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
\((893,226)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{59}{222}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2007 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{56}{111}\right)\) | \(e\left(\frac{1}{111}\right)\) | \(e\left(\frac{73}{74}\right)\) | \(e\left(\frac{53}{111}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{109}{222}\right)\) | \(e\left(\frac{23}{222}\right)\) | \(e\left(\frac{89}{222}\right)\) | \(e\left(\frac{109}{111}\right)\) | \(e\left(\frac{2}{111}\right)\) |