Basic properties
| Modulus: | \(5184\) | |
| Conductor: | \(864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{864}(349,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5184.ck
\(\chi_{5184}(73,\cdot)\) \(\chi_{5184}(361,\cdot)\) \(\chi_{5184}(505,\cdot)\) \(\chi_{5184}(793,\cdot)\) \(\chi_{5184}(937,\cdot)\) \(\chi_{5184}(1225,\cdot)\) \(\chi_{5184}(1369,\cdot)\) \(\chi_{5184}(1657,\cdot)\) \(\chi_{5184}(1801,\cdot)\) \(\chi_{5184}(2089,\cdot)\) \(\chi_{5184}(2233,\cdot)\) \(\chi_{5184}(2521,\cdot)\) \(\chi_{5184}(2665,\cdot)\) \(\chi_{5184}(2953,\cdot)\) \(\chi_{5184}(3097,\cdot)\) \(\chi_{5184}(3385,\cdot)\) \(\chi_{5184}(3529,\cdot)\) \(\chi_{5184}(3817,\cdot)\) \(\chi_{5184}(3961,\cdot)\) \(\chi_{5184}(4249,\cdot)\) \(\chi_{5184}(4393,\cdot)\) \(\chi_{5184}(4681,\cdot)\) \(\chi_{5184}(4825,\cdot)\) \(\chi_{5184}(5113,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,325,1217)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5184 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) |