Basic properties
| Modulus: | \(5184\) | |
| Conductor: | \(1728\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1728}(805,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5184.cq
\(\chi_{5184}(37,\cdot)\) \(\chi_{5184}(181,\cdot)\) \(\chi_{5184}(253,\cdot)\) \(\chi_{5184}(397,\cdot)\) \(\chi_{5184}(469,\cdot)\) \(\chi_{5184}(613,\cdot)\) \(\chi_{5184}(685,\cdot)\) \(\chi_{5184}(829,\cdot)\) \(\chi_{5184}(901,\cdot)\) \(\chi_{5184}(1045,\cdot)\) \(\chi_{5184}(1117,\cdot)\) \(\chi_{5184}(1261,\cdot)\) \(\chi_{5184}(1333,\cdot)\) \(\chi_{5184}(1477,\cdot)\) \(\chi_{5184}(1549,\cdot)\) \(\chi_{5184}(1693,\cdot)\) \(\chi_{5184}(1765,\cdot)\) \(\chi_{5184}(1909,\cdot)\) \(\chi_{5184}(1981,\cdot)\) \(\chi_{5184}(2125,\cdot)\) \(\chi_{5184}(2197,\cdot)\) \(\chi_{5184}(2341,\cdot)\) \(\chi_{5184}(2413,\cdot)\) \(\chi_{5184}(2557,\cdot)\) \(\chi_{5184}(2629,\cdot)\) \(\chi_{5184}(2773,\cdot)\) \(\chi_{5184}(2845,\cdot)\) \(\chi_{5184}(2989,\cdot)\) \(\chi_{5184}(3061,\cdot)\) \(\chi_{5184}(3205,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2431,325,1217)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5184 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{133}{144}\right)\) | \(e\left(\frac{95}{144}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{139}{144}\right)\) | \(e\left(\frac{1}{18}\right)\) |