Basic properties
Modulus: | \(349\) | |
Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(174\) | 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.k
\(\chi_{349}(3,\cdot)\) \(\chi_{349}(4,\cdot)\) \(\chi_{349}(5,\cdot)\) \(\chi_{349}(22,\cdot)\) \(\chi_{349}(29,\cdot)\) \(\chi_{349}(42,\cdot)\) \(\chi_{349}(49,\cdot)\) \(\chi_{349}(56,\cdot)\) \(\chi_{349}(57,\cdot)\) \(\chi_{349}(70,\cdot)\) \(\chi_{349}(73,\cdot)\) \(\chi_{349}(76,\cdot)\) \(\chi_{349}(78,\cdot)\) \(\chi_{349}(83,\cdot)\) \(\chi_{349}(91,\cdot)\) \(\chi_{349}(93,\cdot)\) \(\chi_{349}(95,\cdot)\) \(\chi_{349}(104,\cdot)\) \(\chi_{349}(109,\cdot)\) \(\chi_{349}(124,\cdot)\) \(\chi_{349}(130,\cdot)\) \(\chi_{349}(142,\cdot)\) \(\chi_{349}(153,\cdot)\) \(\chi_{349}(155,\cdot)\) \(\chi_{349}(157,\cdot)\) \(\chi_{349}(164,\cdot)\) \(\chi_{349}(169,\cdot)\) \(\chi_{349}(191,\cdot)\) \(\chi_{349}(198,\cdot)\) \(\chi_{349}(201,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{87})$ |
Fixed field: | Number field defined by a degree 174 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{97}{174}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 349 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{174}\right)\) | \(e\left(\frac{43}{87}\right)\) | \(e\left(\frac{10}{87}\right)\) | \(e\left(\frac{4}{87}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{61}{174}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{86}{87}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{41}{58}\right)\) |