Basic properties
| Modulus: | \(9800\) | |
| Conductor: | \(4900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4900}(279,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.fj
\(\chi_{9800}(279,\cdot)\) \(\chi_{9800}(559,\cdot)\) \(\chi_{9800}(839,\cdot)\) \(\chi_{9800}(1119,\cdot)\) \(\chi_{9800}(1679,\cdot)\) \(\chi_{9800}(2239,\cdot)\) \(\chi_{9800}(2519,\cdot)\) \(\chi_{9800}(3079,\cdot)\) \(\chi_{9800}(3359,\cdot)\) \(\chi_{9800}(3639,\cdot)\) \(\chi_{9800}(4479,\cdot)\) \(\chi_{9800}(4759,\cdot)\) \(\chi_{9800}(5039,\cdot)\) \(\chi_{9800}(5319,\cdot)\) \(\chi_{9800}(6159,\cdot)\) \(\chi_{9800}(6439,\cdot)\) \(\chi_{9800}(6719,\cdot)\) \(\chi_{9800}(7279,\cdot)\) \(\chi_{9800}(7559,\cdot)\) \(\chi_{9800}(8119,\cdot)\) \(\chi_{9800}(8679,\cdot)\) \(\chi_{9800}(8959,\cdot)\) \(\chi_{9800}(9239,\cdot)\) \(\chi_{9800}(9519,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((7351,4901,1177,5001)\) → \((-1,1,e\left(\frac{1}{10}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(279, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) |