Basic properties
| Modulus: | \(7744\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7744.bw
\(\chi_{7744}(257,\cdot)\) \(\chi_{7744}(449,\cdot)\) \(\chi_{7744}(577,\cdot)\) \(\chi_{7744}(641,\cdot)\) \(\chi_{7744}(961,\cdot)\) \(\chi_{7744}(1153,\cdot)\) \(\chi_{7744}(1281,\cdot)\) \(\chi_{7744}(1345,\cdot)\) \(\chi_{7744}(1665,\cdot)\) \(\chi_{7744}(1857,\cdot)\) \(\chi_{7744}(1985,\cdot)\) \(\chi_{7744}(2049,\cdot)\) \(\chi_{7744}(2369,\cdot)\) \(\chi_{7744}(2561,\cdot)\) \(\chi_{7744}(2753,\cdot)\) \(\chi_{7744}(3073,\cdot)\) \(\chi_{7744}(3265,\cdot)\) \(\chi_{7744}(3393,\cdot)\) \(\chi_{7744}(3457,\cdot)\) \(\chi_{7744}(3777,\cdot)\) \(\chi_{7744}(3969,\cdot)\) \(\chi_{7744}(4097,\cdot)\) \(\chi_{7744}(4161,\cdot)\) \(\chi_{7744}(4481,\cdot)\) \(\chi_{7744}(4673,\cdot)\) \(\chi_{7744}(4801,\cdot)\) \(\chi_{7744}(4865,\cdot)\) \(\chi_{7744}(5185,\cdot)\) \(\chi_{7744}(5377,\cdot)\) \(\chi_{7744}(5505,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((5567,4357,6657)\) → \((1,1,e\left(\frac{26}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 7744 }(257, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) |