Basic properties
| Modulus: | \(1125\) | |
| Conductor: | \(1125\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(75\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 1125.bc
\(\chi_{1125}(16,\cdot)\) \(\chi_{1125}(31,\cdot)\) \(\chi_{1125}(61,\cdot)\) \(\chi_{1125}(106,\cdot)\) \(\chi_{1125}(121,\cdot)\) \(\chi_{1125}(166,\cdot)\) \(\chi_{1125}(196,\cdot)\) \(\chi_{1125}(211,\cdot)\) \(\chi_{1125}(241,\cdot)\) \(\chi_{1125}(256,\cdot)\) \(\chi_{1125}(286,\cdot)\) \(\chi_{1125}(331,\cdot)\) \(\chi_{1125}(346,\cdot)\) \(\chi_{1125}(391,\cdot)\) \(\chi_{1125}(421,\cdot)\) \(\chi_{1125}(436,\cdot)\) \(\chi_{1125}(466,\cdot)\) \(\chi_{1125}(481,\cdot)\) \(\chi_{1125}(511,\cdot)\) \(\chi_{1125}(556,\cdot)\) \(\chi_{1125}(571,\cdot)\) \(\chi_{1125}(616,\cdot)\) \(\chi_{1125}(646,\cdot)\) \(\chi_{1125}(661,\cdot)\) \(\chi_{1125}(691,\cdot)\) \(\chi_{1125}(706,\cdot)\) \(\chi_{1125}(736,\cdot)\) \(\chi_{1125}(781,\cdot)\) \(\chi_{1125}(796,\cdot)\) \(\chi_{1125}(841,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\((1001,127)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{22}{25}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1125 }(556, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{7}{75}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{1}{75}\right)\) | \(e\left(\frac{14}{75}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) |