Basic properties
| Modulus: | \(69696\) | |
| Conductor: | \(11616\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(440\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{11616}(4427,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.kq
\(\chi_{69696}(71,\cdot)\) \(\chi_{69696}(647,\cdot)\) \(\chi_{69696}(1367,\cdot)\) \(\chi_{69696}(1511,\cdot)\) \(\chi_{69696}(1655,\cdot)\) \(\chi_{69696}(2231,\cdot)\) \(\chi_{69696}(2951,\cdot)\) \(\chi_{69696}(3095,\cdot)\) \(\chi_{69696}(3239,\cdot)\) \(\chi_{69696}(3815,\cdot)\) \(\chi_{69696}(4535,\cdot)\) \(\chi_{69696}(4823,\cdot)\) \(\chi_{69696}(5399,\cdot)\) \(\chi_{69696}(6119,\cdot)\) \(\chi_{69696}(6263,\cdot)\) \(\chi_{69696}(6407,\cdot)\) \(\chi_{69696}(6983,\cdot)\) \(\chi_{69696}(7703,\cdot)\) \(\chi_{69696}(7847,\cdot)\) \(\chi_{69696}(7991,\cdot)\) \(\chi_{69696}(8567,\cdot)\) \(\chi_{69696}(9287,\cdot)\) \(\chi_{69696}(9431,\cdot)\) \(\chi_{69696}(9575,\cdot)\) \(\chi_{69696}(10151,\cdot)\) \(\chi_{69696}(10871,\cdot)\) \(\chi_{69696}(11015,\cdot)\) \(\chi_{69696}(11735,\cdot)\) \(\chi_{69696}(12455,\cdot)\) \(\chi_{69696}(12599,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{440})$ |
| Fixed field: | Number field defined by a degree 440 polynomial (not computed) |
Values on generators
\((67519,4357,54209,14401)\) → \((-1,e\left(\frac{5}{8}\right),-1,e\left(\frac{47}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{159}{440}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{301}{440}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{353}{440}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{159}{220}\right)\) | \(e\left(\frac{397}{440}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{41}{440}\right)\) |