Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(2028\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2028}(95,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.cz
\(\chi_{4056}(95,\cdot)\) \(\chi_{4056}(335,\cdot)\) \(\chi_{4056}(407,\cdot)\) \(\chi_{4056}(647,\cdot)\) \(\chi_{4056}(719,\cdot)\) \(\chi_{4056}(959,\cdot)\) \(\chi_{4056}(1031,\cdot)\) \(\chi_{4056}(1271,\cdot)\) \(\chi_{4056}(1343,\cdot)\) \(\chi_{4056}(1583,\cdot)\) \(\chi_{4056}(1655,\cdot)\) \(\chi_{4056}(1895,\cdot)\) \(\chi_{4056}(1967,\cdot)\) \(\chi_{4056}(2207,\cdot)\) \(\chi_{4056}(2279,\cdot)\) \(\chi_{4056}(2519,\cdot)\) \(\chi_{4056}(2591,\cdot)\) \(\chi_{4056}(2831,\cdot)\) \(\chi_{4056}(2903,\cdot)\) \(\chi_{4056}(3143,\cdot)\) \(\chi_{4056}(3215,\cdot)\) \(\chi_{4056}(3455,\cdot)\) \(\chi_{4056}(3767,\cdot)\) \(\chi_{4056}(3839,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((-1,1,-1,e\left(\frac{37}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(95, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) |