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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1960.dk
\(\chi_{1960}(37,\cdot)\) \(\chi_{1960}(53,\cdot)\) \(\chi_{1960}(93,\cdot)\) \(\chi_{1960}(277,\cdot)\) \(\chi_{1960}(317,\cdot)\) \(\chi_{1960}(333,\cdot)\) \(\chi_{1960}(597,\cdot)\) \(\chi_{1960}(613,\cdot)\) \(\chi_{1960}(653,\cdot)\) \(\chi_{1960}(837,\cdot)\) \(\chi_{1960}(877,\cdot)\) \(\chi_{1960}(893,\cdot)\) \(\chi_{1960}(933,\cdot)\) \(\chi_{1960}(1117,\cdot)\) \(\chi_{1960}(1173,\cdot)\) \(\chi_{1960}(1213,\cdot)\) \(\chi_{1960}(1397,\cdot)\) \(\chi_{1960}(1437,\cdot)\) \(\chi_{1960}(1453,\cdot)\) \(\chi_{1960}(1493,\cdot)\) \(\chi_{1960}(1677,\cdot)\) \(\chi_{1960}(1717,\cdot)\) \(\chi_{1960}(1773,\cdot)\) \(\chi_{1960}(1957,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,1177,1081)\) → \((1,-1,i,e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 1960 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{3}\right)\) |