Basic properties
Modulus: | \(4014\) | |
Conductor: | \(2007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(111\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2007}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.y
\(\chi_{4014}(31,\cdot)\) \(\chi_{4014}(121,\cdot)\) \(\chi_{4014}(139,\cdot)\) \(\chi_{4014}(175,\cdot)\) \(\chi_{4014}(211,\cdot)\) \(\chi_{4014}(241,\cdot)\) \(\chi_{4014}(259,\cdot)\) \(\chi_{4014}(295,\cdot)\) \(\chi_{4014}(301,\cdot)\) \(\chi_{4014}(349,\cdot)\) \(\chi_{4014}(367,\cdot)\) \(\chi_{4014}(475,\cdot)\) \(\chi_{4014}(493,\cdot)\) \(\chi_{4014}(511,\cdot)\) \(\chi_{4014}(529,\cdot)\) \(\chi_{4014}(535,\cdot)\) \(\chi_{4014}(727,\cdot)\) \(\chi_{4014}(763,\cdot)\) \(\chi_{4014}(769,\cdot)\) \(\chi_{4014}(799,\cdot)\) \(\chi_{4014}(817,\cdot)\) \(\chi_{4014}(835,\cdot)\) \(\chi_{4014}(841,\cdot)\) \(\chi_{4014}(961,\cdot)\) \(\chi_{4014}(1105,\cdot)\) \(\chi_{4014}(1165,\cdot)\) \(\chi_{4014}(1201,\cdot)\) \(\chi_{4014}(1231,\cdot)\) \(\chi_{4014}(1303,\cdot)\) \(\chi_{4014}(1363,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{111})$ |
Fixed field: | Number field defined by a degree 111 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{41}{111}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4014 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{37}\right)\) | \(e\left(\frac{100}{111}\right)\) | \(e\left(\frac{95}{111}\right)\) | \(e\left(\frac{107}{111}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{59}{111}\right)\) | \(e\left(\frac{97}{111}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{68}{111}\right)\) | \(e\left(\frac{106}{111}\right)\) |