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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.x
\(\chi_{4008}(11,\cdot)\) \(\chi_{4008}(107,\cdot)\) \(\chi_{4008}(179,\cdot)\) \(\chi_{4008}(203,\cdot)\) \(\chi_{4008}(251,\cdot)\) \(\chi_{4008}(275,\cdot)\) \(\chi_{4008}(299,\cdot)\) \(\chi_{4008}(395,\cdot)\) \(\chi_{4008}(419,\cdot)\) \(\chi_{4008}(467,\cdot)\) \(\chi_{4008}(491,\cdot)\) \(\chi_{4008}(515,\cdot)\) \(\chi_{4008}(539,\cdot)\) \(\chi_{4008}(563,\cdot)\) \(\chi_{4008}(731,\cdot)\) \(\chi_{4008}(755,\cdot)\) \(\chi_{4008}(851,\cdot)\) \(\chi_{4008}(899,\cdot)\) \(\chi_{4008}(923,\cdot)\) \(\chi_{4008}(947,\cdot)\) \(\chi_{4008}(1067,\cdot)\) \(\chi_{4008}(1091,\cdot)\) \(\chi_{4008}(1139,\cdot)\) \(\chi_{4008}(1187,\cdot)\) \(\chi_{4008}(1211,\cdot)\) \(\chi_{4008}(1235,\cdot)\) \(\chi_{4008}(1283,\cdot)\) \(\chi_{4008}(1331,\cdot)\) \(\chi_{4008}(1355,\cdot)\) \(\chi_{4008}(1451,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((-1,-1,-1,e\left(\frac{49}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4008 }(539, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{83}\right)\) | \(e\left(\frac{27}{166}\right)\) | \(e\left(\frac{5}{166}\right)\) | \(e\left(\frac{51}{166}\right)\) | \(e\left(\frac{131}{166}\right)\) | \(e\left(\frac{20}{83}\right)\) | \(e\left(\frac{37}{83}\right)\) | \(e\left(\frac{15}{83}\right)\) | \(e\left(\frac{46}{83}\right)\) | \(e\left(\frac{105}{166}\right)\) |