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 \(\chi_{1336}(1237,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.s
\(\chi_{4008}(13,\cdot)\) \(\chi_{4008}(37,\cdot)\) \(\chi_{4008}(109,\cdot)\) \(\chi_{4008}(253,\cdot)\) \(\chi_{4008}(277,\cdot)\) \(\chi_{4008}(301,\cdot)\) \(\chi_{4008}(325,\cdot)\) \(\chi_{4008}(349,\cdot)\) \(\chi_{4008}(373,\cdot)\) \(\chi_{4008}(445,\cdot)\) \(\chi_{4008}(469,\cdot)\) \(\chi_{4008}(493,\cdot)\) \(\chi_{4008}(541,\cdot)\) \(\chi_{4008}(637,\cdot)\) \(\chi_{4008}(661,\cdot)\) \(\chi_{4008}(685,\cdot)\) \(\chi_{4008}(709,\cdot)\) \(\chi_{4008}(781,\cdot)\) \(\chi_{4008}(829,\cdot)\) \(\chi_{4008}(925,\cdot)\) \(\chi_{4008}(973,\cdot)\) \(\chi_{4008}(1045,\cdot)\) \(\chi_{4008}(1069,\cdot)\) \(\chi_{4008}(1093,\cdot)\) \(\chi_{4008}(1141,\cdot)\) \(\chi_{4008}(1165,\cdot)\) \(\chi_{4008}(1189,\cdot)\) \(\chi_{4008}(1237,\cdot)\) \(\chi_{4008}(1261,\cdot)\) \(\chi_{4008}(1309,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((1,-1,1,e\left(\frac{133}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(1237, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{155}{166}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{77}{166}\right)\) | \(e\left(\frac{161}{166}\right)\) | \(e\left(\frac{53}{166}\right)\) | \(e\left(\frac{50}{83}\right)\) | \(e\left(\frac{113}{166}\right)\) | \(e\left(\frac{9}{83}\right)\) |