Basic properties
Modulus: | \(237\) | |
Conductor: | \(79\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{79}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 237.m
\(\chi_{237}(4,\cdot)\) \(\chi_{237}(13,\cdot)\) \(\chi_{237}(16,\cdot)\) \(\chi_{237}(19,\cdot)\) \(\chi_{237}(25,\cdot)\) \(\chi_{237}(31,\cdot)\) \(\chi_{237}(40,\cdot)\) \(\chi_{237}(49,\cdot)\) \(\chi_{237}(73,\cdot)\) \(\chi_{237}(76,\cdot)\) \(\chi_{237}(88,\cdot)\) \(\chi_{237}(115,\cdot)\) \(\chi_{237}(121,\cdot)\) \(\chi_{237}(124,\cdot)\) \(\chi_{237}(130,\cdot)\) \(\chi_{237}(151,\cdot)\) \(\chi_{237}(160,\cdot)\) \(\chi_{237}(163,\cdot)\) \(\chi_{237}(169,\cdot)\) \(\chi_{237}(178,\cdot)\) \(\chi_{237}(184,\cdot)\) \(\chi_{237}(190,\cdot)\) \(\chi_{237}(202,\cdot)\) \(\chi_{237}(208,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((80,82)\) → \((1,e\left(\frac{4}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 237 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) |