LMFDB - Embedded newform 345.1.p.a.179.1

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			179.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	345.179
Dual form			345.1.p.a.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25667 + 0.368991i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.601808 + 0.386758i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-1.10181 + 0.708089i) q^{6} +(-0.244123 - 0.281733i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.544078 + 1.19136i) q^{10} +(-0.686393 + 0.201543i) q^{12} +(-0.654861 - 0.755750i) q^{15} +(-0.500000 - 1.09485i) q^{16} +(1.41542 - 0.909632i) q^{17} +(0.186393 - 1.29639i) q^{18} +(0.698939 + 0.449181i) q^{19} +(-0.468468 + 0.540641i) q^{20} +(-0.959493 + 0.281733i) q^{23} +0.372786 q^{24} +(-0.959493 - 0.281733i) q^{25} +(0.841254 + 0.540641i) q^{27} +(-0.544078 - 1.19136i) q^{30} +(-0.544078 - 0.627899i) q^{31} +(-0.171292 - 1.19136i) q^{32} +(2.11435 - 0.620830i) q^{34} +(0.297176 - 0.650724i) q^{36} +(0.712591 + 0.822373i) q^{38} +(0.313607 - 0.201543i) q^{40} +1.00000 q^{45} -1.30972 q^{46} -1.91899 q^{47} +(1.15486 + 0.339098i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-1.10181 - 0.708089i) q^{50} +(-0.239446 + 1.66538i) q^{51} +(-0.797176 - 1.74557i) q^{53} +(0.857685 + 0.989821i) q^{54} +(-0.797176 + 0.234072i) q^{57} +(-0.101808 - 0.708089i) q^{60} +(1.25667 + 1.45027i) q^{61} +(-0.452036 - 0.989821i) q^{62} +(0.0530529 - 0.368991i) q^{64} +1.20362 q^{68} +(0.415415 - 0.909632i) q^{69} +(-0.244123 + 0.281733i) q^{72} +(0.841254 - 0.540641i) q^{75} +(0.246902 + 0.540641i) q^{76} +(-0.118239 + 0.258908i) q^{79} +(1.15486 - 0.339098i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.186393 + 1.29639i) q^{83} +(0.698939 + 1.53046i) q^{85} +(1.25667 + 0.368991i) q^{90} +(-0.686393 - 0.201543i) q^{92} +0.830830 q^{93} +(-2.41153 - 0.708089i) q^{94} +(-0.544078 + 0.627899i) q^{95} +(1.01255 + 0.650724i) q^{96} +(-1.10181 + 0.708089i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$-1$	$e\left(\frac{6}{11}\right)$	$-1$

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 $

$2$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$2$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$3$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$3$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$4$	0.601808	+	0.386758i	0.601808	+	0.386758i
$5$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$5$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$6$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$7$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$7$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$8$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$9$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$10$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$11$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$11$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$12$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$13$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$13$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$14$		0			0
$15$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$16$	−0.500000	−	1.09485i	−0.500000	−	1.09485i
$17$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$17$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$18$	0.186393	−	1.29639i	0.186393	−	1.29639i
$19$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$19$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$20$	−0.468468	+	0.540641i	−0.468468	+	0.540641i
$21$		0			0
$22$		0			0
$23$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$23$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$24$	0.372786			0.372786
$25$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$26$		0			0
$27$	0.841254	+	0.540641i	0.841254	+	0.540641i
$28$		0			0
$29$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$29$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$30$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$31$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$31$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$32$	−0.171292	−	1.19136i	−0.171292	−	1.19136i
$33$		0			0
$34$	2.11435	−	0.620830i	2.11435	−	0.620830i
$35$		0			0
$36$	0.297176	−	0.650724i	0.297176	−	0.650724i
$37$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$37$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$38$	0.712591	+	0.822373i	0.712591	+	0.822373i
$39$		0			0
$40$	0.313607	−	0.201543i	0.313607	−	0.201543i
$41$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$41$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$42$		0			0
$43$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$43$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$44$		0			0
$45$	1.00000			1.00000
$46$	−1.30972			−1.30972
$47$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$47$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$48$	1.15486	+	0.339098i	1.15486	+	0.339098i
$49$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$50$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$51$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$52$		0			0
$53$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$53$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$54$	0.857685	+	0.989821i	0.857685	+	0.989821i
$55$		0			0
$56$		0			0
$57$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$58$		0			0
$59$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$59$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$60$	−0.101808	−	0.708089i	−0.101808	−	0.708089i
$61$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$61$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$62$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$63$		0			0
$64$	0.0530529	−	0.368991i	0.0530529	−	0.368991i
$65$		0			0
$66$		0			0
$67$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$67$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$68$	1.20362			1.20362
$69$	0.415415	−	0.909632i	0.415415	−	0.909632i
$70$		0			0
$71$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$71$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$72$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$73$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$73$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$74$		0			0
$75$	0.841254	−	0.540641i	0.841254	−	0.540641i
$76$	0.246902	+	0.540641i	0.246902	+	0.540641i
$77$		0			0
$78$		0			0
$79$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$79$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$80$	1.15486	−	0.339098i	1.15486	−	0.339098i
$81$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$82$		0			0
$83$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$83$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$84$		0			0
$85$	0.698939	+	1.53046i	0.698939	+	1.53046i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$89$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$90$	1.25667	+	0.368991i	1.25667	+	0.368991i
$91$		0			0
$92$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$93$	0.830830			0.830830
$94$	−2.41153	−	0.708089i	−2.41153	−	0.708089i
$95$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$96$	1.01255	+	0.650724i	1.01255	+	0.650724i
$97$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$97$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$98$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$99$		0			0
$100$	−0.468468	−	0.540641i	−0.468468	−	0.540641i
$101$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$101$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$102$	−0.915415	+	2.00448i	−0.915415	+	2.00448i
$103$		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
$106$	−0.357685	−	2.48775i	−0.357685	−	2.48775i
$107$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$107$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$108$	0.297176	+	0.650724i	0.297176	+	0.650724i
$109$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$109$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$113$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$114$	−1.08816			−1.08816
$115$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$121$	0.841254	−	0.540641i	0.841254	−	0.540641i
$122$	1.04408	+	2.28621i	1.04408	+	2.28621i
$123$		0			0
$124$	−0.0845850	−	0.588302i	−0.0845850	−	0.588302i
$125$	0.415415	−	0.909632i	0.415415	−	0.909632i
$126$		0			0
$127$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$127$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$128$	−0.297176	+	0.650724i	−0.297176	+	0.650724i
$129$		0			0
$130$		0			0
$131$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$131$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$136$	−0.601808	−	0.176707i	−0.601808	−	0.176707i
$137$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$137$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$138$	0.857685	−	0.989821i	0.857685	−	0.989821i
$139$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$139$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$140$		0			0
$141$	1.25667	−	1.45027i	1.25667	−	1.45027i
$142$		0			0
$143$		0			0
$144$	−1.01255	+	0.650724i	−1.01255	+	0.650724i
$145$		0			0
$146$		0			0
$147$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$148$		0			0
$149$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$149$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$150$	1.25667	−	0.368991i	1.25667	−	0.368991i
$151$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$151$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$152$	−0.0440780	−	0.306569i	−0.0440780	−	0.306569i
$153$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$154$		0			0
$155$	0.698939	−	0.449181i	0.698939	−	0.449181i
$156$		0			0
$157$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$157$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$158$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$159$	1.84125	+	0.540641i	1.84125	+	0.540641i
$160$	1.20362			1.20362
$161$		0			0
$162$	−1.30972			−1.30972
$163$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$163$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$164$		0			0
$165$		0			0
$166$	−0.244123	+	1.69791i	−0.244123	+	1.69791i
$167$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$167$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$168$		0			0
$169$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$170$	0.313607	+	2.18119i	0.313607	+	2.18119i
$171$	0.345139	−	0.755750i	0.345139	−	0.755750i
$172$		0			0
$173$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$173$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$179$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$180$	0.601808	+	0.386758i	0.601808	+	0.386758i
$181$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$181$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$182$		0			0
$183$	−1.91899			−1.91899
$184$	0.313607	+	0.201543i	0.313607	+	0.201543i
$185$		0			0
$186$	1.04408	+	0.306569i	1.04408	+	0.306569i
$187$		0			0
$188$	−1.15486	−	0.742184i	−1.15486	−	0.742184i
$189$		0			0
$190$	−0.915415	+	0.588302i	−0.915415	+	0.588302i
$191$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$191$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$192$	0.244123	+	0.281733i	0.244123	+	0.281733i
$193$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$193$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$194$		0			0
$195$		0			0
$196$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$197$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$197$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$198$		0			0
$199$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$199$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$200$	0.154861	+	0.339098i	0.154861	+	0.339098i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.788201	+	0.909632i	−0.788201	+	0.909632i
$205$		0			0
$206$		0			0
$207$	0.415415	+	0.909632i	0.415415	+	0.909632i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$211$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$212$	0.195368	−	1.35881i	0.195368	−	1.35881i
$213$		0			0
$214$	0.154861	+	0.339098i	0.154861	+	0.339098i
$215$		0			0
$216$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$217$		0			0
$218$	−0.357685	+	0.105026i	−0.357685	+	0.105026i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$223$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$224$		0			0
$225$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$226$	1.44306	+	0.927399i	1.44306	+	0.927399i
$227$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$227$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$228$	−0.570276	−	0.167448i	−0.570276	−	0.167448i
$229$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$229$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$230$	0.186393	−	1.29639i	0.186393	−	1.29639i
$231$		0			0
$232$		0			0
$233$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$233$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$234$		0			0
$235$	0.273100	−	1.89945i	0.273100	−	1.89945i
$236$		0			0
$237$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$238$		0			0
$239$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$239$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$240$	−0.500000	+	1.09485i	−0.500000	+	1.09485i
$241$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$241$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$242$	1.25667	−	0.368991i	1.25667	−	0.368991i
$243$	0.415415	−	0.909632i	0.415415	−	0.909632i
$244$	0.195368	+	1.35881i	0.195368	+	1.35881i
$245$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$246$		0			0
$247$		0			0
$248$	−0.0440780	+	0.306569i	−0.0440780	+	0.306569i
$249$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$250$	0.857685	−	0.989821i	0.857685	−	0.989821i
$251$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$251$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$256$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$257$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$257$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$263$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$264$		0			0
$265$	1.84125	−	0.540641i	1.84125	−	0.540641i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$269$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$270$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$271$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$271$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$272$	−1.70362	−	1.09485i	−1.70362	−	1.09485i
$273$		0			0
$274$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$275$		0			0
$276$	0.601808	−	0.386758i	0.601808	−	0.386758i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	−2.41153	−	0.708089i	−2.41153	−	0.708089i
$279$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$280$		0			0
$281$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$281$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$282$	2.11435	−	1.35881i	2.11435	−	1.35881i
$283$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$283$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$284$		0			0
$285$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$286$		0			0
$287$		0			0
$288$	−1.15486	+	0.339098i	−1.15486	+	0.339098i
$289$	0.760554	−	1.66538i	0.760554	−	1.66538i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$293$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$294$	0.186393	−	1.29639i	0.186393	−	1.29639i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.715370			0.715370
$301$		0			0
$302$	1.44306	−	1.66538i	1.44306	−	1.66538i
$303$		0			0
$304$	0.142315	−	0.989821i	0.142315	−	0.989821i
$305$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$306$	−0.915415	−	2.00448i	−0.915415	−	2.00448i
$307$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$307$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$308$		0			0
$309$		0			0
$310$	1.04408	−	0.306569i	1.04408	−	0.306569i
$311$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$311$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$312$		0			0
$313$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$313$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$314$		0			0
$315$		0			0
$316$	−0.171292	+	0.110083i	−0.171292	+	0.110083i
$317$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$317$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$318$	2.11435	+	1.35881i	2.11435	+	1.35881i
$319$		0			0
$320$	0.357685	+	0.105026i	0.357685	+	0.105026i
$321$	−0.284630			−0.284630
$322$		0			0
$323$	1.39788			1.39788
$324$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$325$		0			0
$326$		0			0
$327$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$331$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$332$	−0.389217	+	0.852267i	−0.389217	+	0.852267i
$333$		0			0
$334$	−0.357685	+	0.105026i	−0.357685	+	0.105026i
$335$		0			0
$336$		0			0
$337$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$337$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$338$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$339$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$340$	−0.171292	+	1.19136i	−0.171292	+	1.19136i
$341$		0			0
$342$	0.712591	−	0.822373i	0.712591	−	0.822373i
$343$		0			0
$344$		0			0
$345$	0.841254	+	0.540641i	0.841254	+	0.540641i
$346$	2.51334			2.51334
$347$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$347$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$348$		0			0
$349$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$349$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$353$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−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		−0.142315	−	0.989821i	$-0.545455\pi$
$359$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$360$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$361$	−0.128663	−	0.281733i	−0.128663	−	0.281733i
$362$	−1.85380	+	1.19136i	−1.85380	+	1.19136i
$363$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$364$		0			0
$365$		0			0
$366$	−2.41153	−	0.708089i	−2.41153	−	0.708089i
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	0.788201	+	0.909632i	0.788201	+	0.909632i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.500000	+	0.321330i	0.500000	+	0.321330i
$373$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$373$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$374$		0			0
$375$	0.415415	+	0.909632i	0.415415	+	0.909632i
$376$	0.468468	+	0.540641i	0.468468	+	0.540641i
$377$		0			0
$378$		0			0
$379$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$379$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$380$	−0.570276	+	0.167448i	−0.570276	+	0.167448i
$381$		0			0
$382$		0			0
$383$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$383$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$384$	−0.297176	−	0.650724i	−0.297176	−	0.650724i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$389$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$390$		0			0
$391$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$392$	0.372786			0.372786
$393$		0			0
$394$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$395$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$396$		0			0
$397$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$397$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$398$	0.712591	+	1.56036i	0.712591	+	1.56036i
$399$		0			0
$400$	0.171292	+	1.19136i	0.171292	+	1.19136i
$401$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$401$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$406$		0			0
$407$		0			0
$408$	0.527646	−	0.339098i	0.527646	−	0.339098i
$409$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$409$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$410$		0			0
$411$	0.186393	−	0.215109i	0.186393	−	0.215109i
$412$		0			0
$413$		0			0
$414$	0.186393	+	1.29639i	0.186393	+	1.29639i
$415$	−1.30972			−1.30972
$416$		0			0
$417$	1.25667	−	1.45027i	1.25667	−	1.45027i
$418$		0			0
$419$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$419$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$420$		0			0
$421$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$421$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$422$	1.44306	+	1.66538i	1.44306	+	1.66538i
$423$	0.273100	+	1.89945i	0.273100	+	1.89945i
$424$	−0.297176	+	0.650724i	−0.297176	+	0.650724i
$425$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$426$		0			0
$427$		0			0
$428$	0.0289775	+	0.201543i	0.0289775	+	0.201543i
$429$		0			0
$430$		0			0
$431$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$431$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$432$	0.171292	−	1.19136i	0.171292	−	1.19136i
$433$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$433$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$434$		0			0
$435$		0			0
$436$	−0.203616			−0.203616
$437$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$438$		0			0
$439$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$439$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$440$		0			0
$441$	0.841254	+	0.540641i	0.841254	+	0.540641i
$442$		0			0
$443$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$443$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$449$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$450$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$451$		0			0
$452$	0.613563	+	0.708089i	0.613563	+	0.708089i
$453$	0.698939	+	1.53046i	0.698939	+	1.53046i
$454$	2.11435	−	1.35881i	2.11435	−	1.35881i
$455$		0			0
$456$	0.260554	+	0.167448i	0.260554	+	0.167448i
$457$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$457$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$458$	−1.64589	−	0.483276i	−1.64589	−	0.483276i
$459$	1.68251			1.68251
$460$	0.297176	−	0.650724i	0.297176	−	0.650724i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$463$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$464$		0			0
$465$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$466$	0.313607	−	0.201543i	0.313607	−	0.201543i
$467$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$467$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$468$		0			0
$469$		0			0
$470$	1.04408	−	2.28621i	1.04408	−	2.28621i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$475$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$476$		0			0
$477$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$478$		0			0
$479$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$479$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$480$	−0.788201	+	0.909632i	−0.788201	+	0.909632i
$481$		0			0
$482$	−2.20362			−2.20362
$483$		0			0
$484$	0.715370			0.715370
$485$		0			0
$486$	0.857685	−	0.989821i	0.857685	−	0.989821i
$487$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$487$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$488$	0.101808	−	0.708089i	0.101808	−	0.708089i
$489$		0			0
$490$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$491$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$491$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$497$		0			0
$498$	−1.12333	−	1.29639i	−1.12333	−	1.29639i
$499$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$499$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$500$	0.601808	−	0.386758i	0.601808	−	0.386758i
$501$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$502$		0			0
$503$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$503$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.00000			1.00000
$508$		0			0
$509$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$509$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$510$	−1.85380	−	1.19136i	−1.85380	−	1.19136i
$511$		0			0
$512$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$513$	0.345139	+	0.755750i	0.345139	+	0.755750i
$514$	1.44306	+	1.66538i	1.44306	+	1.66538i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$520$		0			0
$521$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$521$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$522$		0			0
$523$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$523$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$524$		0			0
$525$		0			0
$526$	0.712591	−	0.822373i	0.712591	−	0.822373i
$527$	−1.34125	−	0.393828i	−1.34125	−	0.393828i
$528$		0			0
$529$	0.841254	−	0.540641i	0.841254	−	0.540641i
$530$	2.51334			2.51334
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$541$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$541$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$542$	1.04408	−	2.28621i	1.04408	−	2.28621i
$543$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$544$	−1.32615	−	1.53046i	−1.32615	−	1.53046i
$545$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$546$		0			0
$547$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$547$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$548$	−0.171292	−	0.110083i	−0.171292	−	0.110083i
$549$	1.25667	−	1.45027i	1.25667	−	1.45027i
$550$		0			0
$551$		0			0
$552$	−0.357685	+	0.105026i	−0.357685	+	0.105026i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.15486	−	0.742184i	−1.15486	−	0.742184i
$557$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$557$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$558$	−0.915415	+	0.588302i	−0.915415	+	0.588302i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$563$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$564$	1.31718	−	0.386758i	1.31718	−	0.386758i
$565$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$569$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$570$	0.154861	−	1.07708i	0.154861	−	1.07708i
$571$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$571$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.00000			1.00000
$576$	−0.372786			−0.372786
$577$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$577$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$578$	1.57028	−	1.81219i	1.57028	−	1.81219i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.64589	+	0.483276i	−1.64589	+	0.483276i
$587$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$587$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$588$	0.297176	−	0.650724i	0.297176	−	0.650724i
$589$	−0.0982369	−	0.683252i	−0.0982369	−	0.683252i
$590$		0			0
$591$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$592$		0			0
$593$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$593$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.30972			−1.30972
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$601$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$601$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$602$		0			0
$603$		0			0
$604$	1.01255	−	0.650724i	1.01255	−	0.650724i
$605$	0.415415	+	0.909632i	0.415415	+	0.909632i
$606$		0			0
$607$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$607$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$608$	0.415415	−	0.909632i	0.415415	−	0.909632i
$609$		0			0
$610$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$611$		0			0
$612$	−0.171292	−	1.19136i	−0.171292	−	1.19136i
$613$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$613$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$617$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$618$		0			0
$619$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$619$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$620$	0.594351			0.594351
$621$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.841254	+	0.540641i	0.841254	+	0.540641i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$631$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$632$	0.101808	−	0.0298935i	0.101808	−	0.0298935i
$633$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$634$	−0.915415	+	2.00448i	−0.915415	+	2.00448i
$635$		0			0
$636$	0.898983	+	1.03748i	0.898983	+	1.03748i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.601808	−	0.386758i	−0.601808	−	0.386758i
$641$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$641$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$642$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$	1.75667	+	0.515804i	1.75667	+	0.515804i
$647$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$647$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$648$	0.313607	+	0.201543i	0.313607	+	0.201543i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$653$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$654$	0.154861	−	0.339098i	0.154861	−	0.339098i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$659$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$660$		0			0
$661$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$661$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$662$	−0.244123	+	1.69791i	−0.244123	+	1.69791i
$663$		0			0
$664$	0.319733	−	0.368991i	0.319733	−	0.368991i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.203616			−0.203616
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$673$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$674$		0			0
$675$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$676$	−0.101808	−	0.708089i	−0.101808	−	0.708089i
$677$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$677$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$678$	−1.64589	+	0.483276i	−1.64589	+	0.483276i
$679$		0			0
$680$	0.260554	−	0.570534i	0.260554	−	0.570534i
$681$	0.273100	+	1.89945i	0.273100	+	1.89945i
$682$		0			0
$683$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$683$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$684$	0.500000	−	0.321330i	0.500000	−	0.321330i
$685$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$686$		0			0
$687$	0.857685	−	0.989821i	0.857685	−	0.989821i
$688$		0			0
$689$		0			0
$690$	0.857685	+	0.989821i	0.857685	+	0.989821i
$691$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$691$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$692$	1.31718	+	0.386758i	1.31718	+	0.386758i
$693$		0			0
$694$	−0.915415	−	0.588302i	−0.915415	−	0.588302i
$695$	0.273100	−	1.89945i	0.273100	−	1.89945i
$696$		0			0
$697$		0			0
$698$	−1.12333	−	1.29639i	−1.12333	−	1.29639i
$699$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$700$		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			0
$705$	1.25667	+	1.45027i	1.25667	+	1.45027i
$706$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$707$		0			0
$708$		0			0
$709$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$709$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$710$		0			0
$711$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$712$		0			0
$713$	0.698939	+	0.449181i	0.698939	+	0.449181i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$719$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$720$	−0.500000	−	1.09485i	−0.500000	−	1.09485i
$721$		0			0
$722$	−0.0577299	−	0.401520i	−0.0577299	−	0.401520i
$723$	0.698939	−	1.53046i	0.698939	−	1.53046i
$724$	−1.15486	+	0.339098i	−1.15486	+	0.339098i
$725$		0			0
$726$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$727$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$727$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.415415	+	0.909632i
$730$		0			0
$731$		0			0
$732$	−1.15486	−	0.742184i	−1.15486	−	0.742184i
$733$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$733$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$734$		0			0
$735$	1.00000			1.00000
$736$	0.500000	+	1.09485i	0.500000	+	1.09485i
$737$		0			0
$738$		0			0
$739$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$739$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$743$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$744$	−0.202824	−	0.234072i	−0.202824	−	0.234072i
$745$		0			0
$746$		0			0
$747$	1.25667	−	0.368991i	1.25667	−	0.368991i
$748$		0			0
$749$		0			0
$750$	0.186393	+	1.29639i	0.186393	+	1.29639i
$751$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$751$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$752$	0.959493	+	2.10100i	0.959493	+	2.10100i
$753$		0			0
$754$		0			0
$755$	1.41542	+	0.909632i	1.41542	+	0.909632i
$756$		0			0
$757$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$757$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$758$	1.71537			1.71537
$759$		0			0
$760$	0.309721			0.309721
$761$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$761$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.41542	−	0.909632i	1.41542	−	0.909632i
$766$	0.712591	+	1.56036i	0.712591	+	1.56036i
$767$		0			0
$768$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$769$	0.830830	−	1.81926i	0.830830	−	1.81926i	0.415415	−	0.909632i	$-0.363636\pi$
$769$	0.830830	−	1.81926i	0.830830	−	1.81926i	0.415415	−	0.909632i	$-0.363636\pi$
$770$		0			0
$771$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$772$		0			0
$773$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$773$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$774$		0			0
$775$	0.345139	+	0.755750i	0.345139	+	0.755750i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−1.85380	+	1.19136i	−1.85380	+	1.19136i
$783$		0			0
$784$	1.15486	+	0.339098i	1.15486	+	0.339098i
$785$		0			0
$786$		0			0
$787$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$787$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$788$	−0.171292	+	0.110083i	−0.171292	+	0.110083i
$789$	0.345139	+	0.755750i	0.345139	+	0.755750i
$790$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$796$	0.133340	+	0.927399i	0.133340	+	0.927399i
$797$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$797$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$798$		0			0
$799$	−2.71616	+	1.74557i	−2.71616	+	1.74557i
$800$	−0.171292	+	1.19136i	−0.171292	+	1.19136i
$801$		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		−0.841254	−	0.540641i	$-0.818182\pi$
$809$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$810$	0.186393	−	1.29639i	0.186393	−	1.29639i
$811$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$811$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$812$		0			0
$813$	1.25667	+	1.45027i	1.25667	+	1.45027i
$814$		0			0
$815$		0			0
$816$	1.94306	−	0.570534i	1.94306	−	0.570534i
$817$		0			0
$818$	−0.915415	+	2.00448i	−0.915415	+	2.00448i
$819$		0			0
$820$		0			0
$821$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$821$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$822$	0.313607	−	0.201543i	0.313607	−	0.201543i
$823$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$823$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$827$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$828$	−0.101808	+	0.708089i	−0.101808	+	0.708089i
$829$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$829$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$830$	−1.64589	−	0.483276i	−1.64589	−	0.483276i
$831$		0			0
$832$		0			0
$833$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$834$	2.11435	−	1.35881i	2.11435	−	1.35881i
$835$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$836$		0			0
$837$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$838$		0			0
$839$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$839$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$840$		0			0
$841$	0.415415	−	0.909632i	0.415415	−	0.909632i
$842$	0.154861	+	1.07708i	0.154861	+	1.07708i
$843$		0			0
$844$	0.500000	+	1.09485i	0.500000	+	1.09485i
$845$	0.841254	−	0.540641i	0.841254	−	0.540641i
$846$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$847$		0			0
$848$	−1.51255	+	1.74557i	−1.51255	+	1.74557i
$849$		0			0
$850$	−2.20362			−2.20362
$851$		0			0
$852$		0			0
$853$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$853$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$854$		0			0
$855$	0.698939	+	0.449181i	0.698939	+	0.449181i
$856$	0.0151004	−	0.105026i	0.0151004	−	0.105026i
$857$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$857$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$858$		0			0
$859$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$859$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$863$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$864$	0.500000	−	1.09485i	0.500000	−	1.09485i
$865$	0.273100	+	1.89945i	0.273100	+	1.89945i
$866$		0			0
$867$	0.760554	+	1.66538i	0.760554	+	1.66538i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.101808	+	0.0298935i	0.101808	+	0.0298935i
$873$		0			0
$874$	−0.915415	−	0.588302i	−0.915415	−	0.588302i
$875$		0			0
$876$		0			0
$877$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$877$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$878$	1.44306	+	0.927399i	1.44306	+	0.927399i
$879$	0.186393	−	1.29639i	0.186393	−	1.29639i
$880$		0			0
$881$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$881$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$882$	0.857685	+	0.989821i	0.857685	+	0.989821i
$883$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$883$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$884$		0			0
$885$		0			0
$886$	2.11435	−	0.620830i	2.11435	−	0.620830i
$887$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$887$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.34125	−	0.861971i	−1.34125	−	0.861971i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.468468	+	0.540641i	−0.468468	+	0.540641i
$901$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$902$		0			0
$903$		0			0
$904$	−0.202824	−	0.444124i	−0.202824	−	0.444124i
$905$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$906$	0.313607	+	2.18119i	0.313607	+	2.18119i
$907$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$907$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$908$	1.31718	−	0.386758i	1.31718	−	0.386758i
$909$		0			0
$910$		0			0
$911$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$911$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$912$	0.654861	+	0.755750i	0.654861	+	0.755750i
$913$		0			0
$914$		0			0
$915$	0.273100	−	1.89945i	0.273100	−	1.89945i
$916$	−0.788201	−	0.506546i	−0.788201	−	0.506546i
$917$		0			0
$918$	2.11435	+	0.620830i	2.11435	+	0.620830i
$919$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$919$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$920$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$921$		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		−0.142315	−	0.989821i	$-0.545455\pi$
$929$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$930$	−0.452036	+	0.989821i	−0.452036	+	0.989821i
$931$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$932$	0.195368	−	0.0573652i	0.195368	−	0.0573652i
$933$		0			0
$934$	0.313607	+	2.18119i	0.313607	+	2.18119i
$935$		0			0
$936$		0			0
$937$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$937$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$938$		0			0
$939$		0			0
$940$	0.898983	−	1.03748i	0.898983	−	1.03748i
$941$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$941$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$947$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$948$	0.0289775	−	0.201543i	0.0289775	−	0.201543i
$949$		0			0
$950$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$951$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$952$		0			0
$953$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$953$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$954$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.313607	+	0.201543i	−0.313607	+	0.201543i
$961$	0.0440780	−	0.306569i	0.0440780	−	0.306569i
$962$		0			0
$963$	0.186393	−	0.215109i	0.186393	−	0.215109i
$964$	−1.15486	−	0.339098i	−1.15486	−	0.339098i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$969$	−0.915415	+	1.05645i	−0.915415	+	1.05645i
$970$		0			0
$971$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$971$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$972$	0.601808	−	0.386758i	0.601808	−	0.386758i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.959493	−	2.10100i	0.959493	−	2.10100i
$977$	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			0
$979$		0			0
$980$	−0.101808	−	0.708089i	−0.101808	−	0.708089i
$981$	0.186393	+	0.215109i	0.186393	+	0.215109i
$982$		0			0
$983$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$983$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$984$		0			0
$985$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$991$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$992$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$993$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$994$		0			0
$995$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$996$	−0.389217	−	0.852267i	−0.389217	−	0.852267i
$997$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$997$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$998$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.1.p.a.179.1	✓	10
3.2	odd	2		345.1.p.b.179.1	yes	10
5.2	odd	4		1725.1.bc.a.1076.1		20
5.3	odd	4		1725.1.bc.a.1076.2		20
5.4	even	2		345.1.p.b.179.1	yes	10
15.2	even	4		1725.1.bc.a.1076.2		20
15.8	even	4		1725.1.bc.a.1076.1		20
15.14	odd	2	CM	345.1.p.a.179.1	✓	10
23.9	even	11	inner	345.1.p.a.239.1	yes	10
69.32	odd	22		345.1.p.b.239.1	yes	10
115.9	even	22		345.1.p.b.239.1	yes	10
115.32	odd	44		1725.1.bc.a.101.2		20
115.78	odd	44		1725.1.bc.a.101.1		20
345.32	even	44		1725.1.bc.a.101.1		20
345.239	odd	22	inner	345.1.p.a.239.1	yes	10
345.308	even	44		1725.1.bc.a.101.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.1.p.a.179.1	✓	10	1.1	even	1	trivial
345.1.p.a.179.1	✓	10	15.14	odd	2	CM
345.1.p.a.239.1	yes	10	23.9	even	11	inner
345.1.p.a.239.1	yes	10	345.239	odd	22	inner
345.1.p.b.179.1	yes	10	3.2	odd	2
345.1.p.b.179.1	yes	10	5.4	even	2
345.1.p.b.239.1	yes	10	69.32	odd	22
345.1.p.b.239.1	yes	10	115.9	even	22
1725.1.bc.a.101.1		20	115.78	odd	44
1725.1.bc.a.101.1		20	345.32	even	44
1725.1.bc.a.101.2		20	115.32	odd	44
1725.1.bc.a.101.2		20	345.308	even	44
1725.1.bc.a.1076.1		20	5.2	odd	4
1725.1.bc.a.1076.1		20	15.8	even	4
1725.1.bc.a.1076.2		20	5.3	odd	4
1725.1.bc.a.1076.2		20	15.2	even	4

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	345.p (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25667 + 0.368991i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.601808 + 0.386758i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-1.10181 + 0.708089i) q^{6} +(-0.244123 - 0.281733i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.544078 + 1.19136i) q^{10} +(-0.686393 + 0.201543i) q^{12} +(-0.654861 - 0.755750i) q^{15} +(-0.500000 - 1.09485i) q^{16} +(1.41542 - 0.909632i) q^{17} +(0.186393 - 1.29639i) q^{18} +(0.698939 + 0.449181i) q^{19} +(-0.468468 + 0.540641i) q^{20} +(-0.959493 + 0.281733i) q^{23} +0.372786 q^{24} +(-0.959493 - 0.281733i) q^{25} +(0.841254 + 0.540641i) q^{27} +(-0.544078 - 1.19136i) q^{30} +(-0.544078 - 0.627899i) q^{31} +(-0.171292 - 1.19136i) q^{32} +(2.11435 - 0.620830i) q^{34} +(0.297176 - 0.650724i) q^{36} +(0.712591 + 0.822373i) q^{38} +(0.313607 - 0.201543i) q^{40} +1.00000 q^{45} -1.30972 q^{46} -1.91899 q^{47} +(1.15486 + 0.339098i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-1.10181 - 0.708089i) q^{50} +(-0.239446 + 1.66538i) q^{51} +(-0.797176 - 1.74557i) q^{53} +(0.857685 + 0.989821i) q^{54} +(-0.797176 + 0.234072i) q^{57} +(-0.101808 - 0.708089i) q^{60} +(1.25667 + 1.45027i) q^{61} +(-0.452036 - 0.989821i) q^{62} +(0.0530529 - 0.368991i) q^{64} +1.20362 q^{68} +(0.415415 - 0.909632i) q^{69} +(-0.244123 + 0.281733i) q^{72} +(0.841254 - 0.540641i) q^{75} +(0.246902 + 0.540641i) q^{76} +(-0.118239 + 0.258908i) q^{79} +(1.15486 - 0.339098i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.186393 + 1.29639i) q^{83} +(0.698939 + 1.53046i) q^{85} +(1.25667 + 0.368991i) q^{90} +(-0.686393 - 0.201543i) q^{92} +0.830830 q^{93} +(-2.41153 - 0.708089i) q^{94} +(-0.544078 + 0.627899i) q^{95} +(1.01255 + 0.650724i) q^{96} +(-1.10181 + 0.708089i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - q^{3} - 3 q^{4} - q^{5} - 2 q^{6} + 7 q^{8} - q^{9} - 2 q^{10} - 3 q^{12} - q^{15} - 5 q^{16} + 9 q^{17} - 2 q^{18} - 2 q^{19} - 3 q^{20} - q^{23} - 4 q^{24} - q^{25} - q^{27} - 2 q^{30}+ \cdots - 2 q^{98}+O(q^{100}) \) 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

Introduction

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