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 \(\chi_{637}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1911.ec
\(\chi_{1911}(109,\cdot)\) \(\chi_{1911}(151,\cdot)\) \(\chi_{1911}(268,\cdot)\) \(\chi_{1911}(382,\cdot)\) \(\chi_{1911}(424,\cdot)\) \(\chi_{1911}(499,\cdot)\) \(\chi_{1911}(541,\cdot)\) \(\chi_{1911}(697,\cdot)\) \(\chi_{1911}(772,\cdot)\) \(\chi_{1911}(928,\cdot)\) \(\chi_{1911}(970,\cdot)\) \(\chi_{1911}(1045,\cdot)\) \(\chi_{1911}(1087,\cdot)\) \(\chi_{1911}(1201,\cdot)\) \(\chi_{1911}(1318,\cdot)\) \(\chi_{1911}(1360,\cdot)\) \(\chi_{1911}(1474,\cdot)\) \(\chi_{1911}(1516,\cdot)\) \(\chi_{1911}(1591,\cdot)\) \(\chi_{1911}(1633,\cdot)\) \(\chi_{1911}(1747,\cdot)\) \(\chi_{1911}(1789,\cdot)\) \(\chi_{1911}(1864,\cdot)\) \(\chi_{1911}(1906,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((638,1522,1471)\) → \((1,e\left(\frac{20}{21}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1911 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{28}\right)\) |