Basic properties
Modulus: | \(283\) | |
Conductor: | \(283\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(141\) | 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 283.g
\(\chi_{283}(6,\cdot)\) \(\chi_{283}(7,\cdot)\) \(\chi_{283}(9,\cdot)\) \(\chi_{283}(10,\cdot)\) \(\chi_{283}(11,\cdot)\) \(\chi_{283}(13,\cdot)\) \(\chi_{283}(23,\cdot)\) \(\chi_{283}(24,\cdot)\) \(\chi_{283}(25,\cdot)\) \(\chi_{283}(28,\cdot)\) \(\chi_{283}(34,\cdot)\) \(\chi_{283}(36,\cdot)\) \(\chi_{283}(40,\cdot)\) \(\chi_{283}(41,\cdot)\) \(\chi_{283}(49,\cdot)\) \(\chi_{283}(52,\cdot)\) \(\chi_{283}(57,\cdot)\) \(\chi_{283}(59,\cdot)\) \(\chi_{283}(62,\cdot)\) \(\chi_{283}(63,\cdot)\) \(\chi_{283}(70,\cdot)\) \(\chi_{283}(73,\cdot)\) \(\chi_{283}(74,\cdot)\) \(\chi_{283}(77,\cdot)\) \(\chi_{283}(81,\cdot)\) \(\chi_{283}(83,\cdot)\) \(\chi_{283}(85,\cdot)\) \(\chi_{283}(89,\cdot)\) \(\chi_{283}(90,\cdot)\) \(\chi_{283}(91,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{141})$ |
Fixed field: | Number field defined by a degree 141 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{50}{141}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 283 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{47}\right)\) | \(e\left(\frac{50}{141}\right)\) | \(e\left(\frac{36}{47}\right)\) | \(e\left(\frac{88}{141}\right)\) | \(e\left(\frac{104}{141}\right)\) | \(e\left(\frac{82}{141}\right)\) | \(e\left(\frac{7}{47}\right)\) | \(e\left(\frac{100}{141}\right)\) | \(e\left(\frac{1}{141}\right)\) | \(e\left(\frac{127}{141}\right)\) |