Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(472\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{472}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.bu
\(\chi_{8024}(35,\cdot)\) \(\chi_{8024}(171,\cdot)\) \(\chi_{8024}(307,\cdot)\) \(\chi_{8024}(579,\cdot)\) \(\chi_{8024}(715,\cdot)\) \(\chi_{8024}(851,\cdot)\) \(\chi_{8024}(1259,\cdot)\) \(\chi_{8024}(1667,\cdot)\) \(\chi_{8024}(1939,\cdot)\) \(\chi_{8024}(2211,\cdot)\) \(\chi_{8024}(2347,\cdot)\) \(\chi_{8024}(2483,\cdot)\) \(\chi_{8024}(2755,\cdot)\) \(\chi_{8024}(3163,\cdot)\) \(\chi_{8024}(3707,\cdot)\) \(\chi_{8024}(3979,\cdot)\) \(\chi_{8024}(4251,\cdot)\) \(\chi_{8024}(4387,\cdot)\) \(\chi_{8024}(4659,\cdot)\) \(\chi_{8024}(4795,\cdot)\) \(\chi_{8024}(5339,\cdot)\) \(\chi_{8024}(6155,\cdot)\) \(\chi_{8024}(6971,\cdot)\) \(\chi_{8024}(7107,\cdot)\) \(\chi_{8024}(7243,\cdot)\) \(\chi_{8024}(7379,\cdot)\) \(\chi_{8024}(7515,\cdot)\) \(\chi_{8024}(7923,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,-1,1,e\left(\frac{12}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{41}{58}\right)\) |