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 \(\chi_{1089}(65,\cdot)\) | 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
\((67519,4357,54209,14401)\) → \((1,1,e\left(\frac{1}{6}\right),e\left(\frac{13}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) |