Basic properties
| Modulus: | \(2557\) | |
| Conductor: | \(2557\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(426\) | 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 2557.n
\(\chi_{2557}(12,\cdot)\) \(\chi_{2557}(21,\cdot)\) \(\chi_{2557}(62,\cdot)\) \(\chi_{2557}(64,\cdot)\) \(\chi_{2557}(69,\cdot)\) \(\chi_{2557}(75,\cdot)\) \(\chi_{2557}(97,\cdot)\) \(\chi_{2557}(112,\cdot)\) \(\chi_{2557}(178,\cdot)\) \(\chi_{2557}(197,\cdot)\) \(\chi_{2557}(205,\cdot)\) \(\chi_{2557}(226,\cdot)\) \(\chi_{2557}(241,\cdot)\) \(\chi_{2557}(258,\cdot)\) \(\chi_{2557}(282,\cdot)\) \(\chi_{2557}(283,\cdot)\) \(\chi_{2557}(334,\cdot)\) \(\chi_{2557}(343,\cdot)\) \(\chi_{2557}(353,\cdot)\) \(\chi_{2557}(360,\cdot)\) \(\chi_{2557}(362,\cdot)\) \(\chi_{2557}(368,\cdot)\) \(\chi_{2557}(396,\cdot)\) \(\chi_{2557}(400,\cdot)\) \(\chi_{2557}(415,\cdot)\) \(\chi_{2557}(433,\cdot)\) \(\chi_{2557}(440,\cdot)\) \(\chi_{2557}(467,\cdot)\) \(\chi_{2557}(484,\cdot)\) \(\chi_{2557}(520,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{213})$ |
| Fixed field: | Number field defined by a degree 426 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{383}{426}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2557 }(1061, a) \) | \(1\) | \(1\) | \(e\left(\frac{383}{426}\right)\) | \(e\left(\frac{163}{213}\right)\) | \(e\left(\frac{170}{213}\right)\) | \(e\left(\frac{287}{426}\right)\) | \(e\left(\frac{283}{426}\right)\) | \(e\left(\frac{188}{213}\right)\) | \(e\left(\frac{99}{142}\right)\) | \(e\left(\frac{113}{213}\right)\) | \(e\left(\frac{122}{213}\right)\) | \(e\left(\frac{101}{213}\right)\) |