LMFDB - Embedded newform 799.1.c.d.798.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,1,Mod(798,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("799.798");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$799 = 17 \cdot 47$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	799.c (of order $2$ , degree $1$ , 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:	$0.398752945094$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{10}$
Projective field:	Galois closure of 10.2.6928449225617.1

Embedding invariants

Embedding label			798.2
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	799.798
Dual form			799.1.c.d.798.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{2} +1.17557i q^{3} -0.618034 q^{4} -0.726543i q^{6} +1.90211i q^{7} +1.00000 q^{8} -0.381966 q^{9} -0.726543i q^{12} -1.17557i q^{14} +(-0.809017 - 0.587785i) q^{17} +0.236068 q^{18} -2.23607 q^{21} +1.17557i q^{24} -1.00000 q^{25} +0.726543i q^{27} -1.17557i q^{28} -1.00000 q^{32} +(0.500000 + 0.363271i) q^{34} +0.236068 q^{36} +1.17557i q^{37} +1.38197 q^{42} +1.00000 q^{47} -2.61803 q^{49} +0.618034 q^{50} +(0.690983 - 0.951057i) q^{51} +0.618034 q^{53} -0.449028i q^{54} +1.90211i q^{56} -0.618034 q^{59} -1.90211i q^{61} -0.726543i q^{63} +0.618034 q^{64} +(0.500000 + 0.363271i) q^{68} -1.17557i q^{71} -0.381966 q^{72} -0.726543i q^{74} -1.17557i q^{75} +1.17557i q^{79} -1.23607 q^{81} +2.00000 q^{83} +1.38197 q^{84} +0.618034 q^{89} -0.618034 q^{94} -1.17557i q^{96} +1.90211i q^{97} +1.61803 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 2 q^{2} + 2 q^{4} + 4 q^{8} - 6 q^{9} - q^{17} - 8 q^{18} - 4 q^{25} - 4 q^{32} + 2 q^{34} - 8 q^{36} + 10 q^{42} + 4 q^{47} - 6 q^{49} - 2 q^{50} + 5 q^{51} - 2 q^{53} + 2 q^{59} - 2 q^{64} + 2 q^{68}+ \cdots + 2 q^{98}+O(q^{100})$ 4 * q + 2 * q^2 + 2 * q^4 + 4 * q^8 - 6 * q^9 - q^17 - 8 * q^18 - 4 * q^25 - 4 * q^32 + 2 * q^34 - 8 * q^36 + 10 * q^42 + 4 * q^47 - 6 * q^49 - 2 * q^50 + 5 * q^51 - 2 * q^53 + 2 * q^59 - 2 * q^64 + 2 * q^68 - 6 * q^72 + 4 * q^81 + 8 * q^83 + 10 * q^84 - 2 * q^89 + 2 * q^94 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/799\mathbb{Z}\right)^\times$ .

$n$	$52$	$377$
$\chi(n)$	$-1$	$-1$

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

)

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

$2$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$2$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$3$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$3$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$4$	−0.618034			−0.618034
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		−	0.726543i		−	0.726543i
$7$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$7$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$8$	1.00000			1.00000
$9$	−0.381966			−0.381966
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		−	0.726543i		−	0.726543i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		−	1.17557i		−	1.17557i
$15$		0			0
$16$		0			0
$17$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$17$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$18$	0.236068			0.236068
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	−2.23607			−2.23607
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$			1.17557i			1.17557i
$25$	−1.00000			−1.00000
$26$		0			0
$27$			0.726543i			0.726543i
$28$		−	1.17557i		−	1.17557i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−1.00000			−1.00000
$33$		0			0
$34$	0.500000	+	0.363271i	0.500000	+	0.363271i
$35$		0			0
$36$	0.236068			0.236068
$37$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$37$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	1.38197			1.38197
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.00000			1.00000
$47$	1.00000			1.00000
$48$		0			0
$49$	−2.61803			−2.61803
$50$	0.618034			0.618034
$51$	0.690983	−	0.951057i	0.690983	−	0.951057i
$52$		0			0
$53$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$53$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$54$		−	0.449028i		−	0.449028i
$55$		0			0
$56$			1.90211i			1.90211i
$57$		0			0
$58$		0			0
$59$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$59$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$60$		0			0
$61$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$61$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$62$		0			0
$63$		−	0.726543i		−	0.726543i
$64$	0.618034			0.618034
$65$		0			0
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	0.500000	+	0.363271i	0.500000	+	0.363271i
$69$		0			0
$70$		0			0
$71$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$71$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$72$	−0.381966			−0.381966
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$		−	0.726543i		−	0.726543i
$75$		−	1.17557i		−	1.17557i
$76$		0			0
$77$		0			0
$78$		0			0
$79$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$79$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$80$		0			0
$81$	−1.23607			−1.23607
$82$		0			0
$83$	2.00000			2.00000			1.00000			$0$
$83$	2.00000			2.00000			1.00000			$0$
$84$	1.38197			1.38197
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$89$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.618034			−0.618034
$95$		0			0
$96$		−	1.17557i		−	1.17557i
$97$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$97$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$98$	1.61803			1.61803
$99$		0			0
$100$	0.618034			0.618034
$101$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$101$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$102$	−0.427051	+	0.587785i	−0.427051	+	0.587785i
$103$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$103$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$104$		0			0
$105$		0			0
$106$	−0.381966			−0.381966
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		−	0.449028i		−	0.449028i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−1.38197			−1.38197
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.381966			0.381966
$119$	1.11803	−	1.53884i	1.11803	−	1.53884i
$120$		0			0
$121$	−1.00000			−1.00000
$122$			1.17557i			1.17557i
$123$		0			0
$124$		0			0
$125$		0			0
$126$			0.449028i			0.449028i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	0.618034			0.618034
$129$		0			0
$130$		0			0
$131$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$131$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$			1.17557i			1.17557i
$142$			0.726543i			0.726543i
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	3.07768i		−	3.07768i
$148$		−	0.726543i		−	0.726543i
$149$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$149$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$150$			0.726543i			0.726543i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$	0.309017	+	0.224514i	0.309017	+	0.224514i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$157$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$158$		−	0.726543i		−	0.726543i
$159$			0.726543i			0.726543i
$160$		0			0
$161$		0			0
$162$	0.763932			0.763932
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$		0			0
$165$		0			0
$166$	−1.23607			−1.23607
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	−2.23607			−2.23607
$169$	1.00000			1.00000
$170$		0			0
$171$		0			0
$172$		0			0
$173$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$173$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$174$		0			0
$175$		−	1.90211i		−	1.90211i
$176$		0			0
$177$		−	0.726543i		−	0.726543i
$178$	−0.381966			−0.381966
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	2.23607			2.23607
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.618034			−0.618034
$189$	−1.38197			−1.38197
$190$		0			0
$191$	−2.00000			−2.00000			−1.00000			$\pi$
$191$	−2.00000			−2.00000			−1.00000			$\pi$
$192$			0.726543i			0.726543i
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$		−	1.17557i		−	1.17557i
$195$		0			0
$196$	1.61803			1.61803
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−1.00000			−1.00000
$201$		0			0
$202$	−1.00000			−1.00000
$203$		0			0
$204$	−0.427051	+	0.587785i	−0.427051	+	0.587785i
$205$		0			0
$206$	−1.00000			−1.00000
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	−0.381966			−0.381966
$213$	1.38197			1.38197
$214$		0			0
$215$		0			0
$216$			0.726543i			0.726543i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	0.854102			0.854102
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		−	1.90211i		−	1.90211i
$225$	0.381966			0.381966
$226$		0			0
$227$		0			0			−	1.00000i	$-0.5\pi$
$227$		0			0				1.00000i	$0.5\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$		0			0
$236$	0.381966			0.381966
$237$	−1.38197			−1.38197
$238$	−0.690983	+	0.951057i	−0.690983	+	0.951057i
$239$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$239$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$240$		0			0
$241$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$241$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$242$	0.618034			0.618034
$243$		−	0.726543i		−	0.726543i
$244$			1.17557i			1.17557i
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$			2.35114i			2.35114i
$250$		0			0
$251$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$251$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$252$			0.449028i			0.449028i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−1.00000			−1.00000
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$		0			0
$259$	−2.23607			−2.23607
$260$		0			0
$261$		0			0
$262$		−	1.17557i		−	1.17557i
$263$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$263$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			0.726543i			0.726543i
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$271$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$277$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		−	0.726543i		−	0.726543i
$283$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$283$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$284$			0.726543i			0.726543i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.381966			0.381966
$289$	0.309017	+	0.951057i	0.309017	+	0.951057i
$290$		0			0
$291$	−2.23607			−2.23607
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$			1.90211i			1.90211i
$295$		0			0
$296$			1.17557i			1.17557i
$297$		0			0
$298$	−1.00000			−1.00000
$299$		0			0
$300$			0.726543i			0.726543i
$301$		0			0
$302$		0			0
$303$			1.90211i			1.90211i
$304$		0			0
$305$		0			0
$306$	−0.190983	−	0.138757i	−0.190983	−	0.138757i
$307$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$307$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$308$		0			0
$309$			1.90211i			1.90211i
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$	0.381966			0.381966
$315$		0			0
$316$		−	0.726543i		−	0.726543i
$317$		0			0			−	1.00000i	$-0.5\pi$
$317$		0			0				1.00000i	$0.5\pi$
$318$		−	0.449028i		−	0.449028i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.763932			0.763932
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$			1.90211i			1.90211i
$330$		0			0
$331$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$331$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$332$	−1.23607			−1.23607
$333$		−	0.449028i		−	0.449028i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$337$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$338$	−0.618034			−0.618034
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		−	3.07768i		−	3.07768i
$344$		0			0
$345$		0			0
$346$			1.17557i			1.17557i
$347$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$347$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$			1.17557i			1.17557i
$351$		0			0
$352$		0			0
$353$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$353$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$354$			0.449028i			0.449028i
$355$		0			0
$356$	−0.381966			−0.381966
$357$	1.80902	+	1.31433i	1.80902	+	1.31433i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	1.00000			1.00000
$362$		0			0
$363$		−	1.17557i		−	1.17557i
$364$		0			0
$365$		0			0
$366$	−1.38197			−1.38197
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$			1.17557i			1.17557i
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$	1.00000			1.00000
$377$		0			0
$378$	0.854102			0.854102
$379$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$379$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$380$		0			0
$381$		0			0
$382$	1.23607			1.23607
$383$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$383$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$384$			0.726543i			0.726543i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		−	1.17557i		−	1.17557i
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	−2.61803			−2.61803
$393$	−2.23607			−2.23607
$394$		0			0
$395$		0			0
$396$		0			0
$397$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$397$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$401$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$402$		0			0
$403$		0			0
$404$	−1.00000			−1.00000
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.690983	−	0.951057i	0.690983	−	0.951057i
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−1.00000			−1.00000
$413$		−	1.17557i		−	1.17557i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$	−0.381966			−0.381966
$424$	0.618034			0.618034
$425$	0.809017	+	0.587785i	0.809017	+	0.587785i
$426$	−0.854102			−0.854102
$427$	3.61803			3.61803
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$431$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$432$		0			0
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	1.00000			1.00000
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	0.854102			0.854102
$445$		0			0
$446$		0			0
$447$			1.90211i			1.90211i
$448$			1.17557i			1.17557i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−0.236068			−0.236068
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$458$		0			0
$459$	0.427051	−	0.587785i	0.427051	−	0.587785i
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		−	0.726543i		−	0.726543i
$472$	−0.618034			−0.618034
$473$		0			0
$474$	0.854102			0.854102
$475$		0			0
$476$	−0.690983	+	0.951057i	−0.690983	+	0.951057i
$477$	−0.236068			−0.236068
$478$	1.00000			1.00000
$479$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$479$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$480$		0			0
$481$		0			0
$482$		−	0.726543i		−	0.726543i
$483$		0			0
$484$	0.618034			0.618034
$485$		0			0
$486$			0.449028i			0.449028i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		−	1.90211i		−	1.90211i
$489$		0			0
$490$		0			0
$491$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$491$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.23607			2.23607
$498$		−	1.45309i		−	1.45309i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$		0			0
$501$		0			0
$502$	−1.00000			−1.00000
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		−	0.726543i		−	0.726543i
$505$		0			0
$506$		0			0
$507$			1.17557i			1.17557i
$508$		0			0
$509$		0			0		1.00000			$0$
$509$		0			0		−1.00000			$\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.38197			1.38197
$519$	2.23607			2.23607
$520$		0			0
$521$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$521$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$522$		0			0
$523$	2.00000			2.00000			1.00000			$0$
$523$	2.00000			2.00000			1.00000			$0$
$524$		−	1.17557i		−	1.17557i
$525$	2.23607			2.23607
$526$	0.381966			0.381966
$527$		0			0
$528$		0			0
$529$	−1.00000			−1.00000
$530$		0			0
$531$	0.236068			0.236068
$532$		0			0
$533$		0			0
$534$		−	0.449028i		−	0.449028i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$541$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$542$	−1.00000			−1.00000
$543$		0			0
$544$	0.809017	+	0.587785i	0.809017	+	0.587785i
$545$		0			0
$546$		0			0
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$		0			0
$549$			0.726543i			0.726543i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−2.23607			−2.23607
$554$			0.726543i			0.726543i
$555$		0			0
$556$		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		1.00000			$0$
$563$		0			0		−1.00000			$\pi$
$564$		−	0.726543i		−	0.726543i
$565$		0			0
$566$		−	1.17557i		−	1.17557i
$567$		−	2.35114i		−	2.35114i
$568$		−	1.17557i		−	1.17557i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$571$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$572$		0			0
$573$		−	2.35114i		−	2.35114i
$574$		0			0
$575$		0			0
$576$	−0.236068			−0.236068
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$579$		0			0
$580$		0			0
$581$			3.80423i			3.80423i
$582$	1.38197			1.38197
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$			1.90211i			1.90211i
$589$		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
$596$	−1.00000			−1.00000
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		−	1.17557i		−	1.17557i
$601$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$601$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		−	1.17557i		−	1.17557i
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.190983	−	0.138757i	−0.190983	−	0.138757i
$613$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$613$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$614$	−1.00000			−1.00000
$615$		0			0
$616$		0			0
$617$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$617$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$618$		−	1.17557i		−	1.17557i
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			1.17557i			1.17557i
$624$		0			0
$625$	1.00000			1.00000
$626$		0			0
$627$		0			0
$628$	0.381966			0.381966
$629$	0.690983	−	0.951057i	0.690983	−	0.951057i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$			1.17557i			1.17557i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		−	0.449028i		−	0.449028i
$637$		0			0
$638$		0			0
$639$			0.449028i			0.449028i
$640$		0			0
$641$		0			0			−	1.00000i	$-0.5\pi$
$641$		0			0				1.00000i	$0.5\pi$
$642$		0			0
$643$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$643$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$647$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$648$	−1.23607			−1.23607
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$653$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		−	1.17557i		−	1.17557i
$659$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$659$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$661$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$662$	0.381966			0.381966
$663$		0			0
$664$	2.00000			2.00000
$665$		0			0
$666$			0.277515i			0.277515i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	2.23607			2.23607
$673$		0			0			−	1.00000i	$-0.5\pi$
$673$		0			0				1.00000i	$0.5\pi$
$674$			1.17557i			1.17557i
$675$		−	0.726543i		−	0.726543i
$676$	−0.618034			−0.618034
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$	−3.61803			−3.61803
$680$		0			0
$681$		0			0
$682$		0			0
$683$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$683$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$684$		0			0
$685$		0			0
$686$			1.90211i			1.90211i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$			1.17557i			1.17557i
$693$		0			0
$694$			0.726543i			0.726543i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$			1.17557i			1.17557i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.381966			0.381966
$707$			3.07768i			3.07768i
$708$			0.449028i			0.449028i
$709$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$709$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$710$		0			0
$711$		−	0.449028i		−	0.449028i
$712$	0.618034			0.618034
$713$		0			0
$714$	−1.11803	−	0.812299i	−1.11803	−	0.812299i
$715$		0			0
$716$		0			0
$717$		−	1.90211i		−	1.90211i
$718$		0			0
$719$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$719$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$720$		0			0
$721$			3.07768i			3.07768i
$722$	−0.618034			−0.618034
$723$	−1.38197			−1.38197
$724$		0			0
$725$		0			0
$726$			0.726543i			0.726543i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−0.381966			−0.381966
$730$		0			0
$731$		0			0
$732$	−1.38197			−1.38197
$733$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$733$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$739$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$		0			0
$742$		−	0.726543i		−	0.726543i
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.763932			−0.763932
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$			1.90211i			1.90211i
$754$		0			0
$755$		0			0
$756$	0.854102			0.854102
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$			1.17557i			1.17557i
$759$		0			0
$760$		0			0
$761$	−2.00000			−2.00000			−1.00000			$\pi$
$761$	−2.00000			−2.00000			−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$	1.23607			1.23607
$765$		0			0
$766$	1.00000			1.00000
$767$		0			0
$768$		−	1.17557i		−	1.17557i
$769$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$769$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$773$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$774$		0			0
$775$		0			0
$776$			1.90211i			1.90211i
$777$		−	2.62866i		−	2.62866i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	1.38197			1.38197
$787$		0			0			−	1.00000i	$-0.5\pi$
$787$		0			0				1.00000i	$0.5\pi$
$788$		0			0
$789$		−	0.726543i		−	0.726543i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		−	0.726543i		−	0.726543i
$795$		0			0
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$800$	1.00000			1.00000
$801$	−0.236068			−0.236068
$802$			0.726543i			0.726543i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	1.61803			1.61803
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$		0			0
$811$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$811$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$812$		0			0
$813$			1.90211i			1.90211i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0			−	1.00000i	$-0.5\pi$
$821$		0			0				1.00000i	$0.5\pi$
$822$		0			0
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$	1.61803			1.61803
$825$		0			0
$826$			0.726543i			0.726543i
$827$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$827$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	1.38197			1.38197
$832$		0			0
$833$	2.11803	+	1.53884i	2.11803	+	1.53884i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−1.00000			−1.00000
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	0.236068			0.236068
$847$		−	1.90211i		−	1.90211i
$848$		0			0
$849$	−2.23607			−2.23607
$850$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$851$		0			0
$852$	−0.854102			−0.854102
$853$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$853$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$854$	−2.23607			−2.23607
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$			1.17557i			1.17557i
$863$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$863$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$864$		−	0.726543i		−	0.726543i
$865$		0			0
$866$		0			0
$867$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		−	0.726543i		−	0.726543i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0			−	1.00000i	$-0.5\pi$
$877$		0			0				1.00000i	$0.5\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−0.618034			−0.618034
$883$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$883$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$	−1.38197			−1.38197
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		−	1.17557i		−	1.17557i
$895$		0			0
$896$			1.17557i			1.17557i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.236068			−0.236068
$901$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		1.00000			$0$
$907$		0			0		−1.00000			$\pi$
$908$		0			0
$909$	−0.618034			−0.618034
$910$		0			0
$911$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$911$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$912$		0			0
$913$		0			0
$914$	1.00000			1.00000
$915$		0			0
$916$		0			0
$917$	−3.61803			−3.61803
$918$	−0.263932	+	0.363271i	−0.263932	+	0.363271i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$			1.90211i			1.90211i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		−	1.17557i		−	1.17557i
$926$		0			0
$927$	−0.618034			−0.618034
$928$		0			0
$929$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$929$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$941$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$942$			0.449028i			0.449028i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$	0.854102			0.854102
$949$		0			0
$950$		0			0
$951$		0			0
$952$	1.11803	−	1.53884i	1.11803	−	1.53884i
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$	0.145898			0.145898
$955$		0			0
$956$	1.00000			1.00000
$957$		0			0
$958$			1.17557i			1.17557i
$959$		0			0
$960$		0			0
$961$	−1.00000			−1.00000
$962$		0			0
$963$		0			0
$964$		−	0.726543i		−	0.726543i
$965$		0			0
$966$		0			0
$967$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$967$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$968$	−1.00000			−1.00000
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$			0.449028i			0.449028i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.00000			−2.00000			−1.00000			$\pi$
$977$	−2.00000			−2.00000			−1.00000			$\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.381966			−0.381966
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.23607			−2.23607
$988$		0			0
$989$		0			0
$990$		0			0
$991$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$991$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$992$		0			0
$993$		−	0.726543i		−	0.726543i
$994$	−1.38197			−1.38197
$995$		0			0
$996$		−	1.45309i		−	1.45309i
$997$		0			0			−	1.00000i	$-0.5\pi$
$997$		0			0				1.00000i	$0.5\pi$
$998$		0			0
$999$	−0.854102			−0.854102

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	799.1.c.d.798.2	yes	4
17.16	even	2	inner	799.1.c.d.798.1	✓	4
47.46	odd	2	CM	799.1.c.d.798.2	yes	4
799.798	odd	2	inner	799.1.c.d.798.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.1.c.d.798.1	✓	4	17.16	even	2	inner
799.1.c.d.798.1	✓	4	799.798	odd	2	inner
799.1.c.d.798.2	yes	4	1.1	even	1	trivial
799.1.c.d.798.2	yes	4	47.46	odd	2	CM

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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	799.1.c.d.798.2

Level	$799$
Weight	$1$
Character	799.798
Analytic conductor	$0.399$
Analytic rank	$0$
Dimension	$4$
Projective image	$D_{10}$
CM discriminant	-47
Inner twists	$4$