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.fz
\(\chi_{6031}(200,\cdot)\) \(\chi_{6031}(331,\cdot)\) \(\chi_{6031}(520,\cdot)\) \(\chi_{6031}(779,\cdot)\) \(\chi_{6031}(790,\cdot)\) \(\chi_{6031}(809,\cdot)\) \(\chi_{6031}(986,\cdot)\) \(\chi_{6031}(1239,\cdot)\) \(\chi_{6031}(1352,\cdot)\) \(\chi_{6031}(1609,\cdot)\) \(\chi_{6031}(1771,\cdot)\) \(\chi_{6031}(1983,\cdot)\) \(\chi_{6031}(2054,\cdot)\) \(\chi_{6031}(2309,\cdot)\) \(\chi_{6031}(2424,\cdot)\) \(\chi_{6031}(2788,\cdot)\) \(\chi_{6031}(2928,\cdot)\) \(\chi_{6031}(3199,\cdot)\) \(\chi_{6031}(3273,\cdot)\) \(\chi_{6031}(3288,\cdot)\) \(\chi_{6031}(3291,\cdot)\) \(\chi_{6031}(3550,\cdot)\) \(\chi_{6031}(3591,\cdot)\) \(\chi_{6031}(3685,\cdot)\) \(\chi_{6031}(3724,\cdot)\) \(\chi_{6031}(3890,\cdot)\) \(\chi_{6031}(4011,\cdot)\) \(\chi_{6031}(4083,\cdot)\) \(\chi_{6031}(4938,\cdot)\) \(\chi_{6031}(4976,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{13}{36}\right),e\left(\frac{11}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(200, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) |