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 \(\chi_{2007}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.ba
\(\chi_{4014}(25,\cdot)\) \(\chi_{4014}(43,\cdot)\) \(\chi_{4014}(133,\cdot)\) \(\chi_{4014}(385,\cdot)\) \(\chi_{4014}(499,\cdot)\) \(\chi_{4014}(547,\cdot)\) \(\chi_{4014}(589,\cdot)\) \(\chi_{4014}(625,\cdot)\) \(\chi_{4014}(745,\cdot)\) \(\chi_{4014}(871,\cdot)\) \(\chi_{4014}(889,\cdot)\) \(\chi_{4014}(1069,\cdot)\) \(\chi_{4014}(1093,\cdot)\) \(\chi_{4014}(1177,\cdot)\) \(\chi_{4014}(1267,\cdot)\) \(\chi_{4014}(1327,\cdot)\) \(\chi_{4014}(1357,\cdot)\) \(\chi_{4014}(1393,\cdot)\) \(\chi_{4014}(1465,\cdot)\) \(\chi_{4014}(1519,\cdot)\) \(\chi_{4014}(1537,\cdot)\) \(\chi_{4014}(1555,\cdot)\) \(\chi_{4014}(1579,\cdot)\) \(\chi_{4014}(1597,\cdot)\) \(\chi_{4014}(1633,\cdot)\) \(\chi_{4014}(1687,\cdot)\) \(\chi_{4014}(1705,\cdot)\) \(\chi_{4014}(1717,\cdot)\) \(\chi_{4014}(1813,\cdot)\) \(\chi_{4014}(1831,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 111 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{89}{111}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{111}\right)\) | \(e\left(\frac{5}{111}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{22}{111}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{101}{111}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{43}{111}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{3}{37}\right)\) |