Basic properties
| Modulus: | \(4014\) | |
| Conductor: | \(2007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(222\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2007}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bk
\(\chi_{4014}(5,\cdot)\) \(\chi_{4014}(77,\cdot)\) \(\chi_{4014}(137,\cdot)\) \(\chi_{4014}(149,\cdot)\) \(\chi_{4014}(173,\cdot)\) \(\chi_{4014}(293,\cdot)\) \(\chi_{4014}(311,\cdot)\) \(\chi_{4014}(383,\cdot)\) \(\chi_{4014}(437,\cdot)\) \(\chi_{4014}(497,\cdot)\) \(\chi_{4014}(563,\cdot)\) \(\chi_{4014}(569,\cdot)\) \(\chi_{4014}(689,\cdot)\) \(\chi_{4014}(803,\cdot)\) \(\chi_{4014}(977,\cdot)\) \(\chi_{4014}(1037,\cdot)\) \(\chi_{4014}(1127,\cdot)\) \(\chi_{4014}(1163,\cdot)\) \(\chi_{4014}(1199,\cdot)\) \(\chi_{4014}(1217,\cdot)\) \(\chi_{4014}(1229,\cdot)\) \(\chi_{4014}(1265,\cdot)\) \(\chi_{4014}(1301,\cdot)\) \(\chi_{4014}(1307,\cdot)\) \(\chi_{4014}(1361,\cdot)\) \(\chi_{4014}(1373,\cdot)\) \(\chi_{4014}(1445,\cdot)\) \(\chi_{4014}(1451,\cdot)\) \(\chi_{4014}(1523,\cdot)\) \(\chi_{4014}(1571,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{89}{222}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{94}{111}\right)\) | \(e\left(\frac{58}{111}\right)\) | \(e\left(\frac{27}{37}\right)\) | \(e\left(\frac{133}{222}\right)\) | \(e\left(\frac{17}{74}\right)\) | \(e\left(\frac{106}{111}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{77}{111}\right)\) | \(e\left(\frac{11}{74}\right)\) | \(e\left(\frac{20}{37}\right)\) |