Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.dd
\(\chi_{4056}(49,\cdot)\) \(\chi_{4056}(121,\cdot)\) \(\chi_{4056}(433,\cdot)\) \(\chi_{4056}(673,\cdot)\) \(\chi_{4056}(745,\cdot)\) \(\chi_{4056}(985,\cdot)\) \(\chi_{4056}(1057,\cdot)\) \(\chi_{4056}(1297,\cdot)\) \(\chi_{4056}(1369,\cdot)\) \(\chi_{4056}(1609,\cdot)\) \(\chi_{4056}(1681,\cdot)\) \(\chi_{4056}(1921,\cdot)\) \(\chi_{4056}(1993,\cdot)\) \(\chi_{4056}(2233,\cdot)\) \(\chi_{4056}(2305,\cdot)\) \(\chi_{4056}(2545,\cdot)\) \(\chi_{4056}(2617,\cdot)\) \(\chi_{4056}(2857,\cdot)\) \(\chi_{4056}(2929,\cdot)\) \(\chi_{4056}(3169,\cdot)\) \(\chi_{4056}(3241,\cdot)\) \(\chi_{4056}(3481,\cdot)\) \(\chi_{4056}(3553,\cdot)\) \(\chi_{4056}(3793,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((1,1,1,e\left(\frac{29}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{5}{39}\right)\) |