Basic properties
Modulus: | \(38025\) | |
Conductor: | \(12675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(780\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{12675}(5867,\cdot)\) | 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
\((29576,9127,37351)\) → \((-1,e\left(\frac{13}{20}\right),e\left(\frac{25}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(5867, a) \) | \(1\) | \(1\) | \(e\left(\frac{367}{780}\right)\) | \(e\left(\frac{367}{390}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{107}{260}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{172}{195}\right)\) | \(e\left(\frac{581}{780}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) |