Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(6040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.fh
\(\chi_{6040}(13,\cdot)\) \(\chi_{6040}(77,\cdot)\) \(\chi_{6040}(93,\cdot)\) \(\chi_{6040}(117,\cdot)\) \(\chi_{6040}(133,\cdot)\) \(\chi_{6040}(157,\cdot)\) \(\chi_{6040}(253,\cdot)\) \(\chi_{6040}(277,\cdot)\) \(\chi_{6040}(317,\cdot)\) \(\chi_{6040}(373,\cdot)\) \(\chi_{6040}(413,\cdot)\) \(\chi_{6040}(557,\cdot)\) \(\chi_{6040}(573,\cdot)\) \(\chi_{6040}(693,\cdot)\) \(\chi_{6040}(733,\cdot)\) \(\chi_{6040}(837,\cdot)\) \(\chi_{6040}(957,\cdot)\) \(\chi_{6040}(1197,\cdot)\) \(\chi_{6040}(1317,\cdot)\) \(\chi_{6040}(1373,\cdot)\) \(\chi_{6040}(1413,\cdot)\) \(\chi_{6040}(1493,\cdot)\) \(\chi_{6040}(1517,\cdot)\) \(\chi_{6040}(1573,\cdot)\) \(\chi_{6040}(1717,\cdot)\) \(\chi_{6040}(1757,\cdot)\) \(\chi_{6040}(1773,\cdot)\) \(\chi_{6040}(2077,\cdot)\) \(\chi_{6040}(2093,\cdot)\) \(\chi_{6040}(2277,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((1,-1,-i,e\left(\frac{41}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{19}{300}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{29}{150}\right)\) | \(e\left(\frac{287}{300}\right)\) | \(e\left(\frac{181}{300}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{143}{150}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{67}{100}\right)\) |