from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(280))
M = H._module
chi = DirichletCharacter(H, M([0,220,217]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,6027))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(280\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 2009.cg | 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: | $\Q(\zeta_{280})$ |
| Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6027}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) |
| \(\chi_{6027}(34,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{279}{280}\right)\) | \(e\left(\frac{223}{280}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{9}{280}\right)\) | \(e\left(\frac{31}{40}\right)\) |
| \(\chi_{6027}(76,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{121}{280}\right)\) | \(e\left(\frac{177}{280}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{31}{280}\right)\) | \(e\left(\frac{9}{40}\right)\) |
| \(\chi_{6027}(181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{13}{280}\right)\) | \(e\left(\frac{181}{280}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{163}{280}\right)\) | \(e\left(\frac{37}{40}\right)\) |
| \(\chi_{6027}(265,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{229}{280}\right)\) | \(e\left(\frac{173}{280}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{179}{280}\right)\) | \(e\left(\frac{21}{40}\right)\) |
| \(\chi_{6027}(475,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{153}{280}\right)\) | \(e\left(\frac{41}{280}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{23}{280}\right)\) | \(e\left(\frac{17}{40}\right)\) |
| \(\chi_{6027}(559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{117}{280}\right)\) | \(e\left(\frac{229}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{67}{280}\right)\) | \(e\left(\frac{13}{40}\right)\) |
| \(\chi_{6027}(580,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{101}{280}\right)\) | \(e\left(\frac{157}{280}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{29}{40}\right)\) |
| \(\chi_{6027}(622,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{139}{280}\right)\) | \(e\left(\frac{83}{280}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{149}{280}\right)\) | \(e\left(\frac{11}{40}\right)\) |
| \(\chi_{6027}(643,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{83}{140}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{151}{280}\right)\) | \(e\left(\frac{207}{280}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{41}{280}\right)\) | \(e\left(\frac{39}{40}\right)\) |
| \(\chi_{6027}(727,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{3}{280}\right)\) | \(e\left(\frac{171}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{253}{280}\right)\) | \(e\left(\frac{27}{40}\right)\) |
| \(\chi_{6027}(790,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{263}{280}\right)\) | \(e\left(\frac{151}{280}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{153}{280}\right)\) | \(e\left(\frac{7}{40}\right)\) |
| \(\chi_{6027}(874,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{171}{280}\right)\) | \(e\left(\frac{227}{280}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{141}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) |
| \(\chi_{6027}(895,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{140}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{239}{280}\right)\) | \(e\left(\frac{183}{280}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{89}{280}\right)\) | \(e\left(\frac{31}{40}\right)\) |
| \(\chi_{6027}(937,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{81}{280}\right)\) | \(e\left(\frac{137}{280}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{111}{280}\right)\) | \(e\left(\frac{9}{40}\right)\) |
| \(\chi_{6027}(958,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{177}{280}\right)\) | \(e\left(\frac{9}{280}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{87}{280}\right)\) | \(e\left(\frac{33}{40}\right)\) |
| \(\chi_{6027}(1042,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{253}{280}\right)\) | \(e\left(\frac{141}{280}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{243}{280}\right)\) | \(e\left(\frac{37}{40}\right)\) |
| \(\chi_{6027}(1252,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{9}{280}\right)\) | \(e\left(\frac{233}{280}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{199}{280}\right)\) | \(e\left(\frac{1}{40}\right)\) |
| \(\chi_{6027}(1336,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{113}{280}\right)\) | \(e\left(\frac{1}{280}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{103}{280}\right)\) | \(e\left(\frac{17}{40}\right)\) |
| \(\chi_{6027}(1441,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{53}{140}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{117}{280}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{11}{280}\right)\) | \(e\left(\frac{29}{40}\right)\) |
| \(\chi_{6027}(1483,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{140}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{99}{280}\right)\) | \(e\left(\frac{43}{280}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{229}{280}\right)\) | \(e\left(\frac{11}{40}\right)\) |
| \(\chi_{6027}(1504,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{23}{140}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{111}{280}\right)\) | \(e\left(\frac{167}{280}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{121}{280}\right)\) | \(e\left(\frac{39}{40}\right)\) |
| \(\chi_{6027}(1546,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{219}{280}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{157}{280}\right)\) | \(e\left(\frac{3}{40}\right)\) |
| \(\chi_{6027}(1588,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{243}{280}\right)\) | \(e\left(\frac{131}{280}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{53}{280}\right)\) | \(e\left(\frac{27}{40}\right)\) |
| \(\chi_{6027}(1651,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{223}{280}\right)\) | \(e\left(\frac{111}{280}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{233}{280}\right)\) | \(e\left(\frac{7}{40}\right)\) |
| \(\chi_{6027}(1693,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{247}{280}\right)\) | \(e\left(\frac{79}{280}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{17}{280}\right)\) | \(e\left(\frac{23}{40}\right)\) |
| \(\chi_{6027}(1735,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{131}{280}\right)\) | \(e\left(\frac{187}{280}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{221}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) |
| \(\chi_{6027}(1756,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{199}{280}\right)\) | \(e\left(\frac{143}{280}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{169}{280}\right)\) | \(e\left(\frac{31}{40}\right)\) |
| \(\chi_{6027}(1798,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{41}{280}\right)\) | \(e\left(\frac{97}{280}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{9}{40}\right)\) |
| \(\chi_{6027}(1819,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{137}{280}\right)\) | \(e\left(\frac{249}{280}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{167}{280}\right)\) | \(e\left(\frac{33}{40}\right)\) |
| \(\chi_{6027}(1903,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{213}{280}\right)\) | \(e\left(\frac{101}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{43}{280}\right)\) | \(e\left(\frac{37}{40}\right)\) |