LMFDB - Embedded newform 345.1.p.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,1,Mod(29,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 18]))

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

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

chi := DirichletCharacter("345.29");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$345 = 3 \cdot 5 \cdot 23$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	345.p (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:	$0.172177429358$
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:	$\Z[a_1, a_2, a_3]$
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			59.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	345.59
Dual form			345.1.p.a.269.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10181 - 1.27155i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.260554 + 1.81219i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.239446 - 1.66538i) q^{6} +(1.17597 - 0.755750i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.61435 + 0.474017i) q^{10} +(-1.19894 + 1.38365i) q^{12} +(0.841254 - 0.540641i) q^{15} +(-0.500000 - 0.146813i) q^{16} +(0.0405070 + 0.281733i) q^{17} +(0.698939 - 1.53046i) q^{18} +(0.273100 - 1.89945i) q^{19} +(1.54019 + 0.989821i) q^{20} +(-0.654861 + 0.755750i) q^{23} +1.39788 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(-1.61435 - 0.474017i) q^{30} +(-1.61435 + 1.03748i) q^{31} +(-0.216476 - 0.474017i) q^{32} +(0.313607 - 0.361922i) q^{34} +(-1.75667 + 0.515804i) q^{36} +(-2.71616 + 1.74557i) q^{38} +(-0.198939 - 1.38365i) q^{40} +1.00000 q^{45} +1.68251 q^{46} -1.30972 q^{47} +(-0.341254 - 0.393828i) q^{48} +(0.841254 + 0.540641i) q^{49} +(-0.239446 + 1.66538i) q^{50} +(-0.118239 + 0.258908i) q^{51} +(1.25667 + 0.368991i) q^{53} +(1.41542 - 0.909632i) q^{54} +(1.25667 - 1.45027i) q^{57} +(0.760554 + 1.66538i) q^{60} +(-1.10181 + 0.708089i) q^{61} +(3.09792 + 0.909632i) q^{62} +(-0.580699 + 1.27155i) q^{64} -0.521109 q^{68} +(-0.959493 + 0.281733i) q^{69} +(1.17597 + 0.755750i) q^{72} +(-0.142315 - 0.989821i) q^{75} +(3.37102 + 0.989821i) q^{76} +(-0.797176 + 0.234072i) q^{79} +(-0.341254 + 0.393828i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(0.698939 + 1.53046i) q^{83} +(0.273100 + 0.0801894i) q^{85} +(-1.10181 - 1.27155i) q^{90} +(-1.19894 - 1.38365i) q^{92} -1.91899 q^{93} +(1.44306 + 1.66538i) q^{94} +(-1.61435 - 1.03748i) q^{95} +(0.0741615 - 0.515804i) q^{96} +(-0.239446 - 1.66538i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q - 2 q^{2} - q^{3} - 3 q^{4} - q^{5} - 2 q^{6} + 7 q^{8} - q^{9} - 2 q^{10} - 3 q^{12} - q^{15} - 5 q^{16} + 9 q^{17} - 2 q^{18} - 2 q^{19} - 3 q^{20} - q^{23} - 4 q^{24} - q^{25} - q^{27} - 2 q^{30}+ \cdots - 2 q^{98}+O(q^{100})$ 10 * q - 2 * q^2 - q^3 - 3 * q^4 - q^5 - 2 * q^6 + 7 * q^8 - q^9 - 2 * q^10 - 3 * q^12 - q^15 - 5 * q^16 + 9 * q^17 - 2 * q^18 - 2 * q^19 - 3 * q^20 - q^23 - 4 * q^24 - q^25 - q^27 - 2 * q^30 - 2 * q^31 - 6 * q^32 + 7 * q^34 - 3 * q^36 - 4 * q^38 + 7 * q^40 + 10 * q^45 - 2 * q^46 - 2 * q^47 + 6 * q^48 - q^49 - 2 * q^50 - 2 * q^51 - 2 * q^53 + 9 * q^54 - 2 * q^57 + 8 * q^60 - 2 * q^61 + 7 * q^62 + 4 * q^64 - 6 * q^68 - q^69 + 7 * q^72 - q^75 + 5 * q^76 - 2 * q^79 + 6 * q^80 - q^81 - 2 * q^83 - 2 * q^85 - 2 * q^90 - 3 * q^92 - 2 * q^93 - 4 * q^94 - 2 * q^95 + 5 * q^96 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$ .

$n$	$116$	$166$	$277$
$\chi(n)$	$-1$	$e\left(\frac{7}{11}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$2$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$3$	0.841254	+	0.540641i	0.841254	+	0.540641i
$3$	0.841254	+	0.540641i	0.841254	+	0.540641i
$4$	−0.260554	+	1.81219i	−0.260554	+	1.81219i
$5$	0.415415	−	0.909632i	0.415415	−	0.909632i
$5$	0.415415	−	0.909632i	0.415415	−	0.909632i
$6$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$7$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$7$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$8$	1.17597	−	0.755750i	1.17597	−	0.755750i
$9$	0.415415	+	0.909632i	0.415415	+	0.909632i
$10$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$11$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$11$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$12$	−1.19894	+	1.38365i	−1.19894	+	1.38365i
$13$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$13$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$14$		0			0
$15$	0.841254	−	0.540641i	0.841254	−	0.540641i
$16$	−0.500000	−	0.146813i	−0.500000	−	0.146813i
$17$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$17$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$18$	0.698939	−	1.53046i	0.698939	−	1.53046i
$19$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$19$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$20$	1.54019	+	0.989821i	1.54019	+	0.989821i
$21$		0			0
$22$		0			0
$23$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$23$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$24$	1.39788			1.39788
$25$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$26$		0			0
$27$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$28$		0			0
$29$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$29$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$30$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$31$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$31$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$32$	−0.216476	−	0.474017i	−0.216476	−	0.474017i
$33$		0			0
$34$	0.313607	−	0.361922i	0.313607	−	0.361922i
$35$		0			0
$36$	−1.75667	+	0.515804i	−1.75667	+	0.515804i
$37$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$37$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$38$	−2.71616	+	1.74557i	−2.71616	+	1.74557i
$39$		0			0
$40$	−0.198939	−	1.38365i	−0.198939	−	1.38365i
$41$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$41$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$42$		0			0
$43$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$43$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$44$		0			0
$45$	1.00000			1.00000
$46$	1.68251			1.68251
$47$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$47$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$48$	−0.341254	−	0.393828i	−0.341254	−	0.393828i
$49$	0.841254	+	0.540641i	0.841254	+	0.540641i
$50$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$51$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$52$		0			0
$53$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$53$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$54$	1.41542	−	0.909632i	1.41542	−	0.909632i
$55$		0			0
$56$		0			0
$57$	1.25667	−	1.45027i	1.25667	−	1.45027i
$58$		0			0
$59$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$59$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$60$	0.760554	+	1.66538i	0.760554	+	1.66538i
$61$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$61$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$62$	3.09792	+	0.909632i	3.09792	+	0.909632i
$63$		0			0
$64$	−0.580699	+	1.27155i	−0.580699	+	1.27155i
$65$		0			0
$66$		0			0
$67$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$67$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$68$	−0.521109			−0.521109
$69$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$70$		0			0
$71$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$71$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$72$	1.17597	+	0.755750i	1.17597	+	0.755750i
$73$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$73$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$74$		0			0
$75$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$76$	3.37102	+	0.989821i	3.37102	+	0.989821i
$77$		0			0
$78$		0			0
$79$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$79$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$80$	−0.341254	+	0.393828i	−0.341254	+	0.393828i
$81$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$82$		0			0
$83$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$83$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$84$		0			0
$85$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$89$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$90$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$91$		0			0
$92$	−1.19894	−	1.38365i	−1.19894	−	1.38365i
$93$	−1.91899			−1.91899
$94$	1.44306	+	1.66538i	1.44306	+	1.66538i
$95$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$96$	0.0741615	−	0.515804i	0.0741615	−	0.515804i
$97$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$97$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$98$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$99$		0			0
$100$	1.54019	−	0.989821i	1.54019	−	0.989821i
$101$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$101$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$102$	0.459493	−	0.134919i	0.459493	−	0.134919i
$103$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$103$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$104$		0			0
$105$		0			0
$106$	−0.915415	−	2.00448i	−0.915415	−	2.00448i
$107$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$107$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$108$	−1.75667	−	0.515804i	−1.75667	−	0.515804i
$109$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$109$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$113$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$114$	−3.22871			−3.22871
$115$	0.415415	+	0.909632i	0.415415	+	0.909632i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.580699	−	1.27155i	0.580699	−	1.27155i
$121$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$122$	2.11435	+	0.620830i	2.11435	+	0.620830i
$123$		0			0
$124$	−1.45949	−	3.19584i	−1.45949	−	3.19584i
$125$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$126$		0			0
$127$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$127$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$128$	1.75667	−	0.515804i	1.75667	−	0.515804i
$129$		0			0
$130$		0			0
$131$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$131$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.841254	+	0.540641i	0.841254	+	0.540641i
$136$	0.260554	+	0.300696i	0.260554	+	0.300696i
$137$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$137$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$138$	1.41542	+	0.909632i	1.41542	+	0.909632i
$139$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$139$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$140$		0			0
$141$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$142$		0			0
$143$		0			0
$144$	−0.0741615	−	0.515804i	−0.0741615	−	0.515804i
$145$		0			0
$146$		0			0
$147$	0.415415	+	0.909632i	0.415415	+	0.909632i
$148$		0			0
$149$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$149$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$150$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$151$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$151$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$152$	−1.11435	−	2.44009i	−1.11435	−	2.44009i
$153$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$154$		0			0
$155$	0.273100	+	1.89945i	0.273100	+	1.89945i
$156$		0			0
$157$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$157$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$158$	1.17597	+	0.755750i	1.17597	+	0.755750i
$159$	0.857685	+	0.989821i	0.857685	+	0.989821i
$160$	−0.521109			−0.521109
$161$		0			0
$162$	1.68251			1.68251
$163$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$163$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$164$		0			0
$165$		0			0
$166$	1.17597	−	2.57501i	1.17597	−	2.57501i
$167$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$167$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$168$		0			0
$169$	0.841254	−	0.540641i	0.841254	−	0.540641i
$170$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$171$	1.84125	−	0.540641i	1.84125	−	0.540641i
$172$		0			0
$173$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$173$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$179$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$180$	−0.260554	+	1.81219i	−0.260554	+	1.81219i
$181$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$181$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$182$		0			0
$183$	−1.30972			−1.30972
$184$	−0.198939	+	1.38365i	−0.198939	+	1.38365i
$185$		0			0
$186$	2.11435	+	2.44009i	2.11435	+	2.44009i
$187$		0			0
$188$	0.341254	−	2.37347i	0.341254	−	2.37347i
$189$		0			0
$190$	0.459493	+	3.19584i	0.459493	+	3.19584i
$191$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$191$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$192$	−1.17597	+	0.755750i	−1.17597	+	0.755750i
$193$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$193$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$194$		0			0
$195$		0			0
$196$	−1.19894	+	1.38365i	−1.19894	+	1.38365i
$197$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$197$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$198$		0			0
$199$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$199$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$200$	−1.34125	−	0.393828i	−1.34125	−	0.393828i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.438384	−	0.281733i	−0.438384	−	0.281733i
$205$		0			0
$206$		0			0
$207$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$211$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$212$	−0.996114	+	2.18119i	−0.996114	+	2.18119i
$213$		0			0
$214$	−1.34125	−	0.393828i	−1.34125	−	0.393828i
$215$		0			0
$216$	0.580699	+	1.27155i	0.580699	+	1.27155i
$217$		0			0
$218$	−0.915415	+	1.05645i	−0.915415	+	1.05645i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$223$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$224$		0			0
$225$	0.415415	−	0.909632i	0.415415	−	0.909632i
$226$	−0.402869	+	2.80202i	−0.402869	+	2.80202i
$227$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$227$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$228$	2.30075	+	2.65520i	2.30075	+	2.65520i
$229$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$229$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$230$	0.698939	−	1.53046i	0.698939	−	1.53046i
$231$		0			0
$232$		0			0
$233$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$233$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$234$		0			0
$235$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$236$		0			0
$237$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$238$		0			0
$239$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$239$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$240$	−0.500000	+	0.146813i	−0.500000	+	0.146813i
$241$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$241$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$242$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$243$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$244$	−0.996114	−	2.18119i	−0.996114	−	2.18119i
$245$	0.841254	−	0.540641i	0.841254	−	0.540641i
$246$		0			0
$247$		0			0
$248$	−1.11435	+	2.44009i	−1.11435	+	2.44009i
$249$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$250$	1.41542	+	0.909632i	1.41542	+	0.909632i
$251$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$251$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	0.186393	+	0.215109i	0.186393	+	0.215109i
$256$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$257$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$257$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$263$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$264$		0			0
$265$	0.857685	−	0.989821i	0.857685	−	0.989821i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$269$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$270$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$271$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$271$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$272$	0.0211086	−	0.146813i	0.0211086	−	0.146813i
$273$		0			0
$274$	−0.915415	−	1.05645i	−0.915415	−	1.05645i
$275$		0			0
$276$	−0.260554	−	1.81219i	−0.260554	−	1.81219i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	1.44306	+	1.66538i	1.44306	+	1.66538i
$279$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$280$		0			0
$281$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$281$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$282$	0.313607	+	2.18119i	0.313607	+	2.18119i
$283$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$283$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$284$		0			0
$285$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$286$		0			0
$287$		0			0
$288$	0.341254	−	0.393828i	0.341254	−	0.393828i
$289$	0.881761	−	0.258908i	0.881761	−	0.258908i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$293$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$294$	0.698939	−	1.53046i	0.698939	−	1.53046i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	1.83083			1.83083
$301$		0			0
$302$	−0.402869	−	0.258908i	−0.402869	−	0.258908i
$303$		0			0
$304$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$305$	0.186393	+	1.29639i	0.186393	+	1.29639i
$306$	0.459493	+	0.134919i	0.459493	+	0.134919i
$307$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$307$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$308$		0			0
$309$		0			0
$310$	2.11435	−	2.44009i	2.11435	−	2.44009i
$311$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$311$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$312$		0			0
$313$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$313$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$314$		0			0
$315$		0			0
$316$	−0.216476	−	1.50563i	−0.216476	−	1.50563i
$317$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$317$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$318$	0.313607	−	2.18119i	0.313607	−	2.18119i
$319$		0			0
$320$	0.915415	+	1.05645i	0.915415	+	1.05645i
$321$	0.830830			0.830830
$322$		0			0
$323$	0.546200			0.546200
$324$	−1.19894	−	1.38365i	−1.19894	−	1.38365i
$325$		0			0
$326$		0			0
$327$	0.345139	−	0.755750i	0.345139	−	0.755750i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$331$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$332$	−2.95561	+	0.867845i	−2.95561	+	0.867845i
$333$		0			0
$334$	−0.915415	+	1.05645i	−0.915415	+	1.05645i
$335$		0			0
$336$		0			0
$337$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$337$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$338$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$339$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$340$	−0.216476	+	0.474017i	−0.216476	+	0.474017i
$341$		0			0
$342$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$343$		0			0
$344$		0			0
$345$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$346$	−2.20362			−2.20362
$347$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$347$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$348$		0			0
$349$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$349$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$353$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$359$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$360$	1.17597	−	0.755750i	1.17597	−	0.755750i
$361$	−2.57385	−	0.755750i	−2.57385	−	0.755750i
$362$	0.0681534	+	0.474017i	0.0681534	+	0.474017i
$363$	0.415415	−	0.909632i	0.415415	−	0.909632i
$364$		0			0
$365$		0			0
$366$	1.44306	+	1.66538i	1.44306	+	1.66538i
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	0.438384	−	0.281733i	0.438384	−	0.281733i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.500000	−	3.47758i	0.500000	−	3.47758i
$373$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$373$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$374$		0			0
$375$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$376$	−1.54019	+	0.989821i	−1.54019	+	0.989821i
$377$		0			0
$378$		0			0
$379$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$379$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$380$	2.30075	−	2.65520i	2.30075	−	2.65520i
$381$		0			0
$382$		0			0
$383$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$383$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$384$	1.75667	+	0.515804i	1.75667	+	0.515804i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$389$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$390$		0			0
$391$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$392$	1.39788			1.39788
$393$		0			0
$394$	1.17597	+	0.755750i	1.17597	+	0.755750i
$395$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$396$		0			0
$397$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$397$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$398$	−2.71616	−	0.797537i	−2.71616	−	0.797537i
$399$		0			0
$400$	0.216476	+	0.474017i	0.216476	+	0.474017i
$401$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$401$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.415415	+	0.909632i	0.415415	+	0.909632i
$406$		0			0
$407$		0			0
$408$	0.0566239	+	0.393828i	0.0566239	+	0.393828i
$409$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$409$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$410$		0			0
$411$	0.698939	+	0.449181i	0.698939	+	0.449181i
$412$		0			0
$413$		0			0
$414$	0.698939	+	1.53046i	0.698939	+	1.53046i
$415$	1.68251			1.68251
$416$		0			0
$417$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$418$		0			0
$419$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$419$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$420$		0			0
$421$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$421$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$422$	−0.402869	+	0.258908i	−0.402869	+	0.258908i
$423$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$424$	1.75667	−	0.515804i	1.75667	−	0.515804i
$425$	0.186393	−	0.215109i	0.186393	−	0.215109i
$426$		0			0
$427$		0			0
$428$	0.631891	+	1.38365i	0.631891	+	1.38365i
$429$		0			0
$430$		0			0
$431$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$431$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$432$	0.216476	−	0.474017i	0.216476	−	0.474017i
$433$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$433$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$434$		0			0
$435$		0			0
$436$	1.52111			1.52111
$437$	1.25667	+	1.45027i	1.25667	+	1.45027i
$438$		0			0
$439$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$439$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$440$		0			0
$441$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$442$		0			0
$443$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$443$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$449$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$450$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$451$		0			0
$452$	2.59138	−	1.66538i	2.59138	−	1.66538i
$453$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$454$	0.313607	+	2.18119i	0.313607	+	2.18119i
$455$		0			0
$456$	0.381761	−	2.65520i	0.381761	−	2.65520i
$457$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$457$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$458$	−1.85380	−	2.13940i	−1.85380	−	2.13940i
$459$	−0.284630			−0.284630
$460$	−1.75667	+	0.515804i	−1.75667	+	0.515804i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$463$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$464$		0			0
$465$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$466$	−0.198939	−	1.38365i	−0.198939	−	1.38365i
$467$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$467$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$468$		0			0
$469$		0			0
$470$	2.11435	−	0.620830i	2.11435	−	0.620830i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.580699	+	1.27155i	0.580699	+	1.27155i
$475$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$476$		0			0
$477$	0.186393	+	1.29639i	0.186393	+	1.29639i
$478$		0			0
$479$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$479$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$480$	−0.438384	−	0.281733i	−0.438384	−	0.281733i
$481$		0			0
$482$	−0.478891			−0.478891
$483$		0			0
$484$	1.83083			1.83083
$485$		0			0
$486$	1.41542	+	0.909632i	1.41542	+	0.909632i
$487$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$487$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$488$	−0.760554	+	1.66538i	−0.760554	+	1.66538i
$489$		0			0
$490$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$491$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$491$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.959493	−	0.281733i	0.959493	−	0.281733i
$497$		0			0
$498$	2.38145	−	1.53046i	2.38145	−	1.53046i
$499$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$499$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$500$	−0.260554	−	1.81219i	−0.260554	−	1.81219i
$501$	0.345139	−	0.755750i	0.345139	−	0.755750i
$502$		0			0
$503$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$503$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.00000			1.00000
$508$		0			0
$509$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$509$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$510$	0.0681534	−	0.474017i	0.0681534	−	0.474017i
$511$		0			0
$512$	0.142315	+	0.989821i	0.142315	+	0.989821i
$513$	1.84125	+	0.540641i	1.84125	+	0.540641i
$514$	−0.402869	+	0.258908i	−0.402869	+	0.258908i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.25667	−	0.368991i	1.25667	−	0.368991i
$520$		0			0
$521$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$521$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$522$		0			0
$523$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$523$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$524$		0			0
$525$		0			0
$526$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$527$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$528$		0			0
$529$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$530$	−2.20362			−2.20362
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	−1.19894	+	1.38365i	−1.19894	+	1.38365i
$541$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$541$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$542$	2.11435	−	0.620830i	2.11435	−	0.620830i
$543$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$544$	0.124777	−	0.0801894i	0.124777	−	0.0801894i
$545$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$546$		0			0
$547$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$547$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$548$	−0.216476	+	1.50563i	−0.216476	+	1.50563i
$549$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$550$		0			0
$551$		0			0
$552$	−0.915415	+	1.05645i	−0.915415	+	1.05645i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.341254	−	2.37347i	0.341254	−	2.37347i
$557$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$557$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$558$	0.459493	+	3.19584i	0.459493	+	3.19584i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$563$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$564$	1.57028	−	1.81219i	1.57028	−	1.81219i
$565$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$569$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$570$	−1.34125	+	2.93694i	−1.34125	+	2.93694i
$571$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$571$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.00000			1.00000
$576$	−1.39788			−1.39788
$577$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$577$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$578$	−1.30075	−	0.835939i	−1.30075	−	0.835939i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.85380	+	2.13940i	−1.85380	+	2.13940i
$587$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$587$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$588$	−1.75667	+	0.515804i	−1.75667	+	0.515804i
$589$	1.52977	+	3.34973i	1.52977	+	3.34973i
$590$		0			0
$591$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$592$		0			0
$593$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$593$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.68251			1.68251
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−0.915415	−	1.05645i	−0.915415	−	1.05645i
$601$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$601$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$602$		0			0
$603$		0			0
$604$	0.0741615	+	0.515804i	0.0741615	+	0.515804i
$605$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$606$		0			0
$607$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$607$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$608$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$609$		0			0
$610$	1.44306	−	1.66538i	1.44306	−	1.66538i
$611$		0			0
$612$	−0.216476	−	0.474017i	−0.216476	−	0.474017i
$613$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$613$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$617$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$618$		0			0
$619$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$619$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$620$	−3.51334			−3.51334
$621$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$631$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$632$	−0.760554	+	0.877726i	−0.760554	+	0.877726i
$633$	0.186393	−	0.215109i	0.186393	−	0.215109i
$634$	0.459493	−	0.134919i	0.459493	−	0.134919i
$635$		0			0
$636$	−2.01722	+	1.29639i	−2.01722	+	1.29639i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.260554	−	1.81219i	0.260554	−	1.81219i
$641$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$641$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$642$	−0.915415	−	1.05645i	−0.915415	−	1.05645i
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$	−0.601808	−	0.694523i	−0.601808	−	0.694523i
$647$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$647$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$648$	−0.198939	+	1.38365i	−0.198939	+	1.38365i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$653$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$654$	−1.34125	+	0.393828i	−1.34125	+	0.393828i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$659$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$660$		0			0
$661$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$661$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$662$	1.17597	−	2.57501i	1.17597	−	2.57501i
$663$		0			0
$664$	1.97858	+	1.27155i	1.97858	+	1.27155i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.52111			1.52111
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$673$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$674$		0			0
$675$	0.841254	−	0.540641i	0.841254	−	0.540641i
$676$	0.760554	+	1.66538i	0.760554	+	1.66538i
$677$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$677$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$678$	−1.85380	+	2.13940i	−1.85380	+	2.13940i
$679$		0			0
$680$	0.381761	−	0.112095i	0.381761	−	0.112095i
$681$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$682$		0			0
$683$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$683$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$684$	0.500000	+	3.47758i	0.500000	+	3.47758i
$685$	0.345139	−	0.755750i	0.345139	−	0.755750i
$686$		0			0
$687$	1.41542	+	0.909632i	1.41542	+	0.909632i
$688$		0			0
$689$		0			0
$690$	1.41542	−	0.909632i	1.41542	−	0.909632i
$691$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$691$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$692$	1.57028	+	1.81219i	1.57028	+	1.81219i
$693$		0			0
$694$	0.459493	−	3.19584i	0.459493	−	3.19584i
$695$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$696$		0			0
$697$		0			0
$698$	2.38145	−	1.53046i	2.38145	−	1.53046i
$699$	0.345139	+	0.755750i	0.345139	+	0.755750i
$700$		0			0
$701$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$701$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$706$	3.09792	+	0.909632i	3.09792	+	0.909632i
$707$		0			0
$708$		0			0
$709$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$709$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$710$		0			0
$711$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$712$		0			0
$713$	0.273100	−	1.89945i	0.273100	−	1.89945i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$719$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$720$	−0.500000	−	0.146813i	−0.500000	−	0.146813i
$721$		0			0
$722$	1.87491	+	4.10548i	1.87491	+	4.10548i
$723$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$724$	0.341254	−	0.393828i	0.341254	−	0.393828i
$725$		0			0
$726$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$727$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$727$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$728$		0			0
$729$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$730$		0			0
$731$		0			0
$732$	0.341254	−	2.37347i	0.341254	−	2.37347i
$733$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$733$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$734$		0			0
$735$	1.00000			1.00000
$736$	0.500000	+	0.146813i	0.500000	+	0.146813i
$737$		0			0
$738$		0			0
$739$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$739$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$743$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$744$	−2.25667	+	1.45027i	−2.25667	+	1.45027i
$745$		0			0
$746$		0			0
$747$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$748$		0			0
$749$		0			0
$750$	0.698939	+	1.53046i	0.698939	+	1.53046i
$751$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$751$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$752$	0.654861	+	0.192284i	0.654861	+	0.192284i
$753$		0			0
$754$		0			0
$755$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$756$		0			0
$757$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$757$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$758$	2.83083			2.83083
$759$		0			0
$760$	−2.68251			−2.68251
$761$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$761$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$766$	−2.71616	−	0.797537i	−2.71616	−	0.797537i
$767$		0			0
$768$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$769$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$769$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$770$		0			0
$771$	0.186393	−	0.215109i	0.186393	−	0.215109i
$772$		0			0
$773$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$773$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$774$		0			0
$775$	1.84125	+	0.540641i	1.84125	+	0.540641i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.0681534	+	0.474017i	0.0681534	+	0.474017i
$783$		0			0
$784$	−0.341254	−	0.393828i	−0.341254	−	0.393828i
$785$		0			0
$786$		0			0
$787$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$787$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$788$	−0.216476	−	1.50563i	−0.216476	−	1.50563i
$789$	1.84125	+	0.540641i	1.84125	+	0.540641i
$790$	1.17597	−	0.755750i	1.17597	−	0.755750i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	1.25667	−	0.368991i	1.25667	−	0.368991i
$796$	1.27964	+	2.80202i	1.27964	+	2.80202i
$797$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$797$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$798$		0			0
$799$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$800$	−0.216476	+	0.474017i	−0.216476	+	0.474017i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$809$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$810$	0.698939	−	1.53046i	0.698939	−	1.53046i
$811$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$811$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$812$		0			0
$813$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$814$		0			0
$815$		0			0
$816$	0.0971309	−	0.112095i	0.0971309	−	0.112095i
$817$		0			0
$818$	0.459493	−	0.134919i	0.459493	−	0.134919i
$819$		0			0
$820$		0			0
$821$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$821$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$822$	−0.198939	−	1.38365i	−0.198939	−	1.38365i
$823$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$823$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$827$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$828$	0.760554	−	1.66538i	0.760554	−	1.66538i
$829$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$829$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$830$	−1.85380	−	2.13940i	−1.85380	−	2.13940i
$831$		0			0
$832$		0			0
$833$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$834$	0.313607	+	2.18119i	0.313607	+	2.18119i
$835$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$836$		0			0
$837$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$838$		0			0
$839$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$839$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$840$		0			0
$841$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$842$	−1.34125	−	2.93694i	−1.34125	−	2.93694i
$843$		0			0
$844$	0.500000	+	0.146813i	0.500000	+	0.146813i
$845$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$846$	−0.915415	+	2.00448i	−0.915415	+	2.00448i
$847$		0			0
$848$	−0.574161	−	0.368991i	−0.574161	−	0.368991i
$849$		0			0
$850$	−0.478891			−0.478891
$851$		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
$855$	0.273100	−	1.89945i	0.273100	−	1.89945i
$856$	0.482462	−	1.05645i	0.482462	−	1.05645i
$857$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$857$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$858$		0			0
$859$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$859$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$863$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$864$	0.500000	−	0.146813i	0.500000	−	0.146813i
$865$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$866$		0			0
$867$	0.881761	+	0.258908i	0.881761	+	0.258908i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.760554	−	0.877726i	−0.760554	−	0.877726i
$873$		0			0
$874$	0.459493	−	3.19584i	0.459493	−	3.19584i
$875$		0			0
$876$		0			0
$877$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$877$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$878$	−0.402869	+	2.80202i	−0.402869	+	2.80202i
$879$	0.698939	−	1.53046i	0.698939	−	1.53046i
$880$		0			0
$881$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$881$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$882$	1.41542	−	0.909632i	1.41542	−	0.909632i
$883$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$883$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$884$		0			0
$885$		0			0
$886$	0.313607	−	0.361922i	0.313607	−	0.361922i
$887$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$887$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	1.54019	+	0.989821i	1.54019	+	0.989821i
$901$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$902$		0			0
$903$		0			0
$904$	−2.25667	−	0.662618i	−2.25667	−	0.662618i
$905$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$906$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$907$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$907$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$908$	1.57028	−	1.81219i	1.57028	−	1.81219i
$909$		0			0
$910$		0			0
$911$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$911$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$912$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$913$		0			0
$914$		0			0
$915$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$916$	−0.438384	+	3.04903i	−0.438384	+	3.04903i
$917$		0			0
$918$	0.313607	+	0.361922i	0.313607	+	0.361922i
$919$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$919$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$920$	1.17597	+	0.755750i	1.17597	+	0.755750i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$929$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$930$	3.09792	−	0.909632i	3.09792	−	0.909632i
$931$	1.25667	−	1.45027i	1.25667	−	1.45027i
$932$	−0.996114	+	1.14958i	−0.996114	+	1.14958i
$933$		0			0
$934$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$935$		0			0
$936$		0			0
$937$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$937$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$938$		0			0
$939$		0			0
$940$	−2.01722	−	1.29639i	−2.01722	−	1.29639i
$941$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$941$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$947$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$948$	0.631891	−	1.38365i	0.631891	−	1.38365i
$949$		0			0
$950$	3.09792	+	0.909632i	3.09792	+	0.909632i
$951$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$952$		0			0
$953$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$953$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$954$	1.44306	−	1.66538i	1.44306	−	1.66538i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.198939	+	1.38365i	0.198939	+	1.38365i
$961$	1.11435	−	2.44009i	1.11435	−	2.44009i
$962$		0			0
$963$	0.698939	+	0.449181i	0.698939	+	0.449181i
$964$	0.341254	+	0.393828i	0.341254	+	0.393828i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	−0.915415	−	1.05645i	−0.915415	−	1.05645i
$969$	0.459493	+	0.295298i	0.459493	+	0.295298i
$970$		0			0
$971$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$971$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$972$	−0.260554	−	1.81219i	−0.260554	−	1.81219i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.654861	−	0.192284i	0.654861	−	0.192284i
$977$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$977$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$978$		0			0
$979$		0			0
$980$	0.760554	+	1.66538i	0.760554	+	1.66538i
$981$	0.698939	−	0.449181i	0.698939	−	0.449181i
$982$		0			0
$983$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$983$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$984$		0			0
$985$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$991$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$992$	0.841254	+	0.540641i	0.841254	+	0.540641i
$993$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$994$		0			0
$995$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$996$	−2.95561	−	0.867845i	−2.95561	−	0.867845i
$997$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$997$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$998$	0.580699	+	1.27155i	0.580699	+	1.27155i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.1.p.a.59.1	✓	10
3.2	odd	2		345.1.p.b.59.1	yes	10
5.2	odd	4		1725.1.bc.a.1301.2		20
5.3	odd	4		1725.1.bc.a.1301.1		20
5.4	even	2		345.1.p.b.59.1	yes	10
15.2	even	4		1725.1.bc.a.1301.1		20
15.8	even	4		1725.1.bc.a.1301.2		20
15.14	odd	2	CM	345.1.p.a.59.1	✓	10
23.16	even	11	inner	345.1.p.a.269.1	yes	10
69.62	odd	22		345.1.p.b.269.1	yes	10
115.39	even	22		345.1.p.b.269.1	yes	10
115.62	odd	44		1725.1.bc.a.476.1		20
115.108	odd	44		1725.1.bc.a.476.2		20
345.62	even	44		1725.1.bc.a.476.2		20
345.269	odd	22	inner	345.1.p.a.269.1	yes	10
345.338	even	44		1725.1.bc.a.476.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.1.p.a.59.1	✓	10	1.1	even	1	trivial
345.1.p.a.59.1	✓	10	15.14	odd	2	CM
345.1.p.a.269.1	yes	10	23.16	even	11	inner
345.1.p.a.269.1	yes	10	345.269	odd	22	inner
345.1.p.b.59.1	yes	10	3.2	odd	2
345.1.p.b.59.1	yes	10	5.4	even	2
345.1.p.b.269.1	yes	10	69.62	odd	22
345.1.p.b.269.1	yes	10	115.39	even	22
1725.1.bc.a.476.1		20	115.62	odd	44
1725.1.bc.a.476.1		20	345.338	even	44
1725.1.bc.a.476.2		20	115.108	odd	44
1725.1.bc.a.476.2		20	345.62	even	44
1725.1.bc.a.1301.1		20	5.3	odd	4
1725.1.bc.a.1301.1		20	15.2	even	4
1725.1.bc.a.1301.2		20	5.2	odd	4
1725.1.bc.a.1301.2		20	15.8	even	4

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	345.1.p.a.59.1

Level	$345$
Weight	$1$
Character	345.59
Analytic conductor	$0.172$
Analytic rank	$0$
Dimension	$10$
Projective image	$D_{11}$
CM discriminant	-15
Inner twists	$4$