LMFDB - Embedded newform 3525.1.bg.a.107.1

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			107.1
Root			$0.985460 + 0.169910i$ of defining polynomial
Character	$\chi$	$=$	3525.107
Dual form			3525.1.bg.a.593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34526 - 0.231946i) q^{2} +(-0.994757 - 0.102264i) q^{3} +(0.813657 + 0.289174i) q^{4} +(1.31448 + 0.368301i) q^{6} +(0.162405 + 0.0913155i) q^{8} +(0.979084 + 0.203456i) q^{9} +O(q^{10})$	\(q+(-1.34526 - 0.231946i) q^{2} +(-0.994757 - 0.102264i) q^{3} +(0.813657 + 0.289174i) q^{4} +(1.31448 + 0.368301i) q^{6} +(0.162405 + 0.0913155i) q^{8} +(0.979084 + 0.203456i) q^{9} +(-0.779819 - 0.370865i) q^{12} +(-0.867134 - 0.705466i) q^{16} +(0.217854 - 0.893968i) q^{17} +(-1.26993 - 0.500795i) q^{18} +(1.28629 + 1.37728i) q^{19} +(0.277623 + 1.61018i) q^{23} +(-0.152215 - 0.107445i) q^{24} +(-0.953145 - 0.302515i) q^{27} +(0.655806 - 0.806094i) q^{31} +(0.880441 + 1.00973i) q^{32} +(-0.500422 + 1.15209i) q^{34} +(0.737804 + 0.448669i) q^{36} +(-1.41093 - 2.15114i) q^{38} -2.23050i q^{46} +(0.604236 - 0.796805i) q^{47} +(0.790444 + 0.790444i) q^{48} +(-0.816970 + 0.576680i) q^{49} +(-0.308133 + 0.867003i) q^{51} +(0.199432 + 0.354689i) q^{53} +(1.21206 + 0.628038i) q^{54} +(-1.13870 - 1.50160i) q^{57} +(-1.81734 + 0.249787i) q^{61} +(-1.06920 + 0.932292i) q^{62} +(-0.369395 - 0.607445i) q^{64} +(0.435770 - 0.664385i) q^{68} +(-0.111504 - 1.63013i) q^{69} +(0.140429 + 0.122448i) q^{72} +(0.648323 + 1.49259i) q^{76} +(-1.70486 - 0.116615i) q^{79} +(0.917211 + 0.398401i) q^{81} +(0.455969 + 1.87108i) q^{83} +(-0.239732 + 1.39042i) q^{92} +(-0.734803 + 0.734803i) q^{93} +(-0.997669 + 0.931758i) q^{94} +(-0.772565 - 1.09448i) q^{96} +(1.23279 - 0.586291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{46}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.34526	−	0.231946i	−1.34526	−	0.231946i	−0.548452	−	0.836182i	$-0.684783\pi$
$2$	−1.34526	−	0.231946i	−1.34526	−	0.231946i	−0.796805	+	0.604236i	$0.793478\pi$
$3$	−0.994757	−	0.102264i	−0.994757	−	0.102264i
$3$	−0.994757	−	0.102264i	−0.994757	−	0.102264i
$4$	0.813657	+	0.289174i	0.813657	+	0.289174i
$5$		0			0
$5$		0			0
$6$	1.31448	+	0.368301i	1.31448	+	0.368301i
$7$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$7$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$8$	0.162405	+	0.0913155i	0.162405	+	0.0913155i
$9$	0.979084	+	0.203456i	0.979084	+	0.203456i
$10$		0			0
$11$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$11$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$12$	−0.779819	−	0.370865i	−0.779819	−	0.370865i
$13$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$13$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$14$		0			0
$15$		0			0
$16$	−0.867134	−	0.705466i	−0.867134	−	0.705466i
$17$	0.217854	−	0.893968i	0.217854	−	0.893968i	−0.753713	−	0.657204i	$-0.771739\pi$
$17$	0.217854	−	0.893968i	0.217854	−	0.893968i	0.971567	−	0.236764i	$-0.0760870\pi$
$18$	−1.26993	−	0.500795i	−1.26993	−	0.500795i
$19$	1.28629	+	1.37728i	1.28629	+	1.37728i	0.887885	+	0.460065i	$0.152174\pi$
$19$	1.28629	+	1.37728i	1.28629	+	1.37728i	0.398401	+	0.917211i	$0.369565\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.277623	+	1.61018i	0.277623	+	1.61018i	0.707107	+	0.707107i	$0.250000\pi$
$23$	0.277623	+	1.61018i	0.277623	+	1.61018i	−0.429483	+	0.903075i	$0.641304\pi$
$24$	−0.152215	−	0.107445i	−0.152215	−	0.107445i
$25$		0			0
$26$		0			0
$27$	−0.953145	−	0.302515i	−0.953145	−	0.302515i
$28$		0			0
$29$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$29$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$30$		0			0
$31$	0.655806	−	0.806094i	0.655806	−	0.806094i	−0.334880	−	0.942261i	$-0.608696\pi$
$31$	0.655806	−	0.806094i	0.655806	−	0.806094i	0.990686	+	0.136167i	$0.0434783\pi$
$32$	0.880441	+	1.00973i	0.880441	+	1.00973i
$33$		0			0
$34$	−0.500422	+	1.15209i	−0.500422	+	1.15209i
$35$		0			0
$36$	0.737804	+	0.448669i	0.737804	+	0.448669i
$37$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$37$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$38$	−1.41093	−	2.15114i	−1.41093	−	2.15114i
$39$		0			0
$40$		0			0
$41$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$41$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$42$		0			0
$43$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$43$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$44$		0			0
$45$		0			0
$46$		−	2.23050i		−	2.23050i
$47$	0.604236	−	0.796805i	0.604236	−	0.796805i
$47$	0.604236	−	0.796805i	0.604236	−	0.796805i
$48$	0.790444	+	0.790444i	0.790444	+	0.790444i
$49$	−0.816970	+	0.576680i	−0.816970	+	0.576680i
$50$		0			0
$51$	−0.308133	+	0.867003i	−0.308133	+	0.867003i
$52$		0			0
$53$	0.199432	+	0.354689i	0.199432	+	0.354689i	0.953145	−	0.302515i	$-0.0978261\pi$
$53$	0.199432	+	0.354689i	0.199432	+	0.354689i	−0.753713	+	0.657204i	$0.771739\pi$
$54$	1.21206	+	0.628038i	1.21206	+	0.628038i
$55$		0			0
$56$		0			0
$57$	−1.13870	−	1.50160i	−1.13870	−	1.50160i
$58$		0			0
$59$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$59$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$60$		0			0
$61$	−1.81734	+	0.249787i	−1.81734	+	0.249787i	−0.962917	−	0.269797i	$-0.913043\pi$
$61$	−1.81734	+	0.249787i	−1.81734	+	0.249787i	−0.854419	+	0.519584i	$0.826087\pi$
$62$	−1.06920	+	0.932292i	−1.06920	+	0.932292i
$63$		0			0
$64$	−0.369395	−	0.607445i	−0.369395	−	0.607445i
$65$		0			0
$66$		0			0
$67$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$67$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$68$	0.435770	−	0.664385i	0.435770	−	0.664385i
$69$	−0.111504	−	1.63013i	−0.111504	−	1.63013i
$70$		0			0
$71$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$71$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$72$	0.140429	+	0.122448i	0.140429	+	0.122448i
$73$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$73$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$74$		0			0
$75$		0			0
$76$	0.648323	+	1.49259i	0.648323	+	1.49259i
$77$		0			0
$78$		0			0
$79$	−1.70486	−	0.116615i	−1.70486	−	0.116615i	−0.816970	−	0.576680i	$-0.804348\pi$
$79$	−1.70486	−	0.116615i	−1.70486	−	0.116615i	−0.887885	+	0.460065i	$0.847826\pi$
$80$		0			0
$81$	0.917211	+	0.398401i	0.917211	+	0.398401i
$82$		0			0
$83$	0.455969	+	1.87108i	0.455969	+	1.87108i	0.490110	+	0.871660i	$0.336957\pi$
$83$	0.455969	+	1.87108i	0.455969	+	1.87108i	−0.0341411	+	0.999417i	$0.510870\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$89$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$90$		0			0
$91$		0			0
$92$	−0.239732	+	1.39042i	−0.239732	+	1.39042i
$93$	−0.734803	+	0.734803i	−0.734803	+	0.734803i
$94$	−0.997669	+	0.931758i	−0.997669	+	0.931758i
$95$		0			0
$96$	−0.772565	−	1.09448i	−0.772565	−	1.09448i
$97$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$97$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$98$	1.23279	−	0.586291i	1.23279	−	0.586291i
$99$		0			0
$100$		0			0
$101$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$101$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$102$	0.615615	−	1.09487i	0.615615	−	1.09487i
$103$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$103$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$104$		0			0
$105$		0			0
$106$	−0.186018	−	0.523405i	−0.186018	−	0.523405i
$107$	0.463035	+	1.17418i	0.463035	+	1.17418i	0.953145	+	0.302515i	$0.0978261\pi$
$107$	0.463035	+	1.17418i	0.463035	+	1.17418i	−0.490110	+	0.871660i	$0.663043\pi$
$108$	−0.688053	−	0.521767i	−0.688053	−	0.521767i
$109$	0.0368232	−	0.538336i	0.0368232	−	0.538336i	−0.942261	−	0.334880i	$-0.891304\pi$
$109$	0.0368232	−	0.538336i	0.0368232	−	0.538336i	0.979084	−	0.203456i	$-0.0652174\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.272175	+	0.00929776i	0.272175	+	0.00929776i	0.169910	−	0.985460i	$-0.445652\pi$
$113$	0.272175	+	0.00929776i	0.272175	+	0.00929776i	0.102264	+	0.994757i	$0.467391\pi$
$114$	1.18355	+	2.28415i	1.18355	+	2.28415i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.460065	−	0.887885i	−0.460065	−	0.887885i
$122$	2.50272	+	0.0854955i	2.50272	+	0.0854955i
$123$		0			0
$124$	0.766702	−	0.466242i	0.766702	−	0.466242i
$125$		0			0
$126$		0			0
$127$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$127$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$128$	−0.135429	−	0.343423i	−0.135429	−	0.343423i
$129$		0			0
$130$		0			0
$131$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$131$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.117014	−	0.125291i	0.117014	−	0.125291i
$137$	0.487293	−	0.231746i	0.487293	−	0.231746i	−0.169910	−	0.985460i	$-0.554348\pi$
$137$	0.487293	−	0.231746i	0.487293	−	0.231746i	0.657204	+	0.753713i	$0.271739\pi$
$138$	−0.228100	+	2.21881i	−0.228100	+	2.21881i
$139$	1.15067	+	1.63013i	1.15067	+	1.63013i	0.631088	+	0.775711i	$0.282609\pi$
$139$	1.15067	+	1.63013i	1.15067	+	1.63013i	0.519584	+	0.854419i	$0.326087\pi$
$140$		0			0
$141$	−0.682553	+	0.730836i	−0.682553	+	0.730836i
$142$		0			0
$143$		0			0
$144$	−0.705466	−	0.867134i	−0.705466	−	0.867134i
$145$		0			0
$146$		0			0
$147$	0.871660	−	0.490110i	0.871660	−	0.490110i
$148$		0			0
$149$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$149$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$150$		0			0
$151$	−0.108498	+	0.789381i	−0.108498	+	0.789381i	0.854419	+	0.519584i	$0.173913\pi$
$151$	−0.108498	+	0.789381i	−0.108498	+	0.789381i	−0.962917	+	0.269797i	$0.913043\pi$
$152$	0.0831320	+	0.341134i	0.0831320	+	0.341134i
$153$	0.395181	−	0.830946i	0.395181	−	0.830946i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$157$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$158$	2.26642	+	0.552311i	2.26642	+	0.552311i
$159$	−0.162114	−	0.373224i	−0.162114	−	0.373224i
$160$		0			0
$161$		0			0
$162$	−1.14148	−	0.748695i	−1.14148	−	0.748695i
$163$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$163$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$164$		0			0
$165$		0			0
$166$	−0.179407	−	2.62284i	−0.179407	−	2.62284i
$167$	1.07396	−	1.63739i	1.07396	−	1.63739i	0.366854	−	0.930278i	$-0.380435\pi$
$167$	1.07396	−	1.63739i	1.07396	−	1.63739i	0.707107	−	0.707107i	$-0.250000\pi$
$168$		0			0
$169$	0.730836	−	0.682553i	0.730836	−	0.682553i
$170$		0			0
$171$	0.979167	+	1.61017i	0.979167	+	1.61017i
$172$		0			0
$173$	1.49339	−	1.30216i	1.49339	−	1.30216i	0.657204	−	0.753713i	$-0.271739\pi$
$173$	1.49339	−	1.30216i	1.49339	−	1.30216i	0.836182	−	0.548452i	$-0.184783\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$179$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$180$		0			0
$181$	0.241801	+	0.125291i	0.241801	+	0.125291i	0.576680	−	0.816970i	$-0.304348\pi$
$181$	0.241801	+	0.125291i	0.241801	+	0.125291i	−0.334880	+	0.942261i	$0.608696\pi$
$182$		0			0
$183$	1.83335	−	0.0626292i	1.83335	−	0.0626292i
$184$	−0.101947	+	0.286852i	−0.101947	+	0.286852i
$185$		0			0
$186$	1.15893	−	0.818064i	1.15893	−	0.818064i
$187$		0			0
$188$	0.722056	−	0.473597i	0.722056	−	0.473597i
$189$		0			0
$190$		0			0
$191$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$191$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$192$	0.305339	+	0.642036i	0.305339	+	0.642036i
$193$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$193$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$194$		0			0
$195$		0			0
$196$	−0.831494	+	0.232974i	−0.831494	+	0.232974i
$197$	1.00609	+	1.53391i	1.00609	+	1.53391i	0.836182	+	0.548452i	$0.184783\pi$
$197$	1.00609	+	1.53391i	1.00609	+	1.53391i	0.169910	+	0.985460i	$0.445652\pi$
$198$		0			0
$199$	1.67310	+	1.01743i	1.67310	+	1.01743i	0.942261	+	0.334880i	$0.108696\pi$
$199$	1.67310	+	1.01743i	1.67310	+	1.01743i	0.730836	+	0.682553i	$0.239130\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.501429	+	0.616339i	−0.501429	+	0.616339i
$205$		0			0
$206$		0			0
$207$	−0.0557845	+	1.63299i	−0.0557845	+	1.63299i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.03116	+	0.727872i	1.03116	+	0.727872i	0.962917	−	0.269797i	$-0.0869565\pi$
$211$	1.03116	+	0.727872i	1.03116	+	0.727872i	0.0682424	+	0.997669i	$0.478261\pi$
$212$	0.0597022	+	0.346266i	0.0597022	+	0.346266i
$213$		0			0
$214$	−0.350556	−	1.68697i	−0.350556	−	1.68697i
$215$		0			0
$216$	−0.127171	−	0.136167i	−0.127171	−	0.136167i
$217$		0			0
$218$	−0.174401	+	0.715659i	−0.174401	+	0.715659i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$223$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$224$		0			0
$225$		0			0
$226$	−0.363988	−	0.0756376i	−0.363988	−	0.0756376i
$227$	0.694541	+	0.390521i	0.694541	+	0.390521i	0.796805	−	0.604236i	$-0.206522\pi$
$227$	0.694541	+	0.390521i	0.694541	+	0.390521i	−0.102264	+	0.994757i	$0.532609\pi$
$228$	−0.492286	−	1.55107i	−0.492286	−	1.55107i
$229$	0.767255	+	0.214975i	0.767255	+	0.214975i	0.631088	−	0.775711i	$-0.282609\pi$
$229$	0.767255	+	0.214975i	0.767255	+	0.214975i	0.136167	+	0.990686i	$0.456522\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.92970	−	0.332713i	−1.92970	−	0.332713i	−0.930278	−	0.366854i	$-0.880435\pi$
$233$	−1.92970	−	0.332713i	−1.92970	−	0.332713i	−0.999417	+	0.0341411i	$0.989130\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.68399	+	0.290349i	1.68399	+	0.290349i
$238$		0			0
$239$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$239$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$240$		0			0
$241$	−0.391823	−	0.109784i	−0.391823	−	0.109784i	0.0682424	−	0.997669i	$-0.478261\pi$
$241$	−0.391823	−	0.109784i	−0.391823	−	0.109784i	−0.460065	+	0.887885i	$0.652174\pi$
$242$	0.412965	+	1.30114i	0.412965	+	1.30114i
$243$	−0.871660	−	0.490110i	−0.871660	−	0.490110i
$244$	−1.55092	−	0.322285i	−1.55092	−	0.322285i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.180115	−	0.0710281i	0.180115	−	0.0710281i
$249$	−0.262234	−	1.90790i	−0.262234	−	1.90790i
$250$		0			0
$251$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$251$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.247177	+	1.18948i	0.247177	+	1.18948i
$257$	−1.16704	+	1.33842i	−1.16704	+	1.33842i	−0.236764	+	0.971567i	$0.576087\pi$
$257$	−1.16704	+	1.33842i	−1.16704	+	1.33842i	−0.930278	+	0.366854i	$0.880435\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.0393770	+	1.15269i	−0.0393770	+	1.15269i	0.796805	+	0.604236i	$0.206522\pi$
$263$	−0.0393770	+	1.15269i	−0.0393770	+	1.15269i	−0.836182	+	0.548452i	$0.815217\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$269$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$270$		0			0
$271$	0.572255	+	0.347996i	0.572255	+	0.347996i	0.775711	−	0.631088i	$-0.217391\pi$
$271$	0.572255	+	0.347996i	0.572255	+	0.347996i	−0.203456	+	0.979084i	$0.565217\pi$
$272$	−0.819573	+	0.621502i	−0.819573	+	0.621502i
$273$		0			0
$274$	−0.709287	+	0.198733i	−0.709287	+	0.198733i
$275$		0			0
$276$	0.380665	−	1.35861i	0.380665	−	1.35861i
$277$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$277$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$278$	−1.16985	−	2.45984i	−1.16985	−	2.45984i
$279$	0.806094	−	0.655806i	0.806094	−	0.655806i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	1.08772	−	0.824847i	1.08772	−	0.824847i
$283$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$283$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.656589	+	1.16774i	0.656589	+	1.16774i
$289$	0.136167	+	0.0705559i	0.136167	+	0.0705559i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.42011	−	0.346072i	1.42011	−	0.346072i	0.548452	−	0.836182i	$-0.315217\pi$
$293$	1.42011	−	0.346072i	1.42011	−	0.346072i	0.871660	+	0.490110i	$0.163043\pi$
$294$	−1.28629	+	0.457146i	−1.28629	+	0.457146i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	0.329051	−	1.03675i	0.329051	−	1.03675i
$303$		0			0
$304$	−0.143761	−	2.10171i	−0.143761	−	2.10171i
$305$		0			0
$306$	−0.724354	+	1.02618i	−0.724354	+	1.02618i
$307$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$307$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$311$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$312$		0			0
$313$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$313$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$314$		0			0
$315$		0			0
$316$	−1.35344	−	0.587884i	−1.35344	−	0.587884i
$317$	−0.542084	+	1.13984i	−0.542084	+	1.13984i	0.429483	+	0.903075i	$0.358696\pi$
$317$	−0.542084	+	1.13984i	−0.542084	+	1.13984i	−0.971567	+	0.236764i	$0.923913\pi$
$318$	0.131517	+	0.539684i	0.131517	+	0.539684i
$319$		0			0
$320$		0			0
$321$	−0.340531	−	1.21537i	−0.340531	−	1.21537i
$322$		0			0
$323$	1.51146	−	0.849854i	1.51146	−	0.849854i
$324$	0.631088	+	0.589395i	0.631088	+	0.589395i
$325$		0			0
$326$		0			0
$327$	−0.0916825	+	0.531748i	−0.0916825	+	0.531748i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.11059	+	1.57335i	1.11059	+	1.57335i	0.775711	+	0.631088i	$0.217391\pi$
$331$	1.11059	+	1.57335i	1.11059	+	1.57335i	0.334880	+	0.942261i	$0.391304\pi$
$332$	−0.170064	+	1.65427i	−0.170064	+	1.65427i
$333$		0			0
$334$	−1.82454	+	1.95360i	−1.82454	+	1.95360i
$335$		0			0
$336$		0			0
$337$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$337$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$338$	−1.14148	+	0.748695i	−1.14148	+	0.748695i
$339$	−0.269797	−	0.0370827i	−0.269797	−	0.0370827i
$340$		0			0
$341$		0			0
$342$	−0.943759	−	2.39321i	−0.943759	−	2.39321i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−2.31102	+	1.40536i	−2.31102	+	1.40536i
$347$	0.726875	−	1.84323i	0.726875	−	1.84323i	0.236764	−	0.971567i	$-0.423913\pi$
$347$	0.726875	−	1.84323i	0.726875	−	1.84323i	0.490110	−	0.871660i	$-0.336957\pi$
$348$		0			0
$349$	−0.917985	−	1.77163i	−0.917985	−	1.77163i	−0.519584	−	0.854419i	$-0.673913\pi$
$349$	−0.917985	−	1.77163i	−0.917985	−	1.77163i	−0.398401	−	0.917211i	$-0.630435\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.660021	+	0.113799i	−0.660021	+	0.113799i	−0.490110	−	0.871660i	$-0.663043\pi$
$353$	−0.660021	+	0.113799i	−0.660021	+	0.113799i	−0.169910	+	0.985460i	$0.554348\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$359$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$360$		0			0
$361$	−0.174115	+	2.54547i	−0.174115	+	2.54547i
$362$	−0.296223	−	0.224633i	−0.296223	−	0.224633i
$363$	0.366854	+	0.930278i	0.366854	+	0.930278i
$364$		0			0
$365$		0			0
$366$	−2.48086	−	0.340986i	−2.48086	−	0.340986i
$367$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$367$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$368$	0.895191	−	1.59210i	0.895191	−	1.59210i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.810363	+	0.385391i	−0.810363	+	0.385391i
$373$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$373$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$374$		0			0
$375$		0			0
$376$	0.170891	−	0.0742286i	0.170891	−	0.0742286i
$377$		0			0
$378$		0			0
$379$	−0.979084	−	1.20346i	−0.979084	−	1.20346i	−0.979084	−	0.203456i	$-0.934783\pi$
$379$	−0.979084	−	1.20346i	−0.979084	−	1.20346i		−	1.00000i	$-0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.88853	+	0.599394i	−1.88853	+	0.599394i	−0.903075	+	0.429483i	$0.858696\pi$
$383$	−1.88853	+	0.599394i	−1.88853	+	0.599394i	−0.985460	+	0.169910i	$0.945652\pi$
$384$	0.0995987	+	0.355472i	0.0995987	+	0.355472i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$389$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$390$		0			0
$391$	1.49993	+	0.102598i	1.49993	+	0.102598i
$392$	−0.185339	+	0.0190535i	−0.185339	+	0.0190535i
$393$		0			0
$394$	−0.997669	−	2.29686i	−0.997669	−	2.29686i
$395$		0			0
$396$		0			0
$397$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$397$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$398$	−2.01476	−	1.75678i	−2.01476	−	1.75678i
$399$		0			0
$400$		0			0
$401$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$401$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.129213	+	0.112668i	−0.129213	+	0.112668i
$409$	1.97675	−	0.271698i	1.97675	−	0.271698i	0.979084	−	0.203456i	$-0.0652174\pi$
$409$	1.97675	−	0.271698i	1.97675	−	0.271698i	0.997669	−	0.0682424i	$-0.0217391\pi$
$410$		0			0
$411$	−0.508438	+	0.180699i	−0.508438	+	0.180699i
$412$		0			0
$413$		0			0
$414$	0.453809	−	2.18385i	0.453809	−	2.18385i
$415$		0			0
$416$		0			0
$417$	−0.977935	−	1.73926i	−0.977935	−	1.73926i
$418$		0			0
$419$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$419$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$420$		0			0
$421$	1.03116	−	0.727872i	1.03116	−	0.727872i	0.0682424	−	0.997669i	$-0.478261\pi$
$421$	1.03116	−	0.727872i	1.03116	−	0.727872i	0.962917	+	0.269797i	$0.0869565\pi$
$422$	−1.21835	−	1.21835i	−1.21835	−	1.21835i
$423$	0.753713	−	0.657204i	0.753713	−	0.657204i
$424$			0.0758143i			0.0758143i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.0372107	+	1.08927i	0.0372107	+	1.08927i
$429$		0			0
$430$		0			0
$431$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$431$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$432$	0.613091	+	0.934732i	0.613091	+	0.934732i
$433$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$433$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$434$		0			0
$435$		0			0
$436$	0.185634	−	0.427372i	0.185634	−	0.427372i
$437$	−1.86056	+	2.45352i	−1.86056	+	2.45352i
$438$		0			0
$439$	1.21537	−	1.49389i	1.21537	−	1.49389i	0.398401	−	0.917211i	$-0.369565\pi$
$439$	1.21537	−	1.49389i	1.21537	−	1.49389i	0.816970	−	0.576680i	$-0.195652\pi$
$440$		0			0
$441$	−0.917211	+	0.398401i	−0.917211	+	0.398401i
$442$		0			0
$443$	−0.514311	−	0.163235i	−0.514311	−	0.163235i	0.0341411	−	0.999417i	$-0.489130\pi$
$443$	−0.514311	−	0.163235i	−0.514311	−	0.163235i	−0.548452	+	0.836182i	$0.684783\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$449$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$450$		0			0
$451$		0			0
$452$	0.218768	+	0.0862709i	0.218768	+	0.0862709i
$453$	0.188654	−	0.774147i	0.188654	−	0.774147i
$454$	−0.843756	−	0.686447i	−0.843756	−	0.686447i
$455$		0			0
$456$	−0.0478104	−	0.347847i	−0.0478104	−	0.347847i
$457$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$457$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$458$	−0.982292	−	0.467158i	−0.982292	−	0.467158i
$459$	−0.478085	+	0.786177i	−0.478085	+	0.786177i
$460$		0			0
$461$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$461$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$462$		0			0
$463$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$463$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$464$		0			0
$465$		0			0
$466$	2.51876	+	0.895169i	2.51876	+	0.895169i
$467$	1.98488	+	0.204051i	1.98488	+	0.204051i	0.999417	+	0.0341411i	$0.0108696\pi$
$467$	1.98488	+	0.204051i	1.98488	+	0.204051i	0.985460	+	0.169910i	$0.0543478\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−2.19806	−	0.781189i	−2.19806	−	0.781189i
$475$		0			0
$476$		0			0
$477$	0.123097	+	0.387846i	0.123097	+	0.387846i
$478$		0			0
$479$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$479$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$480$		0			0
$481$		0			0
$482$	0.501638	+	0.238569i	0.501638	+	0.238569i
$483$		0			0
$484$	−0.117582	−	0.855472i	−0.117582	−	0.855472i
$485$		0			0
$486$	1.05893	+	0.861502i	1.05893	+	0.861502i
$487$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$487$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$488$	−0.317953	−	0.125384i	−0.317953	−	0.125384i
$489$		0			0
$490$		0			0
$491$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$491$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−1.13734	+	0.236343i	−1.13734	+	0.236343i
$497$		0			0
$498$	−0.0897559	+	2.62744i	−0.0897559	+	2.62744i
$499$	−1.49867	+	0.650963i	−1.49867	+	0.650963i	−0.979084	−	0.203456i	$-0.934783\pi$
$499$	−1.49867	+	0.650963i	−1.49867	+	0.650963i	−0.519584	+	0.854419i	$0.673913\pi$
$500$		0			0
$501$	−1.23578	+	1.51897i	−1.23578	+	1.51897i
$502$		0			0
$503$	0.883195	−	1.16467i	0.883195	−	1.16467i	−0.102264	−	0.994757i	$-0.532609\pi$
$503$	0.883195	−	1.16467i	0.883195	−	1.16467i	0.985460	−	0.169910i	$-0.0543478\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.796805	+	0.604236i	−0.796805	+	0.604236i
$508$		0			0
$509$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$509$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$510$		0			0
$511$		0			0
$512$	−0.0440179	−	1.28854i	−0.0440179	−	1.28854i
$513$	−0.809371	−	1.70186i	−0.809371	−	1.70186i
$514$	1.88041	−	1.52983i	1.88041	−	1.52983i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.61872	+	1.14262i	−1.61872	+	1.14262i
$520$		0			0
$521$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$521$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$522$		0			0
$523$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$523$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$524$		0			0
$525$		0			0
$526$	0.320333	−	1.54153i	0.320333	−	1.54153i
$527$	−0.577752	−	0.761881i	−0.577752	−	0.761881i
$528$		0			0
$529$	−1.57335	+	0.559168i	−1.57335	+	0.559168i
$530$		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
$541$	−0.985454	+	1.39607i	−0.985454	+	1.39607i	−0.0682424	+	0.997669i	$0.521739\pi$
$541$	−0.985454	+	1.39607i	−0.985454	+	1.39607i	−0.917211	+	0.398401i	$0.869565\pi$
$542$	−0.689114	−	0.600876i	−0.689114	−	0.600876i
$543$	−0.227720	−	0.149362i	−0.227720	−	0.149362i
$544$	1.09448	−	0.567112i	1.09448	−	0.567112i
$545$		0			0
$546$		0			0
$547$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$547$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$548$	0.463504	−	0.0476497i	0.463504	−	0.0476497i
$549$	−1.83015	−	0.125185i	−1.83015	−	0.125185i
$550$		0			0
$551$		0			0
$552$	0.130747	−	0.274923i	0.130747	−	0.274923i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.464861	+	1.65911i	0.464861	+	1.65911i
$557$	−1.69257	+	0.537196i	−1.69257	+	0.537196i	−0.985460	−	0.169910i	$-0.945652\pi$
$557$	−1.69257	+	0.537196i	−1.69257	+	0.537196i	−0.707107	+	0.707107i	$0.750000\pi$
$558$	−1.23652	+	0.695258i	−1.23652	+	0.695258i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.25566	+	1.25566i	−1.25566	+	1.25566i	−0.302515	+	0.953145i	$0.597826\pi$
$563$	−1.25566	+	1.25566i	−1.25566	+	1.25566i	−0.953145	+	0.302515i	$0.902174\pi$
$564$	−0.766702	+	0.397273i	−0.766702	+	0.397273i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$569$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$570$		0			0
$571$	−0.308133	+	0.594669i	−0.308133	+	0.594669i	−0.990686	−	0.136167i	$-0.956522\pi$
$571$	−0.308133	+	0.594669i	−0.308133	+	0.594669i	0.682553	+	0.730836i	$0.260870\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.238081	−	0.669895i	−0.238081	−	0.669895i
$577$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$577$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$578$	−0.166814	−	0.126499i	−0.166814	−	0.126499i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.99069	+	0.136167i	−1.99069	+	0.136167i
$587$	−1.85712	+	0.320200i	−1.85712	+	0.320200i	−0.985460	−	0.169910i	$-0.945652\pi$
$587$	−1.85712	+	0.320200i	−1.85712	+	0.320200i	−0.871660	+	0.490110i	$0.836957\pi$
$588$	0.850959	−	0.146720i	0.850959	−	0.146720i
$589$	1.95377	−	0.133641i	1.95377	−	0.133641i
$590$		0			0
$591$	−0.843954	−	1.62876i	−0.843954	−	1.62876i
$592$		0			0
$593$	−0.536221	+	1.35976i	−0.536221	+	1.35976i	0.366854	+	0.930278i	$0.380435\pi$
$593$	−0.536221	+	1.35976i	−0.536221	+	1.35976i	−0.903075	+	0.429483i	$0.858696\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.56028	−	1.18320i	−1.56028	−	1.18320i
$598$		0			0
$599$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$599$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$600$		0			0
$601$	−1.96292	−	0.269797i	−1.96292	−	0.269797i	−0.962917	−	0.269797i	$-0.913043\pi$
$601$	−1.96292	−	0.269797i	−1.96292	−	0.269797i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	−0.316548	+	0.610910i	−0.316548	+	0.610910i
$605$		0			0
$606$		0			0
$607$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$607$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$608$	−0.258181	+	2.51141i	−0.258181	+	2.51141i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.561829	−	0.561829i	0.561829	−	0.561829i
$613$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$613$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.48953	−	0.837519i	1.48953	−	0.837519i	0.490110	−	0.871660i	$-0.336957\pi$
$617$	1.48953	−	0.837519i	1.48953	−	0.837519i	0.999417	+	0.0341411i	$0.0108696\pi$
$618$		0			0
$619$	0.494921	+	1.76640i	0.494921	+	1.76640i	0.631088	+	0.775711i	$0.282609\pi$
$619$	0.494921	+	1.76640i	0.494921	+	1.76640i	−0.136167	+	0.990686i	$0.543478\pi$
$620$		0			0
$621$	0.222488	−	1.61872i	0.222488	−	1.61872i
$622$		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
$631$	1.45075	−	0.751719i	1.45075	−	0.751719i	0.460065	−	0.887885i	$-0.347826\pi$
$631$	1.45075	−	0.751719i	1.45075	−	0.751719i	0.990686	+	0.136167i	$0.0434783\pi$
$632$	−0.266227	−	0.174619i	−0.266227	−	0.174619i
$633$	−0.951318	−	0.829507i	−0.951318	−	0.829507i
$634$	0.993623	−	1.40764i	0.993623	−	1.40764i
$635$		0			0
$636$	−0.0239787	−	0.350556i	−0.0239787	−	0.350556i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$641$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$642$	0.176202	+	1.71397i	0.176202	+	1.71397i
$643$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$643$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$644$		0			0
$645$		0			0
$646$	−2.23043	+	0.792694i	−2.23043	+	0.792694i
$647$	−0.395342	+	0.0963423i	−0.395342	+	0.0963423i	−0.429483	−	0.903075i	$-0.641304\pi$
$647$	−0.395342	+	0.0963423i	−0.395342	+	0.0963423i	0.0341411	+	0.999417i	$0.489130\pi$
$648$	0.112579	+	0.148458i	0.112579	+	0.148458i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.669369	+	0.0228663i	−0.669369	+	0.0228663i	−0.366854	−	0.930278i	$-0.619565\pi$
$653$	−0.669369	+	0.0228663i	−0.669369	+	0.0228663i	−0.302515	+	0.953145i	$0.597826\pi$
$654$	0.246673	−	0.694072i	0.246673	−	0.694072i
$655$		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
$661$	0.713755	−	0.580683i	0.713755	−	0.580683i	−0.203456	−	0.979084i	$-0.565217\pi$
$661$	0.713755	−	0.580683i	0.713755	−	0.580683i	0.917211	+	0.398401i	$0.130435\pi$
$662$	−1.12910	−	2.37416i	−1.12910	−	2.37416i
$663$		0			0
$664$	−0.0968070	+	0.345509i	−0.0968070	+	0.345509i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.34732	−	1.02171i	1.34732	−	1.02171i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$673$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$674$		0			0
$675$		0			0
$676$	0.792026	−	0.344025i	0.792026	−	0.344025i
$677$	0.0681230	−	1.99417i	0.0681230	−	1.99417i	−0.0341411	−	0.999417i	$-0.510870\pi$
$677$	0.0681230	−	1.99417i	0.0681230	−	1.99417i	0.102264	−	0.994757i	$-0.467391\pi$
$678$	0.354345	+	0.112464i	0.354345	+	0.112464i
$679$		0			0
$680$		0			0
$681$	−0.650963	−	0.459500i	−0.650963	−	0.459500i
$682$		0			0
$683$	0.757993	−	0.869303i	0.757993	−	0.869303i	−0.236764	−	0.971567i	$-0.576087\pi$
$683$	0.757993	−	0.869303i	0.757993	−	0.869303i	0.994757	+	0.102264i	$0.0326087\pi$
$684$	0.331087	+	1.59328i	0.331087	+	1.59328i
$685$		0			0
$686$		0			0
$687$	−0.741248	−	0.292310i	−0.741248	−	0.292310i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.241801	−	1.75923i	−0.241801	−	1.75923i	−0.576680	−	0.816970i	$-0.695652\pi$
$691$	−0.241801	−	1.75923i	−0.241801	−	1.75923i	0.334880	−	0.942261i	$-0.391304\pi$
$692$	1.59165	−	0.627667i	1.59165	−	0.627667i
$693$		0			0
$694$	−1.40536	+	2.31102i	−1.40536	+	2.31102i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.824004	+	2.59622i	0.824004	+	2.59622i
$699$	1.88555	+	0.528307i	1.88555	+	0.528307i
$700$		0			0
$701$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$701$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.914293			0.914293
$707$		0			0
$708$		0			0
$709$	−1.08677	−	0.386237i	−1.08677	−	0.386237i	−0.269797	−	0.962917i	$-0.586957\pi$
$709$	−1.08677	−	0.386237i	−1.08677	−	0.386237i	−0.816970	+	0.576680i	$0.804348\pi$
$710$		0			0
$711$	−1.64547	−	0.461039i	−1.64547	−	0.461039i
$712$		0			0
$713$	1.48003	+	0.832177i	1.48003	+	0.832177i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$719$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$720$		0			0
$721$		0			0
$722$	0.824642	−	3.38393i	0.824642	−	3.38393i
$723$	0.378541	+	0.149277i	0.378541	+	0.149277i
$724$	0.160512	+	0.171866i	0.160512	+	0.171866i
$725$		0			0
$726$	−0.277739	−	1.33655i	−0.277739	−	1.33655i
$727$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$727$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$728$		0			0
$729$	0.816970	+	0.576680i	0.816970	+	0.576680i
$730$		0			0
$731$		0			0
$732$	1.50983	+	0.479199i	1.50983	+	0.479199i
$733$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$733$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$734$		0			0
$735$		0			0
$736$	−1.38142	+	1.69799i	−1.38142	+	1.69799i
$737$		0			0
$738$		0			0
$739$	−0.789381	+	1.81734i	−0.789381	+	1.81734i	−0.269797	+	0.962917i	$0.586957\pi$
$739$	−0.789381	+	1.81734i	−0.789381	+	1.81734i	−0.519584	+	0.854419i	$0.673913\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.03357	−	1.57580i	−1.03357	−	1.57580i	−0.796805	−	0.604236i	$-0.793478\pi$
$743$	−1.03357	−	1.57580i	−1.03357	−	1.57580i	−0.236764	−	0.971567i	$-0.576087\pi$
$744$	−0.186434	+	0.0522364i	−0.186434	+	0.0522364i
$745$		0			0
$746$		0			0
$747$	0.0657501	+	1.92471i	0.0657501	+	1.92471i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		−	1.26218i		−	1.26218i	−0.775711	−	0.631088i	$-0.782609\pi$
$751$		−	1.26218i		−	1.26218i	0.775711	−	0.631088i	$-0.217391\pi$
$752$	−1.08607	+	0.264669i	−1.08607	+	0.264669i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.999417	−	0.0341411i	$-0.0108696\pi$
$757$		0			0		−0.999417	+	0.0341411i	$0.989130\pi$
$758$	1.03798	+	1.84605i	1.03798	+	1.84605i
$759$		0			0
$760$		0			0
$761$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$761$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	2.67959	−	0.368301i	2.67959	−	0.368301i
$767$		0			0
$768$	−0.124240	−	1.20852i	−0.124240	−	1.20852i
$769$	−0.478085	−	0.786177i	−0.478085	−	0.786177i	0.519584	−	0.854419i	$-0.326087\pi$
$769$	−0.478085	−	0.786177i	−0.478085	−	0.786177i	−0.997669	+	0.0682424i	$0.978261\pi$
$770$		0			0
$771$	1.29780	−	1.21206i	1.29780	−	1.21206i
$772$		0			0
$773$	−0.0748554	+	0.114126i	−0.0748554	+	0.114126i	−0.871660	−	0.490110i	$-0.836957\pi$
$773$	−0.0748554	+	0.114126i	−0.0748554	+	0.114126i	0.796805	+	0.604236i	$0.206522\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−1.99400	−	0.485924i	−1.99400	−	0.485924i
$783$		0			0
$784$	1.11525	+	0.0762852i	1.11525	+	0.0762852i
$785$		0			0
$786$		0			0
$787$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$787$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$788$	0.375047	+	1.53901i	0.375047	+	1.53901i
$789$	0.157049	−	1.14262i	0.157049	−	1.14262i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.06711	+	1.31166i	1.06711	+	1.31166i
$797$	0.339029	−	1.96632i	0.339029	−	1.96632i	0.102264	−	0.994757i	$-0.467391\pi$
$797$	0.339029	−	1.96632i	0.339029	−	1.96632i	0.236764	−	0.971567i	$-0.423913\pi$
$798$		0			0
$799$	−0.580683	−	0.713755i	−0.580683	−	0.713755i
$800$		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		−0.990686	−	0.136167i	$-0.956522\pi$
$809$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$810$		0			0
$811$	0.663521	+	1.86697i	0.663521	+	1.86697i	0.460065	+	0.887885i	$0.347826\pi$
$811$	0.663521	+	1.86697i	0.663521	+	1.86697i	0.203456	+	0.979084i	$0.434783\pi$
$812$		0			0
$813$	−0.533668	−	0.404693i	−0.533668	−	0.404693i
$814$		0			0
$815$		0			0
$816$	0.878833	−	0.534430i	0.878833	−	0.534430i
$817$		0			0
$818$	−2.72226	−	0.0929952i	−2.72226	−	0.0929952i
$819$		0			0
$820$		0			0
$821$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$821$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$822$	0.725892	−	0.125156i	0.725892	−	0.125156i
$823$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$823$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.136405	+	0.00465974i	0.136405	+	0.00465974i	0.102264	−	0.994757i	$-0.467391\pi$
$827$	0.136405	+	0.00465974i	0.136405	+	0.00465974i	0.0341411	+	0.999417i	$0.489130\pi$
$828$	−0.517606	+	1.31256i	−0.517606	+	1.31256i
$829$	1.24888	−	0.759461i	1.24888	−	0.759461i	0.269797	−	0.962917i	$-0.413043\pi$
$829$	1.24888	−	0.759461i	1.24888	−	0.759461i	0.979084	+	0.203456i	$0.0652174\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.337554	+	0.855977i	0.337554	+	0.855977i
$834$	0.912161	+	2.56658i	0.912161	+	2.56658i
$835$		0			0
$836$		0			0
$837$	−0.868934	+	0.569934i	−0.868934	+	0.569934i
$838$		0			0
$839$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$839$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$840$		0			0
$841$	0.682553	−	0.730836i	0.682553	−	0.730836i
$842$	−1.55600	+	0.740002i	−1.55600	+	0.740002i
$843$		0			0
$844$	0.628529	+	0.890422i	0.628529	+	0.890422i
$845$		0			0
$846$	−1.16637	+	0.709287i	−1.16637	+	0.709287i
$847$		0			0
$848$	0.0772870	−	0.448255i	0.0772870	−	0.448255i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.953145	−	0.302515i	$-0.0978261\pi$
$853$		0			0		−0.953145	+	0.302515i	$0.902174\pi$
$854$		0			0
$855$		0			0
$856$	−0.0320215	+	0.232974i	−0.0320215	+	0.232974i
$857$	0.298838	+	1.22629i	0.298838	+	1.22629i	0.903075	+	0.429483i	$0.141304\pi$
$857$	0.298838	+	1.22629i	0.298838	+	1.22629i	−0.604236	+	0.796805i	$0.706522\pi$
$858$		0			0
$859$	1.34066	+	0.582332i	1.34066	+	0.582332i	0.942261	−	0.334880i	$-0.108696\pi$
$859$	1.34066	+	0.582332i	1.34066	+	0.582332i	0.398401	+	0.917211i	$0.369565\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.66025	−	0.404592i	−1.66025	−	0.404592i	−0.707107	−	0.707107i	$-0.750000\pi$
$863$	−1.66025	−	0.404592i	−1.66025	−	0.404592i	−0.953145	+	0.302515i	$0.902174\pi$
$864$	−0.533729	−	1.22877i	−0.533729	−	1.22877i
$865$		0			0
$866$		0			0
$867$	−0.128237	−	0.0841109i	−0.128237	−	0.0841109i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.0551386	−	0.0840656i	0.0551386	−	0.0840656i
$873$		0			0
$874$	3.07202	−	2.86906i	3.07202	−	2.86906i
$875$		0			0
$876$		0			0
$877$		0			0		−0.102264	−	0.994757i	$-0.532609\pi$
$877$		0			0		0.102264	+	0.994757i	$0.467391\pi$
$878$	−1.98149	+	1.72777i	−1.98149	+	1.72777i
$879$	−1.44806	+	0.199031i	−1.44806	+	0.199031i
$880$		0			0
$881$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$881$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$882$	1.32629	−	0.323209i	1.32629	−	0.323209i
$883$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$883$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$884$		0			0
$885$		0			0
$886$	0.654019	+	0.338885i	0.654019	+	0.338885i
$887$	0.923623	+	1.64266i	0.923623	+	1.64266i	0.753713	+	0.657204i	$0.228261\pi$
$887$	0.923623	+	1.64266i	0.923623	+	1.64266i	0.169910	+	0.985460i	$0.445652\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.87464	−	0.192719i	1.87464	−	0.192719i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.360528	−	0.101015i	0.360528	−	0.101015i
$902$		0			0
$903$		0			0
$904$	0.0433534	+	0.0263638i	0.0433534	+	0.0263638i
$905$		0			0
$906$	−0.433349	+	0.997669i	−0.433349	+	0.997669i
$907$		0			0		0.604236	−	0.796805i	$-0.293478\pi$
$907$		0			0		−0.604236	+	0.796805i	$0.706522\pi$
$908$	0.452189	+	0.518593i	0.452189	+	0.518593i
$909$		0			0
$910$		0			0
$911$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$911$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$912$	−0.0719225	+	2.10540i	−0.0719225	+	2.10540i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.562117	+	0.396785i	0.562117	+	0.396785i
$917$		0			0
$918$	0.825497	−	0.946720i	0.825497	−	0.946720i
$919$	0.332435	+	1.59976i	0.332435	+	1.59976i	0.730836	+	0.682553i	$0.239130\pi$
$919$	0.332435	+	1.59976i	0.332435	+	1.59976i	−0.398401	+	0.917211i	$0.630435\pi$
$920$		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		0.519584	−	0.854419i	$-0.326087\pi$
$929$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$930$		0			0
$931$	−1.84511	−	0.383417i	−1.84511	−	0.383417i
$932$	−1.47390	−	0.828731i	−1.47390	−	0.828731i
$933$		0			0
$934$	−2.62284	−	0.734885i	−2.62284	−	0.734885i
$935$		0			0
$936$		0			0
$937$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$937$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$938$		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
$947$	−0.0412886	−	0.130090i	−0.0412886	−	0.130090i	0.930278	−	0.366854i	$-0.119565\pi$
$947$	−0.0412886	−	0.130090i	−0.0412886	−	0.130090i	−0.971567	+	0.236764i	$0.923913\pi$
$948$	1.28623	+	0.723211i	1.28623	+	0.723211i
$949$		0			0
$950$		0			0
$951$	0.655806	−	1.07843i	0.655806	−	1.07843i
$952$		0			0
$953$	1.35976	−	0.536221i	1.35976	−	0.536221i	0.429483	−	0.903075i	$-0.358696\pi$
$953$	1.35976	−	0.536221i	1.35976	−	0.536221i	0.930278	+	0.366854i	$0.119565\pi$
$954$	−0.0756376	−	0.550304i	−0.0756376	−	0.550304i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.0162500	−	0.0781994i	−0.0162500	−	0.0781994i
$962$		0			0
$963$	0.214457	+	1.24382i	0.214457	+	1.24382i
$964$	−0.287063	−	0.202631i	−0.287063	−	0.202631i
$965$		0			0
$966$		0			0
$967$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$967$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$968$	0.00636105	−	0.186208i	0.00636105	−	0.186208i
$969$	−1.59045	+	0.690830i	−1.59045	+	0.690830i
$970$		0			0
$971$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$971$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$972$	−0.567505	−	0.650843i	−0.567505	−	0.650843i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.75209	+	1.06547i	1.75209	+	1.06547i
$977$	1.57877	−	1.19722i	1.57877	−	1.19722i	0.707107	−	0.707107i	$-0.250000\pi$
$977$	1.57877	−	1.19722i	1.57877	−	1.19722i	0.871660	−	0.490110i	$-0.163043\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.145581	−	0.519584i	0.145581	−	0.519584i
$982$		0			0
$983$	−0.342213	−	0.719572i	−0.342213	−	0.719572i	0.657204	−	0.753713i	$-0.271739\pi$
$983$	−0.342213	−	0.719572i	−0.342213	−	0.719572i	−0.999417	+	0.0341411i	$0.989130\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.519540	−	1.46184i	0.519540	−	1.46184i	−0.334880	−	0.942261i	$-0.608696\pi$
$991$	0.519540	−	1.46184i	0.519540	−	1.46184i	0.854419	−	0.519584i	$-0.173913\pi$
$992$	1.39134	−	0.0475295i	1.39134	−	0.0475295i
$993$	−0.943871	−	1.67867i	−0.943871	−	1.67867i
$994$		0			0
$995$		0			0
$996$	0.338345	−	1.62820i	0.338345	−	1.62820i
$997$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$997$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$998$	2.16708	−	0.528103i	2.16708	−	0.528103i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.107.1	✓	88
3.2	odd	2	inner	3525.1.bg.a.107.2	yes	88
5.2	odd	4	inner	3525.1.bg.a.3068.2	yes	88
5.3	odd	4	inner	3525.1.bg.a.3068.1	yes	88
5.4	even	2	inner	3525.1.bg.a.107.2	yes	88
15.2	even	4	inner	3525.1.bg.a.3068.1	yes	88
15.8	even	4	inner	3525.1.bg.a.3068.2	yes	88
15.14	odd	2	CM	3525.1.bg.a.107.1	✓	88
47.29	odd	46	inner	3525.1.bg.a.1157.2	yes	88
141.29	even	46	inner	3525.1.bg.a.1157.1	yes	88
235.29	odd	46	inner	3525.1.bg.a.1157.1	yes	88
235.123	even	92	inner	3525.1.bg.a.593.2	yes	88
235.217	even	92	inner	3525.1.bg.a.593.1	yes	88
705.29	even	46	inner	3525.1.bg.a.1157.2	yes	88
705.452	odd	92	inner	3525.1.bg.a.593.2	yes	88
705.593	odd	92	inner	3525.1.bg.a.593.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.107.1	✓	88	1.1	even	1	trivial
3525.1.bg.a.107.1	✓	88	15.14	odd	2	CM
3525.1.bg.a.107.2	yes	88	3.2	odd	2	inner
3525.1.bg.a.107.2	yes	88	5.4	even	2	inner
3525.1.bg.a.593.1	yes	88	235.217	even	92	inner
3525.1.bg.a.593.1	yes	88	705.593	odd	92	inner
3525.1.bg.a.593.2	yes	88	235.123	even	92	inner
3525.1.bg.a.593.2	yes	88	705.452	odd	92	inner
3525.1.bg.a.1157.1	yes	88	141.29	even	46	inner
3525.1.bg.a.1157.1	yes	88	235.29	odd	46	inner
3525.1.bg.a.1157.2	yes	88	47.29	odd	46	inner
3525.1.bg.a.1157.2	yes	88	705.29	even	46	inner
3525.1.bg.a.3068.1	yes	88	5.3	odd	4	inner
3525.1.bg.a.3068.1	yes	88	15.2	even	4	inner
3525.1.bg.a.3068.2	yes	88	5.2	odd	4	inner
3525.1.bg.a.3068.2	yes	88	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.34526 - 0.231946i) q^{2} +(-0.994757 - 0.102264i) q^{3} +(0.813657 + 0.289174i) q^{4} +(1.31448 + 0.368301i) q^{6} +(0.162405 + 0.0913155i) q^{8} +(0.979084 + 0.203456i) q^{9} +O(q^{10})\)	\(q+(-1.34526 - 0.231946i) q^{2} +(-0.994757 - 0.102264i) q^{3} +(0.813657 + 0.289174i) q^{4} +(1.31448 + 0.368301i) q^{6} +(0.162405 + 0.0913155i) q^{8} +(0.979084 + 0.203456i) q^{9} +(-0.779819 - 0.370865i) q^{12} +(-0.867134 - 0.705466i) q^{16} +(0.217854 - 0.893968i) q^{17} +(-1.26993 - 0.500795i) q^{18} +(1.28629 + 1.37728i) q^{19} +(0.277623 + 1.61018i) q^{23} +(-0.152215 - 0.107445i) q^{24} +(-0.953145 - 0.302515i) q^{27} +(0.655806 - 0.806094i) q^{31} +(0.880441 + 1.00973i) q^{32} +(-0.500422 + 1.15209i) q^{34} +(0.737804 + 0.448669i) q^{36} +(-1.41093 - 2.15114i) q^{38} -2.23050i q^{46} +(0.604236 - 0.796805i) q^{47} +(0.790444 + 0.790444i) q^{48} +(-0.816970 + 0.576680i) q^{49} +(-0.308133 + 0.867003i) q^{51} +(0.199432 + 0.354689i) q^{53} +(1.21206 + 0.628038i) q^{54} +(-1.13870 - 1.50160i) q^{57} +(-1.81734 + 0.249787i) q^{61} +(-1.06920 + 0.932292i) q^{62} +(-0.369395 - 0.607445i) q^{64} +(0.435770 - 0.664385i) q^{68} +(-0.111504 - 1.63013i) q^{69} +(0.140429 + 0.122448i) q^{72} +(0.648323 + 1.49259i) q^{76} +(-1.70486 - 0.116615i) q^{79} +(0.917211 + 0.398401i) q^{81} +(0.455969 + 1.87108i) q^{83} +(-0.239732 + 1.39042i) q^{92} +(-0.734803 + 0.734803i) q^{93} +(-0.997669 + 0.931758i) q^{94} +(-0.772565 - 1.09448i) q^{96} +(1.23279 - 0.586291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 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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