Basic properties
Modulus: | \(38025\) | |
Conductor: | \(38025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(780\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.np
\(\chi_{38025}(58,\cdot)\) \(\chi_{38025}(202,\cdot)\) \(\chi_{38025}(223,\cdot)\) \(\chi_{38025}(787,\cdot)\) \(\chi_{38025}(808,\cdot)\) \(\chi_{38025}(817,\cdot)\) \(\chi_{38025}(1228,\cdot)\) \(\chi_{38025}(1372,\cdot)\) \(\chi_{38025}(1402,\cdot)\) \(\chi_{38025}(1813,\cdot)\) \(\chi_{38025}(1978,\cdot)\) \(\chi_{38025}(1987,\cdot)\) \(\chi_{38025}(2398,\cdot)\) \(\chi_{38025}(2542,\cdot)\) \(\chi_{38025}(2563,\cdot)\) \(\chi_{38025}(2572,\cdot)\) \(\chi_{38025}(2983,\cdot)\) \(\chi_{38025}(3127,\cdot)\) \(\chi_{38025}(3148,\cdot)\) \(\chi_{38025}(3712,\cdot)\) \(\chi_{38025}(3733,\cdot)\) \(\chi_{38025}(3742,\cdot)\) \(\chi_{38025}(4153,\cdot)\) \(\chi_{38025}(4297,\cdot)\) \(\chi_{38025}(4327,\cdot)\) \(\chi_{38025}(4738,\cdot)\) \(\chi_{38025}(4903,\cdot)\) \(\chi_{38025}(4912,\cdot)\) \(\chi_{38025}(5323,\cdot)\) \(\chi_{38025}(5467,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{780})$ |
Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{3}{20}\right),e\left(\frac{41}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(58, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{130}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{209}{260}\right)\) | \(e\left(\frac{371}{390}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{251}{780}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) |