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 \(\chi_{2007}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bf
\(\chi_{4014}(13,\cdot)\) \(\chi_{4014}(103,\cdot)\) \(\chi_{4014}(157,\cdot)\) \(\chi_{4014}(193,\cdot)\) \(\chi_{4014}(277,\cdot)\) \(\chi_{4014}(331,\cdot)\) \(\chi_{4014}(439,\cdot)\) \(\chi_{4014}(571,\cdot)\) \(\chi_{4014}(601,\cdot)\) \(\chi_{4014}(637,\cdot)\) \(\chi_{4014}(655,\cdot)\) \(\chi_{4014}(661,\cdot)\) \(\chi_{4014}(787,\cdot)\) \(\chi_{4014}(859,\cdot)\) \(\chi_{4014}(877,\cdot)\) \(\chi_{4014}(979,\cdot)\) \(\chi_{4014}(1003,\cdot)\) \(\chi_{4014}(1033,\cdot)\) \(\chi_{4014}(1051,\cdot)\) \(\chi_{4014}(1087,\cdot)\) \(\chi_{4014}(1111,\cdot)\) \(\chi_{4014}(1141,\cdot)\) \(\chi_{4014}(1219,\cdot)\) \(\chi_{4014}(1321,\cdot)\) \(\chi_{4014}(1429,\cdot)\) \(\chi_{4014}(1501,\cdot)\) \(\chi_{4014}(1615,\cdot)\) \(\chi_{4014}(1669,\cdot)\) \(\chi_{4014}(1735,\cdot)\) \(\chi_{4014}(1777,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{49}{74}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{133}{222}\right)\) | \(e\left(\frac{43}{111}\right)\) | \(e\left(\frac{41}{222}\right)\) | \(e\left(\frac{1}{222}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{133}{222}\right)\) | \(e\left(\frac{22}{111}\right)\) | \(e\left(\frac{10}{111}\right)\) | \(e\left(\frac{107}{111}\right)\) |