Basic properties
| Modulus: | \(2057\) | |
| Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(440\) | 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.bk
\(\chi_{2057}(15,\cdot)\) \(\chi_{2057}(25,\cdot)\) \(\chi_{2057}(26,\cdot)\) \(\chi_{2057}(36,\cdot)\) \(\chi_{2057}(42,\cdot)\) \(\chi_{2057}(49,\cdot)\) \(\chi_{2057}(53,\cdot)\) \(\chi_{2057}(59,\cdot)\) \(\chi_{2057}(60,\cdot)\) \(\chi_{2057}(70,\cdot)\) \(\chi_{2057}(93,\cdot)\) \(\chi_{2057}(104,\cdot)\) \(\chi_{2057}(168,\cdot)\) \(\chi_{2057}(179,\cdot)\) \(\chi_{2057}(185,\cdot)\) \(\chi_{2057}(196,\cdot)\) \(\chi_{2057}(212,\cdot)\) \(\chi_{2057}(213,\cdot)\) \(\chi_{2057}(223,\cdot)\) \(\chi_{2057}(229,\cdot)\) \(\chi_{2057}(236,\cdot)\) \(\chi_{2057}(240,\cdot)\) \(\chi_{2057}(246,\cdot)\) \(\chi_{2057}(247,\cdot)\) \(\chi_{2057}(257,\cdot)\) \(\chi_{2057}(280,\cdot)\) \(\chi_{2057}(291,\cdot)\) \(\chi_{2057}(355,\cdot)\) \(\chi_{2057}(383,\cdot)\) \(\chi_{2057}(389,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{440})$ |
| Fixed field: | Number field defined by a degree 440 polynomial (not computed) |
Values on generators
\((970,122)\) → \((e\left(\frac{26}{55}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2057 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{159}{220}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{377}{440}\right)\) | \(e\left(\frac{307}{440}\right)\) | \(e\left(\frac{191}{440}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{37}{88}\right)\) |