Basic properties
| Modulus: | \(1911\) | |
| Conductor: | \(637\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{637}(85,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1911.ed
\(\chi_{1911}(85,\cdot)\) \(\chi_{1911}(106,\cdot)\) \(\chi_{1911}(232,\cdot)\) \(\chi_{1911}(253,\cdot)\) \(\chi_{1911}(358,\cdot)\) \(\chi_{1911}(379,\cdot)\) \(\chi_{1911}(505,\cdot)\) \(\chi_{1911}(526,\cdot)\) \(\chi_{1911}(631,\cdot)\) \(\chi_{1911}(652,\cdot)\) \(\chi_{1911}(778,\cdot)\) \(\chi_{1911}(799,\cdot)\) \(\chi_{1911}(904,\cdot)\) \(\chi_{1911}(925,\cdot)\) \(\chi_{1911}(1051,\cdot)\) \(\chi_{1911}(1072,\cdot)\) \(\chi_{1911}(1198,\cdot)\) \(\chi_{1911}(1345,\cdot)\) \(\chi_{1911}(1450,\cdot)\) \(\chi_{1911}(1597,\cdot)\) \(\chi_{1911}(1723,\cdot)\) \(\chi_{1911}(1744,\cdot)\) \(\chi_{1911}(1870,\cdot)\) \(\chi_{1911}(1891,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((1,e\left(\frac{2}{7}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1911 }(85, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{84}\right)\) |