Basic properties
Modulus: | \(1728\) | |
Conductor: | \(1728\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(144\) | 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
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1728.cg
\(\chi_{1728}(43,\cdot)\) \(\chi_{1728}(67,\cdot)\) \(\chi_{1728}(115,\cdot)\) \(\chi_{1728}(139,\cdot)\) \(\chi_{1728}(187,\cdot)\) \(\chi_{1728}(211,\cdot)\) \(\chi_{1728}(259,\cdot)\) \(\chi_{1728}(283,\cdot)\) \(\chi_{1728}(331,\cdot)\) \(\chi_{1728}(355,\cdot)\) \(\chi_{1728}(403,\cdot)\) \(\chi_{1728}(427,\cdot)\) \(\chi_{1728}(475,\cdot)\) \(\chi_{1728}(499,\cdot)\) \(\chi_{1728}(547,\cdot)\) \(\chi_{1728}(571,\cdot)\) \(\chi_{1728}(619,\cdot)\) \(\chi_{1728}(643,\cdot)\) \(\chi_{1728}(691,\cdot)\) \(\chi_{1728}(715,\cdot)\) \(\chi_{1728}(763,\cdot)\) \(\chi_{1728}(787,\cdot)\) \(\chi_{1728}(835,\cdot)\) \(\chi_{1728}(859,\cdot)\) \(\chi_{1728}(907,\cdot)\) \(\chi_{1728}(931,\cdot)\) \(\chi_{1728}(979,\cdot)\) \(\chi_{1728}(1003,\cdot)\) \(\chi_{1728}(1051,\cdot)\) \(\chi_{1728}(1075,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{144})$ |
Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((703,325,1217)\) → \((-1,e\left(\frac{15}{16}\right),e\left(\frac{4}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1728 }(499, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{144}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{139}{144}\right)\) | \(e\left(\frac{89}{144}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{109}{144}\right)\) | \(e\left(\frac{8}{9}\right)\) |