Basic properties
Modulus: | \(531\) | |
Conductor: | \(531\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(174\) | 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 531.p
\(\chi_{531}(2,\cdot)\) \(\chi_{531}(11,\cdot)\) \(\chi_{531}(14,\cdot)\) \(\chi_{531}(23,\cdot)\) \(\chi_{531}(32,\cdot)\) \(\chi_{531}(38,\cdot)\) \(\chi_{531}(47,\cdot)\) \(\chi_{531}(50,\cdot)\) \(\chi_{531}(56,\cdot)\) \(\chi_{531}(65,\cdot)\) \(\chi_{531}(77,\cdot)\) \(\chi_{531}(83,\cdot)\) \(\chi_{531}(92,\cdot)\) \(\chi_{531}(101,\cdot)\) \(\chi_{531}(113,\cdot)\) \(\chi_{531}(128,\cdot)\) \(\chi_{531}(131,\cdot)\) \(\chi_{531}(149,\cdot)\) \(\chi_{531}(155,\cdot)\) \(\chi_{531}(158,\cdot)\) \(\chi_{531}(173,\cdot)\) \(\chi_{531}(185,\cdot)\) \(\chi_{531}(191,\cdot)\) \(\chi_{531}(200,\cdot)\) \(\chi_{531}(209,\cdot)\) \(\chi_{531}(221,\cdot)\) \(\chi_{531}(227,\cdot)\) \(\chi_{531}(254,\cdot)\) \(\chi_{531}(266,\cdot)\) \(\chi_{531}(275,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{87})$ |
Fixed field: | Number field defined by a degree 174 polynomial (not computed) |
Values on generators
\((119,415)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{25}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 531 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{87}\right)\) | \(e\left(\frac{17}{87}\right)\) | \(e\left(\frac{73}{174}\right)\) | \(e\left(\frac{37}{87}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{82}{87}\right)\) | \(e\left(\frac{127}{174}\right)\) | \(e\left(\frac{2}{87}\right)\) | \(e\left(\frac{34}{87}\right)\) |