LMFDB - Embedded newform 572.2.bb.a.415.3

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			415.3
Root			$0.115343 - 2.64324i$ of defining polynomial
Character	$\chi$	$=$	572.415
Dual form			572.2.bb.a.51.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.831254 + 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} +(-3.93856 - 1.27972i) q^{7} +(-2.68999 + 0.874032i) q^{8} +(-2.42705 + 1.76336i) q^{9} +O(q^{10})$	\(q+(0.831254 + 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} +(-3.93856 - 1.27972i) q^{7} +(-2.68999 + 0.874032i) q^{8} +(-2.42705 + 1.76336i) q^{9} +(-1.22965 - 3.08025i) q^{11} +(-2.11929 - 2.91695i) q^{13} +(-1.80979 - 5.56997i) q^{14} +(-3.23607 - 2.35114i) q^{16} +(-4.81105 + 6.62184i) q^{17} +(-4.03499 - 1.31105i) q^{18} +(6.69024 - 2.17379i) q^{19} +(2.50203 - 3.96735i) q^{22} +(1.54508 + 4.75528i) q^{25} +(1.57568 - 4.84946i) q^{26} +(4.86833 - 6.70069i) q^{28} +(5.11678 + 1.66254i) q^{29} +(-8.89163 + 6.46015i) q^{31} -5.65685i q^{32} -11.5754 q^{34} +(-1.85410 - 5.70634i) q^{36} +(8.04837 + 5.84749i) q^{38} +(6.61896 - 0.435240i) q^{44} +(-1.03709 - 3.19183i) q^{47} +(8.21149 + 5.96600i) q^{49} +(-4.15627 + 5.72061i) q^{50} +(6.85817 - 2.22835i) q^{52} +(-10.5967 + 7.69899i) q^{53} +11.7132 q^{56} +(2.35119 + 7.23622i) q^{58} +(1.04511 - 3.21652i) q^{59} +(5.97369 - 8.22208i) q^{61} +(-14.7824 - 4.80310i) q^{62} +(11.8157 - 3.83915i) q^{63} +(6.47214 - 4.70228i) q^{64} -5.09902 q^{67} +(-9.62210 - 13.2437i) q^{68} +(-6.64956 - 4.83119i) q^{71} +(4.98752 - 6.86474i) q^{72} +14.0691i q^{76} +(0.901219 + 13.7054i) q^{77} +(2.78115 - 8.55951i) q^{81} +(-6.75321 + 9.29500i) q^{83} +(6.00000 + 7.21110i) q^{88} +(4.61409 + 14.2007i) q^{91} +(2.78976 - 3.83978i) q^{94} +14.3542i q^{98} +(8.41601 + 5.30761i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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	$-0.600000\pi$
$3$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$4$	−0.618034	+	1.90211i	−0.309017	+	0.951057i
$5$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$5$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$6$		0			0
$7$	−3.93856	−	1.27972i	−1.48864	−	0.483688i	−0.551957	−	0.833873i	$-0.686119\pi$
$7$	−3.93856	−	1.27972i	−1.48864	−	0.483688i	−0.936680	+	0.350185i	$0.886119\pi$
$8$	−2.68999	+	0.874032i	−0.951057	+	0.309017i
$9$	−2.42705	+	1.76336i	−0.809017	+	0.587785i
$10$		0			0
$11$	−1.22965	−	3.08025i	−0.370755	−	0.928731i
$11$	−1.22965	−	3.08025i	−0.370755	−	0.928731i
$12$		0			0
$13$	−2.11929	−	2.91695i	−0.587785	−	0.809017i
$13$	−2.11929	−	2.91695i	−0.587785	−	0.809017i
$14$	−1.80979	−	5.56997i	−0.483688	−	1.48864i
$15$		0			0
$16$	−3.23607	−	2.35114i	−0.809017	−	0.587785i
$17$	−4.81105	+	6.62184i	−1.16685	+	1.60603i	−0.485071	+	0.874475i	$0.661206\pi$
$17$	−4.81105	+	6.62184i	−1.16685	+	1.60603i	−0.681780	+	0.731558i	$0.738794\pi$
$18$	−4.03499	−	1.31105i	−0.951057	−	0.309017i
$19$	6.69024	−	2.17379i	1.53485	−	0.498702i	0.584898	−	0.811107i	$-0.301135\pi$
$19$	6.69024	−	2.17379i	1.53485	−	0.498702i	0.949949	+	0.312405i	$0.101135\pi$
$20$		0			0
$21$		0			0
$22$	2.50203	−	3.96735i	0.533435	−	0.845841i
$23$		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
$28$	4.86833	−	6.70069i	0.920028	−	1.26631i
$29$	5.11678	+	1.66254i	0.950162	+	0.308726i	0.742781	−	0.669534i	$-0.233506\pi$
$29$	5.11678	+	1.66254i	0.950162	+	0.308726i	0.207380	+	0.978260i	$0.433506\pi$
$30$		0			0
$31$	−8.89163	+	6.46015i	−1.59698	+	1.16028i	−0.703990	+	0.710210i	$0.748600\pi$
$31$	−8.89163	+	6.46015i	−1.59698	+	1.16028i	−0.892995	+	0.450067i	$0.851400\pi$
$32$		−	5.65685i		−	1.00000i
$33$		0			0
$34$	−11.5754			−1.98517
$35$		0			0
$36$	−1.85410	−	5.70634i	−0.309017	−	0.951057i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$	8.04837	+	5.84749i	1.30562	+	0.948587i
$39$		0			0
$40$		0			0
$41$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$41$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	6.61896	−	0.435240i	0.997845	−	0.0656149i
$45$		0			0
$46$		0			0
$47$	−1.03709	−	3.19183i	−0.151275	−	0.465577i	0.846489	−	0.532406i	$-0.178712\pi$
$47$	−1.03709	−	3.19183i	−0.151275	−	0.465577i	−0.997764	+	0.0668289i	$0.978712\pi$
$48$		0			0
$49$	8.21149	+	5.96600i	1.17307	+	0.852285i
$50$	−4.15627	+	5.72061i	−0.587785	+	0.809017i
$51$		0			0
$52$	6.85817	−	2.22835i	0.951057	−	0.309017i
$53$	−10.5967	+	7.69899i	−1.45557	+	1.05754i	−0.471087	+	0.882087i	$0.656138\pi$
$53$	−10.5967	+	7.69899i	−1.45557	+	1.05754i	−0.984488	+	0.175450i	$0.943862\pi$
$54$		0			0
$55$		0			0
$56$	11.7132			1.56525
$57$		0			0
$58$	2.35119	+	7.23622i	0.308726	+	0.950162i
$59$	1.04511	−	3.21652i	0.136062	−	0.418756i	−0.859692	−	0.510813i	$-0.829344\pi$
$59$	1.04511	−	3.21652i	0.136062	−	0.418756i	0.995754	+	0.0920575i	$0.0293443\pi$
$60$		0			0
$61$	5.97369	−	8.22208i	0.764852	−	1.05273i	−0.231942	−	0.972730i	$-0.574508\pi$
$61$	5.97369	−	8.22208i	0.764852	−	1.05273i	0.996795	−	0.0799995i	$-0.0254919\pi$
$62$	−14.7824	−	4.80310i	−1.87737	−	0.609994i
$63$	11.8157	−	3.83915i	1.48864	−	0.483688i
$64$	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	$0.600822\pi$
$68$	−9.62210	−	13.2437i	−1.16685	−	1.60603i
$69$		0			0
$70$		0			0
$71$	−6.64956	−	4.83119i	−0.789158	−	0.573357i	0.118556	−	0.992947i	$-0.462174\pi$
$71$	−6.64956	−	4.83119i	−0.789158	−	0.573357i	−0.907713	+	0.419591i	$0.862174\pi$
$72$	4.98752	−	6.86474i	0.587785	−	0.809017i
$73$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$73$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$74$		0			0
$75$		0			0
$76$			14.0691i			1.61383i
$77$	0.901219	+	13.7054i	0.102703	+	1.56187i
$78$		0			0
$79$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$79$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$80$		0			0
$81$	2.78115	−	8.55951i	0.309017	−	0.951057i
$82$		0			0
$83$	−6.75321	+	9.29500i	−0.741262	+	1.02026i	0.257283	+	0.966336i	$0.417173\pi$
$83$	−6.75321	+	9.29500i	−0.741262	+	1.02026i	−0.998545	+	0.0539231i	$0.982827\pi$
$84$		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
$91$	4.61409	+	14.2007i	0.483688	+	1.48864i
$92$		0			0
$93$		0			0
$94$	2.78976	−	3.83978i	0.287742	−	0.396043i
$95$		0			0
$96$		0			0
$97$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$97$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$98$			14.3542i			1.44999i
$99$	8.41601	+	5.30761i	0.845841	+	0.533435i
$100$	−10.0000			−1.00000
$101$	−2.02129	−	2.78206i	−0.201125	−	0.276825i	0.696526	−	0.717532i	$-0.254728\pi$
$101$	−2.02129	−	2.78206i	−0.201125	−	0.276825i	−0.897651	+	0.440706i	$0.854728\pi$
$102$		0			0
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$	8.25039	+	5.99426i	0.809017	+	0.587785i
$105$		0			0
$106$	−17.6172	−	5.72417i	−1.71113	−	0.555980i
$107$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$107$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	9.73667	+	13.4014i	0.920028	+	1.26631i
$113$	3.69021	+	11.3573i	0.347145	+	1.06840i	0.960425	+	0.278538i	$0.0898498\pi$
$113$	3.69021	+	11.3573i	0.347145	+	1.06840i	−0.613280	+	0.789866i	$0.710150\pi$
$114$		0			0
$115$		0			0
$116$	−6.32469	+	8.70518i	−0.587232	+	0.808256i
$117$	10.2872	+	3.34253i	0.951057	+	0.309017i
$118$	4.54885	−	1.47801i	0.418756	−	0.136062i
$119$	27.4227	−	19.9238i	2.51384	−	1.82641i
$120$		0			0
$121$	−7.97590	+	7.57529i	−0.725082	+	0.688662i
$122$	14.3727			1.30124
$123$		0			0
$124$	−6.79260	−	20.9055i	−0.609994	−	1.87737i
$125$		0			0
$126$	14.2143	+	10.3273i	1.26631	+	0.920028i
$127$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$127$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$128$	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
$133$	−29.1318			−2.52605
$134$	−4.23858	−	5.83390i	−0.366158	−	0.503973i
$135$		0			0
$136$	7.15399	−	22.0177i	0.613450	−	1.88800i
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$		0			0
$141$		0			0
$142$		−	11.6239i		−	0.975453i
$143$	−6.37896	+	10.1148i	−0.533435	+	0.845841i
$144$	12.0000			1.00000
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$149$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$150$		0			0
$151$	−2.45355	+	0.797207i	−0.199667	+	0.0648758i	−0.407143	−	0.913364i	$-0.633475\pi$
$151$	−2.45355	+	0.797207i	−0.199667	+	0.0648758i	0.207476	+	0.978240i	$0.433475\pi$
$152$	−16.0967	+	11.6950i	−1.30562	+	0.948587i
$153$		−	24.5551i		−	1.98517i
$154$	−14.9315	+	12.4238i	−1.20321	+	1.00113i
$155$		0			0
$156$		0			0
$157$	−7.30979	−	22.4972i	−0.583385	−	1.79547i	−0.605661	−	0.795723i	$-0.707091\pi$
$157$	−7.30979	−	22.4972i	−0.583385	−	1.79547i	0.0222763	−	0.999752i	$-0.492909\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	12.1050	−	3.93314i	0.951057	−	0.309017i
$163$	−16.0143	+	11.6350i	−1.25433	+	0.911327i	−0.998465	−	0.0553849i	$-0.982361\pi$
$163$	−16.0143	+	11.6350i	−1.25433	+	0.911327i	−0.255869	+	0.966712i	$0.582361\pi$
$164$		0			0
$165$		0			0
$166$	−16.2483			−1.26111
$167$	15.0228	+	20.6771i	1.16250	+	1.60004i	0.701556	+	0.712614i	$0.252489\pi$
$167$	15.0228	+	20.6771i	1.16250	+	1.60004i	0.460944	+	0.887429i	$0.347511\pi$
$168$		0			0
$169$	−4.01722	+	12.3637i	−0.309017	+	0.951057i
$170$		0			0
$171$	−12.4044	+	17.0732i	−0.948587	+	1.30562i
$172$		0			0
$173$	13.7163	−	4.45671i	1.04283	−	0.338837i	0.262981	−	0.964801i	$-0.415294\pi$
$173$	13.7163	−	4.45671i	1.04283	−	0.338837i	0.779852	+	0.625964i	$0.215294\pi$
$174$		0			0
$175$		−	20.7063i		−	1.56525i
$176$	−3.26286	+	12.8590i	−0.245948	+	0.969283i
$177$		0			0
$178$		0			0
$179$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$179$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$180$		0			0
$181$	−0.184887	−	0.134328i	−0.0137425	−	0.00998453i	0.580893	−	0.813980i	$-0.302704\pi$
$181$	−0.184887	−	0.134328i	−0.0137425	−	0.00998453i	−0.594635	+	0.803996i	$0.702704\pi$
$182$	−12.4119	+	17.0835i	−0.920028	+	1.26631i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	26.3129	+	6.67667i	1.92419	+	0.488247i
$188$	6.71218			0.489536
$189$		0			0
$190$		0			0
$191$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$191$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$192$		0			0
$193$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$193$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$194$		0			0
$195$		0			0
$196$	−16.4230	+	11.9320i	−1.17307	+	0.852285i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	0.923283	+	14.0409i	0.0656149	+	0.997845i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−8.31254	−	11.4412i	−0.587785	−	0.809017i
$201$		0			0
$202$	1.50282	−	4.62520i	0.105738	−	0.325428i
$203$	−18.0252	−	13.0961i	−1.26512	−	0.919163i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$			14.4222i			1.00000i
$209$	−14.9225	−	17.9346i	−1.03221	−	1.24056i
$210$		0			0
$211$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$211$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$212$	−8.09519	−	24.9144i	−0.555980	−	1.71113i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	43.2874	−	14.0649i	2.93854	−	0.954790i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	29.5116			1.98517
$222$		0			0
$223$	−7.87842	−	24.2473i	−0.527578	−	1.62372i	−0.759161	−	0.650903i	$-0.774391\pi$
$223$	−7.87842	−	24.2473i	−0.527578	−	1.62372i	0.231583	−	0.972815i	$-0.425609\pi$
$224$	−7.23917	+	22.2799i	−0.483688	+	1.48864i
$225$	−12.1353	−	8.81678i	−0.809017	−	0.587785i
$226$	−9.92663	+	13.6628i	−0.660310	+	0.908839i
$227$	20.0002	+	6.49846i	1.32746	+	0.431318i	0.885050	−	0.465495i	$-0.154124\pi$
$227$	20.0002	+	6.49846i	1.32746	+	0.431318i	0.442409	+	0.896813i	$0.354124\pi$
$228$		0			0
$229$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$229$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$230$		0			0
$231$		0			0
$232$	−15.2172			−0.999059
$233$	−0.350997	−	0.483106i	−0.0229946	−	0.0316493i	0.797365	−	0.603497i	$-0.206227\pi$
$233$	−0.350997	−	0.483106i	−0.0229946	−	0.0316493i	−0.820360	+	0.571848i	$0.806227\pi$
$234$	4.72705	+	14.5484i	0.309017	+	0.951057i
$235$		0			0
$236$	5.47228	+	3.97584i	0.356215	+	0.258805i
$237$		0			0
$238$	45.5905	+	14.8132i	2.95519	+	0.960200i
$239$	−12.1231	+	3.93902i	−0.784176	+	0.254794i	−0.673622	−	0.739076i	$-0.735262\pi$
$239$	−12.1231	+	3.93902i	−0.784176	+	0.254794i	−0.110554	+	0.993870i	$0.535262\pi$
$240$		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
$244$	11.9474	+	16.4442i	0.764852	+	1.05273i
$245$		0			0
$246$		0			0
$247$	−20.5194	−	14.9082i	−1.30562	−	0.948587i
$248$	18.2721	−	25.1493i	1.16028	−	1.59698i
$249$		0			0
$250$		0			0
$251$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$251$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$252$			24.8475i			1.56525i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	−1.73917	+	5.35262i	−0.108487	+	0.333887i	−0.990533	−	0.137275i	$-0.956166\pi$
$257$	−1.73917	+	5.35262i	−0.108487	+	0.333887i	0.882046	+	0.471163i	$0.156166\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−15.3503	+	4.98763i	−0.950162	+	0.308726i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$		0			0
$266$	−24.2159	−	33.3303i	−1.48477	−	2.04361i
$267$		0			0
$268$	3.15137	−	9.69891i	0.192500	−	0.592455i
$269$	13.5484	+	9.84347i	0.826059	+	0.600167i	0.918442	−	0.395557i	$-0.129448\pi$
$269$	13.5484	+	9.84347i	0.826059	+	0.600167i	−0.0923827	+	0.995724i	$0.529448\pi$
$270$		0			0
$271$	−27.8773	−	9.05789i	−1.69343	−	0.550228i	−0.705987	−	0.708225i	$-0.749496\pi$
$271$	−27.8773	−	9.05789i	−1.69343	−	0.550228i	−0.987440	+	0.157997i	$0.949496\pi$
$272$	31.1378	−	10.1173i	1.88800	−	0.613450i
$273$		0			0
$274$		0			0
$275$	12.7475	−	10.6066i	0.768706	−	0.639602i
$276$		0			0
$277$	−17.2229	−	23.7053i	−1.03482	−	1.42431i	−0.901263	−	0.433273i	$-0.857359\pi$
$277$	−17.2229	−	23.7053i	−1.03482	−	1.42431i	−0.133562	−	0.991040i	$-0.542641\pi$
$278$		0			0
$279$	10.1889	−	31.3582i	0.609994	−	1.87737i
$280$		0			0
$281$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$281$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$282$		0			0
$283$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$283$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$284$	13.2991	−	9.66238i	0.789158	−	0.573357i
$285$		0			0
$286$	−16.8751	+	1.10965i	−0.997845	+	0.0656149i
$287$		0			0
$288$	9.97505	+	13.7295i	0.587785	+	0.809017i
$289$	−15.4493	−	47.5480i	−0.908782	−	2.79694i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$293$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−2.95163	−	2.14448i	−0.169847	−	0.123401i
$303$		0			0
$304$	−26.7610	−	8.69516i	−1.53485	−	0.498702i
$305$		0			0
$306$	28.0941	−	20.4116i	1.60603	−	1.16685i
$307$			4.46445i			0.254799i	0.991851	+	0.127400i	$0.0406631\pi$
$307$			4.46445i			0.254799i	−0.991851	+	0.127400i	$0.959337\pi$
$308$	−26.6262	−	6.75617i	−1.51717	−	0.384968i
$309$		0			0
$310$		0			0
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$		0			0
$313$	28.6135	+	20.7889i	1.61733	+	1.17506i	0.826003	+	0.563666i	$0.190609\pi$
$313$	28.6135	+	20.7889i	1.61733	+	1.17506i	0.791327	+	0.611393i	$0.209391\pi$
$314$	19.6633	−	27.0642i	1.10966	−	1.52732i
$315$		0			0
$316$		0			0
$317$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$317$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$318$		0			0
$319$	−1.17082	−	17.8053i	−0.0655532	−	0.996906i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−17.7926	+	54.7599i	−0.990006	+	3.04692i
$324$	14.5623	+	10.5801i	0.809017	+	0.587785i
$325$	10.5964	−	14.5848i	0.587785	−	0.809017i
$326$	−26.6238	−	8.65061i	−1.47456	−	0.479113i
$327$		0			0
$328$		0			0
$329$			13.8984i			0.766245i
$330$		0			0
$331$	−17.7548			−0.975890			−0.487945	−	0.872874i	$-0.662253\pi$
$331$	−17.7548			−0.975890			−0.487945	+	0.872874i	$0.662253\pi$
$332$	−13.5064	−	18.5900i	−0.741262	−	1.02026i
$333$		0			0
$334$	−11.1694	+	34.3759i	−0.611162	+	1.88096i
$335$		0			0
$336$		0			0
$337$	−34.6816	−	11.2687i	−1.88923	−	0.613847i	−0.980522	−	0.196407i	$-0.937073\pi$
$337$	−34.6816	−	11.2687i	−1.88923	−	0.613847i	−0.908704	−	0.417440i	$-0.862927\pi$
$338$	−17.4850	+	5.68121i	−0.951057	+	0.309017i
$339$		0			0
$340$		0			0
$341$	30.8325	+	19.4447i	1.66967	+	1.05299i
$342$	−29.8450			−1.61383
$343$	−7.66753	−	10.5535i	−0.414008	−	0.569833i
$344$		0			0
$345$		0			0
$346$	16.5008	+	11.9885i	0.887087	+	0.644506i
$347$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$347$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$348$		0			0
$349$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$349$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$350$	23.6905	−	17.2122i	1.26631	−	0.920028i
$351$		0			0
$352$	−17.4245	+	6.95597i	−0.928731	+	0.370755i
$353$		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
$359$	28.5441	+	9.27454i	1.50650	+	0.489492i	0.941906	−	0.335877i	$-0.109033\pi$
$359$	28.5441	+	9.27454i	1.50650	+	0.489492i	0.564594	+	0.825369i	$0.309033\pi$
$360$		0			0
$361$	24.6626	−	17.9185i	1.29803	−	0.943077i
$362$		−	0.323194i		−	0.0169867i
$363$		0			0
$364$	−29.8630			−1.56525
$365$		0			0
$366$		0			0
$367$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$367$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	51.5885	−	16.7621i	2.67834	−	0.870246i
$372$		0			0
$373$			1.30741i			0.0676954i	0.999427	+	0.0338477i	$0.0107761\pi$
$373$			1.30741i			0.0676954i	−0.999427	+	0.0338477i	$0.989224\pi$
$374$	14.2337	+	35.6552i	0.736009	+	1.84368i
$375$		0			0
$376$	5.57953	+	7.67956i	0.287742	+	0.396043i
$377$	−5.99438	−	18.4488i	−0.308726	−	0.950162i
$378$		0			0
$379$	−28.8764	−	20.9799i	−1.48328	−	1.07767i	−0.976482	−	0.215599i	$-0.930829\pi$
$379$	−28.8764	−	20.9799i	−1.48328	−	1.07767i	−0.506797	−	0.862066i	$-0.669171\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−30.8092	+	22.3842i	−1.57428	+	1.14378i	−0.651369	+	0.758761i	$0.725805\pi$
$383$	−30.8092	+	22.3842i	−1.57428	+	1.14378i	−0.922909	+	0.385019i	$0.874195\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.06859	+	27.9102i	−0.459796	+	1.41511i	0.405616	+	0.914044i	$0.367057\pi$
$389$	−9.06859	+	27.9102i	−0.459796	+	1.41511i	−0.865412	+	0.501062i	$0.832943\pi$
$390$		0			0
$391$		0			0
$392$	−27.3033	−	8.87139i	−1.37903	−	0.448073i
$393$		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	$-0.800000\pi$
$401$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$402$		0			0
$403$	37.6879	+	12.2455i	1.87737	+	0.609994i
$404$	6.54102	−	2.12530i	0.325428	−	0.105738i
$405$		0			0
$406$		−	31.5092i		−	1.56377i
$407$		0			0
$408$		0			0
$409$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$409$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.23248	+	11.3310i	−0.405094	+	0.557564i
$414$		0			0
$415$		0			0
$416$	−16.5008	+	11.9885i	−0.809017	+	0.587785i
$417$		0			0
$418$	8.11502	−	31.9814i	0.396918	−	1.56426i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$421$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$422$		0			0
$423$	8.14541	+	5.91798i	0.396043	+	0.287742i
$424$	21.7760	−	29.9721i	1.05754	−	1.45557i
$425$	−38.9222	−	12.6466i	−1.88800	−	0.613450i
$426$		0			0
$427$	−34.0497	+	24.7385i	−1.64778	+	1.19718i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.24420	−	3.08887i	−0.108099	−	0.148786i	0.751540	−	0.659688i	$-0.229311\pi$
$431$	−2.24420	−	3.08887i	−0.108099	−	0.148786i	−0.859639	+	0.510902i	$0.829311\pi$
$432$		0			0
$433$	−12.7392	+	39.2071i	−0.612206	+	1.88418i	−0.175797	+	0.984426i	$0.556250\pi$
$433$	−12.7392	+	39.2071i	−0.612206	+	1.88418i	−0.436409	+	0.899749i	$0.643750\pi$
$434$	52.0749	+	37.8346i	2.49967	+	1.81612i
$435$		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
$441$	−30.4499			−1.44999
$442$	24.5316	+	33.7649i	1.16685	+	1.60603i
$443$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$443$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$444$		0			0
$445$		0			0
$446$	21.1929	−	29.1695i	1.00351	−	1.38122i
$447$		0			0
$448$	−31.5085	+	10.2377i	−1.48864	+	0.483688i
$449$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$449$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$450$		−	21.2132i		−	1.00000i
$451$		0			0
$452$	−23.8835			−1.12339
$453$		0			0
$454$	9.19021	+	28.2845i	0.431318	+	1.32746i
$455$		0			0
$456$		0			0
$457$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$457$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$458$		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
$463$	11.8352			0.550027			0.275013	−	0.961440i	$-0.411318\pi$
$463$	11.8352			0.550027			0.275013	+	0.961440i	$0.411318\pi$
$464$	−12.6494	−	17.4104i	−0.587232	−	0.808256i
$465$		0			0
$466$	0.260965	−	0.803168i	0.0120890	−	0.0372060i
$467$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$467$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$468$	−12.7157	+	17.5017i	−0.587785	+	0.809017i
$469$	20.0828	+	6.52530i	0.927338	+	0.301310i
$470$		0			0
$471$		0			0
$472$			9.56589i			0.440306i
$473$		0			0
$474$		0			0
$475$	20.6740	+	28.4553i	0.948587	+	1.30562i
$476$	20.9491	+	64.4747i	0.960200	+	2.95519i
$477$	12.1428	−	37.3717i	0.555980	−	1.71113i
$478$	−14.5841	−	10.5959i	−0.667060	−	0.484647i
$479$	−1.10204	+	1.51683i	−0.0503535	+	0.0693056i	−0.833451	−	0.552593i	$-0.813638\pi$
$479$	−1.10204	+	1.51683i	−0.0503535	+	0.0693056i	0.783098	+	0.621899i	$0.213638\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−9.47967	−	19.8529i	−0.430894	−	0.902402i
$485$		0			0
$486$		0			0
$487$	−6.68826	−	20.5844i	−0.303074	−	0.932766i	−0.980389	−	0.197073i	$-0.936856\pi$
$487$	−6.68826	−	20.5844i	−0.303074	−	0.932766i	0.677315	−	0.735693i	$-0.263144\pi$
$488$	−8.88283	+	27.3385i	−0.402107	+	1.23756i
$489$		0			0
$490$		0			0
$491$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$491$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$492$		0			0
$493$	−35.6262	+	25.8839i	−1.60452	+	1.16575i
$494$		−	35.8692i		−	1.61383i
$495$		0			0
$496$	43.9627			1.97398
$497$	20.0072	+	27.5375i	0.897444	+	1.23523i
$498$		0			0
$499$	−4.04272	+	12.4422i	−0.180977	+	0.556991i	−0.999856	−	0.0169761i	$-0.994596\pi$
$499$	−4.04272	+	12.4422i	−0.180977	+	0.556991i	0.818879	+	0.573967i	$0.194596\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$	−28.4286	+	20.6546i	−1.26631	+	0.920028i
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$509$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$510$		0			0
$511$		0			0
$512$	−13.3001	+	18.3060i	−0.587785	+	0.809017i
$513$		0			0
$514$	−7.56975	+	2.45956i	−0.333887	+	0.108487i
$515$		0			0
$516$		0			0
$517$	−8.55639	+	7.11935i	−0.376310	+	0.313108i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.2702	+	40.8415i	−0.581379	+	1.78930i	0.0319726	+	0.999489i	$0.489821\pi$
$521$	−13.2702	+	40.8415i	−0.581379	+	1.78930i	−0.613351	+	0.789810i	$0.710179\pi$
$522$	−18.4665	−	13.4167i	−0.808256	−	0.587232i
$523$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$523$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	89.9591i		−	3.91868i
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$	3.13534	+	9.64957i	0.136062	+	0.418756i
$532$	18.0044	−	55.4119i	0.780591	−	2.40241i
$533$		0			0
$534$		0			0
$535$		0			0
$536$	13.7163	−	4.45671i	0.592455	−	0.192500i
$537$		0			0
$538$			23.6834i			1.02106i
$539$	8.27949	−	32.6296i	0.356623	−	1.40546i
$540$		0			0
$541$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$541$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$542$	−12.8098	−	39.4245i	−0.550228	−	1.69343i
$543$		0			0
$544$	37.4588	+	27.2154i	1.60603	+	1.16685i
$545$		0			0
$546$		0			0
$547$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$547$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$548$		0			0
$549$			30.4891i			1.30124i
$550$	22.7317	+	5.76798i	0.969283	+	0.245948i
$551$	37.8465			1.61232
$552$		0			0
$553$		0			0
$554$	12.8052	−	39.4103i	0.544039	−	1.67438i
$555$		0			0
$556$		0			0
$557$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$557$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$558$	44.3472	−	14.4093i	1.87737	−	0.609994i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$563$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−21.9075	+	30.1531i	−0.920028	+	1.26631i
$568$	22.1099	+	7.18394i	0.927711	+	0.301431i
$569$	43.4361	−	14.1133i	1.82094	−	0.591658i	0.821157	−	0.570702i	$-0.193329\pi$
$569$	43.4361	−	14.1133i	1.82094	−	0.591658i	0.999780	−	0.0209564i	$-0.00667113\pi$
$570$		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	$-0.800000\pi$
$577$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$578$	41.5585	−	57.2004i	1.72861	−	2.37922i
$579$		0			0
$580$		0			0
$581$	38.4929	−	27.9668i	1.59696	−	1.16026i
$582$		0			0
$583$	36.7451	+	23.1736i	1.52183	+	0.959751i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.1812	+	43.6451i	−0.585319	+	1.80143i	0.0126674	+	0.999920i	$0.495968\pi$
$587$	−14.1812	+	43.6451i	−0.585319	+	1.80143i	−0.597986	+	0.801506i	$0.704032\pi$
$588$		0			0
$589$	−45.4442	+	62.5485i	−1.87249	+	2.57727i
$590$		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	$-0.800000\pi$
$599$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$600$		0			0
$601$	20.5745	+	6.68506i	0.839251	+	0.272689i	0.696937	−	0.717132i	$-0.254546\pi$
$601$	20.5745	+	6.68506i	0.839251	+	0.272689i	0.142314	+	0.989822i	$0.454546\pi$
$602$		0			0
$603$	12.3756	−	8.99139i	0.503973	−	0.366158i
$604$		−	5.15963i		−	0.209943i
$605$		0			0
$606$		0			0
$607$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$607$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$608$	−12.2968	−	37.8457i	−0.498702	−	1.53485i
$609$		0			0
$610$		0			0
$611$	−7.11253	+	9.78956i	−0.287742	+	0.396043i
$612$	46.7066	+	15.1759i	1.88800	+	0.613450i
$613$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$613$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$614$	−5.10787	+	3.71109i	−0.206137	+	0.149767i
$615$		0			0
$616$	−14.4032	−	36.0797i	−0.580322	−	1.45369i
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	10.2653	+	31.5932i	0.412596	+	1.26984i	0.914384	+	0.404848i	$0.132676\pi$
$619$	10.2653	+	31.5932i	0.412596	+	1.26984i	−0.501788	+	0.864991i	$0.667324\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$			50.0182i			1.99913i
$627$		0			0
$628$	47.3100			1.88787
$629$		0			0
$630$		0			0
$631$	−15.3451	+	47.2273i	−0.610878	+	1.88009i	−0.161129	+	0.986933i	$0.551513\pi$
$631$	−15.3451	+	47.2273i	−0.610878	+	1.88009i	−0.449749	+	0.893155i	$0.648487\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	36.5962i		−	1.44999i
$638$	19.3982	−	16.1403i	0.767983	−	0.639000i
$639$	24.6579			0.975453
$640$		0			0
$641$	15.2170	+	46.8331i	0.601035	+	1.84980i	0.522040	+	0.852921i	$0.325171\pi$
$641$	15.2170	+	46.8331i	0.601035	+	1.84980i	0.0789953	+	0.996875i	$0.474829\pi$
$642$		0			0
$643$	27.3581	+	19.8768i	1.07890	+	0.783866i	0.977491	−	0.210979i	$-0.0676652\pi$
$643$	27.3581	+	19.8768i	1.07890	+	0.783866i	0.101408	+	0.994845i	$0.467665\pi$
$644$		0			0
$645$		0			0
$646$	−77.4422	+	25.1625i	−3.04692	+	0.990006i
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$			25.4558i			1.00000i
$649$	−11.1928	+	0.736003i	−0.439357	+	0.0288906i
$650$	25.4951			1.00000
$651$		0			0
$652$	−12.2338	−	37.6518i	−0.479113	−	1.47456i
$653$	7.16855	−	22.0625i	0.280527	−	0.863374i	−0.707177	−	0.707037i	$-0.750031\pi$
$653$	7.16855	−	22.0625i	0.280527	−	0.863374i	0.987704	−	0.156337i	$-0.0499685\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−15.9015	+	11.5531i	−0.619905	+	0.450387i
$659$		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			$\pi$
$662$	−14.7587	−	20.3136i	−0.573614	−	0.789512i
$663$		0			0
$664$	10.0420	−	30.9060i	0.389704	−	1.19939i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−48.6148	+	15.7959i	−1.88096	+	0.611162i
$669$		0			0
$670$		0			0
$671$	−32.6716	−	8.29016i	−1.26127	−	0.320038i
$672$		0			0
$673$	−2.46035	−	3.38638i	−0.0948395	−	0.130535i	0.758960	−	0.651137i	$-0.225708\pi$
$673$	−2.46035	−	3.38638i	−0.0948395	−	0.130535i	−0.853800	+	0.520602i	$0.825708\pi$
$674$	−15.9364	−	49.0472i	−0.613847	−	1.88923i
$675$		0			0
$676$	−21.0344	−	15.2824i	−0.809017	−	0.587785i
$677$	30.5704	−	42.0766i	1.17492	−	1.61713i	0.560493	−	0.828159i	$-0.310612\pi$
$677$	30.5704	−	42.0766i	1.17492	−	1.61713i	0.614424	−	0.788976i	$-0.289388\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	3.38250	+	51.4397i	0.129523	+	1.96973i
$683$	−47.3447			−1.81159			−0.905797	−	0.423711i	$-0.860727\pi$
$683$	−47.3447			−1.81159			−0.905797	+	0.423711i	$0.860727\pi$
$684$	−24.8088	−	34.1464i	−0.948587	−	1.30562i
$685$		0			0
$686$	5.70078	−	17.5452i	0.217657	−	0.669879i
$687$		0			0
$688$		0			0
$689$	44.9152	+	14.5938i	1.71113	+	0.555980i
$690$		0			0
$691$	38.9859	−	28.3249i	1.48309	−	1.07753i	0.506549	−	0.862211i	$-0.330921\pi$
$691$	38.9859	−	28.3249i	1.48309	−	1.07753i	0.976544	−	0.215319i	$-0.0690792\pi$
$692$			28.8444i			1.09650i
$693$	−26.3548	−	31.6745i	−1.00113	−	1.20321i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	39.3856	+	12.7972i	1.48864	+	0.483688i
$701$	−29.8943	+	9.71326i	−1.12909	+	0.366865i	−0.813231	−	0.581940i	$-0.802294\pi$
$701$	−29.8943	+	9.71326i	−1.12909	+	0.366865i	−0.315862	+	0.948805i	$0.602294\pi$
$702$		0			0
$703$		0			0
$704$	−22.4427	−	14.1536i	−0.845841	−	0.533435i
$705$		0			0
$706$		0			0
$707$	4.40071	+	13.5440i	0.165506	+	0.509374i
$708$		0			0
$709$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$709$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	13.1162	+	40.3675i	0.489492	+	1.50650i
$719$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$719$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$720$		0			0
$721$		0			0
$722$	41.0018	+	13.3223i	1.52593	+	0.495805i
$723$		0			0
$724$	0.369774	−	0.268656i	0.0137425	−	0.00998453i
$725$			26.9005i			0.999059i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−24.8237	−	34.1669i	−0.920028	−	1.26631i
$729$	8.34346	+	25.6785i	0.309017	+	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$733$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.27003	+	15.7063i	0.230959	+	0.578548i
$738$		0			0
$739$	−31.8341	−	43.8159i	−1.17104	−	1.61179i	−0.656497	−	0.754329i	$-0.727962\pi$
$739$	−31.8341	−	43.8159i	−1.17104	−	1.61179i	−0.514541	−	0.857466i	$-0.672038\pi$
$740$		0			0
$741$		0			0
$742$	62.0610	+	45.0900i	2.27833	+	1.65531i
$743$	−18.0556	+	24.8514i	−0.662394	+	0.911708i	−0.999558	−	0.0297385i	$-0.990533\pi$
$743$	−18.0556	+	24.8514i	−0.662394	+	0.911708i	0.337163	+	0.941446i	$0.390533\pi$
$744$		0			0
$745$		0			0
$746$	−1.49584	+	1.08679i	−0.0547667	+	0.0397903i
$747$		−	34.4678i		−	1.26111i
$748$	−28.9620	+	45.9236i	−1.05896	+	1.67913i
$749$		0			0
$750$		0			0
$751$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$751$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$752$	−4.14836	+	12.7673i	−0.151275	+	0.465577i
$753$		0			0
$754$	16.1248	−	22.1939i	0.587232	−	0.808256i
$755$		0			0
$756$		0			0
$757$	−42.8278	+	31.1162i	−1.55660	+	1.13094i	−0.617876	+	0.786276i	$0.712006\pi$
$757$	−42.8278	+	31.1162i	−1.55660	+	1.13094i	−0.938727	+	0.344662i	$0.887994\pi$
$758$		−	50.4777i		−	1.83343i
$759$		0			0
$760$		0			0
$761$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$761$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−51.2206	−	16.6426i	−1.85067	−	0.601321i
$767$	−11.5973	+	3.76821i	−0.418756	+	0.136062i
$768$		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	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$		0			0
$775$	−44.4582	−	32.3007i	−1.59698	−	1.16028i
$776$		0			0
$777$		0			0
$778$	−39.4710	+	12.8249i	−1.41511	+	0.459796i
$779$		0			0
$780$		0			0
$781$	−6.70462	+	26.4230i	−0.239910	+	0.945490i
$782$		0			0
$783$		0			0
$784$	−12.5460	−	38.6128i	−0.448073	−	1.37903i
$785$		0			0
$786$		0			0
$787$	0.831254	−	1.14412i	0.0296310	−	0.0407836i	−0.793944	−	0.607990i	$-0.791976\pi$
$787$	0.831254	−	1.14412i	0.0296310	−	0.0407836i	0.823575	+	0.567207i	$0.191976\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	49.4538i		−	1.75838i
$792$	−27.2780	−	6.92158i	−0.969283	−	0.245948i
$793$	−36.6434			−1.30124
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.45163	−	6.14047i	−0.299372	−	0.217506i	0.427951	−	0.903802i	$-0.359236\pi$
$797$	−8.45163	−	6.14047i	−0.299372	−	0.217506i	−0.727323	+	0.686296i	$0.759236\pi$
$798$		0			0
$799$	26.1253	+	8.48862i	0.924247	+	0.300306i
$800$	26.8999	−	8.74032i	0.951057	−	0.309017i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	17.3178	+	53.2987i	0.609994	+	1.87737i
$807$		0			0
$808$	7.86885	+	5.71706i	0.276825	+	0.201125i
$809$	21.1929	−	29.1695i	0.745103	−	1.02555i	−0.253206	−	0.967412i	$-0.581485\pi$
$809$	21.1929	−	29.1695i	0.745103	−	1.02555i	0.998309	−	0.0581335i	$-0.0185149\pi$
$810$		0			0
$811$	9.41498	−	3.05911i	0.330605	−	0.107420i	−0.139011	−	0.990291i	$-0.544392\pi$
$811$	9.41498	−	3.05911i	0.330605	−	0.107420i	0.469616	+	0.882871i	$0.344392\pi$
$812$	36.0503	−	26.1921i	1.26512	−	0.919163i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−36.2395	−	26.3295i	−1.26631	−	0.920028i
$820$		0			0
$821$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$821$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$822$		0			0
$823$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$823$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$824$		0			0
$825$		0			0
$826$	−19.8074			−0.689187
$827$	−7.48128	−	10.2971i	−0.260150	−	0.358065i	0.658884	−	0.752245i	$-0.271029\pi$
$827$	−7.48128	−	10.2971i	−0.260150	−	0.358065i	−0.919034	+	0.394179i	$0.871029\pi$
$828$		0			0
$829$	16.3444	−	50.3029i	0.567665	−	1.74709i	−0.0922322	−	0.995738i	$-0.529400\pi$
$829$	16.3444	−	50.3029i	0.567665	−	1.74709i	0.659897	−	0.751356i	$-0.270600\pi$
$830$		0			0
$831$		0			0
$832$	−27.4327	−	8.91341i	−0.951057	−	0.309017i
$833$	−79.0118	+	25.6725i	−2.73760	+	0.889499i
$834$		0			0
$835$		0			0
$836$	43.3363	−	17.3001i	1.49882	−	0.598336i
$837$		0			0
$838$		0			0
$839$	−6.00846	−	18.4921i	−0.207435	−	0.638419i	−0.999605	−	0.0281182i	$-0.991049\pi$
$839$	−6.00846	−	18.4921i	−0.207435	−	0.638419i	0.792170	−	0.610301i	$-0.208951\pi$
$840$		0			0
$841$	−0.0441205	−	0.0320554i	−0.00152140	−	0.00110536i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$			14.2387i			0.489536i
$847$	41.1078	−	19.6289i	1.41248	−	0.674455i
$848$	52.3932			1.79919
$849$		0			0
$850$	−17.8850	−	55.0443i	−0.613450	−	1.88800i
$851$		0			0
$852$		0			0
$853$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$853$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$854$	−56.6079	−	18.3930i	−1.93708	−	0.629396i
$855$		0			0
$856$		0			0
$857$			52.5491i			1.79504i	0.440971	+	0.897521i	$0.354634\pi$
$857$			52.5491i			1.79504i	−0.440971	+	0.897521i	$0.645366\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	1.66855	−	5.13528i	0.0568311	−	0.174908i
$863$	−28.8764	−	20.9799i	−0.982963	−	0.714164i	−0.0245938	−	0.999698i	$-0.507829\pi$
$863$	−28.8764	−	20.9799i	−0.982963	−	0.714164i	−0.958369	+	0.285533i	$0.907829\pi$
$864$		0			0
$865$		0			0
$866$	−55.4473	+	18.0159i	−1.88418	+	0.612206i
$867$		0			0
$868$			91.0302i			3.08977i
$869$		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	$-0.100000\pi$
$877$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	59.1916			1.99421			0.997107	−	0.0760072i	$-0.0242172\pi$
$881$	59.1916			1.99421			0.997107	+	0.0760072i	$0.0242172\pi$
$882$	−25.3116	−	34.8384i	−0.852285	−	1.17307i
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$	−18.2392	+	56.1344i	−0.613450	+	1.88800i
$885$		0			0
$886$		0			0
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−29.7853	+	1.95858i	−0.997845	+	0.0656149i
$892$	50.9902			1.70728
$893$	−13.8768	−	19.0997i	−0.464368	−	0.639148i
$894$		0			0
$895$		0			0
$896$	−37.9048	−	27.5394i	−1.26631	−	0.920028i
$897$		0			0
$898$		0			0
$899$	−56.2368	+	18.2724i	−1.87560	+	0.609420i
$900$	24.2705	−	17.6336i	0.809017	−	0.587785i
$901$		−	107.210i		−	3.57169i
$902$		0			0
$903$		0			0
$904$	−19.8533	−	27.3257i	−0.660310	−	0.908839i
$905$		0			0
$906$		0			0
$907$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$907$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$908$	−24.7216	+	34.0264i	−0.820415	+	1.12920i
$909$	9.81152	+	3.18796i	0.325428	+	0.105738i
$910$		0			0
$911$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$911$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$912$		0			0
$913$	36.9351	+	9.37197i	1.22237	+	0.310167i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$919$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			29.6351i			0.975453i
$924$		0			0
$925$		0			0
$926$	9.83803	+	13.5409i	0.323298	+	0.444981i
$927$		0			0
$928$	9.40476	−	28.9449i	0.308726	−	0.950162i
$929$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$929$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$930$		0			0
$931$	67.9057	+	22.0639i	2.22552	+	0.723115i
$932$	1.13585	−	0.369060i	0.0372060	−	0.0120890i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−30.5941			−1.00000
$937$	−24.9477	−	34.3376i	−0.815007	−	1.12176i	−0.990531	−	0.137286i	$-0.956162\pi$
$937$	−24.9477	−	34.3376i	−0.815007	−	1.12176i	0.175524	−	0.984475i	$-0.443838\pi$
$938$	9.22817	+	28.4014i	0.301310	+	0.927338i
$939$		0			0
$940$		0			0
$941$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$941$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$942$		0			0
$943$		0			0
$944$	−10.9446	+	7.95169i	−0.356215	+	0.258805i
$945$		0			0
$946$		0			0
$947$	61.2331			1.98981			0.994904	−	0.100824i	$-0.0321480\pi$
$947$	61.2331			1.98981			0.994904	+	0.100824i	$0.0321480\pi$
$948$		0			0
$949$		0			0
$950$	−15.3710	+	47.3071i	−0.498702	+	1.53485i
$951$		0			0
$952$	−56.3529	+	77.5631i	−1.82641	+	2.51384i
$953$	−54.8653	−	17.8268i	−1.77726	−	0.577468i	−0.778521	−	0.627619i	$-0.784030\pi$
$953$	−54.8653	−	17.8268i	−1.77726	−	0.577468i	−0.998742	+	0.0501514i	$0.984030\pi$
$954$	52.8515	−	17.1725i	1.71113	−	0.555980i
$955$		0			0
$956$		−	25.4939i		−	0.824532i
$957$		0			0
$958$	−2.65151			−0.0856665
$959$		0			0
$960$		0			0
$961$	27.7481	−	85.3998i	0.895099	−	2.75483i
$962$		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	$-0.142207\pi$
$968$	14.8341	−	27.3487i	0.476786	−	0.879020i
$969$		0			0
$970$		0			0
$971$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$971$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$972$		0			0
$973$		0			0
$974$	17.9914	−	24.7630i	0.576481	−	0.793458i
$975$		0			0
$976$	−38.6625	+	12.5622i	−1.23756	+	0.402107i
$977$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$977$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.3327	−	59.4999i	0.616617	−	1.89775i	0.243950	−	0.969788i	$-0.421557\pi$
$983$	19.3327	−	59.4999i	0.616617	−	1.89775i	0.372667	−	0.927965i	$-0.378443\pi$
$984$		0			0
$985$		0			0
$986$	−59.2288	−	19.2446i	−1.88623	−	0.612873i
$987$		0			0
$988$	41.0388	−	29.8164i	1.30562	−	0.948587i
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	36.5441	+	50.2987i	1.16028	+	1.59698i
$993$		0			0
$994$	−14.8753	+	45.7813i	−0.471814	+	1.45210i
$995$		0			0
$996$		0			0
$997$	59.0050	+	19.1719i	1.86871	+	0.607180i	0.992013	+	0.126132i	$0.0402562\pi$
$997$	59.0050	+	19.1719i	1.86871	+	0.607180i	0.876694	+	0.481048i	$0.159744\pi$
$998$	−17.5960	+	5.71728i	−0.556991	+	0.180977i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bb.a.415.3	yes	16
4.3	odd	2	inner	572.2.bb.a.415.2	yes	16
11.7	odd	10	inner	572.2.bb.a.51.3	yes	16
13.12	even	2	inner	572.2.bb.a.415.2	yes	16
44.7	even	10	inner	572.2.bb.a.51.2	✓	16
52.51	odd	2	CM	572.2.bb.a.415.3	yes	16
143.51	odd	10	inner	572.2.bb.a.51.2	✓	16
572.51	even	10	inner	572.2.bb.a.51.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bb.a.51.2	✓	16	44.7	even	10	inner
572.2.bb.a.51.2	✓	16	143.51	odd	10	inner
572.2.bb.a.51.3	yes	16	11.7	odd	10	inner
572.2.bb.a.51.3	yes	16	572.51	even	10	inner
572.2.bb.a.415.2	yes	16	4.3	odd	2	inner
572.2.bb.a.415.2	yes	16	13.12	even	2	inner
572.2.bb.a.415.3	yes	16	1.1	even	1	trivial
572.2.bb.a.415.3	yes	16	52.51	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(0.831254 + 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} +(-3.93856 - 1.27972i) q^{7} +(-2.68999 + 0.874032i) q^{8} +(-2.42705 + 1.76336i) q^{9} +O(q^{10})\)	\(q+(0.831254 + 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} +(-3.93856 - 1.27972i) q^{7} +(-2.68999 + 0.874032i) q^{8} +(-2.42705 + 1.76336i) q^{9} +(-1.22965 - 3.08025i) q^{11} +(-2.11929 - 2.91695i) q^{13} +(-1.80979 - 5.56997i) q^{14} +(-3.23607 - 2.35114i) q^{16} +(-4.81105 + 6.62184i) q^{17} +(-4.03499 - 1.31105i) q^{18} +(6.69024 - 2.17379i) q^{19} +(2.50203 - 3.96735i) q^{22} +(1.54508 + 4.75528i) q^{25} +(1.57568 - 4.84946i) q^{26} +(4.86833 - 6.70069i) q^{28} +(5.11678 + 1.66254i) q^{29} +(-8.89163 + 6.46015i) q^{31} -5.65685i q^{32} -11.5754 q^{34} +(-1.85410 - 5.70634i) q^{36} +(8.04837 + 5.84749i) q^{38} +(6.61896 - 0.435240i) q^{44} +(-1.03709 - 3.19183i) q^{47} +(8.21149 + 5.96600i) q^{49} +(-4.15627 + 5.72061i) q^{50} +(6.85817 - 2.22835i) q^{52} +(-10.5967 + 7.69899i) q^{53} +11.7132 q^{56} +(2.35119 + 7.23622i) q^{58} +(1.04511 - 3.21652i) q^{59} +(5.97369 - 8.22208i) q^{61} +(-14.7824 - 4.80310i) q^{62} +(11.8157 - 3.83915i) q^{63} +(6.47214 - 4.70228i) q^{64} -5.09902 q^{67} +(-9.62210 - 13.2437i) q^{68} +(-6.64956 - 4.83119i) q^{71} +(4.98752 - 6.86474i) q^{72} +14.0691i q^{76} +(0.901219 + 13.7054i) q^{77} +(2.78115 - 8.55951i) q^{81} +(-6.75321 + 9.29500i) q^{83} +(6.00000 + 7.21110i) q^{88} +(4.61409 + 14.2007i) q^{91} +(2.78976 - 3.83978i) q^{94} +14.3542i q^{98} +(8.41601 + 5.30761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) 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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