Basic properties
Modulus: | \(1875\) | |
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: | no, induced from \(\chi_{625}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1875.v
\(\chi_{1875}(4,\cdot)\) \(\chi_{1875}(19,\cdot)\) \(\chi_{1875}(34,\cdot)\) \(\chi_{1875}(64,\cdot)\) \(\chi_{1875}(79,\cdot)\) \(\chi_{1875}(94,\cdot)\) \(\chi_{1875}(109,\cdot)\) \(\chi_{1875}(139,\cdot)\) \(\chi_{1875}(154,\cdot)\) \(\chi_{1875}(169,\cdot)\) \(\chi_{1875}(184,\cdot)\) \(\chi_{1875}(214,\cdot)\) \(\chi_{1875}(229,\cdot)\) \(\chi_{1875}(244,\cdot)\) \(\chi_{1875}(259,\cdot)\) \(\chi_{1875}(289,\cdot)\) \(\chi_{1875}(304,\cdot)\) \(\chi_{1875}(319,\cdot)\) \(\chi_{1875}(334,\cdot)\) \(\chi_{1875}(364,\cdot)\) \(\chi_{1875}(379,\cdot)\) \(\chi_{1875}(394,\cdot)\) \(\chi_{1875}(409,\cdot)\) \(\chi_{1875}(439,\cdot)\) \(\chi_{1875}(454,\cdot)\) \(\chi_{1875}(469,\cdot)\) \(\chi_{1875}(484,\cdot)\) \(\chi_{1875}(514,\cdot)\) \(\chi_{1875}(529,\cdot)\) \(\chi_{1875}(544,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((626,1252)\) → \((1,e\left(\frac{1}{250}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1875 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{250}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{3}{250}\right)\) | \(e\left(\frac{113}{125}\right)\) | \(e\left(\frac{139}{250}\right)\) | \(e\left(\frac{118}{125}\right)\) | \(e\left(\frac{2}{125}\right)\) | \(e\left(\frac{173}{250}\right)\) | \(e\left(\frac{84}{125}\right)\) |