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.fu
\(\chi_{9800}(139,\cdot)\) \(\chi_{9800}(419,\cdot)\) \(\chi_{9800}(1259,\cdot)\) \(\chi_{9800}(1539,\cdot)\) \(\chi_{9800}(1819,\cdot)\) \(\chi_{9800}(2379,\cdot)\) \(\chi_{9800}(2659,\cdot)\) \(\chi_{9800}(3219,\cdot)\) \(\chi_{9800}(3779,\cdot)\) \(\chi_{9800}(4059,\cdot)\) \(\chi_{9800}(4339,\cdot)\) \(\chi_{9800}(4619,\cdot)\) \(\chi_{9800}(5179,\cdot)\) \(\chi_{9800}(5459,\cdot)\) \(\chi_{9800}(5739,\cdot)\) \(\chi_{9800}(6019,\cdot)\) \(\chi_{9800}(6579,\cdot)\) \(\chi_{9800}(7139,\cdot)\) \(\chi_{9800}(7419,\cdot)\) \(\chi_{9800}(7979,\cdot)\) \(\chi_{9800}(8259,\cdot)\) \(\chi_{9800}(8539,\cdot)\) \(\chi_{9800}(9379,\cdot)\) \(\chi_{9800}(9659,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((7351,4901,1177,5001)\) → \((-1,-1,e\left(\frac{3}{10}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{2}{5}\right)\) |