Basic properties
| Modulus: | \(6008\) | |
| Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(75\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{751}(637,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.bo
\(\chi_{6008}(121,\cdot)\) \(\chi_{6008}(273,\cdot)\) \(\chi_{6008}(881,\cdot)\) \(\chi_{6008}(945,\cdot)\) \(\chi_{6008}(1129,\cdot)\) \(\chi_{6008}(1609,\cdot)\) \(\chi_{6008}(1633,\cdot)\) \(\chi_{6008}(1665,\cdot)\) \(\chi_{6008}(1801,\cdot)\) \(\chi_{6008}(1809,\cdot)\) \(\chi_{6008}(1953,\cdot)\) \(\chi_{6008}(2145,\cdot)\) \(\chi_{6008}(2305,\cdot)\) \(\chi_{6008}(2433,\cdot)\) \(\chi_{6008}(2537,\cdot)\) \(\chi_{6008}(2625,\cdot)\) \(\chi_{6008}(2753,\cdot)\) \(\chi_{6008}(2761,\cdot)\) \(\chi_{6008}(2921,\cdot)\) \(\chi_{6008}(2993,\cdot)\) \(\chi_{6008}(3065,\cdot)\) \(\chi_{6008}(3201,\cdot)\) \(\chi_{6008}(3233,\cdot)\) \(\chi_{6008}(3409,\cdot)\) \(\chi_{6008}(3641,\cdot)\) \(\chi_{6008}(3721,\cdot)\) \(\chi_{6008}(3841,\cdot)\) \(\chi_{6008}(3945,\cdot)\) \(\chi_{6008}(4129,\cdot)\) \(\chi_{6008}(4377,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\((1503,3005,1505)\) → \((1,1,e\left(\frac{31}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(3641, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{75}\right)\) | \(e\left(\frac{16}{75}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{62}{75}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{73}{75}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{74}{75}\right)\) | \(e\left(\frac{58}{75}\right)\) | \(e\left(\frac{37}{75}\right)\) |