Basic properties
| Modulus: | \(3456\) | |
| Conductor: | \(864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{864}(373,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3456.cg
\(\chi_{3456}(49,\cdot)\) \(\chi_{3456}(241,\cdot)\) \(\chi_{3456}(337,\cdot)\) \(\chi_{3456}(529,\cdot)\) \(\chi_{3456}(625,\cdot)\) \(\chi_{3456}(817,\cdot)\) \(\chi_{3456}(913,\cdot)\) \(\chi_{3456}(1105,\cdot)\) \(\chi_{3456}(1201,\cdot)\) \(\chi_{3456}(1393,\cdot)\) \(\chi_{3456}(1489,\cdot)\) \(\chi_{3456}(1681,\cdot)\) \(\chi_{3456}(1777,\cdot)\) \(\chi_{3456}(1969,\cdot)\) \(\chi_{3456}(2065,\cdot)\) \(\chi_{3456}(2257,\cdot)\) \(\chi_{3456}(2353,\cdot)\) \(\chi_{3456}(2545,\cdot)\) \(\chi_{3456}(2641,\cdot)\) \(\chi_{3456}(2833,\cdot)\) \(\chi_{3456}(2929,\cdot)\) \(\chi_{3456}(3121,\cdot)\) \(\chi_{3456}(3217,\cdot)\) \(\chi_{3456}(3409,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,2053,2945)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3456 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{5}{9}\right)\) |