Basic properties
| Modulus: | \(2368\) | |
| Conductor: | \(2368\) | 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 2368.eb
\(\chi_{2368}(19,\cdot)\) \(\chi_{2368}(35,\cdot)\) \(\chi_{2368}(187,\cdot)\) \(\chi_{2368}(203,\cdot)\) \(\chi_{2368}(227,\cdot)\) \(\chi_{2368}(283,\cdot)\) \(\chi_{2368}(355,\cdot)\) \(\chi_{2368}(387,\cdot)\) \(\chi_{2368}(427,\cdot)\) \(\chi_{2368}(459,\cdot)\) \(\chi_{2368}(531,\cdot)\) \(\chi_{2368}(587,\cdot)\) \(\chi_{2368}(611,\cdot)\) \(\chi_{2368}(627,\cdot)\) \(\chi_{2368}(779,\cdot)\) \(\chi_{2368}(795,\cdot)\) \(\chi_{2368}(819,\cdot)\) \(\chi_{2368}(875,\cdot)\) \(\chi_{2368}(947,\cdot)\) \(\chi_{2368}(979,\cdot)\) \(\chi_{2368}(1019,\cdot)\) \(\chi_{2368}(1051,\cdot)\) \(\chi_{2368}(1123,\cdot)\) \(\chi_{2368}(1179,\cdot)\) \(\chi_{2368}(1203,\cdot)\) \(\chi_{2368}(1219,\cdot)\) \(\chi_{2368}(1371,\cdot)\) \(\chi_{2368}(1387,\cdot)\) \(\chi_{2368}(1411,\cdot)\) \(\chi_{2368}(1467,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((1407,1925,705)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{35}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2368 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{144}\right)\) | \(e\left(\frac{115}{144}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{37}{144}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{85}{144}\right)\) | \(e\left(\frac{11}{144}\right)\) |