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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.fh
\(\chi_{9800}(69,\cdot)\) \(\chi_{9800}(629,\cdot)\) \(\chi_{9800}(909,\cdot)\) \(\chi_{9800}(1189,\cdot)\) \(\chi_{9800}(2029,\cdot)\) \(\chi_{9800}(2309,\cdot)\) \(\chi_{9800}(2589,\cdot)\) \(\chi_{9800}(2869,\cdot)\) \(\chi_{9800}(3709,\cdot)\) \(\chi_{9800}(3989,\cdot)\) \(\chi_{9800}(4269,\cdot)\) \(\chi_{9800}(4829,\cdot)\) \(\chi_{9800}(5109,\cdot)\) \(\chi_{9800}(5669,\cdot)\) \(\chi_{9800}(6229,\cdot)\) \(\chi_{9800}(6509,\cdot)\) \(\chi_{9800}(6789,\cdot)\) \(\chi_{9800}(7069,\cdot)\) \(\chi_{9800}(7629,\cdot)\) \(\chi_{9800}(7909,\cdot)\) \(\chi_{9800}(8189,\cdot)\) \(\chi_{9800}(8469,\cdot)\) \(\chi_{9800}(9029,\cdot)\) \(\chi_{9800}(9589,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((7351,4901,1177,5001)\) → \((1,-1,e\left(\frac{9}{10}\right),e\left(\frac{13}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(69, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) |