Basic properties
| Modulus: | \(1011\) | |
| Conductor: | \(1011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1011.bf
\(\chi_{1011}(47,\cdot)\) \(\chi_{1011}(56,\cdot)\) \(\chi_{1011}(137,\cdot)\) \(\chi_{1011}(200,\cdot)\) \(\chi_{1011}(281,\cdot)\) \(\chi_{1011}(290,\cdot)\) \(\chi_{1011}(344,\cdot)\) \(\chi_{1011}(362,\cdot)\) \(\chi_{1011}(380,\cdot)\) \(\chi_{1011}(458,\cdot)\) \(\chi_{1011}(551,\cdot)\) \(\chi_{1011}(626,\cdot)\) \(\chi_{1011}(635,\cdot)\) \(\chi_{1011}(647,\cdot)\) \(\chi_{1011}(668,\cdot)\) \(\chi_{1011}(680,\cdot)\) \(\chi_{1011}(701,\cdot)\) \(\chi_{1011}(713,\cdot)\) \(\chi_{1011}(722,\cdot)\) \(\chi_{1011}(797,\cdot)\) \(\chi_{1011}(890,\cdot)\) \(\chi_{1011}(968,\cdot)\) \(\chi_{1011}(986,\cdot)\) \(\chi_{1011}(1004,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((338,10)\) → \((-1,e\left(\frac{15}{56}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1011 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) |