Basic properties
| Modulus: | \(69696\) | |
| Conductor: | \(8712\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{8712}(4453,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.kg
\(\chi_{69696}(97,\cdot)\) \(\chi_{69696}(1633,\cdot)\) \(\chi_{69696}(2209,\cdot)\) \(\chi_{69696}(2401,\cdot)\) \(\chi_{69696}(4129,\cdot)\) \(\chi_{69696}(4513,\cdot)\) \(\chi_{69696}(5857,\cdot)\) \(\chi_{69696}(6241,\cdot)\) \(\chi_{69696}(6433,\cdot)\) \(\chi_{69696}(7969,\cdot)\) \(\chi_{69696}(8545,\cdot)\) \(\chi_{69696}(8737,\cdot)\) \(\chi_{69696}(10465,\cdot)\) \(\chi_{69696}(10849,\cdot)\) \(\chi_{69696}(12193,\cdot)\) \(\chi_{69696}(12577,\cdot)\) \(\chi_{69696}(12769,\cdot)\) \(\chi_{69696}(14881,\cdot)\) \(\chi_{69696}(15073,\cdot)\) \(\chi_{69696}(16801,\cdot)\) \(\chi_{69696}(18529,\cdot)\) \(\chi_{69696}(18913,\cdot)\) \(\chi_{69696}(19105,\cdot)\) \(\chi_{69696}(20641,\cdot)\) \(\chi_{69696}(21217,\cdot)\) \(\chi_{69696}(21409,\cdot)\) \(\chi_{69696}(23137,\cdot)\) \(\chi_{69696}(23521,\cdot)\) \(\chi_{69696}(24865,\cdot)\) \(\chi_{69696}(25441,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((67519,4357,54209,14401)\) → \((1,-1,e\left(\frac{2}{3}\right),e\left(\frac{18}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(97, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{241}{330}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{1}{110}\right)\) |