Basic properties
| Modulus: | \(2007\) | |
| Conductor: | \(2007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(222\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2007.bl
\(\chi_{2007}(67,\cdot)\) \(\chi_{2007}(70,\cdot)\) \(\chi_{2007}(79,\cdot)\) \(\chi_{2007}(88,\cdot)\) \(\chi_{2007}(97,\cdot)\) \(\chi_{2007}(151,\cdot)\) \(\chi_{2007}(160,\cdot)\) \(\chi_{2007}(187,\cdot)\) \(\chi_{2007}(205,\cdot)\) \(\chi_{2007}(214,\cdot)\) \(\chi_{2007}(229,\cdot)\) \(\chi_{2007}(247,\cdot)\) \(\chi_{2007}(265,\cdot)\) \(\chi_{2007}(274,\cdot)\) \(\chi_{2007}(319,\cdot)\) \(\chi_{2007}(340,\cdot)\) \(\chi_{2007}(346,\cdot)\) \(\chi_{2007}(391,\cdot)\) \(\chi_{2007}(427,\cdot)\) \(\chi_{2007}(457,\cdot)\) \(\chi_{2007}(466,\cdot)\) \(\chi_{2007}(517,\cdot)\) \(\chi_{2007}(580,\cdot)\) \(\chi_{2007}(607,\cdot)\) \(\chi_{2007}(691,\cdot)\) \(\chi_{2007}(715,\cdot)\) \(\chi_{2007}(754,\cdot)\) \(\chi_{2007}(814,\cdot)\) \(\chi_{2007}(895,\cdot)\) \(\chi_{2007}(904,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,226)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{67}{222}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2007 }(1759, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{111}\right)\) | \(e\left(\frac{35}{111}\right)\) | \(e\left(\frac{39}{74}\right)\) | \(e\left(\frac{79}{111}\right)\) | \(e\left(\frac{36}{37}\right)\) | \(e\left(\frac{41}{222}\right)\) | \(e\left(\frac{139}{222}\right)\) | \(e\left(\frac{7}{222}\right)\) | \(e\left(\frac{41}{111}\right)\) | \(e\left(\frac{70}{111}\right)\) |