Basic properties
Modulus: | \(423\) | |
Conductor: | \(423\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(138\) | 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 423.o
\(\chi_{423}(5,\cdot)\) \(\chi_{423}(11,\cdot)\) \(\chi_{423}(20,\cdot)\) \(\chi_{423}(23,\cdot)\) \(\chi_{423}(29,\cdot)\) \(\chi_{423}(38,\cdot)\) \(\chi_{423}(41,\cdot)\) \(\chi_{423}(77,\cdot)\) \(\chi_{423}(86,\cdot)\) \(\chi_{423}(92,\cdot)\) \(\chi_{423}(104,\cdot)\) \(\chi_{423}(113,\cdot)\) \(\chi_{423}(137,\cdot)\) \(\chi_{423}(146,\cdot)\) \(\chi_{423}(164,\cdot)\) \(\chi_{423}(167,\cdot)\) \(\chi_{423}(176,\cdot)\) \(\chi_{423}(182,\cdot)\) \(\chi_{423}(185,\cdot)\) \(\chi_{423}(203,\cdot)\) \(\chi_{423}(218,\cdot)\) \(\chi_{423}(221,\cdot)\) \(\chi_{423}(227,\cdot)\) \(\chi_{423}(245,\cdot)\) \(\chi_{423}(248,\cdot)\) \(\chi_{423}(254,\cdot)\) \(\chi_{423}(257,\cdot)\) \(\chi_{423}(266,\cdot)\) \(\chi_{423}(275,\cdot)\) \(\chi_{423}(293,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((236,334)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{45}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 423 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{138}\right)\) | \(e\left(\frac{61}{69}\right)\) | \(e\left(\frac{10}{69}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{47}{69}\right)\) | \(e\left(\frac{59}{138}\right)\) | \(e\left(\frac{11}{138}\right)\) | \(e\left(\frac{53}{69}\right)\) |