Basic properties
Modulus: | \(1014\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{169}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1014.q
\(\chi_{1014}(55,\cdot)\) \(\chi_{1014}(61,\cdot)\) \(\chi_{1014}(133,\cdot)\) \(\chi_{1014}(139,\cdot)\) \(\chi_{1014}(211,\cdot)\) \(\chi_{1014}(217,\cdot)\) \(\chi_{1014}(289,\cdot)\) \(\chi_{1014}(295,\cdot)\) \(\chi_{1014}(367,\cdot)\) \(\chi_{1014}(373,\cdot)\) \(\chi_{1014}(445,\cdot)\) \(\chi_{1014}(451,\cdot)\) \(\chi_{1014}(523,\cdot)\) \(\chi_{1014}(601,\cdot)\) \(\chi_{1014}(607,\cdot)\) \(\chi_{1014}(679,\cdot)\) \(\chi_{1014}(685,\cdot)\) \(\chi_{1014}(757,\cdot)\) \(\chi_{1014}(763,\cdot)\) \(\chi_{1014}(835,\cdot)\) \(\chi_{1014}(841,\cdot)\) \(\chi_{1014}(913,\cdot)\) \(\chi_{1014}(919,\cdot)\) \(\chi_{1014}(997,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((677,847)\) → \((1,e\left(\frac{35}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 1014 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) |