Basic properties
| Modulus: | \(7744\) | |
| Conductor: | \(3872\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(440\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3872}(491,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7744.cx
\(\chi_{7744}(7,\cdot)\) \(\chi_{7744}(39,\cdot)\) \(\chi_{7744}(151,\cdot)\) \(\chi_{7744}(167,\cdot)\) \(\chi_{7744}(183,\cdot)\) \(\chi_{7744}(327,\cdot)\) \(\chi_{7744}(343,\cdot)\) \(\chi_{7744}(359,\cdot)\) \(\chi_{7744}(391,\cdot)\) \(\chi_{7744}(503,\cdot)\) \(\chi_{7744}(519,\cdot)\) \(\chi_{7744}(535,\cdot)\) \(\chi_{7744}(567,\cdot)\) \(\chi_{7744}(679,\cdot)\) \(\chi_{7744}(695,\cdot)\) \(\chi_{7744}(711,\cdot)\) \(\chi_{7744}(743,\cdot)\) \(\chi_{7744}(855,\cdot)\) \(\chi_{7744}(871,\cdot)\) \(\chi_{7744}(919,\cdot)\) \(\chi_{7744}(1031,\cdot)\) \(\chi_{7744}(1047,\cdot)\) \(\chi_{7744}(1063,\cdot)\) \(\chi_{7744}(1095,\cdot)\) \(\chi_{7744}(1223,\cdot)\) \(\chi_{7744}(1239,\cdot)\) \(\chi_{7744}(1271,\cdot)\) \(\chi_{7744}(1383,\cdot)\) \(\chi_{7744}(1399,\cdot)\) \(\chi_{7744}(1415,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{440})$ |
| Fixed field: | Number field defined by a degree 440 polynomial (not computed) |
Values on generators
\((5567,4357,6657)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{7}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 7744 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{147}{440}\right)\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{353}{440}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{69}{440}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) |