Basic properties
Modulus: | \(349\) | |
Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | 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.g
\(\chi_{349}(31,\cdot)\) \(\chi_{349}(41,\cdot)\) \(\chi_{349}(66,\cdot)\) \(\chi_{349}(67,\cdot)\) \(\chi_{349}(88,\cdot)\) \(\chi_{349}(110,\cdot)\) \(\chi_{349}(118,\cdot)\) \(\chi_{349}(126,\cdot)\) \(\chi_{349}(168,\cdot)\) \(\chi_{349}(171,\cdot)\) \(\chi_{349}(210,\cdot)\) \(\chi_{349}(224,\cdot)\) \(\chi_{349}(228,\cdot)\) \(\chi_{349}(234,\cdot)\) \(\chi_{349}(249,\cdot)\) \(\chi_{349}(257,\cdot)\) \(\chi_{349}(263,\cdot)\) \(\chi_{349}(269,\cdot)\) \(\chi_{349}(274,\cdot)\) \(\chi_{349}(280,\cdot)\) \(\chi_{349}(285,\cdot)\) \(\chi_{349}(289,\cdot)\) \(\chi_{349}(301,\cdot)\) \(\chi_{349}(304,\cdot)\) \(\chi_{349}(312,\cdot)\) \(\chi_{349}(313,\cdot)\) \(\chi_{349}(322,\cdot)\) \(\chi_{349}(332,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(2\) → \(e\left(\frac{27}{29}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 349 }(234, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) |