Basic properties
Modulus: | \(1960\) | |
Conductor: | \(1960\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 1960.dq
\(\chi_{1960}(107,\cdot)\) \(\chi_{1960}(123,\cdot)\) \(\chi_{1960}(163,\cdot)\) \(\chi_{1960}(347,\cdot)\) \(\chi_{1960}(387,\cdot)\) \(\chi_{1960}(403,\cdot)\) \(\chi_{1960}(443,\cdot)\) \(\chi_{1960}(627,\cdot)\) \(\chi_{1960}(683,\cdot)\) \(\chi_{1960}(723,\cdot)\) \(\chi_{1960}(907,\cdot)\) \(\chi_{1960}(947,\cdot)\) \(\chi_{1960}(963,\cdot)\) \(\chi_{1960}(1003,\cdot)\) \(\chi_{1960}(1187,\cdot)\) \(\chi_{1960}(1227,\cdot)\) \(\chi_{1960}(1283,\cdot)\) \(\chi_{1960}(1467,\cdot)\) \(\chi_{1960}(1507,\cdot)\) \(\chi_{1960}(1523,\cdot)\) \(\chi_{1960}(1563,\cdot)\) \(\chi_{1960}(1747,\cdot)\) \(\chi_{1960}(1787,\cdot)\) \(\chi_{1960}(1803,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,1177,1081)\) → \((-1,-1,-i,e\left(\frac{19}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 1960 }(1003, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) |