Basic properties
| Modulus: | \(2025\) | |
| Conductor: | \(2025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(540\) | 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.bv
\(\chi_{2025}(2,\cdot)\) \(\chi_{2025}(23,\cdot)\) \(\chi_{2025}(38,\cdot)\) \(\chi_{2025}(47,\cdot)\) \(\chi_{2025}(77,\cdot)\) \(\chi_{2025}(83,\cdot)\) \(\chi_{2025}(92,\cdot)\) \(\chi_{2025}(113,\cdot)\) \(\chi_{2025}(122,\cdot)\) \(\chi_{2025}(128,\cdot)\) \(\chi_{2025}(137,\cdot)\) \(\chi_{2025}(158,\cdot)\) \(\chi_{2025}(167,\cdot)\) \(\chi_{2025}(173,\cdot)\) \(\chi_{2025}(203,\cdot)\) \(\chi_{2025}(212,\cdot)\) \(\chi_{2025}(227,\cdot)\) \(\chi_{2025}(248,\cdot)\) \(\chi_{2025}(263,\cdot)\) \(\chi_{2025}(272,\cdot)\) \(\chi_{2025}(302,\cdot)\) \(\chi_{2025}(308,\cdot)\) \(\chi_{2025}(317,\cdot)\) \(\chi_{2025}(338,\cdot)\) \(\chi_{2025}(347,\cdot)\) \(\chi_{2025}(353,\cdot)\) \(\chi_{2025}(362,\cdot)\) \(\chi_{2025}(383,\cdot)\) \(\chi_{2025}(392,\cdot)\) \(\chi_{2025}(398,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{540})$ |
| Fixed field: | Number field defined by a degree 540 polynomial (not computed) |
Values on generators
\((326,1702)\) → \((e\left(\frac{1}{54}\right),e\left(\frac{3}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{540}\right)\) | \(e\left(\frac{91}{270}\right)\) | \(e\left(\frac{5}{108}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{173}{270}\right)\) | \(e\left(\frac{539}{540}\right)\) | \(e\left(\frac{29}{135}\right)\) | \(e\left(\frac{91}{135}\right)\) | \(e\left(\frac{101}{180}\right)\) | \(e\left(\frac{53}{90}\right)\) |