Basic properties
| Modulus: | \(4050\) | |
| Conductor: | \(2025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(540\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2025}(203,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4050.bv
\(\chi_{4050}(23,\cdot)\) \(\chi_{4050}(47,\cdot)\) \(\chi_{4050}(77,\cdot)\) \(\chi_{4050}(83,\cdot)\) \(\chi_{4050}(113,\cdot)\) \(\chi_{4050}(137,\cdot)\) \(\chi_{4050}(167,\cdot)\) \(\chi_{4050}(173,\cdot)\) \(\chi_{4050}(203,\cdot)\) \(\chi_{4050}(227,\cdot)\) \(\chi_{4050}(263,\cdot)\) \(\chi_{4050}(317,\cdot)\) \(\chi_{4050}(347,\cdot)\) \(\chi_{4050}(353,\cdot)\) \(\chi_{4050}(383,\cdot)\) \(\chi_{4050}(437,\cdot)\) \(\chi_{4050}(473,\cdot)\) \(\chi_{4050}(497,\cdot)\) \(\chi_{4050}(527,\cdot)\) \(\chi_{4050}(533,\cdot)\) \(\chi_{4050}(563,\cdot)\) \(\chi_{4050}(587,\cdot)\) \(\chi_{4050}(617,\cdot)\) \(\chi_{4050}(623,\cdot)\) \(\chi_{4050}(653,\cdot)\) \(\chi_{4050}(677,\cdot)\) \(\chi_{4050}(713,\cdot)\) \(\chi_{4050}(767,\cdot)\) \(\chi_{4050}(797,\cdot)\) \(\chi_{4050}(803,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{540})$ |
| Fixed field: | Number field defined by a degree 540 polynomial (not computed) |
Values on generators
\((2351,3727)\) → \((e\left(\frac{53}{54}\right),e\left(\frac{7}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4050 }(203, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{108}\right)\) | \(e\left(\frac{97}{270}\right)\) | \(e\left(\frac{271}{540}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{349}{540}\right)\) | \(e\left(\frac{2}{135}\right)\) | \(e\left(\frac{58}{135}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{113}{270}\right)\) |