Basic properties
| Modulus: | \(675\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | 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 675.bc
\(\chi_{675}(16,\cdot)\) \(\chi_{675}(31,\cdot)\) \(\chi_{675}(61,\cdot)\) \(\chi_{675}(106,\cdot)\) \(\chi_{675}(121,\cdot)\) \(\chi_{675}(166,\cdot)\) \(\chi_{675}(196,\cdot)\) \(\chi_{675}(211,\cdot)\) \(\chi_{675}(241,\cdot)\) \(\chi_{675}(256,\cdot)\) \(\chi_{675}(286,\cdot)\) \(\chi_{675}(331,\cdot)\) \(\chi_{675}(346,\cdot)\) \(\chi_{675}(391,\cdot)\) \(\chi_{675}(421,\cdot)\) \(\chi_{675}(436,\cdot)\) \(\chi_{675}(466,\cdot)\) \(\chi_{675}(481,\cdot)\) \(\chi_{675}(511,\cdot)\) \(\chi_{675}(556,\cdot)\) \(\chi_{675}(571,\cdot)\) \(\chi_{675}(616,\cdot)\) \(\chi_{675}(646,\cdot)\) \(\chi_{675}(661,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((326,352)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 675 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) |