Basic properties
| Modulus: | \(2883\) | |
| Conductor: | \(2883\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(310\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2883.z
\(\chi_{2883}(2,\cdot)\) \(\chi_{2883}(8,\cdot)\) \(\chi_{2883}(35,\cdot)\) \(\chi_{2883}(47,\cdot)\) \(\chi_{2883}(95,\cdot)\) \(\chi_{2883}(101,\cdot)\) \(\chi_{2883}(128,\cdot)\) \(\chi_{2883}(140,\cdot)\) \(\chi_{2883}(188,\cdot)\) \(\chi_{2883}(194,\cdot)\) \(\chi_{2883}(221,\cdot)\) \(\chi_{2883}(233,\cdot)\) \(\chi_{2883}(281,\cdot)\) \(\chi_{2883}(287,\cdot)\) \(\chi_{2883}(314,\cdot)\) \(\chi_{2883}(326,\cdot)\) \(\chi_{2883}(380,\cdot)\) \(\chi_{2883}(407,\cdot)\) \(\chi_{2883}(419,\cdot)\) \(\chi_{2883}(467,\cdot)\) \(\chi_{2883}(473,\cdot)\) \(\chi_{2883}(500,\cdot)\) \(\chi_{2883}(512,\cdot)\) \(\chi_{2883}(560,\cdot)\) \(\chi_{2883}(566,\cdot)\) \(\chi_{2883}(593,\cdot)\) \(\chi_{2883}(605,\cdot)\) \(\chi_{2883}(653,\cdot)\) \(\chi_{2883}(659,\cdot)\) \(\chi_{2883}(686,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{155})$ |
| Fixed field: | Number field defined by a degree 310 polynomial (not computed) |
Values on generators
\((962,964)\) → \((-1,e\left(\frac{113}{155}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2883 }(314, a) \) | \(-1\) | \(1\) | \(e\left(\frac{129}{310}\right)\) | \(e\left(\frac{129}{155}\right)\) | \(e\left(\frac{17}{62}\right)\) | \(e\left(\frac{109}{155}\right)\) | \(e\left(\frac{77}{310}\right)\) | \(e\left(\frac{107}{155}\right)\) | \(e\left(\frac{303}{310}\right)\) | \(e\left(\frac{53}{155}\right)\) | \(e\left(\frac{37}{310}\right)\) | \(e\left(\frac{103}{155}\right)\) |