Basic properties
Modulus: | \(2057\) | |
Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | 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 2057.bc
\(\chi_{2057}(100,\cdot)\) \(\chi_{2057}(111,\cdot)\) \(\chi_{2057}(144,\cdot)\) \(\chi_{2057}(155,\cdot)\) \(\chi_{2057}(287,\cdot)\) \(\chi_{2057}(298,\cdot)\) \(\chi_{2057}(331,\cdot)\) \(\chi_{2057}(342,\cdot)\) \(\chi_{2057}(474,\cdot)\) \(\chi_{2057}(518,\cdot)\) \(\chi_{2057}(529,\cdot)\) \(\chi_{2057}(661,\cdot)\) \(\chi_{2057}(672,\cdot)\) \(\chi_{2057}(705,\cdot)\) \(\chi_{2057}(716,\cdot)\) \(\chi_{2057}(859,\cdot)\) \(\chi_{2057}(892,\cdot)\) \(\chi_{2057}(903,\cdot)\) \(\chi_{2057}(1035,\cdot)\) \(\chi_{2057}(1046,\cdot)\) \(\chi_{2057}(1079,\cdot)\) \(\chi_{2057}(1222,\cdot)\) \(\chi_{2057}(1233,\cdot)\) \(\chi_{2057}(1266,\cdot)\) \(\chi_{2057}(1277,\cdot)\) \(\chi_{2057}(1409,\cdot)\) \(\chi_{2057}(1420,\cdot)\) \(\chi_{2057}(1464,\cdot)\) \(\chi_{2057}(1596,\cdot)\) \(\chi_{2057}(1607,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((970,122)\) → \((e\left(\frac{4}{11}\right),e\left(\frac{3}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 2057 }(100, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{87}{88}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(-i\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{53}{88}\right)\) |