Basic properties
Modulus: | \(317\) | |
Conductor: | \(317\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(158\) | 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 317.e
\(\chi_{317}(4,\cdot)\) \(\chi_{317}(6,\cdot)\) \(\chi_{317}(7,\cdot)\) \(\chi_{317}(9,\cdot)\) \(\chi_{317}(25,\cdot)\) \(\chi_{317}(26,\cdot)\) \(\chi_{317}(37,\cdot)\) \(\chi_{317}(39,\cdot)\) \(\chi_{317}(40,\cdot)\) \(\chi_{317}(44,\cdot)\) \(\chi_{317}(53,\cdot)\) \(\chi_{317}(58,\cdot)\) \(\chi_{317}(60,\cdot)\) \(\chi_{317}(61,\cdot)\) \(\chi_{317}(64,\cdot)\) \(\chi_{317}(66,\cdot)\) \(\chi_{317}(70,\cdot)\) \(\chi_{317}(73,\cdot)\) \(\chi_{317}(77,\cdot)\) \(\chi_{317}(82,\cdot)\) \(\chi_{317}(83,\cdot)\) \(\chi_{317}(85,\cdot)\) \(\chi_{317}(87,\cdot)\) \(\chi_{317}(90,\cdot)\) \(\chi_{317}(92,\cdot)\) \(\chi_{317}(94,\cdot)\) \(\chi_{317}(95,\cdot)\) \(\chi_{317}(96,\cdot)\) \(\chi_{317}(99,\cdot)\) \(\chi_{317}(105,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{79})$ |
Fixed field: | Number field defined by a degree 158 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{29}{158}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 317 }(207, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{158}\right)\) | \(e\left(\frac{111}{158}\right)\) | \(e\left(\frac{29}{79}\right)\) | \(e\left(\frac{95}{158}\right)\) | \(e\left(\frac{70}{79}\right)\) | \(e\left(\frac{14}{79}\right)\) | \(e\left(\frac{87}{158}\right)\) | \(e\left(\frac{32}{79}\right)\) | \(e\left(\frac{62}{79}\right)\) | \(e\left(\frac{68}{79}\right)\) |