Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.bo
\(\chi_{8024}(137,\cdot)\) \(\chi_{8024}(953,\cdot)\) \(\chi_{8024}(1089,\cdot)\) \(\chi_{8024}(1225,\cdot)\) \(\chi_{8024}(1361,\cdot)\) \(\chi_{8024}(1497,\cdot)\) \(\chi_{8024}(1905,\cdot)\) \(\chi_{8024}(2041,\cdot)\) \(\chi_{8024}(2177,\cdot)\) \(\chi_{8024}(2313,\cdot)\) \(\chi_{8024}(2585,\cdot)\) \(\chi_{8024}(2721,\cdot)\) \(\chi_{8024}(2857,\cdot)\) \(\chi_{8024}(3265,\cdot)\) \(\chi_{8024}(3673,\cdot)\) \(\chi_{8024}(3945,\cdot)\) \(\chi_{8024}(4217,\cdot)\) \(\chi_{8024}(4353,\cdot)\) \(\chi_{8024}(4489,\cdot)\) \(\chi_{8024}(4761,\cdot)\) \(\chi_{8024}(5169,\cdot)\) \(\chi_{8024}(5713,\cdot)\) \(\chi_{8024}(5985,\cdot)\) \(\chi_{8024}(6257,\cdot)\) \(\chi_{8024}(6393,\cdot)\) \(\chi_{8024}(6665,\cdot)\) \(\chi_{8024}(6801,\cdot)\) \(\chi_{8024}(7345,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\((2007,4013,3777,3129)\) → \((1,1,1,e\left(\frac{19}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) |