Basic properties
Modulus: | \(167\) | |
Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 167.d
\(\chi_{167}(5,\cdot)\) \(\chi_{167}(10,\cdot)\) \(\chi_{167}(13,\cdot)\) \(\chi_{167}(15,\cdot)\) \(\chi_{167}(17,\cdot)\) \(\chi_{167}(20,\cdot)\) \(\chi_{167}(23,\cdot)\) \(\chi_{167}(26,\cdot)\) \(\chi_{167}(30,\cdot)\) \(\chi_{167}(34,\cdot)\) \(\chi_{167}(35,\cdot)\) \(\chi_{167}(37,\cdot)\) \(\chi_{167}(39,\cdot)\) \(\chi_{167}(40,\cdot)\) \(\chi_{167}(41,\cdot)\) \(\chi_{167}(43,\cdot)\) \(\chi_{167}(45,\cdot)\) \(\chi_{167}(46,\cdot)\) \(\chi_{167}(51,\cdot)\) \(\chi_{167}(52,\cdot)\) \(\chi_{167}(53,\cdot)\) \(\chi_{167}(55,\cdot)\) \(\chi_{167}(59,\cdot)\) \(\chi_{167}(60,\cdot)\) \(\chi_{167}(67,\cdot)\) \(\chi_{167}(68,\cdot)\) \(\chi_{167}(69,\cdot)\) \(\chi_{167}(70,\cdot)\) \(\chi_{167}(71,\cdot)\) \(\chi_{167}(73,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{71}{166}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 167 }(78, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{83}\right)\) | \(e\left(\frac{17}{83}\right)\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{71}{166}\right)\) | \(e\left(\frac{26}{83}\right)\) | \(e\left(\frac{39}{83}\right)\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{34}{83}\right)\) | \(e\left(\frac{89}{166}\right)\) | \(e\left(\frac{81}{83}\right)\) |