Basic properties
Modulus: | \(1216\) | |
Conductor: | \(1216\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\((191,837,705)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{2}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 1216 }(301, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{144}\right)\) | \(e\left(\frac{143}{144}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{97}{144}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{131}{144}\right)\) | \(e\left(\frac{41}{72}\right)\) |