Basic properties
| Modulus: | \(4013\) | |
| Conductor: | \(4013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(118\) | 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 4013.h
\(\chi_{4013}(114,\cdot)\) \(\chi_{4013}(119,\cdot)\) \(\chi_{4013}(208,\cdot)\) \(\chi_{4013}(294,\cdot)\) \(\chi_{4013}(366,\cdot)\) \(\chi_{4013}(448,\cdot)\) \(\chi_{4013}(491,\cdot)\) \(\chi_{4013}(547,\cdot)\) \(\chi_{4013}(565,\cdot)\) \(\chi_{4013}(589,\cdot)\) \(\chi_{4013}(717,\cdot)\) \(\chi_{4013}(747,\cdot)\) \(\chi_{4013}(879,\cdot)\) \(\chi_{4013}(977,\cdot)\) \(\chi_{4013}(986,\cdot)\) \(\chi_{4013}(1075,\cdot)\) \(\chi_{4013}(1097,\cdot)\) \(\chi_{4013}(1128,\cdot)\) \(\chi_{4013}(1131,\cdot)\) \(\chi_{4013}(1447,\cdot)\) \(\chi_{4013}(1519,\cdot)\) \(\chi_{4013}(1698,\cdot)\) \(\chi_{4013}(1766,\cdot)\) \(\chi_{4013}(1789,\cdot)\) \(\chi_{4013}(1815,\cdot)\) \(\chi_{4013}(1850,\cdot)\) \(\chi_{4013}(1853,\cdot)\) \(\chi_{4013}(1868,\cdot)\) \(\chi_{4013}(1886,\cdot)\) \(\chi_{4013}(1891,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{59})$ |
| Fixed field: | Number field defined by a degree 118 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{113}{118}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4013 }(114, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{118}\right)\) | \(e\left(\frac{7}{118}\right)\) | \(e\left(\frac{54}{59}\right)\) | \(e\left(\frac{5}{118}\right)\) | \(e\left(\frac{1}{59}\right)\) | \(e\left(\frac{19}{59}\right)\) | \(e\left(\frac{103}{118}\right)\) | \(e\left(\frac{7}{59}\right)\) | \(1\) | \(e\left(\frac{57}{59}\right)\) |