Basic properties
Modulus: | \(7448\) | |
Conductor: | \(7448\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7448.jh
\(\chi_{7448}(51,\cdot)\) \(\chi_{7448}(219,\cdot)\) \(\chi_{7448}(515,\cdot)\) \(\chi_{7448}(907,\cdot)\) \(\chi_{7448}(1003,\cdot)\) \(\chi_{7448}(1115,\cdot)\) \(\chi_{7448}(1283,\cdot)\) \(\chi_{7448}(1523,\cdot)\) \(\chi_{7448}(1579,\cdot)\) \(\chi_{7448}(1971,\cdot)\) \(\chi_{7448}(2067,\cdot)\) \(\chi_{7448}(2179,\cdot)\) \(\chi_{7448}(2347,\cdot)\) \(\chi_{7448}(2587,\cdot)\) \(\chi_{7448}(2643,\cdot)\) \(\chi_{7448}(3035,\cdot)\) \(\chi_{7448}(3131,\cdot)\) \(\chi_{7448}(3243,\cdot)\) \(\chi_{7448}(3651,\cdot)\) \(\chi_{7448}(3707,\cdot)\) \(\chi_{7448}(4099,\cdot)\) \(\chi_{7448}(4307,\cdot)\) \(\chi_{7448}(4475,\cdot)\) \(\chi_{7448}(4715,\cdot)\) \(\chi_{7448}(5259,\cdot)\) \(\chi_{7448}(5539,\cdot)\) \(\chi_{7448}(5779,\cdot)\) \(\chi_{7448}(5835,\cdot)\) \(\chi_{7448}(6227,\cdot)\) \(\chi_{7448}(6323,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((-1,-1,e\left(\frac{13}{21}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 7448 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) |