LMFDB - Embedded newform 729.2.i.a.10.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(10,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(162))

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

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

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

chi := DirichletCharacter("729.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, 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:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.20
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58827 + 0.248401i) q^{2} +(0.556399 + 0.178402i) q^{4} +(-0.870960 - 0.395900i) q^{5} +(-0.334115 - 2.44616i) q^{7} +(-2.03377 - 1.02140i) q^{8} +O(q^{10})$	\(q+(1.58827 + 0.248401i) q^{2} +(0.556399 + 0.178402i) q^{4} +(-0.870960 - 0.395900i) q^{5} +(-0.334115 - 2.44616i) q^{7} +(-2.03377 - 1.02140i) q^{8} +(-1.28498 - 0.845142i) q^{10} +(-2.87435 + 0.223412i) q^{11} +(-1.32760 - 3.88005i) q^{13} +(0.0769621 - 3.96815i) q^{14} +(-3.92717 - 2.80697i) q^{16} +(1.88253 - 4.36419i) q^{17} +(0.182965 - 0.245765i) q^{19} +(-0.413972 - 0.375659i) q^{20} +(-4.62074 - 0.359152i) q^{22} +(6.26337 + 4.85448i) q^{23} +(-2.68577 - 3.07755i) q^{25} +(-1.14478 - 6.49235i) q^{26} +(0.250498 - 1.42064i) q^{28} +(-2.90539 + 1.75341i) q^{29} +(7.87188 - 0.305465i) q^{31} +(-2.29057 - 2.24657i) q^{32} +(4.07402 - 6.46388i) q^{34} +(-0.677432 + 2.26278i) q^{35} +(-3.80493 + 4.03299i) q^{37} +(0.351646 - 0.344892i) q^{38} +(1.36696 + 1.69477i) q^{40} +(-0.445117 + 1.15288i) q^{41} +(-0.557653 - 2.16494i) q^{43} +(-1.63914 - 0.388484i) q^{44} +(8.74206 + 9.26605i) q^{46} +(-8.23233 - 0.319452i) q^{47} +(0.871553 - 0.242613i) q^{49} +(-3.50126 - 5.55513i) q^{50} +(-0.0464646 - 2.39570i) q^{52} +(-0.120579 + 0.0438871i) q^{53} +(2.59189 + 0.943372i) q^{55} +(-1.81898 + 5.31618i) q^{56} +(-5.05008 + 2.06319i) q^{58} +(-4.69182 - 9.81212i) q^{59} +(0.781070 - 0.250440i) q^{61} +(12.5785 + 1.47022i) q^{62} +(2.68522 + 3.60687i) q^{64} +(-0.379828 + 3.90497i) q^{65} +(10.7586 + 6.49283i) q^{67} +(1.82601 - 2.09238i) q^{68} +(-1.63802 + 3.42563i) q^{70} +(0.764363 - 13.1236i) q^{71} +(10.8084 - 7.10878i) q^{73} +(-7.04504 + 5.46032i) q^{74} +(0.145647 - 0.104102i) q^{76} +(1.50687 + 6.95646i) q^{77} +(0.774819 - 0.960625i) q^{79} +(2.30913 + 3.99953i) q^{80} +(-0.993343 + 1.72052i) q^{82} +(0.738540 + 1.91287i) q^{83} +(-3.36739 + 3.05574i) q^{85} +(-0.347930 - 3.57703i) q^{86} +(6.07396 + 2.48149i) q^{88} +(0.471041 + 8.08746i) q^{89} +(-9.04765 + 4.54390i) q^{91} +(2.61888 + 3.81843i) q^{92} +(-12.9958 - 2.55229i) q^{94} +(-0.256654 + 0.141616i) q^{95} +(-8.85687 + 4.02594i) q^{97} +(1.44453 - 0.168841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

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 $

$2$	1.58827	+	0.248401i	1.12308	+	0.175646i	0.688672	−	0.725073i	$-0.258194\pi$
$2$	1.58827	+	0.248401i	1.12308	+	0.175646i	0.434403	+	0.900719i	$0.356959\pi$
$3$		0			0
$3$		0			0
$4$	0.556399	+	0.178402i	0.278199	+	0.0892010i
$5$	−0.870960	−	0.395900i	−0.389505	−	0.177052i	0.209478	−	0.977813i	$-0.432823\pi$
$5$	−0.870960	−	0.395900i	−0.389505	−	0.177052i	−0.598983	+	0.800762i	$0.704428\pi$
$6$		0			0
$7$	−0.334115	−	2.44616i	−0.126284	−	0.924560i	−0.939488	−	0.342582i	$-0.888699\pi$
$7$	−0.334115	−	2.44616i	−0.126284	−	0.924560i	0.813204	−	0.581978i	$-0.197721\pi$
$8$	−2.03377	−	1.02140i	−0.719046	−	0.361118i
$9$		0			0
$10$	−1.28498	−	0.845142i	−0.406345	−	0.267257i
$11$	−2.87435	+	0.223412i	−0.866650	+	0.0673613i	−0.503115	−	0.864219i	$-0.667813\pi$
$11$	−2.87435	+	0.223412i	−0.866650	+	0.0673613i	−0.363534	+	0.931581i	$0.618430\pi$
$12$		0			0
$13$	−1.32760	−	3.88005i	−0.368210	−	1.07613i	−0.962360	−	0.271779i	$-0.912388\pi$
$13$	−1.32760	−	3.88005i	−0.368210	−	1.07613i	0.594150	−	0.804354i	$-0.297489\pi$
$14$	0.0769621	−	3.96815i	0.0205690	−	1.06053i
$15$		0			0
$16$	−3.92717	−	2.80697i	−0.981793	−	0.701744i
$17$	1.88253	−	4.36419i	0.456580	−	1.05847i	−0.522064	−	0.852906i	$-0.674838\pi$
$17$	1.88253	−	4.36419i	0.456580	−	1.05847i	0.978644	−	0.205564i	$-0.0659030\pi$
$18$		0			0
$19$	0.182965	−	0.245765i	0.0419751	−	0.0563824i	−0.780640	−	0.624981i	$-0.785107\pi$
$19$	0.182965	−	0.245765i	0.0419751	−	0.0563824i	0.822615	+	0.568598i	$0.192514\pi$
$20$	−0.413972	−	0.375659i	−0.0925668	−	0.0839999i
$21$		0			0
$22$	−4.62074	−	0.359152i	−0.985145	−	0.0765715i
$23$	6.26337	+	4.85448i	1.30600	+	1.01223i	0.998150	+	0.0607956i	$0.0193638\pi$
$23$	6.26337	+	4.85448i	1.30600	+	1.01223i	0.307854	+	0.951434i	$0.400389\pi$
$24$		0			0
$25$	−2.68577	−	3.07755i	−0.537154	−	0.615511i
$26$	−1.14478	−	6.49235i	−0.224509	−	1.27325i
$27$		0			0
$28$	0.250498	−	1.42064i	0.0473397	−	0.268477i
$29$	−2.90539	+	1.75341i	−0.539517	+	0.325600i	−0.760140	−	0.649759i	$-0.774870\pi$
$29$	−2.90539	+	1.75341i	−0.539517	+	0.325600i	0.220624	+	0.975359i	$0.429191\pi$
$30$		0			0
$31$	7.87188	−	0.305465i	1.41383	−	0.0548631i	0.679511	−	0.733666i	$-0.262192\pi$
$31$	7.87188	−	0.305465i	1.41383	−	0.0548631i	0.734321	+	0.678803i	$0.237501\pi$
$32$	−2.29057	−	2.24657i	−0.404919	−	0.397141i
$33$		0			0
$34$	4.07402	−	6.46388i	0.698689	−	1.10855i
$35$	−0.677432	+	2.26278i	−0.114507	+	0.382480i
$36$		0			0
$37$	−3.80493	+	4.03299i	−0.625526	+	0.663019i	−0.960199	−	0.279315i	$-0.909893\pi$
$37$	−3.80493	+	4.03299i	−0.625526	+	0.663019i	0.334673	+	0.942334i	$0.391374\pi$
$38$	0.351646	−	0.344892i	0.0570446	−	0.0559489i
$39$		0			0
$40$	1.36696	+	1.69477i	0.216135	+	0.267966i
$41$	−0.445117	+	1.15288i	−0.0695156	+	0.180050i	−0.963288	−	0.268472i	$-0.913481\pi$
$41$	−0.445117	+	1.15288i	−0.0695156	+	0.180050i	0.893772	+	0.448522i	$0.148049\pi$
$42$		0			0
$43$	−0.557653	−	2.16494i	−0.0850413	−	0.330151i	0.911696	−	0.410866i	$-0.134773\pi$
$43$	−0.557653	−	2.16494i	−0.0850413	−	0.330151i	−0.996737	+	0.0807150i	$0.974280\pi$
$44$	−1.63914	−	0.388484i	−0.247110	−	0.0585661i
$45$		0			0
$46$	8.74206	+	9.26605i	1.28895	+	1.36620i
$47$	−8.23233	−	0.319452i	−1.20081	−	0.0465968i	−0.569409	−	0.822055i	$-0.692828\pi$
$47$	−8.23233	−	0.319452i	−1.20081	−	0.0465968i	−0.631399	+	0.775458i	$0.717519\pi$
$48$		0			0
$49$	0.871553	−	0.242613i	0.124508	−	0.0346590i
$50$	−3.50126	−	5.55513i	−0.495153	−	0.785614i
$51$		0			0
$52$	−0.0464646	−	2.39570i	−0.00644348	−	0.332224i
$53$	−0.120579	+	0.0438871i	−0.0165628	+	0.00602836i	−0.350288	−	0.936642i	$-0.613916\pi$
$53$	−0.120579	+	0.0438871i	−0.0165628	+	0.00602836i	0.333725	+	0.942670i	$0.391694\pi$
$54$		0			0
$55$	2.59189	+	0.943372i	0.349491	+	0.127204i
$56$	−1.81898	+	5.31618i	−0.243072	+	0.710404i
$57$		0			0
$58$	−5.05008	+	2.06319i	−0.663108	+	0.270910i
$59$	−4.69182	−	9.81212i	−0.610823	−	1.27743i	−0.942554	−	0.334055i	$-0.891583\pi$
$59$	−4.69182	−	9.81212i	−0.610823	−	1.27743i	0.331730	−	0.943374i	$-0.392368\pi$
$60$		0			0
$61$	0.781070	−	0.250440i	0.100006	−	0.0320656i	−0.254902	−	0.966967i	$-0.582043\pi$
$61$	0.781070	−	0.250440i	0.100006	−	0.0320656i	0.354908	+	0.934901i	$0.384512\pi$
$62$	12.5785	+	1.47022i	1.59748	+	0.186718i
$63$		0			0
$64$	2.68522	+	3.60687i	0.335652	+	0.450859i
$65$	−0.379828	+	3.90497i	−0.0471118	+	0.484352i
$66$		0			0
$67$	10.7586	+	6.49283i	1.31437	+	0.793225i	0.988359	−	0.152141i	$-0.0486168\pi$
$67$	10.7586	+	6.49283i	1.31437	+	0.793225i	0.326010	+	0.945366i	$0.394296\pi$
$68$	1.82601	−	2.09238i	0.221437	−	0.253738i
$69$		0			0
$70$	−1.63802	+	3.42563i	−0.195781	+	0.409441i
$71$	0.764363	−	13.1236i	0.0907132	−	1.55748i	−0.579287	−	0.815124i	$-0.696669\pi$
$71$	0.764363	−	13.1236i	0.0907132	−	1.55748i	0.670000	−	0.742361i	$-0.266294\pi$
$72$		0			0
$73$	10.8084	−	7.10878i	1.26502	−	0.832020i	0.273491	−	0.961874i	$-0.411821\pi$
$73$	10.8084	−	7.10878i	1.26502	−	0.832020i	0.991533	+	0.129855i	$0.0414511\pi$
$74$	−7.04504	+	5.46032i	−0.818969	+	0.634749i
$75$		0			0
$76$	0.145647	−	0.104102i	0.0167068	−	0.0119413i
$77$	1.50687	+	6.95646i	0.171723	+	0.792763i
$78$		0			0
$79$	0.774819	−	0.960625i	0.0871740	−	0.108079i	−0.732900	−	0.680337i	$-0.761834\pi$
$79$	0.774819	−	0.960625i	0.0871740	−	0.108079i	0.820074	+	0.572258i	$0.193932\pi$
$80$	2.30913	+	3.99953i	0.258169	+	0.447161i
$81$		0			0
$82$	−0.993343	+	1.72052i	−0.109696	+	0.190000i
$83$	0.738540	+	1.91287i	0.0810652	+	0.209964i	0.967490	−	0.252908i	$-0.0813869\pi$
$83$	0.738540	+	1.91287i	0.0810652	+	0.209964i	−0.886425	+	0.462872i	$0.846819\pi$
$84$		0			0
$85$	−3.36739	+	3.05574i	−0.365244	+	0.331441i
$86$	−0.347930	−	3.57703i	−0.0375182	−	0.385721i
$87$		0			0
$88$	6.07396	+	2.48149i	0.647486	+	0.264527i
$89$	0.471041	+	8.08746i	0.0499303	+	0.857270i	0.926570	+	0.376122i	$0.122743\pi$
$89$	0.471041	+	8.08746i	0.0499303	+	0.857270i	−0.876640	+	0.481147i	$0.840220\pi$
$90$		0			0
$91$	−9.04765	+	4.54390i	−0.948451	+	0.476330i
$92$	2.61888	+	3.81843i	0.273037	+	0.398098i
$93$		0			0
$94$	−12.9958	−	2.55229i	−1.34041	−	0.263249i
$95$	−0.256654	+	0.141616i	−0.0263321	+	0.0145295i
$96$		0			0
$97$	−8.85687	+	4.02594i	−0.899279	+	0.408773i	−0.809453	−	0.587185i	$-0.800236\pi$
$97$	−8.85687	+	4.02594i	−0.899279	+	0.408773i	−0.0898264	+	0.995957i	$0.528631\pi$
$98$	1.44453	−	0.168841i	0.145919	−	0.0170555i
$99$		0			0
$100$	−0.945318	−	2.19149i	−0.0945318	−	0.219149i
$101$	−2.38332	+	11.0026i	−0.237149	+	1.09480i	0.691075	+	0.722783i	$0.257137\pi$
$101$	−2.38332	+	11.0026i	−0.237149	+	1.09480i	−0.928225	+	0.372020i	$0.878665\pi$
$102$		0			0
$103$	8.35148	−	12.1768i	0.822896	−	1.19981i	−0.154416	−	0.988006i	$-0.549350\pi$
$103$	8.35148	−	12.1768i	0.822896	−	1.19981i	0.977312	−	0.211805i	$-0.0679343\pi$
$104$	−1.26305	+	9.24714i	−0.123852	+	0.906757i
$105$		0			0
$106$	−0.202413	+	0.0397527i	−0.0196601	+	0.00386112i
$107$	−4.12013	+	3.45720i	−0.398308	+	0.334220i	−0.819839	−	0.572594i	$-0.805937\pi$
$107$	−4.12013	+	3.45720i	−0.398308	+	0.334220i	0.421531	+	0.906814i	$0.361493\pi$
$108$		0			0
$109$	7.77236	+	6.52179i	0.744457	+	0.624674i	0.934031	−	0.357193i	$-0.116266\pi$
$109$	7.77236	+	6.52179i	0.744457	+	0.624674i	−0.189573	+	0.981867i	$0.560710\pi$
$110$	3.88229	+	2.14216i	0.370162	+	0.204247i
$111$		0			0
$112$	−5.55417	+	10.5443i	−0.524820	+	0.996345i
$113$	0.153311	−	0.595190i	0.0144223	−	0.0559908i	−0.960774	−	0.277332i	$-0.910550\pi$
$113$	0.153311	−	0.595190i	0.0144223	−	0.0559908i	0.975196	+	0.221341i	$0.0710435\pi$
$114$		0			0
$115$	−3.53326	−	6.70773i	−0.329478	−	0.625499i
$116$	−1.92936	+	0.457268i	−0.179137	+	0.0424563i
$117$		0			0
$118$	−5.01454	−	16.7497i	−0.461626	−	1.54194i
$119$	−11.3045	−	3.14681i	−1.03628	−	0.288468i
$120$		0			0
$121$	−2.65591	+	0.415376i	−0.241446	+	0.0377615i
$122$	1.30276	−	0.203748i	0.117946	−	0.0184465i
$123$		0			0
$124$	4.43440	+	1.23440i	0.398221	+	0.110852i
$125$	2.49274	+	8.32635i	0.222958	+	0.744731i
$126$		0			0
$127$	3.12700	−	0.741112i	0.277476	−	0.0657630i	−0.0895217	−	0.995985i	$-0.528534\pi$
$127$	3.12700	−	0.741112i	0.277476	−	0.0657630i	0.366998	+	0.930222i	$0.380386\pi$
$128$	6.35940	+	12.0730i	0.562096	+	1.06711i
$129$		0			0
$130$	−1.57326	+	6.10779i	−0.137984	+	0.535689i
$131$	8.23352	−	15.6309i	0.719366	−	1.36568i	−0.202929	−	0.979194i	$-0.565046\pi$
$131$	8.23352	−	15.6309i	0.719366	−	1.36568i	0.922294	−	0.386488i	$-0.126312\pi$
$132$		0			0
$133$	−0.662311	−	0.365448i	−0.0574297	−	0.0316883i
$134$	15.4747	+	12.9848i	1.33681	+	1.12172i
$135$		0			0
$136$	−8.28619	+	6.95294i	−0.710535	+	0.596210i
$137$	14.4101	−	2.83006i	1.23114	−	0.241788i	0.465495	−	0.885051i	$-0.345876\pi$
$137$	14.4101	−	2.83006i	1.23114	−	0.241788i	0.765646	+	0.643262i	$0.222420\pi$
$138$		0			0
$139$	−2.32648	+	17.0328i	−0.197329	+	1.44471i	0.579488	+	0.814981i	$0.303252\pi$
$139$	−2.32648	+	17.0328i	−0.197329	+	1.44471i	−0.776818	+	0.629726i	$0.783167\pi$
$140$	−0.780606	+	1.13815i	−0.0659733	+	0.0961914i
$141$		0			0
$142$	4.47392	−	20.6539i	0.375443	−	1.73324i
$143$	4.68284	+	10.8560i	0.391599	+	0.907828i
$144$		0			0
$145$	3.22465	−	0.376907i	0.267793	−	0.0313005i
$146$	18.9324	−	8.60584i	1.56686	−	0.712225i
$147$		0			0
$148$	−2.83655	+	1.56514i	−0.233163	+	0.128654i
$149$	−12.8830	−	2.53014i	−1.05542	−	0.207277i	−0.365238	−	0.930914i	$-0.619012\pi$
$149$	−12.8830	−	2.53014i	−1.05542	−	0.207277i	−0.690181	+	0.723637i	$0.742469\pi$
$150$		0			0
$151$	−9.10660	−	13.2777i	−0.741084	−	1.08053i	−0.993602	−	0.112935i	$-0.963975\pi$
$151$	−9.10660	−	13.2777i	−0.741084	−	1.08053i	0.252518	−	0.967592i	$-0.418741\pi$
$152$	−0.623133	+	0.312949i	−0.0505428	+	0.0253835i
$153$		0			0
$154$	0.665316	+	11.4230i	0.0536127	+	0.920495i
$155$	−6.97702	−	2.85043i	−0.560408	−	0.228952i
$156$		0			0
$157$	0.521833	+	5.36492i	0.0416468	+	0.428167i	0.992830	+	0.119539i	$0.0381415\pi$
$157$	0.521833	+	5.36492i	0.0416468	+	0.428167i	−0.951183	+	0.308628i	$0.900130\pi$
$158$	1.46924	−	1.33326i	0.116887	−	0.106069i
$159$		0			0
$160$	1.10557	+	2.86351i	0.0874033	+	0.226380i
$161$	9.78213	−	16.9431i	0.770940	−	1.33531i
$162$		0			0
$163$	−2.64710	−	4.58491i	−0.207337	−	0.359118i	0.743538	−	0.668694i	$-0.233146\pi$
$163$	−2.64710	−	4.58491i	−0.207337	−	0.359118i	−0.950875	+	0.309576i	$0.899813\pi$
$164$	−0.453339	+	0.562052i	−0.0353998	+	0.0438889i
$165$		0			0
$166$	0.697842	+	3.22160i	0.0541631	+	0.250044i
$167$	−0.949486	+	0.678652i	−0.0734734	+	0.0525156i	−0.617636	−	0.786464i	$-0.711909\pi$
$167$	−0.949486	+	0.678652i	−0.0734734	+	0.0525156i	0.544162	+	0.838980i	$0.316848\pi$
$168$		0			0
$169$	−3.01720	+	2.33851i	−0.232092	+	0.179885i
$170$	−6.10736	+	4.01687i	−0.468413	+	0.308080i
$171$		0			0
$172$	0.0759527	−	1.30406i	0.00579134	−	0.0994334i
$173$	4.22792	−	8.84195i	0.321443	−	0.672241i	−0.676494	−	0.736449i	$-0.736501\pi$
$173$	4.22792	−	8.84195i	0.321443	−	0.672241i	0.997937	+	0.0642076i	$0.0204520\pi$
$174$		0			0
$175$	−6.63082	+	7.59807i	−0.501243	+	0.574360i
$176$	11.9152	+	7.19085i	0.898141	+	0.542031i
$177$		0			0
$178$	−1.26079	+	12.9621i	−0.0945003	+	0.971548i
$179$	−6.42149	−	8.62556i	−0.479965	−	0.644705i	0.494518	−	0.869168i	$-0.335345\pi$
$179$	−6.42149	−	8.62556i	−0.479965	−	0.644705i	−0.974483	+	0.224463i	$0.927937\pi$
$180$		0			0
$181$	11.7608	+	1.37464i	0.874174	+	0.102176i	0.541334	−	0.840807i	$-0.317919\pi$
$181$	11.7608	+	1.37464i	0.874174	+	0.102176i	0.332839	+	0.942984i	$0.391993\pi$
$182$	−15.4988	+	4.96949i	−1.14885	+	0.368363i
$183$		0			0
$184$	−7.77990	−	16.2703i	−0.573542	−	1.19946i
$185$	4.91060	−	2.00620i	0.361034	−	0.147499i
$186$		0			0
$187$	−4.43603	+	12.9648i	−0.324395	+	0.948079i
$188$	−4.52346	−	1.64641i	−0.329907	−	0.120076i
$189$		0			0
$190$	−0.442813	+	0.161171i	−0.0321250	+	0.0116925i
$191$	−0.503683	−	25.9697i	−0.0364452	−	1.87911i	−0.360078	−	0.932922i	$-0.617250\pi$
$191$	−0.503683	−	25.9697i	−0.0364452	−	1.87911i	0.323633	−	0.946183i	$-0.395096\pi$
$192$		0			0
$193$	4.79345	+	7.60533i	0.345040	+	0.547444i	0.973001	−	0.230801i	$-0.0741348\pi$
$193$	4.79345	+	7.60533i	0.345040	+	0.547444i	−0.627961	+	0.778245i	$0.716110\pi$
$194$	−15.0671	+	4.19423i	−1.08176	+	0.301128i
$195$		0			0
$196$	0.528213	+	0.0204971i	0.0377295	+	0.00146408i
$197$	−5.19770	−	5.50924i	−0.370321	−	0.392517i	0.515236	−	0.857048i	$-0.327704\pi$
$197$	−5.19770	−	5.50924i	−0.370321	−	0.392517i	−0.885557	+	0.464531i	$0.846223\pi$
$198$		0			0
$199$	18.7069	+	4.43361i	1.32610	+	0.314291i	0.831835	−	0.555023i	$-0.187291\pi$
$199$	18.7069	+	4.43361i	1.32610	+	0.314291i	0.494261	+	0.869313i	$0.335439\pi$
$200$	2.31884	+	9.00228i	0.163966	+	0.636557i
$201$		0			0
$202$	−6.51841	+	16.8831i	−0.458634	+	1.18789i
$203$	5.25985	+	6.52119i	0.369169	+	0.457698i
$204$		0			0
$205$	0.844105	−	0.827893i	0.0589549	−	0.0578225i
$206$	16.2891	−	17.2654i	1.13492	−	1.20294i
$207$		0			0
$208$	−5.67750	+	18.9642i	−0.393664	+	1.31493i
$209$	−0.471000	+	0.747292i	−0.0325797	+	0.0516913i
$210$		0			0
$211$	−16.2457	−	15.9337i	−1.11840	−	1.09692i	−0.994512	−	0.104626i	$-0.966636\pi$
$211$	−16.2457	−	15.9337i	−1.11840	−	1.09692i	−0.123891	−	0.992296i	$-0.539537\pi$
$212$	−0.0749195	+	0.00290722i	−0.00514549	+	0.000199669i
$213$		0			0
$214$	−7.40265	+	4.46752i	−0.506034	+	0.305393i
$215$	−0.371407	+	2.10635i	−0.0253297	+	0.143652i
$216$		0			0
$217$	−3.37733	−	19.1538i	−0.229268	−	1.30024i
$218$	10.7246	+	12.2890i	0.726360	+	0.832317i
$219$		0			0
$220$	1.27383	+	0.987290i	0.0858814	+	0.0665631i
$221$	−19.4325	−	1.51042i	−1.30717	−	0.101602i
$222$		0			0
$223$	7.54546	+	6.84714i	0.505281	+	0.458518i	0.884333	−	0.466857i	$-0.154614\pi$
$223$	7.54546	+	6.84714i	0.505281	+	0.458518i	−0.379051	+	0.925376i	$0.623750\pi$
$224$	−4.73015	+	6.35369i	−0.316046	+	0.424524i
$225$		0			0
$226$	0.391345	−	0.907239i	0.0260319	−	0.0603487i
$227$	10.2204	+	7.30513i	0.678355	+	0.484859i	0.867723	−	0.497047i	$-0.165582\pi$
$227$	10.2204	+	7.30513i	0.678355	+	0.484859i	−0.189369	+	0.981906i	$0.560644\pi$
$228$		0			0
$229$	0.467084	−	24.0827i	0.0308658	−	1.59143i	−0.589927	−	0.807457i	$-0.700843\pi$
$229$	0.467084	−	24.0827i	0.0308658	−	1.59143i	0.620793	−	0.783975i	$-0.286811\pi$
$230$	−3.94556	−	11.5313i	−0.260163	−	0.760354i
$231$		0			0
$232$	7.69981	−	0.598477i	0.505518	−	0.0392919i
$233$	14.1591	+	9.31262i	0.927597	+	0.610090i	0.920863	−	0.389887i	$-0.127486\pi$
$233$	14.1591	+	9.31262i	0.927597	+	0.610090i	0.00673413	+	0.999977i	$0.497856\pi$
$234$		0			0
$235$	7.04355	+	3.53741i	0.459471	+	0.230755i
$236$	−0.860023	−	6.29648i	−0.0559827	−	0.409866i
$237$		0			0
$238$	−17.1728	−	7.80602i	−1.11315	−	0.505989i
$239$	0.586768	+	0.188140i	0.0379549	+	0.0121697i	0.324243	−	0.945974i	$-0.394891\pi$
$239$	0.586768	+	0.188140i	0.0379549	+	0.0121697i	−0.286288	+	0.958144i	$0.592421\pi$
$240$		0			0
$241$	−10.1378	−	1.58553i	−0.653036	−	0.102133i	−0.180682	−	0.983542i	$-0.557830\pi$
$241$	−10.1378	−	1.58553i	−0.653036	−	0.102133i	−0.472355	+	0.881409i	$0.656596\pi$
$242$	−4.32147			−0.277795
$243$		0			0
$244$	0.479265			0.0306818
$245$	−0.855138	−	0.133741i	−0.0546328	−	0.00854441i
$246$		0			0
$247$	−1.19649	−	0.383638i	−0.0761306	−	0.0244103i
$248$	−16.3216	−	7.41907i	−1.03642	−	0.471112i
$249$		0			0
$250$	1.89088	+	13.8437i	0.119590	+	0.875551i
$251$	2.19344	+	1.10159i	0.138449	+	0.0695316i	0.516675	−	0.856182i	$-0.327170\pi$
$251$	2.19344	+	1.10159i	0.138449	+	0.0695316i	−0.378226	+	0.925713i	$0.623466\pi$
$252$		0			0
$253$	−19.0877	−	12.5542i	−1.20003	−	0.789274i
$254$	5.15060	−	0.400336i	0.323178	−	0.0251193i
$255$		0			0
$256$	4.19004	+	12.2459i	0.261878	+	0.765366i
$257$	−0.219847	+	11.3353i	−0.0137137	+	0.707074i	0.928363	+	0.371676i	$0.121217\pi$
$257$	−0.219847	+	11.3353i	−0.0137137	+	0.707074i	−0.942076	+	0.335398i	$0.891129\pi$
$258$		0			0
$259$	11.1366	+	7.95996i	0.691994	+	0.494608i
$260$	−0.907990	+	2.10496i	−0.0563111	+	0.130544i
$261$		0			0
$262$	16.9598	−	22.7809i	1.04778	−	1.40741i
$263$	−17.6116	−	15.9817i	−1.08598	−	0.985473i	−0.0860367	−	0.996292i	$-0.527420\pi$
$263$	−17.6116	−	15.9817i	−1.08598	−	0.985473i	−0.999941	+	0.0108193i	$0.996556\pi$
$264$		0			0
$265$	0.122394	+	0.00951324i	0.00751862	+	0.000584394i
$266$	−0.961151	−	0.744948i	−0.0589319	−	0.0456757i
$267$		0			0
$268$	4.82772	+	5.53195i	0.294900	+	0.337918i
$269$	−0.0624055	−	0.353919i	−0.00380493	−	0.0215788i	0.982846	−	0.184427i	$-0.0590430\pi$
$269$	−0.0624055	−	0.353919i	−0.00380493	−	0.0215788i	−0.986651	+	0.162848i	$0.947932\pi$
$270$		0			0
$271$	0.703818	−	3.99155i	0.0427539	−	0.242469i	−0.955940	−	0.293562i	$-0.905159\pi$
$271$	0.703818	−	3.99155i	0.0427539	−	0.242469i	0.998694	+	0.0510927i	$0.0162704\pi$
$272$	−19.6432	+	11.8547i	−1.19104	+	0.718798i
$273$		0			0
$274$	23.5901	−	0.915405i	1.42513	−	0.0553017i
$275$	8.40742	+	8.24594i	0.506986	+	0.497249i
$276$		0			0
$277$	14.4367	−	22.9054i	0.867419	−	1.37625i	−0.0584025	−	0.998293i	$-0.518601\pi$
$277$	14.4367	−	22.9054i	0.867419	−	1.37625i	0.925822	−	0.377961i	$-0.123375\pi$
$278$	−7.92604	+	26.4748i	−0.475372	+	1.58785i
$279$		0			0
$280$	3.68894	−	3.91004i	0.220456	−	0.233670i
$281$	5.60241	−	5.49480i	0.334212	−	0.327792i	−0.513660	−	0.857994i	$-0.671711\pi$
$281$	5.60241	−	5.49480i	0.334212	−	0.327792i	0.847872	+	0.530201i	$0.177884\pi$
$282$		0			0
$283$	0.821065	+	1.01796i	0.0488073	+	0.0605115i	0.802180	−	0.597082i	$-0.203673\pi$
$283$	0.821065	+	1.01796i	0.0488073	+	0.0605115i	−0.753373	+	0.657593i	$0.771575\pi$
$284$	2.76657	−	7.16559i	0.164166	−	0.425199i
$285$		0			0
$286$	4.74096	+	18.4055i	0.280339	+	1.08834i
$287$	2.96885	+	0.703631i	0.175246	+	0.0415340i
$288$		0			0
$289$	−3.83611	−	4.06604i	−0.225653	−	0.239179i
$290$	5.21523	+	0.202375i	0.306249	+	0.0118839i
$291$		0			0
$292$	7.28198	−	2.02708i	0.426146	−	0.118626i
$293$	9.00289	+	14.2841i	0.525954	+	0.834483i	0.998914	−	0.0466009i	$-0.0148389\pi$
$293$	9.00289	+	14.2841i	0.525954	+	0.834483i	−0.472959	+	0.881084i	$0.656814\pi$
$294$		0			0
$295$	0.201775	+	10.4035i	0.0117478	+	0.605712i
$296$	11.8576	−	4.31582i	0.689210	−	0.250852i
$297$		0			0
$298$	−19.8332	−	7.21870i	−1.14891	−	0.418168i
$299$	10.5204	−	30.7470i	0.608411	−	1.77815i
$300$		0			0
$301$	−5.10946	+	2.08745i	−0.294505	+	0.120318i
$302$	−11.1655	−	23.3507i	−0.642504	−	1.34368i
$303$		0			0
$304$	−1.40839	+	0.451583i	−0.0807769	+	0.0259001i
$305$	−0.779430	−	0.0911023i	−0.0446300	−	0.00521650i
$306$		0			0
$307$	−6.49615	−	8.72584i	−0.370755	−	0.498010i	0.577117	−	0.816661i	$-0.304178\pi$
$307$	−6.49615	−	8.72584i	−0.370755	−	0.498010i	−0.947872	+	0.318651i	$0.896770\pi$
$308$	−0.402630	+	4.13940i	−0.0229420	+	0.235864i
$309$		0			0
$310$	−10.3733	−	6.26034i	−0.589166	−	0.355564i
$311$	12.5544	−	14.3858i	0.711895	−	0.815741i	−0.277541	−	0.960714i	$-0.589519\pi$
$311$	12.5544	−	14.3858i	0.711895	−	0.815741i	0.989436	+	0.144973i	$0.0463095\pi$
$312$		0			0
$313$	−14.1766	+	29.6479i	−0.801311	+	1.67580i	−0.0662447	+	0.997803i	$0.521102\pi$
$313$	−14.1766	+	29.6479i	−0.801311	+	1.67580i	−0.735066	+	0.677996i	$0.762849\pi$
$314$	−0.503837	+	8.65055i	−0.0284332	+	0.488179i
$315$		0			0
$316$	0.602486	−	0.396261i	0.0338925	−	0.0222914i
$317$	6.22316	−	4.82331i	0.349527	−	0.270904i	−0.422674	−	0.906282i	$-0.638909\pi$
$317$	6.22316	−	4.82331i	0.349527	−	0.270904i	0.772202	+	0.635378i	$0.219156\pi$
$318$		0			0
$319$	7.95937	−	5.68901i	0.445639	−	0.318524i
$320$	−0.910756	−	4.20452i	−0.0509128	−	0.235040i
$321$		0			0
$322$	19.7453	−	24.4804i	1.10036	−	1.36424i
$323$	−0.728128	−	1.26115i	−0.0405141	−	0.0701725i
$324$		0			0
$325$	−8.37545	+	14.5067i	−0.464586	+	0.804687i
$326$	−3.06541	−	7.93962i	−0.169778	−	0.439735i
$327$		0			0
$328$	2.08282	−	1.89006i	0.115004	−	0.104361i
$329$	1.96912	+	20.2443i	0.108561	+	1.11610i
$330$		0			0
$331$	30.2181	+	12.3455i	1.66094	+	0.678568i	0.997566	−	0.0697231i	$-0.0222116\pi$
$331$	30.2181	+	12.3455i	1.66094	+	0.678568i	0.663371	+	0.748291i	$0.269125\pi$
$332$	0.0696633	+	1.19607i	0.00382327	+	0.0656430i
$333$		0			0
$334$	−1.67662	+	0.842028i	−0.0917404	+	0.0460737i
$335$	−6.79977	−	9.91431i	−0.371511	−	0.541677i
$336$		0			0
$337$	−0.779026	−	0.152996i	−0.0424363	−	0.00833421i	0.171449	−	0.985193i	$-0.445155\pi$
$337$	−0.779026	−	0.152996i	−0.0424363	−	0.00833421i	−0.213885	+	0.976859i	$0.568612\pi$
$338$	−5.37301	+	2.96470i	−0.292253	+	0.161259i
$339$		0			0
$340$	−2.41876	+	1.09946i	−0.131176	+	0.0596266i
$341$	−22.5583	+	2.63669i	−1.22160	+	0.142785i
$342$		0			0
$343$	−7.72975	−	17.9196i	−0.417367	−	0.967566i
$344$	−1.07713	+	4.97258i	−0.0580749	+	0.268103i
$345$		0			0
$346$	8.91142	−	12.9932i	0.479081	−	0.698517i
$347$	−4.22767	+	30.9520i	−0.226953	+	1.66159i	0.426398	+	0.904536i	$0.359782\pi$
$347$	−4.22767	+	30.9520i	−0.226953	+	1.66159i	−0.653351	+	0.757055i	$0.726637\pi$
$348$		0			0
$349$	−24.2983	+	4.77204i	−1.30066	+	0.255441i	−0.794640	−	0.607080i	$-0.792341\pi$
$349$	−24.2983	+	4.77204i	−1.30066	+	0.255441i	−0.506020	+	0.862522i	$0.668884\pi$
$350$	−12.4189	+	10.4207i	−0.663817	+	0.557009i
$351$		0			0
$352$	7.08580	+	5.94569i	0.377674	+	0.316906i
$353$	−12.8976	−	7.11659i	−0.686470	−	0.378778i	0.101208	−	0.994865i	$-0.467729\pi$
$353$	−12.8976	−	7.11659i	−0.686470	−	0.378778i	−0.787678	+	0.616087i	$0.788717\pi$
$354$		0			0
$355$	−5.86136	+	11.1275i	−0.311089	+	0.590587i
$356$	−1.18073	+	4.58389i	−0.0625787	+	0.242946i
$357$		0			0
$358$	−8.05646	−	15.2948i	−0.425797	−	0.808356i
$359$	−14.7508	+	3.49601i	−0.778520	+	0.184513i	−0.600618	−	0.799536i	$-0.705079\pi$
$359$	−14.7508	+	3.49601i	−0.778520	+	0.184513i	−0.177901	+	0.984048i	$0.556931\pi$
$360$		0			0
$361$	5.42234	+	18.1119i	0.285386	+	0.953256i
$362$	18.3379	+	5.10469i	0.963816	+	0.268297i
$363$		0			0
$364$	−5.84474	+	0.914100i	−0.306348	+	0.0479119i
$365$	−12.2280	+	1.91243i	−0.640044	+	0.100101i
$366$		0			0
$367$	18.7848	+	5.22910i	0.980558	+	0.272957i	0.721126	−	0.692804i	$-0.243625\pi$
$367$	18.7848	+	5.22910i	0.980558	+	0.272957i	0.259432	+	0.965761i	$0.416464\pi$
$368$	−10.9709	−	36.6455i	−0.571900	−	1.91028i
$369$		0			0
$370$	8.29769	−	1.96659i	0.431376	−	0.102238i
$371$	0.147642	+	0.280291i	0.00766519	+	0.0145520i
$372$		0			0
$373$	2.81409	−	10.9249i	0.145708	−	0.565672i	−0.853312	−	0.521401i	$-0.825410\pi$
$373$	2.81409	−	10.9249i	0.145708	−	0.565672i	0.999020	−	0.0442713i	$-0.0140966\pi$
$374$	−10.2661	+	19.4896i	−0.530846	+	1.00779i
$375$		0			0
$376$	16.4164	+	9.05817i	0.846609	+	0.467139i
$377$	10.6605	+	8.94523i	0.549044	+	0.460703i
$378$		0			0
$379$	−6.27259	+	5.26333i	−0.322202	+	0.270359i	−0.789513	−	0.613733i	$-0.789667\pi$
$379$	−6.27259	+	5.26333i	−0.322202	+	0.270359i	0.467312	+	0.884093i	$0.345223\pi$
$380$	−0.168066	+	0.0330072i	−0.00862162	+	0.00169323i
$381$		0			0
$382$	5.65092	−	41.3721i	0.289126	−	2.11678i
$383$	18.7515	−	27.3403i	0.958155	−	1.39702i	0.0407065	−	0.999171i	$-0.487039\pi$
$383$	18.7515	−	27.3403i	0.958155	−	1.39702i	0.917449	−	0.397854i	$-0.130245\pi$
$384$		0			0
$385$	1.44164	−	6.65537i	0.0734730	−	0.339189i
$386$	5.72412	+	13.2700i	0.291350	+	0.675425i
$387$		0			0
$388$	−5.64619	+	0.659945i	−0.286642	+	0.0335036i
$389$	0.971368	−	0.441541i	0.0492503	−	0.0223870i	−0.389034	−	0.921223i	$-0.627191\pi$
$389$	0.971368	−	0.441541i	0.0492503	−	0.0223870i	0.438284	+	0.898836i	$0.355586\pi$
$390$		0			0
$391$	32.9768	−	18.1958i	1.66771	−	0.920203i
$392$	−2.02034	−	0.396782i	−0.102043	−	0.0200405i
$393$		0			0
$394$	−6.88685	−	10.0413i	−0.346954	−	0.505872i
$395$	−1.05515	+	0.529915i	−0.0530902	+	0.0266629i
$396$		0			0
$397$	0.188063	+	3.22892i	0.00943861	+	0.162055i	0.999734	+	0.0230744i	$0.00734546\pi$
$397$	0.188063	+	3.22892i	0.00943861	+	0.162055i	−0.990295	+	0.138980i	$0.955618\pi$
$398$	28.6103	+	11.6886i	1.43410	+	0.585895i
$399$		0			0
$400$	1.90888	+	19.6250i	0.0954439	+	0.981249i
$401$	2.41054	−	2.18745i	0.120377	−	0.109236i	−0.609596	−	0.792712i	$-0.708668\pi$
$401$	2.41054	−	2.18745i	0.120377	−	0.109236i	0.729973	+	0.683476i	$0.239533\pi$
$402$		0			0
$403$	−11.6359	−	30.1378i	−0.579627	−	1.50127i
$404$	−3.28897	+	5.69666i	−0.163632	+	0.283419i
$405$		0			0
$406$	6.73418	+	11.6639i	0.334212	+	0.578872i
$407$	10.0357	−	12.4423i	0.497450	−	0.616741i
$408$		0			0
$409$	1.60288	+	7.39971i	0.0792573	+	0.365892i	0.999687	−	0.0250156i	$-0.00796355\pi$
$409$	1.60288	+	7.39971i	0.0792573	+	0.365892i	−0.920430	+	0.390908i	$0.872161\pi$
$410$	1.54632	−	1.10524i	0.0763671	−	0.0545839i
$411$		0			0
$412$	6.81911	−	5.28521i	0.335953	−	0.260384i
$413$	−22.4344	+	14.7553i	−1.10392	+	0.726061i
$414$		0			0
$415$	0.114065	−	1.95842i	0.00559922	−	0.0961349i
$416$	−5.67586	+	11.8701i	−0.278282	+	0.581978i
$417$		0			0
$418$	−0.933702	+	1.06990i	−0.0456689	+	0.0523307i
$419$	9.14624	+	5.51978i	0.446823	+	0.269659i	0.722209	−	0.691675i	$-0.243127\pi$
$419$	9.14624	+	5.51978i	0.446823	+	0.269659i	−0.275386	+	0.961334i	$0.588806\pi$
$420$		0			0
$421$	2.53977	−	26.1111i	0.123781	−	1.27258i	−0.703462	−	0.710733i	$-0.748363\pi$
$421$	2.53977	−	26.1111i	0.123781	−	1.27258i	0.827242	−	0.561845i	$-0.189908\pi$
$422$	−21.8446	−	29.3425i	−1.06338	−	1.42837i
$423$		0			0
$424$	0.290056	+	0.0339027i	0.0140864	+	0.00164646i
$425$	−18.4871	+	5.92764i	−0.896754	+	0.287533i
$426$		0			0
$427$	−0.873583	−	1.82694i	−0.0422756	−	0.0884120i
$428$	−2.90921	+	1.18854i	−0.140622	+	0.0574503i
$429$		0			0
$430$	−1.11311	+	3.25320i	−0.0536791	+	0.156883i
$431$	−13.2798	−	4.83347i	−0.639668	−	0.232820i	0.00176599	−	0.999998i	$-0.499438\pi$
$431$	−13.2798	−	4.83347i	−0.639668	−	0.232820i	−0.641434	+	0.767178i	$0.721660\pi$
$432$		0			0
$433$	−18.4903	+	6.72993i	−0.888588	+	0.323420i	−0.745670	−	0.666315i	$-0.767871\pi$
$433$	−18.4903	+	6.72993i	−0.888588	+	0.323420i	−0.142918	+	0.989735i	$0.545648\pi$
$434$	−0.606292	−	31.2603i	−0.0291030	−	1.50054i
$435$		0			0
$436$	3.16103	+	5.01532i	0.151386	+	0.240190i
$437$	2.33904	−	0.651117i	0.111892	−	0.0311472i
$438$		0			0
$439$	−31.9056	−	1.23808i	−1.52277	−	0.0590905i	−0.736274	−	0.676684i	$-0.763416\pi$
$439$	−31.9056	−	1.23808i	−1.52277	−	0.0590905i	−0.786498	+	0.617593i	$0.788108\pi$
$440$	−4.30776	−	4.56595i	−0.205364	−	0.217673i
$441$		0			0
$442$	−30.4889	−	7.22600i	−1.45021	−	0.343706i
$443$	2.69326	+	10.4559i	0.127961	+	0.496774i	0.999973	+	0.00729101i	$0.00232082\pi$
$443$	2.69326	+	10.4559i	0.127961	+	0.496774i	−0.872013	+	0.489483i	$0.837185\pi$
$444$		0			0
$445$	2.79157	−	7.23034i	0.132333	−	0.342751i
$446$	10.2834	+	12.7494i	0.486932	+	0.603701i
$447$		0			0
$448$	7.92580	−	7.77357i	0.374459	−	0.367267i
$449$	−24.0171	+	25.4567i	−1.13344	+	1.20137i	−0.156540	+	0.987672i	$0.550034\pi$
$449$	−24.0171	+	25.4567i	−1.13344	+	1.20137i	−0.976899	+	0.213703i	$0.931448\pi$
$450$		0			0
$451$	1.02186	−	3.41323i	0.0481173	−	0.160723i
$452$	0.191485	−	0.303812i	0.00900671	−	0.0142901i
$453$		0			0
$454$	14.4182	+	14.1413i	0.676680	+	0.663683i
$455$	9.67907	−	0.375592i	0.453762	−	0.0176080i
$456$		0			0
$457$	−25.8211	+	15.5831i	−1.20786	+	0.728947i	−0.970178	−	0.242395i	$-0.922067\pi$
$457$	−25.8211	+	15.5831i	−1.20786	+	0.728947i	−0.237683	+	0.971343i	$0.576388\pi$
$458$	6.72402	−	38.1338i	0.314193	−	1.78188i
$459$		0			0
$460$	−0.769228	−	4.36251i	−0.0358655	−	0.203403i
$461$	21.9592	+	25.1625i	1.02274	+	1.17193i	0.984984	+	0.172646i	$0.0552317\pi$
$461$	21.9592	+	25.1625i	1.02274	+	1.17193i	0.0377588	+	0.999287i	$0.487978\pi$
$462$		0			0
$463$	0.716876	+	0.555621i	0.0333161	+	0.0258219i	0.629123	−	0.777306i	$-0.283414\pi$
$463$	0.716876	+	0.555621i	0.0333161	+	0.0258219i	−0.595806	+	0.803128i	$0.703167\pi$
$464$	16.3317	+	1.26940i	0.758182	+	0.0589305i
$465$		0			0
$466$	20.1753	+	18.3081i	0.934601	+	0.848106i
$467$	21.2950	−	28.6042i	0.985417	−	1.32364i	0.0395057	−	0.999219i	$-0.487422\pi$
$467$	21.2950	−	28.6042i	0.985417	−	1.32364i	0.945911	−	0.324425i	$-0.105171\pi$
$468$		0			0
$469$	12.2879	−	28.4865i	0.567401	−	1.31538i
$470$	10.3084	+	7.36797i	0.475489	+	0.339859i
$471$		0			0
$472$	−0.479983	+	24.7478i	−0.0220930	+	1.13911i
$473$	2.08657	+	6.09822i	0.0959404	+	0.280396i
$474$		0			0
$475$	−1.24776	+	0.0969835i	−0.0572511	+	0.00444991i
$476$	−5.72839	−	3.76762i	−0.262560	−	0.172689i
$477$		0			0
$478$	0.885212	+	0.444570i	0.0404886	+	0.0203342i
$479$	−0.439159	−	3.21521i	−0.0200657	−	0.146907i	0.978041	−	0.208412i	$-0.0668296\pi$
$479$	−0.439159	−	3.21521i	−0.0200657	−	0.146907i	−0.998107	+	0.0615055i	$0.980410\pi$
$480$		0			0
$481$	20.6996	+	9.40913i	0.943822	+	0.429020i
$482$	−15.7078	−	5.03650i	−0.715470	−	0.229406i
$483$		0			0
$484$	−1.55185	−	0.242704i	−0.0705385	−	0.0110320i
$485$	9.30785			0.422648
$486$		0			0
$487$	27.4369			1.24329			0.621643	−	0.783301i	$-0.286466\pi$
$487$	27.4369			1.24329			0.621643	+	0.783301i	$0.286466\pi$
$488$	−1.84432	−	0.288446i	−0.0834882	−	0.0130573i
$489$		0			0
$490$	−1.32497	−	0.424834i	−0.0598559	−	0.0191920i
$491$	−2.43554	−	1.10709i	−0.109915	−	0.0499623i	0.358099	−	0.933684i	$-0.383425\pi$
$491$	−2.43554	−	1.10709i	−0.109915	−	0.0499623i	−0.468013	+	0.883721i	$0.655030\pi$
$492$		0			0
$493$	2.18274	+	15.9805i	0.0983057	+	0.719725i
$494$	−1.80505	−	0.906528i	−0.0812129	−	0.0407866i
$495$		0			0
$496$	−31.7717	−	20.8966i	−1.42659	−	0.938283i
$497$	−32.3577	+	2.51504i	−1.45144	+	0.112815i
$498$		0			0
$499$	0.391083	+	1.14298i	0.0175073	+	0.0511670i	0.954556	−	0.298032i	$-0.0963302\pi$
$499$	0.391083	+	1.14298i	0.0175073	+	0.0511670i	−0.937049	+	0.349199i	$0.886454\pi$
$500$	−0.0984776	+	5.07748i	−0.00440405	+	0.227072i
$501$		0			0
$502$	3.21014	+	2.29447i	0.143276	+	0.102407i
$503$	−10.0552	+	23.3106i	−0.448340	+	1.03937i	0.532830	+	0.846223i	$0.321129\pi$
$503$	−10.0552	+	23.3106i	−0.448340	+	1.03937i	−0.981170	+	0.193147i	$0.938131\pi$
$504$		0			0
$505$	6.43172	−	8.63929i	0.286208	−	0.384444i
$506$	−27.1979	−	24.6808i	−1.20909	−	1.09719i
$507$		0			0
$508$	1.87207	+	0.145509i	0.0830598	+	0.00645591i
$509$	20.8817	+	16.1846i	0.925567	+	0.717368i	0.959397	−	0.282059i	$-0.0910175\pi$
$509$	20.8817	+	16.1846i	0.925567	+	0.717368i	−0.0338304	+	0.999428i	$0.510771\pi$
$510$		0			0
$511$	−21.0004	−	24.0638i	−0.929004	−	1.06452i
$512$	−1.12600	−	6.38586i	−0.0497626	−	0.282218i
$513$		0			0
$514$	−3.16486	+	17.9488i	−0.139596	+	0.791689i
$515$	−12.0946	+	7.29912i	−0.532951	+	0.321637i
$516$		0			0
$517$	23.7340	−	0.920986i	1.04382	−	0.0405049i
$518$	15.7106	+	15.4089i	0.690286	+	0.677028i
$519$		0			0
$520$	4.76101	−	7.55385i	0.208784	−	0.331258i
$521$	9.55116	−	31.9031i	0.418444	−	1.39770i	−0.446028	−	0.895019i	$-0.647162\pi$
$521$	9.55116	−	31.9031i	0.418444	−	1.39770i	0.864472	−	0.502681i	$-0.167653\pi$
$522$		0			0
$523$	8.69100	−	9.21192i	0.380031	−	0.402809i	−0.508918	−	0.860815i	$-0.669955\pi$
$523$	8.69100	−	9.21192i	0.380031	−	0.402809i	0.888949	+	0.458006i	$0.151436\pi$
$524$	7.36971	−	7.22816i	0.321947	−	0.315764i
$525$		0			0
$526$	−24.0021	−	29.7579i	−1.04654	−	1.29751i
$527$	13.4859	−	34.9294i	0.587456	−	1.52155i
$528$		0			0
$529$	9.92672	+	38.5379i	0.431597	+	1.67556i
$530$	0.192032	+	0.0455124i	0.00834134	+	0.00197693i
$531$		0			0
$532$	−0.303312	−	0.321492i	−0.0131503	−	0.0139385i
$533$	5.06419	+	0.196513i	0.219354	+	0.00851194i
$534$		0			0
$535$	4.95717	−	1.37992i	0.214317	−	0.0596593i
$536$	−15.2487	−	24.1937i	−0.658643	−	1.04501i
$537$		0			0
$538$	−0.0112029	−	0.577621i	−0.000482993	−	0.0249030i
$539$	−2.45095	+	0.892071i	−0.105570	+	0.0384242i
$540$		0			0
$541$	−38.6113	−	14.0534i	−1.66003	−	0.604201i	−0.669661	−	0.742667i	$-0.733561\pi$
$541$	−38.6113	−	14.0534i	−1.66003	−	0.604201i	−0.990367	+	0.138466i	$0.955783\pi$
$542$	2.10936	−	6.16482i	0.0906046	−	0.264802i
$543$		0			0
$544$	−14.1165	+	5.76723i	−0.605240	+	0.247268i
$545$	−4.18744	−	8.75729i	−0.179370	−	0.375121i
$546$		0			0
$547$	−39.0474	+	12.5201i	−1.66955	+	0.535319i	−0.981683	−	0.190520i	$-0.938983\pi$
$547$	−39.0474	+	12.5201i	−1.66955	+	0.535319i	−0.687865	+	0.725839i	$0.741452\pi$
$548$	8.52267	+	0.996157i	0.364070	+	0.0425537i
$549$		0			0
$550$	11.3049	+	15.1852i	0.482044	+	0.647498i
$551$	−0.100658	+	1.03486i	−0.00428818	+	0.0440863i
$552$		0			0
$553$	−2.60872	−	1.57437i	−0.110934	−	0.0669490i
$554$	28.6191	−	32.7939i	1.21591	−	1.39328i
$555$		0			0
$556$	−4.33314	+	9.06200i	−0.183766	+	0.384314i
$557$	0.843012	−	14.4740i	0.0357196	−	0.613281i	−0.932188	−	0.361974i	$-0.882103\pi$
$557$	0.843012	−	14.4740i	0.0357196	−	0.613281i	0.967908	−	0.251307i	$-0.0808602\pi$
$558$		0			0
$559$	−7.65975	+	5.03790i	−0.323973	+	0.213080i
$560$	9.01196	−	6.98479i	0.380825	−	0.295161i
$561$		0			0
$562$	10.2630	−	7.33558i	0.432920	−	0.309433i
$563$	4.27164	+	19.7201i	0.180028	+	0.831102i	0.974604	+	0.223937i	$0.0718908\pi$
$563$	4.27164	+	19.7201i	0.180028	+	0.831102i	−0.794576	+	0.607165i	$0.792307\pi$
$564$		0			0
$565$	−0.369164	+	0.457691i	−0.0155308	+	0.0192552i
$566$	1.05121	+	1.82075i	0.0441856	+	0.0765318i
$567$		0			0
$568$	−14.9589	+	25.9097i	−0.627663	+	1.08714i
$569$	−11.6620	−	30.2054i	−0.488898	−	1.26628i	−0.929582	−	0.368615i	$-0.879832\pi$
$569$	−11.6620	−	30.2054i	−0.488898	−	1.26628i	0.440685	−	0.897662i	$-0.354736\pi$
$570$		0			0
$571$	17.3908	−	15.7813i	0.727780	−	0.660425i	−0.221391	−	0.975185i	$-0.571060\pi$
$571$	17.3908	−	15.7813i	0.727780	−	0.660425i	0.949171	+	0.314760i	$0.101924\pi$
$572$	0.668785	+	6.87571i	0.0279633	+	0.287488i
$573$		0			0
$574$	4.54055	+	1.85502i	0.189519	+	0.0774270i
$575$	−1.88207	−	32.3139i	−0.0784878	−	1.34758i
$576$		0			0
$577$	−27.9341	+	14.0291i	−1.16291	+	0.584037i	−0.922259	−	0.386574i	$-0.873659\pi$
$577$	−27.9341	+	14.0291i	−1.16291	+	0.584037i	−0.240655	+	0.970611i	$0.577362\pi$
$578$	−5.08276	−	7.41085i	−0.211415	−	0.308251i
$579$		0			0
$580$	1.86143	+	0.365573i	0.0772917	+	0.0151796i
$581$	4.43241	−	2.44570i	0.183887	−	0.101465i
$582$		0			0
$583$	0.336781	−	0.153086i	0.0139481	−	0.00634017i
$584$	−29.2426	+	3.41797i	−1.21007	+	0.141437i
$585$		0			0
$586$	10.7508	+	24.9232i	0.444113	+	1.02957i
$587$	1.08833	−	5.02428i	0.0449201	−	0.207374i	−0.949358	−	0.314196i	$-0.898265\pi$
$587$	1.08833	−	5.02428i	0.0449201	−	0.207374i	0.994278	+	0.106822i	$0.0340675\pi$
$588$		0			0
$589$	1.36521	−	1.99052i	0.0562524	−	0.0820181i
$590$	−2.26375	+	16.5736i	−0.0931972	+	0.682324i
$591$		0			0
$592$	26.2631	−	5.15790i	1.07941	−	0.211989i
$593$	10.0161	−	8.40450i	0.411312	−	0.345131i	−0.413535	−	0.910488i	$-0.635706\pi$
$593$	10.0161	−	8.40450i	0.411312	−	0.345131i	0.824846	+	0.565357i	$0.191262\pi$
$594$		0			0
$595$	8.59991	+	7.21618i	0.352562	+	0.295835i
$596$	−6.71671	−	3.70613i	−0.275127	−	0.151809i
$597$		0			0
$598$	24.3468	−	46.2213i	0.995615	−	1.89013i
$599$	−5.72150	+	22.2122i	−0.233774	+	0.907568i	0.738601	+	0.674143i	$0.235487\pi$
$599$	−5.72150	+	22.2122i	−0.233774	+	0.907568i	−0.972375	+	0.233424i	$0.925007\pi$
$600$		0			0
$601$	14.4187	+	27.3732i	0.588151	+	1.11658i	0.980455	+	0.196741i	$0.0630359\pi$
$601$	14.4187	+	27.3732i	0.588151	+	1.11658i	−0.392305	+	0.919835i	$0.628322\pi$
$602$	−8.63373	+	2.04623i	−0.351884	+	0.0833981i
$603$		0			0
$604$	−2.69812	−	9.01235i	−0.109785	−	0.366707i
$605$	2.47763	+	0.689697i	0.100730	+	0.0280402i
$606$		0			0
$607$	−23.6991	+	3.70648i	−0.961918	+	0.150441i	−0.615933	−	0.787799i	$-0.711221\pi$
$607$	−23.6991	+	3.70648i	−0.961918	+	0.150441i	−0.345985	+	0.938240i	$0.612455\pi$
$608$	−0.971223	+	0.151896i	−0.0393883	+	0.00616022i
$609$		0			0
$610$	−1.21531	−	0.338306i	−0.0492066	−	0.0136976i
$611$	9.68974	+	32.3660i	0.392005	+	1.30939i
$612$		0			0
$613$	−28.9811	+	6.86864i	−1.17053	+	0.277422i	−0.769503	−	0.638643i	$-0.779496\pi$
$613$	−28.9811	+	6.86864i	−1.17053	+	0.277422i	−0.401031	+	0.916065i	$0.631348\pi$
$614$	−8.15012	−	15.4726i	−0.328912	−	0.624424i
$615$		0			0
$616$	4.04070	−	15.6870i	0.162804	−	0.632045i
$617$	4.63194	−	8.79351i	0.186475	−	0.354014i	−0.773638	−	0.633628i	$-0.781565\pi$
$617$	4.63194	−	8.79351i	0.186475	−	0.354014i	0.960112	+	0.279615i	$0.0902068\pi$
$618$		0			0
$619$	−40.1349	−	22.1455i	−1.61316	−	0.890103i	−0.994534	−	0.104415i	$-0.966703\pi$
$619$	−40.1349	−	22.1455i	−1.61316	−	0.890103i	−0.618624	−	0.785687i	$-0.712309\pi$
$620$	−3.37348	−	2.83069i	−0.135482	−	0.113683i
$621$		0			0
$622$	23.5132	−	19.7299i	0.942793	−	0.791097i
$623$	19.6258	−	3.85438i	0.786292	−	0.154423i
$624$		0			0
$625$	−1.63861	+	11.9968i	−0.0655446	+	0.479871i
$626$	−29.8809	+	43.5674i	−1.19428	+	1.74130i
$627$		0			0
$628$	−0.666765	+	3.07813i	−0.0266068	+	0.122831i
$629$	10.4378	+	24.1976i	0.416183	+	0.964822i
$630$		0			0
$631$	36.9816	−	4.32252i	1.47221	−	0.172077i	0.658164	−	0.752874i	$-0.271333\pi$
$631$	36.9816	−	4.32252i	1.47221	−	0.172077i	0.814048	+	0.580797i	$0.197259\pi$
$632$	−2.55698	+	1.16229i	−0.101711	+	0.0462335i
$633$		0			0
$634$	11.0822	−	6.11488i	0.440129	−	0.242853i
$635$	−3.01689	−	0.592499i	−0.119722	−	0.0235126i
$636$		0			0
$637$	−2.09843	−	3.05958i	−0.0831426	−	0.121225i
$638$	14.0548	−	7.05857i	0.556434	−	0.279451i
$639$		0			0
$640$	−0.759074	−	13.0328i	−0.0300050	−	0.515166i
$641$	33.8317	+	13.8218i	1.33627	+	0.545927i	0.929910	−	0.367786i	$-0.119884\pi$
$641$	33.8317	+	13.8218i	1.33627	+	0.545927i	0.406360	+	0.913713i	$0.366798\pi$
$642$		0			0
$643$	3.10371	+	31.9089i	0.122398	+	1.25836i	0.832404	+	0.554169i	$0.186964\pi$
$643$	3.10371	+	31.9089i	0.122398	+	1.25836i	−0.710006	+	0.704196i	$0.751308\pi$
$644$	8.46545	−	7.68199i	0.333586	−	0.302713i
$645$		0			0
$646$	−0.843191	−	2.18392i	−0.0331749	−	0.0859251i
$647$	−15.8319	+	27.4216i	−0.622415	+	1.07805i	0.366620	+	0.930371i	$0.380515\pi$
$647$	−15.8319	+	27.4216i	−0.622415	+	1.07805i	−0.989035	+	0.147683i	$0.952818\pi$
$648$		0			0
$649$	15.6781	+	27.1553i	0.615419	+	1.06594i
$650$	−16.9059	+	20.9601i	−0.663105	+	0.822122i
$651$		0			0
$652$	−0.654886	−	3.02329i	−0.0256473	−	0.118401i
$653$	−9.46047	+	6.76194i	−0.370217	+	0.264615i	−0.751348	−	0.659906i	$-0.770596\pi$
$653$	−9.46047	+	6.76194i	−0.370217	+	0.264615i	0.381132	+	0.924521i	$0.375534\pi$
$654$		0			0
$655$	−13.3594	+	10.3543i	−0.521993	+	0.404575i
$656$	4.98417	−	3.27814i	0.194599	−	0.127990i
$657$		0			0
$658$	−1.90121	+	32.6425i	−0.0741168	+	1.27254i
$659$	−11.6457	+	24.3548i	−0.453651	+	0.948730i	0.540562	+	0.841304i	$0.318211\pi$
$659$	−11.6457	+	24.3548i	−0.453651	+	0.948730i	−0.994213	+	0.107426i	$0.965739\pi$
$660$		0			0
$661$	−16.9179	+	19.3857i	−0.658029	+	0.754017i	−0.981341	−	0.192275i	$-0.938413\pi$
$661$	−16.9179	+	19.3857i	−0.658029	+	0.754017i	0.323312	+	0.946292i	$0.395204\pi$
$662$	44.9279	+	27.1141i	1.74617	+	1.05382i
$663$		0			0
$664$	0.451777	−	4.64467i	0.0175323	−	0.180248i
$665$	0.432166	+	0.580499i	0.0167587	+	0.0225108i
$666$		0			0
$667$	−26.7094	−	3.12188i	−1.03419	−	0.120880i
$668$	−0.649365	+	0.208211i	−0.0251247	+	0.00805591i
$669$		0			0
$670$	−8.33714	−	17.4357i	−0.322092	−	0.673598i
$671$	−2.18912	+	0.894354i	−0.0845100	+	0.0345261i
$672$		0			0
$673$	0.124100	−	0.362697i	0.00478372	−	0.0139809i	−0.943730	−	0.330716i	$-0.892710\pi$
$673$	0.124100	−	0.362697i	0.00478372	−	0.0139809i	0.948514	+	0.316735i	$0.102586\pi$
$674$	−1.19930	−	0.436509i	−0.0461953	−	0.0168137i
$675$		0			0
$676$	−2.09596	+	0.762868i	−0.0806139	+	0.0293411i
$677$	0.754360	+	38.8946i	0.0289924	+	1.49484i	0.678565	+	0.734541i	$0.262602\pi$
$677$	0.754360	+	38.8946i	0.0289924	+	1.49484i	−0.649572	+	0.760300i	$0.725052\pi$
$678$		0			0
$679$	12.8073	+	20.3202i	0.491499	+	0.779816i
$680$	9.96961	−	2.77523i	0.382317	−	0.106425i
$681$		0			0
$682$	−36.4836	−	1.41573i	−1.39703	−	0.0542111i
$683$	−10.5981	−	11.2333i	−0.405525	−	0.429831i	0.492136	−	0.870518i	$-0.336216\pi$
$683$	−10.5981	−	11.2333i	−0.405525	−	0.429831i	−0.897661	+	0.440687i	$0.854735\pi$
$684$		0			0
$685$	−13.6711	−	3.24010i	−0.522345	−	0.123798i
$686$	−7.82568	−	30.3812i	−0.298786	−	1.15996i
$687$		0			0
$688$	−3.88694	+	10.0674i	−0.148188	+	0.383817i
$689$	0.330365	+	0.409588i	0.0125859	+	0.0156041i
$690$		0			0
$691$	24.6957	−	24.2213i	0.939467	−	0.921423i	−0.0575704	−	0.998341i	$-0.518335\pi$
$691$	24.6957	−	24.2213i	0.939467	−	0.921423i	0.997037	+	0.0769187i	$0.0245082\pi$
$692$	3.92983	−	4.16538i	0.149390	−	0.158344i
$693$		0			0
$694$	−14.4032	+	48.1100i	−0.546737	+	1.82623i
$695$	8.76957	−	13.9139i	0.332649	−	0.527783i
$696$		0			0
$697$	4.19345	+	4.11291i	0.158838	+	0.155787i
$698$	−39.7777	+	1.54355i	−1.50561	+	0.0584244i
$699$		0			0
$700$	−5.04489	+	3.04461i	−0.190679	+	0.115075i
$701$	−3.73272	+	21.1693i	−0.140983	+	0.799554i	0.829522	+	0.558474i	$0.188613\pi$
$701$	−3.73272	+	21.1693i	−0.140983	+	0.799554i	−0.970505	+	0.241080i	$0.922498\pi$
$702$		0			0
$703$	0.294998	+	1.67301i	0.0111260	+	0.0630990i
$704$	−8.52408	−	9.76751i	−0.321263	−	0.368127i
$705$		0			0
$706$	−18.7171	−	14.5068i	−0.704427	−	0.545972i
$707$	27.7105	+	2.15383i	1.04216	+	0.0810030i
$708$		0			0
$709$	24.7820	+	22.4885i	0.930709	+	0.844574i	0.988105	−	0.153778i	$-0.0491440\pi$
$709$	24.7820	+	22.4885i	0.930709	+	0.844574i	−0.0573961	+	0.998351i	$0.518280\pi$
$710$	−12.0735	+	16.2175i	−0.453110	+	0.608633i
$711$		0			0
$712$	7.30253	−	16.9292i	0.273674	−	0.634447i
$713$	50.7874	+	36.3007i	1.90200	+	1.35947i
$714$		0			0
$715$	0.219340	−	11.3091i	0.00820285	−	0.422937i
$716$	−2.03409	−	5.94486i	−0.0760176	−	0.222170i
$717$		0			0
$718$	−24.2967	+	1.88849i	−0.906745	+	0.0704778i
$719$	25.6057	+	16.8411i	0.954930	+	0.628068i	0.928401	−	0.371580i	$-0.121184\pi$
$719$	25.6057	+	16.8411i	0.954930	+	0.628068i	0.0265297	+	0.999648i	$0.491554\pi$
$720$		0			0
$721$	−32.5766	−	16.3606i	−1.21322	−	0.609300i
$722$	4.11313	+	30.1134i	0.153075	+	1.12071i
$723$		0			0
$724$	6.29846	+	2.86300i	0.234080	+	0.106403i
$725$	13.1994	+	4.23222i	0.490214	+	0.157181i
$726$		0			0
$727$	46.6071	+	7.28922i	1.72856	+	0.270342i	0.939146	−	0.343518i	$-0.111619\pi$
$727$	46.6071	+	7.28922i	1.72856	+	0.270342i	0.789415	+	0.613860i	$0.210384\pi$
$728$	23.0420			0.853992
$729$		0			0
$730$	−19.8964			−0.736400
$731$	−10.4980	−	1.64186i	−0.388283	−	0.0607263i
$732$		0			0
$733$	−10.7602	−	3.45011i	−0.397437	−	0.127433i	0.0998855	−	0.994999i	$-0.468152\pi$
$733$	−10.7602	−	3.45011i	−0.397437	−	0.127433i	−0.497322	+	0.867566i	$0.665683\pi$
$734$	28.5364	+	12.9714i	1.05330	+	0.478782i
$735$		0			0
$736$	−3.44073	−	25.1906i	−0.126827	−	0.928539i
$737$	−32.3745	−	16.2591i	−1.19253	−	0.598911i
$738$		0			0
$739$	44.8792	+	29.5175i	1.65091	+	1.08582i	0.910363	+	0.413811i	$0.135802\pi$
$739$	44.8792	+	29.5175i	1.65091	+	1.08582i	0.740544	+	0.672008i	$0.234568\pi$
$740$	3.09016	−	0.240186i	0.113597	−	0.00882942i
$741$		0			0
$742$	0.164871	+	0.481853i	0.00605259	+	0.0176894i
$743$	0.0360765	−	1.86010i	0.00132352	−	0.0682403i	−0.998568	−	0.0535002i	$-0.982962\pi$
$743$	0.0360765	−	1.86010i	0.00132352	−	0.0682403i	0.999891	−	0.0147401i	$-0.00469209\pi$
$744$		0			0
$745$	10.2189	+	7.30404i	0.374392	+	0.267599i
$746$	7.18329	−	16.6527i	0.262999	−	0.609700i
$747$		0			0
$748$	−4.78114	+	6.42219i	−0.174816	+	0.234819i
$749$	9.83345	+	8.92338i	0.359306	+	0.326053i
$750$		0			0
$751$	14.4709	+	1.12476i	0.528049	+	0.0410432i	0.338750	−	0.940876i	$-0.389996\pi$
$751$	14.4709	+	1.12476i	0.528049	+	0.0410432i	0.189299	+	0.981920i	$0.439379\pi$
$752$	31.4331	+	24.3625i	1.14625	+	0.888408i
$753$		0			0
$754$	14.7098	+	16.8555i	0.535698	+	0.613842i
$755$	2.67482	+	15.1697i	0.0973468	+	0.552081i
$756$		0			0
$757$	−6.25826	+	35.4924i	−0.227460	+	1.28999i	0.630465	+	0.776218i	$0.282864\pi$
$757$	−6.25826	+	35.4924i	−0.227460	+	1.28999i	−0.857925	+	0.513774i	$0.828247\pi$
$758$	−11.2700	+	6.80147i	−0.409344	+	0.247040i
$759$		0			0
$760$	0.666621	−	0.0258679i	0.0241809	−	0.000938328i
$761$	21.3601	+	20.9498i	0.774301	+	0.759429i	0.975471	−	0.220127i	$-0.0706472\pi$
$761$	21.3601	+	20.9498i	0.774301	+	0.759429i	−0.201170	+	0.979556i	$0.564474\pi$
$762$		0			0
$763$	13.3564	−	21.1914i	0.483536	−	0.767181i
$764$	4.35281	−	14.5394i	0.157479	−	0.526017i
$765$		0			0
$766$	36.5737	−	38.7659i	1.32146	−	1.40067i
$767$	−31.8427	+	31.2311i	−1.14977	+	1.12769i
$768$		0			0
$769$	18.8407	+	23.3588i	0.679412	+	0.842338i	0.994281	−	0.106797i	$-0.0340594\pi$
$769$	18.8407	+	23.3588i	0.679412	+	0.842338i	−0.314869	+	0.949135i	$0.601961\pi$
$770$	3.94292	−	10.2124i	0.142093	−	0.368030i
$771$		0			0
$772$	1.31026	+	5.08676i	0.0471574	+	0.183076i
$773$	15.5272	+	3.68002i	0.558475	+	0.132361i	0.500153	−	0.865937i	$-0.333277\pi$
$773$	15.5272	+	3.68002i	0.558475	+	0.132361i	0.0583215	+	0.998298i	$0.481425\pi$
$774$		0			0
$775$	−22.0822	−	23.4057i	−0.793215	−	0.840758i
$776$	22.1249	+	0.858548i	0.794238	+	0.0308201i
$777$		0			0
$778$	1.65247	−	0.459997i	0.0592440	−	0.0164917i
$779$	0.201897	+	0.320332i	0.00723372	+	0.0114771i
$780$		0			0
$781$	0.734926	+	37.8926i	0.0262977	+	1.35590i
$782$	56.8959	−	20.7084i	2.03459	−	0.740532i
$783$		0			0
$784$	−4.10375	−	1.49364i	−0.146562	−	0.0533444i
$785$	1.66947	−	4.87922i	0.0595861	−	0.174147i
$786$		0			0
$787$	−1.12401	+	0.459209i	−0.0400667	+	0.0163690i	−0.398145	−	0.917323i	$-0.630346\pi$
$787$	−1.12401	+	0.459209i	−0.0400667	+	0.0163690i	0.358078	+	0.933692i	$0.383432\pi$
$788$	−1.90913	−	3.99262i	−0.0680101	−	0.142231i
$789$		0			0
$790$	−1.80749	+	0.579548i	−0.0643076	+	0.0206194i
$791$	−1.50715	−	0.176161i	−0.0535881	−	0.00626355i
$792$		0			0
$793$	−2.00867	−	2.69811i	−0.0713299	−	0.0958127i
$794$	−0.503371	+	5.17510i	−0.0178640	+	0.183658i
$795$		0			0
$796$	9.61752	+	5.80420i	0.340884	+	0.205725i
$797$	3.27129	−	3.74848i	0.115875	−	0.132778i	−0.692568	−	0.721353i	$-0.743521\pi$
$797$	3.27129	−	3.74848i	0.115875	−	0.132778i	0.808443	+	0.588575i	$0.200311\pi$
$798$		0			0
$799$	−16.8917	+	35.3260i	−0.597586	+	1.24974i
$800$	−0.762005	+	13.0831i	−0.0269409	+	0.462558i
$801$		0			0
$802$	4.37195	−	2.87548i	0.154379	−	0.101537i
$803$	−29.4789	+	22.8479i	−1.04029	+	0.806283i
$804$		0			0
$805$	−15.2276	+	10.8841i	−0.536703	+	0.383613i
$806$	−10.9947	−	50.7573i	−0.387273	−	1.78785i
$807$		0			0
$808$	16.0852	−	19.9425i	0.565875	−	0.701575i
$809$	12.7229	+	22.0367i	0.447313	+	0.774770i	0.998210	−	0.0598039i	$-0.0190475\pi$
$809$	12.7229	+	22.0367i	0.447313	+	0.774770i	−0.550897	+	0.834573i	$0.685714\pi$
$810$		0			0
$811$	15.5045	−	26.8547i	0.544438	−	0.942995i	−0.454204	−	0.890898i	$-0.650076\pi$
$811$	15.5045	−	26.8547i	0.544438	−	0.942995i	0.998642	−	0.0520969i	$-0.0165905\pi$
$812$	1.76318	+	4.56675i	0.0618754	+	0.160261i
$813$		0			0
$814$	19.0300	−	17.2688i	0.667002	−	0.605272i
$815$	0.490352	+	5.04126i	0.0171763	+	0.176588i
$816$		0			0
$817$	−0.634098	−	0.259058i	−0.0221843	−	0.00906328i
$818$	0.707709	+	12.1509i	0.0247445	+	0.424846i
$819$		0			0
$820$	0.617357	−	0.310048i	0.0215590	−	0.0108274i
$821$	−9.60209	−	14.0002i	−0.335115	−	0.488610i	0.620100	−	0.784523i	$-0.287092\pi$
$821$	−9.60209	−	14.0002i	−0.335115	−	0.488610i	−0.955215	+	0.295913i	$0.904376\pi$
$822$		0			0
$823$	−8.84800	−	1.73769i	−0.308422	−	0.0605721i	0.0361067	−	0.999348i	$-0.488504\pi$
$823$	−8.84800	−	1.73769i	−0.308422	−	0.0605721i	−0.344528	+	0.938776i	$0.611961\pi$
$824$	−29.4223	+	16.2345i	−1.02497	+	0.565557i
$825$		0			0
$826$	−39.2970	+	17.8627i	−1.36732	+	0.621522i
$827$	−52.6142	+	6.14972i	−1.82957	+	0.213847i	−0.960009	−	0.279970i	$-0.909675\pi$
$827$	−52.6142	+	6.14972i	−1.82957	+	0.213847i	−0.869566	+	0.493817i	$0.835601\pi$
$828$		0			0
$829$	−3.18618	−	7.38639i	−0.110661	−	0.256540i	0.853882	−	0.520466i	$-0.174242\pi$
$829$	−3.18618	−	7.38639i	−0.110661	−	0.256540i	−0.964543	+	0.263926i	$0.914983\pi$
$830$	0.667638	−	3.08216i	0.0231740	−	0.106983i
$831$		0			0
$832$	10.4300	−	15.2073i	0.361594	−	0.527217i
$833$	0.581911	−	4.26034i	0.0201620	−	0.147612i
$834$		0			0
$835$	1.09564	−	0.215177i	0.0379163	−	0.00744651i
$836$	−0.395382	+	0.331765i	−0.0136746	+	0.0114743i
$837$		0			0
$838$	13.1556	+	11.0388i	0.454452	+	0.381330i
$839$	11.5165	+	6.35452i	0.397593	+	0.219382i	0.669292	−	0.743000i	$-0.266598\pi$
$839$	11.5165	+	6.35452i	0.397593	+	0.219382i	−0.271699	+	0.962382i	$0.587585\pi$
$840$		0			0
$841$	−8.14844	+	15.4694i	−0.280981	+	0.533429i
$842$	10.5199	−	40.8406i	0.362538	−	1.40746i
$843$		0			0
$844$	−6.19650	−	11.7638i	−0.213292	−	0.404925i
$845$	3.55368	−	0.842237i	0.122250	−	0.0289738i
$846$		0			0
$847$	1.90345	+	6.35797i	0.0654034	+	0.218463i
$848$	0.596725	+	0.166110i	0.0204916	+	0.00570423i
$849$		0			0
$850$	−30.8348	+	4.82248i	−1.05763	+	0.165410i
$851$	−43.4097	+	6.78916i	−1.48807	+	0.232729i
$852$		0			0
$853$	25.8602	+	7.19868i	0.885436	+	0.246478i	0.680896	−	0.732380i	$-0.261591\pi$
$853$	25.8602	+	7.19868i	0.885436	+	0.246478i	0.204540	+	0.978858i	$0.434430\pi$
$854$	−0.933670	−	3.11868i	−0.0319495	−	0.106719i
$855$		0			0
$856$	11.9106	−	2.82286i	0.407095	−	0.0964833i
$857$	8.77293	+	16.6550i	0.299678	+	0.568924i	0.987624	−	0.156837i	$-0.0501298\pi$
$857$	8.77293	+	16.6550i	0.299678	+	0.568924i	−0.687947	+	0.725761i	$0.741488\pi$
$858$		0			0
$859$	−11.5288	+	44.7575i	−0.393357	+	1.52710i	0.398945	+	0.916975i	$0.369377\pi$
$859$	−11.5288	+	44.7575i	−0.393357	+	1.52710i	−0.792301	+	0.610130i	$0.791117\pi$
$860$	−0.582428	+	1.10571i	−0.0198606	+	0.0377045i
$861$		0			0
$862$	−19.8913	−	10.9756i	−0.677501	−	0.373829i
$863$	−0.366384	−	0.307432i	−0.0124718	−	0.0104651i	0.636530	−	0.771252i	$-0.280369\pi$
$863$	−0.366384	−	0.307432i	−0.0124718	−	0.0104651i	−0.649002	+	0.760786i	$0.724813\pi$
$864$		0			0
$865$	−7.18288	+	6.02715i	−0.244225	+	0.204929i
$866$	−31.0393	+	6.09592i	−1.05476	+	0.207148i
$867$		0			0
$868$	1.53793	−	11.2597i	0.0522008	−	0.382178i
$869$	−2.01249	+	2.93428i	−0.0682689	+	0.0995385i
$870$		0			0
$871$	10.9095	−	50.3637i	0.369653	−	1.70651i
$872$	−9.14586	−	21.2025i	−0.309718	−	0.718007i
$873$		0			0
$874$	3.87677	−	0.453129i	0.131134	−	0.0153273i
$875$	19.5347	−	8.87960i	0.660393	−	0.300185i
$876$		0			0
$877$	−2.44123	+	1.34701i	−0.0824344	+	0.0454854i	−0.523794	−	0.851845i	$-0.675484\pi$
$877$	−2.44123	+	1.34701i	−0.0824344	+	0.0454854i	0.441360	+	0.897330i	$0.354496\pi$
$878$	−50.3671	−	9.89178i	−1.69981	−	0.333831i
$879$		0			0
$880$	−7.53079	−	10.9802i	−0.253863	−	0.370141i
$881$	−0.903870	+	0.453941i	−0.0304522	+	0.0152936i	−0.463960	−	0.885856i	$-0.653572\pi$
$881$	−0.903870	+	0.453941i	−0.0304522	+	0.0152936i	0.433508	+	0.901150i	$0.357276\pi$
$882$		0			0
$883$	−0.475140	−	8.15783i	−0.0159897	−	0.274533i	−0.996821	−	0.0796739i	$-0.974612\pi$
$883$	−0.475140	−	8.15783i	−0.0159897	−	0.274533i	0.980831	−	0.194859i	$-0.0624249\pi$
$884$	−10.5428	−	4.30719i	−0.354592	−	0.144867i
$885$		0			0
$886$	1.68038	+	17.2758i	0.0564533	+	0.580391i
$887$	6.15983	−	5.58975i	0.206827	−	0.187685i	−0.562010	−	0.827131i	$-0.689972\pi$
$887$	6.15983	−	5.58975i	0.206827	−	0.187685i	0.768837	+	0.639445i	$0.220836\pi$
$888$		0			0
$889$	−2.85765	−	7.40150i	−0.0958425	−	0.248238i
$890$	6.22978	−	10.7903i	0.208823	−	0.361692i
$891$		0			0
$892$	2.97674	+	5.15586i	0.0996686	+	0.172631i
$893$	−1.58474	+	1.96477i	−0.0530313	+	0.0657485i
$894$		0			0
$895$	2.17800	+	10.0548i	0.0728026	+	0.336094i
$896$	27.4077	−	19.5898i	0.915627	−	0.654451i
$897$		0			0
$898$	−44.4691	+	34.4662i	−1.48395	+	1.15015i
$899$	−22.3352	+	14.6901i	−0.744922	+	0.489943i
$900$		0			0
$901$	−0.0354613	+	0.608848i	−0.00118139	+	0.0202837i
$902$	2.47083	−	5.16730i	0.0822697	−	0.172052i
$903$		0			0
$904$	−0.919725	+	1.05389i	−0.0305896	+	0.0350518i
$905$	−9.69897	−	5.85336i	−0.322405	−	0.194572i
$906$		0			0
$907$	2.46065	−	25.2977i	0.0817047	−	0.839998i	−0.861494	−	0.507768i	$-0.830471\pi$
$907$	2.46065	−	25.2977i	0.0817047	−	0.839998i	0.943199	−	0.332230i	$-0.107801\pi$
$908$	4.38339	+	5.88791i	0.145468	+	0.195397i
$909$		0			0
$910$	15.4663	+	1.80775i	0.512701	+	0.0599262i
$911$	40.2846	−	12.9167i	1.33469	−	0.427951i	0.449541	−	0.893260i	$-0.351588\pi$
$911$	40.2846	−	12.9167i	1.33469	−	0.427951i	0.885148	+	0.465309i	$0.154057\pi$
$912$		0			0
$913$	−2.55018	−	5.33325i	−0.0843986	−	0.176505i
$914$	−44.8817	+	18.3362i	−1.48455	+	0.606507i
$915$		0			0
$916$	4.55629	−	13.3163i	0.150544	−	0.439982i
$917$	−40.9867	−	14.9179i	−1.35350	−	0.492633i
$918$		0			0
$919$	22.0702	−	8.03288i	0.728027	−	0.264980i	0.0486976	−	0.998814i	$-0.484493\pi$
$919$	22.0702	−	8.03288i	0.728027	−	0.264980i	0.679330	+	0.733833i	$0.262271\pi$
$920$	0.334580	+	17.2508i	0.0110308	+	0.568743i
$921$		0			0
$922$	28.6268	+	45.4194i	0.942772	+	1.49581i
$923$	−51.9351	+	14.4571i	−1.70946	+	0.475862i
$924$		0			0
$925$	22.6309	+	0.878182i	0.744099	+	0.0288744i
$926$	1.00058	+	1.06055i	0.0328809	+	0.0348518i
$927$		0			0
$928$	10.5941	+	2.51086i	0.347770	+	0.0824229i
$929$	−10.5623	−	41.0055i	−0.346539	−	1.34535i	−0.869896	−	0.493235i	$-0.835814\pi$
$929$	−10.5623	−	41.0055i	−0.346539	−	1.34535i	0.523357	−	0.852113i	$-0.324679\pi$
$930$		0			0
$931$	0.0998381	−	0.258587i	0.00327206	−	0.00847485i
$932$	6.21674	+	7.70755i	0.203636	+	0.252469i
$933$		0			0
$934$	40.9275	−	40.1415i	1.33919	−	1.31347i
$935$	8.99636	−	9.53558i	0.294212	−	0.311847i
$936$		0			0
$937$	3.25278	−	10.8651i	0.106264	−	0.354946i	−0.888275	−	0.459312i	$-0.848096\pi$
$937$	3.25278	−	10.8651i	0.106264	−	0.354946i	0.994539	+	0.104366i	$0.0332813\pi$
$938$	26.5925	−	42.1919i	0.868276	−	1.37761i
$939$		0			0
$940$	3.28794	+	3.22479i	0.107241	+	0.105181i
$941$	−26.6752	+	1.03512i	−0.869587	+	0.0337439i	−0.469706	−	0.882823i	$-0.655640\pi$
$941$	−26.6752	+	1.03512i	−0.869587	+	0.0337439i	−0.399881	+	0.916567i	$0.630949\pi$
$942$		0			0
$943$	−8.38458	+	5.06012i	−0.273040	+	0.164780i
$944$	−9.11676	+	51.7037i	−0.296725	+	1.68281i
$945$		0			0
$946$	1.79922	+	10.2039i	0.0584979	+	0.331758i
$947$	−20.1660	−	23.1077i	−0.655307	−	0.750899i	0.325572	−	0.945517i	$-0.394443\pi$
$947$	−20.1660	−	23.1077i	−0.655307	−	0.750899i	−0.980879	+	0.194618i	$0.937653\pi$
$948$		0			0
$949$	−41.9316	−	32.4995i	−1.36116	−	1.05498i
$950$	−2.00587	−	0.155908i	−0.0650789	−	0.00505833i
$951$		0			0
$952$	19.7765	+	17.9462i	0.640961	+	0.581641i
$953$	13.4334	−	18.0442i	0.435151	−	0.584509i	−0.529411	−	0.848366i	$-0.677587\pi$
$953$	13.4334	−	18.0442i	0.435151	−	0.584509i	0.964562	+	0.263856i	$0.0849944\pi$
$954$		0			0
$955$	−9.84273	+	22.8180i	−0.318503	+	0.738374i
$956$	0.292913	+	0.209361i	0.00947347	+	0.00677123i
$957$		0			0
$958$	0.101159	−	5.21571i	0.00326829	−	0.168512i
$959$	−11.7374	−	34.3039i	−0.379021	−	1.10773i
$960$		0			0
$961$	30.9664	−	2.40690i	0.998916	−	0.0776419i
$962$	30.5393	+	20.0860i	0.984627	+	0.647600i
$963$		0			0
$964$	−5.35782	−	2.69080i	−0.172564	−	0.0866648i
$965$	−1.16396	−	8.52166i	−0.0374691	−	0.274322i
$966$		0			0
$967$	−0.817853	−	0.371760i	−0.0263004	−	0.0119550i	0.400617	−	0.916245i	$-0.368796\pi$
$967$	−0.817853	−	0.371760i	−0.0263004	−	0.0119550i	−0.426918	+	0.904290i	$0.640401\pi$
$968$	5.82576	+	1.86796i	0.187247	+	0.0600384i
$969$		0			0
$970$	14.7834	+	2.31208i	0.474665	+	0.0742363i
$971$	30.2813			0.971772			0.485886	−	0.874022i	$-0.338497\pi$
$971$	30.2813			0.971772			0.485886	+	0.874022i	$0.338497\pi$
$972$		0			0
$973$	42.4423			1.36064
$974$	43.5772	+	6.81535i	1.39630	+	0.218378i
$975$		0			0
$976$	−3.77038	−	1.20892i	−0.120687	−	0.0386967i
$977$	−12.3448	−	5.61140i	−0.394945	−	0.179524i	0.206486	−	0.978450i	$-0.433797\pi$
$977$	−12.3448	−	5.61140i	−0.394945	−	0.179524i	−0.601430	+	0.798925i	$0.705402\pi$
$978$		0			0
$979$	−3.16078	−	23.1410i	−0.101019	−	0.739589i
$980$	−0.451938	−	0.226972i	−0.0144366	−	0.00725035i
$981$		0			0
$982$	−3.59330	−	2.36335i	−0.114667	−	0.0754175i
$983$	3.31838	−	0.257925i	0.105840	−	0.00822653i	−0.0244632	−	0.999701i	$-0.507788\pi$
$983$	3.31838	−	0.257925i	0.105840	−	0.00822653i	0.130303	+	0.991474i	$0.458405\pi$
$984$		0			0
$985$	2.34588	+	6.85610i	0.0747460	+	0.218453i
$986$	−0.502786	+	25.9235i	−0.0160120	+	0.825572i
$987$		0			0
$988$	−0.597282	−	0.426911i	−0.0190021	−	0.0135819i
$989$	7.01688	−	16.2670i	0.223124	−	0.517259i
$990$		0			0
$991$	28.4753	−	38.2490i	0.904548	−	1.21502i	−0.0714953	−	0.997441i	$-0.522777\pi$
$991$	28.4753	−	38.2490i	0.904548	−	1.21502i	0.976043	−	0.217578i	$-0.0698155\pi$
$992$	−18.7173	−	16.9850i	−0.594275	−	0.539276i
$993$		0			0
$994$	−52.0175	−	4.04312i	−1.64990	−	0.128240i
$995$	−14.5377	−	11.2676i	−0.460876	−	0.357205i
$996$		0			0
$997$	27.0259	+	30.9683i	0.855919	+	0.980775i	0.999961	−	0.00879677i	$-0.00280014\pi$
$997$	27.0259	+	30.9683i	0.855919	+	0.980775i	−0.144042	+	0.989572i	$0.546010\pi$
$998$	0.337227	+	1.91251i	0.0106747	+	0.0605395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.20		1404
3.2	odd	2		243.2.i.a.13.7	✓	1404
243.56	odd	162		243.2.i.a.187.7	yes	1404
243.187	even	81	inner	729.2.i.a.73.20		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.7	✓	1404	3.2	odd	2
243.2.i.a.187.7	yes	1404	243.56	odd	162
729.2.i.a.10.20		1404	1.1	even	1	trivial
729.2.i.a.73.20		1404	243.187	even	81	inner

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.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.58827 + 0.248401i) q^{2} +(0.556399 + 0.178402i) q^{4} +(-0.870960 - 0.395900i) q^{5} +(-0.334115 - 2.44616i) q^{7} +(-2.03377 - 1.02140i) q^{8} +O(q^{10})\)	\(q+(1.58827 + 0.248401i) q^{2} +(0.556399 + 0.178402i) q^{4} +(-0.870960 - 0.395900i) q^{5} +(-0.334115 - 2.44616i) q^{7} +(-2.03377 - 1.02140i) q^{8} +(-1.28498 - 0.845142i) q^{10} +(-2.87435 + 0.223412i) q^{11} +(-1.32760 - 3.88005i) q^{13} +(0.0769621 - 3.96815i) q^{14} +(-3.92717 - 2.80697i) q^{16} +(1.88253 - 4.36419i) q^{17} +(0.182965 - 0.245765i) q^{19} +(-0.413972 - 0.375659i) q^{20} +(-4.62074 - 0.359152i) q^{22} +(6.26337 + 4.85448i) q^{23} +(-2.68577 - 3.07755i) q^{25} +(-1.14478 - 6.49235i) q^{26} +(0.250498 - 1.42064i) q^{28} +(-2.90539 + 1.75341i) q^{29} +(7.87188 - 0.305465i) q^{31} +(-2.29057 - 2.24657i) q^{32} +(4.07402 - 6.46388i) q^{34} +(-0.677432 + 2.26278i) q^{35} +(-3.80493 + 4.03299i) q^{37} +(0.351646 - 0.344892i) q^{38} +(1.36696 + 1.69477i) q^{40} +(-0.445117 + 1.15288i) q^{41} +(-0.557653 - 2.16494i) q^{43} +(-1.63914 - 0.388484i) q^{44} +(8.74206 + 9.26605i) q^{46} +(-8.23233 - 0.319452i) q^{47} +(0.871553 - 0.242613i) q^{49} +(-3.50126 - 5.55513i) q^{50} +(-0.0464646 - 2.39570i) q^{52} +(-0.120579 + 0.0438871i) q^{53} +(2.59189 + 0.943372i) q^{55} +(-1.81898 + 5.31618i) q^{56} +(-5.05008 + 2.06319i) q^{58} +(-4.69182 - 9.81212i) q^{59} +(0.781070 - 0.250440i) q^{61} +(12.5785 + 1.47022i) q^{62} +(2.68522 + 3.60687i) q^{64} +(-0.379828 + 3.90497i) q^{65} +(10.7586 + 6.49283i) q^{67} +(1.82601 - 2.09238i) q^{68} +(-1.63802 + 3.42563i) q^{70} +(0.764363 - 13.1236i) q^{71} +(10.8084 - 7.10878i) q^{73} +(-7.04504 + 5.46032i) q^{74} +(0.145647 - 0.104102i) q^{76} +(1.50687 + 6.95646i) q^{77} +(0.774819 - 0.960625i) q^{79} +(2.30913 + 3.99953i) q^{80} +(-0.993343 + 1.72052i) q^{82} +(0.738540 + 1.91287i) q^{83} +(-3.36739 + 3.05574i) q^{85} +(-0.347930 - 3.57703i) q^{86} +(6.07396 + 2.48149i) q^{88} +(0.471041 + 8.08746i) q^{89} +(-9.04765 + 4.54390i) q^{91} +(2.61888 + 3.81843i) q^{92} +(-12.9958 - 2.55229i) q^{94} +(-0.256654 + 0.141616i) q^{95} +(-8.85687 + 4.02594i) q^{97} +(1.44453 - 0.168841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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