LMFDB - Embedded newform 3525.1.bg.a.1007.2

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			1007.2
Root			$0.753713 + 0.657204i$ of defining polynomial
Character	$\chi$	$=$	3525.1007
Dual form			3525.1.bg.a.3518.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.869303 + 0.757993i) q^{2} +(0.490110 + 0.871660i) q^{3} +(0.0449678 + 0.327165i) q^{4} +(-0.234658 + 1.12924i) q^{6} +(0.423665 - 0.645929i) q^{8} +(-0.519584 + 0.854419i) q^{9} +O(q^{10})$	\(q+(0.869303 + 0.757993i) q^{2} +(0.490110 + 0.871660i) q^{3} +(0.0449678 + 0.327165i) q^{4} +(-0.234658 + 1.12924i) q^{6} +(0.423665 - 0.645929i) q^{8} +(-0.519584 + 0.854419i) q^{9} +(-0.263138 + 0.199543i) q^{12} +(1.17590 - 0.329471i) q^{16} +(-0.500795 + 1.26993i) q^{17} +(-1.09932 + 0.348908i) q^{18} +(-0.157049 + 0.222488i) q^{19} +(1.31134 + 1.50391i) q^{23} +(0.770673 + 0.0527155i) q^{24} +(-0.999417 - 0.0341411i) q^{27} +(-0.214975 - 0.767255i) q^{31} +(0.574346 + 0.273147i) q^{32} +(-1.39794 + 0.724354i) q^{34} +(-0.302901 - 0.131568i) q^{36} +(-0.305168 + 0.0743674i) q^{38} +2.30134i q^{46} +(0.994757 - 0.102264i) q^{47} +(0.863506 + 0.863506i) q^{48} +(-0.997669 + 0.0682424i) q^{49} +(-1.35239 + 0.185882i) q^{51} +(1.42890 - 0.937216i) q^{53} +(-0.842917 - 0.787230i) q^{54} +(-0.270906 - 0.0278499i) q^{57} +(0.713755 + 0.580683i) q^{61} +(0.394695 - 0.829926i) q^{62} +(-0.194283 - 0.447285i) q^{64} +(-0.437996 - 0.106737i) q^{68} +(-0.668198 + 1.88013i) q^{69} +(0.331765 + 0.697602i) q^{72} +(-0.0798525 - 0.0413762i) q^{76} +(-1.72850 + 0.614311i) q^{79} +(-0.460065 - 0.887885i) q^{81} +(-0.149277 - 0.378541i) q^{83} +(-0.433059 + 0.496653i) q^{92} +(0.563424 - 0.563424i) q^{93} +(0.942261 + 0.665120i) q^{94} +(0.0434014 + 0.634506i) q^{96} +(-0.919004 - 0.696902i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.869303	+	0.757993i	0.869303	+	0.757993i	0.971567	−	0.236764i	$-0.0760870\pi$
$2$	0.869303	+	0.757993i	0.869303	+	0.757993i	−0.102264	+	0.994757i	$0.532609\pi$
$3$	0.490110	+	0.871660i	0.490110	+	0.871660i
$3$	0.490110	+	0.871660i	0.490110	+	0.871660i
$4$	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		−0.0341411	−	0.999417i	$-0.510870\pi$
$7$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$8$	0.423665	−	0.645929i	0.423665	−	0.645929i
$9$	−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	$0.630435\pi$
$12$	−0.263138	+	0.199543i	−0.263138	+	0.199543i
$13$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$13$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$14$		0			0
$15$		0			0
$16$	1.17590	−	0.329471i	1.17590	−	0.329471i
$17$	−0.500795	+	1.26993i	−0.500795	+	1.26993i	0.429483	+	0.903075i	$0.358696\pi$
$17$	−0.500795	+	1.26993i	−0.500795	+	1.26993i	−0.930278	+	0.366854i	$0.880435\pi$
$18$	−1.09932	+	0.348908i	−1.09932	+	0.348908i
$19$	−0.157049	+	0.222488i	−0.157049	+	0.222488i	−0.887885	−	0.460065i	$-0.847826\pi$
$19$	−0.157049	+	0.222488i	−0.157049	+	0.222488i	0.730836	+	0.682553i	$0.239130\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.31134	+	1.50391i	1.31134	+	1.50391i	0.707107	+	0.707107i	$0.250000\pi$
$23$	1.31134	+	1.50391i	1.31134	+	1.50391i	0.604236	+	0.796805i	$0.293478\pi$
$24$	0.770673	+	0.0527155i	0.770673	+	0.0527155i
$25$		0			0
$26$		0			0
$27$	−0.999417	−	0.0341411i	−0.999417	−	0.0341411i
$28$		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	$-0.217391\pi$
$32$	0.574346	+	0.273147i	0.574346	+	0.273147i
$33$		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		0.102264	−	0.994757i	$-0.467391\pi$
$37$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$38$	−0.305168	+	0.0743674i	−0.305168	+	0.0743674i
$39$		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		0.604236	−	0.796805i	$-0.293478\pi$
$43$		0			0		−0.604236	+	0.796805i	$0.706522\pi$
$44$		0			0
$45$		0			0
$46$			2.30134i			2.30134i
$47$	0.994757	−	0.102264i	0.994757	−	0.102264i
$47$	0.994757	−	0.102264i	0.994757	−	0.102264i
$48$	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
$53$	1.42890	−	0.937216i	1.42890	−	0.937216i	0.429483	−	0.903075i	$-0.358696\pi$
$53$	1.42890	−	0.937216i	1.42890	−	0.937216i	0.999417	−	0.0341411i	$-0.0108696\pi$
$54$	−0.842917	−	0.787230i	−0.842917	−	0.787230i
$55$		0			0
$56$		0			0
$57$	−0.270906	−	0.0278499i	−0.270906	−	0.0278499i
$58$		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	$0.565217\pi$
$62$	0.394695	−	0.829926i	0.394695	−	0.829926i
$63$		0			0
$64$	−0.194283	−	0.447285i	−0.194283	−	0.447285i
$65$		0			0
$66$		0			0
$67$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$67$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$68$	−0.437996	−	0.106737i	−0.437996	−	0.106737i
$69$	−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	$0.521739\pi$
$72$	0.331765	+	0.697602i	0.331765	+	0.697602i
$73$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$73$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$74$		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	−0.997669	−	0.0682424i	$-0.978261\pi$
$79$	−1.72850	+	0.614311i	−1.72850	+	0.614311i	−0.730836	+	0.682553i	$0.760870\pi$
$80$		0			0
$81$	−0.460065	−	0.887885i	−0.460065	−	0.887885i
$82$		0			0
$83$	−0.149277	−	0.378541i	−0.149277	−	0.378541i	0.836182	−	0.548452i	$-0.184783\pi$
$83$	−0.149277	−	0.378541i	−0.149277	−	0.378541i	−0.985460	+	0.169910i	$0.945652\pi$
$84$		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
$92$	−0.433059	+	0.496653i	−0.433059	+	0.496653i
$93$	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		0.871660	−	0.490110i	$-0.163043\pi$
$97$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$98$	−0.919004	−	0.696902i	−0.919004	−	0.696902i
$99$		0			0
$100$		0			0
$101$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$101$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$102$	−1.31654	−	0.863515i	−1.31654	−	0.863515i
$103$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$103$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$104$		0			0
$105$		0			0
$106$	1.95255	+	0.268372i	1.95255	+	0.268372i
$107$	0.163235	−	0.514311i	0.163235	−	0.514311i	−0.836182	−	0.548452i	$-0.815217\pi$
$107$	0.163235	−	0.514311i	0.163235	−	0.514311i	0.999417	+	0.0341411i	$0.0108696\pi$
$108$	−0.0337718	−	0.328509i	−0.0337718	−	0.328509i
$109$	−0.655751	−	1.84511i	−0.655751	−	1.84511i	−0.519584	−	0.854419i	$-0.673913\pi$
$109$	−0.655751	−	1.84511i	−0.655751	−	1.84511i	−0.136167	−	0.990686i	$-0.543478\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.214457	−	1.24382i	−0.214457	−	1.24382i	−0.871660	−	0.490110i	$-0.836957\pi$
$113$	−0.214457	−	1.24382i	−0.214457	−	1.24382i	0.657204	−	0.753713i	$-0.271739\pi$
$114$	−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
$122$	0.180316	+	1.04581i	0.180316	+	1.04581i
$123$		0			0
$124$	0.241352	−	0.104834i	0.241352	−	0.104834i
$125$		0			0
$126$		0			0
$127$		0			0		−0.102264	−	0.994757i	$-0.532609\pi$
$127$		0			0		0.102264	+	0.994757i	$0.467391\pi$
$128$	0.362544	−	1.14228i	0.362544	−	1.14228i
$129$		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
$137$	−1.56028	−	1.18320i	−1.56028	−	1.18320i	−0.903075	−	0.429483i	$-0.858696\pi$
$137$	−1.56028	−	1.18320i	−1.56028	−	1.18320i	−0.657204	−	0.753713i	$-0.728261\pi$
$138$	−2.00599	+	1.12791i	−2.00599	+	1.12791i
$139$	−0.128604	−	1.88013i	−0.128604	−	1.88013i	−0.398401	−	0.917211i	$-0.630435\pi$
$139$	−0.128604	−	1.88013i	−0.128604	−	1.88013i	0.269797	−	0.962917i	$-0.413043\pi$
$140$		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
$147$	−0.548452	−	0.836182i	−0.548452	−	0.836182i
$148$		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	$-0.565217\pi$
$152$	0.0771753	+	0.195703i	0.0771753	+	0.195703i
$153$	−0.824847	−	1.08772i	−0.824847	−	1.08772i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$157$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$158$	−1.96824	−	0.776172i	−1.96824	−	0.776172i
$159$	1.51725	+	0.786177i	1.51725	+	0.786177i
$160$		0			0
$161$		0			0
$162$	0.273075	−	1.12057i	0.273075	−	1.12057i
$163$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$163$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$164$		0			0
$165$		0			0
$166$	0.157164	−	0.442218i	0.157164	−	0.442218i
$167$	1.00962	+	0.246038i	1.00962	+	0.246038i	0.707107	−	0.707107i	$-0.250000\pi$
$167$	1.00962	+	0.246038i	1.00962	+	0.246038i	0.302515	+	0.953145i	$0.402174\pi$
$168$		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
$173$	−0.666310	+	1.40105i	−0.666310	+	1.40105i	0.236764	+	0.971567i	$0.423913\pi$
$173$	−0.666310	+	1.40105i	−0.666310	+	1.40105i	−0.903075	+	0.429483i	$0.858696\pi$
$174$		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
$183$	−0.156340	+	0.906751i	−0.156340	+	0.906751i
$184$	1.52699	−	0.209880i	1.52699	−	0.209880i
$185$		0			0
$186$	0.916858	−	0.0627148i	0.916858	−	0.0627148i
$187$		0			0
$188$	0.0781893	+	0.320851i	0.0781893	+	0.320851i
$189$		0			0
$190$		0			0
$191$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$191$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$192$	0.294660	−	0.388568i	0.294660	−	0.388568i
$193$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$193$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$194$		0			0
$195$		0			0
$196$	−0.0671895	−	0.323333i	−0.0671895	−	0.323333i
$197$	0.893968	−	0.217854i	0.893968	−	0.217854i	0.236764	−	0.971567i	$-0.423913\pi$
$197$	0.893968	−	0.217854i	0.893968	−	0.217854i	0.657204	+	0.753713i	$0.271739\pi$
$198$		0			0
$199$	0.953137	+	0.414006i	0.953137	+	0.414006i	0.816970	−	0.576680i	$-0.195652\pi$
$199$	0.953137	+	0.414006i	0.953137	+	0.414006i	0.136167	+	0.990686i	$0.456522\pi$
$200$		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
$207$	−1.96632	+	0.339029i	−1.96632	+	0.339029i
$208$		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	$0.434783\pi$
$212$	0.370879	+	0.425342i	0.370879	+	0.425342i
$213$		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
$218$	0.828531	−	2.10101i	0.828531	−	2.10101i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$223$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$224$		0			0
$225$		0			0
$226$	0.756381	−	1.24382i	0.756381	−	1.24382i
$227$	0.973925	−	1.48487i	0.973925	−	1.48487i	0.102264	−	0.994757i	$-0.467391\pi$
$227$	0.973925	−	1.48487i	0.973925	−	1.48487i	0.871660	−	0.490110i	$-0.163043\pi$
$228$	−0.00307050	−	0.0898831i	−0.00307050	−	0.0898831i
$229$	−0.361291	+	1.73863i	−0.361291	+	1.73863i	0.269797	+	0.962917i	$0.413043\pi$
$229$	−0.361291	+	1.73863i	−0.361291	+	1.73863i	−0.631088	+	0.775711i	$0.717391\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.783234	+	0.682945i	0.783234	+	0.682945i	0.953145	−	0.302515i	$-0.0978261\pi$
$233$	0.783234	+	0.682945i	0.783234	+	0.682945i	−0.169910	+	0.985460i	$0.554348\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.38263	−	1.20559i	−1.38263	−	1.20559i
$238$		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	$0.739130\pi$
$242$	−0.0393770	−	1.15269i	−0.0393770	−	1.15269i
$243$	0.548452	−	0.836182i	0.548452	−	0.836182i
$244$	−0.157883	+	0.259628i	−0.157883	+	0.259628i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.586669	−	0.186200i	−0.586669	−	0.186200i
$249$	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
$257$	1.32000	−	0.627764i	1.32000	−	0.627764i	0.366854	−	0.930278i	$-0.380435\pi$
$257$	1.32000	−	0.627764i	1.32000	−	0.627764i	0.953145	+	0.302515i	$0.0978261\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.134500	+	0.0231902i	−0.134500	+	0.0231902i	−0.236764	−	0.971567i	$-0.576087\pi$
$263$	−0.134500	+	0.0231902i	−0.134500	+	0.0231902i	0.102264	+	0.994757i	$0.467391\pi$
$264$		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	$-0.826087\pi$
$272$	−0.170479	+	1.65830i	−0.170479	+	1.65830i
$273$		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		−0.985460	−	0.169910i	$-0.945652\pi$
$277$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$278$	1.31333	−	1.73188i	1.31333	−	1.73188i
$279$	0.767255	+	0.214975i	0.767255	+	0.214975i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	−0.117947	+	1.14731i	−0.117947	+	1.14731i
$283$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$283$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.531803	+	0.348809i	−0.531803	+	0.348809i
$289$	−0.631088	−	0.589395i	−0.631088	−	0.589395i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.52002	+	0.599418i	−1.52002	+	0.599418i	−0.971567	−	0.236764i	$-0.923913\pi$
$293$	−1.52002	+	0.599418i	−1.52002	+	0.599418i	−0.548452	+	0.836182i	$0.684783\pi$
$294$	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
$302$	0.0699245	−	2.04691i	0.0699245	−	2.04691i
$303$		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		−0.429483	−	0.903075i	$-0.641304\pi$
$307$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$308$		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		0.490110	−	0.871660i	$-0.336957\pi$
$313$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$314$		0			0
$315$		0			0
$316$	−0.278708	−	0.537882i	−0.278708	−	0.537882i
$317$	0.326042	+	0.429951i	0.326042	+	0.429951i	0.930278	−	0.366854i	$-0.119565\pi$
$317$	0.326042	+	0.429951i	0.326042	+	0.429951i	−0.604236	+	0.796805i	$0.706522\pi$
$318$	0.723036	+	1.83349i	0.723036	+	1.83349i
$319$		0			0
$320$		0			0
$321$	0.528307	−	0.109784i	0.528307	−	0.109784i
$322$		0			0
$323$	−0.203895	−	0.310862i	−0.203895	−	0.310862i
$324$	0.269797	−	0.190443i	0.269797	−	0.190443i
$325$		0			0
$326$		0			0
$327$	1.28692	−	1.47590i	1.28692	−	1.47590i
$328$		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	$0.913043\pi$
$332$	0.117133	−	0.0658605i	0.117133	−	0.0658605i
$333$		0			0
$334$	0.691172	+	0.979167i	0.691172	+	0.979167i
$335$		0			0
$336$		0			0
$337$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$337$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$338$	0.273075	+	1.12057i	0.273075	+	1.12057i
$339$	0.979084	−	0.796544i	0.979084	−	0.796544i
$340$		0			0
$341$		0			0
$342$	0.0950194	−	0.299381i	0.0950194	−	0.299381i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.64121	+	0.712879i	−1.64121	+	0.712879i
$347$	0.469328	+	1.47873i	0.469328	+	1.47873i	0.836182	+	0.548452i	$0.184783\pi$
$347$	0.469328	+	1.47873i	0.469328	+	1.47873i	−0.366854	+	0.930278i	$0.619565\pi$
$348$		0			0
$349$	1.28629	+	1.37728i	1.28629	+	1.37728i	0.887885	+	0.460065i	$0.152174\pi$
$349$	1.28629	+	1.37728i	1.28629	+	1.37728i	0.398401	+	0.917211i	$0.369565\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.49339	+	1.30216i	−1.49339	+	1.30216i	−0.657204	+	0.753713i	$0.728261\pi$
$353$	−1.49339	+	1.30216i	−1.49339	+	1.30216i	−0.836182	+	0.548452i	$0.815217\pi$
$354$		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
$362$	−0.148870	−	1.44811i	−0.148870	−	1.44811i
$363$	0.302515	−	0.953145i	0.302515	−	0.953145i
$364$		0			0
$365$		0			0
$366$	−0.823217	+	0.669737i	−0.823217	+	0.669737i
$367$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$367$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$368$	2.03750	+	1.33640i	2.03750	+	1.33640i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.209669	+	0.158997i	0.209669	+	0.158997i
$373$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$373$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$374$		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	$-0.326087\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.55052	+	0.0529673i	−1.55052	+	0.0529673i	−0.796805	−	0.604236i	$-0.793478\pi$
$383$	−1.55052	+	0.0529673i	−1.55052	+	0.0529673i	−0.753713	+	0.657204i	$0.771739\pi$
$384$	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
$392$	−0.378597	+	0.673335i	−0.378597	+	0.673335i
$393$		0			0
$394$	0.942261	+	0.488240i	0.942261	+	0.488240i
$395$		0			0
$396$		0			0
$397$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$397$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$398$	0.514751	+	1.08237i	0.514751	+	1.08237i
$399$		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
$408$	−0.452894	+	0.952300i	−0.452894	+	0.952300i
$409$	−1.46184	−	1.18930i	−1.46184	−	1.18930i	−0.942261	−	0.334880i	$-0.891304\pi$
$409$	−1.46184	−	1.18930i	−1.46184	−	1.18930i	−0.519584	−	0.854419i	$-0.673913\pi$
$410$		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
$417$	1.57580	−	1.03357i	1.57580	−	1.03357i
$418$		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
$423$	−0.429483	+	0.903075i	−0.429483	+	0.903075i
$424$		−	1.32003i		−	1.32003i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.175605	+	0.0302773i	0.175605	+	0.0302773i
$429$		0			0
$430$		0			0
$431$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$431$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$432$	−1.18646	+	0.289132i	−1.18646	+	0.289132i
$433$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$433$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$434$		0			0
$435$		0			0
$436$	0.574166	−	0.297509i	0.574166	−	0.297509i
$437$	−0.540548	+	0.0555700i	−0.540548	+	0.0555700i
$438$		0			0
$439$	0.109784	+	0.391823i	0.109784	+	0.391823i	0.997669	−	0.0682424i	$-0.0217391\pi$
$439$	0.109784	+	0.391823i	0.109784	+	0.391823i	−0.887885	+	0.460065i	$0.847826\pi$
$440$		0			0
$441$	0.460065	−	0.887885i	0.460065	−	0.887885i
$442$		0			0
$443$	1.95703	+	0.0668540i	1.95703	+	0.0668540i	0.985460	−	0.169910i	$-0.0543478\pi$
$443$	1.95703	+	0.0668540i	1.95703	+	0.0668540i	0.971567	+	0.236764i	$0.0760870\pi$
$444$		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
$452$	0.397292	−	0.126095i	0.397292	−	0.126095i
$453$	0.651449	−	1.65196i	0.651449	−	1.65196i
$454$	1.97215	−	0.552572i	1.97215	−	0.552572i
$455$		0			0
$456$	−0.132762	+	0.163187i	−0.132762	+	0.163187i
$457$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$457$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$458$	−1.63194	+	1.23754i	−1.63194	+	1.23754i
$459$	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		−0.0341411	−	0.999417i	$-0.510870\pi$
$463$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$464$		0			0
$465$		0			0
$466$	0.163201	+	1.18737i	0.163201	+	1.18737i
$467$	0.923623	+	1.64266i	0.923623	+	1.64266i	0.753713	+	0.657204i	$0.228261\pi$
$467$	0.923623	+	1.64266i	0.923623	+	1.64266i	0.169910	+	0.985460i	$0.445652\pi$
$468$		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
$477$	0.0583417	+	1.70784i	0.0583417	+	1.70784i
$478$		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
$482$	−1.57043	+	1.19089i	−1.57043	+	1.19089i
$483$		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		0.366854	−	0.930278i	$-0.380435\pi$
$487$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$488$	0.677473	−	0.215020i	0.677473	−	0.215020i
$489$		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
$498$	0.462492	−	0.0797417i	0.462492	−	0.0797417i
$499$	0.917985	−	1.77163i	0.917985	−	1.77163i	0.398401	−	0.917211i	$-0.369565\pi$
$499$	0.917985	−	1.77163i	0.917985	−	1.77163i	0.519584	−	0.854419i	$-0.326087\pi$
$500$		0			0
$501$	0.280364	+	1.00063i	0.280364	+	1.00063i
$502$		0			0
$503$	1.62537	−	0.167093i	1.62537	−	0.167093i	0.753713	−	0.657204i	$-0.228261\pi$
$503$	1.62537	−	0.167093i	1.62537	−	0.167093i	0.871660	+	0.490110i	$0.163043\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.102264	+	0.994757i	−0.102264	+	0.994757i
$508$		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
$512$	−0.164249	−	0.0283194i	−0.164249	−	0.0283194i
$513$	0.164554	−	0.216997i	0.164554	−	0.216997i
$514$	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		0.836182	−	0.548452i	$-0.184783\pi$
$523$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$524$		0			0
$525$		0			0
$526$	−0.134499	−	0.0817909i	−0.134499	−	0.0817909i
$527$	1.08202	+	0.111235i	1.08202	+	0.111235i
$528$		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	$-0.347826\pi$
$542$	−0.981471	−	2.06374i	−0.981471	−	2.06374i
$543$	0.298838	−	1.22629i	0.298838	−	1.22629i
$544$	−0.634506	+	0.592588i	−0.634506	+	0.592588i
$545$		0			0
$546$		0			0
$547$		0			0		−0.930278	−	0.366854i	$-0.880435\pi$
$547$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$548$	0.316938	−	0.563674i	0.316938	−	0.563674i
$549$	−0.867003	+	0.308133i	−0.867003	+	0.308133i
$550$		0			0
$551$		0			0
$552$	0.931337	+	1.22815i	0.931337	+	1.22815i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.609329	−	0.126620i	0.609329	−	0.126620i
$557$	−1.46082	+	0.0499031i	−1.46082	+	0.0499031i	−0.753713	−	0.657204i	$-0.771739\pi$
$557$	−1.46082	+	0.0499031i	−1.46082	+	0.0499031i	−0.707107	+	0.707107i	$0.750000\pi$
$558$	0.504027	+	0.768452i	0.504027	+	0.768452i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.03356	+	1.03356i	−1.03356	+	1.03356i	−0.0341411	+	0.999417i	$0.510870\pi$
$563$	−1.03356	+	1.03356i	−1.03356	+	1.03356i	−0.999417	+	0.0341411i	$0.989130\pi$
$564$	−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		0.302515	−	0.953145i	$-0.402174\pi$
$577$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$578$	−0.101849	−	0.990723i	−0.101849	−	0.990723i
$579$		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
$587$	−0.205261	+	0.178978i	−0.205261	+	0.178978i	−0.753713	−	0.657204i	$-0.771739\pi$
$587$	−0.205261	+	0.178978i	−0.205261	+	0.178978i	0.548452	+	0.836182i	$0.315217\pi$
$588$	0.248907	−	0.217035i	0.248907	−	0.217035i
$589$	0.204467	+	0.0726675i	0.204467	+	0.0726675i
$590$		0			0
$591$	0.628038	+	0.672464i	0.628038	+	0.672464i
$592$		0			0
$593$	−0.494291	−	1.55738i	−0.494291	−	1.55738i	−0.796805	−	0.604236i	$-0.793478\pi$
$593$	−0.494291	−	1.55738i	−0.494291	−	1.55738i	0.302515	−	0.953145i	$-0.402174\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.106270	+	1.03372i	0.106270	+	1.03372i
$598$		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		−0.796805	−	0.604236i	$-0.793478\pi$
$607$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$608$	−0.150972	+	0.0848876i	−0.150972	+	0.0848876i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.318773	−	0.318773i	0.318773	−	0.318773i
$613$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$613$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.00609	+	1.53391i	1.00609	+	1.53391i	0.836182	+	0.548452i	$0.184783\pi$
$617$	1.00609	+	1.53391i	1.00609	+	1.53391i	0.169910	+	0.985460i	$0.445652\pi$
$618$		0			0
$619$	0.900885	−	0.187206i	0.900885	−	0.187206i	0.269797	−	0.962917i	$-0.413043\pi$
$619$	0.900885	−	0.187206i	0.900885	−	0.187206i	0.631088	+	0.775711i	$0.282609\pi$
$620$		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	$-0.217391\pi$
$632$	−0.335506	+	1.37675i	−0.335506	+	1.37675i
$633$	0.231746	+	0.487293i	0.231746	+	0.487293i
$634$	−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	$0.369565\pi$
$642$	0.542474	+	0.305018i	0.542474	+	0.305018i
$643$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$643$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$644$		0			0
$645$		0			0
$646$	0.0583852	−	0.424784i	0.0583852	−	0.424784i
$647$	1.58970	−	0.626895i	1.58970	−	0.626895i	0.604236	−	0.796805i	$-0.293478\pi$
$647$	1.58970	−	0.626895i	1.58970	−	0.626895i	0.985460	+	0.169910i	$0.0543478\pi$
$648$	−0.768424	−	0.0789964i	−0.768424	−	0.0789964i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.336656	+	1.95256i	−0.336656	+	1.95256i	−0.0341411	+	0.999417i	$0.510870\pi$
$653$	−0.336656	+	1.95256i	−0.336656	+	1.95256i	−0.302515	+	0.953145i	$0.597826\pi$
$654$	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	$0.826087\pi$
$662$	−0.283578	+	0.373954i	−0.283578	+	0.373954i
$663$		0			0
$664$	−0.307754	−	0.0639521i	−0.307754	−	0.0639521i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.0350946	+	0.341376i	−0.0350946	+	0.341376i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$673$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$674$		0			0
$675$		0			0
$676$	−0.151932	+	0.293216i	−0.151932	+	0.293216i
$677$	−1.85712	+	0.320200i	−1.85712	+	0.320200i	−0.985460	−	0.169910i	$-0.945652\pi$
$677$	−1.85712	+	0.320200i	−1.85712	+	0.320200i	−0.871660	+	0.490110i	$0.836957\pi$
$678$	1.45490	+	0.0497007i	1.45490	+	0.0497007i
$679$		0			0
$680$		0			0
$681$	1.77163	+	0.121183i	1.77163	+	0.121183i
$682$		0			0
$683$	−0.123256	+	0.0586180i	−0.123256	+	0.0586180i	−0.490110	−	0.871660i	$-0.663043\pi$
$683$	−0.123256	+	0.0586180i	−0.123256	+	0.0586180i	0.366854	+	0.930278i	$0.380435\pi$
$684$	0.0768427	−	0.0467291i	0.0768427	−	0.0467291i
$685$		0			0
$686$		0			0
$687$	−1.69257	+	0.537196i	−1.69257	+	0.537196i
$688$		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	$-0.0434783\pi$
$692$	−0.488337	−	0.154991i	−0.488337	−	0.154991i
$693$		0			0
$694$	−0.712879	+	1.64121i	−0.712879	+	1.64121i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.0742068	+	2.17227i	0.0742068	+	2.17227i
$699$	−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	0.979084	−	0.203456i	$-0.0652174\pi$
$709$	−0.0185847	−	0.135214i	−0.0185847	−	0.135214i	−0.997669	+	0.0682424i	$0.978261\pi$
$710$		0			0
$711$	0.373224	−	1.79605i	0.373224	−	1.79605i
$712$		0			0
$713$	0.871978	−	1.32944i	0.871978	−	1.32944i
$714$		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
$722$	−0.391735	+	0.993371i	−0.391735	+	0.993371i
$723$	−1.62877	+	0.516949i	−1.62877	+	0.516949i
$724$	0.240373	−	0.340531i	0.240373	−	0.340531i
$725$		0			0
$726$	0.985454	−	0.599268i	0.985454	−	0.599268i
$727$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$727$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$728$		0			0
$729$	0.997669	+	0.0682424i	0.997669	+	0.0682424i
$730$		0			0
$731$		0			0
$732$	−0.303687	−	0.0103743i	−0.303687	−	0.0103743i
$733$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$733$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$734$		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	0.398401	−	0.917211i	$-0.369565\pi$
$739$	1.37749	−	0.713755i	1.37749	−	0.713755i	0.979084	+	0.203456i	$0.0652174\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.264590	−	0.0644788i	0.264590	−	0.0644788i	−0.102264	−	0.994757i	$-0.532609\pi$
$743$	0.264590	−	0.0644788i	0.264590	−	0.0644788i	0.366854	+	0.930278i	$0.380435\pi$
$744$	−0.125229	−	0.602635i	−0.125229	−	0.602635i
$745$		0			0
$746$		0			0
$747$	0.400995	+	0.0691386i	0.400995	+	0.0691386i
$748$		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	$-0.0869565\pi$
$752$	1.13604	−	0.447996i	1.13604	−	0.447996i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$757$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$758$	1.85731	−	1.21821i	1.85731	−	1.21821i
$759$		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
$768$	0.779760	+	0.438437i	0.779760	+	0.438437i
$769$	0.543860	+	1.25209i	0.543860	+	1.25209i	0.942261	+	0.334880i	$0.108696\pi$
$769$	0.543860	+	1.25209i	0.543860	+	1.25209i	−0.398401	+	0.917211i	$0.630435\pi$
$770$		0			0
$771$	1.19414	+	0.842917i	1.19414	+	0.842917i
$772$		0			0
$773$	0.650716	+	0.158575i	0.650716	+	0.158575i	0.548452	−	0.836182i	$-0.315217\pi$
$773$	0.650716	+	0.158575i	0.650716	+	0.158575i	0.102264	+	0.994757i	$0.467391\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−2.92254	−	1.15250i	−2.92254	−	1.15250i
$783$		0			0
$784$	−1.15067	+	0.408949i	−1.15067	+	0.408949i
$785$		0			0
$786$		0			0
$787$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$787$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$788$	0.111474	+	0.282679i	0.111474	+	0.282679i
$789$	−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
$797$	−1.23851	+	1.42039i	−1.23851	+	1.42039i	−0.366854	+	0.930278i	$0.619565\pi$
$797$	−1.23851	+	1.42039i	−1.23851	+	1.42039i	−0.871660	+	0.490110i	$0.836957\pi$
$798$		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
$813$	−0.202623	−	1.97098i	−0.202623	−	1.97098i
$814$		0			0
$815$		0			0
$816$	−1.52903	+	0.664152i	−1.52903	+	0.664152i
$817$		0			0
$818$	−0.369306	−	2.14193i	−0.369306	−	2.14193i
$819$		0			0
$820$		0			0
$821$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$821$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$822$	1.70224	−	1.48428i	1.70224	−	1.48428i
$823$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$823$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.113799	+	0.660021i	0.113799	+	0.660021i	0.985460	+	0.169910i	$0.0543478\pi$
$827$	0.113799	+	0.660021i	0.113799	+	0.660021i	−0.871660	+	0.490110i	$0.836957\pi$
$828$	−0.199339	−	0.628067i	−0.199339	−	0.628067i
$829$	−1.49867	+	0.650963i	−1.49867	+	0.650963i	−0.979084	−	0.203456i	$-0.934783\pi$
$829$	−1.49867	+	0.650963i	−1.49867	+	0.650963i	−0.519584	+	0.854419i	$0.673913\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.412965	−	1.30114i	0.412965	−	1.30114i
$834$	2.15329	+	0.295963i	2.15329	+	0.295963i
$835$		0			0
$836$		0			0
$837$	0.188654	+	0.774147i	0.188654	+	0.774147i
$838$		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
$842$	0.495888	+	0.376044i	0.495888	+	0.376044i
$843$		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
$848$	1.37145	−	1.57285i	1.37145	−	1.57285i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$853$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$854$		0			0
$855$		0			0
$856$	−0.263051	−	0.323333i	−0.263051	−	0.323333i
$857$	−0.197952	−	0.501972i	−0.197952	−	0.501972i	0.796805	−	0.604236i	$-0.206522\pi$
$857$	−0.197952	−	0.501972i	−0.197952	−	0.501972i	−0.994757	+	0.102264i	$0.967391\pi$
$858$		0			0
$859$	−0.751719	−	1.45075i	−0.751719	−	1.45075i	−0.887885	−	0.460065i	$-0.847826\pi$
$859$	−0.751719	−	1.45075i	−0.751719	−	1.45075i	0.136167	−	0.990686i	$-0.456522\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.70652	−	0.672966i	−1.70652	−	0.672966i	−0.707107	−	0.707107i	$-0.750000\pi$
$863$	−1.70652	−	0.672966i	−1.70652	−	0.672966i	−0.999417	+	0.0341411i	$0.989130\pi$
$864$	−0.564685	−	0.292596i	−0.564685	−	0.292596i
$865$		0			0
$866$		0			0
$867$	0.204450	−	0.838963i	0.204450	−	0.838963i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.46963	−	0.358138i	−1.46963	−	0.358138i
$873$		0			0
$874$	−0.512022	−	0.361424i	−0.512022	−	0.361424i
$875$		0			0
$876$		0			0
$877$		0			0		−0.871660	−	0.490110i	$-0.836957\pi$
$877$		0			0		0.871660	+	0.490110i	$0.163043\pi$
$878$	−0.201564	+	0.423828i	−0.201564	+	0.423828i
$879$	−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	$0.543478\pi$
$882$	1.07295	−	0.423115i	1.07295	−	0.423115i
$883$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$883$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$884$		0			0
$885$		0			0
$886$	1.65057	+	1.54153i	1.65057	+	1.54153i
$887$	0.227720	−	0.149362i	0.227720	−	0.149362i	−0.429483	−	0.903075i	$-0.641304\pi$
$887$	0.227720	−	0.149362i	0.227720	−	0.149362i	0.657204	+	0.753713i	$0.271739\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.133473	+	0.237382i	−0.133473	+	0.237382i
$894$		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		0.994757	−	0.102264i	$-0.0326087\pi$
$907$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$908$	0.529592	+	0.251863i	0.529592	+	0.251863i
$909$		0			0
$910$		0			0
$911$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$911$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$912$	−0.327733	+	0.0565068i	−0.327733	+	0.0565068i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.585065	−	0.0400195i	−0.585065	−	0.0400195i
$917$		0			0
$918$	1.42185	−	0.676204i	1.42185	−	0.676204i
$919$	1.70486	−	1.03675i	1.70486	−	1.03675i	0.816970	−	0.576680i	$-0.195652\pi$
$919$	1.70486	−	1.03675i	1.70486	−	1.03675i	0.887885	−	0.460065i	$-0.152174\pi$
$920$		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
$932$	−0.188215	+	0.286957i	−0.188215	+	0.286957i
$933$		0			0
$934$	−0.442218	+	2.12807i	−0.442218	+	2.12807i
$935$		0			0
$936$		0			0
$937$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$937$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$938$		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
$947$	−0.0228663	−	0.669369i	−0.0228663	−	0.669369i	−0.953145	−	0.302515i	$-0.902174\pi$
$947$	−0.0228663	−	0.669369i	−0.0228663	−	0.669369i	0.930278	−	0.366854i	$-0.119565\pi$
$948$	0.332253	−	0.506560i	0.332253	−	0.506560i
$949$		0			0
$950$		0			0
$951$	−0.214975	+	0.494921i	−0.214975	+	0.494921i
$952$		0			0
$953$	−1.55738	−	0.494291i	−1.55738	−	0.494291i	−0.604236	−	0.796805i	$-0.706522\pi$
$953$	−1.55738	−	0.494291i	−1.55738	−	0.494291i	−0.953145	+	0.302515i	$0.902174\pi$
$954$	−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
$963$	0.354623	+	0.406699i	0.354623	+	0.406699i
$964$	−0.563013	−	0.0385111i	−0.563013	−	0.0385111i
$965$		0			0
$966$		0			0
$967$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$967$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$968$	−0.761242	+	0.131251i	−0.761242	+	0.131251i
$969$	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	$0.413043\pi$
$972$	0.298232	+	0.141833i	0.298232	+	0.141833i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.03062	+	0.447662i	1.03062	+	0.447662i
$977$	0.158655	−	1.54329i	0.158655	−	1.54329i	−0.548452	−	0.836182i	$-0.684783\pi$
$977$	0.158655	−	1.54329i	0.158655	−	1.54329i	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
$983$	−1.07299	+	1.41494i	−1.07299	+	1.41494i	−0.169910	+	0.985460i	$0.554348\pi$
$983$	−1.07299	+	1.41494i	−1.07299	+	1.41494i	−0.903075	+	0.429483i	$0.858696\pi$
$984$		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	$0.869565\pi$
$992$	0.0861034	−	0.499389i	0.0861034	−	0.499389i
$993$	−0.340253	+	0.223172i	−0.340253	+	0.223172i
$994$		0			0
$995$		0			0
$996$	0.114816	+	0.0698211i	0.114816	+	0.0698211i
$997$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$997$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$998$	2.14089	−	0.844258i	2.14089	−	0.844258i
$999$		0			0

Twists

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

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

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