Basic properties
Modulus: | \(2541\) | |
Conductor: | \(363\) | 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 \(\chi_{363}(305,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2541.cc
\(\chi_{2541}(8,\cdot)\) \(\chi_{2541}(29,\cdot)\) \(\chi_{2541}(50,\cdot)\) \(\chi_{2541}(134,\cdot)\) \(\chi_{2541}(260,\cdot)\) \(\chi_{2541}(281,\cdot)\) \(\chi_{2541}(365,\cdot)\) \(\chi_{2541}(470,\cdot)\) \(\chi_{2541}(491,\cdot)\) \(\chi_{2541}(512,\cdot)\) \(\chi_{2541}(701,\cdot)\) \(\chi_{2541}(722,\cdot)\) \(\chi_{2541}(743,\cdot)\) \(\chi_{2541}(827,\cdot)\) \(\chi_{2541}(932,\cdot)\) \(\chi_{2541}(953,\cdot)\) \(\chi_{2541}(974,\cdot)\) \(\chi_{2541}(1058,\cdot)\) \(\chi_{2541}(1163,\cdot)\) \(\chi_{2541}(1184,\cdot)\) \(\chi_{2541}(1205,\cdot)\) \(\chi_{2541}(1289,\cdot)\) \(\chi_{2541}(1394,\cdot)\) \(\chi_{2541}(1415,\cdot)\) \(\chi_{2541}(1436,\cdot)\) \(\chi_{2541}(1520,\cdot)\) \(\chi_{2541}(1625,\cdot)\) \(\chi_{2541}(1646,\cdot)\) \(\chi_{2541}(1751,\cdot)\) \(\chi_{2541}(1856,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((848,1816,2059)\) → \((-1,1,e\left(\frac{73}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 2541 }(1394, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) |