Basic properties
| Modulus: | \(5472\) | |
| Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{608}(91,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5472.ji
\(\chi_{5472}(91,\cdot)\) \(\chi_{5472}(307,\cdot)\) \(\chi_{5472}(451,\cdot)\) \(\chi_{5472}(523,\cdot)\) \(\chi_{5472}(667,\cdot)\) \(\chi_{5472}(811,\cdot)\) \(\chi_{5472}(1459,\cdot)\) \(\chi_{5472}(1675,\cdot)\) \(\chi_{5472}(1819,\cdot)\) \(\chi_{5472}(1891,\cdot)\) \(\chi_{5472}(2035,\cdot)\) \(\chi_{5472}(2179,\cdot)\) \(\chi_{5472}(2827,\cdot)\) \(\chi_{5472}(3043,\cdot)\) \(\chi_{5472}(3187,\cdot)\) \(\chi_{5472}(3259,\cdot)\) \(\chi_{5472}(3403,\cdot)\) \(\chi_{5472}(3547,\cdot)\) \(\chi_{5472}(4195,\cdot)\) \(\chi_{5472}(4411,\cdot)\) \(\chi_{5472}(4555,\cdot)\) \(\chi_{5472}(4627,\cdot)\) \(\chi_{5472}(4771,\cdot)\) \(\chi_{5472}(4915,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4447,2053,1217,3745)\) → \((-1,e\left(\frac{1}{8}\right),1,e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 5472 }(91, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{72}\right)\) |