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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1216.cg
\(\chi_{1216}(5,\cdot)\) \(\chi_{1216}(61,\cdot)\) \(\chi_{1216}(85,\cdot)\) \(\chi_{1216}(93,\cdot)\) \(\chi_{1216}(101,\cdot)\) \(\chi_{1216}(149,\cdot)\) \(\chi_{1216}(157,\cdot)\) \(\chi_{1216}(213,\cdot)\) \(\chi_{1216}(237,\cdot)\) \(\chi_{1216}(245,\cdot)\) \(\chi_{1216}(253,\cdot)\) \(\chi_{1216}(301,\cdot)\) \(\chi_{1216}(309,\cdot)\) \(\chi_{1216}(365,\cdot)\) \(\chi_{1216}(389,\cdot)\) \(\chi_{1216}(397,\cdot)\) \(\chi_{1216}(405,\cdot)\) \(\chi_{1216}(453,\cdot)\) \(\chi_{1216}(461,\cdot)\) \(\chi_{1216}(517,\cdot)\) \(\chi_{1216}(541,\cdot)\) \(\chi_{1216}(549,\cdot)\) \(\chi_{1216}(557,\cdot)\) \(\chi_{1216}(605,\cdot)\) \(\chi_{1216}(613,\cdot)\) \(\chi_{1216}(669,\cdot)\) \(\chi_{1216}(693,\cdot)\) \(\chi_{1216}(701,\cdot)\) \(\chi_{1216}(709,\cdot)\) \(\chi_{1216}(757,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((191,837,705)\) → \((1,e\left(\frac{5}{16}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1216 }(693, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{144}\right)\) | \(e\left(\frac{61}{144}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{131}{144}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{73}{144}\right)\) | \(e\left(\frac{19}{72}\right)\) |