Basic properties
Modulus: | \(6027\) | |
Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{287}(129,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.dt
\(\chi_{6027}(19,\cdot)\) \(\chi_{6027}(313,\cdot)\) \(\chi_{6027}(766,\cdot)\) \(\chi_{6027}(913,\cdot)\) \(\chi_{6027}(1060,\cdot)\) \(\chi_{6027}(1195,\cdot)\) \(\chi_{6027}(1342,\cdot)\) \(\chi_{6027}(1489,\cdot)\) \(\chi_{6027}(1942,\cdot)\) \(\chi_{6027}(2236,\cdot)\) \(\chi_{6027}(2371,\cdot)\) \(\chi_{6027}(2518,\cdot)\) \(\chi_{6027}(2530,\cdot)\) \(\chi_{6027}(2677,\cdot)\) \(\chi_{6027}(2812,\cdot)\) \(\chi_{6027}(2959,\cdot)\) \(\chi_{6027}(2971,\cdot)\) \(\chi_{6027}(3265,\cdot)\) \(\chi_{6027}(3841,\cdot)\) \(\chi_{6027}(3988,\cdot)\) \(\chi_{6027}(4135,\cdot)\) \(\chi_{6027}(4147,\cdot)\) \(\chi_{6027}(4294,\cdot)\) \(\chi_{6027}(4441,\cdot)\) \(\chi_{6027}(5017,\cdot)\) \(\chi_{6027}(5311,\cdot)\) \(\chi_{6027}(5323,\cdot)\) \(\chi_{6027}(5470,\cdot)\) \(\chi_{6027}(5605,\cdot)\) \(\chi_{6027}(5752,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{1}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(4147, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) |