Basic properties
Modulus: | \(4008\) | |
Conductor: | \(668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{668}(275,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.w
\(\chi_{4008}(7,\cdot)\) \(\chi_{4008}(31,\cdot)\) \(\chi_{4008}(127,\cdot)\) \(\chi_{4008}(175,\cdot)\) \(\chi_{4008}(199,\cdot)\) \(\chi_{4008}(223,\cdot)\) \(\chi_{4008}(295,\cdot)\) \(\chi_{4008}(319,\cdot)\) \(\chi_{4008}(343,\cdot)\) \(\chi_{4008}(367,\cdot)\) \(\chi_{4008}(391,\cdot)\) \(\chi_{4008}(415,\cdot)\) \(\chi_{4008}(559,\cdot)\) \(\chi_{4008}(631,\cdot)\) \(\chi_{4008}(655,\cdot)\) \(\chi_{4008}(679,\cdot)\) \(\chi_{4008}(775,\cdot)\) \(\chi_{4008}(847,\cdot)\) \(\chi_{4008}(871,\cdot)\) \(\chi_{4008}(919,\cdot)\) \(\chi_{4008}(943,\cdot)\) \(\chi_{4008}(967,\cdot)\) \(\chi_{4008}(1063,\cdot)\) \(\chi_{4008}(1087,\cdot)\) \(\chi_{4008}(1135,\cdot)\) \(\chi_{4008}(1159,\cdot)\) \(\chi_{4008}(1183,\cdot)\) \(\chi_{4008}(1207,\cdot)\) \(\chi_{4008}(1231,\cdot)\) \(\chi_{4008}(1399,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((-1,1,1,e\left(\frac{15}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(943, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{83}\right)\) | \(e\left(\frac{137}{166}\right)\) | \(e\left(\frac{93}{166}\right)\) | \(e\left(\frac{51}{83}\right)\) | \(e\left(\frac{48}{83}\right)\) | \(e\left(\frac{163}{166}\right)\) | \(e\left(\frac{65}{166}\right)\) | \(e\left(\frac{30}{83}\right)\) | \(e\left(\frac{9}{83}\right)\) | \(e\left(\frac{127}{166}\right)\) |