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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.br
\(\chi_{2025}(4,\cdot)\) \(\chi_{2025}(34,\cdot)\) \(\chi_{2025}(79,\cdot)\) \(\chi_{2025}(94,\cdot)\) \(\chi_{2025}(139,\cdot)\) \(\chi_{2025}(169,\cdot)\) \(\chi_{2025}(184,\cdot)\) \(\chi_{2025}(214,\cdot)\) \(\chi_{2025}(229,\cdot)\) \(\chi_{2025}(259,\cdot)\) \(\chi_{2025}(304,\cdot)\) \(\chi_{2025}(319,\cdot)\) \(\chi_{2025}(364,\cdot)\) \(\chi_{2025}(394,\cdot)\) \(\chi_{2025}(409,\cdot)\) \(\chi_{2025}(439,\cdot)\) \(\chi_{2025}(454,\cdot)\) \(\chi_{2025}(484,\cdot)\) \(\chi_{2025}(529,\cdot)\) \(\chi_{2025}(544,\cdot)\) \(\chi_{2025}(589,\cdot)\) \(\chi_{2025}(619,\cdot)\) \(\chi_{2025}(634,\cdot)\) \(\chi_{2025}(664,\cdot)\) \(\chi_{2025}(679,\cdot)\) \(\chi_{2025}(709,\cdot)\) \(\chi_{2025}(754,\cdot)\) \(\chi_{2025}(769,\cdot)\) \(\chi_{2025}(814,\cdot)\) \(\chi_{2025}(844,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{135})$ |
| Fixed field: | Number field defined by a degree 270 polynomial (not computed) |
Values on generators
\((326,1702)\) → \((e\left(\frac{1}{27}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{270}\right)\) | \(e\left(\frac{37}{135}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{11}{135}\right)\) | \(e\left(\frac{53}{270}\right)\) | \(e\left(\frac{31}{135}\right)\) | \(e\left(\frac{74}{135}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) |