Basic properties
| Modulus: | \(1859\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | 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 1859.bv
\(\chi_{1859}(2,\cdot)\) \(\chi_{1859}(6,\cdot)\) \(\chi_{1859}(7,\cdot)\) \(\chi_{1859}(24,\cdot)\) \(\chi_{1859}(28,\cdot)\) \(\chi_{1859}(41,\cdot)\) \(\chi_{1859}(46,\cdot)\) \(\chi_{1859}(50,\cdot)\) \(\chi_{1859}(63,\cdot)\) \(\chi_{1859}(72,\cdot)\) \(\chi_{1859}(84,\cdot)\) \(\chi_{1859}(85,\cdot)\) \(\chi_{1859}(106,\cdot)\) \(\chi_{1859}(123,\cdot)\) \(\chi_{1859}(128,\cdot)\) \(\chi_{1859}(145,\cdot)\) \(\chi_{1859}(149,\cdot)\) \(\chi_{1859}(162,\cdot)\) \(\chi_{1859}(167,\cdot)\) \(\chi_{1859}(171,\cdot)\) \(\chi_{1859}(184,\cdot)\) \(\chi_{1859}(189,\cdot)\) \(\chi_{1859}(193,\cdot)\) \(\chi_{1859}(206,\cdot)\) \(\chi_{1859}(215,\cdot)\) \(\chi_{1859}(227,\cdot)\) \(\chi_{1859}(228,\cdot)\) \(\chi_{1859}(266,\cdot)\) \(\chi_{1859}(271,\cdot)\) \(\chi_{1859}(288,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{97}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(288, a) \) | \(1\) | \(1\) | \(e\left(\frac{563}{780}\right)\) | \(e\left(\frac{176}{195}\right)\) | \(e\left(\frac{173}{390}\right)\) | \(e\left(\frac{259}{260}\right)\) | \(e\left(\frac{487}{780}\right)\) | \(e\left(\frac{181}{780}\right)\) | \(e\left(\frac{43}{260}\right)\) | \(e\left(\frac{157}{195}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) |