LMFDB - Embedded newform 1078.2.e.n.177.1

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			177.1
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.n.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 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} + 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}+ \cdots + 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

Character values

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

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

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	−0.776103	−	0.630606i	$-0.782806\pi$
$3$	−1.61803	−	2.80252i	−0.934172	−	1.61803i	−0.158069	−	0.987428i	$-0.550527\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.61803	−	2.80252i	0.723607	−	1.25332i	−0.235938	−	0.971768i	$-0.575816\pi$
$5$	1.61803	−	2.80252i	0.723607	−	1.25332i	0.959545	−	0.281556i	$-0.0908504\pi$
$6$	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	$-0.554833\pi$
$13$	−1.23607			−0.342824			−0.171412	+	0.985199i	$0.554833\pi$
$14$		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	−0.929082	−	0.369875i	$-0.879401\pi$
$17$	−3.23607	−	5.60503i	−0.784862	−	1.35942i	0.144220	−	0.989546i	$-0.453933\pi$
$18$	−3.73607	−	6.47106i	−0.880600	−	1.52524i
$19$	−1.38197	+	2.39364i	−0.317045	+	0.549138i	−0.979870	−	0.199636i	$-0.936024\pi$
$19$	−1.38197	+	2.39364i	−0.317045	+	0.549138i	0.662825	+	0.748774i	$0.269357\pi$
$20$	−3.23607			−0.723607
$21$		0			0
$22$	1.00000			0.213201
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	−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	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−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	0.0716249	−	0.997432i	$-0.477182\pi$
$37$	5.47214	−	9.47802i	0.899614	−	1.55818i	0.827989	−	0.560745i	$-0.189485\pi$
$38$	−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	$-0.668651\pi$
$41$	−6.47214			−1.01078			−0.505389	+	0.862892i	$0.668651\pi$
$42$		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	$-0.879930\pi$
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	0.783830	+	0.620975i	$0.213263\pi$
$48$	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	0.881783	−	0.471655i	$-0.156343\pi$
$53$	0.236068	+	0.408882i	0.0324264	+	0.0561642i	−0.849357	+	0.527819i	$0.823010\pi$
$54$	−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	$-0.0105498\pi$
$59$	3.61803	+	6.26662i	0.471028	+	0.815844i	−0.528423	+	0.848981i	$0.677216\pi$
$60$	5.23607	+	9.06914i	0.675973	+	1.17082i
$61$	−2.61803	+	4.53457i	−0.335205	+	0.580592i	−0.983524	−	0.180777i	$-0.942139\pi$
$61$	−2.61803	+	4.53457i	−0.335205	+	0.580592i	0.648319	+	0.761369i	$0.275472\pi$
$62$	−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	0.762214	+	0.647325i	$0.224112\pi$
$67$	7.70820	+	13.3510i	0.941707	+	1.63108i	0.179493	+	0.983759i	$0.442554\pi$
$68$	−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	$-0.260103\pi$
$73$	−2.47214	−	4.28187i	−0.289342	−	0.501154i	−0.973653	+	0.228036i	$0.926770\pi$
$74$	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	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	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	$-0.688707\pi$
$83$	−10.1803			−1.11744			−0.558719	+	0.829357i	$0.688707\pi$
$84$		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	−0.469389	−	0.882992i	$-0.655526\pi$
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	0.999388	−	0.0349934i	$-0.0111410\pi$
$90$	−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	$-0.557319\pi$
$97$	−3.52786			−0.358200			−0.179100	+	0.983831i	$0.557319\pi$
$98$		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	−0.966511	−	0.256624i	$-0.917390\pi$
$101$	−7.09017	−	12.2805i	−0.705498	−	1.22196i	0.261013	−	0.965335i	$-0.415943\pi$
$102$	−10.4721	−	18.1383i	−1.03690	−	1.79596i
$103$	1.47214	−	2.54981i	0.145054	−	0.251241i	−0.784339	−	0.620332i	$-0.786998\pi$
$103$	1.47214	−	2.54981i	0.145054	−	0.251241i	0.929393	+	0.369092i	$0.120331\pi$
$104$	−1.23607			−0.121206
$105$		0			0
$106$	−0.472136			−0.0458579
$107$	3.23607	−	5.60503i	0.312842	−	0.541859i	−0.666134	−	0.745832i	$-0.732052\pi$
$107$	3.23607	−	5.60503i	0.312842	−	0.541859i	0.978977	+	0.203973i	$0.0653855\pi$
$108$	−7.23607	−	12.5332i	−0.696291	−	1.20601i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	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	$-0.701134\pi$
$131$	4.61803	−	7.99867i	0.403480	−	0.698847i	0.994143	+	0.108071i	$0.0344673\pi$
$132$	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	−0.975365	−	0.220597i	$-0.929200\pi$
$137$	−7.94427	−	13.7599i	−0.678725	−	1.17559i	0.296640	−	0.954989i	$-0.404134\pi$
$138$	−6.47214	+	11.2101i	−0.550945	+	0.954264i
$139$	8.29180			0.703301			0.351650	−	0.936131i	$-0.385621\pi$
$139$	8.29180			0.703301			0.351650	+	0.936131i	$0.385621\pi$
$140$		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	−0.110394	+	0.993888i	$0.535211\pi$
$149$	−11.1803	+	19.3649i	−0.915929	+	1.58644i	−0.805535	+	0.592548i	$0.798122\pi$
$150$	−8.85410	−	15.3358i	−0.722934	−	1.25216i
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	0.511636	−	0.859202i	$-0.329040\pi$
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	−0.999909	+	0.0134886i	$0.995706\pi$
$152$	−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	0.950514	+	0.310681i	$0.100557\pi$
$157$	9.32624	+	16.1535i	0.744315	+	1.28919i	−0.206199	+	0.978510i	$0.566110\pi$
$158$		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	−0.973916	−	0.226909i	$-0.927138\pi$
$163$	−3.70820	+	6.42280i	−0.290449	+	0.503072i	0.683467	+	0.729981i	$0.260471\pi$
$164$	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	$-0.296566\pi$
$167$	15.4164			1.19296			0.596479	+	0.802629i	$0.296566\pi$
$168$		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	$-0.818371\pi$
$173$	0.618034	−	1.07047i	0.0469883	−	0.0813860i	0.888563	+	0.458755i	$0.151704\pi$
$174$	−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	0.649080	−	0.760720i	$-0.275154\pi$
$179$	−4.47214	−	7.74597i	−0.334263	−	0.578961i	−0.983343	+	0.181760i	$0.941821\pi$
$180$	12.0902	−	20.9408i	0.901148	−	1.56083i
$181$	−4.76393			−0.354100			−0.177050	−	0.984202i	$-0.556655\pi$
$181$	−4.76393			−0.354100			−0.177050	+	0.984202i	$0.556655\pi$
$182$		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	−0.959026	−	0.283317i	$-0.908565\pi$
$191$	−3.23607	+	5.60503i	−0.234154	+	0.405566i	0.724873	+	0.688883i	$0.241899\pi$
$192$	−1.61803	−	2.80252i	−0.116772	−	0.202254i
$193$	−1.47214	−	2.54981i	−0.105967	−	0.183540i	0.808166	−	0.588955i	$-0.200460\pi$
$193$	−1.47214	−	2.54981i	−0.105967	−	0.183540i	−0.914133	+	0.405415i	$0.867127\pi$
$194$	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	$-0.154753\pi$
$199$	0.527864	+	0.914287i	0.0374193	+	0.0648121i	−0.846709	+	0.532056i	$0.821420\pi$
$200$	−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	$-0.591551\pi$
$223$	−8.47214			−0.567336			−0.283668	+	0.958923i	$0.591551\pi$
$224$		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	$-0.329655\pi$
$227$	−7.38197	−	12.7859i	−0.489958	−	0.848633i	−0.999933	+	0.0115566i	$0.996321\pi$
$228$	−4.47214	−	7.74597i	−0.296174	−	0.512989i
$229$	6.38197	−	11.0539i	0.421732	−	0.730462i	−0.574377	−	0.818591i	$-0.694756\pi$
$229$	6.38197	−	11.0539i	0.421732	−	0.730462i	0.996109	+	0.0881294i	$0.0280889\pi$
$230$	−12.9443			−0.853520
$231$		0			0
$232$	−4.47214			−0.293610
$233$	−1.47214	+	2.54981i	−0.0964428	+	0.167044i	−0.910210	−	0.414147i	$-0.864080\pi$
$233$	−1.47214	+	2.54981i	−0.0964428	+	0.167044i	0.813767	+	0.581191i	$0.197413\pi$
$234$	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	$-0.286521\pi$
$241$	−5.70820	−	9.88690i	−0.367698	−	0.636871i	−0.989205	+	0.146537i	$0.953187\pi$
$242$	−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	$-0.785567\pi$
$251$	−24.7639			−1.56309			−0.781543	+	0.623852i	$0.785567\pi$
$252$		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	$-0.944215\pi$
$257$	−5.47214	+	9.47802i	−0.341342	+	0.591222i	0.643340	+	0.765581i	$0.277548\pi$
$258$	−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	0.594525	−	0.804077i	$-0.297340\pi$
$263$	−6.47214	−	11.2101i	−0.399089	−	0.691242i	−0.993614	+	0.112835i	$0.964007\pi$
$264$	−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	−0.897796	−	0.440413i	$-0.854832\pi$
$269$	−13.6180	−	23.5871i	−0.830306	−	1.43813i	0.0674893	−	0.997720i	$-0.478501\pi$
$270$	23.4164	+	40.5584i	1.42508	+	2.46831i
$271$	−8.47214	+	14.6742i	−0.514646	+	0.891392i	0.485210	+	0.874398i	$0.338743\pi$
$271$	−8.47214	+	14.6742i	−0.514646	+	0.891392i	−0.999856	+	0.0169947i	$0.994590\pi$
$272$	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	0.615591	−	0.788065i	$-0.288917\pi$
$277$	−6.23607	−	10.8012i	−0.374689	−	0.648980i	−0.990280	+	0.139085i	$0.955584\pi$
$278$	−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	$-0.331478\pi$
$283$	−8.32624	−	14.4215i	−0.494943	−	0.857267i	−0.999983	+	0.00582897i	$0.998145\pi$
$284$	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	$-0.543393\pi$
$293$	−4.65248			−0.271801			−0.135900	+	0.990723i	$0.543393\pi$
$294$		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	$-0.867915\pi$
$307$	−32.0689			−1.83027			−0.915134	+	0.403150i	$0.867915\pi$
$308$		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	$-0.117590\pi$
$311$	2.70820	+	4.69075i	0.153568	+	0.265988i	−0.778969	+	0.627063i	$0.784257\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	14.2361	−	24.6576i	0.804670	−	1.39373i	−0.111843	−	0.993726i	$-0.535675\pi$
$313$	14.2361	−	24.6576i	0.804670	−	1.39373i	0.916514	−	0.400004i	$-0.130991\pi$
$314$	−18.6525			−1.05262
$315$		0			0
$316$		0			0
$317$	6.52786	−	11.3066i	0.366641	−	0.635041i	−0.622397	−	0.782702i	$-0.713841\pi$
$317$	6.52786	−	11.3066i	0.366641	−	0.635041i	0.989038	+	0.147660i	$0.0471743\pi$
$318$	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	−0.878709	−	0.477357i	$-0.841595\pi$
$331$	−0.472136	+	0.817763i	−0.0259509	+	0.0449483i	0.852758	+	0.522306i	$0.174928\pi$
$332$	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	0.939718	−	0.341950i	$-0.111087\pi$
$347$	3.23607	+	5.60503i	0.173721	+	0.300894i	−0.765997	+	0.642844i	$0.777754\pi$
$348$	7.23607	−	12.5332i	0.387894	−	0.671852i
$349$	−8.29180			−0.443850			−0.221925	−	0.975064i	$-0.571234\pi$
$349$	−8.29180			−0.443850			−0.221925	+	0.975064i	$0.571234\pi$
$350$		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	−0.783404	−	0.621513i	$-0.786518\pi$
$353$	−17.4721	−	30.2626i	−0.929948	−	1.61072i	−0.146544	−	0.989204i	$-0.546815\pi$
$354$	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	−0.257473	−	0.966285i	$-0.582890\pi$
$359$	13.4164	−	23.2379i	0.708091	−	1.22645i	0.965564	−	0.260164i	$-0.0837767\pi$
$360$	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	0.997583	+	0.0694807i	$0.0221342\pi$
$367$	10.7082	+	18.5472i	0.558964	+	0.968154i	−0.438620	+	0.898673i	$0.644532\pi$
$368$	−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	−0.777847	−	0.628454i	$-0.783688\pi$
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	0.933181	+	0.359408i	$0.117021\pi$
$374$	−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	$-0.735099\pi$
$383$	5.94427	−	10.2958i	0.303738	−	0.526090i	0.976980	+	0.213333i	$0.0684319\pi$
$384$	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	0.770428	−	0.637527i	$-0.220043\pi$
$389$	−3.29180	−	5.70156i	−0.166901	−	0.289080i	−0.937329	+	0.348447i	$0.886709\pi$
$390$	−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	$-0.916484\pi$
$397$	−5.14590	+	8.91296i	−0.258265	+	0.447328i	0.707512	+	0.706701i	$0.249818\pi$
$398$	−1.05573			−0.0529189
$399$		0			0
$400$	5.47214			0.273607
$401$	15.1803	−	26.2931i	0.758070	−	1.31302i	−0.185764	−	0.982594i	$-0.559476\pi$
$401$	15.1803	−	26.2931i	0.758070	−	1.31302i	0.943834	−	0.330421i	$-0.107191\pi$
$402$	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	−0.995602	−	0.0936836i	$-0.970136\pi$
$409$	−11.7082	−	20.2792i	−0.578933	−	1.00274i	0.416669	−	0.909058i	$-0.363198\pi$
$410$	−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	$-0.600925\pi$
$419$	−12.7639			−0.623559			−0.311779	+	0.950155i	$0.600925\pi$
$420$		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	−0.636905	−	0.770942i	$-0.719786\pi$
$431$	−20.4721	−	35.4588i	−0.986108	−	1.70799i	−0.349203	−	0.937047i	$-0.613548\pi$
$432$	−7.23607	+	12.5332i	−0.348145	+	0.603006i
$433$	−19.5279			−0.938449			−0.469225	−	0.883079i	$-0.655467\pi$
$433$	−19.5279			−0.938449			−0.469225	+	0.883079i	$0.655467\pi$
$434$		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	$-0.901801\pi$
$439$	−4.47214	+	7.74597i	−0.213443	+	0.369695i	0.739347	+	0.673325i	$0.235135\pi$
$440$	−3.23607			−0.154273
$441$		0			0
$442$	−8.00000			−0.380521
$443$	3.52786	−	6.11044i	0.167614	−	0.290316i	−0.769967	−	0.638084i	$-0.779727\pi$
$443$	3.52786	−	6.11044i	0.167614	−	0.290316i	0.937580	+	0.347768i	$0.113060\pi$
$444$	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	−0.952279	−	0.305228i	$-0.901267\pi$
$457$	−4.52786	+	7.84249i	−0.211805	+	0.366856i	0.740475	+	0.672084i	$0.234601\pi$
$458$	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	$-0.738381\pi$
$461$	−29.2361			−1.36166			−0.680830	+	0.732442i	$0.738381\pi$
$462$		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	$-0.735122\pi$
$467$	6.56231	−	11.3662i	0.303667	−	0.525967i	0.976964	+	0.213405i	$0.0684555\pi$
$468$	−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	−0.952812	−	0.303562i	$-0.901824\pi$
$479$	−16.1803	−	28.0252i	−0.739299	−	1.28050i	0.213513	−	0.976940i	$-0.431509\pi$
$480$	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	0.876524	−	0.481357i	$-0.159856\pi$
$487$	0.472136	+	0.817763i	0.0213945	+	0.0370564i	−0.855130	+	0.518414i	$0.826523\pi$
$488$	−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	−0.970555	−	0.240879i	$-0.922564\pi$
$499$	−6.18034	+	10.7047i	−0.276670	+	0.479207i	0.693885	+	0.720086i	$0.255898\pi$
$500$	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	$-0.528423\pi$
$503$	−4.00000			−0.178351			−0.0891756	+	0.996016i	$0.528423\pi$
$504$		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	0.190317	+	0.981723i	$0.439048\pi$
$509$	−17.0344	+	29.5045i	−0.755038	+	1.30776i	−0.945355	+	0.326042i	$0.894285\pi$
$510$	−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	0.946517	+	0.322653i	$0.104575\pi$
$521$	17.1803	+	29.7572i	0.752684	+	1.30369i	−0.193833	+	0.981035i	$0.562092\pi$
$522$	16.7082	+	28.9395i	0.731298	+	1.26665i
$523$	−13.8541	+	23.9960i	−0.605798	+	1.04927i	0.386127	+	0.922446i	$0.373813\pi$
$523$	−13.8541	+	23.9960i	−0.605798	+	1.04927i	−0.991925	+	0.126827i	$0.959521\pi$
$524$	−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	−0.752124	−	0.659022i	$-0.770970\pi$
$541$	4.52786	−	7.84249i	0.194668	−	0.337175i	0.946792	+	0.321847i	$0.104304\pi$
$542$	−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	0.991099	+	0.133129i	$0.0425026\pi$
$557$	14.4164	+	24.9700i	0.610843	+	1.05801i	−0.380256	+	0.924881i	$0.624164\pi$
$558$	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	0.997144	+	0.0755300i	$0.0240648\pi$
$563$	13.3820	+	23.1782i	0.563983	+	0.976847i	−0.433161	+	0.901317i	$0.642602\pi$
$564$	−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	−0.986745	−	0.162280i	$-0.948115\pi$
$569$	−8.41641	+	14.5776i	−0.352834	+	0.611127i	0.633911	+	0.773406i	$0.281449\pi$
$570$	14.4721	+	25.0665i	0.606171	+	1.04992i
$571$	22.9443	+	39.7406i	0.960188	+	1.66309i	0.722022	+	0.691870i	$0.243213\pi$
$571$	22.9443	+	39.7406i	0.960188	+	1.66309i	0.238165	+	0.971225i	$0.423454\pi$
$572$	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	$-0.106305\pi$
$577$	4.52786	+	7.84249i	0.188497	+	0.326487i	−0.756252	+	0.654280i	$0.772972\pi$
$578$	−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	$-0.302441\pi$
$587$	28.1803			1.16313			0.581564	+	0.813501i	$0.302441\pi$
$588$		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	$-0.669314\pi$
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	0.999965	+	0.00831589i	$0.00264706\pi$
$594$	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	0.711698	−	0.702486i	$-0.247927\pi$
$599$	−6.18034	−	10.7047i	−0.252522	−	0.437381i	−0.964219	+	0.265105i	$0.914593\pi$
$600$	−8.85410	+	15.3358i	−0.361467	+	0.626080i
$601$	−18.8328			−0.768207			−0.384103	−	0.923290i	$-0.625489\pi$
$601$	−18.8328			−0.768207			−0.384103	+	0.923290i	$0.625489\pi$
$602$		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	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	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	0.598658	−	0.801005i	$-0.295701\pi$
$613$	−9.76393	−	16.9116i	−0.394362	−	0.683054i	−0.993019	+	0.117951i	$0.962368\pi$
$614$	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	−0.678228	−	0.734852i	$-0.737252\pi$
$619$	−24.2705	−	42.0378i	−0.975514	−	1.68964i	−0.297286	−	0.954788i	$-0.596082\pi$
$620$	−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	−0.960887	−	0.276941i	$-0.910679\pi$
$641$	−18.2361	−	31.5858i	−0.720281	−	1.24756i	0.240606	−	0.970623i	$-0.422654\pi$
$642$	10.4721	−	18.1383i	0.413302	−	0.715860i
$643$	23.2361			0.916341			0.458171	−	0.888864i	$-0.348505\pi$
$643$	23.2361			0.916341			0.458171	+	0.888864i	$0.348505\pi$
$644$		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	$-0.00434244\pi$
$647$	12.4164	+	21.5058i	0.488139	+	0.845482i	−0.511768	+	0.859124i	$0.671009\pi$
$648$	−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	−0.881618	−	0.471964i	$-0.843545\pi$
$653$	−0.819660	+	1.41969i	−0.0320758	+	0.0555569i	0.849542	+	0.527521i	$0.176878\pi$
$654$	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	0.960201	+	0.279310i	$0.0901057\pi$
$661$	18.5623	+	32.1509i	0.721990	+	1.25052i	−0.238211	+	0.971213i	$0.576561\pi$
$662$	−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	−0.373910	−	0.927465i	$-0.621983\pi$
$677$	16.0344	−	27.7725i	0.616254	−	1.06738i	0.990163	−	0.139917i	$-0.0446837\pi$
$678$	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	0.685297	−	0.728263i	$-0.259672\pi$
$683$	−7.52786	−	13.0386i	−0.288046	−	0.498910i	−0.973343	+	0.229353i	$0.926339\pi$
$684$	−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	$-0.948780\pi$
$691$	−9.32624	+	16.1535i	−0.354787	+	0.614509i	0.632295	+	0.774728i	$0.282113\pi$
$692$	−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	−0.820978	−	0.570960i	$-0.806571\pi$
$709$	2.23607	−	3.87298i	0.0839773	−	0.145453i	0.904955	+	0.425507i	$0.139904\pi$
$710$	−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	0.286046	+	0.958216i	$0.407659\pi$
$719$	−18.4164	+	31.8982i	−0.686816	+	1.18960i	−0.972862	+	0.231385i	$0.925674\pi$
$720$	−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	$-0.608328\pi$
$727$	−18.0000			−0.667583			−0.333792	+	0.942647i	$0.608328\pi$
$728$		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	$-0.780923\pi$
$733$	4.43769	−	7.68631i	0.163910	−	0.283900i	0.936268	+	0.351287i	$0.114256\pi$
$734$	−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	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	−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	−0.874511	−	0.485005i	$-0.838818\pi$
$751$	−0.472136	+	0.817763i	−0.0172285	+	0.0298406i	0.857283	+	0.514846i	$0.172151\pi$
$752$	−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	$-0.743190\pi$
$761$	7.70820	−	13.3510i	0.279422	−	0.483973i	0.971241	+	0.238097i	$0.0765238\pi$
$762$	−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	$-0.403344\pi$
$769$	16.5836			0.598020			0.299010	+	0.954250i	$0.403344\pi$
$770$		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	$-0.153544\pi$
$773$	1.14590	+	1.98475i	0.0412151	+	0.0713866i	−0.844682	+	0.535268i	$0.820210\pi$
$774$	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	$-0.199743\pi$
$787$	−2.90983	−	5.03997i	−0.103724	−	0.179656i	−0.913216	+	0.407475i	$0.866409\pi$
$788$	−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	$-0.542957\pi$
$797$	−7.59675			−0.269091			−0.134545	+	0.990907i	$0.542957\pi$
$798$		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	0.973561	+	0.228427i	$0.0733581\pi$
$809$	19.4721	+	33.7267i	0.684604	+	1.18577i	−0.288957	+	0.957342i	$0.593309\pi$
$810$	39.5066	−	68.4274i	1.38812	−	2.40429i
$811$	−9.23607			−0.324322			−0.162161	−	0.986764i	$-0.551846\pi$
$811$	−9.23607			−0.324322			−0.162161	+	0.986764i	$0.551846\pi$
$812$		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	−0.997948	−	0.0640333i	$-0.979604\pi$
$821$	−12.7082	+	22.0113i	−0.443519	+	0.768198i	0.554428	+	0.832231i	$0.312937\pi$
$822$	−25.7082	−	44.5279i	−0.896677	−	1.55309i
$823$	−17.1246	−	29.6607i	−0.596926	−	1.03391i	−0.993272	−	0.115805i	$-0.963055\pi$
$823$	−17.1246	−	29.6607i	−0.596926	−	1.03391i	0.396345	−	0.918101i	$-0.370278\pi$
$824$	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	$-0.176110\pi$
$829$	−0.854102	−	1.47935i	−0.0296642	−	0.0513799i	−0.880476	+	0.474090i	$0.842777\pi$
$830$	−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	$-0.280668\pi$
$839$	36.8328			1.27161			0.635805	+	0.771850i	$0.280668\pi$
$840$		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	$-0.298603\pi$
$853$	34.5410			1.18266			0.591331	+	0.806429i	$0.298603\pi$
$854$		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	−0.985218	−	0.171305i	$-0.945202\pi$
$857$	−18.7639	−	32.5001i	−0.640964	−	1.11018i	0.344254	−	0.938876i	$-0.388132\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	−12.5623	+	21.7586i	−0.428620	+	0.742392i	−0.996751	−	0.0805462i	$-0.974334\pi$
$859$	−12.5623	+	21.7586i	−0.428620	+	0.742392i	0.568131	+	0.822938i	$0.307667\pi$
$860$	4.94427			0.168598
$861$		0			0
$862$	40.9443			1.39457
$863$	−13.7082	+	23.7433i	−0.466633	+	0.808232i	−0.999274	−	0.0381098i	$-0.987866\pi$
$863$	−13.7082	+	23.7433i	−0.466633	+	0.808232i	0.532641	+	0.846341i	$0.321200\pi$
$864$	−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	−0.998684	−	0.0512920i	$-0.983666\pi$
$877$	−13.4721	+	23.3344i	−0.454922	+	0.787948i	0.543762	+	0.839239i	$0.316999\pi$
$878$	−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	$-0.362619\pi$
$881$	24.8328			0.836639			0.418319	+	0.908300i	$0.362619\pi$
$882$		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	$-0.831406\pi$
$887$	0.180340	−	0.312358i	0.00605522	−	0.0104880i	0.869037	+	0.494747i	$0.164739\pi$
$888$	−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	0.646030	−	0.763312i	$-0.276428\pi$
$907$	−10.1803	−	17.6329i	−0.338033	−	0.585490i	−0.984063	+	0.177822i	$0.943095\pi$
$908$	−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	0.219920	−	0.975518i	$-0.429420\pi$
$919$	28.9443	−	50.1329i	0.954783	−	1.65373i	0.734863	−	0.678216i	$-0.237246\pi$
$920$	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	0.320278	+	0.947324i	$0.396224\pi$
$929$	−20.1246	+	34.8569i	−0.660267	+	1.14362i	−0.980545	+	0.196293i	$0.937110\pi$
$930$	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	$-0.388859\pi$
$937$	20.9443			0.684220			0.342110	+	0.939660i	$0.388859\pi$
$938$		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	−0.997735	−	0.0672684i	$-0.978572\pi$
$941$	−17.0902	−	29.6010i	−0.557124	−	0.964966i	0.440611	−	0.897698i	$-0.354762\pi$
$942$	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	−0.858252	−	0.513228i	$-0.828450\pi$
$947$	0.472136	−	0.817763i	0.0153424	−	0.0265737i	0.873595	+	0.486654i	$0.161783\pi$
$948$		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	$-0.918842\pi$
$971$	−8.27051	+	14.3249i	−0.265413	+	0.459709i	0.702259	+	0.711922i	$0.252175\pi$
$972$	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	0.596148	−	0.802875i	$-0.296697\pi$
$977$	−12.4164	−	21.5058i	−0.397236	−	0.688033i	−0.993384	+	0.114842i	$0.963364\pi$
$978$	−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	$-0.0949950\pi$
$983$	7.00000	+	12.1244i	0.223265	+	0.386707i	−0.732532	+	0.680732i	$0.761662\pi$
$984$	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	−0.966842	−	0.255374i	$-0.917801\pi$
$991$	−22.1803	−	38.4175i	−0.704582	−	1.22037i	0.262261	−	0.964997i	$-0.415532\pi$
$992$	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	$-0.157493\pi$
$997$	0.909830	+	1.57587i	0.0288146	+	0.0499084i	−0.851259	+	0.524747i	$0.824160\pi$
$998$	−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.n.177.1		4
7.2	even	3		1078.2.a.w.1.2		2
7.3	odd	6		1078.2.e.q.67.2		4
7.4	even	3	inner	1078.2.e.n.67.1		4
7.5	odd	6		154.2.a.d.1.1	✓	2
7.6	odd	2		1078.2.e.q.177.2		4
21.2	odd	6		9702.2.a.cu.1.2		2
21.5	even	6		1386.2.a.m.1.1		2
28.19	even	6		1232.2.a.p.1.2		2
28.23	odd	6		8624.2.a.bf.1.1		2
35.12	even	12		3850.2.c.q.1849.4		4
35.19	odd	6		3850.2.a.bj.1.2		2
35.33	even	12		3850.2.c.q.1849.1		4
56.5	odd	6		4928.2.a.bt.1.2		2
56.19	even	6		4928.2.a.bk.1.1		2
77.54	even	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	7.5	odd	6
1078.2.a.w.1.2		2	7.2	even	3
1078.2.e.n.67.1		4	7.4	even	3	inner
1078.2.e.n.177.1		4	1.1	even	1	trivial
1078.2.e.q.67.2		4	7.3	odd	6
1078.2.e.q.177.2		4	7.6	odd	2
1232.2.a.p.1.2		2	28.19	even	6
1386.2.a.m.1.1		2	21.5	even	6
1694.2.a.l.1.1		2	77.54	even	6
3850.2.a.bj.1.2		2	35.19	odd	6
3850.2.c.q.1849.1		4	35.33	even	12
3850.2.c.q.1849.4		4	35.12	even	12
4928.2.a.bk.1.1		2	56.19	even	6
4928.2.a.bt.1.2		2	56.5	odd	6
8624.2.a.bf.1.1		2	28.23	odd	6
9702.2.a.cu.1.2		2	21.2	odd	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 $\F_{q}$
Belyi maps

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{8} - 6 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 24 q^{15} - 2 q^{16} - 4 q^{17} - 6 q^{18} - 10 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23}+ \cdots + 12 q^{99}+O(q^{100}) \) 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

Introduction

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