Basic properties
| Modulus: | \(6013\) | |
| Conductor: | \(859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(143\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{859}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6013.ci
\(\chi_{6013}(36,\cdot)\) \(\chi_{6013}(64,\cdot)\) \(\chi_{6013}(71,\cdot)\) \(\chi_{6013}(78,\cdot)\) \(\chi_{6013}(155,\cdot)\) \(\chi_{6013}(267,\cdot)\) \(\chi_{6013}(414,\cdot)\) \(\chi_{6013}(477,\cdot)\) \(\chi_{6013}(526,\cdot)\) \(\chi_{6013}(729,\cdot)\) \(\chi_{6013}(736,\cdot)\) \(\chi_{6013}(743,\cdot)\) \(\chi_{6013}(750,\cdot)\) \(\chi_{6013}(799,\cdot)\) \(\chi_{6013}(848,\cdot)\) \(\chi_{6013}(897,\cdot)\) \(\chi_{6013}(904,\cdot)\) \(\chi_{6013}(918,\cdot)\) \(\chi_{6013}(939,\cdot)\) \(\chi_{6013}(946,\cdot)\) \(\chi_{6013}(1023,\cdot)\) \(\chi_{6013}(1086,\cdot)\) \(\chi_{6013}(1156,\cdot)\) \(\chi_{6013}(1268,\cdot)\) \(\chi_{6013}(1296,\cdot)\) \(\chi_{6013}(1303,\cdot)\) \(\chi_{6013}(1387,\cdot)\) \(\chi_{6013}(1450,\cdot)\) \(\chi_{6013}(1625,\cdot)\) \(\chi_{6013}(1821,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{143})$ |
| Fixed field: | Number field defined by a degree 143 polynomial (not computed) |
Values on generators
\((5155,3438)\) → \((1,e\left(\frac{40}{143}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6013 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{41}{143}\right)\) | \(e\left(\frac{80}{143}\right)\) | \(e\left(\frac{37}{143}\right)\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{120}{143}\right)\) | \(e\left(\frac{82}{143}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{36}{143}\right)\) | \(e\left(\frac{11}{13}\right)\) |