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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1728.ch
\(\chi_{1728}(11,\cdot)\) \(\chi_{1728}(59,\cdot)\) \(\chi_{1728}(83,\cdot)\) \(\chi_{1728}(131,\cdot)\) \(\chi_{1728}(155,\cdot)\) \(\chi_{1728}(203,\cdot)\) \(\chi_{1728}(227,\cdot)\) \(\chi_{1728}(275,\cdot)\) \(\chi_{1728}(299,\cdot)\) \(\chi_{1728}(347,\cdot)\) \(\chi_{1728}(371,\cdot)\) \(\chi_{1728}(419,\cdot)\) \(\chi_{1728}(443,\cdot)\) \(\chi_{1728}(491,\cdot)\) \(\chi_{1728}(515,\cdot)\) \(\chi_{1728}(563,\cdot)\) \(\chi_{1728}(587,\cdot)\) \(\chi_{1728}(635,\cdot)\) \(\chi_{1728}(659,\cdot)\) \(\chi_{1728}(707,\cdot)\) \(\chi_{1728}(731,\cdot)\) \(\chi_{1728}(779,\cdot)\) \(\chi_{1728}(803,\cdot)\) \(\chi_{1728}(851,\cdot)\) \(\chi_{1728}(875,\cdot)\) \(\chi_{1728}(923,\cdot)\) \(\chi_{1728}(947,\cdot)\) \(\chi_{1728}(995,\cdot)\) \(\chi_{1728}(1019,\cdot)\) \(\chi_{1728}(1067,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{144})$ |
Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((703,325,1217)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{1}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1728 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{144}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{59}{144}\right)\) | \(e\left(\frac{1}{144}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{125}{144}\right)\) | \(e\left(\frac{1}{9}\right)\) |