Basic properties
Modulus: | \(311\) | |
Conductor: | \(311\) | 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 311.h
\(\chi_{311}(17,\cdot)\) \(\chi_{311}(19,\cdot)\) \(\chi_{311}(22,\cdot)\) \(\chi_{311}(23,\cdot)\) \(\chi_{311}(29,\cdot)\) \(\chi_{311}(31,\cdot)\) \(\chi_{311}(33,\cdot)\) \(\chi_{311}(34,\cdot)\) \(\chi_{311}(37,\cdot)\) \(\chi_{311}(38,\cdot)\) \(\chi_{311}(43,\cdot)\) \(\chi_{311}(44,\cdot)\) \(\chi_{311}(55,\cdot)\) \(\chi_{311}(57,\cdot)\) \(\chi_{311}(58,\cdot)\) \(\chi_{311}(59,\cdot)\) \(\chi_{311}(62,\cdot)\) \(\chi_{311}(66,\cdot)\) \(\chi_{311}(69,\cdot)\) \(\chi_{311}(71,\cdot)\) \(\chi_{311}(74,\cdot)\) \(\chi_{311}(76,\cdot)\) \(\chi_{311}(82,\cdot)\) \(\chi_{311}(85,\cdot)\) \(\chi_{311}(88,\cdot)\) \(\chi_{311}(92,\cdot)\) \(\chi_{311}(93,\cdot)\) \(\chi_{311}(97,\cdot)\) \(\chi_{311}(99,\cdot)\) \(\chi_{311}(101,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{155})$ |
Fixed field: | Number field defined by a degree 310 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{1}{310}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 311 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{155}\right)\) | \(e\left(\frac{82}{155}\right)\) | \(e\left(\frac{22}{155}\right)\) | \(e\left(\frac{98}{155}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{33}{155}\right)\) | \(e\left(\frac{9}{155}\right)\) | \(e\left(\frac{109}{155}\right)\) | \(e\left(\frac{27}{62}\right)\) |