LMFDB - Embedded newform 3525.1.bg.a.1643.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,1,Mod(107,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(92))

chi = DirichletCharacter(H, H._module([46, 23, 22]))

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

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

chi := DirichletCharacter("3525.107");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.75920416953$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$2$ over $\Q(\zeta_{92})$
Coefficient field:	$\Q(\zeta_{184})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{88} - x^{84} + x^{80} - x^{76} + x^{72} - x^{68} + x^{64} - x^{60} + x^{56} - x^{52} + x^{48} + \cdots + 1 $ x^88 - x^84 + x^80 - x^76 + x^72 - x^68 + x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{46}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{46} - \cdots)$

Embedding invariants

Embedding label			1643.1
Root			$-0.604236 - 0.796805i$ of defining polynomial
Character	$\chi$	$=$	3525.1643
Dual form			3525.1.bg.a.3407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.404693 - 0.533668i) q^{2} +(-0.236764 + 0.971567i) q^{3} +(0.148772 - 0.530974i) q^{4} +(0.614311 - 0.266833i) q^{6} +(-0.966633 + 0.381191i) q^{8} +(-0.887885 - 0.460065i) q^{9} +O(q^{10})$	\(q+(-0.404693 - 0.533668i) q^{2} +(-0.236764 + 0.971567i) q^{3} +(0.148772 - 0.530974i) q^{4} +(0.614311 - 0.266833i) q^{6} +(-0.966633 + 0.381191i) q^{8} +(-0.887885 - 0.460065i) q^{9} +(0.480653 + 0.270258i) q^{12} +(0.123473 + 0.0750854i) q^{16} +(-0.00465974 + 0.136405i) q^{17} +(0.113799 + 0.660021i) q^{18} +(0.180699 - 0.508438i) q^{19} +(-0.216997 - 0.164554i) q^{23} +(-0.141488 - 1.02940i) q^{24} +(0.657204 - 0.753713i) q^{27} +(0.759461 - 1.24888i) q^{31} +(0.0963627 + 0.937352i) q^{32} +(0.0746808 - 0.0527155i) q^{34} +(-0.376375 + 0.402999i) q^{36} +(-0.344464 + 0.109328i) q^{38} +0.182398i q^{46} +(0.836182 - 0.548452i) q^{47} +(-0.102184 + 0.102184i) q^{48} +(0.136167 - 0.990686i) q^{49} +(-0.131424 - 0.0368232i) q^{51} +(0.337554 - 0.855977i) q^{53} +(-0.668198 - 0.0457060i) q^{54} +(0.451198 + 0.295941i) q^{57} +(0.234658 - 1.12924i) q^{61} +(-0.973836 + 0.100113i) q^{62} +(0.566851 - 0.529402i) q^{64} +(0.0717345 + 0.0227675i) q^{68} +(0.211252 - 0.171866i) q^{69} +(1.03363 + 0.106261i) q^{72} +(-0.243085 - 0.171588i) q^{76} +(-0.861502 + 1.05893i) q^{79} +(0.576680 + 0.816970i) q^{81} +(-0.0626292 - 1.83335i) q^{83} +(-0.119657 + 0.0907386i) q^{92} +(1.03356 + 1.03356i) q^{93} +(-0.631088 - 0.224289i) q^{94} +(-0.933516 - 0.128309i) q^{96} +(-0.583803 + 0.328256i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{6}+O(q^{10}) $ 88 * q - 8 * q^6	$ 88 q - 8 q^{6} + 20 q^{16} - 12 q^{36} - 8 q^{51} + 8 q^{61} - 92 q^{76} + 4 q^{81} - 68 q^{96}+O(q^{100}) $ 88 * q - 8 * q^6 + 20 * q^16 - 12 * q^36 - 8 * q^51 + 8 * q^61 - 92 * q^76 + 4 * q^81 - 68 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{41}{46}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.404693	−	0.533668i	−0.404693	−	0.533668i	0.548452	−	0.836182i	$-0.315217\pi$
$2$	−0.404693	−	0.533668i	−0.404693	−	0.533668i	−0.953145	+	0.302515i	$0.902174\pi$
$3$	−0.236764	+	0.971567i	−0.236764	+	0.971567i
$3$	−0.236764	+	0.971567i	−0.236764	+	0.971567i
$4$	0.148772	−	0.530974i	0.148772	−	0.530974i
$5$		0			0
$5$		0			0
$6$	0.614311	−	0.266833i	0.614311	−	0.266833i
$7$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$7$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$8$	−0.966633	+	0.381191i	−0.966633	+	0.381191i
$9$	−0.887885	−	0.460065i	−0.887885	−	0.460065i
$10$		0			0
$11$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$11$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$12$	0.480653	+	0.270258i	0.480653	+	0.270258i
$13$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$13$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$14$		0			0
$15$		0			0
$16$	0.123473	+	0.0750854i	0.123473	+	0.0750854i
$17$	−0.00465974	+	0.136405i	−0.00465974	+	0.136405i	0.994757	+	0.102264i	$0.0326087\pi$
$17$	−0.00465974	+	0.136405i	−0.00465974	+	0.136405i	−0.999417	+	0.0341411i	$0.989130\pi$
$18$	0.113799	+	0.660021i	0.113799	+	0.660021i
$19$	0.180699	−	0.508438i	0.180699	−	0.508438i	−0.816970	−	0.576680i	$-0.804348\pi$
$19$	0.180699	−	0.508438i	0.180699	−	0.508438i	0.997669	+	0.0682424i	$0.0217391\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.216997	−	0.164554i	−0.216997	−	0.164554i	0.490110	−	0.871660i	$-0.336957\pi$
$23$	−0.216997	−	0.164554i	−0.216997	−	0.164554i	−0.707107	+	0.707107i	$0.750000\pi$
$24$	−0.141488	−	1.02940i	−0.141488	−	1.02940i
$25$		0			0
$26$		0			0
$27$	0.657204	−	0.753713i	0.657204	−	0.753713i
$28$		0			0
$29$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$29$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$30$		0			0
$31$	0.759461	−	1.24888i	0.759461	−	1.24888i	−0.203456	−	0.979084i	$-0.565217\pi$
$31$	0.759461	−	1.24888i	0.759461	−	1.24888i	0.962917	−	0.269797i	$-0.0869565\pi$
$32$	0.0963627	+	0.937352i	0.0963627	+	0.937352i
$33$		0			0
$34$	0.0746808	−	0.0527155i	0.0746808	−	0.0527155i
$35$		0			0
$36$	−0.376375	+	0.402999i	−0.376375	+	0.402999i
$37$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$37$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$38$	−0.344464	+	0.109328i	−0.344464	+	0.109328i
$39$		0			0
$40$		0			0
$41$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$41$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$42$		0			0
$43$		0			0		−0.490110	−	0.871660i	$-0.663043\pi$
$43$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$44$		0			0
$45$		0			0
$46$			0.182398i			0.182398i
$47$	0.836182	−	0.548452i	0.836182	−	0.548452i
$47$	0.836182	−	0.548452i	0.836182	−	0.548452i
$48$	−0.102184	+	0.102184i	−0.102184	+	0.102184i
$49$	0.136167	−	0.990686i	0.136167	−	0.990686i
$50$		0			0
$51$	−0.131424	−	0.0368232i	−0.131424	−	0.0368232i
$52$		0			0
$53$	0.337554	−	0.855977i	0.337554	−	0.855977i	−0.657204	−	0.753713i	$-0.728261\pi$
$53$	0.337554	−	0.855977i	0.337554	−	0.855977i	0.994757	−	0.102264i	$-0.0326087\pi$
$54$	−0.668198	−	0.0457060i	−0.668198	−	0.0457060i
$55$		0			0
$56$		0			0
$57$	0.451198	+	0.295941i	0.451198	+	0.295941i
$58$		0			0
$59$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$59$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$60$		0			0
$61$	0.234658	−	1.12924i	0.234658	−	1.12924i	−0.682553	−	0.730836i	$-0.739130\pi$
$61$	0.234658	−	1.12924i	0.234658	−	1.12924i	0.917211	−	0.398401i	$-0.130435\pi$
$62$	−0.973836	+	0.100113i	−0.973836	+	0.100113i
$63$		0			0
$64$	0.566851	−	0.529402i	0.566851	−	0.529402i
$65$		0			0
$66$		0			0
$67$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$67$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$68$	0.0717345	+	0.0227675i	0.0717345	+	0.0227675i
$69$	0.211252	−	0.171866i	0.211252	−	0.171866i
$70$		0			0
$71$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$71$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$72$	1.03363	+	0.106261i	1.03363	+	0.106261i
$73$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$73$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$74$		0			0
$75$		0			0
$76$	−0.243085	−	0.171588i	−0.243085	−	0.171588i
$77$		0			0
$78$		0			0
$79$	−0.861502	+	1.05893i	−0.861502	+	1.05893i	0.136167	+	0.990686i	$0.456522\pi$
$79$	−0.861502	+	1.05893i	−0.861502	+	1.05893i	−0.997669	+	0.0682424i	$0.978261\pi$
$80$		0			0
$81$	0.576680	+	0.816970i	0.576680	+	0.816970i
$82$		0			0
$83$	−0.0626292	−	1.83335i	−0.0626292	−	1.83335i	−0.429483	−	0.903075i	$-0.641304\pi$
$83$	−0.0626292	−	1.83335i	−0.0626292	−	1.83335i	0.366854	−	0.930278i	$-0.380435\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$89$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$90$		0			0
$91$		0			0
$92$	−0.119657	+	0.0907386i	−0.119657	+	0.0907386i
$93$	1.03356	+	1.03356i	1.03356	+	1.03356i
$94$	−0.631088	−	0.224289i	−0.631088	−	0.224289i
$95$		0			0
$96$	−0.933516	−	0.128309i	−0.933516	−	0.128309i
$97$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$97$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$98$	−0.583803	+	0.328256i	−0.583803	+	0.328256i
$99$		0			0
$100$		0			0
$101$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$101$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$102$	0.0335349	+	0.0850386i	0.0335349	+	0.0850386i
$103$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$103$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$104$		0			0
$105$		0			0
$106$	−0.593413	+	0.166266i	−0.593413	+	0.166266i
$107$	−1.02406	−	0.176565i	−1.02406	−	0.176565i	−0.366854	−	0.930278i	$-0.619565\pi$
$107$	−1.02406	−	0.176565i	−1.02406	−	0.176565i	−0.657204	+	0.753713i	$0.728261\pi$
$108$	−0.302429	−	0.461090i	−0.302429	−	0.461090i
$109$	−0.618088	−	0.502852i	−0.618088	−	0.502852i	0.269797	−	0.962917i	$-0.413043\pi$
$109$	−0.618088	−	0.502852i	−0.618088	−	0.502852i	−0.887885	+	0.460065i	$0.847826\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.76837	−	0.841001i	1.76837	−	0.841001i	0.796805	−	0.604236i	$-0.206522\pi$
$113$	1.76837	−	0.841001i	1.76837	−	0.841001i	0.971567	−	0.236764i	$-0.0760870\pi$
$114$	−0.0246627	−	0.360555i	−0.0246627	−	0.360555i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.0682424	+	0.997669i	0.0682424	+	0.997669i
$122$	−0.697602	+	0.331765i	−0.697602	+	0.331765i
$123$		0			0
$124$	−0.550137	−	0.589053i	−0.550137	−	0.589053i
$125$		0			0
$126$		0			0
$127$		0			0		−0.548452	−	0.836182i	$-0.684783\pi$
$127$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$128$	0.416666	+	0.0718405i	0.416666	+	0.0718405i
$129$		0			0
$130$		0			0
$131$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$131$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.0474922	−	0.133630i	−0.0474922	−	0.133630i
$137$	−0.694541	+	0.390521i	−0.694541	+	0.390521i	−0.796805	−	0.604236i	$-0.793478\pi$
$137$	−0.694541	+	0.390521i	−0.694541	+	0.390521i	0.102264	+	0.994757i	$0.467391\pi$
$138$	−0.177212	−	0.0431853i	−0.177212	−	0.0431853i
$139$	1.25042	+	0.171866i	1.25042	+	0.171866i	0.730836	−	0.682553i	$-0.239130\pi$
$139$	1.25042	+	0.171866i	1.25042	+	0.171866i	0.519584	+	0.854419i	$0.326087\pi$
$140$		0			0
$141$	0.334880	+	0.942261i	0.334880	+	0.942261i
$142$		0			0
$143$		0			0
$144$	−0.0750854	−	0.123473i	−0.0750854	−	0.123473i
$145$		0			0
$146$		0			0
$147$	0.930278	+	0.366854i	0.930278	+	0.366854i
$148$		0			0
$149$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$149$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$150$		0			0
$151$	1.59976	−	0.332435i	1.59976	−	0.332435i	0.682553	−	0.730836i	$-0.260870\pi$
$151$	1.59976	−	0.332435i	1.59976	−	0.332435i	0.917211	+	0.398401i	$0.130435\pi$
$152$	0.0191423	+	0.560354i	0.0191423	+	0.560354i
$153$	0.0668926	−	0.118968i	0.0668926	−	0.118968i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$157$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$158$	0.913760	+	0.0312150i	0.913760	+	0.0312150i
$159$	0.751719	+	0.530621i	0.751719	+	0.530621i
$160$		0			0
$161$		0			0
$162$	0.202612	−	0.638377i	0.202612	−	0.638377i
$163$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$163$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$164$		0			0
$165$		0			0
$166$	−0.953056	+	0.775368i	−0.953056	+	0.775368i
$167$	−1.69257	−	0.537196i	−1.69257	−	0.537196i	−0.707107	−	0.707107i	$-0.750000\pi$
$167$	−1.69257	−	0.537196i	−1.69257	−	0.537196i	−0.985460	+	0.169910i	$0.945652\pi$
$168$		0			0
$169$	−0.942261	−	0.334880i	−0.942261	−	0.334880i
$170$		0			0
$171$	−0.394354	+	0.368301i	−0.394354	+	0.368301i
$172$		0			0
$173$	0.404779	−	0.0416125i	0.404779	−	0.0416125i	0.102264	−	0.994757i	$-0.467391\pi$
$173$	0.404779	−	0.0416125i	0.404779	−	0.0416125i	0.302515	+	0.953145i	$0.402174\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$179$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$180$		0			0
$181$	1.95360	+	0.133630i	1.95360	+	0.133630i	0.990686	−	0.136167i	$-0.0434783\pi$
$181$	1.95360	+	0.133630i	1.95360	+	0.133630i	0.962917	+	0.269797i	$0.0869565\pi$
$182$		0			0
$183$	1.04157	+	0.495349i	1.04157	+	0.495349i
$184$	0.272482	+	0.0763460i	0.272482	+	0.0763460i
$185$		0			0
$186$	0.133303	−	0.969850i	0.133303	−	0.969850i
$187$		0			0
$188$	−0.166813	−	0.525586i	−0.166813	−	0.525586i
$189$		0			0
$190$		0			0
$191$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$191$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$192$	0.380139	+	0.676077i	0.380139	+	0.676077i
$193$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$193$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$194$		0			0
$195$		0			0
$196$	−0.505771	−	0.219687i	−0.505771	−	0.219687i
$197$	1.09932	−	0.348908i	1.09932	−	0.348908i	0.302515	−	0.953145i	$-0.402174\pi$
$197$	1.09932	−	0.348908i	1.09932	−	0.348908i	0.796805	+	0.604236i	$0.206522\pi$
$198$		0			0
$199$	−1.21206	+	1.29780i	−1.21206	+	1.29780i	−0.269797	+	0.962917i	$0.586957\pi$
$199$	−1.21206	+	1.29780i	−1.21206	+	1.29780i	−0.942261	+	0.334880i	$0.891304\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.0391043	+	0.0643043i	−0.0391043	+	0.0643043i
$205$		0			0
$206$		0			0
$207$	0.116963	+	0.245937i	0.116963	+	0.245937i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.141500	−	1.02949i	−0.141500	−	1.02949i	−0.917211	−	0.398401i	$-0.869565\pi$
$211$	−0.141500	−	1.02949i	−0.141500	−	1.02949i	0.775711	−	0.631088i	$-0.217391\pi$
$212$	−0.404283	−	0.306578i	−0.404283	−	0.306578i
$213$		0			0
$214$	0.320202	+	0.617961i	0.320202	+	0.617961i
$215$		0			0
$216$	−0.347967	+	0.979084i	−0.347967	+	0.979084i
$217$		0			0
$218$	−0.0182199	+	0.533354i	−0.0182199	+	0.533354i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.871660	−	0.490110i	$-0.836957\pi$
$223$		0			0		0.871660	+	0.490110i	$0.163043\pi$
$224$		0			0
$225$		0			0
$226$	−1.16446	−	0.603376i	−1.16446	−	0.603376i
$227$	−1.52002	+	0.599418i	−1.52002	+	0.599418i	−0.971567	−	0.236764i	$-0.923913\pi$
$227$	−1.52002	+	0.599418i	−1.52002	+	0.599418i	−0.548452	+	0.836182i	$0.684783\pi$
$228$	0.224263	−	0.195547i	0.224263	−	0.195547i
$229$	1.49867	−	0.650963i	1.49867	−	0.650963i	0.519584	−	0.854419i	$-0.326087\pi$
$229$	1.49867	−	0.650963i	1.49867	−	0.650963i	0.979084	+	0.203456i	$0.0652174\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.07299	−	1.41494i	−1.07299	−	1.41494i	−0.903075	−	0.429483i	$-0.858696\pi$
$233$	−1.07299	−	1.41494i	−1.07299	−	1.41494i	−0.169910	−	0.985460i	$-0.554348\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.824847	−	1.08772i	−0.824847	−	1.08772i
$238$		0			0
$239$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$239$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$240$		0			0
$241$	0.843954	−	0.366581i	0.843954	−	0.366581i	0.0682424	−	0.997669i	$-0.478261\pi$
$241$	0.843954	−	0.366581i	0.843954	−	0.366581i	0.775711	+	0.631088i	$0.217391\pi$
$242$	0.504806	−	0.440168i	0.504806	−	0.440168i
$243$	−0.930278	+	0.366854i	−0.930278	+	0.366854i
$244$	−0.564685	−	0.292596i	−0.564685	−	0.292596i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.258059	+	1.49671i	−0.258059	+	1.49671i
$249$	1.79605	+	0.373224i	1.79605	+	0.373224i
$250$		0			0
$251$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$251$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.487118	−	0.940096i	−0.487118	−	0.940096i
$257$	−0.204051	+	1.98488i	−0.204051	+	1.98488i	−0.0341411	+	0.999417i	$0.510870\pi$
$257$	−0.204051	+	1.98488i	−0.204051	+	1.98488i	−0.169910	+	0.985460i	$0.554348\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.850966	−	1.78933i	−0.850966	−	1.78933i	−0.548452	−	0.836182i	$-0.684783\pi$
$263$	−0.850966	−	1.78933i	−0.850966	−	1.78933i	−0.302515	−	0.953145i	$-0.597826\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$269$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$270$		0			0
$271$	−1.31448	+	1.40747i	−1.31448	+	1.40747i	−0.460065	+	0.887885i	$0.652174\pi$
$271$	−1.31448	+	1.40747i	−1.31448	+	1.40747i	−0.854419	+	0.519584i	$0.826087\pi$
$272$	−0.0108174	+	0.0164924i	−0.0108174	+	0.0164924i
$273$		0			0
$274$	0.489484	+	0.212613i	0.489484	+	0.212613i
$275$		0			0
$276$	−0.0598282	−	0.137738i	−0.0598282	−	0.137738i
$277$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$277$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$278$	−0.414317	−	0.736862i	−0.414317	−	0.736862i
$279$	−1.24888	+	0.759461i	−1.24888	+	0.759461i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	0.367331	−	0.560041i	0.367331	−	0.560041i
$283$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$283$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.345684	−	0.876594i	0.345684	−	0.876594i
$289$	0.979084	+	0.0669712i	0.979084	+	0.0669712i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.88342	−	0.0643397i	1.88342	−	0.0643397i	0.930278	−	0.366854i	$-0.119565\pi$
$293$	1.88342	−	0.0643397i	1.88342	−	0.0643397i	0.953145	+	0.302515i	$0.0978261\pi$
$294$	−0.180699	−	0.644923i	−0.180699	−	0.644923i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.824823	−	0.719208i	−0.824823	−	0.719208i
$303$		0			0
$304$	0.0604876	−	0.0492103i	0.0604876	−	0.0492103i
$305$		0			0
$306$	−0.0905606	+	0.0124473i	−0.0905606	+	0.0124473i
$307$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$307$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$311$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$312$		0			0
$313$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$313$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$314$		0			0
$315$		0			0
$316$	0.434096	+	0.614974i	0.434096	+	0.614974i
$317$	0.509307	−	0.905802i	0.509307	−	0.905802i	−0.490110	−	0.871660i	$-0.663043\pi$
$317$	0.509307	−	0.905802i	0.509307	−	0.905802i	0.999417	−	0.0341411i	$-0.0108696\pi$
$318$	−0.0210400	−	0.615906i	−0.0210400	−	0.615906i
$319$		0			0
$320$		0			0
$321$	0.414006	−	0.953137i	0.414006	−	0.953137i
$322$		0			0
$323$	0.0685116	+	0.0270175i	0.0685116	+	0.0270175i
$324$	0.519584	−	0.184660i	0.519584	−	0.184660i
$325$		0			0
$326$		0			0
$327$	0.634896	−	0.481457i	0.634896	−	0.481457i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.81734	−	0.249787i	−1.81734	−	0.249787i	−0.854419	−	0.519584i	$-0.826087\pi$
$331$	−1.81734	−	0.249787i	−1.81734	−	0.249787i	−0.962917	+	0.269797i	$0.913043\pi$
$332$	−0.982781	−	0.239497i	−0.982781	−	0.239497i
$333$		0			0
$334$	0.398285	+	1.12067i	0.398285	+	1.12067i
$335$		0			0
$336$		0			0
$337$		0			0		−0.366854	−	0.930278i	$-0.619565\pi$
$337$		0			0		0.366854	+	0.930278i	$0.380435\pi$
$338$	0.202612	+	0.638377i	0.202612	+	0.638377i
$339$	0.398401	+	1.91721i	0.398401	+	1.91721i
$340$		0			0
$341$		0			0
$342$	0.356143	+	0.0614052i	0.356143	+	0.0614052i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.186018	−	0.199177i	−0.186018	−	0.199177i
$347$	0.400995	−	0.0691386i	0.400995	−	0.0691386i	0.0341411	−	0.999417i	$-0.489130\pi$
$347$	0.400995	−	0.0691386i	0.400995	−	0.0691386i	0.366854	+	0.930278i	$0.380435\pi$
$348$		0			0
$349$	0.0861339	+	1.25923i	0.0861339	+	1.25923i	0.816970	+	0.576680i	$0.195652\pi$
$349$	0.0861339	+	1.25923i	0.0861339	+	1.25923i	−0.730836	+	0.682553i	$0.760870\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.16366	+	1.53451i	−1.16366	+	1.53451i	−0.366854	+	0.930278i	$0.619565\pi$
$353$	−1.16366	+	1.53451i	−1.16366	+	1.53451i	−0.796805	+	0.604236i	$0.793478\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$359$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$360$		0			0
$361$	0.549854	+	0.447340i	0.549854	+	0.447340i
$362$	−0.719295	−	1.09665i	−0.719295	−	1.09665i
$363$	−0.985460	−	0.169910i	−0.985460	−	0.169910i
$364$		0			0
$365$		0			0
$366$	−0.157164	−	0.756317i	−0.157164	−	0.756317i
$367$		0			0		−0.302515	−	0.953145i	$-0.597826\pi$
$367$		0			0		0.302515	+	0.953145i	$0.402174\pi$
$368$	−0.0144376	−	0.0366111i	−0.0144376	−	0.0366111i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.702557	−	0.395028i	0.702557	−	0.395028i
$373$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$373$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$374$		0			0
$375$		0			0
$376$	−0.599217	+	0.848897i	−0.599217	+	0.848897i
$377$		0			0
$378$		0			0
$379$	0.887885	+	1.46007i	0.887885	+	1.46007i	0.887885	+	0.460065i	$0.152174\pi$
$379$	0.887885	+	1.46007i	0.887885	+	1.46007i			1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.267424	−	0.306695i	−0.267424	−	0.306695i	0.604236	−	0.796805i	$-0.293478\pi$
$383$	−0.267424	−	0.306695i	−0.267424	−	0.306695i	−0.871660	+	0.490110i	$0.836957\pi$
$384$	−0.168450	+	0.387810i	−0.168450	+	0.387810i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$389$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$390$		0			0
$391$	0.0234571	−	0.0288327i	0.0234571	−	0.0288327i
$392$	0.246017	+	1.00954i	0.246017	+	1.00954i
$393$		0			0
$394$	−0.631088	−	0.445471i	−0.631088	−	0.445471i
$395$		0			0
$396$		0			0
$397$		0			0		0.302515	−	0.953145i	$-0.402174\pi$
$397$		0			0		−0.302515	+	0.953145i	$0.597826\pi$
$398$	1.18310	+	0.121627i	1.18310	+	0.121627i
$399$		0			0
$400$		0			0
$401$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$401$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.141075	−	0.0145030i	0.141075	−	0.0145030i
$409$	−0.256797	+	1.23578i	−0.256797	+	1.23578i	0.631088	+	0.775711i	$0.282609\pi$
$409$	−0.256797	+	1.23578i	−0.256797	+	1.23578i	−0.887885	+	0.460065i	$0.847826\pi$
$410$		0			0
$411$	−0.214975	−	0.767255i	−0.214975	−	0.767255i
$412$		0			0
$413$		0			0
$414$	0.0839148	−	0.161948i	0.0839148	−	0.161948i
$415$		0			0
$416$		0			0
$417$	−0.463035	+	1.17418i	−0.463035	+	1.17418i
$418$		0			0
$419$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$419$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$420$		0			0
$421$	−0.141500	+	1.02949i	−0.141500	+	1.02949i	0.775711	+	0.631088i	$0.217391\pi$
$421$	−0.141500	+	1.02949i	−0.141500	+	1.02949i	−0.917211	+	0.398401i	$0.869565\pi$
$422$	−0.492141	+	0.492141i	−0.492141	+	0.492141i
$423$	−0.994757	+	0.102264i	−0.994757	+	0.102264i
$424$			0.956088i			0.956088i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.246103	+	0.517480i	−0.246103	+	0.517480i
$429$		0			0
$430$		0			0
$431$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$431$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$432$	0.137739	−	0.0437165i	0.137739	−	0.0437165i
$433$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$433$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$434$		0			0
$435$		0			0
$436$	−0.358956	+	0.253379i	−0.358956	+	0.253379i
$437$	−0.122876	+	0.0805946i	−0.122876	+	0.0805946i
$438$		0			0
$439$	−0.953137	+	1.56737i	−0.953137	+	1.56737i	−0.136167	+	0.990686i	$0.543478\pi$
$439$	−0.953137	+	1.56737i	−0.953137	+	1.56737i	−0.816970	+	0.576680i	$0.804348\pi$
$440$		0			0
$441$	−0.576680	+	0.816970i	−0.576680	+	0.816970i
$442$		0			0
$443$	−0.523661	+	0.600560i	−0.523661	+	0.600560i	−0.953145	−	0.302515i	$-0.902174\pi$
$443$	−0.523661	+	0.600560i	−0.523661	+	0.600560i	0.429483	+	0.903075i	$0.358696\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$449$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$450$		0			0
$451$		0			0
$452$	−0.183466	−	1.06408i	−0.183466	−	1.06408i
$453$	−0.0557845	+	1.63299i	−0.0557845	+	1.63299i
$454$	0.935031	+	0.568605i	0.935031	+	0.568605i
$455$		0			0
$456$	−0.548953	−	0.114074i	−0.548953	−	0.114074i
$457$		0			0		0.169910	−	0.985460i	$-0.445652\pi$
$457$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$458$	−0.953898	−	0.536350i	−0.953898	−	0.536350i
$459$	0.0997480	+	0.0931581i	0.0997480	+	0.0931581i
$460$		0			0
$461$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$461$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$462$		0			0
$463$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$463$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$464$		0			0
$465$		0			0
$466$	−0.320880	+	1.14523i	−0.320880	+	1.14523i
$467$	0.298838	−	1.22629i	0.298838	−	1.22629i	−0.604236	−	0.796805i	$-0.706522\pi$
$467$	0.298838	−	1.22629i	0.298838	−	1.22629i	0.903075	−	0.429483i	$-0.141304\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.246673	+	0.880388i	−0.246673	+	0.880388i
$475$		0			0
$476$		0			0
$477$	−0.693514	+	0.604713i	−0.693514	+	0.604713i
$478$		0			0
$479$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$479$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$480$		0			0
$481$		0			0
$482$	−0.537174	−	0.302038i	−0.537174	−	0.302038i
$483$		0			0
$484$	0.539889	+	0.112190i	0.539889	+	0.112190i
$485$		0			0
$486$	0.572255	+	0.347996i	0.572255	+	0.347996i
$487$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$487$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$488$	0.203626	+	1.18101i	0.203626	+	1.18101i
$489$		0			0
$490$		0			0
$491$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$491$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.187545	−	0.0971782i	0.187545	−	0.0971782i
$497$		0			0
$498$	−0.527673	−	1.10954i	−0.527673	−	1.10954i
$499$	0.157049	−	0.222488i	0.157049	−	0.222488i	−0.730836	−	0.682553i	$-0.760870\pi$
$499$	0.157049	−	0.222488i	0.157049	−	0.222488i	0.887885	+	0.460065i	$0.152174\pi$
$500$		0			0
$501$	0.922662	−	1.51725i	0.922662	−	1.51725i
$502$		0			0
$503$	−1.57580	+	1.03357i	−1.57580	+	1.03357i	−0.604236	+	0.796805i	$0.706522\pi$
$503$	−1.57580	+	1.03357i	−1.57580	+	1.03357i	−0.971567	+	0.236764i	$0.923913\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.548452	−	0.836182i	0.548452	−	0.836182i
$508$		0			0
$509$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$509$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$510$		0			0
$511$		0			0
$512$	−0.122974	+	0.258577i	−0.122974	+	0.258577i
$513$	−0.264460	−	0.470342i	−0.264460	−	0.470342i
$514$	1.14184	−	0.694370i	1.14184	−	0.694370i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.0554078	+	0.403122i	−0.0554078	+	0.403122i
$520$		0			0
$521$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$521$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$522$		0			0
$523$		0			0		0.366854	−	0.930278i	$-0.380435\pi$
$523$		0			0		−0.366854	+	0.930278i	$0.619565\pi$
$524$		0			0
$525$		0			0
$526$	−0.610526	+	1.17826i	−0.610526	+	1.17826i
$527$	0.166815	+	0.109414i	0.166815	+	0.109414i
$528$		0			0
$529$	−0.249787	−	0.891502i	−0.249787	−	0.891502i
$530$		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
$541$	−1.35239	+	0.185882i	−1.35239	+	0.185882i	−0.775711	−	0.631088i	$-0.782609\pi$
$541$	−1.35239	+	0.185882i	−1.35239	+	0.185882i	−0.576680	+	0.816970i	$0.695652\pi$
$542$	1.28308	+	0.131905i	1.28308	+	0.131905i
$543$	−0.592374	+	1.86642i	−0.592374	+	1.86642i
$544$	−0.128309	+	0.00877656i	−0.128309	+	0.00877656i
$545$		0			0
$546$		0			0
$547$		0			0		−0.999417	−	0.0341411i	$-0.989130\pi$
$547$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$548$	0.104028	+	0.426882i	0.104028	+	0.426882i
$549$	−0.727872	+	0.894675i	−0.727872	+	0.894675i
$550$		0			0
$551$		0			0
$552$	−0.138689	+	0.246659i	−0.138689	+	0.246659i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.277284	−	0.638372i	0.277284	−	0.638372i
$557$	1.31134	+	1.50391i	1.31134	+	1.50391i	0.707107	+	0.707107i	$0.250000\pi$
$557$	1.31134	+	1.50391i	1.31134	+	1.50391i	0.604236	+	0.796805i	$0.293478\pi$
$558$	0.910713	+	0.359139i	0.910713	+	0.359139i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.41092	+	1.41092i	1.41092	+	1.41092i	0.753713	+	0.657204i	$0.228261\pi$
$563$	1.41092	+	1.41092i	1.41092	+	1.41092i	0.657204	+	0.753713i	$0.271739\pi$
$564$	0.550137	−	0.0376304i	0.550137	−	0.0376304i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$569$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$570$		0			0
$571$	−0.131424	+	1.92135i	−0.131424	+	1.92135i	0.203456	+	0.979084i	$0.434783\pi$
$571$	−0.131424	+	1.92135i	−0.131424	+	1.92135i	−0.334880	+	0.942261i	$0.608696\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.746857	+	0.209260i	−0.746857	+	0.209260i
$577$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$577$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$578$	−0.360488	−	0.549608i	−0.360488	−	0.549608i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.796544	−	0.979084i	−0.796544	−	0.979084i
$587$	−0.326042	+	0.429951i	−0.326042	+	0.429951i	−0.930278	−	0.366854i	$-0.880435\pi$
$587$	−0.326042	+	0.429951i	−0.326042	+	0.429951i	0.604236	+	0.796805i	$0.293478\pi$
$588$	0.333190	−	0.439376i	0.333190	−	0.439376i
$589$	−0.497745	−	0.611810i	−0.497745	−	0.611810i
$590$		0			0
$591$	0.0787081	+	1.15067i	0.0787081	+	1.15067i
$592$		0			0
$593$	−1.85712	+	0.320200i	−1.85712	+	0.320200i	−0.985460	−	0.169910i	$-0.945652\pi$
$593$	−1.85712	+	0.320200i	−1.85712	+	0.320200i	−0.871660	+	0.490110i	$0.836957\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.973925	−	1.48487i	−0.973925	−	1.48487i
$598$		0			0
$599$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$599$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$600$		0			0
$601$	−0.0827887	−	0.398401i	−0.0827887	−	0.398401i	0.917211	−	0.398401i	$-0.130435\pi$
$601$	−0.0827887	−	0.398401i	−0.0827887	−	0.398401i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	0.0614858	−	0.898891i	0.0614858	−	0.898891i
$605$		0			0
$606$		0			0
$607$		0			0		0.871660	−	0.490110i	$-0.163043\pi$
$607$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$608$	0.493998	+	0.120384i	0.493998	+	0.120384i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.0532174	−	0.0532174i	−0.0532174	−	0.0532174i
$613$		0			0		0.796805	−	0.604236i	$-0.206522\pi$
$613$		0			0		−0.796805	+	0.604236i	$0.793478\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.26993	+	0.500795i	1.26993	+	0.500795i	0.903075	−	0.429483i	$-0.141304\pi$
$617$	1.26993	+	0.500795i	1.26993	+	0.500795i	0.366854	+	0.930278i	$0.380435\pi$
$618$		0			0
$619$	−0.459500	+	1.05788i	−0.459500	+	1.05788i	0.519584	+	0.854419i	$0.326087\pi$
$619$	−0.459500	+	1.05788i	−0.459500	+	1.05788i	−0.979084	+	0.203456i	$0.934783\pi$
$620$		0			0
$621$	−0.266637	+	0.0554078i	−0.266637	+	0.0554078i
$622$		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
$631$	−0.271698	+	0.0185847i	−0.271698	+	0.0185847i	−0.203456	−	0.979084i	$-0.565217\pi$
$631$	−0.271698	+	0.0185847i	−0.271698	+	0.0185847i	−0.0682424	+	0.997669i	$0.521739\pi$
$632$	0.429103	−	1.35199i	0.429103	−	1.35199i
$633$	1.03372	+	0.106270i	1.03372	+	0.106270i
$634$	−0.689510	+	0.0947709i	−0.689510	+	0.0947709i
$635$		0			0
$636$	0.393581	−	0.320202i	0.393581	−	0.320202i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$641$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$642$	−0.676203	+	0.164786i	−0.676203	+	0.164786i
$643$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$643$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$644$		0			0
$645$		0			0
$646$	−0.0133078	−	0.0474962i	−0.0133078	−	0.0474962i
$647$	0.919594	−	0.0314143i	0.919594	−	0.0314143i	0.429483	−	0.903075i	$-0.358696\pi$
$647$	0.919594	−	0.0314143i	0.919594	−	0.0314143i	0.490110	+	0.871660i	$0.336957\pi$
$648$	−0.868860	−	0.569885i	−0.868860	−	0.569885i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.73917	+	0.827114i	1.73917	+	0.827114i	0.985460	+	0.169910i	$0.0543478\pi$
$653$	1.73917	+	0.827114i	1.73917	+	0.827114i	0.753713	+	0.657204i	$0.228261\pi$
$654$	−0.513876	−	0.143981i	−0.513876	−	0.143981i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	0.116615	−	0.0709153i	0.116615	−	0.0709153i	−0.460065	−	0.887885i	$-0.652174\pi$
$661$	0.116615	−	0.0709153i	0.116615	−	0.0709153i	0.576680	+	0.816970i	$0.304348\pi$
$662$	0.602160	+	1.07094i	0.602160	+	1.07094i
$663$		0			0
$664$	0.759397	+	1.74831i	0.759397	+	1.74831i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.537044	+	0.818789i	−0.537044	+	0.818789i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.102264	−	0.994757i	$-0.532609\pi$
$673$		0			0		0.102264	+	0.994757i	$0.467391\pi$
$674$		0			0
$675$		0			0
$676$	−0.317995	+	0.450496i	−0.317995	+	0.450496i
$677$	0.542084	+	1.13984i	0.542084	+	1.13984i	0.971567	+	0.236764i	$0.0760870\pi$
$677$	0.542084	+	1.13984i	0.542084	+	1.13984i	−0.429483	+	0.903075i	$0.641304\pi$
$678$	0.861923	−	0.988496i	0.861923	−	0.988496i
$679$		0			0
$680$		0			0
$681$	−0.222488	−	1.61872i	−0.222488	−	1.61872i
$682$		0			0
$683$	0.202623	−	1.97098i	0.202623	−	1.97098i	−0.0341411	−	0.999417i	$-0.510870\pi$
$683$	0.202623	−	1.97098i	0.202623	−	1.97098i	0.236764	−	0.971567i	$-0.423913\pi$
$684$	0.136890	+	0.264185i	0.136890	+	0.264185i
$685$		0			0
$686$		0			0
$687$	0.277623	+	1.61018i	0.277623	+	1.61018i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−1.95360	−	0.405963i	−1.95360	−	0.405963i	−0.990686	−	0.136167i	$-0.956522\pi$
$691$	−1.95360	−	0.405963i	−1.95360	−	0.405963i	−0.962917	−	0.269797i	$-0.913043\pi$
$692$	0.0381246	−	0.221118i	0.0381246	−	0.221118i
$693$		0			0
$694$	−0.199177	−	0.186018i	−0.199177	−	0.186018i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.637154	−	0.555570i	0.637154	−	0.555570i
$699$	1.62876	−	0.707469i	1.62876	−	0.707469i
$700$		0			0
$701$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$701$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.28985			1.28985
$707$		0			0
$708$		0			0
$709$	0.534568	−	1.90790i	0.534568	−	1.90790i	0.136167	−	0.990686i	$-0.456522\pi$
$709$	0.534568	−	1.90790i	0.534568	−	1.90790i	0.398401	−	0.917211i	$-0.369565\pi$
$710$		0			0
$711$	1.25209	−	0.543860i	1.25209	−	0.543860i
$712$		0			0
$713$	−0.370308	+	0.146031i	−0.370308	+	0.146031i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$719$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$720$		0			0
$721$		0			0
$722$	0.0162085	−	0.474475i	0.0162085	−	0.474475i
$723$	0.156340	+	0.906751i	0.156340	+	0.906751i
$724$	0.361596	−	1.01743i	0.361596	−	1.01743i
$725$		0			0
$726$	0.308133	+	0.594669i	0.308133	+	0.594669i
$727$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$727$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$728$		0			0
$729$	−0.136167	−	0.990686i	−0.136167	−	0.990686i
$730$		0			0
$731$		0			0
$732$	0.417974	−	0.479353i	0.417974	−	0.479353i
$733$		0			0		−0.429483	−	0.903075i	$-0.641304\pi$
$733$		0			0		0.429483	+	0.903075i	$0.358696\pi$
$734$		0			0
$735$		0			0
$736$	0.133334	−	0.219259i	0.133334	−	0.219259i
$737$		0			0
$738$		0			0
$739$	−0.332435	+	0.234658i	−0.332435	+	0.234658i	−0.730836	−	0.682553i	$-0.760870\pi$
$739$	−0.332435	+	0.234658i	−0.332435	+	0.234658i	0.398401	+	0.917211i	$0.369565\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.514311	−	0.163235i	0.514311	−	0.163235i	−0.0341411	−	0.999417i	$-0.510870\pi$
$743$	0.514311	−	0.163235i	0.514311	−	0.163235i	0.548452	+	0.836182i	$0.315217\pi$
$744$	−1.39305	−	0.605089i	−1.39305	−	0.605089i
$745$		0			0
$746$		0			0
$747$	−0.787854	+	1.65662i	−0.787854	+	1.65662i
$748$		0			0
$749$		0			0
$750$		0			0
$751$			1.03917i			1.03917i	0.854419	+	0.519584i	$0.173913\pi$
$751$			1.03917i			1.03917i	−0.854419	+	0.519584i	$0.826087\pi$
$752$	0.144426	−	0.00493375i	0.144426	−	0.00493375i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$757$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$758$	0.419869	−	1.06471i	0.419869	−	1.06471i
$759$		0			0
$760$		0			0
$761$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$761$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−0.0554485	+	0.266833i	−0.0554485	+	0.266833i
$767$		0			0
$768$	1.02870	−	0.250687i	1.02870	−	0.250687i
$769$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i	−0.631088	−	0.775711i	$-0.717391\pi$
$769$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i	0.730836	+	0.682553i	$0.239130\pi$
$770$		0			0
$771$	−1.88013	−	0.668198i	−1.88013	−	0.668198i
$772$		0			0
$773$	−1.47873	−	0.469328i	−1.47873	−	0.469328i	−0.548452	−	0.836182i	$-0.684783\pi$
$773$	−1.47873	−	0.469328i	−1.47873	−	0.469328i	−0.930278	+	0.366854i	$0.880435\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.0248800		0.000849927i	−0.0248800		0.000849927i
$783$		0			0
$784$	0.0911989	−	0.112098i	0.0911989	−	0.112098i
$785$		0			0
$786$		0			0
$787$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$787$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$788$	−0.0217134	−	0.635618i	−0.0217134	−	0.635618i
$789$	1.93993	−	0.403122i	1.93993	−	0.403122i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.508777	+	0.836647i	0.508777	+	0.836647i
$797$	1.00571	−	0.762653i	1.00571	−	0.762653i	0.0341411	−	0.999417i	$-0.489130\pi$
$797$	1.00571	−	0.762653i	1.00571	−	0.762653i	0.971567	+	0.236764i	$0.0760870\pi$
$798$		0			0
$799$	0.0709153	+	0.116615i	0.0709153	+	0.116615i
$800$		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		−0.203456	−	0.979084i	$-0.565217\pi$
$809$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$810$		0			0
$811$	0.391823	−	0.109784i	0.391823	−	0.109784i	−0.0682424	−	0.997669i	$-0.521739\pi$
$811$	0.391823	−	0.109784i	0.391823	−	0.109784i	0.460065	+	0.887885i	$0.347826\pi$
$812$		0			0
$813$	−1.05623	−	1.61035i	−1.05623	−	1.61035i
$814$		0			0
$815$		0			0
$816$	−0.0134623	−	0.0144146i	−0.0134623	−	0.0144146i
$817$		0			0
$818$	0.763418	−	0.363066i	0.763418	−	0.363066i
$819$		0			0
$820$		0			0
$821$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$821$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$822$	−0.322460	+	0.425227i	−0.322460	+	0.425227i
$823$		0			0		0.604236	−	0.796805i	$-0.293478\pi$
$823$		0			0		−0.604236	+	0.796805i	$0.706522\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.40105	−	0.666310i	1.40105	−	0.666310i	0.429483	−	0.903075i	$-0.358696\pi$
$827$	1.40105	−	0.666310i	1.40105	−	0.666310i	0.971567	+	0.236764i	$0.0760870\pi$
$828$	0.147987	−	0.0255156i	0.147987	−	0.0255156i
$829$	−1.28629	−	1.37728i	−1.28629	−	1.37728i	−0.887885	−	0.460065i	$-0.847826\pi$
$829$	−1.28629	−	1.37728i	−1.28629	−	1.37728i	−0.398401	−	0.917211i	$-0.630435\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.134500	+	0.0231902i	0.134500	+	0.0231902i
$834$	0.814006	−	0.228074i	0.814006	−	0.228074i
$835$		0			0
$836$		0			0
$837$	−0.442177	−	1.39318i	−0.442177	−	1.39318i
$838$		0			0
$839$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$839$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$840$		0			0
$841$	−0.334880	−	0.942261i	−0.334880	−	0.942261i
$842$	0.606669	−	0.341113i	0.606669	−	0.341113i
$843$		0			0
$844$	−0.567684	−	0.0780263i	−0.567684	−	0.0780263i
$845$		0			0
$846$	0.457146	+	0.489484i	0.457146	+	0.489484i
$847$		0			0
$848$	0.105950	−	0.0803444i	0.105950	−	0.0803444i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.657204	−	0.753713i	$-0.728261\pi$
$853$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$854$		0			0
$855$		0			0
$856$	1.05719	−	0.219687i	1.05719	−	0.219687i
$857$	0.0354783	+	1.03856i	0.0354783	+	1.03856i	0.871660	+	0.490110i	$0.163043\pi$
$857$	0.0354783	+	1.03856i	0.0354783	+	1.03856i	−0.836182	+	0.548452i	$0.815217\pi$
$858$		0			0
$859$	−1.08677	−	1.53960i	−1.08677	−	1.53960i	−0.816970	−	0.576680i	$-0.804348\pi$
$859$	−1.08677	−	1.53960i	−1.08677	−	1.53960i	−0.269797	−	0.962917i	$-0.586957\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.36431	+	0.0466062i	1.36431	+	0.0466062i	0.707107	−	0.707107i	$-0.250000\pi$
$863$	1.36431	+	0.0466062i	1.36431	+	0.0466062i	0.657204	+	0.753713i	$0.271739\pi$
$864$	0.769824	+	0.543401i	0.769824	+	0.543401i
$865$		0			0
$866$		0			0
$867$	−0.296879	+	0.935389i	−0.296879	+	0.935389i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.789148	+	0.250464i	0.789148	+	0.250464i
$873$		0			0
$874$	0.0927379	+	0.0329591i	0.0927379	+	0.0329591i
$875$		0			0
$876$		0			0
$877$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$877$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$878$	1.22218	−	0.125644i	1.22218	−	0.125644i
$879$	−0.383417	+	1.84511i	−0.383417	+	1.84511i
$880$		0			0
$881$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$881$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$882$	0.669369	−	0.0228663i	0.669369	−	0.0228663i
$883$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$883$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$884$		0			0
$885$		0			0
$886$	0.532422	+	0.0364186i	0.532422	+	0.0364186i
$887$	−0.197952	+	0.501972i	−0.197952	+	0.501972i	−0.994757	−	0.102264i	$-0.967391\pi$
$887$	−0.197952	+	0.501972i	−0.197952	+	0.501972i	0.796805	+	0.604236i	$0.206522\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.127757	−	0.524251i	−0.127757	−	0.524251i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.115187	+	0.0500327i	0.115187	+	0.0500327i
$902$		0			0
$903$		0			0
$904$	−1.38879	+	1.48703i	−1.38879	+	1.48703i
$905$		0			0
$906$	0.894048	−	0.631088i	0.894048	−	0.631088i
$907$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$907$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$908$	0.0921391	+	0.896268i	0.0921391	+	0.896268i
$909$		0			0
$910$		0			0
$911$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$911$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$912$	0.0334898	+	0.0704190i	0.0334898	+	0.0704190i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.122685	−	0.892599i	−0.122685	−	0.892599i
$917$		0			0
$918$	0.00934817	−	0.0909327i	0.00934817	−	0.0909327i
$919$	−0.125291	−	0.241801i	−0.125291	−	0.241801i	0.816970	−	0.576680i	$-0.195652\pi$
$919$	−0.125291	−	0.241801i	−0.125291	−	0.241801i	−0.942261	+	0.334880i	$0.891304\pi$
$920$		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		−0.730836	−	0.682553i	$-0.760870\pi$
$929$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$930$		0			0
$931$	−0.479097	−	0.248248i	−0.479097	−	0.248248i
$932$	−0.910929	+	0.359224i	−0.910929	+	0.359224i
$933$		0			0
$934$	−0.775368	+	0.336790i	−0.775368	+	0.336790i
$935$		0			0
$936$		0			0
$937$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$937$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$938$		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
$947$	1.16933	−	1.01960i	1.16933	−	1.01960i	0.169910	−	0.985460i	$-0.445652\pi$
$947$	1.16933	−	1.01960i	1.16933	−	1.01960i	0.999417	−	0.0341411i	$-0.0108696\pi$
$948$	−0.700268	+	0.276150i	−0.700268	+	0.276150i
$949$		0			0
$950$		0			0
$951$	0.759461	+	0.709287i	0.759461	+	0.709287i
$952$		0			0
$953$	−0.320200	+	1.85712i	−0.320200	+	1.85712i	0.169910	+	0.985460i	$0.445652\pi$
$953$	−0.320200	+	1.85712i	−0.320200	+	1.85712i	−0.490110	+	0.871660i	$0.663043\pi$
$954$	0.603376	+	0.125383i	0.603376	+	0.125383i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.522857	−	1.00907i	−0.522857	−	1.00907i
$962$		0			0
$963$	0.828014	+	0.627903i	0.828014	+	0.627903i
$964$	−0.0690883	−	0.502655i	−0.0690883	−	0.502655i
$965$		0			0
$966$		0			0
$967$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$967$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$968$	−0.446267	−	0.938367i	−0.446267	−	0.938367i
$969$	−0.0424704	+	0.0601668i	−0.0424704	+	0.0601668i
$970$		0			0
$971$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$971$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$972$	0.0563908	+	0.548532i	0.0563908	+	0.548532i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.113763	−	0.121810i	0.113763	−	0.121810i
$977$	0.223172	−	0.340253i	0.223172	−	0.340253i	−0.707107	−	0.707107i	$-0.750000\pi$
$977$	0.223172	−	0.340253i	0.223172	−	0.340253i	0.930278	+	0.366854i	$0.119565\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.317447	+	0.730836i	0.317447	+	0.730836i
$982$		0			0
$983$	−0.800811	−	1.42424i	−0.800811	−	1.42424i	−0.903075	−	0.429483i	$-0.858696\pi$
$983$	−0.800811	−	1.42424i	−0.800811	−	1.42424i	0.102264	−	0.994757i	$-0.467391\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.64547	+	0.461039i	1.64547	+	0.461039i	0.962917	−	0.269797i	$-0.0869565\pi$
$991$	1.64547	+	0.461039i	1.64547	+	0.461039i	0.682553	+	0.730836i	$0.260870\pi$
$992$	1.24382	+	0.591537i	1.24382	+	0.591537i
$993$	0.672966	−	1.70652i	0.672966	−	1.70652i
$994$		0			0
$995$		0			0
$996$	0.465375	−	0.898133i	0.465375	−	0.898133i
$997$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$997$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$998$	−0.182291	+	0.00622726i	−0.182291	+	0.00622726i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bg.a.1643.1	✓	88
3.2	odd	2	inner	3525.1.bg.a.1643.2	yes	88
5.2	odd	4	inner	3525.1.bg.a.2207.2	yes	88
5.3	odd	4	inner	3525.1.bg.a.2207.1	yes	88
5.4	even	2	inner	3525.1.bg.a.1643.2	yes	88
15.2	even	4	inner	3525.1.bg.a.2207.1	yes	88
15.8	even	4	inner	3525.1.bg.a.2207.2	yes	88
15.14	odd	2	CM	3525.1.bg.a.1643.1	✓	88
47.23	odd	46	inner	3525.1.bg.a.2843.1	yes	88
141.23	even	46	inner	3525.1.bg.a.2843.2	yes	88
235.23	even	92	inner	3525.1.bg.a.3407.1	yes	88
235.117	even	92	inner	3525.1.bg.a.3407.2	yes	88
235.164	odd	46	inner	3525.1.bg.a.2843.2	yes	88
705.23	odd	92	inner	3525.1.bg.a.3407.2	yes	88
705.164	even	46	inner	3525.1.bg.a.2843.1	yes	88
705.587	odd	92	inner	3525.1.bg.a.3407.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.1643.1	✓	88	1.1	even	1	trivial
3525.1.bg.a.1643.1	✓	88	15.14	odd	2	CM
3525.1.bg.a.1643.2	yes	88	3.2	odd	2	inner
3525.1.bg.a.1643.2	yes	88	5.4	even	2	inner
3525.1.bg.a.2207.1	yes	88	5.3	odd	4	inner
3525.1.bg.a.2207.1	yes	88	15.2	even	4	inner
3525.1.bg.a.2207.2	yes	88	5.2	odd	4	inner
3525.1.bg.a.2207.2	yes	88	15.8	even	4	inner
3525.1.bg.a.2843.1	yes	88	47.23	odd	46	inner
3525.1.bg.a.2843.1	yes	88	705.164	even	46	inner
3525.1.bg.a.2843.2	yes	88	141.23	even	46	inner
3525.1.bg.a.2843.2	yes	88	235.164	odd	46	inner
3525.1.bg.a.3407.1	yes	88	235.23	even	92	inner
3525.1.bg.a.3407.1	yes	88	705.587	odd	92	inner
3525.1.bg.a.3407.2	yes	88	235.117	even	92	inner
3525.1.bg.a.3407.2	yes	88	705.23	odd	92	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.404693 - 0.533668i) q^{2} +(-0.236764 + 0.971567i) q^{3} +(0.148772 - 0.530974i) q^{4} +(0.614311 - 0.266833i) q^{6} +(-0.966633 + 0.381191i) q^{8} +(-0.887885 - 0.460065i) q^{9} +O(q^{10})\)	\(q+(-0.404693 - 0.533668i) q^{2} +(-0.236764 + 0.971567i) q^{3} +(0.148772 - 0.530974i) q^{4} +(0.614311 - 0.266833i) q^{6} +(-0.966633 + 0.381191i) q^{8} +(-0.887885 - 0.460065i) q^{9} +(0.480653 + 0.270258i) q^{12} +(0.123473 + 0.0750854i) q^{16} +(-0.00465974 + 0.136405i) q^{17} +(0.113799 + 0.660021i) q^{18} +(0.180699 - 0.508438i) q^{19} +(-0.216997 - 0.164554i) q^{23} +(-0.141488 - 1.02940i) q^{24} +(0.657204 - 0.753713i) q^{27} +(0.759461 - 1.24888i) q^{31} +(0.0963627 + 0.937352i) q^{32} +(0.0746808 - 0.0527155i) q^{34} +(-0.376375 + 0.402999i) q^{36} +(-0.344464 + 0.109328i) q^{38} +0.182398i q^{46} +(0.836182 - 0.548452i) q^{47} +(-0.102184 + 0.102184i) q^{48} +(0.136167 - 0.990686i) q^{49} +(-0.131424 - 0.0368232i) q^{51} +(0.337554 - 0.855977i) q^{53} +(-0.668198 - 0.0457060i) q^{54} +(0.451198 + 0.295941i) q^{57} +(0.234658 - 1.12924i) q^{61} +(-0.973836 + 0.100113i) q^{62} +(0.566851 - 0.529402i) q^{64} +(0.0717345 + 0.0227675i) q^{68} +(0.211252 - 0.171866i) q^{69} +(1.03363 + 0.106261i) q^{72} +(-0.243085 - 0.171588i) q^{76} +(-0.861502 + 1.05893i) q^{79} +(0.576680 + 0.816970i) q^{81} +(-0.0626292 - 1.83335i) q^{83} +(-0.119657 + 0.0907386i) q^{92} +(1.03356 + 1.03356i) q^{93} +(-0.631088 - 0.224289i) q^{94} +(-0.933516 - 0.128309i) q^{96} +(-0.583803 + 0.328256i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{6}+O(q^{10}) \) 88 * q - 8 * q^6	\( 88 q - 8 q^{6} + 20 q^{16} - 12 q^{36} - 8 q^{51} + 8 q^{61} - 92 q^{76} + 4 q^{81} - 68 q^{96}+O(q^{100}) \) 88 * q - 8 * q^6 + 20 * q^16 - 12 * q^36 - 8 * q^51 + 8 * q^61 - 92 * q^76 + 4 * q^81 - 68 * q^96

Introduction

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