Basic properties
Modulus: | \(4018\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(27,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.bo
\(\chi_{4018}(27,\cdot)\) \(\chi_{4018}(55,\cdot)\) \(\chi_{4018}(167,\cdot)\) \(\chi_{4018}(601,\cdot)\) \(\chi_{4018}(629,\cdot)\) \(\chi_{4018}(741,\cdot)\) \(\chi_{4018}(1063,\cdot)\) \(\chi_{4018}(1203,\cdot)\) \(\chi_{4018}(1315,\cdot)\) \(\chi_{4018}(1637,\cdot)\) \(\chi_{4018}(1749,\cdot)\) \(\chi_{4018}(1777,\cdot)\) \(\chi_{4018}(1889,\cdot)\) \(\chi_{4018}(2211,\cdot)\) \(\chi_{4018}(2323,\cdot)\) \(\chi_{4018}(2463,\cdot)\) \(\chi_{4018}(2785,\cdot)\) \(\chi_{4018}(2897,\cdot)\) \(\chi_{4018}(2925,\cdot)\) \(\chi_{4018}(3359,\cdot)\) \(\chi_{4018}(3471,\cdot)\) \(\chi_{4018}(3499,\cdot)\) \(\chi_{4018}(3611,\cdot)\) \(\chi_{4018}(3933,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{1}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 4018 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) |