Basic properties
Modulus: | \(349\) | |
Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 349.h
\(\chi_{349}(17,\cdot)\) \(\chi_{349}(27,\cdot)\) \(\chi_{349}(36,\cdot)\) \(\chi_{349}(37,\cdot)\) \(\chi_{349}(45,\cdot)\) \(\chi_{349}(48,\cdot)\) \(\chi_{349}(60,\cdot)\) \(\chi_{349}(64,\cdot)\) \(\chi_{349}(69,\cdot)\) \(\chi_{349}(75,\cdot)\) \(\chi_{349}(80,\cdot)\) \(\chi_{349}(86,\cdot)\) \(\chi_{349}(92,\cdot)\) \(\chi_{349}(100,\cdot)\) \(\chi_{349}(115,\cdot)\) \(\chi_{349}(121,\cdot)\) \(\chi_{349}(125,\cdot)\) \(\chi_{349}(139,\cdot)\) \(\chi_{349}(178,\cdot)\) \(\chi_{349}(181,\cdot)\) \(\chi_{349}(223,\cdot)\) \(\chi_{349}(231,\cdot)\) \(\chi_{349}(239,\cdot)\) \(\chi_{349}(261,\cdot)\) \(\chi_{349}(282,\cdot)\) \(\chi_{349}(283,\cdot)\) \(\chi_{349}(308,\cdot)\) \(\chi_{349}(318,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\(2\) → \(e\left(\frac{41}{58}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 349 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{49}{58}\right)\) |