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.fs
\(\chi_{6031}(13,\cdot)\) \(\chi_{6031}(17,\cdot)\) \(\chi_{6031}(190,\cdot)\) \(\chi_{6031}(261,\cdot)\) \(\chi_{6031}(464,\cdot)\) \(\chi_{6031}(631,\cdot)\) \(\chi_{6031}(738,\cdot)\) \(\chi_{6031}(1169,\cdot)\) \(\chi_{6031}(1312,\cdot)\) \(\chi_{6031}(1495,\cdot)\) \(\chi_{6031}(1498,\cdot)\) \(\chi_{6031}(1678,\cdot)\) \(\chi_{6031}(1757,\cdot)\) \(\chi_{6031}(1892,\cdot)\) \(\chi_{6031}(1993,\cdot)\) \(\chi_{6031}(2313,\cdot)\) \(\chi_{6031}(2462,\cdot)\) \(\chi_{6031}(2572,\cdot)\) \(\chi_{6031}(2873,\cdot)\) \(\chi_{6031}(2947,\cdot)\) \(\chi_{6031}(3032,\cdot)\) \(\chi_{6031}(3402,\cdot)\) \(\chi_{6031}(3757,\cdot)\) \(\chi_{6031}(3998,\cdot)\) \(\chi_{6031}(4050,\cdot)\) \(\chi_{6031}(4102,\cdot)\) \(\chi_{6031}(4112,\cdot)\) \(\chi_{6031}(4569,\cdot)\) \(\chi_{6031}(4612,\cdot)\) \(\chi_{6031}(4721,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{11}{36}\right),e\left(\frac{17}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(-i\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{26}{27}\right)\) |