Basic properties
Modulus: | \(6042\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cr
\(\chi_{6042}(55,\cdot)\) \(\chi_{6042}(61,\cdot)\) \(\chi_{6042}(73,\cdot)\) \(\chi_{6042}(85,\cdot)\) \(\chi_{6042}(139,\cdot)\) \(\chi_{6042}(157,\cdot)\) \(\chi_{6042}(253,\cdot)\) \(\chi_{6042}(283,\cdot)\) \(\chi_{6042}(313,\cdot)\) \(\chi_{6042}(385,\cdot)\) \(\chi_{6042}(397,\cdot)\) \(\chi_{6042}(403,\cdot)\) \(\chi_{6042}(427,\cdot)\) \(\chi_{6042}(499,\cdot)\) \(\chi_{6042}(511,\cdot)\) \(\chi_{6042}(595,\cdot)\) \(\chi_{6042}(631,\cdot)\) \(\chi_{6042}(655,\cdot)\) \(\chi_{6042}(709,\cdot)\) \(\chi_{6042}(739,\cdot)\) \(\chi_{6042}(745,\cdot)\) \(\chi_{6042}(769,\cdot)\) \(\chi_{6042}(853,\cdot)\) \(\chi_{6042}(883,\cdot)\) \(\chi_{6042}(973,\cdot)\) \(\chi_{6042}(985,\cdot)\) \(\chi_{6042}(1081,\cdot)\) \(\chi_{6042}(1087,\cdot)\) \(\chi_{6042}(1099,\cdot)\) \(\chi_{6042}(1111,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{468})$ |
Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{1}{9}\right),e\left(\frac{3}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{451}{468}\right)\) |