Basic properties
| Modulus: | \(4018\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(280\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.cg
\(\chi_{4018}(13,\cdot)\) \(\chi_{4018}(69,\cdot)\) \(\chi_{4018}(111,\cdot)\) \(\chi_{4018}(153,\cdot)\) \(\chi_{4018}(181,\cdot)\) \(\chi_{4018}(265,\cdot)\) \(\chi_{4018}(321,\cdot)\) \(\chi_{4018}(335,\cdot)\) \(\chi_{4018}(363,\cdot)\) \(\chi_{4018}(475,\cdot)\) \(\chi_{4018}(503,\cdot)\) \(\chi_{4018}(545,\cdot)\) \(\chi_{4018}(559,\cdot)\) \(\chi_{4018}(643,\cdot)\) \(\chi_{4018}(671,\cdot)\) \(\chi_{4018}(727,\cdot)\) \(\chi_{4018}(755,\cdot)\) \(\chi_{4018}(839,\cdot)\) \(\chi_{4018}(867,\cdot)\) \(\chi_{4018}(895,\cdot)\) \(\chi_{4018}(909,\cdot)\) \(\chi_{4018}(937,\cdot)\) \(\chi_{4018}(965,\cdot)\) \(\chi_{4018}(1049,\cdot)\) \(\chi_{4018}(1119,\cdot)\) \(\chi_{4018}(1133,\cdot)\) \(\chi_{4018}(1161,\cdot)\) \(\chi_{4018}(1217,\cdot)\) \(\chi_{4018}(1245,\cdot)\) \(\chi_{4018}(1259,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{280})$ |
| Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{31}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{69}{280}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{47}{70}\right)\) |