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 \(\chi_{1225}(37,\cdot)\) | 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
\((1177,101)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 2450 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{383}{420}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{377}{420}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{379}{420}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{14}{15}\right)\) |