Basic properties
Modulus: | \(218\) | |
Conductor: | \(109\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{109}(98,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 218.l
\(\chi_{218}(11,\cdot)\) \(\chi_{218}(13,\cdot)\) \(\chi_{218}(37,\cdot)\) \(\chi_{218}(39,\cdot)\) \(\chi_{218}(47,\cdot)\) \(\chi_{218}(51,\cdot)\) \(\chi_{218}(53,\cdot)\) \(\chi_{218}(57,\cdot)\) \(\chi_{218}(59,\cdot)\) \(\chi_{218}(65,\cdot)\) \(\chi_{218}(67,\cdot)\) \(\chi_{218}(69,\cdot)\) \(\chi_{218}(79,\cdot)\) \(\chi_{218}(85,\cdot)\) \(\chi_{218}(91,\cdot)\) \(\chi_{218}(95,\cdot)\) \(\chi_{218}(99,\cdot)\) \(\chi_{218}(103,\cdot)\) \(\chi_{218}(115,\cdot)\) \(\chi_{218}(119,\cdot)\) \(\chi_{218}(123,\cdot)\) \(\chi_{218}(127,\cdot)\) \(\chi_{218}(133,\cdot)\) \(\chi_{218}(139,\cdot)\) \(\chi_{218}(149,\cdot)\) \(\chi_{218}(151,\cdot)\) \(\chi_{218}(153,\cdot)\) \(\chi_{218}(159,\cdot)\) \(\chi_{218}(161,\cdot)\) \(\chi_{218}(165,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\(115\) → \(e\left(\frac{29}{108}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 218 }(207, a) \) | \(-1\) | \(1\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{19}{27}\right)\) |