Basic properties
Modulus: | \(4008\) | |
Conductor: | \(2004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2004}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.v
\(\chi_{4008}(23,\cdot)\) \(\chi_{4008}(71,\cdot)\) \(\chi_{4008}(95,\cdot)\) \(\chi_{4008}(119,\cdot)\) \(\chi_{4008}(143,\cdot)\) \(\chi_{4008}(287,\cdot)\) \(\chi_{4008}(407,\cdot)\) \(\chi_{4008}(479,\cdot)\) \(\chi_{4008}(527,\cdot)\) \(\chi_{4008}(575,\cdot)\) \(\chi_{4008}(647,\cdot)\) \(\chi_{4008}(719,\cdot)\) \(\chi_{4008}(791,\cdot)\) \(\chi_{4008}(887,\cdot)\) \(\chi_{4008}(983,\cdot)\) \(\chi_{4008}(1007,\cdot)\) \(\chi_{4008}(1055,\cdot)\) \(\chi_{4008}(1103,\cdot)\) \(\chi_{4008}(1127,\cdot)\) \(\chi_{4008}(1151,\cdot)\) \(\chi_{4008}(1199,\cdot)\) \(\chi_{4008}(1247,\cdot)\) \(\chi_{4008}(1271,\cdot)\) \(\chi_{4008}(1391,\cdot)\) \(\chi_{4008}(1415,\cdot)\) \(\chi_{4008}(1439,\cdot)\) \(\chi_{4008}(1487,\cdot)\) \(\chi_{4008}(1583,\cdot)\) \(\chi_{4008}(1607,\cdot)\) \(\chi_{4008}(1775,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((-1,1,-1,e\left(\frac{45}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{64}{83}\right)\) | \(e\left(\frac{81}{166}\right)\) | \(e\left(\frac{49}{83}\right)\) | \(e\left(\frac{153}{166}\right)\) | \(e\left(\frac{72}{83}\right)\) | \(e\left(\frac{37}{166}\right)\) | \(e\left(\frac{139}{166}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{27}{166}\right)\) | \(e\left(\frac{149}{166}\right)\) |