Basic properties
| Modulus: | \(1075\) | |
| Conductor: | \(215\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{215}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1075.bn
\(\chi_{1075}(18,\cdot)\) \(\chi_{1075}(132,\cdot)\) \(\chi_{1075}(157,\cdot)\) \(\chi_{1075}(218,\cdot)\) \(\chi_{1075}(243,\cdot)\) \(\chi_{1075}(407,\cdot)\) \(\chi_{1075}(493,\cdot)\) \(\chi_{1075}(507,\cdot)\) \(\chi_{1075}(593,\cdot)\) \(\chi_{1075}(607,\cdot)\) \(\chi_{1075}(632,\cdot)\) \(\chi_{1075}(657,\cdot)\) \(\chi_{1075}(693,\cdot)\) \(\chi_{1075}(707,\cdot)\) \(\chi_{1075}(718,\cdot)\) \(\chi_{1075}(743,\cdot)\) \(\chi_{1075}(757,\cdot)\) \(\chi_{1075}(793,\cdot)\) \(\chi_{1075}(807,\cdot)\) \(\chi_{1075}(843,\cdot)\) \(\chi_{1075}(893,\cdot)\) \(\chi_{1075}(932,\cdot)\) \(\chi_{1075}(1007,\cdot)\) \(\chi_{1075}(1018,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((302,476)\) → \((-i,e\left(\frac{29}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1075 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) |