Basic properties
| Modulus: | \(4608\) | |
| Conductor: | \(2304\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2304}(1285,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.ce
\(\chi_{4608}(25,\cdot)\) \(\chi_{4608}(121,\cdot)\) \(\chi_{4608}(169,\cdot)\) \(\chi_{4608}(265,\cdot)\) \(\chi_{4608}(313,\cdot)\) \(\chi_{4608}(409,\cdot)\) \(\chi_{4608}(457,\cdot)\) \(\chi_{4608}(553,\cdot)\) \(\chi_{4608}(601,\cdot)\) \(\chi_{4608}(697,\cdot)\) \(\chi_{4608}(745,\cdot)\) \(\chi_{4608}(841,\cdot)\) \(\chi_{4608}(889,\cdot)\) \(\chi_{4608}(985,\cdot)\) \(\chi_{4608}(1033,\cdot)\) \(\chi_{4608}(1129,\cdot)\) \(\chi_{4608}(1177,\cdot)\) \(\chi_{4608}(1273,\cdot)\) \(\chi_{4608}(1321,\cdot)\) \(\chi_{4608}(1417,\cdot)\) \(\chi_{4608}(1465,\cdot)\) \(\chi_{4608}(1561,\cdot)\) \(\chi_{4608}(1609,\cdot)\) \(\chi_{4608}(1705,\cdot)\) \(\chi_{4608}(1753,\cdot)\) \(\chi_{4608}(1849,\cdot)\) \(\chi_{4608}(1897,\cdot)\) \(\chi_{4608}(1993,\cdot)\) \(\chi_{4608}(2041,\cdot)\) \(\chi_{4608}(2137,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((1,e\left(\frac{1}{64}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{192}\right)\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{191}{192}\right)\) | \(e\left(\frac{13}{192}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{53}{96}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{113}{192}\right)\) | \(e\left(\frac{11}{24}\right)\) |