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.iz
\(\chi_{5472}(131,\cdot)\) \(\chi_{5472}(347,\cdot)\) \(\chi_{5472}(443,\cdot)\) \(\chi_{5472}(491,\cdot)\) \(\chi_{5472}(731,\cdot)\) \(\chi_{5472}(1163,\cdot)\) \(\chi_{5472}(1499,\cdot)\) \(\chi_{5472}(1715,\cdot)\) \(\chi_{5472}(1811,\cdot)\) \(\chi_{5472}(1859,\cdot)\) \(\chi_{5472}(2099,\cdot)\) \(\chi_{5472}(2531,\cdot)\) \(\chi_{5472}(2867,\cdot)\) \(\chi_{5472}(3083,\cdot)\) \(\chi_{5472}(3179,\cdot)\) \(\chi_{5472}(3227,\cdot)\) \(\chi_{5472}(3467,\cdot)\) \(\chi_{5472}(3899,\cdot)\) \(\chi_{5472}(4235,\cdot)\) \(\chi_{5472}(4451,\cdot)\) \(\chi_{5472}(4547,\cdot)\) \(\chi_{5472}(4595,\cdot)\) \(\chi_{5472}(4835,\cdot)\) \(\chi_{5472}(5267,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4447,2053,1217,3745)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 5472 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(-1\) | \(e\left(\frac{25}{72}\right)\) |