Basic properties
| Modulus: | \(4014\) | |
| Conductor: | \(669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(222\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{669}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bj
\(\chi_{4014}(35,\cdot)\) \(\chi_{4014}(71,\cdot)\) \(\chi_{4014}(107,\cdot)\) \(\chi_{4014}(161,\cdot)\) \(\chi_{4014}(233,\cdot)\) \(\chi_{4014}(269,\cdot)\) \(\chi_{4014}(377,\cdot)\) \(\chi_{4014}(449,\cdot)\) \(\chi_{4014}(467,\cdot)\) \(\chi_{4014}(503,\cdot)\) \(\chi_{4014}(521,\cdot)\) \(\chi_{4014}(539,\cdot)\) \(\chi_{4014}(575,\cdot)\) \(\chi_{4014}(593,\cdot)\) \(\chi_{4014}(611,\cdot)\) \(\chi_{4014}(791,\cdot)\) \(\chi_{4014}(809,\cdot)\) \(\chi_{4014}(827,\cdot)\) \(\chi_{4014}(845,\cdot)\) \(\chi_{4014}(863,\cdot)\) \(\chi_{4014}(953,\cdot)\) \(\chi_{4014}(971,\cdot)\) \(\chi_{4014}(989,\cdot)\) \(\chi_{4014}(1043,\cdot)\) \(\chi_{4014}(1079,\cdot)\) \(\chi_{4014}(1097,\cdot)\) \(\chi_{4014}(1205,\cdot)\) \(\chi_{4014}(1295,\cdot)\) \(\chi_{4014}(1313,\cdot)\) \(\chi_{4014}(1349,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((-1,e\left(\frac{77}{222}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4014 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{111}\right)\) | \(e\left(\frac{31}{37}\right)\) | \(e\left(\frac{68}{111}\right)\) | \(e\left(\frac{73}{74}\right)\) | \(e\left(\frac{33}{74}\right)\) | \(e\left(\frac{73}{111}\right)\) | \(e\left(\frac{4}{111}\right)\) | \(e\left(\frac{82}{111}\right)\) | \(e\left(\frac{199}{222}\right)\) | \(e\left(\frac{49}{111}\right)\) |