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.r
\(\chi_{4008}(29,\cdot)\) \(\chi_{4008}(77,\cdot)\) \(\chi_{4008}(173,\cdot)\) \(\chi_{4008}(221,\cdot)\) \(\chi_{4008}(293,\cdot)\) \(\chi_{4008}(317,\cdot)\) \(\chi_{4008}(341,\cdot)\) \(\chi_{4008}(365,\cdot)\) \(\chi_{4008}(461,\cdot)\) \(\chi_{4008}(509,\cdot)\) \(\chi_{4008}(533,\cdot)\) \(\chi_{4008}(557,\cdot)\) \(\chi_{4008}(629,\cdot)\) \(\chi_{4008}(653,\cdot)\) \(\chi_{4008}(677,\cdot)\) \(\chi_{4008}(701,\cdot)\) \(\chi_{4008}(725,\cdot)\) \(\chi_{4008}(749,\cdot)\) \(\chi_{4008}(893,\cdot)\) \(\chi_{4008}(965,\cdot)\) \(\chi_{4008}(989,\cdot)\) \(\chi_{4008}(1013,\cdot)\) \(\chi_{4008}(1109,\cdot)\) \(\chi_{4008}(1181,\cdot)\) \(\chi_{4008}(1205,\cdot)\) \(\chi_{4008}(1253,\cdot)\) \(\chi_{4008}(1277,\cdot)\) \(\chi_{4008}(1301,\cdot)\) \(\chi_{4008}(1397,\cdot)\) \(\chi_{4008}(1421,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((1,-1,-1,e\left(\frac{27}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4008 }(1421, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{32}{83}\right)\) | \(e\left(\frac{9}{83}\right)\) | \(e\left(\frac{1}{166}\right)\) | \(e\left(\frac{123}{166}\right)\) | \(e\left(\frac{61}{166}\right)\) | \(e\left(\frac{117}{166}\right)\) | \(e\left(\frac{54}{83}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{23}{83}\right)\) |