Basic properties
| Modulus: | \(1216\) | |
| Conductor: | \(1216\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1216.cf
\(\chi_{1216}(13,\cdot)\) \(\chi_{1216}(21,\cdot)\) \(\chi_{1216}(29,\cdot)\) \(\chi_{1216}(53,\cdot)\) \(\chi_{1216}(109,\cdot)\) \(\chi_{1216}(117,\cdot)\) \(\chi_{1216}(165,\cdot)\) \(\chi_{1216}(173,\cdot)\) \(\chi_{1216}(181,\cdot)\) \(\chi_{1216}(205,\cdot)\) \(\chi_{1216}(261,\cdot)\) \(\chi_{1216}(269,\cdot)\) \(\chi_{1216}(317,\cdot)\) \(\chi_{1216}(325,\cdot)\) \(\chi_{1216}(333,\cdot)\) \(\chi_{1216}(357,\cdot)\) \(\chi_{1216}(413,\cdot)\) \(\chi_{1216}(421,\cdot)\) \(\chi_{1216}(469,\cdot)\) \(\chi_{1216}(477,\cdot)\) \(\chi_{1216}(485,\cdot)\) \(\chi_{1216}(509,\cdot)\) \(\chi_{1216}(565,\cdot)\) \(\chi_{1216}(573,\cdot)\) \(\chi_{1216}(621,\cdot)\) \(\chi_{1216}(629,\cdot)\) \(\chi_{1216}(637,\cdot)\) \(\chi_{1216}(661,\cdot)\) \(\chi_{1216}(717,\cdot)\) \(\chi_{1216}(725,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((191,837,705)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1216 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{144}\right)\) | \(e\left(\frac{55}{144}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{67}{144}\right)\) | \(e\left(\frac{49}{72}\right)\) |