Basic properties
Modulus: | \(7744\) | |
Conductor: | \(3872\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3872}(3827,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7744.cb
\(\chi_{7744}(87,\cdot)\) \(\chi_{7744}(263,\cdot)\) \(\chi_{7744}(439,\cdot)\) \(\chi_{7744}(615,\cdot)\) \(\chi_{7744}(791,\cdot)\) \(\chi_{7744}(1143,\cdot)\) \(\chi_{7744}(1319,\cdot)\) \(\chi_{7744}(1495,\cdot)\) \(\chi_{7744}(1671,\cdot)\) \(\chi_{7744}(1847,\cdot)\) \(\chi_{7744}(2023,\cdot)\) \(\chi_{7744}(2199,\cdot)\) \(\chi_{7744}(2375,\cdot)\) \(\chi_{7744}(2551,\cdot)\) \(\chi_{7744}(2727,\cdot)\) \(\chi_{7744}(3079,\cdot)\) \(\chi_{7744}(3255,\cdot)\) \(\chi_{7744}(3431,\cdot)\) \(\chi_{7744}(3607,\cdot)\) \(\chi_{7744}(3783,\cdot)\) \(\chi_{7744}(3959,\cdot)\) \(\chi_{7744}(4135,\cdot)\) \(\chi_{7744}(4311,\cdot)\) \(\chi_{7744}(4487,\cdot)\) \(\chi_{7744}(4663,\cdot)\) \(\chi_{7744}(5015,\cdot)\) \(\chi_{7744}(5191,\cdot)\) \(\chi_{7744}(5367,\cdot)\) \(\chi_{7744}(5543,\cdot)\) \(\chi_{7744}(5719,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((5567,4357,6657)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{17}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 7744 }(4311, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(i\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{37}{44}\right)\) |