Basic properties
| Modulus: | \(2057\) | |
| Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(880\) | 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 2057.bm
\(\chi_{2057}(6,\cdot)\) \(\chi_{2057}(7,\cdot)\) \(\chi_{2057}(24,\cdot)\) \(\chi_{2057}(28,\cdot)\) \(\chi_{2057}(29,\cdot)\) \(\chi_{2057}(39,\cdot)\) \(\chi_{2057}(41,\cdot)\) \(\chi_{2057}(46,\cdot)\) \(\chi_{2057}(57,\cdot)\) \(\chi_{2057}(61,\cdot)\) \(\chi_{2057}(62,\cdot)\) \(\chi_{2057}(63,\cdot)\) \(\chi_{2057}(73,\cdot)\) \(\chi_{2057}(74,\cdot)\) \(\chi_{2057}(79,\cdot)\) \(\chi_{2057}(90,\cdot)\) \(\chi_{2057}(95,\cdot)\) \(\chi_{2057}(96,\cdot)\) \(\chi_{2057}(105,\cdot)\) \(\chi_{2057}(107,\cdot)\) \(\chi_{2057}(116,\cdot)\) \(\chi_{2057}(129,\cdot)\) \(\chi_{2057}(139,\cdot)\) \(\chi_{2057}(150,\cdot)\) \(\chi_{2057}(156,\cdot)\) \(\chi_{2057}(160,\cdot)\) \(\chi_{2057}(167,\cdot)\) \(\chi_{2057}(173,\cdot)\) \(\chi_{2057}(182,\cdot)\) \(\chi_{2057}(184,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{880})$ |
| Fixed field: | Number field defined by a degree 880 polynomial (not computed) |
Values on generators
\((970,122)\) → \((e\left(\frac{89}{110}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2057 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{411}{440}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{191}{220}\right)\) | \(e\left(\frac{493}{880}\right)\) | \(e\left(\frac{63}{880}\right)\) | \(e\left(\frac{859}{880}\right)\) | \(e\left(\frac{353}{440}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{87}{176}\right)\) | \(e\left(\frac{1}{176}\right)\) |