LMFDB - Embedded newform 630.2.bv.a.577.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(73,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-12,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			577.3
Root			$0.339278 - 0.0446668i$ of defining polynomial
Character	$\chi$	$=$	630.577
Dual form			630.2.bv.a.523.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-2.23385 + 0.0994727i) q^{5} +(2.52756 - 0.781940i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.482081 + 2.18348i) q^{10} +(1.31272 - 2.27370i) q^{11} +(1.21865 + 1.21865i) q^{13} +(-0.101115 - 2.64382i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.95935 - 7.31238i) q^{17} +(-2.32616 - 4.02903i) q^{19} +(1.98431 + 1.03078i) q^{20} +(-1.85647 - 1.85647i) q^{22} +(-4.95766 - 1.32840i) q^{23} +(4.98021 - 0.444415i) q^{25} +(1.49254 - 0.861717i) q^{26} +(-2.57990 - 0.586601i) q^{28} +5.99410i q^{29} +(-8.66177 - 5.00088i) q^{31} +(0.965926 - 0.258819i) q^{32} -7.57033 q^{34} +(-5.56842 + 1.99816i) q^{35} +(1.02429 - 3.82271i) q^{37} +(-4.49380 + 1.20411i) q^{38} +(1.50924 - 1.64991i) q^{40} -5.59423i q^{41} +(-0.545731 + 0.545731i) q^{43} +(-2.27370 + 1.31272i) q^{44} +(-2.56627 + 4.44492i) q^{46} +(6.12372 + 1.64085i) q^{47} +(5.77714 - 3.95280i) q^{49} +(0.859701 - 4.92554i) q^{50} +(-0.446058 - 1.66471i) q^{52} +(2.22057 + 8.28728i) q^{53} +(-2.70626 + 5.20970i) q^{55} +(-1.23434 + 2.34017i) q^{56} +(5.78985 + 1.55139i) q^{58} +(3.86022 - 6.68609i) q^{59} +(4.16543 - 2.40491i) q^{61} +(-7.07231 + 7.07231i) q^{62} -1.00000i q^{64} +(-2.84351 - 2.60107i) q^{65} +(2.47605 - 0.663456i) q^{67} +(-1.95935 + 7.31238i) q^{68} +(0.488864 + 5.89585i) q^{70} +8.36973 q^{71} +(-13.1877 + 3.53363i) q^{73} +(-3.42734 - 1.97878i) q^{74} +4.65232i q^{76} +(1.54009 - 6.77339i) q^{77} +(7.78980 - 4.49744i) q^{79} +(-1.20307 - 1.88484i) q^{80} +(-5.40361 - 1.44789i) q^{82} +(7.99504 + 7.99504i) q^{83} +(5.10428 + 16.1399i) q^{85} +(0.385890 + 0.668382i) q^{86} +(0.679515 + 2.53598i) q^{88} +(0.0812661 + 0.140757i) q^{89} +(4.03313 + 2.12731i) q^{91} +(3.62926 + 3.62926i) q^{92} +(3.16987 - 5.49038i) q^{94} +(5.59708 + 8.76887i) q^{95} +(-4.35278 + 4.35278i) q^{97} +(-2.32288 - 6.60335i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7} + 8 q^{10} - 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{20} + 4 q^{22} - 32 q^{23} - 32 q^{25} + 12 q^{26} - 8 q^{28} - 24 q^{31} + 16 q^{34} - 4 q^{35}+ \cdots + 8 q^{98}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 8 * q^10 - 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^20 + 4 * q^22 - 32 * q^23 - 32 * q^25 + 12 * q^26 - 8 * q^28 - 24 * q^31 + 16 * q^34 - 4 * q^35 - 8 * q^37 + 28 * q^38 - 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 - 8 * q^52 - 44 * q^53 - 56 * q^55 - 8 * q^56 + 48 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 16 * q^65 + 36 * q^67 + 12 * q^68 + 32 * q^70 + 32 * q^71 - 40 * q^73 + 24 * q^74 + 44 * q^77 + 12 * q^79 - 12 * q^80 + 12 * q^82 + 16 * q^83 + 8 * q^85 + 8 * q^86 + 8 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 8 * q^94 + 48 * q^95 + 44 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.23385	+	0.0994727i	−0.999010	+	0.0444856i
$5$	−2.23385	+	0.0994727i	−0.999010	+	0.0444856i
$6$		0			0
$7$	2.52756	−	0.781940i	0.955329	−	0.295546i
$7$	2.52756	−	0.781940i	0.955329	−	0.295546i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−0.482081	+	2.18348i	−0.152447	+	0.690478i
$11$	1.31272	−	2.27370i	0.395800	−	0.685546i	−0.597403	−	0.801942i	$-0.703801\pi$
$11$	1.31272	−	2.27370i	0.395800	−	0.685546i	0.993203	+	0.116395i	$0.0371339\pi$
$12$		0			0
$13$	1.21865	+	1.21865i	0.337993	+	0.337993i	0.855612	−	0.517618i	$-0.173181\pi$
$13$	1.21865	+	1.21865i	0.337993	+	0.337993i	−0.517618	+	0.855612i	$0.673181\pi$
$14$	−0.101115	−	2.64382i	−0.0270242	−	0.706590i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.95935	−	7.31238i	−0.475211	−	1.77351i	−0.620589	−	0.784136i	$-0.713106\pi$
$17$	−1.95935	−	7.31238i	−0.475211	−	1.77351i	0.145377	−	0.989376i	$-0.453560\pi$
$18$		0			0
$19$	−2.32616	−	4.02903i	−0.533658	−	0.924322i	−0.999227	−	0.0393108i	$-0.987484\pi$
$19$	−2.32616	−	4.02903i	−0.533658	−	0.924322i	0.465569	−	0.885011i	$-0.345850\pi$
$20$	1.98431	+	1.03078i	0.443705	+	0.230490i
$21$		0			0
$22$	−1.85647	−	1.85647i	−0.395800	−	0.395800i
$23$	−4.95766	−	1.32840i	−1.03374	−	0.276991i	−0.298225	−	0.954496i	$-0.596395\pi$
$23$	−4.95766	−	1.32840i	−1.03374	−	0.276991i	−0.735518	+	0.677505i	$0.763061\pi$
$24$		0			0
$25$	4.98021	−	0.444415i	0.996042	−	0.0888830i
$26$	1.49254	−	0.861717i	0.292711	−	0.168997i
$27$		0			0
$28$	−2.57990	−	0.586601i	−0.487556	−	0.110857i
$29$			5.99410i			1.11308i	0.830822	+	0.556538i	$0.187871\pi$
$29$			5.99410i			1.11308i	−0.830822	+	0.556538i	$0.812129\pi$
$30$		0			0
$31$	−8.66177	−	5.00088i	−1.55570	−	0.898184i	−0.997660	−	0.0683700i	$-0.978220\pi$
$31$	−8.66177	−	5.00088i	−1.55570	−	0.898184i	−0.558040	−	0.829814i	$-0.688447\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	−7.57033			−1.29830
$35$	−5.56842	+	1.99816i	−0.941235	+	0.337751i
$36$		0			0
$37$	1.02429	−	3.82271i	0.168392	−	0.628449i	−0.829191	−	0.558966i	$-0.811198\pi$
$37$	1.02429	−	3.82271i	0.168392	−	0.628449i	0.997583	−	0.0694832i	$-0.0221350\pi$
$38$	−4.49380	+	1.20411i	−0.728990	+	0.195332i
$39$		0			0
$40$	1.50924	−	1.64991i	0.238631	−	0.260874i
$41$		−	5.59423i		−	0.873671i	−0.899541	−	0.436836i	$-0.856099\pi$
$41$		−	5.59423i		−	0.873671i	0.899541	−	0.436836i	$-0.143901\pi$
$42$		0			0
$43$	−0.545731	+	0.545731i	−0.0832233	+	0.0832233i	−0.747493	−	0.664270i	$-0.768743\pi$
$43$	−0.545731	+	0.545731i	−0.0832233	+	0.0832233i	0.664270	+	0.747493i	$0.268743\pi$
$44$	−2.27370	+	1.31272i	−0.342773	+	0.197900i
$45$		0			0
$46$	−2.56627	+	4.44492i	−0.378376	+	0.655367i
$47$	6.12372	+	1.64085i	0.893237	+	0.239342i	0.676109	−	0.736801i	$-0.263665\pi$
$47$	6.12372	+	1.64085i	0.893237	+	0.239342i	0.217127	+	0.976143i	$0.430331\pi$
$48$		0			0
$49$	5.77714	−	3.95280i	0.825306	−	0.564686i
$50$	0.859701	−	4.92554i	0.121580	−	0.696576i
$51$		0			0
$52$	−0.446058	−	1.66471i	−0.0618571	−	0.230854i
$53$	2.22057	+	8.28728i	0.305019	+	1.13835i	0.932929	+	0.360060i	$0.117244\pi$
$53$	2.22057	+	8.28728i	0.305019	+	1.13835i	−0.627910	+	0.778286i	$0.716089\pi$
$54$		0			0
$55$	−2.70626	+	5.20970i	−0.364912	+	0.702475i
$56$	−1.23434	+	2.34017i	−0.164946	+	0.312719i
$57$		0			0
$58$	5.78985	+	1.55139i	0.760245	+	0.203707i
$59$	3.86022	−	6.68609i	0.502557	−	0.870455i	−0.497438	−	0.867499i	$-0.665726\pi$
$59$	3.86022	−	6.68609i	0.502557	−	0.870455i	0.999996	−	0.00295539i	$-0.000940731\pi$
$60$		0			0
$61$	4.16543	−	2.40491i	0.533328	−	0.307917i	−0.209042	−	0.977907i	$-0.567035\pi$
$61$	4.16543	−	2.40491i	0.533328	−	0.307917i	0.742371	+	0.669989i	$0.233701\pi$
$62$	−7.07231	+	7.07231i	−0.898184	+	0.898184i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−2.84351	−	2.60107i	−0.352694	−	0.322623i
$66$		0			0
$67$	2.47605	−	0.663456i	0.302498	−	0.0810541i	−0.104377	−	0.994538i	$-0.533285\pi$
$67$	2.47605	−	0.663456i	0.302498	−	0.0810541i	0.406875	+	0.913484i	$0.366618\pi$
$68$	−1.95935	+	7.31238i	−0.237606	+	0.886756i
$69$		0			0
$70$	0.488864	+	5.89585i	0.0584305	+	0.704688i
$71$	8.36973			0.993304			0.496652	−	0.867950i	$-0.334563\pi$
$71$	8.36973			0.993304			0.496652	+	0.867950i	$0.334563\pi$
$72$		0			0
$73$	−13.1877	+	3.53363i	−1.54350	+	0.413581i	−0.927396	−	0.374081i	$-0.877958\pi$
$73$	−13.1877	+	3.53363i	−1.54350	+	0.413581i	−0.616108	+	0.787662i	$0.711291\pi$
$74$	−3.42734	−	1.97878i	−0.398421	−	0.230028i
$75$		0			0
$76$			4.65232i			0.533658i
$77$	1.54009	−	6.77339i	0.175509	−	0.771899i
$78$		0			0
$79$	7.78980	−	4.49744i	0.876421	−	0.506002i	0.00694408	−	0.999976i	$-0.497790\pi$
$79$	7.78980	−	4.49744i	0.876421	−	0.506002i	0.869477	+	0.493974i	$0.164456\pi$
$80$	−1.20307	−	1.88484i	−0.134508	−	0.210731i
$81$		0			0
$82$	−5.40361	−	1.44789i	−0.596729	−	0.159893i
$83$	7.99504	+	7.99504i	0.877570	+	0.877570i	0.993283	−	0.115713i	$-0.0369152\pi$
$83$	7.99504	+	7.99504i	0.877570	+	0.877570i	−0.115713	+	0.993283i	$0.536915\pi$
$84$		0			0
$85$	5.10428	+	16.1399i	0.553637	+	1.75062i
$86$	0.385890	+	0.668382i	0.0416116	+	0.0720734i
$87$		0			0
$88$	0.679515	+	2.53598i	0.0724365	+	0.270337i
$89$	0.0812661	+	0.140757i	0.00861419	+	0.0149202i	0.870300	−	0.492521i	$-0.163925\pi$
$89$	0.0812661	+	0.140757i	0.00861419	+	0.0149202i	−0.861686	+	0.507442i	$0.830591\pi$
$90$		0			0
$91$	4.03313	+	2.12731i	0.422787	+	0.223002i
$92$	3.62926	+	3.62926i	0.378376	+	0.378376i
$93$		0			0
$94$	3.16987	−	5.49038i	0.326947	−	0.566289i
$95$	5.59708	+	8.76887i	0.574248	+	0.899667i
$96$		0			0
$97$	−4.35278	+	4.35278i	−0.441958	+	0.441958i	−0.892670	−	0.450711i	$-0.851170\pi$
$97$	−4.35278	+	4.35278i	−0.441958	+	0.441958i	0.450711	+	0.892670i	$0.351170\pi$
$98$	−2.32288	−	6.60335i	−0.234647	−	0.667039i
$99$		0			0
$100$	−4.53520	−	2.10523i	−0.453520	−	0.210523i
$101$	6.64586	+	3.83699i	0.661287	+	0.381795i	0.792767	−	0.609524i	$-0.208640\pi$
$101$	6.64586	+	3.83699i	0.661287	+	0.381795i	−0.131480	+	0.991319i	$0.541973\pi$
$102$		0			0
$103$	−1.05286	+	3.92931i	−0.103741	+	0.387167i	−0.998199	−	0.0599847i	$-0.980895\pi$
$103$	−1.05286	+	3.92931i	−0.103741	+	0.387167i	0.894458	+	0.447151i	$0.147561\pi$
$104$	−1.72343			−0.168997
$105$		0			0
$106$	8.57963			0.833327
$107$	0.729112	−	2.72108i	0.0704859	−	0.263057i	−0.921686	−	0.387937i	$-0.873188\pi$
$107$	0.729112	−	2.72108i	0.0704859	−	0.263057i	0.992172	+	0.124880i	$0.0398545\pi$
$108$		0			0
$109$	−10.5314	−	6.08031i	−1.00872	−	0.582388i	−0.0979069	−	0.995196i	$-0.531215\pi$
$109$	−10.5314	−	6.08031i	−1.00872	−	0.582388i	−0.910818	+	0.412808i	$0.864548\pi$
$110$	4.33175	+	3.96241i	0.413016	+	0.377801i
$111$		0			0
$112$	1.94096	+	1.79796i	0.183404	+	0.169892i
$113$	−1.63875	+	1.63875i	−0.154161	+	0.154161i	−0.779973	−	0.625813i	$-0.784767\pi$
$113$	−1.63875	+	1.63875i	−0.154161	+	0.154161i	0.625813	+	0.779973i	$0.284767\pi$
$114$		0			0
$115$	11.2068	+	2.47430i	1.04504	+	0.230730i
$116$	2.99705	−	5.19104i	0.278269	−	0.481976i
$117$		0			0
$118$	−5.45917	−	5.45917i	−0.502557	−	0.502557i
$119$	−10.6702	−	16.9504i	−0.978137	−	1.55384i
$120$		0			0
$121$	2.05352	+	3.55681i	0.186684	+	0.323346i
$122$	−1.24487	−	4.64593i	−0.112706	−	0.420623i
$123$		0			0
$124$	5.00088	+	8.66177i	0.449092	+	0.777850i
$125$	−11.0809	+	1.48815i	−0.991102	+	0.133105i
$126$		0			0
$127$	6.79622	+	6.79622i	0.603067	+	0.603067i	0.941125	−	0.338058i	$-0.109770\pi$
$127$	6.79622	+	6.79622i	0.603067	+	0.603067i	−0.338058	+	0.941125i	$0.609770\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	−3.24839	+	2.07342i	−0.284903	+	0.181851i
$131$	3.66846	−	2.11799i	0.320515	−	0.185050i	−0.331107	−	0.943593i	$-0.607422\pi$
$131$	3.66846	−	2.11799i	0.320515	−	0.185050i	0.651622	+	0.758544i	$0.274089\pi$
$132$		0			0
$133$	−9.02997	−	8.36470i	−0.782998	−	0.725311i
$134$		−	2.56340i		−	0.221444i
$135$		0			0
$136$	6.55610	+	3.78517i	0.562181	+	0.324575i
$137$	−7.98108	+	2.13852i	−0.681870	+	0.182706i	−0.583096	−	0.812403i	$-0.698159\pi$
$137$	−7.98108	+	2.13852i	−0.681870	+	0.182706i	−0.0987740	+	0.995110i	$0.531492\pi$
$138$		0			0
$139$	9.35059			0.793106			0.396553	−	0.918012i	$-0.370206\pi$
$139$	9.35059			0.793106			0.396553	+	0.918012i	$0.370206\pi$
$140$	5.82148	+	1.05375i	0.492005	+	0.0890582i
$141$		0			0
$142$	2.16624	−	8.08453i	0.181787	−	0.678439i
$143$	4.37060	−	1.17110i	0.365488	−	0.0979322i
$144$		0			0
$145$	−0.596249	−	13.3899i	−0.0495158	−	1.11197i
$146$			13.6529i			1.12992i
$147$		0			0
$148$	−2.79841	+	2.79841i	−0.230028	+	0.230028i
$149$	4.12068	−	2.37908i	0.337579	−	0.194902i	−0.321622	−	0.946868i	$-0.604228\pi$
$149$	4.12068	−	2.37908i	0.337579	−	0.194902i	0.659201	+	0.751967i	$0.270895\pi$
$150$		0			0
$151$	−1.07557	+	1.86294i	−0.0875286	+	0.151604i	−0.906466	−	0.422279i	$-0.861230\pi$
$151$	−1.07557	+	1.86294i	−0.0875286	+	0.151604i	0.818937	+	0.573883i	$0.194564\pi$
$152$	4.49380	+	1.20411i	0.364495	+	0.0976661i
$153$		0			0
$154$	−6.14399	−	3.24069i	−0.495097	−	0.261142i
$155$	19.8466	+	10.3096i	1.59412	+	0.828089i
$156$		0			0
$157$	0.984635	+	3.67471i	0.0785824	+	0.293274i	0.994022	−	0.109182i	$-0.0348233\pi$
$157$	0.984635	+	3.67471i	0.0785824	+	0.293274i	−0.915439	+	0.402456i	$0.868157\pi$
$158$	−2.32805	−	8.68839i	−0.185209	−	0.691211i
$159$		0			0
$160$	−2.13199	+	0.674247i	−0.168549	+	0.0533039i
$161$	−13.5695	+	0.518978i	−1.06943	+	0.0409012i
$162$		0			0
$163$	−4.30925	−	1.15466i	−0.337526	−	0.0904399i	0.0860750	−	0.996289i	$-0.472568\pi$
$163$	−4.30925	−	1.15466i	−0.337526	−	0.0904399i	−0.423601	+	0.905849i	$0.639234\pi$
$164$	−2.79711	+	4.84474i	−0.218418	+	0.378311i
$165$		0			0
$166$	9.79189	−	5.65335i	0.759998	−	0.438785i
$167$	−16.1327	+	16.1327i	−1.24839	+	1.24839i	−0.291956	+	0.956432i	$0.594306\pi$
$167$	−16.1327	+	16.1327i	−1.24839	+	1.24839i	−0.956432	+	0.291956i	$0.905694\pi$
$168$		0			0
$169$		−	10.0298i		−	0.771521i
$170$	16.9110	−	0.753042i	1.29702	−	0.0577557i
$171$		0			0
$172$	0.745483	−	0.199752i	0.0568425	−	0.0152309i
$173$	3.20476	−	11.9603i	0.243653	−	0.909327i	−0.730402	−	0.683017i	$-0.760667\pi$
$173$	3.20476	−	11.9603i	0.243653	−	0.909327i	0.974055	−	0.226309i	$-0.0726660\pi$
$174$		0			0
$175$	12.2403	−	5.01751i	0.925279	−	0.379288i
$176$	2.62544			0.197900
$177$		0			0
$178$	0.156994	−	0.0420664i	0.0117672	−	0.00315301i
$179$	17.5544	+	10.1350i	1.31208	+	0.757528i	0.982440	−	0.186580i	$-0.0597403\pi$
$179$	17.5544	+	10.1350i	1.31208	+	0.757528i	0.329637	+	0.944108i	$0.393074\pi$
$180$		0			0
$181$		−	7.52637i		−	0.559431i	−0.960083	−	0.279715i	$-0.909760\pi$
$181$		−	7.52637i		−	0.559431i	0.960083	−	0.279715i	$-0.0902401\pi$
$182$	3.09867	−	3.34512i	0.229689	−	0.247957i
$183$		0			0
$184$	4.44492	−	2.56627i	0.327684	−	0.189188i
$185$	−1.90786	+	8.64126i	−0.140269	+	0.635318i
$186$		0			0
$187$	−19.1982	−	5.14415i	−1.40391	−	0.376178i
$188$	−4.48288	−	4.48288i	−0.326947	−	0.326947i
$189$		0			0
$190$	9.91871	−	3.13681i	0.719579	−	0.227568i
$191$	2.16395	+	3.74807i	0.156578	+	0.271201i	0.933632	−	0.358233i	$-0.116621\pi$
$191$	2.16395	+	3.74807i	0.156578	+	0.271201i	−0.777055	+	0.629433i	$0.783287\pi$
$192$		0			0
$193$	5.50458	+	20.5434i	0.396228	+	1.47874i	0.819678	+	0.572825i	$0.194153\pi$
$193$	5.50458	+	20.5434i	0.396228	+	1.47874i	−0.423449	+	0.905920i	$0.639181\pi$
$194$	3.07788	+	5.33105i	0.220979	+	0.382747i
$195$		0			0
$196$	−6.97955	+	0.534660i	−0.498539	+	0.0381900i
$197$	14.1314	+	14.1314i	1.00682	+	1.00682i	0.999977	+	0.00684089i	$0.00217754\pi$
$197$	14.1314	+	14.1314i	1.00682	+	1.00682i	0.00684089	+	0.999977i	$0.497822\pi$
$198$		0			0
$199$	0.422034	−	0.730985i	0.0299172	−	0.0518182i	−0.850679	−	0.525685i	$-0.823809\pi$
$199$	0.422034	−	0.730985i	0.0299172	−	0.0518182i	0.880596	+	0.473867i	$0.157142\pi$
$200$	−3.20729	+	3.83579i	−0.226790	+	0.271231i
$201$		0			0
$202$	5.42632	−	5.42632i	0.381795	−	0.381795i
$203$	4.68703	+	15.1505i	0.328965	+	1.06335i
$204$		0			0
$205$	0.556473	+	12.4967i	0.0388657	+	0.872806i
$206$	3.52293	+	2.03396i	0.245454	+	0.141713i
$207$		0			0
$208$	−0.446058	+	1.66471i	−0.0309285	+	0.115427i
$209$	−12.2144			−0.844888
$210$		0			0
$211$	22.1844			1.52724			0.763619	−	0.645667i	$-0.223421\pi$
$211$	22.1844			1.52724			0.763619	+	0.645667i	$0.223421\pi$
$212$	2.22057	−	8.28728i	0.152509	−	0.569173i
$213$		0			0
$214$	−2.43966	−	1.40854i	−0.166771	−	0.0962855i
$215$	1.16480	−	1.27337i	0.0794386	−	0.0868431i
$216$		0			0
$217$	−25.8036	−	5.86704i	−1.75166	−	0.398280i
$218$	−8.59885	+	8.59885i	−0.582388	+	0.582388i
$219$		0			0
$220$	4.94854	−	3.15860i	0.333630	−	0.212953i
$221$	6.52348	−	11.2990i	0.438817	−	0.760053i
$222$		0			0
$223$	10.7632	+	10.7632i	0.720757	+	0.720757i	0.968759	−	0.248002i	$-0.0797741\pi$
$223$	10.7632	+	10.7632i	0.720757	+	0.720757i	−0.248002	+	0.968759i	$0.579774\pi$
$224$	2.23906	−	1.40948i	0.149603	−	0.0941747i
$225$		0			0
$226$	1.15877	+	2.00705i	0.0770804	+	0.133507i
$227$	−0.967615	−	3.61119i	−0.0642229	−	0.239683i	0.926351	−	0.376661i	$-0.122928\pi$
$227$	−0.967615	−	3.61119i	−0.0642229	−	0.239683i	−0.990574	+	0.136978i	$0.956261\pi$
$228$		0			0
$229$	7.59088	+	13.1478i	0.501619	+	0.868830i	0.999998	+	0.00187073i	$0.000595471\pi$
$229$	7.59088	+	13.1478i	0.501619	+	0.868830i	−0.498379	+	0.866959i	$0.666071\pi$
$230$	5.29053	−	10.1846i	0.348847	−	0.671551i
$231$		0			0
$232$	−4.23847	−	4.23847i	−0.278269	−	0.278269i
$233$	−1.17170	−	0.313957i	−0.0767607	−	0.0205680i	0.220234	−	0.975447i	$-0.429318\pi$
$233$	−1.17170	−	0.313957i	−0.0767607	−	0.0205680i	−0.296995	+	0.954879i	$0.595984\pi$
$234$		0			0
$235$	−13.8427	−	3.05627i	−0.903000	−	0.199369i
$236$	−6.68609	+	3.86022i	−0.435227	+	0.251279i
$237$		0			0
$238$	−19.1345	+	5.91955i	−1.24030	+	0.383707i
$239$		−	16.1593i		−	1.04526i	−0.852560	−	0.522630i	$-0.824951\pi$
$239$		−	16.1593i		−	1.04526i	0.852560	−	0.522630i	$-0.175049\pi$
$240$		0			0
$241$	−21.8384	−	12.6084i	−1.40674	−	0.812180i	−0.411665	−	0.911335i	$-0.635053\pi$
$241$	−21.8384	−	12.6084i	−1.40674	−	0.812180i	−0.995072	+	0.0991549i	$0.968386\pi$
$242$	3.96710	−	1.06298i	0.255015	−	0.0683311i
$243$		0			0
$244$	−4.80982			−0.307917
$245$	−12.5121	+	9.40466i	−0.799368	+	0.600842i
$246$		0			0
$247$	2.07520	−	7.74476i	0.132042	−	0.492787i
$248$	9.66095	−	2.58864i	0.613471	−	0.164379i
$249$		0			0
$250$	−1.43049	+	11.0884i	−0.0904722	+	0.701295i
$251$		−	2.07559i		−	0.131010i	−0.997852	−	0.0655051i	$-0.979134\pi$
$251$		−	2.07559i		−	0.131010i	0.997852	−	0.0655051i	$-0.0208659\pi$
$252$		0			0
$253$	−9.52841	+	9.52841i	−0.599046	+	0.599046i
$254$	8.32363	−	4.80565i	0.522271	−	0.301533i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.34881	−	1.16526i	−0.271271	−	0.0726869i	0.120619	−	0.992699i	$-0.461512\pi$
$257$	−4.34881	−	1.16526i	−0.271271	−	0.0726869i	−0.391890	+	0.920012i	$0.628179\pi$
$258$		0			0
$259$	−0.400169	−	10.4631i	−0.0248653	−	0.650143i
$260$	1.16202	+	3.67435i	0.0720655	+	0.227873i
$261$		0			0
$262$	−1.09635	−	4.09164i	−0.0677328	−	0.252782i
$263$	−5.79744	−	21.6364i	−0.357486	−	1.33415i	−0.877327	−	0.479892i	$-0.840676\pi$
$263$	−5.79744	−	21.6364i	−0.357486	−	1.33415i	0.519842	−	0.854263i	$-0.325991\pi$
$264$		0			0
$265$	−5.78479	−	18.2917i	−0.355357	−	1.12365i
$266$	−10.4168	+	6.55734i	−0.638695	+	0.402056i
$267$		0			0
$268$	−2.47605	−	0.663456i	−0.151249	−	0.0405270i
$269$	−5.86211	+	10.1535i	−0.357419	+	0.619068i	−0.987529	−	0.157438i	$-0.949677\pi$
$269$	−5.86211	+	10.1535i	−0.357419	+	0.619068i	0.630110	+	0.776506i	$0.283010\pi$
$270$		0			0
$271$	20.8254	−	12.0235i	1.26505	−	0.730377i	0.291004	−	0.956722i	$-0.406011\pi$
$271$	20.8254	−	12.0235i	1.26505	−	0.730377i	0.974047	+	0.226344i	$0.0726775\pi$
$272$	5.35303	−	5.35303i	0.324575	−	0.324575i
$273$		0			0
$274$			8.26262i			0.499163i
$275$	5.52716	−	11.9069i	0.333300	−	0.718013i
$276$		0			0
$277$	26.2705	−	7.03917i	1.57844	−	0.422943i	0.640000	−	0.768375i	$-0.278934\pi$
$277$	26.2705	−	7.03917i	1.57844	−	0.422943i	0.938444	+	0.345433i	$0.112268\pi$
$278$	2.42011	−	9.03197i	0.145149	−	0.541702i
$279$		0			0
$280$	2.52455	−	5.35039i	0.150871	−	0.319747i
$281$	−22.1913			−1.32382			−0.661910	−	0.749583i	$-0.730254\pi$
$281$	−22.1913			−1.32382			−0.661910	+	0.749583i	$0.730254\pi$
$282$		0			0
$283$	10.7244	−	2.87361i	0.637502	−	0.170818i	0.0744302	−	0.997226i	$-0.476286\pi$
$283$	10.7244	−	2.87361i	0.637502	−	0.170818i	0.563072	+	0.826408i	$0.309620\pi$
$284$	−7.24840	−	4.18486i	−0.430113	−	0.248326i
$285$		0			0
$286$		−	4.52478i		−	0.267556i
$287$	−4.37435	−	14.1398i	−0.258210	−	0.834643i
$288$		0			0
$289$	−34.9094	+	20.1550i	−2.05350	+	1.18559i
$290$	−13.0880	−	2.88964i	−0.768555	−	0.169685i
$291$		0			0
$292$	13.1877	+	3.53363i	0.771752	+	0.206790i
$293$	−6.51580	−	6.51580i	−0.380657	−	0.380657i	0.490682	−	0.871339i	$-0.336748\pi$
$293$	−6.51580	−	6.51580i	−0.380657	−	0.380657i	−0.871339	+	0.490682i	$0.836748\pi$
$294$		0			0
$295$	−7.95808	+	15.3197i	−0.463337	+	0.891950i
$296$	1.97878	+	3.42734i	0.115014	+	0.199210i
$297$		0			0
$298$	−1.23150	−	4.59602i	−0.0713389	−	0.266240i
$299$	−4.42280	−	7.66052i	−0.255777	−	0.443019i
$300$		0			0
$301$	−0.952640	+	1.80610i	−0.0549093	+	0.104102i
$302$	1.52108	+	1.52108i	0.0875286	+	0.0875286i
$303$		0			0
$304$	2.32616	−	4.02903i	0.133414	−	0.231081i
$305$	−9.06574	+	5.78657i	−0.519103	+	0.331338i
$306$		0			0
$307$	−20.6010	+	20.6010i	−1.17576	+	1.17576i	−0.194947	+	0.980814i	$0.562454\pi$
$307$	−20.6010	+	20.6010i	−1.17576	+	1.17576i	−0.980814	+	0.194947i	$0.937546\pi$
$308$	−4.72045	+	5.09588i	−0.268973	+	0.290365i
$309$		0			0
$310$	15.0950	−	16.5020i	0.857339	−	0.937251i
$311$	−28.4631	−	16.4332i	−1.61399	−	0.931840i	−0.988432	−	0.151665i	$-0.951537\pi$
$311$	−28.4631	−	16.4332i	−1.61399	−	0.931840i	−0.625562	−	0.780175i	$-0.715130\pi$
$312$		0			0
$313$	−5.74141	+	21.4272i	−0.324523	+	1.21114i	0.590267	+	0.807208i	$0.299023\pi$
$313$	−5.74141	+	21.4272i	−0.324523	+	1.21114i	−0.914790	+	0.403930i	$0.867644\pi$
$314$	3.80434			0.214691
$315$		0			0
$316$	−8.99488			−0.506002
$317$	3.71781	−	13.8751i	0.208813	−	0.779301i	−0.779440	−	0.626476i	$-0.784496\pi$
$317$	3.71781	−	13.8751i	0.208813	−	0.779301i	0.988253	−	0.152824i	$-0.0488368\pi$
$318$		0			0
$319$	13.6288	+	7.86858i	0.763065	+	0.440556i
$320$	0.0994727	+	2.23385i	0.00556069	+	0.124876i
$321$		0			0
$322$	−3.01076	+	13.2415i	−0.167783	+	0.737918i
$323$	−24.9040	+	24.9040i	−1.38570	+	1.38570i
$324$		0			0
$325$	6.61073	+	5.52756i	0.366697	+	0.306614i
$326$	−2.23063	+	3.86356i	−0.123543	+	0.213983i
$327$		0			0
$328$	3.95571	+	3.95571i	0.218418	+	0.218418i
$329$	16.7611	−	0.641044i	0.924071	−	0.0353419i
$330$		0			0
$331$	1.44533	+	2.50339i	0.0794427	+	0.137599i	0.903010	−	0.429620i	$-0.141353\pi$
$331$	1.44533	+	2.50339i	0.0794427	+	0.137599i	−0.823567	+	0.567219i	$0.808019\pi$
$332$	−2.92639	−	10.9214i	−0.160606	−	0.599391i
$333$		0			0
$334$	11.4076	+	19.7585i	0.624194	+	1.08114i
$335$	−5.46514	+	1.72836i	−0.298593	+	0.0944306i
$336$		0			0
$337$	−23.4453	−	23.4453i	−1.27715	−	1.27715i	−0.942257	−	0.334891i	$-0.891301\pi$
$337$	−23.4453	−	23.4453i	−1.27715	−	1.27715i	−0.334891	−	0.942257i	$-0.608699\pi$
$338$	−9.68802	−	2.59590i	−0.526959	−	0.141198i
$339$		0			0
$340$	3.64951	−	16.5297i	0.197923	−	0.896448i
$341$	−22.7410	+	13.1295i	−1.23149	+	0.711003i
$342$		0			0
$343$	11.5112	−	14.5083i	0.621547	−	0.783377i
$344$		−	0.771781i		−	0.0416116i
$345$		0			0
$346$	−10.7233	−	6.19112i	−0.576490	−	0.332837i
$347$	−10.9516	+	2.93447i	−0.587912	+	0.157531i	−0.540499	−	0.841345i	$-0.681765\pi$
$347$	−10.9516	+	2.93447i	−0.587912	+	0.157531i	−0.0474135	+	0.998875i	$0.515098\pi$
$348$		0			0
$349$	6.80786			0.364417			0.182208	−	0.983260i	$-0.441675\pi$
$349$	6.80786			0.364417			0.182208	+	0.983260i	$0.441675\pi$
$350$	−1.67853	−	13.1218i	−0.0897211	−	0.701392i
$351$		0			0
$352$	0.679515	−	2.53598i	0.0362183	−	0.135168i
$353$	26.8765	−	7.20154i	1.43049	−	0.383299i	0.541299	−	0.840830i	$-0.317933\pi$
$353$	26.8765	−	7.20154i	1.43049	−	0.383299i	0.889194	+	0.457531i	$0.151266\pi$
$354$		0			0
$355$	−18.6967	+	0.832559i	−0.992320	+	0.0441877i
$356$		−	0.162532i		−	0.00861419i
$357$		0			0
$358$	14.3331	−	14.3331i	0.757528	−	0.757528i
$359$	11.8979	−	6.86927i	0.627948	−	0.362546i	−0.152009	−	0.988379i	$-0.548574\pi$
$359$	11.8979	−	6.86927i	0.627948	−	0.362546i	0.779957	+	0.625833i	$0.215241\pi$
$360$		0			0
$361$	−1.32204	+	2.28984i	−0.0695809	+	0.120518i
$362$	−7.26992	−	1.94797i	−0.382098	−	0.102383i
$363$		0			0
$364$	−2.42914	−	3.85887i	−0.127322	−	0.202260i
$365$	29.1079	−	9.20544i	1.52358	−	0.481835i
$366$		0			0
$367$	6.52689	+	24.3587i	0.340701	+	1.27151i	0.897555	+	0.440903i	$0.145342\pi$
$367$	6.52689	+	24.3587i	0.340701	+	1.27151i	−0.556854	+	0.830610i	$0.687992\pi$
$368$	−1.32840	−	4.95766i	−0.0692477	−	0.258436i
$369$		0			0
$370$	7.85302	+	4.07937i	0.408259	+	0.212077i
$371$	12.0928	+	19.2103i	0.627827	+	0.997348i
$372$		0			0
$373$	−25.9391	−	6.95037i	−1.34308	−	0.359876i	−0.485502	−	0.874235i	$-0.661363\pi$
$373$	−25.9391	−	6.95037i	−1.34308	−	0.359876i	−0.857575	+	0.514359i	$0.828030\pi$
$374$	−9.93774	+	17.2127i	−0.513868	+	0.890046i
$375$		0			0
$376$	−5.49038	+	3.16987i	−0.283145	+	0.163474i
$377$	−7.30472	+	7.30472i	−0.376212	+	0.376212i
$378$		0			0
$379$		−	3.51982i		−	0.180801i	−0.995905	−	0.0904005i	$-0.971185\pi$
$379$		−	3.51982i		−	0.180801i	0.995905	−	0.0904005i	$-0.0288147\pi$
$380$	−0.462779	−	10.3926i	−0.0237401	−	0.533129i
$381$		0			0
$382$	4.18042	−	1.12014i	0.213889	−	0.0573114i
$383$	−2.31980	+	8.65762i	−0.118536	+	0.442384i	−0.999527	−	0.0307499i	$-0.990210\pi$
$383$	−2.31980	+	8.65762i	−0.118536	+	0.442384i	0.880991	+	0.473133i	$0.156877\pi$
$384$		0			0
$385$	−2.76656	+	15.2840i	−0.140997	+	0.778943i
$386$	21.2681			1.08252
$387$		0			0
$388$	5.94601	−	1.59323i	0.301863	−	0.0808840i
$389$	27.3119	+	15.7685i	1.38477	+	0.799497i	0.992720	−	0.120447i	$-0.0384329\pi$
$389$	27.3119	+	15.7685i	1.38477	+	0.799497i	0.392049	+	0.919944i	$0.371766\pi$
$390$		0			0
$391$			38.8551i			1.96499i
$392$	−1.29000	+	6.88011i	−0.0651548	+	0.347498i
$393$		0			0
$394$	17.3073	−	9.99238i	0.871930	−	0.503409i
$395$	−16.9539	+	10.8215i	−0.853043	+	0.544489i
$396$		0			0
$397$	−6.00656	−	1.60945i	−0.301461	−	0.0807762i	0.104918	−	0.994481i	$-0.466542\pi$
$397$	−6.00656	−	1.60945i	−0.301461	−	0.0807762i	−0.406379	+	0.913705i	$0.633209\pi$
$398$	−0.596847	−	0.596847i	−0.0299172	−	0.0299172i
$399$		0			0
$400$	2.87498	+	4.09078i	0.143749	+	0.204539i
$401$	−10.2570	−	17.7657i	−0.512211	−	0.887176i	−0.999900	−	0.0141584i	$-0.995493\pi$
$401$	−10.2570	−	17.7657i	−0.512211	−	0.887176i	0.487688	−	0.873018i	$-0.337840\pi$
$402$		0			0
$403$	−4.46136	−	16.6500i	−0.222236	−	0.829396i
$404$	−3.83699	−	6.64586i	−0.190897	−	0.330644i
$405$		0			0
$406$	15.8473	−	0.606094i	0.786489	−	0.0300799i
$407$	−7.34708	−	7.34708i	−0.364181	−	0.364181i
$408$		0			0
$409$	12.8256	−	22.2145i	0.634184	−	1.09844i	−0.352504	−	0.935810i	$-0.614670\pi$
$409$	12.8256	−	22.2145i	0.634184	−	1.09844i	0.986687	−	0.162628i	$-0.0519970\pi$
$410$	12.2149	+	2.69687i	0.603251	+	0.133189i
$411$		0			0
$412$	2.87646	−	2.87646i	0.141713	−	0.141713i
$413$	4.52881	−	19.9180i	0.222848	−	0.980099i
$414$		0			0
$415$	−18.6551	−	17.0645i	−0.915740	−	0.837662i
$416$	1.49254	+	0.861717i	0.0731777	+	0.0422492i
$417$		0			0
$418$	−3.16132	+	11.7982i	−0.154625	+	0.577069i
$419$	−1.54146			−0.0753054			−0.0376527	−	0.999291i	$-0.511988\pi$
$419$	−1.54146			−0.0753054			−0.0376527	+	0.999291i	$0.511988\pi$
$420$		0			0
$421$	−20.0850			−0.978884			−0.489442	−	0.872036i	$-0.662800\pi$
$421$	−20.0850			−0.978884			−0.489442	+	0.872036i	$0.662800\pi$
$422$	5.74175	−	21.4285i	0.279504	−	1.04312i
$423$		0			0
$424$	−7.43018	−	4.28981i	−0.360841	−	0.208332i
$425$	−13.0077	−	35.5464i	−0.630966	−	1.72425i
$426$		0			0
$427$	8.64788	−	9.33568i	0.418500	−	0.451785i
$428$	−1.99197	+	1.99197i	−0.0962855	+	0.0962855i
$429$		0			0
$430$	−0.928509	−	1.45468i	−0.0447767	−	0.0701510i
$431$	10.9503	−	18.9665i	0.527457	−	0.913583i	−0.472030	−	0.881582i	$-0.656479\pi$
$431$	10.9503	−	18.9665i	0.527457	−	0.913583i	0.999488	−	0.0320007i	$-0.0101879\pi$
$432$		0			0
$433$	−5.51584	−	5.51584i	−0.265074	−	0.265074i	0.562038	−	0.827112i	$-0.310018\pi$
$433$	−5.51584	−	5.51584i	−0.265074	−	0.265074i	−0.827112	+	0.562038i	$0.810018\pi$
$434$	−12.3456	+	23.4058i	−0.592606	+	1.12352i
$435$		0			0
$436$	6.08031	+	10.5314i	0.291194	+	0.504362i
$437$	6.18014	+	23.0646i	0.295636	+	1.10333i
$438$		0			0
$439$	2.62203	+	4.54150i	0.125143	+	0.216754i	0.921789	−	0.387692i	$-0.126728\pi$
$439$	2.62203	+	4.54150i	0.125143	+	0.216754i	−0.796646	+	0.604446i	$0.793394\pi$
$440$	−1.77020	−	5.59742i	−0.0843909	−	0.266847i
$441$		0			0
$442$	−9.22560	−	9.22560i	−0.438817	−	0.438817i
$443$	1.25609	+	0.336567i	0.0596784	+	0.0159908i	0.288535	−	0.957469i	$-0.406832\pi$
$443$	1.25609	+	0.336567i	0.0596784	+	0.0159908i	−0.228856	+	0.973460i	$0.573499\pi$
$444$		0			0
$445$	−0.195538	−	0.306347i	−0.00926940	−	0.0145222i
$446$	13.1822	−	7.61073i	0.624194	−	0.360378i
$447$		0			0
$448$	−0.781940	−	2.52756i	−0.0369432	−	0.119416i
$449$			22.3625i			1.05535i	0.849445	+	0.527676i	$0.176937\pi$
$449$			22.3625i			1.05535i	−0.849445	+	0.527676i	$0.823063\pi$
$450$		0			0
$451$	−12.7196	−	7.34366i	−0.598942	−	0.345799i
$452$	2.23858	−	0.599825i	0.105294	−	0.0282134i
$453$		0			0
$454$	−3.73858			−0.175460
$455$	−9.22104	−	4.35090i	−0.432289	−	0.203973i
$456$		0			0
$457$	0.853971	−	3.18706i	0.0399471	−	0.149085i	−0.943072	−	0.332589i	$-0.892078\pi$
$457$	0.853971	−	3.18706i	0.0399471	−	0.149085i	0.983019	+	0.183505i	$0.0587443\pi$
$458$	14.6644	−	3.92933i	0.685225	−	0.183605i
$459$		0			0
$460$	−8.46825	−	7.74622i	−0.394834	−	0.361169i
$461$		−	6.97417i		−	0.324819i	−0.986723	−	0.162410i	$-0.948073\pi$
$461$		−	6.97417i		−	0.324819i	0.986723	−	0.162410i	$-0.0519266\pi$
$462$		0			0
$463$	16.6658	−	16.6658i	0.774527	−	0.774527i	−0.204367	−	0.978894i	$-0.565514\pi$
$463$	16.6658	−	16.6658i	0.774527	−	0.774527i	0.978894	+	0.204367i	$0.0655136\pi$
$464$	−5.19104	+	2.99705i	−0.240988	+	0.139135i
$465$		0			0
$466$	−0.606518	+	1.05052i	−0.0280964	+	0.0486644i
$467$	11.0696	+	2.96609i	0.512240	+	0.137254i	0.505675	−	0.862724i	$-0.331244\pi$
$467$	11.0696	+	2.96609i	0.512240	+	0.137254i	0.00656516	+	0.999978i	$0.497910\pi$
$468$		0			0
$469$	5.73959	−	3.61305i	0.265030	−	0.166835i
$470$	−6.53489	+	12.5800i	−0.301432	+	0.580273i
$471$		0			0
$472$	1.99819	+	7.45736i	0.0919744	+	0.343253i
$473$	0.524436	+	1.95722i	0.0241136	+	0.0899932i
$474$		0			0
$475$	−13.3753	−	19.0316i	−0.613702	−	0.873231i
$476$	0.765475	+	20.0146i	0.0350855	+	0.917367i
$477$		0			0
$478$	−15.6087	−	4.18234i	−0.713926	−	0.191296i
$479$	5.05860	−	8.76174i	0.231133	−	0.400334i	−0.727009	−	0.686628i	$-0.759090\pi$
$479$	5.05860	−	8.76174i	0.231133	−	0.400334i	0.958142	+	0.286294i	$0.0924234\pi$
$480$		0			0
$481$	5.90680	−	3.41029i	0.269327	−	0.155496i
$482$	−17.8310	+	17.8310i	−0.812180	+	0.812180i
$483$		0			0
$484$		−	4.10705i		−	0.186684i
$485$	9.29050	−	10.1565i	0.421860	−	0.461182i
$486$		0			0
$487$	35.6908	−	9.56331i	1.61730	−	0.433355i	0.667095	−	0.744972i	$-0.267537\pi$
$487$	35.6908	−	9.56331i	1.61730	−	0.433355i	0.950208	+	0.311617i	$0.100871\pi$
$488$	−1.24487	+	4.64593i	−0.0563528	+	0.210311i
$489$		0			0
$490$	5.84583	+	14.5199i	0.264088	+	0.655940i
$491$	8.00737			0.361368			0.180684	−	0.983541i	$-0.442169\pi$
$491$	8.00737			0.361368			0.180684	+	0.983541i	$0.442169\pi$
$492$		0			0
$493$	43.8311	−	11.7445i	1.97405	−	0.528946i
$494$	−6.94376	−	4.00898i	−0.312415	−	0.180373i
$495$		0			0
$496$		−	10.0018i		−	0.449092i
$497$	21.1550	−	6.54463i	0.948932	−	0.293567i
$498$		0			0
$499$	−10.3636	+	5.98341i	−0.463937	+	0.267854i	−0.713698	−	0.700453i	$-0.752981\pi$
$499$	−10.3636	+	5.98341i	−0.463937	+	0.267854i	0.249761	+	0.968307i	$0.419648\pi$
$500$	10.3404	+	4.25165i	0.462436	+	0.190140i
$501$		0			0
$502$	−2.00487	−	0.537203i	−0.0894816	−	0.0239765i
$503$	20.3121	+	20.3121i	0.905670	+	0.905670i	0.995919	−	0.0902493i	$-0.0287664\pi$
$503$	20.3121	+	20.3121i	0.905670	+	0.905670i	−0.0902493	+	0.995919i	$0.528766\pi$
$504$		0			0
$505$	−15.2276	−	7.91019i	−0.677617	−	0.351999i
$506$	6.73760	+	11.6699i	0.299523	+	0.518789i
$507$		0			0
$508$	−2.48759	−	9.28381i	−0.110369	−	0.411902i
$509$	14.7797	+	25.5992i	0.655098	+	1.13466i	0.981869	+	0.189559i	$0.0607060\pi$
$509$	14.7797	+	25.5992i	0.655098	+	1.13466i	−0.326771	+	0.945103i	$0.605961\pi$
$510$		0			0
$511$	−30.5696	+	19.2435i	−1.35232	+	0.851281i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−2.25111	+	3.89904i	−0.0992922	+	0.171979i
$515$	1.96107	−	8.88224i	0.0864150	−	0.391398i
$516$		0			0
$517$	11.7695	−	11.7695i	0.517624	−	0.517624i
$518$	−10.2101	−	2.32151i	−0.448607	−	0.102001i
$519$		0			0
$520$	3.84990	−	0.171435i	0.168829	−	0.00751791i
$521$	7.64664	+	4.41479i	0.335005	+	0.193415i	0.658061	−	0.752964i	$-0.271377\pi$
$521$	7.64664	+	4.41479i	0.335005	+	0.193415i	−0.323056	+	0.946380i	$0.604710\pi$
$522$		0			0
$523$	10.6856	−	39.8792i	0.467249	−	1.74380i	−0.182076	−	0.983284i	$-0.558282\pi$
$523$	10.6856	−	39.8792i	0.467249	−	1.74380i	0.649325	−	0.760511i	$-0.275052\pi$
$524$	−4.23598			−0.185050
$525$		0			0
$526$	−22.3996			−0.976669
$527$	−19.5969	+	73.1366i	−0.853654	+	3.18588i
$528$		0			0
$529$	2.89515	+	1.67152i	0.125876	+	0.0726746i
$530$	−19.1656	+	0.853439i	−0.832502	+	0.0370710i
$531$		0			0
$532$	3.63784	+	11.7590i	0.157720	+	0.509818i
$533$	6.81741	−	6.81741i	0.295295	−	0.295295i
$534$		0			0
$535$	−1.35806	+	6.15103i	−0.0587139	+	0.265932i
$536$	−1.28170	+	2.21997i	−0.0553610	+	0.0958880i
$537$		0			0
$538$	8.29027	+	8.29027i	0.357419	+	0.357419i
$539$	−1.40372	−	18.3244i	−0.0604625	−	0.789288i
$540$		0			0
$541$	12.7674	+	22.1137i	0.548911	+	0.950742i	0.998349	+	0.0574309i	$0.0182909\pi$
$541$	12.7674	+	22.1137i	0.548911	+	0.950742i	−0.449438	+	0.893311i	$0.648376\pi$
$542$	−6.22384	−	23.2277i	−0.267337	−	0.997714i
$543$		0			0
$544$	−3.78517	−	6.55610i	−0.162288	−	0.281090i
$545$	24.1304	+	12.5349i	1.03363	+	0.536937i
$546$		0			0
$547$	22.6183	+	22.6183i	0.967087	+	0.967087i	0.999475	−	0.0323883i	$-0.0103113\pi$
$547$	22.6183	+	22.6183i	0.967087	+	0.967087i	−0.0323883	+	0.999475i	$0.510311\pi$
$548$	7.98108	+	2.13852i	0.340935	+	0.0913532i
$549$		0			0
$550$	−10.0706	−	8.42056i	−0.429414	−	0.359054i
$551$	24.1504	−	13.9432i	1.02884	−	0.594002i
$552$		0			0
$553$	16.1725	−	17.4587i	0.687723	−	0.742420i
$554$		−	27.1973i		−	1.15550i
$555$		0			0
$556$	−8.09784	−	4.67529i	−0.343425	−	0.198277i
$557$	−16.9420	+	4.53960i	−0.717856	+	0.192349i	−0.599215	−	0.800588i	$-0.704520\pi$
$557$	−16.9420	+	4.53960i	−0.717856	+	0.192349i	−0.118641	+	0.992937i	$0.537854\pi$
$558$		0			0
$559$	−1.33011			−0.0562578
$560$	−4.51467	−	3.82331i	−0.190780	−	0.161565i
$561$		0			0
$562$	−5.74352	+	21.4351i	−0.242276	+	0.904186i
$563$	−15.0854	+	4.04211i	−0.635772	+	0.170355i	−0.562288	−	0.826942i	$-0.690079\pi$
$563$	−15.0854	+	4.04211i	−0.635772	+	0.170355i	−0.0734847	+	0.997296i	$0.523412\pi$
$564$		0			0
$565$	3.49772	−	3.82374i	0.147150	−	0.160866i
$566$		−	11.1028i		−	0.466684i
$567$		0			0
$568$	−5.91829	+	5.91829i	−0.248326	+	0.248326i
$569$	−15.5107	+	8.95511i	−0.650243	+	0.375418i	−0.788549	−	0.614972i	$-0.789167\pi$
$569$	−15.5107	+	8.95511i	−0.650243	+	0.375418i	0.138307	+	0.990389i	$0.455834\pi$
$570$		0			0
$571$	10.2340	−	17.7258i	0.428278	−	0.741800i	−0.568442	−	0.822723i	$-0.692454\pi$
$571$	10.2340	−	17.7258i	0.428278	−	0.741800i	0.996720	+	0.0809234i	$0.0257869\pi$
$572$	−4.37060	−	1.17110i	−0.182744	−	0.0489661i
$573$		0			0
$574$	−14.7901	+	0.565661i	−0.617327	+	0.0236102i
$575$	−25.2805	−	4.41246i	−1.05427	−	0.184012i
$576$		0			0
$577$	6.62634	+	24.7298i	0.275858	+	1.02952i	0.955264	+	0.295754i	$0.0955708\pi$
$577$	6.62634	+	24.7298i	0.275858	+	1.02952i	−0.679406	+	0.733763i	$0.737762\pi$
$578$	10.4330	+	38.9364i	0.433955	+	1.61954i
$579$		0			0
$580$	−6.17860	+	11.8942i	−0.256553	+	0.493878i
$581$	26.4596	+	13.9563i	1.09773	+	0.579006i
$582$		0			0
$583$	21.7578	+	5.82998i	0.901116	+	0.241453i
$584$	6.82646	−	11.8238i	0.282481	−	0.489271i
$585$		0			0
$586$	−7.98019	+	4.60737i	−0.329659	+	0.190329i
$587$	26.2627	−	26.2627i	1.08398	−	1.08398i	0.0878438	−	0.996134i	$-0.472002\pi$
$587$	26.2627	−	26.2627i	1.08398	−	1.08398i	0.996134	−	0.0878438i	$-0.0279977\pi$
$588$		0			0
$589$			46.5313i			1.91729i
$590$	12.7380	+	11.6520i	0.524416	+	0.479703i
$591$		0			0
$592$	3.82271	−	1.02429i	0.157112	−	0.0420981i
$593$	2.49114	−	9.29705i	0.102299	−	0.381784i	−0.895726	−	0.444606i	$-0.853344\pi$
$593$	2.49114	−	9.29705i	0.102299	−	0.381784i	0.998025	+	0.0628225i	$0.0200102\pi$
$594$		0			0
$595$	25.5218	+	36.8033i	1.04629	+	1.50879i
$596$	−4.75815			−0.194902
$597$		0			0
$598$	−8.54420	+	2.28941i	−0.349398	+	0.0936210i
$599$	−3.36700	−	1.94394i	−0.137572	−	0.0794273i	0.429634	−	0.903003i	$-0.358642\pi$
$599$	−3.36700	−	1.94394i	−0.137572	−	0.0794273i	−0.567206	+	0.823576i	$0.691976\pi$
$600$		0			0
$601$		−	36.4068i		−	1.48506i	−0.669811	−	0.742531i	$-0.733625\pi$
$601$		−	36.4068i		−	1.48506i	0.669811	−	0.742531i	$-0.266375\pi$
$602$	1.49800	+	1.38763i	0.0610538	+	0.0565557i
$603$		0			0
$604$	1.86294	−	1.07557i	0.0758020	−	0.0437643i
$605$	−4.94108	−	7.74112i	−0.200883	−	0.314721i
$606$		0			0
$607$	6.68399	+	1.79097i	0.271295	+	0.0726932i	0.391902	−	0.920007i	$-0.371817\pi$
$607$	6.68399	+	1.79097i	0.271295	+	0.0726932i	−0.120607	+	0.992700i	$0.538484\pi$
$608$	−3.28969	−	3.28969i	−0.133414	−	0.133414i
$609$		0			0
$610$	3.24301	+	10.2545i	0.131306	+	0.415193i
$611$	5.46307	+	9.46231i	0.221012	+	0.382804i
$612$		0			0
$613$	11.5346	+	43.0478i	0.465880	+	1.73869i	0.653957	+	0.756532i	$0.273108\pi$
$613$	11.5346	+	43.0478i	0.465880	+	1.73869i	−0.188077	+	0.982154i	$0.560225\pi$
$614$	14.5671	+	25.2310i	0.587881	+	1.01824i
$615$		0			0
$616$	3.70050	+	5.87851i	0.149098	+	0.236852i
$617$	−8.27627	−	8.27627i	−0.333190	−	0.333190i	0.520607	−	0.853797i	$-0.325706\pi$
$617$	−8.27627	−	8.27627i	−0.333190	−	0.333190i	−0.853797	+	0.520607i	$0.825706\pi$
$618$		0			0
$619$	−5.79761	+	10.0418i	−0.233026	+	0.403612i	−0.958697	−	0.284429i	$-0.908196\pi$
$619$	−5.79761	+	10.0418i	−0.233026	+	0.403612i	0.725671	+	0.688042i	$0.241529\pi$
$620$	−12.0328	−	18.8517i	−0.483250	−	0.757102i
$621$		0			0
$622$	−23.2400	+	23.2400i	−0.931840	+	0.931840i
$623$	0.315469	+	0.292227i	0.0126390	+	0.0117078i
$624$		0			0
$625$	24.6050	−	4.42656i	0.984200	−	0.177062i
$626$	19.2111	+	11.0915i	0.767831	+	0.443307i
$627$		0			0
$628$	0.984635	−	3.67471i	0.0392912	−	0.146637i
$629$	−29.9600			−1.19458
$630$		0			0
$631$	2.25813			0.0898949			0.0449474	−	0.998989i	$-0.485688\pi$
$631$	2.25813			0.0898949			0.0449474	+	0.998989i	$0.485688\pi$
$632$	−2.32805	+	8.68839i	−0.0926047	+	0.345606i
$633$		0			0
$634$	−12.4400	−	7.18226i	−0.494057	−	0.285244i
$635$	−15.8578	−	14.5057i	−0.629298	−	0.575642i
$636$		0			0
$637$	11.8574	+	2.22323i	0.469808	+	0.0880875i
$638$	11.1279	−	11.1279i	0.440556	−	0.440556i
$639$		0			0
$640$	2.18348	+	0.482081i	0.0863097	+	0.0190559i
$641$	9.61246	−	16.6493i	0.379669	−	0.657607i	−0.611345	−	0.791364i	$-0.709371\pi$
$641$	9.61246	−	16.6493i	0.379669	−	0.657607i	0.991014	+	0.133758i	$0.0427044\pi$
$642$		0			0
$643$	15.5634	+	15.5634i	0.613760	+	0.613760i	0.943924	−	0.330163i	$-0.107104\pi$
$643$	15.5634	+	15.5634i	0.613760	+	0.613760i	−0.330163	+	0.943924i	$0.607104\pi$
$644$	12.0110	+	6.33531i	0.473301	+	0.249646i
$645$		0			0
$646$	17.6098	+	30.5011i	0.692848	+	1.20005i
$647$	2.55828	+	9.54764i	0.100577	+	0.375357i	0.997806	−	0.0662082i	$-0.0210902\pi$
$647$	2.55828	+	9.54764i	0.100577	+	0.375357i	−0.897229	+	0.441565i	$0.854423\pi$
$648$		0			0
$649$	−10.1348	−	17.5539i	−0.397825	−	0.689053i
$650$	7.05019	−	4.95484i	0.276531	−	0.194345i
$651$		0			0
$652$	3.15459	+	3.15459i	0.123543	+	0.123543i
$653$	−9.61337	−	2.57589i	−0.376200	−	0.100803i	0.0657640	−	0.997835i	$-0.479052\pi$
$653$	−9.61337	−	2.57589i	−0.376200	−	0.100803i	−0.441964	+	0.897033i	$0.645718\pi$
$654$		0			0
$655$	−7.98413	+	5.09619i	−0.311966	+	0.199125i
$656$	4.84474	−	2.79711i	0.189155	−	0.109209i
$657$		0			0
$658$	3.71890	−	16.3559i	0.144978	−	0.637620i
$659$		−	16.2333i		−	0.632360i	−0.948699	−	0.316180i	$-0.897600\pi$
$659$		−	16.2333i		−	0.632360i	0.948699	−	0.316180i	$-0.102400\pi$
$660$		0			0
$661$	−8.77097	−	5.06392i	−0.341151	−	0.196964i	0.319630	−	0.947543i	$-0.396441\pi$
$661$	−8.77097	−	5.06392i	−0.341151	−	0.196964i	−0.660781	+	0.750579i	$0.729775\pi$
$662$	2.79217	−	0.748160i	0.108521	−	0.0290780i
$663$		0			0
$664$	−11.3067			−0.438785
$665$	21.0037	+	17.7873i	0.814489	+	0.689761i
$666$		0			0
$667$	7.96256	−	29.7167i	0.308312	−	1.15064i
$668$	22.0377	−	5.90499i	0.852665	−	0.228471i
$669$		0			0
$670$	0.254988	+	5.72626i	0.00985105	+	0.221225i
$671$		−	12.6279i		−	0.487495i
$672$		0			0
$673$	15.2038	−	15.2038i	0.586062	−	0.586062i	−0.350501	−	0.936563i	$-0.613989\pi$
$673$	15.2038	−	15.2038i	0.586062	−	0.586062i	0.936563	+	0.350501i	$0.113989\pi$
$674$	−28.7145	+	16.5783i	−1.10604	+	0.638574i
$675$		0			0
$676$	−5.01489	+	8.68604i	−0.192880	+	0.334078i
$677$	−11.6492	−	3.12140i	−0.447716	−	0.119965i	0.0279145	−	0.999610i	$-0.491113\pi$
$677$	−11.6492	−	3.12140i	−0.447716	−	0.119965i	−0.475630	+	0.879645i	$0.657780\pi$
$678$		0			0
$679$	−7.59832	+	14.4056i	−0.291597	+	0.552834i
$680$	−15.0219	−	7.80336i	−0.576063	−	0.299245i
$681$		0			0
$682$	6.79634	+	25.3643i	0.260245	+	0.971248i
$683$	−3.03256	−	11.3177i	−0.116038	−	0.433058i	0.883325	−	0.468761i	$-0.155300\pi$
$683$	−3.03256	−	11.3177i	−0.116038	−	0.433058i	−0.999362	+	0.0357033i	$0.988633\pi$
$684$		0			0
$685$	17.6158	−	5.57105i	0.673067	−	0.212859i
$686$	−11.0347	−	14.8740i	−0.421305	−	0.567893i
$687$		0			0
$688$	−0.745483	−	0.199752i	−0.0284213	−	0.00761546i
$689$	−7.39321	+	12.8054i	−0.281659	+	0.487848i
$690$		0			0
$691$	−24.8579	+	14.3517i	−0.945639	+	0.545965i	−0.891723	−	0.452581i	$-0.850503\pi$
$691$	−24.8579	+	14.3517i	−0.945639	+	0.545965i	−0.0539153	+	0.998546i	$0.517170\pi$
$692$	−8.75557	+	8.75557i	−0.332837	+	0.332837i
$693$		0			0
$694$			11.3379i			0.430382i
$695$	−20.8878	+	0.930128i	−0.792321	+	0.0352818i
$696$		0			0
$697$	−40.9071	+	10.9610i	−1.54947	+	0.415178i
$698$	1.76200	−	6.57589i	0.0666929	−	0.248901i
$699$		0			0
$700$	−13.1092	−	1.77485i	−0.495479	−	0.0670829i
$701$	−47.8761			−1.80825			−0.904127	−	0.427264i	$-0.859477\pi$
$701$	−47.8761			−1.80825			−0.904127	+	0.427264i	$0.859477\pi$
$702$		0			0
$703$	−17.7844	+	4.76533i	−0.670753	+	0.179728i
$704$	−2.27370	−	1.31272i	−0.0856933	−	0.0494751i
$705$		0			0
$706$		−	27.8246i		−	1.04719i
$707$	19.7981	+	4.50156i	0.744585	+	0.169299i
$708$		0			0
$709$	−22.0830	+	12.7496i	−0.829343	+	0.478822i	−0.853628	−	0.520883i	$-0.825603\pi$
$709$	−22.0830	+	12.7496i	−0.829343	+	0.478822i	0.0242844	+	0.999705i	$0.492269\pi$
$710$	−4.03488	+	18.2752i	−0.151427	+	0.685854i
$711$		0			0
$712$	−0.156994	−	0.0420664i	−0.00588360	−	0.00157651i
$713$	36.2989	+	36.2989i	1.35941	+	1.35941i
$714$		0			0
$715$	−9.64679	+	3.05082i	−0.360770	+	0.114094i
$716$	−10.1350	−	17.5544i	−0.378764	−	0.656038i
$717$		0			0
$718$	−3.55579	−	13.2704i	−0.132701	−	0.495247i
$719$	16.0438	+	27.7887i	0.598333	+	1.03634i	0.993067	+	0.117548i	$0.0375033\pi$
$719$	16.0438	+	27.7887i	0.598333	+	1.03634i	−0.394734	+	0.918795i	$0.629163\pi$
$720$		0			0
$721$	0.411329	+	10.7549i	0.0153187	+	0.400532i
$722$	1.86964	+	1.86964i	0.0695809	+	0.0695809i
$723$		0			0
$724$	−3.76319	+	6.51803i	−0.139858	+	0.242241i
$725$	2.66387	+	29.8519i	0.0989336	+	1.10867i
$726$		0			0
$727$	11.3772	−	11.3772i	0.421956	−	0.421956i	−0.463921	−	0.885877i	$-0.653558\pi$
$727$	11.3772	−	11.3772i	0.421956	−	0.421956i	0.885877	+	0.463921i	$0.153558\pi$
$728$	−4.35609	+	1.34762i	−0.161447	+	0.0499462i
$729$		0			0
$730$	−1.35809	−	30.4986i	−0.0502652	−	1.12880i
$731$	5.05987	+	2.92132i	0.187146	+	0.108049i
$732$		0			0
$733$	5.43607	−	20.2877i	0.200786	−	0.749343i	−0.789907	−	0.613226i	$-0.789871\pi$
$733$	5.43607	−	20.2877i	0.200786	−	0.749343i	0.990693	−	0.136116i	$-0.0434620\pi$
$734$	25.2180			0.930812
$735$		0			0
$736$	−5.13255			−0.189188
$737$	1.74187	−	6.50073i	0.0641625	−	0.239458i
$738$		0			0
$739$	31.8347	+	18.3797i	1.17106	+	0.676110i	0.953929	−	0.300033i	$-0.0969977\pi$
$739$	31.8347	+	18.3797i	1.17106	+	0.676110i	0.217128	+	0.976143i	$0.430331\pi$
$740$	5.97289	−	6.52962i	0.219568	−	0.240033i
$741$		0			0
$742$	21.6855	−	6.70876i	0.796101	−	0.246286i
$743$	17.1637	−	17.1637i	0.629676	−	0.629676i	−0.318310	−	0.947987i	$-0.603115\pi$
$743$	17.1637	−	17.1637i	0.629676	−	0.629676i	0.947987	+	0.318310i	$0.103115\pi$
$744$		0			0
$745$	−8.96835	+	5.72441i	−0.328575	+	0.209726i
$746$	−13.4271	+	23.2564i	−0.491600	+	0.851477i
$747$		0			0
$748$	14.0541	+	14.0541i	0.513868	+	0.513868i
$749$	−0.284849	−	7.44782i	−0.0104081	−	0.272138i
$750$		0			0
$751$	−15.1318	−	26.2091i	−0.552168	−	0.956384i	−0.998118	−	0.0613255i	$-0.980467\pi$
$751$	−15.1318	−	26.2091i	−0.552168	−	0.956384i	0.445949	−	0.895058i	$-0.352866\pi$
$752$	1.64085	+	6.12372i	0.0598355	+	0.223309i
$753$		0			0
$754$	5.16522	+	8.94642i	0.188106	+	0.325809i
$755$	2.21735	−	4.26853i	0.0806978	−	0.155348i
$756$		0			0
$757$	−1.48321	−	1.48321i	−0.0539082	−	0.0539082i	0.679639	−	0.733547i	$-0.262137\pi$
$757$	−1.48321	−	1.48321i	−0.0539082	−	0.0539082i	−0.733547	+	0.679639i	$0.762137\pi$
$758$	−3.39988	−	0.910996i	−0.123489	−	0.0330889i
$759$		0			0
$760$	−10.1583	−	2.24279i	−0.368479	−	0.0813547i
$761$	−5.99246	+	3.45975i	−0.217226	+	0.125416i	−0.604665	−	0.796480i	$-0.706693\pi$
$761$	−5.99246	+	3.45975i	−0.217226	+	0.125416i	0.387439	+	0.921895i	$0.373360\pi$
$762$		0			0
$763$	−31.3732	−	7.13342i	−1.13579	−	0.258247i
$764$		−	4.32789i		−	0.156578i
$765$		0			0
$766$	7.76221	+	4.48151i	0.280460	+	0.161924i
$767$	12.8523	−	3.44376i	0.464069	−	0.124347i
$768$		0			0
$769$	16.5757			0.597736			0.298868	−	0.954294i	$-0.403391\pi$
$769$	16.5757			0.597736			0.298868	+	0.954294i	$0.403391\pi$
$770$	14.0471	+	6.62807i	0.506224	+	0.238859i
$771$		0			0
$772$	5.50458	−	20.5434i	0.198114	−	0.739372i
$773$	6.48331	−	1.73720i	0.233189	−	0.0624827i	−0.140332	−	0.990104i	$-0.544817\pi$
$773$	6.48331	−	1.73720i	0.233189	−	0.0624827i	0.373521	+	0.927622i	$0.378150\pi$
$774$		0			0
$775$	−45.3599	−	21.0560i	−1.62938	−	0.756354i
$776$		−	6.15577i		−	0.220979i
$777$		0			0
$778$	22.3001	−	22.3001i	0.799497	−	0.799497i
$779$	−22.5393	+	13.0131i	−0.807554	+	0.466241i
$780$		0			0
$781$	10.9871	−	19.0303i	0.393150	−	0.680956i
$782$	37.5311	+	10.0564i	1.34211	+	0.359617i
$783$		0			0
$784$	6.31180	+	3.02675i	0.225421	+	0.108098i
$785$	−2.56506	−	8.11082i	−0.0915511	−	0.289488i
$786$		0			0
$787$	3.88207	+	14.4881i	0.138381	+	0.516444i	0.999961	+	0.00882263i	$0.00280837\pi$
$787$	3.88207	+	14.4881i	0.138381	+	0.516444i	−0.861580	+	0.507621i	$0.830525\pi$
$788$	−5.17244	−	19.3038i	−0.184260	−	0.687669i
$789$		0			0
$790$	6.06478	+	19.1770i	0.215775	+	0.682288i
$791$	−2.86064	+	5.42345i	−0.101713	+	0.192836i
$792$		0			0
$793$	8.00696	+	2.14546i	0.284335	+	0.0761874i
$794$	−3.10923	+	5.38534i	−0.110342	+	0.191118i
$795$		0			0
$796$	−0.730985	+	0.422034i	−0.0259091	+	0.0149586i
$797$	29.9616	−	29.9616i	1.06130	−	1.06130i	0.0633012	−	0.997994i	$-0.479837\pi$
$797$	29.9616	−	29.9616i	1.06130	−	1.06130i	0.997994	−	0.0633012i	$-0.0201629\pi$
$798$		0			0
$799$		−	47.9940i		−	1.69790i
$800$	4.69549	−	1.71825i	0.166011	−	0.0607491i
$801$		0			0
$802$	−19.8151	+	5.30943i	−0.699694	+	0.187482i
$803$	−9.27735	+	34.6236i	−0.327391	+	1.22184i
$804$		0			0
$805$	30.2607	−	2.50912i	1.06655	−	0.0884348i
$806$	−17.2374			−0.607160
$807$		0			0
$808$	−7.41249	+	1.98617i	−0.260771	+	0.0698732i
$809$	−7.51129	−	4.33664i	−0.264083	−	0.152468i	0.362113	−	0.932134i	$-0.382056\pi$
$809$	−7.51129	−	4.33664i	−0.264083	−	0.152468i	−0.626196	+	0.779666i	$0.715389\pi$
$810$		0			0
$811$		−	21.4366i		−	0.752741i	−0.926469	−	0.376370i	$-0.877172\pi$
$811$		−	21.4366i		−	0.752741i	0.926469	−	0.376370i	$-0.122828\pi$
$812$	3.51614	−	15.4642i	0.123392	−	0.542687i
$813$		0			0
$814$	−8.99830	+	5.19517i	−0.315390	+	0.182091i
$815$	9.74108	+	2.15069i	0.341215	+	0.0753353i
$816$		0			0
$817$	3.46822	+	0.929308i	0.121338	+	0.0325124i
$818$	−18.1381	−	18.1381i	−0.634184	−	0.634184i
$819$		0			0
$820$	5.76642	−	11.1007i	0.201372	−	0.387653i
$821$	9.59996	+	16.6276i	0.335041	+	0.580308i	0.983493	−	0.180948i	$-0.0579165\pi$
$821$	9.59996	+	16.6276i	0.335041	+	0.580308i	−0.648452	+	0.761256i	$0.724583\pi$
$822$		0			0
$823$	2.61193	+	9.74786i	0.0910462	+	0.339789i	0.996390	−	0.0848897i	$-0.0270538\pi$
$823$	2.61193	+	9.74786i	0.0910462	+	0.339789i	−0.905344	+	0.424679i	$0.860387\pi$
$824$	−2.03396	−	3.52293i	−0.0708564	−	0.122727i
$825$		0			0
$826$	−18.0671	−	9.52964i	−0.628636	−	0.331579i
$827$	2.93550	+	2.93550i	0.102077	+	0.102077i	0.756301	−	0.654224i	$-0.227005\pi$
$827$	2.93550	+	2.93550i	0.102077	+	0.102077i	−0.654224	+	0.756301i	$0.727005\pi$
$828$		0			0
$829$	0.316112	−	0.547523i	0.0109790	−	0.0190162i	−0.860484	−	0.509478i	$-0.829839\pi$
$829$	0.316112	−	0.547523i	0.0109790	−	0.0190162i	0.871463	+	0.490462i	$0.163172\pi$
$830$	−21.3113	+	13.6028i	−0.739726	+	0.472160i
$831$		0			0
$832$	1.21865	−	1.21865i	0.0422492	−	0.0422492i
$833$	−40.2238	−	34.4997i	−1.39367	−	1.19534i
$834$		0			0
$835$	34.4334	−	37.6429i	1.19162	−	1.30269i
$836$	10.5780	+	6.10720i	0.365847	+	0.211222i
$837$		0			0
$838$	−0.398960	+	1.48894i	−0.0137818	+	0.0514345i
$839$	7.93406			0.273914			0.136957	−	0.990577i	$-0.456268\pi$
$839$	7.93406			0.273914			0.136957	+	0.990577i	$0.456268\pi$
$840$		0			0
$841$	−6.92921			−0.238938
$842$	−5.19839	+	19.4006i	−0.179148	+	0.668590i
$843$		0			0
$844$	−19.2123	−	11.0922i	−0.661313	−	0.381809i
$845$	0.997689	+	22.4051i	0.0343215	+	0.770757i
$846$		0			0
$847$	7.97162	+	7.38432i	0.273908	+	0.253728i
$848$	−6.06671	+	6.06671i	−0.208332	+	0.208332i
$849$		0			0
$850$	−37.7018	+	3.36437i	−1.29316	+	0.115397i
$851$	−10.1562	+	17.5910i	−0.348149	+	0.603012i
$852$		0			0
$853$	−13.0203	−	13.0203i	−0.445806	−	0.445806i	0.448152	−	0.893957i	$-0.352082\pi$
$853$	−13.0203	−	13.0203i	−0.445806	−	0.445806i	−0.893957	+	0.448152i	$0.852082\pi$
$854$	−6.77934	−	10.7695i	−0.231984	−	0.368523i
$855$		0			0
$856$	1.40854	+	2.43966i	0.0481428	+	0.0833857i
$857$	2.95372	+	11.0234i	0.100897	+	0.376553i	0.997847	−	0.0655783i	$-0.0208892\pi$
$857$	2.95372	+	11.0234i	0.100897	+	0.376553i	−0.896950	+	0.442131i	$0.854223\pi$
$858$		0			0
$859$	−6.44883	−	11.1697i	−0.220031	−	0.381106i	0.734786	−	0.678299i	$-0.237283\pi$
$859$	−6.44883	−	11.1697i	−0.220031	−	0.381106i	−0.954817	+	0.297194i	$0.903949\pi$
$860$	−1.64543	+	0.520371i	−0.0561087	+	0.0177445i
$861$		0			0
$862$	−15.4861	−	15.4861i	−0.527457	−	0.527457i
$863$	−12.2574	−	3.28437i	−0.417248	−	0.111801i	0.0440862	−	0.999028i	$-0.485962\pi$
$863$	−12.2574	−	3.28437i	−0.417248	−	0.111801i	−0.461334	+	0.887226i	$0.652629\pi$
$864$		0			0
$865$	−5.96924	+	27.0364i	−0.202960	+	0.919266i
$866$	−6.75549	+	3.90028i	−0.229561	+	0.132537i
$867$		0			0
$868$	19.4130	+	17.9828i	0.658921	+	0.610375i
$869$		−	23.6156i		−	0.801103i
$870$		0			0
$871$	3.82597	+	2.20892i	0.129638	+	0.0748465i
$872$	11.7462	−	3.14740i	0.397778	−	0.106584i
$873$		0			0
$874$	23.8782			0.807694
$875$	−26.8439	+	12.4260i	−0.907490	+	0.420074i
$876$		0			0
$877$	−6.75617	+	25.2144i	−0.228140	+	0.851429i	0.752983	+	0.658040i	$0.228614\pi$
$877$	−6.75617	+	25.2144i	−0.228140	+	0.851429i	−0.981122	+	0.193388i	$0.938052\pi$
$878$	5.06538	−	1.35726i	0.170948	−	0.0458055i
$879$		0			0
$880$	−5.86486	+	0.261160i	−0.197704	+	0.00880370i
$881$		−	34.2689i		−	1.15455i	−0.816551	−	0.577274i	$-0.804116\pi$
$881$		−	34.2689i		−	1.15455i	0.816551	−	0.577274i	$-0.195884\pi$
$882$		0			0
$883$	−33.0880	+	33.0880i	−1.11350	+	1.11350i	−0.120827	+	0.992674i	$0.538555\pi$
$883$	−33.0880	+	33.0880i	−1.11350	+	1.11350i	−0.992674	+	0.120827i	$0.961445\pi$
$884$	−11.2990	+	6.52348i	−0.380027	+	0.219409i
$885$		0			0
$886$	0.650198	−	1.12618i	0.0218438	−	0.0378346i
$887$	18.3463	+	4.91587i	0.616008	+	0.165059i	0.553312	−	0.832974i	$-0.313364\pi$
$887$	18.3463	+	4.91587i	0.616008	+	0.165059i	0.0626958	+	0.998033i	$0.480030\pi$
$888$		0			0
$889$	22.4921	+	11.8636i	0.754361	+	0.397893i
$890$	−0.346518	+	0.109587i	−0.0116153	+	0.00367336i
$891$		0			0
$892$	−3.93960	−	14.7028i	−0.131908	−	0.492286i
$893$	−7.63374	−	28.4895i	−0.255453	−	0.953365i
$894$		0			0
$895$	−40.2221	−	20.8940i	−1.34448	−	0.698410i
$896$	−2.64382	+	0.101115i	−0.0883238	+	0.00337802i
$897$		0			0
$898$	21.6005	+	5.78785i	0.720819	+	0.193143i
$899$	29.9757	−	51.9195i	0.999747	−	1.73161i
$900$		0			0
$901$	56.2489	−	32.4753i	1.87392	−	1.08191i
$902$	−10.3855	+	10.3855i	−0.345799	+	0.345799i
$903$		0			0
$904$		−	2.31755i		−	0.0770804i
$905$	0.748669	+	16.8128i	0.0248866	+	0.558877i
$906$		0			0
$907$	−54.6185	+	14.6350i	−1.81358	+	0.485947i	−0.995959	−	0.0898120i	$-0.971373\pi$
$907$	−54.6185	+	14.6350i	−1.81358	+	0.485947i	−0.817620	+	0.575759i	$0.804707\pi$
$908$	−0.967615	+	3.61119i	−0.0321114	+	0.119842i
$909$		0			0
$910$	−6.58923	+	7.78074i	−0.218431	+	0.257929i
$911$	18.6286			0.617193			0.308596	−	0.951193i	$-0.400141\pi$
$911$	18.6286			0.617193			0.308596	+	0.951193i	$0.400141\pi$
$912$		0			0
$913$	28.6736	−	7.68307i	0.948958	−	0.254272i
$914$	−2.85744	−	1.64975i	−0.0945158	−	0.0545687i
$915$		0			0
$916$		−	15.1818i		−	0.501619i
$917$	7.61613	−	8.22187i	0.251507	−	0.271510i
$918$		0			0
$919$	−38.3850	+	22.1616i	−1.26620	+	0.731043i	−0.974268	−	0.225395i	$-0.927633\pi$
$919$	−38.3850	+	22.1616i	−1.26620	+	0.731043i	−0.291936	+	0.956438i	$0.594300\pi$
$920$	−9.67402	+	6.17483i	−0.318943	+	0.203578i
$921$		0			0
$922$	−6.73653	−	1.80505i	−0.221856	−	0.0594461i
$923$	10.1998	+	10.1998i	0.335730	+	0.335730i
$924$		0			0
$925$	3.40232	−	19.4931i	0.111867	−	0.640929i
$926$	−11.7845	−	20.4114i	−0.387264	−	0.670760i
$927$		0			0
$928$	1.55139	+	5.78985i	0.0509268	+	0.190061i
$929$	−7.02379	−	12.1656i	−0.230443	−	0.399139i	0.727496	−	0.686112i	$-0.240684\pi$
$929$	−7.02379	−	12.1656i	−0.230443	−	0.399139i	−0.957939	+	0.286973i	$0.907351\pi$
$930$		0			0
$931$	−29.3645	−	14.0814i	−0.962383	−	0.461499i
$932$	0.857745	+	0.857745i	0.0280964	+	0.0280964i
$933$		0			0
$934$	5.73005	−	9.92473i	0.187493	−	0.324747i
$935$	43.3978	+	9.58159i	1.41926	+	0.313351i
$936$		0			0
$937$	24.1561	−	24.1561i	0.789145	−	0.789145i	−0.192209	−	0.981354i	$-0.561565\pi$
$937$	24.1561	−	24.1561i	0.789145	−	0.789145i	0.981354	+	0.192209i	$0.0615652\pi$
$938$	−2.00442	−	6.47915i	−0.0654468	−	0.211552i
$939$		0			0
$940$	10.4600	+	9.56817i	0.341168	+	0.312079i
$941$	−45.3271	−	26.1696i	−1.47762	−	0.853106i	−0.477942	−	0.878391i	$-0.658617\pi$
$941$	−45.3271	−	26.1696i	−1.47762	−	0.853106i	−0.999680	+	0.0252856i	$0.991950\pi$
$942$		0			0
$943$	−7.43137	+	27.7343i	−0.241999	+	0.903152i
$944$	7.72043			0.251279
$945$		0			0
$946$	2.02627			0.0658796
$947$	10.0914	−	37.6614i	0.327925	−	1.22383i	−0.583414	−	0.812175i	$-0.698283\pi$
$947$	10.0914	−	37.6614i	0.327925	−	1.22383i	0.911339	−	0.411657i	$-0.135050\pi$
$948$		0			0
$949$	−20.3775	−	11.7649i	−0.661481	−	0.381906i
$950$	−21.8449	+	7.99383i	−0.708743	+	0.259354i
$951$		0			0
$952$	19.5307	+	4.44076i	0.632994	+	0.143926i
$953$	−1.45944	+	1.45944i	−0.0472759	+	0.0472759i	−0.730350	−	0.683074i	$-0.760643\pi$
$953$	−1.45944	+	1.45944i	−0.0472759	+	0.0472759i	0.683074	+	0.730350i	$0.260643\pi$
$954$		0			0
$955$	−5.20677	−	8.15738i	−0.168487	−	0.263967i
$956$	−8.07967	+	13.9944i	−0.261315	+	0.452611i
$957$		0			0
$958$	−7.15393	−	7.15393i	−0.231133	−	0.231133i
$959$	−18.5005	+	11.6460i	−0.597412	+	0.376068i
$960$		0			0
$961$	34.5175	+	59.7861i	1.11347	+	1.92858i
$962$	−1.76530	−	6.58818i	−0.0569155	−	0.212411i
$963$		0			0
$964$	12.6084	+	21.8384i	0.406090	+	0.703369i
$965$	−14.3399	−	45.3434i	−0.461619	−	1.45965i
$966$		0			0
$967$	11.2656	+	11.2656i	0.362279	+	0.362279i	0.864651	−	0.502373i	$-0.167539\pi$
$967$	11.2656	+	11.2656i	0.362279	+	0.362279i	−0.502373	+	0.864651i	$0.667539\pi$
$968$	−3.96710	−	1.06298i	−0.127508	−	0.0341655i
$969$		0			0
$970$	−7.40584	−	11.6026i	−0.237787	−	0.372538i
$971$	8.48873	−	4.90097i	0.272416	−	0.157280i	−0.357569	−	0.933887i	$-0.616394\pi$
$971$	8.48873	−	4.90097i	0.272416	−	0.157280i	0.629985	+	0.776607i	$0.283061\pi$
$972$		0			0
$973$	23.6342	−	7.31160i	0.757677	−	0.234399i
$974$		−	36.9498i		−	1.18395i
$975$		0			0
$976$	4.16543	+	2.40491i	0.133332	+	0.0769793i
$977$	−47.6370	+	12.7643i	−1.52404	+	0.408366i	−0.921071	−	0.389395i	$-0.872684\pi$
$977$	−47.6370	+	12.7643i	−1.52404	+	0.408366i	−0.602973	+	0.797762i	$0.706017\pi$
$978$		0			0
$979$	0.426719			0.0136380
$980$	15.5381	−	1.88863i	0.496347	−	0.0603300i
$981$		0			0
$982$	2.07246	−	7.73453i	0.0661349	−	0.246819i
$983$	5.77152	−	1.54648i	0.184083	−	0.0493249i	−0.165600	−	0.986193i	$-0.552956\pi$
$983$	5.77152	−	1.54648i	0.184083	−	0.0493249i	0.349683	+	0.936868i	$0.386289\pi$
$984$		0			0
$985$	−32.9731	−	30.1617i	−1.05061	−	0.961032i
$986$		−	45.3773i		−	1.44511i
$987$		0			0
$988$	−5.66956	+	5.66956i	−0.180373	+	0.180373i
$989$	3.43050	−	1.98060i	0.109084	−	0.0629794i
$990$		0			0
$991$	−6.52086	+	11.2945i	−0.207142	+	0.358780i	−0.950813	−	0.309765i	$-0.899749\pi$
$991$	−6.52086	+	11.2945i	−0.207142	+	0.358780i	0.743671	+	0.668546i	$0.233083\pi$
$992$	−9.66095	−	2.58864i	−0.306736	−	0.0821895i
$993$		0			0
$994$	−0.846306	−	22.1280i	−0.0268432	−	0.701859i
$995$	−0.870050	+	1.67490i	−0.0275824	+	0.0530977i
$996$		0			0
$997$	5.49854	+	20.5208i	0.174141	+	0.649901i	0.996696	+	0.0812171i	$0.0258807\pi$
$997$	5.49854	+	20.5208i	0.174141	+	0.649901i	−0.822556	+	0.568684i	$0.807453\pi$
$998$	3.09724	+	11.5591i	0.0980414	+	0.365896i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.a.577.3		16
3.2	odd	2		210.2.u.a.157.2	yes	16
5.3	odd	4		630.2.bv.b.73.2		16
7.5	odd	6		630.2.bv.b.397.2		16
15.2	even	4		1050.2.bc.g.493.1		16
15.8	even	4		210.2.u.b.73.3	yes	16
15.14	odd	2		1050.2.bc.h.157.3		16
21.5	even	6		210.2.u.b.187.3	yes	16
21.11	odd	6		1470.2.m.d.97.2		16
21.17	even	6		1470.2.m.e.97.3		16
35.33	even	12	inner	630.2.bv.a.523.3		16
105.38	odd	12		1470.2.m.d.1273.2		16
105.47	odd	12		1050.2.bc.h.943.3		16
105.53	even	12		1470.2.m.e.1273.3		16
105.68	odd	12		210.2.u.a.103.2	✓	16
105.89	even	6		1050.2.bc.g.607.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.2	✓	16	105.68	odd	12
210.2.u.a.157.2	yes	16	3.2	odd	2
210.2.u.b.73.3	yes	16	15.8	even	4
210.2.u.b.187.3	yes	16	21.5	even	6
630.2.bv.a.523.3		16	35.33	even	12	inner
630.2.bv.a.577.3		16	1.1	even	1	trivial
630.2.bv.b.73.2		16	5.3	odd	4
630.2.bv.b.397.2		16	7.5	odd	6
1050.2.bc.g.493.1		16	15.2	even	4
1050.2.bc.g.607.1		16	105.89	even	6
1050.2.bc.h.157.3		16	15.14	odd	2
1050.2.bc.h.943.3		16	105.47	odd	12
1470.2.m.d.97.2		16	21.11	odd	6
1470.2.m.d.1273.2		16	105.38	odd	12
1470.2.m.e.97.3		16	21.17	even	6
1470.2.m.e.1273.3		16	105.53	even	12

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-2.23385 + 0.0994727i) q^{5} +(2.52756 - 0.781940i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.482081 + 2.18348i) q^{10} +(1.31272 - 2.27370i) q^{11} +(1.21865 + 1.21865i) q^{13} +(-0.101115 - 2.64382i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.95935 - 7.31238i) q^{17} +(-2.32616 - 4.02903i) q^{19} +(1.98431 + 1.03078i) q^{20} +(-1.85647 - 1.85647i) q^{22} +(-4.95766 - 1.32840i) q^{23} +(4.98021 - 0.444415i) q^{25} +(1.49254 - 0.861717i) q^{26} +(-2.57990 - 0.586601i) q^{28} +5.99410i q^{29} +(-8.66177 - 5.00088i) q^{31} +(0.965926 - 0.258819i) q^{32} -7.57033 q^{34} +(-5.56842 + 1.99816i) q^{35} +(1.02429 - 3.82271i) q^{37} +(-4.49380 + 1.20411i) q^{38} +(1.50924 - 1.64991i) q^{40} -5.59423i q^{41} +(-0.545731 + 0.545731i) q^{43} +(-2.27370 + 1.31272i) q^{44} +(-2.56627 + 4.44492i) q^{46} +(6.12372 + 1.64085i) q^{47} +(5.77714 - 3.95280i) q^{49} +(0.859701 - 4.92554i) q^{50} +(-0.446058 - 1.66471i) q^{52} +(2.22057 + 8.28728i) q^{53} +(-2.70626 + 5.20970i) q^{55} +(-1.23434 + 2.34017i) q^{56} +(5.78985 + 1.55139i) q^{58} +(3.86022 - 6.68609i) q^{59} +(4.16543 - 2.40491i) q^{61} +(-7.07231 + 7.07231i) q^{62} -1.00000i q^{64} +(-2.84351 - 2.60107i) q^{65} +(2.47605 - 0.663456i) q^{67} +(-1.95935 + 7.31238i) q^{68} +(0.488864 + 5.89585i) q^{70} +8.36973 q^{71} +(-13.1877 + 3.53363i) q^{73} +(-3.42734 - 1.97878i) q^{74} +4.65232i q^{76} +(1.54009 - 6.77339i) q^{77} +(7.78980 - 4.49744i) q^{79} +(-1.20307 - 1.88484i) q^{80} +(-5.40361 - 1.44789i) q^{82} +(7.99504 + 7.99504i) q^{83} +(5.10428 + 16.1399i) q^{85} +(0.385890 + 0.668382i) q^{86} +(0.679515 + 2.53598i) q^{88} +(0.0812661 + 0.140757i) q^{89} +(4.03313 + 2.12731i) q^{91} +(3.62926 + 3.62926i) q^{92} +(3.16987 - 5.49038i) q^{94} +(5.59708 + 8.76887i) q^{95} +(-4.35278 + 4.35278i) q^{97} +(-2.32288 - 6.60335i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7} + 8 q^{10} - 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{20} + 4 q^{22} - 32 q^{23} - 32 q^{25} + 12 q^{26} - 8 q^{28} - 24 q^{31} + 16 q^{34} - 4 q^{35}+ \cdots + 8 q^{98}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 8 * q^10 - 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^20 + 4 * q^22 - 32 * q^23 - 32 * q^25 + 12 * q^26 - 8 * q^28 - 24 * q^31 + 16 * q^34 - 4 * q^35 - 8 * q^37 + 28 * q^38 - 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 - 8 * q^52 - 44 * q^53 - 56 * q^55 - 8 * q^56 + 48 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 16 * q^65 + 36 * q^67 + 12 * q^68 + 32 * q^70 + 32 * q^71 - 40 * q^73 + 24 * q^74 + 44 * q^77 + 12 * q^79 - 12 * q^80 + 12 * q^82 + 16 * q^83 + 8 * q^85 + 8 * q^86 + 8 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 8 * q^94 + 48 * q^95 + 44 * q^97 + 8 * q^98

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