from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(607, base_ring=CyclotomicField(202))
M = H._module
chi = DirichletCharacter(H, M([195]))
chi.galois_orbit()
[g,chi] = znchar(Mod(6,607))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(607\) | |
| Conductor: | \(607\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(202\) | 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: | $\Q(\zeta_{101})$ |
| Fixed field: | Number field defined by a degree 202 polynomial (not computed) |
First 31 of 100 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{607}(6,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{77}{101}\right)\) | \(e\left(\frac{195}{202}\right)\) | \(e\left(\frac{53}{101}\right)\) | \(e\left(\frac{35}{202}\right)\) | \(e\left(\frac{147}{202}\right)\) | \(e\left(\frac{10}{101}\right)\) | \(e\left(\frac{29}{101}\right)\) | \(e\left(\frac{94}{101}\right)\) | \(e\left(\frac{189}{202}\right)\) | \(e\left(\frac{55}{101}\right)\) |
| \(\chi_{607}(10,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{99}{101}\right)\) | \(e\left(\frac{193}{202}\right)\) | \(e\left(\frac{97}{101}\right)\) | \(e\left(\frac{45}{202}\right)\) | \(e\left(\frac{189}{202}\right)\) | \(e\left(\frac{85}{101}\right)\) | \(e\left(\frac{95}{101}\right)\) | \(e\left(\frac{92}{101}\right)\) | \(e\left(\frac{41}{202}\right)\) | \(e\left(\frac{13}{101}\right)\) |
| \(\chi_{607}(27,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{90}{101}\right)\) | \(e\left(\frac{1}{202}\right)\) | \(e\left(\frac{79}{101}\right)\) | \(e\left(\frac{197}{202}\right)\) | \(e\left(\frac{181}{202}\right)\) | \(e\left(\frac{13}{101}\right)\) | \(e\left(\frac{68}{101}\right)\) | \(e\left(\frac{1}{101}\right)\) | \(e\left(\frac{175}{202}\right)\) | \(e\left(\frac{21}{101}\right)\) |
| \(\chi_{607}(33,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{78}{101}\right)\) | \(e\left(\frac{149}{202}\right)\) | \(e\left(\frac{55}{101}\right)\) | \(e\left(\frac{63}{202}\right)\) | \(e\left(\frac{103}{202}\right)\) | \(e\left(\frac{18}{101}\right)\) | \(e\left(\frac{32}{101}\right)\) | \(e\left(\frac{48}{101}\right)\) | \(e\left(\frac{17}{202}\right)\) | \(e\left(\frac{99}{101}\right)\) |
| \(\chi_{607}(34,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{46}{101}\right)\) | \(e\left(\frac{5}{202}\right)\) | \(e\left(\frac{92}{101}\right)\) | \(e\left(\frac{177}{202}\right)\) | \(e\left(\frac{97}{202}\right)\) | \(e\left(\frac{65}{101}\right)\) | \(e\left(\frac{37}{101}\right)\) | \(e\left(\frac{5}{101}\right)\) | \(e\left(\frac{67}{202}\right)\) | \(e\left(\frac{4}{101}\right)\) |
| \(\chi_{607}(37,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{96}{101}\right)\) | \(e\left(\frac{129}{202}\right)\) | \(e\left(\frac{91}{101}\right)\) | \(e\left(\frac{163}{202}\right)\) | \(e\left(\frac{119}{202}\right)\) | \(e\left(\frac{61}{101}\right)\) | \(e\left(\frac{86}{101}\right)\) | \(e\left(\frac{28}{101}\right)\) | \(e\left(\frac{153}{202}\right)\) | \(e\left(\frac{83}{101}\right)\) |
| \(\chi_{607}(42,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{101}\right)\) | \(e\left(\frac{69}{202}\right)\) | \(e\left(\frac{98}{101}\right)\) | \(e\left(\frac{59}{202}\right)\) | \(e\left(\frac{167}{202}\right)\) | \(e\left(\frac{89}{101}\right)\) | \(e\left(\frac{46}{101}\right)\) | \(e\left(\frac{69}{101}\right)\) | \(e\left(\frac{157}{202}\right)\) | \(e\left(\frac{35}{101}\right)\) |
| \(\chi_{607}(45,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{101}\right)\) | \(e\left(\frac{201}{202}\right)\) | \(e\left(\frac{22}{101}\right)\) | \(e\left(\frac{5}{202}\right)\) | \(e\left(\frac{21}{202}\right)\) | \(e\left(\frac{88}{101}\right)\) | \(e\left(\frac{33}{101}\right)\) | \(e\left(\frac{100}{101}\right)\) | \(e\left(\frac{27}{202}\right)\) | \(e\left(\frac{80}{101}\right)\) |
| \(\chi_{607}(48,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{101}\right)\) | \(e\left(\frac{173}{202}\right)\) | \(e\left(\frac{32}{101}\right)\) | \(e\left(\frac{145}{202}\right)\) | \(e\left(\frac{3}{202}\right)\) | \(e\left(\frac{27}{101}\right)\) | \(e\left(\frac{48}{101}\right)\) | \(e\left(\frac{72}{101}\right)\) | \(e\left(\frac{177}{202}\right)\) | \(e\left(\frac{98}{101}\right)\) |
| \(\chi_{607}(55,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{100}{101}\right)\) | \(e\left(\frac{147}{202}\right)\) | \(e\left(\frac{99}{101}\right)\) | \(e\left(\frac{73}{202}\right)\) | \(e\left(\frac{145}{202}\right)\) | \(e\left(\frac{93}{101}\right)\) | \(e\left(\frac{98}{101}\right)\) | \(e\left(\frac{46}{101}\right)\) | \(e\left(\frac{71}{202}\right)\) | \(e\left(\frac{57}{101}\right)\) |
| \(\chi_{607}(57,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{98}{101}\right)\) | \(e\left(\frac{37}{202}\right)\) | \(e\left(\frac{95}{101}\right)\) | \(e\left(\frac{17}{202}\right)\) | \(e\left(\frac{31}{202}\right)\) | \(e\left(\frac{77}{101}\right)\) | \(e\left(\frac{92}{101}\right)\) | \(e\left(\frac{37}{101}\right)\) | \(e\left(\frac{11}{202}\right)\) | \(e\left(\frac{70}{101}\right)\) |
| \(\chi_{607}(58,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{92}{101}\right)\) | \(e\left(\frac{111}{202}\right)\) | \(e\left(\frac{83}{101}\right)\) | \(e\left(\frac{51}{202}\right)\) | \(e\left(\frac{93}{202}\right)\) | \(e\left(\frac{29}{101}\right)\) | \(e\left(\frac{74}{101}\right)\) | \(e\left(\frac{10}{101}\right)\) | \(e\left(\frac{33}{202}\right)\) | \(e\left(\frac{8}{101}\right)\) |
| \(\chi_{607}(70,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{101}\right)\) | \(e\left(\frac{67}{202}\right)\) | \(e\left(\frac{41}{101}\right)\) | \(e\left(\frac{69}{202}\right)\) | \(e\left(\frac{7}{202}\right)\) | \(e\left(\frac{63}{101}\right)\) | \(e\left(\frac{11}{101}\right)\) | \(e\left(\frac{67}{101}\right)\) | \(e\left(\frac{9}{202}\right)\) | \(e\left(\frac{94}{101}\right)\) |
| \(\chi_{607}(75,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{101}\right)\) | \(e\left(\frac{199}{202}\right)\) | \(e\left(\frac{66}{101}\right)\) | \(e\left(\frac{15}{202}\right)\) | \(e\left(\frac{63}{202}\right)\) | \(e\left(\frac{62}{101}\right)\) | \(e\left(\frac{99}{101}\right)\) | \(e\left(\frac{98}{101}\right)\) | \(e\left(\frac{81}{202}\right)\) | \(e\left(\frac{38}{101}\right)\) |
| \(\chi_{607}(80,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{38}{101}\right)\) | \(e\left(\frac{171}{202}\right)\) | \(e\left(\frac{76}{101}\right)\) | \(e\left(\frac{155}{202}\right)\) | \(e\left(\frac{45}{202}\right)\) | \(e\left(\frac{1}{101}\right)\) | \(e\left(\frac{13}{101}\right)\) | \(e\left(\frac{70}{101}\right)\) | \(e\left(\frac{29}{202}\right)\) | \(e\left(\frac{56}{101}\right)\) |
| \(\chi_{607}(83,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{58}{101}\right)\) | \(e\left(\frac{59}{202}\right)\) | \(e\left(\frac{15}{101}\right)\) | \(e\left(\frac{109}{202}\right)\) | \(e\left(\frac{175}{202}\right)\) | \(e\left(\frac{60}{101}\right)\) | \(e\left(\frac{73}{101}\right)\) | \(e\left(\frac{59}{101}\right)\) | \(e\left(\frac{23}{202}\right)\) | \(e\left(\frac{27}{101}\right)\) |
| \(\chi_{607}(92,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{101}\right)\) | \(e\left(\frac{53}{202}\right)\) | \(e\left(\frac{46}{101}\right)\) | \(e\left(\frac{139}{202}\right)\) | \(e\left(\frac{99}{202}\right)\) | \(e\left(\frac{83}{101}\right)\) | \(e\left(\frac{69}{101}\right)\) | \(e\left(\frac{53}{101}\right)\) | \(e\left(\frac{185}{202}\right)\) | \(e\left(\frac{2}{101}\right)\) |
| \(\chi_{607}(95,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{101}\right)\) | \(e\left(\frac{35}{202}\right)\) | \(e\left(\frac{38}{101}\right)\) | \(e\left(\frac{27}{202}\right)\) | \(e\left(\frac{73}{202}\right)\) | \(e\left(\frac{51}{101}\right)\) | \(e\left(\frac{57}{101}\right)\) | \(e\left(\frac{35}{101}\right)\) | \(e\left(\frac{65}{202}\right)\) | \(e\left(\frac{28}{101}\right)\) |
| \(\chi_{607}(109,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{34}{101}\right)\) | \(e\left(\frac{153}{202}\right)\) | \(e\left(\frac{68}{101}\right)\) | \(e\left(\frac{43}{202}\right)\) | \(e\left(\frac{19}{202}\right)\) | \(e\left(\frac{70}{101}\right)\) | \(e\left(\frac{1}{101}\right)\) | \(e\left(\frac{52}{101}\right)\) | \(e\left(\frac{111}{202}\right)\) | \(e\left(\frac{82}{101}\right)\) |
| \(\chi_{607}(118,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{48}{101}\right)\) | \(e\left(\frac{115}{202}\right)\) | \(e\left(\frac{96}{101}\right)\) | \(e\left(\frac{31}{202}\right)\) | \(e\left(\frac{9}{202}\right)\) | \(e\left(\frac{81}{101}\right)\) | \(e\left(\frac{43}{101}\right)\) | \(e\left(\frac{14}{101}\right)\) | \(e\left(\frac{127}{202}\right)\) | \(e\left(\frac{92}{101}\right)\) |
| \(\chi_{607}(124,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{32}{101}\right)\) | \(e\left(\frac{43}{202}\right)\) | \(e\left(\frac{64}{101}\right)\) | \(e\left(\frac{189}{202}\right)\) | \(e\left(\frac{107}{202}\right)\) | \(e\left(\frac{54}{101}\right)\) | \(e\left(\frac{96}{101}\right)\) | \(e\left(\frac{43}{101}\right)\) | \(e\left(\frac{51}{202}\right)\) | \(e\left(\frac{95}{101}\right)\) |
| \(\chi_{607}(125,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{55}{101}\right)\) | \(e\left(\frac{197}{202}\right)\) | \(e\left(\frac{9}{101}\right)\) | \(e\left(\frac{25}{202}\right)\) | \(e\left(\frac{105}{202}\right)\) | \(e\left(\frac{36}{101}\right)\) | \(e\left(\frac{64}{101}\right)\) | \(e\left(\frac{96}{101}\right)\) | \(e\left(\frac{135}{202}\right)\) | \(e\left(\frac{97}{101}\right)\) |
| \(\chi_{607}(127,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{14}{101}\right)\) | \(e\left(\frac{63}{202}\right)\) | \(e\left(\frac{28}{101}\right)\) | \(e\left(\frac{89}{202}\right)\) | \(e\left(\frac{91}{202}\right)\) | \(e\left(\frac{11}{101}\right)\) | \(e\left(\frac{42}{101}\right)\) | \(e\left(\frac{63}{101}\right)\) | \(e\left(\frac{117}{202}\right)\) | \(e\left(\frac{10}{101}\right)\) |
| \(\chi_{607}(129,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{63}{101}\right)\) | \(e\left(\frac{31}{202}\right)\) | \(e\left(\frac{25}{101}\right)\) | \(e\left(\frac{47}{202}\right)\) | \(e\left(\frac{157}{202}\right)\) | \(e\left(\frac{100}{101}\right)\) | \(e\left(\frac{88}{101}\right)\) | \(e\left(\frac{31}{101}\right)\) | \(e\left(\frac{173}{202}\right)\) | \(e\left(\frac{45}{101}\right)\) |
| \(\chi_{607}(153,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{101}\right)\) | \(e\left(\frac{13}{202}\right)\) | \(e\left(\frac{17}{101}\right)\) | \(e\left(\frac{137}{202}\right)\) | \(e\left(\frac{131}{202}\right)\) | \(e\left(\frac{68}{101}\right)\) | \(e\left(\frac{76}{101}\right)\) | \(e\left(\frac{13}{101}\right)\) | \(e\left(\frac{53}{202}\right)\) | \(e\left(\frac{71}{101}\right)\) |
| \(\chi_{607}(156,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{6}{101}\right)\) | \(e\left(\frac{27}{202}\right)\) | \(e\left(\frac{12}{101}\right)\) | \(e\left(\frac{67}{202}\right)\) | \(e\left(\frac{39}{202}\right)\) | \(e\left(\frac{48}{101}\right)\) | \(e\left(\frac{18}{101}\right)\) | \(e\left(\frac{27}{101}\right)\) | \(e\left(\frac{79}{202}\right)\) | \(e\left(\frac{62}{101}\right)\) |
| \(\chi_{607}(157,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{101}\right)\) | \(e\left(\frac{91}{202}\right)\) | \(e\left(\frac{18}{101}\right)\) | \(e\left(\frac{151}{202}\right)\) | \(e\left(\frac{109}{202}\right)\) | \(e\left(\frac{72}{101}\right)\) | \(e\left(\frac{27}{101}\right)\) | \(e\left(\frac{91}{101}\right)\) | \(e\left(\frac{169}{202}\right)\) | \(e\left(\frac{93}{101}\right)\) |
| \(\chi_{607}(159,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{52}{101}\right)\) | \(e\left(\frac{133}{202}\right)\) | \(e\left(\frac{3}{101}\right)\) | \(e\left(\frac{143}{202}\right)\) | \(e\left(\frac{35}{202}\right)\) | \(e\left(\frac{12}{101}\right)\) | \(e\left(\frac{55}{101}\right)\) | \(e\left(\frac{32}{101}\right)\) | \(e\left(\frac{45}{202}\right)\) | \(e\left(\frac{66}{101}\right)\) |
| \(\chi_{607}(187,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{101}\right)\) | \(e\left(\frac{161}{202}\right)\) | \(e\left(\frac{94}{101}\right)\) | \(e\left(\frac{3}{202}\right)\) | \(e\left(\frac{53}{202}\right)\) | \(e\left(\frac{73}{101}\right)\) | \(e\left(\frac{40}{101}\right)\) | \(e\left(\frac{60}{101}\right)\) | \(e\left(\frac{97}{202}\right)\) | \(e\left(\frac{48}{101}\right)\) |
| \(\chi_{607}(189,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{62}{101}\right)\) | \(e\left(\frac{77}{202}\right)\) | \(e\left(\frac{23}{101}\right)\) | \(e\left(\frac{19}{202}\right)\) | \(e\left(\frac{201}{202}\right)\) | \(e\left(\frac{92}{101}\right)\) | \(e\left(\frac{85}{101}\right)\) | \(e\left(\frac{77}{101}\right)\) | \(e\left(\frac{143}{202}\right)\) | \(e\left(\frac{1}{101}\right)\) |
| \(\chi_{607}(213,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{101}\right)\) | \(e\left(\frac{165}{202}\right)\) | \(e\left(\frac{6}{101}\right)\) | \(e\left(\frac{185}{202}\right)\) | \(e\left(\frac{171}{202}\right)\) | \(e\left(\frac{24}{101}\right)\) | \(e\left(\frac{9}{101}\right)\) | \(e\left(\frac{64}{101}\right)\) | \(e\left(\frac{191}{202}\right)\) | \(e\left(\frac{31}{101}\right)\) |