Basic properties
Modulus: | \(2450\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1225}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bu
\(\chi_{2450}(23,\cdot)\) \(\chi_{2450}(37,\cdot)\) \(\chi_{2450}(53,\cdot)\) \(\chi_{2450}(123,\cdot)\) \(\chi_{2450}(137,\cdot)\) \(\chi_{2450}(163,\cdot)\) \(\chi_{2450}(233,\cdot)\) \(\chi_{2450}(247,\cdot)\) \(\chi_{2450}(277,\cdot)\) \(\chi_{2450}(303,\cdot)\) \(\chi_{2450}(317,\cdot)\) \(\chi_{2450}(333,\cdot)\) \(\chi_{2450}(347,\cdot)\) \(\chi_{2450}(387,\cdot)\) \(\chi_{2450}(403,\cdot)\) \(\chi_{2450}(417,\cdot)\) \(\chi_{2450}(473,\cdot)\) \(\chi_{2450}(487,\cdot)\) \(\chi_{2450}(513,\cdot)\) \(\chi_{2450}(527,\cdot)\) \(\chi_{2450}(583,\cdot)\) \(\chi_{2450}(597,\cdot)\) \(\chi_{2450}(613,\cdot)\) \(\chi_{2450}(627,\cdot)\) \(\chi_{2450}(653,\cdot)\) \(\chi_{2450}(683,\cdot)\) \(\chi_{2450}(697,\cdot)\) \(\chi_{2450}(723,\cdot)\) \(\chi_{2450}(737,\cdot)\) \(\chi_{2450}(767,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{5}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 2450 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{289}{420}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{211}{420}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{377}{420}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{7}{15}\right)\) |