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.dm
\(\chi_{1960}(157,\cdot)\) \(\chi_{1960}(173,\cdot)\) \(\chi_{1960}(213,\cdot)\) \(\chi_{1960}(397,\cdot)\) \(\chi_{1960}(437,\cdot)\) \(\chi_{1960}(453,\cdot)\) \(\chi_{1960}(493,\cdot)\) \(\chi_{1960}(677,\cdot)\) \(\chi_{1960}(733,\cdot)\) \(\chi_{1960}(773,\cdot)\) \(\chi_{1960}(957,\cdot)\) \(\chi_{1960}(997,\cdot)\) \(\chi_{1960}(1013,\cdot)\) \(\chi_{1960}(1053,\cdot)\) \(\chi_{1960}(1237,\cdot)\) \(\chi_{1960}(1277,\cdot)\) \(\chi_{1960}(1333,\cdot)\) \(\chi_{1960}(1517,\cdot)\) \(\chi_{1960}(1557,\cdot)\) \(\chi_{1960}(1573,\cdot)\) \(\chi_{1960}(1613,\cdot)\) \(\chi_{1960}(1797,\cdot)\) \(\chi_{1960}(1837,\cdot)\) \(\chi_{1960}(1853,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,1177,1081)\) → \((1,-1,i,e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 1960 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{6}\right)\) |