from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(464))
M = H._module
chi = DirichletCharacter(H, M([0,319,144]))
chi.galois_orbit()
[g,chi] = znchar(Mod(7,6018))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6018\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1003.s | 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: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
First 31 of 224 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6018}(7,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{139}{464}\right)\) | \(e\left(\frac{69}{464}\right)\) | \(e\left(\frac{265}{464}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{97}{232}\right)\) | \(e\left(\frac{449}{464}\right)\) | \(e\left(\frac{139}{232}\right)\) | \(e\left(\frac{291}{464}\right)\) | \(e\left(\frac{183}{464}\right)\) | \(e\left(\frac{13}{29}\right)\) |
| \(\chi_{6018}(79,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{464}\right)\) | \(e\left(\frac{137}{464}\right)\) | \(e\left(\frac{237}{464}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{85}{232}\right)\) | \(e\left(\frac{293}{464}\right)\) | \(e\left(\frac{7}{232}\right)\) | \(e\left(\frac{255}{464}\right)\) | \(e\left(\frac{323}{464}\right)\) | \(e\left(\frac{9}{29}\right)\) |
| \(\chi_{6018}(133,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{281}{464}\right)\) | \(e\left(\frac{263}{464}\right)\) | \(e\left(\frac{35}{464}\right)\) | \(e\left(\frac{81}{116}\right)\) | \(e\left(\frac{131}{232}\right)\) | \(e\left(\frac{427}{464}\right)\) | \(e\left(\frac{49}{232}\right)\) | \(e\left(\frac{161}{464}\right)\) | \(e\left(\frac{173}{464}\right)\) | \(e\left(\frac{5}{29}\right)\) |
| \(\chi_{6018}(139,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{161}{464}\right)\) | \(e\left(\frac{367}{464}\right)\) | \(e\left(\frac{347}{464}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{99}{232}\right)\) | \(e\left(\frac{243}{464}\right)\) | \(e\left(\frac{161}{232}\right)\) | \(e\left(\frac{297}{464}\right)\) | \(e\left(\frac{5}{464}\right)\) | \(e\left(\frac{4}{29}\right)\) |
| \(\chi_{6018}(163,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{419}{464}\right)\) | \(e\left(\frac{445}{464}\right)\) | \(e\left(\frac{1}{464}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{105}{464}\right)\) | \(e\left(\frac{187}{232}\right)\) | \(e\left(\frac{283}{464}\right)\) | \(e\left(\frac{111}{464}\right)\) | \(e\left(\frac{25}{29}\right)\) |
| \(\chi_{6018}(175,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{309}{464}\right)\) | \(e\left(\frac{347}{464}\right)\) | \(e\left(\frac{55}{464}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{7}{232}\right)\) | \(e\left(\frac{207}{464}\right)\) | \(e\left(\frac{77}{232}\right)\) | \(e\left(\frac{253}{464}\right)\) | \(e\left(\frac{73}{464}\right)\) | \(e\left(\frac{12}{29}\right)\) |
| \(\chi_{6018}(181,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{183}{464}\right)\) | \(e\left(\frac{201}{464}\right)\) | \(e\left(\frac{429}{464}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{101}{232}\right)\) | \(e\left(\frac{37}{464}\right)\) | \(e\left(\frac{183}{232}\right)\) | \(e\left(\frac{303}{464}\right)\) | \(e\left(\frac{291}{464}\right)\) | \(e\left(\frac{24}{29}\right)\) |
| \(\chi_{6018}(193,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{464}\right)\) | \(e\left(\frac{257}{464}\right)\) | \(e\left(\frac{133}{464}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{173}{232}\right)\) | \(e\left(\frac{45}{464}\right)\) | \(e\left(\frac{47}{232}\right)\) | \(e\left(\frac{55}{464}\right)\) | \(e\left(\frac{379}{464}\right)\) | \(e\left(\frac{19}{29}\right)\) |
| \(\chi_{6018}(199,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{349}{464}\right)\) | \(e\left(\frac{3}{464}\right)\) | \(e\left(\frac{415}{464}\right)\) | \(e\left(\frac{49}{116}\right)\) | \(e\left(\frac{95}{232}\right)\) | \(e\left(\frac{423}{464}\right)\) | \(e\left(\frac{117}{232}\right)\) | \(e\left(\frac{53}{464}\right)\) | \(e\left(\frac{129}{464}\right)\) | \(e\left(\frac{22}{29}\right)\) |
| \(\chi_{6018}(241,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{433}{464}\right)\) | \(e\left(\frac{255}{464}\right)\) | \(e\left(\frac{11}{464}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{187}{232}\right)\) | \(e\left(\frac{227}{464}\right)\) | \(e\left(\frac{201}{232}\right)\) | \(e\left(\frac{329}{464}\right)\) | \(e\left(\frac{293}{464}\right)\) | \(e\left(\frac{14}{29}\right)\) |
| \(\chi_{6018}(265,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{387}{464}\right)\) | \(e\left(\frac{349}{464}\right)\) | \(e\left(\frac{177}{464}\right)\) | \(e\left(\frac{55}{116}\right)\) | \(e\left(\frac{225}{232}\right)\) | \(e\left(\frac{25}{464}\right)\) | \(e\left(\frac{155}{232}\right)\) | \(e\left(\frac{443}{464}\right)\) | \(e\left(\frac{159}{464}\right)\) | \(e\left(\frac{17}{29}\right)\) |
| \(\chi_{6018}(277,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{464}\right)\) | \(e\left(\frac{363}{464}\right)\) | \(e\left(\frac{103}{464}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{127}{232}\right)\) | \(e\left(\frac{143}{464}\right)\) | \(e\left(\frac{5}{232}\right)\) | \(e\left(\frac{381}{464}\right)\) | \(e\left(\frac{297}{464}\right)\) | \(e\left(\frac{23}{29}\right)\) |
| \(\chi_{6018}(343,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{417}{464}\right)\) | \(e\left(\frac{207}{464}\right)\) | \(e\left(\frac{331}{464}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{59}{232}\right)\) | \(e\left(\frac{419}{464}\right)\) | \(e\left(\frac{185}{232}\right)\) | \(e\left(\frac{409}{464}\right)\) | \(e\left(\frac{85}{464}\right)\) | \(e\left(\frac{10}{29}\right)\) |
| \(\chi_{6018}(379,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{373}{464}\right)\) | \(e\left(\frac{75}{464}\right)\) | \(e\left(\frac{167}{464}\right)\) | \(e\left(\frac{65}{116}\right)\) | \(e\left(\frac{55}{232}\right)\) | \(e\left(\frac{367}{464}\right)\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{397}{464}\right)\) | \(e\left(\frac{441}{464}\right)\) | \(e\left(\frac{28}{29}\right)\) |
| \(\chi_{6018}(403,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{365}{464}\right)\) | \(e\left(\frac{51}{464}\right)\) | \(e\left(\frac{95}{464}\right)\) | \(e\left(\frac{21}{116}\right)\) | \(e\left(\frac{223}{232}\right)\) | \(e\left(\frac{231}{464}\right)\) | \(e\left(\frac{133}{232}\right)\) | \(e\left(\frac{437}{464}\right)\) | \(e\left(\frac{337}{464}\right)\) | \(e\left(\frac{26}{29}\right)\) |
| \(\chi_{6018}(439,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{265}{464}\right)\) | \(e\left(\frac{215}{464}\right)\) | \(e\left(\frac{355}{464}\right)\) | \(e\left(\frac{109}{116}\right)\) | \(e\left(\frac{3}{232}\right)\) | \(e\left(\frac{155}{464}\right)\) | \(e\left(\frac{33}{232}\right)\) | \(e\left(\frac{241}{464}\right)\) | \(e\left(\frac{429}{464}\right)\) | \(e\left(\frac{1}{29}\right)\) |
| \(\chi_{6018}(481,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{421}{464}\right)\) | \(e\left(\frac{219}{464}\right)\) | \(e\left(\frac{135}{464}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{255}{464}\right)\) | \(e\left(\frac{189}{232}\right)\) | \(e\left(\frac{157}{464}\right)\) | \(e\left(\frac{137}{464}\right)\) | \(e\left(\frac{11}{29}\right)\) |
| \(\chi_{6018}(487,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{455}{464}\right)\) | \(e\left(\frac{89}{464}\right)\) | \(e\left(\frac{93}{464}\right)\) | \(e\left(\frac{23}{116}\right)\) | \(e\left(\frac{189}{232}\right)\) | \(e\left(\frac{21}{464}\right)\) | \(e\left(\frac{223}{232}\right)\) | \(e\left(\frac{335}{464}\right)\) | \(e\left(\frac{115}{464}\right)\) | \(e\left(\frac{5}{29}\right)\) |
| \(\chi_{6018}(499,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{95}{464}\right)\) | \(e\left(\frac{401}{464}\right)\) | \(e\left(\frac{101}{464}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{93}{232}\right)\) | \(e\left(\frac{397}{464}\right)\) | \(e\left(\frac{95}{232}\right)\) | \(e\left(\frac{279}{464}\right)\) | \(e\left(\frac{75}{464}\right)\) | \(e\left(\frac{2}{29}\right)\) |
| \(\chi_{6018}(517,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{187}{464}\right)\) | \(e\left(\frac{213}{464}\right)\) | \(e\left(\frac{233}{464}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{337}{464}\right)\) | \(e\left(\frac{187}{232}\right)\) | \(e\left(\frac{51}{464}\right)\) | \(e\left(\frac{343}{464}\right)\) | \(e\left(\frac{25}{29}\right)\) |
| \(\chi_{6018}(547,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{337}{464}\right)\) | \(e\left(\frac{431}{464}\right)\) | \(e\left(\frac{75}{464}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{115}{232}\right)\) | \(e\left(\frac{451}{464}\right)\) | \(e\left(\frac{105}{232}\right)\) | \(e\left(\frac{345}{464}\right)\) | \(e\left(\frac{437}{464}\right)\) | \(e\left(\frac{19}{29}\right)\) |
| \(\chi_{6018}(607,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{93}{464}\right)\) | \(e\left(\frac{163}{464}\right)\) | \(e\left(\frac{431}{464}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{135}{232}\right)\) | \(e\left(\frac{247}{464}\right)\) | \(e\left(\frac{93}{232}\right)\) | \(e\left(\frac{405}{464}\right)\) | \(e\left(\frac{49}{464}\right)\) | \(e\left(\frac{16}{29}\right)\) |
| \(\chi_{6018}(619,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{155}{464}\right)\) | \(e\left(\frac{117}{464}\right)\) | \(e\left(\frac{409}{464}\right)\) | \(e\left(\frac{55}{116}\right)\) | \(e\left(\frac{225}{232}\right)\) | \(e\left(\frac{257}{464}\right)\) | \(e\left(\frac{155}{232}\right)\) | \(e\left(\frac{211}{464}\right)\) | \(e\left(\frac{391}{464}\right)\) | \(e\left(\frac{17}{29}\right)\) |
| \(\chi_{6018}(643,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{464}\right)\) | \(e\left(\frac{7}{464}\right)\) | \(e\left(\frac{195}{464}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{67}{232}\right)\) | \(e\left(\frac{59}{464}\right)\) | \(e\left(\frac{41}{232}\right)\) | \(e\left(\frac{433}{464}\right)\) | \(e\left(\frac{301}{464}\right)\) | \(e\left(\frac{3}{29}\right)\) |
| \(\chi_{6018}(685,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{464}\right)\) | \(e\left(\frac{43}{464}\right)\) | \(e\left(\frac{71}{464}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{47}{232}\right)\) | \(e\left(\frac{31}{464}\right)\) | \(e\left(\frac{53}{232}\right)\) | \(e\left(\frac{141}{464}\right)\) | \(e\left(\frac{457}{464}\right)\) | \(e\left(\frac{6}{29}\right)\) |
| \(\chi_{6018}(787,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{181}{464}\right)\) | \(e\left(\frac{427}{464}\right)\) | \(e\left(\frac{295}{464}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{143}{232}\right)\) | \(e\left(\frac{351}{464}\right)\) | \(e\left(\frac{181}{232}\right)\) | \(e\left(\frac{429}{464}\right)\) | \(e\left(\frac{265}{464}\right)\) | \(e\left(\frac{9}{29}\right)\) |
| \(\chi_{6018}(793,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{439}{464}\right)\) | \(e\left(\frac{41}{464}\right)\) | \(e\left(\frac{413}{464}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{61}{232}\right)\) | \(e\left(\frac{213}{464}\right)\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{415}{464}\right)\) | \(e\left(\frac{371}{464}\right)\) | \(e\left(\frac{1}{29}\right)\) |
| \(\chi_{6018}(847,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{393}{464}\right)\) | \(e\left(\frac{135}{464}\right)\) | \(e\left(\frac{115}{464}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{99}{232}\right)\) | \(e\left(\frac{11}{464}\right)\) | \(e\left(\frac{161}{232}\right)\) | \(e\left(\frac{65}{464}\right)\) | \(e\left(\frac{237}{464}\right)\) | \(e\left(\frac{4}{29}\right)\) |
| \(\chi_{6018}(853,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{385}{464}\right)\) | \(e\left(\frac{111}{464}\right)\) | \(e\left(\frac{43}{464}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{35}{232}\right)\) | \(e\left(\frac{339}{464}\right)\) | \(e\left(\frac{153}{232}\right)\) | \(e\left(\frac{105}{464}\right)\) | \(e\left(\frac{133}{464}\right)\) | \(e\left(\frac{2}{29}\right)\) |
| \(\chi_{6018}(877,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{115}{464}\right)\) | \(e\left(\frac{461}{464}\right)\) | \(e\left(\frac{49}{464}\right)\) | \(e\left(\frac{67}{116}\right)\) | \(e\left(\frac{137}{232}\right)\) | \(e\left(\frac{41}{464}\right)\) | \(e\left(\frac{115}{232}\right)\) | \(e\left(\frac{411}{464}\right)\) | \(e\left(\frac{335}{464}\right)\) | \(e\left(\frac{7}{29}\right)\) |
| \(\chi_{6018}(889,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{357}{464}\right)\) | \(e\left(\frac{27}{464}\right)\) | \(e\left(\frac{23}{464}\right)\) | \(e\left(\frac{93}{116}\right)\) | \(e\left(\frac{159}{232}\right)\) | \(e\left(\frac{95}{464}\right)\) | \(e\left(\frac{125}{232}\right)\) | \(e\left(\frac{13}{464}\right)\) | \(e\left(\frac{233}{464}\right)\) | \(e\left(\frac{24}{29}\right)\) |