from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(560))
M = H._module
chi = DirichletCharacter(H, M([128,495]))
chi.galois_orbit()
[g,chi] = znchar(Mod(19,8023))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(560\) | 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: | $\Q(\zeta_{560})$ |
| Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
First 31 of 192 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8023}(19,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{463}{560}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{429}{560}\right)\) | \(e\left(\frac{451}{560}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{183}{280}\right)\) | \(e\left(\frac{417}{560}\right)\) | \(e\left(\frac{139}{280}\right)\) |
| \(\chi_{8023}(75,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{531}{560}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{313}{560}\right)\) | \(e\left(\frac{487}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{251}{280}\right)\) | \(e\left(\frac{269}{560}\right)\) | \(e\left(\frac{183}{280}\right)\) |
| \(\chi_{8023}(80,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{69}{140}\right)\) | \(e\left(\frac{271}{560}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{493}{560}\right)\) | \(e\left(\frac{547}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{271}{280}\right)\) | \(e\left(\frac{209}{560}\right)\) | \(e\left(\frac{163}{280}\right)\) |
| \(\chi_{8023}(180,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{81}{560}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{323}{560}\right)\) | \(e\left(\frac{397}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{81}{280}\right)\) | \(e\left(\frac{79}{560}\right)\) | \(e\left(\frac{213}{280}\right)\) |
| \(\chi_{8023}(192,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{140}\right)\) | \(e\left(\frac{381}{560}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{503}{560}\right)\) | \(e\left(\frac{457}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{101}{280}\right)\) | \(e\left(\frac{19}{560}\right)\) | \(e\left(\frac{193}{280}\right)\) |
| \(\chi_{8023}(296,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{19}{560}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{297}{560}\right)\) | \(e\left(\frac{183}{560}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{19}{280}\right)\) | \(e\left(\frac{461}{560}\right)\) | \(e\left(\frac{247}{280}\right)\) |
| \(\chi_{8023}(363,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{9}{560}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{347}{560}\right)\) | \(e\left(\frac{293}{560}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{9}{280}\right)\) | \(e\left(\frac{71}{560}\right)\) | \(e\left(\frac{117}{280}\right)\) |
| \(\chi_{8023}(405,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{451}{560}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{153}{560}\right)\) | \(e\left(\frac{247}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{171}{280}\right)\) | \(e\left(\frac{509}{560}\right)\) | \(e\left(\frac{263}{280}\right)\) |
| \(\chi_{8023}(413,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{107}{560}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{81}{560}\right)\) | \(e\left(\frac{559}{560}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{533}{560}\right)\) | \(e\left(\frac{271}{280}\right)\) |
| \(\chi_{8023}(429,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{293}{560}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{159}{560}\right)\) | \(e\left(\frac{81}{560}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{13}{280}\right)\) | \(e\left(\frac{507}{560}\right)\) | \(e\left(\frac{169}{280}\right)\) |
| \(\chi_{8023}(432,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{191}{560}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{333}{560}\right)\) | \(e\left(\frac{307}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{449}{560}\right)\) | \(e\left(\frac{243}{280}\right)\) |
| \(\chi_{8023}(435,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{481}{560}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{3}{560}\right)\) | \(e\left(\frac{477}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{201}{280}\right)\) | \(e\left(\frac{559}{560}\right)\) | \(e\left(\frac{93}{280}\right)\) |
| \(\chi_{8023}(462,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{347}{560}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{1}{560}\right)\) | \(e\left(\frac{159}{560}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{67}{280}\right)\) | \(e\left(\frac{373}{560}\right)\) | \(e\left(\frac{31}{280}\right)\) |
| \(\chi_{8023}(464,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{221}{560}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{183}{560}\right)\) | \(e\left(\frac{537}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{221}{280}\right)\) | \(e\left(\frac{499}{560}\right)\) | \(e\left(\frac{73}{280}\right)\) |
| \(\chi_{8023}(499,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{283}{560}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{209}{560}\right)\) | \(e\left(\frac{191}{560}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{3}{280}\right)\) | \(e\left(\frac{117}{560}\right)\) | \(e\left(\frac{39}{280}\right)\) |
| \(\chi_{8023}(507,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{17}{560}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{531}{560}\right)\) | \(e\left(\frac{429}{560}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{17}{280}\right)\) | \(e\left(\frac{383}{560}\right)\) | \(e\left(\frac{221}{280}\right)\) |
| \(\chi_{8023}(546,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{109}{140}\right)\) | \(e\left(\frac{71}{560}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{373}{560}\right)\) | \(e\left(\frac{507}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{71}{280}\right)\) | \(e\left(\frac{249}{560}\right)\) | \(e\left(\frac{83}{280}\right)\) |
| \(\chi_{8023}(571,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{433}{560}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{19}{560}\right)\) | \(e\left(\frac{221}{560}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{153}{280}\right)\) | \(e\left(\frac{367}{560}\right)\) | \(e\left(\frac{29}{280}\right)\) |
| \(\chi_{8023}(632,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{193}{560}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{99}{560}\right)\) | \(e\left(\frac{61}{560}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{193}{280}\right)\) | \(e\left(\frac{527}{560}\right)\) | \(e\left(\frac{269}{280}\right)\) |
| \(\chi_{8023}(666,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{389}{560}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{127}{560}\right)\) | \(e\left(\frac{33}{560}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{109}{280}\right)\) | \(e\left(\frac{331}{560}\right)\) | \(e\left(\frac{17}{280}\right)\) |
| \(\chi_{8023}(712,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{213}{560}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{559}{560}\right)\) | \(e\left(\frac{401}{560}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{213}{280}\right)\) | \(e\left(\frac{187}{560}\right)\) | \(e\left(\frac{249}{280}\right)\) |
| \(\chi_{8023}(785,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{41}{560}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{523}{560}\right)\) | \(e\left(\frac{277}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{41}{280}\right)\) | \(e\left(\frac{199}{560}\right)\) | \(e\left(\frac{253}{280}\right)\) |
| \(\chi_{8023}(796,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{447}{560}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{61}{560}\right)\) | \(e\left(\frac{179}{560}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{167}{280}\right)\) | \(e\left(\frac{353}{560}\right)\) | \(e\left(\frac{211}{280}\right)\) |
| \(\chi_{8023}(861,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{69}{140}\right)\) | \(e\left(\frac{131}{560}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{73}{560}\right)\) | \(e\left(\frac{407}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{131}{280}\right)\) | \(e\left(\frac{349}{560}\right)\) | \(e\left(\frac{23}{280}\right)\) |
| \(\chi_{8023}(881,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{69}{560}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{47}{560}\right)\) | \(e\left(\frac{193}{560}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{69}{280}\right)\) | \(e\left(\frac{171}{560}\right)\) | \(e\left(\frac{57}{280}\right)\) |
| \(\chi_{8023}(901,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{141}{560}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{23}{560}\right)\) | \(e\left(\frac{297}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{141}{280}\right)\) | \(e\left(\frac{179}{560}\right)\) | \(e\left(\frac{153}{280}\right)\) |
| \(\chi_{8023}(916,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{333}{560}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{519}{560}\right)\) | \(e\left(\frac{201}{560}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{53}{280}\right)\) | \(e\left(\frac{387}{560}\right)\) | \(e\left(\frac{129}{280}\right)\) |
| \(\chi_{8023}(927,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{461}{560}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{103}{560}\right)\) | \(e\left(\frac{137}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{181}{280}\right)\) | \(e\left(\frac{339}{560}\right)\) | \(e\left(\frac{113}{280}\right)\) |
| \(\chi_{8023}(950,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{249}{560}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{267}{560}\right)\) | \(e\left(\frac{453}{560}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{249}{280}\right)\) | \(e\left(\frac{471}{560}\right)\) | \(e\left(\frac{157}{280}\right)\) |
| \(\chi_{8023}(972,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{1}{560}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{163}{560}\right)\) | \(e\left(\frac{157}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{1}{280}\right)\) | \(e\left(\frac{319}{560}\right)\) | \(e\left(\frac{13}{280}\right)\) |
| \(\chi_{8023}(1023,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{209}{560}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{467}{560}\right)\) | \(e\left(\frac{333}{560}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{209}{280}\right)\) | \(e\left(\frac{31}{560}\right)\) | \(e\left(\frac{197}{280}\right)\) |