Basic properties
Modulus: | \(8027\) | |
Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{349}(92,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8027.v
\(\chi_{8027}(139,\cdot)\) \(\chi_{8027}(231,\cdot)\) \(\chi_{8027}(530,\cdot)\) \(\chi_{8027}(921,\cdot)\) \(\chi_{8027}(1496,\cdot)\) \(\chi_{8027}(1657,\cdot)\) \(\chi_{8027}(1772,\cdot)\) \(\chi_{8027}(2163,\cdot)\) \(\chi_{8027}(2186,\cdot)\) \(\chi_{8027}(2209,\cdot)\) \(\chi_{8027}(2761,\cdot)\) \(\chi_{8027}(3221,\cdot)\) \(\chi_{8027}(3773,\cdot)\) \(\chi_{8027}(4233,\cdot)\) \(\chi_{8027}(4601,\cdot)\) \(\chi_{8027}(4923,\cdot)\) \(\chi_{8027}(4946,\cdot)\) \(\chi_{8027}(5360,\cdot)\) \(\chi_{8027}(5659,\cdot)\) \(\chi_{8027}(5705,\cdot)\) \(\chi_{8027}(5866,\cdot)\) \(\chi_{8027}(5981,\cdot)\) \(\chi_{8027}(6648,\cdot)\) \(\chi_{8027}(6717,\cdot)\) \(\chi_{8027}(6809,\cdot)\) \(\chi_{8027}(7016,\cdot)\) \(\chi_{8027}(7568,\cdot)\) \(\chi_{8027}(7637,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((350,5935)\) → \((1,e\left(\frac{31}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(2186, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{58}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{13}{58}\right)\) |