Basic properties
| Modulus: | \(4029\) | |
| Conductor: | \(4029\) | 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 4029.ce
\(\chi_{4029}(305,\cdot)\) \(\chi_{4029}(458,\cdot)\) \(\chi_{4029}(509,\cdot)\) \(\chi_{4029}(560,\cdot)\) \(\chi_{4029}(662,\cdot)\) \(\chi_{4029}(764,\cdot)\) \(\chi_{4029}(917,\cdot)\) \(\chi_{4029}(1070,\cdot)\) \(\chi_{4029}(1172,\cdot)\) \(\chi_{4029}(1529,\cdot)\) \(\chi_{4029}(1733,\cdot)\) \(\chi_{4029}(2192,\cdot)\) \(\chi_{4029}(2294,\cdot)\) \(\chi_{4029}(2345,\cdot)\) \(\chi_{4029}(2447,\cdot)\) \(\chi_{4029}(2804,\cdot)\) \(\chi_{4029}(2957,\cdot)\) \(\chi_{4029}(3008,\cdot)\) \(\chi_{4029}(3110,\cdot)\) \(\chi_{4029}(3314,\cdot)\) \(\chi_{4029}(3365,\cdot)\) \(\chi_{4029}(3467,\cdot)\) \(\chi_{4029}(3671,\cdot)\) \(\chi_{4029}(3773,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2687,3556,3163)\) → \((-1,-1,e\left(\frac{67}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4029 }(662, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{29}{39}\right)\) |