Basic properties
| Modulus: | \(6008\) | |
| Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(750\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{751}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.cl
\(\chi_{6008}(17,\cdot)\) \(\chi_{6008}(57,\cdot)\) \(\chi_{6008}(113,\cdot)\) \(\chi_{6008}(145,\cdot)\) \(\chi_{6008}(153,\cdot)\) \(\chi_{6008}(161,\cdot)\) \(\chi_{6008}(177,\cdot)\) \(\chi_{6008}(209,\cdot)\) \(\chi_{6008}(257,\cdot)\) \(\chi_{6008}(281,\cdot)\) \(\chi_{6008}(313,\cdot)\) \(\chi_{6008}(329,\cdot)\) \(\chi_{6008}(353,\cdot)\) \(\chi_{6008}(369,\cdot)\) \(\chi_{6008}(393,\cdot)\) \(\chi_{6008}(409,\cdot)\) \(\chi_{6008}(425,\cdot)\) \(\chi_{6008}(449,\cdot)\) \(\chi_{6008}(473,\cdot)\) \(\chi_{6008}(513,\cdot)\) \(\chi_{6008}(521,\cdot)\) \(\chi_{6008}(537,\cdot)\) \(\chi_{6008}(577,\cdot)\) \(\chi_{6008}(609,\cdot)\) \(\chi_{6008}(649,\cdot)\) \(\chi_{6008}(833,\cdot)\) \(\chi_{6008}(889,\cdot)\) \(\chi_{6008}(921,\cdot)\) \(\chi_{6008}(953,\cdot)\) \(\chi_{6008}(1025,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((1,1,e\left(\frac{269}{750}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{269}{750}\right)\) | \(e\left(\frac{367}{375}\right)\) | \(e\left(\frac{123}{250}\right)\) | \(e\left(\frac{269}{375}\right)\) | \(e\left(\frac{67}{150}\right)\) | \(e\left(\frac{76}{375}\right)\) | \(e\left(\frac{253}{750}\right)\) | \(e\left(\frac{1}{750}\right)\) | \(e\left(\frac{46}{375}\right)\) | \(e\left(\frac{319}{375}\right)\) |