Basic properties
| Modulus: | \(4008\) | |
| Conductor: | \(4008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.be
\(\chi_{4008}(35,\cdot)\) \(\chi_{4008}(59,\cdot)\) \(\chi_{4008}(83,\cdot)\) \(\chi_{4008}(131,\cdot)\) \(\chi_{4008}(155,\cdot)\) \(\chi_{4008}(227,\cdot)\) \(\chi_{4008}(323,\cdot)\) \(\chi_{4008}(347,\cdot)\) \(\chi_{4008}(371,\cdot)\) \(\chi_{4008}(443,\cdot)\) \(\chi_{4008}(587,\cdot)\) \(\chi_{4008}(611,\cdot)\) \(\chi_{4008}(635,\cdot)\) \(\chi_{4008}(659,\cdot)\) \(\chi_{4008}(683,\cdot)\) \(\chi_{4008}(707,\cdot)\) \(\chi_{4008}(779,\cdot)\) \(\chi_{4008}(803,\cdot)\) \(\chi_{4008}(827,\cdot)\) \(\chi_{4008}(875,\cdot)\) \(\chi_{4008}(971,\cdot)\) \(\chi_{4008}(995,\cdot)\) \(\chi_{4008}(1019,\cdot)\) \(\chi_{4008}(1043,\cdot)\) \(\chi_{4008}(1115,\cdot)\) \(\chi_{4008}(1163,\cdot)\) \(\chi_{4008}(1259,\cdot)\) \(\chi_{4008}(1307,\cdot)\) \(\chi_{4008}(1379,\cdot)\) \(\chi_{4008}(1403,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((-1,-1,-1,e\left(\frac{35}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4008 }(995, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{166}\right)\) | \(e\left(\frac{63}{166}\right)\) | \(e\left(\frac{67}{166}\right)\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{56}{83}\right)\) | \(e\left(\frac{19}{83}\right)\) | \(e\left(\frac{145}{166}\right)\) | \(e\left(\frac{35}{83}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{79}{166}\right)\) |