LMFDB - Embedded newform 572.2.bb.a.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(51,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7, 5]))

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

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

chi := DirichletCharacter("572.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.855355656503296000000000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 12x^{14} + 95x^{12} + 552x^{10} + 1969x^{8} + 27048x^{6} + 228095x^{4} + 1411788x^{2} + 5764801 $ x^16 + 12x^14 + 95x^12 + 552x^10 + 1969x^8 + 27048x^6 + 228095x^4 + 1411788*x^2 + 5764801
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			51.1
Root			$1.46034 + 2.20622i$ of defining polynomial
Character	$\chi$	$=$	572.51
Dual form			572.2.bb.a.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.831254 + 1.14412i) q^{2} +(-0.618034 - 1.90211i) q^{4} +(-1.76231 + 0.572610i) q^{7} +(2.68999 + 0.874032i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(-0.831254 + 1.14412i) q^{2} +(-0.618034 - 1.90211i) q^{4} +(-1.76231 + 0.572610i) q^{7} +(2.68999 + 0.874032i) q^{8} +(-2.42705 - 1.76336i) q^{9} +(2.80534 + 1.76920i) q^{11} +(2.11929 - 2.91695i) q^{13} +(0.809793 - 2.49229i) q^{14} +(-3.23607 + 2.35114i) q^{16} +(2.04712 + 2.81761i) q^{17} +(4.03499 - 1.31105i) q^{18} +(2.53397 + 0.823337i) q^{19} +(-4.35613 + 1.73899i) q^{22} +(1.54508 - 4.75528i) q^{25} +(1.57568 + 4.84946i) q^{26} +(2.17834 + 2.99823i) q^{28} +(9.35536 - 3.03974i) q^{29} +(6.34212 + 4.60782i) q^{31} -5.65685i q^{32} -4.92537 q^{34} +(-1.85410 + 5.70634i) q^{36} +(-3.04837 + 2.21477i) q^{38} +(1.63143 - 6.42950i) q^{44} +(3.58660 - 11.0384i) q^{47} +(-2.88525 + 2.09626i) q^{49} +(4.15627 + 5.72061i) q^{50} +(-6.85817 - 2.22835i) q^{52} +(11.5967 + 8.42553i) q^{53} -5.24109 q^{56} +(-4.29884 + 13.2305i) q^{58} +(1.87637 + 5.77486i) q^{59} +(0.734516 + 1.01097i) q^{61} +(-10.5438 + 3.42590i) q^{62} +(5.28694 + 1.71783i) q^{63} +(6.47214 + 4.70228i) q^{64} -5.09902 q^{67} +(4.09423 - 5.63523i) q^{68} +(-13.3745 + 9.71718i) q^{71} +(-4.98752 - 6.86474i) q^{72} -5.32875i q^{76} +(-5.95695 - 1.51153i) q^{77} +(2.78115 + 8.55951i) q^{81} +(-10.3494 - 14.2448i) q^{83} +(6.00000 + 7.21110i) q^{88} +(-2.06458 + 6.35411i) q^{91} +(9.64793 + 13.2792i) q^{94} -5.04361i q^{98} +(-3.68896 - 9.24076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 12 * q^9	$ 16 q + 8 q^{4} - 12 q^{9} - 8 q^{14} - 16 q^{16} - 40 q^{17} + 12 q^{22} - 20 q^{25} + 80 q^{29} + 24 q^{36} + 40 q^{38} - 20 q^{49} + 8 q^{53} + 16 q^{56} - 140 q^{62} + 32 q^{64} - 80 q^{68} - 112 q^{77} - 36 q^{81} + 96 q^{88} + 180 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 - 12 * q^9 - 8 * q^14 - 16 * q^16 - 40 * q^17 + 12 * q^22 - 20 * q^25 + 80 * q^29 + 24 * q^36 + 40 * q^38 - 20 * q^49 + 8 * q^53 + 16 * q^56 - 140 * q^62 + 32 * q^64 - 80 * q^68 - 112 * q^77 - 36 * q^81 + 96 * q^88 + 180 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.831254	+	1.14412i	−0.587785	+	0.809017i
$2$	−0.831254	+	1.14412i	−0.587785	+	0.809017i
$3$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$3$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$4$	−0.618034	−	1.90211i	−0.309017	−	0.951057i
$5$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$5$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$6$		0			0
$7$	−1.76231	+	0.572610i	−0.666092	+	0.216426i	−0.622496	−	0.782623i	$-0.713881\pi$
$7$	−1.76231	+	0.572610i	−0.666092	+	0.216426i	−0.0435957	+	0.999049i	$0.513881\pi$
$8$	2.68999	+	0.874032i	0.951057	+	0.309017i
$9$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$10$		0			0
$11$	2.80534	+	1.76920i	0.845841	+	0.533435i
$11$	2.80534	+	1.76920i	0.845841	+	0.533435i
$12$		0			0
$13$	2.11929	−	2.91695i	0.587785	−	0.809017i
$13$	2.11929	−	2.91695i	0.587785	−	0.809017i
$14$	0.809793	−	2.49229i	0.216426	−	0.666092i
$15$		0			0
$16$	−3.23607	+	2.35114i	−0.809017	+	0.587785i
$17$	2.04712	+	2.81761i	0.496499	+	0.683372i	0.981570	−	0.191103i	$-0.0612063\pi$
$17$	2.04712	+	2.81761i	0.496499	+	0.683372i	−0.485071	+	0.874475i	$0.661206\pi$
$18$	4.03499	−	1.31105i	0.951057	−	0.309017i
$19$	2.53397	+	0.823337i	0.581333	+	0.188887i	0.584898	−	0.811107i	$-0.301135\pi$
$19$	2.53397	+	0.823337i	0.581333	+	0.188887i	−0.00356465	+	0.999994i	$0.501135\pi$
$20$		0			0
$21$		0			0
$22$	−4.35613	+	1.73899i	−0.928731	+	0.370755i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	1.57568	+	4.84946i	0.309017	+	0.951057i
$27$		0			0
$28$	2.17834	+	2.99823i	0.411667	+	0.566611i
$29$	9.35536	−	3.03974i	1.73725	−	0.564466i	0.742781	−	0.669534i	$-0.233506\pi$
$29$	9.35536	−	3.03974i	1.73725	−	0.564466i	0.994465	+	0.105069i	$0.0335062\pi$
$30$		0			0
$31$	6.34212	+	4.60782i	1.13908	+	0.827589i	0.986991	−	0.160778i	$-0.0514002\pi$
$31$	6.34212	+	4.60782i	1.13908	+	0.827589i	0.152088	+	0.988367i	$0.451400\pi$
$32$		−	5.65685i		−	1.00000i
$33$		0			0
$34$	−4.92537			−0.844694
$35$		0			0
$36$	−1.85410	+	5.70634i	−0.309017	+	0.951057i
$37$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$37$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$38$	−3.04837	+	2.21477i	−0.494511	+	0.359284i
$39$		0			0
$40$		0			0
$41$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$41$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	1.63143	−	6.42950i	0.245948	−	0.969283i
$45$		0			0
$46$		0			0
$47$	3.58660	−	11.0384i	0.523159	−	1.61012i	−0.244768	−	0.969582i	$-0.578712\pi$
$47$	3.58660	−	11.0384i	0.523159	−	1.61012i	0.767927	−	0.640537i	$-0.221288\pi$
$48$		0			0
$49$	−2.88525	+	2.09626i	−0.412179	+	0.299466i
$50$	4.15627	+	5.72061i	0.587785	+	0.809017i
$51$		0			0
$52$	−6.85817	−	2.22835i	−0.951057	−	0.309017i
$53$	11.5967	+	8.42553i	1.59294	+	1.15734i	0.899595	+	0.436726i	$0.143862\pi$
$53$	11.5967	+	8.42553i	1.59294	+	1.15734i	0.693341	+	0.720610i	$0.256138\pi$
$54$		0			0
$55$		0			0
$56$	−5.24109			−0.700370
$57$		0			0
$58$	−4.29884	+	13.2305i	−0.564466	+	1.73725i
$59$	1.87637	+	5.77486i	0.244282	+	0.751823i	0.995754	+	0.0920575i	$0.0293443\pi$
$59$	1.87637	+	5.77486i	0.244282	+	0.751823i	−0.751472	+	0.659765i	$0.770656\pi$
$60$		0			0
$61$	0.734516	+	1.01097i	0.0940451	+	0.129442i	0.853447	−	0.521180i	$-0.174508\pi$
$61$	0.734516	+	1.01097i	0.0940451	+	0.129442i	−0.759401	+	0.650622i	$0.774508\pi$
$62$	−10.5438	+	3.42590i	−1.33907	+	0.435089i
$63$	5.28694	+	1.71783i	0.666092	+	0.216426i
$64$	6.47214	+	4.70228i	0.809017	+	0.587785i
$65$		0			0
$66$		0			0
$67$	−5.09902			−0.622944			−0.311472	−	0.950255i	$-0.600822\pi$
$67$	−5.09902			−0.622944			−0.311472	+	0.950255i	$0.600822\pi$
$68$	4.09423	−	5.63523i	0.496499	−	0.683372i
$69$		0			0
$70$		0			0
$71$	−13.3745	+	9.71718i	−1.58727	+	1.15322i	−0.679553	+	0.733626i	$0.737826\pi$
$71$	−13.3745	+	9.71718i	−1.58727	+	1.15322i	−0.907713	+	0.419591i	$0.862174\pi$
$72$	−4.98752	−	6.86474i	−0.587785	−	0.809017i
$73$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$73$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$74$		0			0
$75$		0			0
$76$		−	5.32875i		−	0.611250i
$77$	−5.95695	−	1.51153i	−0.678857	−	0.172254i
$78$		0			0
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$		0			0
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$		0			0
$83$	−10.3494	−	14.2448i	−1.13600	−	1.56356i	−0.776145	−	0.630555i	$-0.782827\pi$
$83$	−10.3494	−	14.2448i	−1.13600	−	1.56356i	−0.359851	−	0.933010i	$-0.617173\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	6.00000	+	7.21110i	0.639602	+	0.768706i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$	−2.06458	+	6.35411i	−0.216426	+	0.666092i
$92$		0			0
$93$		0			0
$94$	9.64793	+	13.2792i	0.995108	+	1.36965i
$95$		0			0
$96$		0			0
$97$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$97$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$98$		−	5.04361i		−	0.509481i
$99$	−3.68896	−	9.24076i	−0.370755	−	0.928731i
$100$	−10.0000			−1.00000
$101$	11.6950	−	16.0969i	1.16370	−	1.60170i	0.467175	−	0.884165i	$-0.345272\pi$
$101$	11.6950	−	16.0969i	1.16370	−	1.60170i	0.696526	−	0.717532i	$-0.254728\pi$
$102$		0			0
$103$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$103$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$104$	8.25039	−	5.99426i	0.809017	−	0.587785i
$105$		0			0
$106$	−19.2797	+	6.26435i	−1.87261	+	0.608447i
$107$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$107$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	4.35668	−	5.99645i	0.411667	−	0.566611i
$113$	6.30979	−	19.4195i	0.593575	−	1.82684i	0.0318823	−	0.999492i	$-0.489850\pi$
$113$	6.30979	−	19.4195i	0.593575	−	1.82684i	0.561693	−	0.827346i	$-0.310150\pi$
$114$		0			0
$115$		0			0
$116$	−11.5639	−	15.9163i	−1.07368	−	1.47779i
$117$	−10.2872	+	3.34253i	−0.951057	+	0.309017i
$118$	−8.16689	−	2.65358i	−0.751823	−	0.244282i
$119$	−5.22106	−	3.79332i	−0.478613	−	0.347733i
$120$		0			0
$121$	4.73984	+	9.92643i	0.430894	+	0.902402i
$122$	−1.76725			−0.159999
$123$		0			0
$124$	4.84495	−	14.9112i	0.435089	−	1.33907i
$125$		0			0
$126$	−6.36020	+	4.62095i	−0.566611	+	0.411667i
$127$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$127$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$128$	−10.7600	+	3.49613i	−0.951057	+	0.309017i
$129$		0			0
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−4.93710			−0.428101
$134$	4.23858	−	5.83390i	0.366158	−	0.503973i
$135$		0			0
$136$	3.04405	+	9.36861i	0.261025	+	0.803352i
$137$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$137$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$138$		0			0
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$		0			0
$141$		0			0
$142$		−	23.3796i		−	1.96197i
$143$	11.1060	−	4.43358i	0.928731	−	0.370755i
$144$	12.0000			1.00000
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$149$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$150$		0			0
$151$	11.6778	+	3.79434i	0.950323	+	0.308779i	0.742847	−	0.669461i	$-0.233475\pi$
$151$	11.6778	+	3.79434i	0.950323	+	0.308779i	0.207476	+	0.978240i	$0.433475\pi$
$152$	6.09675	+	4.42955i	0.494511	+	0.359284i
$153$		−	10.4483i		−	0.844694i
$154$	6.68111	−	5.55902i	0.538379	−	0.447958i
$155$		0			0
$156$		0			0
$157$	−4.69021	+	14.4350i	−0.374319	+	1.15204i	0.569618	+	0.821910i	$0.307091\pi$
$157$	−4.69021	+	14.4350i	−0.374319	+	1.15204i	−0.943937	+	0.330126i	$0.892909\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−12.1050	−	3.93314i	−0.951057	−	0.309017i
$163$	−17.3593	−	12.6122i	−1.35968	−	0.987867i	−0.998465	−	0.0553849i	$-0.982361\pi$
$163$	−17.3593	−	12.6122i	−1.35968	−	0.987867i	−0.361217	−	0.932482i	$-0.617639\pi$
$164$		0			0
$165$		0			0
$166$	24.9007			1.93267
$167$	13.4816	−	18.5558i	1.04324	−	1.43589i	0.148707	−	0.988881i	$-0.452489\pi$
$167$	13.4816	−	18.5558i	1.04324	−	1.43589i	0.894529	−	0.447010i	$-0.147511\pi$
$168$		0			0
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$		0			0
$171$	−4.69824	−	6.46658i	−0.359284	−	0.494511i
$172$		0			0
$173$	−13.7163	−	4.45671i	−1.04283	−	0.338837i	−0.262981	−	0.964801i	$-0.584706\pi$
$173$	−13.7163	−	4.45671i	−1.04283	−	0.338837i	−0.779852	+	0.625964i	$0.784706\pi$
$174$		0			0
$175$			9.26503i			0.700370i
$176$	−13.2379	+	0.870480i	−0.997845	+	0.0656149i
$177$		0			0
$178$		0			0
$179$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$179$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$180$		0			0
$181$	−20.7594	+	15.0826i	−1.54303	+	1.12108i	−0.594635	+	0.803996i	$0.702704\pi$
$181$	−20.7594	+	15.0826i	−1.54303	+	1.12108i	−0.948398	+	0.317084i	$0.897296\pi$
$182$	−5.55370	−	7.64401i	−0.411667	−	0.566611i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.757919	+	11.5261i	0.0554245	+	0.842874i
$188$	−23.2130			−1.69298
$189$		0			0
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$		0			0
$193$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$193$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$194$		0			0
$195$		0			0
$196$	5.77051	+	4.19252i	0.412179	+	0.299466i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	13.6390	+	3.46079i	0.969283	+	0.245948i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	8.31254	−	11.4412i	0.587785	−	0.809017i
$201$		0			0
$202$	8.69522	+	26.7611i	0.611794	+	1.88291i
$203$	−14.7465	+	10.7139i	−1.03500	+	0.751972i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$			14.4222i			1.00000i
$209$	5.65199	+	6.79285i	0.390957	+	0.469871i
$210$		0			0
$211$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$211$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$212$	8.85913	−	27.2656i	0.608447	−	1.87261i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−13.8153	−	4.48886i	−0.937843	−	0.304724i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	12.5573			0.844694
$222$		0			0
$223$	−7.87842	+	24.2473i	−0.527578	+	1.62372i	0.231583	+	0.972815i	$0.425609\pi$
$223$	−7.87842	+	24.2473i	−0.527578	+	1.62372i	−0.759161	+	0.650903i	$0.774391\pi$
$224$	3.23917	+	9.96915i	0.216426	+	0.666092i
$225$	−12.1353	+	8.81678i	−0.809017	+	0.587785i
$226$	16.9733	+	23.3618i	1.12905	+	1.55400i
$227$	−25.7011	+	8.35078i	−1.70584	+	0.554261i	−0.989632	−	0.143626i	$-0.954124\pi$
$227$	−25.7011	+	8.35078i	−1.70584	+	0.554261i	−0.716208	+	0.697887i	$0.754124\pi$
$228$		0			0
$229$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$229$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$230$		0			0
$231$		0			0
$232$	27.8227			1.82665
$233$	−10.8293	+	14.9053i	−0.709454	+	0.976479i	0.290355	+	0.956919i	$0.406227\pi$
$233$	−10.8293	+	14.9053i	−0.709454	+	0.976479i	−0.999809	+	0.0195604i	$0.993773\pi$
$234$	4.72705	−	14.5484i	0.309017	−	0.951057i
$235$		0			0
$236$	9.82478	−	7.13812i	0.639539	−	0.464652i
$237$		0			0
$238$	8.68005	−	2.82032i	0.562644	−	0.182814i
$239$	29.2257	+	9.49601i	1.89045	+	0.614246i	0.979390	+	0.201980i	$0.0647375\pi$
$239$	29.2257	+	9.49601i	1.89045	+	0.614246i	0.911064	+	0.412266i	$0.135262\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−15.2971	−	2.82843i	−0.983332	−	0.181818i
$243$		0			0
$244$	1.46903	−	2.02195i	0.0940451	−	0.129442i
$245$		0			0
$246$		0			0
$247$	7.77186	−	5.64658i	0.494511	−	0.359284i
$248$	13.0329	+	17.9382i	0.827589	+	1.13908i
$249$		0			0
$250$		0			0
$251$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$251$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$252$		−	11.1180i		−	0.700370i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	8.73917	+	26.8964i	0.545135	+	1.67775i	0.720670	+	0.693279i	$0.243834\pi$
$257$	8.73917	+	26.8964i	0.545135	+	1.67775i	−0.175535	+	0.984473i	$0.556166\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−28.0661	−	9.11922i	−1.73725	−	0.564466i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$		0			0
$266$	4.10399	−	5.64865i	0.251632	−	0.346341i
$267$		0			0
$268$	3.15137	+	9.69891i	0.192500	+	0.592455i
$269$	2.45163	−	1.78121i	0.149478	−	0.108602i	−0.510532	−	0.859858i	$-0.670552\pi$
$269$	2.45163	−	1.78121i	0.149478	−	0.108602i	0.660011	+	0.751256i	$0.270552\pi$
$270$		0			0
$271$	22.1764	−	7.20556i	1.34712	−	0.437707i	0.455400	−	0.890287i	$-0.349496\pi$
$271$	22.1764	−	7.20556i	1.34712	−	0.437707i	0.891724	+	0.452580i	$0.149496\pi$
$272$	−13.2492	−	4.30493i	−0.803352	−	0.261025i
$273$		0			0
$274$		0			0
$275$	12.7475	−	10.6066i	0.768706	−	0.639602i
$276$		0			0
$277$	−3.50658	+	4.82639i	−0.210690	+	0.289990i	−0.901263	−	0.433273i	$-0.857359\pi$
$277$	−3.50658	+	4.82639i	−0.210690	+	0.289990i	0.690573	+	0.723263i	$0.257359\pi$
$278$		0			0
$279$	−7.26743	−	22.3668i	−0.435089	−	1.33907i
$280$		0			0
$281$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$281$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$282$		0			0
$283$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$283$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$284$	26.7491	+	19.4344i	1.58727	+	1.15322i
$285$		0			0
$286$	−4.15935	+	16.3921i	−0.245948	+	0.969283i
$287$		0			0
$288$	−9.97505	+	13.7295i	−0.587785	+	0.809017i
$289$	1.50502	−	4.63199i	0.0885308	−	0.272470i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$293$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−14.0484	+	10.2067i	−0.808393	+	0.587332i
$303$		0			0
$304$	−10.1359	+	3.29335i	−0.581333	+	0.188887i
$305$		0			0
$306$	11.9541	+	8.68518i	0.683372	+	0.496499i
$307$			34.4357i			1.96535i	0.185335	+	0.982675i	$0.440663\pi$
$307$			34.4357i			1.96535i	−0.185335	+	0.982675i	$0.559337\pi$
$308$	0.806502	+	12.2650i	0.0459547	+	0.698861i
$309$		0			0
$310$		0			0
$311$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$311$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$312$		0			0
$313$	8.03899	−	5.84067i	0.454391	−	0.330134i	−0.336936	−	0.941527i	$-0.609391\pi$
$313$	8.03899	−	5.84067i	0.454391	−	0.330134i	0.791327	+	0.611393i	$0.209391\pi$
$314$	−12.6166	−	17.3653i	−0.711998	−	0.979981i
$315$		0			0
$316$		0			0
$317$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$317$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$318$		0			0
$319$	31.6229	+	8.02404i	1.77054	+	0.449260i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.86749	+	8.82522i	0.159551	+	0.491049i
$324$	14.5623	−	10.5801i	0.809017	−	0.587785i
$325$	−10.5964	−	14.5848i	−0.587785	−	0.809017i
$326$	28.8599	−	9.37715i	1.59840	−	0.519352i
$327$		0			0
$328$		0			0
$329$			21.5069i			1.18571i
$330$		0			0
$331$	−4.30480			−0.236613			−0.118307	−	0.992977i	$-0.537747\pi$
$331$	−4.30480			−0.236613			−0.118307	+	0.992977i	$0.537747\pi$
$332$	−20.6988	+	28.4895i	−1.13600	+	1.56356i
$333$		0			0
$334$	10.0235	+	30.8492i	0.548462	+	1.68799i
$335$		0			0
$336$		0			0
$337$	−30.4430	+	9.89154i	−1.65834	+	0.538826i	−0.980522	−	0.196407i	$-0.937073\pi$
$337$	−30.4430	+	9.89154i	−1.65834	+	0.538826i	−0.677814	+	0.735233i	$0.737073\pi$
$338$	17.4850	+	5.68121i	0.951057	+	0.309017i
$339$		0			0
$340$		0			0
$341$	9.63962	+	24.1470i	0.522015	+	1.30763i
$342$	11.3040			0.611250
$343$	11.5086	−	15.8402i	0.621404	−	0.855290i
$344$		0			0
$345$		0			0
$346$	16.5008	−	11.9885i	0.887087	−	0.644506i
$347$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$347$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$348$		0			0
$349$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$349$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$350$	−10.6003	−	7.70159i	−0.566611	−	0.411667i
$351$		0			0
$352$	10.0081	−	15.8694i	0.533435	−	0.845841i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	36.0254	−	11.7054i	1.90135	−	0.617785i	0.941906	−	0.335877i	$-0.109033\pi$
$359$	36.0254	−	11.7054i	1.90135	−	0.617785i	0.959441	−	0.281908i	$-0.0909673\pi$
$360$		0			0
$361$	−9.62819	−	6.99529i	−0.506747	−	0.368173i
$362$		−	36.2887i		−	1.90729i
$363$		0			0
$364$	13.3622			0.700370
$365$		0			0
$366$		0			0
$367$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$367$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−25.2616	−	8.20800i	−1.31152	−	0.426138i
$372$		0			0
$373$		−	36.3108i		−	1.88010i	−0.341031	−	0.940052i	$-0.610776\pi$
$373$		−	36.3108i		−	1.88010i	0.341031	−	0.940052i	$-0.389224\pi$
$374$	−13.8173	−	8.71399i	−0.714477	−	0.450589i
$375$		0			0
$376$	19.2959	−	26.5585i	0.995108	−	1.36965i
$377$	10.9599	−	33.7312i	0.564466	−	1.73725i
$378$		0			0
$379$	−28.8764	+	20.9799i	−1.48328	+	1.07767i	−0.506797	+	0.862066i	$0.669171\pi$
$379$	−28.8764	+	20.9799i	−1.48328	+	1.07767i	−0.976482	+	0.215599i	$0.930829\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.56429	−	1.86307i	−0.131029	−	0.0951982i	0.520340	−	0.853959i	$-0.325805\pi$
$383$	−2.56429	−	1.86307i	−0.131029	−	0.0951982i	−0.651369	+	0.758761i	$0.725805\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.1243	+	37.3148i	0.614727	+	1.89194i	0.405616	+	0.914044i	$0.367057\pi$
$389$	12.1243	+	37.3148i	0.614727	+	1.89194i	0.209111	+	0.977892i	$0.432943\pi$
$390$		0			0
$391$		0			0
$392$	−9.59351	+	3.11712i	−0.484546	+	0.157438i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−15.2971	+	12.7279i	−0.768706	+	0.639602i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	6.18034	+	19.0211i	0.309017	+	0.951057i
$401$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$401$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$402$		0			0
$403$	26.8816	−	8.73436i	1.33907	−	0.435089i
$404$	−37.8460	−	12.2969i	−1.88291	−	0.611794i
$405$		0			0
$406$		−	25.7778i		−	1.27933i
$407$		0			0
$408$		0			0
$409$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$409$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.61349	−	9.10269i	−0.325429	−	0.447914i
$414$		0			0
$415$		0			0
$416$	−16.5008	−	11.9885i	−0.809017	−	0.587785i
$417$		0			0
$418$	−12.4701	+	0.819991i	−0.609932	+	0.0401071i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$421$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$422$		0			0
$423$	−28.1695	+	20.4664i	−1.36965	+	0.995108i
$424$	23.8310	+	32.8006i	1.15734	+	1.59294i
$425$	16.5615	−	5.38117i	0.803352	−	0.261025i
$426$		0			0
$427$	−1.87334	−	1.36106i	−0.0906573	−	0.0658664i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−22.4192	+	30.8573i	−1.07989	+	1.48634i	−0.220254	+	0.975443i	$0.570689\pi$
$431$	−22.4192	+	30.8573i	−1.07989	+	1.48634i	−0.859639	+	0.510902i	$0.829311\pi$
$432$		0			0
$433$	−2.26083	−	6.95811i	−0.108648	−	0.334385i	0.881921	−	0.471397i	$-0.156250\pi$
$433$	−2.26083	−	6.95811i	−0.108648	−	0.334385i	−0.990569	+	0.137012i	$0.956250\pi$
$434$	16.6198	−	12.0750i	0.797777	−	0.579619i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	10.6991			0.509481
$442$	−10.4383	+	14.3671i	−0.496499	+	0.683372i
$443$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$443$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$444$		0			0
$445$		0			0
$446$	−21.1929	−	29.1695i	−1.00351	−	1.38122i
$447$		0			0
$448$	−14.0985	−	4.58088i	−0.666092	−	0.216426i
$449$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$449$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$450$		−	21.2132i		−	1.00000i
$451$		0			0
$452$	−40.8378			−1.92085
$453$		0			0
$454$	11.8098	−	36.3468i	0.554261	−	1.70584i
$455$		0			0
$456$		0			0
$457$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$457$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	−33.8947			−1.57522			−0.787611	−	0.616173i	$-0.788682\pi$
$463$	−33.8947			−1.57522			−0.787611	+	0.616173i	$0.788682\pi$
$464$	−23.1277	+	31.8326i	−1.07368	+	1.47779i
$465$		0			0
$466$	−8.05157	−	24.7802i	−0.372982	−	1.14792i
$467$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$467$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$468$	12.7157	+	17.5017i	0.587785	+	0.809017i
$469$	8.98607	−	2.91975i	0.414938	−	0.134822i
$470$		0			0
$471$		0			0
$472$			17.1743i			0.790513i
$473$		0			0
$474$		0			0
$475$	7.83040	−	10.7776i	0.359284	−	0.494511i
$476$	−3.98853	+	12.2754i	−0.182814	+	0.562644i
$477$	−13.2887	−	40.8984i	−0.608447	−	1.87261i
$478$	−35.1586	+	25.5442i	−1.60812	+	1.16836i
$479$	−16.0006	−	22.0229i	−0.731086	−	1.00625i	−0.999082	−	0.0428332i	$-0.986362\pi$
$479$	−16.0006	−	22.0229i	−0.731086	−	1.00625i	0.267997	−	0.963420i	$-0.413638\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	15.9518	−	15.1506i	0.725082	−	0.688662i
$485$		0			0
$486$		0			0
$487$	9.23777	−	28.4309i	0.418603	−	1.28833i	−0.490384	−	0.871506i	$-0.663144\pi$
$487$	9.23777	−	28.4309i	0.418603	−	1.28833i	0.908988	−	0.416823i	$-0.136856\pi$
$488$	1.09222	+	3.36150i	0.0494424	+	0.152168i
$489$		0			0
$490$		0			0
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$		0			0
$493$	27.7163	+	20.1371i	1.24828	+	0.906929i
$494$			13.5857i			0.611250i
$495$		0			0
$496$	−31.3572			−1.40798
$497$	18.0060	−	24.7831i	0.807679	−	1.11167i
$498$		0			0
$499$	−13.8038	−	42.4839i	−0.617945	−	1.90184i	−0.325118	−	0.945674i	$-0.605404\pi$
$499$	−13.8038	−	42.4839i	−0.617945	−	1.90184i	−0.292827	−	0.956165i	$-0.594596\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$503$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$504$	12.7204	+	9.24191i	0.566611	+	0.411667i
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$509$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$510$		0			0
$511$		0			0
$512$	13.3001	+	18.3060i	0.587785	+	0.809017i
$513$		0			0
$514$	−38.0373	−	12.3591i	−1.67775	−	0.545135i
$515$		0			0
$516$		0			0
$517$	29.5908	−	24.6211i	1.30140	−	1.08283i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.92269	+	24.3835i	0.347099	+	1.06826i	0.960450	+	0.278451i	$0.0898211\pi$
$521$	7.92269	+	24.3835i	0.347099	+	1.06826i	−0.613351	+	0.789810i	$0.710179\pi$
$522$	33.7635	−	24.5306i	1.47779	−	1.07368i
$523$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$523$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			27.3024i			1.18931i
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$	5.62910	−	17.3246i	0.244282	−	0.751823i
$532$	3.05130	+	9.39093i	0.132291	+	0.407148i
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−13.7163	−	4.45671i	−0.592455	−	0.192500i
$537$		0			0
$538$			4.28560i			0.184765i
$539$	−11.8028	+	0.776113i	−0.508384	+	0.0334296i
$540$		0			0
$541$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$541$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$542$	−10.1902	+	31.3622i	−0.437707	+	1.34712i
$543$		0			0
$544$	15.9388	−	11.5802i	0.683372	−	0.496499i
$545$		0			0
$546$		0			0
$547$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$547$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$548$		0			0
$549$		−	3.74890i		−	0.159999i
$550$	1.53881	+	23.4015i	0.0656149	+	0.997845i
$551$	26.2089			1.11654
$552$		0			0
$553$		0			0
$554$	−2.60713	−	8.02391i	−0.110766	−	0.340903i
$555$		0			0
$556$		0			0
$557$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$557$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$558$	31.6315	+	10.2777i	1.33907	+	0.435089i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$563$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−9.80252	−	13.4920i	−0.411667	−	0.566611i
$568$	−44.4706	+	14.4494i	−1.86594	+	0.606282i
$569$	−0.950846	−	0.308949i	−0.0398615	−	0.0129518i	0.289018	−	0.957324i	$-0.406671\pi$
$569$	−0.950846	−	0.308949i	−0.0398615	−	0.0129518i	−0.328880	+	0.944372i	$0.606671\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$	−15.2971	−	18.3848i	−0.639602	−	0.768706i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−7.41641	−	22.8254i	−0.309017	−	0.951057i
$577$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$577$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$578$	4.04850	+	5.57229i	0.168396	+	0.231777i
$579$		0			0
$580$		0			0
$581$	26.3956	+	19.1775i	1.09507	+	0.795618i
$582$		0			0
$583$	17.6263	+	44.1535i	0.730007	+	1.82865i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.1812	−	43.6451i	−0.585319	−	1.80143i	−0.597986	−	0.801506i	$-0.704032\pi$
$587$	−14.1812	−	43.6451i	−0.585319	−	1.80143i	0.0126674	−	0.999920i	$-0.495968\pi$
$588$		0			0
$589$	12.2770	+	16.8978i	0.505864	+	0.696262i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$599$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$600$		0			0
$601$	−20.5745	+	6.68506i	−0.839251	+	0.272689i	−0.696937	−	0.717132i	$-0.745454\pi$
$601$	−20.5745	+	6.68506i	−0.839251	+	0.272689i	−0.142314	+	0.989822i	$0.545454\pi$
$602$		0			0
$603$	12.3756	+	8.99139i	0.503973	+	0.366158i
$604$		−	24.5575i		−	0.999229i
$605$		0			0
$606$		0			0
$607$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$607$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$608$	4.65750	−	14.3343i	0.188887	−	0.581333i
$609$		0			0
$610$		0			0
$611$	−24.5975	−	33.8555i	−0.995108	−	1.36965i
$612$	−19.8738	+	6.45740i	−0.803352	+	0.261025i
$613$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$613$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$614$	−39.3987	−	28.6248i	−1.59000	−	1.15520i
$615$		0			0
$616$	−14.7030	−	9.27256i	−0.592402	−	0.373602i
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	−7.71575	+	23.7466i	−0.310122	+	0.954458i	0.667594	+	0.744526i	$0.267324\pi$
$619$	−7.71575	+	23.7466i	−0.310122	+	0.954458i	−0.977716	+	0.209932i	$0.932676\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$			14.0527i			0.561658i
$627$		0			0
$628$	30.3557			1.21132
$629$		0			0
$630$		0			0
$631$	−2.50149	−	7.69881i	−0.0995829	−	0.306485i	0.888838	−	0.458222i	$-0.151513\pi$
$631$	−2.50149	−	7.69881i	−0.0995829	−	0.306485i	−0.988421	+	0.151737i	$0.951513\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$			12.8587i			0.509481i
$638$	−35.4671	+	29.5104i	−1.40416	+	1.16833i
$639$	49.5955			1.96197
$640$		0			0
$641$	−14.4531	+	44.4820i	−0.570862	+	1.75693i	0.0789953	+	0.996875i	$0.474829\pi$
$641$	−14.4531	+	44.4820i	−0.570862	+	1.75693i	−0.649857	+	0.760057i	$0.725171\pi$
$642$		0			0
$643$	−40.1057	+	29.1385i	−1.58161	+	1.14911i	−0.666796	+	0.745240i	$0.732335\pi$
$643$	−40.1057	+	29.1385i	−1.58161	+	1.14911i	−0.914817	+	0.403869i	$0.867665\pi$
$644$		0			0
$645$		0			0
$646$	−12.4808	−	4.05524i	−0.491049	−	0.159551i
$647$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$647$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$648$			25.4558i			1.00000i
$649$	−4.95307	+	19.5201i	−0.194425	+	0.766231i
$650$	25.4951			1.00000
$651$		0			0
$652$	−13.2613	+	40.8141i	−0.519352	+	1.59840i
$653$	−11.1686	−	34.3733i	−0.437059	−	1.34513i	−0.890962	−	0.454079i	$-0.849969\pi$
$653$	−11.1686	−	34.3733i	−0.437059	−	1.34513i	0.453902	−	0.891051i	$-0.350031\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−24.6065	−	17.8777i	−0.959261	−	0.696944i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	3.57838	−	4.92522i	0.139078	−	0.191424i
$663$		0			0
$664$	−15.3895	−	47.3640i	−0.597228	−	1.83808i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−43.6273	−	14.1754i	−1.68799	−	0.548462i
$669$		0			0
$670$		0			0
$671$	0.271945	+	4.13563i	0.0104983	+	0.159654i
$672$		0			0
$673$	15.8768	−	21.8525i	0.612004	−	0.842351i	−0.384736	−	0.923026i	$-0.625708\pi$
$673$	15.8768	−	21.8525i	0.612004	−	0.842351i	0.996740	+	0.0806753i	$0.0257077\pi$
$674$	13.9887	−	43.0529i	0.538826	−	1.65834i
$675$		0			0
$676$	−21.0344	+	15.2824i	−0.809017	+	0.587785i
$677$	25.3313	+	34.8655i	0.973560	+	1.33999i	0.940228	+	0.340545i	$0.110612\pi$
$677$	25.3313	+	34.8655i	0.973560	+	1.33999i	0.0333315	+	0.999444i	$0.489388\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−35.6401	−	9.04338i	−1.36473	−	0.346289i
$683$	25.2851			0.967509			0.483754	−	0.875204i	$-0.339273\pi$
$683$	25.2851			0.967509			0.483754	+	0.875204i	$0.339273\pi$
$684$	−9.39648	+	12.9332i	−0.359284	+	0.494511i
$685$		0			0
$686$	8.55657	+	26.3344i	0.326692	+	1.00545i
$687$		0			0
$688$		0			0
$689$	49.1537	−	15.9710i	1.87261	−	0.608447i
$690$		0			0
$691$	−41.5354	−	30.1772i	−1.58008	−	1.14800i	−0.916602	−	0.399801i	$-0.869079\pi$
$691$	−41.5354	−	30.1772i	−1.58008	−	1.14800i	−0.663479	−	0.748195i	$-0.730921\pi$
$692$			28.8444i			1.09650i
$693$	11.7925	+	14.1728i	0.447958	+	0.538379i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	17.6231	−	5.72610i	0.666092	−	0.216426i
$701$	47.7829	+	15.5256i	1.80473	+	0.586394i	0.999974	−	0.00720582i	$-0.00229370\pi$
$701$	47.7829	+	15.5256i	1.80473	+	0.586394i	0.804761	+	0.593600i	$0.202294\pi$
$702$		0			0
$703$		0			0
$704$	9.83723	+	24.6420i	0.370755	+	0.928731i
$705$		0			0
$706$		0			0
$707$	−11.3931	+	35.0644i	−0.428482	+	1.31873i
$708$		0			0
$709$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$709$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−16.5539	+	50.9476i	−0.617785	+	1.90135i
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$		0			0
$721$		0			0
$722$	16.0069	−	5.20097i	0.595717	−	0.193560i
$723$		0			0
$724$	41.5188	+	30.1652i	1.54303	+	1.12108i
$725$		−	49.1840i		−	1.82665i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−11.1074	+	15.2880i	−0.411667	+	0.566611i
$729$	8.34346	−	25.6785i	0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$733$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−14.3045	−	9.02120i	−0.526912	−	0.332300i
$738$		0			0
$739$	7.17078	−	9.86973i	0.263781	−	0.363064i	−0.656497	−	0.754329i	$-0.727962\pi$
$739$	7.17078	−	9.86973i	0.263781	−	0.363064i	0.920278	+	0.391265i	$0.127962\pi$
$740$		0			0
$741$		0			0
$742$	30.3898	−	22.0795i	1.11564	−	0.810563i
$743$	0.952933	+	1.31160i	0.0349597	+	0.0481179i	0.826139	−	0.563466i	$-0.190533\pi$
$743$	0.952933	+	1.31160i	0.0349597	+	0.0481179i	−0.791179	+	0.611584i	$0.790533\pi$
$744$		0			0
$745$		0			0
$746$	41.5441	+	30.1835i	1.52104	+	1.10510i
$747$			52.8224i			1.93267i
$748$	21.4556	−	8.56519i	0.784494	−	0.313174i
$749$		0			0
$750$		0			0
$751$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$751$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$752$	14.3464	+	44.1537i	0.523159	+	1.61012i
$753$		0			0
$754$	29.4822	+	40.5787i	1.07368	+	1.47779i
$755$		0			0
$756$		0			0
$757$	−1.67879	−	1.21971i	−0.0610167	−	0.0443312i	0.556859	−	0.830607i	$-0.312006\pi$
$757$	−1.67879	−	1.21971i	−0.0610167	−	0.0443312i	−0.617876	+	0.786276i	$0.712006\pi$
$758$		−	50.4777i		−	1.83343i
$759$		0			0
$760$		0			0
$761$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$761$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	4.26315	−	1.38518i	0.154034	−	0.0500486i
$767$	20.8216	+	6.76533i	0.751823	+	0.244282i
$768$		0			0
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$		0			0
$775$	31.7106	−	23.0391i	1.13908	−	0.827589i
$776$		0			0
$777$		0			0
$778$	−52.7711	−	17.1464i	−1.89194	−	0.614727i
$779$		0			0
$780$		0			0
$781$	−54.7118	+	3.59766i	−1.95774	+	0.128734i
$782$		0			0
$783$		0			0
$784$	4.40828	−	13.5673i	0.157438	−	0.484546i
$785$		0			0
$786$		0			0
$787$	−0.831254	−	1.14412i	−0.0296310	−	0.0407836i	0.793944	−	0.607990i	$-0.208024\pi$
$787$	−0.831254	−	1.14412i	−0.0296310	−	0.0407836i	−0.823575	+	0.567207i	$0.808024\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			37.8364i			1.34531i
$792$	−1.84657	−	28.0818i	−0.0656149	−	0.997845i
$793$	4.50561			0.159999
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.5484	+	14.2027i	−0.692439	+	0.503086i	−0.877461	−	0.479648i	$-0.840764\pi$
$797$	−19.5484	+	14.2027i	−0.692439	+	0.503086i	0.185022	+	0.982734i	$0.440764\pi$
$798$		0			0
$799$	38.4442	−	12.4913i	1.36006	−	0.441910i
$800$	−26.8999	−	8.74032i	−0.951057	−	0.309017i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−12.3522	+	38.0163i	−0.435089	+	1.33907i
$807$		0			0
$808$	45.5288	−	33.0786i	1.60170	−	1.16370i
$809$	−21.1929	−	29.1695i	−0.745103	−	1.02555i	−0.998309	−	0.0581335i	$-0.981485\pi$
$809$	−21.1929	−	29.1695i	−0.745103	−	1.02555i	0.253206	−	0.967412i	$-0.418515\pi$
$810$		0			0
$811$	−9.41498	−	3.05911i	−0.330605	−	0.107420i	0.139011	−	0.990291i	$-0.455608\pi$
$811$	−9.41498	−	3.05911i	−0.330605	−	0.107420i	−0.469616	+	0.882871i	$0.655608\pi$
$812$	29.4930	+	21.4279i	1.03500	+	0.751972i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	16.2154	−	11.7812i	0.566611	−	0.411667i
$820$		0			0
$821$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$821$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$822$		0			0
$823$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$823$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$824$		0			0
$825$		0			0
$826$	15.9121			0.553652
$827$	7.48128	−	10.2971i	0.260150	−	0.358065i	−0.658884	−	0.752245i	$-0.728971\pi$
$827$	7.48128	−	10.2971i	0.260150	−	0.358065i	0.919034	+	0.394179i	$0.128971\pi$
$828$		0			0
$829$	−9.08706	−	27.9671i	−0.315607	−	0.971338i	−0.975504	−	0.219982i	$-0.929400\pi$
$829$	−9.08706	−	27.9671i	−0.315607	−	0.971338i	0.659897	−	0.751356i	$-0.270600\pi$
$830$		0			0
$831$		0			0
$832$	27.4327	−	8.91341i	0.951057	−	0.309017i
$833$	−11.8129	−	3.83825i	−0.409293	−	0.132987i
$834$		0			0
$835$		0			0
$836$	9.42765	−	14.9489i	0.326062	−	0.517020i
$837$		0			0
$838$		0			0
$839$	14.7729	−	45.4663i	0.510017	−	1.56967i	−0.282153	−	0.959369i	$-0.591049\pi$
$839$	14.7729	−	45.4663i	0.510017	−	1.56967i	0.792170	−	0.610301i	$-0.208951\pi$
$840$		0			0
$841$	54.8212	−	39.8299i	1.89039	−	1.37345i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		−	49.2421i		−	1.69298i
$847$	−14.0370	−	14.7794i	−0.482319	−	0.507826i
$848$	−57.3375			−1.96898
$849$		0			0
$850$	−7.61012	+	23.4215i	−0.261025	+	0.803352i
$851$		0			0
$852$		0			0
$853$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$853$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$854$	3.11444	−	1.01194i	0.106574	−	0.0346280i
$855$		0			0
$856$		0			0
$857$			40.7934i			1.39348i	0.717326	+	0.696738i	$0.245366\pi$
$857$			40.7934i			1.39348i	−0.717326	+	0.696738i	$0.754634\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	−16.6686	−	51.3005i	−0.567733	−	1.74730i
$863$	−28.8764	+	20.9799i	−0.982963	+	0.714164i	−0.958369	−	0.285533i	$-0.907829\pi$
$863$	−28.8764	+	20.9799i	−0.982963	+	0.714164i	−0.0245938	+	0.999698i	$0.507829\pi$
$864$		0			0
$865$		0			0
$866$	9.84025	+	3.19729i	0.334385	+	0.108648i
$867$		0			0
$868$			29.0525i			0.986107i
$869$		0			0
$870$		0			0
$871$	−10.8063	+	14.8736i	−0.366158	+	0.503973i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$877$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−50.5391			−1.70271			−0.851353	−	0.524594i	$-0.824217\pi$
$881$	−50.5391			−1.70271			−0.851353	+	0.524594i	$0.824217\pi$
$882$	−8.89368	+	12.2411i	−0.299466	+	0.412179i
$883$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$883$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$884$	−7.76083	−	23.8854i	−0.261025	−	0.803352i
$885$		0			0
$886$		0			0
$887$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$887$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−7.34144	+	28.9327i	−0.245948	+	0.969283i
$892$	50.9902			1.70728
$893$	18.1767	−	25.0181i	0.608259	−	0.837197i
$894$		0			0
$895$		0			0
$896$	16.9605	−	12.3225i	0.566611	−	0.411667i
$897$		0			0
$898$		0			0
$899$	73.3394	+	23.8294i	2.44601	+	0.794756i
$900$	24.2705	+	17.6336i	0.809017	+	0.587785i
$901$			49.9232i			1.66318i
$902$		0			0
$903$		0			0
$904$	33.9466	−	46.7235i	1.12905	−	1.55400i
$905$		0			0
$906$		0			0
$907$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$907$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$908$	31.7683	+	43.7253i	1.05427	+	1.45107i
$909$	−56.7690	+	18.4454i	−1.88291	+	0.611794i
$910$		0			0
$911$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$911$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$912$		0			0
$913$	−3.83174	−	58.2716i	−0.126812	−	1.92851i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$919$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			59.6064i			1.96197i
$924$		0			0
$925$		0			0
$926$	28.1751	−	38.7797i	0.925892	−	1.27438i
$927$		0			0
$928$	−17.1954	−	52.9219i	−0.564466	−	1.73725i
$929$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$929$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$	−9.03708	+	2.93633i	−0.296178	+	0.0962342i
$932$	35.0445	+	11.3866i	1.14792	+	0.372982i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−30.5941			−1.00000
$937$	−35.4261	+	48.7598i	−1.15732	+	1.59291i	−0.436658	+	0.899628i	$0.643838\pi$
$937$	−35.4261	+	48.7598i	−1.15732	+	1.59291i	−0.720662	+	0.693287i	$0.756162\pi$
$938$	−4.12915	+	12.7082i	−0.134822	+	0.414938i
$939$		0			0
$940$		0			0
$941$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$941$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$942$		0			0
$943$		0			0
$944$	−19.6496	−	14.2762i	−0.639539	−	0.464652i
$945$		0			0
$946$		0			0
$947$	13.0204			0.423105			0.211553	−	0.977367i	$-0.432148\pi$
$947$	13.0204			0.423105			0.211553	+	0.977367i	$0.432148\pi$
$948$		0			0
$949$		0			0
$950$	5.82187	+	17.9179i	0.188887	+	0.581333i
$951$		0			0
$952$	−10.7291	−	14.7674i	−0.347733	−	0.478613i
$953$	54.8653	−	17.8268i	1.77726	−	0.577468i	0.778521	−	0.627619i	$-0.215970\pi$
$953$	54.8653	−	17.8268i	1.77726	−	0.577468i	0.998742	+	0.0501514i	$0.0159704\pi$
$954$	57.8390	+	18.7930i	1.87261	+	0.608447i
$955$		0			0
$956$		−	61.4594i		−	1.98774i
$957$		0			0
$958$	38.4975			1.24380
$959$		0			0
$960$		0			0
$961$	9.41097	+	28.9640i	0.303580	+	0.934323i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	26.8701i		−	0.864083i	−0.901854	−	0.432041i	$-0.857793\pi$
$967$		−	26.8701i		−	0.864083i	0.901854	−	0.432041i	$-0.142207\pi$
$968$	4.07411	+	30.8448i	0.130947	+	0.991389i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$		0			0
$973$		0			0
$974$	24.8496	+	34.2025i	0.796231	+	1.09592i
$975$		0			0
$976$	−4.75389	−	1.54463i	−0.152168	−	0.0494424i
$977$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$977$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−16.4112	−	50.5085i	−0.523437	−	1.61097i	−0.767387	−	0.641184i	$-0.778443\pi$
$983$	−16.4112	−	50.5085i	−0.523437	−	1.61097i	0.243950	−	0.969788i	$-0.421557\pi$
$984$		0			0
$985$		0			0
$986$	−46.0786	+	14.9718i	−1.46744	+	0.476801i
$987$		0			0
$988$	−15.5437	−	11.2932i	−0.494511	−	0.359284i
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	26.0658	−	35.8765i	0.827589	−	1.13908i
$993$		0			0
$994$	13.3874	+	41.2021i	0.424622	+	1.30685i
$995$		0			0
$996$		0			0
$997$	−7.57546	+	2.46141i	−0.239917	+	0.0779538i	−0.426508	−	0.904484i	$-0.640256\pi$
$997$	−7.57546	+	2.46141i	−0.239917	+	0.0779538i	0.186590	+	0.982438i	$0.440256\pi$
$998$	60.0813	+	19.5216i	1.90184	+	0.617945i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bb.a.51.1	✓	16
4.3	odd	2	inner	572.2.bb.a.51.4	yes	16
11.8	odd	10	inner	572.2.bb.a.415.1	yes	16
13.12	even	2	inner	572.2.bb.a.51.4	yes	16
44.19	even	10	inner	572.2.bb.a.415.4	yes	16
52.51	odd	2	CM	572.2.bb.a.51.1	✓	16
143.129	odd	10	inner	572.2.bb.a.415.4	yes	16
572.415	even	10	inner	572.2.bb.a.415.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bb.a.51.1	✓	16	1.1	even	1	trivial
572.2.bb.a.51.1	✓	16	52.51	odd	2	CM
572.2.bb.a.51.4	yes	16	4.3	odd	2	inner
572.2.bb.a.51.4	yes	16	13.12	even	2	inner
572.2.bb.a.415.1	yes	16	11.8	odd	10	inner
572.2.bb.a.415.1	yes	16	572.415	even	10	inner
572.2.bb.a.415.4	yes	16	44.19	even	10	inner
572.2.bb.a.415.4	yes	16	143.129	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831254 + 1.14412i) q^{2} +(-0.618034 - 1.90211i) q^{4} +(-1.76231 + 0.572610i) q^{7} +(2.68999 + 0.874032i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(-0.831254 + 1.14412i) q^{2} +(-0.618034 - 1.90211i) q^{4} +(-1.76231 + 0.572610i) q^{7} +(2.68999 + 0.874032i) q^{8} +(-2.42705 - 1.76336i) q^{9} +(2.80534 + 1.76920i) q^{11} +(2.11929 - 2.91695i) q^{13} +(0.809793 - 2.49229i) q^{14} +(-3.23607 + 2.35114i) q^{16} +(2.04712 + 2.81761i) q^{17} +(4.03499 - 1.31105i) q^{18} +(2.53397 + 0.823337i) q^{19} +(-4.35613 + 1.73899i) q^{22} +(1.54508 - 4.75528i) q^{25} +(1.57568 + 4.84946i) q^{26} +(2.17834 + 2.99823i) q^{28} +(9.35536 - 3.03974i) q^{29} +(6.34212 + 4.60782i) q^{31} -5.65685i q^{32} -4.92537 q^{34} +(-1.85410 + 5.70634i) q^{36} +(-3.04837 + 2.21477i) q^{38} +(1.63143 - 6.42950i) q^{44} +(3.58660 - 11.0384i) q^{47} +(-2.88525 + 2.09626i) q^{49} +(4.15627 + 5.72061i) q^{50} +(-6.85817 - 2.22835i) q^{52} +(11.5967 + 8.42553i) q^{53} -5.24109 q^{56} +(-4.29884 + 13.2305i) q^{58} +(1.87637 + 5.77486i) q^{59} +(0.734516 + 1.01097i) q^{61} +(-10.5438 + 3.42590i) q^{62} +(5.28694 + 1.71783i) q^{63} +(6.47214 + 4.70228i) q^{64} -5.09902 q^{67} +(4.09423 - 5.63523i) q^{68} +(-13.3745 + 9.71718i) q^{71} +(-4.98752 - 6.86474i) q^{72} -5.32875i q^{76} +(-5.95695 - 1.51153i) q^{77} +(2.78115 + 8.55951i) q^{81} +(-10.3494 - 14.2448i) q^{83} +(6.00000 + 7.21110i) q^{88} +(-2.06458 + 6.35411i) q^{91} +(9.64793 + 13.2792i) q^{94} -5.04361i q^{98} +(-3.68896 - 9.24076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^9	\( 16 q + 8 q^{4} - 12 q^{9} - 8 q^{14} - 16 q^{16} - 40 q^{17} + 12 q^{22} - 20 q^{25} + 80 q^{29} + 24 q^{36} + 40 q^{38} - 20 q^{49} + 8 q^{53} + 16 q^{56} - 140 q^{62} + 32 q^{64} - 80 q^{68} - 112 q^{77} - 36 q^{81} + 96 q^{88} + 180 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 - 12 * q^9 - 8 * q^14 - 16 * q^16 - 40 * q^17 + 12 * q^22 - 20 * q^25 + 80 * q^29 + 24 * q^36 + 40 * q^38 - 20 * q^49 + 8 * q^53 + 16 * q^56 - 140 * q^62 + 32 * q^64 - 80 * q^68 - 112 * q^77 - 36 * q^81 + 96 * q^88 + 180 * q^94

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