Basic properties
Modulus: | \(6031\) | |
Conductor: | \(6031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | 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 6031.ge
\(\chi_{6031}(171,\cdot)\) \(\chi_{6031}(467,\cdot)\) \(\chi_{6031}(526,\cdot)\) \(\chi_{6031}(680,\cdot)\) \(\chi_{6031}(917,\cdot)\) \(\chi_{6031}(991,\cdot)\) \(\chi_{6031}(1472,\cdot)\) \(\chi_{6031}(1605,\cdot)\) \(\chi_{6031}(1657,\cdot)\) \(\chi_{6031}(1716,\cdot)\) \(\chi_{6031}(1895,\cdot)\) \(\chi_{6031}(1969,\cdot)\) \(\chi_{6031}(1984,\cdot)\) \(\chi_{6031}(2450,\cdot)\) \(\chi_{6031}(2635,\cdot)\) \(\chi_{6031}(2656,\cdot)\) \(\chi_{6031}(2909,\cdot)\) \(\chi_{6031}(3020,\cdot)\) \(\chi_{6031}(3359,\cdot)\) \(\chi_{6031}(3603,\cdot)\) \(\chi_{6031}(3634,\cdot)\) \(\chi_{6031}(4010,\cdot)\) \(\chi_{6031}(4232,\cdot)\) \(\chi_{6031}(4337,\cdot)\) \(\chi_{6031}(4380,\cdot)\) \(\chi_{6031}(4432,\cdot)\) \(\chi_{6031}(4691,\cdot)\) \(\chi_{6031}(4898,\cdot)\) \(\chi_{6031}(4907,\cdot)\) \(\chi_{6031}(5194,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{1}{54}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6031 }(171, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{108}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{10}{27}\right)\) |