Basic properties
| Modulus: | \(7744\) | |
| Conductor: | \(484\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{484}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7744.cl
\(\chi_{7744}(63,\cdot)\) \(\chi_{7744}(127,\cdot)\) \(\chi_{7744}(255,\cdot)\) \(\chi_{7744}(447,\cdot)\) \(\chi_{7744}(767,\cdot)\) \(\chi_{7744}(831,\cdot)\) \(\chi_{7744}(1151,\cdot)\) \(\chi_{7744}(1471,\cdot)\) \(\chi_{7744}(1535,\cdot)\) \(\chi_{7744}(1663,\cdot)\) \(\chi_{7744}(2239,\cdot)\) \(\chi_{7744}(2367,\cdot)\) \(\chi_{7744}(2559,\cdot)\) \(\chi_{7744}(2879,\cdot)\) \(\chi_{7744}(2943,\cdot)\) \(\chi_{7744}(3071,\cdot)\) \(\chi_{7744}(3263,\cdot)\) \(\chi_{7744}(3583,\cdot)\) \(\chi_{7744}(3647,\cdot)\) \(\chi_{7744}(3775,\cdot)\) \(\chi_{7744}(3967,\cdot)\) \(\chi_{7744}(4287,\cdot)\) \(\chi_{7744}(4351,\cdot)\) \(\chi_{7744}(4479,\cdot)\) \(\chi_{7744}(4671,\cdot)\) \(\chi_{7744}(4991,\cdot)\) \(\chi_{7744}(5183,\cdot)\) \(\chi_{7744}(5375,\cdot)\) \(\chi_{7744}(5695,\cdot)\) \(\chi_{7744}(5759,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((5567,4357,6657)\) → \((-1,1,e\left(\frac{73}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 7744 }(63, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) |