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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3136.da
\(\chi_{3136}(37,\cdot)\) \(\chi_{3136}(53,\cdot)\) \(\chi_{3136}(93,\cdot)\) \(\chi_{3136}(109,\cdot)\) \(\chi_{3136}(149,\cdot)\) \(\chi_{3136}(205,\cdot)\) \(\chi_{3136}(221,\cdot)\) \(\chi_{3136}(261,\cdot)\) \(\chi_{3136}(277,\cdot)\) \(\chi_{3136}(317,\cdot)\) \(\chi_{3136}(333,\cdot)\) \(\chi_{3136}(389,\cdot)\) \(\chi_{3136}(429,\cdot)\) \(\chi_{3136}(445,\cdot)\) \(\chi_{3136}(485,\cdot)\) \(\chi_{3136}(501,\cdot)\) \(\chi_{3136}(541,\cdot)\) \(\chi_{3136}(597,\cdot)\) \(\chi_{3136}(613,\cdot)\) \(\chi_{3136}(653,\cdot)\) \(\chi_{3136}(669,\cdot)\) \(\chi_{3136}(709,\cdot)\) \(\chi_{3136}(725,\cdot)\) \(\chi_{3136}(781,\cdot)\) \(\chi_{3136}(821,\cdot)\) \(\chi_{3136}(837,\cdot)\) \(\chi_{3136}(877,\cdot)\) \(\chi_{3136}(893,\cdot)\) \(\chi_{3136}(933,\cdot)\) \(\chi_{3136}(989,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{221}{336}\right)\) | \(e\left(\frac{151}{168}\right)\) | \(e\left(\frac{97}{336}\right)\) | \(e\left(\frac{65}{112}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{139}{168}\right)\) | \(e\left(\frac{53}{168}\right)\) |