Basic properties
| Modulus: | \(8036\) | |
| 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 8036.em
\(\chi_{8036}(13,\cdot)\) \(\chi_{8036}(69,\cdot)\) \(\chi_{8036}(153,\cdot)\) \(\chi_{8036}(181,\cdot)\) \(\chi_{8036}(265,\cdot)\) \(\chi_{8036}(321,\cdot)\) \(\chi_{8036}(545,\cdot)\) \(\chi_{8036}(909,\cdot)\) \(\chi_{8036}(937,\cdot)\) \(\chi_{8036}(965,\cdot)\) \(\chi_{8036}(1049,\cdot)\) \(\chi_{8036}(1133,\cdot)\) \(\chi_{8036}(1161,\cdot)\) \(\chi_{8036}(1217,\cdot)\) \(\chi_{8036}(1245,\cdot)\) \(\chi_{8036}(1301,\cdot)\) \(\chi_{8036}(1329,\cdot)\) \(\chi_{8036}(1413,\cdot)\) \(\chi_{8036}(1441,\cdot)\) \(\chi_{8036}(1693,\cdot)\) \(\chi_{8036}(1833,\cdot)\) \(\chi_{8036}(2085,\cdot)\) \(\chi_{8036}(2113,\cdot)\) \(\chi_{8036}(2197,\cdot)\) \(\chi_{8036}(2225,\cdot)\) \(\chi_{8036}(2281,\cdot)\) \(\chi_{8036}(2309,\cdot)\) \(\chi_{8036}(2365,\cdot)\) \(\chi_{8036}(2393,\cdot)\) \(\chi_{8036}(2477,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{280})$ |
| Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{11}{14}\right),e\left(\frac{31}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{69}{280}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{47}{70}\right)\) |