Basic properties
| Modulus: | \(4018\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.bw
\(\chi_{4018}(37,\cdot)\) \(\chi_{4018}(51,\cdot)\) \(\chi_{4018}(221,\cdot)\) \(\chi_{4018}(303,\cdot)\) \(\chi_{4018}(305,\cdot)\) \(\chi_{4018}(387,\cdot)\) \(\chi_{4018}(529,\cdot)\) \(\chi_{4018}(543,\cdot)\) \(\chi_{4018}(611,\cdot)\) \(\chi_{4018}(625,\cdot)\) \(\chi_{4018}(795,\cdot)\) \(\chi_{4018}(877,\cdot)\) \(\chi_{4018}(879,\cdot)\) \(\chi_{4018}(1103,\cdot)\) \(\chi_{4018}(1117,\cdot)\) \(\chi_{4018}(1185,\cdot)\) \(\chi_{4018}(1199,\cdot)\) \(\chi_{4018}(1369,\cdot)\) \(\chi_{4018}(1453,\cdot)\) \(\chi_{4018}(1535,\cdot)\) \(\chi_{4018}(1677,\cdot)\) \(\chi_{4018}(1691,\cdot)\) \(\chi_{4018}(1759,\cdot)\) \(\chi_{4018}(1773,\cdot)\) \(\chi_{4018}(1943,\cdot)\) \(\chi_{4018}(2025,\cdot)\) \(\chi_{4018}(2109,\cdot)\) \(\chi_{4018}(2251,\cdot)\) \(\chi_{4018}(2265,\cdot)\) \(\chi_{4018}(2347,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{16}{21}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) |