Basic properties
Modulus: | \(191\) | |
Conductor: | \(191\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(95\) | 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 191.g
\(\chi_{191}(2,\cdot)\) \(\chi_{191}(3,\cdot)\) \(\chi_{191}(4,\cdot)\) \(\chi_{191}(8,\cdot)\) \(\chi_{191}(9,\cdot)\) \(\chi_{191}(10,\cdot)\) \(\chi_{191}(12,\cdot)\) \(\chi_{191}(13,\cdot)\) \(\chi_{191}(15,\cdot)\) \(\chi_{191}(16,\cdot)\) \(\chi_{191}(17,\cdot)\) \(\chi_{191}(18,\cdot)\) \(\chi_{191}(20,\cdot)\) \(\chi_{191}(23,\cdot)\) \(\chi_{191}(24,\cdot)\) \(\chi_{191}(26,\cdot)\) \(\chi_{191}(27,\cdot)\) \(\chi_{191}(34,\cdot)\) \(\chi_{191}(40,\cdot)\) \(\chi_{191}(43,\cdot)\) \(\chi_{191}(45,\cdot)\) \(\chi_{191}(46,\cdot)\) \(\chi_{191}(48,\cdot)\) \(\chi_{191}(50,\cdot)\) \(\chi_{191}(51,\cdot)\) \(\chi_{191}(54,\cdot)\) \(\chi_{191}(59,\cdot)\) \(\chi_{191}(60,\cdot)\) \(\chi_{191}(64,\cdot)\) \(\chi_{191}(65,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{95})$ |
Fixed field: | Number field defined by a degree 95 polynomial |
Values on generators
\(19\) → \(e\left(\frac{47}{95}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 191 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{95}\right)\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{29}{95}\right)\) | \(e\left(\frac{74}{95}\right)\) | \(e\left(\frac{48}{95}\right)\) | \(e\left(\frac{1}{19}\right)\) |