LMFDB - Embedded newform 280.2.ba.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(19,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("280.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.ba (of order $6$, degree $2$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			59.2
Root			$1.72286 + 0.178197i$ of defining polynomial
Character	$\chi$	$=$	280.59
Dual form			280.2.ba.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(1.41421 + 2.23607i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(1.41421 + 2.23607i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(-3.23861 + 5.60944i) q^{11} -2.66291i q^{13} +(1.73861 - 3.31319i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(2.12132 - 3.67423i) q^{18} +(7.23861 - 4.17922i) q^{19} +4.47214i q^{20} +9.16018 q^{22} +(0.184829 + 0.320133i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-3.26139 + 1.88296i) q^{26} +(-5.28720 + 0.213422i) q^{28} +(-2.82843 + 4.89898i) q^{32} +(5.23861 + 2.74899i) q^{35} -6.00000 q^{36} +(-4.76492 - 8.25308i) q^{37} +(-10.2369 - 5.91030i) q^{38} +(5.47723 - 3.16228i) q^{40} +4.59250i q^{41} +(-6.47723 - 11.2189i) q^{44} +(5.80948 + 3.35410i) q^{45} +(0.261387 - 0.452736i) q^{46} +(-7.93080 + 4.57885i) q^{47} +(-3.00000 + 6.32456i) q^{49} -7.07107 q^{50} +(4.61230 + 2.66291i) q^{52} +(4.39526 - 7.61282i) q^{53} +14.4835i q^{55} +(4.00000 + 6.32456i) q^{56} +(-5.47723 - 3.16228i) q^{59} +(-3.68815 + 7.02834i) q^{63} +8.00000 q^{64} +(-2.97723 - 5.15671i) q^{65} +(-0.337449 - 8.35979i) q^{70} +(4.24264 + 7.34847i) q^{72} +(-6.73861 + 11.6716i) q^{74} +16.7169i q^{76} +(-17.1232 + 0.691190i) q^{77} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(5.62465 - 3.24739i) q^{82} +(-9.16018 + 15.8659i) q^{88} +(10.9545 - 6.32456i) q^{89} -9.48683i q^{90} +(5.95445 - 3.76593i) q^{91} -0.739315 q^{92} +(11.2158 + 6.47547i) q^{94} +(9.34501 - 16.1860i) q^{95} +(9.86729 - 0.797901i) q^{98} -19.4317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 12 * q^9	$ 8 q - 8 q^{4} + 12 q^{9} - 4 q^{11} - 8 q^{14} - 16 q^{16} + 36 q^{19} + 20 q^{25} - 48 q^{26} + 20 q^{35} - 48 q^{36} - 8 q^{44} + 24 q^{46} - 24 q^{49} + 32 q^{56} + 64 q^{64} + 20 q^{65} - 32 q^{74} - 36 q^{81} - 40 q^{91} + 24 q^{94} - 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 12 * q^9 - 4 * q^11 - 8 * q^14 - 16 * q^16 + 36 * q^19 + 20 * q^25 - 48 * q^26 + 20 * q^35 - 48 * q^36 - 8 * q^44 + 24 * q^46 - 24 * q^49 + 32 * q^56 + 64 * q^64 + 20 * q^65 - 32 * q^74 - 36 * q^81 - 40 * q^91 + 24 * q^94 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	1.93649	−	1.11803i	0.866025	−	0.500000i
$5$	1.93649	−	1.11803i	0.866025	−	0.500000i
$6$		0			0
$7$	1.41421	+	2.23607i	0.534522	+	0.845154i
$7$	1.41421	+	2.23607i	0.534522	+	0.845154i
$8$	2.82843			1.00000
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−2.73861	−	1.58114i	−0.866025	−	0.500000i
$11$	−3.23861	+	5.60944i	−0.976478	+	1.69131i	−0.301511	+	0.953463i	$0.597491\pi$
$11$	−3.23861	+	5.60944i	−0.976478	+	1.69131i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$		−	2.66291i		−	0.738559i	−0.929318	−	0.369279i	$-0.879605\pi$
$13$		−	2.66291i		−	0.738559i	0.929318	−	0.369279i	$-0.120395\pi$
$14$	1.73861	−	3.31319i	0.464664	−	0.885487i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	2.12132	−	3.67423i	0.500000	−	0.866025i
$19$	7.23861	−	4.17922i	1.66065	−	0.958778i	0.688247	−	0.725476i	$-0.258380\pi$
$19$	7.23861	−	4.17922i	1.66065	−	0.958778i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$			4.47214i			1.00000i
$21$		0			0
$22$	9.16018			1.95296
$23$	0.184829	+	0.320133i	0.0385394	+	0.0667523i	0.884652	−	0.466252i	$-0.154396\pi$
$23$	0.184829	+	0.320133i	0.0385394	+	0.0667523i	−0.846112	+	0.533005i	$0.821063\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	−3.26139	+	1.88296i	−0.639611	+	0.369279i
$27$		0			0
$28$	−5.28720	+	0.213422i	−0.999186	+	0.0403329i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−2.82843	+	4.89898i	−0.500000	+	0.866025i
$33$		0			0
$34$		0			0
$35$	5.23861	+	2.74899i	0.885487	+	0.464664i
$36$	−6.00000			−1.00000
$37$	−4.76492	−	8.25308i	−0.783348	−	1.35680i	−0.929981	−	0.367607i	$-0.880177\pi$
$37$	−4.76492	−	8.25308i	−0.783348	−	1.35680i	0.146633	−	0.989191i	$-0.453156\pi$
$38$	−10.2369	−	5.91030i	−1.66065	−	0.958778i
$39$		0			0
$40$	5.47723	−	3.16228i	0.866025	−	0.500000i
$41$			4.59250i			0.717229i	0.933486	+	0.358614i	$0.116751\pi$
$41$			4.59250i			0.717229i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−6.47723	−	11.2189i	−0.976478	−	1.69131i
$45$	5.80948	+	3.35410i	0.866025	+	0.500000i
$46$	0.261387	−	0.452736i	0.0385394	−	0.0667523i
$47$	−7.93080	+	4.57885i	−1.15683	+	0.667893i	−0.950541	−	0.310599i	$-0.899470\pi$
$47$	−7.93080	+	4.57885i	−1.15683	+	0.667893i	−0.206284	+	0.978492i	$0.566137\pi$
$48$		0			0
$49$	−3.00000	+	6.32456i	−0.428571	+	0.903508i
$50$	−7.07107			−1.00000
$51$		0			0
$52$	4.61230	+	2.66291i	0.639611	+	0.369279i
$53$	4.39526	−	7.61282i	0.603736	−	1.04570i	−0.388514	−	0.921443i	$-0.627012\pi$
$53$	4.39526	−	7.61282i	0.603736	−	1.04570i	0.992250	−	0.124258i	$-0.0396551\pi$
$54$		0			0
$55$			14.4835i			1.95296i
$56$	4.00000	+	6.32456i	0.534522	+	0.845154i
$57$		0			0
$58$		0			0
$59$	−5.47723	−	3.16228i	−0.713074	−	0.411693i	0.0991242	−	0.995075i	$-0.468396\pi$
$59$	−5.47723	−	3.16228i	−0.713074	−	0.411693i	−0.812198	+	0.583382i	$0.801729\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$		0			0
$63$	−3.68815	+	7.02834i	−0.464664	+	0.885487i
$64$	8.00000			1.00000
$65$	−2.97723	−	5.15671i	−0.369279	−	0.639611i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$		0			0
$70$	−0.337449	−	8.35979i	−0.0403329	−	0.999186i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	4.24264	+	7.34847i	0.500000	+	0.866025i
$73$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$73$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$74$	−6.73861	+	11.6716i	−0.783348	+	1.35680i
$75$		0			0
$76$			16.7169i			1.91756i
$77$	−17.1232	+	0.691190i	−1.95137	+	0.0787685i
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	−7.74597	−	4.47214i	−0.866025	−	0.500000i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	5.62465	−	3.24739i	0.621138	−	0.358614i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−9.16018	+	15.8659i	−0.976478	+	1.69131i
$89$	10.9545	−	6.32456i	1.16117	−	0.670402i	0.209585	−	0.977790i	$-0.432789\pi$
$89$	10.9545	−	6.32456i	1.16117	−	0.670402i	0.951584	+	0.307389i	$0.0994552\pi$
$90$		−	9.48683i		−	1.00000i
$91$	5.95445	−	3.76593i	0.624196	−	0.394776i
$92$	−0.739315			−0.0770789
$93$		0			0
$94$	11.2158	+	6.47547i	1.15683	+	0.667893i
$95$	9.34501	−	16.1860i	0.958778	−	1.66065i
$96$		0			0
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	9.86729	−	0.797901i	0.996747	−	0.0806002i
$99$	−19.4317			−1.95296
$100$	5.00000	+	8.66025i	0.500000	+	0.866025i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	3.87298	−	2.23607i	0.381616	−	0.220326i	−0.296905	−	0.954907i	$-0.595954\pi$
$103$	3.87298	−	2.23607i	0.381616	−	0.220326i	0.678521	+	0.734581i	$0.262621\pi$
$104$		−	7.53185i		−	0.738559i
$105$		0			0
$106$	−12.4317			−1.20747
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$		0			0
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$	17.7386	−	10.2414i	1.69131	−	0.976478i
$111$		0			0
$112$	4.91754	−	9.37112i	0.464664	−	0.885487i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$	0.715838	+	0.413289i	0.0667523	+	0.0385394i
$116$		0			0
$117$	6.91845	−	3.99437i	0.639611	−	0.369279i
$118$			8.94427i			0.823387i
$119$		0			0
$120$		0			0
$121$	−15.4772	−	26.8073i	−1.40702	−	2.43703i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	11.1803i		−	1.00000i
$126$	11.2158	−	0.452736i	0.999186	−	0.0403329i
$127$	−17.9507			−1.59287			−0.796434	−	0.604726i	$-0.793283\pi$
$127$	−17.9507			−1.59287			−0.796434	+	0.604726i	$0.793283\pi$
$128$	−5.65685	−	9.79796i	−0.500000	−	0.866025i
$129$		0			0
$130$	−4.21043	+	7.29268i	−0.369279	+	0.639611i
$131$	−13.7614	+	7.94514i	−1.20234	+	0.694170i	−0.961074	−	0.276289i	$-0.910895\pi$
$131$	−13.7614	+	7.94514i	−1.20234	+	0.694170i	−0.241264	+	0.970460i	$0.577562\pi$
$132$		0			0
$133$	19.5820	+	10.2757i	1.69797	+	0.891019i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$		−	18.9737i		−	1.60933i	−0.593732	−	0.804663i	$-0.702346\pi$
$139$		−	18.9737i		−	1.60933i	0.593732	−	0.804663i	$-0.297654\pi$
$140$	−10.0000	+	6.32456i	−0.845154	+	0.534522i
$141$		0			0
$142$		0			0
$143$	14.9374	+	8.62414i	1.24913	+	0.721187i
$144$	6.00000	−	10.3923i	0.500000	−	0.866025i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	19.0597			1.56670
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	20.4739	−	11.8206i	1.66065	−	0.958778i
$153$		0			0
$154$	12.9545	+	20.4828i	1.04390	+	1.65055i
$155$		0			0
$156$		0			0
$157$	18.1677	+	10.4891i	1.44994	+	0.837125i	0.998477	−	0.0551630i	$-0.0175678\pi$
$157$	18.1677	+	10.4891i	1.44994	+	0.837125i	0.451466	+	0.892288i	$0.350901\pi$
$158$		0			0
$159$		0			0
$160$			12.6491i			1.00000i
$161$	−0.454451	+	0.866025i	−0.0358158	+	0.0682524i
$162$	12.7279			1.00000
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−7.95445	−	4.59250i	−0.621138	−	0.358614i
$165$		0			0
$166$		0			0
$167$		−	19.8093i		−	1.53289i	−0.642308	−	0.766446i	$-0.722023\pi$
$167$		−	19.8093i		−	1.53289i	0.642308	−	0.766446i	$-0.277977\pi$
$168$		0			0
$169$	5.90890			0.454531
$170$		0			0
$171$	21.7158	+	12.5376i	1.66065	+	0.958778i
$172$		0			0
$173$	−22.7800	+	13.1521i	−1.73193	+	0.999933i	−0.860165	+	0.510015i	$0.829640\pi$
$173$	−22.7800	+	13.1521i	−1.73193	+	0.999933i	−0.871769	+	0.489917i	$0.837027\pi$
$174$		0			0
$175$	13.2180	−	0.533554i	0.999186	−	0.0403329i
$176$	25.9089			1.95296
$177$		0			0
$178$	−15.4919	−	8.94427i	−1.16117	−	0.670402i
$179$	3.76139	−	6.51491i	0.281139	−	0.486948i	−0.690526	−	0.723307i	$-0.742621\pi$
$179$	3.76139	−	6.51491i	0.281139	−	0.486948i	0.971666	+	0.236360i	$0.0759544\pi$
$180$	−11.6190	+	6.70820i	−0.866025	+	0.500000i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−8.82273	−	4.62977i	−0.653984	−	0.343182i
$183$		0			0
$184$	0.522774	+	0.905472i	0.0385394	+	0.0667523i
$185$	−18.4545	−	10.6547i	−1.35680	−	0.783348i
$186$		0			0
$187$		0			0
$188$		−	18.3154i		−	1.33579i
$189$		0			0
$190$	−26.4317			−1.91756
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$		0			0
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$		0			0
$196$	−7.95445	−	11.5207i	−0.568175	−	0.822908i
$197$	−27.8502			−1.98424			−0.992122	−	0.125274i	$-0.960019\pi$
$197$	−27.8502			−1.98424			−0.992122	+	0.125274i	$0.960019\pi$
$198$	13.7403	+	23.7988i	0.976478	+	1.69131i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	7.07107	−	12.2474i	0.500000	−	0.866025i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.13458	+	8.89335i	0.358614	+	0.621138i
$206$	−5.47723	−	3.16228i	−0.381616	−	0.220326i
$207$	−0.554486	+	0.960398i	−0.0385394	+	0.0667523i
$208$	−9.22460	+	5.32582i	−0.639611	+	0.369279i
$209$			54.1394i			3.74490i
$210$		0			0
$211$	−5.43168			−0.373932			−0.186966	−	0.982366i	$-0.559865\pi$
$211$	−5.43168			−0.373932			−0.186966	+	0.982366i	$0.559865\pi$
$212$	8.79052	+	15.2256i	0.603736	+	1.04570i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−25.0862	−	14.4835i	−1.69131	−	0.976478i
$221$		0			0
$222$		0			0
$223$		−	22.3607i		−	1.49738i	−0.662919	−	0.748691i	$-0.730683\pi$
$223$		−	22.3607i		−	1.49738i	0.662919	−	0.748691i	$-0.269317\pi$
$224$	−14.9545	+	0.603648i	−0.999186	+	0.0403329i
$225$	15.0000			1.00000
$226$		0			0
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$229$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$230$		−	1.16896i		−	0.0770789i
$231$		0			0
$232$		0			0
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$	−9.78416	−	5.64889i	−0.639611	−	0.369279i
$235$	−10.2386	+	17.7338i	−0.667893	+	1.15683i
$236$	10.9545	−	6.32456i	0.713074	−	0.411693i
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	2.54555	+	1.46967i	0.163973	+	0.0946700i	0.579741	−	0.814801i	$-0.303154\pi$
$241$	2.54555	+	1.46967i	0.163973	+	0.0946700i	−0.415768	+	0.909471i	$0.636487\pi$
$242$	−21.8881	+	37.9113i	−1.40702	+	2.43703i
$243$		0			0
$244$		0			0
$245$	1.26159	+	15.6016i	0.0806002	+	0.996747i
$246$		0			0
$247$	−11.1289	−	19.2758i	−0.708114	−	1.22649i
$248$		0			0
$249$		0			0
$250$	−13.6931	+	7.90569i	−0.866025	+	0.500000i
$251$		−	17.5434i		−	1.10733i	−0.832739	−	0.553666i	$-0.813228\pi$
$251$		−	17.5434i		−	1.10733i	0.832739	−	0.553666i	$-0.186772\pi$
$252$	−8.48528	−	13.4164i	−0.534522	−	0.845154i
$253$	−2.39435			−0.150532
$254$	12.6931	+	21.9850i	0.796434	+	1.37946i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$	11.7158	−	22.3263i	0.727987	−	1.38729i
$260$	11.9089			0.738559
$261$		0			0
$262$	19.4615	+	11.2361i	1.20234	+	0.694170i
$263$	4.24264	−	7.34847i	0.261612	−	0.453126i	−0.705058	−	0.709150i	$-0.749079\pi$
$263$	4.24264	−	7.34847i	0.261612	−	0.453126i	0.966671	+	0.256023i	$0.0824124\pi$
$264$		0			0
$265$		−	19.6562i		−	1.20747i
$266$	−1.26139	−	31.2489i	−0.0773406	−	1.91600i
$267$		0			0
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	16.1931	+	28.0472i	0.976478	+	1.69131i
$276$		0			0
$277$	−5.65685	+	9.79796i	−0.339887	+	0.588702i	−0.984411	−	0.175882i	$-0.943722\pi$
$277$	−5.65685	+	9.79796i	−0.339887	+	0.588702i	0.644524	+	0.764584i	$0.277056\pi$
$278$	−23.2379	+	13.4164i	−1.39372	+	0.804663i
$279$		0			0
$280$	14.8170	+	7.77531i	0.885487	+	0.464664i
$281$	32.9089			1.96318			0.981590	−	0.190999i	$-0.0611727\pi$
$281$	32.9089			1.96318			0.981590	+	0.190999i	$0.0611727\pi$
$282$		0			0
$283$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$283$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$284$		0			0
$285$		0			0
$286$		−	24.3927i		−	1.44237i
$287$	−10.2692	+	6.49478i	−0.606169	+	0.383375i
$288$	−16.9706			−1.00000
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			31.6299i			1.84784i	0.382584	+	0.923921i	$0.375034\pi$
$293$			31.6299i			1.84784i	−0.382584	+	0.923921i	$0.624966\pi$
$294$		0			0
$295$	−14.1421			−0.823387
$296$	−13.4772	−	23.3432i	−0.783348	−	1.35680i
$297$		0			0
$298$		0			0
$299$	0.852485	−	0.492182i	0.0493005	−	0.0284636i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−28.9545	−	16.7169i	−1.66065	−	0.958778i
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	15.9260	−	30.3494i	0.907468	−	1.72932i
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$		−	29.6678i		−	1.67425i
$315$	0.715838	+	17.7338i	0.0403329	+	0.999186i
$316$		0			0
$317$	8.48528	+	14.6969i	0.476581	+	0.825462i	0.999640	−	0.0268342i	$-0.00854260\pi$
$317$	8.48528	+	14.6969i	0.476581	+	0.825462i	−0.523059	+	0.852296i	$0.675209\pi$
$318$		0			0
$319$		0			0
$320$	15.4919	−	8.94427i	0.866025	−	0.500000i
$321$		0			0
$322$	1.38201	−	0.0557857i	0.0770162	−	0.00310882i
$323$		0			0
$324$	−9.00000	−	15.5885i	−0.500000	−	0.866025i
$325$	−11.5307	−	6.65728i	−0.639611	−	0.369279i
$326$		0			0
$327$		0			0
$328$			12.9896i			0.717229i
$329$	−21.4545	−	11.2583i	−1.18282	−	0.620692i
$330$		0			0
$331$	9.19306	+	15.9229i	0.505296	+	0.875199i	0.999981	+	0.00612670i	$0.00195020\pi$
$331$	9.19306	+	15.9229i	0.505296	+	0.875199i	−0.494685	+	0.869072i	$0.664716\pi$
$332$		0			0
$333$	14.2948	−	24.7592i	0.783348	−	1.35680i
$334$	−24.2614	+	14.0073i	−1.32752	+	0.766446i
$335$		0			0
$336$		0			0
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−4.17822	−	7.23690i	−0.227265	−	0.393635i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		−	35.4618i		−	1.91756i
$343$	−18.3848	+	2.23607i	−0.992685	+	0.120736i
$344$		0			0
$345$		0			0
$346$	32.2158	+	18.5998i	1.73193	+	0.999933i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	−10.0000	−	15.8114i	−0.534522	−	0.845154i
$351$		0			0
$352$	−18.3204	−	31.7318i	−0.976478	−	1.69131i
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$		0			0
$355$		0			0
$356$			25.2982i			1.34080i
$357$		0			0
$358$	−10.6388			−0.562279
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$	16.4317	+	9.48683i	0.866025	+	0.500000i
$361$	25.4317	−	44.0490i	1.33851	−	2.31837i
$362$		0			0
$363$		0			0
$364$	0.568323	+	14.0793i	0.0297882	+	0.737958i
$365$		0			0
$366$		0			0
$367$	33.0170	+	19.0624i	1.72347	+	0.995047i	0.911438	+	0.411438i	$0.134973\pi$
$367$	33.0170	+	19.0624i	1.72347	+	0.995047i	0.812035	+	0.583609i	$0.198360\pi$
$368$	0.739315	−	1.28053i	0.0385394	−	0.0667523i
$369$	−11.9317	+	6.88876i	−0.621138	+	0.358614i
$370$			30.1360i			1.56670i
$371$	23.2386	−	0.938044i	1.20649	−	0.0487008i
$372$		0			0
$373$	−11.3137	−	19.5959i	−0.585802	−	1.01464i	−0.994775	−	0.102092i	$-0.967446\pi$
$373$	−11.3137	−	19.5959i	−0.585802	−	1.01464i	0.408973	−	0.912546i	$-0.365887\pi$
$374$		0			0
$375$		0			0
$376$	−22.4317	+	12.9509i	−1.15683	+	0.667893i
$377$		0			0
$378$		0			0
$379$	−33.4317			−1.71727			−0.858635	−	0.512588i	$-0.828687\pi$
$379$	−33.4317			−1.71727			−0.858635	+	0.512588i	$0.828687\pi$
$380$	18.6900	+	32.3721i	0.958778	+	1.66065i
$381$		0			0
$382$		0			0
$383$	21.7677	−	12.5676i	1.11228	−	0.642173i	0.172859	−	0.984947i	$-0.444700\pi$
$383$	21.7677	−	12.5676i	1.11228	−	0.642173i	0.939418	+	0.342773i	$0.111366\pi$
$384$		0			0
$385$	−32.3861	+	20.4828i	−1.65055	+	1.04390i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$	−8.48528	+	17.8885i	−0.428571	+	0.903508i
$393$		0			0
$394$	19.6931	+	34.1094i	0.992122	+	1.71841i
$395$		0			0
$396$	19.4317	−	33.6567i	0.976478	−	1.69131i
$397$	3.87298	−	2.23607i	0.194379	−	0.112225i	−0.399652	−	0.916667i	$-0.630869\pi$
$397$	3.87298	−	2.23607i	0.194379	−	0.112225i	0.594031	+	0.804442i	$0.297536\pi$
$398$		0			0
$399$		0			0
$400$	−20.0000			−1.00000
$401$	4.02277	+	6.96765i	0.200888	+	0.347948i	0.948815	−	0.315833i	$-0.102284\pi$
$401$	4.02277	+	6.96765i	0.200888	+	0.347948i	−0.747927	+	0.663781i	$0.768951\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$			20.1246i			1.00000i
$406$		0			0
$407$	61.7269			3.05969
$408$		0			0
$409$	32.8634	+	18.9737i	1.62499	+	0.938187i	0.985558	+	0.169338i	$0.0541630\pi$
$409$	32.8634	+	18.9737i	1.62499	+	0.938187i	0.639430	+	0.768849i	$0.279170\pi$
$410$	7.26139	−	12.5771i	0.358614	−	0.621138i
$411$		0			0
$412$			8.94427i			0.440653i
$413$	−0.674899	−	16.7196i	−0.0332096	−	0.822717i
$414$	1.56832			0.0770789
$415$		0			0
$416$	13.0455	+	7.53185i	0.639611	+	0.369279i
$417$		0			0
$418$	66.3070	−	38.2824i	3.24318	−	1.87245i
$419$			6.70527i			0.327574i	0.986496	+	0.163787i	$0.0523710\pi$
$419$			6.70527i			0.327574i	−0.986496	+	0.163787i	$0.947629\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	3.84078	+	6.65242i	0.186966	+	0.323835i
$423$	−23.7924	−	13.7365i	−1.15683	−	0.667893i
$424$	12.4317	−	21.5323i	0.603736	−	1.04570i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$		0			0
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.67581	+	1.54488i	0.128001	+	0.0739015i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$			40.9656i			1.95296i
$441$	−20.9317	+	1.69260i	−0.996747	+	0.0806002i
$442$		0			0
$443$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$443$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$444$		0			0
$445$	14.1421	−	24.4949i	0.670402	−	1.16117i
$446$	−27.3861	+	15.8114i	−1.29677	+	0.748691i
$447$		0			0
$448$	11.3137	+	17.8885i	0.534522	+	0.845154i
$449$	4.90890			0.231665			0.115833	−	0.993269i	$-0.463046\pi$
$449$	4.90890			0.231665			0.115833	+	0.993269i	$0.463046\pi$
$450$	−10.6066	−	18.3712i	−0.500000	−	0.866025i
$451$	−25.7614	−	14.8733i	−1.21306	−	0.700358i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.32031	−	13.9500i	0.343182	−	0.653984i
$456$		0			0
$457$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$457$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$458$		0			0
$459$		0			0
$460$	−1.43168	+	0.826579i	−0.0667523	+	0.0385394i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	−37.7497			−1.75438			−0.877189	−	0.480146i	$-0.840584\pi$
$463$	−37.7497			−1.75438			−0.877189	+	0.480146i	$0.840584\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$			15.9775i			0.738559i
$469$		0			0
$470$	28.9592			1.33579
$471$		0			0
$472$	−15.4919	−	8.94427i	−0.713074	−	0.411693i
$473$		0			0
$474$		0			0
$475$		−	41.7922i		−	1.91756i
$476$		0			0
$477$	26.3716			1.20747
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−21.9772	+	12.6886i	−1.00208	+	0.578548i
$482$		−	4.15686i		−	0.189340i
$483$		0			0
$484$	61.9089			2.81404
$485$		0			0
$486$		0			0
$487$	−15.5563	+	26.9444i	−0.704925	+	1.22097i	0.261793	+	0.965124i	$0.415686\pi$
$487$	−15.5563	+	26.9444i	−0.704925	+	1.22097i	−0.966718	+	0.255843i	$0.917647\pi$
$488$		0			0
$489$		0			0
$490$	18.2158	−	12.5771i	0.822908	−	0.568175i
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$		0			0
$493$		0			0
$494$	−15.7386	+	27.2601i	−0.708114	+	1.22649i
$495$	−37.6293	+	21.7253i	−1.69131	+	0.976478i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.00000	+	5.19615i	0.134298	+	0.232612i	0.925329	−	0.379165i	$-0.123789\pi$
$499$	3.00000	+	5.19615i	0.134298	+	0.232612i	−0.791031	+	0.611776i	$0.790455\pi$
$500$	19.3649	+	11.1803i	0.866025	+	0.500000i
$501$		0			0
$502$	−21.4862	+	12.4051i	−0.958978	+	0.553666i
$503$			40.2492i			1.79462i	0.441397	+	0.897312i	$0.354483\pi$
$503$			40.2492i			1.79462i	−0.441397	+	0.897312i	$0.645517\pi$
$504$	−10.4317	+	19.8791i	−0.464664	+	0.885487i
$505$		0			0
$506$	1.69306	+	2.93247i	0.0752659	+	0.130364i
$507$		0			0
$508$	17.9507	−	31.0915i	0.796434	−	1.37946i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$		0			0
$512$	22.6274			1.00000
$513$		0			0
$514$		0			0
$515$	5.00000	−	8.66025i	0.220326	−	0.381616i
$516$		0			0
$517$		−	59.3164i		−	2.60873i
$518$	−35.6284	+	1.43817i	−1.56542	+	0.0631894i
$519$		0			0
$520$	−8.42087	−	14.5854i	−0.369279	−	0.639611i
$521$	−39.4545	−	22.7790i	−1.72853	−	0.997968i	−0.896126	−	0.443800i	$-0.853630\pi$
$521$	−39.4545	−	22.7790i	−1.72853	−	0.997968i	−0.832405	−	0.554168i	$-0.813037\pi$
$522$		0			0
$523$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$523$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$524$		−	31.7806i		−	1.38834i
$525$		0			0
$526$	−12.0000			−0.523225
$527$		0			0
$528$		0			0
$529$	11.4317	−	19.8002i	0.497029	−	0.860880i
$530$	−24.0738	+	13.8990i	−1.04570	+	0.603736i
$531$		−	18.9737i		−	0.823387i
$532$	−37.3800	+	23.6412i	−1.62063	+	1.02498i
$533$	12.2294			0.529716
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−25.7614	−	37.3111i	−1.10962	−	1.60710i
$540$		0			0
$541$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$541$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$		0			0
$550$	22.9005	−	39.6647i	0.976478	−	1.69131i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	16.0000			0.679775
$555$		0			0
$556$	32.8634	+	18.9737i	1.39372	+	0.804663i
$557$	−5.50423	+	9.53361i	−0.233222	+	0.403952i	−0.958754	−	0.284236i	$-0.908260\pi$
$557$	−5.50423	+	9.53361i	−0.233222	+	0.403952i	0.725533	+	0.688188i	$0.241594\pi$
$558$		0			0
$559$		0			0
$560$	−0.954451	−	23.6451i	−0.0403329	−	0.999186i
$561$		0			0
$562$	−23.2701	−	40.3050i	−0.981590	−	1.70016i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−23.7924	+	0.960398i	−0.999186	+	0.0403329i
$568$		0			0
$569$	−16.9772	−	29.4054i	−0.711722	−	1.23274i	−0.964210	−	0.265139i	$-0.914582\pi$
$569$	−16.9772	−	29.4054i	−0.711722	−	1.23274i	0.252488	−	0.967600i	$-0.418751\pi$
$570$		0			0
$571$	−9.00000	+	15.5885i	−0.376638	+	0.652357i	−0.990571	−	0.137002i	$-0.956253\pi$
$571$	−9.00000	+	15.5885i	−0.376638	+	0.652357i	0.613933	+	0.789359i	$0.289587\pi$
$572$	−29.8749	+	17.2483i	−1.24913	+	0.721187i
$573$		0			0
$574$	15.2158	+	7.98459i	0.635097	+	0.333270i
$575$	1.84829			0.0770789
$576$	12.0000	+	20.7846i	0.500000	+	0.866025i
$577$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$577$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$578$	12.0208	−	20.8207i	0.500000	−	0.866025i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	28.4691	+	49.3099i	1.17907	+	2.04221i
$584$		0			0
$585$	8.93168	−	15.4701i	0.369279	−	0.639611i
$586$	38.7386	−	22.3657i	1.60028	−	0.923921i
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$		0			0
$589$		0			0
$590$	10.0000	+	17.3205i	0.411693	+	0.713074i
$591$		0			0
$592$	−19.0597	+	33.0123i	−0.783348	+	1.35680i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−1.20560	−	0.696051i	−0.0493005	−	0.0284636i
$599$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$599$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$600$		0			0
$601$			25.2982i			1.03194i	0.856608	+	0.515968i	$0.172568\pi$
$601$			25.2982i			1.03194i	−0.856608	+	0.515968i	$0.827432\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−59.9430	−	34.6081i	−2.43703	−	1.40702i
$606$		0			0
$607$	19.1801	−	11.0736i	0.778496	−	0.449465i	−0.0574012	−	0.998351i	$-0.518281\pi$
$607$	19.1801	−	11.0736i	0.778496	−	0.449465i	0.835897	+	0.548886i	$0.184948\pi$
$608$			47.2824i			1.91756i
$609$		0			0
$610$		0			0
$611$	12.1931	+	21.1190i	0.493279	+	0.854384i
$612$		0			0
$613$	−22.7156	+	39.3446i	−0.917475	+	1.58911i	−0.114239	+	0.993453i	$0.536443\pi$
$613$	−22.7156	+	39.3446i	−0.917475	+	1.58911i	−0.803236	+	0.595661i	$0.796890\pi$
$614$		0			0
$615$		0			0
$616$	−48.4317	+	1.95498i	−1.95137	+	0.0787685i
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	42.7158	+	24.6620i	1.71689	+	0.991250i	0.924448	+	0.381308i	$0.124526\pi$
$619$	42.7158	+	24.6620i	1.71689	+	0.991250i	0.792446	+	0.609941i	$0.208807\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	29.6341	+	15.5506i	1.18726	+	0.623023i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$	−36.3355	+	20.9783i	−1.44994	+	0.837125i
$629$		0			0
$630$	21.2132	−	13.4164i	0.845154	−	0.534522i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$	12.0000	−	20.7846i	0.476581	−	0.825462i
$635$	−34.7614	+	20.0695i	−1.37946	+	0.796434i
$636$		0			0
$637$	16.8417	+	7.98873i	0.667294	+	0.316525i
$638$		0			0
$639$		0			0
$640$	−21.9089	−	12.6491i	−0.866025	−	0.500000i
$641$	−22.4089	+	38.8134i	−0.885098	+	1.53304i	−0.0394976	+	0.999220i	$0.512576\pi$
$641$	−22.4089	+	38.8134i	−0.885098	+	1.53304i	−0.845601	+	0.533816i	$0.820758\pi$
$642$		0			0
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$	−1.04555	−	1.65316i	−0.0412004	−	0.0651435i
$645$		0			0
$646$		0			0
$647$	5.90610	+	3.40989i	0.232193	+	0.134057i	0.611583	−	0.791180i	$-0.290533\pi$
$647$	5.90610	+	3.40989i	0.232193	+	0.134057i	−0.379390	+	0.925237i	$0.623866\pi$
$648$	−12.7279	+	22.0454i	−0.500000	+	0.866025i
$649$	35.4772	−	20.4828i	1.39260	−	0.804020i
$650$			18.8296i			0.738559i
$651$		0			0
$652$		0			0
$653$	−14.6644	−	25.3995i	−0.573863	−	0.993960i	−0.996164	−	0.0875041i	$-0.972111\pi$
$653$	−14.6644	−	25.3995i	−0.573863	−	0.993960i	0.422301	−	0.906456i	$-0.361222\pi$
$654$		0			0
$655$	−17.7659	+	30.7714i	−0.694170	+	1.20234i
$656$	15.9089	−	9.18501i	0.621138	−	0.358614i
$657$		0			0
$658$	1.38201	+	34.2371i	0.0538762	+	1.33470i
$659$	−26.0000			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$659$	−26.0000			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$660$		0			0
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$	13.0010	−	22.5183i	0.505296	−	0.875199i
$663$		0			0
$664$		0			0
$665$	49.4089	−	1.99443i	1.91600	−	0.0773406i
$666$	−40.4317			−1.56670
$667$		0			0
$668$	34.3108	+	19.8093i	1.32752	+	0.766446i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$		0			0
$676$	−5.90890	+	10.2345i	−0.227265	+	0.393635i
$677$	34.0293	−	19.6468i	1.30785	−	0.755090i	0.326116	−	0.945330i	$-0.394260\pi$
$677$	34.0293	−	19.6468i	1.30785	−	0.755090i	0.981738	+	0.190240i	$0.0609267\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$	−43.4317	+	25.0753i	−1.66065	+	0.958778i
$685$		0			0
$686$	15.7386	+	20.9355i	0.600903	+	0.799322i
$687$		0			0
$688$		0			0
$689$	−20.2723	−	11.7042i	−0.772311	−	0.445894i
$690$		0			0
$691$	−27.3861	+	15.8114i	−1.04182	+	0.601494i	−0.920348	−	0.391102i	$-0.872094\pi$
$691$	−27.3861	+	15.8114i	−1.04182	+	0.601494i	−0.121470	+	0.992595i	$0.538761\pi$
$692$		−	52.6082i		−	1.99987i
$693$	−27.4805	−	43.4506i	−1.04390	−	1.65055i
$694$		0			0
$695$	−21.2132	−	36.7423i	−0.804663	−	1.39372i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−12.2938	+	23.4278i	−0.464664	+	0.885487i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−68.9828	−	39.8272i	−2.60174	−	1.50211i
$704$	−25.9089	+	44.8755i	−0.976478	+	1.69131i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$		0			0
$711$		0			0
$712$	30.9839	−	17.8885i	1.16117	−	0.670402i
$713$		0			0
$714$		0			0
$715$	38.5683			1.44237
$716$	7.52277	+	13.0298i	0.281139	+	0.486948i
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		−	26.8328i		−	1.00000i
$721$	10.4772	+	5.49798i	0.390192	+	0.204755i
$722$	−71.9316			−2.67702
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$			48.7764i			1.80902i	0.426457	+	0.904508i	$0.359761\pi$
$727$			48.7764i			1.80902i	−0.426457	+	0.904508i	$0.640239\pi$
$728$	16.8417	−	10.6516i	0.624196	−	0.394776i
$729$	−27.0000			−1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	4.33085	−	2.50041i	0.159963	−	0.0923549i	−0.417881	−	0.908502i	$-0.637227\pi$
$733$	4.33085	−	2.50041i	0.159963	−	0.0923549i	0.577845	+	0.816147i	$0.303894\pi$
$734$		−	53.9165i		−	1.99009i
$735$		0			0
$736$	−2.09110			−0.0770789
$737$		0			0
$738$	16.8739	+	9.74217i	0.621138	+	0.358614i
$739$	10.7614	−	18.6393i	0.395864	−	0.685657i	−0.597347	−	0.801983i	$-0.703778\pi$
$739$	10.7614	−	18.6393i	0.395864	−	0.685657i	0.993211	+	0.116326i	$0.0371118\pi$
$740$	36.9089	−	21.3094i	1.35680	−	0.783348i
$741$		0			0
$742$	−17.5810	−	27.7981i	−0.645420	−	1.02050i
$743$	16.4721			0.604302			0.302151	−	0.953260i	$-0.402295\pi$
$743$	16.4721			0.604302			0.302151	+	0.953260i	$0.402295\pi$
$744$		0			0
$745$		0			0
$746$	−16.0000	+	27.7128i	−0.585802	+	1.01464i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	31.7232	+	18.3154i	1.15683	+	0.667893i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	45.2548			1.64481			0.822407	−	0.568899i	$-0.192630\pi$
$757$	45.2548			1.64481			0.822407	+	0.568899i	$0.192630\pi$
$758$	23.6398	+	40.9453i	0.858635	+	1.48720i
$759$		0			0
$760$	26.4317	−	45.7810i	0.958778	−	1.66065i
$761$	5.40890	−	3.12283i	0.196073	−	0.113203i	−0.398750	−	0.917060i	$-0.630556\pi$
$761$	5.40890	−	3.12283i	0.196073	−	0.113203i	0.594822	+	0.803857i	$0.297222\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−30.7842	−	17.7732i	−1.11228	−	0.642173i
$767$	−8.42087	+	14.5854i	−0.304060	+	0.526647i
$768$		0			0
$769$			53.0899i			1.91447i	0.289309	+	0.957236i	$0.406575\pi$
$769$			53.0899i			1.91447i	−0.289309	+	0.957236i	$0.593425\pi$
$770$	47.9866	+	25.1812i	1.72932	+	0.907468i
$771$		0			0
$772$		0			0
$773$	47.8662	+	27.6356i	1.72163	+	0.993983i	0.915583	+	0.402129i	$0.131730\pi$
$773$	47.8662	+	27.6356i	1.72163	+	0.993983i	0.806045	+	0.591854i	$0.201604\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	19.1931	+	33.2434i	0.687663	+	1.19107i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	27.9089	−	2.25681i	0.996747	−	0.0806002i
$785$	46.9089			1.67425
$786$		0			0
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	27.8502	−	48.2380i	0.992122	−	1.71841i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−54.9611			−1.95296
$793$		0			0
$794$	−5.47723	−	3.16228i	−0.194379	−	0.112225i
$795$		0			0
$796$		0			0
$797$			40.2492i			1.42570i	0.701316	+	0.712850i	$0.252596\pi$
$797$			40.2492i			1.42570i	−0.701316	+	0.712850i	$0.747404\pi$
$798$		0			0
$799$		0			0
$800$	14.1421	+	24.4949i	0.500000	+	0.866025i
$801$	32.8634	+	18.9737i	1.16117	+	0.670402i
$802$	5.68906	−	9.85374i	0.200888	−	0.347948i
$803$		0			0
$804$		0			0
$805$	0.0882050	+	2.18514i	0.00310882	+	0.0770162i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.4089	+	26.6890i	−0.541748	+	0.938335i	0.457056	+	0.889438i	$0.348904\pi$
$809$	−15.4089	+	26.6890i	−0.541748	+	0.938335i	−0.998804	+	0.0488972i	$0.984429\pi$
$810$	24.6475	−	14.2302i	0.866025	−	0.500000i
$811$			26.7284i			0.938563i	0.883049	+	0.469281i	$0.155487\pi$
$811$			26.7284i			0.938563i	−0.883049	+	0.469281i	$0.844513\pi$
$812$		0			0
$813$		0			0
$814$	−43.6475	−	75.5997i	−1.52984	−	2.64977i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		−	53.6656i		−	1.87637i
$819$	18.7158	+	9.82123i	0.653984	+	0.343182i
$820$	−20.5383			−0.717229
$821$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$821$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$822$		0			0
$823$	24.0416	−	41.6413i	0.838039	−	1.45153i	−0.0534937	−	0.998568i	$-0.517036\pi$
$823$	24.0416	−	41.6413i	0.838039	−	1.45153i	0.891532	−	0.452957i	$-0.149631\pi$
$824$	10.9545	−	6.32456i	0.381616	−	0.220326i
$825$		0			0
$826$	−20.0000	+	12.6491i	−0.695889	+	0.440119i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−1.10897	−	1.92080i	−0.0385394	−	0.0667523i
$829$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$829$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$830$		0			0
$831$		0			0
$832$		−	21.3033i		−	0.738559i
$833$		0			0
$834$		0			0
$835$	−22.1475	−	38.3606i	−0.766446	−	1.32752i
$836$	−93.7723	−	54.1394i	−3.24318	−	1.87245i
$837$		0			0
$838$	8.21225	−	4.74134i	0.283687	−	0.163787i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$		0			0
$844$	5.43168	−	9.40794i	0.186966	−	0.323835i
$845$	11.4425	−	6.60635i	0.393635	−	0.227265i
$846$			38.8528i			1.33579i
$847$	38.0549	−	72.5194i	1.30758	−	2.49180i
$848$	−35.1621			−1.20747
$849$		0			0
$850$		0			0
$851$	1.76139	−	3.05081i	0.0603796	−	0.104580i
$852$		0			0
$853$		−	33.9679i		−	1.16304i	−0.813533	−	0.581519i	$-0.802459\pi$
$853$		−	33.9679i		−	1.16304i	0.813533	−	0.581519i	$-0.197541\pi$
$854$		0			0
$855$	56.0701			1.91756
$856$		0			0
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	49.2950	−	28.4605i	1.68192	−	0.971060i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	49.2950	−	28.4605i	1.68192	−	0.971060i	0.960381	−	0.278691i	$-0.0899005\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.2957	+	47.2776i	0.929157	+	1.60935i	0.784736	+	0.619831i	$0.212799\pi$
$863$	27.2957	+	47.2776i	0.929157	+	1.60935i	0.144421	+	0.989516i	$0.453868\pi$
$864$		0			0
$865$	−29.4089	+	50.9377i	−0.999933	+	1.73193i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		−	4.36957i		−	0.147803i
$875$	25.0000	−	15.8114i	0.845154	−	0.534522i
$876$		0			0
$877$	22.3460	+	38.7043i	0.754570	+	1.30695i	0.945588	+	0.325366i	$0.105488\pi$
$877$	22.3460	+	38.7043i	0.754570	+	1.30695i	−0.191018	+	0.981586i	$0.561179\pi$
$878$		0			0
$879$		0			0
$880$	50.1724	−	28.9670i	1.69131	−	0.976478i
$881$		−	43.9049i		−	1.47919i	−0.673050	−	0.739597i	$-0.735016\pi$
$881$		−	43.9049i		−	1.47919i	0.673050	−	0.739597i	$-0.264984\pi$
$882$	16.8739	+	24.4391i	0.568175	+	0.822908i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.87298	−	2.23607i	0.130042	−	0.0750798i	−0.433568	−	0.901121i	$-0.642746\pi$
$887$	3.87298	−	2.23607i	0.130042	−	0.0750798i	0.563610	+	0.826041i	$0.309412\pi$
$888$		0			0
$889$	−25.3861	−	40.1390i	−0.851423	−	1.34622i
$890$	−40.0000			−1.34080
$891$	−29.1475	−	50.4850i	−0.976478	−	1.69131i
$892$	38.7298	+	22.3607i	1.29677	+	0.748691i
$893$	−38.2720	+	66.2890i	−1.28072	+	2.21828i
$894$		0			0
$895$		−	16.8214i		−	0.562279i
$896$	13.9089	−	26.5055i	0.464664	−	0.885487i
$897$		0			0
$898$	−3.47112	−	6.01215i	−0.115833	−	0.200628i
$899$		0			0
$900$	−15.0000	+	25.9808i	−0.500000	+	0.866025i
$901$		0			0
$902$			42.0682i			1.40072i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$907$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$		0			0
$910$	−22.2614	+	0.898598i	−0.737958	+	0.0297882i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−37.2274	−	19.5353i	−1.22936	−	0.645112i
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$	2.02470	+	1.16896i	0.0667523	+	0.0385394i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−47.6492			−1.56670
$926$	26.6931	+	46.2337i	0.877189	+	1.51934i
$927$	11.6190	+	6.70820i	0.381616	+	0.220326i
$928$		0			0
$929$	47.4089	−	27.3715i	1.55544	−	0.898031i	0.557752	−	0.830008i	$-0.311664\pi$
$929$	47.4089	−	27.3715i	1.55544	−	0.898031i	0.997684	−	0.0680235i	$-0.0216693\pi$
$930$		0			0
$931$	4.71584	+	58.3187i	0.154555	+	1.91132i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	19.5683	−	11.2978i	0.639611	−	0.369279i
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$	−20.4772	−	35.4676i	−0.667893	−	1.15683i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	−1.47021	+	0.848827i	−0.0478766	+	0.0276416i
$944$			25.2982i			0.823387i
$945$		0			0
$946$		0			0
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$		0			0
$949$		0			0
$950$	−51.1847	+	29.5515i	−1.66065	+	0.958778i
$951$		0			0
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$	−18.6475	−	32.2984i	−0.603736	−	1.04570i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	31.0805	+	17.9443i	1.00208	+	0.578548i
$963$		0			0
$964$	−5.09110	+	2.93935i	−0.163973	+	0.0946700i
$965$		0			0
$966$		0			0
$967$	−53.7401			−1.72817			−0.864083	−	0.503350i	$-0.832101\pi$
$967$	−53.7401			−1.72817			−0.864083	+	0.503350i	$0.832101\pi$
$968$	−43.7762	−	75.8226i	−1.40702	−	2.43703i
$969$		0			0
$970$		0			0
$971$	49.2386	−	28.4279i	1.58014	−	0.912296i	0.585305	−	0.810813i	$-0.300975\pi$
$971$	49.2386	−	28.4279i	1.58014	−	0.912296i	0.994837	−	0.101482i	$-0.0323585\pi$
$972$		0			0
$973$	42.4264	−	26.8328i	1.36013	−	0.860221i
$974$	44.0000			1.40985
$975$		0			0
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$			81.9311i			2.61853i
$980$	−28.2843	−	13.4164i	−0.903508	−	0.428571i
$981$		0			0
$982$	−1.41421	−	2.44949i	−0.0451294	−	0.0781664i
$983$	−53.4909	−	30.8830i	−1.70609	−	0.985014i	−0.939285	−	0.343138i	$-0.888510\pi$
$983$	−53.4909	−	30.8830i	−1.70609	−	0.985014i	−0.766809	−	0.641875i	$-0.778157\pi$
$984$		0			0
$985$	−53.9317	+	31.1375i	−1.71841	+	0.992122i
$986$		0			0
$987$		0			0
$988$	44.5155			1.41623
$989$		0			0
$990$	53.2158	+	30.7242i	1.69131	+	0.976478i
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−42.6028	−	24.5967i	−1.34924	−	0.778987i	−0.361102	−	0.932526i	$-0.617599\pi$
$997$	−42.6028	−	24.5967i	−1.34924	−	0.778987i	−0.988143	+	0.153539i	$0.950933\pi$
$998$	4.24264	−	7.34847i	0.134298	−	0.232612i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.ba.a.59.2	yes	8
4.3	odd	2		1120.2.bq.a.1039.3		8
5.4	even	2	inner	280.2.ba.a.59.3	yes	8
7.5	odd	6	inner	280.2.ba.a.19.2	✓	8
8.3	odd	2	inner	280.2.ba.a.59.3	yes	8
8.5	even	2		1120.2.bq.a.1039.2		8
20.19	odd	2		1120.2.bq.a.1039.2		8
28.19	even	6		1120.2.bq.a.719.3		8
35.19	odd	6	inner	280.2.ba.a.19.3	yes	8
40.19	odd	2	CM	280.2.ba.a.59.2	yes	8
40.29	even	2		1120.2.bq.a.1039.3		8
56.5	odd	6		1120.2.bq.a.719.2		8
56.19	even	6	inner	280.2.ba.a.19.3	yes	8
140.19	even	6		1120.2.bq.a.719.2		8
280.19	even	6	inner	280.2.ba.a.19.2	✓	8
280.229	odd	6		1120.2.bq.a.719.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.a.19.2	✓	8	7.5	odd	6	inner
280.2.ba.a.19.2	✓	8	280.19	even	6	inner
280.2.ba.a.19.3	yes	8	35.19	odd	6	inner
280.2.ba.a.19.3	yes	8	56.19	even	6	inner
280.2.ba.a.59.2	yes	8	1.1	even	1	trivial
280.2.ba.a.59.2	yes	8	40.19	odd	2	CM
280.2.ba.a.59.3	yes	8	5.4	even	2	inner
280.2.ba.a.59.3	yes	8	8.3	odd	2	inner
1120.2.bq.a.719.2		8	56.5	odd	6
1120.2.bq.a.719.2		8	140.19	even	6
1120.2.bq.a.719.3		8	28.19	even	6
1120.2.bq.a.719.3		8	280.229	odd	6
1120.2.bq.a.1039.2		8	8.5	even	2
1120.2.bq.a.1039.2		8	20.19	odd	2
1120.2.bq.a.1039.3		8	4.3	odd	2
1120.2.bq.a.1039.3		8	40.29	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(1.41421 + 2.23607i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(1.41421 + 2.23607i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(-3.23861 + 5.60944i) q^{11} -2.66291i q^{13} +(1.73861 - 3.31319i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(2.12132 - 3.67423i) q^{18} +(7.23861 - 4.17922i) q^{19} +4.47214i q^{20} +9.16018 q^{22} +(0.184829 + 0.320133i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-3.26139 + 1.88296i) q^{26} +(-5.28720 + 0.213422i) q^{28} +(-2.82843 + 4.89898i) q^{32} +(5.23861 + 2.74899i) q^{35} -6.00000 q^{36} +(-4.76492 - 8.25308i) q^{37} +(-10.2369 - 5.91030i) q^{38} +(5.47723 - 3.16228i) q^{40} +4.59250i q^{41} +(-6.47723 - 11.2189i) q^{44} +(5.80948 + 3.35410i) q^{45} +(0.261387 - 0.452736i) q^{46} +(-7.93080 + 4.57885i) q^{47} +(-3.00000 + 6.32456i) q^{49} -7.07107 q^{50} +(4.61230 + 2.66291i) q^{52} +(4.39526 - 7.61282i) q^{53} +14.4835i q^{55} +(4.00000 + 6.32456i) q^{56} +(-5.47723 - 3.16228i) q^{59} +(-3.68815 + 7.02834i) q^{63} +8.00000 q^{64} +(-2.97723 - 5.15671i) q^{65} +(-0.337449 - 8.35979i) q^{70} +(4.24264 + 7.34847i) q^{72} +(-6.73861 + 11.6716i) q^{74} +16.7169i q^{76} +(-17.1232 + 0.691190i) q^{77} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(5.62465 - 3.24739i) q^{82} +(-9.16018 + 15.8659i) q^{88} +(10.9545 - 6.32456i) q^{89} -9.48683i q^{90} +(5.95445 - 3.76593i) q^{91} -0.739315 q^{92} +(11.2158 + 6.47547i) q^{94} +(9.34501 - 16.1860i) q^{95} +(9.86729 - 0.797901i) q^{98} -19.4317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 12 * q^9	\( 8 q - 8 q^{4} + 12 q^{9} - 4 q^{11} - 8 q^{14} - 16 q^{16} + 36 q^{19} + 20 q^{25} - 48 q^{26} + 20 q^{35} - 48 q^{36} - 8 q^{44} + 24 q^{46} - 24 q^{49} + 32 q^{56} + 64 q^{64} + 20 q^{65} - 32 q^{74} - 36 q^{81} - 40 q^{91} + 24 q^{94} - 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 12 * q^9 - 4 * q^11 - 8 * q^14 - 16 * q^16 + 36 * q^19 + 20 * q^25 - 48 * q^26 + 20 * q^35 - 48 * q^36 - 8 * q^44 + 24 * q^46 - 24 * q^49 + 32 * q^56 + 64 * q^64 + 20 * q^65 - 32 * q^74 - 36 * q^81 - 40 * q^91 + 24 * q^94 - 24 * q^99

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