Basic properties
Modulus: | \(8027\) | |
Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{349}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8027.q
\(\chi_{8027}(415,\cdot)\) \(\chi_{8027}(967,\cdot)\) \(\chi_{8027}(1427,\cdot)\) \(\chi_{8027}(1979,\cdot)\) \(\chi_{8027}(2002,\cdot)\) \(\chi_{8027}(2025,\cdot)\) \(\chi_{8027}(2416,\cdot)\) \(\chi_{8027}(2531,\cdot)\) \(\chi_{8027}(2692,\cdot)\) \(\chi_{8027}(3267,\cdot)\) \(\chi_{8027}(3658,\cdot)\) \(\chi_{8027}(3957,\cdot)\) \(\chi_{8027}(4049,\cdot)\) \(\chi_{8027}(4578,\cdot)\) \(\chi_{8027}(4647,\cdot)\) \(\chi_{8027}(5199,\cdot)\) \(\chi_{8027}(5406,\cdot)\) \(\chi_{8027}(5498,\cdot)\) \(\chi_{8027}(5567,\cdot)\) \(\chi_{8027}(6234,\cdot)\) \(\chi_{8027}(6349,\cdot)\) \(\chi_{8027}(6510,\cdot)\) \(\chi_{8027}(6556,\cdot)\) \(\chi_{8027}(6855,\cdot)\) \(\chi_{8027}(7269,\cdot)\) \(\chi_{8027}(7292,\cdot)\) \(\chi_{8027}(7614,\cdot)\) \(\chi_{8027}(7982,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\((350,5935)\) → \((1,e\left(\frac{23}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(6349, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) |