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 \(\chi_{12675}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.ok
\(\chi_{38025}(71,\cdot)\) \(\chi_{38025}(206,\cdot)\) \(\chi_{38025}(431,\cdot)\) \(\chi_{38025}(566,\cdot)\) \(\chi_{38025}(656,\cdot)\) \(\chi_{38025}(791,\cdot)\) \(\chi_{38025}(1016,\cdot)\) \(\chi_{38025}(1241,\cdot)\) \(\chi_{38025}(1736,\cdot)\) \(\chi_{38025}(1961,\cdot)\) \(\chi_{38025}(2186,\cdot)\) \(\chi_{38025}(2321,\cdot)\) \(\chi_{38025}(2411,\cdot)\) \(\chi_{38025}(2546,\cdot)\) \(\chi_{38025}(2771,\cdot)\) \(\chi_{38025}(2906,\cdot)\) \(\chi_{38025}(2996,\cdot)\) \(\chi_{38025}(3356,\cdot)\) \(\chi_{38025}(3491,\cdot)\) \(\chi_{38025}(3581,\cdot)\) \(\chi_{38025}(3716,\cdot)\) \(\chi_{38025}(3941,\cdot)\) \(\chi_{38025}(4166,\cdot)\) \(\chi_{38025}(4661,\cdot)\) \(\chi_{38025}(4886,\cdot)\) \(\chi_{38025}(5111,\cdot)\) \(\chi_{38025}(5246,\cdot)\) \(\chi_{38025}(5336,\cdot)\) \(\chi_{38025}(5471,\cdot)\) \(\chi_{38025}(5696,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{780})$ |
Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((-1,e\left(\frac{3}{5}\right),e\left(\frac{137}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{763}{780}\right)\) | \(e\left(\frac{373}{390}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{243}{260}\right)\) | \(e\left(\frac{433}{780}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{101}{195}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) |