from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2167, base_ring=CyclotomicField(490))
M = H._module
chi = DirichletCharacter(H, M([49,460]))
chi.galois_orbit()
[g,chi] = znchar(Mod(24,2167))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2167\) | |
| Conductor: | \(2167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(490\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{245})$ |
| Fixed field: | Number field defined by a degree 490 polynomial (not computed) |
First 31 of 168 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2167}(24,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{490}\right)\) | \(e\left(\frac{176}{245}\right)\) | \(e\left(\frac{19}{245}\right)\) | \(e\left(\frac{233}{245}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{373}{490}\right)\) | \(e\left(\frac{57}{490}\right)\) | \(e\left(\frac{107}{245}\right)\) | \(e\left(\frac{97}{98}\right)\) | \(e\left(\frac{39}{49}\right)\) |
| \(\chi_{2167}(28,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{321}{490}\right)\) | \(e\left(\frac{214}{245}\right)\) | \(e\left(\frac{76}{245}\right)\) | \(e\left(\frac{197}{245}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{267}{490}\right)\) | \(e\left(\frac{473}{490}\right)\) | \(e\left(\frac{183}{245}\right)\) | \(e\left(\frac{45}{98}\right)\) | \(e\left(\frac{9}{49}\right)\) |
| \(\chi_{2167}(29,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{433}{490}\right)\) | \(e\left(\frac{207}{245}\right)\) | \(e\left(\frac{188}{245}\right)\) | \(e\left(\frac{36}{245}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{351}{490}\right)\) | \(e\left(\frac{319}{490}\right)\) | \(e\left(\frac{169}{245}\right)\) | \(e\left(\frac{3}{98}\right)\) | \(e\left(\frac{30}{49}\right)\) |
| \(\chi_{2167}(40,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{490}\right)\) | \(e\left(\frac{137}{245}\right)\) | \(e\left(\frac{83}{245}\right)\) | \(e\left(\frac{141}{245}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{211}{490}\right)\) | \(e\left(\frac{249}{490}\right)\) | \(e\left(\frac{29}{245}\right)\) | \(e\left(\frac{73}{98}\right)\) | \(e\left(\frac{44}{49}\right)\) |
| \(\chi_{2167}(51,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{213}{490}\right)\) | \(e\left(\frac{142}{245}\right)\) | \(e\left(\frac{213}{245}\right)\) | \(e\left(\frac{46}{245}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{81}{490}\right)\) | \(e\left(\frac{149}{490}\right)\) | \(e\left(\frac{39}{245}\right)\) | \(e\left(\frac{61}{98}\right)\) | \(e\left(\frac{22}{49}\right)\) |
| \(\chi_{2167}(61,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{111}{490}\right)\) | \(e\left(\frac{74}{245}\right)\) | \(e\left(\frac{111}{245}\right)\) | \(e\left(\frac{162}{245}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{477}{490}\right)\) | \(e\left(\frac{333}{490}\right)\) | \(e\left(\frac{148}{245}\right)\) | \(e\left(\frac{87}{98}\right)\) | \(e\left(\frac{37}{49}\right)\) |
| \(\chi_{2167}(63,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{437}{490}\right)\) | \(e\left(\frac{128}{245}\right)\) | \(e\left(\frac{192}{245}\right)\) | \(e\left(\frac{214}{245}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{249}{490}\right)\) | \(e\left(\frac{331}{490}\right)\) | \(e\left(\frac{11}{245}\right)\) | \(e\left(\frac{75}{98}\right)\) | \(e\left(\frac{15}{49}\right)\) |
| \(\chi_{2167}(85,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{277}{490}\right)\) | \(e\left(\frac{103}{245}\right)\) | \(e\left(\frac{32}{245}\right)\) | \(e\left(\frac{199}{245}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{409}{490}\right)\) | \(e\left(\frac{341}{490}\right)\) | \(e\left(\frac{206}{245}\right)\) | \(e\left(\frac{37}{98}\right)\) | \(e\left(\frac{27}{49}\right)\) |
| \(\chi_{2167}(90,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{199}{490}\right)\) | \(e\left(\frac{51}{245}\right)\) | \(e\left(\frac{199}{245}\right)\) | \(e\left(\frac{158}{245}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{193}{490}\right)\) | \(e\left(\frac{107}{490}\right)\) | \(e\left(\frac{102}{245}\right)\) | \(e\left(\frac{5}{98}\right)\) | \(e\left(\frac{1}{49}\right)\) |
| \(\chi_{2167}(101,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{269}{490}\right)\) | \(e\left(\frac{16}{245}\right)\) | \(e\left(\frac{24}{245}\right)\) | \(e\left(\frac{88}{245}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{123}{490}\right)\) | \(e\left(\frac{317}{490}\right)\) | \(e\left(\frac{32}{245}\right)\) | \(e\left(\frac{89}{98}\right)\) | \(e\left(\frac{8}{49}\right)\) |
| \(\chi_{2167}(105,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{490}\right)\) | \(e\left(\frac{89}{245}\right)\) | \(e\left(\frac{11}{245}\right)\) | \(e\left(\frac{122}{245}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{87}{490}\right)\) | \(e\left(\frac{33}{490}\right)\) | \(e\left(\frac{178}{245}\right)\) | \(e\left(\frac{51}{98}\right)\) | \(e\left(\frac{20}{49}\right)\) |
| \(\chi_{2167}(150,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{263}{490}\right)\) | \(e\left(\frac{12}{245}\right)\) | \(e\left(\frac{18}{245}\right)\) | \(e\left(\frac{66}{245}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{31}{490}\right)\) | \(e\left(\frac{299}{490}\right)\) | \(e\left(\frac{24}{245}\right)\) | \(e\left(\frac{79}{98}\right)\) | \(e\left(\frac{6}{49}\right)\) |
| \(\chi_{2167}(156,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{490}\right)\) | \(e\left(\frac{216}{245}\right)\) | \(e\left(\frac{79}{245}\right)\) | \(e\left(\frac{208}{245}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{313}{490}\right)\) | \(e\left(\frac{237}{490}\right)\) | \(e\left(\frac{187}{245}\right)\) | \(e\left(\frac{1}{98}\right)\) | \(e\left(\frac{10}{49}\right)\) |
| \(\chi_{2167}(171,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{261}{490}\right)\) | \(e\left(\frac{174}{245}\right)\) | \(e\left(\frac{16}{245}\right)\) | \(e\left(\frac{222}{245}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{327}{490}\right)\) | \(e\left(\frac{293}{490}\right)\) | \(e\left(\frac{103}{245}\right)\) | \(e\left(\frac{43}{98}\right)\) | \(e\left(\frac{38}{49}\right)\) |
| \(\chi_{2167}(172,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{490}\right)\) | \(e\left(\frac{117}{245}\right)\) | \(e\left(\frac{53}{245}\right)\) | \(e\left(\frac{31}{245}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{241}{490}\right)\) | \(e\left(\frac{159}{490}\right)\) | \(e\left(\frac{234}{245}\right)\) | \(e\left(\frac{23}{98}\right)\) | \(e\left(\frac{34}{49}\right)\) |
| \(\chi_{2167}(182,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{381}{490}\right)\) | \(e\left(\frac{9}{245}\right)\) | \(e\left(\frac{136}{245}\right)\) | \(e\left(\frac{172}{245}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{207}{490}\right)\) | \(e\left(\frac{163}{490}\right)\) | \(e\left(\frac{18}{245}\right)\) | \(e\left(\frac{47}{98}\right)\) | \(e\left(\frac{29}{49}\right)\) |
| \(\chi_{2167}(193,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{201}{490}\right)\) | \(e\left(\frac{134}{245}\right)\) | \(e\left(\frac{201}{245}\right)\) | \(e\left(\frac{2}{245}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{387}{490}\right)\) | \(e\left(\frac{113}{490}\right)\) | \(e\left(\frac{23}{245}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{18}{49}\right)\) |
| \(\chi_{2167}(226,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{490}\right)\) | \(e\left(\frac{109}{245}\right)\) | \(e\left(\frac{41}{245}\right)\) | \(e\left(\frac{232}{245}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{57}{490}\right)\) | \(e\left(\frac{123}{490}\right)\) | \(e\left(\frac{218}{245}\right)\) | \(e\left(\frac{3}{98}\right)\) | \(e\left(\frac{30}{49}\right)\) |
| \(\chi_{2167}(237,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{181}{490}\right)\) | \(e\left(\frac{39}{245}\right)\) | \(e\left(\frac{181}{245}\right)\) | \(e\left(\frac{92}{245}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{407}{490}\right)\) | \(e\left(\frac{53}{490}\right)\) | \(e\left(\frac{78}{245}\right)\) | \(e\left(\frac{73}{98}\right)\) | \(e\left(\frac{44}{49}\right)\) |
| \(\chi_{2167}(239,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{477}{490}\right)\) | \(e\left(\frac{73}{245}\right)\) | \(e\left(\frac{232}{245}\right)\) | \(e\left(\frac{34}{245}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{209}{490}\right)\) | \(e\left(\frac{451}{490}\right)\) | \(e\left(\frac{146}{245}\right)\) | \(e\left(\frac{11}{98}\right)\) | \(e\left(\frac{12}{49}\right)\) |
| \(\chi_{2167}(248,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{311}{490}\right)\) | \(e\left(\frac{44}{245}\right)\) | \(e\left(\frac{66}{245}\right)\) | \(e\left(\frac{242}{245}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{277}{490}\right)\) | \(e\left(\frac{443}{490}\right)\) | \(e\left(\frac{88}{245}\right)\) | \(e\left(\frac{61}{98}\right)\) | \(e\left(\frac{22}{49}\right)\) |
| \(\chi_{2167}(250,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{327}{490}\right)\) | \(e\left(\frac{218}{245}\right)\) | \(e\left(\frac{82}{245}\right)\) | \(e\left(\frac{219}{245}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{359}{490}\right)\) | \(e\left(\frac{1}{490}\right)\) | \(e\left(\frac{191}{245}\right)\) | \(e\left(\frac{55}{98}\right)\) | \(e\left(\frac{11}{49}\right)\) |
| \(\chi_{2167}(260,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{143}{490}\right)\) | \(e\left(\frac{177}{245}\right)\) | \(e\left(\frac{143}{245}\right)\) | \(e\left(\frac{116}{245}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{151}{490}\right)\) | \(e\left(\frac{429}{490}\right)\) | \(e\left(\frac{109}{245}\right)\) | \(e\left(\frac{75}{98}\right)\) | \(e\left(\frac{15}{49}\right)\) |
| \(\chi_{2167}(282,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{473}{490}\right)\) | \(e\left(\frac{152}{245}\right)\) | \(e\left(\frac{228}{245}\right)\) | \(e\left(\frac{101}{245}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{311}{490}\right)\) | \(e\left(\frac{439}{490}\right)\) | \(e\left(\frac{59}{245}\right)\) | \(e\left(\frac{37}{98}\right)\) | \(e\left(\frac{27}{49}\right)\) |
| \(\chi_{2167}(332,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{159}{490}\right)\) | \(e\left(\frac{106}{245}\right)\) | \(e\left(\frac{159}{245}\right)\) | \(e\left(\frac{93}{245}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{233}{490}\right)\) | \(e\left(\frac{477}{490}\right)\) | \(e\left(\frac{212}{245}\right)\) | \(e\left(\frac{69}{98}\right)\) | \(e\left(\frac{4}{49}\right)\) |
| \(\chi_{2167}(347,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{361}{490}\right)\) | \(e\left(\frac{159}{245}\right)\) | \(e\left(\frac{116}{245}\right)\) | \(e\left(\frac{17}{245}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{227}{490}\right)\) | \(e\left(\frac{103}{490}\right)\) | \(e\left(\frac{73}{245}\right)\) | \(e\left(\frac{79}{98}\right)\) | \(e\left(\frac{6}{49}\right)\) |
| \(\chi_{2167}(369,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{151}{490}\right)\) | \(e\left(\frac{19}{245}\right)\) | \(e\left(\frac{151}{245}\right)\) | \(e\left(\frac{227}{245}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{437}{490}\right)\) | \(e\left(\frac{453}{490}\right)\) | \(e\left(\frac{38}{245}\right)\) | \(e\left(\frac{23}{98}\right)\) | \(e\left(\frac{34}{49}\right)\) |
| \(\chi_{2167}(387,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{169}{490}\right)\) | \(e\left(\frac{31}{245}\right)\) | \(e\left(\frac{169}{245}\right)\) | \(e\left(\frac{48}{245}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{223}{490}\right)\) | \(e\left(\frac{17}{490}\right)\) | \(e\left(\frac{62}{245}\right)\) | \(e\left(\frac{53}{98}\right)\) | \(e\left(\frac{40}{49}\right)\) |
| \(\chi_{2167}(431,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{490}\right)\) | \(e\left(\frac{26}{245}\right)\) | \(e\left(\frac{39}{245}\right)\) | \(e\left(\frac{143}{245}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{353}{490}\right)\) | \(e\left(\frac{117}{490}\right)\) | \(e\left(\frac{52}{245}\right)\) | \(e\left(\frac{65}{98}\right)\) | \(e\left(\frac{13}{49}\right)\) |
| \(\chi_{2167}(436,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{183}{490}\right)\) | \(e\left(\frac{122}{245}\right)\) | \(e\left(\frac{183}{245}\right)\) | \(e\left(\frac{181}{245}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{111}{490}\right)\) | \(e\left(\frac{59}{490}\right)\) | \(e\left(\frac{244}{245}\right)\) | \(e\left(\frac{11}{98}\right)\) | \(e\left(\frac{12}{49}\right)\) |
| \(\chi_{2167}(447,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{490}\right)\) | \(e\left(\frac{22}{245}\right)\) | \(e\left(\frac{33}{245}\right)\) | \(e\left(\frac{121}{245}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{261}{490}\right)\) | \(e\left(\frac{99}{490}\right)\) | \(e\left(\frac{44}{245}\right)\) | \(e\left(\frac{55}{98}\right)\) | \(e\left(\frac{11}{49}\right)\) |