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 \(\chi_{2007}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bc
\(\chi_{4014}(11,\cdot)\) \(\chi_{4014}(23,\cdot)\) \(\chi_{4014}(113,\cdot)\) \(\chi_{4014}(185,\cdot)\) \(\chi_{4014}(245,\cdot)\) \(\chi_{4014}(365,\cdot)\) \(\chi_{4014}(491,\cdot)\) \(\chi_{4014}(545,\cdot)\) \(\chi_{4014}(713,\cdot)\) \(\chi_{4014}(749,\cdot)\) \(\chi_{4014}(761,\cdot)\) \(\chi_{4014}(839,\cdot)\) \(\chi_{4014}(959,\cdot)\) \(\chi_{4014}(1121,\cdot)\) \(\chi_{4014}(1139,\cdot)\) \(\chi_{4014}(1157,\cdot)\) \(\chi_{4014}(1211,\cdot)\) \(\chi_{4014}(1283,\cdot)\) \(\chi_{4014}(1319,\cdot)\) \(\chi_{4014}(1343,\cdot)\) \(\chi_{4014}(1409,\cdot)\) \(\chi_{4014}(1415,\cdot)\) \(\chi_{4014}(1487,\cdot)\) \(\chi_{4014}(1499,\cdot)\) \(\chi_{4014}(1607,\cdot)\) \(\chi_{4014}(1631,\cdot)\) \(\chi_{4014}(1649,\cdot)\) \(\chi_{4014}(1721,\cdot)\) \(\chi_{4014}(1775,\cdot)\) \(\chi_{4014}(1787,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{163}{222}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{58}{111}\right)\) | \(e\left(\frac{44}{111}\right)\) | \(e\left(\frac{133}{222}\right)\) | \(e\left(\frac{17}{74}\right)\) | \(e\left(\frac{32}{111}\right)\) | \(e\left(\frac{94}{111}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{181}{222}\right)\) | \(e\left(\frac{97}{111}\right)\) |