Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.ge
\(\chi_{8624}(81,\cdot)\) \(\chi_{8624}(289,\cdot)\) \(\chi_{8624}(401,\cdot)\) \(\chi_{8624}(625,\cdot)\) \(\chi_{8624}(641,\cdot)\) \(\chi_{8624}(977,\cdot)\) \(\chi_{8624}(1313,\cdot)\) \(\chi_{8624}(1521,\cdot)\) \(\chi_{8624}(1633,\cdot)\) \(\chi_{8624}(1857,\cdot)\) \(\chi_{8624}(1873,\cdot)\) \(\chi_{8624}(1985,\cdot)\) \(\chi_{8624}(2193,\cdot)\) \(\chi_{8624}(2209,\cdot)\) \(\chi_{8624}(2545,\cdot)\) \(\chi_{8624}(2753,\cdot)\) \(\chi_{8624}(2865,\cdot)\) \(\chi_{8624}(3089,\cdot)\) \(\chi_{8624}(3217,\cdot)\) \(\chi_{8624}(3425,\cdot)\) \(\chi_{8624}(3441,\cdot)\) \(\chi_{8624}(3777,\cdot)\) \(\chi_{8624}(3985,\cdot)\) \(\chi_{8624}(4321,\cdot)\) \(\chi_{8624}(4337,\cdot)\) \(\chi_{8624}(4449,\cdot)\) \(\chi_{8624}(4657,\cdot)\) \(\chi_{8624}(5009,\cdot)\) \(\chi_{8624}(5217,\cdot)\) \(\chi_{8624}(5329,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,1,e\left(\frac{10}{21}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(1633, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{1}{35}\right)\) |