Basic properties
| Modulus: | \(38025\) | |
| Conductor: | \(38025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(195\) | 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.lz
\(\chi_{38025}(16,\cdot)\) \(\chi_{38025}(256,\cdot)\) \(\chi_{38025}(841,\cdot)\) \(\chi_{38025}(1186,\cdot)\) \(\chi_{38025}(1771,\cdot)\) \(\chi_{38025}(2011,\cdot)\) \(\chi_{38025}(2356,\cdot)\) \(\chi_{38025}(2596,\cdot)\) \(\chi_{38025}(2941,\cdot)\) \(\chi_{38025}(3181,\cdot)\) \(\chi_{38025}(3766,\cdot)\) \(\chi_{38025}(4111,\cdot)\) \(\chi_{38025}(4696,\cdot)\) \(\chi_{38025}(4936,\cdot)\) \(\chi_{38025}(5281,\cdot)\) \(\chi_{38025}(5521,\cdot)\) \(\chi_{38025}(5866,\cdot)\) \(\chi_{38025}(6691,\cdot)\) \(\chi_{38025}(7036,\cdot)\) \(\chi_{38025}(7621,\cdot)\) \(\chi_{38025}(7861,\cdot)\) \(\chi_{38025}(8206,\cdot)\) \(\chi_{38025}(8446,\cdot)\) \(\chi_{38025}(8791,\cdot)\) \(\chi_{38025}(9031,\cdot)\) \(\chi_{38025}(9616,\cdot)\) \(\chi_{38025}(9961,\cdot)\) \(\chi_{38025}(10546,\cdot)\) \(\chi_{38025}(10786,\cdot)\) \(\chi_{38025}(11371,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 195 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{5}\right),e\left(\frac{1}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{59}{195}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{67}{195}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) |