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.nl
\(\chi_{38025}(29,\cdot)\) \(\chi_{38025}(464,\cdot)\) \(\chi_{38025}(614,\cdot)\) \(\chi_{38025}(1634,\cdot)\) \(\chi_{38025}(1784,\cdot)\) \(\chi_{38025}(2369,\cdot)\) \(\chi_{38025}(2804,\cdot)\) \(\chi_{38025}(2954,\cdot)\) \(\chi_{38025}(3389,\cdot)\) \(\chi_{38025}(3539,\cdot)\) \(\chi_{38025}(4559,\cdot)\) \(\chi_{38025}(5144,\cdot)\) \(\chi_{38025}(5294,\cdot)\) \(\chi_{38025}(5729,\cdot)\) \(\chi_{38025}(5879,\cdot)\) \(\chi_{38025}(6314,\cdot)\) \(\chi_{38025}(6464,\cdot)\) \(\chi_{38025}(7484,\cdot)\) \(\chi_{38025}(7634,\cdot)\) \(\chi_{38025}(8069,\cdot)\) \(\chi_{38025}(8219,\cdot)\) \(\chi_{38025}(8654,\cdot)\) \(\chi_{38025}(8804,\cdot)\) \(\chi_{38025}(9239,\cdot)\) \(\chi_{38025}(9389,\cdot)\) \(\chi_{38025}(10409,\cdot)\) \(\chi_{38025}(10559,\cdot)\) \(\chi_{38025}(10994,\cdot)\) \(\chi_{38025}(11144,\cdot)\) \(\chi_{38025}(11579,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{10}\right),e\left(\frac{10}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{49}{390}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) |