LMFDB - Dirichlet character orbit 41600.ze

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(41600, base_ring=CyclotomicField(480)) M = H._module chi = DirichletCharacter(H, M([0,285,384,320])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(61, 41600)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("41600.61"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$41600$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$41600$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$480$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{480})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 480 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{41600}(61,\cdot)$	$1$	$1$	$e\left(\frac{23}{480}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{449}{480}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{187}{480}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{143}{480}\right)$
$\chi_{41600}(341,\cdot)$	$1$	$1$	$e\left(\frac{217}{480}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{271}{480}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{53}{480}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{57}{160}\right)$	$e\left(\frac{97}{480}\right)$
$\chi_{41600}(581,\cdot)$	$1$	$1$	$e\left(\frac{29}{480}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{107}{480}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{361}{480}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{389}{480}\right)$
$\chi_{41600}(861,\cdot)$	$1$	$1$	$e\left(\frac{463}{480}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{169}{480}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{467}{480}\right)$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{103}{480}\right)$
$\chi_{41600}(1381,\cdot)$	$1$	$1$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{307}{480}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{161}{480}\right)$	$e\left(\frac{73}{160}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{149}{160}\right)$	$e\left(\frac{349}{480}\right)$
$\chi_{41600}(1621,\cdot)$	$1$	$1$	$e\left(\frac{281}{480}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{143}{480}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{157}{160}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{161}{480}\right)$
$\chi_{41600}(2141,\cdot)$	$1$	$1$	$e\left(\frac{47}{480}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{41}{480}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{403}{480}\right)$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{47}{160}\right)$	$e\left(\frac{167}{480}\right)$
$\chi_{41600}(2421,\cdot)$	$1$	$1$	$e\left(\frac{241}{480}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{343}{480}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{269}{480}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{81}{160}\right)$	$e\left(\frac{121}{480}\right)$
$\chi_{41600}(2661,\cdot)$	$1$	$1$	$e\left(\frac{53}{480}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{179}{480}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{97}{480}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{53}{160}\right)$	$e\left(\frac{413}{480}\right)$
$\chi_{41600}(2941,\cdot)$	$1$	$1$	$e\left(\frac{7}{480}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{241}{480}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{203}{480}\right)$	$e\left(\frac{99}{160}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{7}{160}\right)$	$e\left(\frac{127}{480}\right)$
$\chi_{41600}(3181,\cdot)$	$1$	$1$	$e\left(\frac{299}{480}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{77}{480}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{31}{480}\right)$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{419}{480}\right)$
$\chi_{41600}(3461,\cdot)$	$1$	$1$	$e\left(\frac{13}{480}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{379}{480}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{377}{480}\right)$	$e\left(\frac{1}{160}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{373}{480}\right)$
$\chi_{41600}(3981,\cdot)$	$1$	$1$	$e\left(\frac{259}{480}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{277}{480}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{311}{480}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{99}{160}\right)$	$e\left(\frac{379}{480}\right)$
$\chi_{41600}(4221,\cdot)$	$1$	$1$	$e\left(\frac{71}{480}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{113}{480}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{139}{480}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{71}{160}\right)$	$e\left(\frac{191}{480}\right)$
$\chi_{41600}(4741,\cdot)$	$1$	$1$	$e\left(\frac{77}{480}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{251}{480}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{313}{480}\right)$	$e\left(\frac{129}{160}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{437}{480}\right)$
$\chi_{41600}(5021,\cdot)$	$1$	$1$	$e\left(\frac{31}{480}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{313}{480}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{419}{480}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{31}{160}\right)$	$e\left(\frac{151}{480}\right)$
$\chi_{41600}(5261,\cdot)$	$1$	$1$	$e\left(\frac{323}{480}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{149}{480}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{247}{480}\right)$	$e\left(\frac{111}{160}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{3}{160}\right)$	$e\left(\frac{443}{480}\right)$
$\chi_{41600}(5541,\cdot)$	$1$	$1$	$e\left(\frac{37}{480}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{451}{480}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{113}{480}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{397}{480}\right)$
$\chi_{41600}(5781,\cdot)$	$1$	$1$	$e\left(\frac{329}{480}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{287}{480}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{421}{480}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{209}{480}\right)$
$\chi_{41600}(6061,\cdot)$	$1$	$1$	$e\left(\frac{283}{480}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{349}{480}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{47}{480}\right)$	$e\left(\frac{71}{160}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{123}{160}\right)$	$e\left(\frac{403}{480}\right)$
$\chi_{41600}(6581,\cdot)$	$1$	$1$	$e\left(\frac{289}{480}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{7}{480}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{221}{480}\right)$	$e\left(\frac{133}{160}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{129}{160}\right)$	$e\left(\frac{169}{480}\right)$
$\chi_{41600}(6821,\cdot)$	$1$	$1$	$e\left(\frac{101}{480}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{323}{480}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{49}{480}\right)$	$e\left(\frac{57}{160}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{101}{160}\right)$	$e\left(\frac{461}{480}\right)$
$\chi_{41600}(7341,\cdot)$	$1$	$1$	$e\left(\frac{347}{480}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{221}{480}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{463}{480}\right)$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{467}{480}\right)$
$\chi_{41600}(7621,\cdot)$	$1$	$1$	$e\left(\frac{61}{480}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{43}{480}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{329}{480}\right)$	$e\left(\frac{17}{160}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{421}{480}\right)$
$\chi_{41600}(7861,\cdot)$	$1$	$1$	$e\left(\frac{353}{480}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{359}{480}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{157}{480}\right)$	$e\left(\frac{101}{160}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{233}{480}\right)$
$\chi_{41600}(8141,\cdot)$	$1$	$1$	$e\left(\frac{307}{480}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{421}{480}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{263}{480}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{427}{480}\right)$
$\chi_{41600}(8381,\cdot)$	$1$	$1$	$e\left(\frac{119}{480}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{257}{480}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{91}{480}\right)$	$e\left(\frac{83}{160}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{119}{160}\right)$	$e\left(\frac{239}{480}\right)$
$\chi_{41600}(8661,\cdot)$	$1$	$1$	$e\left(\frac{313}{480}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{79}{480}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{437}{480}\right)$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{153}{160}\right)$	$e\left(\frac{193}{480}\right)$
$\chi_{41600}(9181,\cdot)$	$1$	$1$	$e\left(\frac{79}{480}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{457}{480}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{371}{480}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{199}{480}\right)$
$\chi_{41600}(9421,\cdot)$	$1$	$1$	$e\left(\frac{371}{480}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{293}{480}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{199}{480}\right)$	$e\left(\frac{127}{160}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{11}{480}\right)$
$\chi_{41600}(9941,\cdot)$	$1$	$1$	$e\left(\frac{377}{480}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{431}{480}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{373}{480}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{57}{160}\right)$	$e\left(\frac{257}{480}\right)$

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 $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{41600}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{480}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{449}{480}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{187}{480}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{143}{480}\right)\)
\(\chi_{41600}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{480}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{271}{480}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{53}{480}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{57}{160}\right)\)	\(e\left(\frac{97}{480}\right)\)
\(\chi_{41600}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{480}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{107}{480}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{361}{480}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{389}{480}\right)\)
\(\chi_{41600}(861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{463}{480}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{169}{480}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{467}{480}\right)\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{103}{480}\right)\)
\(\chi_{41600}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{307}{480}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{161}{480}\right)\)	\(e\left(\frac{73}{160}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{149}{160}\right)\)	\(e\left(\frac{349}{480}\right)\)
\(\chi_{41600}(1621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{480}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{143}{480}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{157}{160}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{161}{480}\right)\)
\(\chi_{41600}(2141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{480}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{41}{480}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{403}{480}\right)\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{47}{160}\right)\)	\(e\left(\frac{167}{480}\right)\)
\(\chi_{41600}(2421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{480}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{343}{480}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{269}{480}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{81}{160}\right)\)	\(e\left(\frac{121}{480}\right)\)
\(\chi_{41600}(2661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{480}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{179}{480}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{97}{480}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{53}{160}\right)\)	\(e\left(\frac{413}{480}\right)\)
\(\chi_{41600}(2941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{480}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{241}{480}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{203}{480}\right)\)	\(e\left(\frac{99}{160}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{7}{160}\right)\)	\(e\left(\frac{127}{480}\right)\)
\(\chi_{41600}(3181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{480}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{77}{480}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{31}{480}\right)\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{419}{480}\right)\)
\(\chi_{41600}(3461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{480}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{379}{480}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{377}{480}\right)\)	\(e\left(\frac{1}{160}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{373}{480}\right)\)
\(\chi_{41600}(3981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{480}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{277}{480}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{311}{480}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{99}{160}\right)\)	\(e\left(\frac{379}{480}\right)\)
\(\chi_{41600}(4221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{480}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{113}{480}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{139}{480}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{71}{160}\right)\)	\(e\left(\frac{191}{480}\right)\)
\(\chi_{41600}(4741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{480}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{251}{480}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{313}{480}\right)\)	\(e\left(\frac{129}{160}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{437}{480}\right)\)
\(\chi_{41600}(5021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{480}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{313}{480}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{419}{480}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{31}{160}\right)\)	\(e\left(\frac{151}{480}\right)\)
\(\chi_{41600}(5261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{480}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{149}{480}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{247}{480}\right)\)	\(e\left(\frac{111}{160}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{3}{160}\right)\)	\(e\left(\frac{443}{480}\right)\)
\(\chi_{41600}(5541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{480}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{451}{480}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{113}{480}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{397}{480}\right)\)
\(\chi_{41600}(5781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{480}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{287}{480}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{421}{480}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{209}{480}\right)\)
\(\chi_{41600}(6061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{480}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{349}{480}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{47}{480}\right)\)	\(e\left(\frac{71}{160}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{123}{160}\right)\)	\(e\left(\frac{403}{480}\right)\)
\(\chi_{41600}(6581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{289}{480}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{7}{480}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{221}{480}\right)\)	\(e\left(\frac{133}{160}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{129}{160}\right)\)	\(e\left(\frac{169}{480}\right)\)
\(\chi_{41600}(6821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{480}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{323}{480}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{49}{480}\right)\)	\(e\left(\frac{57}{160}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{101}{160}\right)\)	\(e\left(\frac{461}{480}\right)\)
\(\chi_{41600}(7341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{347}{480}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{221}{480}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{463}{480}\right)\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{467}{480}\right)\)
\(\chi_{41600}(7621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{480}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{43}{480}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{329}{480}\right)\)	\(e\left(\frac{17}{160}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{421}{480}\right)\)
\(\chi_{41600}(7861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{480}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{359}{480}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{157}{480}\right)\)	\(e\left(\frac{101}{160}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{233}{480}\right)\)
\(\chi_{41600}(8141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{480}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{421}{480}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{263}{480}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{427}{480}\right)\)
\(\chi_{41600}(8381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{480}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{257}{480}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{91}{480}\right)\)	\(e\left(\frac{83}{160}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{119}{160}\right)\)	\(e\left(\frac{239}{480}\right)\)
\(\chi_{41600}(8661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{480}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{79}{480}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{437}{480}\right)\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{153}{160}\right)\)	\(e\left(\frac{193}{480}\right)\)
\(\chi_{41600}(9181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{480}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{457}{480}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{371}{480}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{199}{480}\right)\)
\(\chi_{41600}(9421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{371}{480}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{293}{480}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{199}{480}\right)\)	\(e\left(\frac{127}{160}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{11}{480}\right)\)
\(\chi_{41600}(9941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{480}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{431}{480}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{373}{480}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{57}{160}\right)\)	\(e\left(\frac{257}{480}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 128 characters in Galois orbit

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	41600.ze
Modulus	$41600$
Conductor	$41600$
Order	$480$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(41600\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(41600\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(480\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);