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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.nn
\(\chi_{38025}(4,\cdot)\) \(\chi_{38025}(439,\cdot)\) \(\chi_{38025}(589,\cdot)\) \(\chi_{38025}(1609,\cdot)\) \(\chi_{38025}(1759,\cdot)\) \(\chi_{38025}(2194,\cdot)\) \(\chi_{38025}(2779,\cdot)\) \(\chi_{38025}(2929,\cdot)\) \(\chi_{38025}(3364,\cdot)\) \(\chi_{38025}(3514,\cdot)\) \(\chi_{38025}(4534,\cdot)\) \(\chi_{38025}(4684,\cdot)\) \(\chi_{38025}(5119,\cdot)\) \(\chi_{38025}(5269,\cdot)\) \(\chi_{38025}(5704,\cdot)\) \(\chi_{38025}(5854,\cdot)\) \(\chi_{38025}(6289,\cdot)\) \(\chi_{38025}(6439,\cdot)\) \(\chi_{38025}(7609,\cdot)\) \(\chi_{38025}(8044,\cdot)\) \(\chi_{38025}(8194,\cdot)\) \(\chi_{38025}(8629,\cdot)\) \(\chi_{38025}(8779,\cdot)\) \(\chi_{38025}(9214,\cdot)\) \(\chi_{38025}(9364,\cdot)\) \(\chi_{38025}(10384,\cdot)\) \(\chi_{38025}(10534,\cdot)\) \(\chi_{38025}(10969,\cdot)\) \(\chi_{38025}(11119,\cdot)\) \(\chi_{38025}(11554,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{195})$ |
Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{10}\right),e\left(\frac{1}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{127}{195}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{67}{390}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) |