Basic properties
Modulus: | \(722\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{361}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 722.k
\(\chi_{722}(5,\cdot)\) \(\chi_{722}(9,\cdot)\) \(\chi_{722}(17,\cdot)\) \(\chi_{722}(23,\cdot)\) \(\chi_{722}(25,\cdot)\) \(\chi_{722}(35,\cdot)\) \(\chi_{722}(43,\cdot)\) \(\chi_{722}(47,\cdot)\) \(\chi_{722}(55,\cdot)\) \(\chi_{722}(61,\cdot)\) \(\chi_{722}(63,\cdot)\) \(\chi_{722}(73,\cdot)\) \(\chi_{722}(81,\cdot)\) \(\chi_{722}(85,\cdot)\) \(\chi_{722}(93,\cdot)\) \(\chi_{722}(101,\cdot)\) \(\chi_{722}(111,\cdot)\) \(\chi_{722}(119,\cdot)\) \(\chi_{722}(123,\cdot)\) \(\chi_{722}(131,\cdot)\) \(\chi_{722}(137,\cdot)\) \(\chi_{722}(139,\cdot)\) \(\chi_{722}(149,\cdot)\) \(\chi_{722}(157,\cdot)\) \(\chi_{722}(161,\cdot)\) \(\chi_{722}(169,\cdot)\) \(\chi_{722}(175,\cdot)\) \(\chi_{722}(177,\cdot)\) \(\chi_{722}(187,\cdot)\) \(\chi_{722}(195,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\(363\) → \(e\left(\frac{13}{171}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 722 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{171}\right)\) | \(e\left(\frac{109}{171}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{23}{171}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{35}{171}\right)\) | \(e\left(\frac{31}{171}\right)\) | \(e\left(\frac{166}{171}\right)\) | \(e\left(\frac{17}{171}\right)\) |