Basic properties
Modulus: | \(6040\) | |
Conductor: | \(755\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{755}(337,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.fl
\(\chi_{6040}(233,\cdot)\) \(\chi_{6040}(257,\cdot)\) \(\chi_{6040}(297,\cdot)\) \(\chi_{6040}(337,\cdot)\) \(\chi_{6040}(353,\cdot)\) \(\chi_{6040}(417,\cdot)\) \(\chi_{6040}(593,\cdot)\) \(\chi_{6040}(617,\cdot)\) \(\chi_{6040}(697,\cdot)\) \(\chi_{6040}(713,\cdot)\) \(\chi_{6040}(737,\cdot)\) \(\chi_{6040}(857,\cdot)\) \(\chi_{6040}(913,\cdot)\) \(\chi_{6040}(977,\cdot)\) \(\chi_{6040}(1017,\cdot)\) \(\chi_{6040}(1113,\cdot)\) \(\chi_{6040}(1153,\cdot)\) \(\chi_{6040}(1177,\cdot)\) \(\chi_{6040}(1297,\cdot)\) \(\chi_{6040}(1337,\cdot)\) \(\chi_{6040}(1473,\cdot)\) \(\chi_{6040}(1673,\cdot)\) \(\chi_{6040}(1713,\cdot)\) \(\chi_{6040}(1873,\cdot)\) \(\chi_{6040}(1953,\cdot)\) \(\chi_{6040}(1977,\cdot)\) \(\chi_{6040}(1993,\cdot)\) \(\chi_{6040}(2017,\cdot)\) \(\chi_{6040}(2097,\cdot)\) \(\chi_{6040}(2177,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{300})$ |
Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((1,1,i,e\left(\frac{29}{150}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 6040 }(337, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{61}{300}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{13}{75}\right)\) | \(e\left(\frac{203}{300}\right)\) | \(e\left(\frac{139}{300}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{46}{75}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{23}{100}\right)\) |