Basic properties
Modulus: | \(2025\) | |
Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{675}(196,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bd
\(\chi_{2025}(46,\cdot)\) \(\chi_{2025}(91,\cdot)\) \(\chi_{2025}(181,\cdot)\) \(\chi_{2025}(316,\cdot)\) \(\chi_{2025}(361,\cdot)\) \(\chi_{2025}(496,\cdot)\) \(\chi_{2025}(586,\cdot)\) \(\chi_{2025}(631,\cdot)\) \(\chi_{2025}(721,\cdot)\) \(\chi_{2025}(766,\cdot)\) \(\chi_{2025}(856,\cdot)\) \(\chi_{2025}(991,\cdot)\) \(\chi_{2025}(1036,\cdot)\) \(\chi_{2025}(1171,\cdot)\) \(\chi_{2025}(1261,\cdot)\) \(\chi_{2025}(1306,\cdot)\) \(\chi_{2025}(1396,\cdot)\) \(\chi_{2025}(1441,\cdot)\) \(\chi_{2025}(1531,\cdot)\) \(\chi_{2025}(1666,\cdot)\) \(\chi_{2025}(1711,\cdot)\) \(\chi_{2025}(1846,\cdot)\) \(\chi_{2025}(1936,\cdot)\) \(\chi_{2025}(1981,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((326,1702)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 2025 }(1396, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) |