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 \(\chi_{2007}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bn
\(\chi_{4014}(29,\cdot)\) \(\chi_{4014}(47,\cdot)\) \(\chi_{4014}(65,\cdot)\) \(\chi_{4014}(83,\cdot)\) \(\chi_{4014}(131,\cdot)\) \(\chi_{4014}(281,\cdot)\) \(\chi_{4014}(317,\cdot)\) \(\chi_{4014}(347,\cdot)\) \(\chi_{4014}(353,\cdot)\) \(\chi_{4014}(371,\cdot)\) \(\chi_{4014}(389,\cdot)\) \(\chi_{4014}(401,\cdot)\) \(\chi_{4014}(515,\cdot)\) \(\chi_{4014}(527,\cdot)\) \(\chi_{4014}(659,\cdot)\) \(\chi_{4014}(707,\cdot)\) \(\chi_{4014}(779,\cdot)\) \(\chi_{4014}(785,\cdot)\) \(\chi_{4014}(857,\cdot)\) \(\chi_{4014}(869,\cdot)\) \(\chi_{4014}(923,\cdot)\) \(\chi_{4014}(929,\cdot)\) \(\chi_{4014}(965,\cdot)\) \(\chi_{4014}(1001,\cdot)\) \(\chi_{4014}(1013,\cdot)\) \(\chi_{4014}(1031,\cdot)\) \(\chi_{4014}(1067,\cdot)\) \(\chi_{4014}(1103,\cdot)\) \(\chi_{4014}(1193,\cdot)\) \(\chi_{4014}(1253,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{52}{111}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{74}\right)\) | \(e\left(\frac{5}{111}\right)\) | \(e\left(\frac{65}{222}\right)\) | \(e\left(\frac{22}{111}\right)\) | \(e\left(\frac{71}{74}\right)\) | \(e\left(\frac{64}{111}\right)\) | \(e\left(\frac{43}{222}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{29}{222}\right)\) | \(e\left(\frac{83}{111}\right)\) |