Basic properties
| Modulus: | \(1875\) | |
| Conductor: | \(625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(125\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{625}(481,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1875.s
\(\chi_{1875}(16,\cdot)\) \(\chi_{1875}(31,\cdot)\) \(\chi_{1875}(46,\cdot)\) \(\chi_{1875}(61,\cdot)\) \(\chi_{1875}(91,\cdot)\) \(\chi_{1875}(106,\cdot)\) \(\chi_{1875}(121,\cdot)\) \(\chi_{1875}(136,\cdot)\) \(\chi_{1875}(166,\cdot)\) \(\chi_{1875}(181,\cdot)\) \(\chi_{1875}(196,\cdot)\) \(\chi_{1875}(211,\cdot)\) \(\chi_{1875}(241,\cdot)\) \(\chi_{1875}(256,\cdot)\) \(\chi_{1875}(271,\cdot)\) \(\chi_{1875}(286,\cdot)\) \(\chi_{1875}(316,\cdot)\) \(\chi_{1875}(331,\cdot)\) \(\chi_{1875}(346,\cdot)\) \(\chi_{1875}(361,\cdot)\) \(\chi_{1875}(391,\cdot)\) \(\chi_{1875}(406,\cdot)\) \(\chi_{1875}(421,\cdot)\) \(\chi_{1875}(436,\cdot)\) \(\chi_{1875}(466,\cdot)\) \(\chi_{1875}(481,\cdot)\) \(\chi_{1875}(496,\cdot)\) \(\chi_{1875}(511,\cdot)\) \(\chi_{1875}(541,\cdot)\) \(\chi_{1875}(556,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\((626,1252)\) → \((1,e\left(\frac{117}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1875 }(481, a) \) | \(1\) | \(1\) | \(e\left(\frac{117}{125}\right)\) | \(e\left(\frac{109}{125}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{101}{125}\right)\) | \(e\left(\frac{67}{125}\right)\) | \(e\left(\frac{13}{125}\right)\) | \(e\left(\frac{112}{125}\right)\) | \(e\left(\frac{93}{125}\right)\) | \(e\left(\frac{116}{125}\right)\) | \(e\left(\frac{31}{125}\right)\) |