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.cr
\(\chi_{3136}(29,\cdot)\) \(\chi_{3136}(85,\cdot)\) \(\chi_{3136}(141,\cdot)\) \(\chi_{3136}(253,\cdot)\) \(\chi_{3136}(309,\cdot)\) \(\chi_{3136}(365,\cdot)\) \(\chi_{3136}(421,\cdot)\) \(\chi_{3136}(477,\cdot)\) \(\chi_{3136}(533,\cdot)\) \(\chi_{3136}(645,\cdot)\) \(\chi_{3136}(701,\cdot)\) \(\chi_{3136}(757,\cdot)\) \(\chi_{3136}(813,\cdot)\) \(\chi_{3136}(869,\cdot)\) \(\chi_{3136}(925,\cdot)\) \(\chi_{3136}(1037,\cdot)\) \(\chi_{3136}(1093,\cdot)\) \(\chi_{3136}(1149,\cdot)\) \(\chi_{3136}(1205,\cdot)\) \(\chi_{3136}(1261,\cdot)\) \(\chi_{3136}(1317,\cdot)\) \(\chi_{3136}(1429,\cdot)\) \(\chi_{3136}(1485,\cdot)\) \(\chi_{3136}(1541,\cdot)\) \(\chi_{3136}(1597,\cdot)\) \(\chi_{3136}(1653,\cdot)\) \(\chi_{3136}(1709,\cdot)\) \(\chi_{3136}(1821,\cdot)\) \(\chi_{3136}(1877,\cdot)\) \(\chi_{3136}(1933,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{3}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 3136 }(2773, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{112}\right)\) | \(e\left(\frac{27}{112}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{23}{112}\right)\) | \(e\left(\frac{37}{112}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{27}{56}\right)\) |