Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1339}(744,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.cq
\(\chi_{8034}(61,\cdot)\) \(\chi_{8034}(133,\cdot)\) \(\chi_{8034}(373,\cdot)\) \(\chi_{8034}(523,\cdot)\) \(\chi_{8034}(529,\cdot)\) \(\chi_{8034}(679,\cdot)\) \(\chi_{8034}(991,\cdot)\) \(\chi_{8034}(1147,\cdot)\) \(\chi_{8034}(1465,\cdot)\) \(\chi_{8034}(1621,\cdot)\) \(\chi_{8034}(1933,\cdot)\) \(\chi_{8034}(2083,\cdot)\) \(\chi_{8034}(2239,\cdot)\) \(\chi_{8034}(2551,\cdot)\) \(\chi_{8034}(3103,\cdot)\) \(\chi_{8034}(3259,\cdot)\) \(\chi_{8034}(3721,\cdot)\) \(\chi_{8034}(3877,\cdot)\) \(\chi_{8034}(3883,\cdot)\) \(\chi_{8034}(4117,\cdot)\) \(\chi_{8034}(4501,\cdot)\) \(\chi_{8034}(4735,\cdot)\) \(\chi_{8034}(4819,\cdot)\) \(\chi_{8034}(5287,\cdot)\) \(\chi_{8034}(5365,\cdot)\) \(\chi_{8034}(5437,\cdot)\) \(\chi_{8034}(5905,\cdot)\) \(\chi_{8034}(5983,\cdot)\) \(\chi_{8034}(6067,\cdot)\) \(\chi_{8034}(6685,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{4}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(2083, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) |