Basic properties
Modulus: | \(625\) | |
Conductor: | \(625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(250\) | 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 625.k
\(\chi_{625}(4,\cdot)\) \(\chi_{625}(9,\cdot)\) \(\chi_{625}(14,\cdot)\) \(\chi_{625}(19,\cdot)\) \(\chi_{625}(29,\cdot)\) \(\chi_{625}(34,\cdot)\) \(\chi_{625}(39,\cdot)\) \(\chi_{625}(44,\cdot)\) \(\chi_{625}(54,\cdot)\) \(\chi_{625}(59,\cdot)\) \(\chi_{625}(64,\cdot)\) \(\chi_{625}(69,\cdot)\) \(\chi_{625}(79,\cdot)\) \(\chi_{625}(84,\cdot)\) \(\chi_{625}(89,\cdot)\) \(\chi_{625}(94,\cdot)\) \(\chi_{625}(104,\cdot)\) \(\chi_{625}(109,\cdot)\) \(\chi_{625}(114,\cdot)\) \(\chi_{625}(119,\cdot)\) \(\chi_{625}(129,\cdot)\) \(\chi_{625}(134,\cdot)\) \(\chi_{625}(139,\cdot)\) \(\chi_{625}(144,\cdot)\) \(\chi_{625}(154,\cdot)\) \(\chi_{625}(159,\cdot)\) \(\chi_{625}(164,\cdot)\) \(\chi_{625}(169,\cdot)\) \(\chi_{625}(179,\cdot)\) \(\chi_{625}(184,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{69}{250}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 625 }(319, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{250}\right)\) | \(e\left(\frac{133}{250}\right)\) | \(e\left(\frac{69}{125}\right)\) | \(e\left(\frac{101}{125}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{207}{250}\right)\) | \(e\left(\frac{8}{125}\right)\) | \(e\left(\frac{47}{125}\right)\) | \(e\left(\frac{21}{250}\right)\) | \(e\left(\frac{91}{250}\right)\) |