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.gf
\(\chi_{6031}(357,\cdot)\) \(\chi_{6031}(424,\cdot)\) \(\chi_{6031}(425,\cdot)\) \(\chi_{6031}(483,\cdot)\) \(\chi_{6031}(494,\cdot)\) \(\chi_{6031}(575,\cdot)\) \(\chi_{6031}(616,\cdot)\) \(\chi_{6031}(794,\cdot)\) \(\chi_{6031}(1189,\cdot)\) \(\chi_{6031}(1240,\cdot)\) \(\chi_{6031}(1445,\cdot)\) \(\chi_{6031}(2094,\cdot)\) \(\chi_{6031}(2420,\cdot)\) \(\chi_{6031}(2645,\cdot)\) \(\chi_{6031}(2869,\cdot)\) \(\chi_{6031}(2962,\cdot)\) \(\chi_{6031}(3239,\cdot)\) \(\chi_{6031}(3254,\cdot)\) \(\chi_{6031}(3362,\cdot)\) \(\chi_{6031}(3428,\cdot)\) \(\chi_{6031}(3436,\cdot)\) \(\chi_{6031}(3454,\cdot)\) \(\chi_{6031}(3460,\cdot)\) \(\chi_{6031}(3713,\cdot)\) \(\chi_{6031}(4092,\cdot)\) \(\chi_{6031}(4161,\cdot)\) \(\chi_{6031}(4216,\cdot)\) \(\chi_{6031}(4418,\cdot)\) \(\chi_{6031}(4754,\cdot)\) \(\chi_{6031}(5101,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{29}{36}\right),e\left(\frac{23}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(357, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{108}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) |