Basic properties
| Modulus: | \(69696\) | |
| Conductor: | \(23232\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(880\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{23232}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.lp
\(\chi_{69696}(35,\cdot)\) \(\chi_{69696}(107,\cdot)\) \(\chi_{69696}(611,\cdot)\) \(\chi_{69696}(755,\cdot)\) \(\chi_{69696}(827,\cdot)\) \(\chi_{69696}(899,\cdot)\) \(\chi_{69696}(1403,\cdot)\) \(\chi_{69696}(1547,\cdot)\) \(\chi_{69696}(1619,\cdot)\) \(\chi_{69696}(2195,\cdot)\) \(\chi_{69696}(2483,\cdot)\) \(\chi_{69696}(2987,\cdot)\) \(\chi_{69696}(3131,\cdot)\) \(\chi_{69696}(3203,\cdot)\) \(\chi_{69696}(3275,\cdot)\) \(\chi_{69696}(3779,\cdot)\) \(\chi_{69696}(3923,\cdot)\) \(\chi_{69696}(3995,\cdot)\) \(\chi_{69696}(4067,\cdot)\) \(\chi_{69696}(4715,\cdot)\) \(\chi_{69696}(4787,\cdot)\) \(\chi_{69696}(4859,\cdot)\) \(\chi_{69696}(5363,\cdot)\) \(\chi_{69696}(5507,\cdot)\) \(\chi_{69696}(5579,\cdot)\) \(\chi_{69696}(5651,\cdot)\) \(\chi_{69696}(6155,\cdot)\) \(\chi_{69696}(6299,\cdot)\) \(\chi_{69696}(6371,\cdot)\) \(\chi_{69696}(6443,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{880})$ |
| Fixed field: | Number field defined by a degree 880 polynomial (not computed) |
Values on generators
\((67519,4357,54209,14401)\) → \((-1,e\left(\frac{13}{16}\right),-1,e\left(\frac{63}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{611}{880}\right)\) | \(e\left(\frac{279}{440}\right)\) | \(e\left(\frac{29}{880}\right)\) | \(e\left(\frac{69}{220}\right)\) | \(e\left(\frac{637}{880}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{171}{440}\right)\) | \(e\left(\frac{153}{880}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{289}{880}\right)\) |