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 \(\chi_{637}(136,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1911.eo
\(\chi_{1911}(136,\cdot)\) \(\chi_{1911}(145,\cdot)\) \(\chi_{1911}(241,\cdot)\) \(\chi_{1911}(271,\cdot)\) \(\chi_{1911}(409,\cdot)\) \(\chi_{1911}(418,\cdot)\) \(\chi_{1911}(514,\cdot)\) \(\chi_{1911}(544,\cdot)\) \(\chi_{1911}(682,\cdot)\) \(\chi_{1911}(691,\cdot)\) \(\chi_{1911}(787,\cdot)\) \(\chi_{1911}(817,\cdot)\) \(\chi_{1911}(955,\cdot)\) \(\chi_{1911}(964,\cdot)\) \(\chi_{1911}(1090,\cdot)\) \(\chi_{1911}(1228,\cdot)\) \(\chi_{1911}(1237,\cdot)\) \(\chi_{1911}(1333,\cdot)\) \(\chi_{1911}(1363,\cdot)\) \(\chi_{1911}(1510,\cdot)\) \(\chi_{1911}(1606,\cdot)\) \(\chi_{1911}(1774,\cdot)\) \(\chi_{1911}(1879,\cdot)\) \(\chi_{1911}(1909,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((1,e\left(\frac{19}{42}\right),e\left(\frac{5}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1911 }(136, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{19}{84}\right)\) |