Basic properties
Modulus: | \(221760\) | |
Conductor: | \(44352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{44352}(7717,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 221760.edh
\(\chi_{221760}(61,\cdot)\) \(\chi_{221760}(2581,\cdot)\) \(\chi_{221760}(3181,\cdot)\) \(\chi_{221760}(5101,\cdot)\) \(\chi_{221760}(13261,\cdot)\) \(\chi_{221760}(15781,\cdot)\) \(\chi_{221760}(17701,\cdot)\) \(\chi_{221760}(18301,\cdot)\) \(\chi_{221760}(27781,\cdot)\) \(\chi_{221760}(30301,\cdot)\) \(\chi_{221760}(30901,\cdot)\) \(\chi_{221760}(32821,\cdot)\) \(\chi_{221760}(40981,\cdot)\) \(\chi_{221760}(43501,\cdot)\) \(\chi_{221760}(45421,\cdot)\) \(\chi_{221760}(46021,\cdot)\) \(\chi_{221760}(55501,\cdot)\) \(\chi_{221760}(58021,\cdot)\) \(\chi_{221760}(58621,\cdot)\) \(\chi_{221760}(60541,\cdot)\) \(\chi_{221760}(68701,\cdot)\) \(\chi_{221760}(71221,\cdot)\) \(\chi_{221760}(73141,\cdot)\) \(\chi_{221760}(73741,\cdot)\) \(\chi_{221760}(83221,\cdot)\) \(\chi_{221760}(85741,\cdot)\) \(\chi_{221760}(86341,\cdot)\) \(\chi_{221760}(88261,\cdot)\) \(\chi_{221760}(96421,\cdot)\) \(\chi_{221760}(98941,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{240})$ |
Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((48511,124741,98561,133057,190081,141121)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{1}{3}\right),1,e\left(\frac{1}{6}\right),e\left(\frac{9}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 221760 }(96421, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{113}{240}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{197}{240}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{7}{60}\right)\) |