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.cf
\(\chi_{1728}(5,\cdot)\) \(\chi_{1728}(29,\cdot)\) \(\chi_{1728}(77,\cdot)\) \(\chi_{1728}(101,\cdot)\) \(\chi_{1728}(149,\cdot)\) \(\chi_{1728}(173,\cdot)\) \(\chi_{1728}(221,\cdot)\) \(\chi_{1728}(245,\cdot)\) \(\chi_{1728}(293,\cdot)\) \(\chi_{1728}(317,\cdot)\) \(\chi_{1728}(365,\cdot)\) \(\chi_{1728}(389,\cdot)\) \(\chi_{1728}(437,\cdot)\) \(\chi_{1728}(461,\cdot)\) \(\chi_{1728}(509,\cdot)\) \(\chi_{1728}(533,\cdot)\) \(\chi_{1728}(581,\cdot)\) \(\chi_{1728}(605,\cdot)\) \(\chi_{1728}(653,\cdot)\) \(\chi_{1728}(677,\cdot)\) \(\chi_{1728}(725,\cdot)\) \(\chi_{1728}(749,\cdot)\) \(\chi_{1728}(797,\cdot)\) \(\chi_{1728}(821,\cdot)\) \(\chi_{1728}(869,\cdot)\) \(\chi_{1728}(893,\cdot)\) \(\chi_{1728}(941,\cdot)\) \(\chi_{1728}(965,\cdot)\) \(\chi_{1728}(1013,\cdot)\) \(\chi_{1728}(1037,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{144})$ |
Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((703,325,1217)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1728 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{133}{144}\right)\) | \(e\left(\frac{23}{144}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{139}{144}\right)\) | \(e\left(\frac{1}{18}\right)\) |