Basic properties
| Modulus: | \(4018\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.bz
\(\chi_{4018}(43,\cdot)\) \(\chi_{4018}(169,\cdot)\) \(\chi_{4018}(225,\cdot)\) \(\chi_{4018}(267,\cdot)\) \(\chi_{4018}(323,\cdot)\) \(\chi_{4018}(449,\cdot)\) \(\chi_{4018}(617,\cdot)\) \(\chi_{4018}(743,\cdot)\) \(\chi_{4018}(771,\cdot)\) \(\chi_{4018}(799,\cdot)\) \(\chi_{4018}(841,\cdot)\) \(\chi_{4018}(869,\cdot)\) \(\chi_{4018}(897,\cdot)\) \(\chi_{4018}(1023,\cdot)\) \(\chi_{4018}(1191,\cdot)\) \(\chi_{4018}(1317,\cdot)\) \(\chi_{4018}(1345,\cdot)\) \(\chi_{4018}(1415,\cdot)\) \(\chi_{4018}(1443,\cdot)\) \(\chi_{4018}(1597,\cdot)\) \(\chi_{4018}(1891,\cdot)\) \(\chi_{4018}(1919,\cdot)\) \(\chi_{4018}(1947,\cdot)\) \(\chi_{4018}(1989,\cdot)\) \(\chi_{4018}(2017,\cdot)\) \(\chi_{4018}(2045,\cdot)\) \(\chi_{4018}(2171,\cdot)\) \(\chi_{4018}(2339,\cdot)\) \(\chi_{4018}(2465,\cdot)\) \(\chi_{4018}(2493,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{1}{7}\right),e\left(\frac{13}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) |