Basic properties
Modulus: | \(6042\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cn
\(\chi_{6042}(25,\cdot)\) \(\chi_{6042}(43,\cdot)\) \(\chi_{6042}(199,\cdot)\) \(\chi_{6042}(271,\cdot)\) \(\chi_{6042}(481,\cdot)\) \(\chi_{6042}(517,\cdot)\) \(\chi_{6042}(541,\cdot)\) \(\chi_{6042}(643,\cdot)\) \(\chi_{6042}(727,\cdot)\) \(\chi_{6042}(859,\cdot)\) \(\chi_{6042}(997,\cdot)\) \(\chi_{6042}(1069,\cdot)\) \(\chi_{6042}(1183,\cdot)\) \(\chi_{6042}(1195,\cdot)\) \(\chi_{6042}(1225,\cdot)\) \(\chi_{6042}(1279,\cdot)\) \(\chi_{6042}(1297,\cdot)\) \(\chi_{6042}(1309,\cdot)\) \(\chi_{6042}(1315,\cdot)\) \(\chi_{6042}(1543,\cdot)\) \(\chi_{6042}(1681,\cdot)\) \(\chi_{6042}(1753,\cdot)\) \(\chi_{6042}(1999,\cdot)\) \(\chi_{6042}(2023,\cdot)\) \(\chi_{6042}(2107,\cdot)\) \(\chi_{6042}(2137,\cdot)\) \(\chi_{6042}(2251,\cdot)\) \(\chi_{6042}(2341,\cdot)\) \(\chi_{6042}(2449,\cdot)\) \(\chi_{6042}(2455,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{7}{9}\right),e\left(\frac{21}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{95}{117}\right)\) | \(e\left(\frac{44}{117}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{89}{234}\right)\) |