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 \(\chi_{637}(115,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1911.eb
\(\chi_{1911}(115,\cdot)\) \(\chi_{1911}(124,\cdot)\) \(\chi_{1911}(262,\cdot)\) \(\chi_{1911}(292,\cdot)\) \(\chi_{1911}(388,\cdot)\) \(\chi_{1911}(397,\cdot)\) \(\chi_{1911}(535,\cdot)\) \(\chi_{1911}(565,\cdot)\) \(\chi_{1911}(661,\cdot)\) \(\chi_{1911}(670,\cdot)\) \(\chi_{1911}(808,\cdot)\) \(\chi_{1911}(838,\cdot)\) \(\chi_{1911}(934,\cdot)\) \(\chi_{1911}(943,\cdot)\) \(\chi_{1911}(1081,\cdot)\) \(\chi_{1911}(1111,\cdot)\) \(\chi_{1911}(1216,\cdot)\) \(\chi_{1911}(1384,\cdot)\) \(\chi_{1911}(1480,\cdot)\) \(\chi_{1911}(1627,\cdot)\) \(\chi_{1911}(1657,\cdot)\) \(\chi_{1911}(1753,\cdot)\) \(\chi_{1911}(1762,\cdot)\) \(\chi_{1911}(1900,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((1,e\left(\frac{25}{42}\right),e\left(\frac{7}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1911 }(115, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(-i\) | \(e\left(\frac{53}{84}\right)\) |