Basic properties
Modulus: | \(2678\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1339}(633,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.bl
\(\chi_{2678}(29,\cdot)\) \(\chi_{2678}(55,\cdot)\) \(\chi_{2678}(139,\cdot)\) \(\chi_{2678}(269,\cdot)\) \(\chi_{2678}(289,\cdot)\) \(\chi_{2678}(347,\cdot)\) \(\chi_{2678}(471,\cdot)\) \(\chi_{2678}(503,\cdot)\) \(\chi_{2678}(575,\cdot)\) \(\chi_{2678}(607,\cdot)\) \(\chi_{2678}(633,\cdot)\) \(\chi_{2678}(841,\cdot)\) \(\chi_{2678}(1231,\cdot)\) \(\chi_{2678}(1277,\cdot)\) \(\chi_{2678}(1355,\cdot)\) \(\chi_{2678}(1407,\cdot)\) \(\chi_{2678}(1563,\cdot)\) \(\chi_{2678}(1595,\cdot)\) \(\chi_{2678}(1667,\cdot)\) \(\chi_{2678}(1745,\cdot)\) \(\chi_{2678}(1803,\cdot)\) \(\chi_{2678}(2109,\cdot)\) \(\chi_{2678}(2167,\cdot)\) \(\chi_{2678}(2245,\cdot)\) \(\chi_{2678}(2291,\cdot)\) \(\chi_{2678}(2395,\cdot)\) \(\chi_{2678}(2401,\cdot)\) \(\chi_{2678}(2427,\cdot)\) \(\chi_{2678}(2479,\cdot)\) \(\chi_{2678}(2505,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{20}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 2678 }(633, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) |