from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6028, base_ring=CyclotomicField(680))
M = H._module
chi = DirichletCharacter(H, M([0,68,125]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,6028))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6028\) | |
| Conductor: | \(1507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(680\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1507.bf | 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: | $\Q(\zeta_{680})$ |
| Fixed field: | Number field defined by a degree 680 polynomial (not computed) |
First 31 of 256 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6028}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{669}{680}\right)\) | \(e\left(\frac{127}{680}\right)\) | \(e\left(\frac{143}{340}\right)\) | \(e\left(\frac{329}{340}\right)\) | \(e\left(\frac{473}{680}\right)\) | \(e\left(\frac{29}{170}\right)\) | \(e\left(\frac{301}{340}\right)\) | \(e\left(\frac{257}{340}\right)\) | \(e\left(\frac{55}{136}\right)\) | \(e\left(\frac{133}{136}\right)\) |
| \(\chi_{6028}(29,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{183}{680}\right)\) | \(e\left(\frac{669}{680}\right)\) | \(e\left(\frac{1}{340}\right)\) | \(e\left(\frac{183}{340}\right)\) | \(e\left(\frac{291}{680}\right)\) | \(e\left(\frac{43}{170}\right)\) | \(e\left(\frac{247}{340}\right)\) | \(e\left(\frac{299}{340}\right)\) | \(e\left(\frac{37}{136}\right)\) | \(e\left(\frac{87}{136}\right)\) |
| \(\chi_{6028}(57,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{99}{680}\right)\) | \(e\left(\frac{217}{680}\right)\) | \(e\left(\frac{73}{340}\right)\) | \(e\left(\frac{99}{340}\right)\) | \(e\left(\frac{503}{680}\right)\) | \(e\left(\frac{79}{170}\right)\) | \(e\left(\frac{11}{340}\right)\) | \(e\left(\frac{67}{340}\right)\) | \(e\left(\frac{49}{136}\right)\) | \(e\left(\frac{27}{136}\right)\) |
| \(\chi_{6028}(85,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{680}\right)\) | \(e\left(\frac{351}{680}\right)\) | \(e\left(\frac{339}{340}\right)\) | \(e\left(\frac{157}{340}\right)\) | \(e\left(\frac{49}{680}\right)\) | \(e\left(\frac{127}{170}\right)\) | \(e\left(\frac{93}{340}\right)\) | \(e\left(\frac{41}{340}\right)\) | \(e\left(\frac{31}{136}\right)\) | \(e\left(\frac{117}{136}\right)\) |
| \(\chi_{6028}(117,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{543}{680}\right)\) | \(e\left(\frac{469}{680}\right)\) | \(e\left(\frac{81}{340}\right)\) | \(e\left(\frac{203}{340}\right)\) | \(e\left(\frac{451}{680}\right)\) | \(e\left(\frac{83}{170}\right)\) | \(e\left(\frac{287}{340}\right)\) | \(e\left(\frac{79}{340}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{111}{136}\right)\) |
| \(\chi_{6028}(149,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{241}{680}\right)\) | \(e\left(\frac{123}{680}\right)\) | \(e\left(\frac{267}{340}\right)\) | \(e\left(\frac{241}{340}\right)\) | \(e\left(\frac{517}{680}\right)\) | \(e\left(\frac{91}{170}\right)\) | \(e\left(\frac{329}{340}\right)\) | \(e\left(\frac{273}{340}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{41}{136}\right)\) |
| \(\chi_{6028}(161,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{563}{680}\right)\) | \(e\left(\frac{609}{680}\right)\) | \(e\left(\frac{161}{340}\right)\) | \(e\left(\frac{223}{340}\right)\) | \(e\left(\frac{271}{680}\right)\) | \(e\left(\frac{123}{170}\right)\) | \(e\left(\frac{327}{340}\right)\) | \(e\left(\frac{199}{340}\right)\) | \(e\left(\frac{41}{136}\right)\) | \(e\left(\frac{67}{136}\right)\) |
| \(\chi_{6028}(189,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{680}\right)\) | \(e\left(\frac{147}{680}\right)\) | \(e\left(\frac{203}{340}\right)\) | \(e\left(\frac{89}{340}\right)\) | \(e\left(\frac{253}{680}\right)\) | \(e\left(\frac{59}{170}\right)\) | \(e\left(\frac{161}{340}\right)\) | \(e\left(\frac{177}{340}\right)\) | \(e\left(\frac{99}{136}\right)\) | \(e\left(\frac{49}{136}\right)\) |
| \(\chi_{6028}(217,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{680}\right)\) | \(e\left(\frac{421}{680}\right)\) | \(e\left(\frac{209}{340}\right)\) | \(e\left(\frac{167}{340}\right)\) | \(e\left(\frac{299}{680}\right)\) | \(e\left(\frac{147}{170}\right)\) | \(e\left(\frac{283}{340}\right)\) | \(e\left(\frac{271}{340}\right)\) | \(e\left(\frac{117}{136}\right)\) | \(e\left(\frac{95}{136}\right)\) |
| \(\chi_{6028}(261,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{680}\right)\) | \(e\left(\frac{331}{680}\right)\) | \(e\left(\frac{279}{340}\right)\) | \(e\left(\frac{57}{340}\right)\) | \(e\left(\frac{269}{680}\right)\) | \(e\left(\frac{97}{170}\right)\) | \(e\left(\frac{233}{340}\right)\) | \(e\left(\frac{121}{340}\right)\) | \(e\left(\frac{123}{136}\right)\) | \(e\left(\frac{65}{136}\right)\) |
| \(\chi_{6028}(277,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{549}{680}\right)\) | \(e\left(\frac{647}{680}\right)\) | \(e\left(\frac{3}{340}\right)\) | \(e\left(\frac{209}{340}\right)\) | \(e\left(\frac{193}{680}\right)\) | \(e\left(\frac{129}{170}\right)\) | \(e\left(\frac{61}{340}\right)\) | \(e\left(\frac{217}{340}\right)\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) |
| \(\chi_{6028}(305,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{637}{680}\right)\) | \(e\left(\frac{311}{680}\right)\) | \(e\left(\frac{219}{340}\right)\) | \(e\left(\frac{297}{340}\right)\) | \(e\left(\frac{489}{680}\right)\) | \(e\left(\frac{67}{170}\right)\) | \(e\left(\frac{33}{340}\right)\) | \(e\left(\frac{201}{340}\right)\) | \(e\left(\frac{79}{136}\right)\) | \(e\left(\frac{13}{136}\right)\) |
| \(\chi_{6028}(321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{639}{680}\right)\) | \(e\left(\frac{597}{680}\right)\) | \(e\left(\frac{193}{340}\right)\) | \(e\left(\frac{299}{340}\right)\) | \(e\left(\frac{403}{680}\right)\) | \(e\left(\frac{139}{170}\right)\) | \(e\left(\frac{71}{340}\right)\) | \(e\left(\frac{247}{340}\right)\) | \(e\left(\frac{69}{136}\right)\) | \(e\left(\frac{63}{136}\right)\) |
| \(\chi_{6028}(325,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{331}{680}\right)\) | \(e\left(\frac{73}{680}\right)\) | \(e\left(\frac{117}{340}\right)\) | \(e\left(\frac{331}{340}\right)\) | \(e\left(\frac{47}{680}\right)\) | \(e\left(\frac{101}{170}\right)\) | \(e\left(\frac{339}{340}\right)\) | \(e\left(\frac{303}{340}\right)\) | \(e\left(\frac{113}{136}\right)\) | \(e\left(\frac{115}{136}\right)\) |
| \(\chi_{6028}(349,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{347}{680}\right)\) | \(e\left(\frac{321}{680}\right)\) | \(e\left(\frac{249}{340}\right)\) | \(e\left(\frac{7}{340}\right)\) | \(e\left(\frac{39}{680}\right)\) | \(e\left(\frac{167}{170}\right)\) | \(e\left(\frac{303}{340}\right)\) | \(e\left(\frac{331}{340}\right)\) | \(e\left(\frac{33}{136}\right)\) | \(e\left(\frac{107}{136}\right)\) |
| \(\chi_{6028}(365,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{680}\right)\) | \(e\left(\frac{237}{680}\right)\) | \(e\left(\frac{133}{340}\right)\) | \(e\left(\frac{199}{340}\right)\) | \(e\left(\frac{283}{680}\right)\) | \(e\left(\frac{109}{170}\right)\) | \(e\left(\frac{211}{340}\right)\) | \(e\left(\frac{327}{340}\right)\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{79}{136}\right)\) |
| \(\chi_{6028}(369,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{680}\right)\) | \(e\left(\frac{223}{680}\right)\) | \(e\left(\frac{227}{340}\right)\) | \(e\left(\frac{61}{340}\right)\) | \(e\left(\frac{97}{680}\right)\) | \(e\left(\frac{71}{170}\right)\) | \(e\left(\frac{309}{340}\right)\) | \(e\left(\frac{213}{340}\right)\) | \(e\left(\frac{103}{136}\right)\) | \(e\left(\frac{29}{136}\right)\) |
| \(\chi_{6028}(437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{447}{680}\right)\) | \(e\left(\frac{341}{680}\right)\) | \(e\left(\frac{309}{340}\right)\) | \(e\left(\frac{107}{340}\right)\) | \(e\left(\frac{499}{680}\right)\) | \(e\left(\frac{27}{170}\right)\) | \(e\left(\frac{163}{340}\right)\) | \(e\left(\frac{251}{340}\right)\) | \(e\left(\frac{77}{136}\right)\) | \(e\left(\frac{23}{136}\right)\) |
| \(\chi_{6028}(453,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{129}{680}\right)\) | \(e\left(\frac{427}{680}\right)\) | \(e\left(\frac{23}{340}\right)\) | \(e\left(\frac{129}{340}\right)\) | \(e\left(\frac{573}{680}\right)\) | \(e\left(\frac{139}{170}\right)\) | \(e\left(\frac{241}{340}\right)\) | \(e\left(\frac{77}{340}\right)\) | \(e\left(\frac{35}{136}\right)\) | \(e\left(\frac{97}{136}\right)\) |
| \(\chi_{6028}(457,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{680}\right)\) | \(e\left(\frac{33}{680}\right)\) | \(e\left(\frac{337}{340}\right)\) | \(e\left(\frac{131}{340}\right)\) | \(e\left(\frac{487}{680}\right)\) | \(e\left(\frac{41}{170}\right)\) | \(e\left(\frac{279}{340}\right)\) | \(e\left(\frac{123}{340}\right)\) | \(e\left(\frac{25}{136}\right)\) | \(e\left(\frac{11}{136}\right)\) |
| \(\chi_{6028}(469,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{680}\right)\) | \(e\left(\frac{339}{680}\right)\) | \(e\left(\frac{31}{340}\right)\) | \(e\left(\frac{233}{340}\right)\) | \(e\left(\frac{181}{680}\right)\) | \(e\left(\frac{143}{170}\right)\) | \(e\left(\frac{177}{340}\right)\) | \(e\left(\frac{89}{340}\right)\) | \(e\left(\frac{59}{136}\right)\) | \(e\left(\frac{113}{136}\right)\) |
| \(\chi_{6028}(481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{680}\right)\) | \(e\left(\frac{161}{680}\right)\) | \(e\left(\frac{109}{340}\right)\) | \(e\left(\frac{227}{340}\right)\) | \(e\left(\frac{439}{680}\right)\) | \(e\left(\frac{97}{170}\right)\) | \(e\left(\frac{63}{340}\right)\) | \(e\left(\frac{291}{340}\right)\) | \(e\left(\frac{89}{136}\right)\) | \(e\left(\frac{99}{136}\right)\) |
| \(\chi_{6028}(497,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{399}{680}\right)\) | \(e\left(\frac{277}{680}\right)\) | \(e\left(\frac{253}{340}\right)\) | \(e\left(\frac{59}{340}\right)\) | \(e\left(\frac{523}{680}\right)\) | \(e\left(\frac{169}{170}\right)\) | \(e\left(\frac{271}{340}\right)\) | \(e\left(\frac{167}{340}\right)\) | \(e\left(\frac{45}{136}\right)\) | \(e\left(\frac{47}{136}\right)\) |
| \(\chi_{6028}(501,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{571}{680}\right)\) | \(e\left(\frac{393}{680}\right)\) | \(e\left(\frac{57}{340}\right)\) | \(e\left(\frac{231}{340}\right)\) | \(e\left(\frac{607}{680}\right)\) | \(e\left(\frac{71}{170}\right)\) | \(e\left(\frac{139}{340}\right)\) | \(e\left(\frac{43}{340}\right)\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{131}{136}\right)\) |
| \(\chi_{6028}(513,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{653}{680}\right)\) | \(e\left(\frac{559}{680}\right)\) | \(e\left(\frac{11}{340}\right)\) | \(e\left(\frac{313}{340}\right)\) | \(e\left(\frac{481}{680}\right)\) | \(e\left(\frac{133}{170}\right)\) | \(e\left(\frac{337}{340}\right)\) | \(e\left(\frac{229}{340}\right)\) | \(e\left(\frac{135}{136}\right)\) | \(e\left(\frac{5}{136}\right)\) |
| \(\chi_{6028}(525,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{557}{680}\right)\) | \(e\left(\frac{431}{680}\right)\) | \(e\left(\frac{239}{340}\right)\) | \(e\left(\frac{217}{340}\right)\) | \(e\left(\frac{529}{680}\right)\) | \(e\left(\frac{77}{170}\right)\) | \(e\left(\frac{213}{340}\right)\) | \(e\left(\frac{61}{340}\right)\) | \(e\left(\frac{71}{136}\right)\) | \(e\left(\frac{53}{136}\right)\) |
| \(\chi_{6028}(545,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{481}{680}\right)\) | \(e\left(\frac{443}{680}\right)\) | \(e\left(\frac{207}{340}\right)\) | \(e\left(\frac{141}{340}\right)\) | \(e\left(\frac{397}{680}\right)\) | \(e\left(\frac{61}{170}\right)\) | \(e\left(\frac{129}{340}\right)\) | \(e\left(\frac{13}{340}\right)\) | \(e\left(\frac{43}{136}\right)\) | \(e\left(\frac{57}{136}\right)\) |
| \(\chi_{6028}(569,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{487}{680}\right)\) | \(e\left(\frac{621}{680}\right)\) | \(e\left(\frac{129}{340}\right)\) | \(e\left(\frac{147}{340}\right)\) | \(e\left(\frac{139}{680}\right)\) | \(e\left(\frac{107}{170}\right)\) | \(e\left(\frac{243}{340}\right)\) | \(e\left(\frac{151}{340}\right)\) | \(e\left(\frac{13}{136}\right)\) | \(e\left(\frac{71}{136}\right)\) |
| \(\chi_{6028}(601,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{383}{680}\right)\) | \(e\left(\frac{29}{680}\right)\) | \(e\left(\frac{121}{340}\right)\) | \(e\left(\frac{43}{340}\right)\) | \(e\left(\frac{531}{680}\right)\) | \(e\left(\frac{103}{170}\right)\) | \(e\left(\frac{307}{340}\right)\) | \(e\left(\frac{139}{340}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{55}{136}\right)\) |
| \(\chi_{6028}(633,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{680}\right)\) | \(e\left(\frac{623}{680}\right)\) | \(e\left(\frac{67}{340}\right)\) | \(e\left(\frac{21}{340}\right)\) | \(e\left(\frac{457}{680}\right)\) | \(e\left(\frac{161}{170}\right)\) | \(e\left(\frac{229}{340}\right)\) | \(e\left(\frac{313}{340}\right)\) | \(e\left(\frac{31}{136}\right)\) | \(e\left(\frac{117}{136}\right)\) |
| \(\chi_{6028}(645,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{593}{680}\right)\) | \(e\left(\frac{139}{680}\right)\) | \(e\left(\frac{111}{340}\right)\) | \(e\left(\frac{253}{340}\right)\) | \(e\left(\frac{341}{680}\right)\) | \(e\left(\frac{13}{170}\right)\) | \(e\left(\frac{217}{340}\right)\) | \(e\left(\frac{209}{340}\right)\) | \(e\left(\frac{27}{136}\right)\) | \(e\left(\frac{1}{136}\right)\) |