Basic properties
| Modulus: | \(4014\) | |
| Conductor: | \(669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(222\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{669}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bd
\(\chi_{4014}(53,\cdot)\) \(\chi_{4014}(89,\cdot)\) \(\chi_{4014}(143,\cdot)\) \(\chi_{4014}(179,\cdot)\) \(\chi_{4014}(323,\cdot)\) \(\chi_{4014}(395,\cdot)\) \(\chi_{4014}(647,\cdot)\) \(\chi_{4014}(719,\cdot)\) \(\chi_{4014}(755,\cdot)\) \(\chi_{4014}(881,\cdot)\) \(\chi_{4014}(917,\cdot)\) \(\chi_{4014}(935,\cdot)\) \(\chi_{4014}(1025,\cdot)\) \(\chi_{4014}(1133,\cdot)\) \(\chi_{4014}(1151,\cdot)\) \(\chi_{4014}(1187,\cdot)\) \(\chi_{4014}(1241,\cdot)\) \(\chi_{4014}(1259,\cdot)\) \(\chi_{4014}(1277,\cdot)\) \(\chi_{4014}(1367,\cdot)\) \(\chi_{4014}(1385,\cdot)\) \(\chi_{4014}(1403,\cdot)\) \(\chi_{4014}(1421,\cdot)\) \(\chi_{4014}(1439,\cdot)\) \(\chi_{4014}(1619,\cdot)\) \(\chi_{4014}(1637,\cdot)\) \(\chi_{4014}(1655,\cdot)\) \(\chi_{4014}(1691,\cdot)\) \(\chi_{4014}(1709,\cdot)\) \(\chi_{4014}(1727,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((-1,e\left(\frac{11}{111}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(89, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{222}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{23}{222}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{57}{74}\right)\) | \(e\left(\frac{5}{111}\right)\) | \(e\left(\frac{145}{222}\right)\) | \(e\left(\frac{71}{111}\right)\) | \(e\left(\frac{41}{222}\right)\) | \(e\left(\frac{14}{111}\right)\) |