Basic properties
Modulus: | \(8026\) | |
Conductor: | \(4013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(118\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4013}(119,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8026.h
\(\chi_{8026}(119,\cdot)\) \(\chi_{8026}(491,\cdot)\) \(\chi_{8026}(547,\cdot)\) \(\chi_{8026}(565,\cdot)\) \(\chi_{8026}(589,\cdot)\) \(\chi_{8026}(717,\cdot)\) \(\chi_{8026}(747,\cdot)\) \(\chi_{8026}(879,\cdot)\) \(\chi_{8026}(977,\cdot)\) \(\chi_{8026}(1075,\cdot)\) \(\chi_{8026}(1097,\cdot)\) \(\chi_{8026}(1131,\cdot)\) \(\chi_{8026}(1447,\cdot)\) \(\chi_{8026}(1519,\cdot)\) \(\chi_{8026}(1789,\cdot)\) \(\chi_{8026}(1815,\cdot)\) \(\chi_{8026}(1853,\cdot)\) \(\chi_{8026}(1891,\cdot)\) \(\chi_{8026}(2143,\cdot)\) \(\chi_{8026}(2413,\cdot)\) \(\chi_{8026}(2419,\cdot)\) \(\chi_{8026}(2535,\cdot)\) \(\chi_{8026}(2601,\cdot)\) \(\chi_{8026}(2963,\cdot)\) \(\chi_{8026}(3065,\cdot)\) \(\chi_{8026}(3323,\cdot)\) \(\chi_{8026}(3339,\cdot)\) \(\chi_{8026}(3495,\cdot)\) \(\chi_{8026}(3715,\cdot)\) \(\chi_{8026}(3811,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{59})$ |
Fixed field: | Number field defined by a degree 118 polynomial (not computed) |
Values on generators
\(4015\) → \(e\left(\frac{37}{118}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8026 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{118}\right)\) | \(e\left(\frac{81}{118}\right)\) | \(e\left(\frac{1}{59}\right)\) | \(e\left(\frac{19}{59}\right)\) | \(e\left(\frac{3}{59}\right)\) | \(e\left(\frac{37}{59}\right)\) | \(e\left(\frac{50}{59}\right)\) | \(e\left(\frac{26}{59}\right)\) | \(e\left(\frac{13}{59}\right)\) | \(e\left(\frac{21}{118}\right)\) |