Basic properties
Modulus: | \(3872\) | |
Conductor: | \(484\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{484}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3872.cd
\(\chi_{3872}(63,\cdot)\) \(\chi_{3872}(95,\cdot)\) \(\chi_{3872}(127,\cdot)\) \(\chi_{3872}(255,\cdot)\) \(\chi_{3872}(415,\cdot)\) \(\chi_{3872}(447,\cdot)\) \(\chi_{3872}(479,\cdot)\) \(\chi_{3872}(607,\cdot)\) \(\chi_{3872}(767,\cdot)\) \(\chi_{3872}(799,\cdot)\) \(\chi_{3872}(831,\cdot)\) \(\chi_{3872}(1119,\cdot)\) \(\chi_{3872}(1151,\cdot)\) \(\chi_{3872}(1311,\cdot)\) \(\chi_{3872}(1471,\cdot)\) \(\chi_{3872}(1503,\cdot)\) \(\chi_{3872}(1535,\cdot)\) \(\chi_{3872}(1663,\cdot)\) \(\chi_{3872}(1823,\cdot)\) \(\chi_{3872}(1887,\cdot)\) \(\chi_{3872}(2015,\cdot)\) \(\chi_{3872}(2207,\cdot)\) \(\chi_{3872}(2239,\cdot)\) \(\chi_{3872}(2367,\cdot)\) \(\chi_{3872}(2527,\cdot)\) \(\chi_{3872}(2559,\cdot)\) \(\chi_{3872}(2591,\cdot)\) \(\chi_{3872}(2719,\cdot)\) \(\chi_{3872}(2879,\cdot)\) \(\chi_{3872}(2911,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1695,485,2785)\) → \((-1,1,e\left(\frac{73}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 3872 }(63, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) |