LMFDB - Embedded newform 27.2.e.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,2,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$0.215596085457$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.2
Root			$0.500000 - 2.22827i$ of defining polynomial
Character	$\chi$	$=$	27.16
Dual form			27.2.e.a.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.318266 - 0.267057i) q^{2} +(0.159815 + 1.72466i) q^{3} +(-0.317323 - 1.79963i) q^{4} +(-2.08159 - 0.757639i) q^{5} +(0.409719 - 0.591580i) q^{6} +(-0.229151 + 1.29958i) q^{7} +(-0.795075 + 1.37711i) q^{8} +(-2.94892 + 0.551252i) q^{9} +O(q^{10})$	\(q+(-0.318266 - 0.267057i) q^{2} +(0.159815 + 1.72466i) q^{3} +(-0.317323 - 1.79963i) q^{4} +(-2.08159 - 0.757639i) q^{5} +(0.409719 - 0.591580i) q^{6} +(-0.229151 + 1.29958i) q^{7} +(-0.795075 + 1.37711i) q^{8} +(-2.94892 + 0.551252i) q^{9} +(0.460168 + 0.797034i) q^{10} +(4.90067 - 1.78370i) q^{11} +(3.05303 - 0.834881i) q^{12} +(-0.0138336 + 0.0116078i) q^{13} +(0.419993 - 0.352416i) q^{14} +(0.974001 - 3.71113i) q^{15} +(-2.81355 + 1.02405i) q^{16} +(1.56640 + 2.71308i) q^{17} +(1.08575 + 0.612083i) q^{18} +(-0.208676 + 0.361438i) q^{19} +(-0.702929 + 3.98651i) q^{20} +(-2.27796 - 0.187516i) q^{21} +(-2.03606 - 0.741067i) q^{22} +(-0.179619 - 1.01867i) q^{23} +(-2.50212 - 1.15115i) q^{24} +(-0.0712019 - 0.0597455i) q^{25} +0.00750270 q^{26} +(-1.42200 - 4.99779i) q^{27} +2.41147 q^{28} +(-5.98068 - 5.01839i) q^{29} +(-1.30107 + 0.921011i) q^{30} +(0.647649 + 3.67300i) q^{31} +(4.15744 + 1.51319i) q^{32} +(3.85948 + 8.16694i) q^{33} +(0.226015 - 1.28180i) q^{34} +(1.46161 - 2.53159i) q^{35} +(1.92781 + 5.13202i) q^{36} +(-2.21238 - 3.83195i) q^{37} +(0.162939 - 0.0593049i) q^{38} +(-0.0222303 - 0.0220032i) q^{39} +(2.69838 - 2.26421i) q^{40} +(-2.81517 + 2.36221i) q^{41} +(0.674919 + 0.668024i) q^{42} +(7.80685 - 2.84146i) q^{43} +(-4.76508 - 8.25337i) q^{44} +(6.55610 + 1.08673i) q^{45} +(-0.214876 + 0.372177i) q^{46} +(-1.23254 + 6.99008i) q^{47} +(-2.21579 - 4.68877i) q^{48} +(4.94145 + 1.79854i) q^{49} +(0.00670569 + 0.0380299i) q^{50} +(-4.42881 + 3.13510i) q^{51} +(0.0252794 + 0.0212119i) q^{52} -1.30057 q^{53} +(-0.882118 + 1.97038i) q^{54} -11.5526 q^{55} +(-1.60747 - 1.34883i) q^{56} +(-0.656707 - 0.302133i) q^{57} +(0.563252 + 3.19436i) q^{58} +(3.47856 + 1.26609i) q^{59} +(-6.98772 - 0.575213i) q^{60} +(1.20064 - 6.80919i) q^{61} +(0.774775 - 1.34195i) q^{62} +(-0.0406486 - 3.95868i) q^{63} +(2.07506 + 3.59410i) q^{64} +(0.0375905 - 0.0136818i) q^{65} +(0.952697 - 3.62996i) q^{66} +(-8.44702 + 7.08789i) q^{67} +(4.38548 - 3.67985i) q^{68} +(1.72816 - 0.472581i) q^{69} +(-1.14126 + 0.415384i) q^{70} +(3.04214 + 5.26914i) q^{71} +(1.58548 - 4.49927i) q^{72} +(0.273486 - 0.473692i) q^{73} +(-0.319224 + 1.81041i) q^{74} +(0.0916617 - 0.132347i) q^{75} +(0.716670 + 0.260847i) q^{76} +(1.19507 + 6.77756i) q^{77} +(0.00119904 + 0.0129396i) q^{78} +(0.374706 + 0.314416i) q^{79} +6.63254 q^{80} +(8.39224 - 3.25120i) q^{81} +1.52681 q^{82} +(3.53428 + 2.96561i) q^{83} +(0.385389 + 4.15898i) q^{84} +(-1.20507 - 6.83430i) q^{85} +(-3.24348 - 1.18053i) q^{86} +(7.69922 - 11.1167i) q^{87} +(-1.44005 + 8.16694i) q^{88} +(1.68653 - 2.92116i) q^{89} +(-1.79636 - 2.09672i) q^{90} +(-0.0119153 - 0.0206379i) q^{91} +(-1.77623 + 0.646495i) q^{92} +(-6.23118 + 1.70398i) q^{93} +(2.25902 - 1.89554i) q^{94} +(0.708218 - 0.594266i) q^{95} +(-1.94531 + 7.41201i) q^{96} +(-9.34182 + 3.40014i) q^{97} +(-1.09238 - 1.89206i) q^{98} +(-13.4684 + 7.96149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

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

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	0.523291	−	0.852154i	$-0.324704\pi$
$2$	−0.318266	−	0.267057i	−0.225048	−	0.188837i	−0.748339	+	0.663316i	$0.769148\pi$
$3$	0.159815	+	1.72466i	0.0922690	+	0.995734i
$3$	0.159815	+	1.72466i	0.0922690	+	0.995734i
$4$	−0.317323	−	1.79963i	−0.158661	−	0.899813i
$5$	−2.08159	−	0.757639i	−0.930917	−	0.338826i	−0.168344	−	0.985728i	$-0.553842\pi$
$5$	−2.08159	−	0.757639i	−0.930917	−	0.338826i	−0.762573	+	0.646902i	$0.776064\pi$
$6$	0.409719	−	0.591580i	0.167267	−	0.241512i
$7$	−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
$9$	−2.94892	+	0.551252i	−0.982973	+	0.183751i
$10$	0.460168	+	0.797034i	0.145518	+	0.252044i
$11$	4.90067	−	1.78370i	1.47761	−	0.537805i	0.527454	−	0.849584i	$-0.323147\pi$
$11$	4.90067	−	1.78370i	1.47761	−	0.537805i	0.950155	+	0.311778i	$0.100925\pi$
$12$	3.05303	−	0.834881i	0.881335	−	0.241009i
$13$	−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
$15$	0.974001	−	3.71113i	0.251486	−	0.958209i
$16$	−2.81355	+	1.02405i	−0.703389	+	0.256012i
$17$	1.56640	+	2.71308i	0.379907	+	0.658019i	0.991048	−	0.133503i	$-0.0426226\pi$
$17$	1.56640	+	2.71308i	0.379907	+	0.658019i	−0.611141	+	0.791522i	$0.709289\pi$
$18$	1.08575	+	0.612083i	0.255915	+	0.144269i
$19$	−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
$21$	−2.27796	−	0.187516i	−0.497092	−	0.0409194i
$22$	−2.03606	−	0.741067i	−0.434090	−	0.157996i
$23$	−0.179619	−	1.01867i	−0.0374532	−	0.212408i	0.960338	−	0.278839i	$-0.0899497\pi$
$23$	−0.179619	−	1.01867i	−0.0374532	−	0.212408i	−0.997791	+	0.0664316i	$0.978839\pi$
$24$	−2.50212	−	1.15115i	−0.510742	−	0.234978i
$25$	−0.0712019	−	0.0597455i	−0.0142404	−	0.0119491i
$26$	0.00750270			0.00147140
$27$	−1.42200	−	4.99779i	−0.273665	−	0.961825i
$28$	2.41147			0.455726
$29$	−5.98068	−	5.01839i	−1.11058	−	0.931891i	−0.112493	−	0.993652i	$-0.535884\pi$
$29$	−5.98068	−	5.01839i	−1.11058	−	0.931891i	−0.998091	+	0.0617615i	$0.980328\pi$
$30$	−1.30107	+	0.921011i	−0.237542	+	0.168153i
$31$	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
$33$	3.85948	+	8.16694i	0.671849	+	1.42168i
$34$	0.226015	−	1.28180i	0.0387613	−	0.219826i
$35$	1.46161	−	2.53159i	0.247058	−	0.427916i
$36$	1.92781	+	5.13202i	0.321301	+	0.855337i
$37$	−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
$39$	−0.0222303	−	0.0220032i	−0.00355970	−	0.00352334i
$40$	2.69838	−	2.26421i	0.426651	−	0.358002i
$41$	−2.81517	+	2.36221i	−0.439655	+	0.368915i	−0.835580	−	0.549368i	$-0.814868\pi$
$41$	−2.81517	+	2.36221i	−0.439655	+	0.368915i	0.395925	+	0.918283i	$0.370424\pi$
$42$	0.674919	+	0.668024i	0.104142	+	0.103078i
$43$	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
$45$	6.55610	+	1.08673i	0.977326	+	0.162000i
$46$	−0.214876	+	0.372177i	−0.0316818	+	0.0548745i
$47$	−1.23254	+	6.99008i	−0.179784	+	1.01961i	0.752691	+	0.658374i	$0.228755\pi$
$47$	−1.23254	+	6.99008i	−0.179784	+	1.01961i	−0.932475	+	0.361234i	$0.882356\pi$
$48$	−2.21579	−	4.68877i	−0.319821	−	0.676766i
$49$	4.94145	+	1.79854i	0.705921	+	0.256934i
$50$	0.00670569	+	0.0380299i	0.000948328	+	0.00537824i
$51$	−4.42881	+	3.13510i	−0.620158	+	0.439001i
$52$	0.0252794	+	0.0212119i	0.00350562	+	0.00294157i
$53$	−1.30057			−0.178648			−0.0893238	−	0.996003i	$-0.528471\pi$
$53$	−1.30057			−0.178648			−0.0893238	+	0.996003i	$0.528471\pi$
$54$	−0.882118	+	1.97038i	−0.120041	+	0.268135i
$55$	−11.5526			−1.55775
$56$	−1.60747	−	1.34883i	−0.214808	−	0.180245i
$57$	−0.656707	−	0.302133i	−0.0869830	−	0.0400185i
$58$	0.563252	+	3.19436i	0.0739586	+	0.419440i
$59$	3.47856	+	1.26609i	0.452871	+	0.164831i	0.558377	−	0.829587i	$-0.311424\pi$
$59$	3.47856	+	1.26609i	0.452871	+	0.164831i	−0.105507	+	0.994419i	$0.533646\pi$
$60$	−6.98772	−	0.575213i	−0.902110	−	0.0742596i
$61$	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
$63$	−0.0406486	−	3.95868i	−0.00512125	−	0.498747i
$64$	2.07506	+	3.59410i	0.259382	+	0.449263i
$65$	0.0375905	−	0.0136818i	0.00466253	−	0.00169702i
$66$	0.952697	−	3.62996i	0.117269	−	0.446817i
$67$	−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
$69$	1.72816	−	0.472581i	0.208046	−	0.0568921i
$70$	−1.14126	+	0.415384i	−0.136406	+	0.0496479i
$71$	3.04214	+	5.26914i	0.361035	+	0.625332i	0.988132	−	0.153610i	$-0.0490900\pi$
$71$	3.04214	+	5.26914i	0.361035	+	0.625332i	−0.627096	+	0.778942i	$0.715757\pi$
$72$	1.58548	−	4.49927i	0.186850	−	0.530245i
$73$	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
$75$	0.0916617	−	0.132347i	0.0105842	−	0.0152822i
$76$	0.716670	+	0.260847i	0.0822077	+	0.0299212i
$77$	1.19507	+	6.77756i	0.136190	+	0.772374i
$78$	0.00119904	+	0.0129396i	0.000135765	+	0.00146512i
$79$	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
$81$	8.39224	−	3.25120i	0.932471	−	0.361244i
$82$	1.52681			0.168608
$83$	3.53428	+	2.96561i	0.387937	+	0.325518i	0.815809	−	0.578321i	$-0.196292\pi$
$83$	3.53428	+	2.96561i	0.387937	+	0.325518i	−0.427872	+	0.903839i	$0.640737\pi$
$84$	0.385389	+	4.15898i	0.0420493	+	0.453782i
$85$	−1.20507	−	6.83430i	−0.130708	−	0.741284i
$86$	−3.24348	−	1.18053i	−0.349754	−	0.127300i
$87$	7.69922	−	11.1167i	0.825443	−	1.19183i
$88$	−1.44005	+	8.16694i	−0.153510	+	0.870599i
$89$	1.68653	−	2.92116i	0.178772	−	0.309642i	−0.762688	−	0.646766i	$-0.776121\pi$
$89$	1.68653	−	2.92116i	0.178772	−	0.309642i	0.941460	+	0.337124i	$0.109454\pi$
$90$	−1.79636	−	2.09672i	−0.189353	−	0.221014i
$91$	−0.0119153	−	0.0206379i	−0.00124906	−	0.00216344i
$92$	−1.77623	+	0.646495i	−0.185185	+	0.0674018i
$93$	−6.23118	+	1.70398i	−0.646144	+	0.176694i
$94$	2.25902	−	1.89554i	0.233000	−	0.195510i
$95$	0.708218	−	0.594266i	0.0726617	−	0.0609704i
$96$	−1.94531	+	7.41201i	−0.198543	+	0.756485i
$97$	−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
$99$	−13.4684	+	7.96149i	−1.35363	+	0.800160i
$100$	−0.0849256	+	0.147095i	−0.00849256	+	0.0147095i
$101$	2.39626	−	13.5898i	0.238436	−	1.35224i	−0.596818	−	0.802377i	$-0.703569\pi$
$101$	2.39626	−	13.5898i	0.238436	−	1.35224i	0.835255	−	0.549863i	$-0.185320\pi$
$102$	2.24679	+	0.184950i	0.222465	+	0.0183128i
$103$	−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
$105$	4.59972	+	2.11620i	0.448887	+	0.206520i
$106$	0.413928	+	0.347327i	0.0402042	+	0.0337354i
$107$	−11.2965			−1.09207			−0.546035	−	0.837762i	$-0.683864\pi$
$107$	−11.2965			−1.09207			−0.546035	+	0.837762i	$0.683864\pi$
$108$	−8.54292	+	4.14499i	−0.822043	+	0.398851i
$109$	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
$111$	6.25525	−	4.42801i	0.593722	−	0.420288i
$112$	−0.686107	−	3.89110i	−0.0648310	−	0.367675i
$113$	−11.8011	−	4.29523i	−1.11015	−	0.404062i	−0.279102	−	0.960262i	$-0.590037\pi$
$113$	−11.8011	−	4.29523i	−1.11015	−	0.404062i	−0.831049	+	0.556200i	$0.812259\pi$
$114$	0.128321	+	0.271536i	0.0120183	+	0.0254317i
$115$	−0.397890	+	2.25655i	−0.0371035	+	0.210424i
$116$	−7.13341	+	12.3554i	−0.662321	+	1.14717i
$117$	0.0343954	−	0.0418563i	0.00317986	−	0.00386961i
$118$	−0.768989	−	1.33193i	−0.0707912	−	0.122614i
$119$	−3.88481	+	1.41395i	−0.356120	+	0.129617i
$120$	4.33623	+	4.29193i	0.395842	+	0.391798i
$121$	12.4085	−	10.4120i	1.12805	−	0.946544i
$122$	−2.20056	+	1.84649i	−0.199230	+	0.167174i
$123$	−4.52391	−	4.47770i	−0.407907	−	0.403740i
$124$	6.40452	−	2.33105i	0.575143	−	0.209335i
$125$	5.64092	+	9.77035i	0.504539	+	0.873887i
$126$	−1.04425	+	1.27077i	−0.0930295	+	0.113209i
$127$	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
$129$	6.14821	+	13.0101i	0.541319	+	1.14547i
$130$	−0.0156176	−	0.00568434i	−0.00136975	−	0.000498549i
$131$	−2.69761	−	15.2989i	−0.235691	−	1.33667i	−0.841154	−	0.540796i	$-0.818123\pi$
$131$	−2.69761	−	15.2989i	−0.235691	−	1.33667i	0.605463	−	0.795874i	$-0.292988\pi$
$132$	13.4727	−	9.53717i	1.17265	−	0.830104i
$133$	−0.421899	−	0.354015i	−0.0365833	−	0.0306970i
$134$	4.58126			0.395761
$135$	−0.826482	+	11.4807i	−0.0711323	+	0.988105i
$136$	−4.98162			−0.427170
$137$	9.19820	+	7.71820i	0.785855	+	0.659411i	0.944716	−	0.327890i	$-0.106338\pi$
$137$	9.19820	+	7.71820i	0.785855	+	0.659411i	−0.158861	+	0.987301i	$0.550782\pi$
$138$	−0.676219	−	0.311110i	−0.0575636	−	0.0264834i
$139$	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
$141$	−12.2525	−	1.00860i	−1.03185	−	0.0849392i
$142$	0.438950	−	2.48941i	0.0368359	−	0.208907i
$143$	−0.0470893	+	0.0815610i	−0.00393780	+	0.00682047i
$144$	7.73243	−	4.57082i	0.644369	−	0.380901i
$145$	8.64723	+	14.9774i	0.718113	+	1.24381i
$146$	−0.213544	+	0.0777237i	−0.0176730	+	0.00643246i
$147$	−2.31216	+	8.80976i	−0.190704	+	0.726617i
$148$	−6.19404	+	5.19742i	−0.509147	+	0.427225i
$149$	0.676280	−	0.567466i	0.0554030	−	0.0464886i	−0.614666	−	0.788788i	$-0.710709\pi$
$149$	0.676280	−	0.567466i	0.0554030	−	0.0464886i	0.670069	+	0.742299i	$0.266265\pi$
$150$	−0.0645170	+	0.0176428i	−0.00526779	+	0.00144053i
$151$	−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
$153$	−6.11477	−	7.13717i	−0.494350	−	0.577006i
$154$	1.42964	−	2.47621i	0.115204	−	0.199539i
$155$	1.43466	−	8.13639i	0.115235	−	0.653530i
$156$	−0.0325434	+	0.0469884i	−0.00260556	+	0.00376208i
$157$	−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
$159$	−0.207851	−	2.24305i	−0.0164836	−	0.177886i
$160$	−7.50766	−	6.29968i	−0.593533	−	0.498033i
$161$	1.36501			0.107578
$162$	−3.53922	−	1.20646i	−0.278067	−	0.0947884i
$163$	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
$165$	−1.84628	−	19.9244i	−0.143732	−	1.55111i
$166$	−0.332853	−	1.88770i	−0.0258344	−	0.146514i
$167$	19.3229	+	7.03295i	1.49525	+	0.544226i	0.954826	−	0.297167i	$-0.0960417\pi$
$167$	19.3229	+	7.03295i	1.49525	+	0.544226i	0.540424	+	0.841393i	$0.318264\pi$
$168$	2.06938	−	2.98791i	0.159656	−	0.230522i
$169$	−2.25737	+	12.8022i	−0.173644	+	0.984783i
$170$	−1.44161	+	2.49694i	−0.110567	+	0.191507i
$171$	0.416126	−	1.18088i	0.0318219	−	0.0903044i
$172$	−7.59085	−	13.1477i	−0.578797	−	1.00251i
$173$	−13.1870	+	4.79966i	−1.00259	+	0.364911i	−0.790581	−	0.612357i	$-0.790221\pi$
$173$	−13.1870	+	4.79966i	−1.00259	+	0.364911i	−0.212005	+	0.977269i	$0.567999\pi$
$174$	−5.41917	+	1.48192i	−0.410827	+	0.112344i
$175$	0.0939601	−	0.0788419i	0.00710272	−	0.00595989i
$176$	−11.9617	+	10.0371i	−0.901648	+	0.756572i
$177$	−1.62766	+	6.20169i	−0.122342	+	0.466148i
$178$	−1.31688	+	0.479305i	−0.0987043	+	0.0359254i
$179$	−5.09500	−	8.82479i	−0.380818	−	0.659596i	0.610361	−	0.792123i	$-0.291024\pi$
$179$	−5.09500	−	8.82479i	−0.380818	−	0.659596i	−0.991179	+	0.132527i	$0.957691\pi$
$180$	−0.124691	−	12.1434i	−0.00929392	−	0.905114i
$181$	−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
$183$	11.9354	+	0.982498i	0.882293	+	0.0726283i
$184$	1.54563	+	0.562565i	0.113946	+	0.0414728i
$185$	1.70204	+	9.65275i	0.125137	+	0.709685i
$186$	2.43823	+	1.12176i	0.178780	+	0.0822516i
$187$	12.5157	+	10.5019i	0.915240	+	0.767978i
$188$	12.9706			0.945981
$189$	6.82089	−	0.702760i	0.496146	−	0.0511182i
$190$	−0.384104			−0.0278658
$191$	8.38541	+	7.03619i	0.606747	+	0.509121i	0.893606	−	0.448852i	$-0.148167\pi$
$191$	8.38541	+	7.03619i	0.606747	+	0.509121i	−0.286860	+	0.957973i	$0.592611\pi$
$192$	−5.86699	+	4.15316i	−0.423414	+	0.299729i
$193$	−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
$195$	0.0296040	+	0.0626444i	0.00211999	+	0.00448606i
$196$	1.66867	−	9.46347i	0.119190	−	0.675962i
$197$	11.0367	−	19.1161i	0.786331	−	1.36196i	−0.141870	−	0.989885i	$-0.545311\pi$
$197$	11.0367	−	19.1161i	0.786331	−	1.36196i	0.928201	−	0.372080i	$-0.121355\pi$
$198$	6.41270	+	1.06296i	0.455731	+	0.0755413i
$199$	−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
$201$	−13.5742	−	13.4355i	−0.957448	−	0.947667i
$202$	−4.39190	+	3.68524i	−0.309013	+	0.259293i
$203$	7.89228	−	6.62241i	0.553929	−	0.464802i
$204$	7.04736	+	6.97537i	0.493414	+	0.488374i
$205$	7.64974	−	2.78428i	0.534281	−	0.194462i
$206$	0.948326	+	1.64255i	0.0660730	+	0.114442i
$207$	1.09123	+	2.90496i	0.0758456	+	0.201909i
$208$	0.0270347	−	0.0468255i	0.00187452	−	0.00324676i
$209$	−0.377957	+	2.14350i	−0.0261439	+	0.148269i
$210$	−0.898786	−	1.90190i	−0.0620222	−	0.131244i
$211$	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
$213$	−8.60131	+	6.08875i	−0.589352	+	0.417194i
$214$	3.59528	+	3.01680i	0.245768	+	0.206224i
$215$	−18.4035			−1.25511
$216$	8.01311	+	2.01536i	0.545223	+	0.137128i
$217$	−4.92177			−0.334112
$218$	−4.61587	−	3.87317i	−0.312626	−	0.262324i
$219$	0.860667	+	0.395969i	0.0581585	+	0.0267571i
$220$	3.66590	+	20.7904i	0.247155	+	1.40169i
$221$	−0.0531618	−	0.0193493i	−0.00357605	−	0.00130158i
$222$	−3.17336	−	0.261224i	−0.212982	−	0.0175322i
$223$	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
$225$	0.242903	+	0.136934i	0.0161936	+	0.00912896i
$226$	2.60880	+	4.51858i	0.173535	+	0.300571i
$227$	−20.3367	+	7.40196i	−1.34979	+	0.491285i	−0.912884	−	0.408220i	$-0.866150\pi$
$227$	−20.3367	+	7.40196i	−1.34979	+	0.491285i	−0.436911	+	0.899505i	$0.643928\pi$
$228$	−0.335338	+	1.27770i	−0.0222083	+	0.0846178i
$229$	−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
$231$	−11.4980	+	3.14424i	−0.756513	+	0.206876i
$232$	11.6660	−	4.24606i	0.765908	−	0.278768i
$233$	−3.81950	−	6.61557i	−0.250224	−	0.433400i	0.713364	−	0.700794i	$-0.247171\pi$
$233$	−3.81950	−	6.61557i	−0.250224	−	0.433400i	−0.963587	+	0.267394i	$0.913838\pi$
$234$	−0.0221249	+	0.00413588i	−0.00144635	+	0.000270371i
$235$	7.86160	−	13.6167i	0.512834	−	0.888255i
$236$	1.17467	−	6.66187i	0.0764644	−	0.433651i
$237$	−0.482377	+	0.696490i	−0.0313338	+	0.0452419i
$238$	1.61401	+	0.587451i	0.104621	+	0.0380788i
$239$	−0.561143	−	3.18240i	−0.0362973	−	0.205852i	0.961266	−	0.275623i	$-0.0888842\pi$
$239$	−0.561143	−	3.18240i	−0.0362973	−	0.205852i	−0.997563	+	0.0697711i	$0.977773\pi$
$240$	1.05998	+	11.4389i	0.0684212	+	0.738377i
$241$	−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
$243$	6.94842	+	13.9542i	0.445741	+	0.895162i
$244$	−12.6350			−0.808873
$245$	−8.92345	−	7.48766i	−0.570098	−	0.478369i
$246$	0.244007	+	2.63324i	0.0155573	+	0.167889i
$247$	−0.00130875	−	0.00742226i	−8.32735e−5	−	0.000472267i
$248$	−5.57306	−	2.02843i	−0.353890	−	0.128805i
$249$	−4.54985	+	6.56938i	−0.288335	+	0.416318i
$250$	0.813927	−	4.61601i	0.0514773	−	0.291942i
$251$	2.24965	−	3.89651i	0.141997	−	0.245945i	−0.786252	−	0.617906i	$-0.787981\pi$
$251$	2.24965	−	3.89651i	0.141997	−	0.245945i	0.928248	+	0.371961i	$0.121314\pi$
$252$	−7.11124	+	1.32933i	−0.447966	+	0.0837399i
$253$	−2.69726	−	4.67179i	−0.169575	−	0.293713i
$254$	−3.27749	+	1.19291i	−0.205648	+	0.0748498i
$255$	11.5943	−	3.17056i	0.726061	−	0.198548i
$256$	2.99340	−	2.51176i	0.187088	−	0.156985i
$257$	10.5219	−	8.82895i	0.656340	−	0.550735i	−0.252647	−	0.967559i	$-0.581301\pi$
$257$	10.5219	−	8.82895i	0.656340	−	0.550735i	0.908987	+	0.416824i	$0.136857\pi$
$258$	1.51766	−	5.78258i	0.0944854	−	0.360007i
$259$	5.48690	−	1.99707i	0.340939	−	0.124092i
$260$	−0.0365505	−	0.0633073i	−0.00226677	−	0.00392615i
$261$	20.4029	+	11.5020i	1.26291	+	0.711953i
$262$	−3.22711	+	5.58952i	−0.199372	+	0.345322i
$263$	−4.20273	+	23.8349i	−0.259151	+	1.46972i	0.526036	+	0.850462i	$0.323678\pi$
$263$	−4.20273	+	23.8349i	−0.259151	+	1.46972i	−0.785187	+	0.619258i	$0.787433\pi$
$264$	−14.3154	−	1.17841i	−0.881049	−	0.0725260i
$265$	2.70727	+	0.985365i	0.166306	+	0.0605305i
$266$	0.0397339	+	0.225342i	0.00243624	+	0.0138166i
$267$	5.30755	+	2.44185i	0.324817	+	0.149439i
$268$	15.4360	+	12.9523i	0.942902	+	0.791189i
$269$	12.0062			0.732032			0.366016	−	0.930609i	$-0.380722\pi$
$269$	12.0062			0.732032			0.366016	+	0.930609i	$0.380722\pi$
$270$	3.32905	−	3.43321i	0.202599	−	0.208938i
$271$	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
$273$	0.0336891	−	0.0238481i	0.00203896	−	0.00144335i
$274$	−0.866273	−	4.91288i	−0.0523335	−	0.296798i
$275$	−0.455505	−	0.165790i	−0.0274680	−	0.00999753i
$276$	−1.39885	−	2.96008i	−0.0842011	−	0.178176i
$277$	−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
$279$	−3.93462	−	10.4744i	−0.235559	−	0.627084i
$280$	2.32418	+	4.02560i	0.138897	+	0.240576i
$281$	19.1432	−	6.96754i	1.14199	−	0.415649i	0.299356	−	0.954142i	$-0.403228\pi$
$281$	19.1432	−	6.96754i	1.14199	−	0.415649i	0.842630	+	0.538493i	$0.181006\pi$
$282$	3.63020	+	3.59311i	0.216175	+	0.213967i
$283$	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
$285$	1.13809	+	1.12646i	0.0674147	+	0.0667260i
$286$	0.0367683	−	0.0133826i	0.00217416	−	0.000791328i
$287$	−2.42478	−	4.19984i	−0.143130	−	0.247909i
$288$	−13.0941	−	2.17046i	−0.771578	−	0.127896i
$289$	3.59280	−	6.22291i	0.211341	−	0.366053i
$290$	1.24771	−	7.07610i	0.0732679	−	0.415523i
$291$	−7.35706	−	15.5681i	−0.431279	−	0.912618i
$292$	−0.939253	−	0.341860i	−0.0549656	−	0.0200058i
$293$	5.48280	+	31.0945i	0.320308	+	1.81656i	0.540779	+	0.841165i	$0.318130\pi$
$293$	5.48280	+	31.0945i	0.320308	+	1.81656i	−0.220470	+	0.975394i	$0.570759\pi$
$294$	3.08858	−	2.18637i	0.180130	−	0.127511i
$295$	−6.28172	−	5.27099i	−0.365736	−	0.306889i
$296$	7.03603			0.408961
$297$	−15.8833	−	21.9561i	−0.921644	−	1.27402i
$298$	−0.366782			−0.0212471
$299$	0.0143093	+	0.0120069i	0.000827529	+	0.000694379i
$300$	−0.267262	−	0.122960i	−0.0154304	−	0.00709909i
$301$	1.90376	+	10.7968i	0.109731	+	0.622315i
$302$	3.21131	+	1.16882i	0.184790	+	0.0672581i
$303$	23.8208	+	1.96088i	1.36847	+	0.112649i
$304$	0.216991	−	1.23062i	0.0124453	−	0.0705809i
$305$	−7.65816	+	13.2643i	−0.438505	+	0.759513i
$306$	0.0400924	+	3.90451i	0.00229193	+	0.223206i
$307$	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
$309$	2.00725	−	7.64800i	0.114188	−	0.435079i
$310$	−2.62948	+	2.20640i	−0.149344	+	0.125315i
$311$	−18.2691	+	15.3296i	−1.03594	+	0.869259i	−0.991546	−	0.129754i	$-0.958581\pi$
$311$	−18.2691	+	15.3296i	−1.03594	+	0.869259i	−0.0443970	+	0.999014i	$0.514137\pi$
$312$	0.0479757	−	0.0131194i	0.00271609	−	0.000742740i
$313$	−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
$315$	−2.91463	+	8.27116i	−0.164221	+	0.466027i
$316$	0.446928	−	0.774102i	0.0251417	−	0.0435466i
$317$	−1.44689	+	8.20574i	−0.0812657	+	0.460881i	0.916834	+	0.399268i	$0.130736\pi$
$317$	−1.44689	+	8.20574i	−0.0812657	+	0.460881i	−0.998100	+	0.0616130i	$0.980376\pi$
$318$	−0.532870	+	0.769394i	−0.0298819	+	0.0431455i
$319$	−38.2606	−	13.9257i	−2.14218	−	0.779692i
$320$	−1.59640	−	9.05361i	−0.0892412	−	0.506112i
$321$	−1.80534	−	19.4826i	−0.100764	−	1.08741i
$322$	−0.434435	−	0.364534i	−0.0242101	−	0.0203147i
$323$	−1.30748			−0.0727501
$324$	−8.51398	−	14.0712i	−0.472999	−	0.781734i
$325$	0.00167849			9.31061e−5
$326$	−1.05494	−	0.885201i	−0.0584278	−	0.0490268i
$327$	2.31782	+	25.0131i	0.128176	+	1.38323i
$328$	−1.01475	−	5.75493i	−0.0560301	−	0.317763i
$329$	−8.80173	−	3.20357i	−0.485255	−	0.176618i
$330$	−4.73332	+	6.83430i	−0.260561	+	0.376216i
$331$	−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
$333$	8.63650	+	10.0805i	0.473277	+	0.552410i
$334$	−4.27161	−	7.39865i	−0.233732	−	0.404836i
$335$	22.9533	−	8.35432i	1.25407	−	0.456446i
$336$	6.60119	−	1.80516i	0.360124	−	0.0984794i
$337$	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
$339$	5.52185	−	21.0393i	0.299906	−	1.14270i
$340$	−11.9168	+	4.33735i	−0.646278	+	0.235226i
$341$	9.72545	+	16.8450i	0.526663	+	0.912206i
$342$	−0.447801	+	0.264706i	−0.0242143	+	0.0143136i
$343$	−8.08839	+	14.0095i	−0.436732	+	0.756442i
$344$	−2.29403	+	13.0101i	−0.123686	+	0.701456i
$345$	−3.95537	−	0.325597i	−0.212950	−	0.0175296i
$346$	5.47874	+	1.99410i	0.294539	+	0.107203i
$347$	−5.46202	−	30.9766i	−0.293216	−	1.66291i	−0.674364	−	0.738399i	$-0.735582\pi$
$347$	−5.46202	−	30.9766i	−0.293216	−	1.66291i	0.381148	−	0.924514i	$-0.375529\pi$
$348$	−22.4490	−	10.3281i	−1.20339	−	0.553647i
$349$	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
$351$	0.0776848	+	0.0526312i	0.00414651	+	0.00280925i
$352$	23.0733			1.22981
$353$	−6.28699	−	5.27541i	−0.334623	−	0.280782i	0.459958	−	0.887941i	$-0.347865\pi$
$353$	−6.28699	−	5.27541i	−0.334623	−	0.280782i	−0.794580	+	0.607159i	$0.792309\pi$
$354$	2.17423	−	1.53911i	0.115559	−	0.0818026i
$355$	−2.34040	−	13.2731i	−0.124215	−	0.704461i
$356$	−5.79217	−	2.10818i	−0.306984	−	0.111733i
$357$	−3.05944	−	6.47401i	−0.161923	−	0.342641i
$358$	−0.735157	+	4.16928i	−0.0388542	+	0.220353i
$359$	−8.86365	+	15.3523i	−0.467806	+	0.810263i	−0.999323	−	0.0367840i	$-0.988289\pi$
$359$	−8.86365	+	15.3523i	−0.467806	+	0.810263i	0.531517	+	0.847047i	$0.321622\pi$
$360$	−6.70914	+	8.16445i	−0.353603	+	0.430304i
$361$	9.41291	+	16.3036i	0.495416	+	0.858086i
$362$	9.39122	−	3.41812i	0.493591	−	0.179653i
$363$	19.9402	+	19.7365i	1.04659	+	1.03590i
$364$	−0.0333594	+	0.0279919i	−0.00174851	+	0.00146717i
$365$	−0.928176	+	0.778832i	−0.0485829	+	0.0407659i
$366$	−3.53626	−	3.50013i	−0.184843	−	0.182955i
$367$	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
$369$	6.99953	−	8.51782i	0.364381	−	0.443420i
$370$	2.03613	−	3.52668i	0.105853	−	0.183343i
$371$	0.298028	−	1.69020i	0.0154728	−	0.0877509i
$372$	5.04381	+	10.6731i	0.261510	+	0.553374i
$373$	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
$375$	−15.9491	+	11.2901i	−0.823606	+	0.583019i
$376$	−8.64615	−	7.25498i	−0.445891	−	0.374147i
$377$	0.140987			0.00726119
$378$	−2.35853	−	1.59790i	−0.121310	−	0.0821870i
$379$	−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
$381$	13.2096	+	6.07736i	0.676748	+	0.311353i
$382$	−0.789725	−	4.47876i	−0.0404059	−	0.229153i
$383$	−4.46371	−	1.62466i	−0.228085	−	0.0830162i	0.225450	−	0.974255i	$-0.427615\pi$
$383$	−4.46371	−	1.62466i	−0.228085	−	0.0830162i	−0.453535	+	0.891239i	$0.649837\pi$
$384$	18.2508	+	1.50236i	0.931357	+	0.0766672i
$385$	2.64729	−	15.0136i	0.134919	−	0.765162i
$386$	−2.24476	+	3.88803i	−0.114255	+	0.197896i
$387$	−21.4554	+	12.6828i	−1.09064	+	0.644702i
$388$	9.08336	+	15.7328i	0.461138	+	0.798714i
$389$	20.4978	−	7.46059i	1.03928	−	0.378267i	0.234673	−	0.972074i	$-0.424598\pi$
$389$	20.4978	−	7.46059i	1.03928	−	0.378267i	0.804607	+	0.593807i	$0.202376\pi$
$390$	0.00730764	−	0.0278435i	0.000370037	−	0.00140991i
$391$	2.48238	−	2.08297i	0.125539	−	0.105340i
$392$	−6.40561	+	5.37495i	−0.323532	+	0.271476i
$393$	25.9543	−	7.09745i	1.30922	−	0.358019i
$394$	−8.61767	+	3.13658i	−0.434152	+	0.158018i
$395$	−0.541773	−	0.938378i	−0.0272595	−	0.0472149i
$396$	18.6015	+	21.7117i	0.934762	+	1.09106i
$397$	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
$399$	0.543131	−	0.784210i	0.0271906	−	0.0392596i
$400$	0.261513	+	0.0951829i	0.0130756	+	0.00475914i
$401$	−3.26911	−	18.5401i	−0.163252	−	0.925847i	−0.950849	−	0.309656i	$-0.899786\pi$
$401$	−3.26911	−	18.5401i	−0.163252	−	0.925847i	0.787597	−	0.616191i	$-0.211325\pi$
$402$	0.732152	+	7.90113i	0.0365164	+	0.394072i
$403$	−0.0515948	−	0.0432932i	−0.00257012	−	0.00215659i
$404$	−25.2170			−1.25459
$405$	−19.9325	+	0.409386i	−0.990453	+	0.0203426i
$406$	−4.28040			−0.212433
$407$	−17.6772	−	14.8329i	−0.876226	−	0.735241i
$408$	−0.796135	−	8.59160i	−0.0394145	−	0.425348i
$409$	−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
$411$	−11.8413	+	17.0973i	−0.584088	+	0.843346i
$412$	−1.44862	+	8.21551i	−0.0713682	+	0.404749i
$413$	−2.44251	+	4.23055i	−0.120188	+	0.208172i
$414$	0.428490	−	1.21597i	0.0210591	−	0.0597617i
$415$	−5.11007	−	8.85090i	−0.250843	−	0.434474i
$416$	−0.0750772	+	0.0273259i	−0.00368096	+	0.00133976i
$417$	−10.2667	+	2.80753i	−0.502763	+	0.137485i
$418$	0.692727	−	0.581267i	0.0338824	−	0.0284307i
$419$	−18.6286	+	15.6313i	−0.910069	+	0.763638i	−0.972132	−	0.234434i	$-0.924676\pi$
$419$	−18.6286	+	15.6313i	−0.910069	+	0.763638i	0.0620632	+	0.998072i	$0.480232\pi$
$420$	2.34878	−	8.94929i	0.114609	−	0.436681i
$421$	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
$423$	−0.218637	−	21.2926i	−0.0106305	−	1.03528i
$424$	1.03405	−	1.79103i	0.0502181	−	0.0869803i
$425$	0.0505638	−	0.286762i	0.00245271	−	0.0139100i
$426$	4.36354	+	0.359197i	0.211414	+	0.0174031i
$427$	8.57397	+	3.12067i	0.414924	+	0.151020i
$428$	3.58462	+	20.3294i	0.173269	+	0.982659i
$429$	−0.148191	−	0.0681784i	−0.00715472	−	0.00329169i
$430$	5.85720	+	4.91477i	0.282459	+	0.237011i
$431$	9.87124			0.475481			0.237740	−	0.971329i	$-0.423593\pi$
$431$	9.87124			0.475481			0.237740	+	0.971329i	$0.423593\pi$
$432$	9.11887	+	12.6053i	0.438732	+	0.606475i
$433$	−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
$435$	−24.4491	+	17.3072i	−1.17224	+	0.829815i
$436$	−4.60219	−	26.1003i	−0.220405	−	1.24998i
$437$	0.405669	+	0.147651i	0.0194058	+	0.00706312i
$438$	−0.168174	−	0.355870i	−0.00803569	−	0.0170041i
$439$	−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
$441$	−15.5634	−	2.57976i	−0.741113	−	0.122846i
$442$	0.0117522	+	0.0203554i	0.000558996	+	0.000968210i
$443$	0.679204	−	0.247210i	0.0322699	−	0.0117453i	−0.325835	−	0.945427i	$-0.605645\pi$
$443$	0.679204	−	0.247210i	0.0322699	−	0.0117453i	0.358105	+	0.933681i	$0.383423\pi$
$444$	−9.95369	−	9.85201i	−0.472381	−	0.467555i
$445$	−5.72386	+	4.80289i	−0.271337	+	0.227679i
$446$	−6.89432	+	5.78502i	−0.326456	+	0.273929i
$447$	1.08677	+	1.07566i	0.0514023	+	0.0508772i
$448$	−5.14633	+	1.87311i	−0.243141	+	0.0884962i
$449$	−0.834224	−	1.44492i	−0.0393695	−	0.0681899i	0.845669	−	0.533707i	$-0.179202\pi$
$449$	−0.834224	−	1.44492i	−0.0393695	−	0.0681899i	−0.885039	+	0.465517i	$0.845868\pi$
$450$	−0.0407386	−	0.108450i	−0.00192044	−	0.00511240i
$451$	−9.58275	+	16.5978i	−0.451234	+	0.781560i
$452$	−3.98507	+	22.6005i	−0.187442	+	1.06304i
$453$	−6.08723	−	12.8810i	−0.286003	−	0.605204i
$454$	8.44922	+	3.07526i	0.396541	+	0.144329i
$455$	0.00916673	+	0.0519871i	0.000429743	+	0.00243719i
$456$	0.938202	−	0.664140i	0.0439353	−	0.0311012i
$457$	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
$459$	11.3320	−	11.6865i	0.528932	−	0.545481i
$460$	4.18720			0.195229
$461$	−16.7644	−	14.0670i	−0.780797	−	0.655166i	0.162653	−	0.986683i	$-0.447995\pi$
$461$	−16.7644	−	14.0670i	−0.780797	−	0.655166i	−0.943449	+	0.331517i	$0.892439\pi$
$462$	4.49911	+	2.06992i	0.209318	+	0.0963012i
$463$	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
$465$	14.2618	+	1.17400i	0.661375	+	0.0544429i
$466$	−0.551115	+	3.12553i	−0.0255299	+	0.144787i
$467$	5.91777	−	10.2499i	0.273842	−	0.474308i	−0.696001	−	0.718041i	$-0.745039\pi$
$467$	5.91777	−	10.2499i	0.273842	−	0.474308i	0.969842	+	0.243734i	$0.0783722\pi$
$468$	−0.0862400	−	0.0486170i	−0.00398645	−	0.00224732i
$469$	−7.27564	−	12.6018i	−0.335958	−	0.581896i
$470$	−6.13850	+	2.23423i	−0.283148	+	0.103057i
$471$	5.52246	−	21.0416i	0.254462	−	0.969547i
$472$	−4.50927	+	3.78373i	−0.207556	+	0.174160i
$473$	33.1905	−	27.8501i	1.52610	−	1.28055i
$474$	0.339526	−	0.0928466i	0.0155950	−	0.00426459i
$475$	0.0364524	−	0.0132676i	0.00167255	−	0.000608759i
$476$	3.77733	+	6.54252i	0.173134	+	0.299876i
$477$	3.83529	−	0.716944i	0.175606	−	0.0328266i
$478$	−0.671288	+	1.16270i	−0.0307040	+	0.0531809i
$479$	0.501383	−	2.84349i	0.0229088	−	0.129922i	−0.971209	−	0.238231i	$-0.923432\pi$
$479$	0.501383	−	2.84349i	0.0229088	−	0.129922i	0.994117	+	0.108309i	$0.0345436\pi$
$480$	9.66498	−	13.9550i	0.441144	−	0.636954i
$481$	0.0750857	+	0.0273290i	0.00342361	+	0.00124609i
$482$	1.91508	+	10.8610i	0.0872297	+	0.494704i
$483$	0.218148	+	2.35417i	0.00992607	+	0.107119i
$484$	−22.6752	−	19.0267i	−1.03069	−	0.864852i
$485$	22.0220			0.999966
$486$	1.51512	−	6.29676i	0.0687271	−	0.285627i
$487$	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
$489$	0.529731	+	5.71667i	0.0239553	+	0.258517i
$490$	0.840397	+	4.76613i	0.0379653	+	0.215312i
$491$	21.2117	+	7.72044i	0.957272	+	0.348418i	0.772964	−	0.634450i	$-0.218773\pi$
$491$	21.2117	+	7.72044i	0.957272	+	0.348418i	0.184308	+	0.982869i	$0.440996\pi$
$492$	−6.62264	+	9.56222i	−0.298572	+	0.431098i
$493$	4.24716	−	24.0869i	0.191283	−	1.08482i
$494$	−0.00156564	+	0.00271176i	−7.04413e−5	+	0.000122008i
$495$	34.0677	−	6.36840i	1.53123	−	0.286238i
$496$	−5.58354	−	9.67097i	−0.250708	−	0.434239i
$497$	−7.54478	+	2.74608i	−0.338430	+	0.123178i
$498$	3.20246	−	0.875741i	0.143505	−	0.0392429i
$499$	−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
$501$	−9.04139	+	34.4494i	−0.403940	+	1.53909i
$502$	−1.75657	+	0.639340i	−0.0783997	+	0.0285352i
$503$	−1.87207	−	3.24252i	−0.0834714	−	0.144577i	0.821267	−	0.570543i	$-0.193267\pi$
$503$	−1.87207	−	3.24252i	−0.0834714	−	0.144577i	−0.904739	+	0.425967i	$0.859934\pi$
$504$	5.48386	+	3.09147i	0.244270	+	0.137705i
$505$	−15.2842	+	26.4731i	−0.680139	+	1.17804i
$506$	−0.389187	+	2.20719i	−0.0173015	+	0.0981216i
$507$	−22.4402	−	1.84723i	−0.996604	−	0.0820382i
$508$	−14.4157	−	5.24690i	−0.639595	−	0.232793i
$509$	4.22831	+	23.9800i	0.187417	+	1.06289i	0.922811	+	0.385253i	$0.125886\pi$
$509$	4.22831	+	23.9800i	0.187417	+	1.06289i	−0.735394	+	0.677640i	$0.763003\pi$
$510$	−4.53677	−	2.08724i	−0.200892	−	0.0924247i
$511$	0.552932	+	0.463965i	0.0244603	+	0.0205246i
$512$	−22.7690			−1.00626
$513$	2.10313	+	0.528954i	0.0928554	+	0.0233539i
$514$	−5.70660			−0.251707
$515$	7.74669	+	6.50025i	0.341360	+	0.286435i
$516$	21.4623	−	15.1929i	0.944824	−	0.668828i
$517$	6.42792	+	36.4546i	0.282700	+	1.60327i
$518$	−2.27962	−	0.829715i	−0.100161	−	0.0364556i
$519$	−10.3853	−	21.9760i	−0.455862	−	0.964639i
$520$	−0.0110459	+	0.0626444i	−0.000484395	+	0.00274714i
$521$	−9.81046	+	16.9922i	−0.429804	+	0.744443i	−0.996856	−	0.0792397i	$-0.974751\pi$
$521$	−9.81046	+	16.9922i	−0.429804	+	0.744443i	0.567051	+	0.823682i	$0.308084\pi$
$522$	−3.42188	−	9.10941i	−0.149772	−	0.398708i
$523$	−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
$525$	0.150992	+	0.149449i	0.00658982	+	0.00652251i
$526$	7.70284	−	6.46345i	0.335860	−	0.281820i
$527$	−8.95067	+	7.51051i	−0.389897	+	0.327163i
$528$	−19.2222	−	19.0258i	−0.836539	−	0.827993i
$529$	20.6075	−	7.50052i	0.895978	−	0.326109i
$530$	−0.598482	−	1.03660i	−0.0259964	−	0.0450271i
$531$	−10.9559	−	1.81604i	−0.475447	−	0.0788095i
$532$	−0.503217	+	0.871598i	−0.0218172	+	0.0377886i
$533$	0.0115240	−	0.0653558i	0.000499159	−	0.00283087i
$534$	−1.03710	−	2.19457i	−0.0448795	−	0.0949685i
$535$	23.5147	+	8.55864i	1.01663	+	0.370022i
$536$	−3.04479	−	17.2679i	−0.131515	−	0.745859i
$537$	14.4055	−	10.1975i	0.621645	−	0.440054i
$538$	−3.82117	−	3.20634i	−0.164742	−	0.138235i
$539$	27.4245			1.18126
$540$	20.9233	−	2.15574i	0.900395	−	0.0927682i
$541$	−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
$543$	−37.8503	−	17.4139i	−1.62431	−	0.747301i
$544$	2.40681	+	13.6497i	0.103191	+	0.585227i
$545$	−30.1898	−	10.9882i	−1.29319	−	0.470682i
$546$	−0.0170909	−	0.00140688i	−0.000731421	−	6.02089e-5i
$547$	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
$549$	0.212980	+	20.7416i	0.00908976	+	0.885231i
$550$	0.100696	+	0.174411i	0.00429370	+	0.00743691i
$551$	3.06186	−	1.11443i	0.130440	−	0.0474761i
$552$	−0.723220	+	2.75560i	−0.0307823	+	0.117286i
$553$	−0.494473	+	0.414912i	−0.0210271	+	0.0176439i
$554$	7.47387	−	6.27132i	0.317534	−	0.266443i
$555$	−16.3757	+	4.47810i	−0.695111	+	0.190085i
$556$	10.5523	−	3.84072i	0.447517	−	0.162883i
$557$	−18.2259	−	31.5682i	−0.772256	−	1.33759i	−0.936324	−	0.351138i	$-0.885795\pi$
$557$	−18.2259	−	31.5682i	−0.772256	−	1.33759i	0.164067	−	0.986449i	$-0.447539\pi$
$558$	−1.54500	+	4.38440i	−0.0654049	+	0.185606i
$559$	−0.0750139	+	0.129928i	−0.00317275	+	0.00549537i
$560$	−1.51985	+	8.61952i	−0.0642256	+	0.364241i
$561$	−16.1121	+	23.2637i	−0.680253	+	0.982196i
$562$	−7.95334	−	2.89478i	−0.335491	−	0.122109i
$563$	4.60450	+	26.1134i	0.194056	+	1.10055i	0.913756	+	0.406263i	$0.133168\pi$
$563$	4.60450	+	26.1134i	0.194056	+	1.10055i	−0.719700	+	0.694285i	$0.755721\pi$
$564$	2.07290	+	22.3700i	0.0872847	+	0.941945i
$565$	21.3108	+	17.8819i	0.896552	+	0.752296i
$566$	−4.81938			−0.202574
$567$	2.30210	+	11.6514i	0.0966791	+	0.489313i
$568$	−9.67492			−0.405950
$569$	17.5941	+	14.7632i	0.737581	+	0.618904i	0.932187	−	0.361978i	$-0.117898\pi$
$569$	17.5941	+	14.7632i	0.737581	+	0.618904i	−0.194606	+	0.980882i	$0.562343\pi$
$570$	−0.0613854	−	0.662450i	−0.00257115	−	0.0277470i
$571$	−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
$573$	−10.7949	+	15.5865i	−0.450965	+	0.651134i
$574$	−0.349871	+	1.98422i	−0.0146033	+	0.0828197i
$575$	−0.0480718	+	0.0832628i	−0.00200473	+	0.00347230i
$576$	−8.10043	−	9.45484i	−0.337518	−	0.393952i
$577$	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
$579$	18.0536	−	4.93693i	0.750283	−	0.205172i
$580$	24.2098	−	20.3145i	1.00526	−	0.843512i
$581$	−4.66393	+	3.91351i	−0.193493	+	0.162360i
$582$	−1.81606	+	6.91954i	−0.0752782	+	0.286824i
$583$	−6.37369	+	2.31983i	−0.263971	+	0.0960777i
$584$	0.434885	+	0.753242i	0.0179957	+	0.0311694i
$585$	−0.103309	+	0.0610685i	−0.00427131	+	0.00252487i
$586$	6.55900	−	11.3605i	0.270950	−	0.469299i
$587$	7.26235	−	41.1868i	0.299749	−	1.69996i	−0.347497	−	0.937681i	$-0.612968\pi$
$587$	7.26235	−	41.1868i	0.299749	−	1.69996i	0.647246	−	0.762281i	$-0.275921\pi$
$588$	16.5880	+	1.36548i	0.684076	+	0.0563116i
$589$	−1.46271	−	0.532383i	−0.0602699	−	0.0219365i
$590$	0.591603	+	3.35515i	0.0243559	+	0.138129i
$591$	34.7326	+	15.9795i	1.42871	+	0.657309i
$592$	10.1488	+	8.51582i	0.417111	+	0.349998i
$593$	−31.5370			−1.29507			−0.647536	−	0.762035i	$-0.724200\pi$
$593$	−31.5370			−1.29507			−0.647536	+	0.762035i	$0.724200\pi$
$594$	−0.808405	+	11.2296i	−0.0331693	+	0.460757i
$595$	9.15786			0.375436
$596$	−1.23583	−	1.03698i	−0.0506214	−	0.0424764i
$597$	18.2179	−	12.8962i	0.745611	−	0.527807i
$598$	−0.00134763	−	0.00764279i	−5.51087e−5	−	0.000312537i
$599$	11.8686	+	4.31982i	0.484938	+	0.176503i	0.572907	−	0.819620i	$-0.305816\pi$
$599$	11.8686	+	4.31982i	0.484938	+	0.176503i	−0.0879695	+	0.996123i	$0.528038\pi$
$600$	0.109379	+	0.231454i	0.00446538	+	0.00944909i
$601$	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
$603$	21.0023	−	25.5580i	0.855282	−	1.04080i
$604$	7.51556	+	13.0173i	0.305804	+	0.529668i
$605$	−33.7180	+	12.2724i	−1.37083	+	0.498942i
$606$	−7.05769	−	6.98559i	−0.286699	−	0.283770i
$607$	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
$609$	12.6827	+	12.5532i	0.513930	+	0.508680i
$610$	5.97966	−	2.17642i	0.242109	−	0.0881205i
$611$	−0.0640889	−	0.111005i	−0.00259276	−	0.00449079i
$612$	−10.9039	+	13.2691i	−0.440763	+	0.536371i
$613$	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
$615$	6.02447	+	12.7482i	0.242930	+	0.514059i
$616$	−10.2836	−	3.74293i	−0.414339	−	0.150807i
$617$	−1.23998	−	7.03230i	−0.0499199	−	0.283110i	0.949621	−	0.313400i	$-0.101468\pi$
$617$	−1.23998	−	7.03230i	−0.0499199	−	0.283110i	−0.999541	+	0.0302901i	$0.990357\pi$
$618$	−2.68129	+	1.89805i	−0.107857	+	0.0763506i
$619$	−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
$621$	−4.83569	+	2.34625i	−0.194049	+	0.0941520i
$622$	9.90827			0.397285
$623$	3.40981	+	2.86117i	0.136611	+	0.114630i
$624$	0.0850787	+	0.0391423i	0.00340587	+	0.00156695i
$625$	−4.25900	−	24.1540i	−0.170360	−	0.966160i
$626$	10.5061	+	3.82392i	0.419909	+	0.152835i
$627$	−3.75722	−	0.309286i	−0.150049	−	0.0123517i
$628$	−3.98552	+	22.6030i	−0.159039	+	0.901957i
$629$	6.93093	−	12.0047i	0.276354	−	0.478660i
$630$	3.13650	−	1.85405i	0.124961	−	0.0738673i
$631$	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
$633$	−10.5507	+	40.2002i	−0.419353	+	1.59781i
$634$	2.65189	−	2.22520i	0.105320	−	0.0883741i
$635$	−14.2457	+	11.9536i	−0.565324	+	0.474363i
$636$	−3.97070	+	1.08582i	−0.157448	+	0.0430557i
$637$	−0.0892352	+	0.0324790i	−0.00353563	+	0.00128686i
$638$	8.45809	+	14.6498i	0.334859	+	0.579993i
$639$	−11.8756	−	13.8613i	−0.469793	−	0.548344i
$640$	−11.7103	+	20.2828i	−0.462890	+	0.801750i
$641$	−0.870188	+	4.93508i	−0.0343704	+	0.194924i	−0.997158	−	0.0753337i	$-0.975998\pi$
$641$	−0.870188	+	4.93508i	−0.0343704	+	0.194924i	0.962788	+	0.270258i	$0.0871089\pi$
$642$	−4.62838	+	6.68277i	−0.182667	+	0.263748i
$643$	−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
$645$	−2.94115	−	31.7398i	−0.115807	−	1.24975i
$646$	0.416126	+	0.349171i	0.0163722	+	0.0137379i
$647$	34.4927			1.35605			0.678024	−	0.735040i	$-0.262836\pi$
$647$	34.4927			1.35605			0.678024	+	0.735040i	$0.262836\pi$
$648$	−2.19521	+	14.1420i	−0.0862359	+	0.555550i
$649$	19.3056			0.757813
$650$	−0.000534207	0	0.000448253i	−2.09533e−5	0	1.75819e-5i
$651$	−0.786571	−	8.48840i	−0.0308282	−	0.332687i
$652$	−1.05182	−	5.96515i	−0.0411923	−	0.233613i
$653$	−36.4230	−	13.2569i	−1.42534	−	0.518783i	−0.489751	−	0.871862i	$-0.662912\pi$
$653$	−36.4230	−	13.2569i	−1.42534	−	0.518783i	−0.935593	+	0.353080i	$0.885134\pi$
$654$	5.94223	−	8.57980i	0.232360	−	0.335497i
$655$	−5.97570	+	33.8899i	−0.233490	+	1.32419i
$656$	5.50161	−	9.52907i	0.214802	−	0.372048i
$657$	−0.545365	+	1.54764i	−0.0212767	+	0.0603792i
$658$	1.94575	+	3.37015i	0.0758534	+	0.131382i
$659$	−8.82552	+	3.21223i	−0.343794	+	0.125131i	−0.508146	−	0.861271i	$-0.669669\pi$
$659$	−8.82552	+	3.21223i	−0.343794	+	0.125131i	0.164352	+	0.986402i	$0.447447\pi$
$660$	−35.2705	+	9.64505i	−1.37290	+	0.375433i
$661$	−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
$663$	0.0248750	−	0.0947785i	0.000966065	−	0.00368089i
$664$	−6.89399	+	2.50921i	−0.267539	+	0.0973761i
$665$	0.610007	+	1.05656i	0.0236551	+	0.0409718i
$666$	−0.0566265	−	5.51472i	−0.00219423	−	0.213691i
$667$	−4.03784	+	6.99375i	−0.156346	+	0.270799i
$668$	6.52510	−	37.0057i	0.252464	−	1.43179i
$669$	37.3935	+	3.07815i	1.44572	+	0.119008i
$670$	−9.53633	−	3.47094i	−0.368421	−	0.134094i
$671$	−6.26159	−	35.5112i	−0.241726	−	1.37090i
$672$	−9.18674	−	4.22656i	−0.354386	−	0.163043i
$673$	−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
$675$	−0.197346	+	0.440811i	−0.00759585	+	0.0169668i
$676$	23.7554			0.913671
$677$	23.7986	+	19.9694i	0.914654	+	0.767486i	0.972999	−	0.230811i	$-0.0741378\pi$
$677$	23.7986	+	19.9694i	0.914654	+	0.767486i	−0.0583448	+	0.998296i	$0.518582\pi$
$678$	−7.37609	+	5.22143i	−0.283277	+	0.200528i
$679$	−2.27807	−	12.9196i	−0.0874245	−	0.495809i
$680$	10.3697	+	3.77426i	0.397660	+	0.144736i
$681$	−16.0160	−	33.8910i	−0.613734	−	1.29871i
$682$	1.40328	−	7.95842i	0.0537345	−	0.304744i
$683$	−19.0681	+	33.0268i	−0.729619	+	1.26374i	0.227425	+	0.973796i	$0.426969\pi$
$683$	−19.0681	+	33.0268i	−0.729619	+	1.26374i	−0.957044	+	0.289942i	$0.906364\pi$
$684$	−2.25719	−	0.374149i	−0.0863060	−	0.0143060i
$685$	−13.2993	−	23.0351i	−0.508140	−	0.880125i
$686$	6.31558	−	2.29868i	0.241130	−	0.0877642i
$687$	−13.3016	−	13.1657i	−0.507487	−	0.502303i
$688$	−19.0552	+	15.9892i	−0.726472	+	0.609583i
$689$	0.0179917	−	0.0150968i	0.000685428	−	0.000575142i
$690$	1.17191	+	1.15993i	0.0446137	+	0.0441579i
$691$	−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
$693$	−7.26030	−	19.3277i	−0.275796	−	0.734198i
$694$	−6.53414	+	11.3175i	−0.248033	+	0.429605i
$695$	2.36380	−	13.4058i	0.0896641	−	0.508510i
$696$	9.18742	+	19.4413i	0.348248	+	0.736919i
$697$	−10.8185	−	3.93762i	−0.409781	−	0.149148i
$698$	−0.855130	−	4.84968i	−0.0323672	−	0.183563i
$699$	10.7992	−	7.64461i	0.408463	−	0.289146i
$700$	−0.171702	−	0.144075i	−0.00648971	−	0.00544551i
$701$	−2.30710			−0.0871381			−0.0435690	−	0.999050i	$-0.513873\pi$
$701$	−2.30710			−0.0871381			−0.0435690	+	0.999050i	$0.513873\pi$
$702$	−0.0106689	−	0.0374969i	−0.000402671	−	0.00141523i
$703$	1.84668			0.0696490
$704$	16.5800	+	13.9123i	0.624881	+	0.524338i
$705$	24.7406	+	11.3825i	0.931784	+	0.428688i
$706$	0.592100	+	3.35796i	0.0222840	+	0.126379i
$707$	17.1120	+	6.22826i	0.643563	+	0.234238i
$708$	11.6772	+	0.961241i	0.438857	+	0.0361257i
$709$	−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
$711$	−1.27830	−	0.720629i	−0.0479400	−	0.0270257i
$712$	2.68184	+	4.64508i	0.100506	+	0.174082i
$713$	3.62525	−	1.31948i	0.135767	−	0.0494151i
$714$	−0.755212	+	2.87750i	−0.0282631	+	0.107688i
$715$	0.159815	−	0.134100i	0.00597673	−	0.00501507i
$716$	−14.2646	+	11.9694i	−0.533092	+	0.447317i
$717$	5.39888	−	1.47637i	0.201625	−	0.0551362i
$718$	6.92093	−	2.51901i	0.258287	−	0.0940087i
$719$	16.0850	+	27.8600i	0.599869	+	1.03900i	0.992840	+	0.119453i	$0.0381140\pi$
$719$	16.0850	+	27.8600i	0.599869	+	1.03900i	−0.392971	+	0.919551i	$0.628553\pi$
$720$	−19.5588	+	3.65620i	−0.728914	+	0.136259i
$721$	3.01213	−	5.21717i	0.112178	−	0.194297i
$722$	1.35819	−	7.70267i	0.0505465	−	0.286664i
$723$	26.1777	−	37.7972i	0.973560	−	1.40569i
$724$	41.3064	+	15.0343i	1.53514	+	0.558745i
$725$	0.126010	+	0.714637i	0.00467989	+	0.0265410i
$726$	−1.07552	−	11.6066i	−0.0399163	−	0.430762i
$727$	−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
$729$	−22.9558	+	14.2138i	−0.850215	+	0.526435i
$730$	0.503399			0.0186316
$731$	19.9377	+	16.7297i	0.737424	+	0.618772i
$732$	−2.01926	−	21.7911i	−0.0746338	−	0.805422i
$733$	−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
$735$	11.4876	−	16.5866i	0.423726	−	0.611805i
$736$	0.794682	−	4.50687i	0.0292924	−	0.166125i
$737$	−28.7534	+	49.8023i	−1.05915	+	1.83449i
$738$	−4.50245	+	0.841659i	−0.165737	+	0.0309819i
$739$	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
$741$	0.0125917	−	0.00344333i	0.000462569	−	0.000126494i
$742$	−0.546231	+	0.458343i	−0.0200528	+	0.0168263i
$743$	6.21431	−	5.21443i	0.227981	−	0.191299i	−0.521641	−	0.853165i	$-0.674680\pi$
$743$	6.21431	−	5.21443i	0.227981	−	0.191299i	0.749622	+	0.661866i	$0.230235\pi$
$744$	2.60770	−	9.93582i	0.0956028	−	0.364265i
$745$	−1.83767	+	0.668859i	−0.0673272	+	0.0245051i
$746$	−2.01116	−	3.48342i	−0.0736336	−	0.127537i
$747$	−12.0571	−	6.79706i	−0.441146	−	0.248692i
$748$	14.9280	−	25.8561i	0.545823	−	0.945393i
$749$	2.58860	−	14.6807i	0.0945854	−	0.536420i
$750$	8.09113	+	0.666044i	0.295446	+	0.0243205i
$751$	−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
$753$	7.07968	+	3.25717i	0.257998	+	0.118698i
$754$	−0.0448713	−	0.0376515i	−0.00163412	−	0.00137119i
$755$	18.2210			0.663129
$756$	−3.42913	−	12.0520i	−0.124716	−	0.438329i
$757$	−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
$759$	7.62620	−	5.39848i	0.276813	−	0.195952i
$760$	0.255283	+	1.44778i	0.00926008	+	0.0525165i
$761$	23.0656	+	8.39520i	0.836128	+	0.304326i	0.724371	−	0.689410i	$-0.242130\pi$
$761$	23.0656	+	8.39520i	0.836128	+	0.304326i	0.111756	+	0.993736i	$0.464352\pi$
$762$	−2.58116	−	5.46192i	−0.0935054	−	0.197865i
$763$	−3.32342	+	18.8481i	−0.120316	+	0.682346i

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.318266 - 0.267057i) q^{2} +(0.159815 + 1.72466i) q^{3} +(-0.317323 - 1.79963i) q^{4} +(-2.08159 - 0.757639i) q^{5} +(0.409719 - 0.591580i) q^{6} +(-0.229151 + 1.29958i) q^{7} +(-0.795075 + 1.37711i) q^{8} +(-2.94892 + 0.551252i) q^{9} +O(q^{10})\)	\(q+(-0.318266 - 0.267057i) q^{2} +(0.159815 + 1.72466i) q^{3} +(-0.317323 - 1.79963i) q^{4} +(-2.08159 - 0.757639i) q^{5} +(0.409719 - 0.591580i) q^{6} +(-0.229151 + 1.29958i) q^{7} +(-0.795075 + 1.37711i) q^{8} +(-2.94892 + 0.551252i) q^{9} +(0.460168 + 0.797034i) q^{10} +(4.90067 - 1.78370i) q^{11} +(3.05303 - 0.834881i) q^{12} +(-0.0138336 + 0.0116078i) q^{13} +(0.419993 - 0.352416i) q^{14} +(0.974001 - 3.71113i) q^{15} +(-2.81355 + 1.02405i) q^{16} +(1.56640 + 2.71308i) q^{17} +(1.08575 + 0.612083i) q^{18} +(-0.208676 + 0.361438i) q^{19} +(-0.702929 + 3.98651i) q^{20} +(-2.27796 - 0.187516i) q^{21} +(-2.03606 - 0.741067i) q^{22} +(-0.179619 - 1.01867i) q^{23} +(-2.50212 - 1.15115i) q^{24} +(-0.0712019 - 0.0597455i) q^{25} +0.00750270 q^{26} +(-1.42200 - 4.99779i) q^{27} +2.41147 q^{28} +(-5.98068 - 5.01839i) q^{29} +(-1.30107 + 0.921011i) q^{30} +(0.647649 + 3.67300i) q^{31} +(4.15744 + 1.51319i) q^{32} +(3.85948 + 8.16694i) q^{33} +(0.226015 - 1.28180i) q^{34} +(1.46161 - 2.53159i) q^{35} +(1.92781 + 5.13202i) q^{36} +(-2.21238 - 3.83195i) q^{37} +(0.162939 - 0.0593049i) q^{38} +(-0.0222303 - 0.0220032i) q^{39} +(2.69838 - 2.26421i) q^{40} +(-2.81517 + 2.36221i) q^{41} +(0.674919 + 0.668024i) q^{42} +(7.80685 - 2.84146i) q^{43} +(-4.76508 - 8.25337i) q^{44} +(6.55610 + 1.08673i) q^{45} +(-0.214876 + 0.372177i) q^{46} +(-1.23254 + 6.99008i) q^{47} +(-2.21579 - 4.68877i) q^{48} +(4.94145 + 1.79854i) q^{49} +(0.00670569 + 0.0380299i) q^{50} +(-4.42881 + 3.13510i) q^{51} +(0.0252794 + 0.0212119i) q^{52} -1.30057 q^{53} +(-0.882118 + 1.97038i) q^{54} -11.5526 q^{55} +(-1.60747 - 1.34883i) q^{56} +(-0.656707 - 0.302133i) q^{57} +(0.563252 + 3.19436i) q^{58} +(3.47856 + 1.26609i) q^{59} +(-6.98772 - 0.575213i) q^{60} +(1.20064 - 6.80919i) q^{61} +(0.774775 - 1.34195i) q^{62} +(-0.0406486 - 3.95868i) q^{63} +(2.07506 + 3.59410i) q^{64} +(0.0375905 - 0.0136818i) q^{65} +(0.952697 - 3.62996i) q^{66} +(-8.44702 + 7.08789i) q^{67} +(4.38548 - 3.67985i) q^{68} +(1.72816 - 0.472581i) q^{69} +(-1.14126 + 0.415384i) q^{70} +(3.04214 + 5.26914i) q^{71} +(1.58548 - 4.49927i) q^{72} +(0.273486 - 0.473692i) q^{73} +(-0.319224 + 1.81041i) q^{74} +(0.0916617 - 0.132347i) q^{75} +(0.716670 + 0.260847i) q^{76} +(1.19507 + 6.77756i) q^{77} +(0.00119904 + 0.0129396i) q^{78} +(0.374706 + 0.314416i) q^{79} +6.63254 q^{80} +(8.39224 - 3.25120i) q^{81} +1.52681 q^{82} +(3.53428 + 2.96561i) q^{83} +(0.385389 + 4.15898i) q^{84} +(-1.20507 - 6.83430i) q^{85} +(-3.24348 - 1.18053i) q^{86} +(7.69922 - 11.1167i) q^{87} +(-1.44005 + 8.16694i) q^{88} +(1.68653 - 2.92116i) q^{89} +(-1.79636 - 2.09672i) q^{90} +(-0.0119153 - 0.0206379i) q^{91} +(-1.77623 + 0.646495i) q^{92} +(-6.23118 + 1.70398i) q^{93} +(2.25902 - 1.89554i) q^{94} +(0.708218 - 0.594266i) q^{95} +(-1.94531 + 7.41201i) q^{96} +(-9.34182 + 3.40014i) q^{97} +(-1.09238 - 1.89206i) q^{98} +(-13.4684 + 7.96149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

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