Basic properties
| Modulus: | \(4029\) | |
| Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1343}(84,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cf
\(\chi_{4029}(16,\cdot)\) \(\chi_{4029}(169,\cdot)\) \(\chi_{4029}(730,\cdot)\) \(\chi_{4029}(832,\cdot)\) \(\chi_{4029}(1036,\cdot)\) \(\chi_{4029}(1138,\cdot)\) \(\chi_{4029}(1189,\cdot)\) \(\chi_{4029}(1393,\cdot)\) \(\chi_{4029}(1495,\cdot)\) \(\chi_{4029}(1546,\cdot)\) \(\chi_{4029}(1699,\cdot)\) \(\chi_{4029}(2056,\cdot)\) \(\chi_{4029}(2158,\cdot)\) \(\chi_{4029}(2209,\cdot)\) \(\chi_{4029}(2311,\cdot)\) \(\chi_{4029}(2770,\cdot)\) \(\chi_{4029}(2974,\cdot)\) \(\chi_{4029}(3331,\cdot)\) \(\chi_{4029}(3433,\cdot)\) \(\chi_{4029}(3586,\cdot)\) \(\chi_{4029}(3739,\cdot)\) \(\chi_{4029}(3841,\cdot)\) \(\chi_{4029}(3943,\cdot)\) \(\chi_{4029}(3994,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2687,3556,3163)\) → \((1,-1,e\left(\frac{31}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4029 }(2770, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) |