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.im
\(\chi_{7448}(13,\cdot)\) \(\chi_{7448}(181,\cdot)\) \(\chi_{7448}(573,\cdot)\) \(\chi_{7448}(629,\cdot)\) \(\chi_{7448}(965,\cdot)\) \(\chi_{7448}(1021,\cdot)\) \(\chi_{7448}(1245,\cdot)\) \(\chi_{7448}(1637,\cdot)\) \(\chi_{7448}(1693,\cdot)\) \(\chi_{7448}(2029,\cdot)\) \(\chi_{7448}(2085,\cdot)\) \(\chi_{7448}(2141,\cdot)\) \(\chi_{7448}(2309,\cdot)\) \(\chi_{7448}(2701,\cdot)\) \(\chi_{7448}(2757,\cdot)\) \(\chi_{7448}(3093,\cdot)\) \(\chi_{7448}(3149,\cdot)\) \(\chi_{7448}(3205,\cdot)\) \(\chi_{7448}(3373,\cdot)\) \(\chi_{7448}(3765,\cdot)\) \(\chi_{7448}(4157,\cdot)\) \(\chi_{7448}(4269,\cdot)\) \(\chi_{7448}(4437,\cdot)\) \(\chi_{7448}(4829,\cdot)\) \(\chi_{7448}(4885,\cdot)\) \(\chi_{7448}(5221,\cdot)\) \(\chi_{7448}(5277,\cdot)\) \(\chi_{7448}(5333,\cdot)\) \(\chi_{7448}(5501,\cdot)\) \(\chi_{7448}(5893,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((1,-1,e\left(\frac{11}{14}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 7448 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) |