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.mx
\(\chi_{38025}(56,\cdot)\) \(\chi_{38025}(491,\cdot)\) \(\chi_{38025}(641,\cdot)\) \(\chi_{38025}(1661,\cdot)\) \(\chi_{38025}(1811,\cdot)\) \(\chi_{38025}(2246,\cdot)\) \(\chi_{38025}(2396,\cdot)\) \(\chi_{38025}(2831,\cdot)\) \(\chi_{38025}(2981,\cdot)\) \(\chi_{38025}(3416,\cdot)\) \(\chi_{38025}(3566,\cdot)\) \(\chi_{38025}(4736,\cdot)\) \(\chi_{38025}(5171,\cdot)\) \(\chi_{38025}(5321,\cdot)\) \(\chi_{38025}(5756,\cdot)\) \(\chi_{38025}(5906,\cdot)\) \(\chi_{38025}(6341,\cdot)\) \(\chi_{38025}(6491,\cdot)\) \(\chi_{38025}(7511,\cdot)\) \(\chi_{38025}(7661,\cdot)\) \(\chi_{38025}(8096,\cdot)\) \(\chi_{38025}(8246,\cdot)\) \(\chi_{38025}(8681,\cdot)\) \(\chi_{38025}(8831,\cdot)\) \(\chi_{38025}(9266,\cdot)\) \(\chi_{38025}(9416,\cdot)\) \(\chi_{38025}(10436,\cdot)\) \(\chi_{38025}(10586,\cdot)\) \(\chi_{38025}(11021,\cdot)\) \(\chi_{38025}(11171,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{2}{5}\right),e\left(\frac{55}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(56, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{195}\right)\) | \(e\left(\frac{106}{195}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{38}{195}\right)\) | \(e\left(\frac{151}{390}\right)\) | \(e\left(\frac{17}{195}\right)\) | \(e\left(\frac{253}{390}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |