LMFDB - Embedded newform 3525.1.bd.a.1076.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,1,Mod(101,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(46))

chi = DirichletCharacter(H, H._module([23, 0, 32]))

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

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

chi := DirichletCharacter("3525.101");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3525.bd (of order $46$, degree $22$, 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:	$44$
Relative dimension:	$2$ over $\Q(\zeta_{46})$
Coefficient field:	$\Q(\zeta_{92})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{44} - x^{42} + x^{40} - x^{38} + x^{36} - x^{34} + x^{32} - x^{30} + x^{28} - x^{26} + x^{24} + \cdots + 1 $ x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Projective image:	$D_{23}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{23} - \cdots)$

Embedding invariants

Embedding label			1076.1
Root			$0.136167 + 0.990686i$ of defining polynomial
Character	$\chi$	$=$	3525.1076
Dual form			3525.1.bd.a.2801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.128604 + 0.0457060i) q^{2} +(0.979084 - 0.203456i) q^{3} +(-0.761261 + 0.619332i) q^{4} +(-0.116615 + 0.0709153i) q^{6} +(0.140510 - 0.231058i) q^{8} +(0.917211 - 0.398401i) q^{9} +O(q^{10})$	\(q+(-0.128604 + 0.0457060i) q^{2} +(0.979084 - 0.203456i) q^{3} +(-0.761261 + 0.619332i) q^{4} +(-0.116615 + 0.0709153i) q^{6} +(0.140510 - 0.231058i) q^{8} +(0.917211 - 0.398401i) q^{9} +(-0.619332 + 0.761261i) q^{12} +(0.192157 - 0.924708i) q^{16} +(1.02405 - 0.530621i) q^{17} +(-0.0997480 + 0.0931581i) q^{18} +(-0.105873 - 1.54781i) q^{19} +(-0.631088 - 0.224289i) q^{23} +(0.0905606 - 0.254813i) q^{24} +(0.816970 - 0.576680i) q^{27} +(0.187206 - 0.900885i) q^{31} +(0.0543757 + 0.395613i) q^{32} +(-0.107445 + 0.115045i) q^{34} +(-0.451495 + 0.871346i) q^{36} +(0.0843597 + 0.194215i) q^{38} +0.0914120 q^{46} +(-0.269797 + 0.962917i) q^{47} -0.944463i q^{48} +(0.334880 + 0.942261i) q^{49} +(0.894675 - 0.727872i) q^{51} +(0.953137 + 1.56737i) q^{53} +(-0.0787081 + 0.111504i) q^{54} +(-0.418569 - 1.49389i) q^{57} +(1.31448 + 0.368301i) q^{61} +(0.0171003 + 0.124414i) q^{62} +(0.409439 + 0.790182i) q^{64} +(-0.450941 + 1.03817i) q^{68} +(-0.663521 - 0.0911989i) q^{69} +(0.0368232 - 0.267908i) q^{72} +(1.03920 + 1.11271i) q^{76} +(0.911560 - 0.125291i) q^{79} +(0.682553 - 0.730836i) q^{81} +(-1.51725 - 0.786177i) q^{83} +(0.619332 - 0.220111i) q^{92} -0.920130i q^{93} +(-0.00931405 - 0.136167i) q^{94} +(0.133728 + 0.376275i) q^{96} +(-0.0861339 - 0.105873i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 44 * q + 6 * q^4 - 4 * q^6 + 2 * q^9	$ 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9} - 10 q^{16} + 4 q^{19} + 8 q^{24} - 4 q^{31} + 8 q^{34} - 6 q^{36} - 8 q^{46} + 2 q^{49} - 4 q^{51} + 4 q^{54} - 4 q^{61} + 14 q^{64} + 4 q^{69} + 34 q^{76} + 4 q^{79} - 2 q^{81} - 42 q^{94} + 34 q^{96}+O(q^{100}) $ 44 * q + 6 * q^4 - 4 * q^6 + 2 * q^9 - 10 * q^16 + 4 * q^19 + 8 * q^24 - 4 * q^31 + 8 * q^34 - 6 * q^36 - 8 * q^46 + 2 * q^49 - 4 * q^51 + 4 * q^54 - 4 * q^61 + 14 * q^64 + 4 * q^69 + 34 * q^76 + 4 * q^79 - 2 * q^81 - 42 * q^94 + 34 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$1$	$e\left(\frac{12}{23}\right)$	$-1$

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 $

$2$	−0.128604	+	0.0457060i	−0.128604	+	0.0457060i	−0.398401	−	0.917211i	$-0.630435\pi$
$2$	−0.128604	+	0.0457060i	−0.128604	+	0.0457060i	0.269797	+	0.962917i	$0.413043\pi$
$3$	0.979084	−	0.203456i	0.979084	−	0.203456i
$3$	0.979084	−	0.203456i	0.979084	−	0.203456i
$4$	−0.761261	+	0.619332i	−0.761261	+	0.619332i
$5$		0			0
$5$		0			0
$6$	−0.116615	+	0.0709153i	−0.116615	+	0.0709153i
$7$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$7$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$8$	0.140510	−	0.231058i	0.140510	−	0.231058i
$9$	0.917211	−	0.398401i	0.917211	−	0.398401i
$10$		0			0
$11$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$11$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$12$	−0.619332	+	0.761261i	−0.619332	+	0.761261i
$13$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$13$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$14$		0			0
$15$		0			0
$16$	0.192157	−	0.924708i	0.192157	−	0.924708i
$17$	1.02405	−	0.530621i	1.02405	−	0.530621i	0.136167	−	0.990686i	$-0.456522\pi$
$17$	1.02405	−	0.530621i	1.02405	−	0.530621i	0.887885	+	0.460065i	$0.152174\pi$
$18$	−0.0997480	+	0.0931581i	−0.0997480	+	0.0931581i
$19$	−0.105873	−	1.54781i	−0.105873	−	1.54781i	−0.682553	−	0.730836i	$-0.739130\pi$
$19$	−0.105873	−	1.54781i	−0.105873	−	1.54781i	0.576680	−	0.816970i	$-0.304348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.631088	−	0.224289i	−0.631088	−	0.224289i		−	1.00000i	$-0.5\pi$
$23$	−0.631088	−	0.224289i	−0.631088	−	0.224289i	−0.631088	+	0.775711i	$0.717391\pi$
$24$	0.0905606	−	0.254813i	0.0905606	−	0.254813i
$25$		0			0
$26$		0			0
$27$	0.816970	−	0.576680i	0.816970	−	0.576680i
$28$		0			0
$29$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$29$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$30$		0			0
$31$	0.187206	−	0.900885i	0.187206	−	0.900885i	−0.775711	−	0.631088i	$-0.782609\pi$
$31$	0.187206	−	0.900885i	0.187206	−	0.900885i	0.962917	−	0.269797i	$-0.0869565\pi$
$32$	0.0543757	+	0.395613i	0.0543757	+	0.395613i
$33$		0			0
$34$	−0.107445	+	0.115045i	−0.107445	+	0.115045i
$35$		0			0
$36$	−0.451495	+	0.871346i	−0.451495	+	0.871346i
$37$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$37$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$38$	0.0843597	+	0.194215i	0.0843597	+	0.194215i
$39$		0			0
$40$		0			0
$41$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$41$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$42$		0			0
$43$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$43$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$44$		0			0
$45$		0			0
$46$	0.0914120			0.0914120
$47$	−0.269797	+	0.962917i	−0.269797	+	0.962917i
$47$	−0.269797	+	0.962917i	−0.269797	+	0.962917i
$48$		−	0.944463i		−	0.944463i
$49$	0.334880	+	0.942261i	0.334880	+	0.942261i
$50$		0			0
$51$	0.894675	−	0.727872i	0.894675	−	0.727872i
$52$		0			0
$53$	0.953137	+	1.56737i	0.953137	+	1.56737i	0.816970	+	0.576680i	$0.195652\pi$
$53$	0.953137	+	1.56737i	0.953137	+	1.56737i	0.136167	+	0.990686i	$0.456522\pi$
$54$	−0.0787081	+	0.111504i	−0.0787081	+	0.111504i
$55$		0			0
$56$		0			0
$57$	−0.418569	−	1.49389i	−0.418569	−	1.49389i
$58$		0			0
$59$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$59$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$60$		0			0
$61$	1.31448	+	0.368301i	1.31448	+	0.368301i	0.854419	−	0.519584i	$-0.173913\pi$
$61$	1.31448	+	0.368301i	1.31448	+	0.368301i	0.460065	+	0.887885i	$0.347826\pi$
$62$	0.0171003	+	0.124414i	0.0171003	+	0.124414i
$63$		0			0
$64$	0.409439	+	0.790182i	0.409439	+	0.790182i
$65$		0			0
$66$		0			0
$67$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$67$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$68$	−0.450941	+	1.03817i	−0.450941	+	1.03817i
$69$	−0.663521	−	0.0911989i	−0.663521	−	0.0911989i
$70$		0			0
$71$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$71$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$72$	0.0368232	−	0.267908i	0.0368232	−	0.267908i
$73$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$73$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$74$		0			0
$75$		0			0
$76$	1.03920	+	1.11271i	1.03920	+	1.11271i
$77$		0			0
$78$		0			0
$79$	0.911560	−	0.125291i	0.911560	−	0.125291i	0.334880	−	0.942261i	$-0.391304\pi$
$79$	0.911560	−	0.125291i	0.911560	−	0.125291i	0.576680	+	0.816970i	$0.304348\pi$
$80$		0			0
$81$	0.682553	−	0.730836i	0.682553	−	0.730836i
$82$		0			0
$83$	−1.51725	−	0.786177i	−1.51725	−	0.786177i	−0.519584	−	0.854419i	$-0.673913\pi$
$83$	−1.51725	−	0.786177i	−1.51725	−	0.786177i	−0.997669	+	0.0682424i	$0.978261\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$89$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$90$		0			0
$91$		0			0
$92$	0.619332	−	0.220111i	0.619332	−	0.220111i
$93$		−	0.920130i		−	0.920130i
$94$	−0.00931405	−	0.136167i	−0.00931405	−	0.136167i
$95$		0			0
$96$	0.133728	+	0.376275i	0.133728	+	0.376275i
$97$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$97$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$98$	−0.0861339	−	0.105873i	−0.0861339	−	0.105873i
$99$		0			0
$100$		0			0
$101$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$101$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$102$	−0.0817909	+	0.134499i	−0.0817909	+	0.134499i
$103$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$103$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$104$		0			0
$105$		0			0
$106$	−0.194215	−	0.158006i	−0.194215	−	0.158006i
$107$	0.297386	+	0.277739i	0.297386	+	0.277739i	0.816970	−	0.576680i	$-0.195652\pi$
$107$	0.297386	+	0.277739i	0.297386	+	0.277739i	−0.519584	+	0.854419i	$0.673913\pi$
$108$	−0.264771	+	0.944980i	−0.264771	+	0.944980i
$109$	1.69292	−	0.232687i	1.69292	−	0.232687i	0.775711	−	0.631088i	$-0.217391\pi$
$109$	1.69292	−	0.232687i	1.69292	−	0.232687i	0.917211	+	0.398401i	$0.130435\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.92135	+	0.131424i	−1.92135	+	0.131424i	−0.979084	−	0.203456i	$-0.934783\pi$
$113$	−1.92135	+	0.131424i	−1.92135	+	0.131424i	−0.942261	+	0.334880i	$0.891304\pi$
$114$	0.122110	+	0.172990i	0.122110	+	0.172990i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.576680	−	0.816970i	−0.576680	−	0.816970i
$122$	−0.185882	+	0.0127147i	−0.185882	+	0.0127147i
$123$		0			0
$124$	0.415434	+	0.801751i	0.415434	+	0.801751i
$125$		0			0
$126$		0			0
$127$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$127$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$128$	−0.380618	−	0.355472i	−0.380618	−	0.355472i
$129$		0			0
$130$		0			0
$131$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$131$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.0212848	−	0.311173i	0.0212848	−	0.311173i
$137$	−1.07843	−	1.32557i	−1.07843	−	1.32557i	−0.942261	−	0.334880i	$-0.891304\pi$
$137$	−1.07843	−	1.32557i	−1.07843	−	1.32557i	−0.136167	−	0.990686i	$-0.543478\pi$
$138$	0.0895000	−	0.0185983i	0.0895000	−	0.0185983i
$139$	−0.663521	−	1.86697i	−0.663521	−	1.86697i	−0.460065	−	0.887885i	$-0.652174\pi$
$139$	−0.663521	−	1.86697i	−0.663521	−	1.86697i	−0.203456	−	0.979084i	$-0.565217\pi$
$140$		0			0
$141$	−0.0682424	+	0.997669i	−0.0682424	+	0.997669i
$142$		0			0
$143$		0			0
$144$	−0.192157	−	0.924708i	−0.192157	−	0.924708i
$145$		0			0
$146$		0			0
$147$	0.519584	+	0.854419i	0.519584	+	0.854419i
$148$		0			0
$149$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$149$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$150$		0			0
$151$	1.31448	−	0.368301i	1.31448	−	0.368301i	0.460065	−	0.887885i	$-0.347826\pi$
$151$	1.31448	−	0.368301i	1.31448	−	0.368301i	0.854419	+	0.519584i	$0.173913\pi$
$152$	−0.372509	−	0.193019i	−0.372509	−	0.193019i
$153$	0.727872	−	0.894675i	0.727872	−	0.894675i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$157$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$158$	−0.111504	+	0.0577767i	−0.111504	+	0.0577767i
$159$	1.25209	+	1.34066i	1.25209	+	1.34066i
$160$		0			0
$161$		0			0
$162$	−0.0543757	+	0.125185i	−0.0543757	+	0.125185i
$163$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$163$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$164$		0			0
$165$		0			0
$166$	0.231058	+	0.0317582i	0.231058	+	0.0317582i
$167$	−0.730836	+	1.68255i	−0.730836	+	1.68255i			1.00000i	$0.5\pi$
$167$	−0.730836	+	1.68255i	−0.730836	+	1.68255i	−0.730836	+	0.682553i	$0.760870\pi$
$168$		0			0
$169$	0.0682424	+	0.997669i	0.0682424	+	0.997669i
$170$		0			0
$171$	−0.713755	−	1.37749i	−0.713755	−	1.37749i
$172$		0			0
$173$	0.262234	+	1.90790i	0.262234	+	1.90790i	0.398401	+	0.917211i	$0.369565\pi$
$173$	0.262234	+	1.90790i	0.262234	+	1.90790i	−0.136167	+	0.990686i	$0.543478\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$179$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$180$		0			0
$181$	−1.11059	+	1.57335i	−1.11059	+	1.57335i	−0.334880	+	0.942261i	$0.608696\pi$
$181$	−1.11059	+	1.57335i	−1.11059	+	1.57335i	−0.775711	+	0.631088i	$0.782609\pi$
$182$		0			0
$183$	1.36192	+	0.0931581i	1.36192	+	0.0931581i
$184$	−0.140498	+	0.114303i	−0.140498	+	0.114303i
$185$		0			0
$186$	0.0420555	+	0.118333i	0.0420555	+	0.118333i
$187$		0			0
$188$	−0.390980	−	0.900125i	−0.390980	−	0.900125i
$189$		0			0
$190$		0			0
$191$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$191$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$192$	0.561643	+	0.690352i	0.561643	+	0.690352i
$193$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$193$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$194$		0			0
$195$		0			0
$196$	−0.838503	−	0.509905i	−0.838503	−	0.509905i
$197$	−0.543860	−	1.25209i	−0.543860	−	1.25209i	−0.942261	−	0.334880i	$-0.891304\pi$
$197$	−0.543860	−	1.25209i	−0.543860	−	1.25209i	0.398401	−	0.917211i	$-0.369565\pi$
$198$		0			0
$199$	0.843954	−	1.62876i	0.843954	−	1.62876i	0.0682424	−	0.997669i	$-0.478261\pi$
$199$	0.843954	−	1.62876i	0.843954	−	1.62876i	0.775711	−	0.631088i	$-0.217391\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.230287	+	1.10820i	−0.230287	+	1.10820i
$205$		0			0
$206$		0			0
$207$	−0.668198	+	0.0457060i	−0.668198	+	0.0457060i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.136267	+	0.383417i	−0.136267	+	0.383417i	−0.990686	−	0.136167i	$-0.956522\pi$
$211$	−0.136267	+	0.383417i	−0.136267	+	0.383417i	0.854419	+	0.519584i	$0.173913\pi$
$212$	−1.69631	−	0.602867i	−1.69631	−	0.602867i
$213$		0			0
$214$	−0.0509395	−	0.0221261i	−0.0509395	−	0.0221261i
$215$		0			0
$216$	−0.0184546	−	0.269797i	−0.0184546	−	0.269797i
$217$		0			0
$218$	−0.207082	+	0.107301i	−0.207082	+	0.107301i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$223$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$224$		0			0
$225$		0			0
$226$	0.241086	−	0.104719i	0.241086	−	0.104719i
$227$	−0.709287	+	1.16637i	−0.709287	+	1.16637i	0.269797	+	0.962917i	$0.413043\pi$
$227$	−0.709287	+	1.16637i	−0.709287	+	1.16637i	−0.979084	+	0.203456i	$0.934783\pi$
$228$	1.24386	+	0.878009i	1.24386	+	0.878009i
$229$	−1.16637	+	0.709287i	−1.16637	+	0.709287i	−0.962917	−	0.269797i	$-0.913043\pi$
$229$	−1.16637	+	0.709287i	−1.16637	+	0.709287i	−0.203456	+	0.979084i	$0.565217\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.72850	−	0.614311i	1.72850	−	0.614311i	0.730836	−	0.682553i	$-0.239130\pi$
$233$	1.72850	−	0.614311i	1.72850	−	0.614311i	0.997669	+	0.0682424i	$0.0217391\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.867003	−	0.308133i	0.867003	−	0.308133i
$238$		0			0
$239$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$239$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$240$		0			0
$241$	−1.56737	+	0.953137i	−1.56737	+	0.953137i	−0.576680	+	0.816970i	$0.695652\pi$
$241$	−1.56737	+	0.953137i	−1.56737	+	0.953137i	−0.990686	+	0.136167i	$0.956522\pi$
$242$	0.111504	+	0.0787081i	0.111504	+	0.0787081i
$243$	0.519584	−	0.854419i	0.519584	−	0.854419i
$244$	−1.22877	+	0.533729i	−1.22877	+	0.533729i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.181853	−	0.169838i	−0.181853	−	0.169838i
$249$	−1.64547	−	0.461039i	−1.64547	−	0.461039i
$250$		0			0
$251$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$251$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.751085	−	0.326242i	−0.751085	−	0.326242i
$257$	−0.157049	+	1.14262i	−0.157049	+	1.14262i	0.730836	+	0.682553i	$0.239130\pi$
$257$	−0.157049	+	1.14262i	−0.157049	+	1.14262i	−0.887885	+	0.460065i	$0.847826\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.668198	−	0.0457060i	0.668198	−	0.0457060i	0.269797	−	0.962917i	$-0.413043\pi$
$263$	0.668198	−	0.0457060i	0.668198	−	0.0457060i	0.398401	+	0.917211i	$0.369565\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$269$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$270$		0			0
$271$	−0.713755	+	1.37749i	−0.713755	+	1.37749i	0.203456	+	0.979084i	$0.434783\pi$
$271$	−0.713755	+	1.37749i	−0.713755	+	1.37749i	−0.917211	+	0.398401i	$0.869565\pi$
$272$	−0.293891	−	1.04891i	−0.293891	−	1.04891i
$273$		0			0
$274$	0.199277	+	0.121183i	0.199277	+	0.121183i
$275$		0			0
$276$	0.561595	−	0.341514i	0.561595	−	0.341514i
$277$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$277$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$278$	0.170663	+	0.209773i	0.170663	+	0.209773i
$279$	−0.187206	−	0.900885i	−0.187206	−	0.900885i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−0.0368232	−	0.131424i	−0.0368232	−	0.131424i
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.207487	+	0.341197i	0.207487	+	0.341197i
$289$	0.190443	−	0.269797i	0.190443	−	0.269797i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.121183	+	0.0627919i	0.121183	+	0.0627919i	0.519584	−	0.854419i	$-0.326087\pi$
$293$	0.121183	+	0.0627919i	0.121183	+	0.0627919i	−0.398401	+	0.917211i	$0.630435\pi$
$294$	−0.105873	−	0.0861339i	−0.105873	−	0.0861339i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.152215	+	0.107445i	−0.152215	+	0.107445i
$303$		0			0
$304$	−1.45161	−	0.199520i	−1.45161	−	0.199520i
$305$		0			0
$306$	−0.0527155	+	0.148327i	−0.0527155	+	0.148327i
$307$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$307$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$311$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$312$		0			0
$313$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$313$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$314$		0			0
$315$		0			0
$316$	−0.616339	+	0.659937i	−0.616339	+	0.659937i
$317$	0.256797	−	0.315646i	0.256797	−	0.315646i	−0.631088	−	0.775711i	$-0.717391\pi$
$317$	0.256797	−	0.315646i	0.256797	−	0.315646i	0.887885	+	0.460065i	$0.152174\pi$
$318$	−0.222301	−	0.115187i	−0.222301	−	0.115187i
$319$		0			0
$320$		0			0
$321$	0.347674	+	0.211425i	0.347674	+	0.211425i
$322$		0			0
$323$	−0.929717	−	1.52886i	−0.929717	−	1.52886i
$324$	−0.0669712	+	0.979084i	−0.0669712	+	0.979084i
$325$		0			0
$326$		0			0
$327$	1.61017	−	0.572255i	1.61017	−	0.572255i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.572255	−	1.61017i	−0.572255	−	1.61017i	−0.775711	−	0.631088i	$-0.782609\pi$
$331$	−0.572255	−	1.61017i	−0.572255	−	1.61017i	0.203456	−	0.979084i	$-0.434783\pi$
$332$	1.64193	−	0.341197i	1.64193	−	0.341197i
$333$		0			0
$334$	0.0170859	−	0.249787i	0.0170859	−	0.249787i
$335$		0			0
$336$		0			0
$337$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$337$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$338$	−0.0543757	−	0.125185i	−0.0543757	−	0.125185i
$339$	−1.85442	+	0.519584i	−1.85442	+	0.519584i
$340$		0			0
$341$		0			0
$342$	0.154751	+	0.144528i	0.154751	+	0.144528i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.120927	−	0.233378i	−0.120927	−	0.233378i
$347$	−1.40747	+	1.31448i	−1.40747	+	1.31448i	−0.519584	+	0.854419i	$0.673913\pi$
$347$	−1.40747	+	1.31448i	−1.40747	+	1.31448i	−0.887885	+	0.460065i	$0.847826\pi$
$348$		0			0
$349$	−1.14262	−	1.61872i	−1.14262	−	1.61872i	−0.682553	−	0.730836i	$-0.739130\pi$
$349$	−1.14262	−	1.61872i	−1.14262	−	1.61872i	−0.460065	−	0.887885i	$-0.652174\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.46184	−	0.519540i	−1.46184	−	0.519540i	−0.519584	−	0.854419i	$-0.673913\pi$
$353$	−1.46184	−	0.519540i	−1.46184	−	0.519540i	−0.942261	+	0.334880i	$0.891304\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$359$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$360$		0			0
$361$	−1.39381	+	0.191574i	−1.39381	+	0.191574i
$362$	0.0709153	−	0.253100i	0.0709153	−	0.253100i
$363$	−0.730836	−	0.682553i	−0.730836	−	0.682553i
$364$		0			0
$365$		0			0
$366$	−0.179407	+	0.0502675i	−0.179407	+	0.0502675i
$367$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$367$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$368$	−0.328669	+	0.540474i	−0.328669	+	0.540474i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.569866	+	0.700459i	0.569866	+	0.700459i
$373$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$373$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$374$		0			0
$375$		0			0
$376$	0.184581	+	0.197638i	0.184581	+	0.197638i
$377$		0			0
$378$		0			0
$379$	−0.0827887	−	0.398401i	−0.0827887	−	0.398401i	0.917211	−	0.398401i	$-0.130435\pi$
$379$	−0.0827887	−	0.398401i	−0.0827887	−	0.398401i	−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.57335	+	1.11059i	1.57335	+	1.11059i	0.942261	+	0.334880i	$0.108696\pi$
$383$	1.57335	+	1.11059i	1.57335	+	1.11059i	0.631088	+	0.775711i	$0.282609\pi$
$384$	−0.444980	−	0.270598i	−0.444980	−	0.270598i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$389$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$390$		0			0
$391$	−0.765279	+	0.105185i	−0.765279	+	0.105185i
$392$	0.264771	+	0.0550200i	0.264771	+	0.0550200i
$393$		0			0
$394$	0.127171	+	0.136167i	0.127171	+	0.136167i
$395$		0			0
$396$		0			0
$397$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$397$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$398$	−0.0340922	+	0.248039i	−0.0340922	+	0.248039i
$399$		0			0
$400$		0			0
$401$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$401$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.0424704	−	0.308995i	−0.0424704	−	0.308995i
$409$	1.90790	+	0.534568i	1.90790	+	0.534568i	0.990686	+	0.136167i	$0.0434783\pi$
$409$	1.90790	+	0.534568i	1.90790	+	0.534568i	0.917211	+	0.398401i	$0.130435\pi$
$410$		0			0
$411$	−1.32557	−	1.07843i	−1.32557	−	1.07843i
$412$		0			0
$413$		0			0
$414$	0.0838441	−	0.0364186i	0.0838441	−	0.0364186i
$415$		0			0
$416$		0			0
$417$	−1.02949	−	1.69292i	−1.02949	−	1.69292i
$418$		0			0
$419$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$419$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$420$		0			0
$421$	−0.136267	−	0.383417i	−0.136267	−	0.383417i	0.854419	−	0.519584i	$-0.173913\pi$
$421$	−0.136267	−	0.383417i	−0.136267	−	0.383417i	−0.990686	+	0.136167i	$0.956522\pi$
$422$		−	0.0555373i		−	0.0555373i
$423$	0.136167	+	0.990686i	0.136167	+	0.990686i
$424$	0.496078			0.496078
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.398401	−	0.0272514i	−0.398401	−	0.0272514i
$429$		0			0
$430$		0			0
$431$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$431$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$432$	−0.376275	−	0.866272i	−0.376275	−	0.866272i
$433$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$433$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$434$		0			0
$435$		0			0
$436$	−1.14465	+	1.22562i	−1.14465	+	1.22562i
$437$	−0.280340	+	1.00055i	−0.280340	+	1.00055i
$438$		0			0
$439$	−0.347674	+	1.67310i	−0.347674	+	1.67310i	0.334880	+	0.942261i	$0.391304\pi$
$439$	−0.347674	+	1.67310i	−0.347674	+	1.67310i	−0.682553	+	0.730836i	$0.739130\pi$
$440$		0			0
$441$	0.682553	+	0.730836i	0.682553	+	0.730836i
$442$		0			0
$443$	−1.39607	+	0.985454i	−1.39607	+	0.985454i	−0.398401	+	0.917211i	$0.630435\pi$
$443$	−1.39607	+	0.985454i	−1.39607	+	0.985454i	−0.997669	+	0.0682424i	$0.978261\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$449$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$450$		0			0
$451$		0			0
$452$	1.38125	−	1.29000i	1.38125	−	1.29000i
$453$	1.21206	−	0.628038i	1.21206	−	0.628038i
$454$	0.0379072	−	0.182419i	0.0379072	−	0.182419i
$455$		0			0
$456$	−0.403989	−	0.113192i	−0.403989	−	0.113192i
$457$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$457$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$458$	0.117582	−	0.144528i	0.117582	−	0.144528i
$459$	0.530621	−	1.02405i	0.530621	−	1.02405i
$460$		0			0
$461$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$461$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$462$		0			0
$463$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$463$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$464$		0			0
$465$		0			0
$466$	−0.194215	+	0.158006i	−0.194215	+	0.158006i
$467$	1.93993	−	0.403122i	1.93993	−	0.403122i	0.942261	−	0.334880i	$-0.108696\pi$
$467$	1.93993	−	0.403122i	1.93993	−	0.403122i	0.997669	−	0.0682424i	$-0.0217391\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.0974168	+	0.0792544i	−0.0974168	+	0.0792544i
$475$		0			0
$476$		0			0
$477$	1.49867	+	1.05788i	1.49867	+	1.05788i
$478$		0			0
$479$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$479$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$480$		0			0
$481$		0			0
$482$	0.158006	−	0.194215i	0.158006	−	0.194215i
$483$		0			0
$484$	0.944980	+	0.264771i	0.944980	+	0.264771i
$485$		0			0
$486$	−0.0277687	+	0.133630i	−0.0277687	+	0.133630i
$487$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$487$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$488$	0.269797	−	0.251973i	0.269797	−	0.251973i
$489$		0			0
$490$		0			0
$491$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$491$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.797083	−	0.346222i	−0.797083	−	0.346222i
$497$		0			0
$498$	0.232687	−	0.0159162i	0.232687	−	0.0159162i
$499$	0.457146	+	0.489484i	0.457146	+	0.489484i	0.917211	−	0.398401i	$-0.130435\pi$
$499$	0.457146	+	0.489484i	0.457146	+	0.489484i	−0.460065	+	0.887885i	$0.652174\pi$
$500$		0			0
$501$	−0.373224	+	1.79605i	−0.373224	+	1.79605i
$502$		0			0
$503$	−0.0368232	+	0.131424i	−0.0368232	+	0.131424i	−0.979084	−	0.203456i	$-0.934783\pi$
$503$	−0.0368232	+	0.131424i	−0.0368232	+	0.131424i	0.942261	+	0.334880i	$0.108696\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.269797	+	0.962917i	0.269797	+	0.962917i
$508$		0			0
$509$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$509$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$510$		0			0
$511$		0			0
$512$	0.631088	+	0.0431676i	0.631088	+	0.0431676i
$513$	−0.979084	−	1.20346i	−0.979084	−	1.20346i
$514$	−0.0320273	−	0.154124i	−0.0320273	−	0.154124i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.644923	+	1.81464i	0.644923	+	1.81464i
$520$		0			0
$521$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$521$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$522$		0			0
$523$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$523$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$524$		0			0
$525$		0			0
$526$	−0.0838441	+	0.0364186i	−0.0838441	+	0.0364186i
$527$	−0.286320	−	1.02189i	−0.286320	−	1.02189i
$528$		0			0
$529$	−0.427745	−	0.347996i	−0.427745	−	0.347996i
$530$		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
$541$	−0.308133	+	0.867003i	−0.308133	+	0.867003i	0.682553	+	0.730836i	$0.260870\pi$
$541$	−0.308133	+	0.867003i	−0.308133	+	0.867003i	−0.990686	+	0.136167i	$0.956522\pi$
$542$	0.0288327	−	0.209773i	0.0288327	−	0.209773i
$543$	−0.767255	+	1.76640i	−0.767255	+	1.76640i
$544$	0.265604	+	0.376275i	0.265604	+	0.376275i
$545$		0			0
$546$		0			0
$547$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$547$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$548$	1.64193	+	0.341197i	1.64193	+	0.341197i
$549$	1.35239	−	0.185882i	1.35239	−	0.185882i
$550$		0			0
$551$		0			0
$552$	−0.114303	+	0.140498i	−0.114303	+	0.140498i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.66139	+	1.01031i	1.66139	+	1.01031i
$557$	0.942261	+	0.665120i	0.942261	+	0.665120i	0.942261	−	0.334880i	$-0.108696\pi$
$557$	0.942261	+	0.665120i	0.942261	+	0.665120i			1.00000i	$0.5\pi$
$558$	0.0652513	+	0.107301i	0.0652513	+	0.107301i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$			1.15336i			1.15336i	0.816970	+	0.576680i	$0.195652\pi$
$563$			1.15336i			1.15336i	−0.816970	+	0.576680i	$0.804348\pi$
$564$	−0.565938	−	0.801751i	−0.565938	−	0.801751i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$569$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$570$		0			0
$571$	0.894675	−	1.26747i	0.894675	−	1.26747i	−0.0682424	−	0.997669i	$-0.521739\pi$
$571$	0.894675	−	1.26747i	0.894675	−	1.26747i	0.962917	−	0.269797i	$-0.0869565\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.690352	+	0.561643i	0.690352	+	0.561643i
$577$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$577$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$578$	−0.0121605	+	0.0434014i	−0.0121605	+	0.0434014i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.0184546	−	0.00253653i	−0.0184546	−	0.00253653i
$587$	1.46184	+	0.519540i	1.46184	+	0.519540i	0.942261	−	0.334880i	$-0.108696\pi$
$587$	1.46184	+	0.519540i	1.46184	+	0.519540i	0.519584	+	0.854419i	$0.326087\pi$
$588$	−0.924708	−	0.328641i	−0.924708	−	0.328641i
$589$	−1.41421	−	0.194379i	−1.41421	−	0.194379i
$590$		0			0
$591$	−0.787230	−	1.11525i	−0.787230	−	1.11525i
$592$		0			0
$593$	−0.0997480	+	0.0931581i	−0.0997480	+	0.0931581i	−0.730836	−	0.682553i	$-0.760870\pi$
$593$	−0.0997480	+	0.0931581i	−0.0997480	+	0.0931581i	0.631088	+	0.775711i	$0.282609\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.494921	−	1.76640i	0.494921	−	1.76640i
$598$		0			0
$599$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$599$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$600$		0			0
$601$	1.85442	−	0.519584i	1.85442	−	0.519584i	0.854419	−	0.519584i	$-0.173913\pi$
$601$	1.85442	−	0.519584i	1.85442	−	0.519584i	1.00000			$0$
$602$		0			0
$603$		0			0
$604$	−0.772565	+	1.09448i	−0.772565	+	1.09448i
$605$		0			0
$606$		0			0
$607$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$607$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$608$	0.606575	−	0.126048i	0.606575	−	0.126048i
$609$		0			0
$610$		0			0
$611$		0			0
$612$			1.13188i			1.13188i
$613$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$613$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.478085	+	0.786177i	0.478085	+	0.786177i	0.997669	−	0.0682424i	$-0.0217391\pi$
$617$	0.478085	+	0.786177i	0.478085	+	0.786177i	−0.519584	+	0.854419i	$0.673913\pi$
$618$		0			0
$619$	−1.16637	−	0.709287i	−1.16637	−	0.709287i	−0.203456	−	0.979084i	$-0.565217\pi$
$619$	−1.16637	−	0.709287i	−1.16637	−	0.709287i	−0.962917	+	0.269797i	$0.913043\pi$
$620$		0			0
$621$	−0.644923	+	0.180699i	−0.644923	+	0.180699i
$622$		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
$631$	0.386237	+	0.547173i	0.386237	+	0.547173i	0.962917	−	0.269797i	$-0.0869565\pi$
$631$	0.386237	+	0.547173i	0.386237	+	0.547173i	−0.576680	+	0.816970i	$0.695652\pi$
$632$	0.0991334	−	0.228228i	0.0991334	−	0.228228i
$633$	−0.0554078	+	0.403122i	−0.0554078	+	0.403122i
$634$	−0.0185983	+	0.0523306i	−0.0185983	+	0.0523306i
$635$		0			0
$636$	−1.78348	−	0.245134i	−1.78348	−	0.245134i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$641$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$642$	−0.0543757	−	0.0112994i	−0.0543757	−	0.0112994i
$643$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$643$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$644$		0			0
$645$		0			0
$646$	0.189444	+	0.154124i	0.189444	+	0.154124i
$647$	−1.62876	−	0.843954i	−1.62876	−	0.843954i	−0.997669	−	0.0682424i	$-0.978261\pi$
$647$	−1.62876	−	0.843954i	−1.62876	−	0.843954i	−0.631088	−	0.775711i	$-0.717391\pi$
$648$	−0.0729604	−	0.260399i	−0.0729604	−	0.260399i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.54781	−	0.105873i	−1.54781	−	0.105873i	−0.730836	−	0.682553i	$-0.760870\pi$
$653$	−1.54781	−	0.105873i	−1.54781	−	0.105873i	−0.816970	+	0.576680i	$0.804348\pi$
$654$	−0.180920	+	0.147189i	−0.180920	+	0.147189i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$	−0.234658	−	1.12924i	−0.234658	−	1.12924i	−0.917211	−	0.398401i	$-0.869565\pi$
$661$	−0.234658	−	1.12924i	−0.234658	−	1.12924i	0.682553	−	0.730836i	$-0.260870\pi$
$662$	0.147189	+	0.180920i	0.147189	+	0.180920i
$663$		0			0
$664$	−0.394841	+	0.240108i	−0.394841	+	0.240108i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.485702	−	1.73349i	−0.485702	−	1.73349i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$673$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$674$		0			0
$675$		0			0
$676$	−0.669838	−	0.717222i	−0.669838	−	0.717222i
$677$	−1.97675	+	0.135214i	−1.97675	+	0.135214i	−0.997669	−	0.0682424i	$-0.978261\pi$
$677$	−1.97675	+	0.135214i	−1.97675	+	0.135214i	−0.979084	+	0.203456i	$0.934783\pi$
$678$	0.214738	−	0.151579i	0.214738	−	0.151579i
$679$		0			0
$680$		0			0
$681$	−0.457146	+	1.28629i	−0.457146	+	1.28629i
$682$		0			0
$683$	0.0911989	−	0.663521i	0.0911989	−	0.663521i	−0.887885	−	0.460065i	$-0.847826\pi$
$683$	0.0911989	−	0.663521i	0.0911989	−	0.663521i	0.979084	−	0.203456i	$-0.0652174\pi$
$684$	1.39647	+	0.606575i	1.39647	+	0.606575i
$685$		0			0
$686$		0			0
$687$	−0.997669	+	0.931758i	−0.997669	+	0.931758i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−1.11059	−	0.311173i	−1.11059	−	0.311173i	−0.334880	−	0.942261i	$-0.608696\pi$
$691$	−1.11059	−	0.311173i	−1.11059	−	0.311173i	−0.775711	+	0.631088i	$0.782609\pi$
$692$	−1.38125	−	1.29000i	−1.38125	−	1.29000i
$693$		0			0
$694$	0.120927	−	0.233378i	0.120927	−	0.233378i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.220931	+	0.155950i	0.220931	+	0.155950i
$699$	1.56737	−	0.953137i	1.56737	−	0.953137i
$700$		0			0
$701$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$701$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.211746			0.211746
$707$		0			0
$708$		0			0
$709$	−0.519540	+	0.422677i	−0.519540	+	0.422677i	−0.854419	−	0.519584i	$-0.826087\pi$
$709$	−0.519540	+	0.422677i	−0.519540	+	0.422677i	0.334880	+	0.942261i	$0.391304\pi$
$710$		0			0
$711$	0.786177	−	0.478085i	0.786177	−	0.478085i
$712$		0			0
$713$	−0.320202	+	0.526549i	−0.320202	+	0.526549i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$719$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$720$		0			0
$721$		0			0
$722$	0.170494	−	0.0883427i	0.170494	−	0.0883427i
$723$	−1.34066	+	1.25209i	−1.34066	+	1.25209i
$724$	−0.128975	−	1.88555i	−0.128975	−	1.88555i
$725$		0			0
$726$	0.125185	+	0.0543757i	0.125185	+	0.0543757i
$727$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$727$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$728$		0			0
$729$	0.334880	−	0.942261i	0.334880	−	0.942261i
$730$		0			0
$731$		0			0
$732$	−1.09448	+	0.772565i	−1.09448	+	0.772565i
$733$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$733$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$734$		0			0
$735$		0			0
$736$	0.0544156	−	0.261862i	0.0544156	−	0.261862i
$737$		0			0
$738$		0			0
$739$	−1.31448	+	1.40747i	−1.31448	+	1.40747i	−0.460065	+	0.887885i	$0.652174\pi$
$739$	−1.31448	+	1.40747i	−1.31448	+	1.40747i	−0.854419	+	0.519584i	$0.826087\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.618088	−	1.42298i	−0.618088	−	1.42298i	−0.887885	−	0.460065i	$-0.847826\pi$
$743$	−0.618088	−	1.42298i	−0.618088	−	1.42298i	0.269797	−	0.962917i	$-0.413043\pi$
$744$	−0.212604	−	0.129287i	−0.212604	−	0.129287i
$745$		0			0
$746$		0			0
$747$	−1.70486	−	0.116615i	−1.70486	−	0.116615i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.406912			0.406912			0.203456	−	0.979084i	$-0.434783\pi$
$751$	0.406912			0.406912			0.203456	+	0.979084i	$0.434783\pi$
$752$	0.838574	+	0.434514i	0.838574	+	0.434514i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$757$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$758$	0.0288563	+	0.0474522i	0.0288563	+	0.0474522i
$759$		0			0
$760$		0			0
$761$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$761$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−0.253100	−	0.0709153i	−0.253100	−	0.0709153i
$767$		0			0
$768$	−0.801751	−	0.166606i	−0.801751	−	0.166606i
$769$	0.530621	+	1.02405i	0.530621	+	1.02405i	0.990686	+	0.136167i	$0.0434783\pi$
$769$	0.530621	+	1.02405i	0.530621	+	1.02405i	−0.460065	+	0.887885i	$0.652174\pi$
$770$		0			0
$771$	0.0787081	+	1.15067i	0.0787081	+	1.15067i
$772$		0			0
$773$	0.789381	−	1.81734i	0.789381	−	1.81734i	0.269797	−	0.962917i	$-0.413043\pi$
$773$	0.789381	−	1.81734i	0.789381	−	1.81734i	0.519584	−	0.854419i	$-0.326087\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.0936106	−	0.0485051i	0.0936106	−	0.0485051i
$783$		0			0
$784$	0.935666	−	0.128604i	0.935666	−	0.128604i
$785$		0			0
$786$		0			0
$787$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$787$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$788$	1.18948	+	0.616339i	1.18948	+	0.616339i
$789$	0.644923	−	0.180699i	0.644923	−	0.180699i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.366272	+	1.76260i	0.366272	+	1.76260i
$797$	−1.86697	+	0.663521i	−1.86697	+	0.663521i	−0.887885	+	0.460065i	$0.847826\pi$
$797$	−1.86697	+	0.663521i	−1.86697	+	0.663521i	−0.979084	+	0.203456i	$0.934783\pi$
$798$		0			0
$799$	0.234658	+	1.12924i	0.234658	+	1.12924i
$800$		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		0.962917	−	0.269797i	$-0.0869565\pi$
$809$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$810$		0			0
$811$	−1.49389	−	1.21537i	−1.49389	−	1.21537i	−0.917211	−	0.398401i	$-0.869565\pi$
$811$	−1.49389	−	1.21537i	−1.49389	−	1.21537i	−0.576680	−	0.816970i	$-0.695652\pi$
$812$		0			0
$813$	−0.418569	+	1.49389i	−0.418569	+	1.49389i
$814$		0			0
$815$		0			0
$816$	−0.501152	−	0.967179i	−0.501152	−	0.967179i
$817$		0			0
$818$	−0.269797	+	0.0184546i	−0.269797	+	0.0184546i
$819$		0			0
$820$		0			0
$821$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$821$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$822$	0.219764	+	0.0781042i	0.219764	+	0.0781042i
$823$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$823$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.97675	+	0.135214i	−1.97675	+	0.135214i	−0.997669	−	0.0682424i	$-0.978261\pi$
$827$	−1.97675	+	0.135214i	−1.97675	+	0.135214i	−0.979084	+	0.203456i	$0.934783\pi$
$828$	0.480366	−	0.448630i	0.480366	−	0.448630i
$829$	0.0627919	+	0.121183i	0.0627919	+	0.121183i	0.917211	−	0.398401i	$-0.130435\pi$
$829$	0.0627919	+	0.121183i	0.0627919	+	0.121183i	−0.854419	+	0.519584i	$0.826087\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.842917	+	0.787230i	0.842917	+	0.787230i
$834$	0.209773	+	0.170663i	0.209773	+	0.170663i
$835$		0			0
$836$		0			0
$837$	−0.366581	−	0.843954i	−0.366581	−	0.843954i
$838$		0			0
$839$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$839$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$840$		0			0
$841$	−0.0682424	+	0.997669i	−0.0682424	+	0.997669i
$842$	0.0350489	+	0.0430809i	0.0350489	+	0.0430809i
$843$		0			0
$844$	−0.133728	−	0.376275i	−0.133728	−	0.376275i
$845$		0			0
$846$	−0.0627919	−	0.121183i	−0.0627919	−	0.121183i
$847$		0			0
$848$	1.63251	−	0.580194i	1.63251	−	0.580194i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$853$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$854$		0			0
$855$		0			0
$856$	0.105959	−	0.0296885i	0.105959	−	0.0296885i
$857$	0.361291	+	0.187206i	0.361291	+	0.187206i	0.631088	−	0.775711i	$-0.282609\pi$
$857$	0.361291	+	0.187206i	0.361291	+	0.187206i	−0.269797	+	0.962917i	$0.586957\pi$
$858$		0			0
$859$	0.0931581	−	0.0997480i	0.0931581	−	0.0997480i	−0.682553	−	0.730836i	$-0.739130\pi$
$859$	0.0931581	−	0.0997480i	0.0931581	−	0.0997480i	0.775711	+	0.631088i	$0.217391\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.816970	−	0.423320i	0.816970	−	0.423320i		−	1.00000i	$-0.5\pi$
$863$	0.816970	−	0.423320i	0.816970	−	0.423320i	0.816970	+	0.576680i	$0.195652\pi$
$864$	0.272565	+	0.291846i	0.272565	+	0.291846i
$865$		0			0
$866$		0			0
$867$	0.131568	−	0.302901i	0.131568	−	0.302901i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.184108	−	0.423858i	0.184108	−	0.423858i
$873$		0			0
$874$	−0.00967804	−	0.141488i	−0.00967804	−	0.141488i
$875$		0			0
$876$		0			0
$877$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$877$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$878$	−0.0317582	−	0.231058i	−0.0317582	−	0.231058i
$879$	0.131424	+	0.0368232i	0.131424	+	0.0368232i
$880$		0			0
$881$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$881$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$882$	−0.121183	−	0.0627919i	−0.121183	−	0.0627919i
$883$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$883$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$884$		0			0
$885$		0			0
$886$	0.134499	−	0.190542i	0.134499	−	0.190542i
$887$	−0.806094	−	1.32557i	−0.806094	−	1.32557i	−0.942261	−	0.334880i	$-0.891304\pi$
$887$	−0.806094	−	1.32557i	−0.806094	−	1.32557i	0.136167	−	0.990686i	$-0.456522\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.51897	+	0.315646i	1.51897	+	0.315646i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	1.80774	+	1.09931i	1.80774	+	1.09931i
$902$		0			0
$903$		0			0
$904$	−0.239601	+	0.462409i	−0.239601	+	0.462409i
$905$		0			0
$906$	−0.127171	+	0.136167i	−0.127171	+	0.136167i
$907$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$907$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$908$	−0.182419	−	1.32720i	−0.182419	−	1.32720i
$909$		0			0
$910$		0			0
$911$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$911$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$912$	−1.46184	+	0.0999929i	−1.46184	+	0.0999929i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.448630	−	1.26233i	0.448630	−	1.26233i
$917$		0			0
$918$	−0.0214348	+	0.155950i	−0.0214348	+	0.155950i
$919$	−0.614311	−	0.266833i	−0.614311	−	0.266833i	0.0682424	−	0.997669i	$-0.478261\pi$
$919$	−0.614311	−	0.266833i	−0.614311	−	0.266833i	−0.682553	+	0.730836i	$0.739130\pi$
$920$		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		0.460065	−	0.887885i	$-0.347826\pi$
$929$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$930$		0			0
$931$	1.42298	−	0.618088i	1.42298	−	0.618088i
$932$	−0.935381	+	1.53817i	−0.935381	+	1.53817i
$933$		0			0
$934$	−0.231058	+	0.140510i	−0.231058	+	0.140510i
$935$		0			0
$936$		0			0
$937$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$937$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.61872	+	1.14262i	1.61872	+	1.14262i	0.887885	+	0.460065i	$0.152174\pi$
$947$	1.61872	+	1.14262i	1.61872	+	1.14262i	0.730836	+	0.682553i	$0.239130\pi$
$948$	−0.469179	+	0.771532i	−0.469179	+	0.771532i
$949$		0			0
$950$		0			0
$951$	0.187206	−	0.361291i	0.187206	−	0.361291i
$952$		0			0
$953$	0.0997480	+	0.0931581i	0.0997480	+	0.0931581i	0.730836	−	0.682553i	$-0.239130\pi$
$953$	0.0997480	+	0.0931581i	0.0997480	+	0.0931581i	−0.631088	+	0.775711i	$0.717391\pi$
$954$	−0.241086	−	0.0675492i	−0.241086	−	0.0675492i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.140664	+	0.0610990i	0.140664	+	0.0610990i
$962$		0			0
$963$	0.383417	+	0.136267i	0.383417	+	0.136267i
$964$	0.602867	−	1.69631i	0.602867	−	1.69631i
$965$		0			0
$966$		0			0
$967$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$967$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$968$	−0.269797	+	0.0184546i	−0.269797	+	0.0184546i
$969$	−1.22133	−	1.30772i	−1.22133	−	1.30772i
$970$		0			0
$971$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$971$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$972$	0.133630	+	0.972231i	0.133630	+	0.972231i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.593158	−	1.14474i	0.593158	−	1.14474i
$977$	0.519584	+	1.85442i	0.519584	+	1.85442i	0.519584	+	0.854419i	$0.326087\pi$
$977$	0.519584	+	1.85442i	0.519584	+	1.85442i			1.00000i	$0.5\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.46007	−	0.887885i	1.46007	−	0.887885i
$982$		0			0
$983$	0.861502	+	1.05893i	0.861502	+	1.05893i	0.997669	+	0.0682424i	$0.0217391\pi$
$983$	0.861502	+	1.05893i	0.861502	+	1.05893i	−0.136167	+	0.990686i	$0.543478\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.315646	+	0.256797i	−0.315646	+	0.256797i	−0.775711	−	0.631088i	$-0.782609\pi$
$991$	−0.315646	+	0.256797i	−0.315646	+	0.256797i	0.460065	+	0.887885i	$0.347826\pi$
$992$	0.366581	+	0.0250748i	0.366581	+	0.0250748i
$993$	−0.887885	−	1.46007i	−0.887885	−	1.46007i
$994$		0			0
$995$		0			0
$996$	1.53817	−	0.668121i	1.53817	−	0.668121i
$997$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$997$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$998$	−0.0811633	−	0.0420555i	−0.0811633	−	0.0420555i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bd.a.1076.1		44
3.2	odd	2	inner	3525.1.bd.a.1076.2		44
5.2	odd	4		705.1.p.b.89.1	yes	22
5.3	odd	4		705.1.p.a.89.1	✓	22
5.4	even	2	inner	3525.1.bd.a.1076.2		44
15.2	even	4		705.1.p.a.89.1	✓	22
15.8	even	4		705.1.p.b.89.1	yes	22
15.14	odd	2	CM	3525.1.bd.a.1076.1		44
47.28	even	23	inner	3525.1.bd.a.2801.2		44
141.122	odd	46	inner	3525.1.bd.a.2801.1		44
235.28	odd	92		705.1.p.a.404.1	yes	22
235.122	odd	92		705.1.p.b.404.1	yes	22
235.169	even	46	inner	3525.1.bd.a.2801.1		44
705.122	even	92		705.1.p.a.404.1	yes	22
705.263	even	92		705.1.p.b.404.1	yes	22
705.404	odd	46	inner	3525.1.bd.a.2801.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.1.p.a.89.1	✓	22	5.3	odd	4
705.1.p.a.89.1	✓	22	15.2	even	4
705.1.p.a.404.1	yes	22	235.28	odd	92
705.1.p.a.404.1	yes	22	705.122	even	92
705.1.p.b.89.1	yes	22	5.2	odd	4
705.1.p.b.89.1	yes	22	15.8	even	4
705.1.p.b.404.1	yes	22	235.122	odd	92
705.1.p.b.404.1	yes	22	705.263	even	92
3525.1.bd.a.1076.1		44	1.1	even	1	trivial
3525.1.bd.a.1076.1		44	15.14	odd	2	CM
3525.1.bd.a.1076.2		44	3.2	odd	2	inner
3525.1.bd.a.1076.2		44	5.4	even	2	inner
3525.1.bd.a.2801.1		44	141.122	odd	46	inner
3525.1.bd.a.2801.1		44	235.169	even	46	inner
3525.1.bd.a.2801.2		44	47.28	even	23	inner
3525.1.bd.a.2801.2		44	705.404	odd	46	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.bd (of order \(46\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.128604 + 0.0457060i) q^{2} +(0.979084 - 0.203456i) q^{3} +(-0.761261 + 0.619332i) q^{4} +(-0.116615 + 0.0709153i) q^{6} +(0.140510 - 0.231058i) q^{8} +(0.917211 - 0.398401i) q^{9} +O(q^{10})\)	\(q+(-0.128604 + 0.0457060i) q^{2} +(0.979084 - 0.203456i) q^{3} +(-0.761261 + 0.619332i) q^{4} +(-0.116615 + 0.0709153i) q^{6} +(0.140510 - 0.231058i) q^{8} +(0.917211 - 0.398401i) q^{9} +(-0.619332 + 0.761261i) q^{12} +(0.192157 - 0.924708i) q^{16} +(1.02405 - 0.530621i) q^{17} +(-0.0997480 + 0.0931581i) q^{18} +(-0.105873 - 1.54781i) q^{19} +(-0.631088 - 0.224289i) q^{23} +(0.0905606 - 0.254813i) q^{24} +(0.816970 - 0.576680i) q^{27} +(0.187206 - 0.900885i) q^{31} +(0.0543757 + 0.395613i) q^{32} +(-0.107445 + 0.115045i) q^{34} +(-0.451495 + 0.871346i) q^{36} +(0.0843597 + 0.194215i) q^{38} +0.0914120 q^{46} +(-0.269797 + 0.962917i) q^{47} -0.944463i q^{48} +(0.334880 + 0.942261i) q^{49} +(0.894675 - 0.727872i) q^{51} +(0.953137 + 1.56737i) q^{53} +(-0.0787081 + 0.111504i) q^{54} +(-0.418569 - 1.49389i) q^{57} +(1.31448 + 0.368301i) q^{61} +(0.0171003 + 0.124414i) q^{62} +(0.409439 + 0.790182i) q^{64} +(-0.450941 + 1.03817i) q^{68} +(-0.663521 - 0.0911989i) q^{69} +(0.0368232 - 0.267908i) q^{72} +(1.03920 + 1.11271i) q^{76} +(0.911560 - 0.125291i) q^{79} +(0.682553 - 0.730836i) q^{81} +(-1.51725 - 0.786177i) q^{83} +(0.619332 - 0.220111i) q^{92} -0.920130i q^{93} +(-0.00931405 - 0.136167i) q^{94} +(0.133728 + 0.376275i) q^{96} +(-0.0861339 - 0.105873i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 44 * q + 6 * q^4 - 4 * q^6 + 2 * q^9	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9} - 10 q^{16} + 4 q^{19} + 8 q^{24} - 4 q^{31} + 8 q^{34} - 6 q^{36} - 8 q^{46} + 2 q^{49} - 4 q^{51} + 4 q^{54} - 4 q^{61} + 14 q^{64} + 4 q^{69} + 34 q^{76} + 4 q^{79} - 2 q^{81} - 42 q^{94} + 34 q^{96}+O(q^{100}) \) 44 * q + 6 * q^4 - 4 * q^6 + 2 * q^9 - 10 * q^16 + 4 * q^19 + 8 * q^24 - 4 * q^31 + 8 * q^34 - 6 * q^36 - 8 * q^46 + 2 * q^49 - 4 * q^51 + 4 * q^54 - 4 * q^61 + 14 * q^64 + 4 * q^69 + 34 * q^76 + 4 * q^79 - 2 * q^81 - 42 * q^94 + 34 * q^96

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