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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3136.cq
\(\chi_{3136}(27,\cdot)\) \(\chi_{3136}(83,\cdot)\) \(\chi_{3136}(139,\cdot)\) \(\chi_{3136}(251,\cdot)\) \(\chi_{3136}(307,\cdot)\) \(\chi_{3136}(363,\cdot)\) \(\chi_{3136}(419,\cdot)\) \(\chi_{3136}(475,\cdot)\) \(\chi_{3136}(531,\cdot)\) \(\chi_{3136}(643,\cdot)\) \(\chi_{3136}(699,\cdot)\) \(\chi_{3136}(755,\cdot)\) \(\chi_{3136}(811,\cdot)\) \(\chi_{3136}(867,\cdot)\) \(\chi_{3136}(923,\cdot)\) \(\chi_{3136}(1035,\cdot)\) \(\chi_{3136}(1091,\cdot)\) \(\chi_{3136}(1147,\cdot)\) \(\chi_{3136}(1203,\cdot)\) \(\chi_{3136}(1259,\cdot)\) \(\chi_{3136}(1315,\cdot)\) \(\chi_{3136}(1427,\cdot)\) \(\chi_{3136}(1483,\cdot)\) \(\chi_{3136}(1539,\cdot)\) \(\chi_{3136}(1595,\cdot)\) \(\chi_{3136}(1651,\cdot)\) \(\chi_{3136}(1707,\cdot)\) \(\chi_{3136}(1819,\cdot)\) \(\chi_{3136}(1875,\cdot)\) \(\chi_{3136}(1931,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{112}\right)\) | \(e\left(\frac{71}{112}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{19}{112}\right)\) | \(e\left(\frac{89}{112}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{15}{56}\right)\) |