Basic properties
| Modulus: | \(3136\) | |
| Conductor: | \(3136\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | 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.cs
\(\chi_{3136}(13,\cdot)\) \(\chi_{3136}(69,\cdot)\) \(\chi_{3136}(125,\cdot)\) \(\chi_{3136}(181,\cdot)\) \(\chi_{3136}(237,\cdot)\) \(\chi_{3136}(349,\cdot)\) \(\chi_{3136}(405,\cdot)\) \(\chi_{3136}(461,\cdot)\) \(\chi_{3136}(517,\cdot)\) \(\chi_{3136}(573,\cdot)\) \(\chi_{3136}(629,\cdot)\) \(\chi_{3136}(741,\cdot)\) \(\chi_{3136}(797,\cdot)\) \(\chi_{3136}(853,\cdot)\) \(\chi_{3136}(909,\cdot)\) \(\chi_{3136}(965,\cdot)\) \(\chi_{3136}(1021,\cdot)\) \(\chi_{3136}(1133,\cdot)\) \(\chi_{3136}(1189,\cdot)\) \(\chi_{3136}(1245,\cdot)\) \(\chi_{3136}(1301,\cdot)\) \(\chi_{3136}(1357,\cdot)\) \(\chi_{3136}(1413,\cdot)\) \(\chi_{3136}(1525,\cdot)\) \(\chi_{3136}(1581,\cdot)\) \(\chi_{3136}(1637,\cdot)\) \(\chi_{3136}(1693,\cdot)\) \(\chi_{3136}(1749,\cdot)\) \(\chi_{3136}(1805,\cdot)\) \(\chi_{3136}(1917,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{112}\right)\) | \(e\left(\frac{81}{112}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{13}{112}\right)\) | \(e\left(\frac{111}{112}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{25}{56}\right)\) |