Basic properties
| Modulus: | \(953\) | |
| Conductor: | \(953\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(119\) | 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.l
\(\chi_{953}(15,\cdot)\) \(\chi_{953}(18,\cdot)\) \(\chi_{953}(28,\cdot)\) \(\chi_{953}(33,\cdot)\) \(\chi_{953}(49,\cdot)\) \(\chi_{953}(53,\cdot)\) \(\chi_{953}(95,\cdot)\) \(\chi_{953}(104,\cdot)\) \(\chi_{953}(114,\cdot)\) \(\chi_{953}(116,\cdot)\) \(\chi_{953}(117,\cdot)\) \(\chi_{953}(136,\cdot)\) \(\chi_{953}(141,\cdot)\) \(\chi_{953}(146,\cdot)\) \(\chi_{953}(153,\cdot)\) \(\chi_{953}(155,\cdot)\) \(\chi_{953}(182,\cdot)\) \(\chi_{953}(186,\cdot)\) \(\chi_{953}(200,\cdot)\) \(\chi_{953}(203,\cdot)\) \(\chi_{953}(209,\cdot)\) \(\chi_{953}(225,\cdot)\) \(\chi_{953}(226,\cdot)\) \(\chi_{953}(230,\cdot)\) \(\chi_{953}(240,\cdot)\) \(\chi_{953}(270,\cdot)\) \(\chi_{953}(288,\cdot)\) \(\chi_{953}(296,\cdot)\) \(\chi_{953}(324,\cdot)\) \(\chi_{953}(328,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{119})$ |
| Fixed field: | Number field defined by a degree 119 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{16}{119}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 953 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{16}{119}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{38}{119}\right)\) | \(e\left(\frac{9}{119}\right)\) | \(e\left(\frac{12}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{32}{119}\right)\) | \(e\left(\frac{31}{119}\right)\) | \(e\left(\frac{97}{119}\right)\) |