LMFDB - Embedded newform 1100.1.x.a.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,1,Mod(21,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("1100.21");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$1100 = 2^{2} \cdot 5^{2} \cdot 11$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1100.x (of order $10$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.548971513896$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1$ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{15}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{15} + \cdots)$

Embedding invariants

Embedding label			241.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	1100.241
Dual form			1100.1.x.a.461.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0646021 - 0.198825i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.773659 - 0.562096i) q^{9} +(-0.809017 - 0.587785i) q^{11} +(-0.139886 + 0.155360i) q^{15} +(-1.08268 - 0.786610i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.330869 - 0.240391i) q^{27} +(0.564602 - 1.73767i) q^{31} +(-0.0646021 + 0.198825i) q^{33} +(0.809017 - 0.587785i) q^{37} +(-0.873619 - 0.388960i) q^{45} +(0.618034 + 1.90211i) q^{47} +1.00000 q^{49} +(-0.500000 - 1.53884i) q^{53} +(-0.104528 + 0.994522i) q^{55} +(0.169131 - 0.122881i) q^{59} +(-0.604528 + 1.86055i) q^{67} +(-0.0864545 + 0.266080i) q^{69} +(-0.0646021 - 0.198825i) q^{71} +(0.204489 + 0.0434654i) q^{75} +(0.269091 - 0.828176i) q^{81} +(1.58268 + 1.14988i) q^{89} -0.381966 q^{93} +(0.564602 + 1.73767i) q^{97} -0.956295 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 2 q^{3} - 4 q^{5} - 2 q^{11} - q^{15} + 2 q^{23} - 4 q^{25} - 7 q^{27} + 2 q^{31} + 2 q^{33} + 2 q^{37} - 4 q^{47} + 8 q^{49} - 4 q^{53} + q^{55} - 3 q^{59} - 3 q^{67} - 7 q^{69} + 2 q^{71} - q^{75}+ \cdots + 10 q^{99}+O(q^{100})$ 8 * q + 2 * q^3 - 4 * q^5 - 2 * q^11 - q^15 + 2 * q^23 - 4 * q^25 - 7 * q^27 + 2 * q^31 + 2 * q^33 + 2 * q^37 - 4 * q^47 + 8 * q^49 - 4 * q^53 + q^55 - 3 * q^59 - 3 * q^67 - 7 * q^69 + 2 * q^71 - q^75 - 3 * q^81 + 2 * q^89 - 12 * q^93 + 2 * q^97 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$ .

$n$	$101$	$177$	$551$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	0.913545	−	0.406737i	$-0.133333\pi$
$3$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	−0.978148	+	0.207912i	$0.933333\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$6$		0			0
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$		0			0
$9$	0.773659	−	0.562096i	0.773659	−	0.562096i
$10$		0			0
$11$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$11$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$12$		0			0
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$		0			0
$15$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$16$		0			0
$17$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$17$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$18$		0			0
$19$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$19$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.08268	−	0.786610i	−1.08268	−	0.786610i	−0.104528	−	0.994522i	$-0.533333\pi$
$23$	−1.08268	−	0.786610i	−1.08268	−	0.786610i	−0.978148	+	0.207912i	$0.933333\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$		0			0
$27$	−0.330869	−	0.240391i	−0.330869	−	0.240391i
$28$		0			0
$29$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$29$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$30$		0			0
$31$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$31$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$32$		0			0
$33$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$37$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$41$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$	−0.873619	−	0.388960i	−0.873619	−	0.388960i
$46$		0			0
$47$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$47$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$48$		0			0
$49$	1.00000			1.00000
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$53$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$54$		0			0
$55$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.169131	−	0.122881i	0.169131	−	0.122881i	−0.500000	−	0.866025i	$-0.666667\pi$
$59$	0.169131	−	0.122881i	0.169131	−	0.122881i	0.669131	+	0.743145i	$0.266667\pi$
$60$		0			0
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.104528	+	0.994522i	$0.533333\pi$
$67$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	−0.0864545	+	0.266080i	−0.0864545	+	0.266080i
$70$		0			0
$71$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	0.913545	−	0.406737i	$-0.133333\pi$
$71$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	−0.978148	+	0.207912i	$0.933333\pi$
$72$		0			0
$73$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$73$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$74$		0			0
$75$	0.204489	+	0.0434654i	0.204489	+	0.0434654i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$79$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$80$		0			0
$81$	0.269091	−	0.828176i	0.269091	−	0.828176i
$82$		0			0
$83$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$83$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.913545	+	0.406737i	$0.133333\pi$
$89$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.669131	+	0.743145i	$0.266667\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.381966			−0.381966
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.564602	+	1.73767i	0.564602	+	1.73767i	0.669131	+	0.743145i	$0.266667\pi$
$97$	0.564602	+	1.73767i	0.564602	+	1.73767i	−0.104528	+	0.994522i	$0.533333\pi$
$98$		0			0
$99$	−0.956295			−0.956295
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		0			0
$103$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$103$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$109$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$110$		0			0
$111$	−0.169131	−	0.122881i	−0.169131	−	0.122881i
$112$		0			0
$113$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.978148	−	0.207912i	$-0.933333\pi$
$113$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.104528	+	0.994522i	$0.533333\pi$
$114$		0			0
$115$	−0.139886	+	1.33093i	−0.139886	+	1.33093i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.309017	+	0.951057i	0.309017	+	0.951057i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			1.00000
$126$		0			0
$127$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$127$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$131$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.0427497	+	0.406737i	−0.0427497	+	0.406737i
$136$		0			0
$137$	1.58268	−	1.14988i	1.58268	−	1.14988i	0.669131	−	0.743145i	$-0.266667\pi$
$137$	1.58268	−	1.14988i	1.58268	−	1.14988i	0.913545	−	0.406737i	$-0.133333\pi$
$138$		0			0
$139$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$139$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$140$		0			0
$141$	0.338261	−	0.245761i	0.338261	−	0.245761i
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.78716	+	0.379874i	−1.78716	+	0.379874i
$156$		0			0
$157$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$157$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$158$		0			0
$159$	−0.273659	+	0.198825i	−0.273659	+	0.198825i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$163$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$164$		0			0
$165$	0.204489	−	0.0434654i	0.204489	−	0.0434654i
$166$		0			0
$167$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$167$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$173$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.0353579	−	0.0256890i	−0.0353579	−	0.0256890i
$178$		0			0
$179$	0.413545	+	1.27276i	0.413545	+	1.27276i	0.913545	+	0.406737i	$0.133333\pi$
$179$	0.413545	+	1.27276i	0.413545	+	1.27276i	−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$181$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.978148	−	0.207912i	$-0.933333\pi$
$191$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.104528	+	0.994522i	$0.533333\pi$
$192$		0			0
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$197$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$198$		0			0
$199$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$199$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$200$		0			0
$201$	0.408977			0.408977
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.27977			−1.27977
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$211$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$212$		0			0
$213$	−0.0353579	+	0.0256890i	−0.0353579	+	0.0256890i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.169131	+	0.122881i	0.169131	+	0.122881i	0.669131	−	0.743145i	$-0.266667\pi$
$223$	0.169131	+	0.122881i	0.169131	+	0.122881i	−0.500000	+	0.866025i	$0.666667\pi$
$224$		0			0
$225$	0.0999601	+	0.951057i	0.0999601	+	0.951057i
$226$		0			0
$227$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$227$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$228$		0			0
$229$	0.413545	+	1.27276i	0.413545	+	1.27276i	0.913545	+	0.406737i	$0.133333\pi$
$229$	0.413545	+	1.27276i	0.413545	+	1.27276i	−0.500000	+	0.866025i	$0.666667\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$233$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$234$		0			0
$235$	1.33826	−	1.48629i	1.33826	−	1.48629i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$239$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$240$		0			0
$241$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$241$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$242$		0			0
$243$	−0.591023			−0.591023
$244$		0			0
$245$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$251$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$252$		0			0
$253$	0.413545	+	1.27276i	0.413545	+	1.27276i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$257$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$263$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$264$		0			0
$265$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$266$		0			0
$267$	0.126381	−	0.388960i	0.126381	−	0.388960i
$268$		0			0
$269$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$269$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$270$		0			0
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.913545	−	0.406737i	0.913545	−	0.406737i
$276$		0			0
$277$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$277$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$278$		0			0
$279$	−0.539926	−	1.66172i	−0.539926	−	1.66172i
$280$		0			0
$281$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$281$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$282$		0			0
$283$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$283$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$290$		0			0
$291$	0.309017	−	0.224514i	0.309017	−	0.224514i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$	−0.190983	−	0.0850311i	−0.190983	−	0.0850311i
$296$		0			0
$297$	0.126381	+	0.388960i	0.126381	+	0.388960i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	0.104528	−	0.0759444i	0.104528	−	0.0759444i
$310$		0			0
$311$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$311$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.978148	−	0.207912i	$-0.933333\pi$
$313$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.104528	+	0.994522i	$0.533333\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$317$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.413545	−	1.27276i	0.413545	−	1.27276i	−0.500000	−	0.866025i	$-0.666667\pi$
$331$	0.413545	−	1.27276i	0.413545	−	1.27276i	0.913545	−	0.406737i	$-0.133333\pi$
$332$		0			0
$333$	0.295511	−	0.909491i	0.295511	−	0.909491i
$334$		0			0
$335$	1.91355	−	0.406737i	1.91355	−	0.406737i
$336$		0			0
$337$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$337$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$338$		0			0
$339$	0.226341	+	0.164446i	0.226341	+	0.164446i
$340$		0			0
$341$	−1.47815	+	1.07394i	−1.47815	+	1.07394i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.273659	−	0.0581680i	0.273659	−	0.0581680i
$346$		0			0
$347$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$347$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$353$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$354$		0			0
$355$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$359$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$360$		0			0
$361$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$362$		0			0
$363$	0.169131	−	0.122881i	0.169131	−	0.122881i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.413545	−	1.27276i	0.413545	−	1.27276i	−0.500000	−	0.866025i	$-0.666667\pi$
$367$	0.413545	−	1.27276i	0.413545	−	1.27276i	0.913545	−	0.406737i	$-0.133333\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$373$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$374$		0			0
$375$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$379$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$383$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.978148	−	0.207912i	$-0.933333\pi$
$389$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.500000	−	0.866025i	$-0.666667\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$397$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$401$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.851767	+	0.181049i	−0.851767	+	0.181049i
$406$		0			0
$407$	−1.00000			−1.00000
$408$		0			0
$409$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$409$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$410$		0			0
$411$	−0.330869	−	0.240391i	−0.330869	−	0.240391i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$419$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$420$		0			0
$421$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$421$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$	1.54732	+	1.12419i	1.54732	+	1.12419i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$		0			0
$433$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$433$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$439$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$440$		0			0
$441$	0.773659	−	0.562096i	0.773659	−	0.562096i
$442$		0			0
$443$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$443$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$444$		0			0
$445$	0.204489	−	1.94558i	0.204489	−	1.94558i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$449$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$461$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$462$		0			0
$463$	1.58268	−	1.14988i	1.58268	−	1.14988i	0.669131	−	0.743145i	$-0.266667\pi$
$463$	1.58268	−	1.14988i	1.58268	−	1.14988i	0.913545	−	0.406737i	$-0.133333\pi$
$464$		0			0
$465$	0.190983	+	0.330792i	0.190983	+	0.330792i
$466$		0			0
$467$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$467$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.126381	+	0.388960i	0.126381	+	0.388960i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.25181	−	0.909491i	−1.25181	−	0.909491i
$478$		0			0
$479$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$479$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.22256	−	1.35779i	1.22256	−	1.35779i
$486$		0			0
$487$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$487$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$488$		0			0
$489$	−0.273659	−	0.198825i	−0.273659	−	0.198825i
$490$		0			0
$491$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$491$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.478148	+	0.828176i	0.478148	+	0.828176i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$499$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$503$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.209057			−0.209057
$508$		0			0
$509$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.978148	−	0.207912i	$-0.933333\pi$
$509$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.104528	+	0.994522i	$0.533333\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.413545	−	0.459289i	0.413545	−	0.459289i
$516$		0			0
$517$	0.618034	−	1.90211i	0.618034	−	1.90211i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.413545	+	1.27276i	0.413545	+	1.27276i	0.913545	+	0.406737i	$0.133333\pi$
$521$	0.413545	+	1.27276i	0.413545	+	1.27276i	−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.244415	+	0.752232i	0.244415	+	0.752232i
$530$		0			0
$531$	0.0617787	−	0.190135i	0.0617787	−	0.190135i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.226341	−	0.164446i	0.226341	−	0.164446i
$538$		0			0
$539$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$540$		0			0
$541$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$541$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$542$		0			0
$543$	0.209057			0.209057
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$547$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.0218524	+	0.207912i	−0.0218524	+	0.207912i
$556$		0			0
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$563$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$564$		0			0
$565$	1.22256	+	0.544320i	1.22256	+	0.544320i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$569$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$570$		0			0
$571$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$571$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$572$		0			0
$573$	0.226341	+	0.164446i	0.226341	+	0.164446i
$574$		0			0
$575$	1.22256	−	0.544320i	1.22256	−	0.544320i
$576$		0			0
$577$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.978148	−	0.207912i	$-0.933333\pi$
$577$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.500000	−	0.866025i	$-0.666667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$587$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.0399263	−	0.122881i	−0.0399263	−	0.122881i
$598$		0			0
$599$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$599$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$600$		0			0
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$	0.578108	+	1.77923i	0.578108	+	1.77923i
$604$		0			0
$605$	0.669131	−	0.743145i	0.669131	−	0.743145i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$613$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$617$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$618$		0			0
$619$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$619$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$620$		0			0
$621$	0.169131	+	0.520530i	0.169131	+	0.520530i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.104528	+	0.994522i	$0.533333\pi$
$631$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.500000	+	0.866025i	$0.666667\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.161739	−	0.117510i	−0.161739	−	0.117510i
$640$		0			0
$641$	−1.47815	+	1.07394i	−1.47815	+	1.07394i	−0.500000	+	0.866025i	$0.666667\pi$
$641$	−1.47815	+	1.07394i	−1.47815	+	1.07394i	−0.978148	+	0.207912i	$0.933333\pi$
$642$		0			0
$643$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$643$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.413545	+	1.27276i	0.413545	+	1.27276i	0.913545	+	0.406737i	$0.133333\pi$
$647$	0.413545	+	1.27276i	0.413545	+	1.27276i	−0.500000	+	0.866025i	$0.666667\pi$
$648$		0			0
$649$	−0.209057			−0.209057
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.564602	+	1.73767i	0.564602	+	1.73767i	0.669131	+	0.743145i	$0.266667\pi$
$653$	0.564602	+	1.73767i	0.564602	+	1.73767i	−0.104528	+	0.994522i	$0.533333\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$659$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.913545	+	0.406737i	$0.133333\pi$
$661$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.669131	+	0.743145i	$0.266667\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	0.0135055	−	0.0415657i	0.0135055	−	0.0415657i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$673$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$674$		0			0
$675$	0.373619	−	0.166346i	0.373619	−	0.166346i
$676$		0			0
$677$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$677$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$683$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$684$		0			0
$685$	−1.78716	−	0.795697i	−1.78716	−	0.795697i
$686$		0			0
$687$	0.226341	−	0.164446i	0.226341	−	0.164446i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.978148	−	0.207912i	$-0.933333\pi$
$691$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.104528	+	0.994522i	$0.533333\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.381966	−	0.170062i	−0.381966	−	0.170062i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.47815	+	1.07394i	−1.47815	+	1.07394i	−0.500000	+	0.866025i	$0.666667\pi$
$709$	−1.47815	+	1.07394i	−1.47815	+	1.07394i	−0.978148	+	0.207912i	$0.933333\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.97815	+	1.43721i	−1.97815	+	1.43721i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.104528	+	0.994522i	$0.533333\pi$
$719$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.978148	−	0.207912i	$-0.933333\pi$
$727$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.500000	−	0.866025i	$-0.666667\pi$
$728$		0			0
$729$	−0.230909	−	0.710666i	−0.230909	−	0.710666i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$736$		0			0
$737$	1.58268	−	1.14988i	1.58268	−	1.14988i
$738$		0			0
$739$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$739$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$751$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$752$		0			0
$753$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$757$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$758$		0			0
$759$	0.226341	−	0.164446i	0.226341	−	0.164446i
$760$		0			0
$761$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$761$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$769$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$770$		0			0
$771$	−0.0399263	−	0.122881i	−0.0399263	−	0.122881i
$772$		0			0
$773$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$773$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$774$		0			0
$775$	1.22256	+	1.35779i	1.22256	+	1.35779i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.978148	+	1.69420i	0.978148	+	1.69420i
$786$		0			0
$787$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$787$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.309017	+	0.137583i	0.309017	+	0.137583i
$796$		0			0
$797$	−0.604528	−	1.86055i	−0.604528	−	1.86055i	−0.500000	−	0.866025i	$-0.666667\pi$
$797$	−0.604528	−	1.86055i	−0.604528	−	1.86055i	−0.104528	−	0.994522i	$-0.533333\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	1.87080			1.87080
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.129204			−0.129204
$808$		0			0
$809$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$809$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$810$		0			0
$811$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$811$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$821$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$822$		0			0
$823$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.978148	−	0.207912i	$-0.933333\pi$
$823$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.500000	−	0.866025i	$-0.666667\pi$
$824$		0			0
$825$	−0.139886	−	0.155360i	−0.139886	−	0.155360i
$826$		0			0
$827$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$827$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$828$		0			0
$829$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	0.913545	−	0.406737i	$-0.133333\pi$
$829$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	−0.978148	+	0.207912i	$0.933333\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.604528	+	0.439216i	−0.604528	+	0.439216i
$838$		0			0
$839$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.913545	+	0.406737i	$0.133333\pi$
$839$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.669131	+	0.743145i	$0.266667\pi$
$840$		0			0
$841$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.33826			−1.33826
$852$		0			0
$853$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$853$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	0.169131	−	0.122881i	0.169131	−	0.122881i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.169131	−	0.122881i	0.169131	−	0.122881i	0.669131	+	0.743145i	$0.266667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$863$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.41355	+	1.02700i	1.41355	+	1.02700i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$877$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i	−0.978148	−	0.207912i	$-0.933333\pi$
$881$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i	0.913545	+	0.406737i	$0.133333\pi$
$882$		0			0
$883$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$883$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$884$		0			0
$885$	−0.00456840	+	0.0434654i	−0.00456840	+	0.0434654i
$886$		0			0
$887$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$887$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.704489	+	0.511841i	−0.704489	+	0.511841i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	0.895472	−	0.994522i	0.895472	−	0.994522i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.978148	−	0.207912i	0.978148	−	0.207912i
$906$		0			0
$907$	2.00000			2.00000			1.00000			$0$
$907$	2.00000			2.00000			1.00000			$0$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$911$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$919$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.104528	+	0.994522i	0.104528	+	0.994522i
$926$		0			0
$927$	0.478148	+	0.347395i	0.478148	+	0.347395i
$928$		0			0
$929$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$929$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.0399263	+	0.122881i	−0.0399263	+	0.122881i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$937$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$938$		0			0
$939$	0.226341	+	0.164446i	0.226341	+	0.164446i
$940$		0			0
$941$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$941$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.564602	+	1.73767i	0.564602	+	1.73767i	0.669131	+	0.743145i	$0.266667\pi$
$947$	0.564602	+	1.73767i	0.564602	+	1.73767i	−0.104528	+	0.994522i	$0.533333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−0.381966			−0.381966
$952$		0			0
$953$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$953$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$954$		0			0
$955$	1.22256	+	0.544320i	1.22256	+	0.544320i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−1.89169	−	1.37440i	−1.89169	−	1.37440i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$967$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.564602	+	1.73767i	0.564602	+	1.73767i	0.669131	+	0.743145i	$0.266667\pi$
$971$	0.564602	+	1.73767i	0.564602	+	1.73767i	−0.104528	+	0.994522i	$0.533333\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$977$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$978$		0			0
$979$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.104528	+	0.994522i	$0.533333\pi$
$983$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.500000	+	0.866025i	$0.666667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$991$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$992$		0			0
$993$	−0.279773			−0.279773
$994$		0			0
$995$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$996$		0			0
$997$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$997$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$998$		0			0
$999$	−0.408977			−0.408977

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.1.x.a.241.1	✓	8
11.10	odd	2	CM	1100.1.x.a.241.1	✓	8
25.11	even	5	inner	1100.1.x.a.461.1	yes	8
275.186	odd	10	inner	1100.1.x.a.461.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.1.x.a.241.1	✓	8	1.1	even	1	trivial
1100.1.x.a.241.1	✓	8	11.10	odd	2	CM
1100.1.x.a.461.1	yes	8	25.11	even	5	inner
1100.1.x.a.461.1	yes	8	275.186	odd	10	inner

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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

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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	1100.1.x.a.241.1

Level	$1100$
Weight	$1$
Character	1100.241
Analytic conductor	$0.549$
Analytic rank	$0$
Dimension	$8$
Projective image	$D_{15}$
CM discriminant	-11
Inner twists	$4$