Basic properties
| Modulus: | \(4014\) | |
| Conductor: | \(223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(111\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{223}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.z
\(\chi_{4014}(19,\cdot)\) \(\chi_{4014}(37,\cdot)\) \(\chi_{4014}(55,\cdot)\) \(\chi_{4014}(73,\cdot)\) \(\chi_{4014}(109,\cdot)\) \(\chi_{4014}(127,\cdot)\) \(\chi_{4014}(181,\cdot)\) \(\chi_{4014}(199,\cdot)\) \(\chi_{4014}(217,\cdot)\) \(\chi_{4014}(361,\cdot)\) \(\chi_{4014}(379,\cdot)\) \(\chi_{4014}(577,\cdot)\) \(\chi_{4014}(649,\cdot)\) \(\chi_{4014}(775,\cdot)\) \(\chi_{4014}(793,\cdot)\) \(\chi_{4014}(847,\cdot)\) \(\chi_{4014}(901,\cdot)\) \(\chi_{4014}(955,\cdot)\) \(\chi_{4014}(973,\cdot)\) \(\chi_{4014}(1027,\cdot)\) \(\chi_{4014}(1045,\cdot)\) \(\chi_{4014}(1153,\cdot)\) \(\chi_{4014}(1189,\cdot)\) \(\chi_{4014}(1225,\cdot)\) \(\chi_{4014}(1261,\cdot)\) \(\chi_{4014}(1315,\cdot)\) \(\chi_{4014}(1333,\cdot)\) \(\chi_{4014}(1369,\cdot)\) \(\chi_{4014}(1459,\cdot)\) \(\chi_{4014}(1477,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 111 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((1,e\left(\frac{86}{111}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{106}{111}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{100}{111}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{29}{111}\right)\) | \(e\left(\frac{32}{111}\right)\) | \(e\left(\frac{101}{111}\right)\) | \(e\left(\frac{19}{111}\right)\) | \(e\left(\frac{59}{111}\right)\) |