Basic properties
Modulus: | \(1225\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | 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 1225.bv
\(\chi_{1225}(2,\cdot)\) \(\chi_{1225}(23,\cdot)\) \(\chi_{1225}(37,\cdot)\) \(\chi_{1225}(53,\cdot)\) \(\chi_{1225}(58,\cdot)\) \(\chi_{1225}(72,\cdot)\) \(\chi_{1225}(88,\cdot)\) \(\chi_{1225}(102,\cdot)\) \(\chi_{1225}(123,\cdot)\) \(\chi_{1225}(137,\cdot)\) \(\chi_{1225}(142,\cdot)\) \(\chi_{1225}(158,\cdot)\) \(\chi_{1225}(163,\cdot)\) \(\chi_{1225}(172,\cdot)\) \(\chi_{1225}(198,\cdot)\) \(\chi_{1225}(212,\cdot)\) \(\chi_{1225}(228,\cdot)\) \(\chi_{1225}(233,\cdot)\) \(\chi_{1225}(242,\cdot)\) \(\chi_{1225}(247,\cdot)\) \(\chi_{1225}(277,\cdot)\) \(\chi_{1225}(298,\cdot)\) \(\chi_{1225}(303,\cdot)\) \(\chi_{1225}(317,\cdot)\) \(\chi_{1225}(333,\cdot)\) \(\chi_{1225}(338,\cdot)\) \(\chi_{1225}(347,\cdot)\) \(\chi_{1225}(352,\cdot)\) \(\chi_{1225}(387,\cdot)\) \(\chi_{1225}(403,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{11}{20}\right),e\left(\frac{8}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(123, a) \) | \(-1\) | \(1\) | \(e\left(\frac{191}{420}\right)\) | \(e\left(\frac{97}{420}\right)\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{59}{420}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{86}{105}\right)\) |