Basic properties
| Modulus: | \(3136\) | |
| Conductor: | \(3136\) | 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 3136.cz
\(\chi_{3136}(5,\cdot)\) \(\chi_{3136}(45,\cdot)\) \(\chi_{3136}(61,\cdot)\) \(\chi_{3136}(101,\cdot)\) \(\chi_{3136}(157,\cdot)\) \(\chi_{3136}(173,\cdot)\) \(\chi_{3136}(213,\cdot)\) \(\chi_{3136}(229,\cdot)\) \(\chi_{3136}(269,\cdot)\) \(\chi_{3136}(285,\cdot)\) \(\chi_{3136}(341,\cdot)\) \(\chi_{3136}(381,\cdot)\) \(\chi_{3136}(397,\cdot)\) \(\chi_{3136}(437,\cdot)\) \(\chi_{3136}(453,\cdot)\) \(\chi_{3136}(493,\cdot)\) \(\chi_{3136}(549,\cdot)\) \(\chi_{3136}(565,\cdot)\) \(\chi_{3136}(605,\cdot)\) \(\chi_{3136}(621,\cdot)\) \(\chi_{3136}(661,\cdot)\) \(\chi_{3136}(677,\cdot)\) \(\chi_{3136}(733,\cdot)\) \(\chi_{3136}(773,\cdot)\) \(\chi_{3136}(789,\cdot)\) \(\chi_{3136}(829,\cdot)\) \(\chi_{3136}(845,\cdot)\) \(\chi_{3136}(885,\cdot)\) \(\chi_{3136}(941,\cdot)\) \(\chi_{3136}(957,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{29}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{295}{336}\right)\) | \(e\left(\frac{29}{336}\right)\) | \(e\left(\frac{127}{168}\right)\) | \(e\left(\frac{313}{336}\right)\) | \(e\left(\frac{81}{112}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{19}{168}\right)\) | \(e\left(\frac{29}{168}\right)\) |