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
\((236,334)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{21}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 423 }(203, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{138}\right)\) | \(e\left(\frac{7}{69}\right)\) | \(e\left(\frac{43}{69}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{2}{69}\right)\) | \(e\left(\frac{95}{138}\right)\) | \(e\left(\frac{137}{138}\right)\) | \(e\left(\frac{14}{69}\right)\) |