Basic properties
| Modulus: | \(69696\) | |
| Conductor: | \(69696\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(528\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.lb
\(\chi_{69696}(67,\cdot)\) \(\chi_{69696}(331,\cdot)\) \(\chi_{69696}(859,\cdot)\) \(\chi_{69696}(1123,\cdot)\) \(\chi_{69696}(1651,\cdot)\) \(\chi_{69696}(1915,\cdot)\) \(\chi_{69696}(2443,\cdot)\) \(\chi_{69696}(2707,\cdot)\) \(\chi_{69696}(3235,\cdot)\) \(\chi_{69696}(3499,\cdot)\) \(\chi_{69696}(4027,\cdot)\) \(\chi_{69696}(4291,\cdot)\) \(\chi_{69696}(4819,\cdot)\) \(\chi_{69696}(5611,\cdot)\) \(\chi_{69696}(5875,\cdot)\) \(\chi_{69696}(6403,\cdot)\) \(\chi_{69696}(6667,\cdot)\) \(\chi_{69696}(7195,\cdot)\) \(\chi_{69696}(7459,\cdot)\) \(\chi_{69696}(8251,\cdot)\) \(\chi_{69696}(8779,\cdot)\) \(\chi_{69696}(9043,\cdot)\) \(\chi_{69696}(9571,\cdot)\) \(\chi_{69696}(9835,\cdot)\) \(\chi_{69696}(10363,\cdot)\) \(\chi_{69696}(10627,\cdot)\) \(\chi_{69696}(11155,\cdot)\) \(\chi_{69696}(11419,\cdot)\) \(\chi_{69696}(11947,\cdot)\) \(\chi_{69696}(12211,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{528})$ |
| Fixed field: | Number field defined by a degree 528 polynomial (not computed) |
Values on generators
\((67519,4357,54209,14401)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{1}{3}\right),e\left(\frac{10}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{528}\right)\) | \(e\left(\frac{19}{264}\right)\) | \(e\left(\frac{157}{528}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{47}{176}\right)\) | \(e\left(\frac{113}{264}\right)\) | \(e\left(\frac{67}{264}\right)\) | \(e\left(\frac{449}{528}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{35}{176}\right)\) |