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 \(\chi_{725}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1450.bg
\(\chi_{1450}(139,\cdot)\) \(\chi_{1450}(169,\cdot)\) \(\chi_{1450}(219,\cdot)\) \(\chi_{1450}(239,\cdot)\) \(\chi_{1450}(339,\cdot)\) \(\chi_{1450}(429,\cdot)\) \(\chi_{1450}(459,\cdot)\) \(\chi_{1450}(489,\cdot)\) \(\chi_{1450}(509,\cdot)\) \(\chi_{1450}(529,\cdot)\) \(\chi_{1450}(629,\cdot)\) \(\chi_{1450}(719,\cdot)\) \(\chi_{1450}(779,\cdot)\) \(\chi_{1450}(819,\cdot)\) \(\chi_{1450}(919,\cdot)\) \(\chi_{1450}(1009,\cdot)\) \(\chi_{1450}(1039,\cdot)\) \(\chi_{1450}(1069,\cdot)\) \(\chi_{1450}(1089,\cdot)\) \(\chi_{1450}(1109,\cdot)\) \(\chi_{1450}(1209,\cdot)\) \(\chi_{1450}(1329,\cdot)\) \(\chi_{1450}(1359,\cdot)\) \(\chi_{1450}(1379,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1277,901)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{5}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1450 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) |