Basic properties
| Modulus: | \(4018\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.cd
\(\chi_{4018}(23,\cdot)\) \(\chi_{4018}(25,\cdot)\) \(\chi_{4018}(107,\cdot)\) \(\chi_{4018}(277,\cdot)\) \(\chi_{4018}(291,\cdot)\) \(\chi_{4018}(359,\cdot)\) \(\chi_{4018}(515,\cdot)\) \(\chi_{4018}(597,\cdot)\) \(\chi_{4018}(599,\cdot)\) \(\chi_{4018}(681,\cdot)\) \(\chi_{4018}(865,\cdot)\) \(\chi_{4018}(933,\cdot)\) \(\chi_{4018}(947,\cdot)\) \(\chi_{4018}(1089,\cdot)\) \(\chi_{4018}(1171,\cdot)\) \(\chi_{4018}(1173,\cdot)\) \(\chi_{4018}(1425,\cdot)\) \(\chi_{4018}(1507,\cdot)\) \(\chi_{4018}(1521,\cdot)\) \(\chi_{4018}(1663,\cdot)\) \(\chi_{4018}(1747,\cdot)\) \(\chi_{4018}(1829,\cdot)\) \(\chi_{4018}(1999,\cdot)\) \(\chi_{4018}(2013,\cdot)\) \(\chi_{4018}(2081,\cdot)\) \(\chi_{4018}(2095,\cdot)\) \(\chi_{4018}(2237,\cdot)\) \(\chi_{4018}(2319,\cdot)\) \(\chi_{4018}(2403,\cdot)\) \(\chi_{4018}(2573,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{19}{21}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{8}{105}\right)\) |