Basic properties
Modulus: | \(2500\) | |
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 \(\chi_{625}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2500.u
\(\chi_{2500}(9,\cdot)\) \(\chi_{2500}(29,\cdot)\) \(\chi_{2500}(69,\cdot)\) \(\chi_{2500}(89,\cdot)\) \(\chi_{2500}(109,\cdot)\) \(\chi_{2500}(129,\cdot)\) \(\chi_{2500}(169,\cdot)\) \(\chi_{2500}(189,\cdot)\) \(\chi_{2500}(209,\cdot)\) \(\chi_{2500}(229,\cdot)\) \(\chi_{2500}(269,\cdot)\) \(\chi_{2500}(289,\cdot)\) \(\chi_{2500}(309,\cdot)\) \(\chi_{2500}(329,\cdot)\) \(\chi_{2500}(369,\cdot)\) \(\chi_{2500}(389,\cdot)\) \(\chi_{2500}(409,\cdot)\) \(\chi_{2500}(429,\cdot)\) \(\chi_{2500}(469,\cdot)\) \(\chi_{2500}(489,\cdot)\) \(\chi_{2500}(509,\cdot)\) \(\chi_{2500}(529,\cdot)\) \(\chi_{2500}(569,\cdot)\) \(\chi_{2500}(589,\cdot)\) \(\chi_{2500}(609,\cdot)\) \(\chi_{2500}(629,\cdot)\) \(\chi_{2500}(669,\cdot)\) \(\chi_{2500}(689,\cdot)\) \(\chi_{2500}(709,\cdot)\) \(\chi_{2500}(729,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((1251,1877)\) → \((1,e\left(\frac{107}{250}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 2500 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{199}{250}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{74}{125}\right)\) | \(e\left(\frac{91}{125}\right)\) | \(e\left(\frac{123}{250}\right)\) | \(e\left(\frac{11}{250}\right)\) | \(e\left(\frac{113}{125}\right)\) | \(e\left(\frac{47}{125}\right)\) | \(e\left(\frac{117}{250}\right)\) | \(e\left(\frac{97}{250}\right)\) |