LMFDB - Embedded newform 3525.1.bg.a.443.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,1,Mod(107,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(92))

chi = DirichletCharacter(H, H._module([46, 23, 22]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3525.107");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3525.bg (of order $92$, degree $44$, 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:	$1.75920416953$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$2$ over $\Q(\zeta_{92})$
Coefficient field:	$\Q(\zeta_{184})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{88} - x^{84} + x^{80} - x^{76} + x^{72} - x^{68} + x^{64} - x^{60} + x^{56} - x^{52} + x^{48} + \cdots + 1 $ x^88 - x^84 + x^80 - x^76 + x^72 - x^68 + x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{46}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{46} - \cdots)$

Embedding invariants

Embedding label			443.1
Root			$-0.657204 + 0.753713i$ of defining polynomial
Character	$\chi$	$=$	3525.443
Dual form			3525.1.bg.a.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.757993 + 0.869303i) q^{2} +(0.871660 - 0.490110i) q^{3} +(-0.0449678 - 0.327165i) q^{4} +(-0.234658 + 1.12924i) q^{6} +(-0.645929 - 0.423665i) q^{8} +(0.519584 - 0.854419i) q^{9} +O(q^{10})$	\(q+(-0.757993 + 0.869303i) q^{2} +(0.871660 - 0.490110i) q^{3} +(-0.0449678 - 0.327165i) q^{4} +(-0.234658 + 1.12924i) q^{6} +(-0.645929 - 0.423665i) q^{8} +(0.519584 - 0.854419i) q^{9} +(-0.199543 - 0.263138i) q^{12} +(1.17590 - 0.329471i) q^{16} +(-1.26993 - 0.500795i) q^{17} +(0.348908 + 1.09932i) q^{18} +(0.157049 - 0.222488i) q^{19} +(1.50391 - 1.31134i) q^{23} +(-0.770673 - 0.0527155i) q^{24} +(0.0341411 - 0.999417i) q^{27} +(-0.214975 - 0.767255i) q^{31} +(-0.273147 + 0.574346i) q^{32} +(1.39794 - 0.724354i) q^{34} +(-0.302901 - 0.131568i) q^{36} +(0.0743674 + 0.305168i) q^{38} +2.30134i q^{46} +(0.102264 + 0.994757i) q^{47} +(0.863506 - 0.863506i) q^{48} +(0.997669 - 0.0682424i) q^{49} +(-1.35239 + 0.185882i) q^{51} +(-0.937216 - 1.42890i) q^{53} +(0.842917 + 0.787230i) q^{54} +(0.0278499 - 0.270906i) q^{57} +(0.713755 + 0.580683i) q^{61} +(0.829926 + 0.394695i) q^{62} +(0.194283 + 0.447285i) q^{64} +(-0.106737 + 0.437996i) q^{68} +(0.668198 - 1.88013i) q^{69} +(-0.697602 + 0.331765i) q^{72} +(-0.0798525 - 0.0413762i) q^{76} +(1.72850 - 0.614311i) q^{79} +(-0.460065 - 0.887885i) q^{81} +(-0.378541 + 0.149277i) q^{83} +(-0.496653 - 0.433059i) q^{92} +(-0.563424 - 0.563424i) q^{93} +(-0.942261 - 0.665120i) q^{94} +(0.0434014 + 0.634506i) q^{96} +(-0.696902 + 0.919004i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{6}+O(q^{10}) $ 88 * q - 8 * q^6	$ 88 q - 8 q^{6} + 20 q^{16} - 12 q^{36} - 8 q^{51} + 8 q^{61} - 92 q^{76} + 4 q^{81} - 68 q^{96}+O(q^{100}) $ 88 * q - 8 * q^6 + 20 * q^16 - 12 * q^36 - 8 * q^51 + 8 * q^61 - 92 * q^76 + 4 * q^81 - 68 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{37}{46}\right)$	$-1$

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 $

$2$	−0.757993	+	0.869303i	−0.757993	+	0.869303i	−0.994757	−	0.102264i	$-0.967391\pi$
$2$	−0.757993	+	0.869303i	−0.757993	+	0.869303i	0.236764	+	0.971567i	$0.423913\pi$
$3$	0.871660	−	0.490110i	0.871660	−	0.490110i
$3$	0.871660	−	0.490110i	0.871660	−	0.490110i
$4$	−0.0449678	−	0.327165i	−0.0449678	−	0.327165i
$5$		0			0
$5$		0			0
$6$	−0.234658	+	1.12924i	−0.234658	+	1.12924i
$7$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$7$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$8$	−0.645929	−	0.423665i	−0.645929	−	0.423665i
$9$	0.519584	−	0.854419i	0.519584	−	0.854419i
$10$		0			0
$11$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$11$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$12$	−0.199543	−	0.263138i	−0.199543	−	0.263138i
$13$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$13$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$14$		0			0
$15$		0			0
$16$	1.17590	−	0.329471i	1.17590	−	0.329471i
$17$	−1.26993	−	0.500795i	−1.26993	−	0.500795i	−0.366854	−	0.930278i	$-0.619565\pi$
$17$	−1.26993	−	0.500795i	−1.26993	−	0.500795i	−0.903075	+	0.429483i	$0.858696\pi$
$18$	0.348908	+	1.09932i	0.348908	+	1.09932i
$19$	0.157049	−	0.222488i	0.157049	−	0.222488i	−0.730836	−	0.682553i	$-0.760870\pi$
$19$	0.157049	−	0.222488i	0.157049	−	0.222488i	0.887885	+	0.460065i	$0.152174\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.50391	−	1.31134i	1.50391	−	1.31134i	0.707107	−	0.707107i	$-0.250000\pi$
$23$	1.50391	−	1.31134i	1.50391	−	1.31134i	0.796805	−	0.604236i	$-0.206522\pi$
$24$	−0.770673	−	0.0527155i	−0.770673	−	0.0527155i
$25$		0			0
$26$		0			0
$27$	0.0341411	−	0.999417i	0.0341411	−	0.999417i
$28$		0			0
$29$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$29$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$30$		0			0
$31$	−0.214975	−	0.767255i	−0.214975	−	0.767255i	−0.990686	−	0.136167i	$-0.956522\pi$
$31$	−0.214975	−	0.767255i	−0.214975	−	0.767255i	0.775711	−	0.631088i	$-0.217391\pi$
$32$	−0.273147	+	0.574346i	−0.273147	+	0.574346i
$33$		0			0
$34$	1.39794	−	0.724354i	1.39794	−	0.724354i
$35$		0			0
$36$	−0.302901	−	0.131568i	−0.302901	−	0.131568i
$37$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$37$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$38$	0.0743674	+	0.305168i	0.0743674	+	0.305168i
$39$		0			0
$40$		0			0
$41$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$41$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$42$		0			0
$43$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$43$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$44$		0			0
$45$		0			0
$46$			2.30134i			2.30134i
$47$	0.102264	+	0.994757i	0.102264	+	0.994757i
$47$	0.102264	+	0.994757i	0.102264	+	0.994757i
$48$	0.863506	−	0.863506i	0.863506	−	0.863506i
$49$	0.997669	−	0.0682424i	0.997669	−	0.0682424i
$50$		0			0
$51$	−1.35239	+	0.185882i	−1.35239	+	0.185882i
$52$		0			0
$53$	−0.937216	−	1.42890i	−0.937216	−	1.42890i	−0.903075	−	0.429483i	$-0.858696\pi$
$53$	−0.937216	−	1.42890i	−0.937216	−	1.42890i	−0.0341411	−	0.999417i	$-0.510870\pi$
$54$	0.842917	+	0.787230i	0.842917	+	0.787230i
$55$		0			0
$56$		0			0
$57$	0.0278499	−	0.270906i	0.0278499	−	0.270906i
$58$		0			0
$59$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$59$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$60$		0			0
$61$	0.713755	+	0.580683i	0.713755	+	0.580683i	0.917211	−	0.398401i	$-0.130435\pi$
$61$	0.713755	+	0.580683i	0.713755	+	0.580683i	−0.203456	+	0.979084i	$0.565217\pi$
$62$	0.829926	+	0.394695i	0.829926	+	0.394695i
$63$		0			0
$64$	0.194283	+	0.447285i	0.194283	+	0.447285i
$65$		0			0
$66$		0			0
$67$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$67$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$68$	−0.106737	+	0.437996i	−0.106737	+	0.437996i
$69$	0.668198	−	1.88013i	0.668198	−	1.88013i
$70$		0			0
$71$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$71$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$72$	−0.697602	+	0.331765i	−0.697602	+	0.331765i
$73$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$73$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$74$		0			0
$75$		0			0
$76$	−0.0798525	−	0.0413762i	−0.0798525	−	0.0413762i
$77$		0			0
$78$		0			0
$79$	1.72850	−	0.614311i	1.72850	−	0.614311i	0.730836	−	0.682553i	$-0.239130\pi$
$79$	1.72850	−	0.614311i	1.72850	−	0.614311i	0.997669	+	0.0682424i	$0.0217391\pi$
$80$		0			0
$81$	−0.460065	−	0.887885i	−0.460065	−	0.887885i
$82$		0			0
$83$	−0.378541	+	0.149277i	−0.378541	+	0.149277i	−0.548452	−	0.836182i	$-0.684783\pi$
$83$	−0.378541	+	0.149277i	−0.378541	+	0.149277i	0.169910	+	0.985460i	$0.445652\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$89$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$90$		0			0
$91$		0			0
$92$	−0.496653	−	0.433059i	−0.496653	−	0.433059i
$93$	−0.563424	−	0.563424i	−0.563424	−	0.563424i
$94$	−0.942261	−	0.665120i	−0.942261	−	0.665120i
$95$		0			0
$96$	0.0434014	+	0.634506i	0.0434014	+	0.634506i
$97$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$97$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$98$	−0.696902	+	0.919004i	−0.696902	+	0.919004i
$99$		0			0
$100$		0			0
$101$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$101$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$102$	0.863515	−	1.31654i	0.863515	−	1.31654i
$103$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$103$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$104$		0			0
$105$		0			0
$106$	1.95255	+	0.268372i	1.95255	+	0.268372i
$107$	0.514311	+	0.163235i	0.514311	+	0.163235i	0.548452	−	0.836182i	$-0.315217\pi$
$107$	0.514311	+	0.163235i	0.514311	+	0.163235i	−0.0341411	+	0.999417i	$0.510870\pi$
$108$	−0.328509	+	0.0337718i	−0.328509	+	0.0337718i
$109$	0.655751	+	1.84511i	0.655751	+	1.84511i	0.519584	+	0.854419i	$0.326087\pi$
$109$	0.655751	+	1.84511i	0.655751	+	1.84511i	0.136167	+	0.990686i	$0.456522\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.24382	+	0.214457i	−1.24382	+	0.214457i	−0.753713	−	0.657204i	$-0.771739\pi$
$113$	−1.24382	+	0.214457i	−1.24382	+	0.214457i	−0.490110	+	0.871660i	$0.663043\pi$
$114$	0.214389	+	0.229554i	0.214389	+	0.229554i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.682553	−	0.730836i	−0.682553	−	0.730836i
$122$	−1.04581	+	0.180316i	−1.04581	+	0.180316i
$123$		0			0
$124$	−0.241352	+	0.104834i	−0.241352	+	0.104834i
$125$		0			0
$126$		0			0
$127$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$127$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$128$	−1.14228	−	0.362544i	−1.14228	−	0.362544i
$129$		0			0
$130$		0			0
$131$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$131$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.608115	+	0.861502i	0.608115	+	0.861502i
$137$	1.18320	−	1.56028i	1.18320	−	1.56028i	0.429483	−	0.903075i	$-0.358696\pi$
$137$	1.18320	−	1.56028i	1.18320	−	1.56028i	0.753713	−	0.657204i	$-0.228261\pi$
$138$	1.12791	+	2.00599i	1.12791	+	2.00599i
$139$	0.128604	+	1.88013i	0.128604	+	1.88013i	0.398401	+	0.917211i	$0.369565\pi$
$139$	0.128604	+	1.88013i	0.128604	+	1.88013i	−0.269797	+	0.962917i	$0.586957\pi$
$140$		0			0
$141$	0.576680	+	0.816970i	0.576680	+	0.816970i
$142$		0			0
$143$		0			0
$144$	0.329471	−	1.17590i	0.329471	−	1.17590i
$145$		0			0
$146$		0			0
$147$	0.836182	−	0.548452i	0.836182	−	0.548452i
$148$		0			0
$149$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$149$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$150$		0			0
$151$	−1.12067	−	1.37749i	−1.12067	−	1.37749i	−0.917211	−	0.398401i	$-0.869565\pi$
$151$	−1.12067	−	1.37749i	−1.12067	−	1.37749i	−0.203456	−	0.979084i	$-0.565217\pi$
$152$	−0.195703	+	0.0771753i	−0.195703	+	0.0771753i
$153$	−1.08772	+	0.824847i	−1.08772	+	0.824847i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.871660	−	0.490110i	$-0.836957\pi$
$157$		0			0		0.871660	+	0.490110i	$0.163043\pi$
$158$	−0.776172	+	1.96824i	−0.776172	+	1.96824i
$159$	−1.51725	−	0.786177i	−1.51725	−	0.786177i
$160$		0			0
$161$		0			0
$162$	1.12057	+	0.273075i	1.12057	+	0.273075i
$163$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$163$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$164$		0			0
$165$		0			0
$166$	0.157164	−	0.442218i	0.157164	−	0.442218i
$167$	−0.246038	+	1.00962i	−0.246038	+	1.00962i	0.707107	+	0.707107i	$0.250000\pi$
$167$	−0.246038	+	1.00962i	−0.246038	+	1.00962i	−0.953145	+	0.302515i	$0.902174\pi$
$168$		0			0
$169$	−0.816970	−	0.576680i	−0.816970	−	0.576680i
$170$		0			0
$171$	−0.108498	−	0.249787i	−0.108498	−	0.249787i
$172$		0			0
$173$	1.40105	+	0.666310i	1.40105	+	0.666310i	0.971567	−	0.236764i	$-0.0760870\pi$
$173$	1.40105	+	0.666310i	1.40105	+	0.666310i	0.429483	+	0.903075i	$0.358696\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$179$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$180$		0			0
$181$	−0.922444	−	0.861502i	−0.922444	−	0.861502i	0.0682424	−	0.997669i	$-0.478261\pi$
$181$	−0.922444	−	0.861502i	−0.922444	−	0.861502i	−0.990686	+	0.136167i	$0.956522\pi$
$182$		0			0
$183$	0.906751	+	0.156340i	0.906751	+	0.156340i
$184$	−1.52699	+	0.209880i	−1.52699	+	0.209880i
$185$		0			0
$186$	0.916858	−	0.0627148i	0.916858	−	0.0627148i
$187$		0			0
$188$	0.320851	−	0.0781893i	0.320851	−	0.0781893i
$189$		0			0
$190$		0			0
$191$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$191$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$192$	0.388568	+	0.294660i	0.388568	+	0.294660i
$193$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$193$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$194$		0			0
$195$		0			0
$196$	−0.0671895	−	0.323333i	−0.0671895	−	0.323333i
$197$	0.217854	+	0.893968i	0.217854	+	0.893968i	0.971567	+	0.236764i	$0.0760870\pi$
$197$	0.217854	+	0.893968i	0.217854	+	0.893968i	−0.753713	+	0.657204i	$0.771739\pi$
$198$		0			0
$199$	−0.953137	−	0.414006i	−0.953137	−	0.414006i	−0.136167	−	0.990686i	$-0.543478\pi$
$199$	−0.953137	−	0.414006i	−0.953137	−	0.414006i	−0.816970	+	0.576680i	$0.804348\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.121628	+	0.434096i	0.121628	+	0.434096i
$205$		0			0
$206$		0			0
$207$	−0.339029	−	1.96632i	−0.339029	−	1.96632i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.538336	+	0.0368232i	0.538336	+	0.0368232i	0.334880	−	0.942261i	$-0.391304\pi$
$211$	0.538336	+	0.0368232i	0.538336	+	0.0368232i	0.203456	+	0.979084i	$0.434783\pi$
$212$	−0.425342	+	0.370879i	−0.425342	+	0.370879i
$213$		0			0
$214$	−0.531744	+	0.323361i	−0.531744	+	0.323361i
$215$		0			0
$216$	−0.445471	+	0.631088i	−0.445471	+	0.631088i
$217$		0			0
$218$	−2.10101	−	0.828531i	−2.10101	−	0.828531i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$223$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$224$		0			0
$225$		0			0
$226$	0.756381	−	1.24382i	0.756381	−	1.24382i
$227$	1.48487	+	0.973925i	1.48487	+	0.973925i	0.994757	+	0.102264i	$0.0326087\pi$
$227$	1.48487	+	0.973925i	1.48487	+	0.973925i	0.490110	+	0.871660i	$0.336957\pi$
$228$	−0.0898831	+	0.00307050i	−0.0898831	+	0.00307050i
$229$	0.361291	−	1.73863i	0.361291	−	1.73863i	−0.269797	−	0.962917i	$-0.586957\pi$
$229$	0.361291	−	1.73863i	0.361291	−	1.73863i	0.631088	−	0.775711i	$-0.282609\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.682945	−	0.783234i	0.682945	−	0.783234i	−0.302515	−	0.953145i	$-0.597826\pi$
$233$	0.682945	−	0.783234i	0.682945	−	0.783234i	0.985460	+	0.169910i	$0.0543478\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.20559	−	1.38263i	1.20559	−	1.38263i
$238$		0			0
$239$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$239$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$240$		0			0
$241$	−0.347674	+	1.67310i	−0.347674	+	1.67310i	0.334880	+	0.942261i	$0.391304\pi$
$241$	−0.347674	+	1.67310i	−0.347674	+	1.67310i	−0.682553	+	0.730836i	$0.739130\pi$
$242$	1.15269	−	0.0393770i	1.15269	−	0.0393770i
$243$	−0.836182	−	0.548452i	−0.836182	−	0.548452i
$244$	0.157883	−	0.259628i	0.157883	−	0.259628i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.186200	+	0.586669i	−0.186200	+	0.586669i
$249$	−0.256797	+	0.315646i	−0.256797	+	0.315646i
$250$		0			0
$251$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$251$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.764337	−	0.464804i	0.764337	−	0.464804i
$257$	0.627764	+	1.32000i	0.627764	+	1.32000i	0.930278	+	0.366854i	$0.119565\pi$
$257$	0.627764	+	1.32000i	0.627764	+	1.32000i	−0.302515	+	0.953145i	$0.597826\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.0231902	+	0.134500i	0.0231902	+	0.134500i	0.994757	−	0.102264i	$-0.0326087\pi$
$263$	0.0231902	+	0.134500i	0.0231902	+	0.134500i	−0.971567	+	0.236764i	$0.923913\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$269$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$270$		0			0
$271$	−1.81734	−	0.789381i	−1.81734	−	0.789381i	−0.962917	−	0.269797i	$-0.913043\pi$
$271$	−1.81734	−	0.789381i	−1.81734	−	0.789381i	−0.854419	−	0.519584i	$-0.826087\pi$
$272$	−1.65830	−	0.170479i	−1.65830	−	0.170479i
$273$		0			0
$274$	0.459500	+	2.21124i	0.459500	+	2.21124i
$275$		0			0
$276$	−0.645159	−	0.134066i	−0.645159	−	0.134066i
$277$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$277$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$278$	−1.73188	−	1.31333i	−1.73188	−	1.31333i
$279$	−0.767255	−	0.214975i	−0.767255	−	0.214975i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	−1.14731	−	0.117947i	−1.14731	−	0.117947i
$283$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$283$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.348809	+	0.531803i	0.348809	+	0.531803i
$289$	0.631088	+	0.589395i	0.631088	+	0.589395i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.599418	+	1.52002i	0.599418	+	1.52002i	0.836182	+	0.548452i	$0.184783\pi$
$293$	0.599418	+	1.52002i	0.599418	+	1.52002i	−0.236764	+	0.971567i	$0.576087\pi$
$294$	−0.157049	+	1.14262i	−0.157049	+	1.14262i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	2.04691	+	0.0699245i	2.04691	+	0.0699245i
$303$		0			0
$304$	0.111370	−	0.313366i	0.111370	−	0.313366i
$305$		0			0
$306$	0.107445	−	1.57079i	0.107445	−	1.57079i
$307$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$307$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$311$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$312$		0			0
$313$		0			0		−0.871660	−	0.490110i	$-0.836957\pi$
$313$		0			0		0.871660	+	0.490110i	$0.163043\pi$
$314$		0			0
$315$		0			0
$316$	−0.278708	−	0.537882i	−0.278708	−	0.537882i
$317$	−0.429951	+	0.326042i	−0.429951	+	0.326042i	−0.796805	−	0.604236i	$-0.793478\pi$
$317$	−0.429951	+	0.326042i	−0.429951	+	0.326042i	0.366854	+	0.930278i	$0.380435\pi$
$318$	1.83349	−	0.723036i	1.83349	−	0.723036i
$319$		0			0
$320$		0			0
$321$	0.528307	−	0.109784i	0.528307	−	0.109784i
$322$		0			0
$323$	−0.310862	+	0.203895i	−0.310862	+	0.203895i
$324$	−0.269797	+	0.190443i	−0.269797	+	0.190443i
$325$		0			0
$326$		0			0
$327$	1.47590	+	1.28692i	1.47590	+	1.28692i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.0277687	+	0.405963i	0.0277687	+	0.405963i	0.990686	+	0.136167i	$0.0434783\pi$
$331$	0.0277687	+	0.405963i	0.0277687	+	0.405963i	−0.962917	+	0.269797i	$0.913043\pi$
$332$	0.0658605	+	0.117133i	0.0658605	+	0.117133i
$333$		0			0
$334$	−0.691172	−	0.979167i	−0.691172	−	0.979167i
$335$		0			0
$336$		0			0
$337$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$337$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$338$	1.12057	−	0.273075i	1.12057	−	0.273075i
$339$	−0.979084	+	0.796544i	−0.979084	+	0.796544i
$340$		0			0
$341$		0			0
$342$	0.299381	+	0.0950194i	0.299381	+	0.0950194i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.64121	+	0.712879i	−1.64121	+	0.712879i
$347$	−1.47873	+	0.469328i	−1.47873	+	0.469328i	−0.930278	−	0.366854i	$-0.880435\pi$
$347$	−1.47873	+	0.469328i	−1.47873	+	0.469328i	−0.548452	+	0.836182i	$0.684783\pi$
$348$		0			0
$349$	−1.28629	−	1.37728i	−1.28629	−	1.37728i	−0.887885	−	0.460065i	$-0.847826\pi$
$349$	−1.28629	−	1.37728i	−1.28629	−	1.37728i	−0.398401	−	0.917211i	$-0.630435\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.30216	+	1.49339i	1.30216	+	1.49339i	0.753713	+	0.657204i	$0.228261\pi$
$353$	1.30216	+	1.49339i	1.30216	+	1.49339i	0.548452	+	0.836182i	$0.315217\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$359$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$360$		0			0
$361$	0.310043	+	0.872378i	0.310043	+	0.872378i
$362$	1.44811	−	0.148870i	1.44811	−	0.148870i
$363$	−0.953145	−	0.302515i	−0.953145	−	0.302515i
$364$		0			0
$365$		0			0
$366$	−0.823217	+	0.669737i	−0.823217	+	0.669737i
$367$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$367$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$368$	1.33640	−	2.03750i	1.33640	−	2.03750i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.158997	+	0.209669i	−0.158997	+	0.209669i
$373$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$373$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$374$		0			0
$375$		0			0
$376$	0.355388	−	0.685868i	0.355388	−	0.685868i
$377$		0			0
$378$		0			0
$379$	−0.519584	+	1.85442i	−0.519584	+	1.85442i			1.00000i	$0.5\pi$
$379$	−0.519584	+	1.85442i	−0.519584	+	1.85442i	−0.519584	+	0.854419i	$0.673913\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.0529673	+	1.55052i	0.0529673	+	1.55052i	0.657204	+	0.753713i	$0.271739\pi$
$383$	0.0529673	+	1.55052i	0.0529673	+	1.55052i	−0.604236	+	0.796805i	$0.706522\pi$
$384$	−1.17337	+	0.243829i	−1.17337	+	0.243829i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$389$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$390$		0			0
$391$	−2.56658	+	0.912161i	−2.56658	+	0.912161i
$392$	−0.673335	−	0.378597i	−0.673335	−	0.378597i
$393$		0			0
$394$	−0.942261	−	0.488240i	−0.942261	−	0.488240i
$395$		0			0
$396$		0			0
$397$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$397$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$398$	1.08237	−	0.514751i	1.08237	−	0.514751i
$399$		0			0
$400$		0			0
$401$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$401$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.952300	+	0.452894i	0.952300	+	0.452894i
$409$	1.46184	+	1.18930i	1.46184	+	1.18930i	0.942261	+	0.334880i	$0.108696\pi$
$409$	1.46184	+	1.18930i	1.46184	+	1.18930i	0.519584	+	0.854419i	$0.326087\pi$
$410$		0			0
$411$	0.266637	−	1.93993i	0.266637	−	1.93993i
$412$		0			0
$413$		0			0
$414$	1.96631	+	1.19574i	1.96631	+	1.19574i
$415$		0			0
$416$		0			0
$417$	1.03357	+	1.57580i	1.03357	+	1.57580i
$418$		0			0
$419$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$419$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$420$		0			0
$421$	0.538336	−	0.0368232i	0.538336	−	0.0368232i	0.203456	−	0.979084i	$-0.434783\pi$
$421$	0.538336	−	0.0368232i	0.538336	−	0.0368232i	0.334880	+	0.942261i	$0.391304\pi$
$422$	−0.440065	+	0.440065i	−0.440065	+	0.440065i
$423$	0.903075	+	0.429483i	0.903075	+	0.429483i
$424$			1.32003i			1.32003i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.0302773	−	0.175605i	0.0302773	−	0.175605i
$429$		0			0
$430$		0			0
$431$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$431$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$432$	−0.289132	−	1.18646i	−0.289132	−	1.18646i
$433$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$433$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$434$		0			0
$435$		0			0
$436$	0.574166	−	0.297509i	0.574166	−	0.297509i
$437$	−0.0555700	−	0.540548i	−0.0555700	−	0.540548i
$438$		0			0
$439$	−0.109784	−	0.391823i	−0.109784	−	0.391823i	0.887885	−	0.460065i	$-0.152174\pi$
$439$	−0.109784	−	0.391823i	−0.109784	−	0.391823i	−0.997669	+	0.0682424i	$0.978261\pi$
$440$		0			0
$441$	0.460065	−	0.887885i	0.460065	−	0.887885i
$442$		0			0
$443$	0.0668540	−	1.95703i	0.0668540	−	1.95703i	−0.169910	−	0.985460i	$-0.554348\pi$
$443$	0.0668540	−	1.95703i	0.0668540	−	1.95703i	0.236764	−	0.971567i	$-0.423913\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$449$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$450$		0			0
$451$		0			0
$452$	0.126095	+	0.397292i	0.126095	+	0.397292i
$453$	−1.65196	−	0.651449i	−1.65196	−	0.651449i
$454$	−1.97215	+	0.552572i	−1.97215	+	0.552572i
$455$		0			0
$456$	−0.132762	+	0.163187i	−0.132762	+	0.163187i
$457$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$457$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$458$	1.23754	+	1.63194i	1.23754	+	1.63194i
$459$	−0.543860	+	1.25209i	−0.543860	+	1.25209i
$460$		0			0
$461$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$461$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$462$		0			0
$463$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$463$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$464$		0			0
$465$		0			0
$466$	0.163201	+	1.18737i	0.163201	+	1.18737i
$467$	−1.64266	+	0.923623i	−1.64266	+	0.923623i	−0.657204	+	0.753713i	$0.728261\pi$
$467$	−1.64266	+	0.923623i	−1.64266	+	0.923623i	−0.985460	+	0.169910i	$0.945652\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.288095	+	2.09604i	0.288095	+	2.09604i
$475$		0			0
$476$		0			0
$477$	−1.70784	+	0.0583417i	−1.70784	+	0.0583417i
$478$		0			0
$479$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$479$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$480$		0			0
$481$		0			0
$482$	−1.19089	−	1.57043i	−1.19089	−	1.57043i
$483$		0			0
$484$	−0.208411	+	0.256171i	−0.208411	+	0.256171i
$485$		0			0
$486$	1.11059	−	0.311173i	1.11059	−	0.311173i
$487$		0			0		−0.930278	−	0.366854i	$-0.880435\pi$
$487$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$488$	−0.215020	−	0.677473i	−0.215020	−	0.677473i
$489$		0			0
$490$		0			0
$491$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$491$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.505576	−	0.831385i	−0.505576	−	0.831385i
$497$		0			0
$498$	−0.0797417	−	0.462492i	−0.0797417	−	0.462492i
$499$	−0.917985	+	1.77163i	−0.917985	+	1.77163i	−0.398401	+	0.917211i	$0.630435\pi$
$499$	−0.917985	+	1.77163i	−0.917985	+	1.77163i	−0.519584	+	0.854419i	$0.673913\pi$
$500$		0			0
$501$	0.280364	+	1.00063i	0.280364	+	1.00063i
$502$		0			0
$503$	−0.167093	−	1.62537i	−0.167093	−	1.62537i	−0.657204	−	0.753713i	$-0.728261\pi$
$503$	−0.167093	−	1.62537i	−0.167093	−	1.62537i	0.490110	−	0.871660i	$-0.336957\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.994757	−	0.102264i	−0.994757	−	0.102264i
$508$		0			0
$509$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$509$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$510$		0			0
$511$		0			0
$512$	0.0283194	−	0.164249i	0.0283194	−	0.164249i
$513$	−0.216997	−	0.164554i	−0.216997	−	0.164554i
$514$	−1.62332	−	0.454833i	−1.62332	−	0.454833i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.54781	−	0.105873i	1.54781	−	0.105873i
$520$		0			0
$521$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$521$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$522$		0			0
$523$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$523$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$524$		0			0
$525$		0			0
$526$	−0.134499	−	0.0817909i	−0.134499	−	0.0817909i
$527$	−0.111235	+	1.08202i	−0.111235	+	1.08202i
$528$		0			0
$529$	0.405963	−	2.95360i	0.405963	−	2.95360i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.125185	−	1.83015i	0.125185	−	1.83015i	−0.334880	−	0.942261i	$-0.608696\pi$
$541$	0.125185	−	1.83015i	0.125185	−	1.83015i	0.460065	−	0.887885i	$-0.347826\pi$
$542$	2.06374	−	0.981471i	2.06374	−	0.981471i
$543$	−1.22629	−	0.298838i	−1.22629	−	0.298838i
$544$	0.634506	−	0.592588i	0.634506	−	0.592588i
$545$		0			0
$546$		0			0
$547$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$547$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$548$	−0.563674	−	0.316938i	−0.563674	−	0.316938i
$549$	0.867003	−	0.308133i	0.867003	−	0.308133i
$550$		0			0
$551$		0			0
$552$	−1.22815	+	0.931337i	−1.22815	+	0.931337i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.609329	−	0.126620i	0.609329	−	0.126620i
$557$	−0.0499031	−	1.46082i	−0.0499031	−	1.46082i	−0.707107	−	0.707107i	$-0.750000\pi$
$557$	−0.0499031	−	1.46082i	−0.0499031	−	1.46082i	0.657204	−	0.753713i	$-0.271739\pi$
$558$	0.768452	−	0.504027i	0.768452	−	0.504027i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.03356	+	1.03356i	1.03356	+	1.03356i	0.999417	+	0.0341411i	$0.0108696\pi$
$563$	1.03356	+	1.03356i	1.03356	+	1.03356i	0.0341411	+	0.999417i	$0.489130\pi$
$564$	0.241352	−	0.225407i	0.241352	−	0.225407i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$569$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$570$		0			0
$571$	−1.35239	+	1.44806i	−1.35239	+	1.44806i	−0.576680	+	0.816970i	$0.695652\pi$
$571$	−1.35239	+	1.44806i	−1.35239	+	1.44806i	−0.775711	+	0.631088i	$0.782609\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.483115	+	0.0664026i	0.483115	+	0.0664026i
$577$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$577$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$578$	−0.990723	+	0.101849i	−0.990723	+	0.101849i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.77571	−	0.631088i	−1.77571	−	0.631088i
$587$	−0.178978	−	0.205261i	−0.178978	−	0.205261i	0.657204	−	0.753713i	$-0.271739\pi$
$587$	−0.178978	−	0.205261i	−0.178978	−	0.205261i	−0.836182	+	0.548452i	$0.815217\pi$
$588$	−0.217035	−	0.248907i	−0.217035	−	0.248907i
$589$	−0.204467	−	0.0726675i	−0.204467	−	0.0726675i
$590$		0			0
$591$	0.628038	+	0.672464i	0.628038	+	0.672464i
$592$		0			0
$593$	−1.55738	+	0.494291i	−1.55738	+	0.494291i	−0.953145	−	0.302515i	$-0.902174\pi$
$593$	−1.55738	+	0.494291i	−1.55738	+	0.494291i	−0.604236	+	0.796805i	$0.706522\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.03372	+	0.106270i	−1.03372	+	0.106270i
$598$		0			0
$599$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$599$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$600$		0			0
$601$	−1.20346	+	0.979084i	−1.20346	+	0.979084i	−0.203456	+	0.979084i	$0.565217\pi$
$601$	−1.20346	+	0.979084i	−1.20346	+	0.979084i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	−0.400271	+	0.428585i	−0.400271	+	0.428585i
$605$		0			0
$606$		0			0
$607$		0			0		0.604236	−	0.796805i	$-0.293478\pi$
$607$		0			0		−0.604236	+	0.796805i	$0.706522\pi$
$608$	0.0848876	+	0.150972i	0.0848876	+	0.150972i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.318773	+	0.318773i	0.318773	+	0.318773i
$613$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$613$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.53391	+	1.00609i	−1.53391	+	1.00609i	−0.548452	+	0.836182i	$0.684783\pi$
$617$	−1.53391	+	1.00609i	−1.53391	+	1.00609i	−0.985460	+	0.169910i	$0.945652\pi$
$618$		0			0
$619$	−0.900885	+	0.187206i	−0.900885	+	0.187206i	−0.631088	−	0.775711i	$-0.717391\pi$
$619$	−0.900885	+	0.187206i	−0.900885	+	0.187206i	−0.269797	+	0.962917i	$0.586957\pi$
$620$		0			0
$621$	−1.25923	−	1.54781i	−1.25923	−	1.54781i
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.45826	−	1.36192i	1.45826	−	1.36192i	0.682553	−	0.730836i	$-0.260870\pi$
$631$	1.45826	−	1.36192i	1.45826	−	1.36192i	0.775711	−	0.631088i	$-0.217391\pi$
$632$	−1.37675	−	0.335506i	−1.37675	−	0.335506i
$633$	0.487293	−	0.231746i	0.487293	−	0.231746i
$634$	0.0424704	−	0.620895i	0.0424704	−	0.620895i
$635$		0			0
$636$	−0.188982	+	0.531744i	−0.188982	+	0.531744i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$641$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$642$	−0.305018	+	0.542474i	−0.305018	+	0.542474i
$643$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$643$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$644$		0			0
$645$		0			0
$646$	0.0583852	−	0.424784i	0.0583852	−	0.424784i
$647$	0.626895	+	1.58970i	0.626895	+	1.58970i	0.796805	+	0.604236i	$0.206522\pi$
$647$	0.626895	+	1.58970i	0.626895	+	1.58970i	−0.169910	+	0.985460i	$0.554348\pi$
$648$	−0.0789964	+	0.768424i	−0.0789964	+	0.768424i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.95256	+	0.336656i	1.95256	+	0.336656i	0.999417	+	0.0341411i	$0.0108696\pi$
$653$	1.95256	+	0.336656i	1.95256	+	0.336656i	0.953145	+	0.302515i	$0.0978261\pi$
$654$	−2.23744	+	0.307529i	−2.23744	+	0.307529i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−1.31448	−	0.368301i	−1.31448	−	0.368301i	−0.460065	−	0.887885i	$-0.652174\pi$
$661$	−1.31448	−	0.368301i	−1.31448	−	0.368301i	−0.854419	+	0.519584i	$0.826087\pi$
$662$	−0.373954	−	0.283578i	−0.373954	−	0.283578i
$663$		0			0
$664$	0.307754	+	0.0639521i	0.307754	+	0.0639521i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.341376	+	0.0350946i	0.341376	+	0.0350946i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$673$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$674$		0			0
$675$		0			0
$676$	−0.151932	+	0.293216i	−0.151932	+	0.293216i
$677$	−0.320200	−	1.85712i	−0.320200	−	1.85712i	−0.490110	−	0.871660i	$-0.663043\pi$
$677$	−0.320200	−	1.85712i	−0.320200	−	1.85712i	0.169910	−	0.985460i	$-0.445652\pi$
$678$	0.0497007	−	1.45490i	0.0497007	−	1.45490i
$679$		0			0
$680$		0			0
$681$	1.77163	+	0.121183i	1.77163	+	0.121183i
$682$		0			0
$683$	0.0586180	+	0.123256i	0.0586180	+	0.123256i	0.930278	−	0.366854i	$-0.119565\pi$
$683$	0.0586180	+	0.123256i	0.0586180	+	0.123256i	−0.871660	+	0.490110i	$0.836957\pi$
$684$	−0.0768427	+	0.0467291i	−0.0768427	+	0.0467291i
$685$		0			0
$686$		0			0
$687$	−0.537196	−	1.69257i	−0.537196	−	1.69257i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.922444	−	1.13384i	0.922444	−	1.13384i	−0.0682424	−	0.997669i	$-0.521739\pi$
$691$	0.922444	−	1.13384i	0.922444	−	1.13384i	0.990686	−	0.136167i	$-0.0434783\pi$
$692$	0.154991	−	0.488337i	0.154991	−	0.488337i
$693$		0			0
$694$	0.712879	−	1.64121i	0.712879	−	1.64121i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	2.17227	−	0.0742068i	2.17227	−	0.0742068i
$699$	0.211425	−	1.01743i	0.211425	−	1.01743i
$700$		0			0
$701$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$701$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−2.28524			−2.28524
$707$		0			0
$708$		0			0
$709$	0.0185847	+	0.135214i	0.0185847	+	0.135214i	0.997669	−	0.0682424i	$-0.0217391\pi$
$709$	0.0185847	+	0.135214i	0.0185847	+	0.135214i	−0.979084	+	0.203456i	$0.934783\pi$
$710$		0			0
$711$	0.373224	−	1.79605i	0.373224	−	1.79605i
$712$		0			0
$713$	−1.32944	−	0.871978i	−1.32944	−	0.871978i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$719$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$720$		0			0
$721$		0			0
$722$	−0.993371	−	0.391735i	−0.993371	−	0.391735i
$723$	0.516949	+	1.62877i	0.516949	+	1.62877i
$724$	−0.240373	+	0.340531i	−0.240373	+	0.340531i
$725$		0			0
$726$	0.985454	−	0.599268i	0.985454	−	0.599268i
$727$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$727$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$728$		0			0
$729$	−0.997669	−	0.0682424i	−0.997669	−	0.0682424i
$730$		0			0
$731$		0			0
$732$	0.0103743	−	0.303687i	0.0103743	−	0.303687i
$733$		0			0		−0.169910	−	0.985460i	$-0.554348\pi$
$733$		0			0		0.169910	+	0.985460i	$0.445652\pi$
$734$		0			0
$735$		0			0
$736$	0.342376	+	1.22195i	0.342376	+	1.22195i
$737$		0			0
$738$		0			0
$739$	−1.37749	+	0.713755i	−1.37749	+	0.713755i	−0.979084	−	0.203456i	$-0.934783\pi$
$739$	−1.37749	+	0.713755i	−1.37749	+	0.713755i	−0.398401	+	0.917211i	$0.630435\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.0644788	−	0.264590i	−0.0644788	−	0.264590i	0.930278	−	0.366854i	$-0.119565\pi$
$743$	−0.0644788	−	0.264590i	−0.0644788	−	0.264590i	−0.994757	+	0.102264i	$0.967391\pi$
$744$	0.125229	+	0.602635i	0.125229	+	0.602635i
$745$		0			0
$746$		0			0
$747$	−0.0691386	+	0.400995i	−0.0691386	+	0.400995i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		−	0.539594i		−	0.539594i	−0.962917	−	0.269797i	$-0.913043\pi$
$751$		−	0.539594i		−	0.539594i	0.962917	−	0.269797i	$-0.0869565\pi$
$752$	0.447996	+	1.13604i	0.447996	+	1.13604i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$757$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$758$	−1.21821	−	1.85731i	−1.21821	−	1.85731i
$759$		0			0
$760$		0			0
$761$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$761$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−1.38802	−	1.12924i	−1.38802	−	1.12924i
$767$		0			0
$768$	0.438437	−	0.779760i	0.438437	−	0.779760i
$769$	−0.543860	−	1.25209i	−0.543860	−	1.25209i	−0.942261	−	0.334880i	$-0.891304\pi$
$769$	−0.543860	−	1.25209i	−0.543860	−	1.25209i	0.398401	−	0.917211i	$-0.369565\pi$
$770$		0			0
$771$	1.19414	+	0.842917i	1.19414	+	0.842917i
$772$		0			0
$773$	0.158575	−	0.650716i	0.158575	−	0.650716i	−0.836182	−	0.548452i	$-0.815217\pi$
$773$	0.158575	−	0.650716i	0.158575	−	0.650716i	0.994757	−	0.102264i	$-0.0326087\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	1.15250	−	2.92254i	1.15250	−	2.92254i
$783$		0			0
$784$	1.15067	−	0.408949i	1.15067	−	0.408949i
$785$		0			0
$786$		0			0
$787$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$787$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$788$	0.282679	−	0.111474i	0.282679	−	0.111474i
$789$	0.0861339	+	0.105873i	0.0861339	+	0.105873i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.0925877	+	0.330450i	−0.0925877	+	0.330450i
$797$	−1.42039	−	1.23851i	−1.42039	−	1.23851i	−0.930278	−	0.366854i	$-0.880435\pi$
$797$	−1.42039	−	1.23851i	−1.42039	−	1.23851i	−0.490110	−	0.871660i	$-0.663043\pi$
$798$		0			0
$799$	0.368301	−	1.31448i	0.368301	−	1.31448i
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$809$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$810$		0			0
$811$	1.53697	+	0.211252i	1.53697	+	0.211252i	0.854419	−	0.519584i	$-0.173913\pi$
$811$	1.53697	+	0.211252i	1.53697	+	0.211252i	0.682553	+	0.730836i	$0.260870\pi$
$812$		0			0
$813$	−1.97098	+	0.202623i	−1.97098	+	0.202623i
$814$		0			0
$815$		0			0
$816$	−1.52903	+	0.664152i	−1.52903	+	0.664152i
$817$		0			0
$818$	−2.14193	+	0.369306i	−2.14193	+	0.369306i
$819$		0			0
$820$		0			0
$821$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$821$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$822$	1.48428	+	1.70224i	1.48428	+	1.70224i
$823$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$823$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.660021	+	0.113799i	−0.660021	+	0.113799i	−0.490110	−	0.871660i	$-0.663043\pi$
$827$	−0.660021	+	0.113799i	−0.660021	+	0.113799i	−0.169910	+	0.985460i	$0.554348\pi$
$828$	−0.628067	+	0.199339i	−0.628067	+	0.199339i
$829$	1.49867	−	0.650963i	1.49867	−	0.650963i	0.519584	−	0.854419i	$-0.326087\pi$
$829$	1.49867	−	0.650963i	1.49867	−	0.650963i	0.979084	+	0.203456i	$0.0652174\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.30114	−	0.412965i	−1.30114	−	0.412965i
$834$	−2.15329	−	0.295963i	−2.15329	−	0.295963i
$835$		0			0
$836$		0			0
$837$	−0.774147	+	0.188654i	−0.774147	+	0.188654i
$838$		0			0
$839$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$839$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$840$		0			0
$841$	−0.576680	−	0.816970i	−0.576680	−	0.816970i
$842$	−0.376044	+	0.495888i	−0.376044	+	0.495888i
$843$		0			0
$844$	−0.0121605	−	0.177780i	−0.0121605	−	0.177780i
$845$		0			0
$846$	−1.05788	+	0.459500i	−1.05788	+	0.459500i
$847$		0			0
$848$	−1.57285	−	1.37145i	−1.57285	−	1.37145i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$853$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$854$		0			0
$855$		0			0
$856$	−0.263051	−	0.323333i	−0.263051	−	0.323333i
$857$	0.501972	−	0.197952i	0.501972	−	0.197952i	−0.102264	−	0.994757i	$-0.532609\pi$
$857$	0.501972	−	0.197952i	0.501972	−	0.197952i	0.604236	+	0.796805i	$0.293478\pi$
$858$		0			0
$859$	0.751719	+	1.45075i	0.751719	+	1.45075i	0.887885	+	0.460065i	$0.152174\pi$
$859$	0.751719	+	1.45075i	0.751719	+	1.45075i	−0.136167	+	0.990686i	$0.543478\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.672966	+	1.70652i	−0.672966	+	1.70652i	0.0341411	+	0.999417i	$0.489130\pi$
$863$	−0.672966	+	1.70652i	−0.672966	+	1.70652i	−0.707107	+	0.707107i	$0.750000\pi$
$864$	0.564685	+	0.292596i	0.564685	+	0.292596i
$865$		0			0
$866$		0			0
$867$	0.838963	+	0.204450i	0.838963	+	0.204450i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.358138	−	1.46963i	0.358138	−	1.46963i
$873$		0			0
$874$	0.512022	+	0.361424i	0.512022	+	0.361424i
$875$		0			0
$876$		0			0
$877$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$877$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$878$	0.423828	+	0.201564i	0.423828	+	0.201564i
$879$	1.26747	+	1.03116i	1.26747	+	1.03116i
$880$		0			0
$881$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$881$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$882$	0.423115	+	1.07295i	0.423115	+	1.07295i
$883$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$883$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$884$		0			0
$885$		0			0
$886$	1.65057	+	1.54153i	1.65057	+	1.54153i
$887$	0.149362	+	0.227720i	0.149362	+	0.227720i	0.903075	−	0.429483i	$-0.141304\pi$
$887$	0.149362	+	0.227720i	0.149362	+	0.227720i	−0.753713	+	0.657204i	$0.771739\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.237382	+	0.133473i	0.237382	+	0.133473i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.474611	+	2.28396i	0.474611	+	2.28396i
$902$		0			0
$903$		0			0
$904$	0.894279	+	0.388440i	0.894279	+	0.388440i
$905$		0			0
$906$	1.81848	−	0.942261i	1.81848	−	0.942261i
$907$		0			0		−0.102264	−	0.994757i	$-0.532609\pi$
$907$		0			0		0.102264	+	0.994757i	$0.467391\pi$
$908$	0.251863	−	0.529592i	0.251863	−	0.529592i
$909$		0			0
$910$		0			0
$911$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$911$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$912$	−0.0565068	−	0.327733i	−0.0565068	−	0.327733i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.585065	−	0.0400195i	−0.585065	−	0.0400195i
$917$		0			0
$918$	−0.676204	−	1.42185i	−0.676204	−	1.42185i
$919$	−1.70486	+	1.03675i	−1.70486	+	1.03675i	−0.816970	+	0.576680i	$0.804348\pi$
$919$	−1.70486	+	1.03675i	−1.70486	+	1.03675i	−0.887885	+	0.460065i	$0.847826\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$929$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$930$		0			0
$931$	0.141500	−	0.232687i	0.141500	−	0.232687i
$932$	−0.286957	−	0.188215i	−0.286957	−	0.188215i
$933$		0			0
$934$	0.442218	−	2.12807i	0.442218	−	2.12807i
$935$		0			0
$936$		0			0
$937$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$937$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.669369	−	0.0228663i	0.669369	−	0.0228663i	0.302515	−	0.953145i	$-0.402174\pi$
$947$	0.669369	−	0.0228663i	0.669369	−	0.0228663i	0.366854	+	0.930278i	$0.380435\pi$
$948$	−0.506560	−	0.332253i	−0.506560	−	0.332253i
$949$		0			0
$950$		0			0
$951$	−0.214975	+	0.494921i	−0.214975	+	0.494921i
$952$		0			0
$953$	−0.494291	+	1.55738i	−0.494291	+	1.55738i	0.302515	+	0.953145i	$0.402174\pi$
$953$	−0.494291	+	1.55738i	−0.494291	+	1.55738i	−0.796805	+	0.604236i	$0.793478\pi$
$954$	1.24382	−	1.52886i	1.24382	−	1.52886i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.311954	−	0.189703i	0.311954	−	0.189703i
$962$		0			0
$963$	0.406699	−	0.354623i	0.406699	−	0.354623i
$964$	0.563013	+	0.0385111i	0.563013	+	0.0385111i
$965$		0			0
$966$		0			0
$967$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$967$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$968$	0.131251	+	0.761242i	0.131251	+	0.761242i
$969$	−0.171036	+	0.330084i	−0.171036	+	0.330084i
$970$		0			0
$971$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$971$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$972$	−0.141833	+	0.298232i	−0.141833	+	0.298232i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.03062	+	0.447662i	1.03062	+	0.447662i
$977$	1.54329	+	0.158655i	1.54329	+	0.158655i	0.836182	−	0.548452i	$-0.184783\pi$
$977$	1.54329	+	0.158655i	1.54329	+	0.158655i	0.707107	+	0.707107i	$0.250000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.91721	+	0.398401i	1.91721	+	0.398401i
$982$		0			0
$983$	1.41494	+	1.07299i	1.41494	+	1.07299i	0.985460	+	0.169910i	$0.0543478\pi$
$983$	1.41494	+	1.07299i	1.41494	+	1.07299i	0.429483	+	0.903075i	$0.358696\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.90790	+	0.262234i	−1.90790	+	0.262234i	−0.990686	−	0.136167i	$-0.956522\pi$
$991$	−1.90790	+	0.262234i	−1.90790	+	0.262234i	−0.917211	+	0.398401i	$0.869565\pi$
$992$	0.499389	+	0.0861034i	0.499389	+	0.0861034i
$993$	0.223172	+	0.340253i	0.223172	+	0.340253i
$994$		0			0
$995$		0			0
$996$	0.114816	+	0.0698211i	0.114816	+	0.0698211i
$997$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$997$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$998$	−0.844258	−	2.14089i	−0.844258	−	2.14089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.443.1	✓	88
3.2	odd	2	inner	3525.1.bg.a.443.2	yes	88
5.2	odd	4	inner	3525.1.bg.a.1007.1	yes	88
5.3	odd	4	inner	3525.1.bg.a.1007.2	yes	88
5.4	even	2	inner	3525.1.bg.a.443.2	yes	88
15.2	even	4	inner	3525.1.bg.a.1007.2	yes	88
15.8	even	4	inner	3525.1.bg.a.1007.1	yes	88
15.14	odd	2	CM	3525.1.bg.a.443.1	✓	88
47.40	odd	46	inner	3525.1.bg.a.3518.2	yes	88
141.134	even	46	inner	3525.1.bg.a.3518.1	yes	88
235.87	even	92	inner	3525.1.bg.a.557.2	yes	88
235.134	odd	46	inner	3525.1.bg.a.3518.1	yes	88
235.228	even	92	inner	3525.1.bg.a.557.1	yes	88
705.134	even	46	inner	3525.1.bg.a.3518.2	yes	88
705.557	odd	92	inner	3525.1.bg.a.557.1	yes	88
705.698	odd	92	inner	3525.1.bg.a.557.2	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.443.1	✓	88	1.1	even	1	trivial
3525.1.bg.a.443.1	✓	88	15.14	odd	2	CM
3525.1.bg.a.443.2	yes	88	3.2	odd	2	inner
3525.1.bg.a.443.2	yes	88	5.4	even	2	inner
3525.1.bg.a.557.1	yes	88	235.228	even	92	inner
3525.1.bg.a.557.1	yes	88	705.557	odd	92	inner
3525.1.bg.a.557.2	yes	88	235.87	even	92	inner
3525.1.bg.a.557.2	yes	88	705.698	odd	92	inner
3525.1.bg.a.1007.1	yes	88	5.2	odd	4	inner
3525.1.bg.a.1007.1	yes	88	15.8	even	4	inner
3525.1.bg.a.1007.2	yes	88	5.3	odd	4	inner
3525.1.bg.a.1007.2	yes	88	15.2	even	4	inner
3525.1.bg.a.3518.1	yes	88	141.134	even	46	inner
3525.1.bg.a.3518.1	yes	88	235.134	odd	46	inner
3525.1.bg.a.3518.2	yes	88	47.40	odd	46	inner
3525.1.bg.a.3518.2	yes	88	705.134	even	46	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3525.bg (of order \(92\), degree \(44\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.757993 + 0.869303i) q^{2} +(0.871660 - 0.490110i) q^{3} +(-0.0449678 - 0.327165i) q^{4} +(-0.234658 + 1.12924i) q^{6} +(-0.645929 - 0.423665i) q^{8} +(0.519584 - 0.854419i) q^{9} +O(q^{10})\)	\(q+(-0.757993 + 0.869303i) q^{2} +(0.871660 - 0.490110i) q^{3} +(-0.0449678 - 0.327165i) q^{4} +(-0.234658 + 1.12924i) q^{6} +(-0.645929 - 0.423665i) q^{8} +(0.519584 - 0.854419i) q^{9} +(-0.199543 - 0.263138i) q^{12} +(1.17590 - 0.329471i) q^{16} +(-1.26993 - 0.500795i) q^{17} +(0.348908 + 1.09932i) q^{18} +(0.157049 - 0.222488i) q^{19} +(1.50391 - 1.31134i) q^{23} +(-0.770673 - 0.0527155i) q^{24} +(0.0341411 - 0.999417i) q^{27} +(-0.214975 - 0.767255i) q^{31} +(-0.273147 + 0.574346i) q^{32} +(1.39794 - 0.724354i) q^{34} +(-0.302901 - 0.131568i) q^{36} +(0.0743674 + 0.305168i) q^{38} +2.30134i q^{46} +(0.102264 + 0.994757i) q^{47} +(0.863506 - 0.863506i) q^{48} +(0.997669 - 0.0682424i) q^{49} +(-1.35239 + 0.185882i) q^{51} +(-0.937216 - 1.42890i) q^{53} +(0.842917 + 0.787230i) q^{54} +(0.0278499 - 0.270906i) q^{57} +(0.713755 + 0.580683i) q^{61} +(0.829926 + 0.394695i) q^{62} +(0.194283 + 0.447285i) q^{64} +(-0.106737 + 0.437996i) q^{68} +(0.668198 - 1.88013i) q^{69} +(-0.697602 + 0.331765i) q^{72} +(-0.0798525 - 0.0413762i) q^{76} +(1.72850 - 0.614311i) q^{79} +(-0.460065 - 0.887885i) q^{81} +(-0.378541 + 0.149277i) q^{83} +(-0.496653 - 0.433059i) q^{92} +(-0.563424 - 0.563424i) q^{93} +(-0.942261 - 0.665120i) q^{94} +(0.0434014 + 0.634506i) q^{96} +(-0.696902 + 0.919004i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 88 * q - 8 * q^6	\( 88 q - 8 q^{6} + 20 q^{16} - 12 q^{36} - 8 q^{51} + 8 q^{61} - 92 q^{76} + 4 q^{81} - 68 q^{96}+O(q^{100}) \) 88 * q - 8 * q^6 + 20 * q^16 - 12 * q^36 - 8 * q^51 + 8 * q^61 - 92 * q^76 + 4 * q^81 - 68 * q^96

Introduction

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