Basic properties
| Modulus: | \(4014\) | |
| Conductor: | \(2007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(111\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2007}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bb
\(\chi_{4014}(7,\cdot)\) \(\chi_{4014}(49,\cdot)\) \(\chi_{4014}(115,\cdot)\) \(\chi_{4014}(169,\cdot)\) \(\chi_{4014}(283,\cdot)\) \(\chi_{4014}(355,\cdot)\) \(\chi_{4014}(463,\cdot)\) \(\chi_{4014}(565,\cdot)\) \(\chi_{4014}(643,\cdot)\) \(\chi_{4014}(673,\cdot)\) \(\chi_{4014}(697,\cdot)\) \(\chi_{4014}(733,\cdot)\) \(\chi_{4014}(751,\cdot)\) \(\chi_{4014}(781,\cdot)\) \(\chi_{4014}(805,\cdot)\) \(\chi_{4014}(907,\cdot)\) \(\chi_{4014}(925,\cdot)\) \(\chi_{4014}(997,\cdot)\) \(\chi_{4014}(1123,\cdot)\) \(\chi_{4014}(1129,\cdot)\) \(\chi_{4014}(1147,\cdot)\) \(\chi_{4014}(1183,\cdot)\) \(\chi_{4014}(1213,\cdot)\) \(\chi_{4014}(1345,\cdot)\) \(\chi_{4014}(1453,\cdot)\) \(\chi_{4014}(1507,\cdot)\) \(\chi_{4014}(1591,\cdot)\) \(\chi_{4014}(1627,\cdot)\) \(\chi_{4014}(1681,\cdot)\) \(\chi_{4014}(1771,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 111 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{33}{37}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{111}\right)\) | \(e\left(\frac{70}{111}\right)\) | \(e\left(\frac{85}{111}\right)\) | \(e\left(\frac{86}{111}\right)\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{15}{37}\right)\) | \(e\left(\frac{5}{111}\right)\) | \(e\left(\frac{10}{111}\right)\) | \(e\left(\frac{55}{111}\right)\) | \(e\left(\frac{89}{111}\right)\) |