Basic properties
| Modulus: | \(4029\) | |
| Conductor: | \(237\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{237}(149,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cb
\(\chi_{4029}(35,\cdot)\) \(\chi_{4029}(86,\cdot)\) \(\chi_{4029}(188,\cdot)\) \(\chi_{4029}(290,\cdot)\) \(\chi_{4029}(443,\cdot)\) \(\chi_{4029}(596,\cdot)\) \(\chi_{4029}(698,\cdot)\) \(\chi_{4029}(1055,\cdot)\) \(\chi_{4029}(1259,\cdot)\) \(\chi_{4029}(1718,\cdot)\) \(\chi_{4029}(1820,\cdot)\) \(\chi_{4029}(1871,\cdot)\) \(\chi_{4029}(1973,\cdot)\) \(\chi_{4029}(2330,\cdot)\) \(\chi_{4029}(2483,\cdot)\) \(\chi_{4029}(2534,\cdot)\) \(\chi_{4029}(2636,\cdot)\) \(\chi_{4029}(2840,\cdot)\) \(\chi_{4029}(2891,\cdot)\) \(\chi_{4029}(2993,\cdot)\) \(\chi_{4029}(3197,\cdot)\) \(\chi_{4029}(3299,\cdot)\) \(\chi_{4029}(3860,\cdot)\) \(\chi_{4029}(4013,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2687,3556,3163)\) → \((-1,1,e\left(\frac{41}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4029 }(2993, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) |