Basic properties
Modulus: | \(1728\) | |
Conductor: | \(1728\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1728.ce
\(\chi_{1728}(13,\cdot)\) \(\chi_{1728}(61,\cdot)\) \(\chi_{1728}(85,\cdot)\) \(\chi_{1728}(133,\cdot)\) \(\chi_{1728}(157,\cdot)\) \(\chi_{1728}(205,\cdot)\) \(\chi_{1728}(229,\cdot)\) \(\chi_{1728}(277,\cdot)\) \(\chi_{1728}(301,\cdot)\) \(\chi_{1728}(349,\cdot)\) \(\chi_{1728}(373,\cdot)\) \(\chi_{1728}(421,\cdot)\) \(\chi_{1728}(445,\cdot)\) \(\chi_{1728}(493,\cdot)\) \(\chi_{1728}(517,\cdot)\) \(\chi_{1728}(565,\cdot)\) \(\chi_{1728}(589,\cdot)\) \(\chi_{1728}(637,\cdot)\) \(\chi_{1728}(661,\cdot)\) \(\chi_{1728}(709,\cdot)\) \(\chi_{1728}(733,\cdot)\) \(\chi_{1728}(781,\cdot)\) \(\chi_{1728}(805,\cdot)\) \(\chi_{1728}(853,\cdot)\) \(\chi_{1728}(877,\cdot)\) \(\chi_{1728}(925,\cdot)\) \(\chi_{1728}(949,\cdot)\) \(\chi_{1728}(997,\cdot)\) \(\chi_{1728}(1021,\cdot)\) \(\chi_{1728}(1069,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{144})$ |
Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((703,325,1217)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{2}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1728 }(421, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{144}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{101}{144}\right)\) | \(e\left(\frac{31}{144}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{59}{144}\right)\) | \(e\left(\frac{17}{18}\right)\) |