Basic properties
Modulus: | \(523\) | |
Conductor: | \(523\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | 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 523.g
\(\chi_{523}(9,\cdot)\) \(\chi_{523}(11,\cdot)\) \(\chi_{523}(43,\cdot)\) \(\chi_{523}(73,\cdot)\) \(\chi_{523}(81,\cdot)\) \(\chi_{523}(99,\cdot)\) \(\chi_{523}(121,\cdot)\) \(\chi_{523}(134,\cdot)\) \(\chi_{523}(150,\cdot)\) \(\chi_{523}(160,\cdot)\) \(\chi_{523}(174,\cdot)\) \(\chi_{523}(191,\cdot)\) \(\chi_{523}(206,\cdot)\) \(\chi_{523}(226,\cdot)\) \(\chi_{523}(280,\cdot)\) \(\chi_{523}(285,\cdot)\) \(\chi_{523}(304,\cdot)\) \(\chi_{523}(345,\cdot)\) \(\chi_{523}(368,\cdot)\) \(\chi_{523}(387,\cdot)\) \(\chi_{523}(394,\cdot)\) \(\chi_{523}(408,\cdot)\) \(\chi_{523}(428,\cdot)\) \(\chi_{523}(465,\cdot)\) \(\chi_{523}(473,\cdot)\) \(\chi_{523}(490,\cdot)\) \(\chi_{523}(496,\cdot)\) \(\chi_{523}(520,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(2\) → \(e\left(\frac{19}{29}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 523 }(99, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) |