Basic properties
| Modulus: | \(5184\) | |
| Conductor: | \(2592\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(216\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2592}(997,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5184.cx
\(\chi_{5184}(25,\cdot)\) \(\chi_{5184}(121,\cdot)\) \(\chi_{5184}(169,\cdot)\) \(\chi_{5184}(265,\cdot)\) \(\chi_{5184}(313,\cdot)\) \(\chi_{5184}(409,\cdot)\) \(\chi_{5184}(457,\cdot)\) \(\chi_{5184}(553,\cdot)\) \(\chi_{5184}(601,\cdot)\) \(\chi_{5184}(697,\cdot)\) \(\chi_{5184}(745,\cdot)\) \(\chi_{5184}(841,\cdot)\) \(\chi_{5184}(889,\cdot)\) \(\chi_{5184}(985,\cdot)\) \(\chi_{5184}(1033,\cdot)\) \(\chi_{5184}(1129,\cdot)\) \(\chi_{5184}(1177,\cdot)\) \(\chi_{5184}(1273,\cdot)\) \(\chi_{5184}(1321,\cdot)\) \(\chi_{5184}(1417,\cdot)\) \(\chi_{5184}(1465,\cdot)\) \(\chi_{5184}(1561,\cdot)\) \(\chi_{5184}(1609,\cdot)\) \(\chi_{5184}(1705,\cdot)\) \(\chi_{5184}(1753,\cdot)\) \(\chi_{5184}(1849,\cdot)\) \(\chi_{5184}(1897,\cdot)\) \(\chi_{5184}(1993,\cdot)\) \(\chi_{5184}(2041,\cdot)\) \(\chi_{5184}(2137,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{216})$ |
| Fixed field: | Number field defined by a degree 216 polynomial (not computed) |
Values on generators
\((2431,325,1217)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{23}{27}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5184 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{155}{216}\right)\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{151}{216}\right)\) | \(e\left(\frac{149}{216}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{47}{108}\right)\) | \(e\left(\frac{193}{216}\right)\) | \(e\left(\frac{1}{27}\right)\) |