Basic properties
| Modulus: | \(731\) | |
| Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | 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)
|
Galois orbit 731.bn
\(\chi_{731}(10,\cdot)\) \(\chi_{731}(14,\cdot)\) \(\chi_{731}(23,\cdot)\) \(\chi_{731}(24,\cdot)\) \(\chi_{731}(31,\cdot)\) \(\chi_{731}(40,\cdot)\) \(\chi_{731}(56,\cdot)\) \(\chi_{731}(57,\cdot)\) \(\chi_{731}(58,\cdot)\) \(\chi_{731}(74,\cdot)\) \(\chi_{731}(95,\cdot)\) \(\chi_{731}(96,\cdot)\) \(\chi_{731}(99,\cdot)\) \(\chi_{731}(109,\cdot)\) \(\chi_{731}(124,\cdot)\) \(\chi_{731}(126,\cdot)\) \(\chi_{731}(139,\cdot)\) \(\chi_{731}(142,\cdot)\) \(\chi_{731}(143,\cdot)\) \(\chi_{731}(146,\cdot)\) \(\chi_{731}(160,\cdot)\) \(\chi_{731}(167,\cdot)\) \(\chi_{731}(181,\cdot)\) \(\chi_{731}(182,\cdot)\) \(\chi_{731}(197,\cdot)\) \(\chi_{731}(210,\cdot)\) \(\chi_{731}(224,\cdot)\) \(\chi_{731}(228,\cdot)\) \(\chi_{731}(232,\cdot)\) \(\chi_{731}(267,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((173,562)\) → \((e\left(\frac{9}{16}\right),e\left(\frac{10}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 731 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{13}{336}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{241}{336}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{25}{112}\right)\) |