from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(430))
M = H._module
chi = DirichletCharacter(H, M([215,167]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,6034))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6034\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(430\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 3017.bb | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{215})$ |
| Fixed field: | Number field defined by a degree 430 polynomial (not computed) |
First 31 of 168 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6034}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{86}\right)\) | \(e\left(\frac{139}{430}\right)\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{73}{215}\right)\) | \(e\left(\frac{77}{215}\right)\) | \(e\left(\frac{122}{215}\right)\) | \(e\left(\frac{116}{215}\right)\) | \(e\left(\frac{33}{430}\right)\) | \(e\left(\frac{131}{215}\right)\) | \(e\left(\frac{139}{215}\right)\) |
| \(\chi_{6034}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{86}\right)\) | \(e\left(\frac{171}{430}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{212}{215}\right)\) | \(e\left(\frac{203}{215}\right)\) | \(e\left(\frac{48}{215}\right)\) | \(e\left(\frac{169}{215}\right)\) | \(e\left(\frac{87}{430}\right)\) | \(e\left(\frac{189}{215}\right)\) | \(e\left(\frac{171}{215}\right)\) |
| \(\chi_{6034}(111,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{86}\right)\) | \(e\left(\frac{159}{430}\right)\) | \(e\left(\frac{20}{43}\right)\) | \(e\left(\frac{133}{215}\right)\) | \(e\left(\frac{102}{215}\right)\) | \(e\left(\frac{22}{215}\right)\) | \(e\left(\frac{176}{215}\right)\) | \(e\left(\frac{13}{430}\right)\) | \(e\left(\frac{6}{215}\right)\) | \(e\left(\frac{159}{215}\right)\) |
| \(\chi_{6034}(153,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{86}\right)\) | \(e\left(\frac{237}{430}\right)\) | \(e\left(\frac{29}{43}\right)\) | \(e\left(\frac{109}{215}\right)\) | \(e\left(\frac{6}{215}\right)\) | \(e\left(\frac{191}{215}\right)\) | \(e\left(\frac{23}{215}\right)\) | \(e\left(\frac{279}{430}\right)\) | \(e\left(\frac{13}{215}\right)\) | \(e\left(\frac{22}{215}\right)\) |
| \(\chi_{6034}(167,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{86}\right)\) | \(e\left(\frac{251}{430}\right)\) | \(e\left(\frac{24}{43}\right)\) | \(e\left(\frac{22}{215}\right)\) | \(e\left(\frac{88}{215}\right)\) | \(e\left(\frac{78}{215}\right)\) | \(e\left(\frac{194}{215}\right)\) | \(e\left(\frac{7}{430}\right)\) | \(e\left(\frac{119}{215}\right)\) | \(e\left(\frac{36}{215}\right)\) |
| \(\chi_{6034}(181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{86}\right)\) | \(e\left(\frac{217}{430}\right)\) | \(e\left(\frac{30}{43}\right)\) | \(e\left(\frac{49}{215}\right)\) | \(e\left(\frac{196}{215}\right)\) | \(e\left(\frac{76}{215}\right)\) | \(e\left(\frac{178}{215}\right)\) | \(e\left(\frac{299}{430}\right)\) | \(e\left(\frac{138}{215}\right)\) | \(e\left(\frac{2}{215}\right)\) |
| \(\chi_{6034}(195,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{86}\right)\) | \(e\left(\frac{13}{430}\right)\) | \(e\left(\frac{23}{43}\right)\) | \(e\left(\frac{211}{215}\right)\) | \(e\left(\frac{199}{215}\right)\) | \(e\left(\frac{64}{215}\right)\) | \(e\left(\frac{82}{215}\right)\) | \(e\left(\frac{331}{430}\right)\) | \(e\left(\frac{37}{215}\right)\) | \(e\left(\frac{13}{215}\right)\) |
| \(\chi_{6034}(237,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{86}\right)\) | \(e\left(\frac{231}{430}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{177}{215}\right)\) | \(e\left(\frac{63}{215}\right)\) | \(e\left(\frac{178}{215}\right)\) | \(e\left(\frac{134}{215}\right)\) | \(e\left(\frac{27}{430}\right)\) | \(e\left(\frac{29}{215}\right)\) | \(e\left(\frac{16}{215}\right)\) |
| \(\chi_{6034}(251,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{86}\right)\) | \(e\left(\frac{369}{430}\right)\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{118}{215}\right)\) | \(e\left(\frac{42}{215}\right)\) | \(e\left(\frac{47}{215}\right)\) | \(e\left(\frac{161}{215}\right)\) | \(e\left(\frac{233}{430}\right)\) | \(e\left(\frac{91}{215}\right)\) | \(e\left(\frac{154}{215}\right)\) |
| \(\chi_{6034}(279,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{86}\right)\) | \(e\left(\frac{353}{430}\right)\) | \(e\left(\frac{6}{43}\right)\) | \(e\left(\frac{156}{215}\right)\) | \(e\left(\frac{194}{215}\right)\) | \(e\left(\frac{84}{215}\right)\) | \(e\left(\frac{27}{215}\right)\) | \(e\left(\frac{421}{430}\right)\) | \(e\left(\frac{62}{215}\right)\) | \(e\left(\frac{138}{215}\right)\) |
| \(\chi_{6034}(293,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{86}\right)\) | \(e\left(\frac{197}{430}\right)\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{204}{215}\right)\) | \(e\left(\frac{171}{215}\right)\) | \(e\left(\frac{176}{215}\right)\) | \(e\left(\frac{118}{215}\right)\) | \(e\left(\frac{319}{430}\right)\) | \(e\left(\frac{48}{215}\right)\) | \(e\left(\frac{197}{215}\right)\) |
| \(\chi_{6034}(349,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{86}\right)\) | \(e\left(\frac{423}{430}\right)\) | \(e\left(\frac{24}{43}\right)\) | \(e\left(\frac{151}{215}\right)\) | \(e\left(\frac{174}{215}\right)\) | \(e\left(\frac{164}{215}\right)\) | \(e\left(\frac{22}{215}\right)\) | \(e\left(\frac{351}{430}\right)\) | \(e\left(\frac{162}{215}\right)\) | \(e\left(\frac{208}{215}\right)\) |
| \(\chi_{6034}(391,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{86}\right)\) | \(e\left(\frac{189}{430}\right)\) | \(e\left(\frac{40}{43}\right)\) | \(e\left(\frac{8}{215}\right)\) | \(e\left(\frac{32}{215}\right)\) | \(e\left(\frac{87}{215}\right)\) | \(e\left(\frac{51}{215}\right)\) | \(e\left(\frac{413}{430}\right)\) | \(e\left(\frac{141}{215}\right)\) | \(e\left(\frac{189}{215}\right)\) |
| \(\chi_{6034}(517,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{69}{86}\right)\) | \(e\left(\frac{211}{430}\right)\) | \(e\left(\frac{26}{43}\right)\) | \(e\left(\frac{117}{215}\right)\) | \(e\left(\frac{38}{215}\right)\) | \(e\left(\frac{63}{215}\right)\) | \(e\left(\frac{74}{215}\right)\) | \(e\left(\frac{47}{430}\right)\) | \(e\left(\frac{154}{215}\right)\) | \(e\left(\frac{211}{215}\right)\) |
| \(\chi_{6034}(573,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{75}{86}\right)\) | \(e\left(\frac{349}{430}\right)\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{58}{215}\right)\) | \(e\left(\frac{17}{215}\right)\) | \(e\left(\frac{147}{215}\right)\) | \(e\left(\frac{101}{215}\right)\) | \(e\left(\frac{253}{430}\right)\) | \(e\left(\frac{1}{215}\right)\) | \(e\left(\frac{134}{215}\right)\) |
| \(\chi_{6034}(587,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{86}\right)\) | \(e\left(\frac{419}{430}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{53}{215}\right)\) | \(e\left(\frac{212}{215}\right)\) | \(e\left(\frac{12}{215}\right)\) | \(e\left(\frac{96}{215}\right)\) | \(e\left(\frac{183}{430}\right)\) | \(e\left(\frac{101}{215}\right)\) | \(e\left(\frac{204}{215}\right)\) |
| \(\chi_{6034}(601,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{86}\right)\) | \(e\left(\frac{61}{430}\right)\) | \(e\left(\frac{12}{43}\right)\) | \(e\left(\frac{97}{215}\right)\) | \(e\left(\frac{173}{215}\right)\) | \(e\left(\frac{168}{215}\right)\) | \(e\left(\frac{54}{215}\right)\) | \(e\left(\frac{197}{430}\right)\) | \(e\left(\frac{124}{215}\right)\) | \(e\left(\frac{61}{215}\right)\) |
| \(\chi_{6034}(657,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{86}\right)\) | \(e\left(\frac{7}{430}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{64}{215}\right)\) | \(e\left(\frac{41}{215}\right)\) | \(e\left(\frac{51}{215}\right)\) | \(e\left(\frac{193}{215}\right)\) | \(e\left(\frac{79}{430}\right)\) | \(e\left(\frac{53}{215}\right)\) | \(e\left(\frac{7}{215}\right)\) |
| \(\chi_{6034}(685,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{86}\right)\) | \(e\left(\frac{333}{430}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{96}{215}\right)\) | \(e\left(\frac{169}{215}\right)\) | \(e\left(\frac{184}{215}\right)\) | \(e\left(\frac{182}{215}\right)\) | \(e\left(\frac{11}{430}\right)\) | \(e\left(\frac{187}{215}\right)\) | \(e\left(\frac{118}{215}\right)\) |
| \(\chi_{6034}(699,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{86}\right)\) | \(e\left(\frac{11}{430}\right)\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{162}{215}\right)\) | \(e\left(\frac{3}{215}\right)\) | \(e\left(\frac{203}{215}\right)\) | \(e\left(\frac{119}{215}\right)\) | \(e\left(\frac{247}{430}\right)\) | \(e\left(\frac{114}{215}\right)\) | \(e\left(\frac{11}{215}\right)\) |
| \(\chi_{6034}(727,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{86}\right)\) | \(e\left(\frac{259}{430}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{3}{215}\right)\) | \(e\left(\frac{12}{215}\right)\) | \(e\left(\frac{167}{215}\right)\) | \(e\left(\frac{46}{215}\right)\) | \(e\left(\frac{343}{430}\right)\) | \(e\left(\frac{26}{215}\right)\) | \(e\left(\frac{44}{215}\right)\) |
| \(\chi_{6034}(741,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{75}{86}\right)\) | \(e\left(\frac{177}{430}\right)\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{144}{215}\right)\) | \(e\left(\frac{146}{215}\right)\) | \(e\left(\frac{61}{215}\right)\) | \(e\left(\frac{58}{215}\right)\) | \(e\left(\frac{339}{430}\right)\) | \(e\left(\frac{173}{215}\right)\) | \(e\left(\frac{177}{215}\right)\) |
| \(\chi_{6034}(839,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{86}\right)\) | \(e\left(\frac{337}{430}\right)\) | \(e\left(\frac{24}{43}\right)\) | \(e\left(\frac{194}{215}\right)\) | \(e\left(\frac{131}{215}\right)\) | \(e\left(\frac{121}{215}\right)\) | \(e\left(\frac{108}{215}\right)\) | \(e\left(\frac{179}{430}\right)\) | \(e\left(\frac{33}{215}\right)\) | \(e\left(\frac{122}{215}\right)\) |
| \(\chi_{6034}(951,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{86}\right)\) | \(e\left(\frac{113}{430}\right)\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{81}{215}\right)\) | \(e\left(\frac{109}{215}\right)\) | \(e\left(\frac{209}{215}\right)\) | \(e\left(\frac{167}{215}\right)\) | \(e\left(\frac{231}{430}\right)\) | \(e\left(\frac{57}{215}\right)\) | \(e\left(\frac{113}{215}\right)\) |
| \(\chi_{6034}(965,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{86}\right)\) | \(e\left(\frac{403}{430}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{91}{215}\right)\) | \(e\left(\frac{149}{215}\right)\) | \(e\left(\frac{49}{215}\right)\) | \(e\left(\frac{177}{215}\right)\) | \(e\left(\frac{371}{430}\right)\) | \(e\left(\frac{72}{215}\right)\) | \(e\left(\frac{188}{215}\right)\) |
| \(\chi_{6034}(979,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{86}\right)\) | \(e\left(\frac{309}{430}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{153}{215}\right)\) | \(e\left(\frac{182}{215}\right)\) | \(e\left(\frac{132}{215}\right)\) | \(e\left(\frac{196}{215}\right)\) | \(e\left(\frac{293}{430}\right)\) | \(e\left(\frac{36}{215}\right)\) | \(e\left(\frac{94}{215}\right)\) |
| \(\chi_{6034}(993,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{86}\right)\) | \(e\left(\frac{73}{430}\right)\) | \(e\left(\frac{20}{43}\right)\) | \(e\left(\frac{176}{215}\right)\) | \(e\left(\frac{59}{215}\right)\) | \(e\left(\frac{194}{215}\right)\) | \(e\left(\frac{47}{215}\right)\) | \(e\left(\frac{271}{430}\right)\) | \(e\left(\frac{92}{215}\right)\) | \(e\left(\frac{73}{215}\right)\) |
| \(\chi_{6034}(1049,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{75}{86}\right)\) | \(e\left(\frac{263}{430}\right)\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{101}{215}\right)\) | \(e\left(\frac{189}{215}\right)\) | \(e\left(\frac{104}{215}\right)\) | \(e\left(\frac{187}{215}\right)\) | \(e\left(\frac{81}{430}\right)\) | \(e\left(\frac{87}{215}\right)\) | \(e\left(\frac{48}{215}\right)\) |
| \(\chi_{6034}(1063,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{86}\right)\) | \(e\left(\frac{331}{430}\right)\) | \(e\left(\frac{20}{43}\right)\) | \(e\left(\frac{47}{215}\right)\) | \(e\left(\frac{188}{215}\right)\) | \(e\left(\frac{108}{215}\right)\) | \(e\left(\frac{4}{215}\right)\) | \(e\left(\frac{357}{430}\right)\) | \(e\left(\frac{49}{215}\right)\) | \(e\left(\frac{116}{215}\right)\) |
| \(\chi_{6034}(1119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{86}\right)\) | \(e\left(\frac{181}{430}\right)\) | \(e\left(\frac{6}{43}\right)\) | \(e\left(\frac{27}{215}\right)\) | \(e\left(\frac{108}{215}\right)\) | \(e\left(\frac{213}{215}\right)\) | \(e\left(\frac{199}{215}\right)\) | \(e\left(\frac{77}{430}\right)\) | \(e\left(\frac{19}{215}\right)\) | \(e\left(\frac{181}{215}\right)\) |
| \(\chi_{6034}(1133,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{86}\right)\) | \(e\left(\frac{169}{430}\right)\) | \(e\left(\frac{41}{43}\right)\) | \(e\left(\frac{163}{215}\right)\) | \(e\left(\frac{7}{215}\right)\) | \(e\left(\frac{187}{215}\right)\) | \(e\left(\frac{206}{215}\right)\) | \(e\left(\frac{3}{430}\right)\) | \(e\left(\frac{51}{215}\right)\) | \(e\left(\frac{169}{215}\right)\) |