Basic properties
| Modulus: | \(1450\) | |
| Conductor: | \(725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{725}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1450.bi
\(\chi_{1450}(73,\cdot)\) \(\chi_{1450}(77,\cdot)\) \(\chi_{1450}(113,\cdot)\) \(\chi_{1450}(127,\cdot)\) \(\chi_{1450}(137,\cdot)\) \(\chi_{1450}(147,\cdot)\) \(\chi_{1450}(153,\cdot)\) \(\chi_{1450}(163,\cdot)\) \(\chi_{1450}(177,\cdot)\) \(\chi_{1450}(213,\cdot)\) \(\chi_{1450}(217,\cdot)\) \(\chi_{1450}(363,\cdot)\) \(\chi_{1450}(367,\cdot)\) \(\chi_{1450}(403,\cdot)\) \(\chi_{1450}(417,\cdot)\) \(\chi_{1450}(427,\cdot)\) \(\chi_{1450}(433,\cdot)\) \(\chi_{1450}(437,\cdot)\) \(\chi_{1450}(453,\cdot)\) \(\chi_{1450}(467,\cdot)\) \(\chi_{1450}(503,\cdot)\) \(\chi_{1450}(653,\cdot)\) \(\chi_{1450}(717,\cdot)\) \(\chi_{1450}(723,\cdot)\) \(\chi_{1450}(727,\cdot)\) \(\chi_{1450}(733,\cdot)\) \(\chi_{1450}(797,\cdot)\) \(\chi_{1450}(947,\cdot)\) \(\chi_{1450}(983,\cdot)\) \(\chi_{1450}(997,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((1277,901)\) → \((e\left(\frac{11}{20}\right),e\left(\frac{27}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1450 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{1}{70}\right)\) |