Basic properties
Modulus: | \(8034\) | |
Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{103}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.ct
\(\chi_{8034}(235,\cdot)\) \(\chi_{8034}(313,\cdot)\) \(\chi_{8034}(391,\cdot)\) \(\chi_{8034}(547,\cdot)\) \(\chi_{8034}(625,\cdot)\) \(\chi_{8034}(781,\cdot)\) \(\chi_{8034}(1093,\cdot)\) \(\chi_{8034}(1171,\cdot)\) \(\chi_{8034}(1327,\cdot)\) \(\chi_{8034}(1483,\cdot)\) \(\chi_{8034}(1561,\cdot)\) \(\chi_{8034}(1873,\cdot)\) \(\chi_{8034}(1951,\cdot)\) \(\chi_{8034}(2419,\cdot)\) \(\chi_{8034}(2497,\cdot)\) \(\chi_{8034}(2809,\cdot)\) \(\chi_{8034}(3355,\cdot)\) \(\chi_{8034}(4135,\cdot)\) \(\chi_{8034}(4291,\cdot)\) \(\chi_{8034}(4447,\cdot)\) \(\chi_{8034}(4993,\cdot)\) \(\chi_{8034}(5305,\cdot)\) \(\chi_{8034}(5461,\cdot)\) \(\chi_{8034}(5617,\cdot)\) \(\chi_{8034}(5851,\cdot)\) \(\chi_{8034}(5929,\cdot)\) \(\chi_{8034}(6007,\cdot)\) \(\chi_{8034}(6319,\cdot)\) \(\chi_{8034}(6787,\cdot)\) \(\chi_{8034}(7021,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((5357,1237,5773)\) → \((1,1,e\left(\frac{22}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(5461, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{8}{51}\right)\) |