Basic properties
Modulus: | \(5184\) | |
Conductor: | \(5184\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(432\) | 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 5184.cy
\(\chi_{5184}(13,\cdot)\) \(\chi_{5184}(61,\cdot)\) \(\chi_{5184}(85,\cdot)\) \(\chi_{5184}(133,\cdot)\) \(\chi_{5184}(157,\cdot)\) \(\chi_{5184}(205,\cdot)\) \(\chi_{5184}(229,\cdot)\) \(\chi_{5184}(277,\cdot)\) \(\chi_{5184}(301,\cdot)\) \(\chi_{5184}(349,\cdot)\) \(\chi_{5184}(373,\cdot)\) \(\chi_{5184}(421,\cdot)\) \(\chi_{5184}(445,\cdot)\) \(\chi_{5184}(493,\cdot)\) \(\chi_{5184}(517,\cdot)\) \(\chi_{5184}(565,\cdot)\) \(\chi_{5184}(589,\cdot)\) \(\chi_{5184}(637,\cdot)\) \(\chi_{5184}(661,\cdot)\) \(\chi_{5184}(709,\cdot)\) \(\chi_{5184}(733,\cdot)\) \(\chi_{5184}(781,\cdot)\) \(\chi_{5184}(805,\cdot)\) \(\chi_{5184}(853,\cdot)\) \(\chi_{5184}(877,\cdot)\) \(\chi_{5184}(925,\cdot)\) \(\chi_{5184}(949,\cdot)\) \(\chi_{5184}(997,\cdot)\) \(\chi_{5184}(1021,\cdot)\) \(\chi_{5184}(1069,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{432})$ |
Fixed field: | Number field defined by a degree 432 polynomial (not computed) |
Values on generators
\((2431,325,1217)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{5}{27}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 5184 }(1429, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{432}\right)\) | \(e\left(\frac{19}{216}\right)\) | \(e\left(\frac{203}{432}\right)\) | \(e\left(\frac{289}{432}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{83}{144}\right)\) | \(e\left(\frac{89}{216}\right)\) | \(e\left(\frac{31}{216}\right)\) | \(e\left(\frac{341}{432}\right)\) | \(e\left(\frac{11}{54}\right)\) |