i
$842$	5.09855	+	87.5388i	0.175708	+	3.01679i
$843$		0			0
$844$	−23.6156	−	5.59700i	−0.812883	−	0.192657i
$845$	−0.695063	+	3.94190i	−0.0239109	+	0.135605i
$846$		0			0
$847$	9.19255	+	52.1335i	0.315860	+	1.79133i
$848$	0.0403892	−	0.693456i	0.00138697	−	0.0238134i
$849$		0			0
$850$	18.0639	−	24.2641i	0.619588	−	0.832251i
$851$	−27.6419	+	37.1296i	−0.947553	+	1.27279i
$852$		0			0
$853$	−0.743310	+	12.7621i	−0.0254505	+	0.436967i	0.961382	+	0.275219i	$0.0887504\pi$
$853$	−0.743310	+	12.7621i	−0.0254505	+	0.436967i	−0.986832	+	0.161748i	$0.948287\pi$
$854$	−17.1441	−	97.2292i	−0.586660	−	3.32711i
$855$		0			0
$856$	2.10213	−	11.9217i	0.0718492	−	0.407477i
$857$	−18.8191	−	4.46020i	−0.642847	−	0.152357i	−0.103753	−	0.994603i	$-0.533085\pi$
$857$	−18.8191	−	4.46020i	−0.642847	−	0.152357i	−0.539094	+	0.842246i	$0.681233\pi$
$858$		0			0
$859$	−1.53806	−	26.4074i	−0.0524778	−	0.901009i	−0.917118	−	0.398616i	$-0.869490\pi$
$859$	−1.53806	−	26.4074i	−0.0524778	−	0.901009i	0.864640	−	0.502392i	$-0.167547\pi$
$860$	−10.9009	+	2.58356i	−0.371718	+	0.0880987i
$861$		0			0
$862$	−0.456806	+	0.0533930i	−0.0155589	+	0.00181857i
$863$	1.63147	+	2.82580i	0.0555360	+	0.0961912i	0.892457	−	0.451133i	$-0.148980\pi$
$863$	1.63147	+	2.82580i	0.0555360	+	0.0961912i	−0.836921	+	0.547324i	$0.815647\pi$
$864$		0			0
$865$	1.36575	−	2.36556i	0.0464370	−	0.0804313i
$866$	7.26161	−	16.8343i	0.246759	−	0.572053i
$867$		0			0
$868$	−24.3694	−	25.8300i	−0.827151	−	0.876729i
$869$	56.0355	+	28.1421i	1.90087	+	0.954655i
$870$		0			0
$871$	4.24013	+	14.1630i	0.143671	+	0.479896i
$872$	−7.97041	−	6.68796i	−0.269912	−	0.226483i
$873$		0			0
$874$	−5.35219	+	4.49102i	−0.181040	+	0.151911i
$875$	18.0362	+	11.8626i	0.609735	+	0.401029i
$876$		0			0
$877$	39.8744	+	4.66065i	1.34646	+	0.157379i	0.758587	−	0.651572i	$-0.225890\pi$
$877$	39.8744	+	4.66065i	1.34646	+	0.157379i	0.587876	+	0.808951i	$0.299964\pi$
$878$	1.96911	+	4.56490i	0.0664541	+	0.154058i
$879$		0			0
$880$	−0.733646	+	0.368451i	−0.0247312	+	0.0124205i
$881$	−42.6866	−	15.5367i	−1.43815	−	0.523443i	−0.498894	−	0.866663i	$-0.666260\pi$
$881$	−42.6866	−	15.5367i	−1.43815	−	0.523443i	−0.939255	+	0.343220i	$0.888482\pi$
$882$		0			0
$883$	28.0681	−	10.2160i	0.944567	−	0.343794i	0.176599	−	0.984283i	$-0.443490\pi$
$883$	28.0681	−	10.2160i	0.944567	−	0.343794i	0.767968	+	0.640488i	$0.221268\pi$
$884$	15.4617	−	16.3884i	0.520033	−	0.551203i
$885$		0			0
$886$	−61.4858	+	40.4399i	−2.06566	+	1.35860i
$887$	7.99268	−	26.6974i	0.268368	−	0.896412i	−0.712489	−	0.701683i	$-0.752432\pi$
$887$	7.99268	−	26.6974i	0.268368	−	0.896412i	0.980857	−	0.194729i	$-0.0623826\pi$
$888$		0			0
$889$	−18.6397	−	25.0374i	−0.625154	−	0.839728i
$890$	0.461102			0.0154562
$891$		0			0
$892$	−26.8317			−0.898391
$893$	−1.64189	−	2.20545i	−0.0549439	−	0.0738025i
$894$		0			0
$895$	−0.584524	+	1.95245i	−0.0195385	+	0.0652631i
$896$	−56.2313	+	36.9839i	−1.87856	+	1.23555i
$897$		0			0
$898$	60.6548	−	64.2904i	2.02408	−	2.14540i
$899$	−14.5858	+	5.30879i	−0.486463	+	0.177058i
$900$		0			0
$901$	−6.65155	−	2.42097i	−0.221595	−	0.0806541i
$902$	−37.0180	+	18.5911i	−1.23256	+	0.619017i
$903$		0			0
$904$	−13.7699	−	31.9222i	−0.457980	−	1.06172i
$905$	8.91412	+	1.04191i	0.296315	+	0.0346343i
$906$		0			0
$907$	23.0222	+	15.1420i	0.764440	+	0.502780i	0.870854	−	0.491542i	$-0.163566\pi$
$907$	23.0222	+	15.1420i	0.764440	+	0.502780i	−0.106414	+	0.994322i	$0.533937\pi$
$908$	−64.9832	+	54.5274i	−2.15654	+	1.80955i
$909$		0			0
$910$	9.68303	+	8.12503i	0.320989	+	0.269342i
$911$	−1.76347	−	5.89040i	−0.0584263	−	0.195157i	0.923794	−	0.382890i	$-0.125071\pi$
$911$	−1.76347	−	5.89040i	−0.0584263	−	0.195157i	−0.982220	+	0.187733i	$0.939886\pi$
$912$		0			0
$913$	−9.35544	−	4.69848i	−0.309620	−	0.155497i
$914$	−46.0811	−	48.8431i	−1.52423	−	1.61558i
$915$		0			0
$916$	−3.86849	+	8.96817i	−0.127819	+	0.296317i
$917$	−3.30614	+	5.72640i	−0.109178	+	0.189102i
$918$		0			0
$919$	−8.38084	−	14.5160i	−0.276459	−	0.478840i	0.694044	−	0.719933i	$-0.255828\pi$
$919$	−8.38084	−	14.5160i	−0.276459	−	0.478840i	−0.970502	+	0.241093i	$0.922494\pi$
$920$	11.4345	−	1.33651i	0.376986	−	0.0440633i
$921$		0			0
$922$	−47.6334	+	11.2893i	−1.56872	+	0.371794i
$923$	0.408374	+	7.01151i	0.0134418	+	0.230787i
$924$		0			0
$925$	28.5048	+	6.75577i	0.937233	+	0.222128i
$926$	13.7988	−	78.2572i	0.453458	−	2.57169i
$927$		0			0
$928$	5.47713	+	31.0624i	0.179796	+	1.01967i
$929$	3.18881	−	54.7498i	0.104621	−	1.79628i	−0.383536	−	0.923526i	$-0.625294\pi$
$929$	3.18881	−	54.7498i	0.104621	−	1.79628i	0.488158	−	0.872755i	$-0.337669\pi$
$930$		0			0
$931$	1.87357	−	2.51664i	0.0614038	−	0.0824796i
$932$	13.4600	−	18.0799i	0.440897	−	0.592228i
$933$		0			0
$934$	−3.32073	+	57.0147i	−0.108657	+	1.86558i
$935$	1.45272	+	8.23876i	0.0475089	+	0.269436i
$936$		0			0
$937$	2.62965	−	14.9135i	0.0859070	−	0.487203i	−0.911250	−	0.411853i	$-0.864882\pi$
$937$	2.62965	−	14.9135i	0.0859070	−	0.487203i	0.997157	−	0.0753496i	$-0.0240073\pi$
$938$	−50.1390	−	11.8832i	−1.63710	−	0.387999i
$939$		0			0
$940$	0.712771	+	12.2378i	0.0232480	+	0.399153i
$941$	20.3114	−	4.81388i	0.662131	−	0.156928i	0.114208	−	0.993457i	$-0.463567\pi$
$941$	20.3114	−	4.81388i	0.662131	−	0.156928i	0.547923	+	0.836529i	$0.315419\pi$
$942$		0			0
$943$	−26.6723	+	3.11755i	−0.868571	+	0.101521i
$944$	−0.649591	−	1.12512i	−0.0211424	−	0.0366197i
$945$		0			0
$946$	−34.1403	+	59.1328i	−1.11000	+	1.92257i
$947$	−20.0506	+	46.4826i	−0.651558	+	1.51048i	0.196458	+	0.980512i	$0.437056\pi$
$947$	−20.0506	+	46.4826i	−0.651558	+	1.51048i	−0.848016	+	0.529970i	$0.822203\pi$
$948$		0			0
$949$	−23.4340	−	24.8385i	−0.760699	−	0.806293i
$950$	3.95133	+	1.98443i	0.128198	+	0.0643835i
$951$		0			0
$952$	8.32370	+	27.8031i	0.269773	+	0.901103i
$953$	−41.7445	−	35.0278i	−1.35224	−	1.13466i	−0.978297	−	0.207208i	$-0.933562\pi$
$953$	−41.7445	−	35.0278i	−1.35224	−	1.13466i	−0.373940	−	0.927453i	$-0.621993\pi$
$954$		0			0
$955$	−10.0647	+	8.44532i	−0.325687	+	0.273284i
$956$	12.1555	+	7.99482i	0.393138	+	0.258571i
$957$		0			0
$958$	−22.1644	−	2.59065i	−0.716101	−	0.0837002i
$959$	4.14651	+	9.61270i	0.133898	+	0.310410i
$960$		0			0
$961$	−19.9876	+	10.0381i	−0.644760	+	0.323811i
$962$	33.4294	+	12.1673i	1.07781	+	0.392290i
$963$		0			0
$964$	−18.3558	+	6.68097i	−0.591201	+	0.215180i
$965$	2.60689	−	2.76314i	0.0839188	−	0.0889487i
$966$		0			0
$967$	−34.4019	+	22.6265i	−1.10629	+	0.727618i	−0.964974	−	0.262346i	$-0.915504\pi$
$967$	−34.4019	+	22.6265i	−1.10629	+	0.727618i	−0.141316	+	0.989965i	$0.545133\pi$
$968$	10.6273	−	35.4975i	0.341573	−	1.14093i
$969$		0			0
$970$	−8.74406	−	11.7453i	−0.280755	−	0.377119i
$971$	−9.59297			−0.307853			−0.153927	−	0.988082i	$-0.549192\pi$
$971$	−9.59297			−0.307853			−0.153927	+	0.988082i	$0.549192\pi$
$972$		0			0
$973$	32.9685			1.05692
$974$	23.1313	+	31.0707i	0.741173	+	0.995569i
$975$		0			0
$976$	0.916258	−	3.06051i	0.0293287	−	0.0979647i
$977$	−12.6018	+	8.28830i	−0.403166	+	0.265166i	−0.734858	−	0.678222i	$-0.762751\pi$
$977$	−12.6018	+	8.28830i	−0.403166	+	0.265166i	0.331692	+	0.943388i	$0.392381\pi$
$978$		0			0
$979$	1.18288	−	1.25378i	0.0378051	−	0.0400711i
$980$	−13.1447	+	4.78426i	−0.419890	+	0.152828i
$981$		0			0
$982$	−17.9721	−	6.54131i	−0.573513	−	0.208741i
$983$	−50.0611	+	25.1417i	−1.59670	+	0.801894i	−1.00000		0.000568285i	$-0.999819\pi$
$983$	−50.0611	+	25.1417i	−1.59670	+	0.801894i	−0.596703	+	0.802462i	$0.703523\pi$
$984$		0			0
$985$	−1.28682	−	2.98318i	−0.0410014	−	0.0950520i
$986$	34.0923	+	3.98482i	1.08572	+	0.126903i
$987$		0			0
$988$	2.75157	+	1.80974i	0.0875392	+	0.0575755i
$989$	−33.9083	+	28.4524i	−1.07822	+	0.904734i
$990$		0			0
$991$	14.6989	+	12.3338i	0.466925	+	0.391796i	0.845671	−	0.533704i	$-0.179200\pi$
$991$	14.6989	+	12.3338i	0.466925	+	0.391796i	−0.378747	+	0.925500i	$0.623645\pi$
$992$	−5.03156	−	16.8066i	−0.159752	−	0.533610i
$993$		0			0
$994$	−21.8753	−	10.9862i	−0.693842	−	0.348460i
$995$	6.76679	+	7.17238i	0.214522	+	0.227380i
$996$		0			0
$997$	12.7363	−	29.5261i	0.403363	−	0.935101i	−0.588582	−	0.808437i	$-0.700314\pi$
$997$	12.7363	−	29.5261i	0.403363	−	0.935101i	0.991946	−	0.126664i	$-0.0404270\pi$
$998$	27.4768	−	47.5913i	0.869764	−	1.50648i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.b.541.1		144
3.2	odd	2		729.2.g.c.541.8		144
9.2	odd	6		729.2.g.d.55.8		144
9.4	even	3		243.2.g.a.19.8		144
9.5	odd	6		81.2.g.a.61.1	yes	144
9.7	even	3		729.2.g.a.55.1		144
81.4	even	27		729.2.g.a.676.1		144
81.23	odd	54		729.2.g.c.190.8		144
81.25	even	27		6561.2.a.d.1.5		72
81.31	even	27		243.2.g.a.64.8		144
81.50	odd	54		81.2.g.a.4.1	✓	144
81.56	odd	54		6561.2.a.c.1.68		72
81.58	even	27	inner	729.2.g.b.190.1		144
81.77	odd	54		729.2.g.d.676.8		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.1	✓	144	81.50	odd	54
81.2.g.a.61.1	yes	144	9.5	odd	6
243.2.g.a.19.8		144	9.4	even	3
243.2.g.a.64.8		144	81.31	even	27
729.2.g.a.55.1		144	9.7	even	3
729.2.g.a.676.1		144	81.4	even	27
729.2.g.b.190.1		144	81.58	even	27	inner
729.2.g.b.541.1		144	1.1	even	1	trivial
729.2.g.c.190.8		144	81.23	odd	54
729.2.g.c.541.8		144	3.2	odd	2
729.2.g.d.55.8		144	9.2	odd	6
729.2.g.d.676.8		144	81.77	odd	54
6561.2.a.c.1.68		72	81.56	odd	54
6561.2.a.d.1.5		72	81.25	even	27

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)

\(f(q)\)	\(=\)	\(q+(-1.35812 - 1.82427i) q^{2} +(-0.909876 + 3.03920i) q^{4} +(-0.490328 + 0.322494i) q^{5} +(-2.61431 + 2.77101i) q^{7} +(2.50575 - 0.912019i) q^{8} +O(q^{10})\)	\(q+(-1.35812 - 1.82427i) q^{2} +(-0.909876 + 3.03920i) q^{4} +(-0.490328 + 0.322494i) q^{5} +(-2.61431 + 2.77101i) q^{7} +(2.50575 - 0.912019i) q^{8} +(1.25424 + 0.456507i) q^{10} +(4.45885 - 2.23932i) q^{11} +(-0.984610 - 2.28258i) q^{13} +(8.60563 + 1.00585i) q^{14} +(0.234238 + 0.154061i) q^{16} +(2.18854 - 1.83640i) q^{17} +(0.319901 + 0.268429i) q^{19} +(-0.533984 - 1.78363i) q^{20} +(-10.1408 - 5.09290i) q^{22} +(-5.04828 - 5.35087i) q^{23} +(-1.84398 + 4.27482i) q^{25} +(-2.82684 + 4.89622i) q^{26} +(-6.04293 - 10.4667i) q^{28} +(-5.24696 + 0.613281i) q^{29} +(2.85906 - 0.677609i) q^{31} +(-0.347168 - 5.96065i) q^{32} +(-6.32240 - 1.49844i) q^{34} +(0.388237 - 2.20180i) q^{35} +(-1.09265 - 6.19675i) q^{37} +(0.0552232 - 0.948146i) q^{38} +(-0.934519 + 1.25528i) q^{40} +(2.17987 - 2.92807i) q^{41} +(0.349862 - 6.00689i) q^{43} +(2.74873 + 15.5888i) q^{44} +(-2.90527 + 16.4766i) q^{46} +(-6.40659 - 1.51839i) q^{47} +(-0.436847 - 7.50038i) q^{49} +(10.3028 - 2.44181i) q^{50} +(7.83309 - 0.915557i) q^{52} +(-1.23882 - 2.14569i) q^{53} +(-1.46413 + 2.53595i) q^{55} +(-4.02360 + 9.32775i) q^{56} +(8.24480 + 8.73898i) q^{58} +(-4.14106 - 2.07972i) q^{59} +(-3.26814 - 10.9163i) q^{61} +(-5.11909 - 4.29543i) q^{62} +(-9.97283 + 8.36820i) q^{64} +(1.21890 + 0.801684i) q^{65} +(-5.90700 - 0.690429i) q^{67} +(3.58989 + 8.32230i) q^{68} +(-4.54396 + 2.28206i) q^{70} +(-2.65492 - 0.966311i) q^{71} +(12.9084 - 4.69828i) q^{73} +(-9.82061 + 10.4092i) q^{74} +(-1.10688 + 0.728005i) q^{76} +(-5.45165 + 18.2098i) q^{77} +(7.50465 + 10.0805i) q^{79} -0.164537 q^{80} -8.30214 q^{82} +(-1.25294 - 1.68299i) q^{83} +(-0.480874 + 1.60623i) q^{85} +(-11.4334 + 7.51985i) q^{86} +(9.13046 - 9.67772i) q^{88} +(0.324629 - 0.118155i) q^{89} +(8.89913 + 3.23902i) q^{91} +(20.8556 - 10.4741i) q^{92} +(5.93097 + 13.7495i) q^{94} +(-0.243423 - 0.0284521i) q^{95} +(-9.16575 - 6.02841i) q^{97} +(-13.0895 + 10.9834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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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