LMFDB - Embedded newform 3525.1.bg.a.218.2

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			218.2
Root			$-0.0341411 + 0.999417i$ of defining polynomial
Character	$\chi$	$=$	3525.218
Dual form			3525.1.bg.a.857.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0314143 - 0.919594i) q^{2} +(0.604236 - 0.796805i) q^{3} +(0.153003 + 0.0104657i) q^{4} +(-0.713755 - 0.580683i) q^{6} +(0.108527 - 1.05568i) q^{8} +(-0.269797 - 0.962917i) q^{9} +O(q^{10})$	\(q+(0.0314143 - 0.919594i) q^{2} +(0.604236 - 0.796805i) q^{3} +(0.153003 + 0.0104657i) q^{4} +(-0.713755 - 0.580683i) q^{6} +(0.108527 - 1.05568i) q^{8} +(-0.269797 - 0.962917i) q^{9} +(0.100789 - 0.115590i) q^{12} +(-0.815453 - 0.112081i) q^{16} +(1.53391 - 1.00609i) q^{17} +(-0.893968 + 0.217854i) q^{18} +(-0.917985 + 1.77163i) q^{19} +(-1.46082 + 0.0499031i) q^{23} +(-0.775594 - 0.724354i) q^{24} +(-0.930278 - 0.366854i) q^{27} +(0.266637 - 1.93993i) q^{31} +(0.0516297 - 0.299446i) q^{32} +(-0.877010 - 1.44218i) q^{34} +(-0.0312021 - 0.150153i) q^{36} +(1.60034 + 0.899828i) q^{38} +1.34493i q^{46} +(0.429483 - 0.903075i) q^{47} +(-0.582034 + 0.582034i) q^{48} +(-0.730836 + 0.682553i) q^{49} +(0.125185 - 1.83015i) q^{51} +(1.91574 - 0.196944i) q^{53} +(-0.366581 + 0.843954i) q^{54} +(0.856964 + 1.80194i) q^{57} +(0.572255 + 1.61017i) q^{61} +(-1.77557 - 0.306139i) q^{62} +(-1.07965 - 0.224354i) q^{64} +(0.245223 - 0.137882i) q^{68} +(-0.842917 + 1.19414i) q^{69} +(-1.04581 + 0.180316i) q^{72} +(-0.158996 + 0.261458i) q^{76} +(-0.332435 + 0.234658i) q^{79} +(-0.854419 + 0.519584i) q^{81} +(1.29727 + 0.850881i) q^{83} +(-0.224032 - 0.00765317i) q^{92} +(-1.38463 - 1.38463i) q^{93} +(-0.816970 - 0.423320i) q^{94} +(-0.207404 - 0.222075i) q^{96} +(0.604713 + 0.693514i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{6}+O(q^{10}) $ 88 * q - 8 * q^6	$ 88 q - 8 q^{6} + 20 q^{16} - 12 q^{36} - 8 q^{51} + 8 q^{61} - 92 q^{76} + 4 q^{81} - 68 q^{96}+O(q^{100}) $ 88 * q - 8 * q^6 + 20 * q^16 - 12 * q^36 - 8 * q^51 + 8 * q^61 - 92 * q^76 + 4 * q^81 - 68 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{39}{46}\right)$	$-1$

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 $

$2$	0.0314143	−	0.919594i	0.0314143	−	0.919594i	−0.871660	−	0.490110i	$-0.836957\pi$
$2$	0.0314143	−	0.919594i	0.0314143	−	0.919594i	0.903075	−	0.429483i	$-0.141304\pi$
$3$	0.604236	−	0.796805i	0.604236	−	0.796805i
$3$	0.604236	−	0.796805i	0.604236	−	0.796805i
$4$	0.153003	+	0.0104657i	0.153003	+	0.0104657i
$5$		0			0
$5$		0			0
$6$	−0.713755	−	0.580683i	−0.713755	−	0.580683i
$7$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$7$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$8$	0.108527	−	1.05568i	0.108527	−	1.05568i
$9$	−0.269797	−	0.962917i	−0.269797	−	0.962917i
$10$		0			0
$11$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$11$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$12$	0.100789	−	0.115590i	0.100789	−	0.115590i
$13$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$13$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$14$		0			0
$15$		0			0
$16$	−0.815453	−	0.112081i	−0.815453	−	0.112081i
$17$	1.53391	−	1.00609i	1.53391	−	1.00609i	0.548452	−	0.836182i	$-0.315217\pi$
$17$	1.53391	−	1.00609i	1.53391	−	1.00609i	0.985460	−	0.169910i	$-0.0543478\pi$
$18$	−0.893968	+	0.217854i	−0.893968	+	0.217854i
$19$	−0.917985	+	1.77163i	−0.917985	+	1.77163i	−0.398401	+	0.917211i	$0.630435\pi$
$19$	−0.917985	+	1.77163i	−0.917985	+	1.77163i	−0.519584	+	0.854419i	$0.673913\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.46082	+	0.0499031i	−1.46082	+	0.0499031i	−0.753713	−	0.657204i	$-0.771739\pi$
$23$	−1.46082	+	0.0499031i	−1.46082	+	0.0499031i	−0.707107	+	0.707107i	$0.750000\pi$
$24$	−0.775594	−	0.724354i	−0.775594	−	0.724354i
$25$		0			0
$26$		0			0
$27$	−0.930278	−	0.366854i	−0.930278	−	0.366854i
$28$		0			0
$29$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$29$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$30$		0			0
$31$	0.266637	−	1.93993i	0.266637	−	1.93993i	−0.0682424	−	0.997669i	$-0.521739\pi$
$31$	0.266637	−	1.93993i	0.266637	−	1.93993i	0.334880	−	0.942261i	$-0.391304\pi$
$32$	0.0516297	−	0.299446i	0.0516297	−	0.299446i
$33$		0			0
$34$	−0.877010	−	1.44218i	−0.877010	−	1.44218i
$35$		0			0
$36$	−0.0312021	−	0.150153i	−0.0312021	−	0.150153i
$37$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$37$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$38$	1.60034	+	0.899828i	1.60034	+	0.899828i
$39$		0			0
$40$		0			0
$41$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$41$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$42$		0			0
$43$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$43$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$44$		0			0
$45$		0			0
$46$			1.34493i			1.34493i
$47$	0.429483	−	0.903075i	0.429483	−	0.903075i
$47$	0.429483	−	0.903075i	0.429483	−	0.903075i
$48$	−0.582034	+	0.582034i	−0.582034	+	0.582034i
$49$	−0.730836	+	0.682553i	−0.730836	+	0.682553i
$50$		0			0
$51$	0.125185	−	1.83015i	0.125185	−	1.83015i
$52$		0			0
$53$	1.91574	−	0.196944i	1.91574	−	0.196944i	0.930278	−	0.366854i	$-0.119565\pi$
$53$	1.91574	−	0.196944i	1.91574	−	0.196944i	0.985460	+	0.169910i	$0.0543478\pi$
$54$	−0.366581	+	0.843954i	−0.366581	+	0.843954i
$55$		0			0
$56$		0			0
$57$	0.856964	+	1.80194i	0.856964	+	1.80194i
$58$		0			0
$59$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$59$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$60$		0			0
$61$	0.572255	+	1.61017i	0.572255	+	1.61017i	0.775711	+	0.631088i	$0.217391\pi$
$61$	0.572255	+	1.61017i	0.572255	+	1.61017i	−0.203456	+	0.979084i	$0.565217\pi$
$62$	−1.77557	−	0.306139i	−1.77557	−	0.306139i
$63$		0			0
$64$	−1.07965	−	0.224354i	−1.07965	−	0.224354i
$65$		0			0
$66$		0			0
$67$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$67$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$68$	0.245223	−	0.137882i	0.245223	−	0.137882i
$69$	−0.842917	+	1.19414i	−0.842917	+	1.19414i
$70$		0			0
$71$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$71$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$72$	−1.04581	+	0.180316i	−1.04581	+	0.180316i
$73$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$73$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$74$		0			0
$75$		0			0
$76$	−0.158996	+	0.261458i	−0.158996	+	0.261458i
$77$		0			0
$78$		0			0
$79$	−0.332435	+	0.234658i	−0.332435	+	0.234658i	−0.730836	−	0.682553i	$-0.760870\pi$
$79$	−0.332435	+	0.234658i	−0.332435	+	0.234658i	0.398401	+	0.917211i	$0.369565\pi$
$80$		0			0
$81$	−0.854419	+	0.519584i	−0.854419	+	0.519584i
$82$		0			0
$83$	1.29727	+	0.850881i	1.29727	+	0.850881i	0.994757	−	0.102264i	$-0.0326087\pi$
$83$	1.29727	+	0.850881i	1.29727	+	0.850881i	0.302515	+	0.953145i	$0.402174\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$89$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$90$		0			0
$91$		0			0
$92$	−0.224032	−	0.00765317i	−0.224032	−	0.00765317i
$93$	−1.38463	−	1.38463i	−1.38463	−	1.38463i
$94$	−0.816970	−	0.423320i	−0.816970	−	0.423320i
$95$		0			0
$96$	−0.207404	−	0.222075i	−0.207404	−	0.222075i
$97$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$97$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$98$	0.604713	+	0.693514i	0.604713	+	0.693514i
$99$		0			0
$100$		0			0
$101$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$101$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$102$	−1.67906	−	0.172612i	−1.67906	−	0.172612i
$103$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$103$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$104$		0			0
$105$		0			0
$106$	−0.120927	−	1.76789i	−0.120927	−	1.76789i
$107$	−0.0644788	+	0.264590i	−0.0644788	+	0.264590i	−0.994757	−	0.102264i	$-0.967391\pi$
$107$	−0.0644788	+	0.264590i	−0.0644788	+	0.264590i	0.930278	+	0.366854i	$0.119565\pi$
$108$	−0.138496	−	0.0658659i	−0.138496	−	0.0658659i
$109$	0.727872	+	1.03116i	0.727872	+	1.03116i	0.997669	+	0.0682424i	$0.0217391\pi$
$109$	0.727872	+	1.03116i	0.727872	+	1.03116i	−0.269797	+	0.962917i	$0.586957\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.79622	+	0.570095i	−1.79622	+	0.570095i	−0.999417	−	0.0341411i	$-0.989130\pi$
$113$	−1.79622	+	0.570095i	−1.79622	+	0.570095i	−0.796805	+	0.604236i	$0.793478\pi$
$114$	1.68397	−	0.731452i	1.68397	−	0.731452i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.917211	−	0.398401i	0.917211	−	0.398401i
$122$	1.49868	−	0.475660i	1.49868	−	0.475660i
$123$		0			0
$124$	0.0610990	−	0.294025i	0.0610990	−	0.294025i
$125$		0			0
$126$		0			0
$127$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$127$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$128$	−0.168287	+	0.690567i	−0.168287	+	0.690567i
$129$		0			0
$130$		0			0
$131$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$131$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.895639	−	1.72850i	−0.895639	−	1.72850i
$137$	0.829507	+	0.951318i	0.829507	+	0.951318i	0.999417	−	0.0341411i	$-0.0108696\pi$
$137$	0.829507	+	0.951318i	0.829507	+	0.951318i	−0.169910	+	0.985460i	$0.554348\pi$
$138$	1.07165	+	0.812655i	1.07165	+	0.812655i
$139$	−1.11525	−	1.19414i	−1.11525	−	1.19414i	−0.979084	−	0.203456i	$-0.934783\pi$
$139$	−1.11525	−	1.19414i	−1.11525	−	1.19414i	−0.136167	−	0.990686i	$-0.543478\pi$
$140$		0			0
$141$	−0.460065	−	0.887885i	−0.460065	−	0.887885i
$142$		0			0
$143$		0			0
$144$	0.112081	+	0.815453i	0.112081	+	0.815453i
$145$		0			0
$146$		0			0
$147$	0.102264	+	0.994757i	0.102264	+	0.994757i
$148$		0			0
$149$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$149$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$150$		0			0
$151$	0.979167	+	0.347996i	0.979167	+	0.347996i	0.775711	−	0.631088i	$-0.217391\pi$
$151$	0.979167	+	0.347996i	0.979167	+	0.347996i	0.203456	+	0.979084i	$0.434783\pi$
$152$	1.77065	+	1.16137i	1.77065	+	1.16137i
$153$	−1.38263	−	1.20559i	−1.38263	−	1.20559i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$157$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$158$	0.205347	+	0.313077i	0.205347	+	0.313077i
$159$	1.00063	−	1.64547i	1.00063	−	1.64547i
$160$		0			0
$161$		0			0
$162$	0.450965	+	0.802041i	0.450965	+	0.802041i
$163$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$163$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$164$		0			0
$165$		0			0
$166$	0.823217	−	1.16623i	0.823217	−	1.16623i
$167$	−0.470342	+	0.264460i	−0.470342	+	0.264460i	−0.707107	−	0.707107i	$-0.750000\pi$
$167$	−0.470342	+	0.264460i	−0.470342	+	0.264460i	0.236764	+	0.971567i	$0.423913\pi$
$168$		0			0
$169$	0.887885	+	0.460065i	0.887885	+	0.460065i
$170$		0			0
$171$	1.95360	+	0.405963i	1.95360	+	0.405963i
$172$		0			0
$173$	−0.660021	−	0.113799i	−0.660021	−	0.113799i	−0.169910	−	0.985460i	$-0.554348\pi$
$173$	−0.660021	−	0.113799i	−0.660021	−	0.113799i	−0.490110	+	0.871660i	$0.663043\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$179$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$180$		0			0
$181$	−0.750796	+	1.72850i	−0.750796	+	1.72850i	−0.0682424	+	0.997669i	$0.521739\pi$
$181$	−0.750796	+	1.72850i	−0.750796	+	1.72850i	−0.682553	+	0.730836i	$0.739130\pi$
$182$		0			0
$183$	1.62877	+	0.516949i	1.62877	+	0.516949i
$184$	−0.105857	+	1.54757i	−0.105857	+	1.54757i
$185$		0			0
$186$	−1.31680	+	1.22980i	−1.31680	+	1.22980i
$187$		0			0
$188$	0.0751636	−	0.133678i	0.0751636	−	0.133678i
$189$		0			0
$190$		0			0
$191$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$191$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$192$	−0.831130	+	0.724708i	−0.831130	+	0.724708i
$193$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$193$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$194$		0			0
$195$		0			0
$196$	−0.118964	+	0.0967841i	−0.118964	+	0.0967841i
$197$	−1.48953	−	0.837519i	−1.48953	−	0.837519i	−0.490110	−	0.871660i	$-0.663043\pi$
$197$	−1.48953	−	0.837519i	−1.48953	−	0.837519i	−0.999417	+	0.0341411i	$0.989130\pi$
$198$		0			0
$199$	−0.109784	−	0.528307i	−0.109784	−	0.528307i	−0.997669	−	0.0682424i	$-0.978261\pi$
$199$	−0.109784	−	0.528307i	−0.109784	−	0.528307i	0.887885	−	0.460065i	$-0.152174\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.0383075	−	0.278708i	0.0383075	−	0.278708i
$205$		0			0
$206$		0			0
$207$	0.442177	+	1.39318i	0.442177	+	1.39318i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.199031	−	0.185882i	−0.199031	−	0.185882i	0.576680	−	0.816970i	$-0.304348\pi$
$211$	−0.199031	−	0.185882i	−0.199031	−	0.185882i	−0.775711	+	0.631088i	$0.782609\pi$
$212$	0.295175	−	0.0100835i	0.295175	−	0.0100835i
$213$		0			0
$214$	0.241290	+	0.0676062i	0.241290	+	0.0676062i
$215$		0			0
$216$	−0.488240	+	0.942261i	−0.488240	+	0.942261i
$217$		0			0
$218$	0.971113	−	0.636953i	0.971113	−	0.636953i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$223$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$224$		0			0
$225$		0			0
$226$	0.467829	+	1.66970i	0.467829	+	1.66970i
$227$	−0.106270	+	1.03372i	−0.106270	+	1.03372i	0.796805	+	0.604236i	$0.206522\pi$
$227$	−0.106270	+	1.03372i	−0.106270	+	1.03372i	−0.903075	+	0.429483i	$0.858696\pi$
$228$	0.112260	+	0.284671i	0.112260	+	0.284671i
$229$	0.806094	+	0.655806i	0.806094	+	0.655806i	0.942261	−	0.334880i	$-0.108696\pi$
$229$	0.806094	+	0.655806i	0.806094	+	0.655806i	−0.136167	+	0.990686i	$0.543478\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.0184223	+	0.539279i	−0.0184223	+	0.539279i	0.953145	+	0.302515i	$0.0978261\pi$
$233$	−0.0184223	+	0.539279i	−0.0184223	+	0.539279i	−0.971567	+	0.236764i	$0.923913\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.0138924	+	0.406675i	−0.0138924	+	0.406675i
$238$		0			0
$239$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$239$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$240$		0			0
$241$	1.49389	+	1.21537i	1.49389	+	1.21537i	0.917211	+	0.398401i	$0.130435\pi$
$241$	1.49389	+	1.21537i	1.49389	+	1.21537i	0.576680	+	0.816970i	$0.304348\pi$
$242$	−0.337554	−	0.855977i	−0.337554	−	0.855977i
$243$	−0.102264	+	0.994757i	−0.102264	+	0.994757i
$244$	0.0707053	+	0.252350i	0.0707053	+	0.252350i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−2.01900	−	0.492018i	−2.01900	−	0.492018i
$249$	1.46184	−	0.519540i	1.46184	−	0.519540i
$250$		0			0
$251$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$251$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.432069	−	0.121060i	−0.432069	−	0.121060i
$257$	−0.135385	−	0.785216i	−0.135385	−	0.785216i	−0.971567	−	0.236764i	$-0.923913\pi$
$257$	−0.135385	−	0.785216i	−0.135385	−	0.785216i	0.836182	−	0.548452i	$-0.184783\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.412965	−	1.30114i	−0.412965	−	1.30114i	−0.903075	−	0.429483i	$-0.858696\pi$
$263$	−0.412965	−	1.30114i	−0.412965	−	1.30114i	0.490110	−	0.871660i	$-0.336957\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$269$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$270$		0			0
$271$	0.0277687	+	0.133630i	0.0277687	+	0.133630i	0.990686	−	0.136167i	$-0.0434783\pi$
$271$	0.0277687	+	0.133630i	0.0277687	+	0.133630i	−0.962917	+	0.269797i	$0.913043\pi$
$272$	−1.36360	+	0.648498i	−1.36360	+	0.648498i
$273$		0			0
$274$	0.900885	−	0.732924i	0.900885	−	0.732924i
$275$		0			0
$276$	−0.141467	+	0.173886i	−0.141467	+	0.173886i
$277$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$277$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$278$	−1.13316	+	0.988064i	−1.13316	+	0.988064i
$279$	−1.93993	+	0.266637i	−1.93993	+	0.266637i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	−0.830946	+	0.395181i	−0.830946	+	0.395181i
$283$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$283$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.302271	+	0.0310744i	−0.302271	+	0.0310744i
$289$	0.942261	−	2.16930i	0.942261	−	2.16930i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.973925	−	1.48487i	0.973925	−	1.48487i	0.102264	−	0.994757i	$-0.467391\pi$
$293$	0.973925	−	1.48487i	0.973925	−	1.48487i	0.871660	−	0.490110i	$-0.163043\pi$
$294$	0.917985	−	0.0627919i	0.917985	−	0.0627919i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	0.350775	−	0.889504i	0.350775	−	0.889504i
$303$		0			0
$304$	0.947141	−	1.34179i	0.947141	−	1.34179i
$305$		0			0
$306$	−1.15209	+	1.23358i	−1.15209	+	1.23358i
$307$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$307$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$311$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$312$		0			0
$313$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$313$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$314$		0			0
$315$		0			0
$316$	−0.0533194	+	0.0324243i	−0.0533194	+	0.0324243i
$317$	0.205261	+	0.178978i	0.205261	+	0.178978i	0.753713	−	0.657204i	$-0.228261\pi$
$317$	0.205261	+	0.178978i	0.205261	+	0.178978i	−0.548452	+	0.836182i	$0.684783\pi$
$318$	−1.48173	−	0.971867i	−1.48173	−	0.971867i
$319$		0			0
$320$		0			0
$321$	0.171866	+	0.211252i	0.171866	+	0.211252i
$322$		0			0
$323$	0.374317	+	3.64110i	0.374317	+	3.64110i
$324$	−0.136167	+	0.0705559i	−0.136167	+	0.0705559i
$325$		0			0
$326$		0			0
$327$	1.26144	+	0.0430921i	1.26144	+	0.0430921i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.05893	+	1.13384i	1.05893	+	1.13384i	0.990686	+	0.136167i	$0.0434783\pi$
$331$	1.05893	+	1.13384i	1.05893	+	1.13384i	0.0682424	+	0.997669i	$0.478261\pi$
$332$	0.189582	+	0.143764i	0.189582	+	0.143764i
$333$		0			0
$334$	0.228421	+	0.440832i	0.228421	+	0.440832i
$335$		0			0
$336$		0			0
$337$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$337$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$338$	0.450965	−	0.802041i	0.450965	−	0.802041i
$339$	−0.631088	+	1.77571i	−0.631088	+	1.77571i
$340$		0			0
$341$		0			0
$342$	0.434692	−	1.78377i	0.434692	−	1.78377i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.125383	+	0.603376i	−0.125383	+	0.603376i
$347$	0.158575	+	0.650716i	0.158575	+	0.650716i	0.994757	+	0.102264i	$0.0326087\pi$
$347$	0.158575	+	0.650716i	0.158575	+	0.650716i	−0.836182	+	0.548452i	$0.815217\pi$
$348$		0			0
$349$	1.49867	−	0.650963i	1.49867	−	0.650963i	0.519584	−	0.854419i	$-0.326087\pi$
$349$	1.49867	−	0.650963i	1.49867	−	0.650963i	0.979084	+	0.203456i	$0.0652174\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.00465974	+	0.136405i	0.00465974	+	0.136405i	0.999417	+	0.0341411i	$0.0108696\pi$
$353$	0.00465974	+	0.136405i	0.00465974	+	0.136405i	−0.994757	+	0.102264i	$0.967391\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$359$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$360$		0			0
$361$	−1.71930	−	2.43569i	−1.71930	−	2.43569i
$362$	1.56594	+	0.744727i	1.56594	+	0.744727i
$363$	0.236764	−	0.971567i	0.236764	−	0.971567i
$364$		0			0
$365$		0			0
$366$	0.526549	−	1.48157i	0.526549	−	1.48157i
$367$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$367$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$368$	1.19682	+	0.123037i	1.19682	+	0.123037i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.197362	−	0.226344i	−0.197362	−	0.226344i
$373$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$373$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$374$		0			0
$375$		0			0
$376$	−0.906746	−	0.551404i	−0.906746	−	0.551404i
$377$		0			0
$378$		0			0
$379$	0.269797	+	1.96292i	0.269797	+	1.96292i	0.269797	+	0.962917i	$0.413043\pi$
$379$	0.269797	+	1.96292i	0.269797	+	1.96292i			1.00000i	$0.500000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.623063	+	0.245704i	−0.623063	+	0.245704i	−0.657204	−	0.753713i	$-0.728261\pi$
$383$	−0.623063	+	0.245704i	−0.623063	+	0.245704i	0.0341411	+	0.999417i	$0.489130\pi$
$384$	0.448562	+	0.551357i	0.448562	+	0.551357i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$389$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$390$		0			0
$391$	−2.19056	+	1.54627i	−2.19056	+	1.54627i
$392$	0.641241	+	0.845603i	0.641241	+	0.845603i
$393$		0			0
$394$	−0.816970	+	1.34345i	−0.816970	+	1.34345i
$395$		0			0
$396$		0			0
$397$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$397$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$398$	−0.489277	+	0.0843599i	−0.489277	+	0.0843599i
$399$		0			0
$400$		0			0
$401$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$401$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.91846	−	0.330776i	−1.91846	−	0.330776i
$409$	0.547173	+	1.53960i	0.547173	+	1.53960i	0.816970	+	0.576680i	$0.195652\pi$
$409$	0.547173	+	1.53960i	0.547173	+	1.53960i	−0.269797	+	0.962917i	$0.586957\pi$
$410$		0			0
$411$	1.25923	−	0.0861339i	1.25923	−	0.0861339i
$412$		0			0
$413$		0			0
$414$	1.29505	−	0.362857i	1.29505	−	0.362857i
$415$		0			0
$416$		0			0
$417$	−1.62537	+	0.167093i	−1.62537	+	0.167093i
$418$		0			0
$419$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$419$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$420$		0			0
$421$	−0.199031	+	0.185882i	−0.199031	+	0.185882i	−0.775711	−	0.631088i	$-0.782609\pi$
$421$	−0.199031	+	0.185882i	−0.199031	+	0.185882i	0.576680	+	0.816970i	$0.304348\pi$
$422$	−0.177188	+	0.177188i	−0.177188	+	0.177188i
$423$	−0.985460	−	0.169910i	−0.985460	−	0.169910i
$424$		−	2.04378i		−	2.04378i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.0126346	+	0.0398083i	−0.0126346	+	0.0398083i
$429$		0			0
$430$		0			0
$431$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$431$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$432$	0.717481	+	0.403419i	0.717481	+	0.403419i
$433$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$433$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$434$		0			0
$435$		0			0
$436$	0.100575	+	0.165388i	0.100575	+	0.165388i
$437$	1.25260	−	2.63384i	1.25260	−	2.63384i
$438$		0			0
$439$	0.211252	−	1.53697i	0.211252	−	1.53697i	−0.519584	−	0.854419i	$-0.673913\pi$
$439$	0.211252	−	1.53697i	0.211252	−	1.53697i	0.730836	−	0.682553i	$-0.239130\pi$
$440$		0			0
$441$	0.854419	+	0.519584i	0.854419	+	0.519584i
$442$		0			0
$443$	−1.17418	−	0.463035i	−1.17418	−	0.463035i	−0.302515	−	0.953145i	$-0.597826\pi$
$443$	−1.17418	−	0.463035i	−1.17418	−	0.463035i	−0.871660	+	0.490110i	$0.836957\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$449$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$450$		0			0
$451$		0			0
$452$	−0.280794	+	0.0684276i	−0.280794	+	0.0684276i
$453$	0.868934	−	0.569934i	0.868934	−	0.569934i
$454$	0.947264	+	0.130198i	0.947264	+	0.130198i
$455$		0			0
$456$	1.99527	−	0.709120i	1.99527	−	0.709120i
$457$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$457$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$458$	0.628398	−	0.720678i	0.628398	−	0.720678i
$459$	−1.79605	+	0.373224i	−1.79605	+	0.373224i
$460$		0			0
$461$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$461$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$462$		0			0
$463$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$463$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$464$		0			0
$465$		0			0
$466$	0.495339	+	0.0338821i	0.495339	+	0.0338821i
$467$	−0.987286	+	1.30193i	−0.987286	+	1.30193i	−0.0341411	+	0.999417i	$0.510870\pi$
$467$	−0.987286	+	1.30193i	−0.987286	+	1.30193i	−0.953145	+	0.302515i	$0.902174\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.373539	+	0.0255508i	0.373539	+	0.0255508i
$475$		0			0
$476$		0			0
$477$	−0.706501	−	1.79156i	−0.706501	−	1.79156i
$478$		0			0
$479$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$479$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$480$		0			0
$481$		0			0
$482$	1.16458	−	1.33559i	1.16458	−	1.33559i
$483$		0			0
$484$	0.144506	−	0.0513574i	0.144506	−	0.0513574i
$485$		0			0
$486$	0.911560	+	0.125291i	0.911560	+	0.125291i
$487$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$487$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$488$	1.76193	−	0.429370i	1.76193	−	0.429370i
$489$		0			0
$490$		0			0
$491$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$491$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.434860	+	1.55204i	−0.434860	+	1.55204i
$497$		0			0
$498$	−0.431843	−	1.36062i	−0.431843	−	1.36062i
$499$	1.24888	+	0.759461i	1.24888	+	0.759461i	0.979084	−	0.203456i	$-0.0652174\pi$
$499$	1.24888	+	0.759461i	1.24888	+	0.759461i	0.269797	+	0.962917i	$0.413043\pi$
$500$		0			0
$501$	−0.0734746	+	0.534568i	−0.0734746	+	0.534568i
$502$		0			0
$503$	0.762664	−	1.60365i	0.762664	−	1.60365i	−0.0341411	−	0.999417i	$-0.510870\pi$
$503$	0.762664	−	1.60365i	0.762664	−	1.60365i	0.796805	−	0.604236i	$-0.206522\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.903075	−	0.429483i	0.903075	−	0.429483i
$508$		0			0
$509$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$509$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$510$		0			0
$511$		0			0
$512$	−0.339919	+	1.07100i	−0.339919	+	1.07100i
$513$	1.50391	−	1.31134i	1.50391	−	1.31134i
$514$	−0.726333	+	0.0998322i	−0.726333	+	0.0998322i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.489484	+	0.457146i	−0.489484	+	0.457146i
$520$		0			0
$521$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$521$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$522$		0			0
$523$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$523$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$524$		0			0
$525$		0			0
$526$	−1.20950	+	0.338885i	−1.20950	+	0.338885i
$527$	−1.54275	−	3.24394i	−1.54275	−	3.24394i
$528$		0			0
$529$	1.13384	−	0.0775565i	1.13384	−	0.0775565i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.277739	−	0.297386i	0.277739	−	0.297386i	−0.576680	−	0.816970i	$-0.695652\pi$
$541$	0.277739	−	0.297386i	0.277739	−	0.297386i	0.854419	+	0.519584i	$0.173913\pi$
$542$	0.123758	−	0.0213380i	0.123758	−	0.0213380i
$543$	0.923623	+	1.64266i	0.923623	+	1.64266i
$544$	−0.222075	−	0.511268i	−0.222075	−	0.511268i
$545$		0			0
$546$		0			0
$547$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$547$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$548$	0.116961	+	0.154236i	0.116961	+	0.154236i
$549$	1.39607	−	0.985454i	1.39607	−	0.985454i
$550$		0			0
$551$		0			0
$552$	1.16915	+	1.01945i	1.16915	+	1.01945i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.158139	−	0.194379i	−0.158139	−	0.194379i
$557$	0.741248	−	0.292310i	0.741248	−	0.292310i	0.0341411	−	0.999417i	$-0.489130\pi$
$557$	0.741248	−	0.292310i	0.741248	−	0.292310i	0.707107	+	0.707107i	$0.250000\pi$
$558$	0.184256	+	1.79232i	0.184256	+	1.79232i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.563424	−	0.563424i	−0.563424	−	0.563424i	0.366854	−	0.930278i	$-0.380435\pi$
$563$	−0.563424	−	0.563424i	−0.563424	−	0.563424i	−0.930278	+	0.366854i	$0.880435\pi$
$564$	−0.0610990	−	0.140664i	−0.0610990	−	0.140664i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$569$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$570$		0			0
$571$	0.125185	+	0.0543757i	0.125185	+	0.0543757i	0.460065	−	0.887885i	$-0.347826\pi$
$571$	0.125185	+	0.0543757i	0.125185	+	0.0543757i	−0.334880	+	0.942261i	$0.608696\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0752519	+	1.10014i	0.0752519	+	1.10014i
$577$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$577$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$578$	−1.96528	−	0.934644i	−1.96528	−	0.934644i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.33488	−	0.942261i	−1.33488	−	0.942261i
$587$	−0.0681230	−	1.99417i	−0.0681230	−	1.99417i	−0.102264	−	0.994757i	$-0.532609\pi$
$587$	−0.0681230	−	1.99417i	−0.0681230	−	1.99417i	0.0341411	−	0.999417i	$-0.489130\pi$
$588$	0.00523590	+	0.153271i	0.00523590	+	0.153271i
$589$	3.19207	+	2.25321i	3.19207	+	2.25321i
$590$		0			0
$591$	−1.56737	+	0.680803i	−1.56737	+	0.680803i
$592$		0			0
$593$	−0.420439	−	1.72528i	−0.420439	−	1.72528i	−0.657204	−	0.753713i	$-0.728261\pi$
$593$	−0.420439	−	1.72528i	−0.420439	−	1.72528i	0.236764	−	0.971567i	$-0.423913\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.487293	−	0.231746i	−0.487293	−	0.231746i
$598$		0			0
$599$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$599$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$600$		0			0
$601$	−0.224289	+	0.631088i	−0.224289	+	0.631088i	0.775711	+	0.631088i	$0.217391\pi$
$601$	−0.224289	+	0.631088i	−0.224289	+	0.631088i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	0.146174	+	0.0634922i	0.146174	+	0.0634922i
$605$		0			0
$606$		0			0
$607$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$607$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$608$	0.483113	+	0.366356i	0.483113	+	0.366356i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.198929	−	0.198929i	−0.198929	−	0.198929i
$613$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$613$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.0416125	+	0.404779i	0.0416125	+	0.404779i	0.994757	+	0.102264i	$0.0326087\pi$
$617$	0.0416125	+	0.404779i	0.0416125	+	0.404779i	−0.953145	+	0.302515i	$0.902174\pi$
$618$		0			0
$619$	−1.07843	−	1.32557i	−1.07843	−	1.32557i	−0.942261	−	0.334880i	$-0.891304\pi$
$619$	−1.07843	−	1.32557i	−1.07843	−	1.32557i	−0.136167	−	0.990686i	$-0.543478\pi$
$620$		0			0
$621$	1.37728	+	0.489484i	1.37728	+	0.489484i
$622$		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
$631$	−0.582332	−	1.34066i	−0.582332	−	1.34066i	−0.917211	−	0.398401i	$-0.869565\pi$
$631$	−0.582332	−	1.34066i	−0.582332	−	1.34066i	0.334880	−	0.942261i	$-0.391304\pi$
$632$	0.211645	+	0.376411i	0.211645	+	0.376411i
$633$	−0.268373	+	0.0462723i	−0.268373	+	0.0462723i
$634$	0.171036	−	0.183134i	0.171036	−	0.183134i
$635$		0			0
$636$	0.170321	−	0.241290i	0.170321	−	0.241290i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$641$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$642$	0.199665	−	0.151411i	0.199665	−	0.151411i
$643$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$643$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$644$		0			0
$645$		0			0
$646$	3.36009	−	0.229837i	3.36009	−	0.229837i
$647$	−1.05623	+	1.61035i	−1.05623	+	1.61035i	−0.302515	+	0.953145i	$0.597826\pi$
$647$	−1.05623	+	1.61035i	−1.05623	+	1.61035i	−0.753713	+	0.657204i	$0.771739\pi$
$648$	0.455786	+	0.958381i	0.455786	+	0.958381i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.130090	+	0.0412886i	0.130090	+	0.0412886i	0.366854	−	0.930278i	$-0.380435\pi$
$653$	0.130090	+	0.0412886i	0.130090	+	0.0412886i	−0.236764	+	0.971567i	$0.576087\pi$
$654$	0.0792544	−	1.15866i	0.0792544	−	1.15866i
$655$		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
$661$	−1.81734	+	0.249787i	−1.81734	+	0.249787i	−0.962917	−	0.269797i	$-0.913043\pi$
$661$	−1.81734	+	0.249787i	−1.81734	+	0.249787i	−0.854419	+	0.519584i	$0.826087\pi$
$662$	1.07593	−	0.938165i	1.07593	−	0.938165i
$663$		0			0
$664$	1.03904	−	1.27716i	1.03904	−	1.27716i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.0747316	+	0.0355408i	−0.0747316	+	0.0355408i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$673$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$674$		0			0
$675$		0			0
$676$	0.131034	+	0.0796837i	0.131034	+	0.0796837i
$677$	−0.494291	−	1.55738i	−0.494291	−	1.55738i	−0.796805	−	0.604236i	$-0.793478\pi$
$677$	−0.494291	−	1.55738i	−0.494291	−	1.55738i	0.302515	−	0.953145i	$-0.402174\pi$
$678$	1.61311	+	0.636127i	1.61311	+	0.636127i
$679$		0			0
$680$		0			0
$681$	0.759461	+	0.709287i	0.759461	+	0.709287i
$682$		0			0
$683$	0.231946	+	1.34526i	0.231946	+	1.34526i	0.836182	+	0.548452i	$0.184783\pi$
$683$	0.231946	+	1.34526i	0.231946	+	1.34526i	−0.604236	+	0.796805i	$0.706522\pi$
$684$	0.294659	+	0.0825595i	0.294659	+	0.0825595i
$685$		0			0
$686$		0			0
$687$	1.00962	−	0.246038i	1.00962	−	0.246038i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.750796	−	0.266833i	0.750796	−	0.266833i	0.0682424	−	0.997669i	$-0.478261\pi$
$691$	0.750796	−	0.266833i	0.750796	−	0.266833i	0.682553	+	0.730836i	$0.260870\pi$
$692$	−0.0997942	−	0.0243192i	−0.0997942	−	0.0243192i
$693$		0			0
$694$	0.603376	−	0.125383i	0.603376	−	0.125383i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.551542	−	1.39862i	−0.551542	−	1.39862i
$699$	0.418569	+	0.340531i	0.418569	+	0.340531i
$700$		0			0
$701$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$701$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.125584			0.125584
$707$		0			0
$708$		0			0
$709$	−1.36192	−	0.0931581i	−1.36192	−	0.0931581i	−0.631088	−	0.775711i	$-0.717391\pi$
$709$	−1.36192	−	0.0931581i	−1.36192	−	0.0931581i	−0.730836	+	0.682553i	$0.760870\pi$
$710$		0			0
$711$	0.315646	+	0.256797i	0.315646	+	0.256797i
$712$		0			0
$713$	−0.292700	+	2.84719i	−0.292700	+	2.84719i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$719$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$720$		0			0
$721$		0			0
$722$	−2.29386	+	1.50454i	−2.29386	+	1.50454i
$723$	1.87108	−	0.455969i	1.87108	−	0.455969i
$724$	−0.132964	+	0.256609i	−0.132964	+	0.256609i
$725$		0			0
$726$	−0.886009	−	0.248248i	−0.886009	−	0.248248i
$727$		0			0		−0.169910	−	0.985460i	$-0.554348\pi$
$727$		0			0		0.169910	+	0.985460i	$0.445652\pi$
$728$		0			0
$729$	0.730836	+	0.682553i	0.730836	+	0.682553i
$730$		0			0
$731$		0			0
$732$	0.243797	+	0.0961410i	0.243797	+	0.0961410i
$733$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$733$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$734$		0			0
$735$		0			0
$736$	−0.0604784	+	0.440013i	−0.0604784	+	0.440013i
$737$		0			0
$738$		0			0
$739$	0.347996	+	0.572255i	0.347996	+	0.572255i	0.979084	−	0.203456i	$-0.0652174\pi$
$739$	0.347996	+	0.572255i	0.347996	+	0.572255i	−0.631088	+	0.775711i	$0.717391\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.73926	+	0.977935i	1.73926	+	0.977935i	0.903075	+	0.429483i	$0.141304\pi$
$743$	1.73926	+	0.977935i	1.73926	+	0.977935i	0.836182	+	0.548452i	$0.184783\pi$
$744$	−1.61200	+	1.31146i	−1.61200	+	1.31146i
$745$		0			0
$746$		0			0
$747$	0.469328	−	1.47873i	0.469328	−	1.47873i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		−	0.272333i		−	0.272333i	−0.990686	−	0.136167i	$-0.956522\pi$
$751$		−	0.272333i		−	0.272333i	0.990686	−	0.136167i	$-0.0434783\pi$
$752$	−0.451442	+	0.688278i	−0.451442	+	0.688278i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$757$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$758$	1.81356	−	0.186440i	1.81356	−	0.186440i
$759$		0			0
$760$		0			0
$761$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$761$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.206375	+	0.580683i	0.206375	+	0.580683i
$767$		0			0
$768$	−0.357533	+	0.271126i	−0.357533	+	0.271126i
$769$	−1.79605	−	0.373224i	−1.79605	−	0.373224i	−0.816970	−	0.576680i	$-0.804348\pi$
$769$	−1.79605	−	0.373224i	−1.79605	−	0.373224i	−0.979084	+	0.203456i	$0.934783\pi$
$770$		0			0
$771$	−0.707469	−	0.366581i	−0.707469	−	0.366581i
$772$		0			0
$773$	−1.00534	+	0.565274i	−1.00534	+	0.565274i	−0.903075	−	0.429483i	$-0.858696\pi$
$773$	−1.00534	+	0.565274i	−1.00534	+	0.565274i	−0.102264	+	0.994757i	$0.532609\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	1.35312	+	2.06300i	1.35312	+	2.06300i
$783$		0			0
$784$	0.672464	−	0.474677i	0.672464	−	0.474677i
$785$		0			0
$786$		0			0
$787$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$787$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$788$	−0.219137	−	0.143732i	−0.219137	−	0.143732i
$789$	−1.28629	−	0.457146i	−1.28629	−	0.457146i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.0112681	−	0.0819817i	−0.0112681	−	0.0819817i
$797$	−1.63299	−	0.0557845i	−1.63299	−	0.0557845i	−0.796805	−	0.604236i	$-0.793478\pi$
$797$	−1.63299	−	0.0557845i	−1.63299	−	0.0557845i	−0.836182	+	0.548452i	$0.815217\pi$
$798$		0			0
$799$	−0.249787	−	1.81734i	−0.249787	−	1.81734i
$800$		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		0.334880	−	0.942261i	$-0.391304\pi$
$809$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$810$		0			0
$811$	0.0457060	+	0.668198i	0.0457060	+	0.668198i	0.962917	+	0.269797i	$0.0869565\pi$
$811$	0.0457060	+	0.668198i	0.0457060	+	0.668198i	−0.917211	+	0.398401i	$0.869565\pi$
$812$		0			0
$813$	0.123256	+	0.0586180i	0.123256	+	0.0586180i
$814$		0			0
$815$		0			0
$816$	−0.307208	+	1.47837i	−0.307208	+	1.47837i
$817$		0			0
$818$	1.43299	−	0.454812i	1.43299	−	0.454812i
$819$		0			0
$820$		0			0
$821$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$821$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$822$	−0.0396503	−	1.16069i	−0.0396503	−	1.16069i
$823$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$823$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.09932	+	0.348908i	−1.09932	+	0.348908i	−0.796805	−	0.604236i	$-0.793478\pi$
$827$	−1.09932	+	0.348908i	−1.09932	+	0.348908i	−0.302515	+	0.953145i	$0.597826\pi$
$828$	0.0530738	+	0.217789i	0.0530738	+	0.217789i
$829$	0.361291	−	1.73863i	0.361291	−	1.73863i	−0.269797	−	0.962917i	$-0.586957\pi$
$829$	0.361291	−	1.73863i	0.361291	−	1.73863i	0.631088	−	0.775711i	$-0.282609\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.434326	+	1.78226i	−0.434326	+	1.78226i
$834$	0.102598	+	1.49993i	0.102598	+	1.49993i
$835$		0			0
$836$		0			0
$837$	−0.959718	+	1.70686i	−0.959718	+	1.70686i
$838$		0			0
$839$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$839$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$840$		0			0
$841$	0.460065	+	0.887885i	0.460065	+	0.887885i
$842$	0.164683	+	0.188867i	0.164683	+	0.188867i
$843$		0			0
$844$	−0.0285070	−	0.0305235i	−0.0285070	−	0.0305235i
$845$		0			0
$846$	−0.187206	+	0.900885i	−0.187206	+	0.900885i
$847$		0			0
$848$	−1.58427	−	0.0541202i	−1.58427	−	0.0541202i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$853$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$854$		0			0
$855$		0			0
$856$	0.272324	+	0.0967841i	0.272324	+	0.0967841i
$857$	0.227720	+	0.149362i	0.227720	+	0.149362i	0.657204	−	0.753713i	$-0.271739\pi$
$857$	0.227720	+	0.149362i	0.227720	+	0.149362i	−0.429483	+	0.903075i	$0.641304\pi$
$858$		0			0
$859$	−1.51725	+	0.922662i	−1.51725	+	0.922662i	−0.519584	+	0.854419i	$0.673913\pi$
$859$	−1.51725	+	0.922662i	−1.51725	+	0.922662i	−0.997669	+	0.0682424i	$0.978261\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.223172	−	0.340253i	−0.223172	−	0.340253i	0.707107	−	0.707107i	$-0.250000\pi$
$863$	−0.223172	−	0.340253i	−0.223172	−	0.340253i	−0.930278	+	0.366854i	$0.880435\pi$
$864$	−0.157883	+	0.259628i	−0.157883	+	0.259628i
$865$		0			0
$866$		0			0
$867$	−1.15916	−	2.06157i	−1.15916	−	2.06157i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.16757	−	0.656490i	1.16757	−	0.656490i
$873$		0			0
$874$	−2.38272	−	1.23462i	−2.38272	−	1.23462i
$875$		0			0
$876$		0			0
$877$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$877$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$878$	−1.40675	−	0.242549i	−1.40675	−	0.242549i
$879$	−0.594669	−	1.67324i	−0.594669	−	1.67324i
$880$		0			0
$881$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$881$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$882$	0.504647	−	0.769396i	0.504647	−	0.769396i
$883$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$883$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$884$		0			0
$885$		0			0
$886$	−0.462689	+	1.06522i	−0.462689	+	1.06522i
$887$	−1.98488	+	0.204051i	−1.98488	+	0.204051i	−0.985460	+	0.169910i	$0.945652\pi$
$887$	−1.98488	+	0.204051i	−1.98488	+	0.204051i	−0.999417	+	0.0341411i	$0.989130\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.20566	+	1.58990i	1.20566	+	1.58990i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	2.74043	−	2.22950i	2.74043	−	2.22950i
$902$		0			0
$903$		0			0
$904$	0.406898	+	1.95810i	0.406898	+	1.95810i
$905$		0			0
$906$	−0.496810	−	0.816970i	−0.496810	−	0.816970i
$907$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$907$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$908$	−0.0270782	+	0.157050i	−0.0270782	+	0.157050i
$909$		0			0
$910$		0			0
$911$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$911$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$912$	−0.496850	−	1.56545i	−0.496850	−	1.56545i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.116471	+	0.108777i	0.116471	+	0.108777i
$917$		0			0
$918$	0.286793	+	1.66336i	0.286793	+	1.66336i
$919$	1.40747	+	0.394354i	1.40747	+	0.394354i	0.887885	−	0.460065i	$-0.152174\pi$
$919$	1.40747	+	0.394354i	1.40747	+	0.394354i	0.519584	+	0.854419i	$0.326087\pi$
$920$		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		0.979084	−	0.203456i	$-0.0652174\pi$
$929$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$930$		0			0
$931$	−0.538336	−	1.92135i	−0.538336	−	1.92135i
$932$	−0.00846261	+	0.0823186i	−0.00846261	+	0.0823186i
$933$		0			0
$934$	1.16623	+	0.948801i	1.16623	+	0.948801i
$935$		0			0
$936$		0			0
$937$		0			0		0.604236	−	0.796805i	$-0.293478\pi$
$937$		0			0		−0.604236	+	0.796805i	$0.706522\pi$
$938$		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
$947$	0.423115	+	1.07295i	0.423115	+	1.07295i	0.971567	+	0.236764i	$0.0760870\pi$
$947$	0.423115	+	1.07295i	0.423115	+	1.07295i	−0.548452	+	0.836182i	$0.684783\pi$
$948$	−0.00638172	+	0.0620771i	−0.00638172	+	0.0620771i
$949$		0			0
$950$		0			0
$951$	0.266637	−	0.0554078i	0.266637	−	0.0554078i
$952$		0			0
$953$	1.72528	+	0.420439i	1.72528	+	0.420439i	0.971567	−	0.236764i	$-0.0760870\pi$
$953$	1.72528	+	0.420439i	1.72528	+	0.420439i	0.753713	+	0.657204i	$0.228261\pi$
$954$	−1.66970	+	0.593413i	−1.66970	+	0.593413i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.72931	−	0.764718i	−2.72931	−	0.764718i
$962$		0			0
$963$	0.272175	−	0.00929776i	0.272175	−	0.00929776i
$964$	0.215850	+	0.201590i	0.215850	+	0.201590i
$965$		0			0
$966$		0			0
$967$		0			0		−0.930278	−	0.366854i	$-0.880435\pi$
$967$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$968$	−0.321041	−	1.01152i	−0.321041	−	1.01152i
$969$	3.12742	+	1.90183i	3.12742	+	1.90183i
$970$		0			0
$971$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$971$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$972$	−0.0260576	+	0.151131i	−0.0260576	+	0.151131i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.286177	−	1.37716i	−0.286177	−	1.37716i
$977$	−0.604843	+	0.287650i	−0.604843	+	0.287650i	−0.707107	−	0.707107i	$-0.750000\pi$
$977$	−0.604843	+	0.287650i	−0.604843	+	0.287650i	0.102264	+	0.994757i	$0.467391\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.796544	−	0.979084i	0.796544	−	0.979084i
$982$		0			0
$983$	0.783234	−	0.682945i	0.783234	−	0.682945i	−0.169910	−	0.985460i	$-0.554348\pi$
$983$	0.783234	−	0.682945i	0.783234	−	0.682945i	0.953145	+	0.302515i	$0.0978261\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.135214	−	1.97675i	0.135214	−	1.97675i	−0.0682424	−	0.997669i	$-0.521739\pi$
$991$	0.135214	−	1.97675i	0.135214	−	1.97675i	0.203456	−	0.979084i	$-0.434783\pi$
$992$	−0.567138	−	0.180002i	−0.567138	−	0.180002i
$993$	1.54329	−	0.158655i	1.54329	−	0.158655i
$994$		0			0
$995$		0			0
$996$	0.229104	−	0.0641920i	0.229104	−	0.0641920i
$997$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$997$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$998$	0.737628	−	1.12461i	0.737628	−	1.12461i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.218.2	yes	88
3.2	odd	2	inner	3525.1.bg.a.218.1	✓	88
5.2	odd	4	inner	3525.1.bg.a.782.2	yes	88
5.3	odd	4	inner	3525.1.bg.a.782.1	yes	88
5.4	even	2	inner	3525.1.bg.a.218.1	✓	88
15.2	even	4	inner	3525.1.bg.a.782.1	yes	88
15.8	even	4	inner	3525.1.bg.a.782.2	yes	88
15.14	odd	2	CM	3525.1.bg.a.218.2	yes	88
47.11	odd	46	inner	3525.1.bg.a.293.1	yes	88
141.11	even	46	inner	3525.1.bg.a.293.2	yes	88
235.58	even	92	inner	3525.1.bg.a.857.2	yes	88
235.152	even	92	inner	3525.1.bg.a.857.1	yes	88
235.199	odd	46	inner	3525.1.bg.a.293.2	yes	88
705.152	odd	92	inner	3525.1.bg.a.857.2	yes	88
705.293	odd	92	inner	3525.1.bg.a.857.1	yes	88
705.434	even	46	inner	3525.1.bg.a.293.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.218.1	✓	88	3.2	odd	2	inner
3525.1.bg.a.218.1	✓	88	5.4	even	2	inner
3525.1.bg.a.218.2	yes	88	1.1	even	1	trivial
3525.1.bg.a.218.2	yes	88	15.14	odd	2	CM
3525.1.bg.a.293.1	yes	88	47.11	odd	46	inner
3525.1.bg.a.293.1	yes	88	705.434	even	46	inner
3525.1.bg.a.293.2	yes	88	141.11	even	46	inner
3525.1.bg.a.293.2	yes	88	235.199	odd	46	inner
3525.1.bg.a.782.1	yes	88	5.3	odd	4	inner
3525.1.bg.a.782.1	yes	88	15.2	even	4	inner
3525.1.bg.a.782.2	yes	88	5.2	odd	4	inner
3525.1.bg.a.782.2	yes	88	15.8	even	4	inner
3525.1.bg.a.857.1	yes	88	235.152	even	92	inner
3525.1.bg.a.857.1	yes	88	705.293	odd	92	inner
3525.1.bg.a.857.2	yes	88	235.58	even	92	inner
3525.1.bg.a.857.2	yes	88	705.152	odd	92	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0314143 - 0.919594i) q^{2} +(0.604236 - 0.796805i) q^{3} +(0.153003 + 0.0104657i) q^{4} +(-0.713755 - 0.580683i) q^{6} +(0.108527 - 1.05568i) q^{8} +(-0.269797 - 0.962917i) q^{9} +O(q^{10})\)	\(q+(0.0314143 - 0.919594i) q^{2} +(0.604236 - 0.796805i) q^{3} +(0.153003 + 0.0104657i) q^{4} +(-0.713755 - 0.580683i) q^{6} +(0.108527 - 1.05568i) q^{8} +(-0.269797 - 0.962917i) q^{9} +(0.100789 - 0.115590i) q^{12} +(-0.815453 - 0.112081i) q^{16} +(1.53391 - 1.00609i) q^{17} +(-0.893968 + 0.217854i) q^{18} +(-0.917985 + 1.77163i) q^{19} +(-1.46082 + 0.0499031i) q^{23} +(-0.775594 - 0.724354i) q^{24} +(-0.930278 - 0.366854i) q^{27} +(0.266637 - 1.93993i) q^{31} +(0.0516297 - 0.299446i) q^{32} +(-0.877010 - 1.44218i) q^{34} +(-0.0312021 - 0.150153i) q^{36} +(1.60034 + 0.899828i) q^{38} +1.34493i q^{46} +(0.429483 - 0.903075i) q^{47} +(-0.582034 + 0.582034i) q^{48} +(-0.730836 + 0.682553i) q^{49} +(0.125185 - 1.83015i) q^{51} +(1.91574 - 0.196944i) q^{53} +(-0.366581 + 0.843954i) q^{54} +(0.856964 + 1.80194i) q^{57} +(0.572255 + 1.61017i) q^{61} +(-1.77557 - 0.306139i) q^{62} +(-1.07965 - 0.224354i) q^{64} +(0.245223 - 0.137882i) q^{68} +(-0.842917 + 1.19414i) q^{69} +(-1.04581 + 0.180316i) q^{72} +(-0.158996 + 0.261458i) q^{76} +(-0.332435 + 0.234658i) q^{79} +(-0.854419 + 0.519584i) q^{81} +(1.29727 + 0.850881i) q^{83} +(-0.224032 - 0.00765317i) q^{92} +(-1.38463 - 1.38463i) q^{93} +(-0.816970 - 0.423320i) q^{94} +(-0.207404 - 0.222075i) q^{96} +(0.604713 + 0.693514i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 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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