Basic properties
Modulus: | \(547\) | |
Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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 547.l
\(\chi_{547}(26,\cdot)\) \(\chi_{547}(59,\cdot)\) \(\chi_{547}(83,\cdot)\) \(\chi_{547}(102,\cdot)\) \(\chi_{547}(106,\cdot)\) \(\chi_{547}(128,\cdot)\) \(\chi_{547}(145,\cdot)\) \(\chi_{547}(222,\cdot)\) \(\chi_{547}(245,\cdot)\) \(\chi_{547}(251,\cdot)\) \(\chi_{547}(308,\cdot)\) \(\chi_{547}(314,\cdot)\) \(\chi_{547}(316,\cdot)\) \(\chi_{547}(330,\cdot)\) \(\chi_{547}(348,\cdot)\) \(\chi_{547}(366,\cdot)\) \(\chi_{547}(411,\cdot)\) \(\chi_{547}(418,\cdot)\) \(\chi_{547}(426,\cdot)\) \(\chi_{547}(451,\cdot)\) \(\chi_{547}(493,\cdot)\) \(\chi_{547}(500,\cdot)\) \(\chi_{547}(526,\cdot)\) \(\chi_{547}(536,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\(2\) → \(e\left(\frac{19}{78}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 547 }(330, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{78}\right)\) | \(-1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) |