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 \(\chi_{2007}(1433,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bl
\(\chi_{4014}(59,\cdot)\) \(\chi_{4014}(95,\cdot)\) \(\chi_{4014}(155,\cdot)\) \(\chi_{4014}(167,\cdot)\) \(\chi_{4014}(191,\cdot)\) \(\chi_{4014}(209,\cdot)\) \(\chi_{4014}(221,\cdot)\) \(\chi_{4014}(275,\cdot)\) \(\chi_{4014}(473,\cdot)\) \(\chi_{4014}(533,\cdot)\) \(\chi_{4014}(587,\cdot)\) \(\chi_{4014}(605,\cdot)\) \(\chi_{4014}(635,\cdot)\) \(\chi_{4014}(641,\cdot)\) \(\chi_{4014}(653,\cdot)\) \(\chi_{4014}(695,\cdot)\) \(\chi_{4014}(851,\cdot)\) \(\chi_{4014}(875,\cdot)\) \(\chi_{4014}(905,\cdot)\) \(\chi_{4014}(983,\cdot)\) \(\chi_{4014}(995,\cdot)\) \(\chi_{4014}(1049,\cdot)\) \(\chi_{4014}(1055,\cdot)\) \(\chi_{4014}(1085,\cdot)\) \(\chi_{4014}(1289,\cdot)\) \(\chi_{4014}(1397,\cdot)\) \(\chi_{4014}(1433,\cdot)\) \(\chi_{4014}(1463,\cdot)\) \(\chi_{4014}(1505,\cdot)\) \(\chi_{4014}(1553,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{13}{74}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(1433, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{111}\right)\) | \(e\left(\frac{62}{111}\right)\) | \(e\left(\frac{107}{111}\right)\) | \(e\left(\frac{35}{222}\right)\) | \(e\left(\frac{59}{74}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{52}{111}\right)\) | \(e\left(\frac{104}{111}\right)\) | \(e\left(\frac{145}{222}\right)\) | \(e\left(\frac{82}{111}\right)\) |