LMFDB - Embedded newform 1078.2.e.q.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	1078.67
Dual form			1078.2.e.q.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.61803 - 2.80252i) q^{5} -3.23607 q^{6} +1.00000 q^{8} +(-3.73607 - 6.47106i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.61803 - 2.80252i) q^{5} -3.23607 q^{6} +1.00000 q^{8} +(-3.73607 - 6.47106i) q^{9} +(-1.61803 + 2.80252i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.61803 + 2.80252i) q^{12} +1.23607 q^{13} -10.4721 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.23607 - 5.60503i) q^{17} +(-3.73607 + 6.47106i) q^{18} +(1.38197 + 2.39364i) q^{19} +3.23607 q^{20} +1.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(1.61803 - 2.80252i) q^{24} +(-2.73607 + 4.73901i) q^{25} +(-0.618034 - 1.07047i) q^{26} -14.4721 q^{27} -4.47214 q^{29} +(5.23607 + 9.06914i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.61803 + 2.80252i) q^{33} -6.47214 q^{34} +7.47214 q^{36} +(5.47214 + 9.47802i) q^{37} +(1.38197 - 2.39364i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-1.61803 - 2.80252i) q^{40} +6.47214 q^{41} -1.52786 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-12.0902 + 20.9408i) q^{45} +(-2.00000 + 3.46410i) q^{46} +(1.00000 + 1.73205i) q^{47} -3.23607 q^{48} +5.47214 q^{50} +(-10.4721 - 18.1383i) q^{51} +(-0.618034 + 1.07047i) q^{52} +(0.236068 - 0.408882i) q^{53} +(7.23607 + 12.5332i) q^{54} +3.23607 q^{55} +8.94427 q^{57} +(2.23607 + 3.87298i) q^{58} +(-3.61803 + 6.26662i) q^{59} +(5.23607 - 9.06914i) q^{60} +(2.61803 + 4.53457i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(1.61803 - 2.80252i) q^{66} +(7.70820 - 13.3510i) q^{67} +(3.23607 + 5.60503i) q^{68} -12.9443 q^{69} -2.47214 q^{71} +(-3.73607 - 6.47106i) q^{72} +(2.47214 - 4.28187i) q^{73} +(5.47214 - 9.47802i) q^{74} +(8.85410 + 15.3358i) q^{75} -2.76393 q^{76} -4.00000 q^{78} +(-1.61803 + 2.80252i) q^{80} +(-12.2082 + 21.1452i) q^{81} +(-3.23607 - 5.60503i) q^{82} +10.1803 q^{83} -20.9443 q^{85} +(0.763932 + 1.32317i) q^{86} +(-7.23607 + 12.5332i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-5.00000 - 8.66025i) q^{89} +24.1803 q^{90} +4.00000 q^{92} +(3.23607 + 5.60503i) q^{93} +(1.00000 - 1.73205i) q^{94} +(4.47214 - 7.74597i) q^{95} +(1.61803 + 2.80252i) q^{96} +3.52786 q^{97} +7.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 24 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{18} + 10 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 40 q^{27} + 12 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} - 8 q^{34} + 12 q^{36} + 4 q^{37} + 10 q^{38} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 24 q^{43} - 2 q^{44} - 26 q^{45} - 8 q^{46} + 4 q^{47} - 4 q^{48} + 4 q^{50} - 24 q^{51} + 2 q^{52} - 8 q^{53} + 20 q^{54} + 4 q^{55} - 10 q^{59} + 12 q^{60} + 6 q^{61} + 8 q^{62} + 4 q^{64} - 8 q^{65} + 2 q^{66} + 4 q^{67} + 4 q^{68} - 16 q^{69} + 8 q^{71} - 6 q^{72} - 8 q^{73} + 4 q^{74} + 22 q^{75} - 20 q^{76} - 16 q^{78} - 2 q^{80} - 22 q^{81} - 4 q^{82} - 4 q^{83} - 48 q^{85} + 12 q^{86} - 20 q^{87} - 2 q^{88} - 20 q^{89} + 52 q^{90} + 16 q^{92} + 4 q^{93} + 4 q^{94} + 2 q^{96} + 32 q^{97} + 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 6 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - 24 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^18 + 10 * q^19 + 4 * q^20 + 4 * q^22 - 8 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 40 * q^27 + 12 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^33 - 8 * q^34 + 12 * q^36 + 4 * q^37 + 10 * q^38 + 8 * q^39 - 2 * q^40 + 8 * q^41 - 24 * q^43 - 2 * q^44 - 26 * q^45 - 8 * q^46 + 4 * q^47 - 4 * q^48 + 4 * q^50 - 24 * q^51 + 2 * q^52 - 8 * q^53 + 20 * q^54 + 4 * q^55 - 10 * q^59 + 12 * q^60 + 6 * q^61 + 8 * q^62 + 4 * q^64 - 8 * q^65 + 2 * q^66 + 4 * q^67 + 4 * q^68 - 16 * q^69 + 8 * q^71 - 6 * q^72 - 8 * q^73 + 4 * q^74 + 22 * q^75 - 20 * q^76 - 16 * q^78 - 2 * q^80 - 22 * q^81 - 4 * q^82 - 4 * q^83 - 48 * q^85 + 12 * q^86 - 20 * q^87 - 2 * q^88 - 20 * q^89 + 52 * q^90 + 16 * q^92 + 4 * q^93 + 4 * q^94 + 2 * q^96 + 32 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.61803	−	2.80252i	0.934172	−	1.61803i	0.158069	−	0.987428i	$-0.449473\pi$
$3$	1.61803	−	2.80252i	0.934172	−	1.61803i	0.776103	−	0.630606i	$-0.217194\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.61803	−	2.80252i	−0.723607	−	1.25332i	−0.959545	−	0.281556i	$-0.909150\pi$
$5$	−1.61803	−	2.80252i	−0.723607	−	1.25332i	0.235938	−	0.971768i	$-0.424184\pi$
$6$	−3.23607			−1.32112
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−3.73607	−	6.47106i	−1.24536	−	2.15702i
$10$	−1.61803	+	2.80252i	−0.511667	+	0.886234i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	1.61803	+	2.80252i	0.467086	+	0.809017i
$13$	1.23607			0.342824			0.171412	−	0.985199i	$-0.445167\pi$
$13$	1.23607			0.342824			0.171412	+	0.985199i	$0.445167\pi$
$14$		0			0
$15$	−10.4721			−2.70389
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.23607	−	5.60503i	0.784862	−	1.35942i	−0.144220	−	0.989546i	$-0.546067\pi$
$17$	3.23607	−	5.60503i	0.784862	−	1.35942i	0.929082	−	0.369875i	$-0.120599\pi$
$18$	−3.73607	+	6.47106i	−0.880600	+	1.52524i
$19$	1.38197	+	2.39364i	0.317045	+	0.549138i	0.979870	−	0.199636i	$-0.0639761\pi$
$19$	1.38197	+	2.39364i	0.317045	+	0.549138i	−0.662825	+	0.748774i	$0.730643\pi$
$20$	3.23607			0.723607
$21$		0			0
$22$	1.00000			0.213201
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	1.61803	−	2.80252i	0.330280	−	0.572061i
$25$	−2.73607	+	4.73901i	−0.547214	+	0.947802i
$26$	−0.618034	−	1.07047i	−0.121206	−	0.209936i
$27$	−14.4721			−2.78516
$28$		0			0
$29$	−4.47214			−0.830455			−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214			−0.830455			−0.415227	+	0.909718i	$0.636298\pi$
$30$	5.23607	+	9.06914i	0.955971	+	1.65579i
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.61803	+	2.80252i	0.281664	+	0.487856i
$34$	−6.47214			−1.10996
$35$		0			0
$36$	7.47214			1.24536
$37$	5.47214	+	9.47802i	0.899614	+	1.55818i	0.827989	+	0.560745i	$0.189485\pi$
$37$	5.47214	+	9.47802i	0.899614	+	1.55818i	0.0716249	+	0.997432i	$0.477182\pi$
$38$	1.38197	−	2.39364i	0.224184	−	0.388299i
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$	−1.61803	−	2.80252i	−0.255834	−	0.443117i
$41$	6.47214			1.01078			0.505389	−	0.862892i	$-0.331349\pi$
$41$	6.47214			1.01078			0.505389	+	0.862892i	$0.331349\pi$
$42$		0			0
$43$	−1.52786			−0.232997			−0.116499	−	0.993191i	$-0.537167\pi$
$43$	−1.52786			−0.232997			−0.116499	+	0.993191i	$0.537167\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−12.0902	+	20.9408i	−1.80230	+	3.12167i
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$	−3.23607			−0.467086
$49$		0			0
$50$	5.47214			0.773877
$51$	−10.4721	−	18.1383i	−1.46639	−	2.53987i
$52$	−0.618034	+	1.07047i	−0.0857059	+	0.148447i
$53$	0.236068	−	0.408882i	0.0324264	−	0.0561642i	−0.849357	−	0.527819i	$-0.823010\pi$
$53$	0.236068	−	0.408882i	0.0324264	−	0.0561642i	0.881783	+	0.471655i	$0.156343\pi$
$54$	7.23607	+	12.5332i	0.984704	+	1.70556i
$55$	3.23607			0.436351
$56$		0			0
$57$	8.94427			1.18470
$58$	2.23607	+	3.87298i	0.293610	+	0.508548i
$59$	−3.61803	+	6.26662i	−0.471028	+	0.815844i	−0.999451	−	0.0331370i	$-0.989450\pi$
$59$	−3.61803	+	6.26662i	−0.471028	+	0.815844i	0.528423	+	0.848981i	$0.322784\pi$
$60$	5.23607	−	9.06914i	0.675973	−	1.17082i
$61$	2.61803	+	4.53457i	0.335205	+	0.580592i	0.983524	−	0.180777i	$-0.0578611\pi$
$61$	2.61803	+	4.53457i	0.335205	+	0.580592i	−0.648319	+	0.761369i	$0.724528\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$	1.61803	−	2.80252i	0.199166	−	0.344966i
$67$	7.70820	−	13.3510i	0.941707	−	1.63108i	0.179493	−	0.983759i	$-0.442554\pi$
$67$	7.70820	−	13.3510i	0.941707	−	1.63108i	0.762214	−	0.647325i	$-0.224112\pi$
$68$	3.23607	+	5.60503i	0.392431	+	0.679710i
$69$	−12.9443			−1.55831
$70$		0			0
$71$	−2.47214			−0.293389			−0.146694	−	0.989182i	$-0.546863\pi$
$71$	−2.47214			−0.293389			−0.146694	+	0.989182i	$0.546863\pi$
$72$	−3.73607	−	6.47106i	−0.440300	−	0.762622i
$73$	2.47214	−	4.28187i	0.289342	−	0.501154i	−0.684311	−	0.729190i	$-0.739897\pi$
$73$	2.47214	−	4.28187i	0.289342	−	0.501154i	0.973653	+	0.228036i	$0.0732303\pi$
$74$	5.47214	−	9.47802i	0.636123	−	1.10180i
$75$	8.85410	+	15.3358i	1.02238	+	1.77082i
$76$	−2.76393			−0.317045
$77$		0			0
$78$	−4.00000			−0.452911
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−1.61803	+	2.80252i	−0.180902	+	0.313331i
$81$	−12.2082	+	21.1452i	−1.35647	+	2.34947i
$82$	−3.23607	−	5.60503i	−0.357364	−	0.618972i
$83$	10.1803			1.11744			0.558719	−	0.829357i	$-0.311293\pi$
$83$	10.1803			1.11744			0.558719	+	0.829357i	$0.311293\pi$
$84$		0			0
$85$	−20.9443			−2.27173
$86$	0.763932	+	1.32317i	0.0823769	+	0.142681i
$87$	−7.23607	+	12.5332i	−0.775788	+	1.34370i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$	24.1803			2.54883
$91$		0			0
$92$	4.00000			0.417029
$93$	3.23607	+	5.60503i	0.335565	+	0.581215i
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$	4.47214	−	7.74597i	0.458831	−	0.794719i
$96$	1.61803	+	2.80252i	0.165140	+	0.286031i
$97$	3.52786			0.358200			0.179100	−	0.983831i	$-0.442681\pi$
$97$	3.52786			0.358200			0.179100	+	0.983831i	$0.442681\pi$
$98$		0			0
$99$	7.47214			0.750978
$100$	−2.73607	−	4.73901i	−0.273607	−	0.473901i
$101$	7.09017	−	12.2805i	0.705498	−	1.22196i	−0.261013	−	0.965335i	$-0.584057\pi$
$101$	7.09017	−	12.2805i	0.705498	−	1.22196i	0.966511	−	0.256624i	$-0.0826101\pi$
$102$	−10.4721	+	18.1383i	−1.03690	+	1.79596i
$103$	−1.47214	−	2.54981i	−0.145054	−	0.251241i	0.784339	−	0.620332i	$-0.213002\pi$
$103$	−1.47214	−	2.54981i	−0.145054	−	0.251241i	−0.929393	+	0.369092i	$0.879669\pi$
$104$	1.23607			0.121206
$105$		0			0
$106$	−0.472136			−0.0458579
$107$	3.23607	+	5.60503i	0.312842	+	0.541859i	0.978977	−	0.203973i	$-0.0653855\pi$
$107$	3.23607	+	5.60503i	0.312842	+	0.541859i	−0.666134	+	0.745832i	$0.732052\pi$
$108$	7.23607	−	12.5332i	0.696291	−	1.20601i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	−1.61803	−	2.80252i	−0.154273	−	0.267210i
$111$	35.4164			3.36158
$112$		0			0
$113$	8.47214			0.796992			0.398496	−	0.917170i	$-0.369532\pi$
$113$	8.47214			0.796992			0.398496	+	0.917170i	$0.369532\pi$
$114$	−4.47214	−	7.74597i	−0.418854	−	0.725476i
$115$	−6.47214	+	11.2101i	−0.603530	+	1.04534i
$116$	2.23607	−	3.87298i	0.207614	−	0.359597i
$117$	−4.61803	−	7.99867i	−0.426937	−	0.739477i
$118$	7.23607			0.666134
$119$		0			0
$120$	−10.4721			−0.955971
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	2.61803	−	4.53457i	0.237026	−	0.410540i
$123$	10.4721	−	18.1383i	0.944241	−	1.63547i
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	1.52786			0.136656
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−2.47214	+	4.28187i	−0.217659	+	0.376997i
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	−4.61803	−	7.99867i	−0.403480	−	0.698847i	0.590664	−	0.806918i	$-0.298866\pi$
$131$	−4.61803	−	7.99867i	−0.403480	−	0.698847i	−0.994143	+	0.108071i	$0.965533\pi$
$132$	−3.23607			−0.281664
$133$		0			0
$134$	−15.4164			−1.33177
$135$	23.4164	+	40.5584i	2.01536	+	3.49071i
$136$	3.23607	−	5.60503i	0.277491	−	0.480628i
$137$	−7.94427	+	13.7599i	−0.678725	+	1.17559i	0.296640	+	0.954989i	$0.404134\pi$
$137$	−7.94427	+	13.7599i	−0.678725	+	1.17559i	−0.975365	+	0.220597i	$0.929200\pi$
$138$	6.47214	+	11.2101i	0.550945	+	0.954264i
$139$	−8.29180			−0.703301			−0.351650	−	0.936131i	$-0.614379\pi$
$139$	−8.29180			−0.703301			−0.351650	+	0.936131i	$0.614379\pi$
$140$		0			0
$141$	6.47214			0.545052
$142$	1.23607	+	2.14093i	0.103729	+	0.179663i
$143$	−0.618034	+	1.07047i	−0.0516826	+	0.0895169i
$144$	−3.73607	+	6.47106i	−0.311339	+	0.539255i
$145$	7.23607	+	12.5332i	0.600923	+	1.04083i
$146$	−4.94427			−0.409191
$147$		0			0
$148$	−10.9443			−0.899614
$149$	−11.1803	−	19.3649i	−0.915929	−	1.58644i	−0.805535	−	0.592548i	$-0.798122\pi$
$149$	−11.1803	−	19.3649i	−0.915929	−	1.58644i	−0.110394	−	0.993888i	$-0.535211\pi$
$150$	8.85410	−	15.3358i	0.722934	−	1.25216i
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	−0.999909	−	0.0134886i	$-0.995706\pi$
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	0.511636	+	0.859202i	$0.329040\pi$
$152$	1.38197	+	2.39364i	0.112092	+	0.194149i
$153$	−48.3607			−3.90973
$154$		0			0
$155$	6.47214			0.519854
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−9.32624	+	16.1535i	−0.744315	+	1.28919i	0.206199	+	0.978510i	$0.433890\pi$
$157$	−9.32624	+	16.1535i	−0.744315	+	1.28919i	−0.950514	+	0.310681i	$0.899443\pi$
$158$		0			0
$159$	−0.763932	−	1.32317i	−0.0605838	−	0.104934i
$160$	3.23607			0.255834
$161$		0			0
$162$	24.4164			1.91833
$163$	−3.70820	−	6.42280i	−0.290449	−	0.503072i	0.683467	−	0.729981i	$-0.260471\pi$
$163$	−3.70820	−	6.42280i	−0.290449	−	0.503072i	−0.973916	+	0.226909i	$0.927138\pi$
$164$	−3.23607	+	5.60503i	−0.252694	+	0.437680i
$165$	5.23607	−	9.06914i	0.407627	−	0.706031i
$166$	−5.09017	−	8.81643i	−0.395074	−	0.684288i
$167$	−15.4164			−1.19296			−0.596479	−	0.802629i	$-0.703434\pi$
$167$	−15.4164			−1.19296			−0.596479	+	0.802629i	$0.703434\pi$
$168$		0			0
$169$	−11.4721			−0.882472
$170$	10.4721	+	18.1383i	0.803176	+	1.39114i
$171$	10.3262	−	17.8856i	0.789667	−	1.36774i
$172$	0.763932	−	1.32317i	0.0582493	−	0.100891i
$173$	−0.618034	−	1.07047i	−0.0469883	−	0.0813860i	0.841575	−	0.540141i	$-0.181629\pi$
$173$	−0.618034	−	1.07047i	−0.0469883	−	0.0813860i	−0.888563	+	0.458755i	$0.848296\pi$
$174$	14.4721			1.09713
$175$		0			0
$176$	1.00000			0.0753778
$177$	11.7082	+	20.2792i	0.880042	+	1.52428i
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$	−4.47214	+	7.74597i	−0.334263	+	0.578961i	−0.983343	−	0.181760i	$-0.941821\pi$
$179$	−4.47214	+	7.74597i	−0.334263	+	0.578961i	0.649080	+	0.760720i	$0.275154\pi$
$180$	−12.0902	−	20.9408i	−0.901148	−	1.56083i
$181$	4.76393			0.354100			0.177050	−	0.984202i	$-0.443345\pi$
$181$	4.76393			0.354100			0.177050	+	0.984202i	$0.443345\pi$
$182$		0			0
$183$	16.9443			1.25256
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$	17.7082	−	30.6715i	1.30193	−	2.25501i
$186$	3.23607	−	5.60503i	0.237280	−	0.410981i
$187$	3.23607	+	5.60503i	0.236645	+	0.409881i
$188$	−2.00000			−0.145865
$189$		0			0
$190$	−8.94427			−0.648886
$191$	−3.23607	−	5.60503i	−0.234154	−	0.405566i	0.724873	−	0.688883i	$-0.241899\pi$
$191$	−3.23607	−	5.60503i	−0.234154	−	0.405566i	−0.959026	+	0.283317i	$0.908565\pi$
$192$	1.61803	−	2.80252i	0.116772	−	0.202254i
$193$	−1.47214	+	2.54981i	−0.105967	+	0.183540i	−0.914133	−	0.405415i	$-0.867127\pi$
$193$	−1.47214	+	2.54981i	−0.105967	+	0.183540i	0.808166	+	0.588955i	$0.200460\pi$
$194$	−1.76393	−	3.05522i	−0.126643	−	0.219352i
$195$	−12.9443			−0.926959
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−3.73607	−	6.47106i	−0.265511	−	0.459878i
$199$	−0.527864	+	0.914287i	−0.0374193	+	0.0648121i	−0.884129	−	0.467244i	$-0.845247\pi$
$199$	−0.527864	+	0.914287i	−0.0374193	+	0.0648121i	0.846709	+	0.532056i	$0.178580\pi$
$200$	−2.73607	+	4.73901i	−0.193469	+	0.335099i
$201$	−24.9443	−	43.2047i	−1.75943	−	3.04743i
$202$	−14.1803			−0.997725
$203$		0			0
$204$	20.9443			1.46639
$205$	−10.4721	−	18.1383i	−0.731406	−	1.26683i
$206$	−1.47214	+	2.54981i	−0.102569	+	0.177654i
$207$	−14.9443	+	25.8842i	−1.03870	+	1.79908i
$208$	−0.618034	−	1.07047i	−0.0428529	−	0.0742235i
$209$	−2.76393			−0.191185
$210$		0			0
$211$	−22.4721			−1.54705			−0.773523	−	0.633768i	$-0.781507\pi$
$211$	−22.4721			−1.54705			−0.773523	+	0.633768i	$0.781507\pi$
$212$	0.236068	+	0.408882i	0.0162132	+	0.0280821i
$213$	−4.00000	+	6.92820i	−0.274075	+	0.474713i
$214$	3.23607	−	5.60503i	0.221213	−	0.383152i
$215$	2.47214	+	4.28187i	0.168598	+	0.292021i
$216$	−14.4721			−0.984704
$217$		0			0
$218$	−10.0000			−0.677285
$219$	−8.00000	−	13.8564i	−0.540590	−	0.936329i
$220$	−1.61803	+	2.80252i	−0.109088	+	0.188946i
$221$	4.00000	−	6.92820i	0.269069	−	0.466041i
$222$	−17.7082	−	30.6715i	−1.18850	−	2.05854i
$223$	8.47214			0.567336			0.283668	−	0.958923i	$-0.408449\pi$
$223$	8.47214			0.567336			0.283668	+	0.958923i	$0.408449\pi$
$224$		0			0
$225$	40.8885			2.72590
$226$	−4.23607	−	7.33708i	−0.281779	−	0.488056i
$227$	7.38197	−	12.7859i	0.489958	−	0.848633i	−0.509975	−	0.860189i	$-0.670345\pi$
$227$	7.38197	−	12.7859i	0.489958	−	0.848633i	0.999933	+	0.0115566i	$0.00367866\pi$
$228$	−4.47214	+	7.74597i	−0.296174	+	0.512989i
$229$	−6.38197	−	11.0539i	−0.421732	−	0.730462i	0.574377	−	0.818591i	$-0.305244\pi$
$229$	−6.38197	−	11.0539i	−0.421732	−	0.730462i	−0.996109	+	0.0881294i	$0.971911\pi$
$230$	12.9443			0.853520
$231$		0			0
$232$	−4.47214			−0.293610
$233$	−1.47214	−	2.54981i	−0.0964428	−	0.167044i	0.813767	−	0.581191i	$-0.197413\pi$
$233$	−1.47214	−	2.54981i	−0.0964428	−	0.167044i	−0.910210	+	0.414147i	$0.864080\pi$
$234$	−4.61803	+	7.99867i	−0.301890	+	0.522889i
$235$	3.23607	−	5.60503i	0.211098	−	0.365632i
$236$	−3.61803	−	6.26662i	−0.235514	−	0.407922i
$237$		0			0
$238$		0			0
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$	5.23607	+	9.06914i	0.337987	+	0.585410i
$241$	5.70820	−	9.88690i	0.367698	−	0.636871i	−0.621507	−	0.783408i	$-0.713479\pi$
$241$	5.70820	−	9.88690i	0.367698	−	0.636871i	0.989205	+	0.146537i	$0.0468128\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	17.7984	+	30.8277i	1.14177	+	1.97760i
$244$	−5.23607			−0.335205
$245$		0			0
$246$	−20.9443			−1.33536
$247$	1.70820	+	2.95870i	0.108690	+	0.188257i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$	16.4721	−	28.5306i	1.04388	−	1.80805i
$250$	−0.763932	−	1.32317i	−0.0483153	−	0.0836846i
$251$	24.7639			1.56309			0.781543	−	0.623852i	$-0.214433\pi$
$251$	24.7639			1.56309			0.781543	+	0.623852i	$0.214433\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$	6.00000	+	10.3923i	0.376473	+	0.652071i
$255$	−33.8885	+	58.6967i	−2.12218	+	3.67573i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.47214	+	9.47802i	0.341342	+	0.591222i	0.984682	−	0.174358i	$-0.0557851\pi$
$257$	5.47214	+	9.47802i	0.341342	+	0.591222i	−0.643340	+	0.765581i	$0.722452\pi$
$258$	4.94427			0.307817
$259$		0			0
$260$	4.00000			0.248069
$261$	16.7082	+	28.9395i	1.03421	+	1.79131i
$262$	−4.61803	+	7.99867i	−0.285303	+	0.494159i
$263$	−6.47214	+	11.2101i	−0.399089	+	0.691242i	−0.993614	−	0.112835i	$-0.964007\pi$
$263$	−6.47214	+	11.2101i	−0.399089	+	0.691242i	0.594525	+	0.804077i	$0.297340\pi$
$264$	1.61803	+	2.80252i	0.0995831	+	0.172483i
$265$	−1.52786			−0.0938559
$266$		0			0
$267$	−32.3607			−1.98044
$268$	7.70820	+	13.3510i	0.470853	+	0.815542i
$269$	13.6180	−	23.5871i	0.830306	−	1.43813i	−0.0674893	−	0.997720i	$-0.521499\pi$
$269$	13.6180	−	23.5871i	0.830306	−	1.43813i	0.897796	−	0.440413i	$-0.145168\pi$
$270$	23.4164	−	40.5584i	1.42508	−	2.46831i
$271$	8.47214	+	14.6742i	0.514646	+	0.891392i	0.999856	+	0.0169947i	$0.00540983\pi$
$271$	8.47214	+	14.6742i	0.514646	+	0.891392i	−0.485210	+	0.874398i	$0.661257\pi$
$272$	−6.47214			−0.392431
$273$		0			0
$274$	15.8885			0.959862
$275$	−2.73607	−	4.73901i	−0.164991	−	0.285773i
$276$	6.47214	−	11.2101i	0.389577	−	0.674767i
$277$	−6.23607	+	10.8012i	−0.374689	+	0.648980i	−0.990280	−	0.139085i	$-0.955584\pi$
$277$	−6.23607	+	10.8012i	−0.374689	+	0.648980i	0.615591	+	0.788065i	$0.288917\pi$
$278$	4.14590	+	7.18091i	0.248654	+	0.430682i
$279$	14.9443			0.894690
$280$		0			0
$281$	−24.8328			−1.48140			−0.740701	−	0.671835i	$-0.765506\pi$
$281$	−24.8328			−1.48140			−0.740701	+	0.671835i	$0.765506\pi$
$282$	−3.23607	−	5.60503i	−0.192705	−	0.333775i
$283$	8.32624	−	14.4215i	0.494943	−	0.857267i	−0.505040	−	0.863096i	$-0.668522\pi$
$283$	8.32624	−	14.4215i	0.494943	−	0.857267i	0.999983	+	0.00582897i	$0.00185543\pi$
$284$	1.23607	−	2.14093i	0.0733471	−	0.127041i
$285$	−14.4721	−	25.0665i	−0.857255	−	1.48481i
$286$	1.23607			0.0730902
$287$		0			0
$288$	7.47214			0.440300
$289$	−12.4443	−	21.5541i	−0.732016	−	1.26789i
$290$	7.23607	−	12.5332i	0.424917	−	0.735977i
$291$	5.70820	−	9.88690i	0.334621	−	0.579580i
$292$	2.47214	+	4.28187i	0.144671	+	0.250577i
$293$	4.65248			0.271801			0.135900	−	0.990723i	$-0.456607\pi$
$293$	4.65248			0.271801			0.135900	+	0.990723i	$0.456607\pi$
$294$		0			0
$295$	23.4164			1.36336
$296$	5.47214	+	9.47802i	0.318061	+	0.550899i
$297$	7.23607	−	12.5332i	0.419879	−	0.727252i
$298$	−11.1803	+	19.3649i	−0.647660	+	1.12178i
$299$	−2.47214	−	4.28187i	−0.142967	−	0.247627i
$300$	−17.7082			−1.02238
$301$		0			0
$302$	12.0000			0.690522
$303$	−22.9443	−	39.7406i	−1.31811	−	2.28304i
$304$	1.38197	−	2.39364i	0.0792612	−	0.137284i
$305$	8.47214	−	14.6742i	0.485113	−	0.840241i
$306$	24.1803	+	41.8816i	1.38230	+	2.39421i
$307$	32.0689			1.83027			0.915134	−	0.403150i	$-0.132085\pi$
$307$	32.0689			1.83027			0.915134	+	0.403150i	$0.132085\pi$
$308$		0			0
$309$	−9.52786			−0.542021
$310$	−3.23607	−	5.60503i	−0.183796	−	0.318345i
$311$	−2.70820	+	4.69075i	−0.153568	+	0.265988i	−0.932537	−	0.361075i	$-0.882410\pi$
$311$	−2.70820	+	4.69075i	−0.153568	+	0.265988i	0.778969	+	0.627063i	$0.215743\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	−14.2361	−	24.6576i	−0.804670	−	1.39373i	−0.916514	−	0.400004i	$-0.869009\pi$
$313$	−14.2361	−	24.6576i	−0.804670	−	1.39373i	0.111843	−	0.993726i	$-0.464325\pi$
$314$	18.6525			1.05262
$315$		0			0
$316$		0			0
$317$	6.52786	+	11.3066i	0.366641	+	0.635041i	0.989038	−	0.147660i	$-0.0471743\pi$
$317$	6.52786	+	11.3066i	0.366641	+	0.635041i	−0.622397	+	0.782702i	$0.713841\pi$
$318$	−0.763932	+	1.32317i	−0.0428392	+	0.0741996i
$319$	2.23607	−	3.87298i	0.125196	−	0.216845i
$320$	−1.61803	−	2.80252i	−0.0904508	−	0.156665i
$321$	20.9443			1.16900
$322$		0			0
$323$	17.8885			0.995345
$324$	−12.2082	−	21.1452i	−0.678234	−	1.17473i
$325$	−3.38197	+	5.85774i	−0.187598	+	0.324929i
$326$	−3.70820	+	6.42280i	−0.205378	+	0.355726i
$327$	−16.1803	−	28.0252i	−0.894775	−	1.54980i
$328$	6.47214			0.357364
$329$		0			0
$330$	−10.4721			−0.576472
$331$	−0.472136	−	0.817763i	−0.0259509	−	0.0449483i	0.852758	−	0.522306i	$-0.174928\pi$
$331$	−0.472136	−	0.817763i	−0.0259509	−	0.0449483i	−0.878709	+	0.477357i	$0.841595\pi$
$332$	−5.09017	+	8.81643i	−0.279359	+	0.483865i
$333$	40.8885	−	70.8210i	2.24068	−	3.88097i
$334$	7.70820	+	13.3510i	0.421774	+	0.730534i
$335$	−49.8885			−2.72570
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	5.73607	+	9.93516i	0.312001	+	0.540402i
$339$	13.7082	−	23.7433i	0.744527	−	1.28956i
$340$	10.4721	−	18.1383i	0.567931	−	0.983686i
$341$	−1.00000	−	1.73205i	−0.0541530	−	0.0937958i
$342$	−20.6525			−1.11676
$343$		0			0
$344$	−1.52786			−0.0823769
$345$	20.9443	+	36.2765i	1.12760	+	1.95306i
$346$	−0.618034	+	1.07047i	−0.0332257	+	0.0575486i
$347$	3.23607	−	5.60503i	0.173721	−	0.300894i	−0.765997	−	0.642844i	$-0.777754\pi$
$347$	3.23607	−	5.60503i	0.173721	−	0.300894i	0.939718	+	0.341950i	$0.111087\pi$
$348$	−7.23607	−	12.5332i	−0.387894	−	0.671852i
$349$	8.29180			0.443850			0.221925	−	0.975064i	$-0.428766\pi$
$349$	8.29180			0.443850			0.221925	+	0.975064i	$0.428766\pi$
$350$		0			0
$351$	−17.8885			−0.954820
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	17.4721	−	30.2626i	0.929948	−	1.61072i	0.146544	−	0.989204i	$-0.453185\pi$
$353$	17.4721	−	30.2626i	0.929948	−	1.61072i	0.783404	−	0.621513i	$-0.213482\pi$
$354$	11.7082	−	20.2792i	0.622284	−	1.07783i
$355$	4.00000	+	6.92820i	0.212298	+	0.367711i
$356$	10.0000			0.529999
$357$		0			0
$358$	8.94427			0.472719
$359$	13.4164	+	23.2379i	0.708091	+	1.22645i	0.965564	+	0.260164i	$0.0837767\pi$
$359$	13.4164	+	23.2379i	0.708091	+	1.22645i	−0.257473	+	0.966285i	$0.582890\pi$
$360$	−12.0902	+	20.9408i	−0.637208	+	1.10368i
$361$	5.68034	−	9.83864i	0.298965	−	0.517823i
$362$	−2.38197	−	4.12569i	−0.125193	−	0.216841i
$363$	−3.23607			−0.169850
$364$		0			0
$365$	−16.0000			−0.837478
$366$	−8.47214	−	14.6742i	−0.442846	−	0.767031i
$367$	−10.7082	+	18.5472i	−0.558964	+	0.968154i	0.438620	+	0.898673i	$0.355468\pi$
$367$	−10.7082	+	18.5472i	−0.558964	+	0.968154i	−0.997583	+	0.0694807i	$0.977866\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$	−24.1803	−	41.8816i	−1.25878	−	2.18027i
$370$	−35.4164			−1.84121
$371$		0			0
$372$	−6.47214			−0.335565
$373$	3.00000	+	5.19615i	0.155334	+	0.269047i	0.933181	−	0.359408i	$-0.117021\pi$
$373$	3.00000	+	5.19615i	0.155334	+	0.269047i	−0.777847	+	0.628454i	$0.783688\pi$
$374$	3.23607	−	5.60503i	0.167333	−	0.289829i
$375$	2.47214	−	4.28187i	0.127661	−	0.221115i
$376$	1.00000	+	1.73205i	0.0515711	+	0.0893237i
$377$	−5.52786			−0.284699
$378$		0			0
$379$	5.52786			0.283947			0.141974	−	0.989870i	$-0.454655\pi$
$379$	5.52786			0.283947			0.141974	+	0.989870i	$0.454655\pi$
$380$	4.47214	+	7.74597i	0.229416	+	0.397360i
$381$	−19.4164	+	33.6302i	−0.994733	+	1.72293i
$382$	−3.23607	+	5.60503i	−0.165572	+	0.286778i
$383$	−5.94427	−	10.2958i	−0.303738	−	0.526090i	0.673241	−	0.739423i	$-0.264901\pi$
$383$	−5.94427	−	10.2958i	−0.303738	−	0.526090i	−0.976980	+	0.213333i	$0.931568\pi$
$384$	−3.23607			−0.165140
$385$		0			0
$386$	2.94427			0.149859
$387$	5.70820	+	9.88690i	0.290164	+	0.502579i
$388$	−1.76393	+	3.05522i	−0.0895501	+	0.155105i
$389$	−3.29180	+	5.70156i	−0.166901	+	0.289080i	−0.937329	−	0.348447i	$-0.886709\pi$
$389$	−3.29180	+	5.70156i	−0.166901	+	0.289080i	0.770428	+	0.637527i	$0.220043\pi$
$390$	6.47214	+	11.2101i	0.327729	+	0.567644i
$391$	−25.8885			−1.30924
$392$		0			0
$393$	−29.8885			−1.50768
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$		0			0
$396$	−3.73607	+	6.47106i	−0.187744	+	0.325183i
$397$	5.14590	+	8.91296i	0.258265	+	0.447328i	0.965777	−	0.259373i	$-0.0835158\pi$
$397$	5.14590	+	8.91296i	0.258265	+	0.447328i	−0.707512	+	0.706701i	$0.750182\pi$
$398$	1.05573			0.0529189
$399$		0			0
$400$	5.47214			0.273607
$401$	15.1803	+	26.2931i	0.758070	+	1.31302i	0.943834	+	0.330421i	$0.107191\pi$
$401$	15.1803	+	26.2931i	0.758070	+	1.31302i	−0.185764	+	0.982594i	$0.559476\pi$
$402$	−24.9443	+	43.2047i	−1.24411	+	2.15486i
$403$	−1.23607	+	2.14093i	−0.0615729	+	0.106647i
$404$	7.09017	+	12.2805i	0.352749	+	0.610979i
$405$	79.0132			3.92620
$406$		0			0
$407$	−10.9443			−0.542487
$408$	−10.4721	−	18.1383i	−0.518448	−	0.897978i
$409$	11.7082	−	20.2792i	0.578933	−	1.00274i	−0.416669	−	0.909058i	$-0.636802\pi$
$409$	11.7082	−	20.2792i	0.578933	−	1.00274i	0.995602	−	0.0936836i	$-0.0298642\pi$
$410$	−10.4721	+	18.1383i	−0.517182	+	0.895785i
$411$	25.7082	+	44.5279i	1.26809	+	2.19640i
$412$	2.94427			0.145054
$413$		0			0
$414$	29.8885			1.46894
$415$	−16.4721	−	28.5306i	−0.808585	−	1.40051i
$416$	−0.618034	+	1.07047i	−0.0303016	+	0.0524839i
$417$	−13.4164	+	23.2379i	−0.657004	+	1.13796i
$418$	1.38197	+	2.39364i	0.0675942	+	0.117077i
$419$	12.7639			0.623559			0.311779	−	0.950155i	$-0.399075\pi$
$419$	12.7639			0.623559			0.311779	+	0.950155i	$0.399075\pi$
$420$		0			0
$421$	7.52786			0.366886			0.183443	−	0.983030i	$-0.441276\pi$
$421$	7.52786			0.366886			0.183443	+	0.983030i	$0.441276\pi$
$422$	11.2361	+	19.4614i	0.546963	+	0.947368i
$423$	7.47214	−	12.9421i	0.363308	−	0.629267i
$424$	0.236068	−	0.408882i	0.0114645	−	0.0198571i
$425$	17.7082	+	30.6715i	0.858974	+	1.48779i
$426$	8.00000			0.387601
$427$		0			0
$428$	−6.47214			−0.312842
$429$	2.00000	+	3.46410i	0.0965609	+	0.167248i
$430$	2.47214	−	4.28187i	0.119217	−	0.206490i
$431$	−20.4721	+	35.4588i	−0.986108	+	1.70799i	−0.349203	+	0.937047i	$0.613548\pi$
$431$	−20.4721	+	35.4588i	−0.986108	+	1.70799i	−0.636905	+	0.770942i	$0.719786\pi$
$432$	7.23607	+	12.5332i	0.348145	+	0.603006i
$433$	19.5279			0.938449			0.469225	−	0.883079i	$-0.344533\pi$
$433$	19.5279			0.938449			0.469225	+	0.883079i	$0.344533\pi$
$434$		0			0
$435$	46.8328			2.24546
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	5.52786	−	9.57454i	0.264434	−	0.458012i
$438$	−8.00000	+	13.8564i	−0.382255	+	0.662085i
$439$	4.47214	+	7.74597i	0.213443	+	0.369695i	0.952790	−	0.303630i	$-0.0981988\pi$
$439$	4.47214	+	7.74597i	0.213443	+	0.369695i	−0.739347	+	0.673325i	$0.764865\pi$
$440$	3.23607			0.154273
$441$		0			0
$442$	−8.00000			−0.380521
$443$	3.52786	+	6.11044i	0.167614	+	0.290316i	0.937580	−	0.347768i	$-0.113060\pi$
$443$	3.52786	+	6.11044i	0.167614	+	0.290316i	−0.769967	+	0.638084i	$0.779727\pi$
$444$	−17.7082	+	30.6715i	−0.840394	+	1.45561i
$445$	−16.1803	+	28.0252i	−0.767022	+	1.32852i
$446$	−4.23607	−	7.33708i	−0.200584	−	0.347421i
$447$	−72.3607			−3.42254
$448$		0			0
$449$	1.05573			0.0498229			0.0249114	−	0.999690i	$-0.492070\pi$
$449$	1.05573			0.0498229			0.0249114	+	0.999690i	$0.492070\pi$
$450$	−20.4443	−	35.4105i	−0.963752	−	1.66927i
$451$	−3.23607	+	5.60503i	−0.152380	+	0.263931i
$452$	−4.23607	+	7.33708i	−0.199248	+	0.345107i
$453$	19.4164	+	33.6302i	0.912262	+	1.58008i
$454$	−14.7639			−0.692906
$455$		0			0
$456$	8.94427			0.418854
$457$	−4.52786	−	7.84249i	−0.211805	−	0.366856i	0.740475	−	0.672084i	$-0.234601\pi$
$457$	−4.52786	−	7.84249i	−0.211805	−	0.366856i	−0.952279	+	0.305228i	$0.901267\pi$
$458$	−6.38197	+	11.0539i	−0.298210	+	0.516514i
$459$	−46.8328	+	81.1168i	−2.18597	+	3.78621i
$460$	−6.47214	−	11.2101i	−0.301765	−	0.522672i
$461$	29.2361			1.36166			0.680830	−	0.732442i	$-0.261619\pi$
$461$	29.2361			1.36166			0.680830	+	0.732442i	$0.261619\pi$
$462$		0			0
$463$	−21.5279			−1.00048			−0.500242	−	0.865885i	$-0.666756\pi$
$463$	−21.5279			−1.00048			−0.500242	+	0.865885i	$0.666756\pi$
$464$	2.23607	+	3.87298i	0.103807	+	0.179799i
$465$	10.4721	−	18.1383i	0.485634	−	0.841142i
$466$	−1.47214	+	2.54981i	−0.0681954	+	0.118118i
$467$	−6.56231	−	11.3662i	−0.303667	−	0.525967i	0.673296	−	0.739373i	$-0.264878\pi$
$467$	−6.56231	−	11.3662i	−0.303667	−	0.525967i	−0.976964	+	0.213405i	$0.931544\pi$
$468$	9.23607			0.426937
$469$		0			0
$470$	−6.47214			−0.298537
$471$	30.1803	+	52.2739i	1.39064	+	2.40865i
$472$	−3.61803	+	6.26662i	−0.166534	+	0.288445i
$473$	0.763932	−	1.32317i	0.0351256	−	0.0608394i
$474$		0			0
$475$	−15.1246			−0.693965
$476$		0			0
$477$	−3.52786			−0.161530
$478$	−10.0000	−	17.3205i	−0.457389	−	0.792222i
$479$	16.1803	−	28.0252i	0.739299	−	1.28050i	−0.213513	−	0.976940i	$-0.568491\pi$
$479$	16.1803	−	28.0252i	0.739299	−	1.28050i	0.952812	−	0.303562i	$-0.0981761\pi$
$480$	5.23607	−	9.06914i	0.238993	−	0.413948i
$481$	6.76393	+	11.7155i	0.308409	+	0.534180i
$482$	−11.4164			−0.520003
$483$		0			0
$484$	1.00000			0.0454545
$485$	−5.70820	−	9.88690i	−0.259196	−	0.448941i
$486$	17.7984	−	30.8277i	0.807351	−	1.39837i
$487$	0.472136	−	0.817763i	0.0213945	−	0.0370564i	−0.855130	−	0.518414i	$-0.826523\pi$
$487$	0.472136	−	0.817763i	0.0213945	−	0.0370564i	0.876524	+	0.481357i	$0.159856\pi$
$488$	2.61803	+	4.53457i	0.118513	+	0.205270i
$489$	−24.0000			−1.08532
$490$		0			0
$491$	0.944272			0.0426144			0.0213072	−	0.999773i	$-0.493217\pi$
$491$	0.944272			0.0426144			0.0213072	+	0.999773i	$0.493217\pi$
$492$	10.4721	+	18.1383i	0.472120	+	0.817736i
$493$	−14.4721	+	25.0665i	−0.651792	+	1.12894i
$494$	1.70820	−	2.95870i	0.0768557	−	0.133118i
$495$	−12.0902	−	20.9408i	−0.543413	−	0.941218i
$496$	2.00000			0.0898027
$497$		0			0
$498$	−32.9443			−1.47627
$499$	−6.18034	−	10.7047i	−0.276670	−	0.479207i	0.693885	−	0.720086i	$-0.255898\pi$
$499$	−6.18034	−	10.7047i	−0.276670	−	0.479207i	−0.970555	+	0.240879i	$0.922564\pi$
$500$	−0.763932	+	1.32317i	−0.0341641	+	0.0591739i
$501$	−24.9443	+	43.2047i	−1.11443	+	1.93025i
$502$	−12.3820	−	21.4462i	−0.552634	−	0.957190i
$503$	4.00000			0.178351			0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000			0.178351			0.0891756	+	0.996016i	$0.471577\pi$
$504$		0			0
$505$	−45.8885			−2.04201
$506$	−2.00000	−	3.46410i	−0.0889108	−	0.153998i
$507$	−18.5623	+	32.1509i	−0.824381	+	1.42787i
$508$	6.00000	−	10.3923i	0.266207	−	0.461084i
$509$	17.0344	+	29.5045i	0.755038	+	1.30776i	0.945355	+	0.326042i	$0.105715\pi$
$509$	17.0344	+	29.5045i	0.755038	+	1.30776i	−0.190317	+	0.981723i	$0.560952\pi$
$510$	67.7771			3.00122
$511$		0			0
$512$	1.00000			0.0441942
$513$	−20.0000	−	34.6410i	−0.883022	−	1.52944i
$514$	5.47214	−	9.47802i	0.241366	−	0.418057i
$515$	−4.76393	+	8.25137i	−0.209924	+	0.363599i
$516$	−2.47214	−	4.28187i	−0.108830	−	0.188499i
$517$	−2.00000			−0.0879599
$518$		0			0
$519$	−4.00000			−0.175581
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	−17.1803	+	29.7572i	−0.752684	+	1.30369i	0.193833	+	0.981035i	$0.437908\pi$
$521$	−17.1803	+	29.7572i	−0.752684	+	1.30369i	−0.946517	+	0.322653i	$0.895425\pi$
$522$	16.7082	−	28.9395i	0.731298	−	1.26665i
$523$	13.8541	+	23.9960i	0.605798	+	1.04927i	0.991925	+	0.126827i	$0.0404792\pi$
$523$	13.8541	+	23.9960i	0.605798	+	1.04927i	−0.386127	+	0.922446i	$0.626187\pi$
$524$	9.23607			0.403480
$525$		0			0
$526$	12.9443			0.564397
$527$	6.47214	+	11.2101i	0.281931	+	0.488318i
$528$	1.61803	−	2.80252i	0.0704159	−	0.121964i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	0.763932	+	1.32317i	0.0331831	+	0.0574748i
$531$	54.0689			2.34639
$532$		0			0
$533$	8.00000			0.346518
$534$	16.1803	+	28.0252i	0.700192	+	1.21277i
$535$	10.4721	−	18.1383i	0.452750	−	0.784186i
$536$	7.70820	−	13.3510i	0.332944	−	0.576675i
$537$	14.4721	+	25.0665i	0.624519	+	1.08170i
$538$	−27.2361			−1.17423
$539$		0			0
$540$	−46.8328			−2.01536
$541$	4.52786	+	7.84249i	0.194668	+	0.337175i	0.946792	−	0.321847i	$-0.104304\pi$
$541$	4.52786	+	7.84249i	0.194668	+	0.337175i	−0.752124	+	0.659022i	$0.770970\pi$
$542$	8.47214	−	14.6742i	0.363909	−	0.630310i
$543$	7.70820	−	13.3510i	0.330791	−	0.572946i
$544$	3.23607	+	5.60503i	0.138745	+	0.240314i
$545$	−32.3607			−1.38618
$546$		0			0
$547$	16.9443			0.724485			0.362242	−	0.932084i	$-0.382011\pi$
$547$	16.9443			0.724485			0.362242	+	0.932084i	$0.382011\pi$
$548$	−7.94427	−	13.7599i	−0.339362	−	0.587793i
$549$	19.5623	−	33.8829i	0.834899	−	1.44609i
$550$	−2.73607	+	4.73901i	−0.116666	+	0.202072i
$551$	−6.18034	−	10.7047i	−0.263291	−	0.456034i
$552$	−12.9443			−0.550945
$553$		0			0
$554$	12.4721			0.529890
$555$	−57.3050	−	99.2551i	−2.43246	−	4.21314i
$556$	4.14590	−	7.18091i	0.175825	−	0.304538i
$557$	14.4164	−	24.9700i	0.610843	−	1.05801i	−0.380256	−	0.924881i	$-0.624164\pi$
$557$	14.4164	−	24.9700i	0.610843	−	1.05801i	0.991099	−	0.133129i	$-0.0425026\pi$
$558$	−7.47214	−	12.9421i	−0.316321	−	0.547884i
$559$	−1.88854			−0.0798769
$560$		0			0
$561$	20.9443			0.884268
$562$	12.4164	+	21.5058i	0.523755	+	0.907169i
$563$	−13.3820	+	23.1782i	−0.563983	+	0.976847i	0.433161	+	0.901317i	$0.357398\pi$
$563$	−13.3820	+	23.1782i	−0.563983	+	0.976847i	−0.997144	+	0.0755300i	$0.975935\pi$
$564$	−3.23607	+	5.60503i	−0.136263	+	0.236015i
$565$	−13.7082	−	23.7433i	−0.576708	−	0.998888i
$566$	−16.6525			−0.699956
$567$		0			0
$568$	−2.47214			−0.103729
$569$	−8.41641	−	14.5776i	−0.352834	−	0.611127i	0.633911	−	0.773406i	$-0.281449\pi$
$569$	−8.41641	−	14.5776i	−0.352834	−	0.611127i	−0.986745	+	0.162280i	$0.948115\pi$
$570$	−14.4721	+	25.0665i	−0.606171	+	1.04992i
$571$	22.9443	−	39.7406i	0.960188	−	1.66309i	0.238165	−	0.971225i	$-0.423454\pi$
$571$	22.9443	−	39.7406i	0.960188	−	1.66309i	0.722022	−	0.691870i	$-0.243213\pi$
$572$	−0.618034	−	1.07047i	−0.0258413	−	0.0447584i
$573$	−20.9443			−0.874960
$574$		0			0
$575$	21.8885			0.912815
$576$	−3.73607	−	6.47106i	−0.155669	−	0.269627i
$577$	−4.52786	+	7.84249i	−0.188497	+	0.326487i	−0.944749	−	0.327793i	$-0.893695\pi$
$577$	−4.52786	+	7.84249i	−0.188497	+	0.326487i	0.756252	+	0.654280i	$0.227028\pi$
$578$	−12.4443	+	21.5541i	−0.517613	+	0.896533i
$579$	4.76393	+	8.25137i	0.197982	+	0.342915i
$580$	−14.4721			−0.600923
$581$		0			0
$582$	−11.4164			−0.473225
$583$	0.236068	+	0.408882i	0.00977694	+	0.0169342i
$584$	2.47214	−	4.28187i	0.102298	−	0.177185i
$585$	−14.9443	+	25.8842i	−0.617870	+	1.07018i
$586$	−2.32624	−	4.02916i	−0.0960960	−	0.166443i
$587$	−28.1803			−1.16313			−0.581564	−	0.813501i	$-0.697559\pi$
$587$	−28.1803			−1.16313			−0.581564	+	0.813501i	$0.697559\pi$
$588$		0			0
$589$	−5.52786			−0.227772
$590$	−11.7082	−	20.2792i	−0.482019	−	0.834882i
$591$	29.1246	−	50.4453i	1.19803	−	2.07504i
$592$	5.47214	−	9.47802i	0.224903	−	0.389544i
$593$	−12.0000	−	20.7846i	−0.492781	−	0.853522i	0.507184	−	0.861838i	$-0.330686\pi$
$593$	−12.0000	−	20.7846i	−0.492781	−	0.853522i	−0.999965	+	0.00831589i	$0.997353\pi$
$594$	−14.4721			−0.593799
$595$		0			0
$596$	22.3607			0.915929
$597$	1.70820	+	2.95870i	0.0699121	+	0.121091i
$598$	−2.47214	+	4.28187i	−0.101093	+	0.175098i
$599$	−6.18034	+	10.7047i	−0.252522	+	0.437381i	−0.964219	−	0.265105i	$-0.914593\pi$
$599$	−6.18034	+	10.7047i	−0.252522	+	0.437381i	0.711698	+	0.702486i	$0.247927\pi$
$600$	8.85410	+	15.3358i	0.361467	+	0.626080i
$601$	18.8328			0.768207			0.384103	−	0.923290i	$-0.374511\pi$
$601$	18.8328			0.768207			0.384103	+	0.923290i	$0.374511\pi$
$602$		0			0
$603$	−115.193			−4.69104
$604$	−6.00000	−	10.3923i	−0.244137	−	0.422857i
$605$	−1.61803	+	2.80252i	−0.0657824	+	0.113939i
$606$	−22.9443	+	39.7406i	−0.932047	+	1.61435i
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	0.983262	+	0.182199i	$0.0583216\pi$
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	−0.333842	+	0.942629i	$0.608345\pi$
$608$	−2.76393			−0.112092
$609$		0			0
$610$	−16.9443			−0.686054
$611$	1.23607	+	2.14093i	0.0500060	+	0.0866129i
$612$	24.1803	−	41.8816i	0.977432	−	1.69296i
$613$	−9.76393	+	16.9116i	−0.394362	+	0.683054i	−0.993019	−	0.117951i	$-0.962368\pi$
$613$	−9.76393	+	16.9116i	−0.394362	+	0.683054i	0.598658	+	0.801005i	$0.295701\pi$
$614$	−16.0344	−	27.7725i	−0.647097	−	1.12081i
$615$	−67.7771			−2.73304
$616$		0			0
$617$	−5.41641			−0.218056			−0.109028	−	0.994039i	$-0.534774\pi$
$617$	−5.41641			−0.218056			−0.109028	+	0.994039i	$0.534774\pi$
$618$	4.76393	+	8.25137i	0.191633	+	0.331919i
$619$	24.2705	−	42.0378i	0.975514	−	1.68964i	0.297286	−	0.954788i	$-0.403918\pi$
$619$	24.2705	−	42.0378i	0.975514	−	1.68964i	0.678228	−	0.734852i	$-0.262748\pi$
$620$	−3.23607	+	5.60503i	−0.129964	+	0.225104i
$621$	28.9443	+	50.1329i	1.16149	+	2.01177i
$622$	5.41641			0.217178
$623$		0			0
$624$	−4.00000			−0.160128
$625$	11.2082	+	19.4132i	0.448328	+	0.776527i
$626$	−14.2361	+	24.6576i	−0.568988	+	0.985516i
$627$	−4.47214	+	7.74597i	−0.178600	+	0.309344i
$628$	−9.32624	−	16.1535i	−0.372157	−	0.644596i
$629$	70.8328			2.82429
$630$		0			0
$631$	−4.58359			−0.182470			−0.0912350	−	0.995829i	$-0.529081\pi$
$631$	−4.58359			−0.182470			−0.0912350	+	0.995829i	$0.529081\pi$
$632$		0			0
$633$	−36.3607	+	62.9785i	−1.44521	+	2.50317i
$634$	6.52786	−	11.3066i	0.259255	−	0.449042i
$635$	19.4164	+	33.6302i	0.770517	+	1.33457i
$636$	1.52786			0.0605838
$637$		0			0
$638$	−4.47214			−0.177054
$639$	9.23607	+	15.9973i	0.365373	+	0.632845i
$640$	−1.61803	+	2.80252i	−0.0639584	+	0.110779i
$641$	−18.2361	+	31.5858i	−0.720281	+	1.24756i	0.240606	+	0.970623i	$0.422654\pi$
$641$	−18.2361	+	31.5858i	−0.720281	+	1.24756i	−0.960887	+	0.276941i	$0.910679\pi$
$642$	−10.4721	−	18.1383i	−0.413302	−	0.715860i
$643$	−23.2361			−0.916341			−0.458171	−	0.888864i	$-0.651495\pi$
$643$	−23.2361			−0.916341			−0.458171	+	0.888864i	$0.651495\pi$
$644$		0			0
$645$	16.0000			0.629999
$646$	−8.94427	−	15.4919i	−0.351908	−	0.609522i
$647$	−12.4164	+	21.5058i	−0.488139	+	0.845482i	−0.999907	−	0.0136418i	$-0.995658\pi$
$647$	−12.4164	+	21.5058i	−0.488139	+	0.845482i	0.511768	+	0.859124i	$0.328991\pi$
$648$	−12.2082	+	21.1452i	−0.479584	+	0.830663i
$649$	−3.61803	−	6.26662i	−0.142020	−	0.245986i
$650$	6.76393			0.265303
$651$		0			0
$652$	7.41641			0.290449
$653$	−0.819660	−	1.41969i	−0.0320758	−	0.0555569i	0.849542	−	0.527521i	$-0.176878\pi$
$653$	−0.819660	−	1.41969i	−0.0320758	−	0.0555569i	−0.881618	+	0.471964i	$0.843545\pi$
$654$	−16.1803	+	28.0252i	−0.632701	+	1.09587i
$655$	−14.9443	+	25.8842i	−0.583921	+	1.01138i
$656$	−3.23607	−	5.60503i	−0.126347	−	0.218840i
$657$	−36.9443			−1.44133
$658$		0			0
$659$	43.4164			1.69126			0.845632	−	0.533767i	$-0.179224\pi$
$659$	43.4164			1.69126			0.845632	+	0.533767i	$0.179224\pi$
$660$	5.23607	+	9.06914i	0.203814	+	0.353016i
$661$	−18.5623	+	32.1509i	−0.721990	+	1.25052i	0.238211	+	0.971213i	$0.423439\pi$
$661$	−18.5623	+	32.1509i	−0.721990	+	1.25052i	−0.960201	+	0.279310i	$0.909894\pi$
$662$	−0.472136	+	0.817763i	−0.0183501	+	0.0317833i
$663$	−12.9443	−	22.4201i	−0.502714	−	0.870726i
$664$	10.1803			0.395074
$665$		0			0
$666$	−81.7771			−3.16880
$667$	8.94427	+	15.4919i	0.346324	+	0.599850i
$668$	7.70820	−	13.3510i	0.298239	−	0.516566i
$669$	13.7082	−	23.7433i	0.529990	−	0.917969i
$670$	24.9443	+	43.2047i	0.963681	+	1.66914i
$671$	−5.23607			−0.202136
$672$		0			0
$673$	31.8885			1.22921			0.614607	−	0.788834i	$-0.289315\pi$
$673$	31.8885			1.22921			0.614607	+	0.788834i	$0.289315\pi$
$674$	−9.00000	−	15.5885i	−0.346667	−	0.600445i
$675$	39.5967	−	68.5836i	1.52408	−	2.63978i
$676$	5.73607	−	9.93516i	0.220618	−	0.382122i
$677$	−16.0344	−	27.7725i	−0.616254	−	1.06738i	−0.990163	−	0.139917i	$-0.955316\pi$
$677$	−16.0344	−	27.7725i	−0.616254	−	1.06738i	0.373910	−	0.927465i	$-0.378017\pi$
$678$	−27.4164			−1.05292
$679$		0			0
$680$	−20.9443			−0.803176
$681$	−23.8885	−	41.3762i	−0.915411	−	1.58554i
$682$	−1.00000	+	1.73205i	−0.0382920	+	0.0663237i
$683$	−7.52786	+	13.0386i	−0.288046	+	0.498910i	−0.973343	−	0.229353i	$-0.926339\pi$
$683$	−7.52786	+	13.0386i	−0.288046	+	0.498910i	0.685297	+	0.728263i	$0.259672\pi$
$684$	10.3262	+	17.8856i	0.394834	+	0.683872i
$685$	51.4164			1.96452
$686$		0			0
$687$	−41.3050			−1.57588
$688$	0.763932	+	1.32317i	0.0291246	+	0.0504453i
$689$	0.291796	−	0.505406i	0.0111165	−	0.0192544i
$690$	20.9443	−	36.2765i	0.797335	−	1.38102i
$691$	9.32624	+	16.1535i	0.354787	+	0.614509i	0.987081	−	0.160219i	$-0.0512201\pi$
$691$	9.32624	+	16.1535i	0.354787	+	0.614509i	−0.632295	+	0.774728i	$0.717887\pi$
$692$	1.23607			0.0469883
$693$		0			0
$694$	−6.47214			−0.245679
$695$	13.4164	+	23.2379i	0.508913	+	0.881464i
$696$	−7.23607	+	12.5332i	−0.274282	+	0.475071i
$697$	20.9443	−	36.2765i	0.793321	−	1.37407i
$698$	−4.14590	−	7.18091i	−0.156925	−	0.271801i
$699$	−9.52786			−0.360377
$700$		0			0
$701$	46.7214			1.76464			0.882321	−	0.470649i	$-0.155980\pi$
$701$	46.7214			1.76464			0.882321	+	0.470649i	$0.155980\pi$
$702$	8.94427	+	15.4919i	0.337580	+	0.584705i
$703$	−15.1246	+	26.1966i	−0.570436	+	0.988023i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−10.4721	−	18.1383i	−0.394403	−	0.683127i
$706$	−34.9443			−1.31515
$707$		0			0
$708$	−23.4164			−0.880042
$709$	2.23607	+	3.87298i	0.0839773	+	0.145453i	0.904955	−	0.425507i	$-0.139904\pi$
$709$	2.23607	+	3.87298i	0.0839773	+	0.145453i	−0.820978	+	0.570960i	$0.806571\pi$
$710$	4.00000	−	6.92820i	0.150117	−	0.260011i
$711$		0			0
$712$	−5.00000	−	8.66025i	−0.187383	−	0.324557i
$713$	8.00000			0.299602
$714$		0			0
$715$	4.00000			0.149592
$716$	−4.47214	−	7.74597i	−0.167132	−	0.289480i
$717$	32.3607	−	56.0503i	1.20853	−	2.09324i
$718$	13.4164	−	23.2379i	0.500696	−	0.867231i
$719$	18.4164	+	31.8982i	0.686816	+	1.18960i	0.972862	+	0.231385i	$0.0743256\pi$
$719$	18.4164	+	31.8982i	0.686816	+	1.18960i	−0.286046	+	0.958216i	$0.592341\pi$
$720$	24.1803			0.901148
$721$		0			0
$722$	−11.3607			−0.422801
$723$	−18.4721	−	31.9947i	−0.686986	−	1.18989i
$724$	−2.38197	+	4.12569i	−0.0885251	+	0.153330i
$725$	12.2361	−	21.1935i	0.454436	−	0.787107i
$726$	1.61803	+	2.80252i	0.0600509	+	0.104011i
$727$	18.0000			0.667583			0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000			0.667583			0.333792	+	0.942647i	$0.391672\pi$
$728$		0			0
$729$	41.9443			1.55349
$730$	8.00000	+	13.8564i	0.296093	+	0.512849i
$731$	−4.94427	+	8.56373i	−0.182871	+	0.316741i
$732$	−8.47214	+	14.6742i	−0.313139	+	0.542373i
$733$	−4.43769	−	7.68631i	−0.163910	−	0.283900i	0.772358	−	0.635188i	$-0.219077\pi$
$733$	−4.43769	−	7.68631i	−0.163910	−	0.283900i	−0.936268	+	0.351287i	$0.885744\pi$
$734$	21.4164			0.790494
$735$		0			0
$736$	4.00000			0.147442
$737$	7.70820	+	13.3510i	0.283935	+	0.491790i
$738$	−24.1803	+	41.8816i	−0.890091	+	1.54168i
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	−0.989230	−	0.146369i	$-0.953241\pi$
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	0.621374	+	0.783514i	$0.286575\pi$
$740$	17.7082	+	30.6715i	0.650967	+	1.12751i
$741$	11.0557			0.406142
$742$		0			0
$743$	−13.8885			−0.509521			−0.254761	−	0.967004i	$-0.581997\pi$
$743$	−13.8885			−0.509521			−0.254761	+	0.967004i	$0.581997\pi$
$744$	3.23607	+	5.60503i	0.118640	+	0.205491i
$745$	−36.1803	+	62.6662i	−1.32555	+	2.29591i
$746$	3.00000	−	5.19615i	0.109838	−	0.190245i
$747$	−38.0344	−	65.8776i	−1.39161	−	2.41033i
$748$	−6.47214			−0.236645
$749$		0			0
$750$	−4.94427			−0.180539
$751$	−0.472136	−	0.817763i	−0.0172285	−	0.0298406i	0.857283	−	0.514846i	$-0.172151\pi$
$751$	−0.472136	−	0.817763i	−0.0172285	−	0.0298406i	−0.874511	+	0.485005i	$0.838818\pi$
$752$	1.00000	−	1.73205i	0.0364662	−	0.0631614i
$753$	40.0689	−	69.4013i	1.46019	−	2.52913i
$754$	2.76393	+	4.78727i	0.100656	+	0.174342i
$755$	38.8328			1.41327
$756$		0			0
$757$	39.3050			1.42856			0.714281	−	0.699859i	$-0.246754\pi$
$757$	39.3050			1.42856			0.714281	+	0.699859i	$0.246754\pi$
$758$	−2.76393	−	4.78727i	−0.100391	−	0.173882i
$759$	6.47214	−	11.2101i	0.234924	−	0.406900i
$760$	4.47214	−	7.74597i	0.162221	−	0.280976i
$761$	−7.70820	−	13.3510i	−0.279422	−	0.483973i	0.691819	−	0.722071i	$-0.256810\pi$
$761$	−7.70820	−	13.3510i	−0.279422	−	0.483973i	−0.971241	+	0.238097i	$0.923476\pi$
$762$	38.8328			1.40676
$763$		0			0
$764$	6.47214			0.234154
$765$	78.2492	+	135.532i	2.82911	+	4.90016i
$766$	−5.94427	+	10.2958i	−0.214775	+	0.372002i
$767$	−4.47214	+	7.74597i	−0.161479	+	0.279691i
$768$	1.61803	+	2.80252i	0.0583858	+	0.101127i
$769$	−16.5836			−0.598020			−0.299010	−	0.954250i	$-0.596656\pi$
$769$	−16.5836			−0.598020			−0.299010	+	0.954250i	$0.596656\pi$
$770$		0			0
$771$	35.4164			1.27549
$772$	−1.47214	−	2.54981i	−0.0529833	−	0.0917698i
$773$	−1.14590	+	1.98475i	−0.0412151	+	0.0713866i	−0.885897	−	0.463882i	$-0.846456\pi$
$773$	−1.14590	+	1.98475i	−0.0412151	+	0.0713866i	0.844682	+	0.535268i	$0.179790\pi$
$774$	5.70820	−	9.88690i	0.205177	−	0.355377i
$775$	−5.47214	−	9.47802i	−0.196565	−	0.340460i
$776$	3.52786			0.126643
$777$		0			0
$778$	6.58359			0.236033
$779$	8.94427	+	15.4919i	0.320462	+	0.555056i
$780$	6.47214	−	11.2101i	0.231740	−	0.401385i
$781$	1.23607	−	2.14093i	0.0442300	−	0.0766086i
$782$	12.9443	+	22.4201i	0.462886	+	0.801742i
$783$	64.7214			2.31295
$784$		0			0
$785$	60.3607			2.15437
$786$	14.9443	+	25.8842i	0.533045	+	0.923260i
$787$	2.90983	−	5.03997i	0.103724	−	0.179656i	−0.809492	−	0.587131i	$-0.800257\pi$
$787$	2.90983	−	5.03997i	0.103724	−	0.179656i	0.913216	+	0.407475i	$0.133591\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$	20.9443	+	36.2765i	0.745636	+	1.29148i
$790$		0			0
$791$		0			0
$792$	7.47214			0.265511
$793$	3.23607	+	5.60503i	0.114916	+	0.199041i
$794$	5.14590	−	8.91296i	0.182621	−	0.316309i
$795$	−2.47214	+	4.28187i	−0.0876776	+	0.151862i
$796$	−0.527864	−	0.914287i	−0.0187096	−	0.0324061i
$797$	7.59675			0.269091			0.134545	−	0.990907i	$-0.457043\pi$
$797$	7.59675			0.269091			0.134545	+	0.990907i	$0.457043\pi$
$798$		0			0
$799$	12.9443			0.457935
$800$	−2.73607	−	4.73901i	−0.0967346	−	0.167549i
$801$	−37.3607	+	64.7106i	−1.32007	+	2.28644i
$802$	15.1803	−	26.2931i	0.536036	−	0.928442i
$803$	2.47214	+	4.28187i	0.0872398	+	0.151104i
$804$	49.8885			1.75943
$805$		0			0
$806$	2.47214			0.0870773
$807$	−44.0689	−	76.3295i	−1.55130	−	2.68693i
$808$	7.09017	−	12.2805i	0.249431	−	0.432028i
$809$	19.4721	−	33.7267i	0.684604	−	1.18577i	−0.288957	−	0.957342i	$-0.593309\pi$
$809$	19.4721	−	33.7267i	0.684604	−	1.18577i	0.973561	−	0.228427i	$-0.0733581\pi$
$810$	−39.5066	−	68.4274i	−1.38812	−	2.40429i
$811$	9.23607			0.324322			0.162161	−	0.986764i	$-0.448154\pi$
$811$	9.23607			0.324322			0.162161	+	0.986764i	$0.448154\pi$
$812$		0			0
$813$	54.8328			1.92307
$814$	5.47214	+	9.47802i	0.191798	+	0.332204i
$815$	−12.0000	+	20.7846i	−0.420342	+	0.728053i
$816$	−10.4721	+	18.1383i	−0.366598	+	0.634967i
$817$	−2.11146	−	3.65715i	−0.0738705	−	0.127947i
$818$	−23.4164			−0.818736
$819$		0			0
$820$	20.9443			0.731406
$821$	−12.7082	−	22.0113i	−0.443519	−	0.768198i	0.554428	−	0.832231i	$-0.312937\pi$
$821$	−12.7082	−	22.0113i	−0.443519	−	0.768198i	−0.997948	+	0.0640333i	$0.979604\pi$
$822$	25.7082	−	44.5279i	0.896677	−	1.55309i
$823$	−17.1246	+	29.6607i	−0.596926	+	1.03391i	0.396345	+	0.918101i	$0.370278\pi$
$823$	−17.1246	+	29.6607i	−0.596926	+	1.03391i	−0.993272	+	0.115805i	$0.963055\pi$
$824$	−1.47214	−	2.54981i	−0.0512843	−	0.0888270i
$825$	−17.7082			−0.616521
$826$		0			0
$827$	−0.944272			−0.0328356			−0.0164178	−	0.999865i	$-0.505226\pi$
$827$	−0.944272			−0.0328356			−0.0164178	+	0.999865i	$0.505226\pi$
$828$	−14.9443	−	25.8842i	−0.519349	−	0.899539i
$829$	0.854102	−	1.47935i	0.0296642	−	0.0513799i	−0.850812	−	0.525470i	$-0.823890\pi$
$829$	0.854102	−	1.47935i	0.0296642	−	0.0513799i	0.880476	+	0.474090i	$0.157223\pi$
$830$	−16.4721	+	28.5306i	−0.571756	+	0.990311i
$831$	20.1803	+	34.9534i	0.700048	+	1.21252i
$832$	1.23607			0.0428529
$833$		0			0
$834$	26.8328			0.929144
$835$	24.9443	+	43.2047i	0.863232	+	1.49516i
$836$	1.38197	−	2.39364i	0.0477963	−	0.0827856i
$837$	14.4721	−	25.0665i	0.500230	−	0.866424i
$838$	−6.38197	−	11.0539i	−0.220461	−	0.381850i
$839$	−36.8328			−1.27161			−0.635805	−	0.771850i	$-0.719332\pi$
$839$	−36.8328			−1.27161			−0.635805	+	0.771850i	$0.719332\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$	−3.76393	−	6.51932i	−0.129714	−	0.224671i
$843$	−40.1803	+	69.5944i	−1.38388	+	2.39696i
$844$	11.2361	−	19.4614i	0.386761	−	0.669890i
$845$	18.5623	+	32.1509i	0.638563	+	1.10602i
$846$	−14.9443			−0.513795
$847$		0			0
$848$	−0.472136			−0.0162132
$849$	−26.9443	−	46.6688i	−0.924725	−	1.60167i
$850$	17.7082	−	30.6715i	0.607386	−	1.05202i
$851$	21.8885	−	37.9121i	0.750330	−	1.29961i
$852$	−4.00000	−	6.92820i	−0.137038	−	0.237356i
$853$	−34.5410			−1.18266			−0.591331	−	0.806429i	$-0.701397\pi$
$853$	−34.5410			−1.18266			−0.591331	+	0.806429i	$0.701397\pi$
$854$		0			0
$855$	−66.8328			−2.28563
$856$	3.23607	+	5.60503i	0.110607	+	0.191576i
$857$	18.7639	−	32.5001i	0.640964	−	1.11018i	−0.344254	−	0.938876i	$-0.611868\pi$
$857$	18.7639	−	32.5001i	0.640964	−	1.11018i	0.985218	−	0.171305i	$-0.0547984\pi$
$858$	2.00000	−	3.46410i	0.0682789	−	0.118262i
$859$	12.5623	+	21.7586i	0.428620	+	0.742392i	0.996751	−	0.0805462i	$-0.0256665\pi$
$859$	12.5623	+	21.7586i	0.428620	+	0.742392i	−0.568131	+	0.822938i	$0.692333\pi$
$860$	−4.94427			−0.168598
$861$		0			0
$862$	40.9443			1.39457
$863$	−13.7082	−	23.7433i	−0.466633	−	0.808232i	0.532641	−	0.846341i	$-0.321200\pi$
$863$	−13.7082	−	23.7433i	−0.466633	−	0.808232i	−0.999274	+	0.0381098i	$0.987866\pi$
$864$	7.23607	−	12.5332i	0.246176	−	0.426389i
$865$	−2.00000	+	3.46410i	−0.0680020	+	0.117783i
$866$	−9.76393	−	16.9116i	−0.331792	−	0.574680i
$867$	−80.5410			−2.73532
$868$		0			0
$869$		0			0
$870$	−23.4164	−	40.5584i	−0.793891	−	1.37506i
$871$	9.52786	−	16.5027i	0.322839	−	0.559174i
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$	−13.1803	−	22.8290i	−0.446087	−	0.772645i
$874$	−11.0557			−0.373966
$875$		0			0
$876$	16.0000			0.540590
$877$	−13.4721	−	23.3344i	−0.454922	−	0.787948i	0.543762	−	0.839239i	$-0.316999\pi$
$877$	−13.4721	−	23.3344i	−0.454922	−	0.787948i	−0.998684	+	0.0512920i	$0.983666\pi$
$878$	4.47214	−	7.74597i	0.150927	−	0.261414i
$879$	7.52786	−	13.0386i	0.253909	−	0.439783i
$880$	−1.61803	−	2.80252i	−0.0545439	−	0.0944728i
$881$	−24.8328			−0.836639			−0.418319	−	0.908300i	$-0.637381\pi$
$881$	−24.8328			−0.836639			−0.418319	+	0.908300i	$0.637381\pi$
$882$		0			0
$883$	50.8328			1.71066			0.855330	−	0.518083i	$-0.173354\pi$
$883$	50.8328			1.71066			0.855330	+	0.518083i	$0.173354\pi$
$884$	4.00000	+	6.92820i	0.134535	+	0.233021i
$885$	37.8885	−	65.6249i	1.27361	−	2.20596i
$886$	3.52786	−	6.11044i	0.118521	−	0.205284i
$887$	−0.180340	−	0.312358i	−0.00605522	−	0.0104880i	0.862982	−	0.505235i	$-0.168594\pi$
$887$	−0.180340	−	0.312358i	−0.00605522	−	0.0104880i	−0.869037	+	0.494747i	$0.835261\pi$
$888$	35.4164			1.18850
$889$		0			0
$890$	32.3607			1.08473
$891$	−12.2082	−	21.1452i	−0.408990	−	0.708392i
$892$	−4.23607	+	7.33708i	−0.141834	+	0.245664i
$893$	−2.76393	+	4.78727i	−0.0924915	+	0.160200i
$894$	36.1803	+	62.6662i	1.21005	+	2.09587i
$895$	28.9443			0.967500
$896$		0			0
$897$	−16.0000			−0.534224
$898$	−0.527864	−	0.914287i	−0.0176151	−	0.0305102i
$899$	4.47214	−	7.74597i	0.149154	−	0.258342i
$900$	−20.4443	+	35.4105i	−0.681476	+	1.18035i
$901$	−1.52786	−	2.64634i	−0.0509005	−	0.0881623i
$902$	6.47214			0.215499
$903$		0			0
$904$	8.47214			0.281779
$905$	−7.70820	−	13.3510i	−0.256229	−	0.443802i
$906$	19.4164	−	33.6302i	0.645067	−	1.11729i
$907$	−10.1803	+	17.6329i	−0.338033	+	0.585490i	−0.984063	−	0.177822i	$-0.943095\pi$
$907$	−10.1803	+	17.6329i	−0.338033	+	0.585490i	0.646030	+	0.763312i	$0.276428\pi$
$908$	7.38197	+	12.7859i	0.244979	+	0.424316i
$909$	−105.957			−3.51439
$910$		0			0
$911$	−28.0000			−0.927681			−0.463841	−	0.885919i	$-0.653529\pi$
$911$	−28.0000			−0.927681			−0.463841	+	0.885919i	$0.653529\pi$
$912$	−4.47214	−	7.74597i	−0.148087	−	0.256495i
$913$	−5.09017	+	8.81643i	−0.168460	+	0.291781i
$914$	−4.52786	+	7.84249i	−0.149768	+	0.259407i
$915$	−27.4164	−	47.4866i	−0.906358	−	1.56986i
$916$	12.7639			0.421732
$917$		0			0
$918$	93.6656			3.09143
$919$	28.9443	+	50.1329i	0.954783	+	1.65373i	0.734863	+	0.678216i	$0.237246\pi$
$919$	28.9443	+	50.1329i	0.954783	+	1.65373i	0.219920	+	0.975518i	$0.429420\pi$
$920$	−6.47214	+	11.2101i	−0.213380	+	0.369585i
$921$	51.8885	−	89.8736i	1.70979	−	2.96144i
$922$	−14.6180	−	25.3192i	−0.481419	−	0.833843i
$923$	−3.05573			−0.100581
$924$		0			0
$925$	−59.8885			−1.96912
$926$	10.7639	+	18.6437i	0.353725	+	0.612669i
$927$	−11.0000	+	19.0526i	−0.361287	+	0.625768i
$928$	2.23607	−	3.87298i	0.0734025	−	0.127137i
$929$	20.1246	+	34.8569i	0.660267	+	1.14362i	0.980545	+	0.196293i	$0.0628903\pi$
$929$	20.1246	+	34.8569i	0.660267	+	1.14362i	−0.320278	+	0.947324i	$0.603776\pi$
$930$	−20.9443			−0.686790
$931$		0			0
$932$	2.94427			0.0964428
$933$	8.76393	+	15.1796i	0.286918	+	0.496957i
$934$	−6.56231	+	11.3662i	−0.214725	+	0.371915i
$935$	10.4721	−	18.1383i	0.342475	−	0.593185i
$936$	−4.61803	−	7.99867i	−0.150945	−	0.261445i
$937$	−20.9443			−0.684220			−0.342110	−	0.939660i	$-0.611141\pi$
$937$	−20.9443			−0.684220			−0.342110	+	0.939660i	$0.611141\pi$
$938$		0			0
$939$	−92.1378			−3.00680
$940$	3.23607	+	5.60503i	0.105549	+	0.182816i
$941$	17.0902	−	29.6010i	0.557124	−	0.964966i	−0.440611	−	0.897698i	$-0.645238\pi$
$941$	17.0902	−	29.6010i	0.557124	−	0.964966i	0.997735	−	0.0672684i	$-0.0214284\pi$
$942$	30.1803	−	52.2739i	0.983329	−	1.70318i
$943$	−12.9443	−	22.4201i	−0.421523	−	0.730100i
$944$	7.23607			0.235514
$945$		0			0
$946$	−1.52786			−0.0496751
$947$	0.472136	+	0.817763i	0.0153424	+	0.0265737i	0.873595	−	0.486654i	$-0.161783\pi$
$947$	0.472136	+	0.817763i	0.0153424	+	0.0265737i	−0.858252	+	0.513228i	$0.828450\pi$
$948$		0			0
$949$	3.05573	−	5.29268i	0.0991931	−	0.171808i
$950$	7.56231	+	13.0983i	0.245354	+	0.424965i
$951$	42.2492			1.37002
$952$		0			0
$953$	5.05573			0.163771			0.0818855	−	0.996642i	$-0.473906\pi$
$953$	5.05573			0.163771			0.0818855	+	0.996642i	$0.473906\pi$
$954$	1.76393	+	3.05522i	0.0571094	+	0.0989164i
$955$	−10.4721	+	18.1383i	−0.338870	+	0.586941i
$956$	−10.0000	+	17.3205i	−0.323423	+	0.560185i
$957$	−7.23607	−	12.5332i	−0.233909	−	0.405142i
$958$	−32.3607			−1.04553
$959$		0			0
$960$	−10.4721			−0.337987
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	6.76393	−	11.7155i	0.218078	−	0.377722i
$963$	24.1803	−	41.8816i	0.779201	−	1.34961i
$964$	5.70820	+	9.88690i	0.183849	+	0.318436i
$965$	9.52786			0.306713
$966$		0			0
$967$	10.1115			0.325163			0.162581	−	0.986695i	$-0.448018\pi$
$967$	10.1115			0.325163			0.162581	+	0.986695i	$0.448018\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	28.9443	−	50.1329i	0.929824	−	1.61050i
$970$	−5.70820	+	9.88690i	−0.183279	+	0.317449i
$971$	8.27051	+	14.3249i	0.265413	+	0.459709i	0.967672	−	0.252213i	$-0.0811583\pi$
$971$	8.27051	+	14.3249i	0.265413	+	0.459709i	−0.702259	+	0.711922i	$0.747825\pi$
$972$	−35.5967			−1.14177
$973$		0			0
$974$	−0.944272			−0.0302564
$975$	10.9443	+	18.9560i	0.350497	+	0.607079i
$976$	2.61803	−	4.53457i	0.0838012	−	0.145148i
$977$	−12.4164	+	21.5058i	−0.397236	+	0.688033i	−0.993384	−	0.114842i	$-0.963364\pi$
$977$	−12.4164	+	21.5058i	−0.397236	+	0.688033i	0.596148	+	0.802875i	$0.296697\pi$
$978$	12.0000	+	20.7846i	0.383718	+	0.664619i
$979$	10.0000			0.319601
$980$		0			0
$981$	−74.7214			−2.38567
$982$	−0.472136	−	0.817763i	−0.0150665	−	0.0260959i
$983$	−7.00000	+	12.1244i	−0.223265	+	0.386707i	−0.955798	−	0.294025i	$-0.905005\pi$
$983$	−7.00000	+	12.1244i	−0.223265	+	0.386707i	0.732532	+	0.680732i	$0.238338\pi$
$984$	10.4721	−	18.1383i	0.333840	−	0.578227i
$985$	−29.1246	−	50.4453i	−0.927987	−	1.60732i
$986$	28.9443			0.921773
$987$		0			0
$988$	−3.41641			−0.108690
$989$	3.05573	+	5.29268i	0.0971665	+	0.168297i
$990$	−12.0902	+	20.9408i	−0.384251	+	0.665542i
$991$	−22.1803	+	38.4175i	−0.704582	+	1.22037i	0.262261	+	0.964997i	$0.415532\pi$
$991$	−22.1803	+	38.4175i	−0.704582	+	1.22037i	−0.966842	+	0.255374i	$0.917801\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$	−3.05573			−0.0969706
$994$		0			0
$995$	3.41641			0.108307
$996$	16.4721	+	28.5306i	0.521940	+	0.904026i
$997$	−0.909830	+	1.57587i	−0.0288146	+	0.0499084i	−0.880073	−	0.474838i	$-0.842507\pi$
$997$	−0.909830	+	1.57587i	−0.0288146	+	0.0499084i	0.851259	+	0.524747i	$0.175840\pi$
$998$	−6.18034	+	10.7047i	−0.195635	+	0.338850i
$999$	−79.1935	−	137.167i	−2.50557	−	4.33978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.q.67.2		4
7.2	even	3	inner	1078.2.e.q.177.2		4
7.3	odd	6		1078.2.a.w.1.2		2
7.4	even	3		154.2.a.d.1.1	✓	2
7.5	odd	6		1078.2.e.n.177.1		4
7.6	odd	2		1078.2.e.n.67.1		4
21.11	odd	6		1386.2.a.m.1.1		2
21.17	even	6		9702.2.a.cu.1.2		2
28.3	even	6		8624.2.a.bf.1.1		2
28.11	odd	6		1232.2.a.p.1.2		2
35.4	even	6		3850.2.a.bj.1.2		2
35.18	odd	12		3850.2.c.q.1849.1		4
35.32	odd	12		3850.2.c.q.1849.4		4
56.11	odd	6		4928.2.a.bk.1.1		2
56.53	even	6		4928.2.a.bt.1.2		2
77.32	odd	6		1694.2.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.a.d.1.1	✓	2	7.4	even	3
1078.2.a.w.1.2		2	7.3	odd	6
1078.2.e.n.67.1		4	7.6	odd	2
1078.2.e.n.177.1		4	7.5	odd	6
1078.2.e.q.67.2		4	1.1	even	1	trivial
1078.2.e.q.177.2		4	7.2	even	3	inner
1232.2.a.p.1.2		2	28.11	odd	6
1386.2.a.m.1.1		2	21.11	odd	6
1694.2.a.l.1.1		2	77.32	odd	6
3850.2.a.bj.1.2		2	35.4	even	6
3850.2.c.q.1849.1		4	35.18	odd	12
3850.2.c.q.1849.4		4	35.32	odd	12
4928.2.a.bk.1.1		2	56.11	odd	6
4928.2.a.bt.1.2		2	56.53	even	6
8624.2.a.bf.1.1		2	28.3	even	6
9702.2.a.cu.1.2		2	21.17	even	6

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.61803 - 2.80252i) q^{5} -3.23607 q^{6} +1.00000 q^{8} +(-3.73607 - 6.47106i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.61803 - 2.80252i) q^{5} -3.23607 q^{6} +1.00000 q^{8} +(-3.73607 - 6.47106i) q^{9} +(-1.61803 + 2.80252i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.61803 + 2.80252i) q^{12} +1.23607 q^{13} -10.4721 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.23607 - 5.60503i) q^{17} +(-3.73607 + 6.47106i) q^{18} +(1.38197 + 2.39364i) q^{19} +3.23607 q^{20} +1.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(1.61803 - 2.80252i) q^{24} +(-2.73607 + 4.73901i) q^{25} +(-0.618034 - 1.07047i) q^{26} -14.4721 q^{27} -4.47214 q^{29} +(5.23607 + 9.06914i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.61803 + 2.80252i) q^{33} -6.47214 q^{34} +7.47214 q^{36} +(5.47214 + 9.47802i) q^{37} +(1.38197 - 2.39364i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-1.61803 - 2.80252i) q^{40} +6.47214 q^{41} -1.52786 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-12.0902 + 20.9408i) q^{45} +(-2.00000 + 3.46410i) q^{46} +(1.00000 + 1.73205i) q^{47} -3.23607 q^{48} +5.47214 q^{50} +(-10.4721 - 18.1383i) q^{51} +(-0.618034 + 1.07047i) q^{52} +(0.236068 - 0.408882i) q^{53} +(7.23607 + 12.5332i) q^{54} +3.23607 q^{55} +8.94427 q^{57} +(2.23607 + 3.87298i) q^{58} +(-3.61803 + 6.26662i) q^{59} +(5.23607 - 9.06914i) q^{60} +(2.61803 + 4.53457i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(1.61803 - 2.80252i) q^{66} +(7.70820 - 13.3510i) q^{67} +(3.23607 + 5.60503i) q^{68} -12.9443 q^{69} -2.47214 q^{71} +(-3.73607 - 6.47106i) q^{72} +(2.47214 - 4.28187i) q^{73} +(5.47214 - 9.47802i) q^{74} +(8.85410 + 15.3358i) q^{75} -2.76393 q^{76} -4.00000 q^{78} +(-1.61803 + 2.80252i) q^{80} +(-12.2082 + 21.1452i) q^{81} +(-3.23607 - 5.60503i) q^{82} +10.1803 q^{83} -20.9443 q^{85} +(0.763932 + 1.32317i) q^{86} +(-7.23607 + 12.5332i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-5.00000 - 8.66025i) q^{89} +24.1803 q^{90} +4.00000 q^{92} +(3.23607 + 5.60503i) q^{93} +(1.00000 - 1.73205i) q^{94} +(4.47214 - 7.74597i) q^{95} +(1.61803 + 2.80252i) q^{96} +3.52786 q^{97} +7.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 24 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{18} + 10 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 40 q^{27} + 12 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} - 8 q^{34} + 12 q^{36} + 4 q^{37} + 10 q^{38} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 24 q^{43} - 2 q^{44} - 26 q^{45} - 8 q^{46} + 4 q^{47} - 4 q^{48} + 4 q^{50} - 24 q^{51} + 2 q^{52} - 8 q^{53} + 20 q^{54} + 4 q^{55} - 10 q^{59} + 12 q^{60} + 6 q^{61} + 8 q^{62} + 4 q^{64} - 8 q^{65} + 2 q^{66} + 4 q^{67} + 4 q^{68} - 16 q^{69} + 8 q^{71} - 6 q^{72} - 8 q^{73} + 4 q^{74} + 22 q^{75} - 20 q^{76} - 16 q^{78} - 2 q^{80} - 22 q^{81} - 4 q^{82} - 4 q^{83} - 48 q^{85} + 12 q^{86} - 20 q^{87} - 2 q^{88} - 20 q^{89} + 52 q^{90} + 16 q^{92} + 4 q^{93} + 4 q^{94} + 2 q^{96} + 32 q^{97} + 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 6 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - 24 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^18 + 10 * q^19 + 4 * q^20 + 4 * q^22 - 8 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 40 * q^27 + 12 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^33 - 8 * q^34 + 12 * q^36 + 4 * q^37 + 10 * q^38 + 8 * q^39 - 2 * q^40 + 8 * q^41 - 24 * q^43 - 2 * q^44 - 26 * q^45 - 8 * q^46 + 4 * q^47 - 4 * q^48 + 4 * q^50 - 24 * q^51 + 2 * q^52 - 8 * q^53 + 20 * q^54 + 4 * q^55 - 10 * q^59 + 12 * q^60 + 6 * q^61 + 8 * q^62 + 4 * q^64 - 8 * q^65 + 2 * q^66 + 4 * q^67 + 4 * q^68 - 16 * q^69 + 8 * q^71 - 6 * q^72 - 8 * q^73 + 4 * q^74 + 22 * q^75 - 20 * q^76 - 16 * q^78 - 2 * q^80 - 22 * q^81 - 4 * q^82 - 4 * q^83 - 48 * q^85 + 12 * q^86 - 20 * q^87 - 2 * q^88 - 20 * q^89 + 52 * q^90 + 16 * q^92 + 4 * q^93 + 4 * q^94 + 2 * q^96 + 32 * q^97 + 12 * q^99

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