Basic properties
| Modulus: | \(2025\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bk
\(\chi_{2025}(19,\cdot)\) \(\chi_{2025}(64,\cdot)\) \(\chi_{2025}(154,\cdot)\) \(\chi_{2025}(289,\cdot)\) \(\chi_{2025}(334,\cdot)\) \(\chi_{2025}(469,\cdot)\) \(\chi_{2025}(559,\cdot)\) \(\chi_{2025}(604,\cdot)\) \(\chi_{2025}(694,\cdot)\) \(\chi_{2025}(739,\cdot)\) \(\chi_{2025}(829,\cdot)\) \(\chi_{2025}(964,\cdot)\) \(\chi_{2025}(1009,\cdot)\) \(\chi_{2025}(1144,\cdot)\) \(\chi_{2025}(1234,\cdot)\) \(\chi_{2025}(1279,\cdot)\) \(\chi_{2025}(1369,\cdot)\) \(\chi_{2025}(1414,\cdot)\) \(\chi_{2025}(1504,\cdot)\) \(\chi_{2025}(1639,\cdot)\) \(\chi_{2025}(1684,\cdot)\) \(\chi_{2025}(1819,\cdot)\) \(\chi_{2025}(1909,\cdot)\) \(\chi_{2025}(1954,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((326,1702)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) |