Basic properties
| Modulus: | \(5472\) | |
| Conductor: | \(1824\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1824}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5472.jr
\(\chi_{5472}(35,\cdot)\) \(\chi_{5472}(251,\cdot)\) \(\chi_{5472}(899,\cdot)\) \(\chi_{5472}(1043,\cdot)\) \(\chi_{5472}(1187,\cdot)\) \(\chi_{5472}(1259,\cdot)\) \(\chi_{5472}(1403,\cdot)\) \(\chi_{5472}(1619,\cdot)\) \(\chi_{5472}(2267,\cdot)\) \(\chi_{5472}(2411,\cdot)\) \(\chi_{5472}(2555,\cdot)\) \(\chi_{5472}(2627,\cdot)\) \(\chi_{5472}(2771,\cdot)\) \(\chi_{5472}(2987,\cdot)\) \(\chi_{5472}(3635,\cdot)\) \(\chi_{5472}(3779,\cdot)\) \(\chi_{5472}(3923,\cdot)\) \(\chi_{5472}(3995,\cdot)\) \(\chi_{5472}(4139,\cdot)\) \(\chi_{5472}(4355,\cdot)\) \(\chi_{5472}(5003,\cdot)\) \(\chi_{5472}(5147,\cdot)\) \(\chi_{5472}(5291,\cdot)\) \(\chi_{5472}(5363,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4447,2053,1217,3745)\) → \((-1,e\left(\frac{3}{8}\right),-1,e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 5472 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{72}\right)\) |