LMFDB - Embedded newform 3525.1.bd.a.476.1

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			476.1
Root			$0.887885 - 0.460065i$ of defining polynomial
Character	$\chi$	$=$	3525.476
Dual form			3525.1.bd.a.3251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.680803 - 1.56737i) q^{2} +(0.997669 + 0.0682424i) q^{3} +(-1.31059 + 1.40330i) q^{4} +(-0.572255 - 1.61017i) q^{6} +(1.48157 + 0.526549i) q^{8} +(0.990686 + 0.136167i) q^{9} +O(q^{10})$	\(q+(-0.680803 - 1.56737i) q^{2} +(0.997669 + 0.0682424i) q^{3} +(-1.31059 + 1.40330i) q^{4} +(-0.572255 - 1.61017i) q^{6} +(1.48157 + 0.526549i) q^{8} +(0.990686 + 0.136167i) q^{9} +(-1.40330 + 1.31059i) q^{12} +(-0.0523262 - 0.764982i) q^{16} +(0.256797 - 0.315646i) q^{17} +(-0.461039 - 1.64547i) q^{18} +(-1.16637 - 0.709287i) q^{19} +(0.730836 - 1.68255i) q^{23} +(1.44218 + 0.626428i) q^{24} +(0.979084 + 0.203456i) q^{27} +(0.105873 + 1.54781i) q^{31} +(0.232687 - 0.120569i) q^{32} +(-0.669562 - 0.187602i) q^{34} +(-1.48947 + 1.21177i) q^{36} +(-0.317642 + 2.31102i) q^{38} -3.13473 q^{46} +(0.816970 - 0.576680i) q^{47} -0.766769i q^{48} +(0.917211 - 0.398401i) q^{49} +(0.277739 - 0.297386i) q^{51} +(1.86697 - 0.663521i) q^{53} +(-0.347674 - 1.67310i) q^{54} +(-1.11525 - 0.787230i) q^{57} +(-1.11059 - 1.57335i) q^{61} +(2.35390 - 1.21969i) q^{62} +(-0.942181 - 0.766521i) q^{64} +(0.106390 + 0.774047i) q^{68} +(0.843954 - 1.62876i) q^{69} +(1.39607 + 0.723385i) q^{72} +(2.52398 - 0.707186i) q^{76} +(0.713755 + 1.37749i) q^{79} +(0.962917 + 0.269797i) q^{81} +(-0.422677 - 0.519540i) q^{83} +(1.40330 + 3.23072i) q^{92} +1.55142i q^{93} +(-1.46007 - 0.887885i) q^{94} +(0.240372 - 0.104408i) q^{96} +(-1.24888 - 1.16637i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$1$	$e\left(\frac{19}{23}\right)$	$-1$

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 $

$2$	−0.680803	−	1.56737i	−0.680803	−	1.56737i	−0.816970	−	0.576680i	$-0.804348\pi$
$2$	−0.680803	−	1.56737i	−0.680803	−	1.56737i	0.136167	−	0.990686i	$-0.456522\pi$
$3$	0.997669	+	0.0682424i	0.997669	+	0.0682424i
$3$	0.997669	+	0.0682424i	0.997669	+	0.0682424i
$4$	−1.31059	+	1.40330i	−1.31059	+	1.40330i
$5$		0			0
$5$		0			0
$6$	−0.572255	−	1.61017i	−0.572255	−	1.61017i
$7$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$7$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$8$	1.48157	+	0.526549i	1.48157	+	0.526549i
$9$	0.990686	+	0.136167i	0.990686	+	0.136167i
$10$		0			0
$11$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$11$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$12$	−1.40330	+	1.31059i	−1.40330	+	1.31059i
$13$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$13$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$14$		0			0
$15$		0			0
$16$	−0.0523262	−	0.764982i	−0.0523262	−	0.764982i
$17$	0.256797	−	0.315646i	0.256797	−	0.315646i	−0.631088	−	0.775711i	$-0.717391\pi$
$17$	0.256797	−	0.315646i	0.256797	−	0.315646i	0.887885	+	0.460065i	$0.152174\pi$
$18$	−0.461039	−	1.64547i	−0.461039	−	1.64547i
$19$	−1.16637	−	0.709287i	−1.16637	−	0.709287i	−0.203456	−	0.979084i	$-0.565217\pi$
$19$	−1.16637	−	0.709287i	−1.16637	−	0.709287i	−0.962917	+	0.269797i	$0.913043\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.730836	−	1.68255i	0.730836	−	1.68255i		−	1.00000i	$-0.5\pi$
$23$	0.730836	−	1.68255i	0.730836	−	1.68255i	0.730836	−	0.682553i	$-0.239130\pi$
$24$	1.44218	+	0.626428i	1.44218	+	0.626428i
$25$		0			0
$26$		0			0
$27$	0.979084	+	0.203456i	0.979084	+	0.203456i
$28$		0			0
$29$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$29$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$30$		0			0
$31$	0.105873	+	1.54781i	0.105873	+	1.54781i	0.682553	+	0.730836i	$0.260870\pi$
$31$	0.105873	+	1.54781i	0.105873	+	1.54781i	−0.576680	+	0.816970i	$0.695652\pi$
$32$	0.232687	−	0.120569i	0.232687	−	0.120569i
$33$		0			0
$34$	−0.669562	−	0.187602i	−0.669562	−	0.187602i
$35$		0			0
$36$	−1.48947	+	1.21177i	−1.48947	+	1.21177i
$37$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$37$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$38$	−0.317642	+	2.31102i	−0.317642	+	2.31102i
$39$		0			0
$40$		0			0
$41$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$41$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$42$		0			0
$43$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$43$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$44$		0			0
$45$		0			0
$46$	−3.13473			−3.13473
$47$	0.816970	−	0.576680i	0.816970	−	0.576680i
$47$	0.816970	−	0.576680i	0.816970	−	0.576680i
$48$		−	0.766769i		−	0.766769i
$49$	0.917211	−	0.398401i	0.917211	−	0.398401i
$50$		0			0
$51$	0.277739	−	0.297386i	0.277739	−	0.297386i
$52$		0			0
$53$	1.86697	−	0.663521i	1.86697	−	0.663521i	0.887885	−	0.460065i	$-0.152174\pi$
$53$	1.86697	−	0.663521i	1.86697	−	0.663521i	0.979084	−	0.203456i	$-0.0652174\pi$
$54$	−0.347674	−	1.67310i	−0.347674	−	1.67310i
$55$		0			0
$56$		0			0
$57$	−1.11525	−	0.787230i	−1.11525	−	0.787230i
$58$		0			0
$59$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$59$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$60$		0			0
$61$	−1.11059	−	1.57335i	−1.11059	−	1.57335i	−0.775711	−	0.631088i	$-0.782609\pi$
$61$	−1.11059	−	1.57335i	−1.11059	−	1.57335i	−0.334880	−	0.942261i	$-0.608696\pi$
$62$	2.35390	−	1.21969i	2.35390	−	1.21969i
$63$		0			0
$64$	−0.942181	−	0.766521i	−0.942181	−	0.766521i
$65$		0			0
$66$		0			0
$67$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$67$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$68$	0.106390	+	0.774047i	0.106390	+	0.774047i
$69$	0.843954	−	1.62876i	0.843954	−	1.62876i
$70$		0			0
$71$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$71$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$72$	1.39607	+	0.723385i	1.39607	+	0.723385i
$73$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$73$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$74$		0			0
$75$		0			0
$76$	2.52398	−	0.707186i	2.52398	−	0.707186i
$77$		0			0
$78$		0			0
$79$	0.713755	+	1.37749i	0.713755	+	1.37749i	0.917211	+	0.398401i	$0.130435\pi$
$79$	0.713755	+	1.37749i	0.713755	+	1.37749i	−0.203456	+	0.979084i	$0.565217\pi$
$80$		0			0
$81$	0.962917	+	0.269797i	0.962917	+	0.269797i
$82$		0			0
$83$	−0.422677	−	0.519540i	−0.422677	−	0.519540i	0.519584	−	0.854419i	$-0.326087\pi$
$83$	−0.422677	−	0.519540i	−0.422677	−	0.519540i	−0.942261	+	0.334880i	$0.891304\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$89$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$90$		0			0
$91$		0			0
$92$	1.40330	+	3.23072i	1.40330	+	3.23072i
$93$			1.55142i			1.55142i
$94$	−1.46007	−	0.887885i	−1.46007	−	0.887885i
$95$		0			0
$96$	0.240372	−	0.104408i	0.240372	−	0.104408i
$97$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$97$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$98$	−1.24888	−	1.16637i	−1.24888	−	1.16637i
$99$		0			0
$100$		0			0
$101$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$101$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$102$	−0.655198	−	0.232858i	−0.655198	−	0.232858i
$103$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$103$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$104$		0			0
$105$		0			0
$106$	−2.31102	−	2.47450i	−2.31102	−	2.47450i
$107$	0.0368232	−	0.131424i	0.0368232	−	0.131424i	−0.942261	−	0.334880i	$-0.891304\pi$
$107$	0.0368232	−	0.131424i	0.0368232	−	0.131424i	0.979084	+	0.203456i	$0.0652174\pi$
$108$	−1.56869	+	1.10730i	−1.56869	+	1.10730i
$109$	0.308133	+	0.594669i	0.308133	+	0.594669i	0.990686	−	0.136167i	$-0.0434783\pi$
$109$	0.308133	+	0.594669i	0.308133	+	0.594669i	−0.682553	+	0.730836i	$0.739130\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.599268	+	0.985454i	−0.599268	+	0.985454i	0.398401	+	0.917211i	$0.369565\pi$
$113$	−0.599268	+	0.985454i	−0.599268	+	0.985454i	−0.997669	+	0.0682424i	$0.978261\pi$
$114$	−0.474611	+	2.28396i	−0.474611	+	2.28396i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.203456	−	0.979084i	0.203456	−	0.979084i
$122$	−1.70992	+	2.81184i	−1.70992	+	2.81184i
$123$		0			0
$124$	−2.31079	−	1.87997i	−2.31079	−	1.87997i
$125$		0			0
$126$		0			0
$127$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$127$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$128$	−0.489274	+	1.74624i	−0.489274	+	1.74624i
$129$		0			0
$130$		0			0
$131$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$131$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.546666	−	0.332435i	0.546666	−	0.332435i
$137$	−0.489484	−	0.457146i	−0.489484	−	0.457146i	0.398401	−	0.917211i	$-0.369565\pi$
$137$	−0.489484	−	0.457146i	−0.489484	−	0.457146i	−0.887885	+	0.460065i	$0.847826\pi$
$138$	−3.12742	−	0.213922i	−3.12742	−	0.213922i
$139$	0.843954	−	0.366581i	0.843954	−	0.366581i	0.0682424	−	0.997669i	$-0.478261\pi$
$139$	0.843954	−	0.366581i	0.843954	−	0.366581i	0.775711	+	0.631088i	$0.217391\pi$
$140$		0			0
$141$	0.854419	−	0.519584i	0.854419	−	0.519584i
$142$		0			0
$143$		0			0
$144$	0.0523262	−	0.764982i	0.0523262	−	0.764982i
$145$		0			0
$146$		0			0
$147$	0.942261	−	0.334880i	0.942261	−	0.334880i
$148$		0			0
$149$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$149$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$150$		0			0
$151$	−1.11059	+	1.57335i	−1.11059	+	1.57335i	−0.334880	+	0.942261i	$0.608696\pi$
$151$	−1.11059	+	1.57335i	−1.11059	+	1.57335i	−0.775711	+	0.631088i	$0.782609\pi$
$152$	−1.35459	−	1.66501i	−1.35459	−	1.66501i
$153$	0.297386	−	0.277739i	0.297386	−	0.277739i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$157$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$158$	1.67310	−	2.05651i	1.67310	−	2.05651i
$159$	1.90790	−	0.534568i	1.90790	−	0.534568i
$160$		0			0
$161$		0			0
$162$	−0.232687	−	1.69292i	−0.232687	−	1.69292i
$163$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$163$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$164$		0			0
$165$		0			0
$166$	−0.526549	+	1.01619i	−0.526549	+	1.01619i
$167$	0.269797	+	1.96292i	0.269797	+	1.96292i	0.269797	+	0.962917i	$0.413043\pi$
$167$	0.269797	+	1.96292i	0.269797	+	1.96292i			1.00000i	$0.500000\pi$
$168$		0			0
$169$	−0.854419	−	0.519584i	−0.854419	−	0.519584i
$170$		0			0
$171$	−1.05893	−	0.861502i	−1.05893	−	0.861502i
$172$		0			0
$173$	−1.02405	+	0.530621i	−1.02405	+	0.530621i	−0.887885	−	0.460065i	$-0.847826\pi$
$173$	−1.02405	+	0.530621i	−1.02405	+	0.530621i	−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		−0.990686	−	0.136167i	$-0.956522\pi$
$179$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$180$		0			0
$181$	−0.234658	−	1.12924i	−0.234658	−	1.12924i	−0.917211	−	0.398401i	$-0.869565\pi$
$181$	−0.234658	−	1.12924i	−0.234658	−	1.12924i	0.682553	−	0.730836i	$-0.260870\pi$
$182$		0			0
$183$	−1.00063	−	1.64547i	−1.00063	−	1.64547i
$184$	1.96873	−	2.10800i	1.96873	−	2.10800i
$185$		0			0
$186$	2.43165	−	1.05621i	2.43165	−	1.05621i
$187$		0			0
$188$	−0.261458	+	1.90225i	−0.261458	+	1.90225i
$189$		0			0
$190$		0			0
$191$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$191$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$192$	−0.887675	−	0.829031i	−0.887675	−	0.829031i
$193$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$193$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$194$		0			0
$195$		0			0
$196$	−0.643012	+	1.80926i	−0.643012	+	1.80926i
$197$	0.262234	−	1.90790i	0.262234	−	1.90790i	−0.136167	−	0.990686i	$-0.543478\pi$
$197$	0.262234	−	1.90790i	0.262234	−	1.90790i	0.398401	−	0.917211i	$-0.369565\pi$
$198$		0			0
$199$	−1.53697	+	1.25042i	−1.53697	+	1.25042i	−0.682553	+	0.730836i	$0.739130\pi$
$199$	−1.53697	+	1.25042i	−1.53697	+	1.25042i	−0.854419	+	0.519584i	$0.826087\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.0533194	+	0.779503i	0.0533194	+	0.779503i
$205$		0			0
$206$		0			0
$207$	0.953137	−	1.56737i	0.953137	−	1.56737i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.125185	+	0.0543757i	0.125185	+	0.0543757i	0.460065	−	0.887885i	$-0.347826\pi$
$211$	0.125185	+	0.0543757i	0.125185	+	0.0543757i	−0.334880	+	0.942261i	$0.608696\pi$
$212$	−1.51571	+	3.48952i	−1.51571	+	3.48952i
$213$		0			0
$214$	−0.231058	+	0.0317582i	−0.231058	+	0.0317582i
$215$		0			0
$216$	1.34345	+	0.816970i	1.34345	+	0.816970i
$217$		0			0
$218$	0.722287	−	0.887810i	0.722287	−	0.887810i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$223$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$224$		0			0
$225$		0			0
$226$	1.95255	+	0.268372i	1.95255	+	0.268372i
$227$	−1.81464	−	0.644923i	−1.81464	−	0.644923i	−0.997669	−	0.0682424i	$-0.978261\pi$
$227$	−1.81464	−	0.644923i	−1.81464	−	0.644923i	−0.816970	−	0.576680i	$-0.804348\pi$
$228$	2.56636	−	0.533295i	2.56636	−	0.533295i
$229$	0.644923	+	1.81464i	0.644923	+	1.81464i	0.576680	+	0.816970i	$0.304348\pi$
$229$	0.644923	+	1.81464i	0.644923	+	1.81464i	0.0682424	+	0.997669i	$0.478261\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.789381	−	1.81734i	−0.789381	−	1.81734i	−0.519584	−	0.854419i	$-0.673913\pi$
$233$	−0.789381	−	1.81734i	−0.789381	−	1.81734i	−0.269797	−	0.962917i	$-0.586957\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.618088	+	1.42298i	0.618088	+	1.42298i
$238$		0			0
$239$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$239$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$240$		0			0
$241$	0.663521	+	1.86697i	0.663521	+	1.86697i	0.460065	+	0.887885i	$0.347826\pi$
$241$	0.663521	+	1.86697i	0.663521	+	1.86697i	0.203456	+	0.979084i	$0.434783\pi$
$242$	−1.67310	+	0.347674i	−1.67310	+	0.347674i
$243$	0.942261	+	0.334880i	0.942261	+	0.334880i
$244$	3.66341	+	0.503524i	3.66341	+	0.503524i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.658138	+	2.34893i	−0.658138	+	2.34893i
$249$	−0.386237	−	0.547173i	−0.386237	−	0.547173i
$250$		0			0
$251$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$251$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	1.86681	−	0.256587i	1.86681	−	0.256587i
$257$	0.361291	+	0.187206i	0.361291	+	0.187206i	0.631088	−	0.775711i	$-0.282609\pi$
$257$	0.361291	+	0.187206i	0.361291	+	0.187206i	−0.269797	+	0.962917i	$0.586957\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.953137	+	1.56737i	−0.953137	+	1.56737i	−0.136167	+	0.990686i	$0.543478\pi$
$263$	−0.953137	+	1.56737i	−0.953137	+	1.56737i	−0.816970	+	0.576680i	$0.804348\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$269$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$270$		0			0
$271$	−1.05893	+	0.861502i	−1.05893	+	0.861502i	−0.990686	−	0.136167i	$-0.956522\pi$
$271$	−1.05893	+	0.861502i	−1.05893	+	0.861502i	−0.0682424	+	0.997669i	$0.521739\pi$
$272$	−0.254901	−	0.179929i	−0.254901	−	0.179929i
$273$		0			0
$274$	−0.383273	+	1.07843i	−0.383273	+	1.07843i
$275$		0			0
$276$	1.17956	+	3.31895i	1.17956	+	3.31895i
$277$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$277$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$278$	−1.14913	−	1.07322i	−1.14913	−	1.07322i
$279$	−0.105873	+	1.54781i	−0.105873	+	1.54781i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−1.39607	−	0.985454i	−1.39607	−	0.985454i
$283$		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
$288$	0.246937	−	0.0877614i	0.246937	−	0.0877614i
$289$	0.169768	+	0.816970i	0.169768	+	0.816970i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.07843	+	1.32557i	1.07843	+	1.32557i	0.942261	+	0.334880i	$0.108696\pi$
$293$	1.07843	+	1.32557i	1.07843	+	1.32557i	0.136167	+	0.990686i	$0.456522\pi$
$294$	−1.16637	−	1.24888i	−1.16637	−	1.24888i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	3.22211	+	0.669562i	3.22211	+	0.669562i
$303$		0			0
$304$	−0.481560	+	0.929369i	−0.481560	+	0.929369i
$305$		0			0
$306$	−0.637780	−	0.277027i	−0.637780	−	0.277027i
$307$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$307$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$311$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$312$		0			0
$313$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$313$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$314$		0			0
$315$		0			0
$316$	−2.86847	−	0.803707i	−2.86847	−	0.803707i
$317$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i	−0.631088	−	0.775711i	$-0.717391\pi$
$317$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i	0.730836	+	0.682553i	$0.239130\pi$
$318$	−2.13677	−	2.62644i	−2.13677	−	2.62644i
$319$		0			0
$320$		0			0
$321$	0.0457060	−	0.128604i	0.0457060	−	0.128604i
$322$		0			0
$323$	−0.523405	+	0.186018i	−0.523405	+	0.186018i
$324$	−1.64060	+	0.997669i	−1.64060	+	0.997669i
$325$		0			0
$326$		0			0
$327$	0.266833	+	0.614311i	0.266833	+	0.614311i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.614311	−	0.266833i	0.614311	−	0.266833i	−0.0682424	−	0.997669i	$-0.521739\pi$
$331$	0.614311	−	0.266833i	0.614311	−	0.266833i	0.682553	+	0.730836i	$0.260870\pi$
$332$	1.28303	+	0.0877614i	1.28303	+	0.0877614i
$333$		0			0
$334$	2.89293	−	1.75923i	2.89293	−	1.75923i
$335$		0			0
$336$		0			0
$337$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$337$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$338$	−0.232687	+	1.69292i	−0.232687	+	1.69292i
$339$	−0.665120	+	0.942261i	−0.665120	+	0.942261i
$340$		0			0
$341$		0			0
$342$	−0.629368	+	2.24624i	−0.629368	+	2.24624i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.52886	+	1.24382i	1.52886	+	1.24382i
$347$	−0.311173	−	1.11059i	−0.311173	−	1.11059i	−0.942261	−	0.334880i	$-0.891304\pi$
$347$	−0.311173	−	1.11059i	−0.311173	−	1.11059i	0.631088	−	0.775711i	$-0.282609\pi$
$348$		0			0
$349$	−0.187206	+	0.900885i	−0.187206	+	0.900885i	0.775711	+	0.631088i	$0.217391\pi$
$349$	−0.187206	+	0.900885i	−0.187206	+	0.900885i	−0.962917	+	0.269797i	$0.913043\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.543860	+	1.25209i	−0.543860	+	1.25209i	0.398401	+	0.917211i	$0.369565\pi$
$353$	−0.543860	+	1.25209i	−0.543860	+	1.25209i	−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		−0.775711	−	0.631088i	$-0.782609\pi$
$359$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$360$		0			0
$361$	0.397273	+	0.766702i	0.397273	+	0.766702i
$362$	−1.61017	+	1.13658i	−1.61017	+	1.13658i
$363$	0.269797	−	0.962917i	0.269797	−	0.962917i
$364$		0			0
$365$		0			0
$366$	−1.89782	+	2.68860i	−1.89782	+	2.68860i
$367$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$367$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$368$	−1.32536	−	0.471035i	−1.32536	−	0.471035i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−2.17711	−	2.03328i	−2.17711	−	2.03328i
$373$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$373$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$374$		0			0
$375$		0			0
$376$	1.51405	−	0.424216i	1.51405	−	0.424216i
$377$		0			0
$378$		0			0
$379$	−0.00931405	+	0.136167i	−0.00931405	+	0.136167i	0.990686	+	0.136167i	$0.0434783\pi$
$379$	−0.00931405	+	0.136167i	−0.00931405	+	0.136167i	−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.12924	+	0.234658i	−1.12924	+	0.234658i	−0.730836	−	0.682553i	$-0.760870\pi$
$383$	−1.12924	+	0.234658i	−1.12924	+	0.234658i	−0.398401	+	0.917211i	$0.630435\pi$
$384$	−0.607301	+	1.70878i	−0.607301	+	1.70878i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$389$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$390$		0			0
$391$	−0.343415	−	0.662761i	−0.343415	−	0.662761i
$392$	1.56869	−	0.107301i	1.56869	−	0.107301i
$393$		0			0
$394$	−3.16890	+	0.887885i	−3.16890	+	0.887885i
$395$		0			0
$396$		0			0
$397$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$397$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$398$	3.00624	+	1.55771i	3.00624	+	1.55771i
$399$		0			0
$400$		0			0
$401$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$401$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.568078	−	0.294354i	0.568078	−	0.294354i
$409$	0.530621	+	0.751719i	0.530621	+	0.751719i	0.990686	−	0.136167i	$-0.0434783\pi$
$409$	0.530621	+	0.751719i	0.530621	+	0.751719i	−0.460065	+	0.887885i	$0.652174\pi$
$410$		0			0
$411$	−0.457146	−	0.489484i	−0.457146	−	0.489484i
$412$		0			0
$413$		0			0
$414$	−3.10554	−	0.426846i	−3.10554	−	0.426846i
$415$		0			0
$416$		0			0
$417$	0.867003	−	0.308133i	0.867003	−	0.308133i
$418$		0			0
$419$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$419$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$420$		0			0
$421$	0.125185	−	0.0543757i	0.125185	−	0.0543757i	−0.334880	−	0.942261i	$-0.608696\pi$
$421$	0.125185	−	0.0543757i	0.125185	−	0.0543757i	0.460065	+	0.887885i	$0.347826\pi$
$422$		−	0.233231i		−	0.233231i
$423$	0.887885	−	0.460065i	0.887885	−	0.460065i
$424$	3.11542			3.11542
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.136167	+	0.223917i	0.136167	+	0.223917i
$429$		0			0
$430$		0			0
$431$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$431$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$432$	0.104408	−	0.759628i	0.104408	−	0.759628i
$433$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$433$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$434$		0			0
$435$		0			0
$436$	−1.23834	−	0.346965i	−1.23834	−	0.346965i
$437$	−2.04584	+	1.44411i	−2.04584	+	1.44411i
$438$		0			0
$439$	−0.0457060	−	0.668198i	−0.0457060	−	0.668198i	−0.962917	−	0.269797i	$-0.913043\pi$
$439$	−0.0457060	−	0.668198i	−0.0457060	−	0.668198i	0.917211	−	0.398401i	$-0.130435\pi$
$440$		0			0
$441$	0.962917	−	0.269797i	0.962917	−	0.269797i
$442$		0			0
$443$	0.655751	+	0.136267i	0.655751	+	0.136267i	0.519584	−	0.854419i	$-0.326087\pi$
$443$	0.655751	+	0.136267i	0.655751	+	0.136267i	0.136167	+	0.990686i	$0.456522\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$449$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$450$		0			0
$451$		0			0
$452$	−0.597493	−	2.13248i	−0.597493	−	2.13248i
$453$	−1.21537	+	1.49389i	−1.21537	+	1.49389i
$454$	0.224582	+	3.28327i	0.224582	+	3.28327i
$455$		0			0
$456$	−1.23780	−	1.75357i	−1.23780	−	1.75357i
$457$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$457$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$458$	2.40514	−	2.24624i	2.40514	−	2.24624i
$459$	0.315646	−	0.256797i	0.315646	−	0.256797i
$460$		0			0
$461$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$461$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$462$		0			0
$463$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$463$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$464$		0			0
$465$		0			0
$466$	−2.31102	+	2.47450i	−2.31102	+	2.47450i
$467$	−0.917985	−	0.0627919i	−0.917985	−	0.0627919i	−0.398401	−	0.917211i	$-0.630435\pi$
$467$	−0.917985	−	0.0627919i	−0.917985	−	0.0627919i	−0.519584	+	0.854419i	$0.673913\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	1.80954	−	1.93754i	1.80954	−	1.93754i
$475$		0			0
$476$		0			0
$477$	1.93993	−	0.403122i	1.93993	−	0.403122i
$478$		0			0
$479$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$479$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$480$		0			0
$481$		0			0
$482$	2.47450	−	2.31102i	2.47450	−	2.31102i
$483$		0			0
$484$	1.10730	+	1.56869i	1.10730	+	1.56869i
$485$		0			0
$486$	−0.116615	−	1.70486i	−0.116615	−	1.70486i
$487$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$487$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$488$	−0.816970	−	2.91580i	−0.816970	−	2.91580i
$489$		0			0
$490$		0			0
$491$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$491$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	1.17850	−	0.161982i	1.17850	−	0.161982i
$497$		0			0
$498$	−0.594669	+	0.977892i	−0.594669	+	0.977892i
$499$	1.76640	−	0.494921i	1.76640	−	0.494921i	0.775711	−	0.631088i	$-0.217391\pi$
$499$	1.76640	−	0.494921i	1.76640	−	0.494921i	0.990686	+	0.136167i	$0.0434783\pi$
$500$		0			0
$501$	0.135214	+	1.97675i	0.135214	+	1.97675i
$502$		0			0
$503$	−1.39607	+	0.985454i	−1.39607	+	0.985454i	−0.398401	+	0.917211i	$0.630435\pi$
$503$	−1.39607	+	0.985454i	−1.39607	+	0.985454i	−0.997669	+	0.0682424i	$0.978261\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.816970	−	0.576680i	−0.816970	−	0.576680i
$508$		0			0
$509$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$509$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$510$		0			0
$511$		0			0
$512$	−0.730836	−	1.20181i	−0.730836	−	1.20181i
$513$	−0.997669	−	0.931758i	−0.997669	−	0.931758i
$514$	0.0474522	−	0.693726i	0.0474522	−	0.693726i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.05788	+	0.459500i	−1.05788	+	0.459500i
$520$		0			0
$521$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$521$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$522$		0			0
$523$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$523$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$524$		0			0
$525$		0			0
$526$	3.10554	+	0.426846i	3.10554	+	0.426846i
$527$	0.515747	+	0.364054i	0.515747	+	0.364054i
$528$		0			0
$529$	−1.61431	−	1.72850i	−1.61431	−	1.72850i
$530$		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
$541$	1.42298	+	0.618088i	1.42298	+	0.618088i	0.962917	−	0.269797i	$-0.0869565\pi$
$541$	1.42298	+	0.618088i	1.42298	+	0.618088i	0.460065	+	0.887885i	$0.347826\pi$
$542$	2.07121	+	1.07322i	2.07121	+	1.07322i
$543$	−0.157049	−	1.14262i	−0.157049	−	1.14262i
$544$	0.0216963	−	0.104408i	0.0216963	−	0.104408i
$545$		0			0
$546$		0			0
$547$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$547$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$548$	1.28303	−	0.0877614i	1.28303	−	0.0877614i
$549$	−0.886009	−	1.70992i	−0.886009	−	1.70992i
$550$		0			0
$551$		0			0
$552$	2.10800	−	1.96873i	2.10800	−	1.96873i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.591655	+	1.66476i	−0.591655	+	1.66476i
$557$	−0.398401	+	0.0827887i	−0.398401	+	0.0827887i	−0.398401	−	0.917211i	$-0.630435\pi$
$557$	−0.398401	+	0.0827887i	−0.398401	+	0.0827887i			1.00000i	$0.5\pi$
$558$	2.49806	−	0.887810i	2.49806	−	0.887810i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	0.406912i		−	0.406912i	−0.979084	−	0.203456i	$-0.934783\pi$
$563$		−	0.406912i		−	0.406912i	0.979084	−	0.203456i	$-0.0652174\pi$
$564$	−0.390662	+	1.87997i	−0.390662	+	1.87997i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$569$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$570$		0			0
$571$	0.277739	+	1.33655i	0.277739	+	1.33655i	0.854419	+	0.519584i	$0.173913\pi$
$571$	0.277739	+	1.33655i	0.277739	+	1.33655i	−0.576680	+	0.816970i	$0.695652\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.829031	−	0.887675i	−0.829031	−	0.887675i
$577$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$577$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$578$	1.16491	−	0.822285i	1.16491	−	0.822285i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	1.34345	−	2.59274i	1.34345	−	2.59274i
$587$	0.543860	−	1.25209i	0.543860	−	1.25209i	−0.398401	−	0.917211i	$-0.630435\pi$
$587$	0.543860	−	1.25209i	0.543860	−	1.25209i	0.942261	−	0.334880i	$-0.108696\pi$
$588$	−0.764982	+	1.76117i	−0.764982	+	1.76117i
$589$	0.974352	−	1.88041i	0.974352	−	1.88041i
$590$		0			0
$591$	0.391823	−	1.88555i	0.391823	−	1.88555i
$592$		0			0
$593$	−0.461039	−	1.64547i	−0.461039	−	1.64547i	−0.730836	−	0.682553i	$-0.760870\pi$
$593$	−0.461039	−	1.64547i	−0.461039	−	1.64547i	0.269797	−	0.962917i	$-0.413043\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.61872	+	1.14262i	−1.61872	+	1.14262i
$598$		0			0
$599$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$599$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$600$		0			0
$601$	0.665120	−	0.942261i	0.665120	−	0.942261i	−0.334880	−	0.942261i	$-0.608696\pi$
$601$	0.665120	−	0.942261i	0.665120	−	0.942261i	1.00000			$0$
$602$		0			0
$603$		0			0
$604$	−0.752350	−	3.62051i	−0.752350	−	3.62051i
$605$		0			0
$606$		0			0
$607$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$607$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$608$	−0.356918	−	0.0244138i	−0.356918	−	0.0244138i
$609$		0			0
$610$		0			0
$611$		0			0
$612$			0.781324i			0.781324i
$613$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$613$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.46184	+	0.519540i	−1.46184	+	0.519540i	−0.942261	−	0.334880i	$-0.891304\pi$
$617$	−1.46184	+	0.519540i	−1.46184	+	0.519540i	−0.519584	+	0.854419i	$0.673913\pi$
$618$		0			0
$619$	0.644923	−	1.81464i	0.644923	−	1.81464i	0.0682424	−	0.997669i	$-0.478261\pi$
$619$	0.644923	−	1.81464i	0.644923	−	1.81464i	0.576680	−	0.816970i	$-0.304348\pi$
$620$		0			0
$621$	1.05788	−	1.49867i	1.05788	−	1.49867i
$622$		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
$631$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	0.203456	+	0.979084i	$0.434783\pi$
$631$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	−0.576680	+	0.816970i	$0.695652\pi$
$632$	0.332163	+	2.41666i	0.332163	+	2.41666i
$633$	0.121183	+	0.0627919i	0.121183	+	0.0627919i
$634$	−0.213922	−	0.0929193i	−0.213922	−	0.0929193i
$635$		0			0
$636$	−1.75031	+	3.37795i	−1.75031	+	3.37795i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$641$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$642$	−0.232687	+	0.0159162i	−0.232687	+	0.0159162i
$643$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$643$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$644$		0			0
$645$		0			0
$646$	0.647895	+	0.693726i	0.647895	+	0.693726i
$647$	1.25042	+	1.53697i	1.25042	+	1.53697i	0.730836	+	0.682553i	$0.239130\pi$
$647$	1.25042	+	1.53697i	1.25042	+	1.53697i	0.519584	+	0.854419i	$0.326087\pi$
$648$	1.28457	+	0.906746i	1.28457	+	0.906746i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.709287	−	1.16637i	−0.709287	−	1.16637i	−0.979084	−	0.203456i	$-0.934783\pi$
$653$	−0.709287	−	1.16637i	−0.709287	−	1.16637i	0.269797	−	0.962917i	$-0.413043\pi$
$654$	0.781189	−	0.836449i	0.781189	−	0.836449i
$655$		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
$661$	−0.0277687	+	0.405963i	−0.0277687	+	0.405963i	0.962917	+	0.269797i	$0.0869565\pi$
$661$	−0.0277687	+	0.405963i	−0.0277687	+	0.405963i	−0.990686	+	0.136167i	$0.956522\pi$
$662$	−0.836449	−	0.781189i	−0.836449	−	0.781189i
$663$		0			0
$664$	−0.352661	−	0.992294i	−0.352661	−	0.992294i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−3.10816	−	2.19398i	−3.10816	−	2.19398i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$673$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$674$		0			0
$675$		0			0
$676$	1.84893	−	0.518045i	1.84893	−	0.518045i
$677$	−0.478085	+	0.786177i	−0.478085	+	0.786177i	−0.997669	−	0.0682424i	$-0.978261\pi$
$677$	−0.478085	+	0.786177i	−0.478085	+	0.786177i	0.519584	+	0.854419i	$0.326087\pi$
$678$	1.92968	+	0.400993i	1.92968	+	0.400993i
$679$		0			0
$680$		0			0
$681$	−1.76640	−	0.767255i	−1.76640	−	0.767255i
$682$		0			0
$683$	1.62876	+	0.843954i	1.62876	+	0.843954i	0.997669	+	0.0682424i	$0.0217391\pi$
$683$	1.62876	+	0.843954i	1.62876	+	0.843954i	0.631088	+	0.775711i	$0.282609\pi$
$684$	2.59677	−	0.356918i	2.59677	−	0.356918i
$685$		0			0
$686$		0			0
$687$	0.519584	+	1.85442i	0.519584	+	1.85442i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.234658	−	0.332435i	−0.234658	−	0.332435i	0.682553	−	0.730836i	$-0.260870\pi$
$691$	−0.234658	−	0.332435i	−0.234658	−	0.332435i	−0.917211	+	0.398401i	$0.869565\pi$
$692$	0.597493	−	2.13248i	0.597493	−	2.13248i
$693$		0			0
$694$	−1.52886	+	1.24382i	−1.52886	+	1.24382i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	1.53947	−	0.319905i	1.53947	−	0.319905i
$699$	−0.663521	−	1.86697i	−0.663521	−	1.86697i
$700$		0			0
$701$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$701$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	2.33275			2.33275
$707$		0			0
$708$		0			0
$709$	1.25209	−	1.34066i	1.25209	−	1.34066i	0.334880	−	0.942261i	$-0.391304\pi$
$709$	1.25209	−	1.34066i	1.25209	−	1.34066i	0.917211	−	0.398401i	$-0.130435\pi$
$710$		0			0
$711$	0.519540	+	1.46184i	0.519540	+	1.46184i
$712$		0			0
$713$	2.68164	+	0.953056i	2.68164	+	0.953056i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$719$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$720$		0			0
$721$		0			0
$722$	0.931239	−	1.14465i	0.931239	−	1.14465i
$723$	0.534568	+	1.90790i	0.534568	+	1.90790i
$724$	1.89220	+	1.15067i	1.89220	+	1.15067i
$725$		0			0
$726$	−1.69292	+	0.232687i	−1.69292	+	0.232687i
$727$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$727$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$728$		0			0
$729$	0.917211	+	0.398401i	0.917211	+	0.398401i
$730$		0			0
$731$		0			0
$732$	3.62051	+	0.752350i	3.62051	+	0.752350i
$733$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$733$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$734$		0			0
$735$		0			0
$736$	−0.0328072	−	0.479624i	−0.0328072	−	0.479624i
$737$		0			0
$738$		0			0
$739$	1.11059	+	0.311173i	1.11059	+	0.311173i	0.775711	−	0.631088i	$-0.217391\pi$
$739$	1.11059	+	0.311173i	1.11059	+	0.311173i	0.334880	+	0.942261i	$0.391304\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.185882	+	1.35239i	−0.185882	+	1.35239i	0.631088	+	0.775711i	$0.282609\pi$
$743$	−0.185882	+	1.35239i	−0.185882	+	1.35239i	−0.816970	+	0.576680i	$0.804348\pi$
$744$	−0.816900	+	2.29854i	−0.816900	+	2.29854i
$745$		0			0
$746$		0			0
$747$	−0.347996	−	0.572255i	−0.347996	−	0.572255i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.136485			−0.136485			−0.0682424	−	0.997669i	$-0.521739\pi$
$751$	−0.136485			−0.136485			−0.0682424	+	0.997669i	$0.521739\pi$
$752$	−0.483899	−	0.594792i	−0.483899	−	0.594792i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$757$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$758$	0.219764	−	0.0781042i	0.219764	−	0.0781042i
$759$		0			0
$760$		0			0
$761$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$761$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	1.13658	+	1.61017i	1.13658	+	1.61017i
$767$		0			0
$768$	1.87997	−	0.128593i	1.87997	−	0.128593i
$769$	0.315646	+	0.256797i	0.315646	+	0.256797i	0.775711	−	0.631088i	$-0.217391\pi$
$769$	0.315646	+	0.256797i	0.315646	+	0.256797i	−0.460065	+	0.887885i	$0.652174\pi$
$770$		0			0
$771$	0.347674	+	0.211425i	0.347674	+	0.211425i
$772$		0			0
$773$	0.125291	+	0.911560i	0.125291	+	0.911560i	0.942261	+	0.334880i	$0.108696\pi$
$773$	0.125291	+	0.911560i	0.125291	+	0.911560i	−0.816970	+	0.576680i	$0.804348\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.804991	+	0.989467i	−0.804991	+	0.989467i
$783$		0			0
$784$	−0.352764	−	0.680803i	−0.352764	−	0.680803i
$785$		0			0
$786$		0			0
$787$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$787$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$788$	2.33367	+	2.86847i	2.33367	+	2.86847i
$789$	−1.05788	+	1.49867i	−1.05788	+	1.49867i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.259628	−	3.79562i	0.259628	−	3.79562i
$797$	−0.366581	−	0.843954i	−0.366581	−	0.843954i	−0.997669	−	0.0682424i	$-0.978261\pi$
$797$	−0.366581	−	0.843954i	−0.366581	−	0.843954i	0.631088	−	0.775711i	$-0.282609\pi$
$798$		0			0
$799$	0.0277687	−	0.405963i	0.0277687	−	0.405963i
$800$		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		0.576680	−	0.816970i	$-0.304348\pi$
$809$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$810$		0			0
$811$	−0.787230	−	0.842917i	−0.787230	−	0.842917i	0.203456	−	0.979084i	$-0.434783\pi$
$811$	−0.787230	−	0.842917i	−0.787230	−	0.842917i	−0.990686	+	0.136167i	$0.956522\pi$
$812$		0			0
$813$	−1.11525	+	0.787230i	−1.11525	+	0.787230i
$814$		0			0
$815$		0			0
$816$	−0.242028	−	0.196904i	−0.242028	−	0.196904i
$817$		0			0
$818$	0.816970	−	1.34345i	0.816970	−	1.34345i
$819$		0			0
$820$		0			0
$821$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$821$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$822$	−0.455974	+	1.04976i	−0.455974	+	1.04976i
$823$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$823$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.478085	+	0.786177i	−0.478085	+	0.786177i	−0.997669	−	0.0682424i	$-0.978261\pi$
$827$	−0.478085	+	0.786177i	−0.478085	+	0.786177i	0.519584	+	0.854419i	$0.326087\pi$
$828$	0.950313	+	3.39171i	0.950313	+	3.39171i
$829$	1.32557	+	1.07843i	1.32557	+	1.07843i	0.990686	+	0.136167i	$0.0434783\pi$
$829$	1.32557	+	1.07843i	1.32557	+	1.07843i	0.334880	+	0.942261i	$0.391304\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.109784	−	0.391823i	0.109784	−	0.391823i
$834$	−1.07322	−	1.14913i	−1.07322	−	1.14913i
$835$		0			0
$836$		0			0
$837$	−0.211252	+	1.53697i	−0.211252	+	1.53697i
$838$		0			0
$839$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$839$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$840$		0			0
$841$	0.854419	−	0.519584i	0.854419	−	0.519584i
$842$	−0.170453	−	0.159192i	−0.170453	−	0.159192i
$843$		0			0
$844$	−0.240372	+	0.104408i	−0.240372	+	0.104408i
$845$		0			0
$846$	−1.32557	−	1.07843i	−1.32557	−	1.07843i
$847$		0			0
$848$	−0.605273	−	1.39348i	−0.605273	−	1.39348i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$853$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$854$		0			0
$855$		0			0
$856$	0.123757	−	0.175324i	0.123757	−	0.175324i
$857$	0.0861339	+	0.105873i	0.0861339	+	0.105873i	0.816970	−	0.576680i	$-0.195652\pi$
$857$	0.0861339	+	0.105873i	0.0861339	+	0.105873i	−0.730836	+	0.682553i	$0.760870\pi$
$858$		0			0
$859$	−1.64547	−	0.461039i	−1.64547	−	0.461039i	−0.682553	−	0.730836i	$-0.739130\pi$
$859$	−1.64547	−	0.461039i	−1.64547	−	0.461039i	−0.962917	+	0.269797i	$0.913043\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.979084	−	1.20346i	0.979084	−	1.20346i		−	1.00000i	$-0.5\pi$
$863$	0.979084	−	1.20346i	0.979084	−	1.20346i	0.979084	−	0.203456i	$-0.0652174\pi$
$864$	0.252350	−	0.0707053i	0.252350	−	0.0707053i
$865$		0			0
$866$		0			0
$867$	0.113621	+	0.826651i	0.113621	+	0.826651i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.143397	+	1.04329i	0.143397	+	1.04329i
$873$		0			0
$874$	3.65627	+	2.22343i	3.65627	+	2.22343i
$875$		0			0
$876$		0			0
$877$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$877$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$878$	−1.01619	+	0.526549i	−1.01619	+	0.526549i
$879$	0.985454	+	1.39607i	0.985454	+	1.39607i
$880$		0			0
$881$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$881$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$882$	−1.07843	−	1.32557i	−1.07843	−	1.32557i
$883$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$883$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$884$		0			0
$885$		0			0
$886$	−0.232858	−	1.12057i	−0.232858	−	1.12057i
$887$	1.28629	−	0.457146i	1.28629	−	0.457146i	0.398401	−	0.917211i	$-0.369565\pi$
$887$	1.28629	−	0.457146i	1.28629	−	0.457146i	0.887885	+	0.460065i	$0.152174\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.36192	+	0.0931581i	−1.36192	+	0.0931581i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.269995	−	0.759692i	0.269995	−	0.759692i
$902$		0			0
$903$		0			0
$904$	−1.40675	+	1.14447i	−1.40675	+	1.14447i
$905$		0			0
$906$	3.16890	+	0.887885i	3.16890	+	0.887885i
$907$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$907$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$908$	3.28327	−	1.70125i	3.28327	−	1.70125i
$909$		0			0
$910$		0			0
$911$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$911$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$912$	−0.543860	+	0.894339i	−0.543860	+	0.894339i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−3.39171	−	1.47323i	−3.39171	−	1.47323i
$917$		0			0
$918$	−0.617388	−	0.319905i	−0.617388	−	0.319905i
$919$	−1.81734	+	0.249787i	−1.81734	+	0.249787i	−0.962917	−	0.269797i	$-0.913043\pi$
$919$	−1.81734	+	0.249787i	−1.81734	+	0.249787i	−0.854419	+	0.519584i	$0.826087\pi$
$920$		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		0.775711	−	0.631088i	$-0.217391\pi$
$929$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$930$		0			0
$931$	−1.35239	−	0.185882i	−1.35239	−	0.185882i
$932$	3.58482	+	1.27405i	3.58482	+	1.27405i
$933$		0			0
$934$	0.526549	+	1.48157i	0.526549	+	1.48157i
$935$		0			0
$936$		0			0
$937$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$937$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$938$		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
$947$	−0.900885	+	0.187206i	−0.900885	+	0.187206i	−0.631088	−	0.775711i	$-0.717391\pi$
$947$	−0.900885	+	0.187206i	−0.900885	+	0.187206i	−0.269797	+	0.962917i	$0.586957\pi$
$948$	−2.80693	−	0.997584i	−2.80693	−	0.997584i
$949$		0			0
$950$		0			0
$951$	0.105873	−	0.0861339i	0.105873	−	0.0861339i
$952$		0			0
$953$	0.461039	−	1.64547i	0.461039	−	1.64547i	−0.269797	−	0.962917i	$-0.586957\pi$
$953$	0.461039	−	1.64547i	0.461039	−	1.64547i	0.730836	−	0.682553i	$-0.239130\pi$
$954$	−1.95255	−	2.76613i	−1.95255	−	2.76613i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−1.39381	+	0.191574i	−1.39381	+	0.191574i
$962$		0			0
$963$	0.0543757	−	0.125185i	0.0543757	−	0.125185i
$964$	−3.48952	−	1.51571i	−3.48952	−	1.51571i
$965$		0			0
$966$		0			0
$967$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$967$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$968$	0.816970	−	1.34345i	0.816970	−	1.34345i
$969$	−0.534880	+	0.149866i	−0.534880	+	0.149866i
$970$		0			0
$971$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$971$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$972$	−1.70486	+	0.883385i	−1.70486	+	0.883385i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−1.14547	+	0.931909i	−1.14547	+	0.931909i
$977$	0.942261	+	0.665120i	0.942261	+	0.665120i	0.942261	−	0.334880i	$-0.108696\pi$
$977$	0.942261	+	0.665120i	0.942261	+	0.665120i			1.00000i	$0.5\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.224289	+	0.631088i	0.224289	+	0.631088i
$982$		0			0
$983$	−1.40747	−	1.31448i	−1.40747	−	1.31448i	−0.887885	−	0.460065i	$-0.847826\pi$
$983$	−1.40747	−	1.31448i	−1.40747	−	1.31448i	−0.519584	−	0.854419i	$-0.673913\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.0931581	+	0.0997480i	−0.0931581	+	0.0997480i	−0.775711	−	0.631088i	$-0.782609\pi$
$991$	−0.0931581	+	0.0997480i	−0.0931581	+	0.0997480i	0.682553	+	0.730836i	$0.260870\pi$
$992$	0.211252	+	0.347389i	0.211252	+	0.347389i
$993$	0.631088	−	0.224289i	0.631088	−	0.224289i
$994$		0			0
$995$		0			0
$996$	1.27405	+	0.175114i	1.27405	+	0.175114i
$997$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$997$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$998$	−1.97829	−	2.43165i	−1.97829	−	2.43165i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bd.a.476.1		44
3.2	odd	2	inner	3525.1.bd.a.476.2		44
5.2	odd	4		705.1.p.b.194.1	yes	22
5.3	odd	4		705.1.p.a.194.1	yes	22
5.4	even	2	inner	3525.1.bd.a.476.2		44
15.2	even	4		705.1.p.a.194.1	yes	22
15.8	even	4		705.1.p.b.194.1	yes	22
15.14	odd	2	CM	3525.1.bd.a.476.1		44
47.8	even	23	inner	3525.1.bd.a.3251.2		44
141.8	odd	46	inner	3525.1.bd.a.3251.1		44
235.8	odd	92		705.1.p.a.149.1	✓	22
235.102	odd	92		705.1.p.b.149.1	yes	22
235.149	even	46	inner	3525.1.bd.a.3251.1		44
705.8	even	92		705.1.p.b.149.1	yes	22
705.149	odd	46	inner	3525.1.bd.a.3251.2		44
705.572	even	92		705.1.p.a.149.1	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.1.p.a.149.1	✓	22	235.8	odd	92
705.1.p.a.149.1	✓	22	705.572	even	92
705.1.p.a.194.1	yes	22	5.3	odd	4
705.1.p.a.194.1	yes	22	15.2	even	4
705.1.p.b.149.1	yes	22	235.102	odd	92
705.1.p.b.149.1	yes	22	705.8	even	92
705.1.p.b.194.1	yes	22	5.2	odd	4
705.1.p.b.194.1	yes	22	15.8	even	4
3525.1.bd.a.476.1		44	1.1	even	1	trivial
3525.1.bd.a.476.1		44	15.14	odd	2	CM
3525.1.bd.a.476.2		44	3.2	odd	2	inner
3525.1.bd.a.476.2		44	5.4	even	2	inner
3525.1.bd.a.3251.1		44	141.8	odd	46	inner
3525.1.bd.a.3251.1		44	235.149	even	46	inner
3525.1.bd.a.3251.2		44	47.8	even	23	inner
3525.1.bd.a.3251.2		44	705.149	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)

\(f(q)\)	\(=\)	\(q+(-0.680803 - 1.56737i) q^{2} +(0.997669 + 0.0682424i) q^{3} +(-1.31059 + 1.40330i) q^{4} +(-0.572255 - 1.61017i) q^{6} +(1.48157 + 0.526549i) q^{8} +(0.990686 + 0.136167i) q^{9} +O(q^{10})\)	\(q+(-0.680803 - 1.56737i) q^{2} +(0.997669 + 0.0682424i) q^{3} +(-1.31059 + 1.40330i) q^{4} +(-0.572255 - 1.61017i) q^{6} +(1.48157 + 0.526549i) q^{8} +(0.990686 + 0.136167i) q^{9} +(-1.40330 + 1.31059i) q^{12} +(-0.0523262 - 0.764982i) q^{16} +(0.256797 - 0.315646i) q^{17} +(-0.461039 - 1.64547i) q^{18} +(-1.16637 - 0.709287i) q^{19} +(0.730836 - 1.68255i) q^{23} +(1.44218 + 0.626428i) q^{24} +(0.979084 + 0.203456i) q^{27} +(0.105873 + 1.54781i) q^{31} +(0.232687 - 0.120569i) q^{32} +(-0.669562 - 0.187602i) q^{34} +(-1.48947 + 1.21177i) q^{36} +(-0.317642 + 2.31102i) q^{38} -3.13473 q^{46} +(0.816970 - 0.576680i) q^{47} -0.766769i q^{48} +(0.917211 - 0.398401i) q^{49} +(0.277739 - 0.297386i) q^{51} +(1.86697 - 0.663521i) q^{53} +(-0.347674 - 1.67310i) q^{54} +(-1.11525 - 0.787230i) q^{57} +(-1.11059 - 1.57335i) q^{61} +(2.35390 - 1.21969i) q^{62} +(-0.942181 - 0.766521i) q^{64} +(0.106390 + 0.774047i) q^{68} +(0.843954 - 1.62876i) q^{69} +(1.39607 + 0.723385i) q^{72} +(2.52398 - 0.707186i) q^{76} +(0.713755 + 1.37749i) q^{79} +(0.962917 + 0.269797i) q^{81} +(-0.422677 - 0.519540i) q^{83} +(1.40330 + 3.23072i) q^{92} +1.55142i q^{93} +(-1.46007 - 0.887885i) q^{94} +(0.240372 - 0.104408i) q^{96} +(-1.24888 - 1.16637i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 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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