Basic properties
Modulus: | \(953\) | |
Conductor: | \(953\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(238\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 953.n
\(\chi_{953}(7,\cdot)\) \(\chi_{953}(26,\cdot)\) \(\chi_{953}(29,\cdot)\) \(\chi_{953}(34,\cdot)\) \(\chi_{953}(50,\cdot)\) \(\chi_{953}(60,\cdot)\) \(\chi_{953}(72,\cdot)\) \(\chi_{953}(81,\cdot)\) \(\chi_{953}(82,\cdot)\) \(\chi_{953}(105,\cdot)\) \(\chi_{953}(110,\cdot)\) \(\chi_{953}(112,\cdot)\) \(\chi_{953}(118,\cdot)\) \(\chi_{953}(126,\cdot)\) \(\chi_{953}(127,\cdot)\) \(\chi_{953}(129,\cdot)\) \(\chi_{953}(132,\cdot)\) \(\chi_{953}(157,\cdot)\) \(\chi_{953}(158,\cdot)\) \(\chi_{953}(166,\cdot)\) \(\chi_{953}(169,\cdot)\) \(\chi_{953}(196,\cdot)\) \(\chi_{953}(206,\cdot)\) \(\chi_{953}(212,\cdot)\) \(\chi_{953}(218,\cdot)\) \(\chi_{953}(231,\cdot)\) \(\chi_{953}(262,\cdot)\) \(\chi_{953}(277,\cdot)\) \(\chi_{953}(289,\cdot)\) \(\chi_{953}(321,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{119})$ |
Fixed field: | Number field defined by a degree 238 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{117}{238}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 953 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{117}{238}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{25}{238}\right)\) | \(e\left(\frac{103}{238}\right)\) | \(e\left(\frac{29}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{117}{119}\right)\) | \(e\left(\frac{11}{238}\right)\) | \(e\left(\frac{211}{238}\right)\) |