Basic properties
Modulus: | \(334\) | |
Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{167}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 334.c
\(\chi_{334}(3,\cdot)\) \(\chi_{334}(7,\cdot)\) \(\chi_{334}(9,\cdot)\) \(\chi_{334}(11,\cdot)\) \(\chi_{334}(19,\cdot)\) \(\chi_{334}(21,\cdot)\) \(\chi_{334}(25,\cdot)\) \(\chi_{334}(27,\cdot)\) \(\chi_{334}(29,\cdot)\) \(\chi_{334}(31,\cdot)\) \(\chi_{334}(33,\cdot)\) \(\chi_{334}(47,\cdot)\) \(\chi_{334}(49,\cdot)\) \(\chi_{334}(57,\cdot)\) \(\chi_{334}(61,\cdot)\) \(\chi_{334}(63,\cdot)\) \(\chi_{334}(65,\cdot)\) \(\chi_{334}(75,\cdot)\) \(\chi_{334}(77,\cdot)\) \(\chi_{334}(81,\cdot)\) \(\chi_{334}(85,\cdot)\) \(\chi_{334}(87,\cdot)\) \(\chi_{334}(89,\cdot)\) \(\chi_{334}(93,\cdot)\) \(\chi_{334}(97,\cdot)\) \(\chi_{334}(99,\cdot)\) \(\chi_{334}(107,\cdot)\) \(\chi_{334}(115,\cdot)\) \(\chi_{334}(121,\cdot)\) \(\chi_{334}(127,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\(5\) → \(e\left(\frac{47}{83}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 334 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{83}\right)\) | \(e\left(\frac{47}{83}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{38}{83}\right)\) | \(e\left(\frac{71}{83}\right)\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{4}{83}\right)\) |