Basic properties
| Modulus: | \(1014\) | |
| 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 \(\chi_{169}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1014.u
\(\chi_{1014}(43,\cdot)\) \(\chi_{1014}(49,\cdot)\) \(\chi_{1014}(121,\cdot)\) \(\chi_{1014}(127,\cdot)\) \(\chi_{1014}(199,\cdot)\) \(\chi_{1014}(205,\cdot)\) \(\chi_{1014}(277,\cdot)\) \(\chi_{1014}(283,\cdot)\) \(\chi_{1014}(355,\cdot)\) \(\chi_{1014}(433,\cdot)\) \(\chi_{1014}(439,\cdot)\) \(\chi_{1014}(511,\cdot)\) \(\chi_{1014}(517,\cdot)\) \(\chi_{1014}(589,\cdot)\) \(\chi_{1014}(595,\cdot)\) \(\chi_{1014}(667,\cdot)\) \(\chi_{1014}(673,\cdot)\) \(\chi_{1014}(745,\cdot)\) \(\chi_{1014}(751,\cdot)\) \(\chi_{1014}(829,\cdot)\) \(\chi_{1014}(901,\cdot)\) \(\chi_{1014}(907,\cdot)\) \(\chi_{1014}(979,\cdot)\) \(\chi_{1014}(985,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((1,e\left(\frac{61}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1014 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) |