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.ce
\(\chi_{1216}(35,\cdot)\) \(\chi_{1216}(43,\cdot)\) \(\chi_{1216}(99,\cdot)\) \(\chi_{1216}(123,\cdot)\) \(\chi_{1216}(131,\cdot)\) \(\chi_{1216}(139,\cdot)\) \(\chi_{1216}(187,\cdot)\) \(\chi_{1216}(195,\cdot)\) \(\chi_{1216}(251,\cdot)\) \(\chi_{1216}(275,\cdot)\) \(\chi_{1216}(283,\cdot)\) \(\chi_{1216}(291,\cdot)\) \(\chi_{1216}(339,\cdot)\) \(\chi_{1216}(347,\cdot)\) \(\chi_{1216}(403,\cdot)\) \(\chi_{1216}(427,\cdot)\) \(\chi_{1216}(435,\cdot)\) \(\chi_{1216}(443,\cdot)\) \(\chi_{1216}(491,\cdot)\) \(\chi_{1216}(499,\cdot)\) \(\chi_{1216}(555,\cdot)\) \(\chi_{1216}(579,\cdot)\) \(\chi_{1216}(587,\cdot)\) \(\chi_{1216}(595,\cdot)\) \(\chi_{1216}(643,\cdot)\) \(\chi_{1216}(651,\cdot)\) \(\chi_{1216}(707,\cdot)\) \(\chi_{1216}(731,\cdot)\) \(\chi_{1216}(739,\cdot)\) \(\chi_{1216}(747,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((191,837,705)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1216 }(731, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{144}\right)\) | \(e\left(\frac{97}{144}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{95}{144}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{109}{144}\right)\) | \(e\left(\frac{19}{72}\right)\) |