Basic properties
| Modulus: | \(1014\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1014.t
\(\chi_{1014}(17,\cdot)\) \(\chi_{1014}(95,\cdot)\) \(\chi_{1014}(101,\cdot)\) \(\chi_{1014}(173,\cdot)\) \(\chi_{1014}(179,\cdot)\) \(\chi_{1014}(251,\cdot)\) \(\chi_{1014}(257,\cdot)\) \(\chi_{1014}(329,\cdot)\) \(\chi_{1014}(335,\cdot)\) \(\chi_{1014}(407,\cdot)\) \(\chi_{1014}(413,\cdot)\) \(\chi_{1014}(491,\cdot)\) \(\chi_{1014}(563,\cdot)\) \(\chi_{1014}(569,\cdot)\) \(\chi_{1014}(641,\cdot)\) \(\chi_{1014}(647,\cdot)\) \(\chi_{1014}(719,\cdot)\) \(\chi_{1014}(725,\cdot)\) \(\chi_{1014}(797,\cdot)\) \(\chi_{1014}(803,\cdot)\) \(\chi_{1014}(875,\cdot)\) \(\chi_{1014}(881,\cdot)\) \(\chi_{1014}(953,\cdot)\) \(\chi_{1014}(959,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((-1,e\left(\frac{35}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1014 }(101, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{43}{78}\right)\) |