LMFDB - Embedded newform 1288.1.bi.e.909.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1288,1,Mod(13,1288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1288, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 14]))

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

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

chi := DirichletCharacter("1288.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1288 = 2^{3} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1288.bi (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:	$0.642795736271$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 11 $
Twist minimal:	yes
Projective image:	$D_{22}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{22} - \cdots)$

Embedding invariants

Embedding label			909.1
Root			$0.989821 + 0.142315i$ of defining polynomial
Character	$\chi$	$=$	1288.909
Dual form			1288.1.bi.e.853.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{2} +(-0.281733 + 1.95949i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-1.45027 + 0.425839i) q^{5} +(-0.822373 - 1.80075i) q^{6} +(0.654861 + 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-2.80075 - 0.822373i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.281733 + 1.95949i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-1.45027 + 0.425839i) q^{5} +(-0.822373 - 1.80075i) q^{6} +(0.654861 + 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-2.80075 - 0.822373i) q^{9} +(0.989821 - 1.14231i) q^{10} +(1.66538 + 1.07028i) q^{12} +(-0.708089 + 0.817178i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-0.425839 - 2.96177i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.80075 - 0.822373i) q^{18} +(0.234072 - 0.512546i) q^{19} +(-0.215109 + 1.49611i) q^{20} +(-1.66538 + 1.07028i) q^{21} +(-0.654861 + 0.755750i) q^{23} -1.97964 q^{24} +(1.08070 - 0.694523i) q^{25} +(0.153882 - 1.07028i) q^{26} +(1.57812 - 3.45561i) q^{27} +(0.959493 - 0.281733i) q^{28} +(1.95949 + 2.26138i) q^{30} +(0.959493 + 0.281733i) q^{32} +(-1.27155 - 0.817178i) q^{35} +(-1.91153 + 2.20602i) q^{36} +(0.0801894 + 0.557730i) q^{38} +(-1.40176 - 1.61772i) q^{39} +(-0.627899 - 1.37491i) q^{40} +(0.822373 - 1.80075i) q^{42} +4.41204 q^{45} +(0.142315 - 0.989821i) q^{46} +(1.66538 - 1.07028i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-0.533654 + 1.16854i) q^{50} +(0.449181 + 0.983568i) q^{52} +(0.540641 + 3.76024i) q^{54} +(-0.654861 + 0.755750i) q^{56} +(0.938384 + 0.603063i) q^{57} +(0.368991 - 0.425839i) q^{59} +(-2.87102 - 0.843008i) q^{60} +(-1.21259 - 2.65520i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(0.678936 - 1.48666i) q^{65} +(-1.29639 - 1.49611i) q^{69} +1.51150 q^{70} +(-1.41542 + 0.909632i) q^{71} +(0.415415 - 2.88927i) q^{72} +(1.05645 + 2.31329i) q^{75} +(-0.368991 - 0.425839i) q^{76} +(2.05384 + 0.603063i) q^{78} +(0.544078 - 0.627899i) q^{79} +(1.27155 + 0.817178i) q^{80} +(3.87102 + 2.48775i) q^{81} +(1.74557 + 0.512546i) q^{83} +(0.281733 + 1.95949i) q^{84} +(-3.71165 + 2.38533i) q^{90} -1.08128 q^{91} +(0.415415 + 0.909632i) q^{92} +(-0.121206 + 0.843008i) q^{95} +(-0.822373 + 1.80075i) q^{96} +(-0.415415 - 0.909632i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 2 * q^8 - 20 * q^9	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9} - 2 q^{14} - 2 q^{16} + 20 q^{18} - 2 q^{23} + 2 q^{25} + 2 q^{28} + 22 q^{30} + 2 q^{32} + 2 q^{36} - 22 q^{39} + 2 q^{46} - 2 q^{49} - 2 q^{50} - 2 q^{56} - 2 q^{63} - 2 q^{64} - 18 q^{71} - 2 q^{72} + 4 q^{79} + 20 q^{81} - 2 q^{92} + 2 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 2 * q^8 - 20 * q^9 - 2 * q^14 - 2 * q^16 + 20 * q^18 - 2 * q^23 + 2 * q^25 + 2 * q^28 + 22 * q^30 + 2 * q^32 + 2 * q^36 - 22 * q^39 + 2 * q^46 - 2 * q^49 - 2 * q^50 - 2 * q^56 - 2 * q^63 - 2 * q^64 - 18 * q^71 - 2 * q^72 + 4 * q^79 + 20 * q^81 - 2 * q^92 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1288\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$645$	$967$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$	$-1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$2$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$3$	−0.281733	+	1.95949i	−0.281733	+	1.95949i			1.00000i	$0.5\pi$
$3$	−0.281733	+	1.95949i	−0.281733	+	1.95949i	−0.281733	+	0.959493i	$0.590909\pi$
$4$	0.415415	−	0.909632i	0.415415	−	0.909632i
$5$	−1.45027	+	0.425839i	−1.45027	+	0.425839i	−0.909632	−	0.415415i	$-0.863636\pi$
$5$	−1.45027	+	0.425839i	−1.45027	+	0.425839i	−0.540641	+	0.841254i	$0.681818\pi$
$6$	−0.822373	−	1.80075i	−0.822373	−	1.80075i
$7$	0.654861	+	0.755750i	0.654861	+	0.755750i
$7$	0.654861	+	0.755750i	0.654861	+	0.755750i
$8$	0.142315	+	0.989821i	0.142315	+	0.989821i
$9$	−2.80075	−	0.822373i	−2.80075	−	0.822373i
$10$	0.989821	−	1.14231i	0.989821	−	1.14231i
$11$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$11$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$12$	1.66538	+	1.07028i	1.66538	+	1.07028i
$13$	−0.708089	+	0.817178i	−0.708089	+	0.817178i	−0.989821	−	0.142315i	$-0.954545\pi$
$13$	−0.708089	+	0.817178i	−0.708089	+	0.817178i	0.281733	+	0.959493i	$0.409091\pi$
$14$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$15$	−0.425839	−	2.96177i	−0.425839	−	2.96177i
$16$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$17$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$17$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$18$	2.80075	−	0.822373i	2.80075	−	0.822373i
$19$	0.234072	−	0.512546i	0.234072	−	0.512546i	−0.755750	−	0.654861i	$-0.772727\pi$
$19$	0.234072	−	0.512546i	0.234072	−	0.512546i	0.989821	+	0.142315i	$0.0454545\pi$
$20$	−0.215109	+	1.49611i	−0.215109	+	1.49611i
$21$	−1.66538	+	1.07028i	−1.66538	+	1.07028i
$22$		0			0
$23$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$23$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$24$	−1.97964			−1.97964
$25$	1.08070	−	0.694523i	1.08070	−	0.694523i
$26$	0.153882	−	1.07028i	0.153882	−	1.07028i
$27$	1.57812	−	3.45561i	1.57812	−	3.45561i
$28$	0.959493	−	0.281733i	0.959493	−	0.281733i
$29$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$29$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$30$	1.95949	+	2.26138i	1.95949	+	2.26138i
$31$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$31$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$32$	0.959493	+	0.281733i	0.959493	+	0.281733i
$33$		0			0
$34$		0			0
$35$	−1.27155	−	0.817178i	−1.27155	−	0.817178i
$36$	−1.91153	+	2.20602i	−1.91153	+	2.20602i
$37$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$37$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$38$	0.0801894	+	0.557730i	0.0801894	+	0.557730i
$39$	−1.40176	−	1.61772i	−1.40176	−	1.61772i
$40$	−0.627899	−	1.37491i	−0.627899	−	1.37491i
$41$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$41$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$42$	0.822373	−	1.80075i	0.822373	−	1.80075i
$43$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$43$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$44$		0			0
$45$	4.41204			4.41204
$46$	0.142315	−	0.989821i	0.142315	−	0.989821i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	1.66538	−	1.07028i	1.66538	−	1.07028i
$49$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$50$	−0.533654	+	1.16854i	−0.533654	+	1.16854i
$51$		0			0
$52$	0.449181	+	0.983568i	0.449181	+	0.983568i
$53$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$53$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$54$	0.540641	+	3.76024i	0.540641	+	3.76024i
$55$		0			0
$56$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$57$	0.938384	+	0.603063i	0.938384	+	0.603063i
$58$		0			0
$59$	0.368991	−	0.425839i	0.368991	−	0.425839i	−0.540641	−	0.841254i	$-0.681818\pi$
$59$	0.368991	−	0.425839i	0.368991	−	0.425839i	0.909632	+	0.415415i	$0.136364\pi$
$60$	−2.87102	−	0.843008i	−2.87102	−	0.843008i
$61$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$61$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$62$		0			0
$63$	−1.21259	−	2.65520i	−1.21259	−	2.65520i
$64$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$65$	0.678936	−	1.48666i	0.678936	−	1.48666i
$66$		0			0
$67$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$67$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$68$		0			0
$69$	−1.29639	−	1.49611i	−1.29639	−	1.49611i
$70$	1.51150			1.51150
$71$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−0.415415	+	0.909632i	$0.636364\pi$
$71$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−1.00000			$\pi$
$72$	0.415415	−	2.88927i	0.415415	−	2.88927i
$73$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$73$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$74$		0			0
$75$	1.05645	+	2.31329i	1.05645	+	2.31329i
$76$	−0.368991	−	0.425839i	−0.368991	−	0.425839i
$77$		0			0
$78$	2.05384	+	0.603063i	2.05384	+	0.603063i
$79$	0.544078	−	0.627899i	0.544078	−	0.627899i	−0.415415	−	0.909632i	$-0.636364\pi$
$79$	0.544078	−	0.627899i	0.544078	−	0.627899i	0.959493	+	0.281733i	$0.0909091\pi$
$80$	1.27155	+	0.817178i	1.27155	+	0.817178i
$81$	3.87102	+	2.48775i	3.87102	+	2.48775i
$82$		0			0
$83$	1.74557	+	0.512546i	1.74557	+	0.512546i	0.989821	−	0.142315i	$-0.0454545\pi$
$83$	1.74557	+	0.512546i	1.74557	+	0.512546i	0.755750	+	0.654861i	$0.227273\pi$
$84$	0.281733	+	1.95949i	0.281733	+	1.95949i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$89$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$90$	−3.71165	+	2.38533i	−3.71165	+	2.38533i
$91$	−1.08128			−1.08128
$92$	0.415415	+	0.909632i	0.415415	+	0.909632i
$93$		0			0
$94$		0			0
$95$	−0.121206	+	0.843008i	−0.121206	+	0.843008i
$96$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$97$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$97$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$98$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$99$		0			0
$100$	−0.182822	−	1.27155i	−0.182822	−	1.27155i
$101$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$101$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$102$		0			0
$103$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$103$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$104$	−0.909632	−	0.584585i	−0.909632	−	0.584585i
$105$	1.95949	−	2.26138i	1.95949	−	2.26138i
$106$		0			0
$107$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$107$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$108$	−2.48775	−	2.87102i	−2.48775	−	2.87102i
$109$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$109$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$110$		0			0
$111$		0			0
$112$	0.142315	−	0.989821i	0.142315	−	0.989821i
$113$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	−0.841254	−	0.540641i	$-0.818182\pi$
$113$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	0.142315	+	0.989821i	$0.454545\pi$
$114$	−1.11546			−1.11546
$115$	0.627899	−	1.37491i	0.627899	−	1.37491i
$116$		0			0
$117$	2.65520	−	1.70640i	2.65520	−	1.70640i
$118$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i
$119$		0			0
$120$	2.87102	−	0.843008i	2.87102	−	0.843008i
$121$	0.415415	+	0.909632i	0.415415	+	0.909632i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.281733	+	0.325137i	−0.281733	+	0.325137i
$126$	2.45561	+	1.57812i	2.45561	+	1.57812i
$127$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$127$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$128$	0.654861	−	0.755750i	0.654861	−	0.755750i
$129$		0			0
$130$	0.232593	+	1.61772i	0.232593	+	1.61772i
$131$	−0.989821	−	1.14231i	−0.989821	−	1.14231i	−0.989821	−	0.142315i	$-0.954545\pi$
$131$	−0.989821	−	1.14231i	−0.989821	−	1.14231i		−	1.00000i	$-0.5\pi$
$132$		0			0
$133$	0.540641	−	0.158746i	0.540641	−	0.158746i
$134$		0			0
$135$	−0.817178	+	5.68360i	−0.817178	+	5.68360i
$136$		0			0
$137$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$137$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$138$	1.89945	+	0.557730i	1.89945	+	0.557730i
$139$	−1.81926			−1.81926			−0.909632	−	0.415415i	$-0.863636\pi$
$139$	−1.81926			−1.81926			−0.909632	+	0.415415i	$0.863636\pi$
$140$	−1.27155	+	0.817178i	−1.27155	+	0.817178i
$141$		0			0
$142$	0.698939	−	1.53046i	0.698939	−	1.53046i
$143$		0			0
$144$	1.21259	+	2.65520i	1.21259	+	2.65520i
$145$		0			0
$146$		0			0
$147$	−1.89945	−	0.557730i	−1.89945	−	0.557730i
$148$		0			0
$149$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$149$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$150$	−2.13940	−	1.37491i	−2.13940	−	1.37491i
$151$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$151$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$152$	0.540641	+	0.158746i	0.540641	+	0.158746i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−2.05384	+	0.603063i	−2.05384	+	0.603063i
$157$	−0.755750	+	1.65486i	−0.755750	+	1.65486i			1.00000i	$0.5\pi$
$157$	−0.755750	+	1.65486i	−0.755750	+	1.65486i	−0.755750	+	0.654861i	$0.772727\pi$
$158$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$159$		0			0
$160$	−1.51150			−1.51150
$161$	−1.00000			−1.00000
$162$	−4.60149			−4.60149
$163$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$163$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$164$		0			0
$165$		0			0
$166$	−1.74557	+	0.512546i	−1.74557	+	0.512546i
$167$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$167$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$168$	−1.29639	−	1.49611i	−1.29639	−	1.49611i
$169$	−0.0240754	−	0.167448i	−0.0240754	−	0.167448i
$170$		0			0
$171$	−1.07708	+	1.24302i	−1.07708	+	1.24302i
$172$		0			0
$173$	−1.53046	−	0.983568i	−1.53046	−	0.983568i	−0.989821	−	0.142315i	$-0.954545\pi$
$173$	−1.53046	−	0.983568i	−1.53046	−	0.983568i	−0.540641	−	0.841254i	$-0.681818\pi$
$174$		0			0
$175$	1.23259	+	0.361922i	1.23259	+	0.361922i
$176$		0			0
$177$	0.730471	+	0.843008i	0.730471	+	0.843008i
$178$		0			0
$179$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$179$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$180$	1.83283	−	4.01334i	1.83283	−	4.01334i
$181$	−0.281733	+	1.95949i	−0.281733	+	1.95949i			1.00000i	$0.5\pi$
$181$	−0.281733	+	1.95949i	−0.281733	+	1.95949i	−0.281733	+	0.959493i	$0.590909\pi$
$182$	0.909632	−	0.584585i	0.909632	−	0.584585i
$183$		0			0
$184$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	3.64502	−	1.07028i	3.64502	−	1.07028i
$190$	−0.353799	−	0.774713i	−0.353799	−	0.774713i
$191$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$191$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$192$	−0.281733	−	1.95949i	−0.281733	−	1.95949i
$193$	−1.25667	−	0.368991i	−1.25667	−	0.368991i	−0.415415	−	0.909632i	$-0.636364\pi$
$193$	−1.25667	−	0.368991i	−1.25667	−	0.368991i	−0.841254	+	0.540641i	$0.818182\pi$
$194$		0			0
$195$	2.72183	+	1.74921i	2.72183	+	1.74921i
$196$	0.841254	+	0.540641i	0.841254	+	0.540641i
$197$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$197$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$198$		0			0
$199$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$199$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$200$	0.841254	+	0.970858i	0.841254	+	0.970858i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.45561	−	1.57812i	2.45561	−	1.57812i
$208$	1.08128			1.08128
$209$		0			0
$210$	−0.425839	+	2.96177i	−0.425839	+	2.96177i
$211$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$211$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$212$		0			0
$213$	−1.38365	−	3.02977i	−1.38365	−	3.02977i
$214$		0			0
$215$		0			0
$216$	3.64502	+	1.07028i	3.64502	+	1.07028i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$223$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$224$	0.415415	+	0.909632i	0.415415	+	0.909632i
$225$	−3.59792	+	1.05645i	−3.59792	+	1.05645i
$226$	0.345139	−	0.755750i	0.345139	−	0.755750i
$227$	−0.258908	+	1.80075i	−0.258908	+	1.80075i	0.281733	+	0.959493i	$0.409091\pi$
$227$	−0.258908	+	1.80075i	−0.258908	+	1.80075i	−0.540641	+	0.841254i	$0.681818\pi$
$228$	0.938384	−	0.603063i	0.938384	−	0.603063i
$229$	−0.563465			−0.563465			−0.281733	−	0.959493i	$-0.590909\pi$
$229$	−0.563465			−0.563465			−0.281733	+	0.959493i	$0.590909\pi$
$230$	0.215109	+	1.49611i	0.215109	+	1.49611i
$231$		0			0
$232$		0			0
$233$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$233$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$234$	−1.31115	+	2.87102i	−1.31115	+	2.87102i
$235$		0			0
$236$	−0.234072	−	0.512546i	−0.234072	−	0.512546i
$237$	1.07708	+	1.24302i	1.07708	+	1.24302i
$238$		0			0
$239$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$239$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$240$	−1.95949	+	2.26138i	−1.95949	+	2.26138i
$241$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$241$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$242$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$243$	−3.47758	+	4.01334i	−3.47758	+	4.01334i
$244$		0			0
$245$	−0.215109	−	1.49611i	−0.215109	−	1.49611i
$246$		0			0
$247$	0.253098	+	0.554206i	0.253098	+	0.554206i
$248$		0			0
$249$	−1.49611	+	3.27603i	−1.49611	+	3.27603i
$250$	0.0612263	−	0.425839i	0.0612263	−	0.425839i
$251$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$251$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.909632	−	0.415415i	$-0.136364\pi$
$252$	−2.91899			−2.91899
$253$		0			0
$254$	1.30972			1.30972
$255$		0			0
$256$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$257$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$257$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$258$		0			0
$259$		0			0
$260$	−1.07028	−	1.23516i	−1.07028	−	1.23516i
$261$		0			0
$262$	1.45027	+	0.425839i	1.45027	+	0.425839i
$263$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$263$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$264$		0			0
$265$		0			0
$266$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$267$		0			0
$268$		0			0
$269$	−0.368991	−	0.425839i	−0.368991	−	0.425839i	0.540641	−	0.841254i	$-0.318182\pi$
$269$	−0.368991	−	0.425839i	−0.368991	−	0.425839i	−0.909632	+	0.415415i	$0.863636\pi$
$270$	−2.38533	−	5.22315i	−2.38533	−	5.22315i
$271$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$271$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$272$		0			0
$273$	0.304632	−	2.11876i	0.304632	−	2.11876i
$274$	1.61435	−	1.03748i	1.61435	−	1.03748i
$275$		0			0
$276$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	1.53046	−	0.983568i	1.53046	−	0.983568i
$279$		0			0
$280$	0.627899	−	1.37491i	0.627899	−	1.37491i
$281$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$281$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$282$		0			0
$283$	−0.708089	−	0.817178i	−0.708089	−	0.817178i	0.281733	−	0.959493i	$-0.409091\pi$
$283$	−0.708089	−	0.817178i	−0.708089	−	0.817178i	−0.989821	+	0.142315i	$0.954545\pi$
$284$	0.239446	+	1.66538i	0.239446	+	1.66538i
$285$	−1.61772	−	0.475006i	−1.61772	−	0.475006i
$286$		0			0
$287$		0			0
$288$	−2.45561	−	1.57812i	−2.45561	−	1.57812i
$289$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.822373	+	1.80075i	0.822373	+	1.80075i	0.540641	+	0.841254i	$0.318182\pi$
$293$	0.822373	+	1.80075i	0.822373	+	1.80075i	0.281733	+	0.959493i	$0.409091\pi$
$294$	1.89945	−	0.557730i	1.89945	−	0.557730i
$295$	−0.353799	+	0.774713i	−0.353799	+	0.774713i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.153882	−	1.07028i	−0.153882	−	1.07028i
$300$	2.54311			2.54311
$301$		0			0
$302$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$303$		0			0
$304$	−0.540641	+	0.158746i	−0.540641	+	0.158746i
$305$		0			0
$306$		0			0
$307$	0.153882	+	1.07028i	0.153882	+	1.07028i	0.909632	+	0.415415i	$0.136364\pi$
$307$	0.153882	+	1.07028i	0.153882	+	1.07028i	−0.755750	+	0.654861i	$0.772727\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$311$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$312$	1.40176	−	1.61772i	1.40176	−	1.61772i
$313$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$313$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$314$	−0.258908	−	1.80075i	−0.258908	−	1.80075i
$315$	2.88927	+	3.33440i	2.88927	+	3.33440i
$316$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$317$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$317$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$318$		0			0
$319$		0			0
$320$	1.27155	−	0.817178i	1.27155	−	0.817178i
$321$		0			0
$322$	0.841254	−	0.540641i	0.841254	−	0.540641i
$323$		0			0
$324$	3.87102	−	2.48775i	3.87102	−	2.48775i
$325$	−0.197682	+	1.37491i	−0.197682	+	1.37491i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$331$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$332$	1.19136	−	1.37491i	1.19136	−	1.37491i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	1.89945	+	0.557730i	1.89945	+	0.557730i
$337$	0.239446	+	1.66538i	0.239446	+	1.66538i	0.654861	+	0.755750i	$0.272727\pi$
$337$	0.239446	+	1.66538i	0.239446	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$338$	0.110783	+	0.127850i	0.110783	+	0.127850i
$339$	−0.683252	−	1.49611i	−0.683252	−	1.49611i
$340$		0			0
$341$		0			0
$342$	0.234072	−	1.62801i	0.234072	−	1.62801i
$343$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$344$		0			0
$345$	2.51722	+	1.61772i	2.51722	+	1.61772i
$346$	1.81926			1.81926
$347$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$347$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$348$		0			0
$349$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$349$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$350$	−1.23259	+	0.361922i	−1.23259	+	0.361922i
$351$	1.70640	+	3.73648i	1.70640	+	3.73648i
$352$		0			0
$353$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$353$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$354$	−1.07028	−	0.314261i	−1.07028	−	0.314261i
$355$	1.66538	−	1.92195i	1.66538	−	1.92195i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$359$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$360$	0.627899	+	4.36714i	0.627899	+	4.36714i
$361$	0.446947	+	0.515804i	0.446947	+	0.515804i
$362$	−0.822373	−	1.80075i	−0.822373	−	1.80075i
$363$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$364$	−0.449181	+	0.983568i	−0.449181	+	0.983568i
$365$		0			0
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	1.00000			1.00000
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$373$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$374$		0			0
$375$	−0.557730	−	0.643655i	−0.557730	−	0.643655i
$376$		0			0
$377$		0			0
$378$	−2.48775	+	2.87102i	−2.48775	+	2.87102i
$379$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$379$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$380$	0.716476	+	0.460451i	0.716476	+	0.460451i
$381$	1.69791	−	1.95949i	1.69791	−	1.95949i
$382$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$383$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$383$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$384$	1.29639	+	1.49611i	1.29639	+	1.49611i
$385$		0			0
$386$	1.25667	−	0.368991i	1.25667	−	0.368991i
$387$		0			0
$388$		0			0
$389$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$389$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$390$	−3.23544			−3.23544
$391$		0			0
$392$	−1.00000			−1.00000
$393$	2.51722	−	1.61772i	2.51722	−	1.61772i
$394$		0			0
$395$	−0.521678	+	1.14231i	−0.521678	+	1.14231i
$396$		0			0
$397$	−0.449181	−	0.983568i	−0.449181	−	0.983568i	−0.989821	−	0.142315i	$-0.954545\pi$
$397$	−0.449181	−	0.983568i	−0.449181	−	0.983568i	0.540641	−	0.841254i	$-0.318182\pi$
$398$		0			0
$399$	0.158746	+	1.10411i	0.158746	+	1.10411i
$400$	−1.23259	−	0.361922i	−1.23259	−	0.361922i
$401$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$401$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−6.67342	−	1.95949i	−6.67342	−	1.95949i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$409$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$410$		0			0
$411$	0.540641	−	3.76024i	0.540641	−	3.76024i
$412$		0			0
$413$	0.563465			0.563465
$414$	−1.21259	+	2.65520i	−1.21259	+	2.65520i
$415$	−2.74982			−2.74982
$416$	−0.909632	+	0.584585i	−0.909632	+	0.584585i
$417$	0.512546	−	3.56484i	0.512546	−	3.56484i
$418$		0			0
$419$	−1.03748	+	0.304632i	−1.03748	+	0.304632i	−0.755750	−	0.654861i	$-0.772727\pi$
$419$	−1.03748	+	0.304632i	−1.03748	+	0.304632i	−0.281733	+	0.959493i	$0.590909\pi$
$420$	−1.24302	−	2.72183i	−1.24302	−	2.72183i
$421$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$421$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	2.80202	+	1.80075i	2.80202	+	1.80075i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$431$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$432$	−3.64502	+	1.07028i	−3.64502	+	1.07028i
$433$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$433$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.234072	+	0.512546i	0.234072	+	0.512546i
$438$		0			0
$439$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$439$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$440$		0			0
$441$	1.21259	−	2.65520i	1.21259	−	2.65520i
$442$		0			0
$443$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$443$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$449$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$449$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$450$	2.45561	−	2.83392i	2.45561	−	2.83392i
$451$		0			0
$452$	0.118239	+	0.822373i	0.118239	+	0.822373i
$453$	0.368991	+	0.425839i	0.368991	+	0.425839i
$454$	−0.755750	−	1.65486i	−0.755750	−	1.65486i
$455$	1.56815	−	0.460451i	1.56815	−	0.460451i
$456$	−0.463379	+	1.01466i	−0.463379	+	1.01466i
$457$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$457$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$458$	0.474017	−	0.304632i	0.474017	−	0.304632i
$459$		0			0
$460$	−0.989821	−	1.14231i	−0.989821	−	1.14231i
$461$	1.81926			1.81926			0.909632	−	0.415415i	$-0.136364\pi$
$461$	1.81926			1.81926			0.909632	+	0.415415i	$0.136364\pi$
$462$		0			0
$463$	0.239446	−	1.66538i	0.239446	−	1.66538i	−0.415415	−	0.909632i	$-0.636364\pi$
$463$	0.239446	−	1.66538i	0.239446	−	1.66538i	0.654861	−	0.755750i	$-0.272727\pi$
$464$		0			0
$465$		0			0
$466$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$467$	1.29639	+	1.49611i	1.29639	+	1.49611i	0.755750	+	0.654861i	$0.227273\pi$
$467$	1.29639	+	1.49611i	1.29639	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$468$	−0.449181	−	3.12412i	−0.449181	−	3.12412i
$469$		0			0
$470$		0			0
$471$	−3.02977	−	1.94711i	−3.02977	−	1.94711i
$472$	0.474017	+	0.304632i	0.474017	+	0.304632i
$473$		0			0
$474$	−1.57812	−	0.463379i	−1.57812	−	0.463379i
$475$	−0.103014	−	0.716476i	−0.103014	−	0.716476i
$476$		0			0
$477$		0			0
$478$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$479$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$479$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$480$	0.425839	−	2.96177i	0.425839	−	2.96177i
$481$		0			0
$482$		0			0
$483$	0.281733	−	1.95949i	0.281733	−	1.95949i
$484$	1.00000			1.00000
$485$		0			0
$486$	0.755750	−	5.25635i	0.755750	−	5.25635i
$487$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$487$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$488$		0			0
$489$		0			0
$490$	0.989821	+	1.14231i	0.989821	+	1.14231i
$491$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$491$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$492$		0			0
$493$		0			0
$494$	−0.512546	−	0.329393i	−0.512546	−	0.329393i
$495$		0			0
$496$		0			0
$497$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$498$	−0.512546	−	3.56484i	−0.512546	−	3.56484i
$499$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$499$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$500$	0.178719	+	0.391340i	0.178719	+	0.391340i
$501$		0			0
$502$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$503$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$503$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$504$	2.45561	−	1.57812i	2.45561	−	1.57812i
$505$		0			0
$506$		0			0
$507$	0.334896			0.334896
$508$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$509$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$509$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$510$		0			0
$511$		0			0
$512$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$513$	−1.40176	−	1.61772i	−1.40176	−	1.61772i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	2.35848	−	2.72183i	2.35848	−	2.72183i
$520$	1.56815	+	0.460451i	1.56815	+	0.460451i
$521$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$521$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$522$		0			0
$523$	0.755750	+	1.65486i	0.755750	+	1.65486i	0.755750	+	0.654861i	$0.227273\pi$
$523$	0.755750	+	1.65486i	0.755750	+	1.65486i			1.00000i	$0.5\pi$
$524$	−1.45027	+	0.425839i	−1.45027	+	0.425839i
$525$	−1.05645	+	2.31329i	−1.05645	+	2.31329i
$526$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$527$		0			0
$528$		0			0
$529$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$530$		0			0
$531$	−1.38365	+	0.889217i	−1.38365	+	0.889217i
$532$	0.0801894	−	0.557730i	0.0801894	−	0.557730i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.540641	+	0.158746i	0.540641	+	0.158746i
$539$		0			0
$540$	4.83052	+	3.10438i	4.83052	+	3.10438i
$541$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$541$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$542$		0			0
$543$	−3.76024	−	1.10411i	−3.76024	−	1.10411i
$544$		0			0
$545$		0			0
$546$	0.889217	+	1.94711i	0.889217	+	1.94711i
$547$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$547$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$548$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	1.29639	−	1.49611i	1.29639	−	1.49611i
$553$	0.830830			0.830830
$554$		0			0
$555$		0			0
$556$	−0.755750	+	1.65486i	−0.755750	+	1.65486i
$557$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$557$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$558$		0			0
$559$		0			0
$560$	0.215109	+	1.49611i	0.215109	+	1.49611i
$561$		0			0
$562$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$563$	−0.909632	−	0.584585i	−0.909632	−	0.584585i		−	1.00000i	$-0.5\pi$
$563$	−0.909632	−	0.584585i	−0.909632	−	0.584585i	−0.909632	+	0.415415i	$0.863636\pi$
$564$		0			0
$565$	0.822373	−	0.949069i	0.822373	−	0.949069i
$566$	1.03748	+	0.304632i	1.03748	+	0.304632i
$567$	0.654861	+	4.55466i	0.654861	+	4.55466i
$568$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$569$	0.118239	+	0.258908i	0.118239	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$569$	0.118239	+	0.258908i	0.118239	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$570$	1.61772	−	0.475006i	1.61772	−	0.475006i
$571$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$571$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$572$		0			0
$573$	0.474017	−	0.304632i	0.474017	−	0.304632i
$574$		0			0
$575$	−0.182822	+	1.27155i	−0.182822	+	1.27155i
$576$	2.91899			2.91899
$577$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$577$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$578$	0.142315	−	0.989821i	0.142315	−	0.989821i
$579$	1.07708	−	2.35848i	1.07708	−	2.35848i
$580$		0			0
$581$	0.755750	+	1.65486i	0.755750	+	1.65486i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−3.12412	+	3.60543i	−3.12412	+	3.60543i
$586$	−1.66538	−	1.07028i	−1.66538	−	1.07028i
$587$	0.909632	+	0.584585i	0.909632	+	0.584585i	0.909632	−	0.415415i	$-0.136364\pi$
$587$	0.909632	+	0.584585i	0.909632	+	0.584585i			1.00000i	$0.5\pi$
$588$	−1.29639	+	1.49611i	−1.29639	+	1.49611i
$589$		0			0
$590$	−0.121206	−	0.843008i	−0.121206	−	0.843008i
$591$		0			0
$592$		0			0
$593$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$593$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.708089	+	0.817178i	0.708089	+	0.817178i
$599$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$599$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$600$	−2.13940	+	1.37491i	−2.13940	+	1.37491i
$601$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$601$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$602$		0			0
$603$		0			0
$604$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$605$	−0.989821	−	1.14231i	−0.989821	−	1.14231i
$606$		0			0
$607$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$607$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$608$	0.368991	−	0.425839i	0.368991	−	0.425839i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$613$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$614$	−0.708089	−	0.817178i	−0.708089	−	0.817178i
$615$		0			0
$616$		0			0
$617$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$617$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$618$		0			0
$619$	1.53046	−	0.983568i	1.53046	−	0.983568i	0.540641	−	0.841254i	$-0.318182\pi$
$619$	1.53046	−	0.983568i	1.53046	−	0.983568i	0.989821	−	0.142315i	$-0.0454545\pi$
$620$		0			0
$621$	1.57812	+	3.45561i	1.57812	+	3.45561i
$622$		0			0
$623$		0			0
$624$	−0.304632	+	2.11876i	−0.304632	+	2.11876i
$625$	−0.263521	+	0.577031i	−0.263521	+	0.577031i
$626$		0			0
$627$		0			0
$628$	1.19136	+	1.37491i	1.19136	+	1.37491i
$629$		0			0
$630$	−4.23333	−	1.24302i	−4.23333	−	1.24302i
$631$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$631$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$632$	0.698939	+	0.449181i	0.698939	+	0.449181i
$633$		0			0
$634$		0			0
$635$	1.89945	+	0.557730i	1.89945	+	0.557730i
$636$		0			0
$637$	−0.708089	−	0.817178i	−0.708089	−	0.817178i
$638$		0			0
$639$	4.71228	−	1.38365i	4.71228	−	1.38365i
$640$	−0.627899	+	1.37491i	−0.627899	+	1.37491i
$641$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$641$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$642$		0			0
$643$	1.97964			1.97964			0.989821	−	0.142315i	$-0.0454545\pi$
$643$	1.97964			1.97964			0.989821	+	0.142315i	$0.0454545\pi$
$644$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$645$		0			0
$646$		0			0
$647$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$647$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$648$	−1.91153	+	4.18567i	−1.91153	+	4.18567i
$649$		0			0
$650$	−0.577031	−	1.26352i	−0.577031	−	1.26352i
$651$		0			0
$652$		0			0
$653$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$653$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$654$		0			0
$655$	1.92195	+	1.23516i	1.92195	+	1.23516i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$659$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$660$		0			0
$661$	0.449181	+	0.983568i	0.449181	+	0.983568i	0.989821	+	0.142315i	$0.0454545\pi$
$661$	0.449181	+	0.983568i	0.449181	+	0.983568i	−0.540641	+	0.841254i	$0.681818\pi$
$662$		0			0
$663$		0			0
$664$	−0.258908	+	1.80075i	−0.258908	+	1.80075i
$665$	−0.716476	+	0.460451i	−0.716476	+	0.460451i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$673$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$673$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$674$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$675$	−0.694523	−	4.83052i	−0.694523	−	4.83052i
$676$	−0.162317	−	0.0476607i	−0.162317	−	0.0476607i
$677$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$677$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.909632	+	0.415415i	$0.863636\pi$
$678$	1.38365	+	0.889217i	1.38365	+	0.889217i
$679$		0			0
$680$		0			0
$681$	−3.45561	−	1.01466i	−3.45561	−	1.01466i
$682$		0			0
$683$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$683$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$684$	0.683252	+	1.49611i	0.683252	+	1.49611i
$685$	2.78305	−	0.817178i	2.78305	−	0.817178i
$686$	0.415415	−	0.909632i	0.415415	−	0.909632i
$687$	0.158746	−	1.10411i	0.158746	−	1.10411i
$688$		0			0
$689$		0			0
$690$	−2.99223			−2.99223
$691$	0.563465			0.563465			0.281733	−	0.959493i	$-0.409091\pi$
$691$	0.563465			0.563465			0.281733	+	0.959493i	$0.409091\pi$
$692$	−1.53046	+	0.983568i	−1.53046	+	0.983568i
$693$		0			0
$694$		0			0
$695$	2.63843	−	0.774713i	2.63843	−	0.774713i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−1.57812	−	0.463379i	−1.57812	−	0.463379i
$700$	0.841254	−	0.970858i	0.841254	−	0.970858i
$701$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$701$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$702$	−3.45561	−	2.22078i	−3.45561	−	2.22078i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$	1.07028	−	0.314261i	1.07028	−	0.314261i
$709$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$709$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$710$	−0.361922	+	2.51722i	−0.361922	+	2.51722i
$711$	−2.04019	+	1.31115i	−2.04019	+	1.31115i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.07708	+	2.35848i	−1.07708	+	2.35848i
$718$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$719$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$719$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$720$	−2.88927	−	3.33440i	−2.88927	−	3.33440i
$721$		0			0
$722$	−0.654861	−	0.192284i	−0.654861	−	0.192284i
$723$		0			0
$724$	1.66538	+	1.07028i	1.66538	+	1.07028i
$725$		0			0
$726$	1.29639	−	1.49611i	1.29639	−	1.49611i
$727$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$727$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$728$	−0.153882	−	1.07028i	−0.153882	−	1.07028i
$729$	−3.87102	−	4.46740i	−3.87102	−	4.46740i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.153882	−	1.07028i	0.153882	−	1.07028i	−0.755750	−	0.654861i	$-0.772727\pi$
$733$	0.153882	−	1.07028i	0.153882	−	1.07028i	0.909632	−	0.415415i	$-0.136364\pi$
$734$		0			0
$735$	2.99223			2.99223
$736$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$737$		0			0
$738$		0			0
$739$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$739$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$740$		0			0
$741$	−1.15727	+	0.339805i	−1.15727	+	0.339805i
$742$		0			0
$743$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$743$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.46740	−	2.87102i	−4.46740	−	2.87102i
$748$		0			0
$749$		0			0
$750$	0.817178	+	0.239945i	0.817178	+	0.239945i
$751$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$751$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$752$		0			0
$753$	1.62801	+	3.56484i	1.62801	+	3.56484i
$754$		0			0
$755$	−0.178719	+	0.391340i	−0.178719	+	0.391340i
$756$	0.540641	−	3.76024i	0.540641	−	3.76024i
$757$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$757$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$758$		0			0
$759$		0			0
$760$	−0.851677			−0.851677
$761$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$761$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$762$	−0.368991	+	2.56639i	−0.368991	+	2.56639i
$763$		0			0
$764$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$765$		0			0
$766$		0			0
$767$	0.0867074	+	0.603063i	0.0867074	+	0.603063i
$768$	−1.89945	−	0.557730i	−1.89945	−	0.557730i
$769$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$769$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$770$		0			0
$771$		0			0
$772$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$773$	1.45027	+	0.425839i	1.45027	+	0.425839i	0.909632	−	0.415415i	$-0.136364\pi$
$773$	1.45027	+	0.425839i	1.45027	+	0.425839i	0.540641	+	0.841254i	$0.318182\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	2.72183	−	1.74921i	2.72183	−	1.74921i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.841254	−	0.540641i	0.841254	−	0.540641i
$785$	0.391340	−	2.72183i	0.391340	−	2.72183i
$786$	−1.24302	+	2.72183i	−1.24302	+	2.72183i
$787$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$787$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$788$		0			0
$789$	2.18119	+	2.51722i	2.18119	+	2.51722i
$790$	−0.178719	−	1.24302i	−0.178719	−	1.24302i
$791$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$792$		0			0
$793$		0			0
$794$	0.909632	+	0.584585i	0.909632	+	0.584585i
$795$		0			0
$796$		0			0
$797$	−0.153882	−	1.07028i	−0.153882	−	1.07028i	−0.909632	−	0.415415i	$-0.863636\pi$
$797$	−0.153882	−	1.07028i	−0.153882	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$798$	−0.730471	−	0.843008i	−0.730471	−	0.843008i
$799$		0			0
$800$	1.23259	−	0.361922i	1.23259	−	0.361922i
$801$		0			0
$802$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$803$		0			0
$804$		0			0
$805$	1.45027	−	0.425839i	1.45027	−	0.425839i
$806$		0			0
$807$	0.938384	−	0.603063i	0.938384	−	0.603063i
$808$		0			0
$809$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	0.654861	+	0.755750i	$0.272727\pi$
$809$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	−1.00000			$\pi$
$810$	6.67342	−	1.95949i	6.67342	−	1.95949i
$811$	−0.234072	−	0.512546i	−0.234072	−	0.512546i	0.755750	−	0.654861i	$-0.227273\pi$
$811$	−0.234072	−	0.512546i	−0.234072	−	0.512546i	−0.989821	+	0.142315i	$0.954545\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	3.02840	+	0.889217i	3.02840	+	0.889217i
$820$		0			0
$821$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$821$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$822$	1.57812	+	3.45561i	1.57812	+	3.45561i
$823$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−0.841254	+	0.540641i	$0.818182\pi$
$823$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−1.00000			$1.00000\pi$
$824$		0			0
$825$		0			0
$826$	−0.474017	+	0.304632i	−0.474017	+	0.304632i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−0.415415	−	2.88927i	−0.415415	−	2.88927i
$829$	−1.51150			−1.51150			−0.755750	−	0.654861i	$-0.772727\pi$
$829$	−1.51150			−1.51150			−0.755750	+	0.654861i	$0.772727\pi$
$830$	2.31329	−	1.48666i	2.31329	−	1.48666i
$831$		0			0
$832$	0.449181	−	0.983568i	0.449181	−	0.983568i
$833$		0			0
$834$	1.49611	+	3.27603i	1.49611	+	3.27603i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.708089	−	0.817178i	0.708089	−	0.817178i
$839$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$839$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$840$	2.51722	+	1.61772i	2.51722	+	1.61772i
$841$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$842$		0			0
$843$	0.368991	+	2.56639i	0.368991	+	2.56639i
$844$		0			0
$845$	0.106222	+	0.232593i	0.106222	+	0.232593i
$846$		0			0
$847$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$848$		0			0
$849$	1.80075	−	1.15727i	1.80075	−	1.15727i
$850$		0			0
$851$		0			0
$852$	−3.33076			−3.33076
$853$	1.53046	−	0.983568i	1.53046	−	0.983568i	0.540641	−	0.841254i	$-0.318182\pi$
$853$	1.53046	−	0.983568i	1.53046	−	0.983568i	0.989821	−	0.142315i	$-0.0454545\pi$
$854$		0			0
$855$	1.03274	−	2.26138i	1.03274	−	2.26138i
$856$		0			0
$857$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$857$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$858$		0			0
$859$	0.215109	+	1.49611i	0.215109	+	1.49611i	0.755750	+	0.654861i	$0.227273\pi$
$859$	0.215109	+	1.49611i	0.215109	+	1.49611i	−0.540641	+	0.841254i	$0.681818\pi$
$860$		0			0
$861$		0			0
$862$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$863$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.959493	+	0.281733i	$0.0909091\pi$
$863$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.654861	+	0.755750i	$0.272727\pi$
$864$	2.48775	−	2.87102i	2.48775	−	2.87102i
$865$	2.63843	+	0.774713i	2.63843	+	0.774713i
$866$		0			0
$867$	−1.29639	−	1.49611i	−1.29639	−	1.49611i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−0.474017	−	0.304632i	−0.474017	−	0.304632i
$875$	−0.430218			−0.430218
$876$		0			0
$877$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$877$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$878$		0			0
$879$	−3.76024	+	1.10411i	−3.76024	+	1.10411i
$880$		0			0
$881$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$881$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$882$	0.415415	+	2.88927i	0.415415	+	2.88927i
$883$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$883$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$884$		0			0
$885$	−1.41837	−	0.911529i	−1.41837	−	0.911529i
$886$		0			0
$887$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$887$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$888$		0			0
$889$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.00000			1.00000
$897$	2.14055			2.14055
$898$	1.91899			1.91899
$899$		0			0
$900$	−0.533654	+	3.71165i	−0.533654	+	3.71165i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$905$	−0.425839	−	2.96177i	−0.425839	−	2.96177i
$906$	−0.540641	−	0.158746i	−0.540641	−	0.158746i
$907$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$907$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$908$	1.53046	+	0.983568i	1.53046	+	0.983568i
$909$		0			0
$910$	−1.07028	+	1.23516i	−1.07028	+	1.23516i
$911$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$911$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$912$	−0.158746	−	1.10411i	−0.158746	−	1.10411i
$913$		0			0
$914$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$915$		0			0
$916$	−0.234072	+	0.512546i	−0.234072	+	0.512546i
$917$	0.215109	−	1.49611i	0.215109	−	1.49611i
$918$		0			0
$919$	−1.68251			−1.68251			−0.841254	−	0.540641i	$-0.818182\pi$
$919$	−1.68251			−1.68251			−0.841254	+	0.540641i	$0.818182\pi$
$920$	1.45027	+	0.425839i	1.45027	+	0.425839i
$921$	−2.14055			−2.14055
$922$	−1.53046	+	0.983568i	−1.53046	+	0.983568i
$923$	0.258908	−	1.80075i	0.258908	−	1.80075i
$924$		0			0
$925$		0			0
$926$	0.698939	+	1.53046i	0.698939	+	1.53046i
$927$		0			0
$928$		0			0
$929$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$929$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$930$		0			0
$931$	0.474017	+	0.304632i	0.474017	+	0.304632i
$932$	0.698939	+	0.449181i	0.698939	+	0.449181i
$933$		0			0
$934$	−1.89945	−	0.557730i	−1.89945	−	0.557730i
$935$		0			0
$936$	2.06690	+	2.38533i	2.06690	+	2.38533i
$937$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$937$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.53046	+	0.983568i	−1.53046	+	0.983568i	−0.540641	+	0.841254i	$0.681818\pi$
$941$	−1.53046	+	0.983568i	−1.53046	+	0.983568i	−0.989821	+	0.142315i	$0.954545\pi$
$942$	3.60149			3.60149
$943$		0			0
$944$	−0.563465			−0.563465
$945$	−4.83052	+	3.10438i	−4.83052	+	3.10438i
$946$		0			0
$947$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$947$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$948$	1.57812	−	0.463379i	1.57812	−	0.463379i
$949$		0			0
$950$	0.474017	+	0.547045i	0.474017	+	0.547045i
$951$		0			0
$952$		0			0
$953$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$953$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$954$		0			0
$955$	0.361922	+	0.232593i	0.361922	+	0.232593i
$956$	0.857685	−	0.989821i	0.857685	−	0.989821i
$957$		0			0
$958$		0			0
$959$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$960$	1.24302	+	2.72183i	1.24302	+	2.72183i
$961$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.97964			1.97964
$966$	0.822373	+	1.80075i	0.822373	+	1.80075i
$967$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$967$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$968$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$969$		0			0
$970$		0			0
$971$	1.45027	−	0.425839i	1.45027	−	0.425839i	0.540641	−	0.841254i	$-0.318182\pi$
$971$	1.45027	−	0.425839i	1.45027	−	0.425839i	0.909632	+	0.415415i	$0.136364\pi$
$972$	2.20602	+	4.83052i	2.20602	+	4.83052i
$973$	−1.19136	−	1.37491i	−1.19136	−	1.37491i
$974$	0.239446	+	1.66538i	0.239446	+	1.66538i
$975$	−2.63843	−	0.774713i	−2.63843	−	0.774713i
$976$		0			0
$977$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$977$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$978$		0			0
$979$		0			0
$980$	−1.45027	−	0.425839i	−1.45027	−	0.425839i
$981$		0			0
$982$		0			0
$983$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$983$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.609264			0.609264
$989$		0			0
$990$		0			0
$991$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.142315	−	0.989821i	$-0.454545\pi$
$991$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.959493	+	0.281733i	$0.0909091\pi$
$992$		0			0
$993$		0			0
$994$	1.61435	−	0.474017i	1.61435	−	0.474017i
$995$		0			0
$996$	2.35848	+	2.72183i	2.35848	+	2.72183i
$997$	−0.215109	−	1.49611i	−0.215109	−	1.49611i	−0.755750	−	0.654861i	$-0.772727\pi$
$997$	−0.215109	−	1.49611i	−0.215109	−	1.49611i	0.540641	−	0.841254i	$-0.318182\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1288.1.bi.e.909.1	yes	20
7.6	odd	2	inner	1288.1.bi.e.909.2	yes	20
8.5	even	2	inner	1288.1.bi.e.909.2	yes	20
23.2	even	11	inner	1288.1.bi.e.853.1	✓	20
56.13	odd	2	CM	1288.1.bi.e.909.1	yes	20
161.48	odd	22	inner	1288.1.bi.e.853.2	yes	20
184.117	even	22	inner	1288.1.bi.e.853.2	yes	20
1288.853	odd	22	inner	1288.1.bi.e.853.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.1.bi.e.853.1	✓	20	23.2	even	11	inner
1288.1.bi.e.853.1	✓	20	1288.853	odd	22	inner
1288.1.bi.e.853.2	yes	20	161.48	odd	22	inner
1288.1.bi.e.853.2	yes	20	184.117	even	22	inner
1288.1.bi.e.909.1	yes	20	1.1	even	1	trivial
1288.1.bi.e.909.1	yes	20	56.13	odd	2	CM
1288.1.bi.e.909.2	yes	20	7.6	odd	2	inner
1288.1.bi.e.909.2	yes	20	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1288.bi (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.281733 + 1.95949i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-1.45027 + 0.425839i) q^{5} +(-0.822373 - 1.80075i) q^{6} +(0.654861 + 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-2.80075 - 0.822373i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.281733 + 1.95949i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-1.45027 + 0.425839i) q^{5} +(-0.822373 - 1.80075i) q^{6} +(0.654861 + 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-2.80075 - 0.822373i) q^{9} +(0.989821 - 1.14231i) q^{10} +(1.66538 + 1.07028i) q^{12} +(-0.708089 + 0.817178i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-0.425839 - 2.96177i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.80075 - 0.822373i) q^{18} +(0.234072 - 0.512546i) q^{19} +(-0.215109 + 1.49611i) q^{20} +(-1.66538 + 1.07028i) q^{21} +(-0.654861 + 0.755750i) q^{23} -1.97964 q^{24} +(1.08070 - 0.694523i) q^{25} +(0.153882 - 1.07028i) q^{26} +(1.57812 - 3.45561i) q^{27} +(0.959493 - 0.281733i) q^{28} +(1.95949 + 2.26138i) q^{30} +(0.959493 + 0.281733i) q^{32} +(-1.27155 - 0.817178i) q^{35} +(-1.91153 + 2.20602i) q^{36} +(0.0801894 + 0.557730i) q^{38} +(-1.40176 - 1.61772i) q^{39} +(-0.627899 - 1.37491i) q^{40} +(0.822373 - 1.80075i) q^{42} +4.41204 q^{45} +(0.142315 - 0.989821i) q^{46} +(1.66538 - 1.07028i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-0.533654 + 1.16854i) q^{50} +(0.449181 + 0.983568i) q^{52} +(0.540641 + 3.76024i) q^{54} +(-0.654861 + 0.755750i) q^{56} +(0.938384 + 0.603063i) q^{57} +(0.368991 - 0.425839i) q^{59} +(-2.87102 - 0.843008i) q^{60} +(-1.21259 - 2.65520i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(0.678936 - 1.48666i) q^{65} +(-1.29639 - 1.49611i) q^{69} +1.51150 q^{70} +(-1.41542 + 0.909632i) q^{71} +(0.415415 - 2.88927i) q^{72} +(1.05645 + 2.31329i) q^{75} +(-0.368991 - 0.425839i) q^{76} +(2.05384 + 0.603063i) q^{78} +(0.544078 - 0.627899i) q^{79} +(1.27155 + 0.817178i) q^{80} +(3.87102 + 2.48775i) q^{81} +(1.74557 + 0.512546i) q^{83} +(0.281733 + 1.95949i) q^{84} +(-3.71165 + 2.38533i) q^{90} -1.08128 q^{91} +(0.415415 + 0.909632i) q^{92} +(-0.121206 + 0.843008i) q^{95} +(-0.822373 + 1.80075i) q^{96} +(-0.415415 - 0.909632i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 2 * q^8 - 20 * q^9	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9} - 2 q^{14} - 2 q^{16} + 20 q^{18} - 2 q^{23} + 2 q^{25} + 2 q^{28} + 22 q^{30} + 2 q^{32} + 2 q^{36} - 22 q^{39} + 2 q^{46} - 2 q^{49} - 2 q^{50} - 2 q^{56} - 2 q^{63} - 2 q^{64} - 18 q^{71} - 2 q^{72} + 4 q^{79} + 20 q^{81} - 2 q^{92} + 2 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 2 * q^8 - 20 * q^9 - 2 * q^14 - 2 * q^16 + 20 * q^18 - 2 * q^23 + 2 * q^25 + 2 * q^28 + 22 * q^30 + 2 * q^32 + 2 * q^36 - 22 * q^39 + 2 * q^46 - 2 * q^49 - 2 * q^50 - 2 * q^56 - 2 * q^63 - 2 * q^64 - 18 * q^71 - 2 * q^72 + 4 * q^79 + 20 * q^81 - 2 * q^92 + 2 * q^98

Introduction

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