LMFDB - Embedded newform 3525.1.bg.a.257.1

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			257.1
Root			$-0.102264 + 0.994757i$ of defining polynomial
Character	$\chi$	$=$	3525.257
Dual form			3525.1.bg.a.2318.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.202623 + 1.97098i) q^{2} +(0.930278 + 0.366854i) q^{3} +(-2.86464 - 0.595279i) q^{4} +(-0.911560 + 1.75923i) q^{6} +(1.15433 - 3.63700i) q^{8} +(0.730836 + 0.682553i) q^{9} +O(q^{10})$	\(q+(-0.202623 + 1.97098i) q^{2} +(0.930278 + 0.366854i) q^{3} +(-2.86464 - 0.595279i) q^{4} +(-0.911560 + 1.75923i) q^{6} +(1.15433 - 3.63700i) q^{8} +(0.730836 + 0.682553i) q^{9} +(-2.44653 - 1.60468i) q^{12} +(4.25097 + 1.84646i) q^{16} +(0.113799 + 0.660021i) q^{17} +(-1.49339 + 1.30216i) q^{18} +(1.93993 - 0.266637i) q^{19} +(-1.25556 + 0.129075i) q^{23} +(2.40810 - 2.95995i) q^{24} +(0.429483 + 0.903075i) q^{27} +(-0.650963 + 1.49867i) q^{31} +(-2.63053 + 4.67839i) q^{32} +(-1.32395 + 0.0905606i) q^{34} +(-1.68727 - 2.39032i) q^{36} +(0.132463 + 3.87760i) q^{38} -2.50084i q^{46} +(0.971567 - 0.236764i) q^{47} +(3.27721 + 3.27721i) q^{48} +(0.631088 + 0.775711i) q^{49} +(-0.136267 + 0.655751i) q^{51} +(-1.30114 + 0.412965i) q^{53} +(-1.86697 + 0.663521i) q^{54} +(1.90249 + 0.463625i) q^{57} +(0.116615 + 0.0709153i) q^{61} +(-2.82195 - 1.58670i) q^{62} +(-4.90164 - 3.45995i) q^{64} +(0.0669031 - 1.95846i) q^{68} +(-1.21537 - 0.340531i) q^{69} +(3.32608 - 1.87016i) q^{72} +(-5.71592 - 0.390980i) q^{76} +(-0.311173 - 1.11059i) q^{79} +(0.0682424 + 0.997669i) q^{81} +(-0.156340 + 0.906751i) q^{83} +(3.67356 + 0.377653i) q^{92} +(-1.15537 + 1.15537i) q^{93} +(0.269797 + 1.96292i) q^{94} +(-4.16341 + 3.38719i) q^{96} +(-1.65679 + 1.08669i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{6}+O(q^{10}) $ 88 * q - 8 * q^6	$ 88 q - 8 q^{6} + 20 q^{16} - 12 q^{36} - 8 q^{51} + 8 q^{61} - 92 q^{76} + 4 q^{81} - 68 q^{96}+O(q^{100}) $ 88 * q - 8 * q^6 + 20 * q^16 - 12 * q^36 - 8 * q^51 + 8 * q^61 - 92 * q^76 + 4 * q^81 - 68 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{25}{46}\right)$	$-1$

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 $

$2$	−0.202623	+	1.97098i	−0.202623	+	1.97098i	0.0341411	+	0.999417i	$0.489130\pi$
$2$	−0.202623	+	1.97098i	−0.202623	+	1.97098i	−0.236764	+	0.971567i	$0.576087\pi$
$3$	0.930278	+	0.366854i	0.930278	+	0.366854i
$3$	0.930278	+	0.366854i	0.930278	+	0.366854i
$4$	−2.86464	−	0.595279i	−2.86464	−	0.595279i
$5$		0			0
$5$		0			0
$6$	−0.911560	+	1.75923i	−0.911560	+	1.75923i
$7$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$7$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$8$	1.15433	−	3.63700i	1.15433	−	3.63700i
$9$	0.730836	+	0.682553i	0.730836	+	0.682553i
$10$		0			0
$11$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$11$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$12$	−2.44653	−	1.60468i	−2.44653	−	1.60468i
$13$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$13$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$14$		0			0
$15$		0			0
$16$	4.25097	+	1.84646i	4.25097	+	1.84646i
$17$	0.113799	+	0.660021i	0.113799	+	0.660021i	0.985460	+	0.169910i	$0.0543478\pi$
$17$	0.113799	+	0.660021i	0.113799	+	0.660021i	−0.871660	+	0.490110i	$0.836957\pi$
$18$	−1.49339	+	1.30216i	−1.49339	+	1.30216i
$19$	1.93993	−	0.266637i	1.93993	−	0.266637i	0.942261	−	0.334880i	$-0.108696\pi$
$19$	1.93993	−	0.266637i	1.93993	−	0.266637i	0.997669	+	0.0682424i	$0.0217391\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.25556	+	0.129075i	−1.25556	+	0.129075i	−0.707107	−	0.707107i	$-0.750000\pi$
$23$	−1.25556	+	0.129075i	−1.25556	+	0.129075i	−0.548452	+	0.836182i	$0.684783\pi$
$24$	2.40810	−	2.95995i	2.40810	−	2.95995i
$25$		0			0
$26$		0			0
$27$	0.429483	+	0.903075i	0.429483	+	0.903075i
$28$		0			0
$29$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$29$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$30$		0			0
$31$	−0.650963	+	1.49867i	−0.650963	+	1.49867i	0.203456	+	0.979084i	$0.434783\pi$
$31$	−0.650963	+	1.49867i	−0.650963	+	1.49867i	−0.854419	+	0.519584i	$0.826087\pi$
$32$	−2.63053	+	4.67839i	−2.63053	+	4.67839i
$33$		0			0
$34$	−1.32395	+	0.0905606i	−1.32395	+	0.0905606i
$35$		0			0
$36$	−1.68727	−	2.39032i	−1.68727	−	2.39032i
$37$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$37$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$38$	0.132463	+	3.87760i	0.132463	+	3.87760i
$39$		0			0
$40$		0			0
$41$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$41$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$42$		0			0
$43$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$43$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$44$		0			0
$45$		0			0
$46$		−	2.50084i		−	2.50084i
$47$	0.971567	−	0.236764i	0.971567	−	0.236764i
$47$	0.971567	−	0.236764i	0.971567	−	0.236764i
$48$	3.27721	+	3.27721i	3.27721	+	3.27721i
$49$	0.631088	+	0.775711i	0.631088	+	0.775711i
$50$		0			0
$51$	−0.136267	+	0.655751i	−0.136267	+	0.655751i
$52$		0			0
$53$	−1.30114	+	0.412965i	−1.30114	+	0.412965i	−0.871660	−	0.490110i	$-0.836957\pi$
$53$	−1.30114	+	0.412965i	−1.30114	+	0.412965i	−0.429483	+	0.903075i	$0.641304\pi$
$54$	−1.86697	+	0.663521i	−1.86697	+	0.663521i
$55$		0			0
$56$		0			0
$57$	1.90249	+	0.463625i	1.90249	+	0.463625i
$58$		0			0
$59$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$59$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$60$		0			0
$61$	0.116615	+	0.0709153i	0.116615	+	0.0709153i	0.576680	−	0.816970i	$-0.304348\pi$
$61$	0.116615	+	0.0709153i	0.116615	+	0.0709153i	−0.460065	+	0.887885i	$0.652174\pi$
$62$	−2.82195	−	1.58670i	−2.82195	−	1.58670i
$63$		0			0
$64$	−4.90164	−	3.45995i	−4.90164	−	3.45995i
$65$		0			0
$66$		0			0
$67$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$67$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$68$	0.0669031	−	1.95846i	0.0669031	−	1.95846i
$69$	−1.21537	−	0.340531i	−1.21537	−	0.340531i
$70$		0			0
$71$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$71$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$72$	3.32608	−	1.87016i	3.32608	−	1.87016i
$73$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$73$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$74$		0			0
$75$		0			0
$76$	−5.71592	−	0.390980i	−5.71592	−	0.390980i
$77$		0			0
$78$		0			0
$79$	−0.311173	−	1.11059i	−0.311173	−	1.11059i	−0.942261	−	0.334880i	$-0.891304\pi$
$79$	−0.311173	−	1.11059i	−0.311173	−	1.11059i	0.631088	−	0.775711i	$-0.282609\pi$
$80$		0			0
$81$	0.0682424	+	0.997669i	0.0682424	+	0.997669i
$82$		0			0
$83$	−0.156340	+	0.906751i	−0.156340	+	0.906751i	0.796805	+	0.604236i	$0.206522\pi$
$83$	−0.156340	+	0.906751i	−0.156340	+	0.906751i	−0.953145	+	0.302515i	$0.902174\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$89$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$90$		0			0
$91$		0			0
$92$	3.67356	+	0.377653i	3.67356	+	0.377653i
$93$	−1.15537	+	1.15537i	−1.15537	+	1.15537i
$94$	0.269797	+	1.96292i	0.269797	+	1.96292i
$95$		0			0
$96$	−4.16341	+	3.38719i	−4.16341	+	3.38719i
$97$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$97$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$98$	−1.65679	+	1.08669i	−1.65679	+	1.08669i
$99$		0			0
$100$		0			0
$101$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$101$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$102$	−1.26486	−	0.401450i	−1.26486	−	0.401450i
$103$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$103$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$104$		0			0
$105$		0			0
$106$	−0.550304	−	2.64821i	−0.550304	−	2.64821i
$107$	0.523661	−	0.600560i	0.523661	−	0.600560i	−0.429483	−	0.903075i	$-0.641304\pi$
$107$	0.523661	−	0.600560i	0.523661	−	0.600560i	0.953145	+	0.302515i	$0.0978261\pi$
$108$	−0.692734	−	2.84264i	−0.692734	−	2.84264i
$109$	1.70992	−	0.479097i	1.70992	−	0.479097i	0.730836	−	0.682553i	$-0.239130\pi$
$109$	1.70992	−	0.479097i	1.70992	−	0.479097i	0.979084	+	0.203456i	$0.0652174\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.627903	−	0.828014i	0.627903	−	0.828014i	−0.366854	−	0.930278i	$-0.619565\pi$
$113$	0.627903	−	0.828014i	0.627903	−	0.828014i	0.994757	+	0.102264i	$0.0326087\pi$
$114$	−1.29929	+	3.65584i	−1.29929	+	3.65584i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.334880	−	0.942261i	0.334880	−	0.942261i
$122$	−0.163402	+	0.215478i	−0.163402	+	0.215478i
$123$		0			0
$124$	2.75690	−	3.90564i	2.75690	−	3.90564i
$125$		0			0
$126$		0			0
$127$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$127$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$128$	4.28535	−	4.91464i	4.28535	−	4.91464i
$129$		0			0
$130$		0			0
$131$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$131$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	2.53186	+	0.347996i	2.53186	+	0.347996i
$137$	−1.48487	+	0.973925i	−1.48487	+	0.973925i	−0.490110	+	0.871660i	$0.663043\pi$
$137$	−1.48487	+	0.973925i	−1.48487	+	0.973925i	−0.994757	+	0.102264i	$0.967391\pi$
$138$	0.917444	−	2.32648i	0.917444	−	2.32648i
$139$	−0.418569	+	0.340531i	−0.418569	+	0.340531i	−0.816970	−	0.576680i	$-0.804348\pi$
$139$	−0.418569	+	0.340531i	−0.418569	+	0.340531i	0.398401	+	0.917211i	$0.369565\pi$
$140$		0			0
$141$	0.990686	+	0.136167i	0.990686	+	0.136167i
$142$		0			0
$143$		0			0
$144$	1.84646	+	4.25097i	1.84646	+	4.25097i
$145$		0			0
$146$		0			0
$147$	0.302515	+	0.953145i	0.302515	+	0.953145i
$148$		0			0
$149$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$149$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$150$		0			0
$151$	−1.03675	−	1.70486i	−1.03675	−	1.70486i	−0.576680	−	0.816970i	$-0.695652\pi$
$151$	−1.03675	−	1.70486i	−1.03675	−	1.70486i	−0.460065	−	0.887885i	$-0.652174\pi$
$152$	1.26956	−	7.36332i	1.26956	−	7.36332i
$153$	−0.367331	+	0.560041i	−0.367331	+	0.560041i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$157$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$158$	2.25201	−	0.388285i	2.25201	−	0.388285i
$159$	−1.36192	−	0.0931581i	−1.36192	−	0.0931581i
$160$		0			0
$161$		0			0
$162$	−1.98022	−	0.0676462i	−1.98022	−	0.0676462i
$163$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$163$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$164$		0			0
$165$		0			0
$166$	−1.75551	−	0.491872i	−1.75551	−	0.491872i
$167$	−0.0499031	+	1.46082i	−0.0499031	+	1.46082i	0.657204	+	0.753713i	$0.271739\pi$
$167$	−0.0499031	+	1.46082i	−0.0499031	+	1.46082i	−0.707107	+	0.707107i	$0.750000\pi$
$168$		0			0
$169$	0.136167	+	0.990686i	0.136167	+	0.990686i
$170$		0			0
$171$	1.59976	+	1.12924i	1.59976	+	1.12924i
$172$		0			0
$173$	−1.48953	−	0.837519i	−1.48953	−	0.837519i	−0.490110	−	0.871660i	$-0.663043\pi$
$173$	−1.48953	−	0.837519i	−1.48953	−	0.837519i	−0.999417	+	0.0341411i	$0.989130\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$179$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$180$		0			0
$181$	0.979167	−	0.347996i	0.979167	−	0.347996i	0.203456	−	0.979084i	$-0.434783\pi$
$181$	0.979167	−	0.347996i	0.979167	−	0.347996i	0.775711	+	0.631088i	$0.217391\pi$
$182$		0			0
$183$	0.0824691	+	0.108752i	0.0824691	+	0.108752i
$184$	−0.979886	+	4.71547i	−0.979886	+	4.71547i
$185$		0			0
$186$	−2.04311	−	2.51132i	−2.04311	−	2.51132i
$187$		0			0
$188$	−2.92413	+	0.0998912i	−2.92413	+	0.0998912i
$189$		0			0
$190$		0			0
$191$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$191$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$192$	−3.29059	−	5.01691i	−3.29059	−	5.01691i
$193$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$193$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$194$		0			0
$195$		0			0
$196$	−1.34607	−	2.59781i	−1.34607	−	2.59781i
$197$	−0.00465974	−	0.136405i	−0.00465974	−	0.136405i	−0.999417	−	0.0341411i	$-0.989130\pi$
$197$	−0.00465974	−	0.136405i	−0.00465974	−	0.136405i	0.994757	−	0.102264i	$-0.0326087\pi$
$198$		0			0
$199$	−0.842917	−	1.19414i	−0.842917	−	1.19414i	−0.979084	−	0.203456i	$-0.934783\pi$
$199$	−0.842917	−	1.19414i	−0.842917	−	1.19414i	0.136167	−	0.990686i	$-0.456522\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.780709	−	1.79737i	0.780709	−	1.79737i
$205$		0			0
$206$		0			0
$207$	−1.00571	−	0.762653i	−1.00571	−	0.762653i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.502852	+	0.618088i	−0.502852	+	0.618088i	−0.962917	−	0.269797i	$-0.913043\pi$
$211$	−0.502852	+	0.618088i	−0.502852	+	0.618088i	0.460065	+	0.887885i	$0.347826\pi$
$212$	3.97314	−	0.408451i	3.97314	−	0.408451i
$213$		0			0
$214$	1.07759	+	1.15382i	1.07759	+	1.15382i
$215$		0			0
$216$	3.78025	−	0.519584i	3.78025	−	0.519584i
$217$		0			0
$218$	0.597823	+	3.46730i	0.597823	+	3.46730i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$223$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$224$		0			0
$225$		0			0
$226$	1.50478	+	1.40536i	1.50478	+	1.40536i
$227$	0.603619	−	1.90185i	0.603619	−	1.90185i	0.236764	−	0.971567i	$-0.423913\pi$
$227$	0.603619	−	1.90185i	0.603619	−	1.90185i	0.366854	−	0.930278i	$-0.380435\pi$
$228$	−5.17396	−	2.46063i	−5.17396	−	2.46063i
$229$	0.917985	−	1.77163i	0.917985	−	1.77163i	0.398401	−	0.917211i	$-0.369565\pi$
$229$	0.917985	−	1.77163i	0.917985	−	1.77163i	0.519584	−	0.854419i	$-0.326087\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.149477	−	1.45401i	0.149477	−	1.45401i	−0.604236	−	0.796805i	$-0.706522\pi$
$233$	0.149477	−	1.45401i	0.149477	−	1.45401i	0.753713	−	0.657204i	$-0.228261\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.117947	−	1.14731i	0.117947	−	1.14731i
$238$		0			0
$239$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$239$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$240$		0			0
$241$	−0.628038	+	1.21206i	−0.628038	+	1.21206i	0.334880	+	0.942261i	$0.391304\pi$
$241$	−0.628038	+	1.21206i	−0.628038	+	1.21206i	−0.962917	+	0.269797i	$0.913043\pi$
$242$	1.78933	+	0.850966i	1.78933	+	0.850966i
$243$	−0.302515	+	0.953145i	−0.302515	+	0.953145i
$244$	−0.291846	−	0.272565i	−0.291846	−	0.272565i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.69923	+	4.09752i	4.69923	+	4.09752i
$249$	−0.478085	+	0.786177i	−0.478085	+	0.786177i
$250$		0			0
$251$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$251$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	4.72321	+	5.05732i	4.72321	+	5.05732i
$257$	0.923623	+	1.64266i	0.923623	+	1.64266i	0.753713	+	0.657204i	$0.228261\pi$
$257$	0.923623	+	1.64266i	0.923623	+	1.64266i	0.169910	+	0.985460i	$0.445652\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.23618	+	0.937426i	1.23618	+	0.937426i	0.999417	−	0.0341411i	$-0.0108696\pi$
$263$	1.23618	+	0.937426i	1.23618	+	0.937426i	0.236764	+	0.971567i	$0.423913\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$269$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$270$		0			0
$271$	0.234658	+	0.332435i	0.234658	+	0.332435i	0.917211	−	0.398401i	$-0.130435\pi$
$271$	0.234658	+	0.332435i	0.234658	+	0.332435i	−0.682553	+	0.730836i	$0.739130\pi$
$272$	−0.734944	+	3.01586i	−0.734944	+	3.01586i
$273$		0			0
$274$	−1.61872	−	3.12399i	−1.61872	−	3.12399i
$275$		0			0
$276$	3.27889	+	1.69898i	3.27889	+	1.69898i
$277$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$277$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$278$	−0.586369	−	0.893992i	−0.586369	−	0.893992i
$279$	−1.49867	+	0.650963i	−1.49867	+	0.650963i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	−0.469118	+	1.92504i	−0.469118	+	1.92504i
$283$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$283$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−5.11573	+	1.62366i	−5.11573	+	1.62366i
$289$	0.519584	−	0.184660i	0.519584	−	0.184660i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.268373	+	0.0462723i	0.268373	+	0.0462723i	0.302515	−	0.953145i	$-0.402174\pi$
$293$	0.268373	+	0.0462723i	0.268373	+	0.0462723i	−0.0341411	+	0.999417i	$0.510870\pi$
$294$	−1.93993	+	0.403122i	−1.93993	+	0.403122i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	3.57031	−	1.69797i	3.57031	−	1.69797i
$303$		0			0
$304$	8.73893	+	2.44853i	8.73893	+	2.44853i
$305$		0			0
$306$	−1.02940	−	0.837480i	−1.02940	−	0.837480i
$307$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$307$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$311$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$312$		0			0
$313$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$313$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$314$		0			0
$315$		0			0
$316$	0.230287	+	3.36668i	0.230287	+	3.36668i
$317$	−0.437008	+	0.666272i	−0.437008	+	0.666272i	−0.985460	−	0.169910i	$-0.945652\pi$
$317$	−0.437008	+	0.666272i	−0.437008	+	0.666272i	0.548452	+	0.836182i	$0.315217\pi$
$318$	0.459571	−	2.66545i	0.459571	−	2.66545i
$319$		0			0
$320$		0			0
$321$	0.707469	−	0.366581i	0.707469	−	0.366581i
$322$		0			0
$323$	0.396748	+	1.25005i	0.396748	+	1.25005i
$324$	0.398401	−	2.89858i	0.398401	−	2.89858i
$325$		0			0
$326$		0			0
$327$	1.76646	+	0.181598i	1.76646	+	0.181598i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.713755	−	0.580683i	0.713755	−	0.580683i	−0.203456	−	0.979084i	$-0.565217\pi$
$331$	0.713755	−	0.580683i	0.713755	−	0.580683i	0.917211	+	0.398401i	$0.130435\pi$
$332$	0.987626	−	2.50445i	0.987626	−	2.50445i
$333$		0			0
$334$	−2.86914	−	0.394354i	−2.86914	−	0.394354i
$335$		0			0
$336$		0			0
$337$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$337$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$338$	−1.98022	+	0.0676462i	−1.98022	+	0.0676462i
$339$	0.887885	−	0.539935i	0.887885	−	0.539935i
$340$		0			0
$341$		0			0
$342$	−2.54986	+	2.92430i	−2.54986	+	2.92430i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.95255	−	2.76613i	1.95255	−	2.76613i
$347$	−1.12306	−	1.28797i	−1.12306	−	1.28797i	−0.953145	−	0.302515i	$-0.902174\pi$
$347$	−1.12306	−	1.28797i	−1.12306	−	1.28797i	−0.169910	−	0.985460i	$-0.554348\pi$
$348$		0			0
$349$	−0.180699	+	0.508438i	−0.180699	+	0.508438i	−0.997669	−	0.0682424i	$-0.978261\pi$
$349$	−0.180699	+	0.508438i	−0.180699	+	0.508438i	0.816970	+	0.576680i	$0.195652\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.0416125	−	0.404779i	−0.0416125	−	0.404779i	−0.994757	−	0.102264i	$-0.967391\pi$
$353$	−0.0416125	−	0.404779i	−0.0416125	−	0.404779i	0.953145	−	0.302515i	$-0.0978261\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$359$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$360$		0			0
$361$	2.72931	−	0.764718i	2.72931	−	0.764718i
$362$	0.487493	+	2.00044i	0.487493	+	2.00044i
$363$	0.657204	−	0.753713i	0.657204	−	0.753713i
$364$		0			0
$365$		0			0
$366$	−0.231058	+	0.140510i	−0.231058	+	0.140510i
$367$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$367$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$368$	−5.57568	−	1.76964i	−5.57568	−	1.76964i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	3.99748	−	2.62195i	3.99748	−	2.62195i
$373$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$373$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$374$		0			0
$375$		0			0
$376$	0.260399	−	3.80690i	0.260399	−	3.80690i
$377$		0			0
$378$		0			0
$379$	−0.730836	−	1.68255i	−0.730836	−	1.68255i	−0.730836	−	0.682553i	$-0.760870\pi$
$379$	−0.730836	−	1.68255i	−0.730836	−	1.68255i		−	1.00000i	$-0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.733918	+	1.54321i	−0.733918	+	1.54321i	0.102264	+	0.994757i	$0.467391\pi$
$383$	−0.733918	+	1.54321i	−0.733918	+	1.54321i	−0.836182	+	0.548452i	$0.815217\pi$
$384$	5.78952	−	2.99989i	5.78952	−	2.99989i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$389$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$390$		0			0
$391$	−0.228074	−	0.814006i	−0.228074	−	0.814006i
$392$	3.54975	−	1.39984i	3.54975	−	1.39984i
$393$		0			0
$394$	0.269797	+	0.0184546i	0.269797	+	0.0184546i
$395$		0			0
$396$		0			0
$397$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$397$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$398$	2.52443	−	1.41942i	2.52443	−	1.41942i
$399$		0			0
$400$		0			0
$401$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$401$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	2.22767	+	1.25256i	2.22767	+	1.25256i
$409$	0.461039	+	0.280364i	0.461039	+	0.280364i	0.730836	−	0.682553i	$-0.239130\pi$
$409$	0.461039	+	0.280364i	0.461039	+	0.280364i	−0.269797	+	0.962917i	$0.586957\pi$
$410$		0			0
$411$	−1.73863	+	0.361291i	−1.73863	+	0.361291i
$412$		0			0
$413$		0			0
$414$	1.70696	−	1.82770i	1.70696	−	1.82770i
$415$		0			0
$416$		0			0
$417$	−0.514311	+	0.163235i	−0.514311	+	0.163235i
$418$		0			0
$419$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$419$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$420$		0			0
$421$	−0.502852	−	0.618088i	−0.502852	−	0.618088i	0.460065	−	0.887885i	$-0.347826\pi$
$421$	−0.502852	−	0.618088i	−0.502852	−	0.618088i	−0.962917	+	0.269797i	$0.913043\pi$
$422$	−1.11635	−	1.11635i	−1.11635	−	1.11635i
$423$	0.871660	+	0.490110i	0.871660	+	0.490110i
$424$			5.20897i			5.20897i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−1.85760	+	1.40866i	−1.85760	+	1.40866i
$429$		0			0
$430$		0			0
$431$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$431$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$432$	0.158233	+	4.63197i	0.158233	+	4.63197i
$433$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$433$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$434$		0			0
$435$		0			0
$436$	−5.18350	+	0.354561i	−5.18350	+	0.354561i
$437$	−2.40128	+	0.585176i	−2.40128	+	0.585176i
$438$		0			0
$439$	0.366581	−	0.843954i	0.366581	−	0.843954i	−0.631088	−	0.775711i	$-0.717391\pi$
$439$	0.366581	−	0.843954i	0.366581	−	0.843954i	0.997669	−	0.0682424i	$-0.0217391\pi$
$440$		0			0
$441$	−0.0682424	+	0.997669i	−0.0682424	+	0.997669i
$442$		0			0
$443$	−0.762664	−	1.60365i	−0.762664	−	1.60365i	−0.796805	−	0.604236i	$-0.793478\pi$
$443$	−0.762664	−	1.60365i	−0.762664	−	1.60365i	0.0341411	−	0.999417i	$-0.489130\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$449$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$450$		0			0
$451$		0			0
$452$	−2.29161	+	1.99818i	−2.29161	+	1.99818i
$453$	−0.339029	−	1.96632i	−0.339029	−	1.96632i
$454$	3.62620	+	1.57508i	3.62620	+	1.57508i
$455$		0			0
$456$	3.88231	−	6.38419i	3.88231	−	6.38419i
$457$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$457$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$458$	3.30585	+	2.16831i	3.30585	+	2.16831i
$459$	−0.547173	+	0.386237i	−0.547173	+	0.386237i
$460$		0			0
$461$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$461$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$462$		0			0
$463$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$463$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$464$		0			0
$465$		0			0
$466$	2.83554	+	0.589232i	2.83554	+	0.589232i
$467$	0.501972	+	0.197952i	0.501972	+	0.197952i	0.604236	−	0.796805i	$-0.293478\pi$
$467$	0.501972	+	0.197952i	0.501972	+	0.197952i	−0.102264	+	0.994757i	$0.532609\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	2.23744	+	0.464945i	2.23744	+	0.464945i
$475$		0			0
$476$		0			0
$477$	−1.23279	−	0.586291i	−1.23279	−	0.586291i
$478$		0			0
$479$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$479$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$480$		0			0
$481$		0			0
$482$	−2.26169	−	1.48344i	−2.26169	−	1.48344i
$483$		0			0
$484$	−1.52022	+	2.49989i	−1.52022	+	2.49989i
$485$		0			0
$486$	−1.81734	−	0.789381i	−1.81734	−	0.789381i
$487$		0			0		−0.169910	−	0.985460i	$-0.554348\pi$
$487$		0			0		0.169910	+	0.985460i	$0.445652\pi$
$488$	0.392532	−	0.342270i	0.392532	−	0.342270i
$489$		0			0
$490$		0			0
$491$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$491$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−5.53446	+	5.16882i	−5.53446	+	5.16882i
$497$		0			0
$498$	−1.45267	−	1.10160i	−1.45267	−	1.10160i
$499$	0.0861339	−	1.25923i	0.0861339	−	1.25923i	−0.730836	−	0.682553i	$-0.760870\pi$
$499$	0.0861339	−	1.25923i	0.0861339	−	1.25923i	0.816970	−	0.576680i	$-0.195652\pi$
$500$		0			0
$501$	−0.582332	+	1.34066i	−0.582332	+	1.34066i
$502$		0			0
$503$	0.264590	−	0.0644788i	0.264590	−	0.0644788i	−0.102264	−	0.994757i	$-0.532609\pi$
$503$	0.264590	−	0.0644788i	0.264590	−	0.0644788i	0.366854	+	0.930278i	$0.380435\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.236764	+	0.971567i	−0.236764	+	0.971567i
$508$		0			0
$509$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$509$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$510$		0			0
$511$		0			0
$512$	−5.72930	+	4.34466i	−5.72930	+	4.34466i
$513$	1.07396	+	1.63739i	1.07396	+	1.63739i
$514$	−3.42481	+	1.48761i	−3.42481	+	1.48761i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.07843	−	1.32557i	−1.07843	−	1.32557i
$520$		0			0
$521$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$521$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$522$		0			0
$523$		0			0		0.953145	−	0.302515i	$-0.0978261\pi$
$523$		0			0		−0.953145	+	0.302515i	$0.902174\pi$
$524$		0			0
$525$		0			0
$526$	−2.09813	+	2.24655i	−2.09813	+	2.24655i
$527$	−1.06323	−	0.259102i	−1.06323	−	0.259102i
$528$		0			0
$529$	0.580683	−	0.120667i	0.580683	−	0.120667i
$530$		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
$541$	0.894675	+	0.727872i	0.894675	+	0.727872i	0.962917	−	0.269797i	$-0.0869565\pi$
$541$	0.894675	+	0.727872i	0.894675	+	0.727872i	−0.0682424	+	0.997669i	$0.521739\pi$
$542$	−0.702771	+	0.395148i	−0.702771	+	0.395148i
$543$	1.03856	+	0.0354783i	1.03856	+	0.0354783i
$544$	−3.38719	−	1.20381i	−3.38719	−	1.20381i
$545$		0			0
$546$		0			0
$547$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$547$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$548$	4.83336	−	1.90603i	4.83336	−	1.90603i
$549$	0.0368232	+	0.131424i	0.0368232	+	0.131424i
$550$		0			0
$551$		0			0
$552$	−2.64146	+	4.02722i	−2.64146	+	4.02722i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.40176	−	0.726333i	1.40176	−	0.726333i
$557$	0.809371	−	1.70186i	0.809371	−	1.70186i	0.102264	−	0.994757i	$-0.467391\pi$
$557$	0.809371	−	1.70186i	0.809371	−	1.70186i	0.707107	−	0.707107i	$-0.250000\pi$
$558$	−0.979373	−	3.08575i	−0.979373	−	3.08575i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.33256	−	1.33256i	1.33256	−	1.33256i	0.429483	−	0.903075i	$-0.358696\pi$
$563$	1.33256	−	1.33256i	1.33256	−	1.33256i	0.903075	−	0.429483i	$-0.141304\pi$
$564$	−2.75690	−	0.979802i	−2.75690	−	0.979802i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$569$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$570$		0			0
$571$	−0.136267	−	0.383417i	−0.136267	−	0.383417i	0.854419	−	0.519584i	$-0.173913\pi$
$571$	−0.136267	−	0.383417i	−0.136267	−	0.383417i	−0.990686	+	0.136167i	$0.956522\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.22069	−	5.87429i	−1.22069	−	5.87429i
$577$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$577$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$578$	0.258682	+	1.06151i	0.258682	+	1.06151i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.145581	+	0.519584i	−0.145581	+	0.519584i
$587$	−0.200250	−	1.94790i	−0.200250	−	1.94790i	−0.302515	−	0.953145i	$-0.597826\pi$
$587$	−0.200250	−	1.94790i	−0.200250	−	1.94790i	0.102264	−	0.994757i	$-0.467391\pi$
$588$	−0.299208	−	2.91050i	−0.299208	−	2.91050i
$589$	−0.863223	+	3.08088i	−0.863223	+	3.08088i
$590$		0			0
$591$	0.0457060	−	0.128604i	0.0457060	−	0.128604i
$592$		0			0
$593$	−0.178978	−	0.205261i	−0.178978	−	0.205261i	0.657204	−	0.753713i	$-0.271739\pi$
$593$	−0.178978	−	0.205261i	−0.178978	−	0.205261i	−0.836182	+	0.548452i	$0.815217\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.346072	−	1.42011i	−0.346072	−	1.42011i
$598$		0			0
$599$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$599$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$600$		0			0
$601$	−1.46007	+	0.887885i	−1.46007	+	0.887885i	−0.460065	+	0.887885i	$0.652174\pi$
$601$	−1.46007	+	0.887885i	−1.46007	+	0.887885i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	1.95504	+	5.50095i	1.95504	+	5.50095i
$605$		0			0
$606$		0			0
$607$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$607$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$608$	−3.85561	+	9.77715i	−3.85561	+	9.77715i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.38565	−	1.38565i	1.38565	−	1.38565i
$613$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$613$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.348908	−	1.09932i	−0.348908	−	1.09932i	−0.953145	−	0.302515i	$-0.902174\pi$
$617$	−0.348908	−	1.09932i	−0.348908	−	1.09932i	0.604236	−	0.796805i	$-0.293478\pi$
$618$		0			0
$619$	−0.121183	+	0.0627919i	−0.121183	+	0.0627919i	−0.519584	−	0.854419i	$-0.673913\pi$
$619$	−0.121183	+	0.0627919i	−0.121183	+	0.0627919i	0.398401	+	0.917211i	$0.369565\pi$
$620$		0			0
$621$	−0.655806	−	1.07843i	−0.655806	−	1.07843i
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.18930	−	0.422677i	−1.18930	−	0.422677i	−0.334880	−	0.942261i	$-0.608696\pi$
$631$	−1.18930	−	0.422677i	−1.18930	−	0.422677i	−0.854419	+	0.519584i	$0.826087\pi$
$632$	−4.39842	−	0.150255i	−4.39842	−	0.150255i
$633$	−0.694541	+	0.390521i	−0.694541	+	0.390521i
$634$	−1.22466	−	0.996337i	−1.22466	−	0.996337i
$635$		0			0
$636$	3.84596	+	1.07759i	3.84596	+	1.07759i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$641$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$642$	0.579175	+	1.46869i	0.579175	+	1.46869i
$643$		0			0		−0.871660	−	0.490110i	$-0.836957\pi$
$643$		0			0		0.871660	+	0.490110i	$0.163043\pi$
$644$		0			0
$645$		0			0
$646$	−2.54422	+	0.528695i	−2.54422	+	0.528695i
$647$	−1.34526	−	0.231946i	−1.34526	−	0.231946i	−0.548452	−	0.836182i	$-0.684783\pi$
$647$	−1.34526	−	0.231946i	−1.34526	−	0.231946i	−0.796805	+	0.604236i	$0.793478\pi$
$648$	3.70730	+	0.903444i	3.70730	+	0.903444i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.245871	+	0.324230i	0.245871	+	0.324230i	0.903075	−	0.429483i	$-0.141304\pi$
$653$	0.245871	+	0.324230i	0.245871	+	0.324230i	−0.657204	+	0.753713i	$0.728261\pi$
$654$	−0.715852	+	3.44487i	−0.715852	+	3.44487i
$655$		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
$661$	−0.614311	+	0.266833i	−0.614311	+	0.266833i	−0.682553	−	0.730836i	$-0.739130\pi$
$661$	−0.614311	+	0.266833i	−0.614311	+	0.266833i	0.0682424	+	0.997669i	$0.478261\pi$
$662$	0.999894	+	1.52446i	0.999894	+	1.52446i
$663$		0			0
$664$	3.11739	+	1.61530i	3.11739	+	1.61530i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.01255	−	4.15501i	1.01255	−	4.15501i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$673$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$674$		0			0
$675$		0			0
$676$	0.199666	−	2.91901i	0.199666	−	2.91901i
$677$	0.429951	+	0.326042i	0.429951	+	0.326042i	0.796805	−	0.604236i	$-0.206522\pi$
$677$	0.429951	+	0.326042i	0.429951	+	0.326042i	−0.366854	+	0.930278i	$0.619565\pi$
$678$	0.884297	+	1.85941i	0.884297	+	1.85941i
$679$		0			0
$680$		0			0
$681$	1.25923	−	1.54781i	1.25923	−	1.54781i
$682$		0			0
$683$	−0.760368	−	1.35231i	−0.760368	−	1.35231i	−0.930278	−	0.366854i	$-0.880435\pi$
$683$	−0.760368	−	1.35231i	−0.760368	−	1.35231i	0.169910	−	0.985460i	$-0.445652\pi$
$684$	−3.91054	−	4.18716i	−3.91054	−	4.18716i
$685$		0			0
$686$		0			0
$687$	1.50391	−	1.31134i	1.50391	−	1.31134i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.979167	+	1.61017i	−0.979167	+	1.61017i	−0.203456	+	0.979084i	$0.565217\pi$
$691$	−0.979167	+	1.61017i	−0.979167	+	1.61017i	−0.775711	+	0.631088i	$0.782609\pi$
$692$	3.76840	+	3.28587i	3.76840	+	3.28587i
$693$		0			0
$694$	2.76613	−	1.95255i	2.76613	−	1.95255i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.965509	−	0.459176i	−0.965509	−	0.459176i
$699$	0.672464	−	1.29780i	0.672464	−	1.29780i
$700$		0			0
$701$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$701$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.806244			0.806244
$707$		0			0
$708$		0			0
$709$	1.51897	+	0.315646i	1.51897	+	0.315646i	0.887885	−	0.460065i	$-0.152174\pi$
$709$	1.51897	+	0.315646i	1.51897	+	0.315646i	0.631088	+	0.775711i	$0.282609\pi$
$710$		0			0
$711$	0.530621	−	1.02405i	0.530621	−	1.02405i
$712$		0			0
$713$	0.623882	−	1.96569i	0.623882	−	1.96569i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$719$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$720$		0			0
$721$		0			0
$722$	0.954224	+	5.53439i	0.954224	+	5.53439i
$723$	−1.02890	+	0.897153i	−1.02890	+	0.897153i
$724$	−3.01211	+	0.414006i	−3.01211	+	0.414006i
$725$		0			0
$726$	1.35239	+	1.44806i	1.35239	+	1.44806i
$727$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$727$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$728$		0			0
$729$	−0.631088	+	0.775711i	−0.631088	+	0.775711i
$730$		0			0
$731$		0			0
$732$	−0.171506	−	0.360627i	−0.171506	−	0.360627i
$733$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$733$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$734$		0			0
$735$		0			0
$736$	2.69892	−	6.21353i	2.69892	−	6.21353i
$737$		0			0
$738$		0			0
$739$	1.70486	−	0.116615i	1.70486	−	0.116615i	0.816970	−	0.576680i	$-0.195652\pi$
$739$	1.70486	−	0.116615i	1.70486	−	0.116615i	0.887885	+	0.460065i	$0.152174\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.0668540	−	1.95703i	−0.0668540	−	1.95703i	−0.236764	−	0.971567i	$-0.576087\pi$
$743$	−0.0668540	−	1.95703i	−0.0668540	−	1.95703i	0.169910	−	0.985460i	$-0.445652\pi$
$744$	2.86840	+	5.53577i	2.86840	+	5.53577i
$745$		0			0
$746$		0			0
$747$	−0.733164	+	0.555976i	−0.733164	+	0.555976i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		−	0.796802i		−	0.796802i	−0.917211	−	0.398401i	$-0.869565\pi$
$751$		−	0.796802i		−	0.796802i	0.917211	−	0.398401i	$-0.130435\pi$
$752$	4.56728	+	0.787479i	4.56728	+	0.787479i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$757$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$758$	3.46437	−	1.09954i	3.46437	−	1.09954i
$759$		0			0
$760$		0			0
$761$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$761$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−2.89293	−	1.75923i	−2.89293	−	1.75923i
$767$		0			0
$768$	2.53860	+	6.43744i	2.53860	+	6.43744i
$769$	−0.547173	−	0.386237i	−0.547173	−	0.386237i	0.269797	−	0.962917i	$-0.413043\pi$
$769$	−0.547173	−	0.386237i	−0.547173	−	0.386237i	−0.816970	+	0.576680i	$0.804348\pi$
$770$		0			0
$771$	0.256609	+	1.86697i	0.256609	+	1.86697i
$772$		0			0
$773$	−0.0657501	+	1.92471i	−0.0657501	+	1.92471i	0.236764	+	0.971567i	$0.423913\pi$
$773$	−0.0657501	+	1.92471i	−0.0657501	+	1.92471i	−0.302515	+	0.953145i	$0.597826\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	1.65061	−	0.284593i	1.65061	−	0.284593i
$783$		0			0
$784$	1.25042	+	4.46281i	1.25042	+	4.46281i
$785$		0			0
$786$		0			0
$787$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$787$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$788$	−0.0678507	+	0.393526i	−0.0678507	+	0.393526i
$789$	0.806094	+	1.32557i	0.806094	+	1.32557i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.70381	+	3.92256i	1.70381	+	3.92256i
$797$	−0.536765	−	0.0551811i	−0.536765	−	0.0551811i	−0.169910	−	0.985460i	$-0.554348\pi$
$797$	−0.536765	−	0.0551811i	−0.536765	−	0.0551811i	−0.366854	+	0.930278i	$0.619565\pi$
$798$		0			0
$799$	0.266833	+	0.614311i	0.266833	+	0.614311i
$800$		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		0.854419	−	0.519584i	$-0.173913\pi$
$809$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$810$		0			0
$811$	0.347674	+	1.67310i	0.347674	+	1.67310i	0.682553	+	0.730836i	$0.260870\pi$
$811$	0.347674	+	1.67310i	0.347674	+	1.67310i	−0.334880	+	0.942261i	$0.608696\pi$
$812$		0			0
$813$	0.0963423	+	0.395342i	0.0963423	+	0.395342i
$814$		0			0
$815$		0			0
$816$	−1.79008	+	2.53597i	−1.79008	+	2.53597i
$817$		0			0
$818$	−0.646011	+	0.851893i	−0.646011	+	0.851893i
$819$		0			0
$820$		0			0
$821$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$821$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$822$	−0.359812	−	3.50002i	−0.359812	−	3.50002i
$823$		0			0		−0.102264	−	0.994757i	$-0.532609\pi$
$823$		0			0		0.102264	+	0.994757i	$0.467391\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.16366	+	1.53451i	−1.16366	+	1.53451i	−0.366854	+	0.930278i	$0.619565\pi$
$827$	−1.16366	+	1.53451i	−1.16366	+	1.53451i	−0.796805	+	0.604236i	$0.793478\pi$
$828$	2.42700	+	2.78340i	2.42700	+	2.78340i
$829$	−0.157049	+	0.222488i	−0.157049	+	0.222488i	−0.887885	−	0.460065i	$-0.847826\pi$
$829$	−0.157049	+	0.222488i	−0.157049	+	0.222488i	0.730836	+	0.682553i	$0.239130\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.440168	+	0.504806i	−0.440168	+	0.504806i
$834$	−0.217522	−	1.04677i	−0.217522	−	1.04677i
$835$		0			0
$836$		0			0
$837$	−1.63299	+	0.0557845i	−1.63299	+	0.0557845i
$838$		0			0
$839$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$839$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$840$		0			0
$841$	−0.990686	−	0.136167i	−0.990686	−	0.136167i
$842$	1.32013	−	0.865875i	1.32013	−	0.865875i
$843$		0			0
$844$	1.80842	−	1.47126i	1.80842	−	1.47126i
$845$		0			0
$846$	−1.14262	+	1.61872i	−1.14262	+	1.61872i
$847$		0			0
$848$	−6.29365	−	0.647007i	−6.29365	−	0.647007i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$853$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$854$		0			0
$855$		0			0
$856$	−1.57976	−	2.59781i	−1.57976	−	2.59781i
$857$	−0.135385	+	0.785216i	−0.135385	+	0.785216i	0.836182	+	0.548452i	$0.184783\pi$
$857$	−0.135385	+	0.785216i	−0.135385	+	0.785216i	−0.971567	+	0.236764i	$0.923913\pi$
$858$		0			0
$859$	0.0185847	+	0.271698i	0.0185847	+	0.271698i	0.997669	+	0.0682424i	$0.0217391\pi$
$859$	0.0185847	+	0.271698i	0.0185847	+	0.271698i	−0.979084	+	0.203456i	$0.934783\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.13659	−	0.195968i	1.13659	−	0.195968i	0.429483	−	0.903075i	$-0.358696\pi$
$863$	1.13659	−	0.195968i	1.13659	−	0.195968i	0.707107	+	0.707107i	$0.250000\pi$
$864$	−5.35470	−	0.366272i	−5.35470	−	0.366272i
$865$		0			0
$866$		0			0
$867$	0.551101	+	0.0188262i	0.551101	+	0.0188262i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.231339	−	6.77202i	0.231339	−	6.77202i
$873$		0			0
$874$	−0.666817	−	4.85145i	−0.666817	−	4.85145i
$875$		0			0
$876$		0			0
$877$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$877$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$878$	1.58914	+	0.893530i	1.58914	+	0.893530i
$879$	0.232687	+	0.141500i	0.232687	+	0.141500i
$880$		0			0
$881$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$881$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$882$	−1.95256	−	0.336656i	−1.95256	−	0.336656i
$883$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$883$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$884$		0			0
$885$		0			0
$886$	3.31531	−	1.17826i	3.31531	−	1.17826i
$887$	1.86642	−	0.592374i	1.86642	−	0.592374i	0.871660	−	0.490110i	$-0.163043\pi$
$887$	1.86642	−	0.592374i	1.86642	−	0.592374i	0.994757	−	0.102264i	$-0.0326087\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.82164	−	0.718362i	1.82164	−	0.718362i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−0.420634	−	0.811787i	−0.420634	−	0.811787i
$902$		0			0
$903$		0			0
$904$	−2.28668	−	3.23949i	−2.28668	−	3.23949i
$905$		0			0
$906$	3.94429	−	0.269797i	3.94429	−	0.269797i
$907$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$907$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$908$	−2.86128	+	5.08878i	−2.86128	+	5.08878i
$909$		0			0
$910$		0			0
$911$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$911$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$912$	7.23138	+	5.48373i	7.23138	+	5.48373i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−3.68431	+	4.52862i	−3.68431	+	4.52862i
$917$		0			0
$918$	−0.650397	−	1.15673i	−0.650397	−	1.15673i
$919$	−0.861502	−	0.922444i	−0.861502	−	0.922444i	0.136167	−	0.990686i	$-0.456522\pi$
$919$	−0.861502	−	0.922444i	−0.861502	−	0.922444i	−0.997669	+	0.0682424i	$0.978261\pi$
$920$		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		0.816970	−	0.576680i	$-0.195652\pi$
$929$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$930$		0			0
$931$	1.43110	+	1.33655i	1.43110	+	1.33655i
$932$	−1.29374	+	4.07623i	−1.29374	+	4.07623i
$933$		0			0
$934$	−0.491872	+	0.949270i	−0.491872	+	0.949270i
$935$		0			0
$936$		0			0
$937$		0			0		−0.930278	−	0.366854i	$-0.880435\pi$
$937$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.73917	−	0.827114i	−1.73917	−	0.827114i	−0.985460	−	0.169910i	$-0.945652\pi$
$947$	−1.73917	−	0.827114i	−1.73917	−	0.827114i	−0.753713	−	0.657204i	$-0.771739\pi$
$948$	−1.02085	+	3.21643i	−1.02085	+	3.21643i
$949$		0			0
$950$		0			0
$951$	−0.650963	+	0.459500i	−0.650963	+	0.459500i
$952$		0			0
$953$	−0.205261	−	0.178978i	−0.205261	−	0.178978i	0.548452	−	0.836182i	$-0.315217\pi$
$953$	−0.205261	−	0.178978i	−0.205261	−	0.178978i	−0.753713	+	0.657204i	$0.771739\pi$
$954$	1.40536	−	2.31102i	1.40536	−	2.31102i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−1.13970	−	1.22032i	−1.13970	−	1.22032i
$962$		0			0
$963$	0.792625	−	0.0814843i	0.792625	−	0.0814843i
$964$	2.52061	−	3.09825i	2.52061	−	3.09825i
$965$		0			0
$966$		0			0
$967$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$967$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$968$	−3.04044	−	2.30564i	−3.04044	−	2.30564i
$969$	−0.0895000	+	1.30844i	−0.0895000	+	1.30844i
$970$		0			0
$971$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$971$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$972$	1.43398	−	2.55033i	1.43398	−	2.55033i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.364786	+	0.516785i	0.364786	+	0.516785i
$977$	−0.404592	+	1.66025i	−0.404592	+	1.66025i	0.302515	+	0.953145i	$0.402174\pi$
$977$	−0.404592	+	1.66025i	−0.404592	+	1.66025i	−0.707107	+	0.707107i	$0.750000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.57668	+	0.816970i	1.57668	+	0.816970i
$982$		0			0
$983$	−1.09435	−	1.66847i	−1.09435	−	1.66847i	−0.604236	−	0.796805i	$-0.706522\pi$
$983$	−1.09435	−	1.66847i	−1.09435	−	1.66847i	−0.490110	−	0.871660i	$-0.663043\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	0.203456	+	0.979084i	$0.434783\pi$
$991$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	−0.576680	+	0.816970i	$0.695652\pi$
$992$	−5.29898	−	6.98775i	−5.29898	−	6.98775i
$993$	0.877017	−	0.278353i	0.877017	−	0.278353i
$994$		0			0
$995$		0			0
$996$	1.83753	−	1.96752i	1.83753	−	1.96752i
$997$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$997$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$998$	2.46448	+	0.424919i	2.46448	+	0.424919i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.257.1	✓	88
3.2	odd	2	inner	3525.1.bg.a.257.2	yes	88
5.2	odd	4	inner	3525.1.bg.a.3218.1	yes	88
5.3	odd	4	inner	3525.1.bg.a.3218.2	yes	88
5.4	even	2	inner	3525.1.bg.a.257.2	yes	88
15.2	even	4	inner	3525.1.bg.a.3218.2	yes	88
15.8	even	4	inner	3525.1.bg.a.3218.1	yes	88
15.14	odd	2	CM	3525.1.bg.a.257.1	✓	88
47.15	odd	46	inner	3525.1.bg.a.2882.1	yes	88
141.62	even	46	inner	3525.1.bg.a.2882.2	yes	88
235.62	even	92	inner	3525.1.bg.a.2318.1	yes	88
235.109	odd	46	inner	3525.1.bg.a.2882.2	yes	88
235.203	even	92	inner	3525.1.bg.a.2318.2	yes	88
705.62	odd	92	inner	3525.1.bg.a.2318.2	yes	88
705.203	odd	92	inner	3525.1.bg.a.2318.1	yes	88
705.344	even	46	inner	3525.1.bg.a.2882.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.257.1	✓	88	1.1	even	1	trivial
3525.1.bg.a.257.1	✓	88	15.14	odd	2	CM
3525.1.bg.a.257.2	yes	88	3.2	odd	2	inner
3525.1.bg.a.257.2	yes	88	5.4	even	2	inner
3525.1.bg.a.2318.1	yes	88	235.62	even	92	inner
3525.1.bg.a.2318.1	yes	88	705.203	odd	92	inner
3525.1.bg.a.2318.2	yes	88	235.203	even	92	inner
3525.1.bg.a.2318.2	yes	88	705.62	odd	92	inner
3525.1.bg.a.2882.1	yes	88	47.15	odd	46	inner
3525.1.bg.a.2882.1	yes	88	705.344	even	46	inner
3525.1.bg.a.2882.2	yes	88	141.62	even	46	inner
3525.1.bg.a.2882.2	yes	88	235.109	odd	46	inner
3525.1.bg.a.3218.1	yes	88	5.2	odd	4	inner
3525.1.bg.a.3218.1	yes	88	15.8	even	4	inner
3525.1.bg.a.3218.2	yes	88	5.3	odd	4	inner
3525.1.bg.a.3218.2	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)

\(f(q)\)	\(=\)	\(q+(-0.202623 + 1.97098i) q^{2} +(0.930278 + 0.366854i) q^{3} +(-2.86464 - 0.595279i) q^{4} +(-0.911560 + 1.75923i) q^{6} +(1.15433 - 3.63700i) q^{8} +(0.730836 + 0.682553i) q^{9} +O(q^{10})\)	\(q+(-0.202623 + 1.97098i) q^{2} +(0.930278 + 0.366854i) q^{3} +(-2.86464 - 0.595279i) q^{4} +(-0.911560 + 1.75923i) q^{6} +(1.15433 - 3.63700i) q^{8} +(0.730836 + 0.682553i) q^{9} +(-2.44653 - 1.60468i) q^{12} +(4.25097 + 1.84646i) q^{16} +(0.113799 + 0.660021i) q^{17} +(-1.49339 + 1.30216i) q^{18} +(1.93993 - 0.266637i) q^{19} +(-1.25556 + 0.129075i) q^{23} +(2.40810 - 2.95995i) q^{24} +(0.429483 + 0.903075i) q^{27} +(-0.650963 + 1.49867i) q^{31} +(-2.63053 + 4.67839i) q^{32} +(-1.32395 + 0.0905606i) q^{34} +(-1.68727 - 2.39032i) q^{36} +(0.132463 + 3.87760i) q^{38} -2.50084i q^{46} +(0.971567 - 0.236764i) q^{47} +(3.27721 + 3.27721i) q^{48} +(0.631088 + 0.775711i) q^{49} +(-0.136267 + 0.655751i) q^{51} +(-1.30114 + 0.412965i) q^{53} +(-1.86697 + 0.663521i) q^{54} +(1.90249 + 0.463625i) q^{57} +(0.116615 + 0.0709153i) q^{61} +(-2.82195 - 1.58670i) q^{62} +(-4.90164 - 3.45995i) q^{64} +(0.0669031 - 1.95846i) q^{68} +(-1.21537 - 0.340531i) q^{69} +(3.32608 - 1.87016i) q^{72} +(-5.71592 - 0.390980i) q^{76} +(-0.311173 - 1.11059i) q^{79} +(0.0682424 + 0.997669i) q^{81} +(-0.156340 + 0.906751i) q^{83} +(3.67356 + 0.377653i) q^{92} +(-1.15537 + 1.15537i) q^{93} +(0.269797 + 1.96292i) q^{94} +(-4.16341 + 3.38719i) q^{96} +(-1.65679 + 1.08669i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 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

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