Basic properties
| Modulus: | \(5472\) | |
| Conductor: | \(5472\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | 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 5472.jn
\(\chi_{5472}(275,\cdot)\) \(\chi_{5472}(587,\cdot)\) \(\chi_{5472}(707,\cdot)\) \(\chi_{5472}(803,\cdot)\) \(\chi_{5472}(947,\cdot)\) \(\chi_{5472}(1355,\cdot)\) \(\chi_{5472}(1643,\cdot)\) \(\chi_{5472}(1955,\cdot)\) \(\chi_{5472}(2075,\cdot)\) \(\chi_{5472}(2171,\cdot)\) \(\chi_{5472}(2315,\cdot)\) \(\chi_{5472}(2723,\cdot)\) \(\chi_{5472}(3011,\cdot)\) \(\chi_{5472}(3323,\cdot)\) \(\chi_{5472}(3443,\cdot)\) \(\chi_{5472}(3539,\cdot)\) \(\chi_{5472}(3683,\cdot)\) \(\chi_{5472}(4091,\cdot)\) \(\chi_{5472}(4379,\cdot)\) \(\chi_{5472}(4691,\cdot)\) \(\chi_{5472}(4811,\cdot)\) \(\chi_{5472}(4907,\cdot)\) \(\chi_{5472}(5051,\cdot)\) \(\chi_{5472}(5459,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4447,2053,1217,3745)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 5472 }(275, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{72}\right)\) | \(i\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{72}\right)\) |