Basic properties
| Modulus: | \(3648\) | |
| 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 \(\chi_{1824}(269,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3648.ee
\(\chi_{3648}(41,\cdot)\) \(\chi_{3648}(89,\cdot)\) \(\chi_{3648}(185,\cdot)\) \(\chi_{3648}(281,\cdot)\) \(\chi_{3648}(713,\cdot)\) \(\chi_{3648}(857,\cdot)\) \(\chi_{3648}(953,\cdot)\) \(\chi_{3648}(1001,\cdot)\) \(\chi_{3648}(1097,\cdot)\) \(\chi_{3648}(1193,\cdot)\) \(\chi_{3648}(1625,\cdot)\) \(\chi_{3648}(1769,\cdot)\) \(\chi_{3648}(1865,\cdot)\) \(\chi_{3648}(1913,\cdot)\) \(\chi_{3648}(2009,\cdot)\) \(\chi_{3648}(2105,\cdot)\) \(\chi_{3648}(2537,\cdot)\) \(\chi_{3648}(2681,\cdot)\) \(\chi_{3648}(2777,\cdot)\) \(\chi_{3648}(2825,\cdot)\) \(\chi_{3648}(2921,\cdot)\) \(\chi_{3648}(3017,\cdot)\) \(\chi_{3648}(3449,\cdot)\) \(\chi_{3648}(3593,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2623,2053,1217,1921)\) → \((1,e\left(\frac{7}{8}\right),-1,e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3648 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{72}\right)\) |