Basic properties
| Modulus: | \(2500\) | |
| Conductor: | \(625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{625}(69,\cdot)\) | 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
\((1251,1877)\) → \((1,e\left(\frac{19}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2500 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{250}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{33}{125}\right)\) | \(e\left(\frac{22}{125}\right)\) | \(e\left(\frac{141}{250}\right)\) | \(e\left(\frac{37}{250}\right)\) | \(e\left(\frac{96}{125}\right)\) | \(e\left(\frac{124}{125}\right)\) | \(e\left(\frac{189}{250}\right)\) | \(e\left(\frac{99}{250}\right)\) |