LMFDB - Embedded newform 3525.1.bg.a.2393.1

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			2393.1
Root			$-0.490110 - 0.871660i$ of defining polynomial
Character	$\chi$	$=$	3525.2393
Dual form			3525.1.bg.a.2432.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.760368 - 1.35231i) q^{2} +(-0.302515 - 0.953145i) q^{3} +(-0.731009 + 1.20209i) q^{4} +(-1.05893 + 1.13384i) q^{6} +(0.630924 + 0.0215530i) q^{8} +(-0.816970 + 0.576680i) q^{9} +O(q^{10})$	\(q+(-0.760368 - 1.35231i) q^{2} +(-0.302515 - 0.953145i) q^{3} +(-0.731009 + 1.20209i) q^{4} +(-1.05893 + 1.13384i) q^{6} +(0.630924 + 0.0215530i) q^{8} +(-0.816970 + 0.576680i) q^{9} +(1.36691 + 0.333107i) q^{12} +(0.196683 + 0.379580i) q^{16} +(1.49339 - 1.30216i) q^{17} +(1.40105 + 0.666310i) q^{18} +(0.806094 + 0.655806i) q^{19} +(0.470342 + 0.264460i) q^{23} +(-0.170321 - 0.607882i) q^{24} +(0.796805 + 0.604236i) q^{27} +(1.77163 - 0.917985i) q^{31} +(0.709994 - 1.08247i) q^{32} +(-2.89646 - 1.02940i) q^{34} +(-0.0960111 - 1.40363i) q^{36} +(0.273928 - 1.58875i) q^{38} -0.837138i q^{46} +(0.366854 + 0.930278i) q^{47} +(0.302296 - 0.302296i) q^{48} +(-0.269797 + 0.962917i) q^{49} +(-1.69292 - 1.02949i) q^{51} +(0.0393770 + 1.15269i) q^{53} +(0.211252 - 1.53697i) q^{54} +(0.381223 - 0.966715i) q^{57} +(-0.614311 - 0.266833i) q^{61} +(-2.58850 - 1.69779i) q^{62} +(-1.57719 - 0.107882i) q^{64} +(0.473645 + 2.74708i) q^{68} +(0.109784 - 0.528307i) q^{69} +(-0.527876 + 0.346234i) q^{72} +(-1.37760 + 0.489600i) q^{76} +(-0.133630 + 0.0277687i) q^{79} +(0.334880 - 0.942261i) q^{81} +(-1.02890 - 0.897153i) q^{83} +(-0.661730 + 0.372072i) q^{92} +(-1.41092 - 1.41092i) q^{93} +(0.979084 - 1.20346i) q^{94} +(-1.24654 - 0.349263i) q^{96} +(1.50731 - 0.367322i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{6}+O(q^{10}) $ 88 * q - 8 * q^6	$ 88 q - 8 q^{6} + 20 q^{16} - 12 q^{36} - 8 q^{51} + 8 q^{61} - 92 q^{76} + 4 q^{81} - 68 q^{96}+O(q^{100}) $ 88 * q - 8 * q^6 + 20 * q^16 - 12 * q^36 - 8 * q^51 + 8 * q^61 - 92 * q^76 + 4 * q^81 - 68 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{46}\right)$	$-1$

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 $

$2$	−0.760368	−	1.35231i	−0.760368	−	1.35231i	−0.930278	−	0.366854i	$-0.880435\pi$
$2$	−0.760368	−	1.35231i	−0.760368	−	1.35231i	0.169910	−	0.985460i	$-0.445652\pi$
$3$	−0.302515	−	0.953145i	−0.302515	−	0.953145i
$3$	−0.302515	−	0.953145i	−0.302515	−	0.953145i
$4$	−0.731009	+	1.20209i	−0.731009	+	1.20209i
$5$		0			0
$5$		0			0
$6$	−1.05893	+	1.13384i	−1.05893	+	1.13384i
$7$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$7$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$8$	0.630924	+	0.0215530i	0.630924	+	0.0215530i
$9$	−0.816970	+	0.576680i	−0.816970	+	0.576680i
$10$		0			0
$11$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$11$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$12$	1.36691	+	0.333107i	1.36691	+	0.333107i
$13$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$13$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$14$		0			0
$15$		0			0
$16$	0.196683	+	0.379580i	0.196683	+	0.379580i
$17$	1.49339	−	1.30216i	1.49339	−	1.30216i	0.657204	−	0.753713i	$-0.271739\pi$
$17$	1.49339	−	1.30216i	1.49339	−	1.30216i	0.836182	−	0.548452i	$-0.184783\pi$
$18$	1.40105	+	0.666310i	1.40105	+	0.666310i
$19$	0.806094	+	0.655806i	0.806094	+	0.655806i	0.942261	−	0.334880i	$-0.108696\pi$
$19$	0.806094	+	0.655806i	0.806094	+	0.655806i	−0.136167	+	0.990686i	$0.543478\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.470342	+	0.264460i	0.470342	+	0.264460i	0.707107	−	0.707107i	$-0.250000\pi$
$23$	0.470342	+	0.264460i	0.470342	+	0.264460i	−0.236764	+	0.971567i	$0.576087\pi$
$24$	−0.170321	−	0.607882i	−0.170321	−	0.607882i
$25$		0			0
$26$		0			0
$27$	0.796805	+	0.604236i	0.796805	+	0.604236i
$28$		0			0
$29$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$29$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$30$		0			0
$31$	1.77163	−	0.917985i	1.77163	−	0.917985i	0.854419	−	0.519584i	$-0.173913\pi$
$31$	1.77163	−	0.917985i	1.77163	−	0.917985i	0.917211	−	0.398401i	$-0.130435\pi$
$32$	0.709994	−	1.08247i	0.709994	−	1.08247i
$33$		0			0
$34$	−2.89646	−	1.02940i	−2.89646	−	1.02940i
$35$		0			0
$36$	−0.0960111	−	1.40363i	−0.0960111	−	1.40363i
$37$		0			0		−0.930278	−	0.366854i	$-0.880435\pi$
$37$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$38$	0.273928	−	1.58875i	0.273928	−	1.58875i
$39$		0			0
$40$		0			0
$41$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$41$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$42$		0			0
$43$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$43$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$44$		0			0
$45$		0			0
$46$		−	0.837138i		−	0.837138i
$47$	0.366854	+	0.930278i	0.366854	+	0.930278i
$47$	0.366854	+	0.930278i	0.366854	+	0.930278i
$48$	0.302296	−	0.302296i	0.302296	−	0.302296i
$49$	−0.269797	+	0.962917i	−0.269797	+	0.962917i
$50$		0			0
$51$	−1.69292	−	1.02949i	−1.69292	−	1.02949i
$52$		0			0
$53$	0.0393770	+	1.15269i	0.0393770	+	1.15269i	0.836182	+	0.548452i	$0.184783\pi$
$53$	0.0393770	+	1.15269i	0.0393770	+	1.15269i	−0.796805	+	0.604236i	$0.793478\pi$
$54$	0.211252	−	1.53697i	0.211252	−	1.53697i
$55$		0			0
$56$		0			0
$57$	0.381223	−	0.966715i	0.381223	−	0.966715i
$58$		0			0
$59$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$59$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$60$		0			0
$61$	−0.614311	−	0.266833i	−0.614311	−	0.266833i	0.0682424	−	0.997669i	$-0.478261\pi$
$61$	−0.614311	−	0.266833i	−0.614311	−	0.266833i	−0.682553	+	0.730836i	$0.739130\pi$
$62$	−2.58850	−	1.69779i	−2.58850	−	1.69779i
$63$		0			0
$64$	−1.57719	−	0.107882i	−1.57719	−	0.107882i
$65$		0			0
$66$		0			0
$67$		0			0		0.604236	−	0.796805i	$-0.293478\pi$
$67$		0			0		−0.604236	+	0.796805i	$0.706522\pi$
$68$	0.473645	+	2.74708i	0.473645	+	2.74708i
$69$	0.109784	−	0.528307i	0.109784	−	0.528307i
$70$		0			0
$71$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$71$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$72$	−0.527876	+	0.346234i	−0.527876	+	0.346234i
$73$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$73$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$74$		0			0
$75$		0			0
$76$	−1.37760	+	0.489600i	−1.37760	+	0.489600i
$77$		0			0
$78$		0			0
$79$	−0.133630	+	0.0277687i	−0.133630	+	0.0277687i	−0.269797	−	0.962917i	$-0.586957\pi$
$79$	−0.133630	+	0.0277687i	−0.133630	+	0.0277687i	0.136167	+	0.990686i	$0.456522\pi$
$80$		0			0
$81$	0.334880	−	0.942261i	0.334880	−	0.942261i
$82$		0			0
$83$	−1.02890	−	0.897153i	−1.02890	−	0.897153i	−0.0341411	−	0.999417i	$-0.510870\pi$
$83$	−1.02890	−	0.897153i	−1.02890	−	0.897153i	−0.994757	+	0.102264i	$0.967391\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$89$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$90$		0			0
$91$		0			0
$92$	−0.661730	+	0.372072i	−0.661730	+	0.372072i
$93$	−1.41092	−	1.41092i	−1.41092	−	1.41092i
$94$	0.979084	−	1.20346i	0.979084	−	1.20346i
$95$		0			0
$96$	−1.24654	−	0.349263i	−1.24654	−	0.349263i
$97$		0			0		0.953145	−	0.302515i	$-0.0978261\pi$
$97$		0			0		−0.953145	+	0.302515i	$0.902174\pi$
$98$	1.50731	−	0.367322i	1.50731	−	0.367322i
$99$		0			0
$100$		0			0
$101$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$101$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$102$	−0.104948	+	3.07215i	−0.104948	+	3.07215i
$103$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$103$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$104$		0			0
$105$		0			0
$106$	1.52886	−	0.929717i	1.52886	−	0.929717i
$107$	−0.762664	−	1.60365i	−0.762664	−	1.60365i	−0.796805	−	0.604236i	$-0.793478\pi$
$107$	−0.762664	−	1.60365i	−0.762664	−	1.60365i	0.0341411	−	0.999417i	$-0.489130\pi$
$108$	−1.30882	+	0.516132i	−1.30882	+	0.516132i
$109$	−0.297386	−	1.43110i	−0.297386	−	1.43110i	−0.816970	−	0.576680i	$-0.804348\pi$
$109$	−0.297386	−	1.43110i	−0.297386	−	1.43110i	0.519584	−	0.854419i	$-0.326087\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.0814843	−	0.792625i	−0.0814843	−	0.792625i	−0.953145	−	0.302515i	$-0.902174\pi$
$113$	−0.0814843	−	0.792625i	−0.0814843	−	0.792625i	0.871660	−	0.490110i	$-0.163043\pi$
$114$	−1.59717	+	0.219526i	−1.59717	+	0.219526i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.990686	−	0.136167i	0.990686	−	0.136167i
$122$	0.106261	+	1.03363i	0.106261	+	1.03363i
$123$		0			0
$124$	−0.191574	+	2.80072i	−0.191574	+	2.80072i
$125$		0			0
$126$		0			0
$127$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$127$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$128$	0.497366	+	1.04581i	0.497366	+	1.04581i
$129$		0			0
$130$		0			0
$131$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$131$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.970279	−	0.789381i	0.970279	−	0.789381i
$137$	−1.42011	+	0.346072i	−1.42011	+	0.346072i	−0.871660	−	0.490110i	$-0.836957\pi$
$137$	−1.42011	+	0.346072i	−1.42011	+	0.346072i	−0.548452	+	0.836182i	$0.684783\pi$
$138$	−0.797913	+	0.253246i	−0.797913	+	0.253246i
$139$	1.88555	+	0.528307i	1.88555	+	0.528307i	0.997669	+	0.0682424i	$0.0217391\pi$
$139$	1.88555	+	0.528307i	1.88555	+	0.528307i	0.887885	+	0.460065i	$0.152174\pi$
$140$		0			0
$141$	0.775711	−	0.631088i	0.775711	−	0.631088i
$142$		0			0
$143$		0			0
$144$	−0.379580	−	0.196683i	−0.379580	−	0.196683i
$145$		0			0
$146$		0			0
$147$	0.999417	−	0.0341411i	0.999417	−	0.0341411i
$148$		0			0
$149$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$149$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$150$		0			0
$151$	−0.750796	−	1.72850i	−0.750796	−	1.72850i	−0.682553	−	0.730836i	$-0.739130\pi$
$151$	−0.750796	−	1.72850i	−0.750796	−	1.72850i	−0.0682424	−	0.997669i	$-0.521739\pi$
$152$	0.494450	+	0.431138i	0.494450	+	0.431138i
$153$	−0.469118	+	1.92504i	−0.469118	+	1.92504i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$157$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$158$	0.139160	+	0.159595i	0.139160	+	0.159595i
$159$	1.08677	−	0.386237i	1.08677	−	0.386237i
$160$		0			0
$161$		0			0
$162$	−1.52886	+	0.263603i	−1.52886	+	0.263603i
$163$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$163$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$164$		0			0
$165$		0			0
$166$	−0.430891	+	2.07356i	−0.430891	+	2.07356i
$167$	0.277623	+	1.61018i	0.277623	+	1.61018i	0.707107	+	0.707107i	$0.250000\pi$
$167$	0.277623	+	1.61018i	0.277623	+	1.61018i	−0.429483	+	0.903075i	$0.641304\pi$
$168$		0			0
$169$	0.631088	−	0.775711i	0.631088	−	0.775711i
$170$		0			0
$171$	−1.03675	−	0.0709153i	−1.03675	−	0.0709153i
$172$		0			0
$173$	−1.53391	−	1.00609i	−1.53391	−	1.00609i	−0.985460	−	0.169910i	$-0.945652\pi$
$173$	−1.53391	−	1.00609i	−1.53391	−	1.00609i	−0.548452	−	0.836182i	$-0.684783\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$179$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$180$		0			0
$181$	−0.108498	+	0.789381i	−0.108498	+	0.789381i	0.854419	+	0.519584i	$0.173913\pi$
$181$	−0.108498	+	0.789381i	−0.108498	+	0.789381i	−0.962917	+	0.269797i	$0.913043\pi$
$182$		0			0
$183$	−0.0684924	+	0.666248i	−0.0684924	+	0.666248i
$184$	0.291051	+	0.176992i	0.291051	+	0.176992i
$185$		0			0
$186$	−0.835186	+	2.98082i	−0.835186	+	2.98082i
$187$		0			0
$188$	−1.38645	−	0.239049i	−1.38645	−	0.239049i
$189$		0			0
$190$		0			0
$191$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$191$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$192$	0.374294	+	1.53592i	0.374294	+	1.53592i
$193$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$193$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$194$		0			0
$195$		0			0
$196$	−0.960292	−	1.02822i	−0.960292	−	1.02822i
$197$	−0.113799	+	0.660021i	−0.113799	+	0.660021i	0.871660	+	0.490110i	$0.163043\pi$
$197$	−0.113799	+	0.660021i	−0.113799	+	0.660021i	−0.985460	+	0.169910i	$0.945652\pi$
$198$		0			0
$199$	0.111504	+	1.63013i	0.111504	+	1.63013i	0.631088	+	0.775711i	$0.282609\pi$
$199$	0.111504	+	1.63013i	0.111504	+	1.63013i	−0.519584	+	0.854419i	$0.673913\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	2.47508	−	1.28248i	2.47508	−	1.28248i
$205$		0			0
$206$		0			0
$207$	−0.536765	+	0.0551811i	−0.536765	+	0.0551811i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.479097	+	1.70992i	0.479097	+	1.70992i	0.682553	+	0.730836i	$0.260870\pi$
$211$	0.479097	+	1.70992i	0.479097	+	1.70992i	−0.203456	+	0.979084i	$0.565217\pi$
$212$	−1.41442	−	0.795291i	−1.41442	−	0.795291i
$213$		0			0
$214$	−1.58874	+	2.25073i	−1.58874	+	2.25073i
$215$		0			0
$216$	0.489701	+	0.398401i	0.489701	+	0.398401i
$217$		0			0
$218$	−1.70917	+	1.49032i	−1.70917	+	1.49032i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$223$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$224$		0			0
$225$		0			0
$226$	−1.00992	+	0.712879i	−1.00992	+	0.712879i
$227$	1.88342	+	0.0643397i	1.88342	+	0.0643397i	0.953145	−	0.302515i	$-0.0978261\pi$
$227$	1.88342	+	0.0643397i	1.88342	+	0.0643397i	0.930278	+	0.366854i	$0.119565\pi$
$228$	0.883404	+	1.16494i	0.883404	+	1.16494i
$229$	1.28629	−	1.37728i	1.28629	−	1.37728i	0.398401	−	0.917211i	$-0.369565\pi$
$229$	1.28629	−	1.37728i	1.28629	−	1.37728i	0.887885	−	0.460065i	$-0.152174\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.800811	−	1.42424i	−0.800811	−	1.42424i	−0.903075	−	0.429483i	$-0.858696\pi$
$233$	−0.800811	−	1.42424i	−0.800811	−	1.42424i	0.102264	−	0.994757i	$-0.467391\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.0668926	+	0.118968i	0.0668926	+	0.118968i
$238$		0			0
$239$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$239$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$240$		0			0
$241$	0.787230	−	0.842917i	0.787230	−	0.842917i	−0.203456	−	0.979084i	$-0.565217\pi$
$241$	0.787230	−	0.842917i	0.787230	−	0.842917i	0.990686	+	0.136167i	$0.0434783\pi$
$242$	−0.937426	−	1.23618i	−0.937426	−	1.23618i
$243$	−0.999417	−	0.0341411i	−0.999417	−	0.0341411i
$244$	0.769824	−	0.543401i	0.769824	−	0.543401i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	1.13755	−	0.540995i	1.13755	−	0.540995i
$249$	−0.543860	+	1.25209i	−0.543860	+	1.25209i
$250$		0			0
$251$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$251$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.124427	−	0.176273i	0.124427	−	0.176273i
$257$	−0.149362	−	0.227720i	−0.149362	−	0.227720i	0.753713	−	0.657204i	$-0.228261\pi$
$257$	−0.149362	−	0.227720i	−0.149362	−	0.227720i	−0.903075	+	0.429483i	$0.858696\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.91574	−	0.196944i	1.91574	−	0.196944i	0.930278	−	0.366854i	$-0.119565\pi$
$263$	1.91574	−	0.196944i	1.91574	−	0.196944i	0.985460	+	0.169910i	$0.0543478\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$269$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$270$		0			0
$271$	0.116615	+	1.70486i	0.116615	+	1.70486i	0.576680	+	0.816970i	$0.304348\pi$
$271$	0.116615	+	1.70486i	0.116615	+	1.70486i	−0.460065	+	0.887885i	$0.652174\pi$
$272$	0.787999	+	0.310747i	0.787999	+	0.310747i
$273$		0			0
$274$	1.54781	+	1.65730i	1.54781	+	1.65730i
$275$		0			0
$276$	0.554822	+	0.518167i	0.554822	+	0.518167i
$277$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$277$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$278$	−0.719278	−	2.95157i	−0.719278	−	2.95157i
$279$	−0.917985	+	1.77163i	−0.917985	+	1.77163i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	−1.44325	−	0.569146i	−1.44325	−	0.569146i
$283$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$283$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0441971	+	1.29379i	0.0441971	+	1.29379i
$289$	0.398401	−	2.89858i	0.398401	−	2.89858i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.829507	−	0.951318i	0.829507	−	0.951318i	−0.169910	−	0.985460i	$-0.554348\pi$
$293$	0.829507	−	0.951318i	0.829507	−	0.951318i	0.999417	+	0.0341411i	$0.0108696\pi$
$294$	−0.806094	−	1.32557i	−0.806094	−	1.32557i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−1.76660	+	2.32961i	−1.76660	+	2.32961i
$303$		0			0
$304$	−0.0903864	+	0.434963i	−0.0903864	+	0.434963i
$305$		0			0
$306$	2.95995	−	0.829340i	2.95995	−	0.829340i
$307$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$307$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$311$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$312$		0			0
$313$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$313$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$314$		0			0
$315$		0			0
$316$	0.0643043	−	0.180935i	0.0643043	−	0.180935i
$317$	−0.420439	+	1.72528i	−0.420439	+	1.72528i	0.236764	+	0.971567i	$0.423913\pi$
$317$	−0.420439	+	1.72528i	−0.420439	+	1.72528i	−0.657204	+	0.753713i	$0.728261\pi$
$318$	−1.34866	−	1.17597i	−1.34866	−	1.17597i
$319$		0			0
$320$		0			0
$321$	−1.29780	+	1.21206i	−1.29780	+	1.21206i
$322$		0			0
$323$	2.05778	−	0.0702958i	2.05778	−	0.0702958i
$324$	0.887885	+	1.09136i	0.887885	+	1.09136i
$325$		0			0
$326$		0			0
$327$	−1.27408	+	0.716380i	−1.27408	+	0.716380i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.31448	−	0.368301i	−1.31448	−	0.368301i	−0.460065	−	0.887885i	$-0.652174\pi$
$331$	−1.31448	−	0.368301i	−1.31448	−	0.368301i	−0.854419	+	0.519584i	$0.826087\pi$
$332$	1.83060	−	0.581005i	1.83060	−	0.581005i
$333$		0			0
$334$	1.96637	−	1.59976i	1.96637	−	1.59976i
$335$		0			0
$336$		0			0
$337$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$337$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$338$	−1.52886	−	0.263603i	−1.52886	−	0.263603i
$339$	−0.730836	+	0.317447i	−0.730836	+	0.317447i
$340$		0			0
$341$		0			0
$342$	0.692408	+	1.45593i	0.692408	+	1.45593i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.194215	+	2.83933i	−0.194215	+	2.83933i
$347$	−0.787854	+	1.65662i	−0.787854	+	1.65662i	−0.0341411	+	0.999417i	$0.510870\pi$
$347$	−0.787854	+	1.65662i	−0.787854	+	1.65662i	−0.753713	+	0.657204i	$0.771739\pi$
$348$		0			0
$349$	−1.93993	+	0.266637i	−1.93993	+	0.266637i	−0.997669	−	0.0682424i	$-0.978261\pi$
$349$	−1.93993	+	0.266637i	−1.93993	+	0.266637i	−0.942261	+	0.334880i	$0.891304\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.837519	+	1.48953i	−0.837519	+	1.48953i	0.0341411	+	0.999417i	$0.489130\pi$
$353$	−0.837519	+	1.48953i	−0.837519	+	1.48953i	−0.871660	+	0.490110i	$0.836957\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$359$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$360$		0			0
$361$	0.0162500	+	0.0781994i	0.0162500	+	0.0781994i
$362$	1.14999	−	0.453497i	1.14999	−	0.453497i
$363$	−0.429483	−	0.903075i	−0.429483	−	0.903075i
$364$		0			0
$365$		0			0
$366$	0.953056	−	0.413970i	0.953056	−	0.413970i
$367$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$367$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$368$	−0.00787574	+	0.230547i	−0.00787574	+	0.230547i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	2.72745	−	0.664660i	2.72745	−	0.664660i
$373$		0			0		0.953145	−	0.302515i	$-0.0978261\pi$
$373$		0			0		−0.953145	+	0.302515i	$0.902174\pi$
$374$		0			0
$375$		0			0
$376$	0.211407	+	0.594842i	0.211407	+	0.594842i
$377$		0			0
$378$		0			0
$379$	0.816970	+	0.423320i	0.816970	+	0.423320i	0.816970	−	0.576680i	$-0.195652\pi$
$379$	0.816970	+	0.423320i	0.816970	+	0.423320i			1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.46168	−	1.10842i	1.46168	−	1.10842i	0.490110	−	0.871660i	$-0.336957\pi$
$383$	1.46168	−	1.10842i	1.46168	−	1.10842i	0.971567	−	0.236764i	$-0.0760870\pi$
$384$	0.846350	−	0.790436i	0.846350	−	0.790436i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$389$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$390$		0			0
$391$	1.04677	−	0.217522i	1.04677	−	0.217522i
$392$	−0.190975	+	0.601713i	−0.190975	+	0.601713i
$393$		0			0
$394$	0.979084	−	0.347967i	0.979084	−	0.347967i
$395$		0			0
$396$		0			0
$397$		0			0		0.985460	−	0.169910i	$-0.0543478\pi$
$397$		0			0		−0.985460	+	0.169910i	$0.945652\pi$
$398$	2.11966	−	1.39029i	2.11966	−	1.39029i
$399$		0			0
$400$		0			0
$401$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$401$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.04592	−	0.686017i	−1.04592	−	0.686017i
$409$	−1.79605	−	0.780136i	−1.79605	−	0.780136i	−0.979084	−	0.203456i	$-0.934783\pi$
$409$	−1.79605	−	0.780136i	−1.79605	−	0.780136i	−0.816970	−	0.576680i	$-0.804348\pi$
$410$		0			0
$411$	0.759461	+	1.24888i	0.759461	+	1.24888i
$412$		0			0
$413$		0			0
$414$	0.482761	+	0.683916i	0.482761	+	0.683916i
$415$		0			0
$416$		0			0
$417$	−0.0668540	−	1.95703i	−0.0668540	−	1.95703i
$418$		0			0
$419$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$419$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$420$		0			0
$421$	0.479097	−	1.70992i	0.479097	−	1.70992i	−0.203456	−	0.979084i	$-0.565217\pi$
$421$	0.479097	−	1.70992i	0.479097	−	1.70992i	0.682553	−	0.730836i	$-0.260870\pi$
$422$	1.94806	−	1.94806i	1.94806	−	1.94806i
$423$	−0.836182	−	0.548452i	−0.836182	−	0.548452i
$424$			0.728108i			0.728108i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	2.48525	+	0.255492i	2.48525	+	0.255492i
$429$		0			0
$430$		0			0
$431$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$431$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$432$	−0.0726385	+	0.421294i	−0.0726385	+	0.421294i
$433$		0			0		−0.930278	−	0.366854i	$-0.880435\pi$
$433$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$434$		0			0
$435$		0			0
$436$	1.93771	+	0.688661i	1.93771	+	0.688661i
$437$	0.205706	+	0.521633i	0.205706	+	0.521633i
$438$		0			0
$439$	1.21206	−	0.628038i	1.21206	−	0.628038i	0.269797	−	0.962917i	$-0.413043\pi$
$439$	1.21206	−	0.628038i	1.21206	−	0.628038i	0.942261	+	0.334880i	$0.108696\pi$
$440$		0			0
$441$	−0.334880	−	0.942261i	−0.334880	−	0.942261i
$442$		0			0
$443$	1.16467	+	0.883195i	1.16467	+	0.883195i	0.994757	−	0.102264i	$-0.0326087\pi$
$443$	1.16467	+	0.883195i	1.16467	+	0.883195i	0.169910	+	0.985460i	$0.445652\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$449$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$450$		0			0
$451$		0			0
$452$	1.01237	+	0.481464i	1.01237	+	0.481464i
$453$	−1.42039	+	1.23851i	−1.42039	+	1.23851i
$454$	−1.34509	−	2.59590i	−1.34509	−	2.59590i
$455$		0			0
$456$	0.261359	−	0.601708i	0.261359	−	0.601708i
$457$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$457$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$458$	−2.84056	−	0.692226i	−2.84056	−	0.692226i
$459$	1.97675	−	0.135214i	1.97675	−	0.135214i
$460$		0			0
$461$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$461$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$462$		0			0
$463$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$463$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$464$		0			0
$465$		0			0
$466$	−1.31711	+	2.16589i	−1.31711	+	2.16589i
$467$	−0.592374	−	1.86642i	−0.592374	−	1.86642i	−0.490110	−	0.871660i	$-0.663043\pi$
$467$	−0.592374	−	1.86642i	−0.592374	−	1.86642i	−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
$474$	0.110020	−	0.180920i	0.110020	−	0.180920i
$475$		0			0
$476$		0			0
$477$	−0.696902	−	0.919004i	−0.696902	−	0.919004i
$478$		0			0
$479$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$479$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$480$		0			0
$481$		0			0
$482$	−1.73847	−	0.423654i	−1.73847	−	0.423654i
$483$		0			0
$484$	−0.560515	+	1.29044i	−0.560515	+	1.29044i
$485$		0			0
$486$	0.713755	+	1.37749i	0.713755	+	1.37749i
$487$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$487$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$488$	−0.381833	−	0.181592i	−0.381833	−	0.181592i
$489$		0			0
$490$		0			0
$491$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$491$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.696898	+	0.491924i	0.696898	+	0.491924i
$497$		0			0
$498$	2.10675	−	0.216581i	2.10675	−	0.216581i
$499$	−0.180699	−	0.508438i	−0.180699	−	0.508438i	0.816970	−	0.576680i	$-0.195652\pi$
$499$	−0.180699	−	0.508438i	−0.180699	−	0.508438i	−0.997669	+	0.0682424i	$0.978261\pi$
$500$		0			0
$501$	1.45075	−	0.751719i	1.45075	−	0.751719i
$502$		0			0
$503$	0.463035	+	1.17418i	0.463035	+	1.17418i	0.953145	+	0.302515i	$0.0978261\pi$
$503$	0.463035	+	1.17418i	0.463035	+	1.17418i	−0.490110	+	0.871660i	$0.663043\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.930278	−	0.366854i	−0.930278	−	0.366854i
$508$		0			0
$509$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$509$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$510$		0			0
$511$		0			0
$512$	0.818998	+	0.0841956i	0.818998	+	0.0841956i
$513$	0.246038	+	1.00962i	0.246038	+	1.00962i
$514$	−0.194379	+	0.375135i	−0.194379	+	0.375135i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.494921	+	1.76640i	−0.494921	+	1.76640i
$520$		0			0
$521$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$521$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$522$		0			0
$523$		0			0		−0.0341411	−	0.999417i	$-0.510870\pi$
$523$		0			0		0.0341411	+	0.999417i	$0.489130\pi$
$524$		0			0
$525$		0			0
$526$	−1.72300	−	2.44093i	−1.72300	−	2.44093i
$527$	1.45036	−	3.67786i	1.45036	−	3.67786i
$528$		0			0
$529$	−0.368301	−	0.605646i	−0.368301	−	0.605646i
$530$		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
$541$	−0.131424	+	0.0368232i	−0.131424	+	0.0368232i	−0.334880	−	0.942261i	$-0.608696\pi$
$541$	−0.131424	+	0.0368232i	−0.131424	+	0.0368232i	0.203456	+	0.979084i	$0.434783\pi$
$542$	2.21683	−	1.45402i	2.21683	−	1.45402i
$543$	0.785216	−	0.135385i	0.785216	−	0.135385i
$544$	−0.349263	−	2.54108i	−0.349263	−	2.54108i
$545$		0			0
$546$		0			0
$547$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$547$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$548$	0.622104	−	1.96009i	0.622104	−	1.96009i
$549$	0.655751	−	0.136267i	0.655751	−	0.136267i
$550$		0			0
$551$		0			0
$552$	0.0806518	−	0.330956i	0.0806518	−	0.330956i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−2.01343	+	1.88041i	−2.01343	+	1.88041i
$557$	−0.216997	+	0.164554i	−0.216997	+	0.164554i	−0.707107	−	0.707107i	$-0.750000\pi$
$557$	−0.216997	+	0.164554i	−0.216997	+	0.164554i	0.490110	+	0.871660i	$0.336957\pi$
$558$	3.09381	−	0.105688i	3.09381	−	0.105688i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.192569	+	0.192569i	0.192569	+	0.192569i	0.796805	−	0.604236i	$-0.206522\pi$
$563$	0.192569	+	0.192569i	0.192569	+	0.192569i	−0.604236	+	0.796805i	$0.706522\pi$
$564$	0.191574	+	1.39381i	0.191574	+	1.39381i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$569$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$570$		0			0
$571$	−1.69292	−	0.232687i	−1.69292	−	0.232687i	−0.775711	−	0.631088i	$-0.782609\pi$
$571$	−1.69292	−	0.232687i	−1.69292	−	0.232687i	−0.917211	+	0.398401i	$0.869565\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.35073	−	0.821395i	1.35073	−	0.821395i
$577$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$577$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$578$	−4.22273	+	1.66523i	−4.22273	+	1.66523i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.91721	−	0.398401i	−1.91721	−	0.398401i
$587$	−0.509307	+	0.905802i	−0.509307	+	0.905802i	0.490110	+	0.871660i	$0.336957\pi$
$587$	−0.509307	+	0.905802i	−0.509307	+	0.905802i	−0.999417	+	0.0341411i	$0.989130\pi$
$588$	−0.689542	+	1.22635i	−0.689542	+	1.22635i
$589$	2.03012	+	0.421864i	2.03012	+	0.421864i
$590$		0			0
$591$	0.663521	−	0.0911989i	0.663521	−	0.0911989i
$592$		0			0
$593$	0.542084	−	1.13984i	0.542084	−	1.13984i	−0.429483	−	0.903075i	$-0.641304\pi$
$593$	0.542084	−	1.13984i	0.542084	−	1.13984i	0.971567	−	0.236764i	$-0.0760870\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.52002	−	0.599418i	1.52002	−	0.599418i
$598$		0			0
$599$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$599$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$600$		0			0
$601$	−1.68255	+	0.730836i	−1.68255	+	0.730836i	−0.682553	+	0.730836i	$0.739130\pi$
$601$	−1.68255	+	0.730836i	−1.68255	+	0.730836i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	2.62666	+	0.361026i	2.62666	+	0.361026i
$605$		0			0
$606$		0			0
$607$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$607$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$608$	1.28221	−	0.406957i	1.28221	−	0.406957i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.97114	−	1.97114i	−1.97114	−	1.97114i
$613$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$613$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.136405	+	0.00465974i	−0.136405	+	0.00465974i	−0.102264	−	0.994757i	$-0.532609\pi$
$617$	−0.136405	+	0.00465974i	−0.136405	+	0.00465974i	−0.0341411	+	0.999417i	$0.510870\pi$
$618$		0			0
$619$	0.489484	−	0.457146i	0.489484	−	0.457146i	−0.398401	−	0.917211i	$-0.630435\pi$
$619$	0.489484	−	0.457146i	0.489484	−	0.457146i	0.887885	+	0.460065i	$0.152174\pi$
$620$		0			0
$621$	0.214975	+	0.494921i	0.214975	+	0.494921i
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.0734746	−	0.534568i	−0.0734746	−	0.534568i	−0.990686	−	0.136167i	$-0.956522\pi$
$631$	−0.0734746	−	0.534568i	−0.0734746	−	0.534568i	0.917211	−	0.398401i	$-0.130435\pi$
$632$	−0.0849090	+	0.0146398i	−0.0849090	+	0.0146398i
$633$	1.48487	−	0.973925i	1.48487	−	0.973925i
$634$	2.65281	−	0.743282i	2.65281	−	0.743282i
$635$		0			0
$636$	−0.330143	+	1.58874i	−0.330143	+	1.58874i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$641$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$642$	2.62589	+	0.833419i	2.62589	+	0.833419i
$643$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$643$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$644$		0			0
$645$		0			0
$646$	−1.65973	−	2.72931i	−1.65973	−	2.72931i
$647$	0.757993	−	0.869303i	0.757993	−	0.869303i	−0.236764	−	0.971567i	$-0.576087\pi$
$647$	0.757993	−	0.869303i	0.757993	−	0.869303i	0.994757	+	0.102264i	$0.0326087\pi$
$648$	0.231592	−	0.587278i	0.231592	−	0.587278i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.174753	+	1.69988i	−0.174753	+	1.69988i	0.429483	+	0.903075i	$0.358696\pi$
$653$	−0.174753	+	1.69988i	−0.174753	+	1.69988i	−0.604236	+	0.796805i	$0.706522\pi$
$654$	1.93754	+	1.17825i	1.93754	+	1.17825i
$655$		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
$661$	0.911560	−	1.75923i	0.911560	−	1.75923i	0.334880	−	0.942261i	$-0.391304\pi$
$661$	0.911560	−	1.75923i	0.911560	−	1.75923i	0.576680	−	0.816970i	$-0.304348\pi$
$662$	0.501433	+	2.05764i	0.501433	+	2.05764i
$663$		0			0
$664$	−0.629821	−	0.588212i	−0.629821	−	0.588212i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−2.13853	−	0.843328i	−2.13853	−	0.843328i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$673$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$674$		0			0
$675$		0			0
$676$	0.471146	+	1.32568i	0.471146	+	1.32568i
$677$	−1.94790	+	0.200250i	−1.94790	+	0.200250i	−0.994757	−	0.102264i	$-0.967391\pi$
$677$	−1.94790	+	0.200250i	−1.94790	+	0.200250i	−0.953145	+	0.302515i	$0.902174\pi$
$678$	0.984992	+	0.746943i	0.984992	+	0.746943i
$679$		0			0
$680$		0			0
$681$	−0.508438	−	1.81464i	−0.508438	−	1.81464i
$682$		0			0
$683$	1.05623	+	1.61035i	1.05623	+	1.61035i	0.753713	+	0.657204i	$0.228261\pi$
$683$	1.05623	+	1.61035i	1.05623	+	1.61035i	0.302515	+	0.953145i	$0.402174\pi$
$684$	0.843117	−	1.19442i	0.843117	−	1.19442i
$685$		0			0
$686$		0			0
$687$	−1.70186	−	0.809371i	−1.70186	−	0.809371i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.108498	−	0.249787i	0.108498	−	0.249787i	−0.854419	−	0.519584i	$-0.826087\pi$
$691$	0.108498	−	0.249787i	0.108498	−	0.249787i	0.962917	+	0.269797i	$0.0869565\pi$
$692$	2.33072	−	1.10844i	2.33072	−	1.10844i
$693$		0			0
$694$	2.83933	−	0.194215i	2.83933	−	0.194215i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	1.83564	+	2.42065i	1.83564	+	2.42065i
$699$	−1.11525	+	1.19414i	−1.11525	+	1.19414i
$700$		0			0
$701$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$701$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	2.65113			2.65113
$707$		0			0
$708$		0			0
$709$	−1.00063	+	1.64547i	−1.00063	+	1.64547i	−0.269797	+	0.962917i	$0.586957\pi$
$709$	−1.00063	+	1.64547i	−1.00063	+	1.64547i	−0.730836	+	0.682553i	$0.760870\pi$
$710$		0			0
$711$	0.0931581	−	0.0997480i	0.0931581	−	0.0997480i
$712$		0			0
$713$	1.07604	+	0.0367588i	1.07604	+	0.0367588i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$719$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$720$		0			0
$721$		0			0
$722$	0.0933941	−	0.0814354i	0.0933941	−	0.0814354i
$723$	−1.04157	−	0.495349i	−1.04157	−	0.495349i
$724$	−0.869596	−	0.707469i	−0.869596	−	0.707469i
$725$		0			0
$726$	−0.894675	+	1.26747i	−0.894675	+	1.26747i
$727$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$727$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$728$		0			0
$729$	0.269797	+	0.962917i	0.269797	+	0.962917i
$730$		0			0
$731$		0			0
$732$	−0.750823	−	0.569367i	−0.750823	−	0.569367i
$733$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$733$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$734$		0			0
$735$		0			0
$736$	0.620211	−	0.321368i	0.620211	−	0.321368i
$737$		0			0
$738$		0			0
$739$	−1.72850	−	0.614311i	−1.72850	−	0.614311i	−0.730836	−	0.682553i	$-0.760870\pi$
$739$	−1.72850	−	0.614311i	−1.72850	−	0.614311i	−0.997669	+	0.0682424i	$0.978261\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.176565	+	1.02406i	−0.176565	+	1.02406i	0.753713	+	0.657204i	$0.228261\pi$
$743$	−0.176565	+	1.02406i	−0.176565	+	1.02406i	−0.930278	+	0.366854i	$0.880435\pi$
$744$	−0.859772	−	0.920591i	−0.859772	−	0.920591i
$745$		0			0
$746$		0			0
$747$	1.35795	+	0.139601i	1.35795	+	0.139601i
$748$		0			0
$749$		0			0
$750$		0			0
$751$			1.77577i			1.77577i	0.460065	+	0.887885i	$0.347826\pi$
$751$			1.77577i			1.77577i	−0.460065	+	0.887885i	$0.652174\pi$
$752$	−0.280962	+	0.322220i	−0.280962	+	0.322220i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$757$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$758$	−0.0487368	−	1.42668i	−0.0487368	−	1.42668i
$759$		0			0
$760$		0			0
$761$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$761$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−2.61035	−	1.13384i	−2.61035	−	1.13384i
$767$		0			0
$768$	−0.205655	−	0.0652720i	−0.205655	−	0.0652720i
$769$	1.97675	+	0.135214i	1.97675	+	0.135214i	0.997669	−	0.0682424i	$-0.0217391\pi$
$769$	1.97675	+	0.135214i	1.97675	+	0.135214i	0.979084	+	0.203456i	$0.0652174\pi$
$770$		0			0
$771$	−0.171866	+	0.211252i	−0.171866	+	0.211252i
$772$		0			0
$773$	−0.0691386	−	0.400995i	−0.0691386	−	0.400995i	−0.999417	−	0.0341411i	$-0.989130\pi$
$773$	−0.0691386	−	0.400995i	−0.0691386	−	0.400995i	0.930278	−	0.366854i	$-0.119565\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−1.09009	−	1.25017i	−1.09009	−	1.25017i
$783$		0			0
$784$	−0.418569	+	0.0869796i	−0.418569	+	0.0869796i
$785$		0			0
$786$		0			0
$787$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$787$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$788$	−0.710218	−	0.619278i	−0.710218	−	0.619278i
$789$	−0.767255	−	1.76640i	−0.767255	−	1.76640i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−2.04108	−	1.05760i	−2.04108	−	1.05760i
$797$	−1.70686	+	0.959718i	−1.70686	+	0.959718i	−0.753713	+	0.657204i	$0.771739\pi$
$797$	−1.70686	+	0.959718i	−1.70686	+	0.959718i	−0.953145	+	0.302515i	$0.902174\pi$
$798$		0			0
$799$	1.75923	+	0.911560i	1.75923	+	0.911560i
$800$		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		0.917211	−	0.398401i	$-0.130435\pi$
$809$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$810$		0			0
$811$	−1.56737	+	0.953137i	−1.56737	+	0.953137i	−0.576680	+	0.816970i	$0.695652\pi$
$811$	−1.56737	+	0.953137i	−1.56737	+	0.953137i	−0.990686	+	0.136167i	$0.956522\pi$
$812$		0			0
$813$	1.58970	−	0.626895i	1.58970	−	0.626895i
$814$		0			0
$815$		0			0
$816$	0.0578052	−	0.845083i	0.0578052	−	0.845083i
$817$		0			0
$818$	0.310673	+	3.02202i	0.310673	+	3.02202i
$819$		0			0
$820$		0			0
$821$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$821$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$822$	1.11141	−	1.97664i	1.11141	−	1.97664i
$823$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$823$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.0416125	+	0.404779i	0.0416125	+	0.404779i	0.994757	+	0.102264i	$0.0326087\pi$
$827$	0.0416125	+	0.404779i	0.0416125	+	0.404779i	−0.953145	+	0.302515i	$0.902174\pi$
$828$	0.326047	−	0.685579i	0.326047	−	0.685579i
$829$	−0.0861339	+	1.25923i	−0.0861339	+	1.25923i	0.730836	+	0.682553i	$0.239130\pi$
$829$	−0.0861339	+	1.25923i	−0.0861339	+	1.25923i	−0.816970	+	0.576680i	$0.804348\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.850966	+	1.78933i	0.850966	+	1.78933i
$834$	−2.59568	+	1.57847i	−2.59568	+	1.57847i
$835$		0			0
$836$		0			0
$837$	1.96632	+	0.339029i	1.96632	+	0.339029i
$838$		0			0
$839$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$839$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$840$		0			0
$841$	−0.775711	+	0.631088i	−0.775711	+	0.631088i
$842$	−2.67664	+	0.652279i	−2.67664	+	0.652279i
$843$		0			0
$844$	−2.40571	−	0.674048i	−2.40571	−	0.674048i
$845$		0			0
$846$	−0.105873	+	1.54781i	−0.105873	+	1.54781i
$847$		0			0
$848$	−0.429793	+	0.241661i	−0.429793	+	0.241661i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$853$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$854$		0			0
$855$		0			0
$856$	−0.446620	−	1.02822i	−0.446620	−	1.02822i
$857$	−1.33842	−	1.16704i	−1.33842	−	1.16704i	−0.971567	−	0.236764i	$-0.923913\pi$
$857$	−1.33842	−	1.16704i	−1.33842	−	1.16704i	−0.366854	−	0.930278i	$-0.619565\pi$
$858$		0			0
$859$	0.422677	−	1.18930i	0.422677	−	1.18930i	−0.519584	−	0.854419i	$-0.673913\pi$
$859$	0.422677	−	1.18930i	0.422677	−	1.18930i	0.942261	−	0.334880i	$-0.108696\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.0896983	+	0.102870i	0.0896983	+	0.102870i	0.796805	−	0.604236i	$-0.206522\pi$
$863$	0.0896983	+	0.102870i	0.0896983	+	0.102870i	−0.707107	+	0.707107i	$0.750000\pi$
$864$	1.21980	−	0.433516i	1.21980	−	0.433516i
$865$		0			0
$866$		0			0
$867$	−2.88329	+	0.497130i	−2.88329	+	0.497130i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.156784	−	0.909325i	−0.156784	−	0.909325i
$873$		0			0
$874$	0.549000	−	0.674812i	0.549000	−	0.674812i
$875$		0			0
$876$		0			0
$877$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$877$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$878$	−1.77091	−	1.16154i	−1.77091	−	1.16154i
$879$	−1.15768	−	0.502852i	−1.15768	−	0.502852i
$880$		0			0
$881$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$881$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$882$	−1.01960	+	1.16933i	−1.01960	+	1.16933i
$883$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$883$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$884$		0			0
$885$		0			0
$886$	0.308781	−	2.24655i	0.308781	−	2.24655i
$887$	0.0354783	+	1.03856i	0.0354783	+	1.03856i	0.871660	+	0.490110i	$0.163043\pi$
$887$	0.0354783	+	1.03856i	0.0354783	+	1.03856i	−0.836182	+	0.548452i	$0.815217\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.314363	+	0.990477i	−0.314363	+	0.990477i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	1.55980	+	1.67013i	1.55980	+	1.67013i
$902$		0			0
$903$		0			0
$904$	−0.0343270	−	0.501843i	−0.0343270	−	0.501843i
$905$		0			0
$906$	2.75488	+	0.979084i	2.75488	+	0.979084i
$907$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$907$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$908$	−1.45414	+	2.21702i	−1.45414	+	2.21702i
$909$		0			0
$910$		0			0
$911$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$911$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$912$	0.441926	−	0.0454314i	0.441926	−	0.0454314i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.715327	+	2.55304i	0.715327	+	2.55304i
$917$		0			0
$918$	−1.68591	−	2.57038i	−1.68591	−	2.57038i
$919$	−0.311173	+	0.440832i	−0.311173	+	0.440832i	−0.942261	−	0.334880i	$-0.891304\pi$
$919$	−0.311173	+	0.440832i	−0.311173	+	0.440832i	0.631088	+	0.775711i	$0.282609\pi$
$920$		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		0.997669	−	0.0682424i	$-0.0217391\pi$
$929$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$930$		0			0
$931$	−0.848969	+	0.599268i	−0.848969	+	0.599268i
$932$	2.29747	+	0.0784839i	2.29747	+	0.0784839i
$933$		0			0
$934$	−2.07356	+	2.22024i	−2.07356	+	2.22024i
$935$		0			0
$936$		0			0
$937$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$937$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$938$		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
$947$	0.245871	+	0.324230i	0.245871	+	0.324230i	0.903075	−	0.429483i	$-0.141304\pi$
$947$	0.245871	+	0.324230i	0.245871	+	0.324230i	−0.657204	+	0.753713i	$0.728261\pi$
$948$	−0.191910	−	0.00655585i	−0.191910	−	0.00655585i
$949$		0			0
$950$		0			0
$951$	1.77163	−	0.121183i	1.77163	−	0.121183i
$952$		0			0
$953$	1.13984	−	0.542084i	1.13984	−	0.542084i	0.236764	−	0.971567i	$-0.423913\pi$
$953$	1.13984	−	0.542084i	1.13984	−	0.542084i	0.903075	+	0.429483i	$0.141304\pi$
$954$	−0.712879	+	1.64121i	−0.712879	+	1.64121i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.71930	−	2.43569i	1.71930	−	2.43569i
$962$		0			0
$963$	1.54787	+	0.870323i	1.54787	+	0.870323i
$964$	0.437793	+	1.56250i	0.437793	+	1.56250i
$965$		0			0
$966$		0			0
$967$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$967$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$968$	0.627983	−	0.0645586i	0.627983	−	0.0645586i
$969$	−0.689510	−	1.94009i	−0.689510	−	1.94009i
$970$		0			0
$971$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$971$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$972$	0.771624	−	1.17643i	0.771624	−	1.17643i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.0195398	−	0.285662i	−0.0195398	−	0.285662i
$977$	1.70652	+	0.672966i	1.70652	+	0.672966i	0.999417	−	0.0341411i	$-0.0108696\pi$
$977$	1.70652	+	0.672966i	1.70652	+	0.672966i	0.707107	+	0.707107i	$0.250000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.06824	+	0.997669i	1.06824	+	0.997669i
$982$		0			0
$983$	−0.446188	−	1.83094i	−0.446188	−	1.83094i	−0.548452	−	0.836182i	$-0.684783\pi$
$983$	−0.446188	−	1.83094i	−0.446188	−	1.83094i	0.102264	−	0.994757i	$-0.467391\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.786177	+	0.478085i	0.786177	+	0.478085i	0.854419	−	0.519584i	$-0.173913\pi$
$991$	0.786177	+	0.478085i	0.786177	+	0.478085i	−0.0682424	+	0.997669i	$0.521739\pi$
$992$	0.264153	−	2.56951i	0.264153	−	2.56951i
$993$	0.0466062	+	1.36431i	0.0466062	+	1.36431i
$994$		0			0
$995$		0			0
$996$	−1.10756	−	1.56906i	−1.10756	−	1.56906i
$997$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$997$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$998$	−0.550170	+	0.630962i	−0.550170	+	0.630962i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.2393.1	yes	88
3.2	odd	2	inner	3525.1.bg.a.2393.2	yes	88
5.2	odd	4	inner	3525.1.bg.a.2957.2	yes	88
5.3	odd	4	inner	3525.1.bg.a.2957.1	yes	88
5.4	even	2	inner	3525.1.bg.a.2393.2	yes	88
15.2	even	4	inner	3525.1.bg.a.2957.1	yes	88
15.8	even	4	inner	3525.1.bg.a.2957.2	yes	88
15.14	odd	2	CM	3525.1.bg.a.2393.1	yes	88
47.35	odd	46	inner	3525.1.bg.a.1868.1	✓	88
141.35	even	46	inner	3525.1.bg.a.1868.2	yes	88
235.82	even	92	inner	3525.1.bg.a.2432.2	yes	88
235.129	odd	46	inner	3525.1.bg.a.1868.2	yes	88
235.223	even	92	inner	3525.1.bg.a.2432.1	yes	88
705.317	odd	92	inner	3525.1.bg.a.2432.1	yes	88
705.458	odd	92	inner	3525.1.bg.a.2432.2	yes	88
705.599	even	46	inner	3525.1.bg.a.1868.1	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.1868.1	✓	88	47.35	odd	46	inner
3525.1.bg.a.1868.1	✓	88	705.599	even	46	inner
3525.1.bg.a.1868.2	yes	88	141.35	even	46	inner
3525.1.bg.a.1868.2	yes	88	235.129	odd	46	inner
3525.1.bg.a.2393.1	yes	88	1.1	even	1	trivial
3525.1.bg.a.2393.1	yes	88	15.14	odd	2	CM
3525.1.bg.a.2393.2	yes	88	3.2	odd	2	inner
3525.1.bg.a.2393.2	yes	88	5.4	even	2	inner
3525.1.bg.a.2432.1	yes	88	235.223	even	92	inner
3525.1.bg.a.2432.1	yes	88	705.317	odd	92	inner
3525.1.bg.a.2432.2	yes	88	235.82	even	92	inner
3525.1.bg.a.2432.2	yes	88	705.458	odd	92	inner
3525.1.bg.a.2957.1	yes	88	5.3	odd	4	inner
3525.1.bg.a.2957.1	yes	88	15.2	even	4	inner
3525.1.bg.a.2957.2	yes	88	5.2	odd	4	inner
3525.1.bg.a.2957.2	yes	88	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.760368 - 1.35231i) q^{2} +(-0.302515 - 0.953145i) q^{3} +(-0.731009 + 1.20209i) q^{4} +(-1.05893 + 1.13384i) q^{6} +(0.630924 + 0.0215530i) q^{8} +(-0.816970 + 0.576680i) q^{9} +O(q^{10})\)	\(q+(-0.760368 - 1.35231i) q^{2} +(-0.302515 - 0.953145i) q^{3} +(-0.731009 + 1.20209i) q^{4} +(-1.05893 + 1.13384i) q^{6} +(0.630924 + 0.0215530i) q^{8} +(-0.816970 + 0.576680i) q^{9} +(1.36691 + 0.333107i) q^{12} +(0.196683 + 0.379580i) q^{16} +(1.49339 - 1.30216i) q^{17} +(1.40105 + 0.666310i) q^{18} +(0.806094 + 0.655806i) q^{19} +(0.470342 + 0.264460i) q^{23} +(-0.170321 - 0.607882i) q^{24} +(0.796805 + 0.604236i) q^{27} +(1.77163 - 0.917985i) q^{31} +(0.709994 - 1.08247i) q^{32} +(-2.89646 - 1.02940i) q^{34} +(-0.0960111 - 1.40363i) q^{36} +(0.273928 - 1.58875i) q^{38} -0.837138i q^{46} +(0.366854 + 0.930278i) q^{47} +(0.302296 - 0.302296i) q^{48} +(-0.269797 + 0.962917i) q^{49} +(-1.69292 - 1.02949i) q^{51} +(0.0393770 + 1.15269i) q^{53} +(0.211252 - 1.53697i) q^{54} +(0.381223 - 0.966715i) q^{57} +(-0.614311 - 0.266833i) q^{61} +(-2.58850 - 1.69779i) q^{62} +(-1.57719 - 0.107882i) q^{64} +(0.473645 + 2.74708i) q^{68} +(0.109784 - 0.528307i) q^{69} +(-0.527876 + 0.346234i) q^{72} +(-1.37760 + 0.489600i) q^{76} +(-0.133630 + 0.0277687i) q^{79} +(0.334880 - 0.942261i) q^{81} +(-1.02890 - 0.897153i) q^{83} +(-0.661730 + 0.372072i) q^{92} +(-1.41092 - 1.41092i) q^{93} +(0.979084 - 1.20346i) q^{94} +(-1.24654 - 0.349263i) q^{96} +(1.50731 - 0.367322i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 88 * q - 8 * q^6	\( 88 q - 8 q^{6} + 20 q^{16} - 12 q^{36} - 8 q^{51} + 8 q^{61} - 92 q^{76} + 4 q^{81} - 68 q^{96}+O(q^{100}) \) 88 * q - 8 * q^6 + 20 * q^16 - 12 * q^36 - 8 * q^51 + 8 * q^61 - 92 * q^76 + 4 * q^81 - 68 * q^96

Introduction

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