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 \(\chi_{3872}(1541,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7744.ce
\(\chi_{7744}(89,\cdot)\) \(\chi_{7744}(265,\cdot)\) \(\chi_{7744}(441,\cdot)\) \(\chi_{7744}(617,\cdot)\) \(\chi_{7744}(793,\cdot)\) \(\chi_{7744}(1145,\cdot)\) \(\chi_{7744}(1321,\cdot)\) \(\chi_{7744}(1497,\cdot)\) \(\chi_{7744}(1673,\cdot)\) \(\chi_{7744}(1849,\cdot)\) \(\chi_{7744}(2025,\cdot)\) \(\chi_{7744}(2201,\cdot)\) \(\chi_{7744}(2377,\cdot)\) \(\chi_{7744}(2553,\cdot)\) \(\chi_{7744}(2729,\cdot)\) \(\chi_{7744}(3081,\cdot)\) \(\chi_{7744}(3257,\cdot)\) \(\chi_{7744}(3433,\cdot)\) \(\chi_{7744}(3609,\cdot)\) \(\chi_{7744}(3785,\cdot)\) \(\chi_{7744}(3961,\cdot)\) \(\chi_{7744}(4137,\cdot)\) \(\chi_{7744}(4313,\cdot)\) \(\chi_{7744}(4489,\cdot)\) \(\chi_{7744}(4665,\cdot)\) \(\chi_{7744}(5017,\cdot)\) \(\chi_{7744}(5193,\cdot)\) \(\chi_{7744}(5369,\cdot)\) \(\chi_{7744}(5545,\cdot)\) \(\chi_{7744}(5721,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((5567,4357,6657)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{6}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 7744 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(-i\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{41}{44}\right)\) |