Basic properties
Modulus: | \(1014\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{169}(158,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1014.w
\(\chi_{1014}(7,\cdot)\) \(\chi_{1014}(37,\cdot)\) \(\chi_{1014}(67,\cdot)\) \(\chi_{1014}(85,\cdot)\) \(\chi_{1014}(97,\cdot)\) \(\chi_{1014}(115,\cdot)\) \(\chi_{1014}(145,\cdot)\) \(\chi_{1014}(163,\cdot)\) \(\chi_{1014}(175,\cdot)\) \(\chi_{1014}(193,\cdot)\) \(\chi_{1014}(223,\cdot)\) \(\chi_{1014}(241,\cdot)\) \(\chi_{1014}(253,\cdot)\) \(\chi_{1014}(271,\cdot)\) \(\chi_{1014}(301,\cdot)\) \(\chi_{1014}(331,\cdot)\) \(\chi_{1014}(349,\cdot)\) \(\chi_{1014}(379,\cdot)\) \(\chi_{1014}(397,\cdot)\) \(\chi_{1014}(409,\cdot)\) \(\chi_{1014}(457,\cdot)\) \(\chi_{1014}(475,\cdot)\) \(\chi_{1014}(487,\cdot)\) \(\chi_{1014}(505,\cdot)\) \(\chi_{1014}(535,\cdot)\) \(\chi_{1014}(553,\cdot)\) \(\chi_{1014}(565,\cdot)\) \(\chi_{1014}(583,\cdot)\) \(\chi_{1014}(613,\cdot)\) \(\chi_{1014}(631,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,847)\) → \((1,e\left(\frac{25}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 1014 }(1003, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{23}{39}\right)\) |