LMFDB - Dirichlet character orbit 416000.bev

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416000, base_ring=CyclotomicField(240)) M = H._module chi = DirichletCharacter(H, M([0,75,168,200])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(49, 416000)) 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("416000.49"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$416000$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$20800$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$240$	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:	no, induced from 20800.ub	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{240})$	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 240 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{416000}(49,\cdot)$	$1$	$1$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{41}{240}\right)$
$\chi_{416000}(849,\cdot)$	$1$	$1$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{127}{240}\right)$
$\chi_{416000}(10449,\cdot)$	$1$	$1$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{119}{240}\right)$
$\chi_{416000}(20849,\cdot)$	$1$	$1$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{197}{240}\right)$
$\chi_{416000}(21649,\cdot)$	$1$	$1$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{43}{240}\right)$
$\chi_{416000}(32049,\cdot)$	$1$	$1$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{121}{240}\right)$
$\chi_{416000}(41649,\cdot)$	$1$	$1$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{113}{240}\right)$
$\chi_{416000}(42449,\cdot)$	$1$	$1$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{199}{240}\right)$
$\chi_{416000}(52049,\cdot)$	$1$	$1$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{191}{240}\right)$
$\chi_{416000}(52849,\cdot)$	$1$	$1$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{37}{240}\right)$
$\chi_{416000}(62449,\cdot)$	$1$	$1$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{29}{240}\right)$
$\chi_{416000}(72849,\cdot)$	$1$	$1$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{107}{240}\right)$
$\chi_{416000}(73649,\cdot)$	$1$	$1$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{193}{240}\right)$
$\chi_{416000}(84049,\cdot)$	$1$	$1$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{31}{240}\right)$
$\chi_{416000}(93649,\cdot)$	$1$	$1$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{23}{240}\right)$
$\chi_{416000}(94449,\cdot)$	$1$	$1$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{109}{240}\right)$
$\chi_{416000}(104049,\cdot)$	$1$	$1$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{101}{240}\right)$
$\chi_{416000}(104849,\cdot)$	$1$	$1$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{187}{240}\right)$
$\chi_{416000}(114449,\cdot)$	$1$	$1$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{179}{240}\right)$
$\chi_{416000}(124849,\cdot)$	$1$	$1$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{17}{240}\right)$
$\chi_{416000}(125649,\cdot)$	$1$	$1$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{103}{240}\right)$
$\chi_{416000}(136049,\cdot)$	$1$	$1$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{181}{240}\right)$
$\chi_{416000}(145649,\cdot)$	$1$	$1$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{173}{240}\right)$
$\chi_{416000}(146449,\cdot)$	$1$	$1$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{19}{240}\right)$
$\chi_{416000}(156049,\cdot)$	$1$	$1$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{11}{240}\right)$
$\chi_{416000}(156849,\cdot)$	$1$	$1$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{97}{240}\right)$
$\chi_{416000}(166449,\cdot)$	$1$	$1$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{89}{240}\right)$
$\chi_{416000}(176849,\cdot)$	$1$	$1$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{167}{240}\right)$
$\chi_{416000}(177649,\cdot)$	$1$	$1$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{13}{240}\right)$
$\chi_{416000}(188049,\cdot)$	$1$	$1$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{91}{240}\right)$
$\chi_{416000}(197649,\cdot)$	$1$	$1$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{83}{240}\right)$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{416000}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{41}{240}\right)\)
\(\chi_{416000}(849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{127}{240}\right)\)
\(\chi_{416000}(10449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{119}{240}\right)\)
\(\chi_{416000}(20849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{197}{240}\right)\)
\(\chi_{416000}(21649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{43}{240}\right)\)
\(\chi_{416000}(32049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{121}{240}\right)\)
\(\chi_{416000}(41649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{113}{240}\right)\)
\(\chi_{416000}(42449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{199}{240}\right)\)
\(\chi_{416000}(52049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{191}{240}\right)\)
\(\chi_{416000}(52849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{37}{240}\right)\)
\(\chi_{416000}(62449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{29}{240}\right)\)
\(\chi_{416000}(72849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{107}{240}\right)\)
\(\chi_{416000}(73649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{193}{240}\right)\)
\(\chi_{416000}(84049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{31}{240}\right)\)
\(\chi_{416000}(93649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{23}{240}\right)\)
\(\chi_{416000}(94449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{109}{240}\right)\)
\(\chi_{416000}(104049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{101}{240}\right)\)
\(\chi_{416000}(104849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{187}{240}\right)\)
\(\chi_{416000}(114449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{179}{240}\right)\)
\(\chi_{416000}(124849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{17}{240}\right)\)
\(\chi_{416000}(125649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{103}{240}\right)\)
\(\chi_{416000}(136049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{181}{240}\right)\)
\(\chi_{416000}(145649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{173}{240}\right)\)
\(\chi_{416000}(146449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{19}{240}\right)\)
\(\chi_{416000}(156049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{11}{240}\right)\)
\(\chi_{416000}(156849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{97}{240}\right)\)
\(\chi_{416000}(166449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{89}{240}\right)\)
\(\chi_{416000}(176849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{167}{240}\right)\)
\(\chi_{416000}(177649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{13}{240}\right)\)
\(\chi_{416000}(188049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{91}{240}\right)\)
\(\chi_{416000}(197649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{83}{240}\right)\)

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First 31 of 64 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	416000.bev
Modulus	$416000$
Conductor	$20800$
Order	$240$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(416000\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(20800\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(240\)	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:	no, induced from 20800.ub	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);