Basic properties
Modulus: | \(317\) | |
Conductor: | \(317\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(79\) | 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.d
\(\chi_{317}(10,\cdot)\) \(\chi_{317}(11,\cdot)\) \(\chi_{317}(15,\cdot)\) \(\chi_{317}(16,\cdot)\) \(\chi_{317}(23,\cdot)\) \(\chi_{317}(24,\cdot)\) \(\chi_{317}(28,\cdot)\) \(\chi_{317}(31,\cdot)\) \(\chi_{317}(34,\cdot)\) \(\chi_{317}(36,\cdot)\) \(\chi_{317}(38,\cdot)\) \(\chi_{317}(42,\cdot)\) \(\chi_{317}(43,\cdot)\) \(\chi_{317}(49,\cdot)\) \(\chi_{317}(51,\cdot)\) \(\chi_{317}(54,\cdot)\) \(\chi_{317}(57,\cdot)\) \(\chi_{317}(59,\cdot)\) \(\chi_{317}(63,\cdot)\) \(\chi_{317}(65,\cdot)\) \(\chi_{317}(67,\cdot)\) \(\chi_{317}(79,\cdot)\) \(\chi_{317}(81,\cdot)\) \(\chi_{317}(89,\cdot)\) \(\chi_{317}(100,\cdot)\) \(\chi_{317}(101,\cdot)\) \(\chi_{317}(103,\cdot)\) \(\chi_{317}(104,\cdot)\) \(\chi_{317}(110,\cdot)\) \(\chi_{317}(113,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{79})$ |
Fixed field: | Number field defined by a degree 79 polynomial |
Values on generators
\(2\) → \(e\left(\frac{44}{79}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 317 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{79}\right)\) | \(e\left(\frac{54}{79}\right)\) | \(e\left(\frac{9}{79}\right)\) | \(e\left(\frac{27}{79}\right)\) | \(e\left(\frac{19}{79}\right)\) | \(e\left(\frac{67}{79}\right)\) | \(e\left(\frac{53}{79}\right)\) | \(e\left(\frac{29}{79}\right)\) | \(e\left(\frac{71}{79}\right)\) | \(e\left(\frac{32}{79}\right)\) |