Basic properties
Modulus: | \(3381\) | |
Conductor: | \(3381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | 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 3381.ca
\(\chi_{3381}(113,\cdot)\) \(\chi_{3381}(134,\cdot)\) \(\chi_{3381}(155,\cdot)\) \(\chi_{3381}(176,\cdot)\) \(\chi_{3381}(218,\cdot)\) \(\chi_{3381}(260,\cdot)\) \(\chi_{3381}(281,\cdot)\) \(\chi_{3381}(365,\cdot)\) \(\chi_{3381}(428,\cdot)\) \(\chi_{3381}(470,\cdot)\) \(\chi_{3381}(596,\cdot)\) \(\chi_{3381}(617,\cdot)\) \(\chi_{3381}(659,\cdot)\) \(\chi_{3381}(701,\cdot)\) \(\chi_{3381}(743,\cdot)\) \(\chi_{3381}(764,\cdot)\) \(\chi_{3381}(848,\cdot)\) \(\chi_{3381}(911,\cdot)\) \(\chi_{3381}(953,\cdot)\) \(\chi_{3381}(1100,\cdot)\) \(\chi_{3381}(1121,\cdot)\) \(\chi_{3381}(1142,\cdot)\) \(\chi_{3381}(1184,\cdot)\) \(\chi_{3381}(1247,\cdot)\) \(\chi_{3381}(1331,\cdot)\) \(\chi_{3381}(1394,\cdot)\) \(\chi_{3381}(1436,\cdot)\) \(\chi_{3381}(1562,\cdot)\) \(\chi_{3381}(1583,\cdot)\) \(\chi_{3381}(1604,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((-1,e\left(\frac{4}{7}\right),e\left(\frac{21}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(1394, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{2}{77}\right)\) | \(e\left(\frac{123}{154}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{73}{77}\right)\) | \(e\left(\frac{17}{77}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{7}{22}\right)\) |