Basic properties
| Modulus: | \(2166\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2166.q
\(\chi_{2166}(7,\cdot)\) \(\chi_{2166}(49,\cdot)\) \(\chi_{2166}(121,\cdot)\) \(\chi_{2166}(163,\cdot)\) \(\chi_{2166}(235,\cdot)\) \(\chi_{2166}(277,\cdot)\) \(\chi_{2166}(349,\cdot)\) \(\chi_{2166}(391,\cdot)\) \(\chi_{2166}(463,\cdot)\) \(\chi_{2166}(505,\cdot)\) \(\chi_{2166}(577,\cdot)\) \(\chi_{2166}(619,\cdot)\) \(\chi_{2166}(691,\cdot)\) \(\chi_{2166}(733,\cdot)\) \(\chi_{2166}(805,\cdot)\) \(\chi_{2166}(847,\cdot)\) \(\chi_{2166}(919,\cdot)\) \(\chi_{2166}(961,\cdot)\) \(\chi_{2166}(1033,\cdot)\) \(\chi_{2166}(1075,\cdot)\) \(\chi_{2166}(1147,\cdot)\) \(\chi_{2166}(1189,\cdot)\) \(\chi_{2166}(1261,\cdot)\) \(\chi_{2166}(1303,\cdot)\) \(\chi_{2166}(1417,\cdot)\) \(\chi_{2166}(1489,\cdot)\) \(\chi_{2166}(1531,\cdot)\) \(\chi_{2166}(1603,\cdot)\) \(\chi_{2166}(1645,\cdot)\) \(\chi_{2166}(1717,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((1445,1807)\) → \((1,e\left(\frac{25}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2166 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{31}{57}\right)\) |