Basic properties
| Modulus: | \(731\) | |
| Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | 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.bk
\(\chi_{731}(19,\cdot)\) \(\chi_{731}(26,\cdot)\) \(\chi_{731}(76,\cdot)\) \(\chi_{731}(77,\cdot)\) \(\chi_{731}(104,\cdot)\) \(\chi_{731}(134,\cdot)\) \(\chi_{731}(155,\cdot)\) \(\chi_{731}(162,\cdot)\) \(\chi_{731}(202,\cdot)\) \(\chi_{731}(206,\cdot)\) \(\chi_{731}(263,\cdot)\) \(\chi_{731}(270,\cdot)\) \(\chi_{731}(287,\cdot)\) \(\chi_{731}(291,\cdot)\) \(\chi_{731}(304,\cdot)\) \(\chi_{731}(321,\cdot)\) \(\chi_{731}(331,\cdot)\) \(\chi_{731}(349,\cdot)\) \(\chi_{731}(372,\cdot)\) \(\chi_{731}(399,\cdot)\) \(\chi_{731}(406,\cdot)\) \(\chi_{731}(416,\cdot)\) \(\chi_{731}(417,\cdot)\) \(\chi_{731}(433,\cdot)\) \(\chi_{731}(450,\cdot)\) \(\chi_{731}(478,\cdot)\) \(\chi_{731}(485,\cdot)\) \(\chi_{731}(491,\cdot)\) \(\chi_{731}(501,\cdot)\) \(\chi_{731}(502,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((173,562)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{19}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 731 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{55}{168}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{115}{168}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{25}{168}\right)\) | \(e\left(\frac{39}{56}\right)\) |