LMFDB - Embedded newform 572.2.bb.a.519.2

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			519.2
Root			$-2.47822 - 0.926503i$ of defining polynomial
Character	$\chi$	$=$	572.519
Dual form			572.2.bb.a.259.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34500 - 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} +(3.10731 - 4.27685i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.927051 - 2.85317i) q^{9} +O(q^{10})$	\(q+(-1.34500 - 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} +(3.10731 - 4.27685i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.927051 - 2.85317i) q^{9} +(-3.30948 + 0.217620i) q^{11} +(3.42908 + 1.11418i) q^{13} +(-6.04837 + 4.39440i) q^{14} +(1.23607 + 3.80423i) q^{16} +(-5.73732 + 1.86417i) q^{17} +(-2.49376 + 3.43237i) q^{18} +(-1.60082 - 2.20335i) q^{19} +(4.54634 + 1.15360i) q^{22} +(-4.04508 + 2.93893i) q^{25} +(-4.12519 - 2.99713i) q^{26} +(10.0555 - 3.26722i) q^{28} +(6.19302 - 8.52395i) q^{29} +(0.523346 - 1.61069i) q^{31} -5.65685i q^{32} +8.53136 q^{34} +(4.85410 - 3.52671i) q^{36} +(1.19021 + 3.66308i) q^{38} +(-5.61067 - 3.53841i) q^{44} +(-8.51837 + 6.18896i) q^{47} +(-6.47291 - 19.9216i) q^{49} +(6.72499 - 2.18508i) q^{50} +(4.23858 + 5.83390i) q^{52} +(3.11959 - 9.60110i) q^{53} -14.9524 q^{56} +(-12.0547 + 8.75825i) q^{58} +(10.6846 + 7.76278i) q^{59} +(7.74264 - 2.51574i) q^{61} +(-1.40780 + 1.93767i) q^{62} +(-9.32193 - 12.8305i) q^{63} +(-2.47214 + 7.60845i) q^{64} -5.09902 q^{67} +(-11.4746 - 3.72834i) q^{68} +(0.617396 + 1.90015i) q^{71} +(-8.06998 + 2.62210i) q^{72} -5.44697i q^{76} +(-9.35285 + 14.8303i) q^{77} +(-7.28115 - 5.29007i) q^{81} +(16.1682 - 5.25336i) q^{83} +(6.00000 + 7.21110i) q^{88} +(15.4204 - 11.2036i) q^{91} +(14.1619 - 4.60147i) q^{94} +29.6232i q^{98} +(-2.44715 + 9.64425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.34500	−	0.437016i	−0.951057	−	0.309017i
$2$	−1.34500	−	0.437016i	−0.951057	−	0.309017i
$3$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$3$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$4$	1.61803	+	1.17557i	0.809017	+	0.587785i
$5$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$5$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$6$		0			0
$7$	3.10731	−	4.27685i	1.17445	−	1.61650i	0.551957	−	0.833873i	$-0.313881\pi$
$7$	3.10731	−	4.27685i	1.17445	−	1.61650i	0.622496	−	0.782623i	$-0.286119\pi$
$8$	−1.66251	−	2.28825i	−0.587785	−	0.809017i
$9$	0.927051	−	2.85317i	0.309017	−	0.951057i
$10$		0			0
$11$	−3.30948	+	0.217620i	−0.997845	+	0.0656149i
$11$	−3.30948	+	0.217620i	−0.997845	+	0.0656149i
$12$		0			0
$13$	3.42908	+	1.11418i	0.951057	+	0.309017i
$13$	3.42908	+	1.11418i	0.951057	+	0.309017i
$14$	−6.04837	+	4.39440i	−1.61650	+	1.17445i
$15$		0			0
$16$	1.23607	+	3.80423i	0.309017	+	0.951057i
$17$	−5.73732	+	1.86417i	−1.39151	+	0.452128i	−0.906434	−	0.422347i	$-0.861206\pi$
$17$	−5.73732	+	1.86417i	−1.39151	+	0.452128i	−0.485071	+	0.874475i	$0.661206\pi$
$18$	−2.49376	+	3.43237i	−0.587785	+	0.809017i
$19$	−1.60082	−	2.20335i	−0.367254	−	0.505482i	0.584898	−	0.811107i	$-0.301135\pi$
$19$	−1.60082	−	2.20335i	−0.367254	−	0.505482i	−0.952152	+	0.305625i	$0.901135\pi$
$20$		0			0
$21$		0			0
$22$	4.54634	+	1.15360i	0.969283	+	0.245948i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	−4.12519	−	2.99713i	−0.809017	−	0.587785i
$27$		0			0
$28$	10.0555	−	3.26722i	1.90030	−	0.617446i
$29$	6.19302	−	8.52395i	1.15001	−	1.58286i	0.407233	−	0.913324i	$-0.366494\pi$
$29$	6.19302	−	8.52395i	1.15001	−	1.58286i	0.742781	−	0.669534i	$-0.233506\pi$
$30$		0			0
$31$	0.523346	−	1.61069i	0.0939957	−	0.289289i	−0.892995	−	0.450067i	$-0.851400\pi$
$31$	0.523346	−	1.61069i	0.0939957	−	0.289289i	0.986991	+	0.160778i	$0.0514002\pi$
$32$		−	5.65685i		−	1.00000i
$33$		0			0
$34$	8.53136			1.46312
$35$		0			0
$36$	4.85410	−	3.52671i	0.809017	−	0.587785i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$	1.19021	+	3.66308i	0.193077	+	0.594230i
$39$		0			0
$40$		0			0
$41$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$41$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−5.61067	−	3.53841i	−0.845841	−	0.533435i
$45$		0			0
$46$		0			0
$47$	−8.51837	+	6.18896i	−1.24253	+	0.902753i	−0.997764	−	0.0668289i	$-0.978712\pi$
$47$	−8.51837	+	6.18896i	−1.24253	+	0.902753i	−0.244768	+	0.969582i	$0.578712\pi$
$48$		0			0
$49$	−6.47291	−	19.9216i	−0.924702	−	2.84594i
$50$	6.72499	−	2.18508i	0.951057	−	0.309017i
$51$		0			0
$52$	4.23858	+	5.83390i	0.587785	+	0.809017i
$53$	3.11959	−	9.60110i	0.428508	−	1.31881i	−0.471087	−	0.882087i	$-0.656138\pi$
$53$	3.11959	−	9.60110i	0.428508	−	1.31881i	0.899595	−	0.436726i	$-0.143862\pi$
$54$		0			0
$55$		0			0
$56$	−14.9524			−1.99810
$57$		0			0
$58$	−12.0547	+	8.75825i	−1.58286	+	1.15001i
$59$	10.6846	+	7.76278i	1.39101	+	1.01063i	0.995754	+	0.0920575i	$0.0293443\pi$
$59$	10.6846	+	7.76278i	1.39101	+	1.01063i	0.395257	+	0.918571i	$0.370656\pi$
$60$		0			0
$61$	7.74264	−	2.51574i	0.991344	−	0.322107i	0.231942	−	0.972730i	$-0.425492\pi$
$61$	7.74264	−	2.51574i	0.991344	−	0.322107i	0.759401	+	0.650622i	$0.225492\pi$
$62$	−1.40780	+	1.93767i	−0.178791	+	0.246084i
$63$	−9.32193	−	12.8305i	−1.17445	−	1.61650i
$64$	−2.47214	+	7.60845i	−0.309017	+	0.951057i
$65$		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	$0.600822\pi$
$68$	−11.4746	−	3.72834i	−1.39151	−	0.452128i
$69$		0			0
$70$		0			0
$71$	0.617396	+	1.90015i	0.0732714	+	0.225506i	0.980985	−	0.194085i	$-0.0621736\pi$
$71$	0.617396	+	1.90015i	0.0732714	+	0.225506i	−0.907713	+	0.419591i	$0.862174\pi$
$72$	−8.06998	+	2.62210i	−0.951057	+	0.309017i
$73$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$73$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$74$		0			0
$75$		0			0
$76$		−	5.44697i		−	0.624810i
$77$	−9.35285	+	14.8303i	−1.06586	+	1.69007i
$78$		0			0
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$		0			0
$81$	−7.28115	−	5.29007i	−0.809017	−	0.587785i
$82$		0			0
$83$	16.1682	−	5.25336i	1.77469	−	0.576632i	0.776145	−	0.630555i	$-0.217173\pi$
$83$	16.1682	−	5.25336i	1.77469	−	0.576632i	0.998545	+	0.0539231i	$0.0171726\pi$
$84$		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
$91$	15.4204	−	11.2036i	1.61650	−	1.17445i
$92$		0			0
$93$		0			0
$94$	14.1619	−	4.60147i	1.46068	−	0.474605i
$95$		0			0
$96$		0			0
$97$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$97$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$98$			29.6232i			2.99240i
$99$	−2.44715	+	9.64425i	−0.245948	+	0.969283i
$100$	−10.0000			−1.00000
$101$	8.42454	+	2.73730i	0.838273	+	0.272371i	0.696526	−	0.717532i	$-0.254728\pi$
$101$	8.42454	+	2.73730i	0.838273	+	0.272371i	0.141747	+	0.989903i	$0.454728\pi$
$102$		0			0
$103$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$103$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$104$	−3.15137	−	9.69891i	−0.309017	−	0.951057i
$105$		0			0
$106$	−8.39167	+	11.5501i	−0.815071	+	1.12185i
$107$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$107$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	20.1109	+	6.53444i	1.90030	+	0.617446i
$113$	−0.548373	+	0.398416i	−0.0515866	+	0.0374798i	−0.613280	−	0.789866i	$-0.710150\pi$
$113$	−0.548373	+	0.398416i	−0.0515866	+	0.0374798i	0.561693	+	0.827346i	$0.310150\pi$
$114$		0			0
$115$		0			0
$116$	20.0410	−	6.51172i	1.86076	−	0.604598i
$117$	6.35787	−	8.75086i	0.587785	−	0.809017i
$118$	−10.9782	−	15.1102i	−1.01063	−	1.39101i
$119$	−9.85488	+	30.3302i	−0.903395	+	2.78036i
$120$		0			0
$121$	10.9053	−	1.44042i	0.991389	−	0.130947i
$122$	−11.5133			−1.04236
$123$		0			0
$124$	2.74028	−	1.99093i	0.246084	−	0.178791i
$125$		0			0
$126$	6.93082	+	21.3309i	0.617446	+	1.90030i
$127$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$127$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$128$	6.65003	−	9.15298i	0.587785	−	0.809017i
$129$		0			0
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−14.3976			−1.24843
$134$	6.85817	+	2.22835i	0.592455	+	0.192500i
$135$		0			0
$136$	13.8040	+	10.0292i	1.18369	+	0.859998i
$137$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$137$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$138$		0			0
$139$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$139$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$140$		0			0
$141$		0			0
$142$		−	2.82551i		−	0.237111i
$143$	−11.5909	−	2.94111i	−0.969283	−	0.245948i
$144$	12.0000			1.00000
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$149$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$150$		0			0
$151$	13.1941	+	18.1602i	1.07372	+	1.47785i	0.866248	+	0.499614i	$0.166525\pi$
$151$	13.1941	+	18.1602i	1.07372	+	1.47785i	0.207476	+	0.978240i	$0.433475\pi$
$152$	−2.38041	+	7.32616i	−0.193077	+	0.594230i
$153$			18.0977i			1.46312i
$154$	19.0606	−	15.8594i	1.53595	−	1.27799i
$155$		0			0
$156$		0			0
$157$	−11.5484	+	8.39038i	−0.921660	+	0.669626i	−0.943937	−	0.330126i	$-0.892909\pi$
$157$	−11.5484	+	8.39038i	−0.921660	+	0.669626i	0.0222763	+	0.999752i	$0.492909\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	7.48128	+	10.2971i	0.587785	+	0.809017i
$163$	−2.01894	+	6.21365i	−0.158135	+	0.486691i	−0.998465	−	0.0553849i	$-0.982361\pi$
$163$	−2.01894	+	6.21365i	−0.158135	+	0.486691i	0.840330	+	0.542076i	$0.182361\pi$
$164$		0			0
$165$		0			0
$166$	−24.0420			−1.86602
$167$	−10.9878	−	3.57016i	−0.850263	−	0.276267i	−0.148707	−	0.988881i	$-0.547511\pi$
$167$	−10.9878	−	3.57016i	−0.850263	−	0.276267i	−0.701556	+	0.712614i	$0.747511\pi$
$168$		0			0
$169$	10.5172	+	7.64121i	0.809017	+	0.587785i
$170$		0			0
$171$	−7.77057	+	2.52481i	−0.594230	+	0.193077i
$172$		0			0
$173$	8.47716	+	11.6678i	0.644506	+	0.887087i	0.998846	−	0.0480298i	$-0.0152942\pi$
$173$	8.47716	+	11.6678i	0.644506	+	0.887087i	−0.354339	+	0.935117i	$0.615294\pi$
$174$		0			0
$175$			26.4324i			1.99810i
$176$	−4.91861	−	12.3210i	−0.370755	−	0.928731i
$177$		0			0
$178$		0			0
$179$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$179$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$180$		0			0
$181$	4.83001	+	14.8652i	0.359011	+	1.10492i	0.953647	+	0.300928i	$0.0972964\pi$
$181$	4.83001	+	14.8652i	0.359011	+	1.10492i	−0.594635	+	0.803996i	$0.702704\pi$
$182$	−25.6365	+	8.32981i	−1.90030	+	0.617446i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	18.5819	−	7.41798i	1.35884	−	0.542457i
$188$	−21.0586			−1.53585
$189$		0			0
$190$		0			0
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$		0			0
$193$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$193$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$194$		0			0
$195$		0			0
$196$	12.9458	−	39.8432i	0.924702	−	2.84594i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	7.50610	−	11.9020i	0.533435	−	0.845841i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	13.4500	+	4.37016i	0.951057	+	0.309017i
$201$		0			0
$202$	−10.1347	−	7.36332i	−0.713078	−	0.518081i
$203$	−17.2120	−	52.9731i	−1.20805	−	3.71799i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$			14.4222i			1.00000i
$209$	5.77739	+	6.94355i	0.399630	+	0.480296i
$210$		0			0
$211$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$211$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$212$	16.3344	−	11.8676i	1.12185	−	0.815071i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.26249	−	7.24320i	−0.357241	−	0.491700i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−21.7508			−1.46312
$222$		0			0
$223$	20.6260	−	14.9856i	1.38122	−	1.00351i	0.384452	−	0.923145i	$-0.374391\pi$
$223$	20.6260	−	14.9856i	1.38122	−	1.00351i	0.996765	−	0.0803677i	$-0.0256095\pi$
$224$	−24.1935	−	17.5776i	−1.61650	−	1.17445i
$225$	4.63525	+	14.2658i	0.309017	+	0.951057i
$226$	0.911674	−	0.296221i	0.0606437	−	0.0197043i
$227$	−2.54386	+	3.50133i	−0.168842	+	0.232391i	−0.885050	−	0.465495i	$-0.845876\pi$
$227$	−2.54386	+	3.50133i	−0.168842	+	0.232391i	0.716208	+	0.697887i	$0.245876\pi$
$228$		0			0
$229$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$229$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$230$		0			0
$231$		0			0
$232$	−29.8008			−1.95652
$233$	27.7837	+	9.02746i	1.82017	+	0.591408i	0.999809	+	0.0195604i	$0.00622666\pi$
$233$	27.7837	+	9.02746i	1.82017	+	0.591408i	0.820360	+	0.571848i	$0.193773\pi$
$234$	−12.3756	+	8.99139i	−0.809017	+	0.587785i
$235$		0			0
$236$	8.16227	+	25.1209i	0.531319	+	1.63523i
$237$		0			0
$238$	26.5096	−	36.4873i	1.71836	−	2.36512i
$239$	−3.67076	−	5.05236i	−0.237441	−	0.326810i	0.673622	−	0.739076i	$-0.264738\pi$
$239$	−3.67076	−	5.05236i	−0.237441	−	0.326810i	−0.911064	+	0.412266i	$0.864738\pi$
$240$		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
$244$	15.4853	+	5.03147i	0.991344	+	0.322107i
$245$		0			0
$246$		0			0
$247$	−3.03444	−	9.33906i	−0.193077	−	0.594230i
$248$	−4.55573	+	1.48025i	−0.289289	+	0.0939957i
$249$		0			0
$250$		0			0
$251$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$251$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$252$		−	31.7188i		−	1.99810i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	−18.6935	−	13.5816i	−1.16607	−	0.847198i	−0.175535	−	0.984473i	$-0.556166\pi$
$257$	−18.6935	−	13.5816i	−1.16607	−	0.847198i	−0.990533	+	0.137275i	$0.956166\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−18.5790	−	25.5719i	−1.15001	−	1.58286i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$		0			0
$266$	19.3648	+	6.29199i	1.18733	+	0.385787i
$267$		0			0
$268$	−8.25039	−	5.99426i	−0.503973	−	0.366158i
$269$	6.69021	+	20.5903i	0.407909	+	1.25542i	0.918442	+	0.395557i	$0.129448\pi$
$269$	6.69021	+	20.5903i	0.407909	+	1.25542i	−0.510532	+	0.859858i	$0.670552\pi$
$270$		0			0
$271$	8.75848	−	12.0550i	0.532040	−	0.732290i	−0.455400	−	0.890287i	$-0.650504\pi$
$271$	8.75848	−	12.0550i	0.532040	−	0.732290i	0.987440	+	0.157997i	$0.0505036\pi$
$272$	−14.1834	−	19.5218i	−0.859998	−	1.18369i
$273$		0			0
$274$		0			0
$275$	12.7475	−	10.6066i	0.768706	−	0.639602i
$276$		0			0
$277$	−31.3738	−	10.1940i	−1.88507	−	0.612497i	−0.983808	−	0.179224i	$-0.942641\pi$
$277$	−31.3738	−	10.1940i	−1.88507	−	0.612497i	−0.901263	−	0.433273i	$-0.857359\pi$
$278$		0			0
$279$	−4.11041	−	2.98639i	−0.246084	−	0.178791i
$280$		0			0
$281$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$281$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$282$		0			0
$283$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$283$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$284$	−1.23479	+	3.80030i	−0.0732714	+	0.225506i
$285$		0			0
$286$	14.3045	+	9.02120i	0.845841	+	0.533435i
$287$		0			0
$288$	−16.1400	−	5.24419i	−0.951057	−	0.309017i
$289$	15.6885	−	11.3983i	0.922851	−	0.670491i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$293$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−9.80979	−	30.1914i	−0.564490	−	1.73732i
$303$		0			0
$304$	6.40330	−	8.81338i	0.367254	−	0.505482i
$305$		0			0
$306$	7.90900	−	24.3414i	0.452128	−	1.39151i
$307$			16.8180i			0.959854i	0.877308	+	0.479927i	$0.159337\pi$
$307$			16.8180i			0.959854i	−0.877308	+	0.479927i	$0.840663\pi$
$308$	−32.5673	+	13.0011i	−1.85570	+	0.740804i
$309$		0			0
$310$		0			0
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$	9.03163	+	27.7965i	0.510498	+	1.57115i	0.791327	+	0.611393i	$0.209391\pi$
$313$	9.03163	+	27.7965i	0.510498	+	1.57115i	−0.280829	+	0.959758i	$0.590609\pi$
$314$	19.1993	−	6.23822i	1.08348	−	0.352043i
$315$		0			0
$316$		0			0
$317$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$317$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$318$		0			0
$319$	−18.6407	+	29.5576i	−1.04368	+	1.65491i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	13.2919	+	9.65710i	0.739579	+	0.537336i
$324$	−5.56231	−	17.1190i	−0.309017	−	0.951057i
$325$	−17.1454	+	5.57088i	−0.951057	+	0.309017i
$326$	5.43093	−	7.47504i	0.300791	−	0.414004i
$327$		0			0
$328$		0			0
$329$			55.6628i			3.06879i
$330$		0			0
$331$	24.7201			1.35874			0.679369	−	0.733796i	$-0.262253\pi$
$331$	24.7201			1.35874			0.679369	+	0.733796i	$0.262253\pi$
$332$	32.3364	+	10.5067i	1.77469	+	0.576632i
$333$		0			0
$334$	13.2184	+	9.60370i	0.723277	+	0.525491i
$335$		0			0
$336$		0			0
$337$	−9.00861	+	12.3993i	−0.490730	+	0.675432i	−0.980522	−	0.196407i	$-0.937073\pi$
$337$	−9.00861	+	12.3993i	−0.490730	+	0.675432i	0.489792	+	0.871839i	$0.337073\pi$
$338$	−10.8063	−	14.8736i	−0.587785	−	0.809017i
$339$		0			0
$340$		0			0
$341$	−1.38148	+	5.44445i	−0.0748115	+	0.294833i
$342$	11.5548			0.624810
$343$	−70.1207	−	22.7836i	−3.78616	−	1.23020i
$344$		0			0
$345$		0			0
$346$	−6.30273	−	19.3978i	−0.338837	−	1.04283i
$347$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$347$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$348$		0			0
$349$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$349$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$350$	11.5514	−	35.5514i	0.617446	−	1.90030i
$351$		0			0
$352$	1.23104	+	18.7212i	0.0656149	+	0.997845i
$353$		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
$359$	18.3842	−	25.3036i	0.970279	−	1.33547i	0.0283731	−	0.999597i	$-0.490967\pi$
$359$	18.3842	−	25.3036i	0.970279	−	1.33547i	0.941906	−	0.335877i	$-0.109033\pi$
$360$		0			0
$361$	3.57923	−	11.0157i	0.188380	−	0.579775i
$362$		−	22.1045i		−	1.16179i
$363$		0			0
$364$	38.1213			1.99810
$365$		0			0
$366$		0			0
$367$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$367$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−31.3689	−	43.1756i	−1.62859	−	2.24156i
$372$		0			0
$373$		−	23.7487i		−	1.22966i	−0.788658	−	0.614832i	$-0.789224\pi$
$373$		−	23.7487i		−	1.22966i	0.788658	−	0.614832i	$-0.210776\pi$
$374$	−28.2343	+	1.85659i	−1.45996	+	0.0960022i
$375$		0			0
$376$	28.3237	+	9.20294i	1.46068	+	0.474605i
$377$	30.7336	−	22.3292i	1.58286	−	1.15001i
$378$		0			0
$379$	11.0298	+	33.9462i	0.566562	+	1.74370i	0.663264	+	0.748385i	$0.269171\pi$
$379$	11.0298	+	33.9462i	0.566562	+	1.74370i	−0.0967022	+	0.995313i	$0.530829\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.1627	+	34.3554i	−0.570389	+	1.75548i	0.0809804	+	0.996716i	$0.474195\pi$
$383$	−11.1627	+	34.3554i	−0.570389	+	1.75548i	−0.651369	+	0.758761i	$0.725805\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	27.6176	+	20.0653i	1.40027	+	1.01735i	0.994649	+	0.103309i	$0.0329430\pi$
$389$	27.6176	+	20.0653i	1.40027	+	1.01735i	0.405616	+	0.914044i	$0.367057\pi$
$390$		0			0
$391$		0			0
$392$	−34.8242	+	47.9314i	−1.75889	+	2.42090i
$393$		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
$400$	−16.1803	−	11.7557i	−0.809017	−	0.587785i
$401$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$401$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$402$		0			0
$403$	3.58919	−	4.94010i	0.178791	−	0.246084i
$404$	10.4133	+	14.3327i	0.518081	+	0.713078i
$405$		0			0
$406$			78.7706i			3.90932i
$407$		0			0
$408$		0			0
$409$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$409$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	66.4004	−	21.5748i	3.26735	−	1.06163i
$414$		0			0
$415$		0			0
$416$	6.30273	−	19.3978i	0.309017	−	0.951057i
$417$		0			0
$418$	−4.73612	−	11.8639i	−0.231651	−	0.580281i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$	9.76119	+	30.0418i	0.474605	+	1.46068i
$424$	−27.1560	+	8.82352i	−1.31881	+	0.428508i
$425$	17.7293	−	24.4023i	0.859998	−	1.18369i
$426$		0			0
$427$	13.2994	−	40.9313i	0.643602	−	1.98080i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−26.0503	−	8.46427i	−1.25480	−	0.407709i	−0.395162	−	0.918612i	$-0.629311\pi$
$431$	−26.0503	−	8.46427i	−1.25480	−	0.407709i	−0.859639	+	0.510902i	$0.829311\pi$
$432$		0			0
$433$	−29.6935	−	21.5736i	−1.42698	−	1.03676i	−0.990569	−	0.137012i	$-0.956250\pi$
$433$	−29.6935	−	21.5736i	−1.42698	−	1.03676i	−0.436409	−	0.899749i	$-0.643750\pi$
$434$	3.91264	+	12.0419i	0.187813	+	0.578028i
$435$		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
$441$	−62.8404			−2.99240
$442$	29.2547	+	9.50544i	1.39151	+	0.452128i
$443$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$443$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$444$		0			0
$445$		0			0
$446$	−34.2908	+	11.1418i	−1.62372	+	0.527578i
$447$		0			0
$448$	24.8585	+	34.2148i	1.17445	+	1.61650i
$449$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$449$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$450$		−	21.2132i		−	1.00000i
$451$		0			0
$452$	−1.35565			−0.0637645
$453$		0			0
$454$	4.95163	−	3.59757i	0.232391	−	0.168842i
$455$		0			0
$456$		0			0
$457$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$457$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$458$		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
$463$	43.0077			1.99874			0.999368	−	0.0355482i	$-0.0113177\pi$
$463$	43.0077			1.99874			0.999368	+	0.0355482i	$0.0113177\pi$
$464$	40.0820	+	13.0234i	1.86076	+	0.604598i
$465$		0			0
$466$	−33.4238	−	24.2838i	−1.54833	−	1.12493i
$467$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$467$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$468$	20.5745	−	6.68506i	0.951057	−	0.309017i
$469$	−15.8442	+	21.8077i	−0.731619	+	1.00699i
$470$		0			0
$471$		0			0
$472$		−	37.3546i		−	1.71938i
$473$		0			0
$474$		0			0
$475$	12.9509	+	4.20802i	0.594230	+	0.193077i
$476$	−51.6008	+	37.4902i	−2.36512	+	1.71836i
$477$	−24.5015	−	17.8014i	−1.12185	−	0.815071i
$478$	2.72919	+	8.39959i	0.124830	+	0.384188i
$479$	40.1070	−	13.0315i	1.83253	−	0.595426i	0.833451	−	0.552593i	$-0.186362\pi$
$479$	40.1070	−	13.0315i	1.83253	−	0.595426i	0.999082	−	0.0428332i	$-0.0136384\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	19.3384	+	10.4893i	0.879020	+	0.476786i
$485$		0			0
$486$		0			0
$487$	−32.4571	+	23.5815i	−1.47077	+	1.06858i	−0.490384	+	0.871506i	$0.663144\pi$
$487$	−32.4571	+	23.5815i	−1.47077	+	1.06858i	−0.980389	+	0.197073i	$0.936856\pi$
$488$	−18.6288	−	13.5346i	−0.843288	−	0.612684i
$489$		0			0
$490$		0			0
$491$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$491$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$492$		0			0
$493$	−19.6412	+	60.4495i	−0.884597	+	2.72251i
$494$			13.8871i			0.624810i
$495$		0			0
$496$	6.77433			0.304177
$497$	10.0451	+	3.26384i	0.450583	+	0.146403i
$498$		0			0
$499$	11.7511	+	8.53767i	0.526051	+	0.382199i	0.818879	−	0.573967i	$-0.194596\pi$
$499$	11.7511	+	8.53767i	0.526051	+	0.382199i	−0.292827	+	0.956165i	$0.594596\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$	−13.8616	+	42.6617i	−0.617446	+	1.90030i
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$509$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	21.5200	−	6.99226i	0.951057	−	0.309017i
$513$		0			0
$514$	19.2073	+	26.4366i	0.847198	+	1.16607i
$515$		0			0
$516$		0			0
$517$	26.8445	−	22.3360i	1.18062	−	0.982336i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.18082	−	0.857918i	−0.0517328	−	0.0375861i	0.561618	−	0.827396i	$-0.310179\pi$
$521$	−1.18082	−	0.857918i	−0.0517328	−	0.0375861i	−0.613351	+	0.789810i	$0.710179\pi$
$522$	13.8134	+	42.5134i	0.604598	+	1.86076i
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			10.2167i			0.445045i
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$	32.0537	−	23.2883i	1.39101	−	1.01063i
$532$	−23.2959	−	16.9254i	−1.01000	−	0.733810i
$533$		0			0
$534$		0			0
$535$		0			0
$536$	8.47716	+	11.6678i	0.366158	+	0.503973i
$537$		0			0
$538$		−	30.6177i		−	1.32002i
$539$	25.7573	+	64.5214i	1.10945	+	2.77913i
$540$		0			0
$541$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$541$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$542$	−17.0484	+	12.3864i	−0.732290	+	0.532040i
$543$		0			0
$544$	10.5453	+	32.4552i	0.452128	+	1.39151i
$545$		0			0
$546$		0			0
$547$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$547$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$548$		0			0
$549$		−	24.4233i		−	1.04236i
$550$	−21.7807	+	8.69496i	−0.928731	+	0.370755i
$551$	−28.6952			−1.22245
$552$		0			0
$553$		0			0
$554$	37.7428	+	27.4217i	1.60354	+	1.16504i
$555$		0			0
$556$		0			0
$557$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$557$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$558$	4.22339	+	5.81300i	0.178791	+	0.246084i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$563$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−45.2496	+	14.7025i	−1.90030	+	0.617446i
$568$	3.32158	−	4.57176i	0.139370	−	0.191827i
$569$	−26.4818	−	36.4491i	−1.11018	−	1.52803i	−0.821157	−	0.570702i	$-0.806671\pi$
$569$	−26.4818	−	36.4491i	−1.11018	−	1.52803i	−0.289018	−	0.957324i	$-0.593329\pi$
$570$		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
$576$	19.4164	+	14.1068i	0.809017	+	0.587785i
$577$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$577$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$578$	−26.0822	+	8.47462i	−1.08488	+	0.352498i
$579$		0			0
$580$		0			0
$581$	27.7718	−	85.4727i	1.15217	−	3.54601i
$582$		0			0
$583$	−8.23481	+	32.4535i	−0.341051	+	1.34409i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	37.1267	+	26.9742i	1.53238	+	1.11334i	0.954895	+	0.296945i	$0.0959677\pi$
$587$	37.1267	+	26.9742i	1.53238	+	1.11334i	0.577490	+	0.816398i	$0.304032\pi$
$588$		0			0
$589$	−4.38670	+	1.42533i	−0.180751	+	0.0587295i
$590$		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		−0.309017	−	0.951057i	$-0.600000\pi$
$599$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$600$		0			0
$601$	12.7157	−	17.5017i	0.518686	−	0.713910i	−0.466668	−	0.884433i	$-0.654546\pi$
$601$	12.7157	−	17.5017i	0.518686	−	0.713910i	0.985354	+	0.170523i	$0.0545457\pi$
$602$		0			0
$603$	−4.72705	+	14.5484i	−0.192500	+	0.592455i
$604$			44.8944i			1.82673i
$605$		0			0
$606$		0			0
$607$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$607$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$608$	−12.4640	+	9.05563i	−0.505482	+	0.367254i
$609$		0			0
$610$		0			0
$611$	−36.1058	+	11.7315i	−1.46068	+	0.474605i
$612$	−21.2752	+	29.2828i	−0.859998	+	1.18369i
$613$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$613$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$614$	7.34974	−	22.6202i	0.296611	−	0.912876i
$615$		0			0
$616$	49.4846	−	3.25394i	1.99379	−	0.131105i
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	39.3591	−	28.5961i	1.58198	−	1.14937i	0.667594	−	0.744526i	$-0.267324\pi$
$619$	39.3591	−	28.5961i	1.58198	−	1.14937i	0.914384	−	0.404848i	$-0.132676\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$		−	41.3332i		−	1.65201i
$627$		0			0
$628$	−28.5491			−1.13924
$629$		0			0
$630$		0			0
$631$	−36.1264	−	26.2474i	−1.43817	−	1.04489i	−0.988421	−	0.151737i	$-0.951513\pi$
$631$	−36.1264	−	26.2474i	−1.43817	−	1.04489i	−0.449749	−	0.893155i	$-0.648487\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	75.5247i		−	2.99240i
$638$	37.9888	−	31.6086i	1.50399	−	1.25139i
$639$	5.99380			0.237111
$640$		0			0
$641$	−21.3855	+	15.5375i	−0.844678	+	0.613695i	−0.923674	−	0.383180i	$-0.874829\pi$
$641$	−21.3855	+	15.5375i	−0.844678	+	0.613695i	0.0789953	+	0.996875i	$0.474829\pi$
$642$		0			0
$643$	−14.3368	−	44.1241i	−0.565388	−	1.74009i	−0.666796	−	0.745240i	$-0.732335\pi$
$643$	−14.3368	−	44.1241i	−0.565388	−	1.74009i	0.101408	−	0.994845i	$-0.467665\pi$
$644$		0			0
$645$		0			0
$646$	−13.6572	−	18.7975i	−0.537336	−	0.739579i
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$			25.4558i			1.00000i
$649$	−37.0496	−	23.3656i	−1.45433	−	0.917179i
$650$	25.4951			1.00000
$651$		0			0
$652$	−10.5713	+	7.68050i	−0.414004	+	0.300791i
$653$	36.8386	+	26.7648i	1.44161	+	1.04739i	0.987704	+	0.156337i	$0.0499685\pi$
$653$	36.8386	+	26.7648i	1.44161	+	1.04739i	0.453902	+	0.891051i	$0.350031\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	24.3255	−	74.8663i	0.948308	−	2.91859i
$659$		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			$\pi$
$662$	−33.2484	−	10.8031i	−1.29224	−	0.419873i
$663$		0			0
$664$	−38.9007	−	28.2630i	−1.50964	−	1.09682i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−13.5817	−	18.6936i	−0.525491	−	0.723277i
$669$		0			0
$670$		0			0
$671$	−25.0766	+	10.0107i	−0.968073	+	0.386460i
$672$		0			0
$673$	−45.5468	−	14.7991i	−1.75570	−	0.570462i	−0.758960	−	0.651137i	$-0.774292\pi$
$673$	−45.5468	−	14.7991i	−1.75570	−	0.570462i	−0.996740	+	0.0806753i	$0.974292\pi$
$674$	17.5352	−	12.7401i	0.675432	−	0.490730i
$675$		0			0
$676$	8.03444	+	24.7275i	0.309017	+	0.951057i
$677$	−16.8541	+	5.47623i	−0.647756	+	0.210469i	−0.614424	−	0.788976i	$-0.710612\pi$
$677$	−16.8541	+	5.47623i	−0.647756	+	0.210469i	−0.0333315	+	0.999444i	$0.510612\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	4.23740	−	6.71903i	0.162258	−	0.257285i
$683$	6.43250			0.246133			0.123066	−	0.992398i	$-0.460727\pi$
$683$	6.43250			0.246133			0.123066	+	0.992398i	$0.460727\pi$
$684$	−15.5411	−	5.04962i	−0.594230	−	0.193077i
$685$		0			0
$686$	84.3553	+	61.2877i	3.22070	+	2.33998i
$687$		0			0
$688$		0			0
$689$	21.3946	−	29.4472i	0.815071	−	1.12185i
$690$		0			0
$691$	−10.7790	+	33.1744i	−0.410053	+	1.26201i	0.506549	+	0.862211i	$0.330921\pi$
$691$	−10.7790	+	33.1744i	−0.410053	+	1.26201i	−0.916602	+	0.399801i	$0.869079\pi$
$692$			28.8444i			1.09650i
$693$	33.6429	+	40.4337i	1.27799	+	1.53595i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−31.0731	+	42.7685i	−1.17445	+	1.61650i
$701$	0.224280	+	0.308695i	0.00847095	+	0.0116593i	0.813231	−	0.581940i	$-0.197706\pi$
$701$	0.224280	+	0.308695i	0.00847095	+	0.0116593i	−0.804761	+	0.593600i	$0.797706\pi$
$702$		0			0
$703$		0			0
$704$	6.52573	−	25.7180i	0.245948	−	0.969283i
$705$		0			0
$706$		0			0
$707$	37.8847	−	27.5248i	1.42480	−	1.03518i
$708$		0			0
$709$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$709$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−35.7847	+	25.9991i	−1.33547	+	0.970279i
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$		0			0
$721$		0			0
$722$	−9.62810	+	13.2519i	−0.358321	+	0.493186i
$723$		0			0
$724$	−9.66001	+	29.7305i	−0.359011	+	1.10492i
$725$			52.6809i			1.95652i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−51.2730	−	16.6596i	−1.90030	−	0.617446i
$729$	−21.8435	+	15.8702i	−0.809017	+	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	16.8751	−	1.10965i	0.621602	−	0.0408744i
$738$		0			0
$739$	−44.3379	−	14.4063i	−1.63100	−	0.529943i	−0.656497	−	0.754329i	$-0.727962\pi$
$739$	−44.3379	−	14.4063i	−1.63100	−	0.529943i	−0.974500	+	0.224386i	$0.927962\pi$
$740$		0			0
$741$		0			0
$742$	23.3227	+	71.7797i	0.856201	+	2.63512i
$743$	−31.7093	+	10.3030i	−1.16330	+	0.377980i	−0.826139	−	0.563466i	$-0.809467\pi$
$743$	−31.7093	+	10.3030i	−1.16330	+	0.377980i	−0.337163	+	0.941446i	$0.609467\pi$
$744$		0			0
$745$		0			0
$746$	−10.3786	+	31.9420i	−0.379987	+	1.16948i
$747$		−	51.0007i		−	1.86602i
$748$	38.7864	+	9.84174i	1.41817	+	0.359850i
$749$		0			0
$750$		0			0
$751$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$751$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$752$	−34.0735	−	24.7558i	−1.24253	−	0.902753i
$753$		0			0
$754$	−51.0948	+	16.6017i	−1.86076	+	0.604598i
$755$		0			0
$756$		0			0
$757$	−15.9625	+	49.1274i	−0.580165	+	1.78556i	0.0377104	+	0.999289i	$0.487994\pi$
$757$	−15.9625	+	49.1274i	−0.580165	+	1.78556i	−0.617876	+	0.786276i	$0.712006\pi$
$758$		−	50.4777i		−	1.83343i
$759$		0			0
$760$		0			0
$761$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$761$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	30.0277	−	41.3296i	1.08494	−	1.49330i
$767$	27.9891	+	38.5237i	1.01063	+	1.39101i
$768$		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		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$		0			0
$775$	2.61673	+	8.05347i	0.0939957	+	0.289289i
$776$		0			0
$777$		0			0
$778$	−28.3767	−	39.0571i	−1.01735	−	1.40027i
$779$		0			0
$780$		0			0
$781$	−2.45677	−	6.15414i	−0.0879100	−	0.220212i
$782$		0			0
$783$		0			0
$784$	67.7852	−	49.2488i	2.42090	−	1.75889i
$785$		0			0
$786$		0			0
$787$	−1.34500	+	0.437016i	−0.0479440	+	0.0155779i	−0.332891	−	0.942965i	$-0.608024\pi$
$787$	−1.34500	+	0.437016i	−0.0479440	+	0.0155779i	0.284947	+	0.958543i	$0.408024\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			3.58331i			0.127408i
$792$	26.1368	−	10.4340i	0.928731	−	0.370755i
$793$	29.3531			1.04236
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.3098	−	47.1187i	−0.542301	−	1.66903i	−0.727323	−	0.686296i	$-0.759236\pi$
$797$	−15.3098	−	47.1187i	−0.542301	−	1.66903i	0.185022	−	0.982734i	$-0.440764\pi$
$798$		0			0
$799$	37.3354	−	51.3878i	1.32083	−	1.81797i
$800$	16.6251	+	22.8825i	0.587785	+	0.809017i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−6.98636	+	5.07589i	−0.246084	+	0.178791i
$807$		0			0
$808$	−7.74225	−	23.8282i	−0.272371	−	0.838273i
$809$	−34.2908	+	11.1418i	−1.20560	+	0.391724i	−0.841819	−	0.539760i	$-0.818515\pi$
$809$	−34.2908	+	11.1418i	−1.20560	+	0.391724i	−0.363783	+	0.931484i	$0.618515\pi$
$810$		0			0
$811$	5.81878	+	8.00886i	0.204325	+	0.281229i	0.898866	−	0.438224i	$-0.144392\pi$
$811$	5.81878	+	8.00886i	0.204325	+	0.281229i	−0.694541	+	0.719453i	$0.744392\pi$
$812$	34.4240	−	105.946i	1.20805	−	3.71799i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−17.6702	−	54.3833i	−0.617446	−	1.90030i
$820$		0			0
$821$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$821$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$822$		0			0
$823$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$823$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$824$		0			0
$825$		0			0
$826$	−98.7369			−3.43550
$827$	12.1050	+	3.93314i	0.420931	+	0.136769i	0.511821	−	0.859092i	$-0.328971\pi$
$827$	12.1050	+	3.93314i	0.420931	+	0.136769i	−0.0908898	+	0.995861i	$0.528971\pi$
$828$		0			0
$829$	4.29682	+	3.12183i	0.149235	+	0.108425i	0.659897	−	0.751356i	$-0.270600\pi$
$829$	4.29682	+	3.12183i	0.149235	+	0.108425i	−0.510662	+	0.859781i	$0.670600\pi$
$830$		0			0
$831$		0			0
$832$	−16.9543	+	23.3356i	−0.587785	+	0.809017i
$833$	74.2744	+	102.230i	2.57345	+	3.54206i
$834$		0			0
$835$		0			0
$836$	1.18537	+	18.0266i	0.0409969	+	0.623464i
$837$		0			0
$838$		0			0
$839$	46.8486	−	34.0375i	1.61739	−	1.17511i	0.792170	−	0.610301i	$-0.208951\pi$
$839$	46.8486	−	34.0375i	1.61739	−	1.17511i	0.825225	−	0.564805i	$-0.191049\pi$
$840$		0			0
$841$	−25.3429	−	77.9973i	−0.873892	−	2.68956i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		−	44.6720i		−	1.53585i
$847$	27.7257	−	51.1160i	0.952665	−	1.75637i
$848$	40.3808			1.38668
$849$		0			0
$850$	−34.5101	+	25.0730i	−1.18369	+	0.859998i
$851$		0			0
$852$		0			0
$853$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$853$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$854$	−35.7752	+	49.2404i	−1.22420	+	1.68497i
$855$		0			0
$856$		0			0
$857$		−	27.3374i		−	0.933827i	−0.884303	−	0.466914i	$-0.845366\pi$
$857$		−	27.3374i		−	0.933827i	0.884303	−	0.466914i	$-0.154634\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	31.3386	+	22.7688i	1.06740	+	0.775510i
$863$	11.0298	+	33.9462i	0.375458	+	1.15554i	0.943169	+	0.332314i	$0.107829\pi$
$863$	11.0298	+	33.9462i	0.375458	+	1.15554i	−0.567711	+	0.823228i	$0.692171\pi$
$864$		0			0
$865$		0			0
$866$	30.5097	+	41.9929i	1.03676	+	1.42698i
$867$		0			0
$868$		−	17.9062i		−	0.607775i
$869$		0			0
$870$		0			0
$871$	−17.4850	−	5.68121i	−0.592455	−	0.192500i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$877$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	22.5824			0.760820			0.380410	−	0.924818i	$-0.375783\pi$
$881$	22.5824			0.760820			0.380410	+	0.924818i	$0.375783\pi$
$882$	84.5201	+	27.4622i	2.84594	+	0.924702i
$883$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$883$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$884$	−35.1935	−	25.5696i	−1.18369	−	0.859998i
$885$		0			0
$886$		0			0
$887$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$887$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	25.2480	+	15.9228i	0.845841	+	0.533435i
$892$	50.9902			1.70728
$893$	27.2728	+	8.86149i	0.912651	+	0.296538i
$894$		0			0
$895$		0			0
$896$	−18.4822	−	56.8823i	−0.617446	−	1.90030i
$897$		0			0
$898$		0			0
$899$	−10.4884	−	14.4360i	−0.349807	−	0.481469i
$900$	−9.27051	+	28.5317i	−0.309017	+	0.951057i
$901$			60.9001i			2.02887i
$902$		0			0
$903$		0			0
$904$	1.82335	+	0.592442i	0.0606437	+	0.0197043i
$905$		0			0
$906$		0			0
$907$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$907$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$908$	−8.23212	+	2.67478i	−0.273192	+	0.0887656i
$909$	15.6200	−	21.4990i	0.518081	−	0.713078i
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$	−52.3650	+	20.9044i	−1.73303	+	0.691835i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$919$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			7.20365i			0.237111i
$924$		0			0
$925$		0			0
$926$	−57.8452	−	18.7950i	−1.90091	−	0.617643i
$927$		0			0
$928$	−48.2188	−	35.0330i	−1.58286	−	1.15001i
$929$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$929$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$930$		0			0
$931$	−33.5321	+	46.1530i	−1.09897	+	1.51260i
$932$	34.3425	+	47.2684i	1.12493	+	1.54833i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−30.5941			−1.00000
$937$	52.3804	+	17.0194i	1.71119	+	0.556000i	0.990531	−	0.137286i	$-0.0438380\pi$
$937$	52.3804	+	17.0194i	1.71119	+	0.556000i	0.720662	+	0.693287i	$0.243838\pi$
$938$	30.8408	−	22.4071i	1.00699	−	0.731619i
$939$		0			0
$940$		0			0
$941$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$941$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$942$		0			0
$943$		0			0
$944$	−16.3245	+	50.2418i	−0.531319	+	1.63523i
$945$		0			0
$946$		0			0
$947$	−53.1861			−1.72831			−0.864157	−	0.503221i	$-0.832148\pi$
$947$	−53.1861			−1.72831			−0.864157	+	0.503221i	$0.832148\pi$
$948$		0			0
$949$		0			0
$950$	−15.5800	−	11.3195i	−0.505482	−	0.367254i
$951$		0			0
$952$	85.7868	−	27.8738i	2.78036	−	0.903395i
$953$	−33.9086	+	46.6712i	−1.09841	+	1.51183i	−0.260931	+	0.965357i	$0.584030\pi$
$953$	−33.9086	+	46.6712i	−1.09841	+	1.51183i	−0.837477	+	0.546472i	$0.815970\pi$
$954$	25.1750	+	34.6504i	0.815071	+	1.12185i
$955$		0			0
$956$		−	12.4901i		−	0.403960i
$957$		0			0
$958$	−59.6387			−1.92684
$959$		0			0
$960$		0			0
$961$	22.7591	+	16.5354i	0.734164	+	0.533401i
$962$		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	$-0.142207\pi$
$968$	−21.4261	−	22.5593i	−0.688662	−	0.725082i
$969$		0			0
$970$		0			0
$971$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$971$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$972$		0			0
$973$		0			0
$974$	53.9602	−	17.5327i	1.72900	−	0.561785i
$975$		0			0
$976$	19.1409	+	26.3451i	0.612684	+	0.843288i
$977$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$977$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.9054	−	13.7356i	−0.602988	−	0.438096i	0.243950	−	0.969788i	$-0.421557\pi$
$983$	−18.9054	−	13.7356i	−0.602988	−	0.438096i	−0.846938	+	0.531691i	$0.821557\pi$
$984$		0			0
$985$		0			0
$986$	52.8348	−	72.7209i	1.68260	−	2.31590i
$987$		0			0
$988$	6.06889	−	18.6781i	0.193077	−	0.594230i
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−9.11146	−	2.96049i	−0.289289	−	0.0939957i
$993$		0			0
$994$	−12.0843	−	8.77972i	−0.383289	−	0.278476i
$995$		0			0
$996$		0			0
$997$	−33.5735	+	46.2100i	−1.06328	+	1.46349i	−0.186590	+	0.982438i	$0.559744\pi$
$997$	−33.5735	+	46.2100i	−1.06328	+	1.46349i	−0.876694	+	0.481048i	$0.840256\pi$
$998$	−12.0741	−	16.6186i	−0.382199	−	0.526051i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bb.a.519.2	yes	16
4.3	odd	2	inner	572.2.bb.a.519.3	yes	16
11.6	odd	10	inner	572.2.bb.a.259.2	✓	16
13.12	even	2	inner	572.2.bb.a.519.3	yes	16
44.39	even	10	inner	572.2.bb.a.259.3	yes	16
52.51	odd	2	CM	572.2.bb.a.519.2	yes	16
143.116	odd	10	inner	572.2.bb.a.259.3	yes	16
572.259	even	10	inner	572.2.bb.a.259.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bb.a.259.2	✓	16	11.6	odd	10	inner
572.2.bb.a.259.2	✓	16	572.259	even	10	inner
572.2.bb.a.259.3	yes	16	44.39	even	10	inner
572.2.bb.a.259.3	yes	16	143.116	odd	10	inner
572.2.bb.a.519.2	yes	16	1.1	even	1	trivial
572.2.bb.a.519.2	yes	16	52.51	odd	2	CM
572.2.bb.a.519.3	yes	16	4.3	odd	2	inner
572.2.bb.a.519.3	yes	16	13.12	even	2	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)

\(f(q)\)	\(=\)	\(q+(-1.34500 - 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} +(3.10731 - 4.27685i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.927051 - 2.85317i) q^{9} +O(q^{10})\)	\(q+(-1.34500 - 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} +(3.10731 - 4.27685i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.927051 - 2.85317i) q^{9} +(-3.30948 + 0.217620i) q^{11} +(3.42908 + 1.11418i) q^{13} +(-6.04837 + 4.39440i) q^{14} +(1.23607 + 3.80423i) q^{16} +(-5.73732 + 1.86417i) q^{17} +(-2.49376 + 3.43237i) q^{18} +(-1.60082 - 2.20335i) q^{19} +(4.54634 + 1.15360i) q^{22} +(-4.04508 + 2.93893i) q^{25} +(-4.12519 - 2.99713i) q^{26} +(10.0555 - 3.26722i) q^{28} +(6.19302 - 8.52395i) q^{29} +(0.523346 - 1.61069i) q^{31} -5.65685i q^{32} +8.53136 q^{34} +(4.85410 - 3.52671i) q^{36} +(1.19021 + 3.66308i) q^{38} +(-5.61067 - 3.53841i) q^{44} +(-8.51837 + 6.18896i) q^{47} +(-6.47291 - 19.9216i) q^{49} +(6.72499 - 2.18508i) q^{50} +(4.23858 + 5.83390i) q^{52} +(3.11959 - 9.60110i) q^{53} -14.9524 q^{56} +(-12.0547 + 8.75825i) q^{58} +(10.6846 + 7.76278i) q^{59} +(7.74264 - 2.51574i) q^{61} +(-1.40780 + 1.93767i) q^{62} +(-9.32193 - 12.8305i) q^{63} +(-2.47214 + 7.60845i) q^{64} -5.09902 q^{67} +(-11.4746 - 3.72834i) q^{68} +(0.617396 + 1.90015i) q^{71} +(-8.06998 + 2.62210i) q^{72} -5.44697i q^{76} +(-9.35285 + 14.8303i) q^{77} +(-7.28115 - 5.29007i) q^{81} +(16.1682 - 5.25336i) q^{83} +(6.00000 + 7.21110i) q^{88} +(15.4204 - 11.2036i) q^{91} +(14.1619 - 4.60147i) q^{94} +29.6232i q^{98} +(-2.44715 + 9.64425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) 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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