LMFDB - Embedded newform 2888.1.bb.a.2699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(115,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(38))

chi = DirichletCharacter(H, H._module([19, 19, 4]))

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

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

chi := DirichletCharacter("2888.115");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2888 = 2^{3} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2888.bb (of order $38$, degree $18$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.44129975648$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\Q(\zeta_{38})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} + \cdots + 1 $ x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{19}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{19} - \cdots)$

Embedding invariants

Embedding label			2699.1
Root			$0.986361 + 0.164595i$ of defining polynomial
Character	$\chi$	$=$	2888.2699
Dual form			2888.1.bb.a.1635.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.879474 - 0.475947i) q^{2} +(1.94582 - 0.324699i) q^{3} +(0.546948 + 0.837166i) q^{4} +(-1.86584 - 0.640542i) q^{6} +(-0.0825793 - 0.996584i) q^{8} +(2.73496 - 0.938912i) q^{9} +O(q^{10})$	\(q+(-0.879474 - 0.475947i) q^{2} +(1.94582 - 0.324699i) q^{3} +(0.546948 + 0.837166i) q^{4} +(-1.86584 - 0.640542i) q^{6} +(-0.0825793 - 0.996584i) q^{8} +(2.73496 - 0.938912i) q^{9} +(1.03463 + 0.355188i) q^{11} +(1.33609 + 1.45138i) q^{12} +(-0.401695 + 0.915773i) q^{16} +(-0.439413 + 0.672572i) q^{17} +(-2.85220 - 0.475947i) q^{18} +(-0.879474 + 0.475947i) q^{19} +(-0.740876 - 0.804806i) q^{22} +(-0.484275 - 1.91236i) q^{24} +(-0.677282 - 0.735724i) q^{25} +(3.28191 - 1.77608i) q^{27} +(0.789141 - 0.614213i) q^{32} +(2.12852 + 0.355188i) q^{33} +(0.706561 - 0.382372i) q^{34} +(2.28191 + 1.77608i) q^{36} +1.00000 q^{38} +(-0.484275 + 1.91236i) q^{41} +(-1.38806 - 1.08037i) q^{43} +(0.268536 + 1.06042i) q^{44} +(-0.484275 + 1.91236i) q^{48} +(-0.401695 - 0.915773i) q^{49} +(0.245485 + 0.969400i) q^{50} +(-0.636634 + 1.45138i) q^{51} -3.73167 q^{54} +(-1.55676 + 1.21167i) q^{57} +(-0.431796 + 1.70512i) q^{59} +(-0.986361 + 0.164595i) q^{64} +(-1.70293 - 1.32544i) q^{66} +(-0.156210 - 1.88517i) q^{67} -0.803391 q^{68} +(-1.16156 - 2.64808i) q^{72} +(0.268536 - 0.411024i) q^{73} +(-1.55676 - 1.21167i) q^{75} +(-0.879474 - 0.475947i) q^{76} +(3.52739 - 2.74548i) q^{81} +(1.33609 - 1.45138i) q^{82} +(0.322718 + 0.735724i) q^{83} +(0.706561 + 1.61080i) q^{86} +(0.268536 - 1.06042i) q^{88} +(-0.439413 - 0.672572i) q^{89} +(1.33609 - 1.45138i) q^{96} +(-0.165159 + 1.99317i) q^{97} +(-0.0825793 + 0.996584i) q^{98} +3.16315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9}+O(q^{10}) $ 18 * q - q^2 + 17 * q^3 - q^4 - 2 * q^6 - q^8 + 16 * q^9	$ 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - q^{19} - 2 q^{22} - 2 q^{24} - q^{25} + 15 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} + 18 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} - 4 q^{54} - 2 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - q^{76} + 14 q^{81} - 2 q^{82} + 17 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) $ 18 * q - q^2 + 17 * q^3 - q^4 - 2 * q^6 - q^8 + 16 * q^9 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - 3 * q^18 - q^19 - 2 * q^22 - 2 * q^24 - q^25 + 15 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 + 18 * q^38 - 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 - 4 * q^54 - 2 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 - 2 * q^75 - q^76 + 14 * q^81 - 2 * q^82 + 17 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{19}\right)$

Coefficient data

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

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

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

$2$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$2$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$3$	1.94582	−	0.324699i	1.94582	−	0.324699i	0.945817	−	0.324699i	$-0.105263\pi$
$3$	1.94582	−	0.324699i	1.94582	−	0.324699i	1.00000			$0$
$4$	0.546948	+	0.837166i	0.546948	+	0.837166i
$5$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$5$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$6$	−1.86584	−	0.640542i	−1.86584	−	0.640542i
$7$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$7$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$8$	−0.0825793	−	0.996584i	−0.0825793	−	0.996584i
$9$	2.73496	−	0.938912i	2.73496	−	0.938912i
$10$		0			0
$11$	1.03463	+	0.355188i	1.03463	+	0.355188i	0.789141	−	0.614213i	$-0.210526\pi$
$11$	1.03463	+	0.355188i	1.03463	+	0.355188i	0.245485	+	0.969400i	$0.421053\pi$
$12$	1.33609	+	1.45138i	1.33609	+	1.45138i
$13$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$13$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$14$		0			0
$15$		0			0
$16$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$17$	−0.439413	+	0.672572i	−0.439413	+	0.672572i	−0.986361	−	0.164595i	$-0.947368\pi$
$17$	−0.439413	+	0.672572i	−0.439413	+	0.672572i	0.546948	+	0.837166i	$0.315789\pi$
$18$	−2.85220	−	0.475947i	−2.85220	−	0.475947i
$19$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$19$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$20$		0			0
$21$		0			0
$22$	−0.740876	−	0.804806i	−0.740876	−	0.804806i
$23$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$23$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$24$	−0.484275	−	1.91236i	−0.484275	−	1.91236i
$25$	−0.677282	−	0.735724i	−0.677282	−	0.735724i
$26$		0			0
$27$	3.28191	−	1.77608i	3.28191	−	1.77608i
$28$		0			0
$29$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$29$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$30$		0			0
$31$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$31$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$32$	0.789141	−	0.614213i	0.789141	−	0.614213i
$33$	2.12852	+	0.355188i	2.12852	+	0.355188i
$34$	0.706561	−	0.382372i	0.706561	−	0.382372i
$35$		0			0
$36$	2.28191	+	1.77608i	2.28191	+	1.77608i
$37$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$37$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$38$	1.00000			1.00000
$39$		0			0
$40$		0			0
$41$	−0.484275	+	1.91236i	−0.484275	+	1.91236i	−0.0825793	+	0.996584i	$0.526316\pi$
$41$	−0.484275	+	1.91236i	−0.484275	+	1.91236i	−0.401695	+	0.915773i	$0.631579\pi$
$42$		0			0
$43$	−1.38806	−	1.08037i	−1.38806	−	1.08037i	−0.986361	−	0.164595i	$-0.947368\pi$
$43$	−1.38806	−	1.08037i	−1.38806	−	1.08037i	−0.401695	−	0.915773i	$-0.631579\pi$
$44$	0.268536	+	1.06042i	0.268536	+	1.06042i
$45$		0			0
$46$		0			0
$47$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$47$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$48$	−0.484275	+	1.91236i	−0.484275	+	1.91236i
$49$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$50$	0.245485	+	0.969400i	0.245485	+	0.969400i
$51$	−0.636634	+	1.45138i	−0.636634	+	1.45138i
$52$		0			0
$53$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$53$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$54$	−3.73167			−3.73167
$55$		0			0
$56$		0			0
$57$	−1.55676	+	1.21167i	−1.55676	+	1.21167i
$58$		0			0
$59$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	0.245485	+	0.969400i	$0.421053\pi$
$59$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	−0.677282	+	0.735724i	$0.736842\pi$
$60$		0			0
$61$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$61$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$62$		0			0
$63$		0			0
$64$	−0.986361	+	0.164595i	−0.986361	+	0.164595i
$65$		0			0
$66$	−1.70293	−	1.32544i	−1.70293	−	1.32544i
$67$	−0.156210	−	1.88517i	−0.156210	−	1.88517i	−0.401695	−	0.915773i	$-0.631579\pi$
$67$	−0.156210	−	1.88517i	−0.156210	−	1.88517i	0.245485	−	0.969400i	$-0.421053\pi$
$68$	−0.803391			−0.803391
$69$		0			0
$70$		0			0
$71$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$71$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$72$	−1.16156	−	2.64808i	−1.16156	−	2.64808i
$73$	0.268536	−	0.411024i	0.268536	−	0.411024i	−0.677282	−	0.735724i	$-0.736842\pi$
$73$	0.268536	−	0.411024i	0.268536	−	0.411024i	0.945817	+	0.324699i	$0.105263\pi$
$74$		0			0
$75$	−1.55676	−	1.21167i	−1.55676	−	1.21167i
$76$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$77$		0			0
$78$		0			0
$79$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$79$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$80$		0			0
$81$	3.52739	−	2.74548i	3.52739	−	2.74548i
$82$	1.33609	−	1.45138i	1.33609	−	1.45138i
$83$	0.322718	+	0.735724i	0.322718	+	0.735724i	1.00000			$0$
$83$	0.322718	+	0.735724i	0.322718	+	0.735724i	−0.677282	+	0.735724i	$0.736842\pi$
$84$		0			0
$85$		0			0
$86$	0.706561	+	1.61080i	0.706561	+	1.61080i
$87$		0			0
$88$	0.268536	−	1.06042i	0.268536	−	1.06042i
$89$	−0.439413	−	0.672572i	−0.439413	−	0.672572i	0.546948	−	0.837166i	$-0.315789\pi$
$89$	−0.439413	−	0.672572i	−0.439413	−	0.672572i	−0.986361	+	0.164595i	$0.947368\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	1.33609	−	1.45138i	1.33609	−	1.45138i
$97$	−0.165159	+	1.99317i	−0.165159	+	1.99317i	−0.0825793	+	0.996584i	$0.526316\pi$
$97$	−0.165159	+	1.99317i	−0.165159	+	1.99317i	−0.0825793	+	0.996584i	$0.526316\pi$
$98$	−0.0825793	+	0.996584i	−0.0825793	+	0.996584i
$99$	3.16315			3.16315
$100$	0.245485	−	0.969400i	0.245485	−	0.969400i
$101$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$101$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$102$	1.25068	−	0.973446i	1.25068	−	0.973446i
$103$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$103$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.431796	−	0.233676i	−0.431796	−	0.233676i	0.245485	−	0.969400i	$-0.421053\pi$
$107$	−0.431796	−	0.233676i	−0.431796	−	0.233676i	−0.677282	+	0.735724i	$0.736842\pi$
$108$	3.28191	+	1.77608i	3.28191	+	1.77608i
$109$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$109$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.962053	−	1.47253i	−0.962053	−	1.47253i	−0.879474	−	0.475947i	$-0.842105\pi$
$113$	−0.962053	−	1.47253i	−0.962053	−	1.47253i	−0.0825793	−	0.996584i	$-0.526316\pi$
$114$	1.94582	−	0.324699i	1.94582	−	0.324699i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.19130	−	1.29410i	1.19130	−	1.29410i
$119$		0			0
$120$		0			0
$121$	0.155152	+	0.120760i	0.155152	+	0.120760i
$122$		0			0
$123$	−0.321369	+	3.87834i	−0.321369	+	3.87834i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	0.945817	+	0.324699i	0.945817	+	0.324699i
$129$	−3.05170	−	1.65150i	−3.05170	−	1.65150i
$130$		0			0
$131$	0.706561	−	0.382372i	0.706561	−	0.382372i	−0.0825793	−	0.996584i	$-0.526316\pi$
$131$	0.706561	−	0.382372i	0.706561	−	0.382372i	0.789141	+	0.614213i	$0.210526\pi$
$132$	0.866840	+	1.97620i	0.866840	+	1.97620i
$133$		0			0
$134$	−0.759861	+	1.73231i	−0.759861	+	1.73231i
$135$		0			0
$136$	0.706561	+	0.382372i	0.706561	+	0.382372i
$137$	−0.130333	−	1.57289i	−0.130333	−	1.57289i	−0.677282	−	0.735724i	$-0.736842\pi$
$137$	−0.130333	−	1.57289i	−0.130333	−	1.57289i	0.546948	−	0.837166i	$-0.315789\pi$
$138$		0			0
$139$	−1.06894	−	0.831990i	−1.06894	−	0.831990i	−0.0825793	−	0.996584i	$-0.526316\pi$
$139$	−1.06894	−	0.831990i	−1.06894	−	0.831990i	−0.986361	+	0.164595i	$0.947368\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.238789	+	2.88176i	−0.238789	+	2.88176i
$145$		0			0
$146$	−0.431796	+	0.233676i	−0.431796	+	0.233676i
$147$	−1.07898	−	1.65150i	−1.07898	−	1.65150i
$148$		0			0
$149$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$149$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$150$	0.792434	+	1.80657i	0.792434	+	1.80657i
$151$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$151$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$152$	0.546948	+	0.837166i	0.546948	+	0.837166i
$153$	−0.570290	+	2.25203i	−0.570290	+	2.25203i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$157$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−4.40895	+	0.735724i	−4.40895	+	0.735724i
$163$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.945817	−	0.324699i	$-0.105263\pi$
$163$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.245485	+	0.969400i	$0.421053\pi$
$164$	−1.86584	+	0.640542i	−1.86584	+	0.640542i
$165$		0			0
$166$	0.0663435	−	0.800647i	0.0663435	−	0.800647i
$167$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$167$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$168$		0			0
$169$	0.945817	−	0.324699i	0.945817	−	0.324699i
$170$		0			0
$171$	−1.95845	+	2.12744i	−1.95845	+	2.12744i
$172$	0.145253	−	1.75294i	0.145253	−	1.75294i
$173$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$173$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$174$		0			0
$175$		0			0
$176$	−0.740876	+	0.804806i	−0.740876	+	0.804806i
$177$	−0.286543	+	3.45806i	−0.286543	+	3.45806i
$178$	0.0663435	+	0.800647i	0.0663435	+	0.800647i
$179$	−1.38806	+	1.08037i	−1.38806	+	1.08037i	−0.401695	+	0.915773i	$0.631579\pi$
$179$	−1.38806	+	1.08037i	−1.38806	+	1.08037i	−0.986361	+	0.164595i	$0.947368\pi$
$180$		0			0
$181$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$181$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.693517	+	0.539786i	−0.693517	+	0.539786i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$191$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$192$	−1.86584	+	0.640542i	−1.86584	+	0.640542i
$193$	1.78914	+	0.614213i	1.78914	+	0.614213i	1.00000			$0$
$193$	1.78914	+	0.614213i	1.78914	+	0.614213i	0.789141	+	0.614213i	$0.210526\pi$
$194$	1.09390	−	1.67433i	1.09390	−	1.67433i
$195$		0			0
$196$	0.546948	−	0.837166i	0.546948	−	0.837166i
$197$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$197$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$198$	−2.78191	−	1.50549i	−2.78191	−	1.50549i
$199$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$199$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$200$	−0.677282	+	0.735724i	−0.677282	+	0.735724i
$201$	−0.916071	−	3.61748i	−0.916071	−	3.61748i
$202$		0			0
$203$		0			0
$204$	−1.56325	+	0.260861i	−1.56325	+	0.260861i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.07898	+	0.180049i	−1.07898	+	0.180049i
$210$		0			0
$211$	0.0663435	+	0.151248i	0.0663435	+	0.151248i	0.945817	−	0.324699i	$-0.105263\pi$
$211$	0.0663435	+	0.151248i	0.0663435	+	0.151248i	−0.879474	+	0.475947i	$0.842105\pi$
$212$		0			0
$213$		0			0
$214$	0.268536	+	0.411024i	0.268536	+	0.411024i
$215$		0			0
$216$	−2.04103	−	3.12403i	−2.04103	−	3.12403i
$217$		0			0
$218$		0			0
$219$	0.389062	−	0.886972i	0.389062	−	0.886972i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$223$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$224$		0			0
$225$	−2.54312	−	1.37627i	−2.54312	−	1.37627i
$226$	0.145253	+	1.75294i	0.145253	+	1.75294i
$227$	0.0663435	−	0.151248i	0.0663435	−	0.151248i	−0.879474	−	0.475947i	$-0.842105\pi$
$227$	0.0663435	−	0.151248i	0.0663435	−	0.151248i	0.945817	+	0.324699i	$0.105263\pi$
$228$	−1.86584	−	0.640542i	−1.86584	−	0.640542i
$229$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$229$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.89163	+	0.649399i	1.89163	+	0.649399i	0.945817	+	0.324699i	$0.105263\pi$
$233$	1.89163	+	0.649399i	1.89163	+	0.649399i	0.945817	+	0.324699i	$0.105263\pi$
$234$		0			0
$235$		0			0
$236$	−1.66364	+	0.571129i	−1.66364	+	0.571129i
$237$		0			0
$238$		0			0
$239$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$239$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$240$		0			0
$241$	−0.484275	−	0.0808112i	−0.484275	−	0.0808112i	−0.0825793	−	0.996584i	$-0.526316\pi$
$241$	−0.484275	−	0.0808112i	−0.484275	−	0.0808112i	−0.401695	+	0.915773i	$0.631579\pi$
$242$	−0.0789770	−	0.180049i	−0.0789770	−	0.180049i
$243$	3.44481	−	3.74206i	3.44481	−	3.74206i
$244$		0			0
$245$		0			0
$246$	2.12852	−	3.25795i	2.12852	−	3.25795i
$247$		0			0
$248$		0			0
$249$	0.866840	+	1.32680i	0.866840	+	1.32680i
$250$		0			0
$251$	1.03463	−	0.355188i	1.03463	−	0.355188i	0.245485	−	0.969400i	$-0.421053\pi$
$251$	1.03463	−	0.355188i	1.03463	−	0.355188i	0.789141	+	0.614213i	$0.210526\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.677282	−	0.735724i	−0.677282	−	0.735724i
$257$	0.464369	+	1.83375i	0.464369	+	1.83375i	0.546948	+	0.837166i	$0.315789\pi$
$257$	0.464369	+	1.83375i	0.464369	+	1.83375i	−0.0825793	+	0.996584i	$0.526316\pi$
$258$	1.89786	+	2.90490i	1.89786	+	2.90490i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.803391			−0.803391
$263$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$263$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$264$	0.178202	−	2.15058i	0.178202	−	2.15058i
$265$		0			0
$266$		0			0
$267$	−1.07340	−	1.16602i	−1.07340	−	1.16602i
$268$	1.49277	−	1.16187i	1.49277	−	1.16187i
$269$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$269$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$270$		0			0
$271$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$271$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$272$	−0.439413	−	0.672572i	−0.439413	−	0.672572i
$273$		0			0
$274$	−0.633988	+	1.44535i	−0.633988	+	1.44535i
$275$	−0.439413	−	1.00176i	−0.439413	−	1.00176i
$276$		0			0
$277$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$277$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$278$	0.544122	+	1.24047i	0.544122	+	1.24047i
$279$		0			0
$280$		0			0
$281$	0.111859	+	0.121511i	0.111859	+	0.121511i	0.789141	−	0.614213i	$-0.210526\pi$
$281$	0.111859	+	0.121511i	0.111859	+	0.121511i	−0.677282	+	0.735724i	$0.736842\pi$
$282$		0			0
$283$	−1.97272	−	0.329189i	−1.97272	−	0.329189i	−0.986361	−	0.164595i	$-0.947368\pi$
$283$	−1.97272	−	0.329189i	−1.97272	−	0.329189i	−0.986361	−	0.164595i	$-0.947368\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.58157	−	2.42078i	1.58157	−	2.42078i
$289$	0.142426	+	0.324699i	0.142426	+	0.324699i
$290$		0			0
$291$	0.325812	+	3.93197i	0.325812	+	3.93197i
$292$	0.490971			0.490971
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	0.162906	+	1.96598i	0.162906	+	1.96598i
$295$		0			0
$296$		0			0
$297$	4.02639	−	0.671885i	4.02639	−	0.671885i
$298$		0			0
$299$		0			0
$300$	0.162906	−	1.96598i	0.162906	−	1.96598i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.0825793	−	0.996584i	−0.0825793	−	0.996584i
$305$		0			0
$306$	1.57340	−	1.70917i	1.57340	−	1.70917i
$307$	−1.97272			−1.97272			−0.986361	−	0.164595i	$-0.947368\pi$
$307$	−1.97272			−1.97272			−0.986361	+	0.164595i	$0.947368\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$311$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$312$		0			0
$313$	0.387445	−	1.52999i	0.387445	−	1.52999i	−0.401695	−	0.915773i	$-0.631579\pi$
$313$	0.387445	−	1.52999i	0.387445	−	1.52999i	0.789141	−	0.614213i	$-0.210526\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$317$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.916071	−	0.314488i	−0.916071	−	0.314488i
$322$		0			0
$323$	0.0663435	−	0.800647i	0.0663435	−	0.800647i
$324$	4.22772	+	1.45138i	4.22772	+	1.45138i
$325$		0			0
$326$	−0.740876	−	1.13399i	−0.740876	−	1.13399i
$327$		0			0
$328$	1.94582	+	0.324699i	1.94582	+	0.324699i
$329$		0			0
$330$		0			0
$331$	0.111859	−	0.121511i	0.111859	−	0.121511i	−0.677282	−	0.735724i	$-0.736842\pi$
$331$	0.111859	−	0.121511i	0.111859	−	0.121511i	0.789141	+	0.614213i	$0.210526\pi$
$332$	−0.439413	+	0.672572i	−0.439413	+	0.672572i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.332526	−	1.31311i	−0.332526	−	1.31311i	−0.879474	−	0.475947i	$-0.842105\pi$
$337$	−0.332526	−	1.31311i	−0.332526	−	1.31311i	0.546948	−	0.837166i	$-0.315789\pi$
$338$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$339$	−2.35011	−	2.55290i	−2.35011	−	2.55290i
$340$		0			0
$341$		0			0
$342$	2.73496	−	0.938912i	2.73496	−	0.938912i
$343$		0			0
$344$	−0.962053	+	1.47253i	−0.962053	+	1.47253i
$345$		0			0
$346$		0			0
$347$	−0.962053	+	0.520637i	−0.962053	+	0.520637i	−0.879474	−	0.475947i	$-0.842105\pi$
$347$	−0.962053	+	0.520637i	−0.962053	+	0.520637i	−0.0825793	+	0.996584i	$0.526316\pi$
$348$		0			0
$349$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$349$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$350$		0			0
$351$		0			0
$352$	1.03463	−	0.355188i	1.03463	−	0.355188i
$353$	0.111859	+	1.34994i	0.111859	+	1.34994i	0.789141	+	0.614213i	$0.210526\pi$
$353$	0.111859	+	1.34994i	0.111859	+	1.34994i	−0.677282	+	0.735724i	$0.736842\pi$
$354$	1.89786	−	2.90490i	1.89786	−	2.90490i
$355$		0			0
$356$	0.322718	−	0.735724i	0.322718	−	0.735724i
$357$		0			0
$358$	1.73496	−	0.289513i	1.73496	−	0.289513i
$359$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$359$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$360$		0			0
$361$	0.546948	−	0.837166i	0.546948	−	0.837166i
$362$		0			0
$363$	0.341109	+	0.184599i	0.341109	+	0.184599i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$367$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$368$		0			0
$369$	0.471065	+	5.68491i	0.471065	+	5.68491i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$373$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$374$	0.866840	−	0.144650i	0.866840	−	0.144650i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.86584	−	0.311353i	−1.86584	−	0.311353i	−0.879474	−	0.475947i	$-0.842105\pi$
$379$	−1.86584	−	0.311353i	−1.86584	−	0.311353i	−0.986361	+	0.164595i	$0.947368\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$383$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$384$	1.94582	+	0.324699i	1.94582	+	0.324699i
$385$		0			0
$386$	−1.28117	−	1.39172i	−1.28117	−	1.39172i
$387$	−4.81065	−	1.65150i	−4.81065	−	1.65150i
$388$	−1.75895	+	0.951895i	−1.75895	+	0.951895i
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$393$	1.25068	−	0.973446i	1.25068	−	0.973446i
$394$		0			0
$395$		0			0
$396$	1.73008	+	2.64808i	1.73008	+	2.64808i
$397$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$397$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$398$		0			0
$399$		0			0
$400$	0.945817	−	0.324699i	0.945817	−	0.324699i
$401$	1.49277	+	0.512467i	1.49277	+	0.512467i	0.945817	−	0.324699i	$-0.105263\pi$
$401$	1.49277	+	0.512467i	1.49277	+	0.512467i	0.546948	+	0.837166i	$0.315789\pi$
$402$	−0.916071	+	3.61748i	−0.916071	+	3.61748i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.49899	+	0.514606i	1.49899	+	0.514606i
$409$	−0.0405441	+	0.160105i	−0.0405441	+	0.160105i	−0.986361	−	0.164595i	$-0.947368\pi$
$409$	−0.0405441	+	0.160105i	−0.0405441	+	0.160105i	0.945817	+	0.324699i	$0.105263\pi$
$410$		0			0
$411$	−0.764322	−	3.01824i	−0.764322	−	3.01824i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.35011	−	1.27182i	−2.35011	−	1.27182i
$418$	1.03463	+	0.355188i	1.03463	+	0.355188i
$419$	−0.962053	+	0.520637i	−0.962053	+	0.520637i	−0.879474	−	0.475947i	$-0.842105\pi$
$419$	−0.962053	+	0.520637i	−0.962053	+	0.520637i	−0.0825793	+	0.996584i	$0.526316\pi$
$420$		0			0
$421$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$421$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$422$	0.0136387	−	0.164595i	0.0136387	−	0.164595i
$423$		0			0
$424$		0			0
$425$	0.792434	−	0.132234i	0.792434	−	0.132234i
$426$		0			0
$427$		0			0
$428$	−0.0405441	−	0.489294i	−0.0405441	−	0.489294i
$429$		0			0
$430$		0			0
$431$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$431$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$432$	0.308159	+	3.71892i	0.308159	+	3.71892i
$433$	0.792434	+	1.80657i	0.792434	+	1.80657i	0.546948	+	0.837166i	$0.315789\pi$
$433$	0.792434	+	1.80657i	0.792434	+	1.80657i	0.245485	+	0.969400i	$0.421053\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.764322	+	0.594895i	−0.764322	+	0.594895i
$439$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$439$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$440$		0			0
$441$	−1.95845	−	2.12744i	−1.95845	−	2.12744i
$442$		0			0
$443$	1.19130	−	1.29410i	1.19130	−	1.29410i	0.245485	−	0.969400i	$-0.421053\pi$
$443$	1.19130	−	1.29410i	1.19130	−	1.29410i	0.945817	−	0.324699i	$-0.105263\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.484275	+	1.91236i	−0.484275	+	1.91236i	−0.0825793	+	0.996584i	$0.526316\pi$
$449$	−0.484275	+	1.91236i	−0.484275	+	1.91236i	−0.401695	+	0.915773i	$0.631579\pi$
$450$	1.58157	+	2.42078i	1.58157	+	2.42078i
$451$	−1.18029	+	1.80657i	−1.18029	+	1.80657i
$452$	0.706561	−	1.61080i	0.706561	−	1.61080i
$453$		0			0
$454$	−0.130333	+	0.101443i	−0.130333	+	0.101443i
$455$		0			0
$456$	1.33609	+	1.45138i	1.33609	+	1.45138i
$457$	0.111859	−	0.121511i	0.111859	−	0.121511i	−0.677282	−	0.735724i	$-0.736842\pi$
$457$	0.111859	−	0.121511i	0.111859	−	0.121511i	0.789141	+	0.614213i	$0.210526\pi$
$458$		0			0
$459$	−0.247572	+	2.98775i	−0.247572	+	2.98775i
$460$		0			0
$461$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$461$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$462$		0			0
$463$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$463$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$464$		0			0
$465$		0			0
$466$	−1.35456	−	1.47145i	−1.35456	−	1.47145i
$467$	−0.332526	−	0.361219i	−0.332526	−	0.361219i	0.546948	−	0.837166i	$-0.315789\pi$
$467$	−0.332526	−	0.361219i	−0.332526	−	0.361219i	−0.879474	+	0.475947i	$0.842105\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.73496	+	0.289513i	1.73496	+	0.289513i
$473$	−1.05239	−	1.61080i	−1.05239	−	1.61080i
$474$		0			0
$475$	0.945817	+	0.324699i	0.945817	+	0.324699i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$479$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$480$		0			0
$481$		0			0
$482$	0.387445	+	0.301561i	0.387445	+	0.301561i
$483$		0			0
$484$	−0.0162359	+	0.195938i	−0.0162359	+	0.195938i
$485$		0			0
$486$	−4.81065	+	1.65150i	−4.81065	+	1.65150i
$487$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$487$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$488$		0			0
$489$	2.52739	+	0.867655i	2.52739	+	0.867655i
$490$		0			0
$491$	−1.06894	+	1.16118i	−1.06894	+	1.16118i	−0.0825793	+	0.996584i	$0.526316\pi$
$491$	−1.06894	+	1.16118i	−1.06894	+	1.16118i	−0.986361	+	0.164595i	$0.947368\pi$
$492$	−3.42259	+	1.85221i	−3.42259	+	1.85221i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.130877	−	1.57945i	−0.130877	−	1.57945i
$499$	0.145253	+	0.0786068i	0.145253	+	0.0786068i	0.546948	−	0.837166i	$-0.315789\pi$
$499$	0.145253	+	0.0786068i	0.145253	+	0.0786068i	−0.401695	+	0.915773i	$0.631579\pi$
$500$		0			0
$501$		0			0
$502$	−1.07898	−	0.180049i	−1.07898	−	0.180049i
$503$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$503$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.73496	−	0.938912i	1.73496	−	0.938912i
$508$		0			0
$509$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$509$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$510$		0			0
$511$		0			0
$512$	0.245485	+	0.969400i	0.245485	+	0.969400i
$513$	−2.04103	+	3.12403i	−2.04103	+	3.12403i
$514$	0.464369	−	1.83375i	0.464369	−	1.83375i
$515$		0			0
$516$	−0.286543	−	3.45806i	−0.286543	−	3.45806i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.268536	+	1.06042i	0.268536	+	1.06042i	0.945817	+	0.324699i	$0.105263\pi$
$521$	0.268536	+	1.06042i	0.268536	+	1.06042i	−0.677282	+	0.735724i	$0.736842\pi$
$522$		0			0
$523$	0.792434	−	0.132234i	0.792434	−	0.132234i	0.245485	−	0.969400i	$-0.421053\pi$
$523$	0.792434	−	0.132234i	0.792434	−	0.132234i	0.546948	+	0.837166i	$0.315789\pi$
$524$	0.706561	+	0.382372i	0.706561	+	0.382372i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.18029	+	1.80657i	−1.18029	+	1.80657i
$529$	0.945817	+	0.324699i	0.945817	+	0.324699i
$530$		0			0
$531$	0.420018	+	5.06886i	0.420018	+	5.06886i
$532$		0			0
$533$		0			0
$534$	0.389062	+	1.53637i	0.389062	+	1.53637i
$535$		0			0
$536$	−1.86584	+	0.311353i	−1.86584	+	0.311353i
$537$	−2.35011	+	2.55290i	−2.35011	+	2.55290i
$538$		0			0
$539$	−0.0903332	−	1.09016i	−0.0903332	−	1.09016i
$540$		0			0
$541$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$541$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$542$		0			0
$543$		0			0
$544$	0.0663435	+	0.800647i	0.0663435	+	0.800647i
$545$		0			0
$546$		0			0
$547$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.986361	−	0.164595i	$-0.947368\pi$
$547$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.879474	+	0.475947i	$0.842105\pi$
$548$	1.24549	−	0.969400i	1.24549	−	0.969400i
$549$		0			0
$550$	−0.0903332	+	1.09016i	−0.0903332	+	1.09016i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.111859	−	1.34994i	0.111859	−	1.34994i
$557$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$557$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.17419	+	1.27551i	−1.17419	+	1.27551i
$562$	−0.0405441	−	0.160105i	−0.0405441	−	0.160105i
$563$	−0.484275	−	0.0808112i	−0.484275	−	0.0808112i	−0.0825793	−	0.996584i	$-0.526316\pi$
$563$	−0.484275	−	0.0808112i	−0.484275	−	0.0808112i	−0.401695	+	0.915773i	$0.631579\pi$
$564$		0			0
$565$		0			0
$566$	1.57828	+	1.22843i	1.57828	+	1.22843i
$567$		0			0
$568$		0			0
$569$	0.387445	−	1.52999i	0.387445	−	1.52999i	−0.401695	−	0.915773i	$-0.631579\pi$
$569$	0.387445	−	1.52999i	0.387445	−	1.52999i	0.789141	−	0.614213i	$-0.210526\pi$
$570$		0			0
$571$	0.120526	+	0.475947i	0.120526	+	0.475947i	1.00000			$0$
$571$	0.120526	+	0.475947i	0.120526	+	0.475947i	−0.879474	+	0.475947i	$0.842105\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−2.54312	+	1.37627i	−2.54312	+	1.37627i
$577$	−1.07898	−	1.65150i	−1.07898	−	1.65150i	−0.677282	−	0.735724i	$-0.736842\pi$
$577$	−1.07898	−	1.65150i	−1.07898	−	1.65150i	−0.401695	−	0.915773i	$-0.631579\pi$
$578$	0.0292796	−	0.353352i	0.0292796	−	0.353352i
$579$	3.68077	+	0.614213i	3.68077	+	0.614213i
$580$		0			0
$581$		0			0
$582$	1.58487	−	3.61313i	1.58487	−	3.61313i
$583$		0			0
$584$	−0.431796	−	0.233676i	−0.431796	−	0.233676i
$585$		0			0
$586$		0			0
$587$	−0.0903332	−	1.09016i	−0.0903332	−	1.09016i	−0.879474	−	0.475947i	$-0.842105\pi$
$587$	−0.0903332	−	1.09016i	−0.0903332	−	1.09016i	0.789141	−	0.614213i	$-0.210526\pi$
$588$	0.792434	−	1.80657i	0.792434	−	1.80657i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.945817	−	0.324699i	$-0.105263\pi$
$593$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.245485	+	0.969400i	$0.421053\pi$
$594$	−3.86088	−	1.32544i	−3.86088	−	1.32544i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$599$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$600$	−1.07898	+	1.65150i	−1.07898	+	1.65150i
$601$	1.57828	+	1.22843i	1.57828	+	1.22843i	0.789141	+	0.614213i	$0.210526\pi$
$601$	1.57828	+	1.22843i	1.57828	+	1.22843i	0.789141	+	0.614213i	$0.210526\pi$
$602$		0			0
$603$	−2.19724	−	5.00920i	−2.19724	−	5.00920i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$607$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$608$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−2.19724	+	0.754313i	−2.19724	+	0.754313i
$613$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$613$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$614$	1.73496	+	0.938912i	1.73496	+	0.938912i
$615$		0			0
$616$		0			0
$617$	0.544122	+	0.591074i	0.544122	+	0.591074i	0.945817	−	0.324699i	$-0.105263\pi$
$617$	0.544122	+	0.591074i	0.544122	+	0.591074i	−0.401695	+	0.915773i	$0.631579\pi$
$618$		0			0
$619$	−0.0903332	−	0.138265i	−0.0903332	−	0.138265i	0.789141	−	0.614213i	$-0.210526\pi$
$619$	−0.0903332	−	0.138265i	−0.0903332	−	0.138265i	−0.879474	+	0.475947i	$0.842105\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.0825793	+	0.996584i	−0.0825793	+	0.996584i
$626$	−1.06894	+	1.16118i	−1.06894	+	1.16118i
$627$	−2.04103	+	0.700687i	−2.04103	+	0.700687i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$631$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$632$		0			0
$633$	0.178202	+	0.272759i	0.178202	+	0.272759i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.38806	+	1.08037i	−1.38806	+	1.08037i	−0.401695	+	0.915773i	$0.631579\pi$
$641$	−1.38806	+	1.08037i	−1.38806	+	1.08037i	−0.986361	+	0.164595i	$0.947368\pi$
$642$	0.655981	+	0.712585i	0.655981	+	0.712585i
$643$	0.387445	+	0.301561i	0.387445	+	0.301561i	0.789141	−	0.614213i	$-0.210526\pi$
$643$	0.387445	+	0.301561i	0.387445	+	0.301561i	−0.401695	+	0.915773i	$0.631579\pi$
$644$		0			0
$645$		0			0
$646$	−0.439413	+	0.672572i	−0.439413	+	0.672572i
$647$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$647$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$648$	−3.02739	−	3.28862i	−3.02739	−	3.28862i
$649$	−1.05239	+	1.61080i	−1.05239	+	1.61080i
$650$		0			0
$651$		0			0
$652$	0.111859	+	1.34994i	0.111859	+	1.34994i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$	−1.55676	−	1.21167i	−1.55676	−	1.21167i
$657$	0.348518	−	1.37627i	0.348518	−	1.37627i
$658$		0			0
$659$	0.268536	−	1.06042i	0.268536	−	1.06042i	−0.677282	−	0.735724i	$-0.736842\pi$
$659$	0.268536	−	1.06042i	0.268536	−	1.06042i	0.945817	−	0.324699i	$-0.105263\pi$
$660$		0			0
$661$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$661$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$662$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i
$663$		0			0
$664$	0.706561	−	0.382372i	0.706561	−	0.382372i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.792434	+	1.80657i	0.792434	+	1.80657i	0.546948	+	0.837166i	$0.315789\pi$
$673$	0.792434	+	1.80657i	0.792434	+	1.80657i	0.245485	+	0.969400i	$0.421053\pi$
$674$	−0.332526	+	1.31311i	−0.332526	+	1.31311i
$675$	−3.52948	−	1.21167i	−3.52948	−	1.21167i
$676$	0.789141	+	0.614213i	0.789141	+	0.614213i
$677$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$677$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$678$	0.851814	+	3.36374i	0.851814	+	3.36374i
$679$		0			0
$680$		0			0
$681$	0.0799822	−	0.315843i	0.0799822	−	0.315843i
$682$		0			0
$683$	−1.86584	+	0.640542i	−1.86584	+	0.640542i	−0.879474	+	0.475947i	$0.842105\pi$
$683$	−1.86584	+	0.640542i	−1.86584	+	0.640542i	−0.986361	+	0.164595i	$0.947368\pi$
$684$	−2.85220	−	0.475947i	−2.85220	−	0.475947i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.54695	−	0.837166i	1.54695	−	0.837166i
$689$		0			0
$690$		0			0
$691$	−1.66364	+	0.900319i	−1.66364	+	0.900319i	−0.677282	+	0.735724i	$0.736842\pi$
$691$	−1.66364	+	0.900319i	−1.66364	+	0.900319i	−0.986361	+	0.164595i	$0.947368\pi$
$692$		0			0
$693$		0			0
$694$	1.09390			1.09390
$695$		0			0
$696$		0			0
$697$	−1.07340	−	1.16602i	−1.07340	−	1.16602i
$698$		0			0
$699$	3.89163	+	0.649399i	3.89163	+	0.649399i
$700$		0			0
$701$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$701$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$702$		0			0
$703$		0			0
$704$	−1.07898	−	0.180049i	−1.07898	−	0.180049i
$705$		0			0
$706$	0.544122	−	1.24047i	0.544122	−	1.24047i
$707$		0			0
$708$	−3.05170	+	1.65150i	−3.05170	+	1.65150i
$709$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$709$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$710$		0			0
$711$		0			0
$712$	−0.633988	+	0.493453i	−0.633988	+	0.493453i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.66364	−	0.571129i	−1.66364	−	0.571129i
$717$		0			0
$718$		0			0
$719$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$719$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$720$		0			0
$721$		0			0
$722$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$723$	−0.968550			−0.968550
$724$		0			0
$725$		0			0
$726$	−0.212137	−	0.324699i	−0.212137	−	0.324699i
$727$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$727$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$728$		0			0
$729$	3.04312	−	4.65784i	3.04312	−	4.65784i
$730$		0			0
$731$	1.33656	−	0.458840i	1.33656	−	0.458840i
$732$		0			0
$733$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$733$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.507971	−	2.00593i	0.507971	−	2.00593i
$738$	2.29143	−	5.22393i	2.29143	−	5.22393i
$739$	−0.740876	+	1.13399i	−0.740876	+	1.13399i	0.245485	+	0.969400i	$0.421053\pi$
$739$	−0.740876	+	1.13399i	−0.740876	+	1.13399i	−0.986361	+	0.164595i	$0.947368\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$743$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.57340	+	1.70917i	1.57340	+	1.70917i
$748$	−0.831209	−	0.285354i	−0.831209	−	0.285354i
$749$		0			0
$750$		0			0
$751$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$751$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$752$		0			0
$753$	1.89786	−	1.02707i	1.89786	−	1.02707i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$757$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$758$	1.49277	+	1.16187i	1.49277	+	1.16187i
$759$		0			0
$760$		0			0
$761$	0.464369	−	0.159418i	0.464369	−	0.159418i	−0.0825793	−	0.996584i	$-0.526316\pi$
$761$	0.464369	−	0.159418i	0.464369	−	0.159418i	0.546948	+	0.837166i	$0.315789\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.55676	−	1.21167i	−1.55676	−	1.21167i
$769$	1.78914	+	0.614213i	1.78914	+	0.614213i	1.00000			$0$
$769$	1.78914	+	0.614213i	1.78914	+	0.614213i	0.789141	+	0.614213i	$0.210526\pi$
$770$		0			0
$771$	1.49899	+	3.41736i	1.49899	+	3.41736i
$772$	0.464369	+	1.83375i	0.464369	+	1.83375i
$773$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$773$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$774$	3.44481	+	3.74206i	3.44481	+	3.74206i
$775$		0			0
$776$	2.00000			2.00000
$777$		0			0
$778$		0			0
$779$	−0.484275	−	1.91236i	−0.484275	−	1.91236i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.00000			1.00000
$785$		0			0
$786$	−1.56325	+	0.260861i	−1.56325	+	0.260861i
$787$	0.464369	−	1.83375i	0.464369	−	1.83375i	−0.0825793	−	0.996584i	$-0.526316\pi$
$787$	0.464369	−	1.83375i	0.464369	−	1.83375i	0.546948	−	0.837166i	$-0.315789\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.261211	−	3.15234i	−0.261211	−	3.15234i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$797$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$798$		0			0
$799$		0			0
$800$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$801$	−1.83326	−	1.42689i	−1.83326	−	1.42689i
$802$	−1.06894	−	1.16118i	−1.06894	−	1.16118i
$803$	0.423825	−	0.329876i	0.423825	−	0.329876i
$804$	2.52739	−	2.74548i	2.52739	−	2.74548i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.792434	−	1.80657i	0.792434	−	1.80657i	0.245485	−	0.969400i	$-0.421053\pi$
$809$	0.792434	−	1.80657i	0.792434	−	1.80657i	0.546948	−	0.837166i	$-0.315789\pi$
$810$		0			0
$811$	0.268536	+	0.411024i	0.268536	+	0.411024i	0.945817	−	0.324699i	$-0.105263\pi$
$811$	0.268536	+	0.411024i	0.268536	+	0.411024i	−0.677282	+	0.735724i	$0.736842\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.07340	−	1.16602i	−1.07340	−	1.16602i
$817$	1.73496	+	0.289513i	1.73496	+	0.289513i
$818$	0.111859	−	0.121511i	0.111859	−	0.121511i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−0.764322	+	3.01824i	−0.764322	+	3.01824i
$823$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$823$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$824$		0			0
$825$	−1.18029	−	1.80657i	−1.18029	−	1.80657i
$826$		0			0
$827$	1.33609	+	1.45138i	1.33609	+	1.45138i	0.789141	+	0.614213i	$0.210526\pi$
$827$	1.33609	+	1.45138i	1.33609	+	1.45138i	0.546948	+	0.837166i	$0.315789\pi$
$828$		0			0
$829$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$829$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.792434	+	0.132234i	0.792434	+	0.132234i
$834$	1.46154	+	2.23706i	1.46154	+	2.23706i
$835$		0			0
$836$	−0.740876	−	0.804806i	−0.740876	−	0.804806i
$837$		0			0
$838$	1.09390			1.09390
$839$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$839$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$840$		0			0
$841$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$842$		0			0
$843$	0.257112	+	0.200118i	0.257112	+	0.200118i
$844$	−0.0903332	+	0.138265i	−0.0903332	+	0.138265i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.94545			−3.94545
$850$	−0.759861	−	0.260861i	−0.759861	−	0.260861i
$851$		0			0
$852$		0			0
$853$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$853$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$854$		0			0
$855$		0			0
$856$	−0.197221	+	0.449618i	−0.197221	+	0.449618i
$857$	0.0136387	+	0.164595i	0.0136387	+	0.164595i	1.00000			$0$
$857$	0.0136387	+	0.164595i	0.0136387	+	0.164595i	−0.986361	+	0.164595i	$0.947368\pi$
$858$		0			0
$859$	0.0663435	+	0.800647i	0.0663435	+	0.800647i	0.945817	+	0.324699i	$0.105263\pi$
$859$	0.0663435	+	0.800647i	0.0663435	+	0.800647i	−0.879474	+	0.475947i	$0.842105\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$863$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$864$	1.49899	−	3.41736i	1.49899	−	3.41736i
$865$		0			0
$866$	0.162906	−	1.96598i	0.162906	−	1.96598i
$867$	0.382565	+	0.585560i	0.382565	+	0.585560i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.41971	+	5.60630i	1.41971	+	5.60630i
$874$		0			0
$875$		0			0
$876$	0.955340	−	0.159418i	0.955340	−	0.159418i
$877$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$877$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.73496	+	0.289513i	1.73496	+	0.289513i	0.945817	−	0.324699i	$-0.105263\pi$
$881$	1.73496	+	0.289513i	1.73496	+	0.289513i	0.789141	+	0.614213i	$0.210526\pi$
$882$	0.709854	+	2.80315i	0.709854	+	2.80315i
$883$	0.544122	−	0.591074i	0.544122	−	0.591074i	−0.401695	−	0.915773i	$-0.631579\pi$
$883$	0.544122	−	0.591074i	0.544122	−	0.591074i	0.945817	+	0.324699i	$0.105263\pi$
$884$		0			0
$885$		0			0
$886$	−1.66364	+	0.571129i	−1.66364	+	0.571129i
$887$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$887$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.62469	−	1.58766i	4.62469	−	1.58766i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.33609	−	1.45138i	1.33609	−	1.45138i
$899$		0			0
$900$	−0.238789	−	2.88176i	−0.238789	−	2.88176i
$901$		0			0
$902$	1.89786	−	1.02707i	1.89786	−	1.02707i
$903$		0			0
$904$	−1.38806	+	1.08037i	−1.38806	+	1.08037i
$905$		0			0
$906$		0			0
$907$	0.917421	−	0.996584i	0.917421	−	0.996584i	−0.0825793	−	0.996584i	$-0.526316\pi$
$907$	0.917421	−	0.996584i	0.917421	−	0.996584i	1.00000			$0$
$908$	0.162906	−	0.0271842i	0.162906	−	0.0271842i
$909$		0			0
$910$		0			0
$911$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$911$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$912$	−0.484275	−	1.91236i	−0.484275	−	1.91236i
$913$	0.0725729	+	0.875825i	0.0725729	+	0.875825i
$914$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.63974	−	2.50982i	1.63974	−	2.50982i
$919$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$919$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$920$		0			0
$921$	−3.83856	+	0.640542i	−3.83856	+	0.640542i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.55676	+	0.259777i	−1.55676	+	0.259777i	−0.879474	−	0.475947i	$-0.842105\pi$
$929$	−1.55676	+	0.259777i	−1.55676	+	0.259777i	−0.677282	+	0.735724i	$0.736842\pi$
$930$		0			0
$931$	0.789141	+	0.614213i	0.789141	+	0.614213i
$932$	0.490971	+	1.93880i	0.490971	+	1.93880i
$933$		0			0
$934$	0.120526	+	0.475947i	0.120526	+	0.475947i
$935$		0			0
$936$		0			0
$937$	1.54695	−	0.837166i	1.54695	−	0.837166i	0.546948	−	0.837166i	$-0.315789\pi$
$937$	1.54695	−	0.837166i	1.54695	−	0.837166i	1.00000			$0$
$938$		0			0
$939$	0.257112	−	3.10288i	0.257112	−	3.10288i
$940$		0			0
$941$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$941$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$942$		0			0
$943$		0			0
$944$	−1.38806	−	1.08037i	−1.38806	−	1.08037i
$945$		0			0
$946$	0.158891	+	1.91753i	0.158891	+	1.91753i
$947$	1.54695	+	0.837166i	1.54695	+	0.837166i	1.00000			$0$
$947$	1.54695	+	0.837166i	1.54695	+	0.837166i	0.546948	+	0.837166i	$0.315789\pi$
$948$		0			0
$949$		0			0
$950$	−0.677282	−	0.735724i	−0.677282	−	0.735724i
$951$		0			0
$952$		0			0
$953$	0.917421	−	0.996584i	0.917421	−	0.996584i	−0.0825793	−	0.996584i	$-0.526316\pi$
$953$	0.917421	−	0.996584i	0.917421	−	0.996584i	1.00000			$0$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.546948	−	0.837166i	0.546948	−	0.837166i
$962$		0			0
$963$	−1.40035	−	0.233676i	−1.40035	−	0.233676i
$964$	−0.197221	−	0.449618i	−0.197221	−	0.449618i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.107535	−	0.164595i	0.107535	−	0.164595i
$969$	−0.130877	−	1.57945i	−0.130877	−	1.57945i
$970$		0			0
$971$	1.09390	+	1.67433i	1.09390	+	1.67433i	0.546948	+	0.837166i	$0.315789\pi$
$971$	1.09390	+	1.67433i	1.09390	+	1.67433i	0.546948	+	0.837166i	$0.315789\pi$
$972$	5.01686	+	0.837166i	5.01686	+	0.837166i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.06894	−	1.16118i	−1.06894	−	1.16118i	−0.986361	−	0.164595i	$-0.947368\pi$
$977$	−1.06894	−	1.16118i	−1.06894	−	1.16118i	−0.0825793	−	0.996584i	$-0.526316\pi$
$978$	−1.80982	−	1.96598i	−1.80982	−	1.96598i
$979$	−0.215739	−	0.851934i	−0.215739	−	0.851934i
$980$		0			0
$981$		0			0
$982$	1.49277	−	0.512467i	1.49277	−	0.512467i
$983$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$983$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$984$	3.89163			3.89163
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$991$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$992$		0			0
$993$	0.178202	−	0.272759i	0.178202	−	0.272759i
$994$		0			0
$995$		0			0
$996$	−0.636634	+	1.45138i	−0.636634	+	1.45138i
$997$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$997$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$998$	−0.0903332	−	0.138265i	−0.0903332	−	0.138265i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bb.a.2699.1	yes	18
8.3	odd	2	CM	2888.1.bb.a.2699.1	yes	18
361.191	even	19	inner	2888.1.bb.a.1635.1	✓	18
2888.1635	odd	38	inner	2888.1.bb.a.1635.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bb.a.1635.1	✓	18	361.191	even	19	inner
2888.1.bb.a.1635.1	✓	18	2888.1635	odd	38	inner
2888.1.bb.a.2699.1	yes	18	1.1	even	1	trivial
2888.1.bb.a.2699.1	yes	18	8.3	odd	2	CM

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:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2888.bb (of order \(38\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.879474 - 0.475947i) q^{2} +(1.94582 - 0.324699i) q^{3} +(0.546948 + 0.837166i) q^{4} +(-1.86584 - 0.640542i) q^{6} +(-0.0825793 - 0.996584i) q^{8} +(2.73496 - 0.938912i) q^{9} +O(q^{10})\)	\(q+(-0.879474 - 0.475947i) q^{2} +(1.94582 - 0.324699i) q^{3} +(0.546948 + 0.837166i) q^{4} +(-1.86584 - 0.640542i) q^{6} +(-0.0825793 - 0.996584i) q^{8} +(2.73496 - 0.938912i) q^{9} +(1.03463 + 0.355188i) q^{11} +(1.33609 + 1.45138i) q^{12} +(-0.401695 + 0.915773i) q^{16} +(-0.439413 + 0.672572i) q^{17} +(-2.85220 - 0.475947i) q^{18} +(-0.879474 + 0.475947i) q^{19} +(-0.740876 - 0.804806i) q^{22} +(-0.484275 - 1.91236i) q^{24} +(-0.677282 - 0.735724i) q^{25} +(3.28191 - 1.77608i) q^{27} +(0.789141 - 0.614213i) q^{32} +(2.12852 + 0.355188i) q^{33} +(0.706561 - 0.382372i) q^{34} +(2.28191 + 1.77608i) q^{36} +1.00000 q^{38} +(-0.484275 + 1.91236i) q^{41} +(-1.38806 - 1.08037i) q^{43} +(0.268536 + 1.06042i) q^{44} +(-0.484275 + 1.91236i) q^{48} +(-0.401695 - 0.915773i) q^{49} +(0.245485 + 0.969400i) q^{50} +(-0.636634 + 1.45138i) q^{51} -3.73167 q^{54} +(-1.55676 + 1.21167i) q^{57} +(-0.431796 + 1.70512i) q^{59} +(-0.986361 + 0.164595i) q^{64} +(-1.70293 - 1.32544i) q^{66} +(-0.156210 - 1.88517i) q^{67} -0.803391 q^{68} +(-1.16156 - 2.64808i) q^{72} +(0.268536 - 0.411024i) q^{73} +(-1.55676 - 1.21167i) q^{75} +(-0.879474 - 0.475947i) q^{76} +(3.52739 - 2.74548i) q^{81} +(1.33609 - 1.45138i) q^{82} +(0.322718 + 0.735724i) q^{83} +(0.706561 + 1.61080i) q^{86} +(0.268536 - 1.06042i) q^{88} +(-0.439413 - 0.672572i) q^{89} +(1.33609 - 1.45138i) q^{96} +(-0.165159 + 1.99317i) q^{97} +(-0.0825793 + 0.996584i) q^{98} +3.16315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9}+O(q^{10}) \) 18 * q - q^2 + 17 * q^3 - q^4 - 2 * q^6 - q^8 + 16 * q^9	\( 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - q^{19} - 2 q^{22} - 2 q^{24} - q^{25} + 15 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} + 18 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} - 4 q^{54} - 2 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - q^{76} + 14 q^{81} - 2 q^{82} + 17 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - q^2 + 17 * q^3 - q^4 - 2 * q^6 - q^8 + 16 * q^9 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - 3 * q^18 - q^19 - 2 * q^22 - 2 * q^24 - q^25 + 15 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 + 18 * q^38 - 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 - 4 * q^54 - 2 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 - 2 * q^75 - q^76 + 14 * q^81 - 2 * q^82 + 17 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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