Basic properties
Modulus: | \(531\) | |
Conductor: | \(531\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(174\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 531.o
\(\chi_{531}(13,\cdot)\) \(\chi_{531}(31,\cdot)\) \(\chi_{531}(34,\cdot)\) \(\chi_{531}(40,\cdot)\) \(\chi_{531}(43,\cdot)\) \(\chi_{531}(52,\cdot)\) \(\chi_{531}(61,\cdot)\) \(\chi_{531}(67,\cdot)\) \(\chi_{531}(70,\cdot)\) \(\chi_{531}(97,\cdot)\) \(\chi_{531}(103,\cdot)\) \(\chi_{531}(106,\cdot)\) \(\chi_{531}(115,\cdot)\) \(\chi_{531}(124,\cdot)\) \(\chi_{531}(142,\cdot)\) \(\chi_{531}(148,\cdot)\) \(\chi_{531}(151,\cdot)\) \(\chi_{531}(157,\cdot)\) \(\chi_{531}(160,\cdot)\) \(\chi_{531}(187,\cdot)\) \(\chi_{531}(211,\cdot)\) \(\chi_{531}(214,\cdot)\) \(\chi_{531}(220,\cdot)\) \(\chi_{531}(229,\cdot)\) \(\chi_{531}(232,\cdot)\) \(\chi_{531}(238,\cdot)\) \(\chi_{531}(247,\cdot)\) \(\chi_{531}(250,\cdot)\) \(\chi_{531}(259,\cdot)\) \(\chi_{531}(268,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{87})$ |
Fixed field: | Number field defined by a degree 174 polynomial (not computed) |
Values on generators
\((119,415)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{41}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 531 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{174}\right)\) | \(e\left(\frac{65}{87}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{34}{87}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{59}{174}\right)\) | \(e\left(\frac{25}{174}\right)\) | \(e\left(\frac{133}{174}\right)\) | \(e\left(\frac{43}{87}\right)\) |