Basic properties
Modulus: | \(8027\) | |
Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(87\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{349}(20,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8027.ba
\(\chi_{8027}(116,\cdot)\) \(\chi_{8027}(185,\cdot)\) \(\chi_{8027}(254,\cdot)\) \(\chi_{8027}(300,\cdot)\) \(\chi_{8027}(346,\cdot)\) \(\chi_{8027}(369,\cdot)\) \(\chi_{8027}(484,\cdot)\) \(\chi_{8027}(507,\cdot)\) \(\chi_{8027}(622,\cdot)\) \(\chi_{8027}(714,\cdot)\) \(\chi_{8027}(783,\cdot)\) \(\chi_{8027}(806,\cdot)\) \(\chi_{8027}(990,\cdot)\) \(\chi_{8027}(1059,\cdot)\) \(\chi_{8027}(1128,\cdot)\) \(\chi_{8027}(1243,\cdot)\) \(\chi_{8027}(1266,\cdot)\) \(\chi_{8027}(1473,\cdot)\) \(\chi_{8027}(1588,\cdot)\) \(\chi_{8027}(1703,\cdot)\) \(\chi_{8027}(2117,\cdot)\) \(\chi_{8027}(2301,\cdot)\) \(\chi_{8027}(2370,\cdot)\) \(\chi_{8027}(2439,\cdot)\) \(\chi_{8027}(2462,\cdot)\) \(\chi_{8027}(2554,\cdot)\) \(\chi_{8027}(2623,\cdot)\) \(\chi_{8027}(2807,\cdot)\) \(\chi_{8027}(3037,\cdot)\) \(\chi_{8027}(3635,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{87})$ |
Fixed field: | Number field defined by a degree 87 polynomial |
Values on generators
\((350,5935)\) → \((1,e\left(\frac{79}{87}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(369, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{87}\right)\) | \(e\left(\frac{53}{87}\right)\) | \(e\left(\frac{71}{87}\right)\) | \(e\left(\frac{11}{87}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{73}{87}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{19}{87}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) |