LMFDB - Embedded newform 3525.1.bg.a.1718.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3525.107");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.75920416953$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$2$ over $\Q(\zeta_{92})$
Coefficient field:	$\Q(\zeta_{184})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{88} - x^{84} + x^{80} - x^{76} + x^{72} - x^{68} + x^{64} - x^{60} + x^{56} - x^{52} + x^{48} + \cdots + 1 $ x^88 - x^84 + x^80 - x^76 + x^72 - x^68 + x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{46}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{46} - \cdots)$

Embedding invariants

Embedding label			1718.1
Root			$-0.302515 + 0.953145i$ of defining polynomial
Character	$\chi$	$=$	3525.1718
Dual form			3525.1.bg.a.1307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.554940 + 1.74847i) q^{2} +(-0.429483 - 0.903075i) q^{3} +(-1.93222 - 1.36391i) q^{4} +(1.81734 - 0.249787i) q^{6} +(1.99534 - 1.51312i) q^{8} +(-0.631088 + 0.775711i) q^{9} +O(q^{10})$	\(q+(-0.554940 + 1.74847i) q^{2} +(-0.429483 - 0.903075i) q^{3} +(-1.93222 - 1.36391i) q^{4} +(1.81734 - 0.249787i) q^{6} +(1.99534 - 1.51312i) q^{8} +(-0.631088 + 0.775711i) q^{9} +(-0.401856 + 2.33072i) q^{12} +(0.746320 + 2.09994i) q^{16} +(-0.837519 - 1.48953i) q^{17} +(-1.00609 - 1.53391i) q^{18} +(1.49867 - 0.650963i) q^{19} +(-1.69257 + 0.537196i) q^{23} +(-2.22343 - 1.15209i) q^{24} +(0.971567 + 0.236764i) q^{27} +(-0.508438 + 0.180699i) q^{31} +(-1.58313 + 0.0540813i) q^{32} +(3.06917 - 0.637780i) q^{34} +(2.27740 - 0.638098i) q^{36} +(0.306520 + 2.98162i) q^{38} -3.25751i q^{46} +(-0.753713 + 0.657204i) q^{47} +(1.57587 - 1.57587i) q^{48} +(-0.887885 + 0.460065i) q^{49} +(-0.985454 + 1.39607i) q^{51} +(-0.937426 + 1.23618i) q^{53} +(-0.953137 + 1.56737i) q^{54} +(-1.23152 - 1.07383i) q^{57} +(0.0277687 - 0.405963i) q^{61} +(-0.0337943 - 0.989266i) q^{62} +(0.182706 - 0.652087i) q^{64} +(-0.413309 + 4.02040i) q^{68} +(1.21206 + 1.29780i) q^{69} +(-0.0854955 + 2.50272i) q^{72} +(-3.78361 - 0.786244i) q^{76} +(-1.40747 - 1.31448i) q^{79} +(-0.203456 - 0.979084i) q^{81} +(0.971091 - 1.72708i) q^{83} +(4.00310 + 1.27053i) q^{92} +(0.381550 + 0.381550i) q^{93} +(-0.730836 - 1.68255i) q^{94} +(0.728767 + 1.40646i) q^{96} +(-0.311687 - 1.80775i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{29}{46}\right)$	$-1$

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 $

$2$	−0.554940	+	1.74847i	−0.554940	+	1.74847i	0.102264	+	0.994757i	$0.467391\pi$
$2$	−0.554940	+	1.74847i	−0.554940	+	1.74847i	−0.657204	+	0.753713i	$0.728261\pi$
$3$	−0.429483	−	0.903075i	−0.429483	−	0.903075i
$3$	−0.429483	−	0.903075i	−0.429483	−	0.903075i
$4$	−1.93222	−	1.36391i	−1.93222	−	1.36391i
$5$		0			0
$5$		0			0
$6$	1.81734	−	0.249787i	1.81734	−	0.249787i
$7$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$7$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$8$	1.99534	−	1.51312i	1.99534	−	1.51312i
$9$	−0.631088	+	0.775711i	−0.631088	+	0.775711i
$10$		0			0
$11$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$11$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$12$	−0.401856	+	2.33072i	−0.401856	+	2.33072i
$13$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$13$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$14$		0			0
$15$		0			0
$16$	0.746320	+	2.09994i	0.746320	+	2.09994i
$17$	−0.837519	−	1.48953i	−0.837519	−	1.48953i	−0.871660	−	0.490110i	$-0.836957\pi$
$17$	−0.837519	−	1.48953i	−0.837519	−	1.48953i	0.0341411	−	0.999417i	$-0.489130\pi$
$18$	−1.00609	−	1.53391i	−1.00609	−	1.53391i
$19$	1.49867	−	0.650963i	1.49867	−	0.650963i	0.519584	−	0.854419i	$-0.326087\pi$
$19$	1.49867	−	0.650963i	1.49867	−	0.650963i	0.979084	+	0.203456i	$0.0652174\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.69257	+	0.537196i	−1.69257	+	0.537196i	−0.985460	−	0.169910i	$-0.945652\pi$
$23$	−1.69257	+	0.537196i	−1.69257	+	0.537196i	−0.707107	+	0.707107i	$0.750000\pi$
$24$	−2.22343	−	1.15209i	−2.22343	−	1.15209i
$25$		0			0
$26$		0			0
$27$	0.971567	+	0.236764i	0.971567	+	0.236764i
$28$		0			0
$29$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$29$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$30$		0			0
$31$	−0.508438	+	0.180699i	−0.508438	+	0.180699i	−0.576680	−	0.816970i	$-0.695652\pi$
$31$	−0.508438	+	0.180699i	−0.508438	+	0.180699i	0.0682424	+	0.997669i	$0.478261\pi$
$32$	−1.58313	+	0.0540813i	−1.58313	+	0.0540813i
$33$		0			0
$34$	3.06917	−	0.637780i	3.06917	−	0.637780i
$35$		0			0
$36$	2.27740	−	0.638098i	2.27740	−	0.638098i
$37$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$37$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$38$	0.306520	+	2.98162i	0.306520	+	2.98162i
$39$		0			0
$40$		0			0
$41$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$41$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$42$		0			0
$43$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$43$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$44$		0			0
$45$		0			0
$46$		−	3.25751i		−	3.25751i
$47$	−0.753713	+	0.657204i	−0.753713	+	0.657204i
$47$	−0.753713	+	0.657204i	−0.753713	+	0.657204i
$48$	1.57587	−	1.57587i	1.57587	−	1.57587i
$49$	−0.887885	+	0.460065i	−0.887885	+	0.460065i
$50$		0			0
$51$	−0.985454	+	1.39607i	−0.985454	+	1.39607i
$52$		0			0
$53$	−0.937426	+	1.23618i	−0.937426	+	1.23618i	0.0341411	+	0.999417i	$0.489130\pi$
$53$	−0.937426	+	1.23618i	−0.937426	+	1.23618i	−0.971567	+	0.236764i	$0.923913\pi$
$54$	−0.953137	+	1.56737i	−0.953137	+	1.56737i
$55$		0			0
$56$		0			0
$57$	−1.23152	−	1.07383i	−1.23152	−	1.07383i
$58$		0			0
$59$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$59$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$60$		0			0
$61$	0.0277687	−	0.405963i	0.0277687	−	0.405963i	−0.962917	−	0.269797i	$-0.913043\pi$
$61$	0.0277687	−	0.405963i	0.0277687	−	0.405963i	0.990686	−	0.136167i	$-0.0434783\pi$
$62$	−0.0337943	−	0.989266i	−0.0337943	−	0.989266i
$63$		0			0
$64$	0.182706	−	0.652087i	0.182706	−	0.652087i
$65$		0			0
$66$		0			0
$67$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$67$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$68$	−0.413309	+	4.02040i	−0.413309	+	4.02040i
$69$	1.21206	+	1.29780i	1.21206	+	1.29780i
$70$		0			0
$71$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$71$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$72$	−0.0854955	+	2.50272i	−0.0854955	+	2.50272i
$73$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$73$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$74$		0			0
$75$		0			0
$76$	−3.78361	−	0.786244i	−3.78361	−	0.786244i
$77$		0			0
$78$		0			0
$79$	−1.40747	−	1.31448i	−1.40747	−	1.31448i	−0.887885	−	0.460065i	$-0.847826\pi$
$79$	−1.40747	−	1.31448i	−1.40747	−	1.31448i	−0.519584	−	0.854419i	$-0.673913\pi$
$80$		0			0
$81$	−0.203456	−	0.979084i	−0.203456	−	0.979084i
$82$		0			0
$83$	0.971091	−	1.72708i	0.971091	−	1.72708i	0.366854	−	0.930278i	$-0.380435\pi$
$83$	0.971091	−	1.72708i	0.971091	−	1.72708i	0.604236	−	0.796805i	$-0.293478\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$89$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$90$		0			0
$91$		0			0
$92$	4.00310	+	1.27053i	4.00310	+	1.27053i
$93$	0.381550	+	0.381550i	0.381550	+	0.381550i
$94$	−0.730836	−	1.68255i	−0.730836	−	1.68255i
$95$		0			0
$96$	0.728767	+	1.40646i	0.728767	+	1.40646i
$97$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$97$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$98$	−0.311687	−	1.80775i	−0.311687	−	1.80775i
$99$		0			0
$100$		0			0
$101$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$101$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$102$	−1.89412	−	2.49777i	−1.89412	−	2.49777i
$103$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$103$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$104$		0			0
$105$		0			0
$106$	−1.64121	−	2.32507i	−1.64121	−	2.32507i
$107$	−1.57580	−	1.03357i	−1.57580	−	1.03357i	−0.971567	−	0.236764i	$-0.923913\pi$
$107$	−1.57580	−	1.03357i	−1.57580	−	1.03357i	−0.604236	−	0.796805i	$-0.706522\pi$
$108$	−1.55436	−	1.78261i	−1.55436	−	1.78261i
$109$	0.185882	−	0.199031i	0.185882	−	0.199031i	−0.631088	−	0.775711i	$-0.717391\pi$
$109$	0.185882	−	0.199031i	0.185882	−	0.199031i	0.816970	+	0.576680i	$0.195652\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.85622	−	0.731998i	−1.85622	−	0.731998i	−0.953145	−	0.302515i	$-0.902174\pi$
$113$	−1.85622	−	0.731998i	−1.85622	−	0.731998i	−0.903075	−	0.429483i	$-0.858696\pi$
$114$	2.56098	−	1.55737i	2.56098	−	1.55737i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.854419	+	0.519584i	−0.854419	+	0.519584i
$122$	0.694405	+	0.273838i	0.694405	+	0.273838i
$123$		0			0
$124$	1.22887	+	0.344314i	1.22887	+	0.344314i
$125$		0			0
$126$		0			0
$127$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$127$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$128$	−0.285793	−	0.187451i	−0.285793	−	0.187451i
$129$		0			0
$130$		0			0
$131$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$131$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−3.92497	−	1.70486i	−3.92497	−	1.70486i
$137$	−0.0462723	−	0.268373i	−0.0462723	−	0.268373i	0.953145	−	0.302515i	$-0.0978261\pi$
$137$	−0.0462723	−	0.268373i	−0.0462723	−	0.268373i	−0.999417	+	0.0341411i	$0.989130\pi$
$138$	−2.94178	+	1.39905i	−2.94178	+	1.39905i
$139$	−0.672464	−	1.29780i	−0.672464	−	1.29780i	−0.942261	−	0.334880i	$-0.891304\pi$
$139$	−0.672464	−	1.29780i	−0.672464	−	1.29780i	0.269797	−	0.962917i	$-0.413043\pi$
$140$		0			0
$141$	0.917211	+	0.398401i	0.917211	+	0.398401i
$142$		0			0
$143$		0			0
$144$	−2.09994	−	0.746320i	−2.09994	−	0.746320i
$145$		0			0
$146$		0			0
$147$	0.796805	+	0.604236i	0.796805	+	0.604236i
$148$		0			0
$149$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$149$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$150$		0			0
$151$	1.95360	−	0.133630i	1.95360	−	0.133630i	0.962917	−	0.269797i	$-0.0869565\pi$
$151$	1.95360	−	0.133630i	1.95360	−	0.133630i	0.990686	+	0.136167i	$0.0434783\pi$
$152$	2.00538	−	3.56656i	2.00538	−	3.56656i
$153$	1.68399	+	0.290349i	1.68399	+	0.290349i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$157$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$158$	3.07940	−	1.73146i	3.07940	−	1.73146i
$159$	1.51897	+	0.315646i	1.51897	+	0.315646i
$160$		0			0
$161$		0			0
$162$	1.82481	+	0.187596i	1.82481	+	0.187596i
$163$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$163$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$164$		0			0
$165$		0			0
$166$	2.48086	+	2.65635i	2.48086	+	2.65635i
$167$	0.129075	−	1.25556i	0.129075	−	1.25556i	−0.707107	−	0.707107i	$-0.750000\pi$
$167$	0.129075	−	1.25556i	0.129075	−	1.25556i	0.836182	−	0.548452i	$-0.184783\pi$
$168$		0			0
$169$	−0.398401	−	0.917211i	−0.398401	−	0.917211i
$170$		0			0
$171$	−0.440832	+	1.57335i	−0.440832	+	1.57335i
$172$		0			0
$173$	−0.00465974	−	0.136405i	−0.00465974	−	0.136405i	−0.999417	−	0.0341411i	$-0.989130\pi$
$173$	−0.00465974	−	0.136405i	−0.00465974	−	0.136405i	0.994757	−	0.102264i	$-0.0326087\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$179$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$180$		0			0
$181$	−1.03675	+	1.70486i	−1.03675	+	1.70486i	−0.460065	+	0.887885i	$0.652174\pi$
$181$	−1.03675	+	1.70486i	−1.03675	+	1.70486i	−0.576680	+	0.816970i	$0.695652\pi$
$182$		0			0
$183$	−0.378541	+	0.149277i	−0.378541	+	0.149277i
$184$	−2.56441	+	3.63294i	−2.56441	+	3.63294i
$185$		0			0
$186$	−0.878867	+	0.455392i	−0.878867	+	0.455392i
$187$		0			0
$188$	2.35271	−	0.241866i	2.35271	−	0.241866i
$189$		0			0
$190$		0			0
$191$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$191$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$192$	−0.667352	+	0.115063i	−0.667352	+	0.115063i
$193$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$193$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$194$		0			0
$195$		0			0
$196$	2.34308	+	0.322049i	2.34308	+	0.322049i
$197$	0.0416125	+	0.404779i	0.0416125	+	0.404779i	0.994757	+	0.102264i	$0.0326087\pi$
$197$	0.0416125	+	0.404779i	0.0416125	+	0.404779i	−0.953145	+	0.302515i	$0.902174\pi$
$198$		0			0
$199$	−1.21537	+	0.340531i	−1.21537	+	0.340531i	−0.816970	−	0.576680i	$-0.804348\pi$
$199$	−1.21537	+	0.340531i	−1.21537	+	0.340531i	−0.398401	+	0.917211i	$0.630435\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	3.80823	−	1.35344i	3.80823	−	1.35344i
$205$		0			0
$206$		0			0
$207$	0.651449	−	1.65196i	0.651449	−	1.65196i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.67324	−	0.867003i	−1.67324	−	0.867003i	−0.990686	−	0.136167i	$-0.956522\pi$
$211$	−1.67324	−	0.867003i	−1.67324	−	0.867003i	−0.682553	−	0.730836i	$-0.739130\pi$
$212$	3.49735	−	1.11001i	3.49735	−	1.11001i
$213$		0			0
$214$	2.68164	−	2.18168i	2.68164	−	2.18168i
$215$		0			0
$216$	2.29686	−	0.997669i	2.29686	−	0.997669i
$217$		0			0
$218$	0.244846	+	0.435459i	0.244846	+	0.435459i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$223$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$224$		0			0
$225$		0			0
$226$	2.30997	−	2.83933i	2.30997	−	2.83933i
$227$	1.56028	−	1.18320i	1.56028	−	1.18320i	0.657204	−	0.753713i	$-0.271739\pi$
$227$	1.56028	−	1.18320i	1.56028	−	1.18320i	0.903075	−	0.429483i	$-0.141304\pi$
$228$	0.914962	+	3.75456i	0.914962	+	3.75456i
$229$	−1.93993	+	0.266637i	−1.93993	+	0.266637i	−0.997669	−	0.0682424i	$-0.978261\pi$
$229$	−1.93993	+	0.266637i	−1.93993	+	0.266637i	−0.942261	+	0.334880i	$0.891304\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.381827	+	1.20304i	−0.381827	+	1.20304i	0.548452	+	0.836182i	$0.315217\pi$
$233$	−0.381827	+	1.20304i	−0.381827	+	1.20304i	−0.930278	+	0.366854i	$0.880435\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.582593	+	1.83560i	−0.582593	+	1.83560i
$238$		0			0
$239$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$239$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$240$		0			0
$241$	−1.53697	+	0.211252i	−1.53697	+	0.211252i	−0.854419	−	0.519584i	$-0.826087\pi$
$241$	−1.53697	+	0.211252i	−1.53697	+	0.211252i	−0.682553	+	0.730836i	$0.739130\pi$
$242$	−0.434326	−	1.78226i	−0.434326	−	1.78226i
$243$	−0.796805	+	0.604236i	−0.796805	+	0.604236i
$244$	−0.607353	+	0.746537i	−0.607353	+	0.746537i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.741090	+	1.12988i	−0.741090	+	1.12988i
$249$	−1.97675	−	0.135214i	−1.97675	−	0.135214i
$250$		0			0
$251$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$251$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	1.01166	−	0.823048i	1.01166	−	0.823048i
$257$	1.03856	+	0.0354783i	1.03856	+	0.0354783i	0.548452	−	0.836182i	$-0.315217\pi$
$257$	1.03856	+	0.0354783i	1.03856	+	0.0354783i	0.490110	+	0.871660i	$0.336957\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.337554	+	0.855977i	−0.337554	+	0.855977i	0.657204	+	0.753713i	$0.271739\pi$
$263$	−0.337554	+	0.855977i	−0.337554	+	0.855977i	−0.994757	+	0.102264i	$0.967391\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$269$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$270$		0			0
$271$	1.11059	−	0.311173i	1.11059	−	0.311173i	0.334880	−	0.942261i	$-0.391304\pi$
$271$	1.11059	−	0.311173i	1.11059	−	0.311173i	0.775711	+	0.631088i	$0.217391\pi$
$272$	2.50286	−	2.87041i	2.50286	−	2.87041i
$273$		0			0
$274$	0.494921	+	0.0680254i	0.494921	+	0.0680254i
$275$		0			0
$276$	−0.571884	−	4.16077i	−0.571884	−	4.16077i
$277$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$277$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$278$	2.64234	−	0.455585i	2.64234	−	0.455585i
$279$	0.180699	−	0.508438i	0.180699	−	0.508438i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	−1.20559	+	1.38263i	−1.20559	+	1.38263i
$283$		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
$288$	0.957142	−	1.26218i	0.957142	−	1.26218i
$289$	−0.997669	+	1.64060i	−0.997669	+	1.64060i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.694541	+	0.390521i	0.694541	+	0.390521i	0.796805	−	0.604236i	$-0.206522\pi$
$293$	0.694541	+	0.390521i	0.694541	+	0.390521i	−0.102264	+	0.994757i	$0.532609\pi$
$294$	−1.49867	+	1.05788i	−1.49867	+	1.05788i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.850483	+	3.48997i	−0.850483	+	3.48997i
$303$		0			0
$304$	2.48547	+	2.66129i	2.48547	+	2.66129i
$305$		0			0
$306$	−1.44218	+	2.78328i	−1.44218	+	2.78328i
$307$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$307$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$311$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$312$		0			0
$313$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$313$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$314$		0			0
$315$		0			0
$316$	0.926702	+	4.45954i	0.926702	+	4.45954i
$317$	1.85712	+	0.320200i	1.85712	+	0.320200i	0.985460	−	0.169910i	$-0.0543478\pi$
$317$	1.85712	+	0.320200i	1.85712	+	0.320200i	0.871660	+	0.490110i	$0.163043\pi$
$318$	−1.39484	+	2.48071i	−1.39484	+	2.48071i
$319$		0			0
$320$		0			0
$321$	−0.256609	+	1.86697i	−0.256609	+	1.86697i
$322$		0			0
$323$	−2.22479	−	1.68711i	−2.22479	−	1.68711i
$324$	−0.942261	+	2.16930i	−0.942261	+	2.16930i
$325$		0			0
$326$		0			0
$327$	−0.259573	−	0.0823848i	−0.259573	−	0.0823848i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.911560	+	1.75923i	0.911560	+	1.75923i	0.576680	+	0.816970i	$0.304348\pi$
$331$	0.911560	+	1.75923i	0.911560	+	1.75923i	0.334880	+	0.942261i	$0.391304\pi$
$332$	−4.23195	+	2.01263i	−4.23195	+	2.01263i
$333$		0			0
$334$	2.12368	+	0.922444i	2.12368	+	0.922444i
$335$		0			0
$336$		0			0
$337$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$337$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$338$	1.82481	−	0.187596i	1.82481	−	0.187596i
$339$	0.136167	+	1.99069i	0.136167	+	1.99069i
$340$		0			0
$341$		0			0
$342$	−2.50632	−	1.64389i	−2.50632	−	1.64389i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.241086	+	0.0675492i	0.241086	+	0.0675492i
$347$	0.114126	−	0.0748554i	0.114126	−	0.0748554i	−0.490110	−	0.871660i	$-0.663043\pi$
$347$	0.114126	−	0.0748554i	0.114126	−	0.0748554i	0.604236	+	0.796805i	$0.293478\pi$
$348$		0			0
$349$	−1.24888	+	0.759461i	−1.24888	+	0.759461i	−0.979084	−	0.203456i	$-0.934783\pi$
$349$	−1.24888	+	0.759461i	−1.24888	+	0.759461i	−0.269797	+	0.962917i	$0.586957\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.348908	+	1.09932i	0.348908	+	1.09932i	0.953145	+	0.302515i	$0.0978261\pi$
$353$	0.348908	+	1.09932i	0.348908	+	1.09932i	−0.604236	+	0.796805i	$0.706522\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$359$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$360$		0			0
$361$	1.13970	−	1.22032i	1.13970	−	1.22032i
$362$	−2.40556	−	2.75881i	−2.40556	−	2.75881i
$363$	0.836182	+	0.548452i	0.836182	+	0.548452i
$364$		0			0
$365$		0			0
$366$	−0.0509395	−	0.744708i	−0.0509395	−	0.744708i
$367$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$367$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$368$	−2.39128	−	3.15337i	−2.39128	−	3.15337i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.216839	−	1.25764i	−0.216839	−	1.25764i
$373$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$373$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$374$		0			0
$375$		0			0
$376$	−0.509491	+	2.45180i	−0.509491	+	2.45180i
$377$		0			0
$378$		0			0
$379$	0.631088	+	0.224289i	0.631088	+	0.224289i	0.631088	−	0.775711i	$-0.282609\pi$
$379$	0.631088	+	0.224289i	0.631088	+	0.224289i			1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.132604	−	0.0323148i	0.132604	−	0.0323148i	−0.169910	−	0.985460i	$-0.554348\pi$
$383$	0.132604	−	0.0323148i	0.132604	−	0.0323148i	0.302515	+	0.953145i	$0.402174\pi$
$384$	−0.0465394	+	0.338599i	−0.0465394	+	0.338599i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$389$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$390$		0			0
$391$	2.21773	+	2.07121i	2.21773	+	2.07121i
$392$	−1.07550	+	2.26146i	−1.07550	+	2.26146i
$393$		0			0
$394$	−0.730836	−	0.151869i	−0.730836	−	0.151869i
$395$		0			0
$396$		0			0
$397$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$397$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$398$	0.0790491	−	2.31401i	0.0790491	−	2.31401i
$399$		0			0
$400$		0			0
$401$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$401$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.146098	+	4.27675i	0.146098	+	4.27675i
$409$	0.0997480	−	1.45826i	0.0997480	−	1.45826i	−0.631088	−	0.775711i	$-0.717391\pi$
$409$	0.0997480	−	1.45826i	0.0997480	−	1.45826i	0.730836	−	0.682553i	$-0.239130\pi$
$410$		0			0
$411$	−0.222488	+	0.157049i	−0.222488	+	0.157049i
$412$		0			0
$413$		0			0
$414$	2.52689	+	2.05578i	2.52689	+	2.05578i
$415$		0			0
$416$		0			0
$417$	−0.883195	+	1.16467i	−0.883195	+	1.16467i
$418$		0			0
$419$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$419$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$420$		0			0
$421$	−1.67324	+	0.867003i	−1.67324	+	0.867003i	−0.682553	+	0.730836i	$0.739130\pi$
$421$	−1.67324	+	0.867003i	−1.67324	+	0.867003i	−0.990686	+	0.136167i	$0.956522\pi$
$422$	2.44447	−	2.44447i	2.44447	−	2.44447i
$423$	−0.0341411	−	0.999417i	−0.0341411	−	0.999417i
$424$			3.88504i			3.88504i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.63510	+	4.14634i	1.63510	+	4.14634i
$429$		0			0
$430$		0			0
$431$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$431$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$432$	0.227908	+	2.21694i	0.227908	+	2.21694i
$433$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$433$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$434$		0			0
$435$		0			0
$436$	−0.630625	+	0.131045i	−0.630625	+	0.131045i
$437$	−2.18690	+	1.90688i	−2.18690	+	1.90688i
$438$		0			0
$439$	1.86697	−	0.663521i	1.86697	−	0.663521i	0.887885	−	0.460065i	$-0.152174\pi$
$439$	1.86697	−	0.663521i	1.86697	−	0.663521i	0.979084	−	0.203456i	$-0.0652174\pi$
$440$		0			0
$441$	0.203456	−	0.979084i	0.203456	−	0.979084i
$442$		0			0
$443$	−0.264590	−	0.0644788i	−0.264590	−	0.0644788i	0.102264	−	0.994757i	$-0.467391\pi$
$443$	−0.264590	−	0.0644788i	−0.264590	−	0.0644788i	−0.366854	+	0.930278i	$0.619565\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$449$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$450$		0			0
$451$		0			0
$452$	2.58825	+	3.94610i	2.58825	+	3.94610i
$453$	−0.959718	−	1.70686i	−0.959718	−	1.70686i
$454$	1.20292	+	3.38470i	1.20292	+	3.38470i
$455$		0			0
$456$	−4.08214	−	0.279226i	−4.08214	−	0.279226i
$457$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$457$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$458$	0.610336	−	3.53988i	0.610336	−	3.53988i
$459$	−0.461039	−	1.64547i	−0.461039	−	1.64547i
$460$		0			0
$461$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$461$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$462$		0			0
$463$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$463$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$464$		0			0
$465$		0			0
$466$	−1.89158	−	1.33522i	−1.89158	−	1.33522i
$467$	0.627764	+	1.32000i	0.627764	+	1.32000i	0.930278	+	0.366854i	$0.119565\pi$
$467$	0.627764	+	1.32000i	0.627764	+	1.32000i	−0.302515	+	0.953145i	$0.597826\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−2.88619	−	2.03729i	−2.88619	−	2.03729i
$475$		0			0
$476$		0			0
$477$	−0.367322	−	1.50731i	−0.367322	−	1.50731i
$478$		0			0
$479$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$479$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$480$		0			0
$481$		0			0
$482$	0.483559	−	2.80458i	0.483559	−	2.80458i
$483$		0			0
$484$	2.35959	+	0.161401i	2.35959	+	0.161401i
$485$		0			0
$486$	−0.614311	−	1.72850i	−0.614311	−	1.72850i
$487$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$487$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$488$	−0.558862	−	0.852054i	−0.558862	−	0.852054i
$489$		0			0
$490$		0			0
$491$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$491$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.758915	−	0.932831i	−0.758915	−	0.932831i
$497$		0			0
$498$	1.33340	−	3.38126i	1.33340	−	3.38126i
$499$	0.361291	−	1.73863i	0.361291	−	1.73863i	−0.269797	−	0.962917i	$-0.586957\pi$
$499$	0.361291	−	1.73863i	0.361291	−	1.73863i	0.631088	−	0.775711i	$-0.282609\pi$
$500$		0			0
$501$	−1.18930	+	0.422677i	−1.18930	+	0.422677i
$502$		0			0
$503$	0.600560	−	0.523661i	0.600560	−	0.523661i	−0.302515	−	0.953145i	$-0.597826\pi$
$503$	0.600560	−	0.523661i	0.600560	−	0.523661i	0.903075	+	0.429483i	$0.141304\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.657204	+	0.753713i	−0.657204	+	0.753713i
$508$		0			0
$509$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$509$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$510$		0			0
$511$		0			0
$512$	0.752279	+	1.90765i	0.752279	+	1.90765i
$513$	1.61018	−	0.277623i	1.61018	−	0.277623i
$514$	−0.638372	+	1.79621i	−0.638372	+	1.79621i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.121183	+	0.0627919i	−0.121183	+	0.0627919i
$520$		0			0
$521$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$521$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$522$		0			0
$523$		0			0		0.604236	−	0.796805i	$-0.293478\pi$
$523$		0			0		−0.604236	+	0.796805i	$0.706522\pi$
$524$		0			0
$525$		0			0
$526$	−1.30933	−	1.06522i	−1.30933	−	1.06522i
$527$	0.694982	+	0.605993i	0.694982	+	0.605993i
$528$		0			0
$529$	1.75923	−	1.24180i	1.75923	−	1.24180i
$530$		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
$541$	0.886009	−	1.70992i	0.886009	−	1.70992i	0.203456	−	0.979084i	$-0.434783\pi$
$541$	0.886009	−	1.70992i	0.886009	−	1.70992i	0.682553	−	0.730836i	$-0.260870\pi$
$542$	−0.0722341	+	2.11452i	−0.0722341	+	2.11452i
$543$	1.98488	+	0.204051i	1.98488	+	0.204051i
$544$	1.40646	+	2.31282i	1.40646	+	2.31282i
$545$		0			0
$546$		0			0
$547$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$547$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$548$	−0.276629	+	0.581668i	−0.276629	+	0.581668i
$549$	0.297386	+	0.277739i	0.297386	+	0.277739i
$550$		0			0
$551$		0			0
$552$	4.38219	+	0.755566i	4.38219	+	0.755566i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.470729	+	3.42481i	−0.470729	+	3.42481i
$557$	1.00962	−	0.246038i	1.00962	−	0.246038i	0.302515	−	0.953145i	$-0.402174\pi$
$557$	1.00962	−	0.246038i	1.00962	−	0.246038i	0.707107	+	0.707107i	$0.250000\pi$
$558$	0.788712	+	0.598099i	0.788712	+	0.598099i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.734803	+	0.734803i	0.734803	+	0.734803i	0.971567	−	0.236764i	$-0.0760870\pi$
$563$	0.734803	+	0.734803i	0.734803	+	0.734803i	−0.236764	+	0.971567i	$0.576087\pi$
$564$	−1.22887	−	2.02079i	−1.22887	−	2.02079i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$569$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$570$		0			0
$571$	−0.985454	−	0.599268i	−0.985454	−	0.599268i	−0.0682424	−	0.997669i	$-0.521739\pi$
$571$	−0.985454	−	0.599268i	−0.985454	−	0.599268i	−0.917211	+	0.398401i	$0.869565\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.390527	+	0.553251i	0.390527	+	0.553251i
$577$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$577$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$578$	−2.31489	−	2.65483i	−2.31489	−	2.65483i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.06824	+	0.997669i	−1.06824	+	0.997669i
$587$	−0.494291	−	1.55738i	−0.494291	−	1.55738i	−0.796805	−	0.604236i	$-0.793478\pi$
$587$	−0.494291	−	1.55738i	−0.494291	−	1.55738i	0.302515	−	0.953145i	$-0.402174\pi$
$588$	−0.715479	−	2.25429i	−0.715479	−	2.25429i
$589$	−0.644351	+	0.601782i	−0.644351	+	0.601782i
$590$		0			0
$591$	0.347674	−	0.211425i	0.347674	−	0.211425i
$592$		0			0
$593$	0.666272	−	0.437008i	0.666272	−	0.437008i	−0.169910	−	0.985460i	$-0.554348\pi$
$593$	0.666272	−	0.437008i	0.666272	−	0.437008i	0.836182	+	0.548452i	$0.184783\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.829507	+	0.951318i	0.829507	+	0.951318i
$598$		0			0
$599$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$599$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$600$		0			0
$601$	−0.00931405	−	0.136167i	−0.00931405	−	0.136167i	0.990686	−	0.136167i	$-0.0434783\pi$
$601$	−0.00931405	−	0.136167i	−0.00931405	−	0.136167i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	−3.95705	−	2.40634i	−3.95705	−	2.40634i
$605$		0			0
$606$		0			0
$607$		0			0		−0.169910	−	0.985460i	$-0.554348\pi$
$607$		0			0		0.169910	+	0.985460i	$0.445652\pi$
$608$	−2.33738	+	1.11161i	−2.33738	+	1.11161i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−2.85783	−	2.85783i	−2.85783	−	2.85783i
$613$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$613$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.53451	+	1.16366i	1.53451	+	1.16366i	0.930278	+	0.366854i	$0.119565\pi$
$617$	1.53451	+	1.16366i	1.53451	+	1.16366i	0.604236	+	0.796805i	$0.293478\pi$
$618$		0			0
$619$	0.0554078	−	0.403122i	0.0554078	−	0.403122i	−0.942261	−	0.334880i	$-0.891304\pi$
$619$	0.0554078	−	0.403122i	0.0554078	−	0.403122i	0.997669	−	0.0682424i	$-0.0217391\pi$
$620$		0			0
$621$	−1.77163	+	0.121183i	−1.77163	+	0.121183i
$622$		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
$631$	0.922662	+	1.51725i	0.922662	+	1.51725i	0.854419	+	0.519584i	$0.173913\pi$
$631$	0.922662	+	1.51725i	0.922662	+	1.51725i	0.0682424	+	0.997669i	$0.478261\pi$
$632$	−4.79736	−	0.493183i	−4.79736	−	0.493183i
$633$	−0.0643397	+	1.88342i	−0.0643397	+	1.88342i
$634$	−1.59045	+	3.06943i	−1.59045	+	3.06943i
$635$		0			0
$636$	−2.50448	−	2.68164i	−2.50448	−	2.68164i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$641$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$642$	−3.12194	−	1.48473i	−3.12194	−	1.48473i
$643$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$643$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$644$		0			0
$645$		0			0
$646$	4.18449	−	2.95374i	4.18449	−	2.95374i
$647$	−1.35231	−	0.760368i	−1.35231	−	0.760368i	−0.366854	−	0.930278i	$-0.619565\pi$
$647$	−1.35231	−	0.760368i	−1.35231	−	0.760368i	−0.985460	+	0.169910i	$0.945652\pi$
$648$	−1.88743	−	1.64576i	−1.88743	−	1.64576i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.07295	+	0.423115i	−1.07295	+	0.423115i	−0.836182	−	0.548452i	$-0.815217\pi$
$653$	−1.07295	+	0.423115i	−1.07295	+	0.423115i	−0.236764	+	0.971567i	$0.576087\pi$
$654$	0.288095	−	0.408137i	0.288095	−	0.408137i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	0.572255	−	1.61017i	0.572255	−	1.61017i	−0.203456	−	0.979084i	$-0.565217\pi$
$661$	0.572255	−	1.61017i	0.572255	−	1.61017i	0.775711	−	0.631088i	$-0.217391\pi$
$662$	−3.58182	+	0.617569i	−3.58182	+	0.617569i
$663$		0			0
$664$	−0.675620	−	4.91550i	−0.675620	−	4.91550i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.96187	+	2.24997i	−1.96187	+	2.24997i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$673$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$674$		0			0
$675$		0			0
$676$	−0.481195	+	2.31564i	−0.481195	+	2.31564i
$677$	−0.536221	+	1.35976i	−0.536221	+	1.35976i	0.366854	+	0.930278i	$0.380435\pi$
$677$	−0.536221	+	1.35976i	−0.536221	+	1.35976i	−0.903075	+	0.429483i	$0.858696\pi$
$678$	−3.55622	−	0.866627i	−3.55622	−	0.866627i
$679$		0			0
$680$		0			0
$681$	−1.73863	−	0.900885i	−1.73863	−	0.900885i
$682$		0			0
$683$	0.919594	+	0.0314143i	0.919594	+	0.0314143i	0.490110	−	0.871660i	$-0.336957\pi$
$683$	0.919594	+	0.0314143i	0.919594	+	0.0314143i	0.429483	+	0.903075i	$0.358696\pi$
$684$	2.99769	−	2.43880i	2.99769	−	2.43880i
$685$		0			0
$686$		0			0
$687$	1.07396	+	1.63739i	1.07396	+	1.63739i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	1.03675	+	0.0709153i	1.03675	+	0.0709153i	0.576680	−	0.816970i	$-0.304348\pi$
$691$	1.03675	+	0.0709153i	1.03675	+	0.0709153i	0.460065	+	0.887885i	$0.347826\pi$
$692$	−0.177041	+	0.269921i	−0.177041	+	0.269921i
$693$		0			0
$694$	0.0675492	+	0.241086i	0.0675492	+	0.241086i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.634842	−	2.60509i	−0.634842	−	2.60509i
$699$	1.25042	−	0.171866i	1.25042	−	0.171866i
$700$		0			0
$701$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$701$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−2.11575			−2.11575
$707$		0			0
$708$		0			0
$709$	−0.751719	−	0.530621i	−0.751719	−	0.530621i	0.136167	−	0.990686i	$-0.456522\pi$
$709$	−0.751719	−	0.530621i	−0.751719	−	0.530621i	−0.887885	+	0.460065i	$0.847826\pi$
$710$		0			0
$711$	1.90790	−	0.262234i	1.90790	−	0.262234i
$712$		0			0
$713$	0.763494	−	0.578976i	0.763494	−	0.578976i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$719$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$720$		0			0
$721$		0			0
$722$	1.50123	+	2.66993i	1.50123	+	2.66993i
$723$	0.850881	+	1.29727i	0.850881	+	1.29727i
$724$	4.32849	−	1.88013i	4.32849	−	1.88013i
$725$		0			0
$726$	−1.42298	+	1.15768i	−1.42298	+	1.15768i
$727$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$727$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$728$		0			0
$729$	0.887885	+	0.460065i	0.887885	+	0.460065i
$730$		0			0
$731$		0			0
$732$	0.935027	+	0.227860i	0.935027	+	0.227860i
$733$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$733$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$734$		0			0
$735$		0			0
$736$	2.65050	−	0.941987i	2.65050	−	0.941987i
$737$		0			0
$738$		0			0
$739$	−0.133630	+	0.0277687i	−0.133630	+	0.0277687i	−0.269797	−	0.962917i	$-0.586957\pi$
$739$	−0.133630	+	0.0277687i	−0.133630	+	0.0277687i	0.136167	+	0.990686i	$0.456522\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.167093	−	1.62537i	−0.167093	−	1.62537i	−0.657204	−	0.753713i	$-0.728261\pi$
$743$	−0.167093	−	1.62537i	−0.167093	−	1.62537i	0.490110	−	0.871660i	$-0.336957\pi$
$744$	1.33865	+	0.183994i	1.33865	+	0.183994i
$745$		0			0
$746$		0			0
$747$	0.726875	+	1.84323i	0.726875	+	1.84323i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		−	1.88452i		−	1.88452i	−0.334880	−	0.942261i	$-0.608696\pi$
$751$		−	1.88452i		−	1.88452i	0.334880	−	0.942261i	$-0.391304\pi$
$752$	−1.94260	−	1.09227i	−1.94260	−	1.09227i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$757$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$758$	−0.742378	+	0.978972i	−0.742378	+	0.978972i
$759$		0			0
$760$		0			0
$761$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$761$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−0.0170859	+	0.249787i	−0.0170859	+	0.249787i
$767$		0			0
$768$	−1.17777	−	0.560121i	−1.17777	−	0.560121i
$769$	−0.461039	+	1.64547i	−0.461039	+	1.64547i	0.269797	+	0.962917i	$0.413043\pi$
$769$	−0.461039	+	1.64547i	−0.461039	+	1.64547i	−0.730836	+	0.682553i	$0.760870\pi$
$770$		0			0
$771$	−0.414006	−	0.953137i	−0.414006	−	0.953137i
$772$		0			0
$773$	−0.139601	+	1.35795i	−0.139601	+	1.35795i	0.657204	+	0.753713i	$0.271739\pi$
$773$	−0.139601	+	1.35795i	−0.139601	+	1.35795i	−0.796805	+	0.604236i	$0.793478\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−4.85215	+	2.72823i	−4.85215	+	2.72823i
$783$		0			0
$784$	−1.62876	−	1.52115i	−1.62876	−	1.52115i
$785$		0			0
$786$		0			0
$787$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$787$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$788$	0.471677	−	0.838877i	0.471677	−	0.838877i
$789$	0.917985	−	0.0627919i	0.917985	−	0.0627919i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	2.81282	+	0.999676i	2.81282	+	0.999676i
$797$	−1.39318	−	0.442177i	−1.39318	−	0.442177i	−0.490110	−	0.871660i	$-0.663043\pi$
$797$	−1.39318	−	0.442177i	−1.39318	−	0.442177i	−0.903075	+	0.429483i	$0.858696\pi$
$798$		0			0
$799$	1.61017	+	0.572255i	1.61017	+	0.572255i
$800$		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		−0.0682424	−	0.997669i	$-0.521739\pi$
$809$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$810$		0			0
$811$	0.0787081	+	0.111504i	0.0787081	+	0.111504i	0.854419	−	0.519584i	$-0.173913\pi$
$811$	0.0787081	+	0.111504i	0.0787081	+	0.111504i	−0.775711	+	0.631088i	$0.782609\pi$
$812$		0			0
$813$	−0.757993	−	0.869303i	−0.757993	−	0.869303i
$814$		0			0
$815$		0			0
$816$	−3.66713	−	1.02748i	−3.66713	−	1.02748i
$817$		0			0
$818$	2.49438	+	0.983655i	2.49438	+	0.983655i
$819$		0			0
$820$		0			0
$821$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$821$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$822$	−0.151129	−	0.476167i	−0.151129	−	0.476167i
$823$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$823$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.26993	−	0.500795i	−1.26993	−	0.500795i	−0.366854	−	0.930278i	$-0.619565\pi$
$827$	−1.26993	−	0.500795i	−1.26993	−	0.500795i	−0.903075	+	0.429483i	$0.858696\pi$
$828$	−3.51187	+	2.30344i	−3.51187	+	2.30344i
$829$	−0.767255	−	0.214975i	−0.767255	−	0.214975i	−0.136167	−	0.990686i	$-0.543478\pi$
$829$	−0.767255	−	0.214975i	−0.767255	−	0.214975i	−0.631088	+	0.775711i	$0.717391\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.42890	+	0.937216i	1.42890	+	0.937216i
$834$	−1.54627	−	2.19056i	−1.54627	−	2.19056i
$835$		0			0
$836$		0			0
$837$	−0.536765	+	0.0551811i	−0.536765	+	0.0551811i
$838$		0			0
$839$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$839$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$840$		0			0
$841$	−0.917211	−	0.398401i	−0.917211	−	0.398401i
$842$	−0.587382	−	3.40674i	−0.587382	−	3.40674i
$843$		0			0
$844$	2.05055	+	3.95739i	2.05055	+	3.95739i
$845$		0			0
$846$	1.76640	+	0.494921i	1.76640	+	0.494921i
$847$		0			0
$848$	−3.29553	−	1.04595i	−3.29553	−	1.04595i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$853$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$854$		0			0
$855$		0			0
$856$	−4.70818	+	0.322049i	−4.70818	+	0.322049i
$857$	0.923623	−	1.64266i	0.923623	−	1.64266i	0.169910	−	0.985460i	$-0.445652\pi$
$857$	0.923623	−	1.64266i	0.923623	−	1.64266i	0.753713	−	0.657204i	$-0.228261\pi$
$858$		0			0
$859$	0.162114	+	0.780136i	0.162114	+	0.780136i	0.979084	+	0.203456i	$0.0652174\pi$
$859$	0.162114	+	0.780136i	0.162114	+	0.780136i	−0.816970	+	0.576680i	$0.804348\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.67867	−	0.943871i	1.67867	−	0.943871i	0.707107	−	0.707107i	$-0.250000\pi$
$863$	1.67867	−	0.943871i	1.67867	−	0.943871i	0.971567	−	0.236764i	$-0.0760870\pi$
$864$	−1.55092	−	0.322285i	−1.55092	−	0.322285i
$865$		0			0
$866$		0			0
$867$	1.91006	+	0.196360i	1.91006	+	0.196360i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.0697413	−	0.678397i	0.0697413	−	0.678397i
$873$		0			0
$874$	−2.12052	−	4.88193i	−2.12052	−	4.88193i
$875$		0			0
$876$		0			0
$877$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$877$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$878$	0.124092	+	3.63255i	0.124092	+	3.63255i
$879$	0.0543757	−	0.794945i	0.0543757	−	0.794945i
$880$		0			0
$881$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$881$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$882$	1.59899	+	0.899069i	1.59899	+	0.899069i
$883$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$883$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$884$		0			0
$885$		0			0
$886$	0.259571	−	0.426846i	0.259571	−	0.426846i
$887$	−0.987286	+	1.30193i	−0.987286	+	1.30193i	−0.0341411	+	0.999417i	$0.510870\pi$
$887$	−0.987286	+	1.30193i	−0.987286	+	1.30193i	−0.953145	+	0.302515i	$0.902174\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.701750	+	1.47557i	−0.701750	+	1.47557i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	2.62644	+	0.360996i	2.62644	+	0.360996i
$902$		0			0
$903$		0			0
$904$	−4.81140	+	1.34809i	−4.81140	+	1.34809i
$905$		0			0
$906$	3.51698	−	0.730836i	3.51698	−	0.730836i
$907$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$907$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$908$	−4.62858	+	0.158117i	−4.62858	+	0.158117i
$909$		0			0
$910$		0			0
$911$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$911$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$912$	1.33588	−	3.38755i	1.33588	−	3.38755i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	4.11204	+	2.13069i	4.11204	+	2.13069i
$917$		0			0
$918$	3.13291	+	0.107023i	3.13291	+	0.107023i
$919$	−1.37749	+	1.12067i	−1.37749	+	1.12067i	−0.398401	+	0.917211i	$0.630435\pi$
$919$	−1.37749	+	1.12067i	−1.37749	+	1.12067i	−0.979084	+	0.203456i	$0.934783\pi$
$920$		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		−0.269797	−	0.962917i	$-0.586957\pi$
$929$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$930$		0			0
$931$	−1.03116	+	1.26747i	−1.03116	+	1.26747i
$932$	2.37861	−	1.80375i	2.37861	−	1.80375i
$933$		0			0
$934$	−2.65635	+	0.365107i	−2.65635	+	0.365107i
$935$		0			0
$936$		0			0
$937$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$937$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$938$		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
$947$	0.323209	+	1.32629i	0.323209	+	1.32629i	0.871660	+	0.490110i	$0.163043\pi$
$947$	0.323209	+	1.32629i	0.323209	+	1.32629i	−0.548452	+	0.836182i	$0.684783\pi$
$948$	3.62929	−	2.75218i	3.62929	−	2.75218i
$949$		0			0
$950$		0			0
$951$	−0.508438	−	1.81464i	−0.508438	−	1.81464i
$952$		0			0
$953$	0.437008	−	0.666272i	0.437008	−	0.666272i	−0.548452	−	0.836182i	$-0.684783\pi$
$953$	0.437008	−	0.666272i	0.437008	−	0.666272i	0.985460	+	0.169910i	$0.0543478\pi$
$954$	2.83933	+	0.194215i	2.83933	+	0.194215i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.549854	+	0.447340i	−0.549854	+	0.447340i
$962$		0			0
$963$	1.79622	−	0.570095i	1.79622	−	0.570095i
$964$	3.25790	+	1.68811i	3.25790	+	1.68811i
$965$		0			0
$966$		0			0
$967$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$967$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$968$	−0.918670	+	2.32959i	−0.918670	+	2.32959i
$969$	−0.568078	+	2.73374i	−0.568078	+	2.73374i
$970$		0			0
$971$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$971$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$972$	2.36373	−	0.0807474i	2.36373	−	0.0807474i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.873224	−	0.244666i	0.873224	−	0.244666i
$977$	0.0896983	−	0.102870i	0.0896983	−	0.102870i	−0.707107	−	0.707107i	$-0.750000\pi$
$977$	0.0896983	−	0.102870i	0.0896983	−	0.102870i	0.796805	+	0.604236i	$0.206522\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.0370827	+	0.269797i	0.0370827	+	0.269797i
$982$		0			0
$983$	−1.92970	+	0.332713i	−1.92970	+	0.332713i	−0.999417	−	0.0341411i	$-0.989130\pi$
$983$	−1.92970	+	0.332713i	−1.92970	+	0.332713i	−0.930278	+	0.366854i	$0.880435\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.386237	−	0.547173i	0.386237	−	0.547173i	−0.576680	−	0.816970i	$-0.695652\pi$
$991$	0.386237	−	0.547173i	0.386237	−	0.547173i	0.962917	+	0.269797i	$0.0869565\pi$
$992$	0.795150	−	0.313566i	0.795150	−	0.313566i
$993$	1.19722	−	1.57877i	1.19722	−	1.57877i
$994$		0			0
$995$		0			0
$996$	3.63510	+	2.95738i	3.63510	+	2.95738i
$997$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$997$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$998$	2.83945	+	1.59654i	2.83945	+	1.59654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.1718.1	yes	88
3.2	odd	2	inner	3525.1.bg.a.1718.2	yes	88
5.2	odd	4	inner	3525.1.bg.a.2282.1	yes	88
5.3	odd	4	inner	3525.1.bg.a.2282.2	yes	88
5.4	even	2	inner	3525.1.bg.a.1718.2	yes	88
15.2	even	4	inner	3525.1.bg.a.2282.2	yes	88
15.8	even	4	inner	3525.1.bg.a.2282.1	yes	88
15.14	odd	2	CM	3525.1.bg.a.1718.1	yes	88
47.38	odd	46	inner	3525.1.bg.a.743.2	yes	88
141.38	even	46	inner	3525.1.bg.a.743.1	✓	88
235.38	even	92	inner	3525.1.bg.a.1307.1	yes	88
235.132	even	92	inner	3525.1.bg.a.1307.2	yes	88
235.179	odd	46	inner	3525.1.bg.a.743.1	✓	88
705.38	odd	92	inner	3525.1.bg.a.1307.2	yes	88
705.179	even	46	inner	3525.1.bg.a.743.2	yes	88
705.602	odd	92	inner	3525.1.bg.a.1307.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.743.1	✓	88	141.38	even	46	inner
3525.1.bg.a.743.1	✓	88	235.179	odd	46	inner
3525.1.bg.a.743.2	yes	88	47.38	odd	46	inner
3525.1.bg.a.743.2	yes	88	705.179	even	46	inner
3525.1.bg.a.1307.1	yes	88	235.38	even	92	inner
3525.1.bg.a.1307.1	yes	88	705.602	odd	92	inner
3525.1.bg.a.1307.2	yes	88	235.132	even	92	inner
3525.1.bg.a.1307.2	yes	88	705.38	odd	92	inner
3525.1.bg.a.1718.1	yes	88	1.1	even	1	trivial
3525.1.bg.a.1718.1	yes	88	15.14	odd	2	CM
3525.1.bg.a.1718.2	yes	88	3.2	odd	2	inner
3525.1.bg.a.1718.2	yes	88	5.4	even	2	inner
3525.1.bg.a.2282.1	yes	88	5.2	odd	4	inner
3525.1.bg.a.2282.1	yes	88	15.8	even	4	inner
3525.1.bg.a.2282.2	yes	88	5.3	odd	4	inner
3525.1.bg.a.2282.2	yes	88	15.2	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)

\(f(q)\)	\(=\)	\(q+(-0.554940 + 1.74847i) q^{2} +(-0.429483 - 0.903075i) q^{3} +(-1.93222 - 1.36391i) q^{4} +(1.81734 - 0.249787i) q^{6} +(1.99534 - 1.51312i) q^{8} +(-0.631088 + 0.775711i) q^{9} +O(q^{10})\)	\(q+(-0.554940 + 1.74847i) q^{2} +(-0.429483 - 0.903075i) q^{3} +(-1.93222 - 1.36391i) q^{4} +(1.81734 - 0.249787i) q^{6} +(1.99534 - 1.51312i) q^{8} +(-0.631088 + 0.775711i) q^{9} +(-0.401856 + 2.33072i) q^{12} +(0.746320 + 2.09994i) q^{16} +(-0.837519 - 1.48953i) q^{17} +(-1.00609 - 1.53391i) q^{18} +(1.49867 - 0.650963i) q^{19} +(-1.69257 + 0.537196i) q^{23} +(-2.22343 - 1.15209i) q^{24} +(0.971567 + 0.236764i) q^{27} +(-0.508438 + 0.180699i) q^{31} +(-1.58313 + 0.0540813i) q^{32} +(3.06917 - 0.637780i) q^{34} +(2.27740 - 0.638098i) q^{36} +(0.306520 + 2.98162i) q^{38} -3.25751i q^{46} +(-0.753713 + 0.657204i) q^{47} +(1.57587 - 1.57587i) q^{48} +(-0.887885 + 0.460065i) q^{49} +(-0.985454 + 1.39607i) q^{51} +(-0.937426 + 1.23618i) q^{53} +(-0.953137 + 1.56737i) q^{54} +(-1.23152 - 1.07383i) q^{57} +(0.0277687 - 0.405963i) q^{61} +(-0.0337943 - 0.989266i) q^{62} +(0.182706 - 0.652087i) q^{64} +(-0.413309 + 4.02040i) q^{68} +(1.21206 + 1.29780i) q^{69} +(-0.0854955 + 2.50272i) q^{72} +(-3.78361 - 0.786244i) q^{76} +(-1.40747 - 1.31448i) q^{79} +(-0.203456 - 0.979084i) q^{81} +(0.971091 - 1.72708i) q^{83} +(4.00310 + 1.27053i) q^{92} +(0.381550 + 0.381550i) q^{93} +(-0.730836 - 1.68255i) q^{94} +(0.728767 + 1.40646i) q^{96} +(-0.311687 - 1.80775i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 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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