Basic properties
| Modulus: | \(4864\) | |
| Conductor: | \(1216\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1216}(1005,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4864.cs
\(\chi_{4864}(17,\cdot)\) \(\chi_{4864}(81,\cdot)\) \(\chi_{4864}(177,\cdot)\) \(\chi_{4864}(465,\cdot)\) \(\chi_{4864}(529,\cdot)\) \(\chi_{4864}(593,\cdot)\) \(\chi_{4864}(625,\cdot)\) \(\chi_{4864}(689,\cdot)\) \(\chi_{4864}(785,\cdot)\) \(\chi_{4864}(1073,\cdot)\) \(\chi_{4864}(1137,\cdot)\) \(\chi_{4864}(1201,\cdot)\) \(\chi_{4864}(1233,\cdot)\) \(\chi_{4864}(1297,\cdot)\) \(\chi_{4864}(1393,\cdot)\) \(\chi_{4864}(1681,\cdot)\) \(\chi_{4864}(1745,\cdot)\) \(\chi_{4864}(1809,\cdot)\) \(\chi_{4864}(1841,\cdot)\) \(\chi_{4864}(1905,\cdot)\) \(\chi_{4864}(2001,\cdot)\) \(\chi_{4864}(2289,\cdot)\) \(\chi_{4864}(2353,\cdot)\) \(\chi_{4864}(2417,\cdot)\) \(\chi_{4864}(2449,\cdot)\) \(\chi_{4864}(2513,\cdot)\) \(\chi_{4864}(2609,\cdot)\) \(\chi_{4864}(2897,\cdot)\) \(\chi_{4864}(2961,\cdot)\) \(\chi_{4864}(3025,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((3839,2053,4353)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4864 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{144}\right)\) | \(e\left(\frac{47}{144}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{49}{144}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{35}{144}\right)\) | \(e\left(\frac{17}{72}\right)\) |