Basic properties
| Modulus: | \(1450\) | |
| Conductor: | \(725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{725}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1450.bh
\(\chi_{1450}(9,\cdot)\) \(\chi_{1450}(109,\cdot)\) \(\chi_{1450}(129,\cdot)\) \(\chi_{1450}(179,\cdot)\) \(\chi_{1450}(209,\cdot)\) \(\chi_{1450}(419,\cdot)\) \(\chi_{1450}(439,\cdot)\) \(\chi_{1450}(469,\cdot)\) \(\chi_{1450}(589,\cdot)\) \(\chi_{1450}(689,\cdot)\) \(\chi_{1450}(709,\cdot)\) \(\chi_{1450}(729,\cdot)\) \(\chi_{1450}(759,\cdot)\) \(\chi_{1450}(789,\cdot)\) \(\chi_{1450}(879,\cdot)\) \(\chi_{1450}(979,\cdot)\) \(\chi_{1450}(1019,\cdot)\) \(\chi_{1450}(1079,\cdot)\) \(\chi_{1450}(1169,\cdot)\) \(\chi_{1450}(1269,\cdot)\) \(\chi_{1450}(1289,\cdot)\) \(\chi_{1450}(1309,\cdot)\) \(\chi_{1450}(1339,\cdot)\) \(\chi_{1450}(1369,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1277,901)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1450 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) |