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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bu
\(\chi_{2025}(13,\cdot)\) \(\chi_{2025}(22,\cdot)\) \(\chi_{2025}(52,\cdot)\) \(\chi_{2025}(58,\cdot)\) \(\chi_{2025}(67,\cdot)\) \(\chi_{2025}(88,\cdot)\) \(\chi_{2025}(97,\cdot)\) \(\chi_{2025}(103,\cdot)\) \(\chi_{2025}(112,\cdot)\) \(\chi_{2025}(133,\cdot)\) \(\chi_{2025}(142,\cdot)\) \(\chi_{2025}(148,\cdot)\) \(\chi_{2025}(178,\cdot)\) \(\chi_{2025}(187,\cdot)\) \(\chi_{2025}(202,\cdot)\) \(\chi_{2025}(223,\cdot)\) \(\chi_{2025}(238,\cdot)\) \(\chi_{2025}(247,\cdot)\) \(\chi_{2025}(277,\cdot)\) \(\chi_{2025}(283,\cdot)\) \(\chi_{2025}(292,\cdot)\) \(\chi_{2025}(313,\cdot)\) \(\chi_{2025}(322,\cdot)\) \(\chi_{2025}(328,\cdot)\) \(\chi_{2025}(337,\cdot)\) \(\chi_{2025}(358,\cdot)\) \(\chi_{2025}(367,\cdot)\) \(\chi_{2025}(373,\cdot)\) \(\chi_{2025}(403,\cdot)\) \(\chi_{2025}(412,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{540})$ |
| Fixed field: | Number field defined by a degree 540 polynomial (not computed) |
Values on generators
\((326,1702)\) → \((e\left(\frac{7}{27}\right),e\left(\frac{17}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{540}\right)\) | \(e\left(\frac{59}{270}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{131}{135}\right)\) | \(e\left(\frac{121}{540}\right)\) | \(e\left(\frac{137}{270}\right)\) | \(e\left(\frac{59}{135}\right)\) | \(e\left(\frac{109}{180}\right)\) | \(e\left(\frac{67}{90}\right)\) |