LMFDB - Embedded newform 536.1.t.a.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [536,1,Mod(59,536)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(536, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("536.59");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 536 = 2^{3} \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	536.t (of order $22$, degree $10$, 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:	$0.267498846771$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{11}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{11} - \cdots)$

Embedding invariants

Embedding label			91.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	536.91
Dual form			536.1.t.a.483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-1.61435 + 1.03748i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.273100 + 1.89945i) q^{6} +(-0.959493 + 0.281733i) q^{8} +(1.11435 - 2.44009i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-1.61435 + 1.03748i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.273100 + 1.89945i) q^{6} +(-0.959493 + 0.281733i) q^{8} +(1.11435 - 2.44009i) q^{9} +(0.273100 - 1.89945i) q^{11} +(1.84125 + 0.540641i) q^{12} +(-0.142315 + 0.989821i) q^{16} +(0.857685 - 0.989821i) q^{17} +(-1.75667 - 2.02730i) q^{18} +(-0.118239 - 0.258908i) q^{19} +(-1.61435 - 1.03748i) q^{22} +(1.25667 - 1.45027i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(0.459493 + 3.19584i) q^{27} +(0.841254 + 0.540641i) q^{32} +(1.52977 + 3.34973i) q^{33} +(-0.544078 - 1.19136i) q^{34} +(-2.57385 + 0.755750i) q^{36} -0.284630 q^{38} +(-0.544078 + 0.627899i) q^{41} +(0.186393 - 0.215109i) q^{43} +(-1.61435 + 1.03748i) q^{44} +(-0.797176 - 1.74557i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-0.357685 + 2.48775i) q^{51} +(3.09792 + 0.909632i) q^{54} +(0.459493 + 0.295298i) q^{57} +(1.84125 - 0.540641i) q^{59} +(0.841254 - 0.540641i) q^{64} +3.68251 q^{66} +(-0.142315 + 0.989821i) q^{67} -1.30972 q^{68} +(-0.381761 + 2.65520i) q^{72} +(0.186393 + 1.29639i) q^{73} +(1.84125 - 0.540641i) q^{75} +(-0.118239 + 0.258908i) q^{76} +(-2.30075 - 2.65520i) q^{81} +(0.345139 + 0.755750i) q^{82} +(0.0405070 - 0.281733i) q^{83} +(-0.118239 - 0.258908i) q^{86} +(0.273100 + 1.89945i) q^{88} +(0.698939 + 0.449181i) q^{89} -1.91899 q^{96} -1.30972 q^{97} +(-0.959493 + 0.281733i) q^{98} +(-4.33052 - 2.78305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9	$ 10 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} + 9 q^{12} - q^{16} + 9 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 2 q^{24} - q^{25} - 4 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} - 2 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} + 7 q^{54} - 4 q^{57} + 9 q^{59} - q^{64} + 18 q^{66} - q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} + 9 q^{75} - 2 q^{76} - 5 q^{81} + 9 q^{82} + 9 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) $ 10 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9 - 2 * q^11 + 9 * q^12 - q^16 + 9 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^22 - 2 * q^24 - q^25 - 4 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 - 2 * q^38 - 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 + 7 * q^54 - 4 * q^57 + 9 * q^59 - q^64 + 18 * q^66 - q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 + 9 * q^75 - 2 * q^76 - 5 * q^81 + 9 * q^82 + 9 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$.

$n$	$135$	$269$	$337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.415415	−	0.909632i
$2$	0.415415	−	0.909632i	0.415415	−	0.909632i
$3$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$3$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$4$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$5$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$5$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$6$	0.273100	+	1.89945i	0.273100	+	1.89945i
$7$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$7$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$8$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$9$	1.11435	−	2.44009i	1.11435	−	2.44009i
$10$		0			0
$11$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$11$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$12$	1.84125	+	0.540641i	1.84125	+	0.540641i
$13$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$13$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$14$		0			0
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$17$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$17$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$18$	−1.75667	−	2.02730i	−1.75667	−	2.02730i
$19$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$19$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$20$		0			0
$21$		0			0
$22$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$23$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$23$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$24$	1.25667	−	1.45027i	1.25667	−	1.45027i
$25$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$26$		0			0
$27$	0.459493	+	3.19584i	0.459493	+	3.19584i
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$31$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$32$	0.841254	+	0.540641i	0.841254	+	0.540641i
$33$	1.52977	+	3.34973i	1.52977	+	3.34973i
$34$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$35$		0			0
$36$	−2.57385	+	0.755750i	−2.57385	+	0.755750i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−0.284630			−0.284630
$39$		0			0
$40$		0			0
$41$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$41$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$42$		0			0
$43$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$43$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$44$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$45$		0			0
$46$		0			0
$47$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$47$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$48$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$49$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$50$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$51$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$52$		0			0
$53$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$53$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$54$	3.09792	+	0.909632i	3.09792	+	0.909632i
$55$		0			0
$56$		0			0
$57$	0.459493	+	0.295298i	0.459493	+	0.295298i
$58$		0			0
$59$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$59$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$60$		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			0
$64$	0.841254	−	0.540641i	0.841254	−	0.540641i
$65$		0			0
$66$	3.68251			3.68251
$67$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$67$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$68$	−1.30972			−1.30972
$69$		0			0
$70$		0			0
$71$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$71$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$72$	−0.381761	+	2.65520i	−0.381761	+	2.65520i
$73$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$73$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$74$		0			0
$75$	1.84125	−	0.540641i	1.84125	−	0.540641i
$76$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$77$		0			0
$78$		0			0
$79$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$79$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$80$		0			0
$81$	−2.30075	−	2.65520i	−2.30075	−	2.65520i
$82$	0.345139	+	0.755750i	0.345139	+	0.755750i
$83$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$83$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$84$		0			0
$85$		0			0
$86$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$87$		0			0
$88$	0.273100	+	1.89945i	0.273100	+	1.89945i
$89$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$89$	0.698939	+	0.449181i	0.698939	+	0.449181i	−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
$96$	−1.91899			−1.91899
$97$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$97$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$98$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$99$	−4.33052	−	2.78305i	−4.33052	−	2.78305i
$100$	0.415415	+	0.909632i	0.415415	+	0.909632i
$101$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$101$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$102$	2.11435	+	1.35881i	2.11435	+	1.35881i
$103$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$103$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$107$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$108$	2.11435	−	2.44009i	2.11435	−	2.44009i
$109$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$109$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$113$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$114$	0.459493	−	0.295298i	0.459493	−	0.295298i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.273100	−	1.89945i	0.273100	−	1.89945i
$119$		0			0
$120$		0			0
$121$	−2.57385	−	0.755750i	−2.57385	−	0.755750i
$122$		0			0
$123$	0.226900	−	1.57812i	0.226900	−	1.57812i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$127$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$128$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$129$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$130$		0			0
$131$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$131$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$132$	1.52977	−	3.34973i	1.52977	−	3.34973i
$133$		0			0
$134$	0.841254	+	0.540641i	0.841254	+	0.540641i
$135$		0			0
$136$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$137$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$137$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$138$		0			0
$139$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$139$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.25667	+	1.45027i	2.25667	+	1.45027i
$145$		0			0
$146$	1.25667	+	0.368991i	1.25667	+	0.368991i
$147$	1.84125	+	0.540641i	1.84125	+	0.540641i
$148$		0			0
$149$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$149$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$150$	0.273100	−	1.89945i	0.273100	−	1.89945i
$151$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$151$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$152$	0.186393	+	0.215109i	0.186393	+	0.215109i
$153$	−1.45949	−	3.19584i	−1.45949	−	3.19584i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$157$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−3.37102	+	0.989821i	−3.37102	+	0.989821i
$163$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$163$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$164$	0.830830			0.830830
$165$		0			0
$166$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$167$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$167$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$168$		0			0
$169$	0.841254	+	0.540641i	0.841254	+	0.540641i
$170$		0			0
$171$	−0.763521			−0.763521
$172$	−0.284630			−0.284630
$173$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$173$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$174$		0			0
$175$		0			0
$176$	1.84125	+	0.540641i	1.84125	+	0.540641i
$177$	−2.41153	+	2.78305i	−2.41153	+	2.78305i
$178$	0.698939	−	0.449181i	0.698939	−	0.449181i
$179$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$179$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$180$		0			0
$181$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$181$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.64589	−	1.89945i	−1.64589	−	1.89945i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$191$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$192$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$193$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$193$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$194$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$195$		0			0
$196$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$197$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$197$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$198$	−4.33052	+	2.78305i	−4.33052	+	2.78305i
$199$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$199$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$200$	1.00000			1.00000
$201$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$202$		0			0
$203$		0			0
$204$	2.11435	−	1.35881i	2.11435	−	1.35881i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.524075	+	0.153882i	−0.524075	+	0.153882i
$210$		0			0
$211$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$211$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$212$		0			0
$213$		0			0
$214$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$215$		0			0
$216$	−1.34125	−	2.93694i	−1.34125	−	2.93694i
$217$		0			0
$218$		0			0
$219$	−1.64589	−	1.89945i	−1.64589	−	1.89945i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$223$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$224$		0			0
$225$	−1.75667	+	2.02730i	−1.75667	+	2.02730i
$226$	1.84125	+	0.540641i	1.84125	+	0.540641i
$227$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$227$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$228$	−0.0777324	−	0.540641i	−0.0777324	−	0.540641i
$229$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$229$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$233$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$234$		0			0
$235$		0			0
$236$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$241$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$242$	−1.75667	+	2.02730i	−1.75667	+	2.02730i
$243$	3.37102	+	0.989821i	3.37102	+	0.989821i
$244$		0			0
$245$		0			0
$246$	−1.34125	−	0.861971i	−1.34125	−	0.861971i
$247$		0			0
$248$		0			0
$249$	0.226900	+	0.496841i	0.226900	+	0.496841i
$250$		0			0
$251$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$251$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$257$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$257$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$258$	0.459493	+	0.295298i	0.459493	+	0.295298i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$263$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$263$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$264$	−2.41153	−	2.78305i	−2.41153	−	2.78305i
$265$		0			0
$266$		0			0
$267$	−1.59435			−1.59435
$268$	0.841254	−	0.540641i	0.841254	−	0.540641i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$271$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$272$	0.857685	+	0.989821i	0.857685	+	0.989821i
$273$		0			0
$274$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$275$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$276$		0			0
$277$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$277$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$278$	1.68251	+	1.08128i	1.68251	+	1.08128i
$279$		0			0
$280$		0			0
$281$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$281$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$282$		0			0
$283$	0.830830	+	1.81926i	0.830830	+	1.81926i	0.415415	+	0.909632i	$0.363636\pi$
$283$	0.830830	+	1.81926i	0.830830	+	1.81926i	0.415415	+	0.909632i	$0.363636\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.25667	−	1.45027i	2.25667	−	1.45027i
$289$	−0.101808	−	0.708089i	−0.101808	−	0.708089i
$290$		0			0
$291$	2.11435	−	1.35881i	2.11435	−	1.35881i
$292$	0.857685	−	0.989821i	0.857685	−	0.989821i
$293$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$293$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$294$	1.25667	−	1.45027i	1.25667	−	1.45027i
$295$		0			0
$296$		0			0
$297$	6.19584			6.19584
$298$		0			0
$299$		0			0
$300$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$305$		0			0
$306$	−3.51334			−3.51334
$307$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$307$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$311$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$312$		0			0
$313$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$313$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$317$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	2.11435	+	2.44009i	2.11435	+	2.44009i
$322$		0			0
$323$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$324$	−0.500000	+	3.47758i	−0.500000	+	3.47758i
$325$		0			0
$326$	0.345139	−	0.755750i	0.345139	−	0.755750i
$327$		0			0
$328$	0.345139	−	0.755750i	0.345139	−	0.755750i
$329$		0			0
$330$		0			0
$331$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$331$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$332$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$337$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$338$	0.841254	−	0.540641i	0.841254	−	0.540641i
$339$	−2.41153	−	2.78305i	−2.41153	−	2.78305i
$340$		0			0
$341$		0			0
$342$	−0.317178	+	0.694523i	−0.317178	+	0.694523i
$343$		0			0
$344$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$345$		0			0
$346$		0			0
$347$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$347$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$348$		0			0
$349$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$349$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$350$		0			0
$351$		0			0
$352$	1.25667	−	1.45027i	1.25667	−	1.45027i
$353$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$353$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$354$	1.52977	+	3.34973i	1.52977	+	3.34973i
$355$		0			0
$356$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$357$		0			0
$358$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$359$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$359$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$360$		0			0
$361$	0.601808	−	0.694523i	0.601808	−	0.694523i
$362$		0			0
$363$	4.93918	−	1.45027i	4.93918	−	1.45027i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$367$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$368$		0			0
$369$	0.925839	+	2.02730i	0.925839	+	2.02730i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$379$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$383$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$384$	1.25667	+	1.45027i	1.25667	+	1.45027i
$385$		0			0
$386$	0.186393	−	1.29639i	0.186393	−	1.29639i
$387$	−0.317178	−	0.694523i	−0.317178	−	0.694523i
$388$	0.857685	+	0.989821i	0.857685	+	0.989821i
$389$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$389$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$390$		0			0
$391$		0			0
$392$	0.841254	+	0.540641i	0.841254	+	0.540641i
$393$	−0.662317	+	1.45027i	−0.662317	+	1.45027i
$394$		0			0
$395$		0			0
$396$	0.732593	+	5.09530i	0.732593	+	5.09530i
$397$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$397$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$398$		0			0
$399$		0			0
$400$	0.415415	−	0.909632i	0.415415	−	0.909632i
$401$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$401$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$402$	−1.91899			−1.91899
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.357685	−	2.48775i	−0.357685	−	2.48775i
$409$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$409$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$410$		0			0
$411$	−1.34125	+	2.93694i	−1.34125	+	2.93694i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.59435	−	3.49114i	−1.59435	−	3.49114i
$418$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$419$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$419$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$420$		0			0
$421$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$421$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$422$	0.698939	−	0.449181i	0.698939	−	0.449181i
$423$		0			0
$424$		0			0
$425$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$426$		0			0
$427$		0			0
$428$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$429$		0			0
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	−3.22871			−3.22871
$433$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$433$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	−2.57385	+	0.755750i	−2.57385	+	0.755750i
$442$		0			0
$443$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$443$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$449$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$450$	1.11435	+	2.44009i	1.11435	+	2.44009i
$451$	1.04408	+	1.20493i	1.04408	+	1.20493i
$452$	1.25667	−	1.45027i	1.25667	−	1.45027i
$453$		0			0
$454$	0.345139	+	0.755750i	0.345139	+	0.755750i
$455$		0			0
$456$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$457$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$457$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$458$		0			0
$459$	3.55742	+	2.28621i	3.55742	+	2.28621i
$460$		0			0
$461$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$461$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$462$		0			0
$463$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$463$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$464$		0			0
$465$		0			0
$466$	1.68251	−	1.08128i	1.68251	−	1.08128i
$467$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$467$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$473$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$474$		0			0
$475$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$479$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$480$		0			0
$481$		0			0
$482$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$483$		0			0
$484$	1.11435	+	2.44009i	1.11435	+	2.44009i
$485$		0			0
$486$	2.30075	−	2.65520i	2.30075	−	2.65520i
$487$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$487$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$488$		0			0
$489$	−1.34125	+	0.861971i	−1.34125	+	0.861971i
$490$		0			0
$491$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$491$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$492$	−1.34125	+	0.861971i	−1.34125	+	0.861971i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.546200			0.546200
$499$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$499$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$500$		0			0
$501$		0			0
$502$	0.345139	+	0.755750i	0.345139	+	0.755750i
$503$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$503$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.91899			−1.91899
$508$		0			0
$509$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$509$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$510$		0			0
$511$		0			0
$512$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$513$	0.773100	−	0.496841i	0.773100	−	0.496841i
$514$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$515$		0			0
$516$	0.459493	−	0.295298i	0.459493	−	0.295298i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$521$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$522$		0			0
$523$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$523$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$524$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−3.53334	+	1.03748i	−3.53334	+	1.03748i
$529$	0.415415	−	0.909632i	0.415415	−	0.909632i
$530$		0			0
$531$	0.732593	−	5.09530i	0.732593	−	5.09530i
$532$		0			0
$533$		0			0
$534$	−0.662317	+	1.45027i	−0.662317	+	1.45027i
$535$		0			0
$536$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$537$	0.546200			0.546200
$538$		0			0
$539$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$540$		0			0
$541$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$541$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$542$		0			0
$543$		0			0
$544$	1.25667	−	0.368991i	1.25667	−	0.368991i
$545$		0			0
$546$		0			0
$547$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$547$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$548$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$549$		0			0
$550$	1.25667	+	1.45027i	1.25667	+	1.45027i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.68251	−	1.08128i	1.68251	−	1.08128i
$557$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$557$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	4.62769	+	1.35881i	4.62769	+	1.35881i
$562$	0.857685	−	0.989821i	0.857685	−	0.989821i
$563$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$563$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$564$		0			0
$565$		0			0
$566$	2.00000			2.00000
$567$		0			0
$568$		0			0
$569$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$569$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$570$		0			0
$571$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$571$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.381761	−	2.65520i	−0.381761	−	2.65520i
$577$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$577$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$578$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$579$	−1.64589	+	1.89945i	−1.64589	+	1.89945i
$580$		0			0
$581$		0			0
$582$	−0.357685	−	2.48775i	−0.357685	−	2.48775i
$583$		0			0
$584$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$585$		0			0
$586$		0			0
$587$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$587$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$588$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$593$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$594$	2.57385	−	5.63594i	2.57385	−	5.63594i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$599$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$600$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$601$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$601$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$602$		0			0
$603$	2.25667	+	1.45027i	2.25667	+	1.45027i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$607$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$608$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.45949	+	3.19584i	−1.45949	+	3.19584i
$613$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$613$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$614$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$615$		0			0
$616$		0			0
$617$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$617$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$618$		0			0
$619$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$619$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.841254	+	0.540641i	0.841254	+	0.540641i
$626$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$627$	0.686393	−	0.792140i	0.686393	−	0.792140i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$631$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$632$		0			0
$633$	−1.59435			−1.59435
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$641$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$642$	3.09792	−	0.909632i	3.09792	−	0.909632i
$643$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$643$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$644$		0			0
$645$		0			0
$646$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$647$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$647$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$648$	2.95561	+	1.89945i	2.95561	+	1.89945i
$649$	−0.524075	−	3.64502i	−0.524075	−	3.64502i
$650$		0			0
$651$		0			0
$652$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$653$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$653$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$654$		0			0
$655$		0			0
$656$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$657$	3.37102	+	0.989821i	3.37102	+	0.989821i
$658$		0			0
$659$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$659$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$660$		0			0
$661$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$661$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$662$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$663$		0			0
$664$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$673$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$674$	0.857685	+	0.989821i	0.857685	+	0.989821i
$675$	0.459493	−	3.19584i	0.459493	−	3.19584i
$676$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$677$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$677$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$678$	−3.53334	+	1.03748i	−3.53334	+	1.03748i
$679$		0			0
$680$		0			0
$681$	0.226900	−	1.57812i	0.226900	−	1.57812i
$682$		0			0
$683$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$683$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$684$	0.500000	+	0.577031i	0.500000	+	0.577031i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.186393	+	0.215109i	0.186393	+	0.215109i
$689$		0			0
$690$		0			0
$691$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$691$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$692$		0			0
$693$		0			0
$694$	−1.30972	+	1.51150i	−1.30972	+	1.51150i
$695$		0			0
$696$		0			0
$697$	0.154861	+	1.07708i	0.154861	+	1.07708i
$698$		0			0
$699$	−3.83797			−3.83797
$700$		0			0
$701$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$701$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$702$		0			0
$703$		0			0
$704$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$705$		0			0
$706$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$707$		0			0
$708$	3.68251			3.68251
$709$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$709$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$710$		0			0
$711$		0			0
$712$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$717$		0			0
$718$		0			0
$719$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$719$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$720$		0			0
$721$		0			0
$722$	−0.381761	−	0.835939i	−0.381761	−	0.835939i
$723$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$724$		0			0
$725$		0			0
$726$	0.732593	−	5.09530i	0.732593	−	5.09530i
$727$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$727$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$728$		0			0
$729$	−3.09792	+	0.909632i	−3.09792	+	0.909632i
$730$		0			0
$731$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$732$		0			0
$733$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$733$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.84125	+	0.540641i	1.84125	+	0.540641i
$738$	2.22871			2.22871
$739$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$739$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$743$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.642315	−	0.412791i	−0.642315	−	0.412791i
$748$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$749$		0			0
$750$		0			0
$751$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$751$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$752$		0			0
$753$	0.226900	−	1.57812i	0.226900	−	1.57812i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$757$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$758$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$759$		0			0
$760$		0			0
$761$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$761$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.84125	−	0.540641i	1.84125	−	0.540641i
$769$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$769$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$770$		0			0
$771$	1.04408	+	2.28621i	1.04408	+	2.28621i
$772$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$773$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$773$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$774$	−0.763521			−0.763521
$775$		0			0
$776$	1.25667	−	0.368991i	1.25667	−	0.368991i
$777$		0			0
$778$		0			0
$779$	0.226900	+	0.0666238i	0.226900	+	0.0666238i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.841254	−	0.540641i	0.841254	−	0.540641i
$785$		0			0
$786$	1.04408	+	1.20493i	1.04408	+	1.20493i
$787$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$787$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	4.93918	+	1.45027i	4.93918	+	1.45027i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$797$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$798$		0			0
$799$		0			0
$800$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$801$	1.87491	−	1.20493i	1.87491	−	1.20493i
$802$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$803$	2.51334			2.51334
$804$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$809$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$810$		0			0
$811$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$811$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−2.41153	−	0.708089i	−2.41153	−	0.708089i
$817$	−0.0777324	−	0.0228243i	−0.0777324	−	0.0228243i
$818$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$819$		0			0
$820$		0			0
$821$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$821$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$822$	2.11435	+	2.44009i	2.11435	+	2.44009i
$823$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$823$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$824$		0			0
$825$	−0.524075	−	3.64502i	−0.524075	−	3.64502i
$826$		0			0
$827$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$827$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$828$		0			0
$829$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$829$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.30972			−1.30972
$834$	−3.83797			−3.83797
$835$		0			0
$836$	0.459493	+	0.295298i	0.459493	+	0.295298i
$837$		0			0
$838$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$839$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$839$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$840$		0			0
$841$	1.00000			1.00000
$842$		0			0
$843$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$844$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.22871	−	2.07496i	−3.22871	−	2.07496i
$850$	0.186393	+	1.29639i	0.186393	+	1.29639i
$851$		0			0
$852$		0			0
$853$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$853$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$854$		0			0
$855$		0			0
$856$	0.698939	+	1.53046i	0.698939	+	1.53046i
$857$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$857$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$858$		0			0
$859$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$859$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$863$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$864$	−1.34125	+	2.93694i	−1.34125	+	2.93694i
$865$		0			0
$866$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$867$	0.898983	+	1.03748i	0.898983	+	1.03748i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.45949	+	3.19584i	−1.45949	+	3.19584i
$874$		0			0
$875$		0			0
$876$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$877$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$877$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$881$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$882$	−0.381761	+	2.65520i	−0.381761	+	2.65520i
$883$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$883$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$884$		0			0
$885$		0			0
$886$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$887$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$887$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−5.67177	+	3.64502i	−5.67177	+	3.64502i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.273100	+	1.89945i	0.273100	+	1.89945i
$899$		0			0
$900$	2.68251			2.68251
$901$		0			0
$902$	1.52977	−	0.449181i	1.52977	−	0.449181i
$903$		0			0
$904$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$905$		0			0
$906$		0			0
$907$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$907$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$908$	0.830830			0.830830
$909$		0			0
$910$		0			0
$911$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$911$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$912$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$913$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$914$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	3.55742	−	2.28621i	3.55742	−	2.28621i
$919$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$919$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$920$		0			0
$921$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$929$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$930$		0			0
$931$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$932$	−0.284630	−	1.97964i	−0.284630	−	1.97964i
$933$		0			0
$934$	1.25667	+	1.45027i	1.25667	+	1.45027i
$935$		0			0
$936$		0			0
$937$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$937$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$938$		0			0
$939$	0.546200			0.546200
$940$		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
$944$	0.273100	+	1.89945i	0.273100	+	1.89945i
$945$		0			0
$946$	−0.524075	+	0.153882i	−0.524075	+	0.153882i
$947$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$947$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$948$		0			0
$949$		0			0
$950$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$951$		0			0
$952$		0			0
$953$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$953$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.841254	−	0.540641i	0.841254	−	0.540641i
$962$		0			0
$963$	−4.33052	−	1.27155i	−4.33052	−	1.27155i
$964$	0.186393	−	0.215109i	0.186393	−	0.215109i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	2.68251			2.68251
$969$	0.686393	−	0.201543i	0.686393	−	0.201543i
$970$		0			0
$971$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$971$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$972$	−1.45949	−	3.19584i	−1.45949	−	3.19584i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$977$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$978$	0.226900	+	1.57812i	0.226900	+	1.57812i
$979$	1.04408	−	1.20493i	1.04408	−	1.20493i
$980$		0			0
$981$		0			0
$982$	1.68251	−	1.08128i	1.68251	−	1.08128i
$983$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$983$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$984$	0.226900	+	1.57812i	0.226900	+	1.57812i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$991$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$992$		0			0
$993$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$994$		0			0
$995$		0			0
$996$	0.226900	−	0.496841i	0.226900	−	0.496841i
$997$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$997$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$998$	0.698939	−	1.53046i	0.698939	−	1.53046i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	536.1.t.a.91.1	✓	10
4.3	odd	2		2144.1.bf.a.1967.1		10
8.3	odd	2	CM	536.1.t.a.91.1	✓	10
8.5	even	2		2144.1.bf.a.1967.1		10
67.14	even	11	inner	536.1.t.a.483.1	yes	10
268.215	odd	22		2144.1.bf.a.751.1		10
536.349	even	22		2144.1.bf.a.751.1		10
536.483	odd	22	inner	536.1.t.a.483.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
536.1.t.a.91.1	✓	10	1.1	even	1	trivial
536.1.t.a.91.1	✓	10	8.3	odd	2	CM
536.1.t.a.483.1	yes	10	67.14	even	11	inner
536.1.t.a.483.1	yes	10	536.483	odd	22	inner
2144.1.bf.a.751.1		10	268.215	odd	22
2144.1.bf.a.751.1		10	536.349	even	22
2144.1.bf.a.1967.1		10	4.3	odd	2
2144.1.bf.a.1967.1		10	8.5	even	2

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:	\( N \)	\(=\)	\( 536 = 2^{3} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	536.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-1.61435 + 1.03748i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.273100 + 1.89945i) q^{6} +(-0.959493 + 0.281733i) q^{8} +(1.11435 - 2.44009i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-1.61435 + 1.03748i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.273100 + 1.89945i) q^{6} +(-0.959493 + 0.281733i) q^{8} +(1.11435 - 2.44009i) q^{9} +(0.273100 - 1.89945i) q^{11} +(1.84125 + 0.540641i) q^{12} +(-0.142315 + 0.989821i) q^{16} +(0.857685 - 0.989821i) q^{17} +(-1.75667 - 2.02730i) q^{18} +(-0.118239 - 0.258908i) q^{19} +(-1.61435 - 1.03748i) q^{22} +(1.25667 - 1.45027i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(0.459493 + 3.19584i) q^{27} +(0.841254 + 0.540641i) q^{32} +(1.52977 + 3.34973i) q^{33} +(-0.544078 - 1.19136i) q^{34} +(-2.57385 + 0.755750i) q^{36} -0.284630 q^{38} +(-0.544078 + 0.627899i) q^{41} +(0.186393 - 0.215109i) q^{43} +(-1.61435 + 1.03748i) q^{44} +(-0.797176 - 1.74557i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-0.357685 + 2.48775i) q^{51} +(3.09792 + 0.909632i) q^{54} +(0.459493 + 0.295298i) q^{57} +(1.84125 - 0.540641i) q^{59} +(0.841254 - 0.540641i) q^{64} +3.68251 q^{66} +(-0.142315 + 0.989821i) q^{67} -1.30972 q^{68} +(-0.381761 + 2.65520i) q^{72} +(0.186393 + 1.29639i) q^{73} +(1.84125 - 0.540641i) q^{75} +(-0.118239 + 0.258908i) q^{76} +(-2.30075 - 2.65520i) q^{81} +(0.345139 + 0.755750i) q^{82} +(0.0405070 - 0.281733i) q^{83} +(-0.118239 - 0.258908i) q^{86} +(0.273100 + 1.89945i) q^{88} +(0.698939 + 0.449181i) q^{89} -1.91899 q^{96} -1.30972 q^{97} +(-0.959493 + 0.281733i) q^{98} +(-4.33052 - 2.78305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9	\( 10 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} + 9 q^{12} - q^{16} + 9 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 2 q^{24} - q^{25} - 4 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} - 2 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} + 7 q^{54} - 4 q^{57} + 9 q^{59} - q^{64} + 18 q^{66} - q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} + 9 q^{75} - 2 q^{76} - 5 q^{81} + 9 q^{82} + 9 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) \) 10 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9 - 2 * q^11 + 9 * q^12 - q^16 + 9 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^22 - 2 * q^24 - q^25 - 4 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 - 2 * q^38 - 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 + 7 * q^54 - 4 * q^57 + 9 * q^59 - q^64 + 18 * q^66 - q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 + 9 * q^75 - 2 * q^76 - 5 * q^81 + 9 * q^82 + 9 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 - 6 * q^99

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