Basic properties
| Modulus: | \(38025\) | |
| Conductor: | \(12675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{12675}(5327,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.oj
\(\chi_{38025}(17,\cdot)\) \(\chi_{38025}(62,\cdot)\) \(\chi_{38025}(413,\cdot)\) \(\chi_{38025}(602,\cdot)\) \(\chi_{38025}(647,\cdot)\) \(\chi_{38025}(953,\cdot)\) \(\chi_{38025}(998,\cdot)\) \(\chi_{38025}(1187,\cdot)\) \(\chi_{38025}(1538,\cdot)\) \(\chi_{38025}(1583,\cdot)\) \(\chi_{38025}(1772,\cdot)\) \(\chi_{38025}(1817,\cdot)\) \(\chi_{38025}(2123,\cdot)\) \(\chi_{38025}(2402,\cdot)\) \(\chi_{38025}(2708,\cdot)\) \(\chi_{38025}(2753,\cdot)\) \(\chi_{38025}(2942,\cdot)\) \(\chi_{38025}(2987,\cdot)\) \(\chi_{38025}(3338,\cdot)\) \(\chi_{38025}(3878,\cdot)\) \(\chi_{38025}(3923,\cdot)\) \(\chi_{38025}(4112,\cdot)\) \(\chi_{38025}(4463,\cdot)\) \(\chi_{38025}(4508,\cdot)\) \(\chi_{38025}(4697,\cdot)\) \(\chi_{38025}(4742,\cdot)\) \(\chi_{38025}(5327,\cdot)\) \(\chi_{38025}(5633,\cdot)\) \(\chi_{38025}(5678,\cdot)\) \(\chi_{38025}(5867,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((-1,e\left(\frac{1}{20}\right),e\left(\frac{53}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(5327, a) \) | \(1\) | \(1\) | \(e\left(\frac{179}{780}\right)\) | \(e\left(\frac{179}{390}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{179}{260}\right)\) | \(e\left(\frac{56}{195}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{179}{195}\right)\) | \(e\left(\frac{277}{780}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) |