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 \(\chi_{2004}(767,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.bc
\(\chi_{4008}(47,\cdot)\) \(\chi_{4008}(191,\cdot)\) \(\chi_{4008}(215,\cdot)\) \(\chi_{4008}(239,\cdot)\) \(\chi_{4008}(263,\cdot)\) \(\chi_{4008}(311,\cdot)\) \(\chi_{4008}(359,\cdot)\) \(\chi_{4008}(383,\cdot)\) \(\chi_{4008}(431,\cdot)\) \(\chi_{4008}(455,\cdot)\) \(\chi_{4008}(503,\cdot)\) \(\chi_{4008}(551,\cdot)\) \(\chi_{4008}(599,\cdot)\) \(\chi_{4008}(623,\cdot)\) \(\chi_{4008}(671,\cdot)\) \(\chi_{4008}(695,\cdot)\) \(\chi_{4008}(743,\cdot)\) \(\chi_{4008}(767,\cdot)\) \(\chi_{4008}(815,\cdot)\) \(\chi_{4008}(839,\cdot)\) \(\chi_{4008}(863,\cdot)\) \(\chi_{4008}(911,\cdot)\) \(\chi_{4008}(935,\cdot)\) \(\chi_{4008}(959,\cdot)\) \(\chi_{4008}(1031,\cdot)\) \(\chi_{4008}(1079,\cdot)\) \(\chi_{4008}(1175,\cdot)\) \(\chi_{4008}(1223,\cdot)\) \(\chi_{4008}(1295,\cdot)\) \(\chi_{4008}(1319,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((-1,1,-1,e\left(\frac{25}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(767, a) \) | \(1\) | \(1\) | \(e\left(\frac{133}{166}\right)\) | \(e\left(\frac{7}{166}\right)\) | \(e\left(\frac{36}{83}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{77}{166}\right)\) | \(e\left(\frac{161}{166}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{50}{83}\right)\) | \(e\left(\frac{113}{166}\right)\) | \(e\left(\frac{101}{166}\right)\) |