LMFDB - Embedded newform 3703.1.l.g.1392.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3703,1,Mod(118,3703)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3703, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 16]))

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

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

chi := DirichletCharacter("3703.118");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3703 = 7 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3703.l (of order $22$, degree $10$, not 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:	$1.84803774178$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 161)
Projective image:	$D_{11}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{11} - \cdots)$

Embedding invariants

Embedding label			1392.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	3703.1392
Dual form			3703.1.l.g.3429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.239446 + 0.153882i) q^{2} +(-0.381761 + 0.835939i) q^{4} +(0.654861 + 0.755750i) q^{7} +(-0.0777324 - 0.540641i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-1.41542 - 0.909632i) q^{11} +(-0.273100 - 0.0801894i) q^{14} +(-0.500000 - 0.577031i) q^{16} +(0.273100 - 0.0801894i) q^{18} +0.478891 q^{22} +(0.841254 - 0.540641i) q^{25} +(-0.881761 + 0.258908i) q^{28} +(-0.544078 - 1.19136i) q^{29} +(0.732593 + 0.215109i) q^{32} +(0.601808 - 0.694523i) q^{36} +(-1.84125 - 0.540641i) q^{37} +(0.118239 - 0.822373i) q^{43} +(1.30075 - 0.835939i) q^{44} +(-0.142315 + 0.989821i) q^{49} +(-0.118239 + 0.258908i) q^{50} +(-0.857685 - 0.989821i) q^{53} +(0.357685 - 0.412791i) q^{56} +(0.313607 + 0.201543i) q^{58} +(-0.415415 - 0.909632i) q^{63} +(0.524075 - 0.153882i) q^{64} +(0.239446 - 0.153882i) q^{67} +(1.41542 - 0.909632i) q^{71} +(-0.0777324 + 0.540641i) q^{72} +(0.524075 - 0.153882i) q^{74} +(-0.239446 - 1.66538i) q^{77} +(-0.857685 + 0.989821i) q^{79} +(0.841254 + 0.540641i) q^{81} +(0.0982369 + 0.215109i) q^{86} +(-0.381761 + 0.835939i) q^{88} +(-0.118239 - 0.258908i) q^{98} +(1.10181 + 1.27155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 3 q^{4} + q^{7} + 7 q^{8} - q^{9} - 9 q^{11} + 2 q^{14} - 5 q^{16} - 2 q^{18} + 4 q^{22} - q^{25} - 8 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 9 q^{37} + 2 q^{43} - 5 q^{44} - q^{49}+ \cdots + 2 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 3 * q^4 + q^7 + 7 * q^8 - q^9 - 9 * q^11 + 2 * q^14 - 5 * q^16 - 2 * q^18 + 4 * q^22 - q^25 - 8 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 9 * q^37 + 2 * q^43 - 5 * q^44 - q^49 - 2 * q^50 - 9 * q^53 + 4 * q^56 + 7 * q^58 + q^63 + 4 * q^64 + 2 * q^67 + 9 * q^71 + 7 * q^72 + 4 * q^74 - 2 * q^77 - 9 * q^79 - q^81 + 4 * q^86 - 3 * q^88 - 2 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3703\mathbb{Z}\right)^\times$.

$n$	$2117$	$3179$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$2$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$3$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$3$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$4$	−0.381761	+	0.835939i	−0.381761	+	0.835939i
$5$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$5$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$6$		0			0
$7$	0.654861	+	0.755750i	0.654861	+	0.755750i
$7$	0.654861	+	0.755750i	0.654861	+	0.755750i
$8$	−0.0777324	−	0.540641i	−0.0777324	−	0.540641i
$9$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$10$		0			0
$11$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$11$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$12$		0			0
$13$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$13$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$14$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$15$		0			0
$16$	−0.500000	−	0.577031i	−0.500000	−	0.577031i
$17$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$17$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$18$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$19$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$19$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$20$		0			0
$21$		0			0
$22$	0.478891			0.478891
$23$		0			0
$23$		0			0
$24$		0			0
$25$	0.841254	−	0.540641i	0.841254	−	0.540641i
$26$		0			0
$27$		0			0
$28$	−0.881761	+	0.258908i	−0.881761	+	0.258908i
$29$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$29$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$30$		0			0
$31$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$31$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$32$	0.732593	+	0.215109i	0.732593	+	0.215109i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.601808	−	0.694523i	0.601808	−	0.694523i
$37$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$37$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$41$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$42$		0			0
$43$	0.118239	−	0.822373i	0.118239	−	0.822373i	−0.841254	−	0.540641i	$-0.818182\pi$
$43$	0.118239	−	0.822373i	0.118239	−	0.822373i	0.959493	−	0.281733i	$-0.0909091\pi$
$44$	1.30075	−	0.835939i	1.30075	−	0.835939i
$45$		0			0
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$50$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$51$		0			0
$52$		0			0
$53$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	0.142315	−	0.989821i	$-0.454545\pi$
$53$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$	0.357685	−	0.412791i	0.357685	−	0.412791i
$57$		0			0
$58$	0.313607	+	0.201543i	0.313607	+	0.201543i
$59$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$59$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$60$		0			0
$61$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$61$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$62$		0			0
$63$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$64$	0.524075	−	0.153882i	0.524075	−	0.153882i
$65$		0			0
$66$		0			0
$67$	0.239446	−	0.153882i	0.239446	−	0.153882i	−0.415415	−	0.909632i	$-0.636364\pi$
$67$	0.239446	−	0.153882i	0.239446	−	0.153882i	0.654861	+	0.755750i	$0.272727\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$71$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$72$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$73$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$73$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$74$	0.524075	−	0.153882i	0.524075	−	0.153882i
$75$		0			0
$76$		0			0
$77$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$78$		0			0
$79$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	0.142315	+	0.989821i	$0.454545\pi$
$79$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	−1.00000			$\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.841254	+	0.540641i
$82$		0			0
$83$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$83$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$84$		0			0
$85$		0			0
$86$	0.0982369	+	0.215109i	0.0982369	+	0.215109i
$87$		0			0
$88$	−0.381761	+	0.835939i	−0.381761	+	0.835939i
$89$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$89$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$97$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$98$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$99$	1.10181	+	1.27155i	1.10181	+	1.27155i
$100$	0.130785	+	0.909632i	0.130785	+	0.909632i
$101$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$101$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$102$		0			0
$103$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$103$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$104$		0			0
$105$		0			0
$106$	0.357685	+	0.105026i	0.357685	+	0.105026i
$107$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	−0.415415	−	0.909632i	$-0.636364\pi$
$107$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	0.142315	−	0.989821i	$-0.454545\pi$
$108$		0			0
$109$	0.118239	+	0.258908i	0.118239	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$109$	0.118239	+	0.258908i	0.118239	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$110$		0			0
$111$		0			0
$112$	0.108660	−	0.755750i	0.108660	−	0.755750i
$113$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	−0.841254	−	0.540641i	$-0.818182\pi$
$113$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	0.142315	+	0.989821i	$0.454545\pi$
$114$		0			0
$115$		0			0
$116$	1.20362			1.20362
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.760554	+	1.66538i	0.760554	+	1.66538i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.239446	+	0.153882i	0.239446	+	0.153882i
$127$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$127$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$128$	−0.601808	+	0.694523i	−0.601808	+	0.694523i
$129$		0			0
$130$		0			0
$131$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$131$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$132$		0			0
$133$		0			0
$134$	−0.0336545	+	0.0736930i	−0.0336545	+	0.0736930i
$135$		0			0
$136$		0			0
$137$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$137$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		0			0
$141$		0			0
$142$	−0.198939	+	0.435615i	−0.198939	+	0.435615i
$143$		0			0
$144$	0.317178	+	0.694523i	0.317178	+	0.694523i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	1.15486	−	1.33278i	1.15486	−	1.33278i
$149$	−0.698939	−	0.449181i	−0.698939	−	0.449181i	0.142315	−	0.989821i	$-0.454545\pi$
$149$	−0.698939	−	0.449181i	−0.698939	−	0.449181i	−0.841254	+	0.540641i	$0.818182\pi$
$150$		0			0
$151$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$151$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$152$		0			0
$153$		0			0
$154$	0.313607	+	0.361922i	0.313607	+	0.361922i
$155$		0			0
$156$		0			0
$157$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$157$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$158$	0.0530529	−	0.368991i	0.0530529	−	0.368991i
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.284630			−0.284630
$163$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$163$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$167$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$168$		0			0
$169$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$170$		0			0
$171$		0			0
$172$	0.642315	+	0.412791i	0.642315	+	0.412791i
$173$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$173$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$174$		0			0
$175$	0.959493	+	0.281733i	0.959493	+	0.281733i
$176$	0.182822	+	1.27155i	0.182822	+	1.27155i
$177$		0			0
$178$		0			0
$179$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$179$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$180$		0			0
$181$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$181$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.841254	−	0.540641i	$-0.818182\pi$
$191$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.415415	−	0.909632i	$-0.636364\pi$
$192$		0			0
$193$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$193$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$194$		0			0
$195$		0			0
$196$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$197$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$197$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$198$	−0.459493	−	0.134919i	−0.459493	−	0.134919i
$199$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$199$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$200$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$201$		0			0
$202$		0			0
$203$	0.544078	−	1.19136i	0.544078	−	1.19136i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$211$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$212$	1.15486	−	0.339098i	1.15486	−	0.339098i
$213$		0			0
$214$	0.357685	+	0.412791i	0.357685	+	0.412791i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.0681534	−	0.0437995i	−0.0681534	−	0.0437995i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$223$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$224$	0.317178	+	0.694523i	0.317178	+	0.694523i
$225$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$226$	0.0982369	−	0.215109i	0.0982369	−	0.215109i
$227$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$227$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$	−0.601808	+	0.386758i	−0.601808	+	0.386758i
$233$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$233$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$239$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$240$		0			0
$241$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$241$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$242$	−0.438384	−	0.281733i	−0.438384	−	0.281733i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$251$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$252$	0.918986			0.918986
$253$		0			0
$254$	−0.236479			−0.236479
$255$		0			0
$256$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$257$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$257$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$258$		0			0
$259$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$260$		0			0
$261$	0.186393	+	1.29639i	0.186393	+	1.29639i
$262$		0			0
$263$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$263$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.0372254	+	0.258908i	0.0372254	+	0.258908i
$269$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$269$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$270$		0			0
$271$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$271$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$272$		0			0
$273$		0			0
$274$	−0.0681534	+	0.0437995i	−0.0681534	+	0.0437995i
$275$	−1.68251			−1.68251
$276$		0			0
$277$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$277$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$281$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$282$		0			0
$283$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$283$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$284$	0.220047	+	1.53046i	0.220047	+	1.53046i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.642315	−	0.412791i	−0.642315	−	0.412791i
$289$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$293$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$294$		0			0
$295$		0			0
$296$	−0.149167	+	1.03748i	−0.149167	+	1.03748i
$297$		0			0
$298$	0.236479			0.236479
$299$		0			0
$300$		0			0
$301$	0.698939	−	0.449181i	0.698939	−	0.449181i
$302$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$307$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$308$	1.48357	+	0.435615i	1.48357	+	0.435615i
$309$		0			0
$310$		0			0
$311$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$311$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$312$		0			0
$313$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$313$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$314$		0			0
$315$		0			0
$316$	−0.500000	−	1.09485i	−0.500000	−	1.09485i
$317$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$317$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$318$		0			0
$319$	−0.313607	+	2.18119i	−0.313607	+	2.18119i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$325$		0			0
$326$	0.154861	−	0.339098i	0.154861	−	0.339098i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$331$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$332$		0			0
$333$	1.61435	+	1.03748i	1.61435	+	1.03748i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.239446	+	1.66538i	0.239446	+	1.66538i	0.654861	+	0.755750i	$0.272727\pi$
$337$	0.239446	+	1.66538i	0.239446	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$338$	0.186393	+	0.215109i	0.186393	+	0.215109i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$344$	−0.453800			−0.453800
$345$		0			0
$346$		0			0
$347$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$347$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$348$		0			0
$349$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$349$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$350$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$351$		0			0
$352$	−0.841254	−	0.970858i	−0.841254	−	0.970858i
$353$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$353$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.154861	−	0.178719i	0.154861	−	0.178719i
$359$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.654861	−	0.755750i	$-0.272727\pi$
$359$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.142315	+	0.989821i	$0.454545\pi$
$360$		0			0
$361$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.186393	−	1.29639i	0.186393	−	1.29639i
$372$		0			0
$373$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$373$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$379$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$380$		0			0
$381$		0			0
$382$	0.524075	+	0.153882i	0.524075	+	0.153882i
$383$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$383$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$384$		0			0
$385$		0			0
$386$	0.459493	−	0.134919i	0.459493	−	0.134919i
$387$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$388$		0			0
$389$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−0.415415	+	0.909632i	$0.636364\pi$
$389$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	0.546200			0.546200
$393$		0			0
$394$	0.0336545	−	0.234072i	0.0336545	−	0.234072i
$395$		0			0
$396$	−1.48357	+	0.435615i	−1.48357	+	0.435615i
$397$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$397$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$398$		0			0
$399$		0			0
$400$	−0.732593	−	0.215109i	−0.732593	−	0.215109i
$401$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$401$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.0530529	+	0.368991i	0.0530529	+	0.368991i
$407$	2.11435	+	2.44009i	2.11435	+	2.44009i
$408$		0			0
$409$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$409$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$419$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$420$		0			0
$421$	0.544078	+	0.627899i	0.544078	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$421$	0.544078	+	0.627899i	0.544078	+	0.627899i	−0.415415	+	0.909632i	$0.636364\pi$
$422$	0.0681534	+	0.474017i	0.0681534	+	0.474017i
$423$		0			0
$424$	−0.468468	+	0.540641i	−0.468468	+	0.540641i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.69209	+	0.496841i	1.69209	+	0.496841i
$429$		0			0
$430$		0			0
$431$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$431$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$432$		0			0
$433$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$433$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$434$		0			0
$435$		0			0
$436$	−0.261571			−0.261571
$437$		0			0
$438$		0			0
$439$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$439$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$440$		0			0
$441$	0.415415	−	0.909632i	0.415415	−	0.909632i
$442$		0			0
$443$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$443$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.459493	+	0.295298i	0.459493	+	0.295298i
$449$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$449$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$450$	0.186393	−	0.215109i	0.186393	−	0.215109i
$451$		0			0
$452$	−0.108660	−	0.755750i	−0.108660	−	0.755750i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$457$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$463$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$464$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$465$		0			0
$466$	0.226900	+	0.496841i	0.226900	+	0.496841i
$467$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$467$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$468$		0			0
$469$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.915415	+	1.05645i	−0.915415	+	1.05645i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.544078	+	1.19136i	0.544078	+	1.19136i
$478$	−0.524075	+	0.153882i	−0.524075	+	0.153882i
$479$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$479$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.68251			−1.68251
$485$		0			0
$486$		0			0
$487$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$487$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$491$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.61435	+	0.474017i	1.61435	+	0.474017i
$498$		0			0
$499$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$499$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$503$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$504$	−0.459493	+	0.295298i	−0.459493	+	0.295298i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−0.642315	+	0.412791i	−0.642315	+	0.412791i
$509$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$509$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$510$		0			0
$511$		0			0
$512$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.459493	+	0.295298i	0.459493	+	0.295298i
$519$		0			0
$520$		0			0
$521$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$521$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$522$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$523$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$523$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$524$		0			0
$525$		0			0
$526$	0.0115295	−	0.0801894i	0.0115295	−	0.0801894i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.101808	−	0.117492i	−0.101808	−	0.117492i
$537$		0			0
$538$		0			0
$539$	1.10181	−	1.27155i	1.10181	−	1.27155i
$540$		0			0
$541$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$541$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$547$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$548$	−0.108660	+	0.237933i	−0.108660	+	0.237933i
$549$		0			0
$550$	0.402869	−	0.258908i	0.402869	−	0.258908i
$551$		0			0
$552$		0			0
$553$	−1.30972			−1.30972
$554$	0.459493	−	0.295298i	0.459493	−	0.295298i
$555$		0			0
$556$		0			0
$557$	1.91899	−	0.563465i	1.91899	−	0.563465i	0.959493	−	0.281733i	$-0.0909091\pi$
$557$	1.91899	−	0.563465i	1.91899	−	0.563465i	0.959493	−	0.281733i	$-0.0909091\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.244123	−	0.281733i	0.244123	−	0.281733i
$563$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$563$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.142315	+	0.989821i	0.142315	+	0.989821i
$568$	−0.601808	−	0.694523i	−0.601808	−	0.694523i
$569$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.654861	+	0.755750i	$0.272727\pi$
$569$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.142315	+	0.989821i	$0.454545\pi$
$570$		0			0
$571$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$571$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.546200			−0.546200
$577$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$577$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$578$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.313607	+	2.18119i	0.313607	+	2.18119i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$587$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.608660	+	1.33278i	0.608660	+	1.33278i
$593$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$593$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$594$		0			0
$595$		0			0
$596$	0.642315	−	0.412791i	0.642315	−	0.412791i
$597$		0			0
$598$		0			0
$599$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$599$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$600$		0			0
$601$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$601$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$602$	−0.0982369	+	0.215109i	−0.0982369	+	0.215109i
$603$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$604$	0.500000	+	1.09485i	0.500000	+	1.09485i
$605$		0			0
$606$		0			0
$607$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$607$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	0.959493	−	0.281733i	$-0.0909091\pi$
$613$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$	−0.881761	+	0.258908i	−0.881761	+	0.258908i
$617$	0.118239	−	0.258908i	0.118239	−	0.258908i	−0.841254	−	0.540641i	$-0.818182\pi$
$617$	0.118239	−	0.258908i	0.118239	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$618$		0			0
$619$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$619$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.415415	−	0.909632i	0.415415	−	0.909632i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.544078	−	0.627899i	0.544078	−	0.627899i	−0.415415	−	0.909632i	$-0.636364\pi$
$631$	0.544078	−	0.627899i	0.544078	−	0.627899i	0.959493	+	0.281733i	$0.0909091\pi$
$632$	0.601808	+	0.386758i	0.601808	+	0.386758i
$633$		0			0
$634$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.260554	−	0.570534i	−0.260554	−	0.570534i
$639$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$640$		0			0
$641$	0.284630	−	1.97964i	0.284630	−	1.97964i	0.142315	−	0.989821i	$-0.454545\pi$
$641$	0.284630	−	1.97964i	0.284630	−	1.97964i	0.142315	−	0.989821i	$-0.454545\pi$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$647$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$648$	0.226900	−	0.496841i	0.226900	−	0.496841i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.171292	−	1.19136i	−0.171292	−	1.19136i
$653$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$653$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	−0.841254	−	0.540641i	$-0.818182\pi$
$659$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	0.654861	−	0.755750i	$-0.272727\pi$
$660$		0			0
$661$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$661$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$662$	0.226900	−	0.0666238i	0.226900	−	0.0666238i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.546200			−0.546200
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$673$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$674$	−0.313607	−	0.361922i	−0.313607	−	0.361922i
$675$		0			0
$676$	0.881761	+	0.258908i	0.881761	+	0.258908i
$677$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$677$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$683$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$684$		0			0
$685$		0			0
$686$	0.118239	−	0.258908i	0.118239	−	0.258908i
$687$		0			0
$688$	−0.533654	+	0.342959i	−0.533654	+	0.342959i
$689$		0			0
$690$		0			0
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$694$	0.226900	−	0.496841i	0.226900	−	0.496841i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.601808	+	0.694523i	−0.601808	+	0.694523i
$701$	0.239446	+	0.153882i	0.239446	+	0.153882i	0.654861	−	0.755750i	$-0.272727\pi$
$701$	0.239446	+	0.153882i	0.239446	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$702$		0			0
$703$		0			0
$704$	−0.881761	−	0.258908i	−0.881761	−	0.258908i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$709$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	−0.841254	+	0.540641i	$0.818182\pi$
$710$		0			0
$711$	1.10181	−	0.708089i	1.10181	−	0.708089i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.108660	−	0.755750i	0.108660	−	0.755750i
$717$		0			0
$718$	−0.226900	+	0.0666238i	−0.226900	+	0.0666238i
$719$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$719$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$720$		0			0
$721$		0			0
$722$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$723$		0			0
$724$		0			0
$725$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$726$		0			0
$727$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$727$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$733$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.478891			−0.478891
$738$		0			0
$739$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$739$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$740$		0			0
$741$		0			0
$742$	0.154861	+	0.339098i	0.154861	+	0.339098i
$743$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$743$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$744$		0			0
$745$		0			0
$746$	−0.313607	+	0.361922i	−0.313607	+	0.361922i
$747$		0			0
$748$		0			0
$749$	1.25667	−	1.45027i	1.25667	−	1.45027i
$750$		0			0
$751$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	−0.841254	−	0.540641i	$-0.818182\pi$
$751$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	0.654861	−	0.755750i	$-0.272727\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−0.415415	+	0.909632i	$0.636364\pi$
$757$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−1.00000			$\pi$
$758$	−0.372786			−0.372786
$759$		0			0
$760$		0			0
$761$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$761$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$762$		0			0
$763$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$764$	1.69209	−	0.496841i	1.69209	−	0.496841i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$769$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$770$		0			0
$771$		0			0
$772$	1.01255	−	1.16854i	1.01255	−	1.16854i
$773$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$773$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$774$	−0.0336545	−	0.234072i	−0.0336545	−	0.234072i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.198939	−	0.435615i	0.198939	−	0.435615i
$779$		0			0
$780$		0			0
$781$	−2.83083			−2.83083
$782$		0			0
$783$		0			0
$784$	0.642315	−	0.412791i	0.642315	−	0.412791i
$785$		0			0
$786$		0			0
$787$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$787$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$788$	−0.317178	−	0.694523i	−0.317178	−	0.694523i
$789$		0			0
$790$		0			0
$791$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$792$	0.601808	−	0.694523i	0.601808	−	0.694523i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$797$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$798$		0			0
$799$		0			0
$800$	0.732593	−	0.215109i	0.732593	−	0.215109i
$801$		0			0
$802$	0.0777324	−	0.540641i	0.0777324	−	0.540641i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$809$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$810$		0			0
$811$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$811$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$812$	0.788201	+	0.909632i	0.788201	+	0.909632i
$813$		0			0
$814$	−0.881761	−	0.258908i	−0.881761	−	0.258908i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$821$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$822$		0			0
$823$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$823$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$827$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$839$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$840$		0			0
$841$	−0.468468	+	0.540641i	−0.468468	+	0.540641i
$842$	−0.226900	−	0.0666238i	−0.226900	−	0.0666238i
$843$		0			0
$844$	1.01255	+	1.16854i	1.01255	+	1.16854i
$845$		0			0
$846$		0			0
$847$	−0.760554	+	1.66538i	−0.760554	+	1.66538i
$848$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$853$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$854$		0			0
$855$		0			0
$856$	−1.00569	+	0.295298i	−1.00569	+	0.295298i
$857$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$857$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$858$		0			0
$859$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$859$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$860$		0			0
$861$		0			0
$862$	0.198939	+	0.127850i	0.198939	+	0.127850i
$863$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$863$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.11435	−	0.620830i	2.11435	−	0.620830i
$870$		0			0
$871$		0			0
$872$	0.130785	−	0.0840506i	0.130785	−	0.0840506i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$877$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$881$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$882$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$883$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$883$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$884$		0			0
$885$		0			0
$886$	−0.402869	−	0.258908i	−0.402869	−	0.258908i
$887$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$887$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$888$		0			0
$889$	0.118239	+	0.822373i	0.118239	+	0.822373i
$890$		0			0
$891$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.918986			−0.918986
$897$		0			0
$898$	0.546200			0.546200
$899$		0			0
$900$	0.130785	−	0.909632i	0.130785	−	0.909632i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.297176	+	0.342959i	0.297176	+	0.342959i
$905$		0			0
$906$		0			0
$907$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$907$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i	0.142315	−	0.989821i	$-0.454545\pi$
$911$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i	−0.415415	+	0.909632i	$0.636364\pi$
$912$		0			0
$913$		0			0
$914$	−0.154861	−	0.339098i	−0.154861	−	0.339098i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$919$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$926$	0.0336545	+	0.0736930i	0.0336545	+	0.0736930i
$927$		0			0
$928$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$929$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$929$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$930$		0			0
$931$		0			0
$932$	1.48357	+	0.953431i	1.48357	+	0.953431i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$937$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$938$	−0.0777324	+	0.0228243i	−0.0777324	+	0.0228243i
$939$		0			0
$940$		0			0
$941$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$941$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.0566239	−	0.393828i	0.0566239	−	0.393828i
$947$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$947$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$953$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$954$	−0.313607	−	0.201543i	−0.313607	−	0.201543i
$955$		0			0
$956$	−1.15486	+	1.33278i	−1.15486	+	1.33278i
$957$		0			0
$958$		0			0
$959$	0.186393	+	0.215109i	0.186393	+	0.215109i
$960$		0			0
$961$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$962$		0			0
$963$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$967$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$968$	0.841254	−	0.540641i	0.841254	−	0.540641i
$969$		0			0
$970$		0			0
$971$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$971$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$972$		0			0
$973$		0			0
$974$	0.0336545	+	0.234072i	0.0336545	+	0.234072i
$975$		0			0
$976$		0			0
$977$	−1.68251	−	1.08128i	−1.68251	−	1.08128i	−0.841254	−	0.540641i	$-0.818182\pi$
$977$	−1.68251	−	1.08128i	−1.68251	−	1.08128i	−0.841254	−	0.540641i	$-0.818182\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$982$	−0.0530529	−	0.0612263i	−0.0530529	−	0.0612263i
$983$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$983$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$991$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$992$		0			0
$993$		0			0
$994$	−0.459493	+	0.134919i	−0.459493	+	0.134919i
$995$		0			0
$996$		0			0
$997$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$997$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$998$	−0.0777324	−	0.0228243i	−0.0777324	−	0.0228243i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3703.1.l.g.1392.1		10
7.6	odd	2	CM	3703.1.l.g.1392.1		10
23.2	even	11	inner	3703.1.l.g.3429.1		10
23.3	even	11		3703.1.l.f.706.1		10
23.4	even	11		3703.1.l.i.3044.1		10
23.5	odd	22		3703.1.b.c.1588.3		5
23.6	even	11		3703.1.l.d.2617.1		10
23.7	odd	22		161.1.l.a.13.1	✓	10
23.8	even	11		3703.1.l.d.699.1		10
23.9	even	11		3703.1.l.e.2582.1		10
23.10	odd	22		3703.1.l.a.2603.1		10
23.11	odd	22		3703.1.l.h.118.1		10
23.12	even	11		3703.1.l.i.118.1		10
23.13	even	11		3703.1.l.e.2603.1		10
23.14	odd	22		3703.1.l.a.2582.1		10
23.15	odd	22		3703.1.l.b.699.1		10
23.16	even	11		3703.1.l.f.2911.1		10
23.17	odd	22		3703.1.l.b.2617.1		10
23.18	even	11		3703.1.b.b.1588.3		5
23.19	odd	22		3703.1.l.h.3044.1		10
23.20	odd	22		161.1.l.a.62.1	yes	10
23.21	odd	22		3703.1.l.c.3429.1		10
23.22	odd	2		3703.1.l.c.1392.1		10
69.20	even	22		1449.1.bq.a.1189.1		10
69.53	even	22		1449.1.bq.a.496.1		10
92.7	even	22		2576.1.cj.a.657.1		10
92.43	even	22		2576.1.cj.a.545.1		10
161.6	odd	22		3703.1.l.d.2617.1		10
161.13	odd	22		3703.1.l.e.2603.1		10
161.20	even	22		161.1.l.a.62.1	yes	10
161.27	odd	22		3703.1.l.i.3044.1		10
161.30	odd	66		1127.1.v.a.864.1		20
161.34	even	22		3703.1.l.h.118.1		10
161.41	odd	22		3703.1.b.b.1588.3		5
161.48	odd	22	inner	3703.1.l.g.3429.1		10
161.53	odd	66		1127.1.v.a.1048.1		20
161.55	odd	22		3703.1.l.e.2582.1		10
161.62	odd	22		3703.1.l.f.2911.1		10
161.66	even	66		1127.1.v.a.1097.1		20
161.76	even	22		161.1.l.a.13.1	✓	10
161.83	even	22		3703.1.l.a.2582.1		10
161.89	even	66		1127.1.v.a.913.1		20
161.90	even	22		3703.1.l.c.3429.1		10
161.97	even	22		3703.1.b.c.1588.3		5
161.104	odd	22		3703.1.l.i.118.1		10
161.111	even	22		3703.1.l.h.3044.1		10
161.118	odd	22		3703.1.l.f.706.1		10
161.122	even	66		1127.1.v.a.1048.1		20
161.125	even	22		3703.1.l.a.2603.1		10
161.132	even	22		3703.1.l.b.2617.1		10
161.135	odd	66		1127.1.v.a.913.1		20
161.145	even	66		1127.1.v.a.864.1		20
161.146	odd	22		3703.1.l.d.699.1		10
161.153	even	22		3703.1.l.b.699.1		10
161.158	odd	66		1127.1.v.a.1097.1		20
161.160	even	2		3703.1.l.c.1392.1		10
483.20	odd	22		1449.1.bq.a.1189.1		10
483.398	odd	22		1449.1.bq.a.496.1		10
644.503	odd	22		2576.1.cj.a.545.1		10
644.559	odd	22		2576.1.cj.a.657.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.1.l.a.13.1	✓	10	23.7	odd	22
161.1.l.a.13.1	✓	10	161.76	even	22
161.1.l.a.62.1	yes	10	23.20	odd	22
161.1.l.a.62.1	yes	10	161.20	even	22
1127.1.v.a.864.1		20	161.30	odd	66
1127.1.v.a.864.1		20	161.145	even	66
1127.1.v.a.913.1		20	161.89	even	66
1127.1.v.a.913.1		20	161.135	odd	66
1127.1.v.a.1048.1		20	161.53	odd	66
1127.1.v.a.1048.1		20	161.122	even	66
1127.1.v.a.1097.1		20	161.66	even	66
1127.1.v.a.1097.1		20	161.158	odd	66
1449.1.bq.a.496.1		10	69.53	even	22
1449.1.bq.a.496.1		10	483.398	odd	22
1449.1.bq.a.1189.1		10	69.20	even	22
1449.1.bq.a.1189.1		10	483.20	odd	22
2576.1.cj.a.545.1		10	92.43	even	22
2576.1.cj.a.545.1		10	644.503	odd	22
2576.1.cj.a.657.1		10	92.7	even	22
2576.1.cj.a.657.1		10	644.559	odd	22
3703.1.b.b.1588.3		5	23.18	even	11
3703.1.b.b.1588.3		5	161.41	odd	22
3703.1.b.c.1588.3		5	23.5	odd	22
3703.1.b.c.1588.3		5	161.97	even	22
3703.1.l.a.2582.1		10	23.14	odd	22
3703.1.l.a.2582.1		10	161.83	even	22
3703.1.l.a.2603.1		10	23.10	odd	22
3703.1.l.a.2603.1		10	161.125	even	22
3703.1.l.b.699.1		10	23.15	odd	22
3703.1.l.b.699.1		10	161.153	even	22
3703.1.l.b.2617.1		10	23.17	odd	22
3703.1.l.b.2617.1		10	161.132	even	22
3703.1.l.c.1392.1		10	23.22	odd	2
3703.1.l.c.1392.1		10	161.160	even	2
3703.1.l.c.3429.1		10	23.21	odd	22
3703.1.l.c.3429.1		10	161.90	even	22
3703.1.l.d.699.1		10	23.8	even	11
3703.1.l.d.699.1		10	161.146	odd	22
3703.1.l.d.2617.1		10	23.6	even	11
3703.1.l.d.2617.1		10	161.6	odd	22
3703.1.l.e.2582.1		10	23.9	even	11
3703.1.l.e.2582.1		10	161.55	odd	22
3703.1.l.e.2603.1		10	23.13	even	11
3703.1.l.e.2603.1		10	161.13	odd	22
3703.1.l.f.706.1		10	23.3	even	11
3703.1.l.f.706.1		10	161.118	odd	22
3703.1.l.f.2911.1		10	23.16	even	11
3703.1.l.f.2911.1		10	161.62	odd	22
3703.1.l.g.1392.1		10	1.1	even	1	trivial
3703.1.l.g.1392.1		10	7.6	odd	2	CM
3703.1.l.g.3429.1		10	23.2	even	11	inner
3703.1.l.g.3429.1		10	161.48	odd	22	inner
3703.1.l.h.118.1		10	23.11	odd	22
3703.1.l.h.118.1		10	161.34	even	22
3703.1.l.h.3044.1		10	23.19	odd	22
3703.1.l.h.3044.1		10	161.111	even	22
3703.1.l.i.118.1		10	23.12	even	11
3703.1.l.i.118.1		10	161.104	odd	22
3703.1.l.i.3044.1		10	23.4	even	11
3703.1.l.i.3044.1		10	161.27	odd	22

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:	\( N \)	\(=\)	\( 3703 = 7 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3703.l (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.239446 + 0.153882i) q^{2} +(-0.381761 + 0.835939i) q^{4} +(0.654861 + 0.755750i) q^{7} +(-0.0777324 - 0.540641i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-1.41542 - 0.909632i) q^{11} +(-0.273100 - 0.0801894i) q^{14} +(-0.500000 - 0.577031i) q^{16} +(0.273100 - 0.0801894i) q^{18} +0.478891 q^{22} +(0.841254 - 0.540641i) q^{25} +(-0.881761 + 0.258908i) q^{28} +(-0.544078 - 1.19136i) q^{29} +(0.732593 + 0.215109i) q^{32} +(0.601808 - 0.694523i) q^{36} +(-1.84125 - 0.540641i) q^{37} +(0.118239 - 0.822373i) q^{43} +(1.30075 - 0.835939i) q^{44} +(-0.142315 + 0.989821i) q^{49} +(-0.118239 + 0.258908i) q^{50} +(-0.857685 - 0.989821i) q^{53} +(0.357685 - 0.412791i) q^{56} +(0.313607 + 0.201543i) q^{58} +(-0.415415 - 0.909632i) q^{63} +(0.524075 - 0.153882i) q^{64} +(0.239446 - 0.153882i) q^{67} +(1.41542 - 0.909632i) q^{71} +(-0.0777324 + 0.540641i) q^{72} +(0.524075 - 0.153882i) q^{74} +(-0.239446 - 1.66538i) q^{77} +(-0.857685 + 0.989821i) q^{79} +(0.841254 + 0.540641i) q^{81} +(0.0982369 + 0.215109i) q^{86} +(-0.381761 + 0.835939i) q^{88} +(-0.118239 - 0.258908i) q^{98} +(1.10181 + 1.27155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 3 q^{4} + q^{7} + 7 q^{8} - q^{9} - 9 q^{11} + 2 q^{14} - 5 q^{16} - 2 q^{18} + 4 q^{22} - q^{25} - 8 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 9 q^{37} + 2 q^{43} - 5 q^{44} - q^{49}+ \cdots + 2 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 3 * q^4 + q^7 + 7 * q^8 - q^9 - 9 * q^11 + 2 * q^14 - 5 * q^16 - 2 * q^18 + 4 * q^22 - q^25 - 8 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 9 * q^37 + 2 * q^43 - 5 * q^44 - q^49 - 2 * q^50 - 9 * q^53 + 4 * q^56 + 7 * q^58 + q^63 + 4 * q^64 + 2 * q^67 + 9 * q^71 + 7 * q^72 + 4 * q^74 - 2 * q^77 - 9 * q^79 - q^81 + 4 * q^86 - 3 * q^88 - 2 * q^98 + 2 * q^99

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