Basic properties
Modulus: | \(4008\) | |
Conductor: | \(501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{501}(428,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.ba
\(\chi_{4008}(65,\cdot)\) \(\chi_{4008}(89,\cdot)\) \(\chi_{4008}(137,\cdot)\) \(\chi_{4008}(185,\cdot)\) \(\chi_{4008}(209,\cdot)\) \(\chi_{4008}(233,\cdot)\) \(\chi_{4008}(281,\cdot)\) \(\chi_{4008}(329,\cdot)\) \(\chi_{4008}(353,\cdot)\) \(\chi_{4008}(449,\cdot)\) \(\chi_{4008}(545,\cdot)\) \(\chi_{4008}(617,\cdot)\) \(\chi_{4008}(689,\cdot)\) \(\chi_{4008}(761,\cdot)\) \(\chi_{4008}(809,\cdot)\) \(\chi_{4008}(857,\cdot)\) \(\chi_{4008}(929,\cdot)\) \(\chi_{4008}(1049,\cdot)\) \(\chi_{4008}(1193,\cdot)\) \(\chi_{4008}(1217,\cdot)\) \(\chi_{4008}(1241,\cdot)\) \(\chi_{4008}(1265,\cdot)\) \(\chi_{4008}(1313,\cdot)\) \(\chi_{4008}(1361,\cdot)\) \(\chi_{4008}(1385,\cdot)\) \(\chi_{4008}(1433,\cdot)\) \(\chi_{4008}(1457,\cdot)\) \(\chi_{4008}(1505,\cdot)\) \(\chi_{4008}(1553,\cdot)\) \(\chi_{4008}(1601,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((1,1,-1,e\left(\frac{3}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(929, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{166}\right)\) | \(e\left(\frac{22}{83}\right)\) | \(e\left(\frac{85}{166}\right)\) | \(e\left(\frac{60}{83}\right)\) | \(e\left(\frac{69}{166}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{153}{166}\right)\) | \(e\left(\frac{21}{83}\right)\) |