Basic properties
Modulus: | \(38025\) | |
Conductor: | \(38025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(780\) | 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.of
\(\chi_{38025}(38,\cdot)\) \(\chi_{38025}(77,\cdot)\) \(\chi_{38025}(272,\cdot)\) \(\chi_{38025}(428,\cdot)\) \(\chi_{38025}(623,\cdot)\) \(\chi_{38025}(662,\cdot)\) \(\chi_{38025}(1208,\cdot)\) \(\chi_{38025}(1247,\cdot)\) \(\chi_{38025}(1442,\cdot)\) \(\chi_{38025}(1598,\cdot)\) \(\chi_{38025}(2183,\cdot)\) \(\chi_{38025}(2378,\cdot)\) \(\chi_{38025}(2417,\cdot)\) \(\chi_{38025}(2612,\cdot)\) \(\chi_{38025}(2963,\cdot)\) \(\chi_{38025}(3002,\cdot)\) \(\chi_{38025}(3197,\cdot)\) \(\chi_{38025}(3353,\cdot)\) \(\chi_{38025}(3587,\cdot)\) \(\chi_{38025}(3938,\cdot)\) \(\chi_{38025}(4133,\cdot)\) \(\chi_{38025}(4172,\cdot)\) \(\chi_{38025}(4367,\cdot)\) \(\chi_{38025}(4523,\cdot)\) \(\chi_{38025}(4952,\cdot)\) \(\chi_{38025}(5108,\cdot)\) \(\chi_{38025}(5303,\cdot)\) \(\chi_{38025}(5342,\cdot)\) \(\chi_{38025}(5537,\cdot)\) \(\chi_{38025}(5888,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{780})$ |
Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{19}{20}\right),e\left(\frac{11}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(38, a) \) | \(1\) | \(1\) | \(e\left(\frac{421}{780}\right)\) | \(e\left(\frac{31}{390}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{161}{260}\right)\) | \(e\left(\frac{184}{195}\right)\) | \(e\left(\frac{44}{195}\right)\) | \(e\left(\frac{31}{195}\right)\) | \(e\left(\frac{161}{260}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{29}{60}\right)\) |