Basic properties
Modulus: | \(527\) | |
Conductor: | \(527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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 527.bj
\(\chi_{527}(23,\cdot)\) \(\chi_{527}(27,\cdot)\) \(\chi_{527}(29,\cdot)\) \(\chi_{527}(46,\cdot)\) \(\chi_{527}(54,\cdot)\) \(\chi_{527}(58,\cdot)\) \(\chi_{527}(91,\cdot)\) \(\chi_{527}(108,\cdot)\) \(\chi_{527}(116,\cdot)\) \(\chi_{527}(122,\cdot)\) \(\chi_{527}(139,\cdot)\) \(\chi_{527}(147,\cdot)\) \(\chi_{527}(182,\cdot)\) \(\chi_{527}(184,\cdot)\) \(\chi_{527}(201,\cdot)\) \(\chi_{527}(209,\cdot)\) \(\chi_{527}(215,\cdot)\) \(\chi_{527}(232,\cdot)\) \(\chi_{527}(244,\cdot)\) \(\chi_{527}(275,\cdot)\) \(\chi_{527}(277,\cdot)\) \(\chi_{527}(294,\cdot)\) \(\chi_{527}(333,\cdot)\) \(\chi_{527}(337,\cdot)\) \(\chi_{527}(364,\cdot)\) \(\chi_{527}(368,\cdot)\) \(\chi_{527}(401,\cdot)\) \(\chi_{527}(418,\cdot)\) \(\chi_{527}(430,\cdot)\) \(\chi_{527}(432,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((156,375)\) → \((e\left(\frac{13}{16}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 527 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) |