Basic properties
| Modulus: | \(2025\) | |
| Conductor: | \(2025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(270\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bs
\(\chi_{2025}(14,\cdot)\) \(\chi_{2025}(29,\cdot)\) \(\chi_{2025}(59,\cdot)\) \(\chi_{2025}(104,\cdot)\) \(\chi_{2025}(119,\cdot)\) \(\chi_{2025}(164,\cdot)\) \(\chi_{2025}(194,\cdot)\) \(\chi_{2025}(209,\cdot)\) \(\chi_{2025}(239,\cdot)\) \(\chi_{2025}(254,\cdot)\) \(\chi_{2025}(284,\cdot)\) \(\chi_{2025}(329,\cdot)\) \(\chi_{2025}(344,\cdot)\) \(\chi_{2025}(389,\cdot)\) \(\chi_{2025}(419,\cdot)\) \(\chi_{2025}(434,\cdot)\) \(\chi_{2025}(464,\cdot)\) \(\chi_{2025}(479,\cdot)\) \(\chi_{2025}(509,\cdot)\) \(\chi_{2025}(554,\cdot)\) \(\chi_{2025}(569,\cdot)\) \(\chi_{2025}(614,\cdot)\) \(\chi_{2025}(644,\cdot)\) \(\chi_{2025}(659,\cdot)\) \(\chi_{2025}(689,\cdot)\) \(\chi_{2025}(704,\cdot)\) \(\chi_{2025}(734,\cdot)\) \(\chi_{2025}(779,\cdot)\) \(\chi_{2025}(794,\cdot)\) \(\chi_{2025}(839,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{135})$ |
| Fixed field: | Number field defined by a degree 270 polynomial (not computed) |
Values on generators
\((326,1702)\) → \((e\left(\frac{31}{54}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(2009, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{135}\right)\) | \(e\left(\frac{74}{135}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{179}{270}\right)\) | \(e\left(\frac{241}{270}\right)\) | \(e\left(\frac{259}{270}\right)\) | \(e\left(\frac{13}{135}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) |