Basic properties
| Modulus: | \(9800\) | |
| Conductor: | \(4900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4900}(159,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.hb
\(\chi_{9800}(159,\cdot)\) \(\chi_{9800}(439,\cdot)\) \(\chi_{9800}(479,\cdot)\) \(\chi_{9800}(719,\cdot)\) \(\chi_{9800}(759,\cdot)\) \(\chi_{9800}(1039,\cdot)\) \(\chi_{9800}(1279,\cdot)\) \(\chi_{9800}(1319,\cdot)\) \(\chi_{9800}(1559,\cdot)\) \(\chi_{9800}(1839,\cdot)\) \(\chi_{9800}(1879,\cdot)\) \(\chi_{9800}(2119,\cdot)\) \(\chi_{9800}(2159,\cdot)\) \(\chi_{9800}(2439,\cdot)\) \(\chi_{9800}(2679,\cdot)\) \(\chi_{9800}(2719,\cdot)\) \(\chi_{9800}(3239,\cdot)\) \(\chi_{9800}(3279,\cdot)\) \(\chi_{9800}(3519,\cdot)\) \(\chi_{9800}(3839,\cdot)\) \(\chi_{9800}(4079,\cdot)\) \(\chi_{9800}(4119,\cdot)\) \(\chi_{9800}(4359,\cdot)\) \(\chi_{9800}(4639,\cdot)\) \(\chi_{9800}(4679,\cdot)\) \(\chi_{9800}(4959,\cdot)\) \(\chi_{9800}(5239,\cdot)\) \(\chi_{9800}(5479,\cdot)\) \(\chi_{9800}(5759,\cdot)\) \(\chi_{9800}(6039,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((7351,4901,1177,5001)\) → \((-1,1,e\left(\frac{7}{10}\right),e\left(\frac{11}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(159, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{14}{15}\right)\) |