Basic properties
Modulus: | \(2151\) | |
Conductor: | \(2151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | 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 2151.u
\(\chi_{2151}(22,\cdot)\) \(\chi_{2151}(40,\cdot)\) \(\chi_{2151}(67,\cdot)\) \(\chi_{2151}(166,\cdot)\) \(\chi_{2151}(187,\cdot)\) \(\chi_{2151}(211,\cdot)\) \(\chi_{2151}(310,\cdot)\) \(\chi_{2151}(340,\cdot)\) \(\chi_{2151}(367,\cdot)\) \(\chi_{2151}(484,\cdot)\) \(\chi_{2151}(529,\cdot)\) \(\chi_{2151}(553,\cdot)\) \(\chi_{2151}(610,\cdot)\) \(\chi_{2151}(880,\cdot)\) \(\chi_{2151}(904,\cdot)\) \(\chi_{2151}(1057,\cdot)\) \(\chi_{2151}(1084,\cdot)\) \(\chi_{2151}(1201,\cdot)\) \(\chi_{2151}(1231,\cdot)\) \(\chi_{2151}(1246,\cdot)\) \(\chi_{2151}(1327,\cdot)\) \(\chi_{2151}(1411,\cdot)\) \(\chi_{2151}(1456,\cdot)\) \(\chi_{2151}(1474,\cdot)\) \(\chi_{2151}(1501,\cdot)\) \(\chi_{2151}(1597,\cdot)\) \(\chi_{2151}(1600,\cdot)\) \(\chi_{2151}(1645,\cdot)\) \(\chi_{2151}(1744,\cdot)\) \(\chi_{2151}(1948,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((479,1441)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2151 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(1\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{50}{51}\right)\) |