LMFDB - Dirichlet character orbit 24200.lt

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(24200, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([110,110,143,200])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(67, 24200)) 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("24200.67"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$24200$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$24200$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$220$	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:	$\Q(\zeta_{220})$	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 220 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{24200}(67,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{24200}(683,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{24200}(947,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{24200}(1123,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{24200}(1387,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{24200}(1563,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{24200}(1827,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{24200}(2003,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{24200}(2267,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{24200}(2883,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{24200}(3323,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{24200}(3587,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{24200}(3763,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{24200}(4027,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{24200}(4203,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{24200}(4467,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{24200}(5347,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{24200}(5523,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{24200}(5787,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{24200}(5963,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{24200}(6227,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{24200}(6403,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{24200}(6667,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{24200}(7283,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{24200}(7547,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{24200}(7723,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{24200}(8163,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{24200}(8427,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{24200}(8603,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{24200}(8867,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{24200}(9483,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{24}{55}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{24200}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{24200}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{24200}(947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{24200}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{24200}(1387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{24200}(1563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{24200}(1827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{24200}(2003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{24200}(2267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{24200}(2883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{24200}(3323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{24200}(3587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{24200}(3763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{24200}(4027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{24200}(4203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{24200}(4467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{24200}(5347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{24200}(5523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{24200}(5787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{24200}(5963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{24200}(6227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{24200}(6403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{24200}(6667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{24200}(7283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{24200}(7547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{24200}(7723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{24200}(8163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{24200}(8427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{24200}(8603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{24200}(8867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{24200}(9483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{24}{55}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 80 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	24200.lt
Modulus	$24200$
Conductor	$24200$
Order	$220$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(24200\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(24200\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(220\)	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);