LMFDB - Embedded newform 3800.1.cq.b.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3800,1,Mod(99,3800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3800, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 9, 2]))

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

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

chi := DirichletCharacter("3800.99");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$3800 = 2^{3} \cdot 5^{2} \cdot 19$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	3800.cq (of order $18$ , degree $6$ , not 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:	$1.89644704801$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - x^{6} + 1$ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 152)
Projective image:	$D_{9}$
Projective field:	Galois closure of 9.1.69564674215936.1

Embedding invariants

Embedding label			99.1
Root			$-0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	3800.99
Dual form			3800.1.cq.b.499.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 + 0.939693i) q^{2} +(1.85083 - 0.326352i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{6} +(0.866025 - 0.500000i) q^{8} +(2.37939 - 0.866025i) q^{9} +(-0.173648 - 0.300767i) q^{11} +(-1.62760 - 0.939693i) q^{12} +(0.173648 + 0.984808i) q^{16} +(0.342020 - 0.939693i) q^{17} +2.53209i q^{18} +(-0.766044 - 0.642788i) q^{19} +(0.342020 - 0.0603074i) q^{22} +(1.43969 - 1.20805i) q^{24} +(2.49362 - 1.43969i) q^{27} +(-0.984808 - 0.173648i) q^{32} +(-0.419550 - 0.500000i) q^{33} +(0.766044 + 0.642788i) q^{34} +(-2.37939 - 0.866025i) q^{36} +(0.866025 - 0.500000i) q^{38} +(0.266044 + 1.50881i) q^{41} +(-0.642788 - 0.766044i) q^{43} +(-0.0603074 + 0.342020i) q^{44} +(0.642788 + 1.76604i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.326352 - 1.85083i) q^{51} +(0.500000 + 2.83564i) q^{54} +(-1.62760 - 0.939693i) q^{57} +(0.326352 + 0.118782i) q^{59} +(0.500000 - 0.866025i) q^{64} +(0.613341 - 0.223238i) q^{66} +(0.524005 + 1.43969i) q^{67} +(-0.866025 + 0.500000i) q^{68} +(1.62760 - 1.93969i) q^{72} +(-0.342020 + 0.0603074i) q^{73} +(0.173648 + 0.984808i) q^{76} +(2.20574 - 1.85083i) q^{81} +(-1.50881 - 0.266044i) q^{82} +(-1.32683 - 0.766044i) q^{83} +(0.939693 - 0.342020i) q^{86} +(-0.300767 - 0.173648i) q^{88} +(0.173648 - 0.984808i) q^{89} -1.87939 q^{96} +(-0.524005 + 1.43969i) q^{97} +(-0.984808 + 0.173648i) q^{98} +(-0.673648 - 0.565258i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 6 q^{6} + 6 q^{9} + 6 q^{24} - 6 q^{36} - 6 q^{41} - 12 q^{44} + 6 q^{49} + 6 q^{51} + 6 q^{54} + 6 q^{59} + 6 q^{64} - 6 q^{66} + 6 q^{81} - 6 q^{99}+O(q^{100})$ 12 * q - 6 * q^6 + 6 * q^9 + 6 * q^24 - 6 * q^36 - 6 * q^41 - 12 * q^44 + 6 * q^49 + 6 * q^51 + 6 * q^54 + 6 * q^59 + 6 * q^64 - 6 * q^66 + 6 * q^81 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times$ .

$n$	$401$	$951$	$1901$	$1977$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$2$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$3$	1.85083	−	0.326352i	1.85083	−	0.326352i	0.866025	−	0.500000i	$-0.166667\pi$
$3$	1.85083	−	0.326352i	1.85083	−	0.326352i	0.984808	+	0.173648i	$0.0555556\pi$
$4$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$5$		0			0
$5$		0			0
$6$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	0.866025	−	0.500000i	0.866025	−	0.500000i
$9$	2.37939	−	0.866025i	2.37939	−	0.866025i
$10$		0			0
$11$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$11$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$12$	−1.62760	−	0.939693i	−1.62760	−	0.939693i
$13$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$13$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$14$		0			0
$15$		0			0
$16$	0.173648	+	0.984808i	0.173648	+	0.984808i
$17$	0.342020	−	0.939693i	0.342020	−	0.939693i	−0.642788	−	0.766044i	$-0.722222\pi$
$17$	0.342020	−	0.939693i	0.342020	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$18$			2.53209i			2.53209i
$19$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$19$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$20$		0			0
$21$		0			0
$22$	0.342020	−	0.0603074i	0.342020	−	0.0603074i
$23$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$23$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$24$	1.43969	−	1.20805i	1.43969	−	1.20805i
$25$		0			0
$26$		0			0
$27$	2.49362	−	1.43969i	2.49362	−	1.43969i
$28$		0			0
$29$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$29$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$33$	−0.419550	−	0.500000i	−0.419550	−	0.500000i
$34$	0.766044	+	0.642788i	0.766044	+	0.642788i
$35$		0			0
$36$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	0.866025	−	0.500000i	0.866025	−	0.500000i
$39$		0			0
$40$		0			0
$41$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$41$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$42$		0			0
$43$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	0.342020	−	0.939693i	$-0.388889\pi$
$43$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	−0.984808	+	0.173648i	$0.944444\pi$
$44$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$45$		0			0
$46$		0			0
$47$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$47$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$48$	0.642788	+	1.76604i	0.642788	+	1.76604i
$49$	0.500000	+	0.866025i	0.500000	+	0.866025i
$50$		0			0
$51$	0.326352	−	1.85083i	0.326352	−	1.85083i
$52$		0			0
$53$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$53$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$54$	0.500000	+	2.83564i	0.500000	+	2.83564i
$55$		0			0
$56$		0			0
$57$	−1.62760	−	0.939693i	−1.62760	−	0.939693i
$58$		0			0
$59$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$59$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$60$		0			0
$61$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$61$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$62$		0			0
$63$		0			0
$64$	0.500000	−	0.866025i	0.500000	−	0.866025i
$65$		0			0
$66$	0.613341	−	0.223238i	0.613341	−	0.223238i
$67$	0.524005	+	1.43969i	0.524005	+	1.43969i	0.866025	+	0.500000i	$0.166667\pi$
$67$	0.524005	+	1.43969i	0.524005	+	1.43969i	−0.342020	+	0.939693i	$0.611111\pi$
$68$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$69$		0			0
$70$		0			0
$71$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$71$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$72$	1.62760	−	1.93969i	1.62760	−	1.93969i
$73$	−0.342020	+	0.0603074i	−0.342020	+	0.0603074i	−0.342020	−	0.939693i	$-0.611111\pi$
$73$	−0.342020	+	0.0603074i	−0.342020	+	0.0603074i			1.00000i	$0.5\pi$
$74$		0			0
$75$		0			0
$76$	0.173648	+	0.984808i	0.173648	+	0.984808i
$77$		0			0
$78$		0			0
$79$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$79$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$80$		0			0
$81$	2.20574	−	1.85083i	2.20574	−	1.85083i
$82$	−1.50881	−	0.266044i	−1.50881	−	0.266044i
$83$	−1.32683	−	0.766044i	−1.32683	−	0.766044i	−0.342020	−	0.939693i	$-0.611111\pi$
$83$	−1.32683	−	0.766044i	−1.32683	−	0.766044i	−0.984808	+	0.173648i	$0.944444\pi$
$84$		0			0
$85$		0			0
$86$	0.939693	−	0.342020i	0.939693	−	0.342020i
$87$		0			0
$88$	−0.300767	−	0.173648i	−0.300767	−	0.173648i
$89$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$89$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.87939			−1.87939
$97$	−0.524005	+	1.43969i	−0.524005	+	1.43969i	0.342020	+	0.939693i	$0.388889\pi$
$97$	−0.524005	+	1.43969i	−0.524005	+	1.43969i	−0.866025	+	0.500000i	$0.833333\pi$
$98$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$99$	−0.673648	−	0.565258i	−0.673648	−	0.565258i
$100$		0			0
$101$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$101$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$102$	1.62760	+	0.939693i	1.62760	+	0.939693i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$107$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$108$	−2.83564	−	0.500000i	−2.83564	−	0.500000i
$109$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$109$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			0.347296i			0.347296i	0.984808	+	0.173648i	$0.0555556\pi$
$113$			0.347296i			0.347296i	−0.984808	+	0.173648i	$0.944444\pi$
$114$	1.43969	−	1.20805i	1.43969	−	1.20805i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.223238	+	0.266044i	−0.223238	+	0.266044i
$119$		0			0
$120$		0			0
$121$	0.439693	−	0.761570i	0.439693	−	0.761570i
$122$		0			0
$123$	0.984808	+	2.70574i	0.984808	+	2.70574i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$127$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$128$	0.642788	+	0.766044i	0.642788	+	0.766044i
$129$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$130$		0			0
$131$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$131$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$132$			0.652704i			0.652704i
$133$		0			0
$134$	−1.53209			−1.53209
$135$		0			0
$136$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$137$	−1.20805	+	1.43969i	−1.20805	+	1.43969i	−0.342020	+	0.939693i	$0.611111\pi$
$137$	−1.20805	+	1.43969i	−1.20805	+	1.43969i	−0.866025	+	0.500000i	$0.833333\pi$
$138$		0			0
$139$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$139$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.26604	+	2.19285i	1.26604	+	2.19285i
$145$		0			0
$146$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$147$	1.20805	+	1.43969i	1.20805	+	1.43969i
$148$		0			0
$149$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$149$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$153$		−	2.53209i		−	2.53209i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$157$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.984808	+	2.70574i	0.984808	+	2.70574i
$163$	−1.62760	+	0.939693i	−1.62760	+	0.939693i	−0.642788	+	0.766044i	$0.722222\pi$
$163$	−1.62760	+	0.939693i	−1.62760	+	0.939693i	−0.984808	+	0.173648i	$0.944444\pi$
$164$	0.766044	−	1.32683i	0.766044	−	1.32683i
$165$		0			0
$166$	1.17365	−	0.984808i	1.17365	−	0.984808i
$167$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$167$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$168$		0			0
$169$	0.939693	+	0.342020i	0.939693	+	0.342020i
$170$		0			0
$171$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$172$			1.00000i			1.00000i
$173$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$173$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$174$		0			0
$175$		0			0
$176$	0.266044	−	0.223238i	0.266044	−	0.223238i
$177$	0.642788	+	0.113341i	0.642788	+	0.113341i
$178$	0.866025	+	0.500000i	0.866025	+	0.500000i
$179$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$179$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$180$		0			0
$181$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$181$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.342020	+	0.0603074i	−0.342020	+	0.0603074i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	0.642788	−	1.76604i	0.642788	−	1.76604i
$193$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$193$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$194$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$195$		0			0
$196$	0.173648	−	0.984808i	0.173648	−	0.984808i
$197$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$197$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$198$	0.761570	−	0.439693i	0.761570	−	0.439693i
$199$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$199$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$200$		0			0
$201$	1.43969	+	2.49362i	1.43969	+	2.49362i
$202$		0			0
$203$		0			0
$204$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$210$		0			0
$211$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$211$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$212$		0			0
$213$		0			0
$214$	0.766044	−	0.642788i	0.766044	−	0.642788i
$215$		0			0
$216$	1.43969	−	2.49362i	1.43969	−	2.49362i
$217$		0			0
$218$		0			0
$219$	−0.613341	+	0.223238i	−0.613341	+	0.223238i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$223$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$224$		0			0
$225$		0			0
$226$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$227$		−	1.53209i		−	1.53209i	−0.642788	−	0.766044i	$-0.722222\pi$
$227$		−	1.53209i		−	1.53209i	0.642788	−	0.766044i	$-0.277778\pi$
$228$	0.642788	+	1.76604i	0.642788	+	1.76604i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.20805	−	1.43969i	−1.20805	−	1.43969i	−0.866025	−	0.500000i	$-0.833333\pi$
$233$	−1.20805	−	1.43969i	−1.20805	−	1.43969i	−0.342020	−	0.939693i	$-0.611111\pi$
$234$		0			0
$235$		0			0
$236$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$		0			0
$241$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$241$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$242$	0.565258	+	0.673648i	0.565258	+	0.673648i
$243$	1.62760	−	1.93969i	1.62760	−	1.93969i
$244$		0			0
$245$		0			0
$246$	−2.87939			−2.87939
$247$		0			0
$248$		0			0
$249$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$250$		0			0
$251$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$251$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$257$	−0.642788	−	1.76604i	−0.642788	−	1.76604i	−0.642788	−	0.766044i	$-0.722222\pi$
$257$	−0.642788	−	1.76604i	−0.642788	−	1.76604i		−	1.00000i	$-0.5\pi$
$258$	1.62760	−	0.939693i	1.62760	−	0.939693i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.20805	+	1.43969i	−1.20805	+	1.43969i
$263$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$263$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$264$	−0.613341	−	0.223238i	−0.613341	−	0.223238i
$265$		0			0
$266$		0			0
$267$		−	1.87939i		−	1.87939i
$268$	0.524005	−	1.43969i	0.524005	−	1.43969i
$269$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$269$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$270$		0			0
$271$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$271$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$272$	0.984808	+	0.173648i	0.984808	+	0.173648i
$273$		0			0
$274$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$275$		0			0
$276$		0			0
$277$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$277$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$278$	−1.32683	−	0.766044i	−1.32683	−	0.766044i
$279$		0			0
$280$		0			0
$281$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$281$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$282$		0			0
$283$	0.118782	−	0.326352i	0.118782	−	0.326352i	−0.866025	−	0.500000i	$-0.833333\pi$
$283$	0.118782	−	0.326352i	0.118782	−	0.326352i	0.984808	+	0.173648i	$0.0555556\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.49362	+	0.439693i	−2.49362	+	0.439693i
$289$		0			0
$290$		0			0
$291$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$292$	0.300767	+	0.173648i	0.300767	+	0.173648i
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$295$		0			0
$296$		0			0
$297$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.500000	−	0.866025i	0.500000	−	0.866025i
$305$		0			0
$306$	2.37939	+	0.866025i	2.37939	+	0.866025i
$307$	0.342020	−	0.0603074i	0.342020	−	0.0603074i		−	1.00000i	$-0.5\pi$
$307$	0.342020	−	0.0603074i	0.342020	−	0.0603074i	0.342020	+	0.939693i	$0.388889\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$311$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$312$		0			0
$313$	0.642788	+	1.76604i	0.642788	+	1.76604i	0.642788	+	0.766044i	$0.277778\pi$
$313$	0.642788	+	1.76604i	0.642788	+	1.76604i			1.00000i	$0.5\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$317$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$322$		0			0
$323$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$324$	−2.87939			−2.87939
$325$		0			0
$326$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$327$		0			0
$328$	0.984808	+	1.17365i	0.984808	+	1.17365i
$329$		0			0
$330$		0			0
$331$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$331$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$332$	0.524005	+	1.43969i	0.524005	+	1.43969i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.20805	+	1.43969i	1.20805	+	1.43969i	0.866025	+	0.500000i	$0.166667\pi$
$337$	1.20805	+	1.43969i	1.20805	+	1.43969i	0.342020	+	0.939693i	$0.388889\pi$
$338$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$339$	0.113341	+	0.642788i	0.113341	+	0.642788i
$340$		0			0
$341$		0			0
$342$	1.62760	−	1.93969i	1.62760	−	1.93969i
$343$		0			0
$344$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$345$		0			0
$346$		0			0
$347$	−0.984808	−	1.17365i	−0.984808	−	1.17365i	−0.984808	−	0.173648i	$-0.944444\pi$
$347$	−0.984808	−	1.17365i	−0.984808	−	1.17365i		−	1.00000i	$-0.5\pi$
$348$		0			0
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$		0			0
$351$		0			0
$352$	0.118782	+	0.326352i	0.118782	+	0.326352i
$353$	1.32683	−	0.766044i	1.32683	−	0.766044i	0.342020	−	0.939693i	$-0.388889\pi$
$353$	1.32683	−	0.766044i	1.32683	−	0.766044i	0.984808	+	0.173648i	$0.0555556\pi$
$354$	−0.326352	+	0.565258i	−0.326352	+	0.565258i
$355$		0			0
$356$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$357$		0			0
$358$	−1.50881	+	0.266044i	−1.50881	+	0.266044i
$359$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$359$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$360$		0			0
$361$	0.173648	+	0.984808i	0.173648	+	0.984808i
$362$		0			0
$363$	0.565258	−	1.55303i	0.565258	−	1.55303i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$367$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$368$		0			0
$369$	1.93969	+	3.35965i	1.93969	+	3.35965i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−2.00000			−2.00000			−1.00000			$\pi$
$379$	−2.00000			−2.00000			−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$383$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$384$	1.43969	+	1.20805i	1.43969	+	1.20805i
$385$		0			0
$386$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$387$	−2.19285	−	1.26604i	−2.19285	−	1.26604i
$388$	1.32683	−	0.766044i	1.32683	−	0.766044i
$389$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$389$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$390$		0			0
$391$		0			0
$392$	0.866025	+	0.500000i	0.866025	+	0.500000i
$393$	3.47843	+	0.613341i	3.47843	+	0.613341i
$394$		0			0
$395$		0			0
$396$	0.152704	+	0.866025i	0.152704	+	0.866025i
$397$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$397$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$401$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$402$	−2.83564	+	0.500000i	−2.83564	+	0.500000i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.642788	−	1.76604i	−0.642788	−	1.76604i
$409$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$409$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$410$		0			0
$411$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$			2.87939i			2.87939i
$418$	−0.300767	−	0.173648i	−0.300767	−	0.173648i
$419$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$419$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$420$		0			0
$421$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$421$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$422$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.342020	+	0.939693i	0.342020	+	0.939693i
$429$		0			0
$430$		0			0
$431$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$431$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$432$	1.85083	+	2.20574i	1.85083	+	2.20574i
$433$	−1.28558	+	1.53209i	−1.28558	+	1.53209i	−0.642788	+	0.766044i	$0.722222\pi$
$433$	−1.28558	+	1.53209i	−1.28558	+	1.53209i	−0.642788	+	0.766044i	$0.722222\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		−	0.652704i		−	0.652704i
$439$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$439$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$440$		0			0
$441$	1.93969	+	1.62760i	1.93969	+	1.62760i
$442$		0			0
$443$	−1.85083	−	0.326352i	−1.85083	−	0.326352i	−0.866025	−	0.500000i	$-0.833333\pi$
$443$	−1.85083	−	0.326352i	−1.85083	−	0.326352i	−0.984808	+	0.173648i	$0.944444\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$449$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$450$		0			0
$451$	0.407604	−	0.342020i	0.407604	−	0.342020i
$452$	0.223238	−	0.266044i	0.223238	−	0.266044i
$453$		0			0
$454$	1.43969	+	0.524005i	1.43969	+	0.524005i
$455$		0			0
$456$	−1.87939			−1.87939
$457$		−	1.53209i		−	1.53209i	−0.642788	−	0.766044i	$-0.722222\pi$
$457$		−	1.53209i		−	1.53209i	0.642788	−	0.766044i	$-0.277778\pi$
$458$		0			0
$459$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$460$		0			0
$461$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$461$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$462$		0			0
$463$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$463$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$464$		0			0
$465$		0			0
$466$	1.76604	−	0.642788i	1.76604	−	0.642788i
$467$	−1.32683	+	0.766044i	−1.32683	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$467$	−1.32683	+	0.766044i	−1.32683	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.342020	−	0.0603074i	0.342020	−	0.0603074i
$473$	−0.118782	+	0.326352i	−0.118782	+	0.326352i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$479$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$480$		0			0
$481$		0			0
$482$	−1.62760	−	0.939693i	−1.62760	−	0.939693i
$483$		0			0
$484$	−0.826352	+	0.300767i	−0.826352	+	0.300767i
$485$		0			0
$486$	1.26604	+	2.19285i	1.26604	+	2.19285i
$487$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$487$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$488$		0			0
$489$	−2.70574	+	2.27038i	−2.70574	+	2.27038i
$490$		0			0
$491$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$491$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$492$	0.984808	−	2.70574i	0.984808	−	2.70574i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.85083	−	2.20574i	1.85083	−	2.20574i
$499$	−0.266044	+	0.223238i	−0.266044	+	0.223238i	−0.766044	−	0.642788i	$-0.777778\pi$
$499$	−0.266044	+	0.223238i	−0.266044	+	0.223238i	0.500000	+	0.866025i	$0.333333\pi$
$500$		0			0
$501$		0			0
$502$	1.62760	−	0.939693i	1.62760	−	0.939693i
$503$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$503$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.85083	+	0.326352i	1.85083	+	0.326352i
$508$		0			0
$509$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$509$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	1.00000i
$513$	−2.83564	−	0.500000i	−2.83564	−	0.500000i
$514$	1.87939			1.87939
$515$		0			0
$516$	0.326352	+	1.85083i	0.326352	+	1.85083i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$521$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$522$		0			0
$523$	−0.684040	−	1.87939i	−0.684040	−	1.87939i	−0.342020	−	0.939693i	$-0.611111\pi$
$523$	−0.684040	−	1.87939i	−0.684040	−	1.87939i	−0.342020	−	0.939693i	$-0.611111\pi$
$524$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.419550	−	0.500000i	0.419550	−	0.500000i
$529$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$530$		0			0
$531$	0.879385			0.879385
$532$		0			0
$533$		0			0
$534$	1.76604	+	0.642788i	1.76604	+	0.642788i
$535$		0			0
$536$	1.17365	+	0.984808i	1.17365	+	0.984808i
$537$	1.85083	+	2.20574i	1.85083	+	2.20574i
$538$		0			0
$539$	0.173648	−	0.300767i	0.173648	−	0.300767i
$540$		0			0
$541$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$541$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$542$		0			0
$543$		0			0
$544$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$545$		0			0
$546$		0			0
$547$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$547$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$548$	1.85083	−	0.326352i	1.85083	−	0.326352i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.17365	−	0.984808i	1.17365	−	0.984808i
$557$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$557$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.613341	+	0.223238i	−0.613341	+	0.223238i
$562$	1.62760	−	0.939693i	1.62760	−	0.939693i
$563$	−0.300767	−	0.173648i	−0.300767	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$563$	−0.300767	−	0.173648i	−0.300767	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$564$		0			0
$565$		0			0
$566$	0.266044	+	0.223238i	0.266044	+	0.223238i
$567$		0			0
$568$		0			0
$569$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$569$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$571$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.439693	−	2.49362i	0.439693	−	2.49362i
$577$	0.300767	+	0.173648i	0.300767	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$577$	0.300767	+	0.173648i	0.300767	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$578$		0			0
$579$	1.76604	−	0.642788i	1.76604	−	0.642788i
$580$		0			0
$581$		0			0
$582$	−2.49362	−	1.43969i	−2.49362	−	1.43969i
$583$		0			0
$584$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$585$		0			0
$586$		0			0
$587$	0.342020	−	0.939693i	0.342020	−	0.939693i	−0.642788	−	0.766044i	$-0.722222\pi$
$587$	0.342020	−	0.939693i	0.342020	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$588$		−	1.87939i		−	1.87939i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.223238	+	0.266044i	−0.223238	+	0.266044i	−0.866025	−	0.500000i	$-0.833333\pi$
$593$	−0.223238	+	0.266044i	−0.223238	+	0.266044i	0.642788	+	0.766044i	$0.277778\pi$
$594$	0.766044	−	0.642788i	0.766044	−	0.642788i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$599$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$600$		0			0
$601$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$601$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$602$		0			0
$603$	2.49362	+	2.97178i	2.49362	+	2.97178i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	0.642788	+	0.766044i	0.642788	+	0.766044i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.62760	+	1.93969i	−1.62760	+	1.93969i
$613$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$613$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$614$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$615$		0			0
$616$		0			0
$617$	0.118782	+	0.326352i	0.118782	+	0.326352i	0.984808	−	0.173648i	$-0.0555556\pi$
$617$	0.118782	+	0.326352i	0.118782	+	0.326352i	−0.866025	+	0.500000i	$0.833333\pi$
$618$		0			0
$619$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$619$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$	−1.87939			−1.87939
$627$			0.652704i			0.652704i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$631$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$632$		0			0
$633$	1.85083	+	0.326352i	1.85083	+	0.326352i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$641$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$642$	1.20805	−	1.43969i	1.20805	−	1.43969i
$643$	1.85083	−	0.326352i	1.85083	−	0.326352i	0.866025	−	0.500000i	$-0.166667\pi$
$643$	1.85083	−	0.326352i	1.85083	−	0.326352i	0.984808	+	0.173648i	$0.0555556\pi$
$644$		0			0
$645$		0			0
$646$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	0.984808	−	2.70574i	0.984808	−	2.70574i
$649$	−0.0209445	−	0.118782i	−0.0209445	−	0.118782i
$650$		0			0
$651$		0			0
$652$	1.85083	+	0.326352i	1.85083	+	0.326352i
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$		0			0
$655$		0			0
$656$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$657$	−0.761570	+	0.439693i	−0.761570	+	0.439693i
$658$		0			0
$659$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$659$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$660$		0			0
$661$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$661$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$662$	0.342020	−	0.0603074i	0.342020	−	0.0603074i
$663$		0			0
$664$	−1.53209			−1.53209
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$673$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$674$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$675$		0			0
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$677$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$678$	−0.642788	−	0.113341i	−0.642788	−	0.113341i
$679$		0			0
$680$		0			0
$681$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$682$		0			0
$683$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$683$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$684$	1.26604	+	2.19285i	1.26604	+	2.19285i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.642788	−	0.766044i	0.642788	−	0.766044i
$689$		0			0
$690$		0			0
$691$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$691$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$692$		0			0
$693$		0			0
$694$	1.43969	−	0.524005i	1.43969	−	0.524005i
$695$		0			0
$696$		0			0
$697$	1.50881	+	0.266044i	1.50881	+	0.266044i
$698$		0			0
$699$	−2.70574	−	2.27038i	−2.70574	−	2.27038i
$700$		0			0
$701$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$701$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$702$		0			0
$703$		0			0
$704$	−0.347296			−0.347296
$705$		0			0
$706$	0.266044	+	1.50881i	0.266044	+	1.50881i
$707$		0			0
$708$	−0.419550	−	0.500000i	−0.419550	−	0.500000i
$709$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$709$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$710$		0			0
$711$		0			0
$712$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.266044	−	1.50881i	0.266044	−	1.50881i
$717$		0			0
$718$		0			0
$719$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$719$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$720$		0			0
$721$		0			0
$722$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$723$			3.53209i			3.53209i
$724$		0			0
$725$		0			0
$726$	1.26604	+	1.06234i	1.26604	+	1.06234i
$727$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$727$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$728$		0			0
$729$	0.939693	−	1.62760i	0.939693	−	1.62760i
$730$		0			0
$731$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$732$		0			0
$733$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$733$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.342020	−	0.407604i	0.342020	−	0.407604i
$738$	−3.82045	+	0.673648i	−3.82045	+	0.673648i
$739$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.939693	−	0.342020i	$-0.111111\pi$
$739$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$743$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.82045	−	0.673648i	−3.82045	−	0.673648i
$748$	0.300767	+	0.173648i	0.300767	+	0.173648i
$749$		0			0
$750$		0			0
$751$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$751$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$752$		0			0
$753$	−3.05888	−	1.76604i	−3.05888	−	1.76604i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$757$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$758$	0.684040	−	1.87939i	0.684040	−	1.87939i
$759$		0			0
$760$		0			0
$761$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$761$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.62760	+	0.939693i	−1.62760	+	0.939693i
$769$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$769$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$770$		0			0
$771$	−1.76604	−	3.05888i	−1.76604	−	3.05888i
$772$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$773$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$773$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$774$	1.93969	−	1.62760i	1.93969	−	1.62760i
$775$		0			0
$776$	0.266044	+	1.50881i	0.266044	+	1.50881i
$777$		0			0
$778$		0			0
$779$	0.766044	−	1.32683i	0.766044	−	1.32683i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$785$		0			0
$786$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$787$	−0.300767	+	0.173648i	−0.300767	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$787$	−0.300767	+	0.173648i	−0.300767	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.866025	−	0.152704i	−0.866025	−	0.152704i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−0.439693	−	2.49362i	−0.439693	−	2.49362i
$802$	0.223238	−	0.266044i	0.223238	−	0.266044i
$803$	0.0775297	+	0.0923963i	0.0775297	+	0.0923963i
$804$	0.500000	−	2.83564i	0.500000	−	2.83564i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$809$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$810$		0			0
$811$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$811$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.87939			1.87939
$817$			1.00000i			1.00000i
$818$			0.347296i			0.347296i
$819$		0			0
$820$		0			0
$821$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$821$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$822$	−2.27038	−	2.70574i	−2.27038	−	2.70574i
$823$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$823$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.118782	+	0.326352i	0.118782	+	0.326352i	0.984808	−	0.173648i	$-0.0555556\pi$
$827$	0.118782	+	0.326352i	0.118782	+	0.326352i	−0.866025	+	0.500000i	$0.833333\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.984808	−	0.173648i	0.984808	−	0.173648i
$834$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$835$		0			0
$836$	0.266044	−	0.223238i	0.266044	−	0.223238i
$837$		0			0
$838$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$839$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$839$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$840$		0			0
$841$	0.766044	−	0.642788i	0.766044	−	0.642788i
$842$		0			0
$843$	−3.05888	−	1.76604i	−3.05888	−	1.76604i
$844$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.113341	−	0.642788i	0.113341	−	0.642788i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$853$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$854$		0			0
$855$		0			0
$856$	−1.00000			−1.00000
$857$	0.642788	−	1.76604i	0.642788	−	1.76604i		−	1.00000i	$-0.5\pi$
$857$	0.642788	−	1.76604i	0.642788	−	1.76604i	0.642788	−	0.766044i	$-0.277778\pi$
$858$		0			0
$859$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	0.500000	−	0.866025i	$-0.333333\pi$
$859$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	−0.766044	+	0.642788i	$0.777778\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$863$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$864$	−2.70574	+	0.984808i	−2.70574	+	0.984808i
$865$		0			0
$866$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$			3.87939i			3.87939i
$874$		0			0
$875$		0			0
$876$	0.613341	+	0.223238i	0.613341	+	0.223238i
$877$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$877$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$881$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$882$	−2.19285	+	1.26604i	−2.19285	+	1.26604i
$883$	−0.524005	−	1.43969i	−0.524005	−	1.43969i	−0.866025	−	0.500000i	$-0.833333\pi$
$883$	−0.524005	−	1.43969i	−0.524005	−	1.43969i	0.342020	−	0.939693i	$-0.388889\pi$
$884$		0			0
$885$		0			0
$886$	0.939693	−	1.62760i	0.939693	−	1.62760i
$887$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$887$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.20805	−	1.43969i	−1.20805	−	1.43969i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	0.181985	+	0.500000i	0.181985	+	0.500000i
$903$		0			0
$904$	0.173648	+	0.300767i	0.173648	+	0.300767i
$905$		0			0
$906$		0			0
$907$	−0.223238	−	0.266044i	−0.223238	−	0.266044i	0.642788	−	0.766044i	$-0.277778\pi$
$907$	−0.223238	−	0.266044i	−0.223238	−	0.266044i	−0.866025	+	0.500000i	$0.833333\pi$
$908$	−0.984808	+	1.17365i	−0.984808	+	1.17365i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	0.642788	−	1.76604i	0.642788	−	1.76604i
$913$			0.532089i			0.532089i
$914$	1.43969	+	0.524005i	1.43969	+	0.524005i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	2.83564	+	0.500000i	2.83564	+	0.500000i
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	0.613341	−	0.223238i	0.613341	−	0.223238i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$929$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$930$		0			0
$931$	0.173648	−	0.984808i	0.173648	−	0.984808i
$932$			1.87939i			1.87939i
$933$		0			0
$934$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$935$		0			0
$936$		0			0
$937$	1.85083	+	0.326352i	1.85083	+	0.326352i	0.984808	−	0.173648i	$-0.0555556\pi$
$937$	1.85083	+	0.326352i	1.85083	+	0.326352i	0.866025	+	0.500000i	$0.166667\pi$
$938$		0			0
$939$	1.76604	+	3.05888i	1.76604	+	3.05888i
$940$		0			0
$941$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$941$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$942$		0			0
$943$		0			0
$944$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$945$		0			0
$946$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$947$	1.96962	−	0.347296i	1.96962	−	0.347296i	0.984808	−	0.173648i	$-0.0555556\pi$
$947$	1.96962	−	0.347296i	1.96962	−	0.347296i	0.984808	−	0.173648i	$-0.0555556\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.342020	+	0.0603074i	−0.342020	+	0.0603074i	−0.342020	−	0.939693i	$-0.611111\pi$
$953$	−0.342020	+	0.0603074i	−0.342020	+	0.0603074i			1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$	−2.49362	−	0.439693i	−2.49362	−	0.439693i
$964$	1.43969	−	1.20805i	1.43969	−	1.20805i
$965$		0			0
$966$		0			0
$967$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$967$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$968$		−	0.879385i		−	0.879385i
$969$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$970$		0			0
$971$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$971$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$972$	−2.49362	+	0.439693i	−2.49362	+	0.439693i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.62760	−	0.939693i	1.62760	−	0.939693i	0.642788	−	0.766044i	$-0.277778\pi$
$977$	1.62760	−	0.939693i	1.62760	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$978$	−1.20805	−	3.31908i	−1.20805	−	3.31908i
$979$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$980$		0			0
$981$		0			0
$982$	0.984808	+	0.173648i	0.984808	+	0.173648i
$983$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$983$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$984$	2.20574	+	1.85083i	2.20574	+	1.85083i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$991$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$992$		0			0
$993$	−0.419550	−	0.500000i	−0.419550	−	0.500000i
$994$		0			0
$995$		0			0
$996$	1.43969	+	2.49362i	1.43969	+	2.49362i
$997$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$997$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$998$	−0.118782	−	0.326352i	−0.118782	−	0.326352i
$999$		0			0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3800.1.cq.b.99.1		12
5.2	odd	4		152.1.u.a.99.1	yes	6
5.3	odd	4		3800.1.cv.c.251.1		6
5.4	even	2	inner	3800.1.cq.b.99.2		12
8.3	odd	2	CM	3800.1.cq.b.99.1		12
15.2	even	4		1368.1.eh.a.1315.1		6
19.5	even	9	inner	3800.1.cq.b.499.2		12
20.7	even	4		608.1.bg.a.175.1		6
40.3	even	4		3800.1.cv.c.251.1		6
40.19	odd	2	inner	3800.1.cq.b.99.2		12
40.27	even	4		152.1.u.a.99.1	yes	6
40.37	odd	4		608.1.bg.a.175.1		6
95.2	even	36		2888.1.u.a.1859.1		6
95.7	odd	12		2888.1.u.g.595.1		6
95.12	even	12		2888.1.u.a.595.1		6
95.17	odd	36		2888.1.u.g.1859.1		6
95.22	even	36		2888.1.u.f.2411.1		6
95.24	even	18	inner	3800.1.cq.b.499.1		12
95.27	even	12		2888.1.u.f.2555.1		6
95.32	even	36		2888.1.k.c.2595.1		6
95.37	even	4		2888.1.u.e.99.1		6
95.42	odd	36		2888.1.k.b.2819.3		6
95.43	odd	36		3800.1.cv.c.651.1		6
95.47	odd	36		2888.1.f.d.723.1		3
95.52	even	36		2888.1.u.e.1867.1		6
95.62	odd	36		152.1.u.a.43.1	✓	6
95.67	even	36		2888.1.f.c.723.3		3
95.72	even	36		2888.1.k.c.2819.1		6
95.82	odd	36		2888.1.k.b.2595.3		6
95.87	odd	12		2888.1.u.b.2555.1		6
95.92	odd	36		2888.1.u.b.2411.1		6
120.107	odd	4		1368.1.eh.a.1315.1		6
152.43	odd	18	inner	3800.1.cq.b.499.2		12
285.62	even	36		1368.1.eh.a.955.1		6
380.347	even	36		608.1.bg.a.271.1		6
760.27	odd	12		2888.1.u.f.2555.1		6
760.43	even	36		3800.1.cv.c.651.1		6
760.67	odd	36		2888.1.f.c.723.3		3
760.107	odd	12		2888.1.u.a.595.1		6
760.147	odd	36		2888.1.u.e.1867.1		6
760.157	odd	36		608.1.bg.a.271.1		6
760.187	even	36		2888.1.u.b.2411.1		6
760.227	odd	4		2888.1.u.e.99.1		6
760.307	odd	36		2888.1.u.f.2411.1		6
760.347	even	36		152.1.u.a.43.1	✓	6
760.387	even	12		2888.1.u.g.595.1		6
760.427	even	36		2888.1.f.d.723.1		3
760.467	even	12		2888.1.u.b.2555.1		6
760.499	odd	18	inner	3800.1.cq.b.499.1		12
760.507	odd	36		2888.1.k.c.2595.1		6
760.547	odd	36		2888.1.k.c.2819.1		6
760.587	even	36		2888.1.u.g.1859.1		6
760.667	odd	36		2888.1.u.a.1859.1		6
760.707	even	36		2888.1.k.b.2819.3		6
760.747	even	36		2888.1.k.b.2595.3		6
2280.347	odd	36		1368.1.eh.a.955.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.1.u.a.43.1	✓	6	95.62	odd	36
152.1.u.a.43.1	✓	6	760.347	even	36
152.1.u.a.99.1	yes	6	5.2	odd	4
152.1.u.a.99.1	yes	6	40.27	even	4
608.1.bg.a.175.1		6	20.7	even	4
608.1.bg.a.175.1		6	40.37	odd	4
608.1.bg.a.271.1		6	380.347	even	36
608.1.bg.a.271.1		6	760.157	odd	36
1368.1.eh.a.955.1		6	285.62	even	36
1368.1.eh.a.955.1		6	2280.347	odd	36
1368.1.eh.a.1315.1		6	15.2	even	4
1368.1.eh.a.1315.1		6	120.107	odd	4
2888.1.f.c.723.3		3	95.67	even	36
2888.1.f.c.723.3		3	760.67	odd	36
2888.1.f.d.723.1		3	95.47	odd	36
2888.1.f.d.723.1		3	760.427	even	36
2888.1.k.b.2595.3		6	95.82	odd	36
2888.1.k.b.2595.3		6	760.747	even	36
2888.1.k.b.2819.3		6	95.42	odd	36
2888.1.k.b.2819.3		6	760.707	even	36
2888.1.k.c.2595.1		6	95.32	even	36
2888.1.k.c.2595.1		6	760.507	odd	36
2888.1.k.c.2819.1		6	95.72	even	36
2888.1.k.c.2819.1		6	760.547	odd	36
2888.1.u.a.595.1		6	95.12	even	12
2888.1.u.a.595.1		6	760.107	odd	12
2888.1.u.a.1859.1		6	95.2	even	36
2888.1.u.a.1859.1		6	760.667	odd	36
2888.1.u.b.2411.1		6	95.92	odd	36
2888.1.u.b.2411.1		6	760.187	even	36
2888.1.u.b.2555.1		6	95.87	odd	12
2888.1.u.b.2555.1		6	760.467	even	12
2888.1.u.e.99.1		6	95.37	even	4
2888.1.u.e.99.1		6	760.227	odd	4
2888.1.u.e.1867.1		6	95.52	even	36
2888.1.u.e.1867.1		6	760.147	odd	36
2888.1.u.f.2411.1		6	95.22	even	36
2888.1.u.f.2411.1		6	760.307	odd	36
2888.1.u.f.2555.1		6	95.27	even	12
2888.1.u.f.2555.1		6	760.27	odd	12
2888.1.u.g.595.1		6	95.7	odd	12
2888.1.u.g.595.1		6	760.387	even	12
2888.1.u.g.1859.1		6	95.17	odd	36
2888.1.u.g.1859.1		6	760.587	even	36
3800.1.cq.b.99.1		12	1.1	even	1	trivial
3800.1.cq.b.99.1		12	8.3	odd	2	CM
3800.1.cq.b.99.2		12	5.4	even	2	inner
3800.1.cq.b.99.2		12	40.19	odd	2	inner
3800.1.cq.b.499.1		12	95.24	even	18	inner
3800.1.cq.b.499.1		12	760.499	odd	18	inner
3800.1.cq.b.499.2		12	19.5	even	9	inner
3800.1.cq.b.499.2		12	152.43	odd	18	inner
3800.1.cv.c.251.1		6	5.3	odd	4
3800.1.cv.c.251.1		6	40.3	even	4
3800.1.cv.c.651.1		6	95.43	odd	36
3800.1.cv.c.651.1		6	760.43	even	36

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	3800.1.cq.b.99.1

Level	$3800$
Weight	$1$
Character	3800.99
Analytic conductor	$1.896$
Analytic rank	$0$
Dimension	$12$
Projective image	$D_{9}$
CM discriminant	-8
Inner twists	$8$