LMFDB - Embedded newform 3525.1.bg.a.932.1

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			932.1
Root			$0.930278 - 0.366854i$ of defining polynomial
Character	$\chi$	$=$	3525.932
Dual form			3525.1.bg.a.3143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58970 + 0.626895i) q^{2} +(0.657204 - 0.753713i) q^{3} +(1.40330 - 1.31059i) q^{4} +(-0.572255 + 1.61017i) q^{6} +(-0.675300 + 1.41995i) q^{8} +(-0.136167 - 0.990686i) q^{9} +O(q^{10})$	\(q+(-1.58970 + 0.626895i) q^{2} +(0.657204 - 0.753713i) q^{3} +(1.40330 - 1.31059i) q^{4} +(-0.572255 + 1.61017i) q^{6} +(-0.675300 + 1.41995i) q^{8} +(-0.136167 - 0.990686i) q^{9} +(-0.0655554 - 1.91901i) q^{12} +(0.0523262 - 0.764982i) q^{16} +(-0.0416125 + 0.404779i) q^{17} +(0.837519 + 1.48953i) q^{18} +(1.24888 - 0.759461i) q^{19} +(-0.292310 + 0.741248i) q^{23} +(0.626428 + 1.44218i) q^{24} +(-0.836182 - 0.548452i) q^{27} +(1.25923 + 0.0861339i) q^{31} +(-0.0792796 - 0.249789i) q^{32} +(-0.187602 - 0.669562i) q^{34} +(-1.48947 - 1.21177i) q^{36} +(-1.50924 + 1.99023i) q^{38} -1.36161i q^{46} +(-0.169910 - 0.985460i) q^{47} +(-0.542188 - 0.542188i) q^{48} +(-0.398401 + 0.917211i) q^{49} +(0.277739 + 0.297386i) q^{51} +(1.78933 - 0.850966i) q^{53} +(1.67310 + 0.347674i) q^{54} +(0.248353 - 1.44042i) q^{57} +(1.11059 - 1.57335i) q^{61} +(-2.05580 + 0.652480i) q^{62} +(0.766521 + 0.942181i) q^{64} +(0.472104 + 0.622563i) q^{68} +(0.366581 + 0.707469i) q^{69} +(1.49868 + 0.475660i) q^{72} +(0.757212 - 2.70252i) q^{76} +(-1.37749 - 0.713755i) q^{79} +(-0.962917 + 0.269797i) q^{81} +(0.0684924 + 0.666248i) q^{83} +(0.561274 + 1.42329i) q^{92} +(0.892493 - 0.892493i) q^{93} +(0.887885 + 1.46007i) q^{94} +(-0.240372 - 0.104408i) q^{96} +(0.0583417 - 1.70784i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{31}{46}\right)$	$-1$

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 $

$2$	−1.58970	+	0.626895i	−1.58970	+	0.626895i	−0.985460	−	0.169910i	$-0.945652\pi$
$2$	−1.58970	+	0.626895i	−1.58970	+	0.626895i	−0.604236	+	0.796805i	$0.706522\pi$
$3$	0.657204	−	0.753713i	0.657204	−	0.753713i
$3$	0.657204	−	0.753713i	0.657204	−	0.753713i
$4$	1.40330	−	1.31059i	1.40330	−	1.31059i
$5$		0			0
$5$		0			0
$6$	−0.572255	+	1.61017i	−0.572255	+	1.61017i
$7$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$7$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$8$	−0.675300	+	1.41995i	−0.675300	+	1.41995i
$9$	−0.136167	−	0.990686i	−0.136167	−	0.990686i
$10$		0			0
$11$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$11$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$12$	−0.0655554	−	1.91901i	−0.0655554	−	1.91901i
$13$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$13$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$14$		0			0
$15$		0			0
$16$	0.0523262	−	0.764982i	0.0523262	−	0.764982i
$17$	−0.0416125	+	0.404779i	−0.0416125	+	0.404779i	0.953145	+	0.302515i	$0.0978261\pi$
$17$	−0.0416125	+	0.404779i	−0.0416125	+	0.404779i	−0.994757	+	0.102264i	$0.967391\pi$
$18$	0.837519	+	1.48953i	0.837519	+	1.48953i
$19$	1.24888	−	0.759461i	1.24888	−	0.759461i	0.269797	−	0.962917i	$-0.413043\pi$
$19$	1.24888	−	0.759461i	1.24888	−	0.759461i	0.979084	+	0.203456i	$0.0652174\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.292310	+	0.741248i	−0.292310	+	0.741248i	0.707107	+	0.707107i	$0.250000\pi$
$23$	−0.292310	+	0.741248i	−0.292310	+	0.741248i	−0.999417	+	0.0341411i	$0.989130\pi$
$24$	0.626428	+	1.44218i	0.626428	+	1.44218i
$25$		0			0
$26$		0			0
$27$	−0.836182	−	0.548452i	−0.836182	−	0.548452i
$28$		0			0
$29$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$29$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$30$		0			0
$31$	1.25923	+	0.0861339i	1.25923	+	0.0861339i	0.682553	−	0.730836i	$-0.260870\pi$
$31$	1.25923	+	0.0861339i	1.25923	+	0.0861339i	0.576680	+	0.816970i	$0.304348\pi$
$32$	−0.0792796	−	0.249789i	−0.0792796	−	0.249789i
$33$		0			0
$34$	−0.187602	−	0.669562i	−0.187602	−	0.669562i
$35$		0			0
$36$	−1.48947	−	1.21177i	−1.48947	−	1.21177i
$37$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$37$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$38$	−1.50924	+	1.99023i	−1.50924	+	1.99023i
$39$		0			0
$40$		0			0
$41$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$41$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$42$		0			0
$43$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$43$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$44$		0			0
$45$		0			0
$46$		−	1.36161i		−	1.36161i
$47$	−0.169910	−	0.985460i	−0.169910	−	0.985460i
$47$	−0.169910	−	0.985460i	−0.169910	−	0.985460i
$48$	−0.542188	−	0.542188i	−0.542188	−	0.542188i
$49$	−0.398401	+	0.917211i	−0.398401	+	0.917211i
$50$		0			0
$51$	0.277739	+	0.297386i	0.277739	+	0.297386i
$52$		0			0
$53$	1.78933	−	0.850966i	1.78933	−	0.850966i	0.836182	−	0.548452i	$-0.184783\pi$
$53$	1.78933	−	0.850966i	1.78933	−	0.850966i	0.953145	−	0.302515i	$-0.0978261\pi$
$54$	1.67310	+	0.347674i	1.67310	+	0.347674i
$55$		0			0
$56$		0			0
$57$	0.248353	−	1.44042i	0.248353	−	1.44042i
$58$		0			0
$59$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$59$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$60$		0			0
$61$	1.11059	−	1.57335i	1.11059	−	1.57335i	0.334880	−	0.942261i	$-0.391304\pi$
$61$	1.11059	−	1.57335i	1.11059	−	1.57335i	0.775711	−	0.631088i	$-0.217391\pi$
$62$	−2.05580	+	0.652480i	−2.05580	+	0.652480i
$63$		0			0
$64$	0.766521	+	0.942181i	0.766521	+	0.942181i
$65$		0			0
$66$		0			0
$67$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$67$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$68$	0.472104	+	0.622563i	0.472104	+	0.622563i
$69$	0.366581	+	0.707469i	0.366581	+	0.707469i
$70$		0			0
$71$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$71$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$72$	1.49868	+	0.475660i	1.49868	+	0.475660i
$73$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$73$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$74$		0			0
$75$		0			0
$76$	0.757212	−	2.70252i	0.757212	−	2.70252i
$77$		0			0
$78$		0			0
$79$	−1.37749	−	0.713755i	−1.37749	−	0.713755i	−0.398401	−	0.917211i	$-0.630435\pi$
$79$	−1.37749	−	0.713755i	−1.37749	−	0.713755i	−0.979084	+	0.203456i	$0.934783\pi$
$80$		0			0
$81$	−0.962917	+	0.269797i	−0.962917	+	0.269797i
$82$		0			0
$83$	0.0684924	+	0.666248i	0.0684924	+	0.666248i	0.971567	+	0.236764i	$0.0760870\pi$
$83$	0.0684924	+	0.666248i	0.0684924	+	0.666248i	−0.903075	+	0.429483i	$0.858696\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$89$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$90$		0			0
$91$		0			0
$92$	0.561274	+	1.42329i	0.561274	+	1.42329i
$93$	0.892493	−	0.892493i	0.892493	−	0.892493i
$94$	0.887885	+	1.46007i	0.887885	+	1.46007i
$95$		0			0
$96$	−0.240372	−	0.104408i	−0.240372	−	0.104408i
$97$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$97$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$98$	0.0583417	−	1.70784i	0.0583417	−	1.70784i
$99$		0			0
$100$		0			0
$101$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$101$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$102$	−0.627950	−	0.298640i	−0.627950	−	0.298640i
$103$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$103$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$104$		0			0
$105$		0			0
$106$	−2.31102	+	2.47450i	−2.31102	+	2.47450i
$107$	1.73926	+	0.977935i	1.73926	+	0.977935i	0.903075	+	0.429483i	$0.141304\pi$
$107$	1.73926	+	0.977935i	1.73926	+	0.977935i	0.836182	+	0.548452i	$0.184783\pi$
$108$	−1.89221	+	0.326250i	−1.89221	+	0.326250i
$109$	−0.867003	+	1.67324i	−0.867003	+	1.67324i	−0.136167	+	0.990686i	$0.543478\pi$
$109$	−0.867003	+	1.67324i	−0.867003	+	1.67324i	−0.730836	+	0.682553i	$0.760870\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.386859	−	1.58748i	0.386859	−	1.58748i	−0.366854	−	0.930278i	$-0.619565\pi$
$113$	0.386859	−	1.58748i	0.386859	−	1.58748i	0.753713	−	0.657204i	$-0.228261\pi$
$114$	0.508185	+	2.44552i	0.508185	+	2.44552i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.203456	−	0.979084i	−0.203456	−	0.979084i
$122$	−0.779178	+	3.19737i	−0.779178	+	3.19737i
$123$		0			0
$124$	1.87997	−	1.52947i	1.87997	−	1.52947i
$125$		0			0
$126$		0			0
$127$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$127$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$128$	−1.58075	−	0.888811i	−1.58075	−	0.888811i
$129$		0			0
$130$		0			0
$131$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$131$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.546666	−	0.332435i	−0.546666	−	0.332435i
$137$	0.0643397	−	1.88342i	0.0643397	−	1.88342i	−0.302515	−	0.953145i	$-0.597826\pi$
$137$	0.0643397	−	1.88342i	0.0643397	−	1.88342i	0.366854	−	0.930278i	$-0.380435\pi$
$138$	−1.02626	−	0.894853i	−1.02626	−	0.894853i
$139$	−1.62876	−	0.707469i	−1.62876	−	0.707469i	−0.631088	−	0.775711i	$-0.717391\pi$
$139$	−1.62876	−	0.707469i	−1.62876	−	0.707469i	−0.997669	+	0.0682424i	$0.978261\pi$
$140$		0			0
$141$	−0.854419	−	0.519584i	−0.854419	−	0.519584i
$142$		0			0
$143$		0			0
$144$	−0.764982	+	0.0523262i	−0.764982	+	0.0523262i
$145$		0			0
$146$		0			0
$147$	0.429483	+	0.903075i	0.429483	+	0.903075i
$148$		0			0
$149$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$149$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$150$		0			0
$151$	−0.440832	+	0.311173i	−0.440832	+	0.311173i	−0.775711	−	0.631088i	$-0.782609\pi$
$151$	−0.440832	+	0.311173i	−0.440832	+	0.311173i	0.334880	+	0.942261i	$0.391304\pi$
$152$	0.235030	+	2.28622i	0.235030	+	2.28622i
$153$	0.406675	−	0.0138924i	0.406675	−	0.0138924i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$157$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$158$	2.63723	+	0.271116i	2.63723	+	0.271116i
$159$	0.534568	−	1.90790i	0.534568	−	1.90790i
$160$		0			0
$161$		0			0
$162$	1.36161	−	1.03254i	1.36161	−	1.03254i
$163$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$163$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$164$		0			0
$165$		0			0
$166$	−0.526549	−	1.01619i	−0.526549	−	1.01619i
$167$	−0.164554	−	0.216997i	−0.164554	−	0.216997i	0.707107	−	0.707107i	$-0.250000\pi$
$167$	−0.164554	−	0.216997i	−0.164554	−	0.216997i	−0.871660	+	0.490110i	$0.836957\pi$
$168$		0			0
$169$	−0.519584	−	0.854419i	−0.519584	−	0.854419i
$170$		0			0
$171$	−0.922444	−	1.13384i	−0.922444	−	1.13384i
$172$		0			0
$173$	−1.09932	+	0.348908i	−1.09932	+	0.348908i	−0.796805	−	0.604236i	$-0.793478\pi$
$173$	−1.09932	+	0.348908i	−1.09932	+	0.348908i	−0.302515	+	0.953145i	$0.597826\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$179$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$180$		0			0
$181$	1.59976	+	0.332435i	1.59976	+	0.332435i	0.917211	−	0.398401i	$-0.130435\pi$
$181$	1.59976	+	0.332435i	1.59976	+	0.332435i	0.682553	+	0.730836i	$0.260870\pi$
$182$		0			0
$183$	−0.455969	−	1.87108i	−0.455969	−	1.87108i
$184$	−0.855140	−	0.915632i	−0.855140	−	0.915632i
$185$		0			0
$186$	−0.859293	+	1.97829i	−0.859293	+	1.97829i
$187$		0			0
$188$	−1.52997	−	1.16021i	−1.52997	−	1.16021i
$189$		0			0
$190$		0			0
$191$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$191$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$192$	1.21389	+	0.0414679i	1.21389	+	0.0414679i
$193$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$193$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$194$		0			0
$195$		0			0
$196$	0.643012	+	1.80926i	0.643012	+	1.80926i
$197$	−1.16366	+	1.53451i	−1.16366	+	1.53451i	−0.366854	+	0.930278i	$0.619565\pi$
$197$	−1.16366	+	1.53451i	−1.16366	+	1.53451i	−0.796805	+	0.604236i	$0.793478\pi$
$198$		0			0
$199$	0.211252	+	0.171866i	0.211252	+	0.171866i	0.730836	−	0.682553i	$-0.239130\pi$
$199$	0.211252	+	0.171866i	0.211252	+	0.171866i	−0.519584	+	0.854419i	$0.673913\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.779503	+	0.0533194i	0.779503	+	0.0533194i
$205$		0			0
$206$		0			0
$207$	0.774147	+	0.188654i	0.774147	+	0.188654i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.794945	−	1.83015i	−0.794945	−	1.83015i	−0.460065	−	0.887885i	$-0.652174\pi$
$211$	−0.794945	−	1.83015i	−0.794945	−	1.83015i	−0.334880	−	0.942261i	$-0.608696\pi$
$212$	1.39569	−	3.53924i	1.39569	−	3.53924i
$213$		0			0
$214$	−3.37795	−	0.464289i	−3.37795	−	0.464289i
$215$		0			0
$216$	1.34345	−	0.816970i	1.34345	−	0.816970i
$217$		0			0
$218$	0.329326	−	3.20346i	0.329326	−	3.20346i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$223$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$224$		0			0
$225$		0			0
$226$	0.380196	+	2.76613i	0.380196	+	2.76613i
$227$	0.231746	−	0.487293i	0.231746	−	0.487293i	−0.753713	−	0.657204i	$-0.771739\pi$
$227$	0.231746	−	0.487293i	0.231746	−	0.487293i	0.985460	+	0.169910i	$0.0543478\pi$
$228$	−1.53929	−	2.34683i	−1.53929	−	2.34683i
$229$	−0.180699	+	0.508438i	−0.180699	+	0.508438i	−0.997669	−	0.0682424i	$-0.978261\pi$
$229$	−0.180699	+	0.508438i	−0.180699	+	0.508438i	0.816970	+	0.576680i	$0.195652\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.253346	−	0.0999066i	0.253346	−	0.0999066i	−0.236764	−	0.971567i	$-0.576087\pi$
$233$	0.253346	−	0.0999066i	0.253346	−	0.0999066i	0.490110	+	0.871660i	$0.336957\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.44325	+	0.569146i	−1.44325	+	0.569146i
$238$		0			0
$239$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$239$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$240$		0			0
$241$	−0.663521	+	1.86697i	−0.663521	+	1.86697i	−0.203456	+	0.979084i	$0.565217\pi$
$241$	−0.663521	+	1.86697i	−0.663521	+	1.86697i	−0.460065	+	0.887885i	$0.652174\pi$
$242$	0.937216	+	1.42890i	0.937216	+	1.42890i
$243$	−0.429483	+	0.903075i	−0.429483	+	0.903075i
$244$	−0.503524	−	3.66341i	−0.503524	−	3.66341i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.972667	+	1.72989i	−0.972667	+	1.72989i
$249$	0.547173	+	0.386237i	0.547173	+	0.386237i
$250$		0			0
$251$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$251$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	1.86681	+	0.256587i	1.86681	+	0.256587i
$257$	0.592374	−	1.86642i	0.592374	−	1.86642i	0.102264	−	0.994757i	$-0.467391\pi$
$257$	0.592374	−	1.86642i	0.592374	−	1.86642i	0.490110	−	0.871660i	$-0.336957\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.78226	+	0.434326i	1.78226	+	0.434326i	0.985460	−	0.169910i	$-0.0543478\pi$
$263$	1.78226	+	0.434326i	1.78226	+	0.434326i	0.796805	+	0.604236i	$0.206522\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$269$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$270$		0			0
$271$	1.05893	+	0.861502i	1.05893	+	0.861502i	0.990686	−	0.136167i	$-0.0434783\pi$
$271$	1.05893	+	0.861502i	1.05893	+	0.861502i	0.0682424	+	0.997669i	$0.478261\pi$
$272$	0.307471	+	0.0530133i	0.307471	+	0.0530133i
$273$		0			0
$274$	1.07843	+	3.03440i	1.07843	+	3.03440i
$275$		0			0
$276$	1.44163	+	0.512354i	1.44163	+	0.512354i
$277$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$277$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$278$	3.03274	+	0.103601i	3.03274	+	0.103601i
$279$	−0.0861339	−	1.25923i	−0.0861339	−	1.25923i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	1.68399	+	0.290349i	1.68399	+	0.290349i
$283$		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
$288$	−0.236668	+	0.112554i	−0.236668	+	0.112554i
$289$	0.816970	+	0.169768i	0.816970	+	0.169768i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.03372	−	0.106270i	1.03372	−	0.106270i	0.429483	−	0.903075i	$-0.358696\pi$
$293$	1.03372	−	0.106270i	1.03372	−	0.106270i	0.604236	+	0.796805i	$0.293478\pi$
$294$	−1.24888	−	1.16637i	−1.24888	−	1.16637i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	0.505716	−	0.771025i	0.505716	−	0.771025i
$303$		0			0
$304$	−0.515625	−	0.995111i	−0.515625	−	0.995111i
$305$		0			0
$306$	−0.637780	+	0.277027i	−0.637780	+	0.277027i
$307$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$307$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$311$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$312$		0			0
$313$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$313$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$314$		0			0
$315$		0			0
$316$	−2.86847	+	0.803707i	−2.86847	+	0.803707i
$317$	1.99417	−	0.0681230i	1.99417	−	0.0681230i	0.994757	−	0.102264i	$-0.0326087\pi$
$317$	1.99417	−	0.0681230i	1.99417	−	0.0681230i	0.999417	+	0.0341411i	$0.0108696\pi$
$318$	0.346251	+	3.36809i	0.346251	+	3.36809i
$319$		0			0
$320$		0			0
$321$	1.88013	−	0.668198i	1.88013	−	0.668198i
$322$		0			0
$323$	0.255445	+	0.537123i	0.255445	+	0.537123i
$324$	−0.997669	+	1.64060i	−0.997669	+	1.64060i
$325$		0			0
$326$		0			0
$327$	0.691345	+	1.75313i	0.691345	+	1.75313i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.614311	−	0.266833i	−0.614311	−	0.266833i	0.0682424	−	0.997669i	$-0.478261\pi$
$331$	−0.614311	−	0.266833i	−0.614311	−	0.266833i	−0.682553	+	0.730836i	$0.739130\pi$
$332$	0.969294	+	0.845180i	0.969294	+	0.845180i
$333$		0			0
$334$	0.397624	+	0.241801i	0.397624	+	0.241801i
$335$		0			0
$336$		0			0
$337$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$337$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$338$	1.36161	+	1.03254i	1.36161	+	1.03254i
$339$	−0.942261	−	1.33488i	−0.942261	−	1.33488i
$340$		0			0
$341$		0			0
$342$	2.17720	+	1.22418i	2.17720	+	1.22418i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.52886	−	1.24382i	1.52886	−	1.24382i
$347$	−1.00534	+	0.565274i	−1.00534	+	0.565274i	−0.903075	−	0.429483i	$-0.858696\pi$
$347$	−1.00534	+	0.565274i	−1.00534	+	0.565274i	−0.102264	+	0.994757i	$0.532609\pi$
$348$		0			0
$349$	0.361291	+	1.73863i	0.361291	+	1.73863i	0.631088	+	0.775711i	$0.282609\pi$
$349$	0.361291	+	1.73863i	0.361291	+	1.73863i	−0.269797	+	0.962917i	$0.586957\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.26993	+	0.500795i	1.26993	+	0.500795i	0.903075	−	0.429483i	$-0.141304\pi$
$353$	1.26993	+	0.500795i	1.26993	+	0.500795i	0.366854	+	0.930278i	$0.380435\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$359$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$360$		0			0
$361$	0.522857	−	1.00907i	0.522857	−	1.00907i
$362$	−2.75154	+	0.474414i	−2.75154	+	0.474414i
$363$	−0.871660	−	0.490110i	−0.871660	−	0.490110i
$364$		0			0
$365$		0			0
$366$	1.89782	+	2.68860i	1.89782	+	2.68860i
$367$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$367$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$368$	0.551746	+	0.262399i	0.551746	+	0.262399i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.0827424	−	2.42213i	0.0827424	−	2.42213i
$373$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$373$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$374$		0			0
$375$		0			0
$376$	1.51405	+	0.424216i	1.51405	+	0.424216i
$377$		0			0
$378$		0			0
$379$	0.136167	−	0.00931405i	0.136167	−	0.00931405i		−	1.00000i	$-0.5\pi$
$379$	0.136167	−	0.00931405i	0.136167	−	0.00931405i	0.136167	+	0.990686i	$0.456522\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.964420	+	0.632563i	−0.964420	+	0.632563i	−0.930278	−	0.366854i	$-0.880435\pi$
$383$	−0.964420	+	0.632563i	−0.964420	+	0.632563i	−0.0341411	+	0.999417i	$0.510870\pi$
$384$	−1.70878	+	0.607301i	−1.70878	+	0.607301i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$389$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$390$		0			0
$391$	−0.287878	−	0.149166i	−0.287878	−	0.149166i
$392$	−1.03336	−	1.18510i	−1.03336	−	1.18510i
$393$		0			0
$394$	0.887885	−	3.16890i	0.887885	−	3.16890i
$395$		0			0
$396$		0			0
$397$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$397$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$398$	−0.443569	−	0.140782i	−0.443569	−	0.140782i
$399$		0			0
$400$		0			0
$401$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$401$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.609831	+	0.193552i	−0.609831	+	0.193552i
$409$	−1.02405	+	1.45075i	−1.02405	+	1.45075i	−0.136167	+	0.990686i	$0.543478\pi$
$409$	−1.02405	+	1.45075i	−1.02405	+	1.45075i	−0.887885	+	0.460065i	$0.847826\pi$
$410$		0			0
$411$	−1.37728	−	1.28629i	−1.37728	−	1.28629i
$412$		0			0
$413$		0			0
$414$	−1.34892	+	0.185405i	−1.34892	+	0.185405i
$415$		0			0
$416$		0			0
$417$	−1.60365	+	0.762664i	−1.60365	+	0.762664i
$418$		0			0
$419$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$419$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$420$		0			0
$421$	−0.794945	+	1.83015i	−0.794945	+	1.83015i	−0.334880	+	0.942261i	$0.608696\pi$
$421$	−0.794945	+	1.83015i	−0.794945	+	1.83015i	−0.460065	+	0.887885i	$0.652174\pi$
$422$	2.41103	+	2.41103i	2.41103	+	2.41103i
$423$	−0.953145	+	0.302515i	−0.953145	+	0.302515i
$424$			3.11542i			3.11542i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	3.72237	−	0.907117i	3.72237	−	0.907117i
$429$		0			0
$430$		0			0
$431$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$431$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$432$	−0.463310	+	0.610966i	−0.463310	+	0.610966i
$433$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$433$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$434$		0			0
$435$		0			0
$436$	0.976267	+	3.48434i	0.976267	+	3.48434i
$437$	0.197888	+	1.14773i	0.197888	+	1.14773i
$438$		0			0
$439$	0.668198	+	0.0457060i	0.668198	+	0.0457060i	0.398401	−	0.917211i	$-0.369565\pi$
$439$	0.668198	+	0.0457060i	0.668198	+	0.0457060i	0.269797	+	0.962917i	$0.413043\pi$
$440$		0			0
$441$	0.962917	+	0.269797i	0.962917	+	0.269797i
$442$		0			0
$443$	−1.57580	−	1.03357i	−1.57580	−	1.03357i	−0.971567	−	0.236764i	$-0.923913\pi$
$443$	−1.57580	−	1.03357i	−1.57580	−	1.03357i	−0.604236	−	0.796805i	$-0.706522\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$449$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$450$		0			0
$451$		0			0
$452$	−1.53766	−	2.73473i	−1.53766	−	2.73473i
$453$	−0.0551811	+	0.536765i	−0.0551811	+	0.536765i
$454$	−0.0629249	+	0.919929i	−0.0629249	+	0.919929i
$455$		0			0
$456$	1.87761	+	1.32536i	1.87761	+	1.32536i
$457$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$457$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$458$	−0.0314808	−	0.921541i	−0.0314808	−	0.921541i
$459$	0.256797	−	0.315646i	0.256797	−	0.315646i
$460$		0			0
$461$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$461$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$462$		0			0
$463$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$463$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$464$		0			0
$465$		0			0
$466$	−0.340112	+	0.317642i	−0.340112	+	0.317642i
$467$	1.16704	−	1.33842i	1.16704	−	1.33842i	0.236764	−	0.971567i	$-0.423913\pi$
$467$	1.16704	−	1.33842i	1.16704	−	1.33842i	0.930278	−	0.366854i	$-0.119565\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	1.93754	−	1.80954i	1.93754	−	1.80954i
$475$		0			0
$476$		0			0
$477$	−1.08669	−	1.65679i	−1.08669	−	1.65679i
$478$		0			0
$479$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$479$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$480$		0			0
$481$		0			0
$482$	−0.115597	−	3.38387i	−0.115597	−	3.38387i
$483$		0			0
$484$	−1.56869	−	1.10730i	−1.56869	−	1.10730i
$485$		0			0
$486$	0.116615	−	1.70486i	0.116615	−	1.70486i
$487$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$487$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$488$	1.48410	+	2.63947i	1.48410	+	2.63947i
$489$		0			0
$490$		0			0
$491$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$491$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.131782	−	0.958784i	0.131782	−	0.958784i
$497$		0			0
$498$	−1.11197	−	0.270979i	−1.11197	−	0.270979i
$499$	0.767255	+	0.214975i	0.767255	+	0.214975i	0.631088	−	0.775711i	$-0.282609\pi$
$499$	0.767255	+	0.214975i	0.767255	+	0.214975i	0.136167	+	0.990686i	$0.456522\pi$
$500$		0			0
$501$	−0.271698	−	0.0185847i	−0.271698	−	0.0185847i
$502$		0			0
$503$	0.176565	+	1.02406i	0.176565	+	1.02406i	0.930278	+	0.366854i	$0.119565\pi$
$503$	0.176565	+	1.02406i	0.176565	+	1.02406i	−0.753713	+	0.657204i	$0.771739\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.985460	−	0.169910i	−0.985460	−	0.169910i
$508$		0			0
$509$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$509$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$510$		0			0
$511$		0			0
$512$	−1.36659	+	0.333028i	−1.36659	+	0.333028i
$513$	−1.46082	−	0.0499031i	−1.46082	−	0.0499031i
$514$	0.228352	+	3.33839i	0.228352	+	3.33839i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.459500	+	1.05788i	−0.459500	+	1.05788i
$520$		0			0
$521$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$521$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$522$		0			0
$523$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$523$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$524$		0			0
$525$		0			0
$526$	−3.10554	+	0.426846i	−3.10554	+	0.426846i
$527$	−0.0872650	+	0.506127i	−0.0872650	+	0.506127i
$528$		0			0
$529$	0.266833	+	0.249204i	0.266833	+	0.249204i
$530$		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
$541$	1.42298	−	0.618088i	1.42298	−	0.618088i	0.460065	−	0.887885i	$-0.347826\pi$
$541$	1.42298	−	0.618088i	1.42298	−	0.618088i	0.962917	+	0.269797i	$0.0869565\pi$
$542$	−2.22345	−	0.705690i	−2.22345	−	0.705690i
$543$	1.30193	−	0.987286i	1.30193	−	0.987286i
$544$	0.104408	−	0.0216963i	0.104408	−	0.0216963i
$545$		0			0
$546$		0			0
$547$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$547$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$548$	−2.37811	−	2.72733i	−2.37811	−	2.72733i
$549$	−1.70992	−	0.886009i	−1.70992	−	0.886009i
$550$		0			0
$551$		0			0
$552$	−1.25212	+	0.0427739i	−1.25212	+	0.0427739i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−3.21284	+	1.14184i	−3.21284	+	1.14184i
$557$	−1.63739	+	1.07396i	−1.63739	+	1.07396i	−0.707107	+	0.707107i	$0.750000\pi$
$557$	−1.63739	+	1.07396i	−1.63739	+	1.07396i	−0.930278	+	0.366854i	$0.880435\pi$
$558$	0.926334	+	1.94780i	0.926334	+	1.94780i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.38463	+	1.38463i	−1.38463	+	1.38463i	−0.548452	+	0.836182i	$0.684783\pi$
$563$	−1.38463	+	1.38463i	−1.38463	+	1.38463i	−0.836182	+	0.548452i	$0.815217\pi$
$564$	−1.87997	+	0.390662i	−1.87997	+	0.390662i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$569$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$570$		0			0
$571$	0.277739	−	1.33655i	0.277739	−	1.33655i	−0.576680	−	0.816970i	$-0.695652\pi$
$571$	0.277739	−	1.33655i	0.277739	−	1.33655i	0.854419	−	0.519584i	$-0.173913\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.829031	−	0.887675i	0.829031	−	0.887675i
$577$		0			0		−0.871660	−	0.490110i	$-0.836957\pi$
$577$		0			0		0.871660	+	0.490110i	$0.163043\pi$
$578$	−1.40516	+	0.242274i	−1.40516	+	0.242274i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.57668	+	0.816970i	−1.57668	+	0.816970i
$587$	−1.35976	−	0.536221i	−1.35976	−	0.536221i	−0.429483	−	0.903075i	$-0.641304\pi$
$587$	−1.35976	−	0.536221i	−1.35976	−	0.536221i	−0.930278	+	0.366854i	$0.880435\pi$
$588$	1.78626	+	0.704408i	1.78626	+	0.704408i
$589$	1.63805	−	0.848768i	1.63805	−	0.848768i
$590$		0			0
$591$	0.391823	+	1.88555i	0.391823	+	1.88555i
$592$		0			0
$593$	−0.905802	+	0.509307i	−0.905802	+	0.509307i	−0.871660	−	0.490110i	$-0.836957\pi$
$593$	−0.905802	+	0.509307i	−0.905802	+	0.509307i	−0.0341411	+	0.999417i	$0.510870\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.268373	−	0.0462723i	0.268373	−	0.0462723i
$598$		0			0
$599$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$599$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$600$		0			0
$601$	−0.665120	−	0.942261i	−0.665120	−	0.942261i	0.334880	−	0.942261i	$-0.391304\pi$
$601$	−0.665120	−	0.942261i	−0.665120	−	0.942261i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	−0.210799	+	1.01442i	−0.210799	+	1.01442i
$605$		0			0
$606$		0			0
$607$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$607$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$608$	−0.288716	−	0.251747i	−0.288716	−	0.251747i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.552480	−	0.552480i	0.552480	−	0.552480i
$613$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$613$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.666310	−	1.40105i	−0.666310	−	1.40105i	−0.903075	−	0.429483i	$-0.858696\pi$
$617$	−0.666310	−	1.40105i	−0.666310	−	1.40105i	0.236764	−	0.971567i	$-0.423913\pi$
$618$		0			0
$619$	−1.81464	+	0.644923i	−1.81464	+	0.644923i	−0.816970	+	0.576680i	$0.804348\pi$
$619$	−1.81464	+	0.644923i	−1.81464	+	0.644923i	−0.997669	+	0.0682424i	$0.978261\pi$
$620$		0			0
$621$	0.650963	−	0.459500i	0.650963	−	0.459500i
$622$		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
$631$	0.780136	−	0.162114i	0.780136	−	0.162114i	0.203456	−	0.979084i	$-0.434783\pi$
$631$	0.780136	−	0.162114i	0.780136	−	0.162114i	0.576680	+	0.816970i	$0.304348\pi$
$632$	1.94371	−	1.47397i	1.94371	−	1.47397i
$633$	−1.90185	−	0.603619i	−1.90185	−	0.603619i
$634$	−3.12742	+	1.35843i	−3.12742	+	1.35843i
$635$		0			0
$636$	−1.75031	−	3.37795i	−1.75031	−	3.37795i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$641$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$642$	−2.56994	+	2.24087i	−2.56994	+	2.24087i
$643$		0			0		0.953145	−	0.302515i	$-0.0978261\pi$
$643$		0			0		−0.953145	+	0.302515i	$0.902174\pi$
$644$		0			0
$645$		0			0
$646$	−0.742799	−	0.693726i	−0.742799	−	0.693726i
$647$	−1.97098	+	0.202623i	−1.97098	+	0.202623i	−0.999417	−	0.0341411i	$-0.989130\pi$
$647$	−1.97098	+	0.202623i	−1.97098	+	0.202623i	−0.971567	+	0.236764i	$0.923913\pi$
$648$	0.267159	−	1.54949i	0.267159	−	1.54949i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.323209	+	1.32629i	0.323209	+	1.32629i	0.871660	+	0.490110i	$0.163043\pi$
$653$	0.323209	+	1.32629i	0.323209	+	1.32629i	−0.548452	+	0.836182i	$0.684783\pi$
$654$	−2.19806	−	2.35354i	−2.19806	−	2.35354i
$655$		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
$661$	0.0277687	+	0.405963i	0.0277687	+	0.405963i	0.990686	+	0.136167i	$0.0434783\pi$
$661$	0.0277687	+	0.405963i	0.0277687	+	0.405963i	−0.962917	+	0.269797i	$0.913043\pi$
$662$	1.14384	+	0.0390749i	1.14384	+	0.0390749i
$663$		0			0
$664$	−0.992294	−	0.352661i	−0.992294	−	0.352661i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.515312	−	0.0888487i	−0.515312	−	0.0888487i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$673$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$674$		0			0
$675$		0			0
$676$	−1.84893	−	0.518045i	−1.84893	−	0.518045i
$677$	1.72528	+	0.420439i	1.72528	+	0.420439i	0.971567	−	0.236764i	$-0.0760870\pi$
$677$	1.72528	+	0.420439i	1.72528	+	0.420439i	0.753713	+	0.657204i	$0.228261\pi$
$678$	2.33474	+	1.53135i	2.33474	+	1.53135i
$679$		0			0
$680$		0			0
$681$	−0.214975	−	0.494921i	−0.214975	−	0.494921i
$682$		0			0
$683$	−0.554940	+	1.74847i	−0.554940	+	1.74847i	0.102264	+	0.994757i	$0.467391\pi$
$683$	−0.554940	+	1.74847i	−0.554940	+	1.74847i	−0.657204	+	0.753713i	$0.728261\pi$
$684$	−2.78046	−	0.382165i	−2.78046	−	0.382165i
$685$		0			0
$686$		0			0
$687$	0.264460	+	0.470342i	0.264460	+	0.470342i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−1.59976	−	1.12924i	−1.59976	−	1.12924i	−0.917211	−	0.398401i	$-0.869565\pi$
$691$	−1.59976	−	1.12924i	−1.59976	−	1.12924i	−0.682553	−	0.730836i	$-0.739130\pi$
$692$	−1.08540	+	1.93038i	−1.08540	+	1.93038i
$693$		0			0
$694$	1.24382	−	1.52886i	1.24382	−	1.52886i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−1.66428	−	2.53740i	−1.66428	−	2.53740i
$699$	0.0911989	−	0.256609i	0.0911989	−	0.256609i
$700$		0			0
$701$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$701$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−2.33275			−2.33275
$707$		0			0
$708$		0			0
$709$	−1.34066	+	1.25209i	−1.34066	+	1.25209i	−0.398401	+	0.917211i	$0.630435\pi$
$709$	−1.34066	+	1.25209i	−1.34066	+	1.25209i	−0.942261	+	0.334880i	$0.891304\pi$
$710$		0			0
$711$	−0.519540	+	1.46184i	−0.519540	+	1.46184i
$712$		0			0
$713$	−0.431933	+	0.908226i	−0.431933	+	0.908226i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$719$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$720$		0			0
$721$		0			0
$722$	−0.198604	+	1.93189i	−0.198604	+	1.93189i
$723$	0.971091	+	1.72708i	0.971091	+	1.72708i
$724$	2.68064	−	1.63013i	2.68064	−	1.63013i
$725$		0			0
$726$	1.69292	+	0.232687i	1.69292	+	0.232687i
$727$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$727$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$728$		0			0
$729$	0.398401	+	0.917211i	0.398401	+	0.917211i
$730$		0			0
$731$		0			0
$732$	−3.09208	−	2.02809i	−3.09208	−	2.02809i
$733$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$733$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$734$		0			0
$735$		0			0
$736$	0.208330	+	0.0142502i	0.208330	+	0.0142502i
$737$		0			0
$738$		0			0
$739$	−0.311173	−	1.11059i	−0.311173	−	1.11059i	−0.942261	−	0.334880i	$-0.891304\pi$
$739$	−0.311173	−	1.11059i	−0.311173	−	1.11059i	0.631088	−	0.775711i	$-0.282609\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.883195	+	1.16467i	−0.883195	+	1.16467i	0.102264	+	0.994757i	$0.467391\pi$
$743$	−0.883195	+	1.16467i	−0.883195	+	1.16467i	−0.985460	+	0.169910i	$0.945652\pi$
$744$	0.664598	+	1.87000i	0.664598	+	1.87000i
$745$		0			0
$746$		0			0
$747$	0.650716	−	0.158575i	0.650716	−	0.158575i
$748$		0			0
$749$		0			0
$750$		0			0
$751$			1.99534i			1.99534i	0.0682424	+	0.997669i	$0.478261\pi$
$751$			1.99534i			1.99534i	−0.0682424	+	0.997669i	$0.521739\pi$
$752$	−0.762749	+	0.0784130i	−0.762749	+	0.0784130i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$757$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$758$	−0.210625	+	0.100169i	−0.210625	+	0.100169i
$759$		0			0
$760$		0			0
$761$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$761$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	1.13658	−	1.61017i	1.13658	−	1.61017i
$767$		0			0
$768$	1.42027	−	1.23841i	1.42027	−	1.23841i
$769$	0.256797	+	0.315646i	0.256797	+	0.315646i	0.887885	−	0.460065i	$-0.152174\pi$
$769$	0.256797	+	0.315646i	0.256797	+	0.315646i	−0.631088	+	0.775711i	$0.717391\pi$
$770$		0			0
$771$	−1.01743	−	1.67310i	−1.01743	−	1.67310i
$772$		0			0
$773$	0.555976	+	0.733164i	0.555976	+	0.733164i	0.985460	−	0.169910i	$-0.0543478\pi$
$773$	0.555976	+	0.733164i	0.555976	+	0.733164i	−0.429483	+	0.903075i	$0.641304\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.551149	+	0.0566599i	0.551149	+	0.0566599i
$783$		0			0
$784$	0.680803	+	0.352764i	0.680803	+	0.352764i
$785$		0			0
$786$		0			0
$787$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$787$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$788$	0.378158	+	3.67847i	0.378158	+	3.67847i
$789$	1.49867	−	1.05788i	1.49867	−	1.05788i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.521696	−	0.0356850i	0.521696	−	0.0356850i
$797$	0.651449	+	1.65196i	0.651449	+	1.65196i	0.753713	+	0.657204i	$0.228261\pi$
$797$	0.651449	+	1.65196i	0.651449	+	1.65196i	−0.102264	+	0.994757i	$0.532609\pi$
$798$		0			0
$799$	0.405963	−	0.0277687i	0.405963	−	0.0277687i
$800$		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		−0.576680	−	0.816970i	$-0.695652\pi$
$809$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$810$		0			0
$811$	−0.787230	+	0.842917i	−0.787230	+	0.842917i	−0.990686	−	0.136167i	$-0.956522\pi$
$811$	−0.787230	+	0.842917i	−0.787230	+	0.842917i	0.203456	+	0.979084i	$0.434783\pi$
$812$		0			0
$813$	1.34526	−	0.231946i	1.34526	−	0.231946i
$814$		0			0
$815$		0			0
$816$	0.242028	−	0.196904i	0.242028	−	0.196904i
$817$		0			0
$818$	0.718463	−	2.94823i	0.718463	−	2.94823i
$819$		0			0
$820$		0			0
$821$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$821$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$822$	2.99582	+	1.18140i	2.99582	+	1.18140i
$823$		0			0		−0.930278	−	0.366854i	$-0.880435\pi$
$823$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.217854	+	0.893968i	−0.217854	+	0.893968i	0.753713	+	0.657204i	$0.228261\pi$
$827$	−0.217854	+	0.893968i	−0.217854	+	0.893968i	−0.971567	+	0.236764i	$0.923913\pi$
$828$	1.33361	−	0.749851i	1.33361	−	0.749851i
$829$	0.806094	−	0.655806i	0.806094	−	0.655806i	−0.136167	−	0.990686i	$-0.543478\pi$
$829$	0.806094	−	0.655806i	0.806094	−	0.655806i	0.942261	+	0.334880i	$0.108696\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.354689	−	0.199432i	−0.354689	−	0.199432i
$834$	2.07121	−	2.21773i	2.07121	−	2.21773i
$835$		0			0
$836$		0			0
$837$	−1.00571	−	0.762653i	−1.00571	−	0.762653i
$838$		0			0
$839$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$839$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$840$		0			0
$841$	0.854419	+	0.519584i	0.854419	+	0.519584i
$842$	0.116411	−	3.40772i	0.116411	−	3.40772i
$843$		0			0
$844$	−3.51412	−	1.52640i	−3.51412	−	1.52640i
$845$		0			0
$846$	1.32557	−	1.07843i	1.32557	−	1.07843i
$847$		0			0
$848$	−0.557345	−	1.41333i	−0.557345	−	1.41333i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$853$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$854$		0			0
$855$		0			0
$856$	−2.56314	+	1.80926i	−2.56314	+	1.80926i
$857$	0.204051	+	1.98488i	0.204051	+	1.98488i	0.169910	+	0.985460i	$0.445652\pi$
$857$	0.204051	+	1.98488i	0.204051	+	1.98488i	0.0341411	+	0.999417i	$0.489130\pi$
$858$		0			0
$859$	1.00063	−	0.280364i	1.00063	−	0.280364i	0.269797	−	0.962917i	$-0.413043\pi$
$859$	1.00063	−	0.280364i	1.00063	−	0.280364i	0.730836	+	0.682553i	$0.239130\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.54329	−	0.158655i	−1.54329	−	0.158655i	−0.707107	−	0.707107i	$-0.750000\pi$
$863$	−1.54329	−	0.158655i	−1.54329	−	0.158655i	−0.836182	+	0.548452i	$0.815217\pi$
$864$	−0.0707053	+	0.252350i	−0.0707053	+	0.252350i
$865$		0			0
$866$		0			0
$867$	0.664872	−	0.504189i	0.664872	−	0.504189i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.79043	−	2.36104i	−1.79043	−	2.36104i
$873$		0			0
$874$	−1.03409	−	1.70048i	−1.03409	−	1.70048i
$875$		0			0
$876$		0			0
$877$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$877$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$878$	−1.09088	+	0.346231i	−1.09088	+	0.346231i
$879$	0.599268	−	0.848969i	0.599268	−	0.848969i
$880$		0			0
$881$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$881$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$882$	−1.69988	+	0.174753i	−1.69988	+	0.174753i
$883$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$883$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$884$		0			0
$885$		0			0
$886$	3.15299	+	0.655198i	3.15299	+	0.655198i
$887$	−1.32000	+	0.627764i	−1.32000	+	0.627764i	−0.953145	−	0.302515i	$-0.902174\pi$
$887$	−1.32000	+	0.627764i	−1.32000	+	0.627764i	−0.366854	+	0.930278i	$0.619565\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.960616	−	1.10168i	−0.960616	−	1.10168i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.269995	+	0.759692i	0.269995	+	0.759692i
$902$		0			0
$903$		0			0
$904$	1.99290	+	1.62135i	1.99290	+	1.62135i
$905$		0			0
$906$	−0.248774	−	0.887885i	−0.248774	−	0.887885i
$907$		0			0		−0.169910	−	0.985460i	$-0.554348\pi$
$907$		0			0		0.169910	+	0.985460i	$0.445652\pi$
$908$	−0.313432	−	0.987544i	−0.313432	−	0.987544i
$909$		0			0
$910$		0			0
$911$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$911$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$912$	−1.08890	−	0.265357i	−1.08890	−	0.265357i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.412779	+	0.950313i	0.412779	+	0.950313i
$917$		0			0
$918$	−0.210353	+	0.662766i	−0.210353	+	0.662766i
$919$	−0.789381	−	0.108498i	−0.789381	−	0.108498i	−0.269797	−	0.962917i	$-0.586957\pi$
$919$	−0.789381	−	0.108498i	−0.789381	−	0.108498i	−0.519584	+	0.854419i	$0.673913\pi$
$920$		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		0.631088	−	0.775711i	$-0.282609\pi$
$929$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$930$		0			0
$931$	0.199031	+	1.44806i	0.199031	+	1.44806i
$932$	0.224583	−	0.472232i	0.224583	−	0.472232i
$933$		0			0
$934$	−1.01619	+	2.85930i	−1.01619	+	2.85930i
$935$		0			0
$936$		0			0
$937$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$937$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$938$		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
$947$	0.504647	+	0.769396i	0.504647	+	0.769396i	0.994757	−	0.102264i	$-0.0326087\pi$
$947$	0.504647	+	0.769396i	0.504647	+	0.769396i	−0.490110	+	0.871660i	$0.663043\pi$
$948$	−1.27940	+	2.69020i	−1.27940	+	2.69020i
$949$		0			0
$950$		0			0
$951$	1.25923	−	1.54781i	1.25923	−	1.54781i
$952$		0			0
$953$	0.509307	−	0.905802i	0.509307	−	0.905802i	−0.490110	−	0.871660i	$-0.663043\pi$
$953$	0.509307	−	0.905802i	0.509307	−	0.905802i	0.999417	−	0.0341411i	$-0.0108696\pi$
$954$	2.76613	+	1.95255i	2.76613	+	1.95255i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.587564	+	0.0807588i	0.587564	+	0.0807588i
$962$		0			0
$963$	0.731998	−	1.85622i	0.731998	−	1.85622i
$964$	1.51571	+	3.48952i	1.51571	+	3.48952i
$965$		0			0
$966$		0			0
$967$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$967$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$968$	1.52765	+	0.372277i	1.52765	+	0.372277i
$969$	0.572716	+	0.160468i	0.572716	+	0.160468i
$970$		0			0
$971$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$971$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$972$	0.580867	+	1.83016i	0.580867	+	1.83016i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−1.14547	−	0.931909i	−1.14547	−	0.931909i
$977$	1.13659	+	0.195968i	1.13659	+	0.195968i	0.707107	−	0.707107i	$-0.250000\pi$
$977$	1.13659	+	0.195968i	1.13659	+	0.195968i	0.429483	+	0.903075i	$0.358696\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.77571	+	0.631088i	1.77571	+	0.631088i
$982$		0			0
$983$	−0.539279	−	0.0184223i	−0.539279	−	0.0184223i	−0.236764	−	0.971567i	$-0.576087\pi$
$983$	−0.539279	−	0.0184223i	−0.539279	−	0.0184223i	−0.302515	+	0.953145i	$0.597826\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.0931581	−	0.0997480i	−0.0931581	−	0.0997480i	0.682553	−	0.730836i	$-0.260870\pi$
$991$	−0.0931581	−	0.0997480i	−0.0931581	−	0.0997480i	−0.775711	+	0.631088i	$0.782609\pi$
$992$	−0.0783162	−	0.321372i	−0.0783162	−	0.321372i
$993$	−0.604843	+	0.287650i	−0.604843	+	0.287650i
$994$		0			0
$995$		0			0
$996$	1.27405	−	0.175114i	1.27405	−	0.175114i
$997$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$997$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$998$	−1.35447	+	0.139244i	−1.35447	+	0.139244i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.932.1	yes	88
3.2	odd	2	inner	3525.1.bg.a.932.2	yes	88
5.2	odd	4	inner	3525.1.bg.a.368.1	yes	88
5.3	odd	4	inner	3525.1.bg.a.368.2	yes	88
5.4	even	2	inner	3525.1.bg.a.932.2	yes	88
15.2	even	4	inner	3525.1.bg.a.368.2	yes	88
15.8	even	4	inner	3525.1.bg.a.368.1	yes	88
15.14	odd	2	CM	3525.1.bg.a.932.1	yes	88
47.41	odd	46	inner	3525.1.bg.a.182.1	✓	88
141.41	even	46	inner	3525.1.bg.a.182.2	yes	88
235.88	even	92	inner	3525.1.bg.a.3143.2	yes	88
235.182	even	92	inner	3525.1.bg.a.3143.1	yes	88
235.229	odd	46	inner	3525.1.bg.a.182.2	yes	88
705.182	odd	92	inner	3525.1.bg.a.3143.2	yes	88
705.323	odd	92	inner	3525.1.bg.a.3143.1	yes	88
705.464	even	46	inner	3525.1.bg.a.182.1	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.182.1	✓	88	47.41	odd	46	inner
3525.1.bg.a.182.1	✓	88	705.464	even	46	inner
3525.1.bg.a.182.2	yes	88	141.41	even	46	inner
3525.1.bg.a.182.2	yes	88	235.229	odd	46	inner
3525.1.bg.a.368.1	yes	88	5.2	odd	4	inner
3525.1.bg.a.368.1	yes	88	15.8	even	4	inner
3525.1.bg.a.368.2	yes	88	5.3	odd	4	inner
3525.1.bg.a.368.2	yes	88	15.2	even	4	inner
3525.1.bg.a.932.1	yes	88	1.1	even	1	trivial
3525.1.bg.a.932.1	yes	88	15.14	odd	2	CM
3525.1.bg.a.932.2	yes	88	3.2	odd	2	inner
3525.1.bg.a.932.2	yes	88	5.4	even	2	inner
3525.1.bg.a.3143.1	yes	88	235.182	even	92	inner
3525.1.bg.a.3143.1	yes	88	705.323	odd	92	inner
3525.1.bg.a.3143.2	yes	88	235.88	even	92	inner
3525.1.bg.a.3143.2	yes	88	705.182	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)

\(f(q)\)	\(=\)	\(q+(-1.58970 + 0.626895i) q^{2} +(0.657204 - 0.753713i) q^{3} +(1.40330 - 1.31059i) q^{4} +(-0.572255 + 1.61017i) q^{6} +(-0.675300 + 1.41995i) q^{8} +(-0.136167 - 0.990686i) q^{9} +O(q^{10})\)	\(q+(-1.58970 + 0.626895i) q^{2} +(0.657204 - 0.753713i) q^{3} +(1.40330 - 1.31059i) q^{4} +(-0.572255 + 1.61017i) q^{6} +(-0.675300 + 1.41995i) q^{8} +(-0.136167 - 0.990686i) q^{9} +(-0.0655554 - 1.91901i) q^{12} +(0.0523262 - 0.764982i) q^{16} +(-0.0416125 + 0.404779i) q^{17} +(0.837519 + 1.48953i) q^{18} +(1.24888 - 0.759461i) q^{19} +(-0.292310 + 0.741248i) q^{23} +(0.626428 + 1.44218i) q^{24} +(-0.836182 - 0.548452i) q^{27} +(1.25923 + 0.0861339i) q^{31} +(-0.0792796 - 0.249789i) q^{32} +(-0.187602 - 0.669562i) q^{34} +(-1.48947 - 1.21177i) q^{36} +(-1.50924 + 1.99023i) q^{38} -1.36161i q^{46} +(-0.169910 - 0.985460i) q^{47} +(-0.542188 - 0.542188i) q^{48} +(-0.398401 + 0.917211i) q^{49} +(0.277739 + 0.297386i) q^{51} +(1.78933 - 0.850966i) q^{53} +(1.67310 + 0.347674i) q^{54} +(0.248353 - 1.44042i) q^{57} +(1.11059 - 1.57335i) q^{61} +(-2.05580 + 0.652480i) q^{62} +(0.766521 + 0.942181i) q^{64} +(0.472104 + 0.622563i) q^{68} +(0.366581 + 0.707469i) q^{69} +(1.49868 + 0.475660i) q^{72} +(0.757212 - 2.70252i) q^{76} +(-1.37749 - 0.713755i) q^{79} +(-0.962917 + 0.269797i) q^{81} +(0.0684924 + 0.666248i) q^{83} +(0.561274 + 1.42329i) q^{92} +(0.892493 - 0.892493i) q^{93} +(0.887885 + 1.46007i) q^{94} +(-0.240372 - 0.104408i) q^{96} +(0.0583417 - 1.70784i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more