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 \(\chi_{675}(254,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bl
\(\chi_{2025}(44,\cdot)\) \(\chi_{2025}(89,\cdot)\) \(\chi_{2025}(179,\cdot)\) \(\chi_{2025}(314,\cdot)\) \(\chi_{2025}(359,\cdot)\) \(\chi_{2025}(494,\cdot)\) \(\chi_{2025}(584,\cdot)\) \(\chi_{2025}(629,\cdot)\) \(\chi_{2025}(719,\cdot)\) \(\chi_{2025}(764,\cdot)\) \(\chi_{2025}(854,\cdot)\) \(\chi_{2025}(989,\cdot)\) \(\chi_{2025}(1034,\cdot)\) \(\chi_{2025}(1169,\cdot)\) \(\chi_{2025}(1259,\cdot)\) \(\chi_{2025}(1304,\cdot)\) \(\chi_{2025}(1394,\cdot)\) \(\chi_{2025}(1439,\cdot)\) \(\chi_{2025}(1529,\cdot)\) \(\chi_{2025}(1664,\cdot)\) \(\chi_{2025}(1709,\cdot)\) \(\chi_{2025}(1844,\cdot)\) \(\chi_{2025}(1934,\cdot)\) \(\chi_{2025}(1979,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((326,1702)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(1979, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) |