Basic properties
Modulus: | \(349\) | |
Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(116\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 349.j
\(\chi_{349}(6,\cdot)\) \(\chi_{349}(8,\cdot)\) \(\chi_{349}(10,\cdot)\) \(\chi_{349}(11,\cdot)\) \(\chi_{349}(21,\cdot)\) \(\chi_{349}(28,\cdot)\) \(\chi_{349}(35,\cdot)\) \(\chi_{349}(38,\cdot)\) \(\chi_{349}(39,\cdot)\) \(\chi_{349}(47,\cdot)\) \(\chi_{349}(52,\cdot)\) \(\chi_{349}(53,\cdot)\) \(\chi_{349}(58,\cdot)\) \(\chi_{349}(61,\cdot)\) \(\chi_{349}(65,\cdot)\) \(\chi_{349}(79,\cdot)\) \(\chi_{349}(98,\cdot)\) \(\chi_{349}(101,\cdot)\) \(\chi_{349}(102,\cdot)\) \(\chi_{349}(103,\cdot)\) \(\chi_{349}(127,\cdot)\) \(\chi_{349}(131,\cdot)\) \(\chi_{349}(133,\cdot)\) \(\chi_{349}(146,\cdot)\) \(\chi_{349}(162,\cdot)\) \(\chi_{349}(163,\cdot)\) \(\chi_{349}(167,\cdot)\) \(\chi_{349}(170,\cdot)\) \(\chi_{349}(179,\cdot)\) \(\chi_{349}(182,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{116})$ |
Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{7}{116}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 349 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{116}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{21}{116}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{31}{116}\right)\) |