Basic properties
Modulus: | \(24704\) | |
Conductor: | \(24704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(192\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.sy
\(\chi_{24704}(19,\cdot)\) \(\chi_{24704}(875,\cdot)\) \(\chi_{24704}(883,\cdot)\) \(\chi_{24704}(1203,\cdot)\) \(\chi_{24704}(1299,\cdot)\) \(\chi_{24704}(1851,\cdot)\) \(\chi_{24704}(2779,\cdot)\) \(\chi_{24704}(4395,\cdot)\) \(\chi_{24704}(4579,\cdot)\) \(\chi_{24704}(4683,\cdot)\) \(\chi_{24704}(4747,\cdot)\) \(\chi_{24704}(5539,\cdot)\) \(\chi_{24704}(5619,\cdot)\) \(\chi_{24704}(5627,\cdot)\) \(\chi_{24704}(5699,\cdot)\) \(\chi_{24704}(6035,\cdot)\) \(\chi_{24704}(6715,\cdot)\) \(\chi_{24704}(6835,\cdot)\) \(\chi_{24704}(6907,\cdot)\) \(\chi_{24704}(7315,\cdot)\) \(\chi_{24704}(7643,\cdot)\) \(\chi_{24704}(7683,\cdot)\) \(\chi_{24704}(7971,\cdot)\) \(\chi_{24704}(8931,\cdot)\) \(\chi_{24704}(9419,\cdot)\) \(\chi_{24704}(10051,\cdot)\) \(\chi_{24704}(10195,\cdot)\) \(\chi_{24704}(11523,\cdot)\) \(\chi_{24704}(12203,\cdot)\) \(\chi_{24704}(12555,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((24319,773,23937)\) → \((-1,e\left(\frac{23}{32}\right),e\left(\frac{145}{192}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 24704 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{91}{192}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{109}{192}\right)\) | \(e\left(\frac{103}{192}\right)\) | \(e\left(\frac{103}{192}\right)\) | \(e\left(\frac{31}{96}\right)\) |