Basic properties
Modulus: | \(38025\) | |
Conductor: | \(38025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(390\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.mu
\(\chi_{38025}(14,\cdot)\) \(\chi_{38025}(209,\cdot)\) \(\chi_{38025}(794,\cdot)\) \(\chi_{38025}(1379,\cdot)\) \(\chi_{38025}(1769,\cdot)\) \(\chi_{38025}(1964,\cdot)\) \(\chi_{38025}(2354,\cdot)\) \(\chi_{38025}(2939,\cdot)\) \(\chi_{38025}(3134,\cdot)\) \(\chi_{38025}(4109,\cdot)\) \(\chi_{38025}(4304,\cdot)\) \(\chi_{38025}(4694,\cdot)\) \(\chi_{38025}(4889,\cdot)\) \(\chi_{38025}(5279,\cdot)\) \(\chi_{38025}(5864,\cdot)\) \(\chi_{38025}(6059,\cdot)\) \(\chi_{38025}(6644,\cdot)\) \(\chi_{38025}(7034,\cdot)\) \(\chi_{38025}(7229,\cdot)\) \(\chi_{38025}(7619,\cdot)\) \(\chi_{38025}(7814,\cdot)\) \(\chi_{38025}(8204,\cdot)\) \(\chi_{38025}(8984,\cdot)\) \(\chi_{38025}(9569,\cdot)\) \(\chi_{38025}(9959,\cdot)\) \(\chi_{38025}(10154,\cdot)\) \(\chi_{38025}(10544,\cdot)\) \(\chi_{38025}(10739,\cdot)\) \(\chi_{38025}(11129,\cdot)\) \(\chi_{38025}(11714,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{195})$ |
Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{7}{10}\right),e\left(\frac{10}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(4109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{195}\right)\) | \(e\left(\frac{118}{195}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{103}{390}\right)\) | \(e\left(\frac{173}{390}\right)\) | \(e\left(\frac{41}{195}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{30}\right)\) |