Basic properties
Modulus: | \(4008\) | |
Conductor: | \(1336\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1336}(571,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.u
\(\chi_{4008}(43,\cdot)\) \(\chi_{4008}(67,\cdot)\) \(\chi_{4008}(91,\cdot)\) \(\chi_{4008}(139,\cdot)\) \(\chi_{4008}(163,\cdot)\) \(\chi_{4008}(187,\cdot)\) \(\chi_{4008}(235,\cdot)\) \(\chi_{4008}(259,\cdot)\) \(\chi_{4008}(307,\cdot)\) \(\chi_{4008}(331,\cdot)\) \(\chi_{4008}(379,\cdot)\) \(\chi_{4008}(403,\cdot)\) \(\chi_{4008}(451,\cdot)\) \(\chi_{4008}(499,\cdot)\) \(\chi_{4008}(547,\cdot)\) \(\chi_{4008}(571,\cdot)\) \(\chi_{4008}(619,\cdot)\) \(\chi_{4008}(643,\cdot)\) \(\chi_{4008}(691,\cdot)\) \(\chi_{4008}(739,\cdot)\) \(\chi_{4008}(763,\cdot)\) \(\chi_{4008}(787,\cdot)\) \(\chi_{4008}(811,\cdot)\) \(\chi_{4008}(955,\cdot)\) \(\chi_{4008}(1075,\cdot)\) \(\chi_{4008}(1147,\cdot)\) \(\chi_{4008}(1195,\cdot)\) \(\chi_{4008}(1243,\cdot)\) \(\chi_{4008}(1315,\cdot)\) \(\chi_{4008}(1387,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((-1,-1,1,e\left(\frac{159}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(571, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{83}\right)\) | \(e\left(\frac{87}{166}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{13}{83}\right)\) | \(e\left(\frac{127}{166}\right)\) | \(e\left(\frac{46}{83}\right)\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{29}{166}\right)\) | \(e\left(\frac{117}{166}\right)\) |