Basic properties
Modulus: | \(7360\) | |
Conductor: | \(3680\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3680}(2387,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7360.ew
\(\chi_{7360}(87,\cdot)\) \(\chi_{7360}(407,\cdot)\) \(\chi_{7360}(423,\cdot)\) \(\chi_{7360}(583,\cdot)\) \(\chi_{7360}(887,\cdot)\) \(\chi_{7360}(903,\cdot)\) \(\chi_{7360}(1047,\cdot)\) \(\chi_{7360}(1223,\cdot)\) \(\chi_{7360}(1383,\cdot)\) \(\chi_{7360}(1527,\cdot)\) \(\chi_{7360}(1543,\cdot)\) \(\chi_{7360}(1687,\cdot)\) \(\chi_{7360}(2007,\cdot)\) \(\chi_{7360}(2327,\cdot)\) \(\chi_{7360}(2487,\cdot)\) \(\chi_{7360}(2647,\cdot)\) \(\chi_{7360}(2663,\cdot)\) \(\chi_{7360}(2983,\cdot)\) \(\chi_{7360}(3463,\cdot)\) \(\chi_{7360}(3623,\cdot)\) \(\chi_{7360}(3767,\cdot)\) \(\chi_{7360}(4087,\cdot)\) \(\chi_{7360}(4103,\cdot)\) \(\chi_{7360}(4263,\cdot)\) \(\chi_{7360}(4567,\cdot)\) \(\chi_{7360}(4583,\cdot)\) \(\chi_{7360}(4727,\cdot)\) \(\chi_{7360}(4903,\cdot)\) \(\chi_{7360}(5063,\cdot)\) \(\chi_{7360}(5207,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1151,5061,4417,6721)\) → \((-1,e\left(\frac{7}{8}\right),i,e\left(\frac{6}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 7360 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{83}{88}\right)\) |