Basic properties
Modulus: | \(261\) | |
Conductor: | \(261\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 261.x
\(\chi_{261}(2,\cdot)\) \(\chi_{261}(11,\cdot)\) \(\chi_{261}(14,\cdot)\) \(\chi_{261}(32,\cdot)\) \(\chi_{261}(47,\cdot)\) \(\chi_{261}(50,\cdot)\) \(\chi_{261}(56,\cdot)\) \(\chi_{261}(68,\cdot)\) \(\chi_{261}(77,\cdot)\) \(\chi_{261}(95,\cdot)\) \(\chi_{261}(101,\cdot)\) \(\chi_{261}(113,\cdot)\) \(\chi_{261}(119,\cdot)\) \(\chi_{261}(131,\cdot)\) \(\chi_{261}(137,\cdot)\) \(\chi_{261}(155,\cdot)\) \(\chi_{261}(164,\cdot)\) \(\chi_{261}(176,\cdot)\) \(\chi_{261}(182,\cdot)\) \(\chi_{261}(185,\cdot)\) \(\chi_{261}(200,\cdot)\) \(\chi_{261}(218,\cdot)\) \(\chi_{261}(221,\cdot)\) \(\chi_{261}(230,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((146,118)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{9}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 261 }(164, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{20}{21}\right)\) |