LMFDB - Embedded newform 81.2.e.a.46.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(10,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			46.1
Root			$0.500000 - 2.22827i$ of defining polynomial
Character	$\chi$	$=$	81.46
Dual form			81.2.e.a.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.318266 + 0.267057i) q^{2} +(-0.317323 - 1.79963i) q^{4} +(2.08159 + 0.757639i) q^{5} +(-0.229151 + 1.29958i) q^{7} +(0.795075 - 1.37711i) q^{8} +(0.460168 + 0.797034i) q^{10} +(-4.90067 + 1.78370i) q^{11} +(-0.0138336 + 0.0116078i) q^{13} +(-0.419993 + 0.352416i) q^{14} +(-2.81355 + 1.02405i) q^{16} +(-1.56640 - 2.71308i) q^{17} +(-0.208676 + 0.361438i) q^{19} +(0.702929 - 3.98651i) q^{20} +(-2.03606 - 0.741067i) q^{22} +(0.179619 + 1.01867i) q^{23} +(-0.0712019 - 0.0597455i) q^{25} -0.00750270 q^{26} +2.41147 q^{28} +(5.98068 + 5.01839i) q^{29} +(0.647649 + 3.67300i) q^{31} +(-4.15744 - 1.51319i) q^{32} +(0.226015 - 1.28180i) q^{34} +(-1.46161 + 2.53159i) q^{35} +(-2.21238 - 3.83195i) q^{37} +(-0.162939 + 0.0593049i) q^{38} +(2.69838 - 2.26421i) q^{40} +(2.81517 - 2.36221i) q^{41} +(7.80685 - 2.84146i) q^{43} +(4.76508 + 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(1.23254 - 6.99008i) q^{47} +(4.94145 + 1.79854i) q^{49} +(-0.00670569 - 0.0380299i) q^{50} +(0.0252794 + 0.0212119i) q^{52} +1.30057 q^{53} -11.5526 q^{55} +(1.60747 + 1.34883i) q^{56} +(0.563252 + 3.19436i) q^{58} +(-3.47856 - 1.26609i) q^{59} +(1.20064 - 6.80919i) q^{61} +(-0.774775 + 1.34195i) q^{62} +(2.07506 + 3.59410i) q^{64} +(-0.0375905 + 0.0136818i) q^{65} +(-8.44702 + 7.08789i) q^{67} +(-4.38548 + 3.67985i) q^{68} +(-1.14126 + 0.415384i) q^{70} +(-3.04214 - 5.26914i) q^{71} +(0.273486 - 0.473692i) q^{73} +(0.319224 - 1.81041i) q^{74} +(0.716670 + 0.260847i) q^{76} +(-1.19507 - 6.77756i) q^{77} +(0.374706 + 0.314416i) q^{79} -6.63254 q^{80} +1.52681 q^{82} +(-3.53428 - 2.96561i) q^{83} +(-1.20507 - 6.83430i) q^{85} +(3.24348 + 1.18053i) q^{86} +(-1.44005 + 8.16694i) q^{88} +(-1.68653 + 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(1.77623 - 0.646495i) q^{92} +(2.25902 - 1.89554i) q^{94} +(-0.708218 + 0.594266i) q^{95} +(-9.34182 + 3.40014i) q^{97} +(1.09238 + 1.89206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29}+ \cdots + 45 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.318266	+	0.267057i	0.225048	+	0.188837i	0.748339	−	0.663316i	$-0.230852\pi$
$2$	0.318266	+	0.267057i	0.225048	+	0.188837i	−0.523291	+	0.852154i	$0.675296\pi$
$3$		0			0
$3$		0			0
$4$	−0.317323	−	1.79963i	−0.158661	−	0.899813i
$5$	2.08159	+	0.757639i	0.930917	+	0.338826i	0.762573	−	0.646902i	$-0.223936\pi$
$5$	2.08159	+	0.757639i	0.930917	+	0.338826i	0.168344	+	0.985728i	$0.446158\pi$
$6$		0			0
$7$	−0.229151	+	1.29958i	−0.0866110	+	0.491195i	0.910386	+	0.413759i	$0.135784\pi$
$7$	−0.229151	+	1.29958i	−0.0866110	+	0.491195i	−0.996997	+	0.0774361i	$0.975327\pi$
$8$	0.795075	−	1.37711i	0.281102	−	0.486882i
$9$		0			0
$10$	0.460168	+	0.797034i	0.145518	+	0.252044i
$11$	−4.90067	+	1.78370i	−1.47761	+	0.537805i	−0.950155	−	0.311778i	$-0.899075\pi$
$11$	−4.90067	+	1.78370i	−1.47761	+	0.537805i	−0.527454	+	0.849584i	$0.676853\pi$
$12$		0			0
$13$	−0.0138336	+	0.0116078i	−0.00383676	+	0.00321942i	−0.644704	−	0.764432i	$-0.723019\pi$
$13$	−0.0138336	+	0.0116078i	−0.00383676	+	0.00321942i	0.640867	+	0.767652i	$0.278575\pi$
$14$	−0.419993	+	0.352416i	−0.112248	+	0.0941870i
$15$		0			0
$16$	−2.81355	+	1.02405i	−0.703389	+	0.256012i
$17$	−1.56640	−	2.71308i	−0.379907	−	0.658019i	0.611141	−	0.791522i	$-0.290711\pi$
$17$	−1.56640	−	2.71308i	−0.379907	−	0.658019i	−0.991048	+	0.133503i	$0.957377\pi$
$18$		0			0
$19$	−0.208676	+	0.361438i	−0.0478736	+	0.0829195i	−0.888969	−	0.457967i	$-0.848578\pi$
$19$	−0.208676	+	0.361438i	−0.0478736	+	0.0829195i	0.841096	+	0.540886i	$0.181911\pi$
$20$	0.702929	−	3.98651i	0.157180	−	0.891410i
$21$		0			0
$22$	−2.03606	−	0.741067i	−0.434090	−	0.157996i
$23$	0.179619	+	1.01867i	0.0374532	+	0.212408i	0.997791	−	0.0664316i	$-0.0211614\pi$
$23$	0.179619	+	1.01867i	0.0374532	+	0.212408i	−0.960338	+	0.278839i	$0.910050\pi$
$24$		0			0
$25$	−0.0712019	−	0.0597455i	−0.0142404	−	0.0119491i
$26$	−0.00750270			−0.00147140
$27$		0			0
$28$	2.41147			0.455726
$29$	5.98068	+	5.01839i	1.11058	+	0.931891i	0.998091	−	0.0617615i	$-0.0196718\pi$
$29$	5.98068	+	5.01839i	1.11058	+	0.931891i	0.112493	+	0.993652i	$0.464116\pi$
$30$		0			0
$31$	0.647649	+	3.67300i	0.116321	+	0.659691i	0.986088	+	0.166227i	$0.0531584\pi$
$31$	0.647649	+	3.67300i	0.116321	+	0.659691i	−0.869766	+	0.493464i	$0.835730\pi$
$32$	−4.15744	−	1.51319i	−0.734939	−	0.267496i
$33$		0			0
$34$	0.226015	−	1.28180i	0.0387613	−	0.219826i
$35$	−1.46161	+	2.53159i	−0.247058	+	0.427916i
$36$		0			0
$37$	−2.21238	−	3.83195i	−0.363713	−	0.629969i	0.624856	−	0.780740i	$-0.285158\pi$
$37$	−2.21238	−	3.83195i	−0.363713	−	0.629969i	−0.988569	+	0.150771i	$0.951824\pi$
$38$	−0.162939	+	0.0593049i	−0.0264322	+	0.00962052i
$39$		0			0
$40$	2.69838	−	2.26421i	0.426651	−	0.358002i
$41$	2.81517	−	2.36221i	0.439655	−	0.368915i	−0.395925	−	0.918283i	$-0.629576\pi$
$41$	2.81517	−	2.36221i	0.439655	−	0.368915i	0.835580	+	0.549368i	$0.185132\pi$
$42$		0			0
$43$	7.80685	−	2.84146i	1.19053	−	0.433319i	0.330622	−	0.943763i	$-0.392741\pi$
$43$	7.80685	−	2.84146i	1.19053	−	0.433319i	0.859911	+	0.510445i	$0.170519\pi$
$44$	4.76508	+	8.25337i	0.718363	+	1.24424i
$45$		0			0
$46$	−0.214876	+	0.372177i	−0.0316818	+	0.0548745i
$47$	1.23254	−	6.99008i	0.179784	−	1.01961i	−0.752691	−	0.658374i	$-0.771245\pi$
$47$	1.23254	−	6.99008i	0.179784	−	1.01961i	0.932475	−	0.361234i	$-0.117644\pi$
$48$		0			0
$49$	4.94145	+	1.79854i	0.705921	+	0.256934i
$50$	−0.00670569	−	0.0380299i	−0.000948328	−	0.00537824i
$51$		0			0
$52$	0.0252794	+	0.0212119i	0.00350562	+	0.00294157i
$53$	1.30057			0.178648			0.0893238	−	0.996003i	$-0.471529\pi$
$53$	1.30057			0.178648			0.0893238	+	0.996003i	$0.471529\pi$
$54$		0			0
$55$	−11.5526			−1.55775
$56$	1.60747	+	1.34883i	0.214808	+	0.180245i
$57$		0			0
$58$	0.563252	+	3.19436i	0.0739586	+	0.419440i
$59$	−3.47856	−	1.26609i	−0.452871	−	0.164831i	0.105507	−	0.994419i	$-0.466354\pi$
$59$	−3.47856	−	1.26609i	−0.452871	−	0.164831i	−0.558377	+	0.829587i	$0.688576\pi$
$60$		0			0
$61$	1.20064	−	6.80919i	0.153727	−	0.871828i	−0.806214	−	0.591624i	$-0.798487\pi$
$61$	1.20064	−	6.80919i	0.153727	−	0.871828i	0.959941	−	0.280204i	$-0.0904020\pi$
$62$	−0.774775	+	1.34195i	−0.0983965	+	0.170428i
$63$		0			0
$64$	2.07506	+	3.59410i	0.259382	+	0.449263i
$65$	−0.0375905	+	0.0136818i	−0.00466253	+	0.00169702i
$66$		0			0
$67$	−8.44702	+	7.08789i	−1.03197	+	0.865923i	−0.991084	−	0.133241i	$-0.957462\pi$
$67$	−8.44702	+	7.08789i	−1.03197	+	0.865923i	−0.0408835	+	0.999164i	$0.513017\pi$
$68$	−4.38548	+	3.67985i	−0.531817	+	0.446247i
$69$		0			0
$70$	−1.14126	+	0.415384i	−0.136406	+	0.0496479i
$71$	−3.04214	−	5.26914i	−0.361035	−	0.625332i	0.627096	−	0.778942i	$-0.284243\pi$
$71$	−3.04214	−	5.26914i	−0.361035	−	0.625332i	−0.988132	+	0.153610i	$0.950910\pi$
$72$		0			0
$73$	0.273486	−	0.473692i	0.0320092	−	0.0554415i	−0.849577	−	0.527465i	$-0.823143\pi$
$73$	0.273486	−	0.473692i	0.0320092	−	0.0554415i	0.881586	+	0.472023i	$0.156476\pi$
$74$	0.319224	−	1.81041i	0.0371090	−	0.210456i
$75$		0			0
$76$	0.716670	+	0.260847i	0.0822077	+	0.0299212i
$77$	−1.19507	−	6.77756i	−0.136190	−	0.772374i
$78$		0			0
$79$	0.374706	+	0.314416i	0.0421577	+	0.0353745i	0.663623	−	0.748067i	$-0.269018\pi$
$79$	0.374706	+	0.314416i	0.0421577	+	0.0353745i	−0.621465	+	0.783442i	$0.713462\pi$
$80$	−6.63254			−0.741540
$81$		0			0
$82$	1.52681			0.168608
$83$	−3.53428	−	2.96561i	−0.387937	−	0.325518i	0.427872	−	0.903839i	$-0.359263\pi$
$83$	−3.53428	−	2.96561i	−0.387937	−	0.325518i	−0.815809	+	0.578321i	$0.803708\pi$
$84$		0			0
$85$	−1.20507	−	6.83430i	−0.130708	−	0.741284i
$86$	3.24348	+	1.18053i	0.349754	+	0.127300i
$87$		0			0
$88$	−1.44005	+	8.16694i	−0.153510	+	0.870599i
$89$	−1.68653	+	2.92116i	−0.178772	+	0.309642i	−0.941460	−	0.337124i	$-0.890546\pi$
$89$	−1.68653	+	2.92116i	−0.178772	+	0.309642i	0.762688	+	0.646766i	$0.223879\pi$
$90$		0			0
$91$	−0.0119153	−	0.0206379i	−0.00124906	−	0.00216344i
$92$	1.77623	−	0.646495i	0.185185	−	0.0674018i
$93$		0			0
$94$	2.25902	−	1.89554i	0.233000	−	0.195510i
$95$	−0.708218	+	0.594266i	−0.0726617	+	0.0609704i
$96$		0			0
$97$	−9.34182	+	3.40014i	−0.948518	+	0.345232i	−0.769524	−	0.638618i	$-0.779507\pi$
$97$	−9.34182	+	3.40014i	−0.948518	+	0.345232i	−0.178994	+	0.983850i	$0.557284\pi$
$98$	1.09238	+	1.89206i	0.110347	+	0.191127i
$99$		0			0
$100$	−0.0849256	+	0.147095i	−0.00849256	+	0.0147095i
$101$	−2.39626	+	13.5898i	−0.238436	+	1.35224i	0.596818	+	0.802377i	$0.296431\pi$
$101$	−2.39626	+	13.5898i	−0.238436	+	1.35224i	−0.835255	+	0.549863i	$0.814680\pi$
$102$		0			0
$103$	−4.28981	−	1.56136i	−0.422687	−	0.153846i	0.121914	−	0.992541i	$-0.461097\pi$
$103$	−4.28981	−	1.56136i	−0.422687	−	0.153846i	−0.544601	+	0.838695i	$0.683319\pi$
$104$	0.00498644	+	0.0282795i	0.000488961	+	0.00277303i
$105$		0			0
$106$	0.413928	+	0.347327i	0.0402042	+	0.0337354i
$107$	11.2965			1.09207			0.546035	−	0.837762i	$-0.316136\pi$
$107$	11.2965			1.09207			0.546035	+	0.837762i	$0.316136\pi$
$108$		0			0
$109$	14.5032			1.38915			0.694577	−	0.719419i	$-0.255592\pi$
$109$	14.5032			1.38915			0.694577	+	0.719419i	$0.255592\pi$
$110$	−3.67680	−	3.08520i	−0.350569	−	0.294162i
$111$		0			0
$112$	−0.686107	−	3.89110i	−0.0648310	−	0.367675i
$113$	11.8011	+	4.29523i	1.11015	+	0.404062i	0.831049	−	0.556200i	$-0.187741\pi$
$113$	11.8011	+	4.29523i	1.11015	+	0.404062i	0.279102	+	0.960262i	$0.409963\pi$
$114$		0			0
$115$	−0.397890	+	2.25655i	−0.0371035	+	0.210424i
$116$	7.13341	−	12.3554i	0.662321	−	1.14717i
$117$		0			0
$118$	−0.768989	−	1.33193i	−0.0707912	−	0.122614i
$119$	3.88481	−	1.41395i	0.356120	−	0.129617i
$120$		0			0
$121$	12.4085	−	10.4120i	1.12805	−	0.946544i
$122$	2.20056	−	1.84649i	0.199230	−	0.167174i
$123$		0			0
$124$	6.40452	−	2.33105i	0.575143	−	0.209335i
$125$	−5.64092	−	9.77035i	−0.504539	−	0.873887i
$126$		0			0
$127$	4.19749	−	7.27027i	0.372467	−	0.645132i	−0.617477	−	0.786589i	$-0.711845\pi$
$127$	4.19749	−	7.27027i	0.372467	−	0.645132i	0.989944	+	0.141456i	$0.0451785\pi$
$128$	−1.83594	+	10.4121i	−0.162276	+	0.920310i
$129$		0			0
$130$	−0.0156176	−	0.00568434i	−0.00136975	−	0.000498549i
$131$	2.69761	+	15.2989i	0.235691	+	1.33667i	0.841154	+	0.540796i	$0.181877\pi$
$131$	2.69761	+	15.2989i	0.235691	+	1.33667i	−0.605463	+	0.795874i	$0.707012\pi$
$132$		0			0
$133$	−0.421899	−	0.354015i	−0.0365833	−	0.0306970i
$134$	−4.58126			−0.395761
$135$		0			0
$136$	−4.98162			−0.427170
$137$	−9.19820	−	7.71820i	−0.785855	−	0.659411i	0.158861	−	0.987301i	$-0.449218\pi$
$137$	−9.19820	−	7.71820i	−0.785855	−	0.659411i	−0.944716	+	0.327890i	$0.893662\pi$
$138$		0			0
$139$	1.06709	+	6.05176i	0.0905093	+	0.513304i	0.996031	+	0.0890042i	$0.0283685\pi$
$139$	1.06709	+	6.05176i	0.0905093	+	0.513304i	−0.905522	+	0.424299i	$0.860520\pi$
$140$	5.01971	+	1.82703i	0.424243	+	0.154412i
$141$		0			0
$142$	0.438950	−	2.48941i	0.0368359	−	0.208907i
$143$	0.0470893	−	0.0815610i	0.00393780	−	0.00682047i
$144$		0			0
$145$	8.64723	+	14.9774i	0.718113	+	1.24381i
$146$	0.213544	−	0.0777237i	0.0176730	−	0.00643246i
$147$		0			0
$148$	−6.19404	+	5.19742i	−0.509147	+	0.427225i
$149$	−0.676280	+	0.567466i	−0.0554030	+	0.0464886i	−0.670069	−	0.742299i	$-0.733735\pi$
$149$	−0.676280	+	0.567466i	−0.0554030	+	0.0464886i	0.614666	+	0.788788i	$0.289291\pi$
$150$		0			0
$151$	−7.72942	+	2.81328i	−0.629011	+	0.228941i	−0.636801	−	0.771028i	$-0.719743\pi$
$151$	−7.72942	+	2.81328i	−0.629011	+	0.228941i	0.00778980	+	0.999970i	$0.497520\pi$
$152$	0.331826	+	0.574740i	0.0269147	+	0.0466176i
$153$		0			0
$154$	1.42964	−	2.47621i	0.115204	−	0.199539i
$155$	−1.43466	+	8.13639i	−0.115235	+	0.653530i
$156$		0			0
$157$	−11.8024	−	4.29571i	−0.941932	−	0.342835i	−0.175003	−	0.984568i	$-0.555994\pi$
$157$	−11.8024	−	4.29571i	−0.941932	−	0.342835i	−0.766928	+	0.641733i	$0.778216\pi$
$158$	0.0352893	+	0.200135i	0.00280746	+	0.0159219i
$159$		0			0
$160$	−7.50766	−	6.29968i	−0.593533	−	0.498033i
$161$	−1.36501			−0.107578
$162$		0			0
$163$	3.31466			0.259624			0.129812	−	0.991539i	$-0.458563\pi$
$163$	3.31466			0.259624			0.129812	+	0.991539i	$0.458563\pi$
$164$	−5.14440	−	4.31667i	−0.401710	−	0.337075i
$165$		0			0
$166$	−0.332853	−	1.88770i	−0.0258344	−	0.146514i
$167$	−19.3229	−	7.03295i	−1.49525	−	0.544226i	−0.540424	−	0.841393i	$-0.681736\pi$
$167$	−19.3229	−	7.03295i	−1.49525	−	0.544226i	−0.954826	+	0.297167i	$0.903958\pi$
$168$		0			0
$169$	−2.25737	+	12.8022i	−0.173644	+	0.984783i
$170$	1.44161	−	2.49694i	0.110567	−	0.191507i
$171$		0			0
$172$	−7.59085	−	13.1477i	−0.578797	−	1.00251i
$173$	13.1870	−	4.79966i	1.00259	−	0.364911i	0.212005	−	0.977269i	$-0.432001\pi$
$173$	13.1870	−	4.79966i	1.00259	−	0.364911i	0.790581	+	0.612357i	$0.209779\pi$
$174$		0			0
$175$	0.0939601	−	0.0788419i	0.00710272	−	0.00595989i
$176$	11.9617	−	10.0371i	0.901648	−	0.756572i
$177$		0			0
$178$	−1.31688	+	0.479305i	−0.0987043	+	0.0359254i
$179$	5.09500	+	8.82479i	0.380818	+	0.659596i	0.991179	−	0.132527i	$-0.0423091\pi$
$179$	5.09500	+	8.82479i	0.380818	+	0.659596i	−0.610361	+	0.792123i	$0.708976\pi$
$180$		0			0
$181$	−12.0274	+	20.8320i	−0.893987	+	1.54843i	−0.0589331	+	0.998262i	$0.518770\pi$
$181$	−12.0274	+	20.8320i	−0.893987	+	1.54843i	−0.835054	+	0.550169i	$0.814563\pi$
$182$	0.00171925	−	0.00975037i	0.000127440	−	0.000722746i
$183$		0			0
$184$	1.54563	+	0.562565i	0.113946	+	0.0414728i
$185$	−1.70204	−	9.65275i	−0.125137	−	0.709685i
$186$		0			0
$187$	12.5157	+	10.5019i	0.915240	+	0.767978i
$188$	−12.9706			−0.945981
$189$		0			0
$190$	−0.384104			−0.0278658
$191$	−8.38541	−	7.03619i	−0.606747	−	0.509121i	0.286860	−	0.957973i	$-0.407389\pi$
$191$	−8.38541	−	7.03619i	−0.606747	−	0.509121i	−0.893606	+	0.448852i	$0.851833\pi$
$192$		0			0
$193$	−1.87644	−	10.6418i	−0.135069	−	0.766013i	−0.974812	−	0.223029i	$-0.928405\pi$
$193$	−1.87644	−	10.6418i	−0.135069	−	0.766013i	0.839743	−	0.542984i	$-0.182706\pi$
$194$	−3.88121	−	1.41265i	−0.278655	−	0.101422i
$195$		0			0
$196$	1.66867	−	9.46347i	0.119190	−	0.675962i
$197$	−11.0367	+	19.1161i	−0.786331	+	1.36196i	0.141870	+	0.989885i	$0.454689\pi$
$197$	−11.0367	+	19.1161i	−0.786331	+	1.36196i	−0.928201	+	0.372080i	$0.878645\pi$
$198$		0			0
$199$	−6.44338	−	11.1603i	−0.456759	−	0.791130i	0.542028	−	0.840360i	$-0.317657\pi$
$199$	−6.44338	−	11.1603i	−0.456759	−	0.791130i	−0.998787	+	0.0492301i	$0.984323\pi$
$200$	−0.138887	+	0.0505508i	−0.00982080	+	0.00357448i
$201$		0			0
$202$	−4.39190	+	3.68524i	−0.309013	+	0.259293i
$203$	−7.89228	+	6.62241i	−0.553929	+	0.464802i
$204$		0			0
$205$	7.64974	−	2.78428i	0.534281	−	0.194462i
$206$	−0.948326	−	1.64255i	−0.0660730	−	0.114442i
$207$		0			0
$208$	0.0270347	−	0.0468255i	0.00187452	−	0.00324676i
$209$	0.377957	−	2.14350i	0.0261439	−	0.148269i
$210$		0			0
$211$	22.5485	+	8.20699i	1.55230	+	0.564992i	0.968957	−	0.247230i	$-0.0795204\pi$
$211$	22.5485	+	8.20699i	1.55230	+	0.564992i	0.583347	+	0.812223i	$0.301743\pi$
$212$	−0.412702	−	2.34055i	−0.0283445	−	0.160749i
$213$		0			0
$214$	3.59528	+	3.01680i	0.245768	+	0.206224i
$215$	18.4035			1.25511
$216$		0			0
$217$	−4.92177			−0.334112
$218$	4.61587	+	3.87317i	0.312626	+	0.262324i
$219$		0			0
$220$	3.66590	+	20.7904i	0.247155	+	1.40169i
$221$	0.0531618	+	0.0193493i	0.00357605	+	0.00130158i
$222$		0			0
$223$	3.76160	−	21.3331i	0.251895	−	1.42857i	−0.552023	−	0.833829i	$-0.686144\pi$
$223$	3.76160	−	21.3331i	0.251895	−	1.42857i	0.803918	−	0.594740i	$-0.202745\pi$
$224$	2.91919	−	5.05618i	0.195047	−	0.337831i
$225$		0			0
$226$	2.60880	+	4.51858i	0.173535	+	0.300571i
$227$	20.3367	−	7.40196i	1.34979	−	0.491285i	0.436911	−	0.899505i	$-0.356072\pi$
$227$	20.3367	−	7.40196i	1.34979	−	0.491285i	0.912884	+	0.408220i	$0.133850\pi$
$228$		0			0
$229$	−8.27739	+	6.94555i	−0.546985	+	0.458975i	−0.873919	−	0.486072i	$-0.838429\pi$
$229$	−8.27739	+	6.94555i	−0.546985	+	0.458975i	0.326934	+	0.945047i	$0.393985\pi$
$230$	−0.729261	+	0.611922i	−0.0480860	+	0.0403490i
$231$		0			0
$232$	11.6660	−	4.24606i	0.765908	−	0.278768i
$233$	3.81950	+	6.61557i	0.250224	+	0.433400i	0.963587	−	0.267394i	$-0.0861625\pi$
$233$	3.81950	+	6.61557i	0.250224	+	0.433400i	−0.713364	+	0.700794i	$0.752829\pi$
$234$		0			0
$235$	7.86160	−	13.6167i	0.512834	−	0.888255i
$236$	−1.17467	+	6.66187i	−0.0764644	+	0.433651i
$237$		0			0
$238$	1.61401	+	0.587451i	0.104621	+	0.0380788i
$239$	0.561143	+	3.18240i	0.0362973	+	0.205852i	0.997563	−	0.0697711i	$-0.0222269\pi$
$239$	0.561143	+	3.18240i	0.0362973	+	0.205852i	−0.961266	+	0.275623i	$0.911116\pi$
$240$		0			0
$241$	−20.3346	−	17.0628i	−1.30987	−	1.09911i	−0.988349	−	0.152206i	$-0.951362\pi$
$241$	−20.3346	−	17.0628i	−1.30987	−	1.09911i	−0.321518	−	0.946903i	$-0.604193\pi$
$242$	6.72979			0.432608
$243$		0			0
$244$	−12.6350			−0.808873
$245$	8.92345	+	7.48766i	0.570098	+	0.478369i
$246$		0			0
$247$	−0.00130875	−	0.00742226i	−8.32735e−5	−	0.000472267i
$248$	5.57306	+	2.02843i	0.353890	+	0.128805i
$249$		0			0
$250$	0.813927	−	4.61601i	0.0514773	−	0.291942i
$251$	−2.24965	+	3.89651i	−0.141997	+	0.245945i	−0.928248	−	0.371961i	$-0.878686\pi$
$251$	−2.24965	+	3.89651i	−0.141997	+	0.245945i	0.786252	+	0.617906i	$0.212019\pi$
$252$		0			0
$253$	−2.69726	−	4.67179i	−0.169575	−	0.293713i
$254$	3.27749	−	1.19291i	0.205648	−	0.0748498i
$255$		0			0
$256$	2.99340	−	2.51176i	0.187088	−	0.156985i
$257$	−10.5219	+	8.82895i	−0.656340	+	0.550735i	−0.908987	−	0.416824i	$-0.863143\pi$
$257$	−10.5219	+	8.82895i	−0.656340	+	0.550735i	0.252647	+	0.967559i	$0.418699\pi$
$258$		0			0
$259$	5.48690	−	1.99707i	0.340939	−	0.124092i
$260$	0.0365505	+	0.0633073i	0.00226677	+	0.00392615i
$261$		0			0
$262$	−3.22711	+	5.58952i	−0.199372	+	0.345322i
$263$	4.20273	−	23.8349i	0.259151	−	1.46972i	−0.526036	−	0.850462i	$-0.676322\pi$
$263$	4.20273	−	23.8349i	0.259151	−	1.46972i	0.785187	−	0.619258i	$-0.212567\pi$
$264$		0			0
$265$	2.70727	+	0.985365i	0.166306	+	0.0605305i
$266$	−0.0397339	−	0.225342i	−0.00243624	−	0.0138166i
$267$		0			0
$268$	15.4360	+	12.9523i	0.942902	+	0.791189i
$269$	−12.0062			−0.732032			−0.366016	−	0.930609i	$-0.619278\pi$
$269$	−12.0062			−0.732032			−0.366016	+	0.930609i	$0.619278\pi$
$270$		0			0
$271$	3.71777			0.225839			0.112919	−	0.993604i	$-0.463980\pi$
$271$	3.71777			0.225839			0.112919	+	0.993604i	$0.463980\pi$
$272$	7.18547	+	6.02933i	0.435683	+	0.365582i
$273$		0			0
$274$	−0.866273	−	4.91288i	−0.0523335	−	0.296798i
$275$	0.455505	+	0.165790i	0.0274680	+	0.00999753i
$276$		0			0
$277$	−4.07780	+	23.1264i	−0.245011	+	1.38953i	0.575455	+	0.817833i	$0.304825\pi$
$277$	−4.07780	+	23.1264i	−0.245011	+	1.38953i	−0.820466	+	0.571695i	$0.806286\pi$
$278$	−1.27654	+	2.21104i	−0.0765621	+	0.132609i
$279$		0			0
$280$	2.32418	+	4.02560i	0.138897	+	0.240576i
$281$	−19.1432	+	6.96754i	−1.14199	+	0.415649i	−0.842630	−	0.538493i	$-0.818994\pi$
$281$	−19.1432	+	6.96754i	−1.14199	+	0.415649i	−0.299356	+	0.954142i	$0.596772\pi$
$282$		0			0
$283$	8.88607	−	7.45630i	0.528222	−	0.443231i	−0.339265	−	0.940691i	$-0.610178\pi$
$283$	8.88607	−	7.45630i	0.528222	−	0.443231i	0.867487	+	0.497460i	$0.165734\pi$
$284$	−8.51714	+	7.14673i	−0.505399	+	0.424080i
$285$		0			0
$286$	0.0367683	−	0.0133826i	0.00217416	−	0.000791328i
$287$	2.42478	+	4.19984i	0.143130	+	0.247909i
$288$		0			0
$289$	3.59280	−	6.22291i	0.211341	−	0.366053i
$290$	−1.24771	+	7.07610i	−0.0732679	+	0.415523i
$291$		0			0
$292$	−0.939253	−	0.341860i	−0.0549656	−	0.0200058i
$293$	−5.48280	−	31.0945i	−0.320308	−	1.81656i	−0.540779	−	0.841165i	$-0.681870\pi$
$293$	−5.48280	−	31.0945i	−0.320308	−	1.81656i	0.220470	−	0.975394i	$-0.429241\pi$
$294$		0			0
$295$	−6.28172	−	5.27099i	−0.365736	−	0.306889i
$296$	−7.03603			−0.408961
$297$		0			0
$298$	−0.366782			−0.0212471
$299$	−0.0143093	−	0.0120069i	−0.000827529	−	0.000694379i
$300$		0			0
$301$	1.90376	+	10.7968i	0.109731	+	0.622315i
$302$	−3.21131	−	1.16882i	−0.184790	−	0.0672581i
$303$		0			0
$304$	0.216991	−	1.23062i	0.0124453	−	0.0705809i
$305$	7.65816	−	13.2643i	0.438505	−	0.759513i
$306$		0			0
$307$	4.06027	+	7.03259i	0.231732	+	0.401371i	0.958318	−	0.285704i	$-0.0922275\pi$
$307$	4.06027	+	7.03259i	0.231732	+	0.401371i	−0.726586	+	0.687075i	$0.758894\pi$
$308$	−11.8178	+	4.30134i	−0.673384	+	0.245092i
$309$		0			0
$310$	−2.62948	+	2.20640i	−0.149344	+	0.125315i
$311$	18.2691	−	15.3296i	1.03594	−	0.869259i	0.0443970	−	0.999014i	$-0.485863\pi$
$311$	18.2691	−	15.3296i	1.03594	−	0.869259i	0.991546	+	0.129754i	$0.0414189\pi$
$312$		0			0
$313$	−25.2876	+	9.20392i	−1.42934	+	0.520236i	−0.936742	−	0.350022i	$-0.886174\pi$
$313$	−25.2876	+	9.20392i	−1.42934	+	0.520236i	−0.492596	+	0.870258i	$0.663952\pi$
$314$	−2.60909	−	4.51908i	−0.147240	−	0.255026i
$315$		0			0
$316$	0.446928	−	0.774102i	0.0251417	−	0.0435466i
$317$	1.44689	−	8.20574i	0.0812657	−	0.460881i	−0.916834	−	0.399268i	$-0.869264\pi$
$317$	1.44689	−	8.20574i	0.0812657	−	0.460881i	0.998100	−	0.0616130i	$-0.0196244\pi$
$318$		0			0
$319$	−38.2606	−	13.9257i	−2.14218	−	0.779692i
$320$	1.59640	+	9.05361i	0.0892412	+	0.506112i
$321$		0			0
$322$	−0.434435	−	0.364534i	−0.0242101	−	0.0203147i
$323$	1.30748			0.0727501
$324$		0			0
$325$	0.00167849			9.31061e−5
$326$	1.05494	+	0.885201i	0.0584278	+	0.0490268i
$327$		0			0
$328$	−1.01475	−	5.75493i	−0.0560301	−	0.317763i
$329$	8.80173	+	3.20357i	0.485255	+	0.176618i
$330$		0			0
$331$	−1.11487	+	6.32272i	−0.0612786	+	0.347528i	0.938717	+	0.344688i	$0.112015\pi$
$331$	−1.11487	+	6.32272i	−0.0612786	+	0.347528i	−0.999996	+	0.00284030i	$0.999096\pi$
$332$	−4.21548	+	7.30143i	−0.231355	+	0.400718i
$333$		0			0
$334$	−4.27161	−	7.39865i	−0.233732	−	0.404836i
$335$	−22.9533	+	8.35432i	−1.25407	+	0.456446i
$336$		0			0
$337$	5.72610	−	4.80477i	0.311921	−	0.261732i	−0.473365	−	0.880867i	$-0.656961\pi$
$337$	5.72610	−	4.80477i	0.311921	−	0.261732i	0.785285	+	0.619134i	$0.212516\pi$
$338$	−4.13735	+	3.47165i	−0.225042	+	0.188833i
$339$		0			0
$340$	−11.9168	+	4.33735i	−0.646278	+	0.235226i
$341$	−9.72545	−	16.8450i	−0.526663	−	0.912206i
$342$		0			0
$343$	−8.08839	+	14.0095i	−0.436732	+	0.756442i
$344$	2.29403	−	13.0101i	0.123686	−	0.701456i
$345$		0			0
$346$	5.47874	+	1.99410i	0.294539	+	0.107203i
$347$	5.46202	+	30.9766i	0.293216	+	1.66291i	0.674364	+	0.738399i	$0.264418\pi$
$347$	5.46202	+	30.9766i	0.293216	+	1.66291i	−0.381148	+	0.924514i	$0.624471\pi$
$348$		0			0
$349$	9.07988	+	7.61893i	0.486035	+	0.407832i	0.852603	−	0.522560i	$-0.175023\pi$
$349$	9.07988	+	7.61893i	0.486035	+	0.407832i	−0.366568	+	0.930391i	$0.619467\pi$
$350$	0.0509595			0.00272390
$351$		0			0
$352$	23.0733			1.22981
$353$	6.28699	+	5.27541i	0.334623	+	0.280782i	0.794580	−	0.607159i	$-0.207691\pi$
$353$	6.28699	+	5.27541i	0.334623	+	0.280782i	−0.459958	+	0.887941i	$0.652135\pi$
$354$		0			0
$355$	−2.34040	−	13.2731i	−0.124215	−	0.704461i
$356$	5.79217	+	2.10818i	0.306984	+	0.111733i
$357$		0			0
$358$	−0.735157	+	4.16928i	−0.0388542	+	0.220353i
$359$	8.86365	−	15.3523i	0.467806	−	0.810263i	−0.531517	−	0.847047i	$-0.678378\pi$
$359$	8.86365	−	15.3523i	0.467806	−	0.810263i	0.999323	+	0.0367840i	$0.0117114\pi$
$360$		0			0
$361$	9.41291	+	16.3036i	0.495416	+	0.858086i
$362$	−9.39122	+	3.41812i	−0.493591	+	0.179653i
$363$		0			0
$364$	−0.0333594	+	0.0279919i	−0.00174851	+	0.00146717i
$365$	0.928176	−	0.778832i	0.0485829	−	0.0407659i
$366$		0			0
$367$	19.0941	−	6.94969i	0.996704	−	0.362771i	0.208392	−	0.978045i	$-0.433177\pi$
$367$	19.0941	−	6.94969i	0.996704	−	0.362771i	0.788313	+	0.615275i	$0.210955\pi$
$368$	−1.54854	−	2.68215i	−0.0807232	−	0.139817i
$369$		0			0
$370$	2.03613	−	3.52668i	0.105853	−	0.183343i
$371$	−0.298028	+	1.69020i	−0.0154728	+	0.0877509i
$372$		0			0
$373$	9.09758	+	3.31125i	0.471055	+	0.171450i	0.566630	−	0.823972i	$-0.308247\pi$
$373$	9.09758	+	3.31125i	0.471055	+	0.171450i	−0.0955754	+	0.995422i	$0.530469\pi$
$374$	1.17871	+	6.68481i	0.0609498	+	0.345663i
$375$		0			0
$376$	−8.64615	−	7.25498i	−0.445891	−	0.374147i
$377$	−0.140987			−0.00726119
$378$		0			0
$379$	−4.12905			−0.212095			−0.106048	−	0.994361i	$-0.533820\pi$
$379$	−4.12905			−0.212095			−0.106048	+	0.994361i	$0.533820\pi$
$380$	1.29419	+	1.08595i	0.0663905	+	0.0557083i
$381$		0			0
$382$	−0.789725	−	4.47876i	−0.0404059	−	0.229153i
$383$	4.46371	+	1.62466i	0.228085	+	0.0830162i	0.453535	−	0.891239i	$-0.350163\pi$
$383$	4.46371	+	1.62466i	0.228085	+	0.0830162i	−0.225450	+	0.974255i	$0.572385\pi$
$384$		0			0
$385$	2.64729	−	15.0136i	0.134919	−	0.765162i
$386$	2.24476	−	3.88803i	0.114255	−	0.197896i
$387$		0			0
$388$	9.08336	+	15.7328i	0.461138	+	0.798714i
$389$	−20.4978	+	7.46059i	−1.03928	+	0.378267i	−0.804607	−	0.593807i	$-0.797624\pi$
$389$	−20.4978	+	7.46059i	−1.03928	+	0.378267i	−0.234673	+	0.972074i	$0.575402\pi$
$390$		0			0
$391$	2.48238	−	2.08297i	0.125539	−	0.105340i
$392$	6.40561	−	5.37495i	0.323532	−	0.271476i
$393$		0			0
$394$	−8.61767	+	3.13658i	−0.434152	+	0.158018i
$395$	0.541773	+	0.938378i	0.0272595	+	0.0472149i
$396$		0			0
$397$	17.4245	−	30.1802i	0.874512	−	1.51470i	0.0172294	−	0.999852i	$-0.494515\pi$
$397$	17.4245	−	30.1802i	0.874512	−	1.51470i	0.857282	−	0.514847i	$-0.172151\pi$
$398$	0.929715	−	5.27268i	0.0466024	−	0.264295i
$399$		0			0
$400$	0.261513	+	0.0951829i	0.0130756	+	0.00475914i
$401$	3.26911	+	18.5401i	0.163252	+	0.925847i	0.950849	+	0.309656i	$0.100214\pi$
$401$	3.26911	+	18.5401i	0.163252	+	0.925847i	−0.787597	+	0.616191i	$0.788675\pi$
$402$		0			0
$403$	−0.0515948	−	0.0432932i	−0.00257012	−	0.00215659i
$404$	25.2170			1.25459
$405$		0			0
$406$	−4.28040			−0.212433
$407$	17.6772	+	14.8329i	0.876226	+	0.735241i
$408$		0			0
$409$	−1.10439	−	6.26334i	−0.0546088	−	0.309702i	0.945253	−	0.326339i	$-0.105815\pi$
$409$	−1.10439	−	6.26334i	−0.0546088	−	0.309702i	−0.999862	+	0.0166371i	$0.994704\pi$
$410$	3.17821	+	1.15677i	0.156960	+	0.0571289i
$411$		0			0
$412$	−1.44862	+	8.21551i	−0.0713682	+	0.404749i
$413$	2.44251	−	4.23055i	0.120188	−	0.208172i
$414$		0			0
$415$	−5.11007	−	8.85090i	−0.250843	−	0.434474i
$416$	0.0750772	−	0.0273259i	0.00368096	−	0.00133976i
$417$		0			0
$418$	0.692727	−	0.581267i	0.0338824	−	0.0284307i
$419$	18.6286	−	15.6313i	0.910069	−	0.763638i	−0.0620632	−	0.998072i	$-0.519768\pi$
$419$	18.6286	−	15.6313i	0.910069	−	0.763638i	0.972132	+	0.234434i	$0.0753236\pi$
$420$		0			0
$421$	7.50818	−	2.73275i	0.365926	−	0.133186i	−0.152511	−	0.988302i	$-0.548736\pi$
$421$	7.50818	−	2.73275i	0.365926	−	0.133186i	0.518438	+	0.855115i	$0.326514\pi$
$422$	4.98469	+	8.63373i	0.242651	+	0.420283i
$423$		0			0
$424$	1.03405	−	1.79103i	0.0502181	−	0.0869803i
$425$	−0.0505638	+	0.286762i	−0.00245271	+	0.0139100i
$426$		0			0
$427$	8.57397	+	3.12067i	0.414924	+	0.151020i
$428$	−3.58462	−	20.3294i	−0.173269	−	0.982659i
$429$		0			0
$430$	5.85720	+	4.91477i	0.282459	+	0.237011i
$431$	−9.87124			−0.475481			−0.237740	−	0.971329i	$-0.576407\pi$
$431$	−9.87124			−0.475481			−0.237740	+	0.971329i	$0.576407\pi$
$432$		0			0
$433$	−6.10369			−0.293325			−0.146662	−	0.989187i	$-0.546853\pi$
$433$	−6.10369			−0.293325			−0.146662	+	0.989187i	$0.546853\pi$
$434$	−1.56643	−	1.31439i	−0.0751911	−	0.0630928i
$435$		0			0
$436$	−4.60219	−	26.1003i	−0.220405	−	1.24998i
$437$	−0.405669	−	0.147651i	−0.0194058	−	0.00706312i
$438$		0			0
$439$	−2.62800	+	14.9041i	−0.125427	+	0.711334i	0.855626	+	0.517595i	$0.173173\pi$
$439$	−2.62800	+	14.9041i	−0.125427	+	0.711334i	−0.981053	+	0.193739i	$0.937938\pi$
$440$	−9.18520	+	15.9092i	−0.437887	+	0.758443i
$441$		0			0
$442$	0.0117522	+	0.0203554i	0.000558996	+	0.000968210i
$443$	−0.679204	+	0.247210i	−0.0322699	+	0.0117453i	−0.358105	−	0.933681i	$-0.616577\pi$
$443$	−0.679204	+	0.247210i	−0.0322699	+	0.0117453i	0.325835	+	0.945427i	$0.394355\pi$
$444$		0			0
$445$	−5.72386	+	4.80289i	−0.271337	+	0.227679i
$446$	6.89432	−	5.78502i	0.326456	−	0.273929i
$447$		0			0
$448$	−5.14633	+	1.87311i	−0.243141	+	0.0884962i
$449$	0.834224	+	1.44492i	0.0393695	+	0.0681899i	0.885039	−	0.465517i	$-0.154132\pi$
$449$	0.834224	+	1.44492i	0.0393695	+	0.0681899i	−0.845669	+	0.533707i	$0.820798\pi$
$450$		0			0
$451$	−9.58275	+	16.5978i	−0.451234	+	0.781560i
$452$	3.98507	−	22.6005i	0.187442	−	1.06304i
$453$		0			0
$454$	8.44922	+	3.07526i	0.396541	+	0.144329i
$455$	−0.00916673	−	0.0519871i	−0.000429743	−	0.00243719i
$456$		0			0
$457$	8.49041	+	7.12430i	0.397165	+	0.333261i	0.819397	−	0.573227i	$-0.194309\pi$
$457$	8.49041	+	7.12430i	0.397165	+	0.333261i	−0.422232	+	0.906488i	$0.638753\pi$
$458$	−4.48926			−0.209769
$459$		0			0
$460$	4.18720			0.195229
$461$	16.7644	+	14.0670i	0.780797	+	0.655166i	0.943449	−	0.331517i	$-0.107561\pi$
$461$	16.7644	+	14.0670i	0.780797	+	0.655166i	−0.162653	+	0.986683i	$0.552005\pi$
$462$		0			0
$463$	4.31546	+	24.4742i	0.200556	+	1.13741i	0.904281	+	0.426938i	$0.140408\pi$
$463$	4.31546	+	24.4742i	0.200556	+	1.13741i	−0.703724	+	0.710473i	$0.748481\pi$
$464$	−21.9660	−	7.99499i	−1.01975	−	0.371158i
$465$		0			0
$466$	−0.551115	+	3.12553i	−0.0255299	+	0.144787i
$467$	−5.91777	+	10.2499i	−0.273842	+	0.474308i	−0.969842	−	0.243734i	$-0.921628\pi$
$467$	−5.91777	+	10.2499i	−0.273842	+	0.474308i	0.696001	+	0.718041i	$0.254961\pi$
$468$		0			0
$469$	−7.27564	−	12.6018i	−0.335958	−	0.581896i
$470$	6.13850	−	2.23423i	0.283148	−	0.103057i
$471$		0			0
$472$	−4.50927	+	3.78373i	−0.207556	+	0.174160i
$473$	−33.1905	+	27.8501i	−1.52610	+	1.28055i
$474$		0			0
$475$	0.0364524	−	0.0132676i	0.00167255	−	0.000608759i
$476$	−3.77733	−	6.54252i	−0.173134	−	0.299876i
$477$		0			0
$478$	−0.671288	+	1.16270i	−0.0307040	+	0.0531809i
$479$	−0.501383	+	2.84349i	−0.0229088	+	0.129922i	−0.994117	−	0.108309i	$-0.965456\pi$
$479$	−0.501383	+	2.84349i	−0.0229088	+	0.129922i	0.971209	+	0.238231i	$0.0765676\pi$
$480$		0			0
$481$	0.0750857	+	0.0273290i	0.00342361	+	0.00124609i
$482$	−1.91508	−	10.8610i	−0.0872297	−	0.494704i
$483$		0			0
$484$	−22.6752	−	19.0267i	−1.03069	−	0.864852i
$485$	−22.0220			−0.999966
$486$		0			0
$487$	8.75903			0.396910			0.198455	−	0.980110i	$-0.436408\pi$
$487$	8.75903			0.396910			0.198455	+	0.980110i	$0.436408\pi$
$488$	−8.42241	−	7.06724i	−0.381265	−	0.319919i
$489$		0			0
$490$	0.840397	+	4.76613i	0.0379653	+	0.215312i
$491$	−21.2117	−	7.72044i	−0.957272	−	0.348418i	−0.184308	−	0.982869i	$-0.559004\pi$
$491$	−21.2117	−	7.72044i	−0.957272	−	0.348418i	−0.772964	+	0.634450i	$0.781227\pi$
$492$		0			0
$493$	4.24716	−	24.0869i	0.191283	−	1.08482i
$494$	0.00156564	−	0.00271176i	7.04413e−5	−	0.000122008i
$495$		0			0
$496$	−5.58354	−	9.67097i	−0.250708	−	0.434239i
$497$	7.54478	−	2.74608i	0.338430	−	0.123178i
$498$		0			0
$499$	−19.4061	+	16.2836i	−0.868734	+	0.728955i	−0.963831	−	0.266513i	$-0.914128\pi$
$499$	−19.4061	+	16.2836i	−0.868734	+	0.728955i	0.0950968	+	0.995468i	$0.469684\pi$
$500$	−15.7930	+	13.2519i	−0.706284	+	0.592642i
$501$		0			0
$502$	−1.75657	+	0.639340i	−0.0783997	+	0.0285352i
$503$	1.87207	+	3.24252i	0.0834714	+	0.144577i	0.904739	−	0.425967i	$-0.140066\pi$
$503$	1.87207	+	3.24252i	0.0834714	+	0.144577i	−0.821267	+	0.570543i	$0.806733\pi$
$504$		0			0
$505$	−15.2842	+	26.4731i	−0.680139	+	1.17804i
$506$	0.389187	−	2.20719i	0.0173015	−	0.0981216i
$507$		0			0
$508$	−14.4157	−	5.24690i	−0.639595	−	0.232793i
$509$	−4.22831	−	23.9800i	−0.187417	−	1.06289i	−0.922811	−	0.385253i	$-0.874114\pi$
$509$	−4.22831	−	23.9800i	−0.187417	−	1.06289i	0.735394	−	0.677640i	$-0.236997\pi$
$510$		0			0
$511$	0.552932	+	0.463965i	0.0244603	+	0.0205246i
$512$	22.7690			1.00626
$513$		0			0
$514$	−5.70660			−0.251707
$515$	−7.74669	−	6.50025i	−0.341360	−	0.286435i
$516$		0			0
$517$	6.42792	+	36.4546i	0.282700	+	1.60327i
$518$	2.27962	+	0.829715i	0.100161	+	0.0364556i
$519$		0			0
$520$	−0.0110459	+	0.0626444i	−0.000484395	+	0.00274714i
$521$	9.81046	−	16.9922i	0.429804	−	0.744443i	−0.567051	−	0.823682i	$-0.691916\pi$
$521$	9.81046	−	16.9922i	0.429804	−	0.744443i	0.996856	+	0.0792397i	$0.0252492\pi$
$522$		0			0
$523$	−10.4077	−	18.0267i	−0.455097	−	0.788251i	0.543597	−	0.839346i	$-0.317062\pi$
$523$	−10.4077	−	18.0267i	−0.455097	−	0.788251i	−0.998694	+	0.0510956i	$0.983729\pi$
$524$	26.6763	−	9.70937i	1.16536	−	0.424156i
$525$		0			0
$526$	7.70284	−	6.46345i	0.335860	−	0.281820i
$527$	8.95067	−	7.51051i	0.389897	−	0.327163i
$528$		0			0
$529$	20.6075	−	7.50052i	0.895978	−	0.326109i
$530$	0.598482	+	1.03660i	0.0259964	+	0.0450271i
$531$		0			0
$532$	−0.503217	+	0.871598i	−0.0218172	+	0.0377886i
$533$	−0.0115240	+	0.0653558i	−0.000499159	+	0.00283087i
$534$		0			0
$535$	23.5147	+	8.55864i	1.01663	+	0.370022i
$536$	3.04479	+	17.2679i	0.131515	+	0.745859i
$537$		0			0
$538$	−3.82117	−	3.20634i	−0.164742	−	0.138235i
$539$	−27.4245			−1.18126
$540$		0			0
$541$	−30.6272			−1.31676			−0.658382	−	0.752684i	$-0.728759\pi$
$541$	−30.6272			−1.31676			−0.658382	+	0.752684i	$0.728759\pi$
$542$	1.18324	+	0.992856i	0.0508245	+	0.0426468i
$543$		0			0
$544$	2.40681	+	13.6497i	0.103191	+	0.585227i
$545$	30.1898	+	10.9882i	1.29319	+	0.470682i
$546$		0			0
$547$	3.93273	−	22.3036i	0.168151	−	0.953633i	−0.777604	−	0.628754i	$-0.783565\pi$
$547$	3.93273	−	22.3036i	0.168151	−	0.953633i	0.945756	−	0.324879i	$-0.105324\pi$
$548$	−10.9711	+	19.0025i	−0.468661	+	0.811745i
$549$		0			0
$550$	0.100696	+	0.174411i	0.00429370	+	0.00743691i
$551$	−3.06186	+	1.11443i	−0.130440	+	0.0474761i
$552$		0			0
$553$	−0.494473	+	0.414912i	−0.0210271	+	0.0176439i
$554$	−7.47387	+	6.27132i	−0.317534	+	0.266443i
$555$		0			0
$556$	10.5523	−	3.84072i	0.447517	−	0.162883i
$557$	18.2259	+	31.5682i	0.772256	+	1.33759i	0.936324	+	0.351138i	$0.114205\pi$
$557$	18.2259	+	31.5682i	0.772256	+	1.33759i	−0.164067	+	0.986449i	$0.552461\pi$
$558$		0			0
$559$	−0.0750139	+	0.129928i	−0.00317275	+	0.00549537i
$560$	1.51985	−	8.61952i	0.0642256	−	0.364241i
$561$		0			0
$562$	−7.95334	−	2.89478i	−0.335491	−	0.122109i
$563$	−4.60450	−	26.1134i	−0.194056	−	1.10055i	−0.913756	−	0.406263i	$-0.866832\pi$
$563$	−4.60450	−	26.1134i	−0.194056	−	1.10055i	0.719700	−	0.694285i	$-0.244279\pi$
$564$		0			0
$565$	21.3108	+	17.8819i	0.896552	+	0.752296i
$566$	4.81938			0.202574
$567$		0			0
$568$	−9.67492			−0.405950
$569$	−17.5941	−	14.7632i	−0.737581	−	0.618904i	0.194606	−	0.980882i	$-0.437657\pi$
$569$	−17.5941	−	14.7632i	−0.737581	−	0.618904i	−0.932187	+	0.361978i	$0.882102\pi$
$570$		0			0
$571$	−0.833165	−	4.72511i	−0.0348669	−	0.197740i	0.962399	−	0.271641i	$-0.0875662\pi$
$571$	−0.833165	−	4.72511i	−0.0348669	−	0.197740i	−0.997266	+	0.0739009i	$0.976455\pi$
$572$	−0.161722	−	0.0588619i	−0.00676193	−	0.00246114i
$573$		0			0
$574$	−0.349871	+	1.98422i	−0.0146033	+	0.0828197i
$575$	0.0480718	−	0.0832628i	0.00200473	−	0.00347230i
$576$		0			0
$577$	2.15666	+	3.73545i	0.0897831	+	0.155509i	0.907419	−	0.420226i	$-0.138049\pi$
$577$	2.15666	+	3.73545i	0.0897831	+	0.155509i	−0.817636	+	0.575735i	$0.804716\pi$
$578$	2.80533	−	1.02106i	0.116686	−	0.0424704i
$579$		0			0
$580$	24.2098	−	20.3145i	1.00526	−	0.843512i
$581$	4.66393	−	3.91351i	0.193493	−	0.162360i
$582$		0			0
$583$	−6.37369	+	2.31983i	−0.263971	+	0.0960777i
$584$	−0.434885	−	0.753242i	−0.0179957	−	0.0311694i
$585$		0			0
$586$	6.55900	−	11.3605i	0.270950	−	0.469299i
$587$	−7.26235	+	41.1868i	−0.299749	+	1.69996i	0.347497	+	0.937681i	$0.387032\pi$
$587$	−7.26235	+	41.1868i	−0.299749	+	1.69996i	−0.647246	+	0.762281i	$0.724079\pi$
$588$		0			0
$589$	−1.46271	−	0.532383i	−0.0602699	−	0.0219365i
$590$	−0.591603	−	3.35515i	−0.0243559	−	0.138129i
$591$		0			0
$592$	10.1488	+	8.51582i	0.417111	+	0.349998i
$593$	31.5370			1.29507			0.647536	−	0.762035i	$-0.275800\pi$
$593$	31.5370			1.29507			0.647536	+	0.762035i	$0.275800\pi$
$594$		0			0
$595$	9.15786			0.375436
$596$	1.23583	+	1.03698i	0.0506214	+	0.0424764i
$597$		0			0
$598$	−0.00134763	−	0.00764279i	−5.51087e−5	−	0.000312537i
$599$	−11.8686	−	4.31982i	−0.484938	−	0.176503i	0.0879695	−	0.996123i	$-0.471962\pi$
$599$	−11.8686	−	4.31982i	−0.484938	−	0.176503i	−0.572907	+	0.819620i	$0.694184\pi$
$600$		0			0
$601$	3.56725	−	20.2309i	0.145511	−	0.825235i	−0.821444	−	0.570289i	$-0.806831\pi$
$601$	3.56725	−	20.2309i	0.145511	−	0.825235i	0.966955	−	0.254946i	$-0.0820577\pi$
$602$	−2.27744	+	3.94465i	−0.0928216	+	0.160772i
$603$		0			0
$604$	7.51556	+	13.0173i	0.305804	+	0.529668i
$605$	33.7180	−	12.2724i	1.37083	−	0.498942i
$606$		0			0
$607$	9.89160	−	8.30003i	0.401487	−	0.336888i	−0.419581	−	0.907718i	$-0.637823\pi$
$607$	9.89160	−	8.30003i	0.401487	−	0.336888i	0.821068	+	0.570830i	$0.193378\pi$
$608$	1.41448	−	1.18689i	0.0573648	−	0.0481348i
$609$		0			0
$610$	5.97966	−	2.17642i	0.242109	−	0.0881205i
$611$	0.0640889	+	0.111005i	0.00259276	+	0.00449079i
$612$		0			0
$613$	15.5799	−	26.9851i	0.629265	−	1.08992i	−0.358434	−	0.933555i	$-0.616689\pi$
$613$	15.5799	−	26.9851i	0.629265	−	1.08992i	0.987699	−	0.156364i	$-0.0499774\pi$
$614$	−0.585856	+	3.32255i	−0.0236432	+	0.134087i
$615$		0			0
$616$	−10.2836	−	3.74293i	−0.414339	−	0.150807i
$617$	1.23998	+	7.03230i	0.0499199	+	0.283110i	0.999541	−	0.0302901i	$-0.00964312\pi$
$617$	1.23998	+	7.03230i	0.0499199	+	0.283110i	−0.949621	+	0.313400i	$0.898532\pi$
$618$		0			0
$619$	−7.68412	−	6.44774i	−0.308851	−	0.259157i	0.475166	−	0.879896i	$-0.342388\pi$
$619$	−7.68412	−	6.44774i	−0.308851	−	0.259157i	−0.784017	+	0.620740i	$0.786832\pi$
$620$	15.0977			0.606338
$621$		0			0
$622$	9.90827			0.397285
$623$	−3.40981	−	2.86117i	−0.136611	−	0.114630i
$624$		0			0
$625$	−4.25900	−	24.1540i	−0.170360	−	0.966160i
$626$	−10.5061	−	3.82392i	−0.419909	−	0.152835i
$627$		0			0
$628$	−3.98552	+	22.6030i	−0.159039	+	0.901957i
$629$	−6.93093	+	12.0047i	−0.276354	+	0.478660i
$630$		0			0
$631$	3.53780	+	6.12765i	0.140838	+	0.243938i	0.927812	−	0.373047i	$-0.121687\pi$
$631$	3.53780	+	6.12765i	0.140838	+	0.243938i	−0.786975	+	0.616985i	$0.788354\pi$
$632$	0.730905	−	0.266028i	0.0290738	−	0.0105820i
$633$		0			0
$634$	2.65189	−	2.22520i	0.105320	−	0.0883741i
$635$	14.2457	−	11.9536i	0.565324	−	0.474363i
$636$		0			0
$637$	−0.0892352	+	0.0324790i	−0.00353563	+	0.00128686i
$638$	−8.45809	−	14.6498i	−0.334859	−	0.579993i
$639$		0			0
$640$	−11.7103	+	20.2828i	−0.462890	+	0.801750i
$641$	0.870188	−	4.93508i	0.0343704	−	0.194924i	−0.962788	−	0.270258i	$-0.912891\pi$
$641$	0.870188	−	4.93508i	0.0343704	−	0.194924i	0.997158	+	0.0753337i	$0.0240022\pi$
$642$		0			0
$643$	−1.53960	−	0.560367i	−0.0607157	−	0.0220987i	0.311484	−	0.950251i	$-0.399174\pi$
$643$	−1.53960	−	0.560367i	−0.0607157	−	0.0220987i	−0.372199	+	0.928153i	$0.621396\pi$
$644$	0.433147	+	2.45650i	0.0170684	+	0.0967997i
$645$		0			0
$646$	0.416126	+	0.349171i	0.0163722	+	0.0137379i
$647$	−34.4927			−1.35605			−0.678024	−	0.735040i	$-0.737164\pi$
$647$	−34.4927			−1.35605			−0.678024	+	0.735040i	$0.737164\pi$
$648$		0			0
$649$	19.3056			0.757813
$650$	0.000534207	0	0.000448253i	2.09533e−5	0	1.75819e-5i
$651$		0			0
$652$	−1.05182	−	5.96515i	−0.0411923	−	0.233613i
$653$	36.4230	+	13.2569i	1.42534	+	0.518783i	0.935593	−	0.353080i	$-0.114866\pi$
$653$	36.4230	+	13.2569i	1.42534	+	0.518783i	0.489751	+	0.871862i	$0.337088\pi$
$654$		0			0
$655$	−5.97570	+	33.8899i	−0.233490	+	1.32419i
$656$	−5.50161	+	9.52907i	−0.214802	+	0.372048i
$657$		0			0
$658$	1.94575	+	3.37015i	0.0758534	+	0.131382i
$659$	8.82552	−	3.21223i	0.343794	−	0.125131i	−0.164352	−	0.986402i	$-0.552553\pi$
$659$	8.82552	−	3.21223i	0.343794	−	0.125131i	0.508146	+	0.861271i	$0.330331\pi$
$660$		0			0
$661$	−18.4980	+	15.5217i	−0.719489	+	0.603723i	−0.927244	−	0.374458i	$-0.877829\pi$
$661$	−18.4980	+	15.5217i	−0.719489	+	0.603723i	0.207755	+	0.978181i	$0.433384\pi$
$662$	−2.04335	+	1.71457i	−0.0794169	+	0.0666387i
$663$		0			0
$664$	−6.89399	+	2.50921i	−0.267539	+	0.0973761i
$665$	−0.610007	−	1.05656i	−0.0236551	−	0.0409718i
$666$		0			0
$667$	−4.03784	+	6.99375i	−0.156346	+	0.270799i
$668$	−6.52510	+	37.0057i	−0.252464	+	1.43179i
$669$		0			0
$670$	−9.53633	−	3.47094i	−0.368421	−	0.134094i
$671$	6.26159	+	35.5112i	0.241726	+	1.37090i
$672$		0			0
$673$	−20.2742	−	17.0121i	−0.781514	−	0.655768i	0.162115	−	0.986772i	$-0.448168\pi$
$673$	−20.2742	−	17.0121i	−0.781514	−	0.655768i	−0.943630	+	0.331003i	$0.892613\pi$
$674$	3.10557			0.119622
$675$		0			0
$676$	23.7554			0.913671
$677$	−23.7986	−	19.9694i	−0.914654	−	0.767486i	0.0583448	−	0.998296i	$-0.481418\pi$
$677$	−23.7986	−	19.9694i	−0.914654	−	0.767486i	−0.972999	+	0.230811i	$0.925862\pi$
$678$		0			0
$679$	−2.27807	−	12.9196i	−0.0874245	−	0.495809i
$680$	−10.3697	−	3.77426i	−0.397660	−	0.144736i
$681$		0			0
$682$	1.40328	−	7.95842i	0.0537345	−	0.304744i
$683$	19.0681	−	33.0268i	0.729619	−	1.26374i	−0.227425	−	0.973796i	$-0.573031\pi$
$683$	19.0681	−	33.0268i	0.729619	−	1.26374i	0.957044	−	0.289942i	$-0.0936359\pi$
$684$		0			0
$685$	−13.2993	−	23.0351i	−0.508140	−	0.880125i
$686$	−6.31558	+	2.29868i	−0.241130	+	0.0877642i
$687$		0			0
$688$	−19.0552	+	15.9892i	−0.726472	+	0.609583i
$689$	−0.0179917	+	0.0150968i	−0.000685428	+	0.000575142i
$690$		0			0
$691$	−30.9436	+	11.2626i	−1.17715	+	0.428448i	−0.855195	−	0.518306i	$-0.826563\pi$
$691$	−30.9436	+	11.2626i	−1.17715	+	0.428448i	−0.321957	+	0.946754i	$0.604341\pi$
$692$	−12.8221	−	22.2085i	−0.487424	−	0.844242i
$693$		0			0
$694$	−6.53414	+	11.3175i	−0.248033	+	0.429605i
$695$	−2.36380	+	13.4058i	−0.0896641	+	0.508510i
$696$		0			0
$697$	−10.8185	−	3.93762i	−0.409781	−	0.149148i
$698$	0.855130	+	4.84968i	0.0323672	+	0.183563i
$699$		0			0
$700$	−0.171702	−	0.144075i	−0.00648971	−	0.00544551i
$701$	2.30710			0.0871381			0.0435690	−	0.999050i	$-0.486127\pi$
$701$	2.30710			0.0871381			0.0435690	+	0.999050i	$0.486127\pi$
$702$		0			0
$703$	1.84668			0.0696490
$704$	−16.5800	−	13.9123i	−0.624881	−	0.524338i
$705$		0			0
$706$	0.592100	+	3.35796i	0.0222840	+	0.126379i
$707$	−17.1120	−	6.22826i	−0.643563	−	0.234238i
$708$		0			0
$709$	−1.93654	+	10.9826i	−0.0727281	+	0.412462i	0.926608	+	0.376029i	$0.122711\pi$
$709$	−1.93654	+	10.9826i	−0.0727281	+	0.412462i	−0.999336	+	0.0364329i	$0.988400\pi$
$710$	2.79979	−	4.84937i	0.105074	−	0.181994i
$711$		0			0
$712$	2.68184	+	4.64508i	0.100506	+	0.174082i
$713$	−3.62525	+	1.31948i	−0.135767	+	0.0494151i
$714$		0			0
$715$	0.159815	−	0.134100i	0.00597673	−	0.00501507i
$716$	14.2646	−	11.9694i	0.533092	−	0.447317i
$717$		0			0
$718$	6.92093	−	2.51901i	0.258287	−	0.0940087i
$719$	−16.0850	−	27.8600i	−0.599869	−	1.03900i	−0.992840	−	0.119453i	$-0.961886\pi$
$719$	−16.0850	−	27.8600i	−0.599869	−	1.03900i	0.392971	−	0.919551i	$-0.371447\pi$
$720$		0			0
$721$	3.01213	−	5.21717i	0.112178	−	0.194297i
$722$	−1.35819	+	7.70267i	−0.0505465	+	0.286664i
$723$		0			0
$724$	41.3064	+	15.0343i	1.53514	+	0.558745i
$725$	−0.126010	−	0.714637i	−0.00467989	−	0.0265410i
$726$		0			0
$727$	−4.11022	−	3.44888i	−0.152440	−	0.127912i	0.563378	−	0.826199i	$-0.309501\pi$
$727$	−4.11022	−	3.44888i	−0.152440	−	0.127912i	−0.715818	+	0.698287i	$0.753946\pi$
$728$	−0.0378942			−0.00140445
$729$		0			0
$730$	0.503399			0.0186316
$731$	−19.9377	−	16.7297i	−0.737424	−	0.618772i
$732$		0			0
$733$	−2.53463	−	14.3746i	−0.0936187	−	0.530938i	−0.995162	−	0.0982489i	$-0.968676\pi$
$733$	−2.53463	−	14.3746i	−0.0936187	−	0.530938i	0.901543	−	0.432689i	$-0.142435\pi$
$734$	7.93296	+	2.88736i	0.292811	+	0.106574i
$735$		0			0
$736$	0.794682	−	4.50687i	0.0292924	−	0.166125i
$737$	28.7534	−	49.8023i	1.05915	−	1.83449i
$738$		0			0
$739$	21.6083	+	37.4266i	0.794873	+	1.37676i	0.922920	+	0.384992i	$0.125796\pi$
$739$	21.6083	+	37.4266i	0.794873	+	1.37676i	−0.128047	+	0.991768i	$0.540871\pi$
$740$	−16.8312	+	6.12607i	−0.618729	+	0.225199i
$741$		0			0
$742$	−0.546231	+	0.458343i	−0.0200528	+	0.0168263i
$743$	−6.21431	+	5.21443i	−0.227981	+	0.191299i	−0.749622	−	0.661866i	$-0.769765\pi$
$743$	−6.21431	+	5.21443i	−0.227981	+	0.191299i	0.521641	+	0.853165i	$0.325320\pi$
$744$		0			0
$745$	−1.83767	+	0.668859i	−0.0673272	+	0.0245051i
$746$	2.01116	+	3.48342i	0.0736336	+	0.127537i
$747$		0			0
$748$	14.9280	−	25.8561i	0.545823	−	0.945393i
$749$	−2.58860	+	14.6807i	−0.0945854	+	0.536420i
$750$		0			0
$751$	−8.22744	−	2.99454i	−0.300223	−	0.109272i	0.187516	−	0.982261i	$-0.439956\pi$
$751$	−8.22744	−	2.99454i	−0.300223	−	0.109272i	−0.487740	+	0.872989i	$0.662178\pi$
$752$	3.69037	+	20.9291i	0.134574	+	0.763207i
$753$		0			0
$754$	−0.0448713	−	0.0376515i	−0.00163412	−	0.00137119i
$755$	−18.2210			−0.663129
$756$		0			0
$757$	−32.1511			−1.16855			−0.584276	−	0.811555i	$-0.698622\pi$
$757$	−32.1511			−1.16855			−0.584276	+	0.811555i	$0.698622\pi$
$758$	−1.31414	−	1.10269i	−0.0477316	−	0.0400515i
$759$		0			0
$760$	0.255283	+	1.44778i	0.00926008	+	0.0525165i
$761$	−23.0656	−	8.39520i	−0.836128	−	0.304326i	−0.111756	−	0.993736i	$-0.535648\pi$
$761$	−23.0656	−	8.39520i	−0.836128	−	0.304326i	−0.724371	+	0.689410i	$0.757870\pi$
$762$		0			0
$763$	−3.32342	+	18.8481i	−0.120316	+	0.682346i
$764$	−10.0016	+	17.3233i	−0.361846	+	0.626736i
$765$		0			0
$766$	0.986770	+	1.70914i	0.0356535	+	0.0617536i
$767$	0.0628177	−	0.0228638i	0.00226822	−	0.000825563i
$768$		0			0
$769$	24.0648	−	20.1928i	0.867800	−	0.728170i	−0.0958338	−	0.995397i	$-0.530552\pi$
$769$	24.0648	−	20.1928i	0.867800	−	0.728170i	0.963634	+	0.267227i	$0.0861073\pi$
$770$	4.85201	−	4.07132i	0.174854	−	0.146720i
$771$		0			0
$772$	−18.5558	+	6.75377i	−0.667839	+	0.243073i
$773$	14.3573	+	24.8675i	0.516395	+	0.894422i	0.999819	+	0.0190355i	$0.00605954\pi$
$773$	14.3573	+	24.8675i	0.516395	+	0.894422i	−0.483424	+	0.875386i	$0.660607\pi$
$774$		0			0
$775$	0.173332	−	0.300219i	0.00622625	−	0.0107842i
$776$	−2.74507	+	15.5681i	−0.0985424	+	0.558862i
$777$		0			0
$778$	−8.51615	−	3.09962i	−0.305319	−	0.111127i
$779$	0.266332	+	1.51044i	0.00954233	+	0.0541173i
$780$		0			0
$781$	24.3071	+	20.3961i	0.869776	+	0.729829i
$782$	1.34633			0.0481446
$783$		0			0
$784$	−15.7448			−0.562315
$785$	−21.3132	−	17.8839i	−0.760699	−	0.638303i
$786$		0			0
$787$	−6.74033	−	38.2263i	−0.240267	−	1.36262i	−0.831233	−	0.555925i	$-0.812364\pi$
$787$	−6.74033	−	38.2263i	−0.240267	−	1.36262i	0.590966	−	0.806697i	$-0.298747\pi$
$788$	37.9040	+	13.7959i	1.35027	+	0.491459i
$789$		0			0
$790$	−0.0781723	+	0.443337i	−0.00278125	+	0.0157732i
$791$	−8.28623	+	14.3522i	−0.294625	+	0.510305i
$792$		0			0
$793$	0.0624304	+	0.108133i	0.00221697	+	0.00383990i
$794$	13.6054	−	4.95197i	0.482839	−	0.175739i
$795$		0			0
$796$	−18.0397	+	15.1371i	−0.639399	+	0.536520i
$797$	3.09030	−	2.59307i	0.109464	−	0.0918512i	−0.586413	−	0.810012i	$-0.699460\pi$
$797$	3.09030	−	2.59307i	0.109464	−	0.0918512i	0.695877	+	0.718161i	$0.255016\pi$
$798$		0			0
$799$	−20.8953	+	7.60526i	−0.739222	+	0.269055i
$800$	0.205612	+	0.356130i	0.00726948	+	0.0125911i
$801$		0			0
$802$	−3.91080	+	6.77371i	−0.138095	+	0.239188i
$803$	−0.495343	+	2.80923i	−0.0174803	+	0.0991355i
$804$		0			0
$805$	−2.84139	−	1.03418i	−0.100146	−	0.0364501i
$806$	−0.00485912	−	0.0275575i	−0.000171155	−	0.000970670i
$807$		0			0
$808$	16.8095	+	14.1049i	0.591357	+	0.496207i
$809$	29.9454			1.05283			0.526413	−	0.850229i	$-0.323537\pi$
$809$	29.9454			1.05283			0.526413	+	0.850229i	$0.323537\pi$
$810$		0			0
$811$	20.2173			0.709927			0.354963	−	0.934880i	$-0.384493\pi$
$811$	20.2173			0.709927			0.354963	+	0.934880i	$0.384493\pi$
$812$	14.4223	+	12.1017i	0.506122	+	0.424687i
$813$		0			0
$814$	1.66481	+	9.44162i	0.0583516	+	0.330929i
$815$	6.89978	+	2.51131i	0.241689	+	0.0879675i
$816$		0			0
$817$	−0.602092	+	3.41463i	−0.0210645	+	0.119463i
$818$	1.32117	−	2.28834i	0.0461938	−	0.0800099i
$819$		0			0
$820$	−7.43809	−	12.8831i	−0.259749	−	0.449899i
$821$	25.2530	−	9.19133i	0.881334	−	0.320779i	0.138586	−	0.990350i	$-0.455744\pi$
$821$	25.2530	−	9.19133i	0.881334	−	0.320779i	0.742748	+	0.669571i	$0.233522\pi$
$822$		0			0
$823$	17.6606	−	14.8190i	0.615611	−	0.516559i	−0.280809	−	0.959764i	$-0.590603\pi$
$823$	17.6606	−	14.8190i	0.615611	−	0.516559i	0.896421	+	0.443204i	$0.146158\pi$
$824$	−5.56089	+	4.66614i	−0.193723	+	0.162553i
$825$		0			0
$826$	1.90716	−	0.694150i	0.0663587	−	0.0241526i
$827$	−2.55476	−	4.42498i	−0.0888378	−	0.153872i	0.818182	−	0.574959i	$-0.194982\pi$
$827$	−2.55476	−	4.42498i	−0.0888378	−	0.153872i	−0.907020	+	0.421087i	$0.861649\pi$
$828$		0			0
$829$	15.2991	−	26.4988i	0.531360	−	0.920343i	−0.467970	−	0.883744i	$-0.655014\pi$
$829$	15.2991	−	26.4988i	0.531360	−	0.920343i	0.999330	−	0.0365985i	$-0.0116523\pi$
$830$	0.737332	−	4.18162i	0.0255932	−	0.145146i
$831$		0			0
$832$	−0.0704252	−	0.0256327i	−0.00244155	−	0.000888653i
$833$	−2.86069	−	16.2238i	−0.0991170	−	0.562120i
$834$		0			0
$835$	−34.8940	−	29.2795i	−1.20756	−	1.01326i
$836$	−3.97744			−0.137563
$837$		0			0
$838$	10.1033			0.349013
$839$	43.1350	+	36.1945i	1.48918	+	1.24957i	0.895645	+	0.444769i	$0.146714\pi$
$839$	43.1350	+	36.1945i	1.48918	+	1.24957i	0.593539	+	0.804805i	$0.297730\pi$
$840$		0			0
$841$	5.54853	+	31.4673i	0.191329	+	1.08508i
$842$	3.11939	+	1.13537i	0.107501	+	0.0391273i
$843$		0			0
$844$	7.61436	−	43.1832i	0.262097	−	1.48643i
$845$	−14.3984	+	24.9387i	−0.495318	+	0.857917i
$846$		0			0
$847$	10.6878	+	18.5118i	0.367237	+	0.636073i
$848$	−3.65924	+	1.33185i	−0.125659	+	0.0457360i
$849$		0			0
$850$	−0.0926743	+	0.0777630i	−0.00317870	+	0.00266725i
$851$	3.50612	−	2.94198i	0.120188	−	0.100850i
$852$		0			0
$853$	42.7983	−	15.5773i	1.46539	−	0.533357i	0.518542	−	0.855052i	$-0.326475\pi$
$853$	42.7983	−	15.5773i	1.46539	−	0.533357i	0.946843	+	0.321695i	$0.104253\pi$
$854$	1.89540	+	3.28294i	0.0648594	+	0.112340i
$855$		0			0
$856$	8.98154	−	15.5565i	0.306983	−	0.531710i
$857$	3.03696	−	17.2235i	0.103741	−	0.588343i	−0.887975	−	0.459892i	$-0.847888\pi$
$857$	3.03696	−	17.2235i	0.103741	−	0.588343i	0.991716	−	0.128451i	$-0.0410006\pi$
$858$		0			0
$859$	−17.2396	−	6.27471i	−0.588208	−	0.214090i	0.0307329	−	0.999528i	$-0.490216\pi$
$859$	−17.2396	−	6.27471i	−0.588208	−	0.214090i	−0.618941	+	0.785437i	$0.712438\pi$
$860$	−5.83984	−	33.1194i	−0.199137	−	1.12936i
$861$		0			0
$862$	−3.14167	−	2.63618i	−0.107006	−	0.0897886i
$863$	−4.65373			−0.158415			−0.0792073	−	0.996858i	$-0.525239\pi$
$863$	−4.65373			−0.158415			−0.0792073	+	0.996858i	$0.525239\pi$
$864$		0			0
$865$	31.0863			1.05697
$866$	−1.94259	−	1.63003i	−0.0660120	−	0.0553907i
$867$		0			0
$868$	1.56179	+	8.85735i	0.0530106	+	0.300638i
$869$	−2.39713	−	0.872486i	−0.0813172	−	0.0295971i
$870$		0			0
$871$	0.0345781	−	0.196102i	0.00117164	−	0.00664468i
$872$	11.5311	−	19.9725i	0.390493	−	0.676354i
$873$		0			0
$874$	−0.0896791	−	0.155329i	−0.00303344	−	0.00525407i
$875$	13.9900	−	5.09194i	0.472948	−	0.172139i
$876$		0			0
$877$	−2.80916	+	2.35716i	−0.0948585	+	0.0795958i	−0.688984	−	0.724777i	$-0.741943\pi$
$877$	−2.80916	+	2.35716i	−0.0948585	+	0.0795958i	0.594125	+	0.804373i	$0.297498\pi$
$878$	−4.81664	+	4.04164i	−0.162554	+	0.136399i
$879$		0			0
$880$	32.5039	−	11.8305i	1.09571	−	0.398804i
$881$	19.1504	+	33.1694i	0.645193	+	1.11751i	0.984257	+	0.176744i	$0.0565564\pi$
$881$	19.1504	+	33.1694i	0.645193	+	1.11751i	−0.339064	+	0.940763i	$0.610110\pi$
$882$		0			0
$883$	−11.3071	+	19.5844i	−0.380513	+	0.659069i	−0.991136	−	0.132853i	$-0.957586\pi$
$883$	−11.3071	+	19.5844i	−0.380513	+	0.659069i	0.610622	+	0.791922i	$0.290919\pi$
$884$	0.0179521	−	0.101811i	0.000603794	−	0.00342429i
$885$		0			0
$886$	−0.282186	−	0.102707i	−0.00948023	−	0.00345052i
$887$	0.329334	+	1.86774i	0.0110579	+	0.0627127i	0.989837	−	0.142204i	$-0.0454188\pi$
$887$	0.329334	+	1.86774i	0.0110579	+	0.0627127i	−0.978779	+	0.204916i	$0.934308\pi$
$888$		0			0
$889$	8.48645	+	7.12097i	0.284626	+	0.238830i
$890$	−3.10435			−0.104058
$891$		0			0
$892$	−39.5852			−1.32541
$893$	2.26928	+	1.90415i	0.0759384	+	0.0637199i
$894$		0			0
$895$	3.91971	+	22.2298i	0.131022	+	0.743061i
$896$	−13.1107	−	4.77190i	−0.437997	−	0.159418i
$897$		0			0
$898$	−0.120370	+	0.682653i	−0.00401680	+	0.0227804i
$899$	−14.5592	+	25.2172i	−0.485575	+	0.841041i
$900$		0			0
$901$	−2.03722	−	3.52856i	−0.0678695	−	0.117553i
$902$	−7.48241	+	2.72338i	−0.249137	+	0.0906785i
$903$		0			0
$904$	15.2977	−	12.8363i	0.508795	−	0.426930i
$905$	−40.8192	+	34.2514i	−1.35688	+	1.13855i
$906$		0			0
$907$	−6.13708	+	2.23371i	−0.203778	+	0.0741693i	−0.441893	−	0.897068i	$-0.645693\pi$
$907$	−6.13708	+	2.23371i	−0.203778	+	0.0741693i	0.238115	+	0.971237i	$0.423471\pi$
$908$	−19.7740	−	34.2497i	−0.656225	−	1.13661i
$909$		0			0
$910$	0.0109660	−	0.0189938i	0.000363521	−	0.000629637i
$911$	7.47332	−	42.3833i	0.247602	−	1.40422i	−0.566769	−	0.823877i	$-0.691807\pi$
$911$	7.47332	−	42.3833i	0.247602	−	1.40422i	0.814371	−	0.580344i	$-0.197082\pi$
$912$		0			0
$913$	22.6101	+	8.22940i	0.748285	+	0.272353i
$914$	0.799615	+	4.53484i	0.0264489	+	0.149999i
$915$		0			0
$916$	15.1260	+	12.6922i	0.499777	+	0.419363i
$917$	−20.5003			−0.676980
$918$		0			0
$919$	−16.7911			−0.553887			−0.276943	−	0.960886i	$-0.589321\pi$
$919$	−16.7911			−0.553887			−0.276943	+	0.960886i	$0.589321\pi$
$920$	2.79116	+	2.34206i	0.0920219	+	0.0772156i
$921$		0			0
$922$	1.57885	+	8.95409i	0.0519966	+	0.294887i
$923$	0.103247	+	0.0375788i	0.00339841	+	0.00123692i
$924$		0			0
$925$	−0.0714163	+	0.405022i	−0.00234815	+	0.0133170i
$926$	−5.16253	+	8.94176i	−0.169651	+	0.293844i
$927$		0			0
$928$	−17.2706	−	29.9135i	−0.566935	−	0.981960i
$929$	−10.9004	+	3.96744i	−0.357632	+	0.130167i	−0.514587	−	0.857438i	$-0.672055\pi$
$929$	−10.9004	+	3.96744i	−0.357632	+	0.130167i	0.156955	+	0.987606i	$0.449832\pi$
$930$		0			0
$931$	−1.68122	+	1.41071i	−0.0550998	+	0.0462343i
$932$	10.6935	−	8.97294i	0.350278	−	0.293918i
$933$		0			0
$934$	−4.62072	+	1.68180i	−0.151195	+	0.0550303i
$935$	18.0960	+	31.3432i	0.591802	+	1.02503i
$936$		0			0
$937$	−23.8976	+	41.3919i	−0.780702	+	1.35222i	0.150832	+	0.988559i	$0.451805\pi$
$937$	−23.8976	+	41.3919i	−0.780702	+	1.35222i	−0.931533	+	0.363656i	$0.881528\pi$
$938$	1.04980	−	5.95372i	0.0342772	−	0.194396i
$939$		0			0
$940$	−26.9996	−	9.82705i	−0.880630	−	0.320523i
$941$	−1.95534	−	11.0893i	−0.0637422	−	0.361500i	−0.999949	−	0.0100518i	$-0.996800\pi$
$941$	−1.95534	−	11.0893i	−0.0637422	−	0.361500i	0.936207	−	0.351448i	$-0.114311\pi$
$942$		0			0
$943$	2.91197	+	2.44343i	0.0948268	+	0.0795691i
$944$	11.0837			0.360743
$945$		0			0
$946$	−18.0010			−0.585261
$947$	−5.61656	−	4.71285i	−0.182514	−	0.153147i	0.546954	−	0.837163i	$-0.315787\pi$
$947$	−5.61656	−	4.71285i	−0.182514	−	0.153147i	−0.729467	+	0.684016i	$0.760232\pi$
$948$		0			0
$949$	0.00171521	+	0.00972746i	5.56782e−5	+	0.000315767i
$950$	0.0151447	+	0.00551224i	0.000491361	+	0.000178841i
$951$		0			0
$952$	1.14154	−	6.47401i	0.0369976	−	0.209824i
$953$	−12.4377	+	21.5427i	−0.402895	+	0.697835i	−0.994074	−	0.108705i	$-0.965329\pi$
$953$	−12.4377	+	21.5427i	−0.402895	+	0.697835i	0.591179	+	0.806541i	$0.298663\pi$
$954$		0			0
$955$	−12.1241	−	20.9996i	−0.392328	−	0.679531i
$956$	5.54906	−	2.01969i	0.179469	−	0.0653215i
$957$		0			0
$958$	−0.918945	+	0.771086i	−0.0296898	+	0.0249127i
$959$	12.1382	−	10.1852i	0.391963	−	0.328896i
$960$		0			0
$961$	16.0590	−	5.84499i	0.518031	−	0.188548i
$962$	0.0165988	+	0.0287500i	0.000535168	+	0.000926937i
$963$		0			0
$964$	−24.2540	+	42.0091i	−0.781167	+	1.35302i
$965$	4.15666	−	23.5736i	0.133808	−	0.758860i
$966$		0			0
$967$	31.9777	+	11.6389i	1.02833	+	0.374283i	0.800446	−	0.599404i	$-0.204596\pi$
$967$	31.9777	+	11.6389i	1.02833	+	0.374283i	0.227888	+	0.973687i	$0.426818\pi$
$968$	−4.47275	−	25.3662i	−0.143760	−	0.815301i
$969$		0			0
$970$	−7.00883	−	5.88111i	−0.225040	−	0.188831i
$971$	34.2476			1.09906			0.549530	−	0.835474i	$-0.314807\pi$
$971$	34.2476			1.09906			0.549530	+	0.835474i	$0.314807\pi$
$972$		0			0
$973$	−8.10928			−0.259971
$974$	2.78770	+	2.33916i	0.0893236	+	0.0749514i
$975$		0			0
$976$	3.59488	+	20.3876i	0.115069	+	0.652590i
$977$	−22.0051	−	8.00919i	−0.704004	−	0.256237i	−0.0348848	−	0.999391i	$-0.511106\pi$
$977$	−22.0051	−	8.00919i	−0.704004	−	0.256237i	−0.669120	+	0.743155i	$0.733329\pi$
$978$		0			0
$979$	3.05467	−	17.3239i	0.0976278	−	0.553675i
$980$	10.6434	−	18.4349i	0.339990	−	0.588880i
$981$		0			0
$982$	−4.68917	−	8.12188i	−0.149637	−	0.259180i
$983$	−31.2007	+	11.3561i	−0.995149	+	0.362205i	−0.787712	−	0.616044i	$-0.788734\pi$
$983$	−31.2007	+	11.3561i	−0.995149	+	0.362205i	−0.207437	+	0.978248i	$0.566512\pi$
$984$		0			0
$985$	−37.4570	+	31.4301i	−1.19348	+	1.00145i
$986$	7.78428	−	6.53178i	0.247902	−	0.208014i
$987$		0			0
$988$	−0.0129420	+	0.00471050i	−0.000411740	+	0.000149861i
$989$	4.29678	+	7.44223i	0.136630	+	0.236649i
$990$		0			0
$991$	14.0903	−	24.4051i	0.447594	−	0.775255i	−0.550635	−	0.834746i	$-0.685614\pi$
$991$	14.0903	−	24.4051i	0.447594	−	0.775255i	0.998229	+	0.0594912i	$0.0189478\pi$
$992$	2.86537	−	16.2503i	0.0909755	−	0.515948i
$993$		0			0
$994$	3.13460	+	1.14090i	0.0994236	+	0.0361872i
$995$	−4.95706	−	28.1129i	−0.157149	−	0.891239i
$996$		0			0
$997$	−34.4342	−	28.8938i	−1.09054	−	0.915075i	−0.0937901	−	0.995592i	$-0.529898\pi$
$997$	−34.4342	−	28.8938i	−1.09054	−	0.915075i	−0.996753	+	0.0805175i	$0.974343\pi$
$998$	−10.5249			−0.333161
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.e.a.46.1		12
3.2	odd	2		27.2.e.a.16.2	✓	12
9.2	odd	6		243.2.e.d.217.2		12
9.4	even	3		243.2.e.b.55.2		12
9.5	odd	6		243.2.e.c.55.1		12
9.7	even	3		243.2.e.a.217.1		12
12.11	even	2		432.2.u.c.97.1		12
15.2	even	4		675.2.u.b.124.3		24
15.8	even	4		675.2.u.b.124.2		24
15.14	odd	2		675.2.l.c.151.1		12
27.2	odd	18		729.2.c.e.244.3		12
27.4	even	9		243.2.e.a.28.1		12
27.5	odd	18		27.2.e.a.22.2	yes	12
27.7	even	9		729.2.a.d.1.3		6
27.11	odd	18		729.2.c.e.487.3		12
27.13	even	9		243.2.e.b.190.2		12
27.14	odd	18		243.2.e.c.190.1		12
27.16	even	9		729.2.c.b.487.4		12
27.20	odd	18		729.2.a.a.1.4		6
27.22	even	9	inner	81.2.e.a.37.1		12
27.23	odd	18		243.2.e.d.28.2		12
27.25	even	9		729.2.c.b.244.4		12
108.59	even	18		432.2.u.c.49.1		12
135.32	even	36		675.2.u.b.49.2		24
135.59	odd	18		675.2.l.c.76.1		12
135.113	even	36		675.2.u.b.49.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.2	✓	12	3.2	odd	2
27.2.e.a.22.2	yes	12	27.5	odd	18
81.2.e.a.37.1		12	27.22	even	9	inner
81.2.e.a.46.1		12	1.1	even	1	trivial
243.2.e.a.28.1		12	27.4	even	9
243.2.e.a.217.1		12	9.7	even	3
243.2.e.b.55.2		12	9.4	even	3
243.2.e.b.190.2		12	27.13	even	9
243.2.e.c.55.1		12	9.5	odd	6
243.2.e.c.190.1		12	27.14	odd	18
243.2.e.d.28.2		12	27.23	odd	18
243.2.e.d.217.2		12	9.2	odd	6
432.2.u.c.49.1		12	108.59	even	18
432.2.u.c.97.1		12	12.11	even	2
675.2.l.c.76.1		12	135.59	odd	18
675.2.l.c.151.1		12	15.14	odd	2
675.2.u.b.49.2		24	135.32	even	36
675.2.u.b.49.3		24	135.113	even	36
675.2.u.b.124.2		24	15.8	even	4
675.2.u.b.124.3		24	15.2	even	4
729.2.a.a.1.4		6	27.20	odd	18
729.2.a.d.1.3		6	27.7	even	9
729.2.c.b.244.4		12	27.25	even	9
729.2.c.b.487.4		12	27.16	even	9
729.2.c.e.244.3		12	27.2	odd	18
729.2.c.e.487.3		12	27.11	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.318266 + 0.267057i) q^{2} +(-0.317323 - 1.79963i) q^{4} +(2.08159 + 0.757639i) q^{5} +(-0.229151 + 1.29958i) q^{7} +(0.795075 - 1.37711i) q^{8} +(0.460168 + 0.797034i) q^{10} +(-4.90067 + 1.78370i) q^{11} +(-0.0138336 + 0.0116078i) q^{13} +(-0.419993 + 0.352416i) q^{14} +(-2.81355 + 1.02405i) q^{16} +(-1.56640 - 2.71308i) q^{17} +(-0.208676 + 0.361438i) q^{19} +(0.702929 - 3.98651i) q^{20} +(-2.03606 - 0.741067i) q^{22} +(0.179619 + 1.01867i) q^{23} +(-0.0712019 - 0.0597455i) q^{25} -0.00750270 q^{26} +2.41147 q^{28} +(5.98068 + 5.01839i) q^{29} +(0.647649 + 3.67300i) q^{31} +(-4.15744 - 1.51319i) q^{32} +(0.226015 - 1.28180i) q^{34} +(-1.46161 + 2.53159i) q^{35} +(-2.21238 - 3.83195i) q^{37} +(-0.162939 + 0.0593049i) q^{38} +(2.69838 - 2.26421i) q^{40} +(2.81517 - 2.36221i) q^{41} +(7.80685 - 2.84146i) q^{43} +(4.76508 + 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(1.23254 - 6.99008i) q^{47} +(4.94145 + 1.79854i) q^{49} +(-0.00670569 - 0.0380299i) q^{50} +(0.0252794 + 0.0212119i) q^{52} +1.30057 q^{53} -11.5526 q^{55} +(1.60747 + 1.34883i) q^{56} +(0.563252 + 3.19436i) q^{58} +(-3.47856 - 1.26609i) q^{59} +(1.20064 - 6.80919i) q^{61} +(-0.774775 + 1.34195i) q^{62} +(2.07506 + 3.59410i) q^{64} +(-0.0375905 + 0.0136818i) q^{65} +(-8.44702 + 7.08789i) q^{67} +(-4.38548 + 3.67985i) q^{68} +(-1.14126 + 0.415384i) q^{70} +(-3.04214 - 5.26914i) q^{71} +(0.273486 - 0.473692i) q^{73} +(0.319224 - 1.81041i) q^{74} +(0.716670 + 0.260847i) q^{76} +(-1.19507 - 6.77756i) q^{77} +(0.374706 + 0.314416i) q^{79} -6.63254 q^{80} +1.52681 q^{82} +(-3.53428 - 2.96561i) q^{83} +(-1.20507 - 6.83430i) q^{85} +(3.24348 + 1.18053i) q^{86} +(-1.44005 + 8.16694i) q^{88} +(-1.68653 + 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(1.77623 - 0.646495i) q^{92} +(2.25902 - 1.89554i) q^{94} +(-0.708218 + 0.594266i) q^{95} +(-9.34182 + 3.40014i) q^{97} +(1.09238 + 1.89206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29}+ \cdots + 45 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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