LMFDB - Embedded newform 3525.1.bg.a.2207.2

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			2207.2
Root			$0.796805 - 0.604236i$ of defining polynomial
Character	$\chi$	$=$	3525.2207
Dual form			3525.1.bg.a.2843.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.533668 - 0.404693i) q^{2} +(0.971567 + 0.236764i) q^{3} +(-0.148772 + 0.530974i) q^{4} +(0.614311 - 0.266833i) q^{6} +(0.381191 + 0.966633i) q^{8} +(0.887885 + 0.460065i) q^{9} +O(q^{10})$	\(q+(0.533668 - 0.404693i) q^{2} +(0.971567 + 0.236764i) q^{3} +(-0.148772 + 0.530974i) q^{4} +(0.614311 - 0.266833i) q^{6} +(0.381191 + 0.966633i) q^{8} +(0.887885 + 0.460065i) q^{9} +(-0.270258 + 0.480653i) q^{12} +(0.123473 + 0.0750854i) q^{16} +(-0.136405 - 0.00465974i) q^{17} +(0.660021 - 0.113799i) q^{18} +(-0.180699 + 0.508438i) q^{19} +(-0.164554 + 0.216997i) q^{23} +(0.141488 + 1.02940i) q^{24} +(0.753713 + 0.657204i) q^{27} +(0.759461 - 1.24888i) q^{31} +(-0.937352 + 0.0963627i) q^{32} +(-0.0746808 + 0.0527155i) q^{34} +(-0.376375 + 0.402999i) q^{36} +(0.109328 + 0.344464i) q^{38} +0.182398i q^{46} +(0.548452 + 0.836182i) q^{47} +(0.102184 + 0.102184i) q^{48} +(-0.136167 + 0.990686i) q^{49} +(-0.131424 - 0.0368232i) q^{51} +(-0.855977 - 0.337554i) q^{53} +(0.668198 + 0.0457060i) q^{54} +(-0.295941 + 0.451198i) q^{57} +(0.234658 - 1.12924i) q^{61} +(-0.100113 - 0.973836i) q^{62} +(-0.566851 + 0.529402i) q^{64} +(0.0227675 - 0.0717345i) q^{68} +(-0.211252 + 0.171866i) q^{69} +(-0.106261 + 1.03363i) q^{72} +(-0.243085 - 0.171588i) q^{76} +(0.861502 - 1.05893i) q^{79} +(0.576680 + 0.816970i) q^{81} +(-1.83335 + 0.0626292i) q^{83} +(-0.0907386 - 0.119657i) q^{92} +(1.03356 - 1.03356i) q^{93} +(0.631088 + 0.224289i) q^{94} +(-0.933516 - 0.128309i) q^{96} +(0.328256 + 0.583803i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.533668	−	0.404693i	0.533668	−	0.404693i	−0.302515	−	0.953145i	$-0.597826\pi$
$2$	0.533668	−	0.404693i	0.533668	−	0.404693i	0.836182	+	0.548452i	$0.184783\pi$
$3$	0.971567	+	0.236764i	0.971567	+	0.236764i
$3$	0.971567	+	0.236764i	0.971567	+	0.236764i
$4$	−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		−0.657204	−	0.753713i	$-0.728261\pi$
$7$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$8$	0.381191	+	0.966633i	0.381191	+	0.966633i
$9$	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	$0.239130\pi$
$12$	−0.270258	+	0.480653i	−0.270258	+	0.480653i
$13$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$13$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$14$		0			0
$15$		0			0
$16$	0.123473	+	0.0750854i	0.123473	+	0.0750854i
$17$	−0.136405	−	0.00465974i	−0.136405	−	0.00465974i	−0.0341411	−	0.999417i	$-0.510870\pi$
$17$	−0.136405	−	0.00465974i	−0.136405	−	0.00465974i	−0.102264	+	0.994757i	$0.532609\pi$
$18$	0.660021	−	0.113799i	0.660021	−	0.113799i
$19$	−0.180699	+	0.508438i	−0.180699	+	0.508438i	−0.997669	−	0.0682424i	$-0.978261\pi$
$19$	−0.180699	+	0.508438i	−0.180699	+	0.508438i	0.816970	+	0.576680i	$0.195652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.164554	+	0.216997i	−0.164554	+	0.216997i	−0.871660	−	0.490110i	$-0.836957\pi$
$23$	−0.164554	+	0.216997i	−0.164554	+	0.216997i	0.707107	+	0.707107i	$0.250000\pi$
$24$	0.141488	+	1.02940i	0.141488	+	1.02940i
$25$		0			0
$26$		0			0
$27$	0.753713	+	0.657204i	0.753713	+	0.657204i
$28$		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	$-0.0869565\pi$
$32$	−0.937352	+	0.0963627i	−0.937352	+	0.0963627i
$33$		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		−0.836182	−	0.548452i	$-0.815217\pi$
$37$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$38$	0.109328	+	0.344464i	0.109328	+	0.344464i
$39$		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		0.871660	−	0.490110i	$-0.163043\pi$
$43$		0			0		−0.871660	+	0.490110i	$0.836957\pi$
$44$		0			0
$45$		0			0
$46$			0.182398i			0.182398i
$47$	0.548452	+	0.836182i	0.548452	+	0.836182i
$47$	0.548452	+	0.836182i	0.548452	+	0.836182i
$48$	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
$53$	−0.855977	−	0.337554i	−0.855977	−	0.337554i	−0.102264	−	0.994757i	$-0.532609\pi$
$53$	−0.855977	−	0.337554i	−0.855977	−	0.337554i	−0.753713	+	0.657204i	$0.771739\pi$
$54$	0.668198	+	0.0457060i	0.668198	+	0.0457060i
$55$		0			0
$56$		0			0
$57$	−0.295941	+	0.451198i	−0.295941	+	0.451198i
$58$		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	$-0.130435\pi$
$62$	−0.100113	−	0.973836i	−0.100113	−	0.973836i
$63$		0			0
$64$	−0.566851	+	0.529402i	−0.566851	+	0.529402i
$65$		0			0
$66$		0			0
$67$		0			0		0.657204	−	0.753713i	$-0.271739\pi$
$67$		0			0		−0.657204	+	0.753713i	$0.728261\pi$
$68$	0.0227675	−	0.0717345i	0.0227675	−	0.0717345i
$69$	−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	$0.956522\pi$
$72$	−0.106261	+	1.03363i	−0.106261	+	1.03363i
$73$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$73$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$74$		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	$-0.543478\pi$
$79$	0.861502	−	1.05893i	0.861502	−	1.05893i	0.997669	−	0.0682424i	$-0.0217391\pi$
$80$		0			0
$81$	0.576680	+	0.816970i	0.576680	+	0.816970i
$82$		0			0
$83$	−1.83335	+	0.0626292i	−1.83335	+	0.0626292i	−0.930278	−	0.366854i	$-0.880435\pi$
$83$	−1.83335	+	0.0626292i	−1.83335	+	0.0626292i	−0.903075	+	0.429483i	$0.858696\pi$
$84$		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
$92$	−0.0907386	−	0.119657i	−0.0907386	−	0.119657i
$93$	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		0.236764	−	0.971567i	$-0.423913\pi$
$97$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$98$	0.328256	+	0.583803i	0.328256	+	0.583803i
$99$		0			0
$100$		0			0
$101$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$101$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$102$	−0.0850386	+	0.0335349i	−0.0850386	+	0.0335349i
$103$		0			0		0.953145	−	0.302515i	$-0.0978261\pi$
$103$		0			0		−0.953145	+	0.302515i	$0.902174\pi$
$104$		0			0
$105$		0			0
$106$	−0.593413	+	0.166266i	−0.593413	+	0.166266i
$107$	0.176565	−	1.02406i	0.176565	−	1.02406i	−0.753713	−	0.657204i	$-0.771739\pi$
$107$	0.176565	−	1.02406i	0.176565	−	1.02406i	0.930278	−	0.366854i	$-0.119565\pi$
$108$	−0.461090	+	0.302429i	−0.461090	+	0.302429i
$109$	0.618088	+	0.502852i	0.618088	+	0.502852i	0.887885	−	0.460065i	$-0.152174\pi$
$109$	0.618088	+	0.502852i	0.618088	+	0.502852i	−0.269797	+	0.962917i	$0.586957\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.841001	−	1.76837i	−0.841001	−	1.76837i	−0.604236	−	0.796805i	$-0.706522\pi$
$113$	−0.841001	−	1.76837i	−0.841001	−	1.76837i	−0.236764	−	0.971567i	$-0.576087\pi$
$114$	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
$122$	−0.331765	−	0.697602i	−0.331765	−	0.697602i
$123$		0			0
$124$	0.550137	+	0.589053i	0.550137	+	0.589053i
$125$		0			0
$126$		0			0
$127$		0			0		0.836182	−	0.548452i	$-0.184783\pi$
$127$		0			0		−0.836182	+	0.548452i	$0.815217\pi$
$128$	0.0718405	−	0.416666i	0.0718405	−	0.416666i
$129$		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
$137$	−0.390521	−	0.694541i	−0.390521	−	0.694541i	0.604236	−	0.796805i	$-0.293478\pi$
$137$	−0.390521	−	0.694541i	−0.390521	−	0.694541i	−0.994757	+	0.102264i	$0.967391\pi$
$138$	−0.0431853	+	0.177212i	−0.0431853	+	0.177212i
$139$	−1.25042	−	0.171866i	−1.25042	−	0.171866i	−0.519584	−	0.854419i	$-0.673913\pi$
$139$	−1.25042	−	0.171866i	−1.25042	−	0.171866i	−0.730836	+	0.682553i	$0.760870\pi$
$140$		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
$147$	−0.366854	+	0.930278i	−0.366854	+	0.930278i
$148$		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	$0.130435\pi$
$152$	−0.560354	+	0.0191423i	−0.560354	+	0.0191423i
$153$	−0.118968	−	0.0668926i	−0.118968	−	0.0668926i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.971567	−	0.236764i	$-0.0760870\pi$
$157$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$158$	0.0312150	−	0.913760i	0.0312150	−	0.913760i
$159$	−0.751719	−	0.530621i	−0.751719	−	0.530621i
$160$		0			0
$161$		0			0
$162$	0.638377	+	0.202612i	0.638377	+	0.202612i
$163$		0			0		0.102264	−	0.994757i	$-0.467391\pi$
$163$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$164$		0			0
$165$		0			0
$166$	−0.953056	+	0.775368i	−0.953056	+	0.775368i
$167$	0.537196	−	1.69257i	0.537196	−	1.69257i	−0.169910	−	0.985460i	$-0.554348\pi$
$167$	0.537196	−	1.69257i	0.537196	−	1.69257i	0.707107	−	0.707107i	$-0.250000\pi$
$168$		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
$173$	−0.0416125	−	0.404779i	−0.0416125	−	0.404779i	−0.994757	−	0.102264i	$-0.967391\pi$
$173$	−0.0416125	−	0.404779i	−0.0416125	−	0.404779i	0.953145	−	0.302515i	$-0.0978261\pi$
$174$		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
$183$	0.495349	−	1.04157i	0.495349	−	1.04157i
$184$	−0.272482	−	0.0763460i	−0.272482	−	0.0763460i
$185$		0			0
$186$	0.133303	−	0.969850i	0.133303	−	0.969850i
$187$		0			0
$188$	−0.525586	+	0.166813i	−0.525586	+	0.166813i
$189$		0			0
$190$		0			0
$191$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$191$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$192$	−0.676077	+	0.380139i	−0.676077	+	0.380139i
$193$		0			0		−0.903075	−	0.429483i	$-0.858696\pi$
$193$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$194$		0			0
$195$		0			0
$196$	−0.505771	−	0.219687i	−0.505771	−	0.219687i
$197$	0.348908	+	1.09932i	0.348908	+	1.09932i	0.953145	+	0.302515i	$0.0978261\pi$
$197$	0.348908	+	1.09932i	0.348908	+	1.09932i	−0.604236	+	0.796805i	$0.706522\pi$
$198$		0			0
$199$	1.21206	−	1.29780i	1.21206	−	1.29780i	0.269797	−	0.962917i	$-0.413043\pi$
$199$	1.21206	−	1.29780i	1.21206	−	1.29780i	0.942261	−	0.334880i	$-0.108696\pi$
$200$		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
$207$	−0.245937	+	0.116963i	−0.245937	+	0.116963i
$208$		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	$-0.217391\pi$
$212$	0.306578	−	0.404283i	0.306578	−	0.404283i
$213$		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
$218$	0.533354	+	0.0182199i	0.533354	+	0.0182199i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.490110	−	0.871660i	$-0.336957\pi$
$223$		0			0		−0.490110	+	0.871660i	$0.663043\pi$
$224$		0			0
$225$		0			0
$226$	−1.16446	−	0.603376i	−1.16446	−	0.603376i
$227$	−0.599418	−	1.52002i	−0.599418	−	1.52002i	−0.836182	−	0.548452i	$-0.815217\pi$
$227$	−0.599418	−	1.52002i	−0.599418	−	1.52002i	0.236764	−	0.971567i	$-0.423913\pi$
$228$	−0.195547	−	0.224263i	−0.195547	−	0.224263i
$229$	−1.49867	+	0.650963i	−1.49867	+	0.650963i	−0.979084	−	0.203456i	$-0.934783\pi$
$229$	−1.49867	+	0.650963i	−1.49867	+	0.650963i	−0.519584	+	0.854419i	$0.673913\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.41494	+	1.07299i	−1.41494	+	1.07299i	−0.429483	+	0.903075i	$0.641304\pi$
$233$	−1.41494	+	1.07299i	−1.41494	+	1.07299i	−0.985460	+	0.169910i	$0.945652\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.08772	−	0.824847i	1.08772	−	0.824847i
$238$		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	$0.217391\pi$
$242$	0.440168	+	0.504806i	0.440168	+	0.504806i
$243$	0.366854	+	0.930278i	0.366854	+	0.930278i
$244$	0.564685	+	0.292596i	0.564685	+	0.292596i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	1.49671	+	0.258059i	1.49671	+	0.258059i
$249$	−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
$257$	−1.98488	−	0.204051i	−1.98488	−	0.204051i	−0.999417	−	0.0341411i	$-0.989130\pi$
$257$	−1.98488	−	0.204051i	−1.98488	−	0.204051i	−0.985460	−	0.169910i	$-0.945652\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.78933	+	0.850966i	−1.78933	+	0.850966i	−0.836182	+	0.548452i	$0.815217\pi$
$263$	−1.78933	+	0.850966i	−1.78933	+	0.850966i	−0.953145	+	0.302515i	$0.902174\pi$
$264$		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	$0.826087\pi$
$272$	−0.0164924	−	0.0108174i	−0.0164924	−	0.0108174i
$273$		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		−0.903075	−	0.429483i	$-0.858696\pi$
$277$		0			0		0.903075	+	0.429483i	$0.141304\pi$
$278$	−0.736862	+	0.414317i	−0.736862	+	0.414317i
$279$	1.24888	−	0.759461i	1.24888	−	0.759461i
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	0.560041	+	0.367331i	0.560041	+	0.367331i
$283$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$283$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.876594	−	0.345684i	−0.876594	−	0.345684i
$289$	−0.979084	−	0.0669712i	−0.979084	−	0.0669712i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.0643397	−	1.88342i	−0.0643397	−	1.88342i	−0.366854	−	0.930278i	$-0.619565\pi$
$293$	−0.0643397	−	1.88342i	−0.0643397	−	1.88342i	0.302515	−	0.953145i	$-0.402174\pi$
$294$	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
$302$	0.719208	−	0.824823i	0.719208	−	0.824823i
$303$		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		0.102264	−	0.994757i	$-0.467391\pi$
$307$		0			0		−0.102264	+	0.994757i	$0.532609\pi$
$308$		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		0.971567	−	0.236764i	$-0.0760870\pi$
$313$		0			0		−0.971567	+	0.236764i	$0.923913\pi$
$314$		0			0
$315$		0			0
$316$	0.434096	+	0.614974i	0.434096	+	0.614974i
$317$	0.905802	+	0.509307i	0.905802	+	0.509307i	0.871660	−	0.490110i	$-0.163043\pi$
$317$	0.905802	+	0.509307i	0.905802	+	0.509307i	0.0341411	+	0.999417i	$0.489130\pi$
$318$	−0.615906	+	0.0210400i	−0.615906	+	0.0210400i
$319$		0			0
$320$		0			0
$321$	0.414006	−	0.953137i	0.414006	−	0.953137i
$322$		0			0
$323$	0.0270175	−	0.0685116i	0.0270175	−	0.0685116i
$324$	−0.519584	+	0.184660i	−0.519584	+	0.184660i
$325$		0			0
$326$		0			0
$327$	0.481457	+	0.634896i	0.481457	+	0.634896i
$328$		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	$0.913043\pi$
$332$	0.239497	−	0.982781i	0.239497	−	0.982781i
$333$		0			0
$334$	−0.398285	−	1.12067i	−0.398285	−	1.12067i
$335$		0			0
$336$		0			0
$337$		0			0		0.930278	−	0.366854i	$-0.119565\pi$
$337$		0			0		−0.930278	+	0.366854i	$0.880435\pi$
$338$	0.638377	−	0.202612i	0.638377	−	0.202612i
$339$	−0.398401	−	1.91721i	−0.398401	−	1.91721i
$340$		0			0
$341$		0			0
$342$	−0.0614052	+	0.356143i	−0.0614052	+	0.356143i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.186018	−	0.199177i	−0.186018	−	0.199177i
$347$	0.0691386	+	0.400995i	0.0691386	+	0.400995i	0.999417	+	0.0341411i	$0.0108696\pi$
$347$	0.0691386	+	0.400995i	0.0691386	+	0.400995i	−0.930278	+	0.366854i	$0.880435\pi$
$348$		0			0
$349$	−0.0861339	−	1.25923i	−0.0861339	−	1.25923i	−0.816970	−	0.576680i	$-0.804348\pi$
$349$	−0.0861339	−	1.25923i	−0.0861339	−	1.25923i	0.730836	−	0.682553i	$-0.239130\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.53451	+	1.16366i	1.53451	+	1.16366i	0.930278	+	0.366854i	$0.119565\pi$
$353$	1.53451	+	1.16366i	1.53451	+	1.16366i	0.604236	+	0.796805i	$0.293478\pi$
$354$		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
$362$	1.09665	−	0.719295i	1.09665	−	0.719295i
$363$	−0.169910	+	0.985460i	−0.169910	+	0.985460i
$364$		0			0
$365$		0			0
$366$	−0.157164	−	0.756317i	−0.157164	−	0.756317i
$367$		0			0		0.953145	−	0.302515i	$-0.0978261\pi$
$367$		0			0		−0.953145	+	0.302515i	$0.902174\pi$
$368$	−0.0366111	+	0.0144376i	−0.0366111	+	0.0144376i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.395028	+	0.702557i	0.395028	+	0.702557i
$373$		0			0		0.236764	−	0.971567i	$-0.423913\pi$
$373$		0			0		−0.236764	+	0.971567i	$0.576087\pi$
$374$		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	$-0.847826\pi$
$379$	−0.887885	−	1.46007i	−0.887885	−	1.46007i		−	1.00000i	$-0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.306695	+	0.267424i	−0.306695	+	0.267424i	−0.796805	−	0.604236i	$-0.793478\pi$
$383$	−0.306695	+	0.267424i	−0.306695	+	0.267424i	0.490110	+	0.871660i	$0.336957\pi$
$384$	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
$392$	−1.00954	+	0.246017i	−1.00954	+	0.246017i
$393$		0			0
$394$	0.631088	+	0.445471i	0.631088	+	0.445471i
$395$		0			0
$396$		0			0
$397$		0			0		−0.953145	−	0.302515i	$-0.902174\pi$
$397$		0			0		0.953145	+	0.302515i	$0.0978261\pi$
$398$	0.121627	−	1.18310i	0.121627	−	1.18310i
$399$		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
$408$	−0.0145030	−	0.141075i	−0.0145030	−	0.141075i
$409$	0.256797	−	1.23578i	0.256797	−	1.23578i	−0.631088	−	0.775711i	$-0.717391\pi$
$409$	0.256797	−	1.23578i	0.256797	−	1.23578i	0.887885	−	0.460065i	$-0.152174\pi$
$410$		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
$417$	−1.17418	−	0.463035i	−1.17418	−	0.463035i
$418$		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
$423$	0.102264	+	0.994757i	0.102264	+	0.994757i
$424$		−	0.956088i		−	0.956088i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.517480	+	0.246103i	0.517480	+	0.246103i
$429$		0			0
$430$		0			0
$431$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$431$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$432$	0.0437165	+	0.137739i	0.0437165	+	0.137739i
$433$		0			0		−0.836182	−	0.548452i	$-0.815217\pi$
$433$		0			0		0.836182	+	0.548452i	$0.184783\pi$
$434$		0			0
$435$		0			0
$436$	−0.358956	+	0.253379i	−0.358956	+	0.253379i
$437$	−0.0805946	−	0.122876i	−0.0805946	−	0.122876i
$438$		0			0
$439$	0.953137	−	1.56737i	0.953137	−	1.56737i	0.136167	−	0.990686i	$-0.456522\pi$
$439$	0.953137	−	1.56737i	0.953137	−	1.56737i	0.816970	−	0.576680i	$-0.195652\pi$
$440$		0			0
$441$	−0.576680	+	0.816970i	−0.576680	+	0.816970i
$442$		0			0
$443$	0.600560	+	0.523661i	0.600560	+	0.523661i	0.903075	−	0.429483i	$-0.141304\pi$
$443$	0.600560	+	0.523661i	0.600560	+	0.523661i	−0.302515	+	0.953145i	$0.597826\pi$
$444$		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
$452$	1.06408	−	0.183466i	1.06408	−	0.183466i
$453$	1.63299	+	0.0557845i	1.63299	+	0.0557845i
$454$	−0.935031	−	0.568605i	−0.935031	−	0.568605i
$455$		0			0
$456$	−0.548953	−	0.114074i	−0.548953	−	0.114074i
$457$		0			0		−0.985460	−	0.169910i	$-0.945652\pi$
$457$		0			0		0.985460	+	0.169910i	$0.0543478\pi$
$458$	−0.536350	+	0.953898i	−0.536350	+	0.953898i
$459$	−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		−0.657204	−	0.753713i	$-0.728261\pi$
$463$		0			0		0.657204	+	0.753713i	$0.271739\pi$
$464$		0			0
$465$		0			0
$466$	−0.320880	+	1.14523i	−0.320880	+	1.14523i
$467$	1.22629	+	0.298838i	1.22629	+	0.298838i	0.796805	−	0.604236i	$-0.206522\pi$
$467$	1.22629	+	0.298838i	1.22629	+	0.298838i	0.429483	+	0.903075i	$0.358696\pi$
$468$		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
$477$	−0.604713	−	0.693514i	−0.604713	−	0.693514i
$478$		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
$482$	0.302038	−	0.537174i	0.302038	−	0.537174i
$483$		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		−0.999417	−	0.0341411i	$-0.989130\pi$
$487$		0			0		0.999417	+	0.0341411i	$0.0108696\pi$
$488$	1.18101	−	0.203626i	1.18101	−	0.203626i
$489$		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
$498$	−1.10954	+	0.527673i	−1.10954	+	0.527673i
$499$	−0.157049	+	0.222488i	−0.157049	+	0.222488i	−0.887885	−	0.460065i	$-0.847826\pi$
$499$	−0.157049	+	0.222488i	−0.157049	+	0.222488i	0.730836	+	0.682553i	$0.239130\pi$
$500$		0			0
$501$	0.922662	−	1.51725i	0.922662	−	1.51725i
$502$		0			0
$503$	1.03357	+	1.57580i	1.03357	+	1.57580i	0.796805	+	0.604236i	$0.206522\pi$
$503$	1.03357	+	1.57580i	1.03357	+	1.57580i	0.236764	+	0.971567i	$0.423913\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.836182	+	0.548452i	0.836182	+	0.548452i
$508$		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
$512$	−0.258577	−	0.122974i	−0.258577	−	0.122974i
$513$	−0.470342	+	0.264460i	−0.470342	+	0.264460i
$514$	−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		−0.930278	−	0.366854i	$-0.880435\pi$
$523$		0			0		0.930278	+	0.366854i	$0.119565\pi$
$524$		0			0
$525$		0			0
$526$	−0.610526	+	1.17826i	−0.610526	+	1.17826i
$527$	−0.109414	+	0.166815i	−0.109414	+	0.166815i
$528$		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	$0.695652\pi$
$542$	−0.131905	+	1.28308i	−0.131905	+	1.28308i
$543$	1.86642	+	0.592374i	1.86642	+	0.592374i
$544$	0.128309	−	0.00877656i	0.128309	−	0.00877656i
$545$		0			0
$546$		0			0
$547$		0			0		0.0341411	−	0.999417i	$-0.489130\pi$
$547$		0			0		−0.0341411	+	0.999417i	$0.510870\pi$
$548$	0.426882	−	0.104028i	0.426882	−	0.104028i
$549$	0.727872	−	0.894675i	0.727872	−	0.894675i
$550$		0			0
$551$		0			0
$552$	−0.246659	−	0.138689i	−0.246659	−	0.138689i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.277284	−	0.638372i	0.277284	−	0.638372i
$557$	−1.50391	+	1.31134i	−1.50391	+	1.31134i	−0.707107	+	0.707107i	$0.750000\pi$
$557$	−1.50391	+	1.31134i	−1.50391	+	1.31134i	−0.796805	+	0.604236i	$0.793478\pi$
$558$	0.359139	−	0.910713i	0.359139	−	0.910713i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.41092	−	1.41092i	1.41092	−	1.41092i	0.657204	−	0.753713i	$-0.271739\pi$
$563$	1.41092	−	1.41092i	1.41092	−	1.41092i	0.753713	−	0.657204i	$-0.228261\pi$
$564$	−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		0.169910	−	0.985460i	$-0.445652\pi$
$577$		0			0		−0.169910	+	0.985460i	$0.554348\pi$
$578$	−0.549608	+	0.360488i	−0.549608	+	0.360488i
$579$		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
$587$	−0.429951	−	0.326042i	−0.429951	−	0.326042i	0.366854	−	0.930278i	$-0.380435\pi$
$587$	−0.429951	−	0.326042i	−0.429951	−	0.326042i	−0.796805	+	0.604236i	$0.793478\pi$
$588$	−0.439376	−	0.333190i	−0.439376	−	0.333190i
$589$	0.497745	+	0.611810i	0.497745	+	0.611810i
$590$		0			0
$591$	0.0787081	+	1.15067i	0.0787081	+	1.15067i
$592$		0			0
$593$	0.320200	+	1.85712i	0.320200	+	1.85712i	0.490110	+	0.871660i	$0.336957\pi$
$593$	0.320200	+	1.85712i	0.320200	+	1.85712i	−0.169910	+	0.985460i	$0.554348\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.48487	−	0.973925i	1.48487	−	0.973925i
$598$		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		−0.490110	−	0.871660i	$-0.663043\pi$
$607$		0			0		0.490110	+	0.871660i	$0.336957\pi$
$608$	0.120384	−	0.493998i	0.120384	−	0.493998i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.0532174	−	0.0532174i	0.0532174	−	0.0532174i
$613$		0			0		−0.604236	−	0.796805i	$-0.706522\pi$
$613$		0			0		0.604236	+	0.796805i	$0.293478\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.500795	+	1.26993i	−0.500795	+	1.26993i	0.429483	+	0.903075i	$0.358696\pi$
$617$	−0.500795	+	1.26993i	−0.500795	+	1.26993i	−0.930278	+	0.366854i	$0.880435\pi$
$618$		0			0
$619$	0.459500	−	1.05788i	0.459500	−	1.05788i	−0.519584	−	0.854419i	$-0.673913\pi$
$619$	0.459500	−	1.05788i	0.459500	−	1.05788i	0.979084	−	0.203456i	$-0.0652174\pi$
$620$		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	$0.521739\pi$
$632$	1.35199	+	0.429103i	1.35199	+	0.429103i
$633$	0.106270	−	1.03372i	0.106270	−	1.03372i
$634$	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	$0.760870\pi$
$642$	−0.164786	−	0.676203i	−0.164786	−	0.676203i
$643$		0			0		−0.102264	−	0.994757i	$-0.532609\pi$
$643$		0			0		0.102264	+	0.994757i	$0.467391\pi$
$644$		0			0
$645$		0			0
$646$	−0.0133078	−	0.0474962i	−0.0133078	−	0.0474962i
$647$	0.0314143	+	0.919594i	0.0314143	+	0.919594i	0.903075	+	0.429483i	$0.141304\pi$
$647$	0.0314143	+	0.919594i	0.0314143	+	0.919594i	−0.871660	+	0.490110i	$0.836957\pi$
$648$	−0.569885	+	0.868860i	−0.569885	+	0.868860i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.827114	−	1.73917i	0.827114	−	1.73917i	0.169910	−	0.985460i	$-0.445652\pi$
$653$	0.827114	−	1.73917i	0.827114	−	1.73917i	0.657204	−	0.753713i	$-0.271739\pi$
$654$	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	$0.304348\pi$
$662$	−1.07094	+	0.602160i	−1.07094	+	0.602160i
$663$		0			0
$664$	−0.759397	−	1.74831i	−0.759397	−	1.74831i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.818789	+	0.537044i	0.818789	+	0.537044i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.994757	−	0.102264i	$-0.0326087\pi$
$673$		0			0		−0.994757	+	0.102264i	$0.967391\pi$
$674$		0			0
$675$		0			0
$676$	−0.317995	+	0.450496i	−0.317995	+	0.450496i
$677$	−1.13984	+	0.542084i	−1.13984	+	0.542084i	−0.903075	−	0.429483i	$-0.858696\pi$
$677$	−1.13984	+	0.542084i	−1.13984	+	0.542084i	−0.236764	+	0.971567i	$0.576087\pi$
$678$	−0.988496	−	0.861923i	−0.988496	−	0.861923i
$679$		0			0
$680$		0			0
$681$	−0.222488	−	1.61872i	−0.222488	−	1.61872i
$682$		0			0
$683$	−1.97098	−	0.202623i	−1.97098	−	0.202623i	−0.971567	−	0.236764i	$-0.923913\pi$
$683$	−1.97098	−	0.202623i	−1.97098	−	0.202623i	−0.999417	+	0.0341411i	$0.989130\pi$
$684$	−0.136890	−	0.264185i	−0.136890	−	0.264185i
$685$		0			0
$686$		0			0
$687$	−1.61018	+	0.277623i	−1.61018	+	0.277623i
$688$		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	$-0.913043\pi$
$692$	0.221118	+	0.0381246i	0.221118	+	0.0381246i
$693$		0			0
$694$	0.199177	+	0.186018i	0.199177	+	0.186018i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.555570	−	0.637154i	−0.555570	−	0.637154i
$699$	−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	$0.543478\pi$
$709$	−0.534568	+	1.90790i	−0.534568	+	1.90790i	−0.398401	+	0.917211i	$0.630435\pi$
$710$		0			0
$711$	1.25209	−	0.543860i	1.25209	−	0.543860i
$712$		0			0
$713$	0.146031	+	0.370308i	0.146031	+	0.370308i
$714$		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
$722$	0.474475	+	0.0162085i	0.474475	+	0.0162085i
$723$	0.906751	−	0.156340i	0.906751	−	0.156340i
$724$	−0.361596	+	1.01743i	−0.361596	+	1.01743i
$725$		0			0
$726$	0.308133	+	0.594669i	0.308133	+	0.594669i
$727$		0			0		−0.994757	−	0.102264i	$-0.967391\pi$
$727$		0			0		0.994757	+	0.102264i	$0.0326087\pi$
$728$		0			0
$729$	0.136167	+	0.990686i	0.136167	+	0.990686i
$730$		0			0
$731$		0			0
$732$	0.479353	+	0.417974i	0.479353	+	0.417974i
$733$		0			0		0.903075	−	0.429483i	$-0.141304\pi$
$733$		0			0		−0.903075	+	0.429483i	$0.858696\pi$
$734$		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	−0.398401	−	0.917211i	$-0.630435\pi$
$739$	0.332435	−	0.234658i	0.332435	−	0.234658i	0.730836	+	0.682553i	$0.239130\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.163235	−	0.514311i	−0.163235	−	0.514311i	0.836182	−	0.548452i	$-0.184783\pi$
$743$	−0.163235	−	0.514311i	−0.163235	−	0.514311i	−0.999417	+	0.0341411i	$0.989130\pi$
$744$	1.39305	+	0.605089i	1.39305	+	0.605089i
$745$		0			0
$746$		0			0
$747$	−1.65662	−	0.787854i	−1.65662	−	0.787854i
$748$		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	$0.826087\pi$
$752$	0.00493375	+	0.144426i	0.00493375	+	0.144426i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.429483	−	0.903075i	$-0.358696\pi$
$757$		0			0		−0.429483	+	0.903075i	$0.641304\pi$
$758$	−1.06471	−	0.419869i	−1.06471	−	0.419869i
$759$		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
$768$	−0.250687	−	1.02870i	−0.250687	−	1.02870i
$769$	−0.0997480	+	0.0931581i	−0.0997480	+	0.0931581i	−0.730836	−	0.682553i	$-0.760870\pi$
$769$	−0.0997480	+	0.0931581i	−0.0997480	+	0.0931581i	0.631088	+	0.775711i	$0.282609\pi$
$770$		0			0
$771$	−1.88013	−	0.668198i	−1.88013	−	0.668198i
$772$		0			0
$773$	−0.469328	+	1.47873i	−0.469328	+	1.47873i	0.366854	+	0.930278i	$0.380435\pi$
$773$	−0.469328	+	1.47873i	−0.469328	+	1.47873i	−0.836182	+	0.548452i	$0.815217\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.000849927	−	0.0248800i	0.000849927	−	0.0248800i
$783$		0			0
$784$	−0.0911989	+	0.112098i	−0.0911989	+	0.112098i
$785$		0			0
$786$		0			0
$787$		0			0		−0.871660	−	0.490110i	$-0.836957\pi$
$787$		0			0		0.871660	+	0.490110i	$0.163043\pi$
$788$	−0.635618	+	0.0217134i	−0.635618	+	0.0217134i
$789$	−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
$797$	0.762653	+	1.00571i	0.762653	+	1.00571i	0.999417	+	0.0341411i	$0.0108696\pi$
$797$	0.762653	+	1.00571i	0.762653	+	1.00571i	−0.236764	+	0.971567i	$0.576087\pi$
$798$		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
$813$	−1.61035	+	1.05623i	−1.61035	+	1.05623i
$814$		0			0
$815$		0			0
$816$	−0.0134623	−	0.0144146i	−0.0134623	−	0.0144146i
$817$		0			0
$818$	−0.363066	−	0.763418i	−0.363066	−	0.763418i
$819$		0			0
$820$		0			0
$821$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$821$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$822$	−0.425227	−	0.322460i	−0.425227	−	0.322460i
$823$		0			0		−0.796805	−	0.604236i	$-0.793478\pi$
$823$		0			0		0.796805	+	0.604236i	$0.206522\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.666310	+	1.40105i	0.666310	+	1.40105i	0.903075	+	0.429483i	$0.141304\pi$
$827$	0.666310	+	1.40105i	0.666310	+	1.40105i	−0.236764	+	0.971567i	$0.576087\pi$
$828$	−0.0255156	−	0.147987i	−0.0255156	−	0.147987i
$829$	1.28629	+	1.37728i	1.28629	+	1.37728i	0.887885	+	0.460065i	$0.152174\pi$
$829$	1.28629	+	1.37728i	1.28629	+	1.37728i	0.398401	+	0.917211i	$0.369565\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.0231902	−	0.134500i	0.0231902	−	0.134500i
$834$	−0.814006	+	0.228074i	−0.814006	+	0.228074i
$835$		0			0
$836$		0			0
$837$	1.39318	−	0.442177i	1.39318	−	0.442177i
$838$		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
$842$	0.341113	+	0.606669i	0.341113	+	0.606669i
$843$		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
$848$	−0.0803444	−	0.105950i	−0.0803444	−	0.105950i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.753713	−	0.657204i	$-0.228261\pi$
$853$		0			0		−0.753713	+	0.657204i	$0.771739\pi$
$854$		0			0
$855$		0			0
$856$	1.05719	−	0.219687i	1.05719	−	0.219687i
$857$	−1.03856	+	0.0354783i	−1.03856	+	0.0354783i	−0.548452	−	0.836182i	$-0.684783\pi$
$857$	−1.03856	+	0.0354783i	−1.03856	+	0.0354783i	−0.490110	+	0.871660i	$0.663043\pi$
$858$		0			0
$859$	1.08677	+	1.53960i	1.08677	+	1.53960i	0.816970	+	0.576680i	$0.195652\pi$
$859$	1.08677	+	1.53960i	1.08677	+	1.53960i	0.269797	+	0.962917i	$0.413043\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.0466062	−	1.36431i	0.0466062	−	1.36431i	−0.707107	−	0.707107i	$-0.750000\pi$
$863$	0.0466062	−	1.36431i	0.0466062	−	1.36431i	0.753713	−	0.657204i	$-0.228261\pi$
$864$	−0.769824	−	0.543401i	−0.769824	−	0.543401i
$865$		0			0
$866$		0			0
$867$	−0.935389	−	0.296879i	−0.935389	−	0.296879i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.250464	+	0.789148i	−0.250464	+	0.789148i
$873$		0			0
$874$	−0.0927379	−	0.0329591i	−0.0927379	−	0.0329591i
$875$		0			0
$876$		0			0
$877$		0			0		−0.236764	−	0.971567i	$-0.576087\pi$
$877$		0			0		0.236764	+	0.971567i	$0.423913\pi$
$878$	−0.125644	−	1.22218i	−0.125644	−	1.22218i
$879$	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	$0.413043\pi$
$882$	0.0228663	+	0.669369i	0.0228663	+	0.669369i
$883$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$883$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$884$		0			0
$885$		0			0
$886$	0.532422	+	0.0364186i	0.532422	+	0.0364186i
$887$	−0.501972	−	0.197952i	−0.501972	−	0.197952i	0.102264	−	0.994757i	$-0.467391\pi$
$887$	−0.501972	−	0.197952i	−0.501972	−	0.197952i	−0.604236	+	0.796805i	$0.706522\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.524251	+	0.127757i	−0.524251	+	0.127757i
$894$		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		−0.548452	−	0.836182i	$-0.684783\pi$
$907$		0			0		0.548452	+	0.836182i	$0.315217\pi$
$908$	0.896268	−	0.0921391i	0.896268	−	0.0921391i
$909$		0			0
$910$		0			0
$911$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$911$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$912$	−0.0704190	+	0.0334898i	−0.0704190	+	0.0334898i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.122685	−	0.892599i	−0.122685	−	0.892599i
$917$		0			0
$918$	−0.0909327	−	0.00934817i	−0.0909327	−	0.00934817i
$919$	0.125291	+	0.241801i	0.125291	+	0.241801i	0.942261	−	0.334880i	$-0.108696\pi$
$919$	0.125291	+	0.241801i	0.125291	+	0.241801i	−0.816970	+	0.576680i	$0.804348\pi$
$920$		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
$932$	−0.359224	−	0.910929i	−0.359224	−	0.910929i
$933$		0			0
$934$	0.775368	−	0.336790i	0.775368	−	0.336790i
$935$		0			0
$936$		0			0
$937$		0			0		−0.971567	−	0.236764i	$-0.923913\pi$
$937$		0			0		0.971567	+	0.236764i	$0.0760870\pi$
$938$		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
$947$	1.01960	+	1.16933i	1.01960	+	1.16933i	0.985460	+	0.169910i	$0.0543478\pi$
$947$	1.01960	+	1.16933i	1.01960	+	1.16933i	0.0341411	+	0.999417i	$0.489130\pi$
$948$	0.276150	+	0.700268i	0.276150	+	0.700268i
$949$		0			0
$950$		0			0
$951$	0.759461	+	0.709287i	0.759461	+	0.709287i
$952$		0			0
$953$	1.85712	+	0.320200i	1.85712	+	0.320200i	0.985460	−	0.169910i	$-0.0543478\pi$
$953$	1.85712	+	0.320200i	1.85712	+	0.320200i	0.871660	+	0.490110i	$0.163043\pi$
$954$	−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
$963$	0.627903	−	0.828014i	0.627903	−	0.828014i
$964$	0.0690883	+	0.502655i	0.0690883	+	0.502655i
$965$		0			0
$966$		0			0
$967$		0			0		−0.753713	−	0.657204i	$-0.771739\pi$
$967$		0			0		0.753713	+	0.657204i	$0.228261\pi$
$968$	−0.938367	+	0.446267i	−0.938367	+	0.446267i
$969$	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	$0.673913\pi$
$972$	−0.548532	+	0.0563908i	−0.548532	+	0.0563908i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.113763	−	0.121810i	0.113763	−	0.121810i
$977$	0.340253	+	0.223172i	0.340253	+	0.223172i	0.707107	−	0.707107i	$-0.250000\pi$
$977$	0.340253	+	0.223172i	0.340253	+	0.223172i	−0.366854	+	0.930278i	$0.619565\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.317447	+	0.730836i	0.317447	+	0.730836i
$982$		0			0
$983$	−1.42424	+	0.800811i	−1.42424	+	0.800811i	−0.994757	−	0.102264i	$-0.967391\pi$
$983$	−1.42424	+	0.800811i	−1.42424	+	0.800811i	−0.429483	+	0.903075i	$0.641304\pi$
$984$		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	$0.260870\pi$
$992$	−0.591537	+	1.24382i	−0.591537	+	1.24382i
$993$	−1.70652	−	0.672966i	−1.70652	−	0.672966i
$994$		0			0
$995$		0			0
$996$	0.465375	−	0.898133i	0.465375	−	0.898133i
$997$		0			0		0.548452	−	0.836182i	$-0.315217\pi$
$997$		0			0		−0.548452	+	0.836182i	$0.684783\pi$
$998$	0.00622726	+	0.182291i	0.00622726	+	0.182291i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.1.bg.a.1643.1	✓	88	5.3	odd	4	inner
3525.1.bg.a.1643.1	✓	88	15.2	even	4	inner
3525.1.bg.a.1643.2	yes	88	5.2	odd	4	inner
3525.1.bg.a.1643.2	yes	88	15.8	even	4	inner
3525.1.bg.a.2207.1	yes	88	3.2	odd	2	inner
3525.1.bg.a.2207.1	yes	88	5.4	even	2	inner
3525.1.bg.a.2207.2	yes	88	1.1	even	1	trivial
3525.1.bg.a.2207.2	yes	88	15.14	odd	2	CM
3525.1.bg.a.2843.1	yes	88	235.23	even	92	inner
3525.1.bg.a.2843.1	yes	88	705.587	odd	92	inner
3525.1.bg.a.2843.2	yes	88	235.117	even	92	inner
3525.1.bg.a.2843.2	yes	88	705.23	odd	92	inner
3525.1.bg.a.3407.1	yes	88	141.23	even	46	inner
3525.1.bg.a.3407.1	yes	88	235.164	odd	46	inner
3525.1.bg.a.3407.2	yes	88	47.23	odd	46	inner
3525.1.bg.a.3407.2	yes	88	705.164	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.bg (of order \(92\), degree \(44\), minimal)

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