LMFDB - Embedded newform 81.2.e.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(10,81)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			37.1
Root			$0.500000 + 2.22827i$ of defining polynomial
Character	$\chi$	$=$	81.37
Dual form			81.2.e.a.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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	−0.523291	−	0.852154i	$-0.675296\pi$
$2$	0.318266	−	0.267057i	0.225048	−	0.188837i	0.748339	+	0.663316i	$0.230852\pi$
$3$		0			0
$3$		0			0
$4$	−0.317323	+	1.79963i	−0.158661	+	0.899813i
$5$	2.08159	−	0.757639i	0.930917	−	0.338826i	0.168344	−	0.985728i	$-0.446158\pi$
$5$	2.08159	−	0.757639i	0.930917	−	0.338826i	0.762573	+	0.646902i	$0.223936\pi$
$6$		0			0
$7$	−0.229151	−	1.29958i	−0.0866110	−	0.491195i	−0.996997	−	0.0774361i	$-0.975327\pi$
$7$	−0.229151	−	1.29958i	−0.0866110	−	0.491195i	0.910386	−	0.413759i	$-0.135784\pi$
$8$	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	−0.527454	−	0.849584i	$-0.676853\pi$
$11$	−4.90067	−	1.78370i	−1.47761	−	0.537805i	−0.950155	+	0.311778i	$0.899075\pi$
$12$		0			0
$13$	−0.0138336	−	0.0116078i	−0.00383676	−	0.00321942i	0.640867	−	0.767652i	$-0.278575\pi$
$13$	−0.0138336	−	0.0116078i	−0.00383676	−	0.00321942i	−0.644704	+	0.764432i	$0.723019\pi$
$14$	−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	−0.991048	−	0.133503i	$-0.957377\pi$
$17$	−1.56640	+	2.71308i	−0.379907	+	0.658019i	0.611141	+	0.791522i	$0.290711\pi$
$18$		0			0
$19$	−0.208676	−	0.361438i	−0.0478736	−	0.0829195i	0.841096	−	0.540886i	$-0.181911\pi$
$19$	−0.208676	−	0.361438i	−0.0478736	−	0.0829195i	−0.888969	+	0.457967i	$0.848578\pi$
$20$	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	−0.960338	−	0.278839i	$-0.910050\pi$
$23$	0.179619	−	1.01867i	0.0374532	−	0.212408i	0.997791	+	0.0664316i	$0.0211614\pi$
$24$		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	0.112493	−	0.993652i	$-0.464116\pi$
$29$	5.98068	−	5.01839i	1.11058	−	0.931891i	0.998091	+	0.0617615i	$0.0196718\pi$
$30$		0			0
$31$	0.647649	−	3.67300i	0.116321	−	0.659691i	−0.869766	−	0.493464i	$-0.835730\pi$
$31$	0.647649	−	3.67300i	0.116321	−	0.659691i	0.986088	−	0.166227i	$-0.0531584\pi$
$32$	−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	−0.988569	−	0.150771i	$-0.951824\pi$
$37$	−2.21238	+	3.83195i	−0.363713	+	0.629969i	0.624856	+	0.780740i	$0.285158\pi$
$38$	−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	0.835580	−	0.549368i	$-0.185132\pi$
$41$	2.81517	+	2.36221i	0.439655	+	0.368915i	−0.395925	+	0.918283i	$0.629576\pi$
$42$		0			0
$43$	7.80685	+	2.84146i	1.19053	+	0.433319i	0.859911	−	0.510445i	$-0.170519\pi$
$43$	7.80685	+	2.84146i	1.19053	+	0.433319i	0.330622	+	0.943763i	$0.392741\pi$
$44$	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	0.932475	+	0.361234i	$0.117644\pi$
$47$	1.23254	+	6.99008i	0.179784	+	1.01961i	−0.752691	+	0.658374i	$0.771245\pi$
$48$		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	−0.558377	−	0.829587i	$-0.688576\pi$
$59$	−3.47856	+	1.26609i	−0.452871	+	0.164831i	0.105507	+	0.994419i	$0.466354\pi$
$60$		0			0
$61$	1.20064	+	6.80919i	0.153727	+	0.871828i	0.959941	+	0.280204i	$0.0904020\pi$
$61$	1.20064	+	6.80919i	0.153727	+	0.871828i	−0.806214	+	0.591624i	$0.798487\pi$
$62$	−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	−0.0408835	−	0.999164i	$-0.513017\pi$
$67$	−8.44702	−	7.08789i	−1.03197	−	0.865923i	−0.991084	+	0.133241i	$0.957462\pi$
$68$	−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	−0.988132	−	0.153610i	$-0.950910\pi$
$71$	−3.04214	+	5.26914i	−0.361035	+	0.625332i	0.627096	+	0.778942i	$0.284243\pi$
$72$		0			0
$73$	0.273486	+	0.473692i	0.0320092	+	0.0554415i	0.881586	−	0.472023i	$-0.156476\pi$
$73$	0.273486	+	0.473692i	0.0320092	+	0.0554415i	−0.849577	+	0.527465i	$0.823143\pi$
$74$	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	−0.621465	−	0.783442i	$-0.713462\pi$
$79$	0.374706	−	0.314416i	0.0421577	−	0.0353745i	0.663623	+	0.748067i	$0.269018\pi$
$80$	−6.63254			−0.741540
$81$		0			0
$82$	1.52681			0.168608
$83$	−3.53428	+	2.96561i	−0.387937	+	0.325518i	−0.815809	−	0.578321i	$-0.803708\pi$
$83$	−3.53428	+	2.96561i	−0.387937	+	0.325518i	0.427872	+	0.903839i	$0.359263\pi$
$84$		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	0.762688	−	0.646766i	$-0.223879\pi$
$89$	−1.68653	−	2.92116i	−0.178772	−	0.309642i	−0.941460	+	0.337124i	$0.890546\pi$
$90$		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	−0.178994	−	0.983850i	$-0.557284\pi$
$97$	−9.34182	−	3.40014i	−0.948518	−	0.345232i	−0.769524	+	0.638618i	$0.779507\pi$
$98$	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	−0.835255	−	0.549863i	$-0.814680\pi$
$101$	−2.39626	−	13.5898i	−0.238436	−	1.35224i	0.596818	−	0.802377i	$-0.296431\pi$
$102$		0			0
$103$	−4.28981	+	1.56136i	−0.422687	+	0.153846i	−0.544601	−	0.838695i	$-0.683319\pi$
$103$	−4.28981	+	1.56136i	−0.422687	+	0.153846i	0.121914	+	0.992541i	$0.461097\pi$
$104$	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	0.279102	−	0.960262i	$-0.409963\pi$
$113$	11.8011	−	4.29523i	1.11015	−	0.404062i	0.831049	+	0.556200i	$0.187741\pi$
$114$		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	0.989944	−	0.141456i	$-0.0451785\pi$
$127$	4.19749	+	7.27027i	0.372467	+	0.645132i	−0.617477	+	0.786589i	$0.711845\pi$
$128$	−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	−0.605463	−	0.795874i	$-0.707012\pi$
$131$	2.69761	−	15.2989i	0.235691	−	1.33667i	0.841154	−	0.540796i	$-0.181877\pi$
$132$		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	−0.944716	−	0.327890i	$-0.893662\pi$
$137$	−9.19820	+	7.71820i	−0.785855	+	0.659411i	0.158861	+	0.987301i	$0.449218\pi$
$138$		0			0
$139$	1.06709	−	6.05176i	0.0905093	−	0.513304i	−0.905522	−	0.424299i	$-0.860520\pi$
$139$	1.06709	−	6.05176i	0.0905093	−	0.513304i	0.996031	−	0.0890042i	$-0.0283685\pi$
$140$	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	0.614666	−	0.788788i	$-0.289291\pi$
$149$	−0.676280	−	0.567466i	−0.0554030	−	0.0464886i	−0.670069	+	0.742299i	$0.733735\pi$
$150$		0			0
$151$	−7.72942	−	2.81328i	−0.629011	−	0.228941i	0.00778980	−	0.999970i	$-0.497520\pi$
$151$	−7.72942	−	2.81328i	−0.629011	−	0.228941i	−0.636801	+	0.771028i	$0.719743\pi$
$152$	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	−0.766928	−	0.641733i	$-0.778216\pi$
$157$	−11.8024	+	4.29571i	−0.941932	+	0.342835i	−0.175003	+	0.984568i	$0.555994\pi$
$158$	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	−0.954826	−	0.297167i	$-0.903958\pi$
$167$	−19.3229	+	7.03295i	−1.49525	+	0.544226i	−0.540424	+	0.841393i	$0.681736\pi$
$168$		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	0.790581	−	0.612357i	$-0.209779\pi$
$173$	13.1870	+	4.79966i	1.00259	+	0.364911i	0.212005	+	0.977269i	$0.432001\pi$
$174$		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	−0.610361	−	0.792123i	$-0.708976\pi$
$179$	5.09500	−	8.82479i	0.380818	−	0.659596i	0.991179	+	0.132527i	$0.0423091\pi$
$180$		0			0
$181$	−12.0274	−	20.8320i	−0.893987	−	1.54843i	−0.835054	−	0.550169i	$-0.814563\pi$
$181$	−12.0274	−	20.8320i	−0.893987	−	1.54843i	−0.0589331	−	0.998262i	$-0.518770\pi$
$182$	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	−0.893606	−	0.448852i	$-0.851833\pi$
$191$	−8.38541	+	7.03619i	−0.606747	+	0.509121i	0.286860	+	0.957973i	$0.407389\pi$
$192$		0			0
$193$	−1.87644	+	10.6418i	−0.135069	+	0.766013i	0.839743	+	0.542984i	$0.182706\pi$
$193$	−1.87644	+	10.6418i	−0.135069	+	0.766013i	−0.974812	+	0.223029i	$0.928405\pi$
$194$	−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	−0.928201	−	0.372080i	$-0.878645\pi$
$197$	−11.0367	−	19.1161i	−0.786331	−	1.36196i	0.141870	−	0.989885i	$-0.454689\pi$
$198$		0			0
$199$	−6.44338	+	11.1603i	−0.456759	+	0.791130i	−0.998787	−	0.0492301i	$-0.984323\pi$
$199$	−6.44338	+	11.1603i	−0.456759	+	0.791130i	0.542028	+	0.840360i	$0.317657\pi$
$200$	−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	0.583347	−	0.812223i	$-0.301743\pi$
$211$	22.5485	−	8.20699i	1.55230	−	0.564992i	0.968957	+	0.247230i	$0.0795204\pi$
$212$	−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	0.803918	+	0.594740i	$0.202745\pi$
$223$	3.76160	+	21.3331i	0.251895	+	1.42857i	−0.552023	+	0.833829i	$0.686144\pi$
$224$	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	0.912884	−	0.408220i	$-0.133850\pi$
$227$	20.3367	+	7.40196i	1.34979	+	0.491285i	0.436911	+	0.899505i	$0.356072\pi$
$228$		0			0
$229$	−8.27739	−	6.94555i	−0.546985	−	0.458975i	0.326934	−	0.945047i	$-0.393985\pi$
$229$	−8.27739	−	6.94555i	−0.546985	−	0.458975i	−0.873919	+	0.486072i	$0.838429\pi$
$230$	−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	−0.713364	−	0.700794i	$-0.752829\pi$
$233$	3.81950	−	6.61557i	0.250224	−	0.433400i	0.963587	+	0.267394i	$0.0861625\pi$
$234$		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	−0.961266	−	0.275623i	$-0.911116\pi$
$239$	0.561143	−	3.18240i	0.0362973	−	0.205852i	0.997563	+	0.0697711i	$0.0222269\pi$
$240$		0			0
$241$	−20.3346	+	17.0628i	−1.30987	+	1.09911i	−0.321518	+	0.946903i	$0.604193\pi$
$241$	−20.3346	+	17.0628i	−1.30987	+	1.09911i	−0.988349	+	0.152206i	$0.951362\pi$
$242$	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	0.786252	−	0.617906i	$-0.212019\pi$
$251$	−2.24965	−	3.89651i	−0.141997	−	0.245945i	−0.928248	+	0.371961i	$0.878686\pi$
$252$		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	0.252647	−	0.967559i	$-0.418699\pi$
$257$	−10.5219	−	8.82895i	−0.656340	−	0.550735i	−0.908987	+	0.416824i	$0.863143\pi$
$258$		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	0.785187	+	0.619258i	$0.212567\pi$
$263$	4.20273	+	23.8349i	0.259151	+	1.46972i	−0.526036	+	0.850462i	$0.676322\pi$
$264$		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	−0.820466	−	0.571695i	$-0.806286\pi$
$277$	−4.07780	−	23.1264i	−0.245011	−	1.38953i	0.575455	−	0.817833i	$-0.304825\pi$
$278$	−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	−0.299356	−	0.954142i	$-0.596772\pi$
$281$	−19.1432	−	6.96754i	−1.14199	−	0.415649i	−0.842630	+	0.538493i	$0.818994\pi$
$282$		0			0
$283$	8.88607	+	7.45630i	0.528222	+	0.443231i	0.867487	−	0.497460i	$-0.165734\pi$
$283$	8.88607	+	7.45630i	0.528222	+	0.443231i	−0.339265	+	0.940691i	$0.610178\pi$
$284$	−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	0.220470	+	0.975394i	$0.429241\pi$
$293$	−5.48280	+	31.0945i	−0.320308	+	1.81656i	−0.540779	+	0.841165i	$0.681870\pi$
$294$		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	−0.726586	−	0.687075i	$-0.758894\pi$
$307$	4.06027	−	7.03259i	0.231732	−	0.401371i	0.958318	+	0.285704i	$0.0922275\pi$
$308$	−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	0.991546	−	0.129754i	$-0.0414189\pi$
$311$	18.2691	+	15.3296i	1.03594	+	0.869259i	0.0443970	+	0.999014i	$0.485863\pi$
$312$		0			0
$313$	−25.2876	−	9.20392i	−1.42934	−	0.520236i	−0.492596	−	0.870258i	$-0.663952\pi$
$313$	−25.2876	−	9.20392i	−1.42934	−	0.520236i	−0.936742	+	0.350022i	$0.886174\pi$
$314$	−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	0.998100	+	0.0616130i	$0.0196244\pi$
$317$	1.44689	+	8.20574i	0.0812657	+	0.460881i	−0.916834	+	0.399268i	$0.869264\pi$
$318$		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	−0.999996	−	0.00284030i	$-0.999096\pi$
$331$	−1.11487	−	6.32272i	−0.0612786	−	0.347528i	0.938717	−	0.344688i	$-0.112015\pi$
$332$	−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	0.785285	−	0.619134i	$-0.212516\pi$
$337$	5.72610	+	4.80477i	0.311921	+	0.261732i	−0.473365	+	0.880867i	$0.656961\pi$
$338$	−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	−0.381148	−	0.924514i	$-0.624471\pi$
$347$	5.46202	−	30.9766i	0.293216	−	1.66291i	0.674364	−	0.738399i	$-0.264418\pi$
$348$		0			0
$349$	9.07988	−	7.61893i	0.486035	−	0.407832i	−0.366568	−	0.930391i	$-0.619467\pi$
$349$	9.07988	−	7.61893i	0.486035	−	0.407832i	0.852603	+	0.522560i	$0.175023\pi$
$350$	0.0509595			0.00272390
$351$		0			0
$352$	23.0733			1.22981
$353$	6.28699	−	5.27541i	0.334623	−	0.280782i	−0.459958	−	0.887941i	$-0.652135\pi$
$353$	6.28699	−	5.27541i	0.334623	−	0.280782i	0.794580	+	0.607159i	$0.207691\pi$
$354$		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	0.999323	−	0.0367840i	$-0.0117114\pi$
$359$	8.86365	+	15.3523i	0.467806	+	0.810263i	−0.531517	+	0.847047i	$0.678378\pi$
$360$		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	0.788313	−	0.615275i	$-0.210955\pi$
$367$	19.0941	+	6.94969i	0.996704	+	0.362771i	0.208392	+	0.978045i	$0.433177\pi$
$368$	−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	−0.0955754	−	0.995422i	$-0.530469\pi$
$373$	9.09758	−	3.31125i	0.471055	−	0.171450i	0.566630	+	0.823972i	$0.308247\pi$
$374$	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	−0.225450	−	0.974255i	$-0.572385\pi$
$383$	4.46371	−	1.62466i	0.228085	−	0.0830162i	0.453535	+	0.891239i	$0.350163\pi$
$384$		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	−0.234673	−	0.972074i	$-0.575402\pi$
$389$	−20.4978	−	7.46059i	−1.03928	−	0.378267i	−0.804607	+	0.593807i	$0.797624\pi$
$390$		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	0.857282	+	0.514847i	$0.172151\pi$
$397$	17.4245	+	30.1802i	0.874512	+	1.51470i	0.0172294	+	0.999852i	$0.494515\pi$
$398$	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	−0.787597	−	0.616191i	$-0.788675\pi$
$401$	3.26911	−	18.5401i	0.163252	−	0.925847i	0.950849	−	0.309656i	$-0.100214\pi$
$402$		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	−0.999862	−	0.0166371i	$-0.994704\pi$
$409$	−1.10439	+	6.26334i	−0.0546088	+	0.309702i	0.945253	+	0.326339i	$0.105815\pi$
$410$	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	0.972132	−	0.234434i	$-0.0753236\pi$
$419$	18.6286	+	15.6313i	0.910069	+	0.763638i	−0.0620632	+	0.998072i	$0.519768\pi$
$420$		0			0
$421$	7.50818	+	2.73275i	0.365926	+	0.133186i	0.518438	−	0.855115i	$-0.326514\pi$
$421$	7.50818	+	2.73275i	0.365926	+	0.133186i	−0.152511	+	0.988302i	$0.548736\pi$
$422$	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	−0.981053	−	0.193739i	$-0.937938\pi$
$439$	−2.62800	−	14.9041i	−0.125427	−	0.711334i	0.855626	−	0.517595i	$-0.173173\pi$
$440$	−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	0.325835	−	0.945427i	$-0.394355\pi$
$443$	−0.679204	−	0.247210i	−0.0322699	−	0.0117453i	−0.358105	+	0.933681i	$0.616577\pi$
$444$		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	−0.845669	−	0.533707i	$-0.820798\pi$
$449$	0.834224	−	1.44492i	0.0393695	−	0.0681899i	0.885039	+	0.465517i	$0.154132\pi$
$450$		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	−0.422232	−	0.906488i	$-0.638753\pi$
$457$	8.49041	−	7.12430i	0.397165	−	0.333261i	0.819397	+	0.573227i	$0.194309\pi$
$458$	−4.48926			−0.209769
$459$		0			0
$460$	4.18720			0.195229
$461$	16.7644	−	14.0670i	0.780797	−	0.655166i	−0.162653	−	0.986683i	$-0.552005\pi$
$461$	16.7644	−	14.0670i	0.780797	−	0.655166i	0.943449	+	0.331517i	$0.107561\pi$
$462$		0			0
$463$	4.31546	−	24.4742i	0.200556	−	1.13741i	−0.703724	−	0.710473i	$-0.748481\pi$
$463$	4.31546	−	24.4742i	0.200556	−	1.13741i	0.904281	−	0.426938i	$-0.140408\pi$
$464$	−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	0.696001	−	0.718041i	$-0.254961\pi$
$467$	−5.91777	−	10.2499i	−0.273842	−	0.474308i	−0.969842	+	0.243734i	$0.921628\pi$
$468$		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	0.971209	−	0.238231i	$-0.0765676\pi$
$479$	−0.501383	−	2.84349i	−0.0229088	−	0.129922i	−0.994117	+	0.108309i	$0.965456\pi$
$480$		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	−0.772964	−	0.634450i	$-0.781227\pi$
$491$	−21.2117	+	7.72044i	−0.957272	+	0.348418i	−0.184308	+	0.982869i	$0.559004\pi$
$492$		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	0.0950968	−	0.995468i	$-0.469684\pi$
$499$	−19.4061	−	16.2836i	−0.868734	−	0.728955i	−0.963831	+	0.266513i	$0.914128\pi$
$500$	−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	−0.821267	−	0.570543i	$-0.806733\pi$
$503$	1.87207	−	3.24252i	0.0834714	−	0.144577i	0.904739	+	0.425967i	$0.140066\pi$
$504$		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	0.735394	+	0.677640i	$0.236997\pi$
$509$	−4.22831	+	23.9800i	−0.187417	+	1.06289i	−0.922811	+	0.385253i	$0.874114\pi$
$510$		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	0.996856	−	0.0792397i	$-0.0252492\pi$
$521$	9.81046	+	16.9922i	0.429804	+	0.744443i	−0.567051	+	0.823682i	$0.691916\pi$
$522$		0			0
$523$	−10.4077	+	18.0267i	−0.455097	+	0.788251i	−0.998694	−	0.0510956i	$-0.983729\pi$
$523$	−10.4077	+	18.0267i	−0.455097	+	0.788251i	0.543597	+	0.839346i	$0.317062\pi$
$524$	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	0.945756	+	0.324879i	$0.105324\pi$
$547$	3.93273	+	22.3036i	0.168151	+	0.953633i	−0.777604	+	0.628754i	$0.783565\pi$
$548$	−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	−0.164067	−	0.986449i	$-0.552461\pi$
$557$	18.2259	−	31.5682i	0.772256	−	1.33759i	0.936324	−	0.351138i	$-0.114205\pi$
$558$		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	0.719700	+	0.694285i	$0.244279\pi$
$563$	−4.60450	+	26.1134i	−0.194056	+	1.10055i	−0.913756	+	0.406263i	$0.866832\pi$
$564$		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	−0.932187	−	0.361978i	$-0.882102\pi$
$569$	−17.5941	+	14.7632i	−0.737581	+	0.618904i	0.194606	+	0.980882i	$0.437657\pi$
$570$		0			0
$571$	−0.833165	+	4.72511i	−0.0348669	+	0.197740i	−0.997266	−	0.0739009i	$-0.976455\pi$
$571$	−0.833165	+	4.72511i	−0.0348669	+	0.197740i	0.962399	+	0.271641i	$0.0875662\pi$
$572$	−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	−0.817636	−	0.575735i	$-0.804716\pi$
$577$	2.15666	−	3.73545i	0.0897831	−	0.155509i	0.907419	+	0.420226i	$0.138049\pi$
$578$	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	−0.647246	−	0.762281i	$-0.724079\pi$
$587$	−7.26235	−	41.1868i	−0.299749	−	1.69996i	0.347497	−	0.937681i	$-0.387032\pi$
$588$		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	−0.572907	−	0.819620i	$-0.694184\pi$
$599$	−11.8686	+	4.31982i	−0.484938	+	0.176503i	0.0879695	+	0.996123i	$0.471962\pi$
$600$		0			0
$601$	3.56725	+	20.2309i	0.145511	+	0.825235i	0.966955	+	0.254946i	$0.0820577\pi$
$601$	3.56725	+	20.2309i	0.145511	+	0.825235i	−0.821444	+	0.570289i	$0.806831\pi$
$602$	−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	0.821068	−	0.570830i	$-0.193378\pi$
$607$	9.89160	+	8.30003i	0.401487	+	0.336888i	−0.419581	+	0.907718i	$0.637823\pi$
$608$	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	0.987699	+	0.156364i	$0.0499774\pi$
$613$	15.5799	+	26.9851i	0.629265	+	1.08992i	−0.358434	+	0.933555i	$0.616689\pi$
$614$	−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	−0.949621	−	0.313400i	$-0.898532\pi$
$617$	1.23998	−	7.03230i	0.0499199	−	0.283110i	0.999541	+	0.0302901i	$0.00964312\pi$
$618$		0			0
$619$	−7.68412	+	6.44774i	−0.308851	+	0.259157i	−0.784017	−	0.620740i	$-0.786832\pi$
$619$	−7.68412	+	6.44774i	−0.308851	+	0.259157i	0.475166	+	0.879896i	$0.342388\pi$
$620$	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	−0.786975	−	0.616985i	$-0.788354\pi$
$631$	3.53780	−	6.12765i	0.140838	−	0.243938i	0.927812	+	0.373047i	$0.121687\pi$
$632$	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	0.997158	−	0.0753337i	$-0.0240022\pi$
$641$	0.870188	+	4.93508i	0.0343704	+	0.194924i	−0.962788	+	0.270258i	$0.912891\pi$
$642$		0			0
$643$	−1.53960	+	0.560367i	−0.0607157	+	0.0220987i	−0.372199	−	0.928153i	$-0.621396\pi$
$643$	−1.53960	+	0.560367i	−0.0607157	+	0.0220987i	0.311484	+	0.950251i	$0.399174\pi$
$644$	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	0.489751	−	0.871862i	$-0.337088\pi$
$653$	36.4230	−	13.2569i	1.42534	−	0.518783i	0.935593	+	0.353080i	$0.114866\pi$
$654$		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	0.508146	−	0.861271i	$-0.330331\pi$
$659$	8.82552	+	3.21223i	0.343794	+	0.125131i	−0.164352	+	0.986402i	$0.552553\pi$
$660$		0			0
$661$	−18.4980	−	15.5217i	−0.719489	−	0.603723i	0.207755	−	0.978181i	$-0.433384\pi$
$661$	−18.4980	−	15.5217i	−0.719489	−	0.603723i	−0.927244	+	0.374458i	$0.877829\pi$
$662$	−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	−0.943630	−	0.331003i	$-0.892613\pi$
$673$	−20.2742	+	17.0121i	−0.781514	+	0.655768i	0.162115	+	0.986772i	$0.448168\pi$
$674$	3.10557			0.119622
$675$		0			0
$676$	23.7554			0.913671
$677$	−23.7986	+	19.9694i	−0.914654	+	0.767486i	−0.972999	−	0.230811i	$-0.925862\pi$
$677$	−23.7986	+	19.9694i	−0.914654	+	0.767486i	0.0583448	+	0.998296i	$0.481418\pi$
$678$		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	0.957044	+	0.289942i	$0.0936359\pi$
$683$	19.0681	+	33.0268i	0.729619	+	1.26374i	−0.227425	+	0.973796i	$0.573031\pi$
$684$		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	−0.321957	−	0.946754i	$-0.604341\pi$
$691$	−30.9436	−	11.2626i	−1.17715	−	0.428448i	−0.855195	+	0.518306i	$0.826563\pi$
$692$	−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	−0.999336	−	0.0364329i	$-0.988400\pi$
$709$	−1.93654	−	10.9826i	−0.0727281	−	0.412462i	0.926608	−	0.376029i	$-0.122711\pi$
$710$	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	0.392971	+	0.919551i	$0.371447\pi$
$719$	−16.0850	+	27.8600i	−0.599869	+	1.03900i	−0.992840	+	0.119453i	$0.961886\pi$
$720$		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	−0.715818	−	0.698287i	$-0.753946\pi$
$727$	−4.11022	+	3.44888i	−0.152440	+	0.127912i	0.563378	+	0.826199i	$0.309501\pi$
$728$	−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	0.901543	+	0.432689i	$0.142435\pi$
$733$	−2.53463	+	14.3746i	−0.0936187	+	0.530938i	−0.995162	+	0.0982489i	$0.968676\pi$
$734$	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	−0.128047	−	0.991768i	$-0.540871\pi$
$739$	21.6083	−	37.4266i	0.794873	−	1.37676i	0.922920	−	0.384992i	$-0.125796\pi$
$740$	−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	0.521641	−	0.853165i	$-0.325320\pi$
$743$	−6.21431	−	5.21443i	−0.227981	−	0.191299i	−0.749622	+	0.661866i	$0.769765\pi$
$744$		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	−0.487740	−	0.872989i	$-0.662178\pi$
$751$	−8.22744	+	2.99454i	−0.300223	+	0.109272i	0.187516	+	0.982261i	$0.439956\pi$
$752$	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	−0.724371	−	0.689410i	$-0.757870\pi$
$761$	−23.0656	+	8.39520i	−0.836128	+	0.304326i	−0.111756	+	0.993736i	$0.535648\pi$
$762$		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	0.963634	−	0.267227i	$-0.0861073\pi$
$769$	24.0648	+	20.1928i	0.867800	+	0.728170i	−0.0958338	+	0.995397i	$0.530552\pi$
$770$	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	−0.483424	−	0.875386i	$-0.660607\pi$
$773$	14.3573	−	24.8675i	0.516395	−	0.894422i	0.999819	−	0.0190355i	$-0.00605954\pi$
$774$		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

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

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

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Database

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