Basic properties
| Modulus: | \(9800\) | |
| Conductor: | \(9800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.fi
\(\chi_{9800}(141,\cdot)\) \(\chi_{9800}(421,\cdot)\) \(\chi_{9800}(1261,\cdot)\) \(\chi_{9800}(1541,\cdot)\) \(\chi_{9800}(1821,\cdot)\) \(\chi_{9800}(2381,\cdot)\) \(\chi_{9800}(2661,\cdot)\) \(\chi_{9800}(3221,\cdot)\) \(\chi_{9800}(3781,\cdot)\) \(\chi_{9800}(4061,\cdot)\) \(\chi_{9800}(4341,\cdot)\) \(\chi_{9800}(4621,\cdot)\) \(\chi_{9800}(5181,\cdot)\) \(\chi_{9800}(5461,\cdot)\) \(\chi_{9800}(5741,\cdot)\) \(\chi_{9800}(6021,\cdot)\) \(\chi_{9800}(6581,\cdot)\) \(\chi_{9800}(7141,\cdot)\) \(\chi_{9800}(7421,\cdot)\) \(\chi_{9800}(7981,\cdot)\) \(\chi_{9800}(8261,\cdot)\) \(\chi_{9800}(8541,\cdot)\) \(\chi_{9800}(9381,\cdot)\) \(\chi_{9800}(9661,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((7351,4901,1177,5001)\) → \((1,-1,e\left(\frac{1}{5}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) |