LMFDB - Embedded newform 637.2.h.m.471.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(165,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-8,0,24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	16.0.468066644398978174550016.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 $ x^16 + 8x^14 + 45x^12 + 124x^10 + 248x^8 + 250x^6 + 177x^4 + 14*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.4
Root			$-0.141226 + 0.244611i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.m.165.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.52077 q^{2} +(1.06311 - 1.84135i) q^{3} +0.312752 q^{4} +(-0.294696 + 0.510428i) q^{5} +(-1.61674 + 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 - 1.31703i) q^{9} +(0.448165 - 0.776245i) q^{10} +(-0.760387 + 1.31703i) q^{11} +(0.332488 - 0.575886i) q^{12} +(3.32565 + 1.39285i) q^{13} +(0.626585 + 1.08528i) q^{15} -4.52769 q^{16} +4.79479 q^{17} +(1.15638 + 2.00290i) q^{18} +(-0.841957 - 1.45831i) q^{19} +(-0.0921666 + 0.159637i) q^{20} +(1.15638 - 2.00290i) q^{22} +1.77394 q^{23} +(2.72785 - 4.72477i) q^{24} +(2.32631 + 4.02929i) q^{25} +(-5.05756 - 2.11821i) q^{26} +3.14515 q^{27} +(-3.44625 - 5.96909i) q^{29} +(-0.952894 - 1.65046i) q^{30} +(3.04320 + 5.27098i) q^{31} +1.75375 q^{32} +(1.61674 + 2.80028i) q^{33} -7.29179 q^{34} +(-0.237812 - 0.411903i) q^{36} +1.40913 q^{37} +(1.28043 + 2.21776i) q^{38} +(6.10025 - 4.64295i) q^{39} +(-0.756166 + 1.30972i) q^{40} +(-0.677729 - 1.17386i) q^{41} +(5.77978 - 10.0109i) q^{43} +(-0.237812 + 0.411903i) q^{44} +0.896331 q^{45} -2.69777 q^{46} +(0.232416 - 0.402556i) q^{47} +(-4.81341 + 8.33707i) q^{48} +(-3.53779 - 6.12763i) q^{50} +(5.09737 - 8.82890i) q^{51} +(1.04010 + 0.435617i) q^{52} +(-4.12340 - 7.14194i) q^{53} -4.78306 q^{54} +(-0.448165 - 0.776245i) q^{55} -3.58035 q^{57} +(5.24097 + 9.07763i) q^{58} -11.8756 q^{59} +(0.195966 + 0.339422i) q^{60} +(-1.24009 - 2.14789i) q^{61} +(-4.62802 - 8.01596i) q^{62} +6.38833 q^{64} +(-1.69101 + 1.28704i) q^{65} +(-2.45870 - 4.25859i) q^{66} +(3.78642 - 6.55827i) q^{67} +1.49958 q^{68} +(1.88589 - 3.26646i) q^{69} +(-3.30235 + 5.71984i) q^{71} +(-1.95109 - 3.37939i) q^{72} +(8.18558 + 14.1778i) q^{73} -2.14296 q^{74} +9.89245 q^{75} +(-0.263323 - 0.456090i) q^{76} +(-9.27710 + 7.06087i) q^{78} +(7.48116 - 12.9577i) q^{79} +(1.33429 - 2.31106i) q^{80} +(5.62478 - 9.74241i) q^{81} +(1.03067 + 1.78518i) q^{82} +10.1222 q^{83} +(-1.41300 + 2.44740i) q^{85} +(-8.78973 + 15.2243i) q^{86} -14.6549 q^{87} +(-1.95109 + 3.37939i) q^{88} +16.4850 q^{89} -1.36312 q^{90} +0.554804 q^{92} +12.9410 q^{93} +(-0.353452 + 0.612196i) q^{94} +0.992484 q^{95} +(1.86442 - 3.22927i) q^{96} +(0.486935 - 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} + 8 q^{16} + 28 q^{18} + 28 q^{22} - 24 q^{23} + 12 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} + 16 q^{37} + 20 q^{39} + 32 q^{43} + 4 q^{44}+ \cdots + 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 24 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 + 8 * q^16 + 28 * q^18 + 28 * q^22 - 24 * q^23 + 12 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 + 16 * q^37 + 20 * q^39 + 32 * q^43 + 4 * q^44 + 8 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 - 48 * q^58 - 64 * q^60 - 64 * q^64 - 68 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 - 152 * q^74 + 28 * q^78 + 4 * q^79 + 56 * q^81 + 36 * q^85 - 4 * q^86 + 28 * q^88 - 160 * q^92 - 16 * q^93 - 104 * q^95 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.52077			−1.07535			−0.537675	−	0.843152i	$-0.680697\pi$
$2$	−1.52077			−1.07535			−0.537675	+	0.843152i	$0.680697\pi$
$3$	1.06311	−	1.84135i	0.613784	−	1.06311i	−0.376812	−	0.926290i	$-0.622980\pi$
$3$	1.06311	−	1.84135i	0.613784	−	1.06311i	0.990596	−	0.136816i	$-0.0436869\pi$
$4$	0.312752			0.156376
$5$	−0.294696	+	0.510428i	−0.131792	+	0.228270i	−0.924367	−	0.381504i	$-0.875406\pi$
$5$	−0.294696	+	0.510428i	−0.131792	+	0.228270i	0.792575	+	0.609774i	$0.208740\pi$
$6$	−1.61674	+	2.80028i	−0.660032	+	1.14321i
$7$		0			0
$7$		0			0
$8$	2.56592			0.907190
$9$	−0.760387	−	1.31703i	−0.253462	−	0.439009i
$10$	0.448165	−	0.776245i	0.141722	−	0.245470i
$11$	−0.760387	+	1.31703i	−0.229265	+	0.397099i	−0.957591	−	0.288132i	$-0.906966\pi$
$11$	−0.760387	+	1.31703i	−0.229265	+	0.397099i	0.728325	+	0.685232i	$0.240299\pi$
$12$	0.332488	−	0.575886i	0.0959811	−	0.166244i
$13$	3.32565	+	1.39285i	0.922370	+	0.386308i
$13$	3.32565	+	1.39285i	0.922370	+	0.386308i
$14$		0			0
$15$	0.626585	+	1.08528i	0.161784	+	0.280217i
$16$	−4.52769			−1.13192
$17$	4.79479			1.16291			0.581454	−	0.813579i	$-0.302484\pi$
$17$	4.79479			1.16291			0.581454	+	0.813579i	$0.302484\pi$
$18$	1.15638	+	2.00290i	0.272560	+	0.472088i
$19$	−0.841957	−	1.45831i	−0.193158	−	0.334560i	0.753137	−	0.657864i	$-0.228540\pi$
$19$	−0.841957	−	1.45831i	−0.193158	−	0.334560i	−0.946295	+	0.323304i	$0.895206\pi$
$20$	−0.0921666	+	0.159637i	−0.0206091	+	0.0356960i
$21$		0			0
$22$	1.15638	−	2.00290i	0.246540	−	0.427020i
$23$	1.77394			0.369893			0.184946	−	0.982749i	$-0.440789\pi$
$23$	1.77394			0.369893			0.184946	+	0.982749i	$0.440789\pi$
$24$	2.72785	−	4.72477i	0.556819	−	0.964439i
$25$	2.32631	+	4.02929i	0.465262	+	0.805857i
$26$	−5.05756	−	2.11821i	−0.991870	−	0.415416i
$27$	3.14515			0.605284
$28$		0			0
$29$	−3.44625	−	5.96909i	−0.639953	−	1.10843i	−0.985443	−	0.170009i	$-0.945620\pi$
$29$	−3.44625	−	5.96909i	−0.639953	−	1.10843i	0.345489	−	0.938423i	$-0.387713\pi$
$30$	−0.952894	−	1.65046i	−0.173974	−	0.301332i
$31$	3.04320	+	5.27098i	0.546575	+	0.946695i	0.998506	+	0.0546426i	$0.0174019\pi$
$31$	3.04320	+	5.27098i	0.546575	+	0.946695i	−0.451931	+	0.892053i	$0.649265\pi$
$32$	1.75375			0.310021
$33$	1.61674	+	2.80028i	0.281439	+	0.487466i
$34$	−7.29179			−1.25053
$35$		0			0
$36$	−0.237812	−	0.411903i	−0.0396354	−	0.0686505i
$37$	1.40913			0.231659			0.115830	−	0.993269i	$-0.463047\pi$
$37$	1.40913			0.231659			0.115830	+	0.993269i	$0.463047\pi$
$38$	1.28043	+	2.21776i	0.207712	+	0.359768i
$39$	6.10025	−	4.64295i	0.976822	−	0.743467i
$40$	−0.756166	+	1.30972i	−0.119560	+	0.207085i
$41$	−0.677729	−	1.17386i	−0.105843	−	0.183326i	0.808239	−	0.588855i	$-0.200421\pi$
$41$	−0.677729	−	1.17386i	−0.105843	−	0.183326i	−0.914082	+	0.405528i	$0.867088\pi$
$42$		0			0
$43$	5.77978	−	10.0109i	0.881408	−	1.52664i	0.0316319	−	0.999500i	$-0.489930\pi$
$43$	5.77978	−	10.0109i	0.881408	−	1.52664i	0.849776	−	0.527144i	$-0.176737\pi$
$44$	−0.237812	+	0.411903i	−0.0358516	+	0.0620967i
$45$	0.896331			0.133617
$46$	−2.69777			−0.397764
$47$	0.232416	−	0.402556i	0.0339013	−	0.0587188i	−0.848577	−	0.529072i	$-0.822540\pi$
$47$	0.232416	−	0.402556i	0.0339013	−	0.0587188i	0.882478	+	0.470353i	$0.155873\pi$
$48$	−4.81341	+	8.33707i	−0.694756	+	1.20335i
$49$		0			0
$50$	−3.53779	−	6.12763i	−0.500319	−	0.866578i
$51$	5.09737	−	8.82890i	0.713775	−	1.23629i
$52$	1.04010	+	0.435617i	0.144236	+	0.0604093i
$53$	−4.12340	−	7.14194i	−0.566393	−	0.981021i	−0.996919	−	0.0784430i	$-0.975005\pi$
$53$	−4.12340	−	7.14194i	−0.566393	−	0.981021i	0.430526	−	0.902578i	$-0.358328\pi$
$54$	−4.78306			−0.650892
$55$	−0.448165	−	0.776245i	−0.0604306	−	0.104669i
$56$		0			0
$57$	−3.58035			−0.474230
$58$	5.24097	+	9.07763i	0.688173	+	1.19195i
$59$	−11.8756			−1.54608			−0.773038	−	0.634359i	$-0.781264\pi$
$59$	−11.8756			−1.54608			−0.773038	+	0.634359i	$0.781264\pi$
$60$	0.195966	+	0.339422i	0.0252991	+	0.0438193i
$61$	−1.24009	−	2.14789i	−0.158777	−	0.275009i	0.775651	−	0.631162i	$-0.217422\pi$
$61$	−1.24009	−	2.14789i	−0.158777	−	0.275009i	−0.934428	+	0.356153i	$0.884088\pi$
$62$	−4.62802	−	8.01596i	−0.587759	−	1.01803i
$63$		0			0
$64$	6.38833			0.798541
$65$	−1.69101	+	1.28704i	−0.209744	+	0.159637i
$66$	−2.45870	−	4.25859i	−0.302645	−	0.524196i
$67$	3.78642	−	6.55827i	0.462585	−	0.801220i	−0.536504	−	0.843898i	$-0.680255\pi$
$67$	3.78642	−	6.55827i	0.462585	−	0.801220i	0.999089	+	0.0426774i	$0.0135888\pi$
$68$	1.49958			0.181851
$69$	1.88589	−	3.26646i	0.227034	−	0.393235i
$70$		0			0
$71$	−3.30235	+	5.71984i	−0.391917	+	0.678821i	−0.992702	−	0.120590i	$-0.961521\pi$
$71$	−3.30235	+	5.71984i	−0.391917	+	0.678821i	0.600785	+	0.799411i	$0.294855\pi$
$72$	−1.95109	−	3.37939i	−0.229939	−	0.398265i
$73$	8.18558	+	14.1778i	0.958049	+	1.65939i	0.727231	+	0.686393i	$0.240807\pi$
$73$	8.18558	+	14.1778i	0.958049	+	1.65939i	0.230819	+	0.972997i	$0.425860\pi$
$74$	−2.14296			−0.249114
$75$	9.89245			1.14228
$76$	−0.263323	−	0.456090i	−0.0302053	−	0.0523171i
$77$		0			0
$78$	−9.27710	+	7.06087i	−1.05042	+	0.799486i
$79$	7.48116	−	12.9577i	0.841696	−	1.45786i	−0.0467635	−	0.998906i	$-0.514891\pi$
$79$	7.48116	−	12.9577i	0.841696	−	1.45786i	0.888460	−	0.458955i	$-0.151776\pi$
$80$	1.33429	−	2.31106i	0.149178	−	0.258384i
$81$	5.62478	−	9.74241i	0.624976	−	1.08249i
$82$	1.03067	+	1.78518i	0.113819	+	0.197140i
$83$	10.1222			1.11105			0.555526	−	0.831499i	$-0.312517\pi$
$83$	10.1222			1.11105			0.555526	+	0.831499i	$0.312517\pi$
$84$		0			0
$85$	−1.41300	+	2.44740i	−0.153262	+	0.265457i
$86$	−8.78973	+	15.2243i	−0.947821	+	1.64167i
$87$	−14.6549			−1.57117
$88$	−1.95109	+	3.37939i	−0.207987	+	0.360244i
$89$	16.4850			1.74741			0.873703	−	0.486460i	$-0.161712\pi$
$89$	16.4850			1.74741			0.873703	+	0.486460i	$0.161712\pi$
$90$	−1.36312			−0.143685
$91$		0			0
$92$	0.554804			0.0578423
$93$	12.9410			1.34192
$94$	−0.353452	+	0.612196i	−0.0364558	+	0.0631432i
$95$	0.992484			0.101827
$96$	1.86442	−	3.22927i	0.190286	−	0.329586i
$97$	0.486935	−	0.843396i	0.0494407	−	0.0856338i	−0.840246	−	0.542205i	$-0.817589\pi$
$97$	0.486935	−	0.843396i	0.0494407	−	0.0856338i	0.889687	+	0.456572i	$0.150923\pi$
$98$		0			0
$99$	2.31275			0.232440
$100$	0.727557	+	1.26017i	0.0727557	+	0.126017i
$101$	1.47012	−	2.54632i	0.146282	−	0.253368i	−0.783568	−	0.621305i	$-0.786603\pi$
$101$	1.47012	−	2.54632i	0.146282	−	0.253368i	0.929851	+	0.367937i	$0.119936\pi$
$102$	−7.75195	+	13.4268i	−0.767557	+	1.32945i
$103$	−0.264341	+	0.457852i	−0.0260463	+	0.0451135i	−0.878755	−	0.477274i	$-0.841625\pi$
$103$	−0.264341	+	0.457852i	−0.0260463	+	0.0451135i	0.852708	+	0.522387i	$0.174958\pi$
$104$	8.53336	+	3.57395i	0.836765	+	0.350455i
$105$		0			0
$106$	6.27076	+	10.8613i	0.609070	+	1.05494i
$107$	−19.3224			−1.86797			−0.933983	−	0.357318i	$-0.883691\pi$
$107$	−19.3224			−1.86797			−0.933983	+	0.357318i	$0.883691\pi$
$108$	0.983651			0.0946518
$109$	2.86620	+	4.96440i	0.274532	+	0.475503i	0.970017	−	0.243037i	$-0.0781437\pi$
$109$	2.86620	+	4.96440i	0.274532	+	0.475503i	−0.695485	+	0.718541i	$0.744810\pi$
$110$	0.681558	+	1.18049i	0.0649840	+	0.112556i
$111$	1.49805	−	2.59470i	0.142189	−	0.246278i
$112$		0			0
$113$	−2.57480	+	4.45968i	−0.242216	+	0.419531i	−0.961345	−	0.275346i	$-0.911208\pi$
$113$	−2.57480	+	4.45968i	−0.242216	+	0.419531i	0.719129	+	0.694877i	$0.244541\pi$
$114$	5.44491			0.509962
$115$	−0.522774	+	0.905470i	−0.0487489	+	0.0844355i
$116$	−1.07782	−	1.86684i	−0.100073	−	0.173332i
$117$	−0.694354	−	5.43908i	−0.0641931	−	0.502844i
$118$	18.0602			1.66257
$119$		0			0
$120$	1.60777	+	2.78474i	0.146769	+	0.254211i
$121$	4.34362	+	7.52338i	0.394875	+	0.683943i
$122$	1.88589	+	3.26646i	0.170740	+	0.295731i
$123$	−2.88199			−0.259860
$124$	0.951766	+	1.64851i	0.0854711	+	0.148040i
$125$	−5.68917			−0.508855
$126$		0			0
$127$	4.50166	+	7.79710i	0.399457	+	0.691881i	0.993659	−	0.112436i	$-0.0358652\pi$
$127$	4.50166	+	7.79710i	0.399457	+	0.691881i	−0.594202	+	0.804316i	$0.702532\pi$
$128$	−13.2227			−1.16873
$129$	−12.2890	−	21.2852i	−1.08199	−	1.87406i
$130$	2.57164	−	1.95729i	0.225548	−	0.171666i
$131$	−3.39920	+	5.88758i	−0.296989	+	0.514401i	−0.975446	−	0.220240i	$-0.929316\pi$
$131$	−3.39920	+	5.88758i	−0.296989	+	0.514401i	0.678456	+	0.734641i	$0.262649\pi$
$132$	0.505639	+	0.875793i	0.0440102	+	0.0762280i
$133$		0			0
$134$	−5.75829	+	9.97364i	−0.497440	+	0.861592i
$135$	−0.926861	+	1.60537i	−0.0797715	+	0.138168i
$136$	12.3031			1.05498
$137$	−14.0756			−1.20256			−0.601279	−	0.799039i	$-0.705342\pi$
$137$	−14.0756			−1.20256			−0.601279	+	0.799039i	$0.705342\pi$
$138$	−2.86801	+	4.96754i	−0.244141	+	0.422865i
$139$	−8.64313	+	14.9703i	−0.733101	+	1.26977i	0.222451	+	0.974944i	$0.428594\pi$
$139$	−8.64313	+	14.9703i	−0.733101	+	1.26977i	−0.955552	+	0.294824i	$0.904739\pi$
$140$		0			0
$141$	−0.494165	−	0.855919i	−0.0416162	−	0.0720814i
$142$	5.02213	−	8.69859i	0.421448	−	0.729969i
$143$	−4.36321	+	3.32087i	−0.364870	+	0.277705i
$144$	3.44280	+	5.96310i	0.286900	+	0.496925i
$145$	4.06238			0.337363
$146$	−12.4484	−	21.5613i	−1.03024	−	1.78442i
$147$		0			0
$148$	0.440707			0.0362259
$149$	8.56260	+	14.8309i	0.701475	+	1.21499i	0.967949	+	0.251148i	$0.0808082\pi$
$149$	8.56260	+	14.8309i	0.701475	+	1.21499i	−0.266473	+	0.963842i	$0.585858\pi$
$150$	−15.0442			−1.22835
$151$	−7.89873	−	13.6810i	−0.642789	−	1.11334i	−0.984807	−	0.173650i	$-0.944444\pi$
$151$	−7.89873	−	13.6810i	−0.642789	−	1.11334i	0.342018	−	0.939693i	$-0.388890\pi$
$152$	−2.16040	−	3.74191i	−0.175231	−	0.303509i
$153$	−3.64590	−	6.31488i	−0.294753	−	0.510528i
$154$		0			0
$155$	−3.58727			−0.288137
$156$	1.90787	−	1.45209i	0.152751	−	0.116260i
$157$	1.89176	+	3.27662i	0.150979	+	0.261503i	0.931587	−	0.363517i	$-0.118424\pi$
$157$	1.89176	+	3.27662i	0.150979	+	0.261503i	−0.780609	+	0.625020i	$0.785091\pi$
$158$	−11.3771	+	19.7058i	−0.905117	+	1.56771i
$159$	−17.5344			−1.39057
$160$	−0.516821	+	0.895161i	−0.0408583	+	0.0707687i
$161$		0			0
$162$	−8.55402	+	14.8160i	−0.672067	+	1.16406i
$163$	−0.857757	−	1.48568i	−0.0671847	−	0.116367i	0.830476	−	0.557054i	$-0.188068\pi$
$163$	−0.857757	−	1.48568i	−0.0671847	−	0.116367i	−0.897661	+	0.440687i	$0.854735\pi$
$164$	−0.211961	−	0.367127i	−0.0165514	−	0.0286678i
$165$	−1.90579			−0.148365
$166$	−15.3935			−1.19477
$167$	−6.32605	−	10.9570i	−0.489524	−	0.847881i	0.510403	−	0.859935i	$-0.329496\pi$
$167$	−6.32605	−	10.9570i	−0.489524	−	0.847881i	−0.999927	+	0.0120542i	$0.996163\pi$
$168$		0			0
$169$	9.11992	+	9.26429i	0.701532	+	0.712638i
$170$	2.14886	−	3.72193i	0.164810	−	0.285459i
$171$	−1.28043	+	2.21776i	−0.0979166	+	0.169596i
$172$	1.80764	−	3.13092i	0.137831	−	0.238730i
$173$	5.74371	+	9.94839i	0.436686	+	0.756362i	0.997432	−	0.0716259i	$-0.0228188\pi$
$173$	5.74371	+	9.94839i	0.436686	+	0.756362i	−0.560746	+	0.827988i	$0.689485\pi$
$174$	22.2868			1.68956
$175$		0			0
$176$	3.44280	−	5.96310i	0.259510	−	0.449485i
$177$	−12.6251	+	21.8672i	−0.948958	+	1.64364i
$178$	−25.0699			−1.87907
$179$	1.09225	−	1.89184i	0.0816389	−	0.141403i	−0.822315	−	0.569032i	$-0.807318\pi$
$179$	1.09225	−	1.89184i	0.0816389	−	0.141403i	0.903954	+	0.427630i	$0.140651\pi$
$180$	0.280329			0.0208945
$181$	−11.5981			−0.862081			−0.431041	−	0.902333i	$-0.641853\pi$
$181$	−11.5981			−0.862081			−0.431041	+	0.902333i	$0.641853\pi$
$182$		0			0
$183$	−5.27337			−0.389819
$184$	4.55180			0.335563
$185$	−0.415264	+	0.719258i	−0.0305308	+	0.0528809i
$186$	−19.6803			−1.44303
$187$	−3.64590	+	6.31488i	−0.266614	+	0.461790i
$188$	0.0726885	−	0.125900i	0.00530135	−	0.00918221i
$189$		0			0
$190$	−1.50934			−0.109499
$191$	−8.87961	−	15.3799i	−0.642506	−	1.11285i	−0.984871	−	0.173286i	$-0.944561\pi$
$191$	−8.87961	−	15.3799i	−0.642506	−	1.11285i	0.342365	−	0.939567i	$-0.388772\pi$
$192$	6.79147	−	11.7632i	0.490132	−	0.848934i
$193$	−11.3189	+	19.6050i	−0.814756	+	1.41120i	0.0947474	+	0.995501i	$0.469796\pi$
$193$	−11.3189	+	19.6050i	−0.814756	+	1.41120i	−0.909503	+	0.415697i	$0.863538\pi$
$194$	−0.740517	+	1.28261i	−0.0531660	+	0.0920863i
$195$	0.572172	+	4.48200i	0.0409741	+	0.320962i
$196$		0			0
$197$	−10.0032	−	17.3260i	−0.712696	−	1.23442i	−0.963842	−	0.266476i	$-0.914141\pi$
$197$	−10.0032	−	17.3260i	−0.712696	−	1.23442i	0.251146	−	0.967949i	$-0.419193\pi$
$198$	−3.51717			−0.249954
$199$	−1.84885			−0.131062			−0.0655309	−	0.997851i	$-0.520874\pi$
$199$	−1.84885			−0.131062			−0.0655309	+	0.997851i	$0.520874\pi$
$200$	5.96913	+	10.3388i	0.422081	+	0.731066i
$201$	−8.05073	−	13.9443i	−0.567854	−	0.983553i
$202$	−2.23572	+	3.87237i	−0.157304	+	0.272459i
$203$		0			0
$204$	1.59421	−	2.76126i	0.111617	−	0.193327i
$205$	0.798895			0.0557972
$206$	0.402003	−	0.696289i	0.0280088	−	0.0485127i
$207$	−1.34888	−	2.33633i	−0.0937539	−	0.162386i
$208$	−15.0575	−	6.30641i	−1.04405	−	0.437271i
$209$	2.56085			0.177138
$210$		0			0
$211$	8.08474	+	14.0032i	0.556576	+	0.964019i	0.997779	+	0.0666110i	$0.0212187\pi$
$211$	8.08474	+	14.0032i	0.556576	+	0.964019i	−0.441203	+	0.897407i	$0.645448\pi$
$212$	−1.28960	−	2.23366i	−0.0885702	−	0.153408i
$213$	7.02150	+	12.1616i	0.481105	+	0.833299i
$214$	29.3850			2.00871
$215$	3.40655	+	5.90032i	0.232325	+	0.402399i
$216$	8.07020			0.549108
$217$		0			0
$218$	−4.35884	−	7.54973i	−0.295218	−	0.511332i
$219$	34.8085			2.35214
$220$	−0.140165	−	0.242772i	−0.00944989	−	0.0163677i
$221$	15.9458	+	6.67844i	1.07263	+	0.449241i
$222$	−2.27820	+	3.94595i	−0.152902	+	0.264835i
$223$	6.21589	+	10.7662i	0.416247	+	0.720961i	0.995558	−	0.0941455i	$-0.0300119\pi$
$223$	6.21589	+	10.7662i	0.416247	+	0.720961i	−0.579312	+	0.815106i	$0.696679\pi$
$224$		0			0
$225$	3.53779	−	6.12763i	0.235853	−	0.408509i
$226$	3.91568	−	6.78216i	0.260467	−	0.451142i
$227$	1.23497			0.0819681			0.0409841	−	0.999160i	$-0.486951\pi$
$227$	1.23497			0.0819681			0.0409841	+	0.999160i	$0.486951\pi$
$228$	−1.11976			−0.0741581
$229$	−3.27757	+	5.67692i	−0.216588	+	0.375141i	−0.953763	−	0.300561i	$-0.902826\pi$
$229$	−3.27757	+	5.67692i	−0.216588	+	0.375141i	0.737175	+	0.675702i	$0.236159\pi$
$230$	0.795020	−	1.37702i	0.0524221	−	0.0907977i
$231$		0			0
$232$	−8.84282	−	15.3162i	−0.580559	−	1.00556i
$233$	−3.14944	+	5.45498i	−0.206326	+	0.357368i	−0.950555	−	0.310558i	$-0.899484\pi$
$233$	−3.14944	+	5.45498i	−0.206326	+	0.357368i	0.744228	+	0.667925i	$0.232818\pi$
$234$	1.05596	+	8.27162i	0.0690300	+	0.540732i
$235$	0.136984	+	0.237263i	0.00893584	+	0.0154773i
$236$	−3.71413			−0.241769
$237$	−15.9065	−	27.5509i	−1.03324	−	1.78962i
$238$		0			0
$239$	−18.9193			−1.22379			−0.611895	−	0.790939i	$-0.709592\pi$
$239$	−18.9193			−1.22379			−0.611895	+	0.790939i	$0.709592\pi$
$240$	−2.83698	−	4.91380i	−0.183126	−	0.317184i
$241$	22.2968			1.43626			0.718131	−	0.695908i	$-0.244998\pi$
$241$	22.2968			1.43626			0.718131	+	0.695908i	$0.244998\pi$
$242$	−6.60567	−	11.4414i	−0.424628	−	0.735478i
$243$	−7.24176	−	12.5431i	−0.464559	−	0.804640i
$244$	−0.387839	−	0.671757i	−0.0248289	−	0.0430048i
$245$		0			0
$246$	4.38285			0.279440
$247$	−0.768841	−	6.02256i	−0.0489202	−	0.383206i
$248$	7.80861	+	13.5249i	0.495847	+	0.858833i
$249$	10.7609	−	18.6385i	0.681947	−	1.18117i
$250$	8.65194			0.547197
$251$	3.47657	−	6.02160i	0.219439	−	0.380080i	−0.735197	−	0.677853i	$-0.762910\pi$
$251$	3.47657	−	6.02160i	0.219439	−	0.380080i	0.954637	+	0.297773i	$0.0962438\pi$
$252$		0			0
$253$	−1.34888	+	2.33633i	−0.0848036	+	0.146884i
$254$	−6.84600	−	11.8576i	−0.429556	−	0.744013i
$255$	3.00435	+	5.20368i	0.188139	+	0.325867i
$256$	7.33206			0.458254
$257$	21.1551			1.31962			0.659811	−	0.751432i	$-0.270636\pi$
$257$	21.1551			1.31962			0.659811	+	0.751432i	$0.270636\pi$
$258$	18.6888	+	32.3700i	1.16352	+	2.01527i
$259$		0			0
$260$	−0.528865	+	0.402523i	−0.0327988	+	0.0249634i
$261$	−5.24097	+	9.07763i	−0.324408	+	0.561891i
$262$	5.16941	−	8.95368i	0.319367	−	0.553160i
$263$	4.21496	−	7.30053i	0.259906	−	0.450170i	−0.706311	−	0.707902i	$-0.749642\pi$
$263$	4.21496	−	7.30053i	0.259906	−	0.450170i	0.966216	+	0.257732i	$0.0829752\pi$
$264$	4.14844	+	7.18530i	0.255319	+	0.442225i
$265$	4.86060			0.298584
$266$		0			0
$267$	17.5253	−	30.3547i	1.07253	−	1.85768i
$268$	1.18421	−	2.05111i	0.0723371	−	0.125292i
$269$	−5.83039			−0.355485			−0.177743	−	0.984077i	$-0.556879\pi$
$269$	−5.83039			−0.355485			−0.177743	+	0.984077i	$0.556879\pi$
$270$	1.40955	−	2.44141i	0.0857823	−	0.148579i
$271$	18.4299			1.11954			0.559769	−	0.828648i	$-0.310890\pi$
$271$	18.4299			1.11954			0.559769	+	0.828648i	$0.310890\pi$
$272$	−21.7093			−1.31632
$273$		0			0
$274$	21.4058			1.29317
$275$	−7.07558			−0.426673
$276$	0.589815	−	1.02159i	0.0355027	−	0.0614925i
$277$	−6.18307			−0.371505			−0.185752	−	0.982597i	$-0.559472\pi$
$277$	−6.18307			−0.371505			−0.185752	+	0.982597i	$0.559472\pi$
$278$	13.1442	−	22.7665i	0.788340	−	1.36544i
$279$	4.62802	−	8.01596i	0.277072	−	0.479903i
$280$		0			0
$281$	−5.64049			−0.336483			−0.168242	−	0.985746i	$-0.553809\pi$
$281$	−5.64049			−0.336483			−0.168242	+	0.985746i	$0.553809\pi$
$282$	0.751513	+	1.30166i	0.0447520	+	0.0775127i
$283$	8.22771	−	14.2508i	0.489086	−	0.847123i	−0.510835	−	0.859679i	$-0.670664\pi$
$283$	8.22771	−	14.2508i	0.489086	−	0.847123i	0.999921	+	0.0125564i	$0.00399694\pi$
$284$	−1.03282	+	1.78889i	−0.0612864	+	0.106151i
$285$	1.05512	−	1.82751i	0.0624996	−	0.108253i
$286$	6.63545	−	5.05029i	0.392362	−	0.298630i
$287$		0			0
$288$	−1.33353	−	2.30973i	−0.0785787	−	0.136102i
$289$	5.99003			0.352355
$290$	−6.17797			−0.362783
$291$	−1.03533	−	1.79324i	−0.0606919	−	0.105121i
$292$	2.56005	+	4.43414i	0.149816	+	0.259489i
$293$	−15.3086	+	26.5152i	−0.894335	+	1.54903i	−0.0597104	+	0.998216i	$0.519018\pi$
$293$	−15.3086	+	26.5152i	−0.894335	+	1.54903i	−0.834625	+	0.550819i	$0.814316\pi$
$294$		0			0
$295$	3.49970	−	6.06166i	0.203760	−	0.352923i
$296$	3.61571			0.210159
$297$	−2.39153	+	4.14225i	−0.138771	+	0.240358i
$298$	−13.0218	−	22.5544i	−0.754331	−	1.30654i
$299$	5.89952	+	2.47084i	0.341178	+	0.142893i
$300$	3.09388			0.178625
$301$		0			0
$302$	12.0122	+	20.8057i	0.691223	+	1.19723i
$303$	−3.12578	−	5.41401i	−0.179571	−	0.311027i
$304$	3.81212	+	6.60278i	0.218640	+	0.378696i
$305$	1.46179			0.0837019
$306$	5.54458	+	9.60350i	0.316963	+	0.548995i
$307$	−9.96020			−0.568459			−0.284229	−	0.958756i	$-0.591738\pi$
$307$	−9.96020			−0.568459			−0.284229	+	0.958756i	$0.591738\pi$
$308$		0			0
$309$	0.562044	+	0.973489i	0.0319736	+	0.0553799i
$310$	5.45543			0.309847
$311$	−13.8734	−	24.0294i	−0.786687	−	1.36258i	−0.927986	−	0.372615i	$-0.878461\pi$
$311$	−13.8734	−	24.0294i	−0.786687	−	1.36258i	0.141299	−	0.989967i	$-0.454872\pi$
$312$	15.6528	−	11.9134i	0.886164	−	0.674466i
$313$	8.26136	−	14.3091i	0.466960	−	0.808798i	−0.532328	−	0.846538i	$-0.678683\pi$
$313$	8.26136	−	14.3091i	0.466960	−	0.808798i	0.999288	+	0.0377401i	$0.0120159\pi$
$314$	−2.87693	−	4.98300i	−0.162355	−	0.281207i
$315$		0			0
$316$	2.33975	−	4.05256i	0.131621	−	0.227974i
$317$	−11.8396	+	20.5069i	−0.664980	+	1.15178i	0.314310	+	0.949320i	$0.398227\pi$
$317$	−11.8396	+	20.5069i	−0.664980	+	1.15178i	−0.979291	+	0.202459i	$0.935107\pi$
$318$	26.6659			1.49535
$319$	10.4819			0.586876
$320$	−1.88261	+	3.26078i	−0.105241	+	0.182283i
$321$	−20.5417	+	35.5793i	−1.14653	+	1.98584i
$322$		0			0
$323$	−4.03701	−	6.99230i	−0.224625	−	0.389062i
$324$	1.75916	−	3.04696i	0.0977312	−	0.169275i
$325$	2.12429	+	16.6402i	0.117834	+	0.923033i
$326$	1.30445	+	2.25938i	0.0722470	+	0.125136i
$327$	12.1883			0.674014
$328$	−1.73900	−	3.01203i	−0.0960202	−	0.166312i
$329$		0			0
$330$	2.89827			0.159545
$331$	−3.97604	−	6.88671i	−0.218543	−	0.378528i	0.735820	−	0.677178i	$-0.236797\pi$
$331$	−3.97604	−	6.88671i	−0.218543	−	0.378528i	−0.954363	+	0.298650i	$0.903464\pi$
$332$	3.16573			0.173742
$333$	−1.07148	−	1.85586i	−0.0587168	−	0.101700i
$334$	9.62049	+	16.6632i	0.526410	+	0.911768i
$335$	2.23168	+	3.86539i	0.121930	+	0.211189i
$336$		0			0
$337$	−7.91326			−0.431063			−0.215531	−	0.976497i	$-0.569148\pi$
$337$	−7.91326			−0.431063			−0.215531	+	0.976497i	$0.569148\pi$
$338$	−13.8693	−	14.0889i	−0.754392	−	0.766334i
$339$	5.47456	+	9.48221i	0.297337	+	0.515003i
$340$	−0.441920	+	0.765427i	−0.0239665	+	0.0415111i
$341$	−9.25603			−0.501242
$342$	1.94724	−	3.37271i	0.105294	−	0.182375i
$343$		0			0
$344$	14.8305	−	25.6871i	0.799605	−	1.38496i
$345$	1.11153	+	1.92522i	0.0598426	+	0.103650i
$346$	−8.73488	−	15.1292i	−0.469590	−	0.813353i
$347$	7.13571			0.383065			0.191533	−	0.981486i	$-0.438654\pi$
$347$	7.13571			0.383065			0.191533	+	0.981486i	$0.438654\pi$
$348$	−4.58335			−0.245694
$349$	0.688402	+	1.19235i	0.0368493	+	0.0638249i	0.883862	−	0.467748i	$-0.154935\pi$
$349$	0.688402	+	1.19235i	0.0368493	+	0.0638249i	−0.847013	+	0.531573i	$0.821601\pi$
$350$		0			0
$351$	10.4597	+	4.38073i	0.558296	+	0.233826i
$352$	−1.33353	+	2.30973i	−0.0710771	+	0.123109i
$353$	0.346608	−	0.600342i	0.0184481	−	0.0319530i	−0.856654	−	0.515891i	$-0.827461\pi$
$353$	0.346608	−	0.600342i	0.0184481	−	0.0319530i	0.875102	+	0.483938i	$0.160794\pi$
$354$	19.1999	−	33.2551i	1.02046	−	1.76749i
$355$	−1.94638	−	3.37123i	−0.103303	−	0.178926i
$356$	5.15571			0.273252
$357$		0			0
$358$	−1.66107	+	2.87706i	−0.0877904	+	0.152057i
$359$	2.90182	−	5.02611i	0.153152	−	0.265268i	−0.779232	−	0.626735i	$-0.784391\pi$
$359$	2.90182	−	5.02611i	0.153152	−	0.265268i	0.932385	+	0.361467i	$0.117724\pi$
$360$	2.29991			0.121216
$361$	8.08222	−	13.9988i	0.425380	−	0.736780i
$362$	17.6381			0.927038
$363$	18.4709			0.969472
$364$		0			0
$365$	−9.64902			−0.505053
$366$	8.01960			0.419191
$367$	3.67578	−	6.36664i	0.191874	−	0.332336i	−0.753997	−	0.656878i	$-0.771877\pi$
$367$	3.67578	−	6.36664i	0.191874	−	0.332336i	0.945871	+	0.324542i	$0.105210\pi$
$368$	−8.03187			−0.418690
$369$	−1.03067	+	1.78518i	−0.0536546	+	0.0929325i
$370$	0.631522	−	1.09383i	0.0328313	−	0.0568654i
$371$		0			0
$372$	4.04731			0.209843
$373$	−9.19942	−	15.9339i	−0.476328	−	0.825024i	0.523304	−	0.852146i	$-0.324699\pi$
$373$	−9.19942	−	15.9339i	−0.476328	−	0.825024i	−0.999632	+	0.0271216i	$0.991366\pi$
$374$	5.54458	−	9.60350i	0.286704	−	0.496585i
$375$	−6.04819	+	10.4758i	−0.312327	+	0.540966i
$376$	0.596361	−	1.03293i	0.0307550	−	0.0532692i
$377$	−3.14698	−	24.6512i	−0.162078	−	1.26960i
$378$		0			0
$379$	2.42550	+	4.20110i	0.124590	+	0.215796i	0.921573	−	0.388206i	$-0.126905\pi$
$379$	2.42550	+	4.20110i	0.124590	+	0.215796i	−0.796983	+	0.604002i	$0.793572\pi$
$380$	0.310401			0.0159232
$381$	19.1429			0.980723
$382$	13.5039	+	23.3894i	0.690918	+	1.19671i
$383$	−11.4103	−	19.7631i	−0.583037	−	1.00985i	−0.995117	−	0.0987019i	$-0.968531\pi$
$383$	−11.4103	−	19.7631i	−0.583037	−	1.00985i	0.412080	−	0.911148i	$-0.364802\pi$
$384$	−14.0571	+	24.3476i	−0.717349	+	1.24249i
$385$		0			0
$386$	17.2136	−	29.8148i	0.876147	−	1.51753i
$387$	−17.5795			−0.893615
$388$	0.152290	−	0.263773i	0.00773134	−	0.0133911i
$389$	10.1561	+	17.5908i	0.514933	+	0.891891i	0.999850	+	0.0173304i	$0.00551672\pi$
$389$	10.1561	+	17.5908i	0.514933	+	0.891891i	−0.484916	+	0.874561i	$0.661150\pi$
$390$	−0.870144	−	6.81610i	−0.0440615	−	0.345147i
$391$	8.50569			0.430151
$392$		0			0
$393$	7.22741	+	12.5182i	0.364575	+	0.631462i
$394$	15.2125	+	26.3489i	0.766397	+	1.32744i
$395$	4.40933	+	7.63719i	0.221858	+	0.384268i
$396$	0.723317			0.0363481
$397$	−17.0689	−	29.5641i	−0.856662	−	1.48378i	−0.875095	−	0.483952i	$-0.839201\pi$
$397$	−17.0689	−	29.5641i	−0.856662	−	1.48378i	0.0184326	−	0.999830i	$-0.494132\pi$
$398$	2.81169			0.140937
$399$		0			0
$400$	−10.5328	−	18.2434i	−0.526640	−	0.912168i
$401$	−3.02596			−0.151109			−0.0755547	−	0.997142i	$-0.524073\pi$
$401$	−3.02596			−0.151109			−0.0755547	+	0.997142i	$0.524073\pi$
$402$	12.2433	+	21.2061i	0.610642	+	1.05766i
$403$	2.77893	+	21.7682i	0.138428	+	1.08435i
$404$	0.459782	−	0.796365i	0.0228750	−	0.0396207i
$405$	3.31520	+	5.74209i	0.164734	+	0.285327i
$406$		0			0
$407$	−1.07148	+	1.85586i	−0.0531114	+	0.0919916i
$408$	13.0795	−	22.6543i	0.647530	−	1.12155i
$409$	−5.38325			−0.266184			−0.133092	−	0.991104i	$-0.542491\pi$
$409$	−5.38325			−0.266184			−0.133092	+	0.991104i	$0.542491\pi$
$410$	−1.21494			−0.0600015
$411$	−14.9638	+	25.9181i	−0.738111	+	1.27845i
$412$	−0.0826731	+	0.143194i	−0.00407301	+	0.00705466i
$413$		0			0
$414$	2.05135	+	3.55304i	0.100818	+	0.174622i
$415$	−2.98296	+	5.16664i	−0.146428	+	0.253620i
$416$	5.83235	+	2.44271i	0.285954	+	0.119764i
$417$	18.3771	+	31.8301i	0.899932	+	1.55873i
$418$	−3.89447			−0.190485
$419$	2.94117	+	5.09426i	0.143686	+	0.248871i	0.928882	−	0.370376i	$-0.120771\pi$
$419$	2.94117	+	5.09426i	0.143686	+	0.248871i	−0.785196	+	0.619247i	$0.787438\pi$
$420$		0			0
$421$	−28.7614			−1.40174			−0.700872	−	0.713287i	$-0.747206\pi$
$421$	−28.7614			−1.40174			−0.700872	+	0.713287i	$0.747206\pi$
$422$	−12.2951	−	21.2957i	−0.598514	−	1.03666i
$423$	−0.706904			−0.0343708
$424$	−10.5803	−	18.3257i	−0.513826	−	0.889973i
$425$	11.1542	+	19.3196i	0.541057	+	0.937138i
$426$	−10.6781	−	18.4950i	−0.517356	−	0.896087i
$427$		0			0
$428$	−6.04311			−0.292105
$429$	1.47634	+	11.5646i	0.0712786	+	0.558346i
$430$	−5.18059	−	8.97305i	−0.249830	−	0.432719i
$431$	−4.19294	+	7.26238i	−0.201967	+	0.349817i	−0.949162	−	0.314788i	$-0.898067\pi$
$431$	−4.19294	+	7.26238i	−0.201967	+	0.349817i	0.747195	+	0.664605i	$0.231400\pi$
$432$	−14.2403			−0.685135
$433$	−13.7996	+	23.9017i	−0.663168	+	1.14864i	0.316611	+	0.948556i	$0.397455\pi$
$433$	−13.7996	+	23.9017i	−0.663168	+	1.14864i	−0.979779	+	0.200085i	$0.935878\pi$
$434$		0			0
$435$	4.31874	−	7.48028i	0.207068	−	0.358652i
$436$	0.896409	+	1.55263i	0.0429302	+	0.0743573i
$437$	−1.49358	−	2.58696i	−0.0714478	−	0.123751i
$438$	−52.9359			−2.52937
$439$	−31.1737			−1.48784			−0.743921	−	0.668268i	$-0.767036\pi$
$439$	−31.1737			−1.48784			−0.743921	+	0.668268i	$0.767036\pi$
$440$	−1.14996	−	1.99178i	−0.0548221	−	0.0949546i
$441$		0			0
$442$	−24.2500	−	10.1564i	−1.15345	−	0.483090i
$443$	11.7941	−	20.4281i	0.560357	−	0.970566i	−0.437109	−	0.899409i	$-0.643997\pi$
$443$	11.7941	−	20.4281i	0.560357	−	0.970566i	0.997465	−	0.0711573i	$-0.0226692\pi$
$444$	0.468518	−	0.811497i	0.0222349	−	0.0385119i
$445$	−4.85806	+	8.41440i	−0.230294	+	0.398881i
$446$	−9.45296	−	16.3730i	−0.447611	−	0.775284i
$447$	36.4118			1.72222
$448$		0			0
$449$	−1.41328	+	2.44787i	−0.0666968	+	0.115522i	−0.897445	−	0.441125i	$-0.854579\pi$
$449$	−1.41328	+	2.44787i	−0.0666968	+	0.115522i	0.830749	+	0.556648i	$0.187913\pi$
$450$	−5.38018	+	9.31874i	−0.253624	+	0.439289i
$451$	2.06134			0.0970649
$452$	−0.805272	+	1.39477i	−0.0378768	+	0.0656046i
$453$	−33.5887			−1.57814
$454$	−1.87812			−0.0881444
$455$		0			0
$456$	−9.18691			−0.430217
$457$	−37.7432			−1.76555			−0.882776	−	0.469795i	$-0.844328\pi$
$457$	−37.7432			−1.76555			−0.882776	+	0.469795i	$0.844328\pi$
$458$	4.98444	−	8.63330i	0.232908	−	0.403408i
$459$	15.0803			0.703890
$460$	−0.163498	+	0.283188i	−0.00762315	+	0.0132037i
$461$	17.3293	−	30.0152i	0.807106	−	1.39795i	−0.107754	−	0.994178i	$-0.534366\pi$
$461$	17.3293	−	30.0152i	0.807106	−	1.39795i	0.914860	−	0.403771i	$-0.132301\pi$
$462$		0			0
$463$	18.5114			0.860296			0.430148	−	0.902758i	$-0.358461\pi$
$463$	18.5114			0.860296			0.430148	+	0.902758i	$0.358461\pi$
$464$	15.6036	+	27.0262i	0.724377	+	1.25466i
$465$	−3.81365	+	6.60543i	−0.176854	+	0.306320i
$466$	4.78958	−	8.29579i	0.221873	−	0.384295i
$467$	3.31392	−	5.73987i	0.153350	−	0.265610i	−0.779107	−	0.626891i	$-0.784327\pi$
$467$	3.31392	−	5.73987i	0.153350	−	0.265610i	0.932457	+	0.361281i	$0.117661\pi$
$468$	−0.217161	−	1.70108i	−0.0100383	−	0.0786326i
$469$		0			0
$470$	−0.208321	−	0.360823i	−0.00960915	−	0.0166435i
$471$	8.04455			0.370673
$472$	−30.4720			−1.40259
$473$	8.78973	+	15.2243i	0.404152	+	0.700012i
$474$	24.1902	+	41.8987i	1.11109	+	1.92447i
$475$	3.91730	−	6.78497i	0.179738	−	0.311316i
$476$		0			0
$477$	−6.27076	+	10.8613i	−0.287118	+	0.497304i
$478$	28.7720			1.31600
$479$	−8.72630	+	15.1144i	−0.398715	+	0.690594i	−0.993568	−	0.113240i	$-0.963877\pi$
$479$	−8.72630	+	15.1144i	−0.398715	+	0.690594i	0.594853	+	0.803835i	$0.297210\pi$
$480$	1.09887	+	1.90330i	0.0501564	+	0.0868734i
$481$	4.68626	+	1.96271i	0.213675	+	0.0894917i
$482$	−33.9083			−1.54448
$483$		0			0
$484$	1.35848	+	2.35295i	0.0617489	+	0.106952i
$485$	0.286995	+	0.497090i	0.0130318	+	0.0225717i
$486$	11.0131	+	19.0752i	0.499563	+	0.865269i
$487$	−35.5138			−1.60928			−0.804641	−	0.593762i	$-0.797642\pi$
$487$	−35.5138			−1.60928			−0.804641	+	0.593762i	$0.797642\pi$
$488$	−3.18196	−	5.51132i	−0.144041	−	0.249486i
$489$	−3.64754			−0.164948
$490$		0			0
$491$	14.9059	+	25.8178i	0.672695	+	1.16514i	0.977137	+	0.212611i	$0.0681966\pi$
$491$	14.9059	+	25.8178i	0.672695	+	1.16514i	−0.304442	+	0.952531i	$0.598470\pi$
$492$	−0.901347			−0.0406359
$493$	−16.5241	−	28.6205i	−0.744207	−	1.28900i
$494$	1.16923	+	9.15895i	0.0526063	+	0.412081i
$495$	−0.681558	+	1.18049i	−0.0306338	+	0.0530592i
$496$	−13.7787	−	23.8653i	−0.618680	−	1.07159i
$497$		0			0
$498$	−16.3649	+	28.3449i	−0.733331	+	1.27017i
$499$	3.75483	−	6.50355i	0.168089	−	0.291139i	−0.769659	−	0.638455i	$-0.779574\pi$
$499$	3.75483	−	6.50355i	0.168089	−	0.291139i	0.937748	+	0.347316i	$0.112907\pi$
$500$	−1.77930			−0.0795726
$501$	−26.9010			−1.20185
$502$	−5.28708	+	9.15750i	−0.235974	+	0.408719i
$503$	0.492171	−	0.852466i	0.0219448	−	0.0380096i	−0.854844	−	0.518884i	$-0.826348\pi$
$503$	0.492171	−	0.852466i	0.0219448	−	0.0380096i	0.876789	+	0.480875i	$0.159681\pi$
$504$		0			0
$505$	0.866474	+	1.50078i	0.0385576	+	0.0667837i
$506$	2.05135	−	3.55304i	0.0911934	−	0.157952i
$507$	26.7543	−	6.94407i	1.18820	−	0.308397i
$508$	1.40790	+	2.43856i	0.0624655	+	0.108193i
$509$	−12.9792			−0.575291			−0.287646	−	0.957737i	$-0.592873\pi$
$509$	−12.9792			−0.575291			−0.287646	+	0.957737i	$0.592873\pi$
$510$	−4.56893	−	7.91362i	−0.202316	−	0.350421i
$511$		0			0
$512$	15.2950			0.675949
$513$	−2.64808	−	4.58661i	−0.116916	−	0.202504i
$514$	−32.1722			−1.41905
$515$	−0.155800	−	0.269854i	−0.00686538	−	0.0118912i
$516$	−3.84342	−	6.65699i	−0.169197	−	0.293058i
$517$	0.353452	+	0.612196i	0.0155448	+	0.0269244i
$518$		0			0
$519$	24.4247			1.07212
$520$	−4.33899	+	3.30244i	−0.190277	+	0.144822i
$521$	−9.70730	−	16.8135i	−0.425285	−	0.736614i	0.571162	−	0.820837i	$-0.306493\pi$
$521$	−9.70730	−	16.8135i	−0.425285	−	0.736614i	−0.996447	+	0.0842226i	$0.973159\pi$
$522$	7.97033	−	13.8050i	0.348852	−	0.604229i
$523$	−27.2719			−1.19252			−0.596259	−	0.802792i	$-0.703347\pi$
$523$	−27.2719			−1.19252			−0.596259	+	0.802792i	$0.703347\pi$
$524$	−1.06311	+	1.84135i	−0.0464420	+	0.0804399i
$525$		0			0
$526$	−6.41000	+	11.1024i	−0.279489	+	0.484090i
$527$	14.5915	+	25.2732i	0.635616	+	1.10092i
$528$	−7.32011	−	12.6788i	−0.318567	−	0.551774i
$529$	−19.8531			−0.863179
$530$	−7.39187			−0.321082
$531$	9.03008	+	15.6406i	0.391872	+	0.678742i
$532$		0			0
$533$	−0.618874	−	4.84783i	−0.0268064	−	0.209983i
$534$	−26.6520	+	46.1626i	−1.15334	+	1.99765i
$535$	5.69422	−	9.86268i	0.246183	−	0.426401i
$536$	9.71566	−	16.8280i	0.419652	−	0.726859i
$537$	−2.32236	−	4.02245i	−0.100217	−	0.173582i
$538$	8.86670			0.382271
$539$		0			0
$540$	−0.289878	+	0.502083i	−0.0124743	+	0.0216062i
$541$	15.0495	−	26.0665i	0.647029	−	1.12069i	−0.336799	−	0.941576i	$-0.609344\pi$
$541$	15.0495	−	26.0665i	0.647029	−	1.12069i	0.983829	−	0.179111i	$-0.0573223\pi$
$542$	−28.0278			−1.20389
$543$	−12.3300	+	21.3562i	−0.529132	+	0.916483i
$544$	8.40885			0.360526
$545$	−3.37863			−0.144724
$546$		0			0
$547$	−26.1451			−1.11788			−0.558942	−	0.829207i	$-0.688793\pi$
$547$	−26.1451			−1.11788			−0.558942	+	0.829207i	$0.688793\pi$
$548$	−4.40216			−0.188051
$549$	−1.88589	+	3.26646i	−0.0804878	+	0.139409i
$550$	10.7604			0.458823
$551$	−5.80319	+	10.0514i	−0.247224	+	0.428205i
$552$	4.83905	−	8.38147i	0.205963	−	0.356739i
$553$		0			0
$554$	9.40305			0.399497
$555$	0.882938	+	1.52929i	0.0374786	+	0.0649149i
$556$	−2.70316	+	4.68200i	−0.114639	+	0.198561i
$557$	−8.95317	+	15.5073i	−0.379358	+	0.657067i	−0.990969	−	0.134091i	$-0.957188\pi$
$557$	−8.95317	+	15.5073i	−0.379358	+	0.657067i	0.611611	+	0.791159i	$0.290522\pi$
$558$	−7.03817	+	12.1905i	−0.297949	+	0.516063i
$559$	33.1652	−	25.2423i	1.40274	−	1.06764i
$560$		0			0
$561$	7.75195	+	13.4268i	0.327287	+	0.566878i
$562$	8.57790			0.361837
$563$	31.6549			1.33410			0.667048	−	0.745015i	$-0.267558\pi$
$563$	31.6549			1.33410			0.667048	+	0.745015i	$0.267558\pi$
$564$	−0.154551	−	0.267690i	−0.00650777	−	0.0112718i
$565$	−1.51756	−	2.62850i	−0.0638443	−	0.110582i
$566$	−12.5125	+	21.6722i	−0.525939	+	0.910953i
$567$		0			0
$568$	−8.47358	+	14.6767i	−0.355544	+	0.615820i
$569$	−26.1111			−1.09463			−0.547317	−	0.836925i	$-0.684351\pi$
$569$	−26.1111			−1.09463			−0.547317	+	0.836925i	$0.684351\pi$
$570$	−1.60459	+	2.77923i	−0.0672089	+	0.116409i
$571$	−6.65205	−	11.5217i	−0.278380	−	0.482168i	0.692602	−	0.721320i	$-0.256464\pi$
$571$	−6.65205	−	11.5217i	−0.278380	−	0.482168i	−0.970982	+	0.239152i	$0.923131\pi$
$572$	−1.36460	+	1.03861i	−0.0570569	+	0.0434264i
$573$	−37.7599			−1.57744
$574$		0			0
$575$	4.12674	+	7.14773i	0.172097	+	0.298081i
$576$	−4.85760	−	8.41361i	−0.202400	−	0.350567i
$577$	−8.38564	−	14.5244i	−0.349099	−	0.604657i	0.636991	−	0.770871i	$-0.280179\pi$
$577$	−8.38564	−	14.5244i	−0.349099	−	0.604657i	−0.986090	+	0.166214i	$0.946846\pi$
$578$	−9.10948			−0.378905
$579$	24.0665	+	41.6844i	1.00017	+	1.73234i
$580$	1.27052			0.0527554
$581$		0			0
$582$	1.57450	+	2.72711i	0.0652650	+	0.113042i
$583$	12.5415			0.519417
$584$	21.0036	+	36.3792i	0.869133	+	1.50538i
$585$	2.98088	+	1.24846i	0.123244	+	0.0516173i
$586$	23.2808	−	40.3236i	0.961723	−	1.66575i
$587$	−5.03261	−	8.71673i	−0.207718	−	0.359778i	0.743277	−	0.668983i	$-0.233270\pi$
$587$	−5.03261	−	8.71673i	−0.207718	−	0.359778i	−0.950995	+	0.309205i	$0.899937\pi$
$588$		0			0
$589$	5.12448	−	8.87587i	0.211151	−	0.365724i
$590$	−5.32225	+	9.21841i	−0.219114	+	0.379516i
$591$	−42.5377			−1.74977
$592$	−6.38009			−0.262220
$593$	19.7161	−	34.1493i	0.809643	−	1.40234i	−0.103468	−	0.994633i	$-0.532994\pi$
$593$	19.7161	−	34.1493i	0.809643	−	1.40234i	0.913111	−	0.407710i	$-0.133673\pi$
$594$	3.63697	−	6.29942i	0.149227	−	0.258468i
$595$		0			0
$596$	2.67797	+	4.63838i	0.109694	+	0.189995i
$597$	−1.96553	+	3.40439i	−0.0804436	+	0.139332i
$598$	−8.97183	−	3.75759i	−0.366886	−	0.153659i
$599$	−6.88601	−	11.9269i	−0.281355	−	0.487321i	0.690364	−	0.723462i	$-0.257450\pi$
$599$	−6.88601	−	11.9269i	−0.281355	−	0.487321i	−0.971719	+	0.236142i	$0.924117\pi$
$600$	25.3833			1.03627
$601$	16.6312	+	28.8060i	0.678399	+	1.17502i	0.975463	+	0.220164i	$0.0706592\pi$
$601$	16.6312	+	28.8060i	0.678399	+	1.17502i	−0.297064	+	0.954858i	$0.596007\pi$
$602$		0			0
$603$	−11.5166			−0.468991
$604$	−2.47034	−	4.27876i	−0.100517	−	0.174100i
$605$	−5.12019			−0.208165
$606$	4.75360	+	8.23348i	0.193102	+	0.334462i
$607$	21.9824	+	38.0747i	0.892240	+	1.54540i	0.837184	+	0.546921i	$0.184200\pi$
$607$	21.9824	+	38.0747i	0.892240	+	1.54540i	0.0550554	+	0.998483i	$0.482466\pi$
$608$	−1.47658	−	2.55751i	−0.0598831	−	0.103721i
$609$		0			0
$610$	−2.22305			−0.0900088
$611$	1.33364	−	1.01504i	0.0539531	−	0.0410641i
$612$	−1.14026	−	1.97499i	−0.0460923	−	0.0798342i
$613$	−1.35045	+	2.33906i	−0.0545443	+	0.0944736i	−0.892008	−	0.452019i	$-0.850704\pi$
$613$	−1.35045	+	2.33906i	−0.0545443	+	0.0944736i	0.837464	+	0.546492i	$0.184037\pi$
$614$	15.1472			0.611292
$615$	0.849310	−	1.47105i	0.0342475	−	0.0593184i
$616$		0			0
$617$	−3.00208	+	5.19975i	−0.120859	+	0.209334i	−0.920107	−	0.391668i	$-0.871898\pi$
$617$	−3.00208	+	5.19975i	−0.120859	+	0.209334i	0.799248	+	0.601002i	$0.205232\pi$
$618$	−0.854742	−	1.48046i	−0.0343828	−	0.0595527i
$619$	−6.68204	−	11.5736i	−0.268574	−	0.465184i	0.699920	−	0.714221i	$-0.253219\pi$
$619$	−6.68204	−	11.5736i	−0.268574	−	0.465184i	−0.968494	+	0.249038i	$0.919886\pi$
$620$	−1.12193			−0.0450576
$621$	5.57932			0.223890
$622$	21.0983	+	36.5433i	0.845963	+	1.46525i
$623$		0			0
$624$	−27.6201	+	21.0218i	−1.10569	+	0.841547i
$625$	−9.95497	+	17.2425i	−0.398199	+	0.689701i
$626$	−12.5637	+	21.7609i	−0.502145	+	0.869741i
$627$	2.72245	−	4.71543i	0.108724	−	0.188316i
$628$	0.591650	+	1.02477i	0.0236094	+	0.0408927i
$629$	6.75647			0.269398
$630$		0			0
$631$	−20.2228	+	35.0270i	−0.805059	+	1.39440i	0.111192	+	0.993799i	$0.464533\pi$
$631$	−20.2228	+	35.0270i	−0.805059	+	1.39440i	−0.916251	+	0.400604i	$0.868800\pi$
$632$	19.1961	−	33.2486i	0.763579	−	1.32256i
$633$	34.3797			1.36647
$634$	18.0054	−	31.1863i	0.715086	−	1.23857i
$635$	−5.30648			−0.210581
$636$	−5.48393			−0.217452
$637$		0			0
$638$	−15.9407			−0.631097
$639$	10.0443			0.397345
$640$	3.89667	−	6.74923i	0.154029	−	0.266787i
$641$	10.2198			0.403658			0.201829	−	0.979421i	$-0.435311\pi$
$641$	10.2198			0.403658			0.201829	+	0.979421i	$0.435311\pi$
$642$	31.2393	−	54.1081i	1.23292	−	2.13548i
$643$	15.9014	−	27.5420i	0.627088	−	1.08615i	−0.361045	−	0.932548i	$-0.617580\pi$
$643$	15.9014	−	27.5420i	0.627088	−	1.08615i	0.988133	−	0.153600i	$-0.0490868\pi$
$644$		0			0
$645$	14.4861			0.570389
$646$	6.13937	+	10.6337i	0.241550	+	0.418378i
$647$	−17.2617	+	29.8981i	−0.678626	+	1.17541i	0.296769	+	0.954949i	$0.404091\pi$
$647$	−17.2617	+	29.8981i	−0.678626	+	1.17541i	−0.975395	+	0.220465i	$0.929243\pi$
$648$	14.4328	−	24.9983i	0.566972	−	0.982025i
$649$	9.03008	−	15.6406i	0.354462	−	0.613946i
$650$	−3.23057	−	25.3060i	−0.126713	−	0.992582i
$651$		0			0
$652$	−0.268265	−	0.464649i	−0.0105061	−	0.0181970i
$653$	10.1180			0.395947			0.197974	−	0.980207i	$-0.436564\pi$
$653$	10.1180			0.395947			0.197974	+	0.980207i	$0.436564\pi$
$654$	−18.5356			−0.724800
$655$	−2.00346	−	3.47009i	−0.0782816	−	0.135588i
$656$	3.06855	+	5.31488i	0.119807	+	0.207511i
$657$	12.4484	−	21.5613i	0.485659	−	0.841185i
$658$		0			0
$659$	17.3841	−	30.1101i	0.677187	−	1.17292i	−0.298637	−	0.954367i	$-0.596532\pi$
$659$	17.3841	−	30.1101i	0.677187	−	1.17292i	0.975824	−	0.218556i	$-0.0701345\pi$
$660$	−0.596039			−0.0232008
$661$	−8.28076	+	14.3427i	−0.322084	+	0.557866i	−0.980918	−	0.194422i	$-0.937717\pi$
$661$	−8.28076	+	14.3427i	−0.322084	+	0.557866i	0.658834	+	0.752289i	$0.271050\pi$
$662$	6.04666	+	10.4731i	0.235010	+	0.407050i
$663$	29.2494	−	22.2620i	1.13595	−	0.864583i
$664$	25.9727			1.00794
$665$		0			0
$666$	1.62948	+	2.82234i	0.0631411	+	0.109364i
$667$	−6.11346	−	10.5888i	−0.236714	−	0.410001i
$668$	−1.97848	−	3.42683i	−0.0765498	−	0.132588i
$669$	26.4326			1.02194
$670$	−3.39388	−	5.87838i	−0.131117	−	0.227102i
$671$	3.77178			0.145608
$672$		0			0
$673$	20.9437	+	36.2756i	0.807321	+	1.39832i	0.914713	+	0.404104i	$0.132417\pi$
$673$	20.9437	+	36.2756i	0.807321	+	1.39832i	−0.107393	+	0.994217i	$0.534250\pi$
$674$	12.0343			0.463543
$675$	7.31659	+	12.6727i	0.281616	+	0.487772i
$676$	2.85227	+	2.89742i	0.109703	+	0.111439i
$677$	−15.7858	+	27.3417i	−0.606696	+	1.05083i	0.385085	+	0.922881i	$0.374172\pi$
$677$	−15.7858	+	27.3417i	−0.606696	+	1.05083i	−0.991781	+	0.127947i	$0.959161\pi$
$678$	−8.32556	−	14.4203i	−0.319741	−	0.553808i
$679$		0			0
$680$	−3.62566	+	6.27983i	−0.139038	+	0.240820i
$681$	1.31291	−	2.27402i	0.0503107	−	0.0871408i
$682$	14.0763			0.539011
$683$	−26.2676			−1.00510			−0.502551	−	0.864548i	$-0.667605\pi$
$683$	−26.2676			−1.00510			−0.502551	+	0.864548i	$0.667605\pi$
$684$	−0.400455	+	0.693609i	−0.0153118	+	0.0265208i
$685$	4.14801	−	7.18457i	0.158487	−	0.274508i
$686$		0			0
$687$	6.96880	+	12.0703i	0.265876	+	0.460512i
$688$	−26.1690	+	45.3261i	−0.997686	+	1.72804i
$689$	−3.76532	−	29.4949i	−0.143447	−	1.12367i
$690$	−1.69038	−	2.92783i	−0.0643517	−	0.111460i
$691$	−6.10095			−0.232091			−0.116046	−	0.993244i	$-0.537022\pi$
$691$	−6.10095			−0.232091			−0.116046	+	0.993244i	$0.537022\pi$
$692$	1.79635	+	3.11138i	0.0682872	+	0.118277i
$693$		0			0
$694$	−10.8518			−0.411929
$695$	−5.09419	−	8.82339i	−0.193234	−	0.334690i
$696$	−37.6034			−1.42535
$697$	−3.24957	−	5.62842i	−0.123086	−	0.213192i
$698$	−1.04690	−	1.81329i	−0.0396259	−	0.0686341i
$699$	6.69636	+	11.5984i	0.253280	+	0.438693i
$700$		0			0
$701$	−20.5701			−0.776921			−0.388461	−	0.921465i	$-0.626993\pi$
$701$	−20.5701			−0.776921			−0.388461	+	0.921465i	$0.626993\pi$
$702$	−15.9068	−	6.66210i	−0.600363	−	0.251445i
$703$	−1.18642	−	2.05495i	−0.0447468	−	0.0775038i
$704$	−4.85760	+	8.41361i	−0.183078	+	0.317100i
$705$	0.582513			0.0219387
$706$	−0.527111	+	0.912984i	−0.0198381	+	0.0343606i
$707$		0			0
$708$	−3.94851	+	6.83902i	−0.148394	+	0.257026i
$709$	21.5764	+	37.3715i	0.810320	+	1.40352i	0.912640	+	0.408764i	$0.134040\pi$
$709$	21.5764	+	37.3715i	0.810320	+	1.40352i	−0.102320	+	0.994751i	$0.532627\pi$
$710$	2.96000	+	5.12687i	0.111087	+	0.192408i
$711$	−22.7543			−0.853353
$712$	42.2992			1.58523
$713$	5.39847	+	9.35042i	0.202174	+	0.350176i
$714$		0			0
$715$	−0.409246	−	3.20575i	−0.0153050	−	0.119888i
$716$	0.341605	−	0.591677i	0.0127664	−	0.0221120i
$717$	−20.1132	+	34.8372i	−0.751143	+	1.30102i
$718$	−4.41302	+	7.64357i	−0.164692	+	0.285255i
$719$	14.1042	+	24.4292i	0.525999	+	0.911057i	0.999541	+	0.0302857i	$0.00964171\pi$
$719$	14.1042	+	24.4292i	0.525999	+	0.911057i	−0.473542	+	0.880771i	$0.657025\pi$
$720$	−4.05831			−0.151244
$721$		0			0
$722$	−12.2912	+	21.2890i	−0.457432	+	0.792295i
$723$	23.7038	−	41.0562i	0.881555	−	1.52690i
$724$	−3.62733			−0.134809
$725$	16.0341	−	27.7719i	0.595492	−	1.03142i
$726$	−28.0901			−1.04252
$727$	−19.5116			−0.723646			−0.361823	−	0.932247i	$-0.617845\pi$
$727$	−19.5116			−0.723646			−0.361823	+	0.932247i	$0.617845\pi$
$728$		0			0
$729$	2.95370			0.109396
$730$	14.6740			0.543108
$731$	27.7128	−	48.0000i	1.02500	−	1.77535i
$732$	−1.64926			−0.0609582
$733$	−10.1833	+	17.6380i	−0.376129	+	0.651475i	−0.990495	−	0.137546i	$-0.956078\pi$
$733$	−10.1833	+	17.6380i	−0.376129	+	0.651475i	0.614366	+	0.789021i	$0.289412\pi$
$734$	−5.59003	+	9.68222i	−0.206332	+	0.357377i
$735$		0			0
$736$	3.11105			0.114675
$737$	5.75829	+	9.97364i	0.212109	+	0.367384i
$738$	1.56742	−	2.71485i	0.0576975	−	0.0999349i
$739$	5.20995	−	9.02391i	0.191651	−	0.331950i	−0.754146	−	0.656706i	$-0.771949\pi$
$739$	5.20995	−	9.02391i	0.191651	−	0.331950i	0.945798	+	0.324757i	$0.105282\pi$
$740$	−0.129874	+	0.224949i	−0.00477428	+	0.00826929i
$741$	−11.9070	−	4.98691i	−0.437415	−	0.183199i
$742$		0			0
$743$	8.70470	+	15.0770i	0.319344	+	0.553121i	0.980351	−	0.197259i	$-0.0632040\pi$
$743$	8.70470	+	15.0770i	0.319344	+	0.553121i	−0.661007	+	0.750380i	$0.729871\pi$
$744$	33.2055			1.21737
$745$	−10.0934			−0.369795
$746$	13.9902	+	24.2318i	0.512219	+	0.887189i
$747$	−7.69677	−	13.3312i	−0.281610	−	0.487763i
$748$	−1.14026	+	1.97499i	−0.0416921	+	0.0722128i
$749$		0			0
$750$	9.19792	−	15.9313i	0.335861	−	0.581728i
$751$	−1.81525			−0.0662395			−0.0331197	−	0.999451i	$-0.510544\pi$
$751$	−1.81525			−0.0662395			−0.0331197	+	0.999451i	$0.510544\pi$
$752$	−1.05231	+	1.82265i	−0.0383737	+	0.0664652i
$753$	−7.39193	−	12.8032i	−0.269377	−	0.466575i
$754$	4.78584	+	37.4889i	0.174290	+	1.36527i
$755$	9.31088			0.338858
$756$		0			0
$757$	−26.7814	−	46.3867i	−0.973385	−	1.68595i	−0.685165	−	0.728388i	$-0.740270\pi$
$757$	−26.7814	−	46.3867i	−0.973385	−	1.68595i	−0.288220	−	0.957564i	$-0.593063\pi$
$758$	−3.68864	−	6.38892i	−0.133978	−	0.232056i
$759$	2.86801	+	4.96754i	0.104102	+	0.180310i
$760$	2.54664			0.0923762
$761$	−1.84083	−	3.18841i	−0.0667300	−	0.115580i	0.830730	−	0.556675i	$-0.187923\pi$
$761$	−1.84083	−	3.18841i	−0.0667300	−	0.115580i	−0.897460	+	0.441096i	$0.854590\pi$
$762$	−29.1121			−1.05462
$763$		0			0
$764$	−2.77711	−	4.81010i	−0.100472	−	0.174023i
$765$	4.29772			0.155384
$766$	17.3524	+	30.0553i	0.626968	+	1.08594i
$767$	−39.4942	−	16.5410i	−1.42605	−	0.597262i
$768$	7.79476	−	13.5009i	0.281269	−	0.487172i
$769$	−2.61897	−	4.53619i	−0.0944424	−	0.163579i	0.814933	−	0.579555i	$-0.196773\pi$
$769$	−2.61897	−	4.53619i	−0.0944424	−	0.163579i	−0.909376	+	0.415976i	$0.863440\pi$
$770$		0			0
$771$	22.4902	−	38.9541i	0.809963	−	1.40290i
$772$	−3.54002	+	6.13150i	−0.127408	+	0.220677i
$773$	−40.6138			−1.46078			−0.730388	−	0.683032i	$-0.760661\pi$
$773$	−40.6138			−1.46078			−0.730388	+	0.683032i	$0.760661\pi$
$774$	26.7344			0.960948
$775$	−14.1588	+	24.5238i	−0.508601	+	0.880922i
$776$	1.24944	−	2.16409i	0.0448522	−	0.0776862i
$777$		0			0
$778$	−15.4451	−	26.7517i	−0.553733	−	0.959094i
$779$	−1.14124	+	1.97668i	−0.0408890	+	0.0708219i
$780$	0.178948	+	1.40175i	0.00640736	+	0.0501908i
$781$	−5.02213	−	8.69859i	−0.179706	−	0.311260i
$782$	−12.9352			−0.462563
$783$	−10.8390	−	18.7737i	−0.387353	−	0.670916i
$784$		0			0
$785$	−2.22997			−0.0795911
$786$	−10.9913	−	19.0374i	−0.392045	−	0.679042i
$787$	34.2000			1.21910			0.609550	−	0.792748i	$-0.291350\pi$
$787$	34.2000			1.21910			0.609550	+	0.792748i	$0.291350\pi$
$788$	−3.12851	−	5.41873i	−0.111448	−	0.193034i
$789$	−8.96190	−	15.5225i	−0.319052	−	0.552614i
$790$	−6.70559	−	11.6144i	−0.238574	−	0.413223i
$791$		0			0
$792$	5.93434			0.210868
$793$	−1.13240	−	8.87040i	−0.0402126	−	0.314997i
$794$	25.9579	+	44.9604i	0.921211	+	1.59558i
$795$	5.16733	−	8.95007i	0.183266	−	0.317426i
$796$	−0.578232			−0.0204949
$797$	−15.6903	+	27.1763i	−0.555778	+	0.962635i	0.442065	+	0.896983i	$0.354246\pi$
$797$	−15.6903	+	27.1763i	−0.555778	+	0.962635i	−0.997843	+	0.0656522i	$0.979087\pi$
$798$		0			0
$799$	1.11439	−	1.93017i	0.0394241	−	0.0682846i
$800$	4.07976	+	7.06634i	0.144241	+	0.249833i
$801$	−12.5350	−	21.7112i	−0.442901	−	0.767128i
$802$	4.60180			0.162495
$803$	−24.8968			−0.878590
$804$	−2.51788	−	4.36109i	−0.0887988	−	0.153804i
$805$		0			0
$806$	−4.22612	−	33.1044i	−0.148859	−	1.16605i
$807$	−6.19832	+	10.7358i	−0.218191	+	0.377918i
$808$	3.77221	−	6.53365i	0.132706	−	0.229853i
$809$	18.9709	−	32.8585i	0.666981	−	1.15524i	−0.311764	−	0.950160i	$-0.600920\pi$
$809$	18.9709	−	32.8585i	0.666981	−	1.15524i	0.978744	−	0.205085i	$-0.0657470\pi$
$810$	−5.04167	−	8.73242i	−0.177146	−	0.306826i
$811$	−32.1023			−1.12726			−0.563632	−	0.826026i	$-0.690597\pi$
$811$	−32.1023			−1.12726			−0.563632	+	0.826026i	$0.690597\pi$
$812$		0			0
$813$	19.5930	−	33.9360i	0.687155	−	1.19019i
$814$	1.62948	−	2.82234i	0.0571133	−	0.0989231i
$815$	1.01111			0.0354176
$816$	−23.0793	+	39.9745i	−0.807938	+	1.39939i
$817$	−19.4653			−0.681004
$818$	8.18670			0.286241
$819$		0			0
$820$	0.249856			0.00872534
$821$	−16.9223			−0.590594			−0.295297	−	0.955406i	$-0.595419\pi$
$821$	−16.9223			−0.590594			−0.295297	+	0.955406i	$0.595419\pi$
$822$	22.7566	−	39.4156i	0.793727	−	1.37478i
$823$	−14.4733			−0.504508			−0.252254	−	0.967661i	$-0.581172\pi$
$823$	−14.4733			−0.504508			−0.252254	+	0.967661i	$0.581172\pi$
$824$	−0.678278	+	1.17481i	−0.0236289	+	0.0409265i
$825$	−7.52209	+	13.0286i	−0.261885	+	0.453599i
$826$		0			0
$827$	27.5792			0.959021			0.479511	−	0.877536i	$-0.340814\pi$
$827$	27.5792			0.959021			0.479511	+	0.877536i	$0.340814\pi$
$828$	−0.421866	−	0.730693i	−0.0146608	−	0.0253933i
$829$	−10.5465	+	18.2671i	−0.366296	+	0.634443i	−0.988983	−	0.148028i	$-0.952708\pi$
$829$	−10.5465	+	18.2671i	−0.366296	+	0.634443i	0.622687	+	0.782471i	$0.286041\pi$
$830$	4.53641	−	7.85729i	0.157461	−	0.272730i
$831$	−6.57326	+	11.3852i	−0.228024	+	0.394949i
$832$	21.2454	+	8.89800i	0.736550	+	0.308483i
$833$		0			0
$834$	−27.9474	−	48.4064i	−0.967741	−	1.67618i
$835$	7.45704			0.258061
$836$	0.800911			0.0277001
$837$	9.57131	+	16.5780i	0.330833	+	0.573020i
$838$	−4.47286	−	7.74722i	−0.154512	−	0.267623i
$839$	6.35488	−	11.0070i	0.219395	−	0.380003i	−0.735228	−	0.677819i	$-0.762925\pi$
$839$	6.35488	−	11.0070i	0.219395	−	0.380003i	0.954623	+	0.297817i	$0.0962584\pi$
$840$		0			0
$841$	−9.25333	+	16.0272i	−0.319080	+	0.552663i
$842$	43.7396			1.50736
$843$	−5.99643	+	10.3861i	−0.206528	+	0.357717i
$844$	2.52852	+	4.37952i	0.0870351	+	0.150749i
$845$	−7.41635	+	1.92492i	−0.255130	+	0.0662191i
$846$	1.07504			0.0369606
$847$		0			0
$848$	18.6695	+	32.3365i	0.641113	+	1.11044i
$849$	−17.4938	−	30.3002i	−0.600387	−	1.03990i
$850$	−16.9630	−	29.3807i	−0.581825	−	1.00775i
$851$	2.49971			0.0856890
$852$	2.19599	+	3.80356i	0.0752333	+	0.130308i
$853$	−35.0471			−1.19999			−0.599996	−	0.800003i	$-0.704831\pi$
$853$	−35.0471			−1.19999			−0.599996	+	0.800003i	$0.704831\pi$
$854$		0			0
$855$	−0.754672	−	1.30713i	−0.0258092	−	0.0447029i
$856$	−49.5797			−1.69460
$857$	12.7970	+	22.1651i	0.437138	+	0.757145i	0.997467	−	0.0711250i	$-0.0226589\pi$
$857$	12.7970	+	22.1651i	0.437138	+	0.757145i	−0.560330	+	0.828270i	$0.689326\pi$
$858$	−2.24518	−	17.5872i	−0.0766493	−	0.600417i
$859$	−0.372743	+	0.645610i	−0.0127178	+	0.0220279i	−0.872314	−	0.488946i	$-0.837382\pi$
$859$	−0.372743	+	0.645610i	−0.0127178	+	0.0220279i	0.859596	+	0.510974i	$0.170715\pi$
$860$	1.06541	+	1.84534i	0.0363300	+	0.0629254i
$861$		0			0
$862$	6.37651	−	11.0444i	0.217185	−	0.376175i
$863$	10.9908	−	19.0367i	0.374132	−	0.648015i	−0.616065	−	0.787695i	$-0.711274\pi$
$863$	10.9908	−	19.0367i	0.374132	−	0.648015i	0.990197	+	0.139680i	$0.0446075\pi$
$864$	5.51579			0.187651
$865$	−6.77058			−0.230207
$866$	20.9861	−	36.3490i	0.713137	−	1.23519i
$867$	6.36804	−	11.0298i	0.216270	−	0.374590i
$868$		0			0
$869$	11.3771	+	19.7058i	0.385943	+	0.668473i
$870$	−6.56783	+	11.3758i	−0.222670	+	0.385676i
$871$	21.7270	−	16.5366i	0.736192	−	0.560321i
$872$	7.35444	+	12.7383i	0.249053	+	0.431372i
$873$	−1.48103			−0.0501254
$874$	2.27140	+	3.93418i	0.0768313	+	0.133076i
$875$		0			0
$876$	10.8864			0.367818
$877$	−14.7095	−	25.4776i	−0.496705	−	0.860319i	0.503287	−	0.864119i	$-0.332124\pi$
$877$	−14.7095	−	25.4776i	−0.496705	−	0.860319i	−0.999993	+	0.00380023i	$0.998790\pi$
$878$	47.4082			1.59995
$879$	32.5492	+	56.3769i	1.09786	+	1.90155i
$880$	2.02915	+	3.51460i	0.0684028	+	0.118477i
$881$	24.1414	+	41.8142i	0.813345	+	1.40876i	0.910510	+	0.413487i	$0.135689\pi$
$881$	24.1414	+	41.8142i	0.813345	+	1.40876i	−0.0971649	+	0.995268i	$0.530977\pi$
$882$		0			0
$883$	16.4465			0.553469			0.276735	−	0.960946i	$-0.410748\pi$
$883$	16.4465			0.553469			0.276735	+	0.960946i	$0.410748\pi$
$884$	4.98708	+	2.08869i	0.167734	+	0.0702504i
$885$	−7.44110	−	12.8884i	−0.250130	−	0.433238i
$886$	−17.9362	+	31.0664i	−0.602579	+	1.04370i
$887$	−29.1653			−0.979276			−0.489638	−	0.871926i	$-0.662871\pi$
$887$	−29.1653			−0.979276			−0.489638	+	0.871926i	$0.662871\pi$
$888$	3.84388	−	6.65780i	0.128992	−	0.223421i
$889$		0			0
$890$	7.38800	−	12.7964i	0.247646	−	0.428936i
$891$	8.55402	+	14.8160i	0.286571	+	0.496355i
$892$	1.94403	+	3.36716i	0.0650910	+	0.112741i
$893$	−0.782736			−0.0261933
$894$	−55.3741			−1.85199
$895$	0.643765	+	1.11503i	0.0215187	+	0.0372715i
$896$		0			0
$897$	10.8215	−	8.23633i	0.361320	−	0.275003i
$898$	2.14928	−	3.72266i	0.0717224	−	0.124227i
$899$	20.9753	−	36.3302i	0.699565	−	1.21168i
$900$	1.10645	−	1.91643i	0.0368817	−	0.0638809i
$901$	−19.7709	−	34.2441i	−0.658663	−	1.14084i
$902$	−3.13484			−0.104379
$903$		0			0
$904$	−6.60673	+	11.4432i	−0.219736	+	0.380595i
$905$	3.41791	−	5.92000i	0.113615	−	0.196787i
$906$	51.0808			1.69705
$907$	17.6607	−	30.5893i	0.586416	−	1.01570i	−0.408282	−	0.912856i	$-0.633872\pi$
$907$	17.6607	−	30.5893i	0.586416	−	1.01570i	0.994697	−	0.102846i	$-0.0327947\pi$
$908$	0.386240			0.0128178
$909$	−4.47143			−0.148308
$910$		0			0
$911$	−43.6496			−1.44617			−0.723087	−	0.690757i	$-0.757278\pi$
$911$	−43.6496			−1.44617			−0.723087	+	0.690757i	$0.757278\pi$
$912$	16.2107			0.536791
$913$	−7.69677	+	13.3312i	−0.254726	+	0.441198i
$914$	57.3988			1.89858
$915$	1.55404	−	2.69167i	0.0513749	−	0.0889840i
$916$	−1.02507	+	1.77547i	−0.0338691	+	0.0586630i
$917$		0			0
$918$	−22.9338			−0.756927
$919$	8.89389	+	15.4047i	0.293382	+	0.508153i	0.974607	−	0.223921i	$-0.0718858\pi$
$919$	8.89389	+	15.4047i	0.293382	+	0.508153i	−0.681225	+	0.732074i	$0.738552\pi$
$920$	−1.34140	+	2.32337i	−0.0442245	+	0.0765991i
$921$	−10.5887	+	18.3403i	−0.348911	+	0.604332i
$922$	−26.3539	+	45.6463i	−0.867921	+	1.50328i
$923$	−18.9494	+	14.4225i	−0.623726	+	0.474723i
$924$		0			0
$925$	3.27806	+	5.67777i	0.107782	+	0.186684i
$926$	−28.1516			−0.925118
$927$	0.804005			0.0264070
$928$	−6.04385	−	10.4683i	−0.198399	−	0.343638i
$929$	1.95710	+	3.38980i	0.0642103	+	0.111216i	0.896343	−	0.443360i	$-0.146214\pi$
$929$	1.95710	+	3.38980i	0.0642103	+	0.111216i	−0.832133	+	0.554576i	$0.812880\pi$
$930$	5.79969	−	10.0454i	0.190179	−	0.329401i
$931$		0			0
$932$	−0.984992	+	1.70606i	−0.0322645	+	0.0558837i
$933$	−58.9955			−1.93142
$934$	−5.03972	+	8.72905i	−0.164905	+	0.285623i
$935$	−2.14886	−	3.72193i	−0.0702752	−	0.121720i
$936$	−1.78166	−	13.9563i	−0.0582354	−	0.456175i
$937$	0.207362			0.00677421			0.00338710	−	0.999994i	$-0.498922\pi$
$937$	0.207362			0.00677421			0.00338710	+	0.999994i	$0.498922\pi$
$938$		0			0
$939$	−17.5654	−	30.4242i	−0.573225	−	0.992855i
$940$	0.0428420	+	0.0742044i	0.00139735	+	0.00242028i
$941$	13.7328	+	23.7859i	0.447677	+	0.775400i	0.998234	−	0.0593977i	$-0.0189180\pi$
$941$	13.7328	+	23.7859i	0.447677	+	0.775400i	−0.550557	+	0.834797i	$0.685585\pi$
$942$	−12.2339			−0.398603
$943$	−1.20225	−	2.08236i	−0.0391507	−	0.0678111i
$944$	53.7692			1.75004
$945$		0			0
$946$	−13.3672	−	23.1527i	−0.434605	−	0.752758i
$947$	−23.0363			−0.748580			−0.374290	−	0.927312i	$-0.622114\pi$
$947$	−23.0363			−0.748580			−0.374290	+	0.927312i	$0.622114\pi$
$948$	−4.97479	−	8.61660i	−0.161574	−	0.279854i
$949$	7.47474	+	58.5518i	0.242640	+	1.90067i
$950$	−5.95733	+	10.3184i	−0.193281	+	0.334773i
$951$	25.1736	+	43.6019i	0.816309	+	1.41389i
$952$		0			0
$953$	−7.22808	+	12.5194i	−0.234140	+	0.405543i	−0.959022	−	0.283330i	$-0.908561\pi$
$953$	−7.22808	+	12.5194i	−0.234140	+	0.405543i	0.724882	+	0.688873i	$0.241894\pi$
$954$	9.53641	−	16.5175i	0.308753	−	0.534775i
$955$	10.4671			0.338708
$956$	−5.91706			−0.191371
$957$	11.1434	−	19.3010i	0.360215	−	0.623911i
$958$	13.2707	−	22.9856i	0.428758	−	0.742630i
$959$		0			0
$960$	4.00283	+	6.93311i	0.129191	+	0.223765i
$961$	−3.02213	+	5.23448i	−0.0974881	+	0.168854i
$962$	−7.12675	−	2.98483i	−0.229776	−	0.0962348i
$963$	14.6925	+	25.4481i	0.473459	+	0.820054i
$964$	6.97336			0.224597
$965$	−6.67129	−	11.5550i	−0.214756	−	0.371969i
$966$		0			0
$967$	32.3357			1.03984			0.519922	−	0.854213i	$-0.325961\pi$
$967$	32.3357			1.03984			0.519922	+	0.854213i	$0.325961\pi$
$968$	11.1454	+	19.3044i	0.358227	+	0.620467i
$969$	−17.1671			−0.551485
$970$	−0.436454	−	0.755961i	−0.0140137	−	0.0242725i
$971$	12.3118	+	21.3246i	0.395103	+	0.684338i	0.993114	−	0.117149i	$-0.0373756\pi$
$971$	12.3118	+	21.3246i	0.395103	+	0.684338i	−0.598011	+	0.801488i	$0.704042\pi$
$972$	−2.26487	−	3.92287i	−0.0726458	−	0.125826i
$973$		0			0
$974$	54.0084			1.73054
$975$	32.8988	+	13.7787i	1.05361	+	0.441272i
$976$	5.61472	+	9.72499i	0.179723	+	0.311289i
$977$	−3.00496	+	5.20474i	−0.0961372	+	0.166514i	−0.910083	−	0.414427i	$-0.863982\pi$
$977$	−3.00496	+	5.20474i	−0.0961372	+	0.166514i	0.813945	+	0.580941i	$0.197315\pi$
$978$	5.54709			0.177376
$979$	−12.5350	+	21.7112i	−0.400619	+	0.693893i
$980$		0			0
$981$	4.35884	−	7.54973i	0.139167	−	0.241044i
$982$	−22.6685	−	39.2630i	−0.723382	−	1.25293i
$983$	−17.9546	−	31.0984i	−0.572664	−	0.991884i	−0.996291	−	0.0860467i	$-0.972577\pi$
$983$	−17.9546	−	31.0984i	−0.572664	−	0.991884i	0.423627	−	0.905837i	$-0.360757\pi$
$984$	−7.39496			−0.235743
$985$	11.7916			0.375710
$986$	25.1294	+	43.5253i	0.800282	+	1.38613i
$987$		0			0
$988$	−0.240456	−	1.88357i	−0.00764994	−	0.0599242i
$989$	10.2530	−	17.7587i	0.326027	−	0.564694i
$990$	1.03650	−	1.79526i	0.0329420	−	0.0570572i
$991$	−14.0000	+	24.2487i	−0.444724	+	0.770285i	−0.998033	−	0.0626912i	$-0.980032\pi$
$991$	−14.0000	+	24.2487i	−0.444724	+	0.770285i	0.553309	+	0.832976i	$0.313365\pi$
$992$	5.33700	+	9.24396i	0.169450	+	0.293496i
$993$	−16.9078			−0.536553
$994$		0			0
$995$	0.544849	−	0.943706i	0.0172729	−	0.0299175i
$996$	3.36550	−	5.82922i	0.106640	−	0.184706i
$997$	33.0081			1.04538			0.522688	−	0.852524i	$-0.324929\pi$
$997$	33.0081			1.04538			0.522688	+	0.852524i	$0.324929\pi$
$998$	−5.71024	+	9.89043i	−0.180755	+	0.313076i
$999$	4.43191			0.140219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.m.471.4		16
7.2	even	3		637.2.f.l.393.6	yes	16
7.3	odd	6		637.2.g.m.263.6		16
7.4	even	3		637.2.g.m.263.5		16
7.5	odd	6		637.2.f.l.393.5	yes	16
7.6	odd	2	inner	637.2.h.m.471.3		16
13.9	even	3		637.2.g.m.373.5		16
91.9	even	3		637.2.f.l.295.6	yes	16
91.16	even	3		8281.2.a.ci.1.3		8
91.23	even	6		8281.2.a.cl.1.5		8
91.48	odd	6		637.2.g.m.373.6		16
91.61	odd	6		637.2.f.l.295.5	✓	16
91.68	odd	6		8281.2.a.ci.1.4		8
91.74	even	3	inner	637.2.h.m.165.4		16
91.75	odd	6		8281.2.a.cl.1.6		8
91.87	odd	6	inner	637.2.h.m.165.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.5	✓	16	91.61	odd	6
637.2.f.l.295.6	yes	16	91.9	even	3
637.2.f.l.393.5	yes	16	7.5	odd	6
637.2.f.l.393.6	yes	16	7.2	even	3
637.2.g.m.263.5		16	7.4	even	3
637.2.g.m.263.6		16	7.3	odd	6
637.2.g.m.373.5		16	13.9	even	3
637.2.g.m.373.6		16	91.48	odd	6
637.2.h.m.165.3		16	91.87	odd	6	inner
637.2.h.m.165.4		16	91.74	even	3	inner
637.2.h.m.471.3		16	7.6	odd	2	inner
637.2.h.m.471.4		16	1.1	even	1	trivial
8281.2.a.ci.1.3		8	91.16	even	3
8281.2.a.ci.1.4		8	91.68	odd	6
8281.2.a.cl.1.5		8	91.23	even	6
8281.2.a.cl.1.6		8	91.75	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.52077 q^{2} +(1.06311 - 1.84135i) q^{3} +0.312752 q^{4} +(-0.294696 + 0.510428i) q^{5} +(-1.61674 + 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 - 1.31703i) q^{9} +(0.448165 - 0.776245i) q^{10} +(-0.760387 + 1.31703i) q^{11} +(0.332488 - 0.575886i) q^{12} +(3.32565 + 1.39285i) q^{13} +(0.626585 + 1.08528i) q^{15} -4.52769 q^{16} +4.79479 q^{17} +(1.15638 + 2.00290i) q^{18} +(-0.841957 - 1.45831i) q^{19} +(-0.0921666 + 0.159637i) q^{20} +(1.15638 - 2.00290i) q^{22} +1.77394 q^{23} +(2.72785 - 4.72477i) q^{24} +(2.32631 + 4.02929i) q^{25} +(-5.05756 - 2.11821i) q^{26} +3.14515 q^{27} +(-3.44625 - 5.96909i) q^{29} +(-0.952894 - 1.65046i) q^{30} +(3.04320 + 5.27098i) q^{31} +1.75375 q^{32} +(1.61674 + 2.80028i) q^{33} -7.29179 q^{34} +(-0.237812 - 0.411903i) q^{36} +1.40913 q^{37} +(1.28043 + 2.21776i) q^{38} +(6.10025 - 4.64295i) q^{39} +(-0.756166 + 1.30972i) q^{40} +(-0.677729 - 1.17386i) q^{41} +(5.77978 - 10.0109i) q^{43} +(-0.237812 + 0.411903i) q^{44} +0.896331 q^{45} -2.69777 q^{46} +(0.232416 - 0.402556i) q^{47} +(-4.81341 + 8.33707i) q^{48} +(-3.53779 - 6.12763i) q^{50} +(5.09737 - 8.82890i) q^{51} +(1.04010 + 0.435617i) q^{52} +(-4.12340 - 7.14194i) q^{53} -4.78306 q^{54} +(-0.448165 - 0.776245i) q^{55} -3.58035 q^{57} +(5.24097 + 9.07763i) q^{58} -11.8756 q^{59} +(0.195966 + 0.339422i) q^{60} +(-1.24009 - 2.14789i) q^{61} +(-4.62802 - 8.01596i) q^{62} +6.38833 q^{64} +(-1.69101 + 1.28704i) q^{65} +(-2.45870 - 4.25859i) q^{66} +(3.78642 - 6.55827i) q^{67} +1.49958 q^{68} +(1.88589 - 3.26646i) q^{69} +(-3.30235 + 5.71984i) q^{71} +(-1.95109 - 3.37939i) q^{72} +(8.18558 + 14.1778i) q^{73} -2.14296 q^{74} +9.89245 q^{75} +(-0.263323 - 0.456090i) q^{76} +(-9.27710 + 7.06087i) q^{78} +(7.48116 - 12.9577i) q^{79} +(1.33429 - 2.31106i) q^{80} +(5.62478 - 9.74241i) q^{81} +(1.03067 + 1.78518i) q^{82} +10.1222 q^{83} +(-1.41300 + 2.44740i) q^{85} +(-8.78973 + 15.2243i) q^{86} -14.6549 q^{87} +(-1.95109 + 3.37939i) q^{88} +16.4850 q^{89} -1.36312 q^{90} +0.554804 q^{92} +12.9410 q^{93} +(-0.353452 + 0.612196i) q^{94} +0.992484 q^{95} +(1.86442 - 3.22927i) q^{96} +(0.486935 - 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} + 8 q^{16} + 28 q^{18} + 28 q^{22} - 24 q^{23} + 12 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} + 16 q^{37} + 20 q^{39} + 32 q^{43} + 4 q^{44}+ \cdots + 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 24 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 + 8 * q^16 + 28 * q^18 + 28 * q^22 - 24 * q^23 + 12 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 + 16 * q^37 + 20 * q^39 + 32 * q^43 + 4 * q^44 + 8 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 - 48 * q^58 - 64 * q^60 - 64 * q^64 - 68 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 - 152 * q^74 + 28 * q^78 + 4 * q^79 + 56 * q^81 + 36 * q^85 - 4 * q^86 + 28 * q^88 - 160 * q^92 - 16 * q^93 - 104 * q^95 + 56 * q^99

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