Basic properties
Modulus: | \(4008\) | |
Conductor: | \(668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{668}(583,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.bf
\(\chi_{4008}(55,\cdot)\) \(\chi_{4008}(79,\cdot)\) \(\chi_{4008}(103,\cdot)\) \(\chi_{4008}(151,\cdot)\) \(\chi_{4008}(247,\cdot)\) \(\chi_{4008}(271,\cdot)\) \(\chi_{4008}(439,\cdot)\) \(\chi_{4008}(463,\cdot)\) \(\chi_{4008}(487,\cdot)\) \(\chi_{4008}(511,\cdot)\) \(\chi_{4008}(535,\cdot)\) \(\chi_{4008}(583,\cdot)\) \(\chi_{4008}(607,\cdot)\) \(\chi_{4008}(703,\cdot)\) \(\chi_{4008}(727,\cdot)\) \(\chi_{4008}(751,\cdot)\) \(\chi_{4008}(799,\cdot)\) \(\chi_{4008}(823,\cdot)\) \(\chi_{4008}(895,\cdot)\) \(\chi_{4008}(991,\cdot)\) \(\chi_{4008}(1015,\cdot)\) \(\chi_{4008}(1039,\cdot)\) \(\chi_{4008}(1111,\cdot)\) \(\chi_{4008}(1255,\cdot)\) \(\chi_{4008}(1279,\cdot)\) \(\chi_{4008}(1303,\cdot)\) \(\chi_{4008}(1327,\cdot)\) \(\chi_{4008}(1351,\cdot)\) \(\chi_{4008}(1375,\cdot)\) \(\chi_{4008}(1447,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((-1,1,1,e\left(\frac{137}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(583, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{166}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{101}{166}\right)\) | \(e\left(\frac{1}{166}\right)\) | \(e\left(\frac{123}{166}\right)\) | \(e\left(\frac{61}{166}\right)\) | \(e\left(\frac{17}{83}\right)\) | \(e\left(\frac{54}{83}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{129}{166}\right)\) |