Basic properties
Modulus: | \(967\) | |
Conductor: | \(967\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(138\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 967.l
\(\chi_{967}(20,\cdot)\) \(\chi_{967}(52,\cdot)\) \(\chi_{967}(54,\cdot)\) \(\chi_{967}(55,\cdot)\) \(\chi_{967}(92,\cdot)\) \(\chi_{967}(93,\cdot)\) \(\chi_{967}(96,\cdot)\) \(\chi_{967}(147,\cdot)\) \(\chi_{967}(197,\cdot)\) \(\chi_{967}(210,\cdot)\) \(\chi_{967}(211,\cdot)\) \(\chi_{967}(239,\cdot)\) \(\chi_{967}(249,\cdot)\) \(\chi_{967}(382,\cdot)\) \(\chi_{967}(413,\cdot)\) \(\chi_{967}(428,\cdot)\) \(\chi_{967}(443,\cdot)\) \(\chi_{967}(454,\cdot)\) \(\chi_{967}(473,\cdot)\) \(\chi_{967}(522,\cdot)\) \(\chi_{967}(546,\cdot)\) \(\chi_{967}(567,\cdot)\) \(\chi_{967}(590,\cdot)\) \(\chi_{967}(615,\cdot)\) \(\chi_{967}(626,\cdot)\) \(\chi_{967}(632,\cdot)\) \(\chi_{967}(646,\cdot)\) \(\chi_{967}(687,\cdot)\) \(\chi_{967}(726,\cdot)\) \(\chi_{967}(742,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{53}{138}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 967 }(147, a) \) | \(-1\) | \(1\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{19}{69}\right)\) | \(e\left(\frac{53}{138}\right)\) | \(e\left(\frac{91}{138}\right)\) | \(e\left(\frac{101}{138}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) |