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 \(\chi_{725}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1450.bf
\(\chi_{1450}(71,\cdot)\) \(\chi_{1450}(91,\cdot)\) \(\chi_{1450}(121,\cdot)\) \(\chi_{1450}(241,\cdot)\) \(\chi_{1450}(341,\cdot)\) \(\chi_{1450}(361,\cdot)\) \(\chi_{1450}(381,\cdot)\) \(\chi_{1450}(411,\cdot)\) \(\chi_{1450}(441,\cdot)\) \(\chi_{1450}(531,\cdot)\) \(\chi_{1450}(631,\cdot)\) \(\chi_{1450}(671,\cdot)\) \(\chi_{1450}(731,\cdot)\) \(\chi_{1450}(821,\cdot)\) \(\chi_{1450}(921,\cdot)\) \(\chi_{1450}(941,\cdot)\) \(\chi_{1450}(961,\cdot)\) \(\chi_{1450}(991,\cdot)\) \(\chi_{1450}(1021,\cdot)\) \(\chi_{1450}(1111,\cdot)\) \(\chi_{1450}(1211,\cdot)\) \(\chi_{1450}(1231,\cdot)\) \(\chi_{1450}(1281,\cdot)\) \(\chi_{1450}(1311,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1277,901)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1450 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) |