LMFDB - Embedded newform 3525.1.bg.a.407.2

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			407.2
Root			$-0.971567 + 0.236764i$ of defining polynomial
Character	$\chi$	$=$	3525.407
Dual form			3525.1.bg.a.2018.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.395342 - 0.0963423i) q^{2} +(0.169910 - 0.985460i) q^{3} +(-0.740871 + 0.383889i) q^{4} +(-0.0277687 - 0.405963i) q^{6} +(-0.562608 + 0.490569i) q^{8} +(-0.942261 - 0.334880i) q^{9} +O(q^{10})$	\(q+(0.395342 - 0.0963423i) q^{2} +(0.169910 - 0.985460i) q^{3} +(-0.740871 + 0.383889i) q^{4} +(-0.0277687 - 0.405963i) q^{6} +(-0.562608 + 0.490569i) q^{8} +(-0.942261 - 0.334880i) q^{9} +(0.252425 + 0.795326i) q^{12} +(0.306035 - 0.433553i) q^{16} +(-1.53451 + 1.16366i) q^{17} +(-0.404779 - 0.0416125i) q^{18} +(0.361291 + 1.73863i) q^{19} +(-0.246038 + 1.00962i) q^{23} +(0.387843 + 0.637780i) q^{24} +(-0.490110 + 0.871660i) q^{27} +(-0.222488 - 0.157049i) q^{31} +(0.353057 - 0.895291i) q^{32} +(-0.494549 + 0.607882i) q^{34} +(0.826651 - 0.113621i) q^{36} +(0.310337 + 0.652546i) q^{38} +0.422850i q^{46} +(-0.999417 - 0.0341411i) q^{47} +(-0.375250 - 0.375250i) q^{48} +(0.519584 - 0.854419i) q^{49} +(0.886009 + 1.70992i) q^{51} +(-0.440168 + 0.504806i) q^{53} +(-0.109784 + 0.391823i) q^{54} +(1.77474 - 0.0606268i) q^{57} +(1.05893 + 1.13384i) q^{61} +(-0.103089 - 0.0406532i) q^{62} +(-0.0189375 + 0.137780i) q^{64} +(0.690163 - 1.45120i) q^{68} +(0.953137 + 0.414006i) q^{69} +(0.694405 - 0.273838i) q^{72} +(-0.935110 - 1.14940i) q^{76} +(0.789381 + 1.81734i) q^{79} +(0.775711 + 0.631088i) q^{81} +(0.108752 + 0.0824691i) q^{83} +(-0.205300 - 0.842451i) q^{92} +(-0.192569 + 0.192569i) q^{93} +(-0.398401 + 0.0827887i) q^{94} +(-0.822285 - 0.500042i) q^{96} +(0.123097 - 0.387846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.395342	−	0.0963423i	0.395342	−	0.0963423i	−0.0341411	−	0.999417i	$-0.510870\pi$
$2$	0.395342	−	0.0963423i	0.395342	−	0.0963423i	0.429483	+	0.903075i	$0.358696\pi$
$3$	0.169910	−	0.985460i	0.169910	−	0.985460i
$3$	0.169910	−	0.985460i	0.169910	−	0.985460i
$4$	−0.740871	+	0.383889i	−0.740871	+	0.383889i
$5$		0			0
$5$		0			0
$6$	−0.0277687	−	0.405963i	−0.0277687	−	0.405963i
$7$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$7$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$8$	−0.562608	+	0.490569i	−0.562608	+	0.490569i
$9$	−0.942261	−	0.334880i	−0.942261	−	0.334880i
$10$		0			0
$11$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$11$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$12$	0.252425	+	0.795326i	0.252425	+	0.795326i
$13$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$13$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$14$		0			0
$15$		0			0
$16$	0.306035	−	0.433553i	0.306035	−	0.433553i
$17$	−1.53451	+	1.16366i	−1.53451	+	1.16366i	−0.604236	+	0.796805i	$0.706522\pi$
$17$	−1.53451	+	1.16366i	−1.53451	+	1.16366i	−0.930278	+	0.366854i	$0.880435\pi$
$18$	−0.404779	−	0.0416125i	−0.404779	−	0.0416125i
$19$	0.361291	+	1.73863i	0.361291	+	1.73863i	0.631088	+	0.775711i	$0.282609\pi$
$19$	0.361291	+	1.73863i	0.361291	+	1.73863i	−0.269797	+	0.962917i	$0.586957\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.246038	+	1.00962i	−0.246038	+	1.00962i	0.707107	+	0.707107i	$0.250000\pi$
$23$	−0.246038	+	1.00962i	−0.246038	+	1.00962i	−0.953145	+	0.302515i	$0.902174\pi$
$24$	0.387843	+	0.637780i	0.387843	+	0.637780i
$25$		0			0
$26$		0			0
$27$	−0.490110	+	0.871660i	−0.490110	+	0.871660i
$28$		0			0
$29$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$29$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$30$		0			0
$31$	−0.222488	−	0.157049i	−0.222488	−	0.157049i	0.460065	−	0.887885i	$-0.347826\pi$
$31$	−0.222488	−	0.157049i	−0.222488	−	0.157049i	−0.682553	+	0.730836i	$0.739130\pi$
$32$	0.353057	−	0.895291i	0.353057	−	0.895291i
$33$		0			0
$34$	−0.494549	+	0.607882i	−0.494549	+	0.607882i
$35$		0			0
$36$	0.826651	−	0.113621i	0.826651	−	0.113621i
$37$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$37$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$38$	0.310337	+	0.652546i	0.310337	+	0.652546i
$39$		0			0
$40$		0			0
$41$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$41$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$42$		0			0
$43$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$43$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$44$		0			0
$45$		0			0
$46$			0.422850i			0.422850i
$47$	−0.999417	−	0.0341411i	−0.999417	−	0.0341411i
$47$	−0.999417	−	0.0341411i	−0.999417	−	0.0341411i
$48$	−0.375250	−	0.375250i	−0.375250	−	0.375250i
$49$	0.519584	−	0.854419i	0.519584	−	0.854419i
$50$		0			0
$51$	0.886009	+	1.70992i	0.886009	+	1.70992i
$52$		0			0
$53$	−0.440168	+	0.504806i	−0.440168	+	0.504806i	−0.930278	−	0.366854i	$-0.880435\pi$
$53$	−0.440168	+	0.504806i	−0.440168	+	0.504806i	0.490110	+	0.871660i	$0.336957\pi$
$54$	−0.109784	+	0.391823i	−0.109784	+	0.391823i
$55$		0			0
$56$		0			0
$57$	1.77474	−	0.0606268i	1.77474	−	0.0606268i
$58$		0			0
$59$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$59$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$60$		0			0
$61$	1.05893	+	1.13384i	1.05893	+	1.13384i	0.990686	+	0.136167i	$0.0434783\pi$
$61$	1.05893	+	1.13384i	1.05893	+	1.13384i	0.0682424	+	0.997669i	$0.478261\pi$
$62$	−0.103089	−	0.0406532i	−0.103089	−	0.0406532i
$63$		0			0
$64$	−0.0189375	+	0.137780i	−0.0189375	+	0.137780i
$65$		0			0
$66$		0			0
$67$		0			0		−0.871660	−	0.490110i	$-0.836957\pi$
$67$		0			0		0.871660	+	0.490110i	$0.163043\pi$
$68$	0.690163	−	1.45120i	0.690163	−	1.45120i
$69$	0.953137	+	0.414006i	0.953137	+	0.414006i
$70$		0			0
$71$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$71$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$72$	0.694405	−	0.273838i	0.694405	−	0.273838i
$73$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$73$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$74$		0			0
$75$		0			0
$76$	−0.935110	−	1.14940i	−0.935110	−	1.14940i
$77$		0			0
$78$		0			0
$79$	0.789381	+	1.81734i	0.789381	+	1.81734i	0.519584	+	0.854419i	$0.326087\pi$
$79$	0.789381	+	1.81734i	0.789381	+	1.81734i	0.269797	+	0.962917i	$0.413043\pi$
$80$		0			0
$81$	0.775711	+	0.631088i	0.775711	+	0.631088i
$82$		0			0
$83$	0.108752	+	0.0824691i	0.108752	+	0.0824691i	0.657204	−	0.753713i	$-0.271739\pi$
$83$	0.108752	+	0.0824691i	0.108752	+	0.0824691i	−0.548452	+	0.836182i	$0.684783\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$89$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$90$		0			0
$91$		0			0
$92$	−0.205300	−	0.842451i	−0.205300	−	0.842451i
$93$	−0.192569	+	0.192569i	−0.192569	+	0.192569i
$94$	−0.398401	+	0.0827887i	−0.398401	+	0.0827887i
$95$		0			0
$96$	−0.822285	−	0.500042i	−0.822285	−	0.500042i
$97$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$97$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$98$	0.123097	−	0.387846i	0.123097	−	0.387846i
$99$		0			0
$100$		0			0
$101$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$101$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$102$	0.515015	+	0.590644i	0.515015	+	0.590644i
$103$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$103$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$104$		0			0
$105$		0			0
$106$	−0.125383	+	0.241978i	−0.125383	+	0.241978i
$107$	−0.167093	−	1.62537i	−0.167093	−	1.62537i	−0.657204	−	0.753713i	$-0.728261\pi$
$107$	−0.167093	−	1.62537i	−0.167093	−	1.62537i	0.490110	−	0.871660i	$-0.336957\pi$
$108$	0.0284881	−	0.833936i	0.0284881	−	0.833936i
$109$	−1.83015	+	0.794945i	−1.83015	+	0.794945i	−0.887885	+	0.460065i	$0.847826\pi$
$109$	−1.83015	+	0.794945i	−1.83015	+	0.794945i	−0.942261	+	0.334880i	$0.891304\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.22222	+	0.801657i	1.22222	+	0.801657i	0.985460	−	0.169910i	$-0.0543478\pi$
$113$	1.22222	+	0.801657i	1.22222	+	0.801657i	0.236764	+	0.971567i	$0.423913\pi$
$114$	0.695787	−	0.194950i	0.695787	−	0.194950i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.962917	+	0.269797i	−0.962917	+	0.269797i
$122$	0.527876	+	0.346234i	0.527876	+	0.346234i
$123$		0			0
$124$	0.225125	+	0.0309427i	0.225125	+	0.0309427i
$125$		0			0
$126$		0			0
$127$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$127$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$128$	0.104205	+	1.01364i	0.104205	+	1.01364i
$129$		0			0
$130$		0			0
$131$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$131$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.292475	−	1.40747i	0.292475	−	1.40747i
$137$	−0.603619	+	1.90185i	−0.603619	+	1.90185i	−0.236764	+	0.971567i	$0.576087\pi$
$137$	−0.603619	+	1.90185i	−0.603619	+	1.90185i	−0.366854	+	0.930278i	$0.619565\pi$
$138$	0.416701	+	0.0718466i	0.416701	+	0.0718466i
$139$	−0.680803	−	0.414006i	−0.680803	−	0.414006i	0.136167	−	0.990686i	$-0.456522\pi$
$139$	−0.680803	−	0.414006i	−0.680803	−	0.414006i	−0.816970	+	0.576680i	$0.804348\pi$
$140$		0			0
$141$	−0.203456	+	0.979084i	−0.203456	+	0.979084i
$142$		0			0
$143$		0			0
$144$	−0.433553	+	0.306035i	−0.433553	+	0.306035i
$145$		0			0
$146$		0			0
$147$	−0.753713	−	0.657204i	−0.753713	−	0.657204i
$148$		0			0
$149$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$149$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$150$		0			0
$151$	−0.922444	−	0.861502i	−0.922444	−	0.861502i	0.0682424	−	0.997669i	$-0.478261\pi$
$151$	−0.922444	−	0.861502i	−0.922444	−	0.861502i	−0.990686	+	0.136167i	$0.956522\pi$
$152$	−1.05618	−	0.800928i	−1.05618	−	0.800928i
$153$	1.83560	−	0.582593i	1.83560	−	0.582593i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.169910	−	0.985460i	$-0.554348\pi$
$157$		0			0		0.169910	+	0.985460i	$0.445652\pi$
$158$	0.487162	+	0.642419i	0.487162	+	0.642419i
$159$	0.422677	+	0.519540i	0.422677	+	0.519540i
$160$		0			0
$161$		0			0
$162$	0.367472	+	0.174762i	0.367472	+	0.174762i
$163$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$163$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$164$		0			0
$165$		0			0
$166$	0.0509395	+	0.0221261i	0.0509395	+	0.0221261i
$167$	0.809371	−	1.70186i	0.809371	−	1.70186i	0.102264	−	0.994757i	$-0.467391\pi$
$167$	0.809371	−	1.70186i	0.809371	−	1.70186i	0.707107	−	0.707107i	$-0.250000\pi$
$168$		0			0
$169$	0.979084	−	0.203456i	0.979084	−	0.203456i
$170$		0			0
$171$	0.241801	−	1.75923i	0.241801	−	1.75923i
$172$		0			0
$173$	−1.26993	−	0.500795i	−1.26993	−	0.500795i	−0.366854	−	0.930278i	$-0.619565\pi$
$173$	−1.26993	−	0.500795i	−1.26993	−	0.500795i	−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		0.334880	−	0.942261i	$-0.391304\pi$
$179$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$180$		0			0
$181$	−0.394354	+	1.40747i	−0.394354	+	1.40747i	0.460065	+	0.887885i	$0.347826\pi$
$181$	−0.394354	+	1.40747i	−0.394354	+	1.40747i	−0.854419	+	0.519584i	$0.826087\pi$
$182$		0			0
$183$	1.29727	−	0.850881i	1.29727	−	0.850881i
$184$	−0.356866	−	0.688720i	−0.356866	−	0.688720i
$185$		0			0
$186$	−0.0575781	+	0.0946831i	−0.0575781	+	0.0946831i
$187$		0			0
$188$	0.753546	−	0.358371i	0.753546	−	0.358371i
$189$		0			0
$190$		0			0
$191$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$191$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$192$	0.132559	+	0.0420724i	0.132559	+	0.0420724i
$193$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$193$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$194$		0			0
$195$		0			0
$196$	−0.0569430	+	0.832477i	−0.0569430	+	0.832477i
$197$	−0.666310	−	1.40105i	−0.666310	−	1.40105i	−0.903075	−	0.429483i	$-0.858696\pi$
$197$	−0.666310	−	1.40105i	−0.666310	−	1.40105i	0.236764	−	0.971567i	$-0.423913\pi$
$198$		0			0
$199$	1.86697	−	0.256609i	1.86697	−	0.256609i	0.887885	−	0.460065i	$-0.152174\pi$
$199$	1.86697	−	0.256609i	1.86697	−	0.256609i	0.979084	+	0.203456i	$0.0652174\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−1.31284	−	0.926702i	−1.31284	−	0.926702i
$205$		0			0
$206$		0			0
$207$	0.569934	−	0.868934i	0.569934	−	0.868934i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.848969	+	1.39607i	0.848969	+	1.39607i	0.917211	+	0.398401i	$0.130435\pi$
$211$	0.848969	+	1.39607i	0.848969	+	1.39607i	−0.0682424	+	0.997669i	$0.521739\pi$
$212$	0.132319	−	0.542972i	0.132319	−	0.542972i
$213$		0			0
$214$	−0.222651	−	0.626481i	−0.222651	−	0.626481i
$215$		0			0
$216$	−0.151869	−	0.730836i	−0.151869	−	0.730836i
$217$		0			0
$218$	−0.646947	+	0.490596i	−0.646947	+	0.490596i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$223$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$224$		0			0
$225$		0			0
$226$	0.560430	+	0.199177i	0.560430	+	0.199177i
$227$	−0.951318	+	0.829507i	−0.951318	+	0.829507i	−0.985460	−	0.169910i	$-0.945652\pi$
$227$	−0.951318	+	0.829507i	−0.951318	+	0.829507i	0.0341411	+	0.999417i	$0.489130\pi$
$228$	−1.29158	+	0.726217i	−1.29158	+	0.726217i
$229$	−0.0861339	−	1.25923i	−0.0861339	−	1.25923i	−0.816970	−	0.576680i	$-0.804348\pi$
$229$	−0.0861339	−	1.25923i	−0.0861339	−	1.25923i	0.730836	−	0.682553i	$-0.239130\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.83094	+	0.446188i	−1.83094	+	0.446188i	−0.994757	−	0.102264i	$-0.967391\pi$
$233$	−1.83094	+	0.446188i	−1.83094	+	0.446188i	−0.836182	+	0.548452i	$0.815217\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.92504	−	0.469118i	1.92504	−	0.469118i
$238$		0			0
$239$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$239$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$240$		0			0
$241$	−0.0457060	−	0.668198i	−0.0457060	−	0.668198i	−0.962917	−	0.269797i	$-0.913043\pi$
$241$	−0.0457060	−	0.668198i	−0.0457060	−	0.668198i	0.917211	−	0.398401i	$-0.130435\pi$
$242$	−0.354689	+	0.199432i	−0.354689	+	0.199432i
$243$	0.753713	−	0.657204i	0.753713	−	0.657204i
$244$	−1.21980	−	0.433516i	−1.21980	−	0.433516i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.202217	−	0.0207885i	0.202217	−	0.0207885i
$249$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i
$250$		0			0
$251$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$251$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.0922795	+	0.259650i	0.0922795	+	0.259650i
$257$	−0.197952	−	0.501972i	−0.197952	−	0.501972i	0.796805	−	0.604236i	$-0.206522\pi$
$257$	−0.197952	−	0.501972i	−0.197952	−	0.501972i	−0.994757	+	0.102264i	$0.967391\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.937216	−	1.42890i	0.937216	−	1.42890i	0.0341411	−	0.999417i	$-0.489130\pi$
$263$	0.937216	−	1.42890i	0.937216	−	1.42890i	0.903075	−	0.429483i	$-0.141304\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$269$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$270$		0			0
$271$	0.911560	−	0.125291i	0.911560	−	0.125291i	0.334880	−	0.942261i	$-0.391304\pi$
$271$	0.911560	−	0.125291i	0.911560	−	0.125291i	0.576680	+	0.816970i	$0.304348\pi$
$272$	0.0348925	+	1.02141i	0.0348925	+	1.02141i
$273$		0			0
$274$	−0.0554078	+	0.810034i	−0.0554078	+	0.810034i
$275$		0			0
$276$	−0.865084	+	0.0591734i	−0.865084	+	0.0591734i
$277$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$277$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$278$	−0.309037	−	0.0980838i	−0.309037	−	0.0980838i
$279$	0.157049	+	0.222488i	0.157049	+	0.222488i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	0.0138924	+	0.406675i	0.0138924	+	0.406675i
$283$		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
$288$	−0.632486	+	0.725366i	−0.632486	+	0.725366i
$289$	0.730836	−	2.60839i	0.730836	−	2.60839i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.18320	+	1.56028i	−1.18320	+	1.56028i	−0.429483	+	0.903075i	$0.641304\pi$
$293$	−1.18320	+	1.56028i	−1.18320	+	1.56028i	−0.753713	+	0.657204i	$0.771739\pi$
$294$	−0.361291	−	0.187206i	−0.361291	−	0.187206i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.447680	−	0.251718i	−0.447680	−	0.251718i
$303$		0			0
$304$	0.864355	+	0.375442i	0.864355	+	0.375442i
$305$		0			0
$306$	0.669562	−	0.407169i	0.669562	−	0.407169i
$307$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$307$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$311$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$312$		0			0
$313$		0			0		−0.169910	−	0.985460i	$-0.554348\pi$
$313$		0			0		0.169910	+	0.985460i	$0.445652\pi$
$314$		0			0
$315$		0			0
$316$	−1.28248	−	1.04338i	−1.28248	−	1.04338i
$317$	1.55738	−	0.494291i	1.55738	−	0.494291i	0.604236	−	0.796805i	$-0.293478\pi$
$317$	1.55738	−	0.494291i	1.55738	−	0.494291i	0.953145	+	0.302515i	$0.0978261\pi$
$318$	0.217156	+	0.164674i	0.217156	+	0.164674i
$319$		0			0
$320$		0			0
$321$	−1.63013	−	0.111504i	−1.63013	−	0.111504i
$322$		0			0
$323$	−2.57758	−	2.24753i	−2.57758	−	2.24753i
$324$	−0.816970	−	0.169768i	−0.816970	−	0.169768i
$325$		0			0
$326$		0			0
$327$	0.472425	+	1.93860i	0.472425	+	1.93860i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.116615	+	0.0709153i	0.116615	+	0.0709153i	0.576680	−	0.816970i	$-0.304348\pi$
$331$	0.116615	+	0.0709153i	0.116615	+	0.0709153i	−0.460065	+	0.887885i	$0.652174\pi$
$332$	−0.112230	−	0.0193504i	−0.112230	−	0.0193504i
$333$		0			0
$334$	0.156017	−	0.750796i	0.156017	−	0.750796i
$335$		0			0
$336$		0			0
$337$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$337$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$338$	0.367472	−	0.174762i	0.367472	−	0.174762i
$339$	0.997669	−	1.06824i	0.997669	−	1.06824i
$340$		0			0
$341$		0			0
$342$	−0.0738943	−	0.718794i	−0.0738943	−	0.718794i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.550304	−	0.0756376i	−0.550304	−	0.0756376i
$347$	−0.139601	+	1.35795i	−0.139601	+	1.35795i	0.657204	+	0.753713i	$0.271739\pi$
$347$	−0.139601	+	1.35795i	−0.139601	+	1.35795i	−0.796805	+	0.604236i	$0.793478\pi$
$348$		0			0
$349$	−0.767255	+	0.214975i	−0.767255	+	0.214975i	−0.631088	−	0.775711i	$-0.717391\pi$
$349$	−0.767255	+	0.214975i	−0.767255	+	0.214975i	−0.136167	+	0.990686i	$0.543478\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.893968	−	0.217854i	−0.893968	−	0.217854i	−0.236764	−	0.971567i	$-0.576087\pi$
$353$	−0.893968	−	0.217854i	−0.893968	−	0.217854i	−0.657204	+	0.753713i	$0.728261\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$359$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$360$		0			0
$361$	−1.97509	+	0.857901i	−1.97509	+	0.857901i
$362$	−0.0203062	+	0.594425i	−0.0203062	+	0.594425i
$363$	0.102264	+	0.994757i	0.102264	+	0.994757i
$364$		0			0
$365$		0			0
$366$	0.430891	−	0.461371i	0.430891	−	0.461371i
$367$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$367$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$368$	0.362428	+	0.415650i	0.362428	+	0.415650i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.0687437	−	0.216594i	0.0687437	−	0.216594i
$373$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$373$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$374$		0			0
$375$		0			0
$376$	0.579029	−	0.471075i	0.579029	−	0.471075i
$377$		0			0
$378$		0			0
$379$	0.942261	−	0.665120i	0.942261	−	0.665120i		−	1.00000i	$-0.5\pi$
$379$	0.942261	−	0.665120i	0.942261	−	0.665120i	0.942261	+	0.334880i	$0.108696\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.669053	+	1.18991i	0.669053	+	1.18991i	0.971567	+	0.236764i	$0.0760870\pi$
$383$	0.669053	+	1.18991i	0.669053	+	1.18991i	−0.302515	+	0.953145i	$0.597826\pi$
$384$	1.01661	+	0.0695378i	1.01661	+	0.0695378i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$389$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$390$		0			0
$391$	−0.797306	−	1.83558i	−0.797306	−	1.83558i
$392$	0.126829	+	0.735595i	0.126829	+	0.735595i
$393$		0			0
$394$	−0.398401	−	0.489701i	−0.398401	−	0.489701i
$395$		0			0
$396$		0			0
$397$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$397$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$398$	0.713370	−	0.281317i	0.713370	−	0.281317i
$399$		0			0
$400$		0			0
$401$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$401$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.33731	−	0.527366i	−1.33731	−	0.527366i
$409$	−0.543860	−	0.582332i	−0.543860	−	0.582332i	0.398401	−	0.917211i	$-0.369565\pi$
$409$	−0.543860	−	0.582332i	−0.543860	−	0.582332i	−0.942261	+	0.334880i	$0.891304\pi$
$410$		0			0
$411$	1.77163	+	0.917985i	1.77163	+	0.917985i
$412$		0			0
$413$		0			0
$414$	0.141604	−	0.398435i	0.141604	−	0.398435i
$415$		0			0
$416$		0			0
$417$	−0.523661	+	0.600560i	−0.523661	+	0.600560i
$418$		0			0
$419$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$419$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$420$		0			0
$421$	0.848969	−	1.39607i	0.848969	−	1.39607i	−0.0682424	−	0.997669i	$-0.521739\pi$
$421$	0.848969	−	1.39607i	0.848969	−	1.39607i	0.917211	−	0.398401i	$-0.130435\pi$
$422$	0.470134	+	0.470134i	0.470134	+	0.470134i
$423$	0.930278	+	0.366854i	0.930278	+	0.366854i
$424$		−	0.499941i		−	0.499941i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.747757	+	1.14005i	0.747757	+	1.14005i
$429$		0			0
$430$		0			0
$431$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$431$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$432$	0.227920	+	0.479247i	0.227920	+	0.479247i
$433$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$433$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$434$		0			0
$435$		0			0
$436$	1.05073	−	1.29152i	1.05073	−	1.29152i
$437$	−1.84425	−	0.0630014i	−1.84425	−	0.0630014i
$438$		0			0
$439$	0.111504	+	0.0787081i	0.111504	+	0.0787081i	0.631088	−	0.775711i	$-0.282609\pi$
$439$	0.111504	+	0.0787081i	0.111504	+	0.0787081i	−0.519584	+	0.854419i	$0.673913\pi$
$440$		0			0
$441$	−0.775711	+	0.631088i	−0.775711	+	0.631088i
$442$		0			0
$443$	0.977935	−	1.73926i	0.977935	−	1.73926i	0.429483	−	0.903075i	$-0.358696\pi$
$443$	0.977935	−	1.73926i	0.977935	−	1.73926i	0.548452	−	0.836182i	$-0.315217\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$449$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$450$		0			0
$451$		0			0
$452$	−1.21326	−	0.124727i	−1.21326	−	0.124727i
$453$	−1.00571	+	0.762653i	−1.00571	+	0.762653i
$454$	−0.296180	+	0.419591i	−0.296180	+	0.419591i
$455$		0			0
$456$	−0.968739	+	0.904739i	−0.968739	+	0.904739i
$457$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$457$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$458$	−0.155370	−	0.489530i	−0.155370	−	0.489530i
$459$	−0.262234	−	1.90790i	−0.262234	−	1.90790i
$460$		0			0
$461$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$461$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$462$		0			0
$463$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$463$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$464$		0			0
$465$		0			0
$466$	−0.680861	+	0.352794i	−0.680861	+	0.352794i
$467$	−0.135385	+	0.785216i	−0.135385	+	0.785216i	0.836182	+	0.548452i	$0.184783\pi$
$467$	−0.135385	+	0.785216i	−0.135385	+	0.785216i	−0.971567	+	0.236764i	$0.923913\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.715852	−	0.370925i	0.715852	−	0.370925i
$475$		0			0
$476$		0			0
$477$	0.583803	−	0.328256i	0.583803	−	0.328256i
$478$		0			0
$479$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$479$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$480$		0			0
$481$		0			0
$482$	−0.0824452	−	0.259763i	−0.0824452	−	0.259763i
$483$		0			0
$484$	0.609826	−	0.569538i	0.609826	−	0.569538i
$485$		0			0
$486$	0.234658	−	0.332435i	0.234658	−	0.332435i
$487$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$487$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$488$	−1.15199	−	0.118428i	−1.15199	−	0.118428i
$489$		0			0
$490$		0			0
$491$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$491$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.136178	+	0.0483978i	−0.136178	+	0.0483978i
$497$		0			0
$498$	0.0304595	−	0.0464393i	0.0304595	−	0.0464393i
$499$	0.806094	−	0.655806i	0.806094	−	0.655806i	−0.136167	−	0.990686i	$-0.543478\pi$
$499$	0.806094	−	0.655806i	0.806094	−	0.655806i	0.942261	+	0.334880i	$0.108696\pi$
$500$		0			0
$501$	−1.53960	−	1.08677i	−1.53960	−	1.08677i
$502$		0			0
$503$	−1.95703	−	0.0668540i	−1.95703	−	0.0668540i	−0.971567	−	0.236764i	$-0.923913\pi$
$503$	−1.95703	−	0.0668540i	−1.95703	−	0.0668540i	−0.985460	+	0.169910i	$0.945652\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0341411	−	0.999417i	−0.0341411	−	0.999417i
$508$		0			0
$509$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$509$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$510$		0			0
$511$		0			0
$512$	−0.497365	−	0.758294i	−0.497365	−	0.758294i
$513$	−1.69257	−	0.537196i	−1.69257	−	0.537196i
$514$	−0.126620	−	0.179380i	−0.126620	−	0.179380i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.709287	+	1.16637i	−0.709287	+	1.16637i
$520$		0			0
$521$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$521$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$522$		0			0
$523$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$523$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$524$		0			0
$525$		0			0
$526$	0.232858	−	0.655198i	0.232858	−	0.655198i
$527$	0.524163	−	0.0179059i	0.524163	−	0.0179059i
$528$		0			0
$529$	−0.0709153	−	0.0367454i	−0.0709153	−	0.0367454i
$530$		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
$541$	−1.69292	+	1.02949i	−1.69292	+	1.02949i	−0.775711	+	0.631088i	$0.782609\pi$
$541$	−1.69292	+	1.02949i	−1.69292	+	1.02949i	−0.917211	+	0.398401i	$0.869565\pi$
$542$	0.348307	−	0.137355i	0.348307	−	0.137355i
$543$	1.32000	+	0.627764i	1.32000	+	0.627764i
$544$	0.500042	+	1.78468i	0.500042	+	1.78468i
$545$		0			0
$546$		0			0
$547$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$547$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$548$	−0.282893	−	1.64075i	−0.282893	−	1.64075i
$549$	−0.618088	−	1.42298i	−0.618088	−	1.42298i
$550$		0			0
$551$		0			0
$552$	−0.739341	+	0.234656i	−0.739341	+	0.234656i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.663320	+	0.0453723i	0.663320	+	0.0453723i
$557$	0.264460	+	0.470342i	0.264460	+	0.470342i	0.971567	−	0.236764i	$-0.0760870\pi$
$557$	0.264460	+	0.470342i	0.264460	+	0.470342i	−0.707107	+	0.707107i	$0.750000\pi$
$558$	0.0835232	+	0.0728285i	0.0835232	+	0.0728285i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.381550	−	0.381550i	0.381550	−	0.381550i	−0.490110	−	0.871660i	$-0.663043\pi$
$563$	0.381550	−	0.381550i	0.381550	−	0.381550i	0.871660	+	0.490110i	$0.163043\pi$
$564$	−0.225125	−	0.803480i	−0.225125	−	0.803480i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$569$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$570$		0			0
$571$	0.886009	+	0.248248i	0.886009	+	0.248248i	0.682553	−	0.730836i	$-0.260870\pi$
$571$	0.886009	+	0.248248i	0.886009	+	0.248248i	0.203456	+	0.979084i	$0.434783\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0639838	−	0.123483i	0.0639838	−	0.123483i
$577$		0			0		−0.102264	−	0.994757i	$-0.532609\pi$
$577$		0			0		0.102264	+	0.994757i	$0.467391\pi$
$578$	0.0376323	−	1.10162i	0.0376323	−	1.10162i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.317447	+	0.730836i	−0.317447	+	0.730836i
$587$	1.72528	+	0.420439i	1.72528	+	0.420439i	0.971567	−	0.236764i	$-0.0760870\pi$
$587$	1.72528	+	0.420439i	1.72528	+	0.420439i	0.753713	+	0.657204i	$0.228261\pi$
$588$	0.810698	+	0.197562i	0.810698	+	0.197562i
$589$	0.192667	−	0.443565i	0.192667	−	0.443565i
$590$		0			0
$591$	−1.49389	+	0.418569i	−1.49389	+	0.418569i
$592$		0			0
$593$	−0.200250	+	1.94790i	−0.200250	+	1.94790i	0.102264	+	0.994757i	$0.467391\pi$
$593$	−0.200250	+	1.94790i	−0.200250	+	1.94790i	−0.302515	+	0.953145i	$0.597826\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.0643397	−	1.88342i	0.0643397	−	1.88342i
$598$		0			0
$599$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$599$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$600$		0			0
$601$	−0.931758	+	0.997669i	−0.931758	+	0.997669i	0.0682424	+	0.997669i	$0.478261\pi$
$601$	−0.931758	+	0.997669i	−0.931758	+	0.997669i	−1.00000			$1.00000\pi$
$602$		0			0
$603$		0			0
$604$	1.01413	+	0.284147i	1.01413	+	0.284147i
$605$		0			0
$606$		0			0
$607$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$607$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$608$	1.68413	+	0.290374i	1.68413	+	0.290374i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.13629	+	1.13629i	−1.13629	+	1.13629i
$613$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$613$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.49339	+	1.30216i	1.49339	+	1.30216i	0.836182	+	0.548452i	$0.184783\pi$
$617$	1.49339	+	1.30216i	1.49339	+	1.30216i	0.657204	+	0.753713i	$0.271739\pi$
$618$		0			0
$619$	−1.54781	−	0.105873i	−1.54781	−	0.105873i	−0.730836	−	0.682553i	$-0.760870\pi$
$619$	−1.54781	−	0.105873i	−1.54781	−	0.105873i	−0.816970	+	0.576680i	$0.804348\pi$
$620$		0			0
$621$	−0.759461	−	0.709287i	−0.759461	−	0.709287i
$622$		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
$631$	0.280364	+	1.00063i	0.280364	+	1.00063i	0.962917	+	0.269797i	$0.0869565\pi$
$631$	0.280364	+	1.00063i	0.280364	+	1.00063i	−0.682553	+	0.730836i	$0.739130\pi$
$632$	−1.33564	−	0.635203i	−1.33564	−	0.635203i
$633$	1.52002	−	0.599418i	1.52002	−	0.599418i
$634$	0.568078	−	0.345456i	0.568078	−	0.345456i
$635$		0			0
$636$	−0.512595	−	0.222651i	−0.512595	−	0.222651i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$641$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$642$	−0.655202	+	0.112968i	−0.655202	+	0.112968i
$643$		0			0		−0.930278	−	0.366854i	$-0.880435\pi$
$643$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$644$		0			0
$645$		0			0
$646$	−1.23556	−	0.640215i	−1.23556	−	0.640215i
$647$	−0.404693	+	0.533668i	−0.404693	+	0.533668i	−0.953145	−	0.302515i	$-0.902174\pi$
$647$	−0.404693	+	0.533668i	−0.404693	+	0.533668i	0.548452	+	0.836182i	$0.315217\pi$
$648$	−0.746013	+	0.0254846i	−0.746013	+	0.0254846i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.769396	−	0.504647i	0.769396	−	0.504647i	−0.102264	−	0.994757i	$-0.532609\pi$
$653$	0.769396	−	0.504647i	0.769396	−	0.504647i	0.871660	+	0.490110i	$0.163043\pi$
$654$	0.373539	+	0.720898i	0.373539	+	0.720898i
$655$		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
$661$	1.11059	+	1.57335i	1.11059	+	1.57335i	0.775711	+	0.631088i	$0.217391\pi$
$661$	1.11059	+	1.57335i	1.11059	+	1.57335i	0.334880	+	0.942261i	$0.391304\pi$
$662$	0.0529351	+	0.0168008i	0.0529351	+	0.0168008i
$663$		0			0
$664$	−0.101641	+	0.00695246i	−0.101641	+	0.00695246i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.0536865	+	1.57157i	0.0536865	+	1.57157i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$673$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$674$		0			0
$675$		0			0
$676$	−0.647271	+	0.526594i	−0.647271	+	0.526594i
$677$	0.437008	−	0.666272i	0.437008	−	0.666272i	−0.548452	−	0.836182i	$-0.684783\pi$
$677$	0.437008	−	0.666272i	0.437008	−	0.666272i	0.985460	+	0.169910i	$0.0543478\pi$
$678$	0.291504	−	0.518439i	0.291504	−	0.518439i
$679$		0			0
$680$		0			0
$681$	0.655806	+	1.07843i	0.655806	+	1.07843i
$682$		0			0
$683$	0.626895	+	1.58970i	0.626895	+	1.58970i	0.796805	+	0.604236i	$0.206522\pi$
$683$	0.626895	+	1.58970i	0.626895	+	1.58970i	−0.169910	+	0.985460i	$0.554348\pi$
$684$	0.496206	+	1.39619i	0.496206	+	1.39619i
$685$		0			0
$686$		0			0
$687$	−1.25556	−	0.129075i	−1.25556	−	0.129075i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.394354	−	0.368301i	0.394354	−	0.368301i	−0.460065	−	0.887885i	$-0.652174\pi$
$691$	0.394354	−	0.368301i	0.394354	−	0.368301i	0.854419	+	0.519584i	$0.173913\pi$
$692$	1.13310	−	0.116487i	1.13310	−	0.116487i
$693$		0			0
$694$	0.0756376	+	0.550304i	0.0756376	+	0.550304i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.282617	+	0.158908i	−0.282617	+	0.158908i
$699$	0.128604	+	1.88013i	0.128604	+	1.88013i
$700$		0			0
$701$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$701$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.374412			−0.374412
$707$		0			0
$708$		0			0
$709$	1.51725	−	0.786177i	1.51725	−	0.786177i	0.519584	−	0.854419i	$-0.326087\pi$
$709$	1.51725	−	0.786177i	1.51725	−	0.786177i	0.997669	+	0.0682424i	$0.0217391\pi$
$710$		0			0
$711$	−0.135214	−	1.97675i	−0.135214	−	1.97675i
$712$		0			0
$713$	0.213301	−	0.185989i	0.213301	−	0.185989i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$719$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$720$		0			0
$721$		0			0
$722$	−0.698183	+	0.529449i	−0.698183	+	0.529449i
$723$	−0.666248	−	0.0684924i	−0.666248	−	0.0684924i
$724$	−0.248146	−	1.19414i	−0.248146	−	1.19414i
$725$		0			0
$726$	0.136267	+	0.383417i	0.136267	+	0.383417i
$727$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$727$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$728$		0			0
$729$	−0.519584	−	0.854419i	−0.519584	−	0.854419i
$730$		0			0
$731$		0			0
$732$	−0.634468	+	1.12840i	−0.634468	+	1.12840i
$733$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$733$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$734$		0			0
$735$		0			0
$736$	0.817039	+	0.576729i	0.817039	+	0.576729i
$737$		0			0
$738$		0			0
$739$	0.861502	−	1.05893i	0.861502	−	1.05893i	−0.136167	−	0.990686i	$-0.543478\pi$
$739$	0.861502	−	1.05893i	0.861502	−	1.05893i	0.997669	−	0.0682424i	$-0.0217391\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.762664	+	1.60365i	0.762664	+	1.60365i	0.796805	+	0.604236i	$0.206522\pi$
$743$	0.762664	+	1.60365i	0.762664	+	1.60365i	−0.0341411	+	0.999417i	$0.510870\pi$
$744$	0.0138725	−	0.202809i	0.0138725	−	0.202809i
$745$		0			0
$746$		0			0
$747$	−0.0748554	−	0.114126i	−0.0748554	−	0.114126i
$748$		0			0
$749$		0			0
$750$		0			0
$751$			1.63394i			1.63394i	0.576680	+	0.816970i	$0.304348\pi$
$751$			1.63394i			1.63394i	−0.576680	+	0.816970i	$0.695652\pi$
$752$	−0.320658	+	0.422851i	−0.320658	+	0.422851i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$757$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$758$	0.308436	−	0.353730i	0.308436	−	0.353730i
$759$		0			0
$760$		0			0
$761$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$761$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.379143	+	0.405963i	0.379143	+	0.405963i
$767$		0			0
$768$	0.271554	−	0.0468206i	0.271554	−	0.0468206i
$769$	−0.262234	+	1.90790i	−0.262234	+	1.90790i	0.136167	+	0.990686i	$0.456522\pi$
$769$	−0.262234	+	1.90790i	−0.262234	+	1.90790i	−0.398401	+	0.917211i	$0.630435\pi$
$770$		0			0
$771$	−0.528307	+	0.109784i	−0.528307	+	0.109784i
$772$		0			0
$773$	0.787854	−	1.65662i	0.787854	−	1.65662i	0.0341411	−	0.999417i	$-0.489130\pi$
$773$	0.787854	−	1.65662i	0.787854	−	1.65662i	0.753713	−	0.657204i	$-0.228261\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.492053	−	0.648869i	−0.492053	−	0.648869i
$783$		0			0
$784$	−0.211425	−	0.486749i	−0.211425	−	0.486749i
$785$		0			0
$786$		0			0
$787$		0			0		0.953145	−	0.302515i	$-0.0978261\pi$
$787$		0			0		−0.953145	+	0.302515i	$0.902174\pi$
$788$	1.03150	+	0.782209i	1.03150	+	0.782209i
$789$	−1.24888	−	1.16637i	−1.24888	−	1.16637i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−1.28468	+	0.906823i	−1.28468	+	0.906823i
$797$	0.188654	+	0.774147i	0.188654	+	0.774147i	0.985460	+	0.169910i	$0.0543478\pi$
$797$	0.188654	+	0.774147i	0.188654	+	0.774147i	−0.796805	+	0.604236i	$0.793478\pi$
$798$		0			0
$799$	1.57335	−	1.11059i	1.57335	−	1.11059i
$800$		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		0.682553	−	0.730836i	$-0.260870\pi$
$809$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$810$		0			0
$811$	0.628038	−	1.21206i	0.628038	−	1.21206i	−0.334880	−	0.942261i	$-0.608696\pi$
$811$	0.628038	−	1.21206i	0.628038	−	1.21206i	0.962917	−	0.269797i	$-0.0869565\pi$
$812$		0			0
$813$	0.0314143	−	0.919594i	0.0314143	−	0.919594i
$814$		0			0
$815$		0			0
$816$	1.01249	+	0.139164i	1.01249	+	0.139164i
$817$		0			0
$818$	−0.271114	−	0.177824i	−0.271114	−	0.177824i
$819$		0			0
$820$		0			0
$821$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$821$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$822$	0.788841	+	0.192235i	0.788841	+	0.192235i
$823$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$823$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.53391	+	1.00609i	1.53391	+	1.00609i	0.985460	+	0.169910i	$0.0543478\pi$
$827$	1.53391	+	1.00609i	1.53391	+	1.00609i	0.548452	+	0.836182i	$0.315217\pi$
$828$	−0.0886738	+	0.862559i	−0.0886738	+	0.862559i
$829$	−1.93993	−	0.266637i	−1.93993	−	0.266637i	−0.942261	−	0.334880i	$-0.891304\pi$
$829$	−1.93993	−	0.266637i	−1.93993	−	0.266637i	−0.997669	+	0.0682424i	$0.978261\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.196944	+	1.91574i	0.196944	+	1.91574i
$834$	−0.149166	+	0.287878i	−0.149166	+	0.287878i
$835$		0			0
$836$		0			0
$837$	0.245937	−	0.116963i	0.245937	−	0.116963i
$838$		0			0
$839$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$839$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$840$		0			0
$841$	0.203456	−	0.979084i	0.203456	−	0.979084i
$842$	0.201133	−	0.633717i	0.201133	−	0.633717i
$843$		0			0
$844$	−1.16491	−	0.708399i	−1.16491	−	0.708399i
$845$		0			0
$846$	0.403122	+	0.0554078i	0.403122	+	0.0554078i
$847$		0			0
$848$	0.0841532	+	0.345324i	0.0841532	+	0.345324i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$853$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$854$		0			0
$855$		0			0
$856$	0.891366	+	0.832477i	0.891366	+	0.832477i
$857$	1.30193	+	0.987286i	1.30193	+	0.987286i	0.999417	+	0.0341411i	$0.0108696\pi$
$857$	1.30193	+	0.987286i	1.30193	+	0.987286i	0.302515	+	0.953145i	$0.402174\pi$
$858$		0			0
$859$	1.51897	+	1.23578i	1.51897	+	1.23578i	0.887885	+	0.460065i	$0.152174\pi$
$859$	1.51897	+	1.23578i	1.51897	+	1.23578i	0.631088	+	0.775711i	$0.282609\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.19722	−	1.57877i	−1.19722	−	1.57877i	−0.707107	−	0.707107i	$-0.750000\pi$
$863$	−1.19722	−	1.57877i	−1.19722	−	1.57877i	−0.490110	−	0.871660i	$-0.663043\pi$
$864$	0.607353	+	0.746537i	0.607353	+	0.746537i
$865$		0			0
$866$		0			0
$867$	−2.44628	−	1.16340i	−2.44628	−	1.16340i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.639680	−	1.34505i	0.639680	−	1.34505i
$873$		0			0
$874$	−0.735179	+	0.152772i	−0.735179	+	0.152772i
$875$		0			0
$876$		0			0
$877$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$877$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$878$	0.0516652	+	0.0203741i	0.0516652	+	0.0203741i
$879$	1.33655	+	1.43110i	1.33655	+	1.43110i
$880$		0			0
$881$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$881$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$882$	−0.245871	+	0.324230i	−0.245871	+	0.324230i
$883$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$883$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$884$		0			0
$885$		0			0
$886$	0.219055	−	0.781818i	0.219055	−	0.781818i
$887$	1.16704	−	1.33842i	1.16704	−	1.33842i	0.236764	−	0.971567i	$-0.423913\pi$
$887$	1.16704	−	1.33842i	1.16704	−	1.33842i	0.930278	−	0.366854i	$-0.119565\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.301722	−	1.74995i	−0.301722	−	1.74995i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.0880222	−	1.28684i	0.0880222	−	1.28684i
$902$		0			0
$903$		0			0
$904$	−1.08090	+	0.148566i	−1.08090	+	0.148566i
$905$		0			0
$906$	−0.324123	+	0.398401i	−0.324123	+	0.398401i
$907$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$907$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$908$	0.386366	−	0.979758i	0.386366	−	0.979758i
$909$		0			0
$910$		0			0
$911$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$911$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$912$	0.516846	−	0.787995i	0.516846	−	0.787995i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.547220	+	0.899864i	0.547220	+	0.899864i
$917$		0			0
$918$	−0.287484	−	0.729008i	−0.287484	−	0.729008i
$919$	0.347996	+	0.979167i	0.347996	+	0.979167i	0.979084	+	0.203456i	$0.0652174\pi$
$919$	0.347996	+	0.979167i	0.347996	+	0.979167i	−0.631088	+	0.775711i	$0.717391\pi$
$920$		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		−0.136167	−	0.990686i	$-0.543478\pi$
$929$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$930$		0			0
$931$	1.67324	+	0.594669i	1.67324	+	0.594669i
$932$	1.18520	−	1.03344i	1.18520	−	1.03344i
$933$		0			0
$934$	0.0221261	+	0.323473i	0.0221261	+	0.323473i
$935$		0			0
$936$		0			0
$937$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$937$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$938$		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
$947$	1.59899	−	0.899069i	1.59899	−	0.899069i	0.604236	−	0.796805i	$-0.293478\pi$
$947$	1.59899	−	0.899069i	1.59899	−	0.899069i	0.994757	−	0.102264i	$-0.0326087\pi$
$948$	−1.24611	+	1.08656i	−1.24611	+	1.08656i
$949$		0			0
$950$		0			0
$951$	−0.222488	−	1.61872i	−0.222488	−	1.61872i
$952$		0			0
$953$	1.94790	−	0.200250i	1.94790	−	0.200250i	0.953145	−	0.302515i	$-0.0978261\pi$
$953$	1.94790	−	0.200250i	1.94790	−	0.200250i	0.994757	+	0.102264i	$0.0326087\pi$
$954$	0.199177	−	0.186018i	0.199177	−	0.186018i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.310043	−	0.872378i	−0.310043	−	0.872378i
$962$		0			0
$963$	−0.386859	+	1.58748i	−0.386859	+	1.58748i
$964$	0.290376	+	0.477503i	0.290376	+	0.477503i
$965$		0			0
$966$		0			0
$967$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$967$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$968$	0.409391	−	0.624167i	0.409391	−	0.624167i
$969$	−2.65281	+	2.15822i	−2.65281	+	2.15822i
$970$		0			0
$971$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$971$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$972$	−0.306111	+	0.776245i	−0.306111	+	0.776245i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.815646	−	0.112108i	0.815646	−	0.112108i
$977$	−0.0466062	−	1.36431i	−0.0466062	−	1.36431i	−0.753713	−	0.657204i	$-0.771739\pi$
$977$	−0.0466062	−	1.36431i	−0.0466062	−	1.36431i	0.707107	−	0.707107i	$-0.250000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.99069	−	0.136167i	1.99069	−	0.136167i
$982$		0			0
$983$	−1.20304	−	0.381827i	−1.20304	−	0.381827i	−0.366854	−	0.930278i	$-0.619565\pi$
$983$	−1.20304	−	0.381827i	−1.20304	−	0.381827i	−0.836182	+	0.548452i	$0.815217\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.530621	−	1.02405i	−0.530621	−	1.02405i	−0.990686	−	0.136167i	$-0.956522\pi$
$991$	−0.530621	−	1.02405i	−0.530621	−	1.02405i	0.460065	−	0.887885i	$-0.347826\pi$
$992$	−0.219156	+	0.143744i	−0.219156	+	0.143744i
$993$	0.0896983	−	0.102870i	0.0896983	−	0.102870i
$994$		0			0
$995$		0			0
$996$	−0.0381381	+	0.107310i	−0.0381381	+	0.107310i
$997$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$997$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$998$	0.255501	−	0.336929i	0.255501	−	0.336929i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.407.2	yes	88
3.2	odd	2	inner	3525.1.bg.a.407.1	✓	88
5.2	odd	4	inner	3525.1.bg.a.3368.2	yes	88
5.3	odd	4	inner	3525.1.bg.a.3368.1	yes	88
5.4	even	2	inner	3525.1.bg.a.407.1	✓	88
15.2	even	4	inner	3525.1.bg.a.3368.1	yes	88
15.8	even	4	inner	3525.1.bg.a.3368.2	yes	88
15.14	odd	2	CM	3525.1.bg.a.407.2	yes	88
47.44	odd	46	inner	3525.1.bg.a.2582.2	yes	88
141.44	even	46	inner	3525.1.bg.a.2582.1	yes	88
235.44	odd	46	inner	3525.1.bg.a.2582.1	yes	88
235.138	even	92	inner	3525.1.bg.a.2018.1	yes	88
235.232	even	92	inner	3525.1.bg.a.2018.2	yes	88
705.44	even	46	inner	3525.1.bg.a.2582.2	yes	88
705.467	odd	92	inner	3525.1.bg.a.2018.1	yes	88
705.608	odd	92	inner	3525.1.bg.a.2018.2	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.407.1	✓	88	3.2	odd	2	inner
3525.1.bg.a.407.1	✓	88	5.4	even	2	inner
3525.1.bg.a.407.2	yes	88	1.1	even	1	trivial
3525.1.bg.a.407.2	yes	88	15.14	odd	2	CM
3525.1.bg.a.2018.1	yes	88	235.138	even	92	inner
3525.1.bg.a.2018.1	yes	88	705.467	odd	92	inner
3525.1.bg.a.2018.2	yes	88	235.232	even	92	inner
3525.1.bg.a.2018.2	yes	88	705.608	odd	92	inner
3525.1.bg.a.2582.1	yes	88	141.44	even	46	inner
3525.1.bg.a.2582.1	yes	88	235.44	odd	46	inner
3525.1.bg.a.2582.2	yes	88	47.44	odd	46	inner
3525.1.bg.a.2582.2	yes	88	705.44	even	46	inner
3525.1.bg.a.3368.1	yes	88	5.3	odd	4	inner
3525.1.bg.a.3368.1	yes	88	15.2	even	4	inner
3525.1.bg.a.3368.2	yes	88	5.2	odd	4	inner
3525.1.bg.a.3368.2	yes	88	15.8	even	4	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)

\(f(q)\)	\(=\)	\(q+(0.395342 - 0.0963423i) q^{2} +(0.169910 - 0.985460i) q^{3} +(-0.740871 + 0.383889i) q^{4} +(-0.0277687 - 0.405963i) q^{6} +(-0.562608 + 0.490569i) q^{8} +(-0.942261 - 0.334880i) q^{9} +O(q^{10})\)	\(q+(0.395342 - 0.0963423i) q^{2} +(0.169910 - 0.985460i) q^{3} +(-0.740871 + 0.383889i) q^{4} +(-0.0277687 - 0.405963i) q^{6} +(-0.562608 + 0.490569i) q^{8} +(-0.942261 - 0.334880i) q^{9} +(0.252425 + 0.795326i) q^{12} +(0.306035 - 0.433553i) q^{16} +(-1.53451 + 1.16366i) q^{17} +(-0.404779 - 0.0416125i) q^{18} +(0.361291 + 1.73863i) q^{19} +(-0.246038 + 1.00962i) q^{23} +(0.387843 + 0.637780i) q^{24} +(-0.490110 + 0.871660i) q^{27} +(-0.222488 - 0.157049i) q^{31} +(0.353057 - 0.895291i) q^{32} +(-0.494549 + 0.607882i) q^{34} +(0.826651 - 0.113621i) q^{36} +(0.310337 + 0.652546i) q^{38} +0.422850i q^{46} +(-0.999417 - 0.0341411i) q^{47} +(-0.375250 - 0.375250i) q^{48} +(0.519584 - 0.854419i) q^{49} +(0.886009 + 1.70992i) q^{51} +(-0.440168 + 0.504806i) q^{53} +(-0.109784 + 0.391823i) q^{54} +(1.77474 - 0.0606268i) q^{57} +(1.05893 + 1.13384i) q^{61} +(-0.103089 - 0.0406532i) q^{62} +(-0.0189375 + 0.137780i) q^{64} +(0.690163 - 1.45120i) q^{68} +(0.953137 + 0.414006i) q^{69} +(0.694405 - 0.273838i) q^{72} +(-0.935110 - 1.14940i) q^{76} +(0.789381 + 1.81734i) q^{79} +(0.775711 + 0.631088i) q^{81} +(0.108752 + 0.0824691i) q^{83} +(-0.205300 - 0.842451i) q^{92} +(-0.192569 + 0.192569i) q^{93} +(-0.398401 + 0.0827887i) q^{94} +(-0.822285 - 0.500042i) q^{96} +(0.123097 - 0.387846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 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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