LMFDB - Embedded newform 3525.1.bd.a.401.2

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			401.2
Root			$-0.269797 - 0.962917i$ of defining polynomial
Character	$\chi$	$=$	3525.401
Dual form			3525.1.bd.a.1301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25042 + 1.53697i) q^{2} +(0.398401 + 0.917211i) q^{3} +(-0.595279 + 2.86464i) q^{4} +(-0.911560 + 1.75923i) q^{6} +(-3.38799 + 1.75551i) q^{8} +(-0.682553 + 0.730836i) q^{9} +O(q^{10})$	\(q+(1.25042 + 1.53697i) q^{2} +(0.398401 + 0.917211i) q^{3} +(-0.595279 + 2.86464i) q^{4} +(-0.911560 + 1.75923i) q^{6} +(-3.38799 + 1.75551i) q^{8} +(-0.682553 + 0.730836i) q^{9} +(-2.86464 + 0.595279i) q^{12} +(-4.25097 - 1.84646i) q^{16} +(0.547173 + 0.386237i) q^{17} +(-1.97675 - 0.135214i) q^{18} +(0.403122 - 0.0554078i) q^{19} +(0.979084 - 1.20346i) q^{23} +(-2.95995 - 2.40810i) q^{24} +(-0.942261 - 0.334880i) q^{27} +(1.05788 + 0.459500i) q^{31} +(-1.44806 - 5.16819i) q^{32} +(0.0905606 + 1.32395i) q^{34} +(-1.68727 - 2.39032i) q^{36} +(0.589232 + 0.550304i) q^{38} +3.07395 q^{46} +(-0.519584 + 0.854419i) q^{47} -4.63467i q^{48} +(0.775711 - 0.631088i) q^{49} +(-0.136267 + 0.655751i) q^{51} +(-1.21206 - 0.628038i) q^{53} +(-0.663521 - 1.86697i) q^{54} +(0.211425 + 0.347674i) q^{57} +(-0.116615 - 0.0709153i) q^{61} +(0.616549 + 2.20049i) q^{62} +(3.45995 - 4.90164i) q^{64} +(-1.43215 + 1.33753i) q^{68} +(1.49389 + 0.418569i) q^{69} +(1.02949 - 3.67429i) q^{72} +(-0.0812465 + 1.18778i) q^{76} +(1.11059 - 0.311173i) q^{79} +(-0.0682424 - 0.997669i) q^{81} +(-0.751719 + 0.530621i) q^{83} +(2.86464 + 3.52111i) q^{92} +1.15336i q^{93} +(-1.96292 + 0.269797i) q^{94} +(4.16341 - 3.38719i) q^{96} +(1.93993 + 0.403122i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.25042	+	1.53697i	1.25042	+	1.53697i	0.730836	+	0.682553i	$0.239130\pi$
$2$	1.25042	+	1.53697i	1.25042	+	1.53697i	0.519584	+	0.854419i	$0.326087\pi$
$3$	0.398401	+	0.917211i	0.398401	+	0.917211i
$3$	0.398401	+	0.917211i	0.398401	+	0.917211i
$4$	−0.595279	+	2.86464i	−0.595279	+	2.86464i
$5$		0			0
$5$		0			0
$6$	−0.911560	+	1.75923i	−0.911560	+	1.75923i
$7$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$7$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$8$	−3.38799	+	1.75551i	−3.38799	+	1.75551i
$9$	−0.682553	+	0.730836i	−0.682553	+	0.730836i
$10$		0			0
$11$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$11$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$12$	−2.86464	+	0.595279i	−2.86464	+	0.595279i
$13$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$13$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$14$		0			0
$15$		0			0
$16$	−4.25097	−	1.84646i	−4.25097	−	1.84646i
$17$	0.547173	+	0.386237i	0.547173	+	0.386237i	0.816970	−	0.576680i	$-0.195652\pi$
$17$	0.547173	+	0.386237i	0.547173	+	0.386237i	−0.269797	+	0.962917i	$0.586957\pi$
$18$	−1.97675	−	0.135214i	−1.97675	−	0.135214i
$19$	0.403122	−	0.0554078i	0.403122	−	0.0554078i	0.0682424	−	0.997669i	$-0.478261\pi$
$19$	0.403122	−	0.0554078i	0.403122	−	0.0554078i	0.334880	+	0.942261i	$0.391304\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.979084	−	1.20346i	0.979084	−	1.20346i		−	1.00000i	$-0.5\pi$
$23$	0.979084	−	1.20346i	0.979084	−	1.20346i	0.979084	−	0.203456i	$-0.0652174\pi$
$24$	−2.95995	−	2.40810i	−2.95995	−	2.40810i
$25$		0			0
$26$		0			0
$27$	−0.942261	−	0.334880i	−0.942261	−	0.334880i
$28$		0			0
$29$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$29$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$30$		0			0
$31$	1.05788	+	0.459500i	1.05788	+	0.459500i	0.854419	−	0.519584i	$-0.173913\pi$
$31$	1.05788	+	0.459500i	1.05788	+	0.459500i	0.203456	+	0.979084i	$0.434783\pi$
$32$	−1.44806	−	5.16819i	−1.44806	−	5.16819i
$33$		0			0
$34$	0.0905606	+	1.32395i	0.0905606	+	1.32395i
$35$		0			0
$36$	−1.68727	−	2.39032i	−1.68727	−	2.39032i
$37$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$37$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$38$	0.589232	+	0.550304i	0.589232	+	0.550304i
$39$		0			0
$40$		0			0
$41$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$41$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$42$		0			0
$43$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$43$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$44$		0			0
$45$		0			0
$46$	3.07395			3.07395
$47$	−0.519584	+	0.854419i	−0.519584	+	0.854419i
$47$	−0.519584	+	0.854419i	−0.519584	+	0.854419i
$48$		−	4.63467i		−	4.63467i
$49$	0.775711	−	0.631088i	0.775711	−	0.631088i
$50$		0			0
$51$	−0.136267	+	0.655751i	−0.136267	+	0.655751i
$52$		0			0
$53$	−1.21206	−	0.628038i	−1.21206	−	0.628038i	−0.269797	−	0.962917i	$-0.586957\pi$
$53$	−1.21206	−	0.628038i	−1.21206	−	0.628038i	−0.942261	+	0.334880i	$0.891304\pi$
$54$	−0.663521	−	1.86697i	−0.663521	−	1.86697i
$55$		0			0
$56$		0			0
$57$	0.211425	+	0.347674i	0.211425	+	0.347674i
$58$		0			0
$59$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$59$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$60$		0			0
$61$	−0.116615	−	0.0709153i	−0.116615	−	0.0709153i	0.460065	−	0.887885i	$-0.347826\pi$
$61$	−0.116615	−	0.0709153i	−0.116615	−	0.0709153i	−0.576680	+	0.816970i	$0.695652\pi$
$62$	0.616549	+	2.20049i	0.616549	+	2.20049i
$63$		0			0
$64$	3.45995	−	4.90164i	3.45995	−	4.90164i
$65$		0			0
$66$		0			0
$67$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$67$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$68$	−1.43215	+	1.33753i	−1.43215	+	1.33753i
$69$	1.49389	+	0.418569i	1.49389	+	0.418569i
$70$		0			0
$71$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$71$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$72$	1.02949	−	3.67429i	1.02949	−	3.67429i
$73$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$73$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$74$		0			0
$75$		0			0
$76$	−0.0812465	+	1.18778i	−0.0812465	+	1.18778i
$77$		0			0
$78$		0			0
$79$	1.11059	−	0.311173i	1.11059	−	0.311173i	0.334880	−	0.942261i	$-0.391304\pi$
$79$	1.11059	−	0.311173i	1.11059	−	0.311173i	0.775711	+	0.631088i	$0.217391\pi$
$80$		0			0
$81$	−0.0682424	−	0.997669i	−0.0682424	−	0.997669i
$82$		0			0
$83$	−0.751719	+	0.530621i	−0.751719	+	0.530621i	−0.887885	−	0.460065i	$-0.847826\pi$
$83$	−0.751719	+	0.530621i	−0.751719	+	0.530621i	0.136167	+	0.990686i	$0.456522\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$89$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$90$		0			0
$91$		0			0
$92$	2.86464	+	3.52111i	2.86464	+	3.52111i
$93$			1.15336i			1.15336i
$94$	−1.96292	+	0.269797i	−1.96292	+	0.269797i
$95$		0			0
$96$	4.16341	−	3.38719i	4.16341	−	3.38719i
$97$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$97$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$98$	1.93993	+	0.403122i	1.93993	+	0.403122i
$99$		0			0
$100$		0			0
$101$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$101$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$102$	−1.17826	+	0.610526i	−1.17826	+	0.610526i
$103$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$103$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$104$		0			0
$105$		0			0
$106$	−0.550304	−	2.64821i	−0.550304	−	2.64821i
$107$	−1.83015	+	0.125185i	−1.83015	+	0.125185i	−0.942261	−	0.334880i	$-0.891304\pi$
$107$	−1.83015	+	0.125185i	−1.83015	+	0.125185i	−0.887885	+	0.460065i	$0.847826\pi$
$108$	1.52022	−	2.49989i	1.52022	−	2.49989i
$109$	−0.886009	+	0.248248i	−0.886009	+	0.248248i	−0.682553	−	0.730836i	$-0.739130\pi$
$109$	−0.886009	+	0.248248i	−0.886009	+	0.248248i	−0.203456	+	0.979084i	$0.565217\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.232687	+	1.69292i	0.232687	+	1.69292i	0.631088	+	0.775711i	$0.282609\pi$
$113$	0.232687	+	1.69292i	0.232687	+	1.69292i	−0.398401	+	0.917211i	$0.630435\pi$
$114$	−0.269995	+	0.759692i	−0.269995	+	0.759692i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.334880	+	0.942261i	−0.334880	+	0.942261i
$122$	−0.0368232	−	0.267908i	−0.0368232	−	0.267908i
$123$		0			0
$124$	−1.94603	+	2.75690i	−1.94603	+	2.75690i
$125$		0			0
$126$		0			0
$127$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$127$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$128$	6.50538	−	0.444980i	6.50538	−	0.444980i
$129$		0			0
$130$		0			0
$131$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$131$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−2.53186	−	0.347996i	−2.53186	−	0.347996i
$137$	0.900885	+	0.187206i	0.900885	+	0.187206i	0.631088	−	0.775711i	$-0.282609\pi$
$137$	0.900885	+	0.187206i	0.900885	+	0.187206i	0.269797	+	0.962917i	$0.413043\pi$
$138$	1.22466	+	2.81946i	1.22466	+	2.81946i
$139$	1.49389	−	1.21537i	1.49389	−	1.21537i	0.576680	−	0.816970i	$-0.304348\pi$
$139$	1.49389	−	1.21537i	1.49389	−	1.21537i	0.917211	−	0.398401i	$-0.130435\pi$
$140$		0			0
$141$	−0.990686	−	0.136167i	−0.990686	−	0.136167i
$142$		0			0
$143$		0			0
$144$	4.25097	−	1.84646i	4.25097	−	1.84646i
$145$		0			0
$146$		0			0
$147$	0.887885	+	0.460065i	0.887885	+	0.460065i
$148$		0			0
$149$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$149$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$150$		0			0
$151$	−0.116615	+	0.0709153i	−0.116615	+	0.0709153i	−0.576680	−	0.816970i	$-0.695652\pi$
$151$	−0.116615	+	0.0709153i	−0.116615	+	0.0709153i	0.460065	+	0.887885i	$0.347826\pi$
$152$	−1.26850	+	0.895407i	−1.26850	+	0.895407i
$153$	−0.655751	+	0.136267i	−0.655751	+	0.136267i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$157$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$158$	1.86697	+	1.31785i	1.86697	+	1.31785i
$159$	0.0931581	−	1.36192i	0.0931581	−	1.36192i
$160$		0			0
$161$		0			0
$162$	1.44806	−	1.35239i	1.44806	−	1.35239i
$163$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$163$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$164$		0			0
$165$		0			0
$166$	−1.75551	−	0.491872i	−1.75551	−	0.491872i
$167$	−0.997669	+	0.931758i	−0.997669	+	0.931758i	−0.997669	−	0.0682424i	$-0.978261\pi$
$167$	−0.997669	+	0.931758i	−0.997669	+	0.931758i			1.00000i	$0.5\pi$
$168$		0			0
$169$	0.990686	−	0.136167i	0.990686	−	0.136167i
$170$		0			0
$171$	−0.234658	+	0.332435i	−0.234658	+	0.332435i
$172$		0			0
$173$	−0.461039	−	1.64547i	−0.461039	−	1.64547i	−0.730836	−	0.682553i	$-0.760870\pi$
$173$	−0.461039	−	1.64547i	−0.461039	−	1.64547i	0.269797	−	0.962917i	$-0.413043\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$179$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$180$		0			0
$181$	−0.572255	−	1.61017i	−0.572255	−	1.61017i	−0.775711	−	0.631088i	$-0.782609\pi$
$181$	−0.572255	−	1.61017i	−0.572255	−	1.61017i	0.203456	−	0.979084i	$-0.434783\pi$
$182$		0			0
$183$	0.0185847	−	0.135214i	0.0185847	−	0.135214i
$184$	−1.20444	+	5.79609i	−1.20444	+	5.79609i
$185$		0			0
$186$	−1.77268	+	1.44219i	−1.77268	+	1.44219i
$187$		0			0
$188$	−2.13831	−	1.99704i	−2.13831	−	1.99704i
$189$		0			0
$190$		0			0
$191$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$191$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$192$	5.87429	+	1.22069i	5.87429	+	1.22069i
$193$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$193$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$194$		0			0
$195$		0			0
$196$	1.34607	+	2.59781i	1.34607	+	2.59781i
$197$	−0.0997480	−	0.0931581i	−0.0997480	−	0.0931581i	0.631088	−	0.775711i	$-0.282609\pi$
$197$	−0.0997480	−	0.0931581i	−0.0997480	−	0.0931581i	−0.730836	+	0.682553i	$0.760870\pi$
$198$		0			0
$199$	0.787230	+	1.11525i	0.787230	+	1.11525i	0.990686	+	0.136167i	$0.0434783\pi$
$199$	0.787230	+	1.11525i	0.787230	+	1.11525i	−0.203456	+	0.979084i	$0.565217\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−1.79737	−	0.780709i	−1.79737	−	0.780709i
$205$		0			0
$206$		0			0
$207$	0.211252	+	1.53697i	0.211252	+	1.53697i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.42298	+	1.15768i	1.42298	+	1.15768i	0.962917	+	0.269797i	$0.0869565\pi$
$211$	1.42298	+	1.15768i	1.42298	+	1.15768i	0.460065	+	0.887885i	$0.347826\pi$
$212$	2.52061	−	3.09825i	2.52061	−	3.09825i
$213$		0			0
$214$	−2.48086	−	2.65635i	−2.48086	−	2.65635i
$215$		0			0
$216$	3.78025	−	0.519584i	3.78025	−	0.519584i
$217$		0			0
$218$	−1.48943	−	1.05136i	−1.48943	−	1.05136i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$223$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$224$		0			0
$225$		0			0
$226$	−2.31102	+	2.47450i	−2.31102	+	2.47450i
$227$	0.121183	−	0.0627919i	0.121183	−	0.0627919i	−0.398401	−	0.917211i	$-0.630435\pi$
$227$	0.121183	−	0.0627919i	0.121183	−	0.0627919i	0.519584	+	0.854419i	$0.326087\pi$
$228$	−1.12182	+	0.398693i	−1.12182	+	0.398693i
$229$	0.0627919	−	0.121183i	0.0627919	−	0.121183i	−0.854419	−	0.519584i	$-0.826087\pi$
$229$	0.0627919	−	0.121183i	0.0627919	−	0.121183i	0.917211	+	0.398401i	$0.130435\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.861502	+	1.05893i	0.861502	+	1.05893i	0.997669	+	0.0682424i	$0.0217391\pi$
$233$	0.861502	+	1.05893i	0.861502	+	1.05893i	−0.136167	+	0.990686i	$0.543478\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.727872	+	0.894675i	0.727872	+	0.894675i
$238$		0			0
$239$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$239$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$240$		0			0
$241$	0.628038	−	1.21206i	0.628038	−	1.21206i	−0.334880	−	0.942261i	$-0.608696\pi$
$241$	0.628038	−	1.21206i	0.628038	−	1.21206i	0.962917	−	0.269797i	$-0.0869565\pi$
$242$	−1.86697	+	0.663521i	−1.86697	+	0.663521i
$243$	0.887885	−	0.460065i	0.887885	−	0.460065i
$244$	0.272565	−	0.291846i	0.272565	−	0.291846i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−4.39073	+	0.300334i	−4.39073	+	0.300334i
$249$	−0.786177	−	0.478085i	−0.786177	−	0.478085i
$250$		0			0
$251$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$251$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	4.72321	+	5.05732i	4.72321	+	5.05732i
$257$	0.180699	−	0.644923i	0.180699	−	0.644923i	−0.816970	−	0.576680i	$-0.804348\pi$
$257$	0.180699	−	0.644923i	0.180699	−	0.644923i	0.997669	−	0.0682424i	$-0.0217391\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.211252	−	1.53697i	−0.211252	−	1.53697i	−0.730836	−	0.682553i	$-0.760870\pi$
$263$	−0.211252	−	1.53697i	−0.211252	−	1.53697i	0.519584	−	0.854419i	$-0.326087\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$269$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$270$		0			0
$271$	−0.234658	−	0.332435i	−0.234658	−	0.332435i	0.682553	−	0.730836i	$-0.260870\pi$
$271$	−0.234658	−	0.332435i	−0.234658	−	0.332435i	−0.917211	+	0.398401i	$0.869565\pi$
$272$	−1.61285	−	2.65222i	−1.61285	−	2.65222i
$273$		0			0
$274$	0.838754	+	1.61872i	0.838754	+	1.61872i
$275$		0			0
$276$	−2.08833	+	4.03029i	−2.08833	+	4.03029i
$277$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$277$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$278$	3.73598	+	0.776346i	3.73598	+	0.776346i
$279$	−1.05788	+	0.459500i	−1.05788	+	0.459500i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−1.02949	−	1.69292i	−1.02949	−	1.69292i
$283$		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
$288$	4.76547	+	2.46927i	4.76547	+	2.46927i
$289$	−0.184660	−	0.519584i	−0.184660	−	0.519584i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.61872	−	1.14262i	1.61872	−	1.14262i	0.730836	−	0.682553i	$-0.239130\pi$
$293$	1.61872	−	1.14262i	1.61872	−	1.14262i	0.887885	−	0.460065i	$-0.152174\pi$
$294$	0.403122	+	1.93993i	0.403122	+	1.93993i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.254813	−	0.0905606i	−0.254813	−	0.0905606i
$303$		0			0
$304$	−1.81597	−	0.508811i	−1.81597	−	0.508811i
$305$		0			0
$306$	−1.02940	−	0.837480i	−1.02940	−	0.837480i
$307$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$307$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$311$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$312$		0			0
$313$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$313$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$314$		0			0
$315$		0			0
$316$	0.230287	+	3.36668i	0.230287	+	3.36668i
$317$	1.79605	−	0.373224i	1.79605	−	0.373224i	0.816970	−	0.576680i	$-0.195652\pi$
$317$	1.79605	−	0.373224i	1.79605	−	0.373224i	0.979084	+	0.203456i	$0.0652174\pi$
$318$	2.20973	−	1.55980i	2.20973	−	1.55980i
$319$		0			0
$320$		0			0
$321$	−0.843954	−	1.62876i	−0.843954	−	1.62876i
$322$		0			0
$323$	0.241978	+	0.125383i	0.241978	+	0.125383i
$324$	2.89858	+	0.398401i	2.89858	+	0.398401i
$325$		0			0
$326$		0			0
$327$	−0.580683	−	0.713755i	−0.580683	−	0.713755i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.713755	+	0.580683i	−0.713755	+	0.580683i	−0.917211	−	0.398401i	$-0.869565\pi$
$331$	−0.713755	+	0.580683i	−0.713755	+	0.580683i	0.203456	+	0.979084i	$0.434783\pi$
$332$	−1.07255	−	2.46927i	−1.07255	−	2.46927i
$333$		0			0
$334$	−2.67959	−	0.368301i	−2.67959	−	0.368301i
$335$		0			0
$336$		0			0
$337$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$337$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$338$	1.44806	+	1.35239i	1.44806	+	1.35239i
$339$	−1.46007	+	0.887885i	−1.46007	+	0.887885i
$340$		0			0
$341$		0			0
$342$	−0.804365	+	0.0550200i	−0.804365	+	0.0550200i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.95255	−	2.76613i	1.95255	−	2.76613i
$347$	−1.70486	−	0.116615i	−1.70486	−	0.116615i	−0.816970	−	0.576680i	$-0.804348\pi$
$347$	−1.70486	−	0.116615i	−1.70486	−	0.116615i	−0.887885	+	0.460065i	$0.847826\pi$
$348$		0			0
$349$	0.644923	−	1.81464i	0.644923	−	1.81464i	0.0682424	−	0.997669i	$-0.478261\pi$
$349$	0.644923	−	1.81464i	0.644923	−	1.81464i	0.576680	−	0.816970i	$-0.304348\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.256797	+	0.315646i	−0.256797	+	0.315646i	−0.887885	−	0.460065i	$-0.847826\pi$
$353$	−0.256797	+	0.315646i	−0.256797	+	0.315646i	0.631088	+	0.775711i	$0.282609\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$359$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$360$		0			0
$361$	−0.803480	+	0.225125i	−0.803480	+	0.225125i
$362$	1.75923	−	2.89293i	1.75923	−	2.89293i
$363$	−0.997669	+	0.0682424i	−0.997669	+	0.0682424i
$364$		0			0
$365$		0			0
$366$	0.231058	−	0.140510i	0.231058	−	0.140510i
$367$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$367$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$368$	−6.38419	+	3.30802i	−6.38419	+	3.30802i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−3.30396	−	0.686571i	−3.30396	−	0.686571i
$373$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$373$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$374$		0			0
$375$		0			0
$376$	0.260399	−	3.80690i	0.260399	−	3.80690i
$377$		0			0
$378$		0			0
$379$	−1.68255	+	0.730836i	−1.68255	+	0.730836i	−0.682553	+	0.730836i	$0.739130\pi$
$379$	−1.68255	+	0.730836i	−1.68255	+	0.730836i	−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.61017	+	0.572255i	−1.61017	+	0.572255i	−0.979084	−	0.203456i	$-0.934783\pi$
$383$	−1.61017	+	0.572255i	−1.61017	+	0.572255i	−0.631088	+	0.775711i	$0.717391\pi$
$384$	2.99989	+	5.78952i	2.99989	+	5.78952i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$389$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$390$		0			0
$391$	1.00055	−	0.280340i	1.00055	−	0.280340i
$392$	−1.52022	+	3.49989i	−1.52022	+	3.49989i
$393$		0			0
$394$	0.0184546	−	0.269797i	0.0184546	−	0.269797i
$395$		0			0
$396$		0			0
$397$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$397$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$398$	−0.729742	+	2.60448i	−0.729742	+	2.60448i
$399$		0			0
$400$		0			0
$401$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$401$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.689510	−	2.46089i	−0.689510	−	2.46089i
$409$	−1.64547	−	1.00063i	−1.64547	−	1.00063i	−0.962917	−	0.269797i	$-0.913043\pi$
$409$	−1.64547	−	1.00063i	−1.64547	−	1.00063i	−0.682553	−	0.730836i	$-0.739130\pi$
$410$		0			0
$411$	0.187206	+	0.900885i	0.187206	+	0.900885i
$412$		0			0
$413$		0			0
$414$	−2.09813	+	2.24655i	−2.09813	+	2.24655i
$415$		0			0
$416$		0			0
$417$	1.70992	+	0.886009i	1.70992	+	0.886009i
$418$		0			0
$419$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$419$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$420$		0			0
$421$	1.42298	−	1.15768i	1.42298	−	1.15768i	0.460065	−	0.887885i	$-0.347826\pi$
$421$	1.42298	−	1.15768i	1.42298	−	1.15768i	0.962917	−	0.269797i	$-0.0869565\pi$
$422$			3.63467i			3.63467i
$423$	−0.269797	−	0.962917i	−0.269797	−	0.962917i
$424$	5.20897			5.20897
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.730836	−	5.31723i	0.730836	−	5.31723i
$429$		0			0
$430$		0			0
$431$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$431$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$432$	3.38719	+	3.16341i	3.38719	+	3.16341i
$433$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$433$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$434$		0			0
$435$		0			0
$436$	−0.183719	−	2.68587i	−0.183719	−	2.68587i
$437$	0.328009	−	0.539389i	0.328009	−	0.539389i
$438$		0			0
$439$	0.843954	+	0.366581i	0.843954	+	0.366581i	0.775711	−	0.631088i	$-0.217391\pi$
$439$	0.843954	+	0.366581i	0.843954	+	0.366581i	0.0682424	+	0.997669i	$0.478261\pi$
$440$		0			0
$441$	−0.0682424	+	0.997669i	−0.0682424	+	0.997669i
$442$		0			0
$443$	0.867003	+	0.308133i	0.867003	+	0.308133i	0.730836	−	0.682553i	$-0.239130\pi$
$443$	0.867003	+	0.308133i	0.867003	+	0.308133i	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		−0.682553	−	0.730836i	$-0.739130\pi$
$449$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$450$		0			0
$451$		0			0
$452$	−4.98812	−	0.341197i	−4.98812	−	0.341197i
$453$	−0.111504	−	0.0787081i	−0.111504	−	0.0787081i
$454$	0.248039	+	0.107738i	0.248039	+	0.107738i
$455$		0			0
$456$	−1.32665	−	0.806754i	−1.32665	−	0.806754i
$457$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$457$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$458$	0.264771	−	0.0550200i	0.264771	−	0.0550200i
$459$	−0.386237	−	0.547173i	−0.386237	−	0.547173i
$460$		0			0
$461$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$461$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$462$		0			0
$463$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$463$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$464$		0			0
$465$		0			0
$466$	−0.550304	+	2.64821i	−0.550304	+	2.64821i
$467$	−0.767255	−	1.76640i	−0.767255	−	1.76640i	−0.631088	−	0.775711i	$-0.717391\pi$
$467$	−0.767255	−	1.76640i	−0.767255	−	1.76640i	−0.136167	−	0.990686i	$-0.543478\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.464945	+	2.23744i	−0.464945	+	2.23744i
$475$		0			0
$476$		0			0
$477$	1.28629	−	0.457146i	1.28629	−	0.457146i
$478$		0			0
$479$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$479$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$480$		0			0
$481$		0			0
$482$	2.64821	−	0.550304i	2.64821	−	0.550304i
$483$		0			0
$484$	−2.49989	−	1.52022i	−2.49989	−	1.52022i
$485$		0			0
$486$	1.81734	+	0.789381i	1.81734	+	0.789381i
$487$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$487$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$488$	0.519584	+	0.0355405i	0.519584	+	0.0355405i
$489$		0			0
$490$		0			0
$491$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$491$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−3.64855	−	3.90665i	−3.64855	−	3.90665i
$497$		0			0
$498$	−0.248248	−	1.80614i	−0.248248	−	1.80614i
$499$	−0.105873	+	1.54781i	−0.105873	+	1.54781i	0.576680	+	0.816970i	$0.304348\pi$
$499$	−0.105873	+	1.54781i	−0.105873	+	1.54781i	−0.682553	+	0.730836i	$0.739130\pi$
$500$		0			0
$501$	−1.25209	−	0.543860i	−1.25209	−	0.543860i
$502$		0			0
$503$	−1.02949	+	1.69292i	−1.02949	+	1.69292i	−0.398401	+	0.917211i	$0.630435\pi$
$503$	−1.02949	+	1.69292i	−1.02949	+	1.69292i	−0.631088	+	0.775711i	$0.717391\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.519584	+	0.854419i	0.519584	+	0.854419i
$508$		0			0
$509$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$509$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$510$		0			0
$511$		0			0
$512$	−0.979084	+	7.12337i	−0.979084	+	7.12337i
$513$	−0.398401	−	0.0827887i	−0.398401	−	0.0827887i
$514$	1.21718	−	0.528695i	1.21718	−	0.528695i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.32557	−	1.07843i	1.32557	−	1.07843i
$520$		0			0
$521$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$521$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$522$		0			0
$523$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$523$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$524$		0			0
$525$		0			0
$526$	2.09813	−	2.24655i	2.09813	−	2.24655i
$527$	0.401365	+	0.660017i	0.401365	+	0.660017i
$528$		0			0
$529$	−0.286245	−	1.37749i	−0.286245	−	1.37749i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.894675	+	0.727872i	0.894675	+	0.727872i	0.962917	−	0.269797i	$-0.0869565\pi$
$541$	0.894675	+	0.727872i	0.894675	+	0.727872i	−0.0682424	+	0.997669i	$0.521739\pi$
$542$	0.217522	−	0.776346i	0.217522	−	0.776346i
$543$	1.24888	−	1.16637i	1.24888	−	1.16637i
$544$	1.20381	−	3.38719i	1.20381	−	3.38719i
$545$		0			0
$546$		0			0
$547$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$547$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$548$	−1.07255	+	2.46927i	−1.07255	+	2.46927i
$549$	0.131424	−	0.0368232i	0.131424	−	0.0368232i
$550$		0			0
$551$		0			0
$552$	−5.79609	+	1.20444i	−5.79609	+	1.20444i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	2.59232	+	5.00294i	2.59232	+	5.00294i
$557$	−0.631088	+	0.224289i	−0.631088	+	0.224289i	−0.631088	−	0.775711i	$-0.717391\pi$
$557$	−0.631088	+	0.224289i	−0.631088	+	0.224289i			1.00000i	$0.5\pi$
$558$	−2.02903	−	1.05136i	−2.02903	−	1.05136i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$			0.669759i			0.669759i	0.942261	+	0.334880i	$0.108696\pi$
$563$			0.669759i			0.669759i	−0.942261	+	0.334880i	$0.891304\pi$
$564$	0.979802	−	2.75690i	0.979802	−	2.75690i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$569$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$570$		0			0
$571$	−0.136267	−	0.383417i	−0.136267	−	0.383417i	0.854419	−	0.519584i	$-0.173913\pi$
$571$	−0.136267	−	0.383417i	−0.136267	−	0.383417i	−0.990686	+	0.136167i	$0.956522\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.22069	+	5.87429i	1.22069	+	5.87429i
$577$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$577$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$578$	0.567684	−	0.933516i	0.567684	−	0.933516i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	3.78025	+	1.05918i	3.78025	+	1.05918i
$587$	0.256797	−	0.315646i	0.256797	−	0.315646i	−0.631088	−	0.775711i	$-0.717391\pi$
$587$	0.256797	−	0.315646i	0.256797	−	0.315646i	0.887885	+	0.460065i	$0.152174\pi$
$588$	−1.84646	+	2.26960i	−1.84646	+	2.26960i
$589$	0.451913	+	0.126620i	0.451913	+	0.126620i
$590$		0			0
$591$	0.0457060	−	0.128604i	0.0457060	−	0.128604i
$592$		0			0
$593$	−1.97675	−	0.135214i	−1.97675	−	0.135214i	−0.979084	−	0.203456i	$-0.934783\pi$
$593$	−1.97675	−	0.135214i	−1.97675	−	0.135214i	−0.997669	+	0.0682424i	$0.978261\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.709287	+	1.16637i	−0.709287	+	1.16637i
$598$		0			0
$599$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$599$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$600$		0			0
$601$	1.46007	−	0.887885i	1.46007	−	0.887885i	0.460065	−	0.887885i	$-0.347826\pi$
$601$	1.46007	−	0.887885i	1.46007	−	0.887885i	1.00000			$0$
$602$		0			0
$603$		0			0
$604$	−0.133728	−	0.376275i	−0.133728	−	0.376275i
$605$		0			0
$606$		0			0
$607$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$607$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$608$	−0.870102	−	2.00318i	−0.870102	−	2.00318i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		−	1.95960i		−	1.95960i
$613$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$613$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.02405	−	0.530621i	−1.02405	−	0.530621i	−0.136167	−	0.990686i	$-0.543478\pi$
$617$	−1.02405	−	0.530621i	−1.02405	−	0.530621i	−0.887885	+	0.460065i	$0.847826\pi$
$618$		0			0
$619$	0.0627919	+	0.121183i	0.0627919	+	0.121183i	0.917211	−	0.398401i	$-0.130435\pi$
$619$	0.0627919	+	0.121183i	0.0627919	+	0.121183i	−0.854419	+	0.519584i	$0.826087\pi$
$620$		0			0
$621$	−1.32557	+	0.806094i	−1.32557	+	0.806094i
$622$		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
$631$	0.519540	−	1.46184i	0.519540	−	1.46184i	−0.334880	−	0.942261i	$-0.608696\pi$
$631$	0.519540	−	1.46184i	0.519540	−	1.46184i	0.854419	−	0.519584i	$-0.173913\pi$
$632$	−3.21640	+	3.00391i	−3.21640	+	3.00391i
$633$	−0.494921	+	1.76640i	−0.494921	+	1.76640i
$634$	2.81946	+	2.29380i	2.81946	+	2.29380i
$635$		0			0
$636$	3.84596	+	1.07759i	3.84596	+	1.07759i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$641$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$642$	1.44806	−	3.33376i	1.44806	−	3.33376i
$643$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$643$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$644$		0			0
$645$		0			0
$646$	0.109864	+	0.528695i	0.109864	+	0.528695i
$647$	1.11525	−	0.787230i	1.11525	−	0.787230i	0.136167	−	0.990686i	$-0.456522\pi$
$647$	1.11525	−	0.787230i	1.11525	−	0.787230i	0.979084	+	0.203456i	$0.0652174\pi$
$648$	1.98263	+	3.26029i	1.98263	+	3.26029i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.0554078	+	0.403122i	−0.0554078	+	0.403122i	0.942261	+	0.334880i	$0.108696\pi$
$653$	−0.0554078	+	0.403122i	−0.0554078	+	0.403122i	−0.997669	+	0.0682424i	$0.978261\pi$
$654$	0.370925	−	1.78499i	0.370925	−	1.78499i
$655$		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
$661$	0.614311	−	0.266833i	0.614311	−	0.266833i	−0.0682424	−	0.997669i	$-0.521739\pi$
$661$	0.614311	−	0.266833i	0.614311	−	0.266833i	0.682553	+	0.730836i	$0.260870\pi$
$662$	−1.78499	−	0.370925i	−1.78499	−	0.370925i
$663$		0			0
$664$	1.61530	−	3.11739i	1.61530	−	3.11739i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−2.07526	−	3.41262i	−2.07526	−	3.41262i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$673$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$674$		0			0
$675$		0			0
$676$	−0.199666	+	2.91901i	−0.199666	+	2.91901i
$677$	−0.262234	−	1.90790i	−0.262234	−	1.90790i	−0.398401	−	0.917211i	$-0.630435\pi$
$677$	−0.262234	−	1.90790i	−0.262234	−	1.90790i	0.136167	−	0.990686i	$-0.456522\pi$
$678$	−3.19035	−	1.13385i	−3.19035	−	1.13385i
$679$		0			0
$680$		0			0
$681$	0.105873	+	0.0861339i	0.105873	+	0.0861339i
$682$		0			0
$683$	−0.418569	+	1.49389i	−0.418569	+	1.49389i	0.398401	+	0.917211i	$0.369565\pi$
$683$	−0.418569	+	1.49389i	−0.418569	+	1.49389i	−0.816970	+	0.576680i	$0.804348\pi$
$684$	−0.812619	−	0.870102i	−0.812619	−	0.870102i
$685$		0			0
$686$		0			0
$687$	0.136167	+	0.00931405i	0.136167	+	0.00931405i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.572255	−	0.347996i	−0.572255	−	0.347996i	0.203456	−	0.979084i	$-0.434783\pi$
$691$	−0.572255	−	0.347996i	−0.572255	−	0.347996i	−0.775711	+	0.631088i	$0.782609\pi$
$692$	4.98812	−	0.341197i	4.98812	−	0.341197i
$693$		0			0
$694$	−1.95255	−	2.76613i	−1.95255	−	2.76613i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	3.59547	−	1.27783i	3.59547	−	1.27783i
$699$	−0.628038	+	1.21206i	−0.628038	+	1.21206i
$700$		0			0
$701$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$701$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.806244			−0.806244
$707$		0			0
$708$		0			0
$709$	0.315646	−	1.51897i	0.315646	−	1.51897i	−0.460065	−	0.887885i	$-0.652174\pi$
$709$	0.315646	−	1.51897i	0.315646	−	1.51897i	0.775711	−	0.631088i	$-0.217391\pi$
$710$		0			0
$711$	−0.530621	+	1.02405i	−0.530621	+	1.02405i
$712$		0			0
$713$	1.58874	−	0.823217i	1.58874	−	0.823217i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$719$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$720$		0			0
$721$		0			0
$722$	−1.35070	−	0.953426i	−1.35070	−	0.953426i
$723$	1.36192	+	0.0931581i	1.36192	+	0.0931581i
$724$	4.95321	−	0.680803i	4.95321	−	0.680803i
$725$		0			0
$726$	−1.35239	−	1.44806i	−1.35239	−	1.44806i
$727$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$727$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$728$		0			0
$729$	0.775711	+	0.631088i	0.775711	+	0.631088i
$730$		0			0
$731$		0			0
$732$	0.376275	+	0.133728i	0.376275	+	0.133728i
$733$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$733$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$734$		0			0
$735$		0			0
$736$	−7.63746	−	3.31741i	−7.63746	−	3.31741i
$737$		0			0
$738$		0			0
$739$	0.116615	+	1.70486i	0.116615	+	1.70486i	0.576680	+	0.816970i	$0.304348\pi$
$739$	0.116615	+	1.70486i	0.116615	+	1.70486i	−0.460065	+	0.887885i	$0.652174\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.297386	−	0.277739i	−0.297386	−	0.277739i	0.519584	−	0.854419i	$-0.326087\pi$
$743$	−0.297386	−	0.277739i	−0.297386	−	0.277739i	−0.816970	+	0.576680i	$0.804348\pi$
$744$	−2.02474	−	3.90757i	−2.02474	−	3.90757i
$745$		0			0
$746$		0			0
$747$	0.125291	−	0.911560i	0.125291	−	0.911560i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.83442			−1.83442			−0.917211	−	0.398401i	$-0.869565\pi$
$751$	−1.83442			−1.83442			−0.917211	+	0.398401i	$0.869565\pi$
$752$	3.78639	−	2.67272i	3.78639	−	2.67272i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$757$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$758$	−3.22717	−	1.67219i	−3.22717	−	1.67219i
$759$		0			0
$760$		0			0
$761$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$761$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−2.89293	−	1.75923i	−2.89293	−	1.75923i
$767$		0			0
$768$	−2.75690	+	6.34702i	−2.75690	+	6.34702i
$769$	−0.386237	+	0.547173i	−0.386237	+	0.547173i	−0.962917	−	0.269797i	$-0.913043\pi$
$769$	−0.386237	+	0.547173i	−0.386237	+	0.547173i	0.576680	+	0.816970i	$0.304348\pi$
$770$		0			0
$771$	0.663521	−	0.0911989i	0.663521	−	0.0911989i
$772$		0			0
$773$	1.40747	−	1.31448i	1.40747	−	1.31448i	0.519584	−	0.854419i	$-0.326087\pi$
$773$	1.40747	−	1.31448i	1.40747	−	1.31448i	0.887885	−	0.460065i	$-0.152174\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	1.68198	+	1.18727i	1.68198	+	1.18727i
$783$		0			0
$784$	−4.46281	+	1.25042i	−4.46281	+	1.25042i
$785$		0			0
$786$		0			0
$787$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$787$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$788$	0.326242	−	0.230287i	0.326242	−	0.230287i
$789$	1.32557	−	0.806094i	1.32557	−	0.806094i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−3.66341	+	1.59124i	−3.66341	+	1.59124i
$797$	−1.21537	−	1.49389i	−1.21537	−	1.49389i	−0.816970	−	0.576680i	$-0.804348\pi$
$797$	−1.21537	−	1.49389i	−1.21537	−	1.49389i	−0.398401	−	0.917211i	$-0.630435\pi$
$798$		0			0
$799$	−0.614311	+	0.266833i	−0.614311	+	0.266833i
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$809$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$810$		0			0
$811$	0.347674	+	1.67310i	0.347674	+	1.67310i	0.682553	+	0.730836i	$0.260870\pi$
$811$	0.347674	+	1.67310i	0.347674	+	1.67310i	−0.334880	+	0.942261i	$0.608696\pi$
$812$		0			0
$813$	0.211425	−	0.347674i	0.211425	−	0.347674i
$814$		0			0
$815$		0			0
$816$	1.79008	−	2.53597i	1.79008	−	2.53597i
$817$		0			0
$818$	−0.519584	−	3.78025i	−0.519584	−	3.78025i
$819$		0			0
$820$		0			0
$821$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$821$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$822$	−1.15055	+	1.41421i	−1.15055	+	1.41421i
$823$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$823$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.262234	−	1.90790i	−0.262234	−	1.90790i	−0.398401	−	0.917211i	$-0.630435\pi$
$827$	−0.262234	−	1.90790i	−0.262234	−	1.90790i	0.136167	−	0.990686i	$-0.456522\pi$
$828$	−4.52862	−	0.309766i	−4.52862	−	0.309766i
$829$	−1.14262	+	1.61872i	−1.14262	+	1.61872i	−0.460065	+	0.887885i	$0.652174\pi$
$829$	−1.14262	+	1.61872i	−1.14262	+	1.61872i	−0.682553	+	0.730836i	$0.739130\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.668198	−	0.0457060i	0.668198	−	0.0457060i
$834$	0.776346	+	3.73598i	0.776346	+	3.73598i
$835$		0			0
$836$		0			0
$837$	−0.842917	−	0.787230i	−0.842917	−	0.787230i
$838$		0			0
$839$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$839$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$840$		0			0
$841$	−0.990686	−	0.136167i	−0.990686	−	0.136167i
$842$	3.55865	+	0.739496i	3.55865	+	0.739496i
$843$		0			0
$844$	−4.16341	+	3.38719i	−4.16341	+	3.38719i
$845$		0			0
$846$	1.14262	−	1.61872i	1.14262	−	1.61872i
$847$		0			0
$848$	3.99278	+	4.90779i	3.99278	+	4.90779i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$853$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$854$		0			0
$855$		0			0
$856$	5.98075	−	3.63697i	5.98075	−	3.63697i
$857$	−1.49867	+	1.05788i	−1.49867	+	1.05788i	−0.519584	+	0.854419i	$0.673913\pi$
$857$	−1.49867	+	1.05788i	−1.49867	+	1.05788i	−0.979084	+	0.203456i	$0.934783\pi$
$858$		0			0
$859$	−0.135214	−	1.97675i	−0.135214	−	1.97675i	−0.203456	−	0.979084i	$-0.565217\pi$
$859$	−0.135214	−	1.97675i	−0.135214	−	1.97675i	0.0682424	−	0.997669i	$-0.478261\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.942261	−	0.665120i	−0.942261	−	0.665120i		−	1.00000i	$-0.5\pi$
$863$	−0.942261	−	0.665120i	−0.942261	−	0.665120i	−0.942261	+	0.334880i	$0.891304\pi$
$864$	−0.366272	+	5.35470i	−0.366272	+	5.35470i
$865$		0			0
$866$		0			0
$867$	0.402999	−	0.376375i	0.402999	−	0.376375i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	2.56599	−	2.39646i	2.56599	−	2.39646i
$873$		0			0
$874$	1.23917	−	0.170321i	1.23917	−	0.170321i
$875$		0			0
$876$		0			0
$877$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$877$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$878$	0.491872	+	1.75551i	0.491872	+	1.75551i
$879$	1.69292	+	1.02949i	1.69292	+	1.02949i
$880$		0			0
$881$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$881$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$882$	−1.61872	+	1.14262i	−1.61872	+	1.14262i
$883$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$883$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$884$		0			0
$885$		0			0
$886$	0.610526	+	1.71785i	0.610526	+	1.71785i
$887$	0.361291	+	0.187206i	0.361291	+	0.187206i	0.631088	−	0.775711i	$-0.282609\pi$
$887$	0.361291	+	0.187206i	0.361291	+	0.187206i	−0.269797	+	0.962917i	$0.586957\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.162114	+	0.373224i	−0.162114	+	0.373224i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−0.420634	−	0.811787i	−0.420634	−	0.811787i
$902$		0			0
$903$		0			0
$904$	−3.76029	−	5.32712i	−3.76029	−	5.32712i
$905$		0			0
$906$	−0.0184546	−	0.269797i	−0.0184546	−	0.269797i
$907$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$907$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$908$	0.107738	+	0.384524i	0.107738	+	0.384524i
$909$		0			0
$910$		0			0
$911$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$911$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$912$	−0.256797	−	1.86834i	−0.256797	−	1.86834i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.309766	+	0.252014i	0.309766	+	0.252014i
$917$		0			0
$918$	0.358032	−	1.27783i	0.358032	−	1.27783i
$919$	1.05893	+	1.13384i	1.05893	+	1.13384i	0.990686	+	0.136167i	$0.0434783\pi$
$919$	1.05893	+	1.13384i	1.05893	+	1.13384i	0.0682424	+	0.997669i	$0.478261\pi$
$920$		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		−0.576680	−	0.816970i	$-0.695652\pi$
$929$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$930$		0			0
$931$	0.277739	−	0.297386i	0.277739	−	0.297386i
$932$	−3.54628	+	1.83753i	−3.54628	+	1.83753i
$933$		0			0
$934$	1.75551	−	3.38799i	1.75551	−	3.38799i
$935$		0			0
$936$		0			0
$937$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$937$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$938$		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
$947$	1.81464	−	0.644923i	1.81464	−	0.644923i	0.816970	−	0.576680i	$-0.195652\pi$
$947$	1.81464	−	0.644923i	1.81464	−	0.644923i	0.997669	−	0.0682424i	$-0.0217391\pi$
$948$	−2.99621	+	1.55251i	−2.99621	+	1.55251i
$949$		0			0
$950$		0			0
$951$	1.05788	+	1.49867i	1.05788	+	1.49867i
$952$		0			0
$953$	1.97675	−	0.135214i	1.97675	−	0.135214i	0.979084	−	0.203456i	$-0.0652174\pi$
$953$	1.97675	−	0.135214i	1.97675	−	0.135214i	0.997669	+	0.0682424i	$0.0217391\pi$
$954$	2.31102	+	1.40536i	2.31102	+	1.40536i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.225407	+	0.241352i	0.225407	+	0.241352i
$962$		0			0
$963$	1.15768	−	1.42298i	1.15768	−	1.42298i
$964$	3.09825	+	2.52061i	3.09825	+	2.52061i
$965$		0			0
$966$		0			0
$967$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$967$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$968$	−0.519584	−	3.78025i	−0.519584	−	3.78025i
$969$	−0.0185983	+	0.271898i	−0.0185983	+	0.271898i
$970$		0			0
$971$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$971$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$972$	0.789381	+	2.81734i	0.789381	+	2.81734i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.364786	+	0.516785i	0.364786	+	0.516785i
$977$	0.887885	+	1.46007i	0.887885	+	1.46007i	0.887885	+	0.460065i	$0.152174\pi$
$977$	0.887885	+	1.46007i	0.887885	+	1.46007i			1.00000i	$0.5\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.423320	−	0.816970i	0.423320	−	0.816970i
$982$		0			0
$983$	0.133630	+	0.0277687i	0.133630	+	0.0277687i	0.269797	−	0.962917i	$-0.413043\pi$
$983$	0.133630	+	0.0277687i	0.133630	+	0.0277687i	−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
$991$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	0.203456	+	0.979084i	$0.434783\pi$
$991$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	−0.576680	+	0.816970i	$0.695652\pi$
$992$	0.842917	−	6.13268i	0.842917	−	6.13268i
$993$	−0.816970	−	0.423320i	−0.816970	−	0.423320i
$994$		0			0
$995$		0			0
$996$	1.83753	−	1.96752i	1.83753	−	1.96752i
$997$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$997$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$998$	−2.51132	+	1.77268i	−2.51132	+	1.77268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bd.a.401.2		44
3.2	odd	2	inner	3525.1.bd.a.401.1		44
5.2	odd	4		705.1.p.b.119.1	yes	22
5.3	odd	4		705.1.p.a.119.1	✓	22
5.4	even	2	inner	3525.1.bd.a.401.1		44
15.2	even	4		705.1.p.a.119.1	✓	22
15.8	even	4		705.1.p.b.119.1	yes	22
15.14	odd	2	CM	3525.1.bd.a.401.2		44
47.32	even	23	inner	3525.1.bd.a.1301.1		44
141.32	odd	46	inner	3525.1.bd.a.1301.2		44
235.32	odd	92		705.1.p.b.314.1	yes	22
235.79	even	46	inner	3525.1.bd.a.1301.2		44
235.173	odd	92		705.1.p.a.314.1	yes	22
705.32	even	92		705.1.p.a.314.1	yes	22
705.173	even	92		705.1.p.b.314.1	yes	22
705.314	odd	46	inner	3525.1.bd.a.1301.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.1.p.a.119.1	✓	22	5.3	odd	4
705.1.p.a.119.1	✓	22	15.2	even	4
705.1.p.a.314.1	yes	22	235.173	odd	92
705.1.p.a.314.1	yes	22	705.32	even	92
705.1.p.b.119.1	yes	22	5.2	odd	4
705.1.p.b.119.1	yes	22	15.8	even	4
705.1.p.b.314.1	yes	22	235.32	odd	92
705.1.p.b.314.1	yes	22	705.173	even	92
3525.1.bd.a.401.1		44	3.2	odd	2	inner
3525.1.bd.a.401.1		44	5.4	even	2	inner
3525.1.bd.a.401.2		44	1.1	even	1	trivial
3525.1.bd.a.401.2		44	15.14	odd	2	CM
3525.1.bd.a.1301.1		44	47.32	even	23	inner
3525.1.bd.a.1301.1		44	705.314	odd	46	inner
3525.1.bd.a.1301.2		44	141.32	odd	46	inner
3525.1.bd.a.1301.2		44	235.79	even	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)

\(f(q)\)	\(=\)	\(q+(1.25042 + 1.53697i) q^{2} +(0.398401 + 0.917211i) q^{3} +(-0.595279 + 2.86464i) q^{4} +(-0.911560 + 1.75923i) q^{6} +(-3.38799 + 1.75551i) q^{8} +(-0.682553 + 0.730836i) q^{9} +O(q^{10})\)	\(q+(1.25042 + 1.53697i) q^{2} +(0.398401 + 0.917211i) q^{3} +(-0.595279 + 2.86464i) q^{4} +(-0.911560 + 1.75923i) q^{6} +(-3.38799 + 1.75551i) q^{8} +(-0.682553 + 0.730836i) q^{9} +(-2.86464 + 0.595279i) q^{12} +(-4.25097 - 1.84646i) q^{16} +(0.547173 + 0.386237i) q^{17} +(-1.97675 - 0.135214i) q^{18} +(0.403122 - 0.0554078i) q^{19} +(0.979084 - 1.20346i) q^{23} +(-2.95995 - 2.40810i) q^{24} +(-0.942261 - 0.334880i) q^{27} +(1.05788 + 0.459500i) q^{31} +(-1.44806 - 5.16819i) q^{32} +(0.0905606 + 1.32395i) q^{34} +(-1.68727 - 2.39032i) q^{36} +(0.589232 + 0.550304i) q^{38} +3.07395 q^{46} +(-0.519584 + 0.854419i) q^{47} -4.63467i q^{48} +(0.775711 - 0.631088i) q^{49} +(-0.136267 + 0.655751i) q^{51} +(-1.21206 - 0.628038i) q^{53} +(-0.663521 - 1.86697i) q^{54} +(0.211425 + 0.347674i) q^{57} +(-0.116615 - 0.0709153i) q^{61} +(0.616549 + 2.20049i) q^{62} +(3.45995 - 4.90164i) q^{64} +(-1.43215 + 1.33753i) q^{68} +(1.49389 + 0.418569i) q^{69} +(1.02949 - 3.67429i) q^{72} +(-0.0812465 + 1.18778i) q^{76} +(1.11059 - 0.311173i) q^{79} +(-0.0682424 - 0.997669i) q^{81} +(-0.751719 + 0.530621i) q^{83} +(2.86464 + 3.52111i) q^{92} +1.15336i q^{93} +(-1.96292 + 0.269797i) q^{94} +(4.16341 - 3.38719i) q^{96} +(1.93993 + 0.403122i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 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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