Basic properties
Modulus: | \(311\) | |
Conductor: | \(311\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(155\) | 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 311.g
\(\chi_{311}(2,\cdot)\) \(\chi_{311}(3,\cdot)\) \(\chi_{311}(4,\cdot)\) \(\chi_{311}(5,\cdot)\) \(\chi_{311}(8,\cdot)\) \(\chi_{311}(9,\cdot)\) \(\chi_{311}(10,\cdot)\) \(\chi_{311}(12,\cdot)\) \(\chi_{311}(14,\cdot)\) \(\chi_{311}(16,\cdot)\) \(\chi_{311}(21,\cdot)\) \(\chi_{311}(25,\cdot)\) \(\chi_{311}(26,\cdot)\) \(\chi_{311}(27,\cdot)\) \(\chi_{311}(28,\cdot)\) \(\chi_{311}(30,\cdot)\) \(\chi_{311}(35,\cdot)\) \(\chi_{311}(39,\cdot)\) \(\chi_{311}(40,\cdot)\) \(\chi_{311}(42,\cdot)\) \(\chi_{311}(45,\cdot)\) \(\chi_{311}(48,\cdot)\) \(\chi_{311}(50,\cdot)\) \(\chi_{311}(53,\cdot)\) \(\chi_{311}(54,\cdot)\) \(\chi_{311}(56,\cdot)\) \(\chi_{311}(60,\cdot)\) \(\chi_{311}(63,\cdot)\) \(\chi_{311}(64,\cdot)\) \(\chi_{311}(65,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{155})$ |
Fixed field: | Number field defined by a degree 155 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{87}{155}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 311 }(158, a) \) | \(1\) | \(1\) | \(e\left(\frac{54}{155}\right)\) | \(e\left(\frac{8}{155}\right)\) | \(e\left(\frac{108}{155}\right)\) | \(e\left(\frac{2}{155}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{7}{155}\right)\) | \(e\left(\frac{16}{155}\right)\) | \(e\left(\frac{56}{155}\right)\) | \(e\left(\frac{24}{31}\right)\) |