Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(483\) | 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 8033.cm
\(\chi_{8033}(23,\cdot)\) \(\chi_{8033}(49,\cdot)\) \(\chi_{8033}(81,\cdot)\) \(\chi_{8033}(136,\cdot)\) \(\chi_{8033}(165,\cdot)\) \(\chi_{8033}(190,\cdot)\) \(\chi_{8033}(194,\cdot)\) \(\chi_{8033}(248,\cdot)\) \(\chi_{8033}(252,\cdot)\) \(\chi_{8033}(255,\cdot)\) \(\chi_{8033}(286,\cdot)\) \(\chi_{8033}(326,\cdot)\) \(\chi_{8033}(344,\cdot)\) \(\chi_{8033}(368,\cdot)\) \(\chi_{8033}(413,\cdot)\) \(\chi_{8033}(431,\cdot)\) \(\chi_{8033}(442,\cdot)\) \(\chi_{8033}(471,\cdot)\) \(\chi_{8033}(484,\cdot)\) \(\chi_{8033}(518,\cdot)\) \(\chi_{8033}(529,\cdot)\) \(\chi_{8033}(542,\cdot)\) \(\chi_{8033}(547,\cdot)\) \(\chi_{8033}(603,\cdot)\) \(\chi_{8033}(625,\cdot)\) \(\chi_{8033}(633,\cdot)\) \(\chi_{8033}(645,\cdot)\) \(\chi_{8033}(654,\cdot)\) \(\chi_{8033}(690,\cdot)\) \(\chi_{8033}(719,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{483})$ |
Fixed field: | Number field defined by a degree 483 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{11}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(326, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{161}\right)\) | \(e\left(\frac{55}{483}\right)\) | \(e\left(\frac{117}{161}\right)\) | \(e\left(\frac{284}{483}\right)\) | \(e\left(\frac{472}{483}\right)\) | \(e\left(\frac{314}{483}\right)\) | \(e\left(\frac{95}{161}\right)\) | \(e\left(\frac{110}{483}\right)\) | \(e\left(\frac{218}{483}\right)\) | \(e\left(\frac{401}{483}\right)\) |