LMFDB - Embedded newform 2888.1.bb.a.2395.1

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			2395.1
Root			$0.677282 - 0.735724i$ of defining polynomial
Character	$\chi$	$=$	2888.2395
Dual form			2888.1.bb.a.1939.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.789141 + 0.614213i) q^{2} +(0.917421 + 0.996584i) q^{3} +(0.245485 + 0.969400i) q^{4} +(0.111859 + 1.34994i) q^{6} +(-0.401695 + 0.915773i) q^{8} +(-0.0689406 + 0.831990i) q^{9} +(-0.0405441 - 0.489294i) q^{11} +(-0.740876 + 1.13399i) q^{12} +(-0.879474 + 0.475947i) q^{16} +(-0.431796 + 1.70512i) q^{17} +(-0.565423 + 0.614213i) q^{18} +(0.789141 - 0.614213i) q^{19} +(0.268536 - 0.411024i) q^{22} +(-1.28117 + 0.439826i) q^{24} +(0.546948 - 0.837166i) q^{25} +(0.176545 - 0.137410i) q^{27} +(-0.986361 - 0.164595i) q^{32} +(0.450427 - 0.489294i) q^{33} +(-1.38806 + 1.08037i) q^{34} +(-0.823455 + 0.137410i) q^{36} +1.00000 q^{38} +(-1.28117 - 0.439826i) q^{41} +(-1.55676 + 0.259777i) q^{43} +(0.464369 - 0.159418i) q^{44} +(-1.28117 - 0.439826i) q^{48} +(-0.879474 - 0.475947i) q^{49} +(0.945817 - 0.324699i) q^{50} +(-2.09544 + 1.13399i) q^{51} +0.223718 q^{54} +(1.33609 + 0.222954i) q^{57} +(1.49277 + 0.512467i) q^{59} +(-0.677282 - 0.735724i) q^{64} +(0.655981 - 0.109464i) q^{66} +(0.0663435 - 0.151248i) q^{67} -1.75895 q^{68} +(-0.734221 - 0.397341i) q^{72} +(0.464369 - 1.83375i) q^{73} +(1.33609 - 0.222954i) q^{75} +(0.789141 + 0.614213i) q^{76} +(1.12236 + 0.187289i) q^{81} +(-0.740876 - 1.13399i) q^{82} +(1.54695 + 0.837166i) q^{83} +(-1.38806 - 0.751179i) q^{86} +(0.464369 + 0.159418i) q^{88} +(-0.431796 - 1.70512i) q^{89} +(-0.740876 - 1.13399i) q^{96} +(-0.803391 - 1.83155i) q^{97} +(-0.401695 - 0.915773i) q^{98} +0.409883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} - 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}+ \cdots - 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

Character values

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

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{4}{19}\right)$

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 $

$2$	0.789141	+	0.614213i	0.789141	+	0.614213i
$2$	0.789141	+	0.614213i	0.789141	+	0.614213i
$3$	0.917421	+	0.996584i	0.917421	+	0.996584i	1.00000			$0$
$3$	0.917421	+	0.996584i	0.917421	+	0.996584i	−0.0825793	+	0.996584i	$0.526316\pi$
$4$	0.245485	+	0.969400i	0.245485	+	0.969400i
$5$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$5$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$6$	0.111859	+	1.34994i	0.111859	+	1.34994i
$7$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$7$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$8$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$9$	−0.0689406	+	0.831990i	−0.0689406	+	0.831990i
$10$		0			0
$11$	−0.0405441	−	0.489294i	−0.0405441	−	0.489294i	−0.986361	−	0.164595i	$-0.947368\pi$
$11$	−0.0405441	−	0.489294i	−0.0405441	−	0.489294i	0.945817	−	0.324699i	$-0.105263\pi$
$12$	−0.740876	+	1.13399i	−0.740876	+	1.13399i
$13$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$13$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$14$		0			0
$15$		0			0
$16$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$17$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	0.245485	+	0.969400i	$0.421053\pi$
$17$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	−0.677282	+	0.735724i	$0.736842\pi$
$18$	−0.565423	+	0.614213i	−0.565423	+	0.614213i
$19$	0.789141	−	0.614213i	0.789141	−	0.614213i
$19$	0.789141	−	0.614213i	0.789141	−	0.614213i
$20$		0			0
$21$		0			0
$22$	0.268536	−	0.411024i	0.268536	−	0.411024i
$23$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$23$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$24$	−1.28117	+	0.439826i	−1.28117	+	0.439826i
$25$	0.546948	−	0.837166i	0.546948	−	0.837166i
$26$		0			0
$27$	0.176545	−	0.137410i	0.176545	−	0.137410i
$28$		0			0
$29$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$29$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$30$		0			0
$31$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$31$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$32$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$33$	0.450427	−	0.489294i	0.450427	−	0.489294i
$34$	−1.38806	+	1.08037i	−1.38806	+	1.08037i
$35$		0			0
$36$	−0.823455	+	0.137410i	−0.823455	+	0.137410i
$37$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$37$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$38$	1.00000			1.00000
$39$		0			0
$40$		0			0
$41$	−1.28117	−	0.439826i	−1.28117	−	0.439826i	−0.401695	−	0.915773i	$-0.631579\pi$
$41$	−1.28117	−	0.439826i	−1.28117	−	0.439826i	−0.879474	+	0.475947i	$0.842105\pi$
$42$		0			0
$43$	−1.55676	+	0.259777i	−1.55676	+	0.259777i	−0.879474	−	0.475947i	$-0.842105\pi$
$43$	−1.55676	+	0.259777i	−1.55676	+	0.259777i	−0.677282	+	0.735724i	$0.736842\pi$
$44$	0.464369	−	0.159418i	0.464369	−	0.159418i
$45$		0			0
$46$		0			0
$47$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$47$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$48$	−1.28117	−	0.439826i	−1.28117	−	0.439826i
$49$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$50$	0.945817	−	0.324699i	0.945817	−	0.324699i
$51$	−2.09544	+	1.13399i	−2.09544	+	1.13399i
$52$		0			0
$53$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$53$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$54$	0.223718			0.223718
$55$		0			0
$56$		0			0
$57$	1.33609	+	0.222954i	1.33609	+	0.222954i
$58$		0			0
$59$	1.49277	+	0.512467i	1.49277	+	0.512467i	0.945817	−	0.324699i	$-0.105263\pi$
$59$	1.49277	+	0.512467i	1.49277	+	0.512467i	0.546948	+	0.837166i	$0.315789\pi$
$60$		0			0
$61$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$61$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$62$		0			0
$63$		0			0
$64$	−0.677282	−	0.735724i	−0.677282	−	0.735724i
$65$		0			0
$66$	0.655981	−	0.109464i	0.655981	−	0.109464i
$67$	0.0663435	−	0.151248i	0.0663435	−	0.151248i	−0.879474	−	0.475947i	$-0.842105\pi$
$67$	0.0663435	−	0.151248i	0.0663435	−	0.151248i	0.945817	+	0.324699i	$0.105263\pi$
$68$	−1.75895			−1.75895
$69$		0			0
$70$		0			0
$71$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$71$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$72$	−0.734221	−	0.397341i	−0.734221	−	0.397341i
$73$	0.464369	−	1.83375i	0.464369	−	1.83375i	−0.0825793	−	0.996584i	$-0.526316\pi$
$73$	0.464369	−	1.83375i	0.464369	−	1.83375i	0.546948	−	0.837166i	$-0.315789\pi$
$74$		0			0
$75$	1.33609	−	0.222954i	1.33609	−	0.222954i
$76$	0.789141	+	0.614213i	0.789141	+	0.614213i
$77$		0			0
$78$		0			0
$79$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$79$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$80$		0			0
$81$	1.12236	+	0.187289i	1.12236	+	0.187289i
$82$	−0.740876	−	1.13399i	−0.740876	−	1.13399i
$83$	1.54695	+	0.837166i	1.54695	+	0.837166i	1.00000			$0$
$83$	1.54695	+	0.837166i	1.54695	+	0.837166i	0.546948	+	0.837166i	$0.315789\pi$
$84$		0			0
$85$		0			0
$86$	−1.38806	−	0.751179i	−1.38806	−	0.751179i
$87$		0			0
$88$	0.464369	+	0.159418i	0.464369	+	0.159418i
$89$	−0.431796	−	1.70512i	−0.431796	−	1.70512i	−0.677282	−	0.735724i	$-0.736842\pi$
$89$	−0.431796	−	1.70512i	−0.431796	−	1.70512i	0.245485	−	0.969400i	$-0.421053\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.740876	−	1.13399i	−0.740876	−	1.13399i
$97$	−0.803391	−	1.83155i	−0.803391	−	1.83155i	−0.401695	−	0.915773i	$-0.631579\pi$
$97$	−0.803391	−	1.83155i	−0.803391	−	1.83155i	−0.401695	−	0.915773i	$-0.631579\pi$
$98$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$99$	0.409883			0.409883
$100$	0.945817	+	0.324699i	0.945817	+	0.324699i
$101$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$101$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$102$	−2.35011	−	0.392164i	−2.35011	−	0.392164i
$103$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$103$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.49277	+	1.16187i	1.49277	+	1.16187i	0.945817	+	0.324699i	$0.105263\pi$
$107$	1.49277	+	1.16187i	1.49277	+	1.16187i	0.546948	+	0.837166i	$0.315789\pi$
$108$	0.176545	+	0.137410i	0.176545	+	0.137410i
$109$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$109$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.387445	+	1.52999i	0.387445	+	1.52999i	0.789141	+	0.614213i	$0.210526\pi$
$113$	0.387445	+	1.52999i	0.387445	+	1.52999i	−0.401695	+	0.915773i	$0.631579\pi$
$114$	0.917421	+	0.996584i	0.917421	+	0.996584i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.863238	+	1.32128i	0.863238	+	1.32128i
$119$		0			0
$120$		0			0
$121$	0.748596	−	0.124919i	0.748596	−	0.124919i
$122$		0			0
$123$	−0.737047	−	1.68030i	−0.737047	−	1.68030i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−0.0825793	−	0.996584i	−0.0825793	−	0.996584i
$129$	−1.68709	−	1.31311i	−1.68709	−	1.31311i
$130$		0			0
$131$	−1.38806	+	1.08037i	−1.38806	+	1.08037i	−0.401695	+	0.915773i	$0.631579\pi$
$131$	−1.38806	+	1.08037i	−1.38806	+	1.08037i	−0.986361	+	0.164595i	$0.947368\pi$
$132$	0.584895	+	0.316529i	0.584895	+	0.316529i
$133$		0			0
$134$	0.145253	−	0.0786068i	0.145253	−	0.0786068i
$135$		0			0
$136$	−1.38806	−	1.08037i	−1.38806	−	1.08037i
$137$	0.792434	−	1.80657i	0.792434	−	1.80657i	0.245485	−	0.969400i	$-0.421053\pi$
$137$	0.792434	−	1.80657i	0.792434	−	1.80657i	0.546948	−	0.837166i	$-0.315789\pi$
$138$		0			0
$139$	−1.07898	+	0.180049i	−1.07898	+	0.180049i	−0.677282	−	0.735724i	$-0.736842\pi$
$139$	−1.07898	+	0.180049i	−1.07898	+	0.180049i	−0.401695	+	0.915773i	$0.631579\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.335352	−	0.764525i	−0.335352	−	0.764525i
$145$		0			0
$146$	1.49277	−	1.16187i	1.49277	−	1.16187i
$147$	−0.332526	−	1.31311i	−0.332526	−	1.31311i
$148$		0			0
$149$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$149$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$150$	1.19130	+	0.644701i	1.19130	+	0.644701i
$151$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$151$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$152$	0.245485	+	0.969400i	0.245485	+	0.969400i
$153$	−1.38888	−	0.476802i	−1.38888	−	0.476802i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$157$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.770666	+	0.837166i	0.770666	+	0.837166i
$163$	0.863238	+	0.671885i	0.863238	+	0.671885i	0.945817	−	0.324699i	$-0.105263\pi$
$163$	0.863238	+	0.671885i	0.863238	+	0.671885i	−0.0825793	+	0.996584i	$0.526316\pi$
$164$	0.111859	−	1.34994i	0.111859	−	1.34994i
$165$		0			0
$166$	0.706561	+	1.61080i	0.706561	+	1.61080i
$167$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$167$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$168$		0			0
$169$	−0.0825793	+	0.996584i	−0.0825793	+	0.996584i
$170$		0			0
$171$	0.456615	+	0.698901i	0.456615	+	0.698901i
$172$	−0.633988	−	1.44535i	−0.633988	−	1.44535i
$173$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$173$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$174$		0			0
$175$		0			0
$176$	0.268536	+	0.411024i	0.268536	+	0.411024i
$177$	0.858777	+	1.95781i	0.858777	+	1.95781i
$178$	0.706561	−	1.61080i	0.706561	−	1.61080i
$179$	−1.55676	−	0.259777i	−1.55676	−	0.259777i	−0.677282	−	0.735724i	$-0.736842\pi$
$179$	−1.55676	−	0.259777i	−1.55676	−	0.259777i	−0.879474	+	0.475947i	$0.842105\pi$
$180$		0			0
$181$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$181$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.851814	+	0.142143i	0.851814	+	0.142143i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$191$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$192$	0.111859	−	1.34994i	0.111859	−	1.34994i
$193$	0.0136387	+	0.164595i	0.0136387	+	0.164595i	1.00000			$0$
$193$	0.0136387	+	0.164595i	0.0136387	+	0.164595i	−0.986361	+	0.164595i	$0.947368\pi$
$194$	0.490971	−	1.93880i	0.490971	−	1.93880i
$195$		0			0
$196$	0.245485	−	0.969400i	0.245485	−	0.969400i
$197$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$197$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$198$	0.323455	+	0.251755i	0.323455	+	0.251755i
$199$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$199$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$200$	0.546948	+	0.837166i	0.546948	+	0.837166i
$201$	0.211596	−	0.0726411i	0.211596	−	0.0726411i
$202$		0			0
$203$		0			0
$204$	−1.61369	−	1.75294i	−1.61369	−	1.75294i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.332526	−	0.361219i	−0.332526	−	0.361219i
$210$		0			0
$211$	0.706561	+	0.382372i	0.706561	+	0.382372i	0.789141	−	0.614213i	$-0.210526\pi$
$211$	0.706561	+	0.382372i	0.706561	+	0.382372i	−0.0825793	+	0.996584i	$0.526316\pi$
$212$		0			0
$213$		0			0
$214$	0.464369	+	1.83375i	0.464369	+	1.83375i
$215$		0			0
$216$	0.0549195	+	0.216872i	0.0549195	+	0.216872i
$217$		0			0
$218$		0			0
$219$	2.25351	−	1.21954i	2.25351	−	1.21954i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$223$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$224$		0			0
$225$	0.658807	+	0.512770i	0.658807	+	0.512770i
$226$	−0.633988	+	1.44535i	−0.633988	+	1.44535i
$227$	0.706561	−	0.382372i	0.706561	−	0.382372i	−0.0825793	−	0.996584i	$-0.526316\pi$
$227$	0.706561	−	0.382372i	0.706561	−	0.382372i	0.789141	+	0.614213i	$0.210526\pi$
$228$	0.111859	+	1.34994i	0.111859	+	1.34994i
$229$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$229$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.165159	−	1.99317i	−0.165159	−	1.99317i	−0.0825793	−	0.996584i	$-0.526316\pi$
$233$	−0.165159	−	1.99317i	−0.165159	−	1.99317i	−0.0825793	−	0.996584i	$-0.526316\pi$
$234$		0			0
$235$		0			0
$236$	−0.130333	+	1.57289i	−0.130333	+	1.57289i
$237$		0			0
$238$		0			0
$239$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$239$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$240$		0			0
$241$	−1.28117	+	1.39172i	−1.28117	+	1.39172i	−0.401695	+	0.915773i	$0.631579\pi$
$241$	−1.28117	+	1.39172i	−1.28117	+	1.39172i	−0.879474	+	0.475947i	$0.842105\pi$
$242$	0.667474	+	0.361219i	0.667474	+	0.361219i
$243$	0.720667	+	1.10306i	0.720667	+	1.10306i
$244$		0			0
$245$		0			0
$246$	0.450427	−	1.77870i	0.450427	−	1.77870i
$247$		0			0
$248$		0			0
$249$	0.584895	+	2.30970i	0.584895	+	2.30970i
$250$		0			0
$251$	−0.0405441	+	0.489294i	−0.0405441	+	0.489294i	0.945817	+	0.324699i	$0.105263\pi$
$251$	−0.0405441	+	0.489294i	−0.0405441	+	0.489294i	−0.986361	+	0.164595i	$0.947368\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.546948	−	0.837166i	0.546948	−	0.837166i
$257$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i	−0.401695	−	0.915773i	$-0.631579\pi$
$257$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i	0.245485	+	0.969400i	$0.421053\pi$
$258$	−0.524819	−	2.07246i	−0.524819	−	2.07246i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.75895			−1.75895
$263$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$263$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$264$	0.267148	+	0.609036i	0.267148	+	0.609036i
$265$		0			0
$266$		0			0
$267$	1.30316	−	1.99464i	1.30316	−	1.99464i
$268$	0.162906	+	0.0271842i	0.162906	+	0.0271842i
$269$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$269$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$270$		0			0
$271$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$271$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$272$	−0.431796	−	1.70512i	−0.431796	−	1.70512i
$273$		0			0
$274$	1.73496	−	0.938912i	1.73496	−	0.938912i
$275$	−0.431796	−	0.233676i	−0.431796	−	0.233676i
$276$		0			0
$277$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$277$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$278$	−0.962053	−	0.520637i	−0.962053	−	0.520637i
$279$		0			0
$280$		0			0
$281$	−0.439413	+	0.672572i	−0.439413	+	0.672572i	−0.986361	−	0.164595i	$-0.947368\pi$
$281$	−0.439413	+	0.672572i	−0.439413	+	0.672572i	0.546948	+	0.837166i	$0.315789\pi$
$282$		0			0
$283$	−1.35456	+	1.47145i	−1.35456	+	1.47145i	−0.677282	+	0.735724i	$0.736842\pi$
$283$	−1.35456	+	1.47145i	−1.35456	+	1.47145i	−0.677282	+	0.735724i	$0.736842\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.204941	−	0.809295i	0.204941	−	0.809295i
$289$	−1.84153	−	0.996584i	−1.84153	−	0.996584i
$290$		0			0
$291$	1.08824	−	2.48095i	1.08824	−	2.48095i
$292$	1.89163			1.89163
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	0.544122	−	1.24047i	0.544122	−	1.24047i
$295$		0			0
$296$		0			0
$297$	−0.0743919	−	0.0808112i	−0.0743919	−	0.0808112i
$298$		0			0
$299$		0			0
$300$	0.544122	+	1.24047i	0.544122	+	1.24047i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$305$		0			0
$306$	−0.803162	−	1.22933i	−0.803162	−	1.22933i
$307$	−1.35456			−1.35456			−0.677282	−	0.735724i	$-0.736842\pi$
$307$	−1.35456			−1.35456			−0.677282	+	0.735724i	$0.736842\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$311$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$312$		0			0
$313$	−1.86584	−	0.640542i	−1.86584	−	0.640542i	−0.986361	−	0.164595i	$-0.947368\pi$
$313$	−1.86584	−	0.640542i	−1.86584	−	0.640542i	−0.879474	−	0.475947i	$-0.842105\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$317$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.211596	+	2.55359i	0.211596	+	2.55359i
$322$		0			0
$323$	0.706561	+	1.61080i	0.706561	+	1.61080i
$324$	0.0939655	+	1.13399i	0.0939655	+	1.13399i
$325$		0			0
$326$	0.268536	+	1.06042i	0.268536	+	1.06042i
$327$		0			0
$328$	0.917421	−	0.996584i	0.917421	−	0.996584i
$329$		0			0
$330$		0			0
$331$	−0.439413	−	0.672572i	−0.439413	−	0.672572i	0.546948	−	0.837166i	$-0.315789\pi$
$331$	−0.439413	−	0.672572i	−0.439413	−	0.672572i	−0.986361	+	0.164595i	$0.947368\pi$
$332$	−0.431796	+	1.70512i	−0.431796	+	1.70512i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.03463	−	0.355188i	1.03463	−	0.355188i	0.245485	−	0.969400i	$-0.421053\pi$
$337$	1.03463	−	0.355188i	1.03463	−	0.355188i	0.789141	+	0.614213i	$0.210526\pi$
$338$	−0.677282	+	0.735724i	−0.677282	+	0.735724i
$339$	−1.16931	+	1.78976i	−1.16931	+	1.78976i
$340$		0			0
$341$		0			0
$342$	−0.0689406	+	0.831990i	−0.0689406	+	0.831990i
$343$		0			0
$344$	0.387445	−	1.52999i	0.387445	−	1.52999i
$345$		0			0
$346$		0			0
$347$	0.387445	−	0.301561i	0.387445	−	0.301561i	−0.401695	−	0.915773i	$-0.631579\pi$
$347$	0.387445	−	0.301561i	0.387445	−	0.301561i	0.789141	+	0.614213i	$0.210526\pi$
$348$		0			0
$349$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$349$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$350$		0			0
$351$		0			0
$352$	−0.0405441	+	0.489294i	−0.0405441	+	0.489294i
$353$	−0.439413	+	1.00176i	−0.439413	+	1.00176i	0.546948	+	0.837166i	$0.315789\pi$
$353$	−0.439413	+	1.00176i	−0.439413	+	1.00176i	−0.986361	+	0.164595i	$0.947368\pi$
$354$	−0.524819	+	2.07246i	−0.524819	+	2.07246i
$355$		0			0
$356$	1.54695	−	0.837166i	1.54695	−	0.837166i
$357$		0			0
$358$	−1.06894	−	1.16118i	−1.06894	−	1.16118i
$359$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$359$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$360$		0			0
$361$	0.245485	−	0.969400i	0.245485	−	0.969400i
$362$		0			0
$363$	0.811270	+	0.631437i	0.811270	+	0.631437i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$367$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$368$		0			0
$369$	0.454255	−	1.03560i	0.454255	−	1.03560i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$373$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$374$	0.584895	+	0.635365i	0.584895	+	0.635365i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.111859	−	0.121511i	0.111859	−	0.121511i	−0.677282	−	0.735724i	$-0.736842\pi$
$379$	0.111859	−	0.121511i	0.111859	−	0.121511i	0.789141	+	0.614213i	$0.210526\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$383$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$384$	0.917421	−	0.996584i	0.917421	−	0.996584i
$385$		0			0
$386$	−0.0903332	+	0.138265i	−0.0903332	+	0.138265i
$387$	−0.108808	−	1.31311i	−0.108808	−	1.31311i
$388$	1.57828	−	1.22843i	1.57828	−	1.22843i
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	0.789141	−	0.614213i	0.789141	−	0.614213i
$393$	−2.35011	−	0.392164i	−2.35011	−	0.392164i
$394$		0			0
$395$		0			0
$396$	0.100620	+	0.397341i	0.100620	+	0.397341i
$397$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$397$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$398$		0			0
$399$		0			0
$400$	−0.0825793	+	0.996584i	−0.0825793	+	0.996584i
$401$	0.162906	+	1.96598i	0.162906	+	1.96598i	0.245485	+	0.969400i	$0.421053\pi$
$401$	0.162906	+	1.96598i	0.162906	+	1.96598i	−0.0825793	+	0.996584i	$0.526316\pi$
$402$	0.211596	+	0.0726411i	0.211596	+	0.0726411i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.196754	−	2.37447i	−0.196754	−	2.37447i
$409$	−0.759861	−	0.260861i	−0.759861	−	0.260861i	−0.0825793	−	0.996584i	$-0.526316\pi$
$409$	−0.759861	−	0.260861i	−0.759861	−	0.260861i	−0.677282	+	0.735724i	$0.736842\pi$
$410$		0			0
$411$	2.52739	−	0.867655i	2.52739	−	0.867655i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.16931	−	0.910111i	−1.16931	−	0.910111i
$418$	−0.0405441	−	0.489294i	−0.0405441	−	0.489294i
$419$	0.387445	−	0.301561i	0.387445	−	0.301561i	−0.401695	−	0.915773i	$-0.631579\pi$
$419$	0.387445	−	0.301561i	0.387445	−	0.301561i	0.789141	+	0.614213i	$0.210526\pi$
$420$		0			0
$421$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$421$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$422$	0.322718	+	0.735724i	0.322718	+	0.735724i
$423$		0			0
$424$		0			0
$425$	1.19130	+	1.29410i	1.19130	+	1.29410i
$426$		0			0
$427$		0			0
$428$	−0.759861	+	1.73231i	−0.759861	+	1.73231i
$429$		0			0
$430$		0			0
$431$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$431$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$432$	−0.0898664	+	0.204875i	−0.0898664	+	0.204875i
$433$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.945817	−	0.324699i	$-0.105263\pi$
$433$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.245485	+	0.969400i	$0.421053\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	2.52739	+	0.421747i	2.52739	+	0.421747i
$439$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$439$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$440$		0			0
$441$	0.456615	−	0.698901i	0.456615	−	0.698901i
$442$		0			0
$443$	0.863238	+	1.32128i	0.863238	+	1.32128i	0.945817	+	0.324699i	$0.105263\pi$
$443$	0.863238	+	1.32128i	0.863238	+	1.32128i	−0.0825793	+	0.996584i	$0.526316\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.28117	−	0.439826i	−1.28117	−	0.439826i	−0.401695	−	0.915773i	$-0.631579\pi$
$449$	−1.28117	−	0.439826i	−1.28117	−	0.439826i	−0.879474	+	0.475947i	$0.842105\pi$
$450$	0.204941	+	0.809295i	0.204941	+	0.809295i
$451$	−0.163260	+	0.644701i	−0.163260	+	0.644701i
$452$	−1.38806	+	0.751179i	−1.38806	+	0.751179i
$453$		0			0
$454$	0.792434	+	0.132234i	0.792434	+	0.132234i
$455$		0			0
$456$	−0.740876	+	1.13399i	−0.740876	+	1.13399i
$457$	−0.439413	−	0.672572i	−0.439413	−	0.672572i	0.546948	−	0.837166i	$-0.315789\pi$
$457$	−0.439413	−	0.672572i	−0.439413	−	0.672572i	−0.986361	+	0.164595i	$0.947368\pi$
$458$		0			0
$459$	0.158070	+	0.360364i	0.158070	+	0.360364i
$460$		0			0
$461$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$461$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$462$		0			0
$463$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$463$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$464$		0			0
$465$		0			0
$466$	1.09390	−	1.67433i	1.09390	−	1.67433i
$467$	1.03463	−	1.58361i	1.03463	−	1.58361i	0.245485	−	0.969400i	$-0.421053\pi$
$467$	1.03463	−	1.58361i	1.03463	−	1.58361i	0.789141	−	0.614213i	$-0.210526\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.06894	+	1.16118i	−1.06894	+	1.16118i
$473$	0.190224	+	0.751179i	0.190224	+	0.751179i
$474$		0			0
$475$	−0.0825793	−	0.996584i	−0.0825793	−	0.996584i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$479$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$480$		0			0
$481$		0			0
$482$	−1.86584	+	0.311353i	−1.86584	+	0.311353i
$483$		0			0
$484$	0.304866	+	0.695024i	0.304866	+	0.695024i
$485$		0			0
$486$	−0.108808	+	1.31311i	−0.108808	+	1.31311i
$487$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$487$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$488$		0			0
$489$	0.122362	+	1.47669i	0.122362	+	1.47669i
$490$		0			0
$491$	−1.07898	−	1.65150i	−1.07898	−	1.65150i	−0.677282	−	0.735724i	$-0.736842\pi$
$491$	−1.07898	−	1.65150i	−1.07898	−	1.65150i	−0.401695	−	0.915773i	$-0.631579\pi$
$492$	1.44795	−	1.12698i	1.44795	−	1.12698i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.957082	+	2.18193i	−0.957082	+	2.18193i
$499$	−0.633988	−	0.493453i	−0.633988	−	0.493453i	0.245485	−	0.969400i	$-0.421053\pi$
$499$	−0.633988	−	0.493453i	−0.633988	−	0.493453i	−0.879474	+	0.475947i	$0.842105\pi$
$500$		0			0
$501$		0			0
$502$	−0.332526	+	0.361219i	−0.332526	+	0.361219i
$503$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$503$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.06894	+	0.831990i	−1.06894	+	0.831990i
$508$		0			0
$509$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$509$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$510$		0			0
$511$		0			0
$512$	0.945817	−	0.324699i	0.945817	−	0.324699i
$513$	0.0549195	−	0.216872i	0.0549195	−	0.216872i
$514$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i
$515$		0			0
$516$	0.858777	−	1.95781i	0.858777	−	1.95781i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.464369	−	0.159418i	0.464369	−	0.159418i	−0.0825793	−	0.996584i	$-0.526316\pi$
$521$	0.464369	−	0.159418i	0.464369	−	0.159418i	0.546948	+	0.837166i	$0.315789\pi$
$522$		0			0
$523$	1.19130	+	1.29410i	1.19130	+	1.29410i	0.945817	+	0.324699i	$0.105263\pi$
$523$	1.19130	+	1.29410i	1.19130	+	1.29410i	0.245485	+	0.969400i	$0.421053\pi$
$524$	−1.38806	−	1.08037i	−1.38806	−	1.08037i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.163260	+	0.644701i	−0.163260	+	0.644701i
$529$	−0.0825793	−	0.996584i	−0.0825793	−	0.996584i
$530$		0			0
$531$	−0.529280	+	1.20664i	−0.529280	+	1.20664i
$532$		0			0
$533$		0			0
$534$	2.25351	−	0.773631i	2.25351	−	0.773631i
$535$		0			0
$536$	0.111859	+	0.121511i	0.111859	+	0.121511i
$537$	−1.16931	−	1.78976i	−1.16931	−	1.78976i
$538$		0			0
$539$	−0.197221	+	0.449618i	−0.197221	+	0.449618i
$540$		0			0
$541$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$541$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$542$		0			0
$543$		0			0
$544$	0.706561	−	1.61080i	0.706561	−	1.61080i
$545$		0			0
$546$		0			0
$547$	0.111859	+	0.121511i	0.111859	+	0.121511i	0.789141	−	0.614213i	$-0.210526\pi$
$547$	0.111859	+	0.121511i	0.111859	+	0.121511i	−0.677282	+	0.735724i	$0.736842\pi$
$548$	1.94582	+	0.324699i	1.94582	+	0.324699i
$549$		0			0
$550$	−0.197221	−	0.449618i	−0.197221	−	0.449618i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.439413	−	1.00176i	−0.439413	−	1.00176i
$557$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$557$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.639815	+	0.979309i	0.639815	+	0.979309i
$562$	−0.759861	+	0.260861i	−0.759861	+	0.260861i
$563$	−1.28117	+	1.39172i	−1.28117	+	1.39172i	−0.401695	+	0.915773i	$0.631579\pi$
$563$	−1.28117	+	1.39172i	−1.28117	+	1.39172i	−0.879474	+	0.475947i	$0.842105\pi$
$564$		0			0
$565$		0			0
$566$	−1.97272	+	0.329189i	−1.97272	+	0.329189i
$567$		0			0
$568$		0			0
$569$	−1.86584	−	0.640542i	−1.86584	−	0.640542i	−0.986361	−	0.164595i	$-0.947368\pi$
$569$	−1.86584	−	0.640542i	−1.86584	−	0.640542i	−0.879474	−	0.475947i	$-0.842105\pi$
$570$		0			0
$571$	1.78914	−	0.614213i	1.78914	−	0.614213i	0.789141	−	0.614213i	$-0.210526\pi$
$571$	1.78914	−	0.614213i	1.78914	−	0.614213i	1.00000			$0$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.658807	−	0.512770i	0.658807	−	0.512770i
$577$	−0.332526	−	1.31311i	−0.332526	−	1.31311i	−0.879474	−	0.475947i	$-0.842105\pi$
$577$	−0.332526	−	1.31311i	−0.332526	−	1.31311i	0.546948	−	0.837166i	$-0.315789\pi$
$578$	−0.841109	−	1.91753i	−0.841109	−	1.91753i
$579$	−0.151520	+	0.164595i	−0.151520	+	0.164595i
$580$		0			0
$581$		0			0
$582$	2.38261	−	1.28940i	2.38261	−	1.28940i
$583$		0			0
$584$	1.49277	+	1.16187i	1.49277	+	1.16187i
$585$		0			0
$586$		0			0
$587$	−0.197221	+	0.449618i	−0.197221	+	0.449618i	−0.986361	−	0.164595i	$-0.947368\pi$
$587$	−0.197221	+	0.449618i	−0.197221	+	0.449618i	0.789141	+	0.614213i	$0.210526\pi$
$588$	1.19130	−	0.644701i	1.19130	−	0.644701i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.863238	+	0.671885i	0.863238	+	0.671885i	0.945817	−	0.324699i	$-0.105263\pi$
$593$	0.863238	+	0.671885i	0.863238	+	0.671885i	−0.0825793	+	0.996584i	$0.526316\pi$
$594$	−0.00907043	−	0.109464i	−0.00907043	−	0.109464i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$599$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$600$	−0.332526	+	1.31311i	−0.332526	+	1.31311i
$601$	−1.97272	+	0.329189i	−1.97272	+	0.329189i	−0.986361	+	0.164595i	$0.947368\pi$
$601$	−1.97272	+	0.329189i	−1.97272	+	0.329189i	−0.986361	+	0.164595i	$0.947368\pi$
$602$		0			0
$603$	0.121263	+	0.0656242i	0.121263	+	0.0656242i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$607$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$608$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.121263	−	1.46343i	0.121263	−	1.46343i
$613$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$613$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$614$	−1.06894	−	0.831990i	−1.06894	−	0.831990i
$615$		0			0
$616$		0			0
$617$	−0.962053	+	1.47253i	−0.962053	+	1.47253i	−0.0825793	+	0.996584i	$0.526316\pi$
$617$	−0.962053	+	1.47253i	−0.962053	+	1.47253i	−0.879474	+	0.475947i	$0.842105\pi$
$618$		0			0
$619$	−0.197221	−	0.778807i	−0.197221	−	0.778807i	−0.986361	−	0.164595i	$-0.947368\pi$
$619$	−0.197221	−	0.778807i	−0.197221	−	0.778807i	0.789141	−	0.614213i	$-0.210526\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$626$	−1.07898	−	1.65150i	−1.07898	−	1.65150i
$627$	0.0549195	−	0.662780i	0.0549195	−	0.662780i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$631$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$632$		0			0
$633$	0.267148	+	1.05494i	0.267148	+	1.05494i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.55676	−	0.259777i	−1.55676	−	0.259777i	−0.677282	−	0.735724i	$-0.736842\pi$
$641$	−1.55676	−	0.259777i	−1.55676	−	0.259777i	−0.879474	+	0.475947i	$0.842105\pi$
$642$	−1.40147	+	2.14510i	−1.40147	+	2.14510i
$643$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.986361	−	0.164595i	$-0.947368\pi$
$643$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.879474	+	0.475947i	$0.842105\pi$
$644$		0			0
$645$		0			0
$646$	−0.431796	+	1.70512i	−0.431796	+	1.70512i
$647$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$647$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$648$	−0.622362	+	0.952596i	−0.622362	+	0.952596i
$649$	0.190224	−	0.751179i	0.190224	−	0.751179i
$650$		0			0
$651$		0			0
$652$	−0.439413	+	1.00176i	−0.439413	+	1.00176i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$	1.33609	−	0.222954i	1.33609	−	0.222954i
$657$	1.49365	+	0.512770i	1.49365	+	0.512770i
$658$		0			0
$659$	0.464369	+	0.159418i	0.464369	+	0.159418i	0.546948	−	0.837166i	$-0.315789\pi$
$659$	0.464369	+	0.159418i	0.464369	+	0.159418i	−0.0825793	+	0.996584i	$0.526316\pi$
$660$		0			0
$661$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$661$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$662$	0.0663435	−	0.800647i	0.0663435	−	0.800647i
$663$		0			0
$664$	−1.38806	+	1.08037i	−1.38806	+	1.08037i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.945817	−	0.324699i	$-0.105263\pi$
$673$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.245485	+	0.969400i	$0.421053\pi$
$674$	1.03463	+	0.355188i	1.03463	+	0.355188i
$675$	−0.0184745	−	0.222954i	−0.0184745	−	0.222954i
$676$	−0.986361	+	0.164595i	−0.986361	+	0.164595i
$677$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$677$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$678$	−2.02204	+	0.694169i	−2.02204	+	0.694169i
$679$		0			0
$680$		0			0
$681$	1.02928	+	0.353352i	1.02928	+	0.353352i
$682$		0			0
$683$	0.111859	−	1.34994i	0.111859	−	1.34994i	−0.677282	−	0.735724i	$-0.736842\pi$
$683$	0.111859	−	1.34994i	0.111859	−	1.34994i	0.789141	−	0.614213i	$-0.210526\pi$
$684$	−0.565423	+	0.614213i	−0.565423	+	0.614213i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.24549	−	0.969400i	1.24549	−	0.969400i
$689$		0			0
$690$		0			0
$691$	−0.130333	+	0.101443i	−0.130333	+	0.101443i	−0.677282	−	0.735724i	$-0.736842\pi$
$691$	−0.130333	+	0.101443i	−0.130333	+	0.101443i	0.546948	+	0.837166i	$0.315789\pi$
$692$		0			0
$693$		0			0
$694$	0.490971			0.490971
$695$		0			0
$696$		0			0
$697$	1.30316	−	1.99464i	1.30316	−	1.99464i
$698$		0			0
$699$	1.83484	−	1.99317i	1.83484	−	1.99317i
$700$		0			0
$701$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$701$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$702$		0			0
$703$		0			0
$704$	−0.332526	+	0.361219i	−0.332526	+	0.361219i
$705$		0			0
$706$	−0.962053	+	0.520637i	−0.962053	+	0.520637i
$707$		0			0
$708$	−1.68709	+	1.31311i	−1.68709	+	1.31311i
$709$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$709$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$710$		0			0
$711$		0			0
$712$	1.73496	+	0.289513i	1.73496	+	0.289513i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.130333	−	1.57289i	−0.130333	−	1.57289i
$717$		0			0
$718$		0			0
$719$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$719$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$720$		0			0
$721$		0			0
$722$	0.789141	−	0.614213i	0.789141	−	0.614213i
$723$	−2.56234			−2.56234
$724$		0			0
$725$		0			0
$726$	0.252369	+	0.996584i	0.252369	+	0.996584i
$727$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$727$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$728$		0			0
$729$	−0.158807	+	0.627115i	−0.158807	+	0.627115i
$730$		0			0
$731$	0.229250	−	2.76663i	0.229250	−	2.76663i
$732$		0			0
$733$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$733$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.0766945	−	0.0263293i	−0.0766945	−	0.0263293i
$738$	0.994549	−	0.538223i	0.994549	−	0.538223i
$739$	0.268536	−	1.06042i	0.268536	−	1.06042i	−0.677282	−	0.735724i	$-0.736842\pi$
$739$	0.268536	−	1.06042i	0.268536	−	1.06042i	0.945817	−	0.324699i	$-0.105263\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$743$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.803162	+	1.22933i	−0.803162	+	1.22933i
$748$	0.0713149	+	0.860643i	0.0713149	+	0.860643i
$749$		0			0
$750$		0			0
$751$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$751$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$752$		0			0
$753$	−0.524819	+	0.408483i	−0.524819	+	0.408483i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$757$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$758$	0.162906	−	0.0271842i	0.162906	−	0.0271842i
$759$		0			0
$760$		0			0
$761$	−0.156210	+	1.88517i	−0.156210	+	1.88517i	0.245485	+	0.969400i	$0.421053\pi$
$761$	−0.156210	+	1.88517i	−0.156210	+	1.88517i	−0.401695	+	0.915773i	$0.631579\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.33609	−	0.222954i	1.33609	−	0.222954i
$769$	0.0136387	+	0.164595i	0.0136387	+	0.164595i	1.00000			$0$
$769$	0.0136387	+	0.164595i	0.0136387	+	0.164595i	−0.986361	+	0.164595i	$0.947368\pi$
$770$		0			0
$771$	−0.196754	−	0.106478i	−0.196754	−	0.106478i
$772$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i
$773$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$773$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$774$	0.720667	−	1.10306i	0.720667	−	1.10306i
$775$		0			0
$776$	2.00000			2.00000
$777$		0			0
$778$		0			0
$779$	−1.28117	+	0.439826i	−1.28117	+	0.439826i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.00000			1.00000
$785$		0			0
$786$	−1.61369	−	1.75294i	−1.61369	−	1.75294i
$787$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i	0.245485	−	0.969400i	$-0.421053\pi$
$787$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i	−0.401695	+	0.915773i	$0.631579\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.164648	+	0.375360i	−0.164648	+	0.375360i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$797$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$798$		0			0
$799$		0			0
$800$	−0.677282	+	0.735724i	−0.677282	+	0.735724i
$801$	1.44841	−	0.241698i	1.44841	−	0.241698i
$802$	−1.07898	+	1.65150i	−1.07898	+	1.65150i
$803$	−0.916071	−	0.152865i	−0.916071	−	0.152865i
$804$	0.122362	+	0.187289i	0.122362	+	0.187289i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.19130	−	0.644701i	1.19130	−	0.644701i	0.245485	−	0.969400i	$-0.421053\pi$
$809$	1.19130	−	0.644701i	1.19130	−	0.644701i	0.945817	+	0.324699i	$0.105263\pi$
$810$		0			0
$811$	0.464369	+	1.83375i	0.464369	+	1.83375i	0.546948	+	0.837166i	$0.315789\pi$
$811$	0.464369	+	1.83375i	0.464369	+	1.83375i	−0.0825793	+	0.996584i	$0.526316\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.30316	−	1.99464i	1.30316	−	1.99464i
$817$	−1.06894	+	1.16118i	−1.06894	+	1.16118i
$818$	−0.439413	−	0.672572i	−0.439413	−	0.672572i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	2.52739	+	0.867655i	2.52739	+	0.867655i
$823$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$823$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$824$		0			0
$825$	−0.163260	−	0.644701i	−0.163260	−	0.644701i
$826$		0			0
$827$	−0.740876	+	1.13399i	−0.740876	+	1.13399i	0.245485	+	0.969400i	$0.421053\pi$
$827$	−0.740876	+	1.13399i	−0.740876	+	1.13399i	−0.986361	+	0.164595i	$0.947368\pi$
$828$		0			0
$829$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$829$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.19130	−	1.29410i	1.19130	−	1.29410i
$834$	−0.363749	−	1.43641i	−0.363749	−	1.43641i
$835$		0			0
$836$	0.268536	−	0.411024i	0.268536	−	0.411024i
$837$		0			0
$838$	0.490971			0.490971
$839$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$839$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$840$		0			0
$841$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$842$		0			0
$843$	−1.07340	+	0.179119i	−1.07340	+	0.179119i
$844$	−0.197221	+	0.778807i	−0.197221	+	0.778807i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.70913			−2.70913
$850$	0.145253	+	1.75294i	0.145253	+	1.75294i
$851$		0			0
$852$		0			0
$853$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$853$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$854$		0			0
$855$		0			0
$856$	−1.66364	+	0.900319i	−1.66364	+	0.900319i
$857$	0.322718	−	0.735724i	0.322718	−	0.735724i	−0.677282	−	0.735724i	$-0.736842\pi$
$857$	0.322718	−	0.735724i	0.322718	−	0.735724i	1.00000			$0$
$858$		0			0
$859$	0.706561	−	1.61080i	0.706561	−	1.61080i	−0.0825793	−	0.996584i	$-0.526316\pi$
$859$	0.706561	−	1.61080i	0.706561	−	1.61080i	0.789141	−	0.614213i	$-0.210526\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$863$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$864$	−0.196754	+	0.106478i	−0.196754	+	0.106478i
$865$		0			0
$866$	0.544122	+	1.24047i	0.544122	+	1.24047i
$867$	−0.696274	−	2.74952i	−0.696274	−	2.74952i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.57921	−	0.542145i	1.57921	−	0.542145i
$874$		0			0
$875$		0			0
$876$	1.73542	+	1.88517i	1.73542	+	1.88517i
$877$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$877$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.06894	+	1.16118i	−1.06894	+	1.16118i	−0.0825793	+	0.996584i	$0.526316\pi$
$881$	−1.06894	+	1.16118i	−1.06894	+	1.16118i	−0.986361	+	0.164595i	$0.947368\pi$
$882$	0.789607	−	0.271073i	0.789607	−	0.271073i
$883$	−0.962053	−	1.47253i	−0.962053	−	1.47253i	−0.879474	−	0.475947i	$-0.842105\pi$
$883$	−0.962053	−	1.47253i	−0.962053	−	1.47253i	−0.0825793	−	0.996584i	$-0.526316\pi$
$884$		0			0
$885$		0			0
$886$	−0.130333	+	1.57289i	−0.130333	+	1.57289i
$887$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$887$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.0461343	−	0.556759i	0.0461343	−	0.556759i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.740876	−	1.13399i	−0.740876	−	1.13399i
$899$		0			0
$900$	−0.335352	+	0.764525i	−0.335352	+	0.764525i
$901$		0			0
$902$	−0.524819	+	0.408483i	−0.524819	+	0.408483i
$903$		0			0
$904$	−1.55676	−	0.259777i	−1.55676	−	0.259777i
$905$		0			0
$906$		0			0
$907$	0.598305	+	0.915773i	0.598305	+	0.915773i	1.00000			$0$
$907$	0.598305	+	0.915773i	0.598305	+	0.915773i	−0.401695	+	0.915773i	$0.631579\pi$
$908$	0.544122	+	0.591074i	0.544122	+	0.591074i
$909$		0			0
$910$		0			0
$911$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$911$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$912$	−1.28117	+	0.439826i	−1.28117	+	0.439826i
$913$	0.346901	−	0.790855i	0.346901	−	0.790855i
$914$	0.0663435	−	0.800647i	0.0663435	−	0.800647i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.0966005	+	0.381467i	−0.0966005	+	0.381467i
$919$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$919$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$920$		0			0
$921$	−1.24270	−	1.34994i	−1.24270	−	1.34994i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.33609	+	1.45138i	1.33609	+	1.45138i	0.789141	+	0.614213i	$0.210526\pi$
$929$	1.33609	+	1.45138i	1.33609	+	1.45138i	0.546948	+	0.837166i	$0.315789\pi$
$930$		0			0
$931$	−0.986361	+	0.164595i	−0.986361	+	0.164595i
$932$	1.89163	−	0.649399i	1.89163	−	0.649399i
$933$		0			0
$934$	1.78914	−	0.614213i	1.78914	−	0.614213i
$935$		0			0
$936$		0			0
$937$	1.24549	−	0.969400i	1.24549	−	0.969400i	0.245485	−	0.969400i	$-0.421053\pi$
$937$	1.24549	−	0.969400i	1.24549	−	0.969400i	1.00000			$0$
$938$		0			0
$939$	−1.07340	−	2.44711i	−1.07340	−	2.44711i
$940$		0			0
$941$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$941$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$942$		0			0
$943$		0			0
$944$	−1.55676	+	0.259777i	−1.55676	+	0.259777i
$945$		0			0
$946$	−0.311270	+	0.709624i	−0.311270	+	0.709624i
$947$	1.24549	+	0.969400i	1.24549	+	0.969400i	1.00000			$0$
$947$	1.24549	+	0.969400i	1.24549	+	0.969400i	0.245485	+	0.969400i	$0.421053\pi$
$948$		0			0
$949$		0			0
$950$	0.546948	−	0.837166i	0.546948	−	0.837166i
$951$		0			0
$952$		0			0
$953$	0.598305	+	0.915773i	0.598305	+	0.915773i	1.00000			$0$
$953$	0.598305	+	0.915773i	0.598305	+	0.915773i	−0.401695	+	0.915773i	$0.631579\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.245485	−	0.969400i	0.245485	−	0.969400i
$962$		0			0
$963$	−1.06957	+	1.16187i	−1.06957	+	1.16187i
$964$	−1.66364	−	0.900319i	−1.66364	−	0.900319i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	−0.186311	+	0.735724i	−0.186311	+	0.735724i
$969$	−0.957082	+	2.18193i	−0.957082	+	2.18193i
$970$		0			0
$971$	0.490971	+	1.93880i	0.490971	+	1.93880i	0.245485	+	0.969400i	$0.421053\pi$
$971$	0.490971	+	1.93880i	0.490971	+	1.93880i	0.245485	+	0.969400i	$0.421053\pi$
$972$	−0.892396	+	0.969400i	−0.892396	+	0.969400i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.07898	+	1.65150i	−1.07898	+	1.65150i	−0.401695	+	0.915773i	$0.631579\pi$
$977$	−1.07898	+	1.65150i	−1.07898	+	1.65150i	−0.677282	+	0.735724i	$0.736842\pi$
$978$	−0.810441	+	1.24047i	−0.810441	+	1.24047i
$979$	−0.816800	+	0.280408i	−0.816800	+	0.280408i
$980$		0			0
$981$		0			0
$982$	0.162906	−	1.96598i	0.162906	−	1.96598i
$983$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$983$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$984$	1.83484			1.83484
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$991$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$992$		0			0
$993$	0.267148	−	1.05494i	0.267148	−	1.05494i
$994$		0			0
$995$		0			0
$996$	−2.09544	+	1.13399i	−2.09544	+	1.13399i
$997$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$997$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$998$	−0.197221	−	0.778807i	−0.197221	−	0.778807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bb.a.2395.1	yes	18
8.3	odd	2	CM	2888.1.bb.a.2395.1	yes	18
361.134	even	19	inner	2888.1.bb.a.1939.1	✓	18
2888.1939	odd	38	inner	2888.1.bb.a.1939.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bb.a.1939.1	✓	18	361.134	even	19	inner
2888.1.bb.a.1939.1	✓	18	2888.1939	odd	38	inner
2888.1.bb.a.2395.1	yes	18	1.1	even	1	trivial
2888.1.bb.a.2395.1	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)

\(f(q)\)	\(=\)	\(q+(0.789141 + 0.614213i) q^{2} +(0.917421 + 0.996584i) q^{3} +(0.245485 + 0.969400i) q^{4} +(0.111859 + 1.34994i) q^{6} +(-0.401695 + 0.915773i) q^{8} +(-0.0689406 + 0.831990i) q^{9} +(-0.0405441 - 0.489294i) q^{11} +(-0.740876 + 1.13399i) q^{12} +(-0.879474 + 0.475947i) q^{16} +(-0.431796 + 1.70512i) q^{17} +(-0.565423 + 0.614213i) q^{18} +(0.789141 - 0.614213i) q^{19} +(0.268536 - 0.411024i) q^{22} +(-1.28117 + 0.439826i) q^{24} +(0.546948 - 0.837166i) q^{25} +(0.176545 - 0.137410i) q^{27} +(-0.986361 - 0.164595i) q^{32} +(0.450427 - 0.489294i) q^{33} +(-1.38806 + 1.08037i) q^{34} +(-0.823455 + 0.137410i) q^{36} +1.00000 q^{38} +(-1.28117 - 0.439826i) q^{41} +(-1.55676 + 0.259777i) q^{43} +(0.464369 - 0.159418i) q^{44} +(-1.28117 - 0.439826i) q^{48} +(-0.879474 - 0.475947i) q^{49} +(0.945817 - 0.324699i) q^{50} +(-2.09544 + 1.13399i) q^{51} +0.223718 q^{54} +(1.33609 + 0.222954i) q^{57} +(1.49277 + 0.512467i) q^{59} +(-0.677282 - 0.735724i) q^{64} +(0.655981 - 0.109464i) q^{66} +(0.0663435 - 0.151248i) q^{67} -1.75895 q^{68} +(-0.734221 - 0.397341i) q^{72} +(0.464369 - 1.83375i) q^{73} +(1.33609 - 0.222954i) q^{75} +(0.789141 + 0.614213i) q^{76} +(1.12236 + 0.187289i) q^{81} +(-0.740876 - 1.13399i) q^{82} +(1.54695 + 0.837166i) q^{83} +(-1.38806 - 0.751179i) q^{86} +(0.464369 + 0.159418i) q^{88} +(-0.431796 - 1.70512i) q^{89} +(-0.740876 - 1.13399i) q^{96} +(-0.803391 - 1.83155i) q^{97} +(-0.401695 - 0.915773i) q^{98} +0.409883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - q^{19} - 2 q^{22} - 2 q^{24} - q^{25} + 15 q^{27} - q^{32} - 4 q^{33} - 2 q^{34}+ \cdots - 6 q^{99}+O(q^{100}) \) 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

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Database

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