Basic properties
Modulus: | \(6001\) | |
Conductor: | \(353\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{353}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.df
\(\chi_{6001}(324,\cdot)\) \(\chi_{6001}(426,\cdot)\) \(\chi_{6001}(698,\cdot)\) \(\chi_{6001}(817,\cdot)\) \(\chi_{6001}(834,\cdot)\) \(\chi_{6001}(1038,\cdot)\) \(\chi_{6001}(1140,\cdot)\) \(\chi_{6001}(1344,\cdot)\) \(\chi_{6001}(1395,\cdot)\) \(\chi_{6001}(1429,\cdot)\) \(\chi_{6001}(1480,\cdot)\) \(\chi_{6001}(1684,\cdot)\) \(\chi_{6001}(1786,\cdot)\) \(\chi_{6001}(1990,\cdot)\) \(\chi_{6001}(2007,\cdot)\) \(\chi_{6001}(2126,\cdot)\) \(\chi_{6001}(2398,\cdot)\) \(\chi_{6001}(2500,\cdot)\) \(\chi_{6001}(2908,\cdot)\) \(\chi_{6001}(3469,\cdot)\) \(\chi_{6001}(3486,\cdot)\) \(\chi_{6001}(3639,\cdot)\) \(\chi_{6001}(3707,\cdot)\) \(\chi_{6001}(3724,\cdot)\) \(\chi_{6001}(3792,\cdot)\) \(\chi_{6001}(3894,\cdot)\) \(\chi_{6001}(4234,\cdot)\) \(\chi_{6001}(4268,\cdot)\) \(\chi_{6001}(4319,\cdot)\) \(\chi_{6001}(4506,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((1,e\left(\frac{81}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(3639, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{22}\right)\) |