Basic properties
Modulus: | \(239\) | |
Conductor: | \(239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(238\) | 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 239.h
\(\chi_{239}(7,\cdot)\) \(\chi_{239}(13,\cdot)\) \(\chi_{239}(14,\cdot)\) \(\chi_{239}(19,\cdot)\) \(\chi_{239}(21,\cdot)\) \(\chi_{239}(26,\cdot)\) \(\chi_{239}(35,\cdot)\) \(\chi_{239}(37,\cdot)\) \(\chi_{239}(39,\cdot)\) \(\chi_{239}(41,\cdot)\) \(\chi_{239}(42,\cdot)\) \(\chi_{239}(43,\cdot)\) \(\chi_{239}(46,\cdot)\) \(\chi_{239}(47,\cdot)\) \(\chi_{239}(53,\cdot)\) \(\chi_{239}(56,\cdot)\) \(\chi_{239}(57,\cdot)\) \(\chi_{239}(59,\cdot)\) \(\chi_{239}(63,\cdot)\) \(\chi_{239}(65,\cdot)\) \(\chi_{239}(69,\cdot)\) \(\chi_{239}(70,\cdot)\) \(\chi_{239}(74,\cdot)\) \(\chi_{239}(77,\cdot)\) \(\chi_{239}(78,\cdot)\) \(\chi_{239}(79,\cdot)\) \(\chi_{239}(82,\cdot)\) \(\chi_{239}(84,\cdot)\) \(\chi_{239}(86,\cdot)\) \(\chi_{239}(89,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{119})$ |
Fixed field: | Number field defined by a degree 238 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{185}{238}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 239 }(237, a) \) | \(-1\) | \(1\) | \(e\left(\frac{36}{119}\right)\) | \(e\left(\frac{62}{119}\right)\) | \(e\left(\frac{72}{119}\right)\) | \(e\left(\frac{32}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{185}{238}\right)\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{5}{119}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{13}{119}\right)\) |