Basic properties
| Modulus: | \(925\) | |
| Conductor: | \(925\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | 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 925.ca
\(\chi_{925}(21,\cdot)\) \(\chi_{925}(41,\cdot)\) \(\chi_{925}(136,\cdot)\) \(\chi_{925}(141,\cdot)\) \(\chi_{925}(206,\cdot)\) \(\chi_{925}(321,\cdot)\) \(\chi_{925}(336,\cdot)\) \(\chi_{925}(361,\cdot)\) \(\chi_{925}(391,\cdot)\) \(\chi_{925}(411,\cdot)\) \(\chi_{925}(506,\cdot)\) \(\chi_{925}(511,\cdot)\) \(\chi_{925}(521,\cdot)\) \(\chi_{925}(546,\cdot)\) \(\chi_{925}(596,\cdot)\) \(\chi_{925}(691,\cdot)\) \(\chi_{925}(696,\cdot)\) \(\chi_{925}(706,\cdot)\) \(\chi_{925}(731,\cdot)\) \(\chi_{925}(761,\cdot)\) \(\chi_{925}(781,\cdot)\) \(\chi_{925}(881,\cdot)\) \(\chi_{925}(891,\cdot)\) \(\chi_{925}(916,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((852,76)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 925 }(696, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{61}{90}\right)\) |