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 \(\chi_{2007}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bm
\(\chi_{4014}(67,\cdot)\) \(\chi_{4014}(79,\cdot)\) \(\chi_{4014}(97,\cdot)\) \(\chi_{4014}(151,\cdot)\) \(\chi_{4014}(187,\cdot)\) \(\chi_{4014}(205,\cdot)\) \(\chi_{4014}(229,\cdot)\) \(\chi_{4014}(247,\cdot)\) \(\chi_{4014}(265,\cdot)\) \(\chi_{4014}(319,\cdot)\) \(\chi_{4014}(391,\cdot)\) \(\chi_{4014}(427,\cdot)\) \(\chi_{4014}(457,\cdot)\) \(\chi_{4014}(517,\cdot)\) \(\chi_{4014}(607,\cdot)\) \(\chi_{4014}(691,\cdot)\) \(\chi_{4014}(715,\cdot)\) \(\chi_{4014}(895,\cdot)\) \(\chi_{4014}(913,\cdot)\) \(\chi_{4014}(1039,\cdot)\) \(\chi_{4014}(1159,\cdot)\) \(\chi_{4014}(1195,\cdot)\) \(\chi_{4014}(1237,\cdot)\) \(\chi_{4014}(1285,\cdot)\) \(\chi_{4014}(1399,\cdot)\) \(\chi_{4014}(1651,\cdot)\) \(\chi_{4014}(1741,\cdot)\) \(\chi_{4014}(1759,\cdot)\) \(\chi_{4014}(1789,\cdot)\) \(\chi_{4014}(1861,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{167}{222}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(79, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{74}\right)\) | \(e\left(\frac{71}{111}\right)\) | \(e\left(\frac{35}{222}\right)\) | \(e\left(\frac{203}{222}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{43}{111}\right)\) | \(e\left(\frac{211}{222}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{106}{111}\right)\) | \(e\left(\frac{2}{111}\right)\) |