Basic properties
Modulus: | \(5269\) | |
Conductor: | \(5269\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1195\) | 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 5269.m
\(\chi_{5269}(3,\cdot)\) \(\chi_{5269}(4,\cdot)\) \(\chi_{5269}(5,\cdot)\) \(\chi_{5269}(9,\cdot)\) \(\chi_{5269}(14,\cdot)\) \(\chi_{5269}(15,\cdot)\) \(\chi_{5269}(16,\cdot)\) \(\chi_{5269}(20,\cdot)\) \(\chi_{5269}(25,\cdot)\) \(\chi_{5269}(27,\cdot)\) \(\chi_{5269}(36,\cdot)\) \(\chi_{5269}(42,\cdot)\) \(\chi_{5269}(48,\cdot)\) \(\chi_{5269}(49,\cdot)\) \(\chi_{5269}(60,\cdot)\) \(\chi_{5269}(64,\cdot)\) \(\chi_{5269}(69,\cdot)\) \(\chi_{5269}(70,\cdot)\) \(\chi_{5269}(71,\cdot)\) \(\chi_{5269}(75,\cdot)\) \(\chi_{5269}(80,\cdot)\) \(\chi_{5269}(81,\cdot)\) \(\chi_{5269}(92,\cdot)\) \(\chi_{5269}(97,\cdot)\) \(\chi_{5269}(103,\cdot)\) \(\chi_{5269}(108,\cdot)\) \(\chi_{5269}(115,\cdot)\) \(\chi_{5269}(125,\cdot)\) \(\chi_{5269}(126,\cdot)\) \(\chi_{5269}(135,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1195})$ |
Fixed field: | Number field defined by a degree 1195 polynomial (not computed) |
Values on generators
\((959,4324)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{223}{239}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 5269 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{676}{1195}\right)\) | \(e\left(\frac{648}{1195}\right)\) | \(e\left(\frac{157}{1195}\right)\) | \(e\left(\frac{274}{1195}\right)\) | \(e\left(\frac{129}{1195}\right)\) | \(e\left(\frac{92}{1195}\right)\) | \(e\left(\frac{833}{1195}\right)\) | \(e\left(\frac{101}{1195}\right)\) | \(e\left(\frac{190}{239}\right)\) | \(e\left(\frac{161}{239}\right)\) |