Basic properties
Modulus: | \(69696\) | |
Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(66\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1089}(1022,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.gh
\(\chi_{69696}(65,\cdot)\) \(\chi_{69696}(4289,\cdot)\) \(\chi_{69696}(6401,\cdot)\) \(\chi_{69696}(10625,\cdot)\) \(\chi_{69696}(12737,\cdot)\) \(\chi_{69696}(16961,\cdot)\) \(\chi_{69696}(19073,\cdot)\) \(\chi_{69696}(23297,\cdot)\) \(\chi_{69696}(29633,\cdot)\) \(\chi_{69696}(31745,\cdot)\) \(\chi_{69696}(35969,\cdot)\) \(\chi_{69696}(38081,\cdot)\) \(\chi_{69696}(42305,\cdot)\) \(\chi_{69696}(44417,\cdot)\) \(\chi_{69696}(50753,\cdot)\) \(\chi_{69696}(54977,\cdot)\) \(\chi_{69696}(57089,\cdot)\) \(\chi_{69696}(61313,\cdot)\) \(\chi_{69696}(63425,\cdot)\) \(\chi_{69696}(67649,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{33})\) |
Fixed field: | Number field defined by a degree 66 polynomial |
Values on generators
\((67519,4357,54209,14401)\) → \((1,1,e\left(\frac{5}{6}\right),e\left(\frac{9}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 69696 }(4289, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) |