Basic properties
| Modulus: | \(1343\) | |
| Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1343.bb
\(\chi_{1343}(16,\cdot)\) \(\chi_{1343}(50,\cdot)\) \(\chi_{1343}(84,\cdot)\) \(\chi_{1343}(152,\cdot)\) \(\chi_{1343}(169,\cdot)\) \(\chi_{1343}(203,\cdot)\) \(\chi_{1343}(288,\cdot)\) \(\chi_{1343}(356,\cdot)\) \(\chi_{1343}(645,\cdot)\) \(\chi_{1343}(713,\cdot)\) \(\chi_{1343}(730,\cdot)\) \(\chi_{1343}(747,\cdot)\) \(\chi_{1343}(815,\cdot)\) \(\chi_{1343}(832,\cdot)\) \(\chi_{1343}(866,\cdot)\) \(\chi_{1343}(900,\cdot)\) \(\chi_{1343}(968,\cdot)\) \(\chi_{1343}(1036,\cdot)\) \(\chi_{1343}(1053,\cdot)\) \(\chi_{1343}(1138,\cdot)\) \(\chi_{1343}(1155,\cdot)\) \(\chi_{1343}(1189,\cdot)\) \(\chi_{1343}(1257,\cdot)\) \(\chi_{1343}(1308,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((870,477)\) → \((-1,e\left(\frac{34}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1343 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{61}{78}\right)\) |