Basic properties
| Modulus: | \(968\) | |
| Conductor: | \(968\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | 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 968.z
\(\chi_{968}(59,\cdot)\) \(\chi_{968}(75,\cdot)\) \(\chi_{968}(91,\cdot)\) \(\chi_{968}(115,\cdot)\) \(\chi_{968}(147,\cdot)\) \(\chi_{968}(163,\cdot)\) \(\chi_{968}(179,\cdot)\) \(\chi_{968}(203,\cdot)\) \(\chi_{968}(235,\cdot)\) \(\chi_{968}(267,\cdot)\) \(\chi_{968}(291,\cdot)\) \(\chi_{968}(339,\cdot)\) \(\chi_{968}(355,\cdot)\) \(\chi_{968}(379,\cdot)\) \(\chi_{968}(411,\cdot)\) \(\chi_{968}(427,\cdot)\) \(\chi_{968}(443,\cdot)\) \(\chi_{968}(467,\cdot)\) \(\chi_{968}(499,\cdot)\) \(\chi_{968}(515,\cdot)\) \(\chi_{968}(531,\cdot)\) \(\chi_{968}(555,\cdot)\) \(\chi_{968}(587,\cdot)\) \(\chi_{968}(603,\cdot)\) \(\chi_{968}(619,\cdot)\) \(\chi_{968}(643,\cdot)\) \(\chi_{968}(675,\cdot)\) \(\chi_{968}(691,\cdot)\) \(\chi_{968}(707,\cdot)\) \(\chi_{968}(731,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,485,849)\) → \((-1,-1,e\left(\frac{48}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 968 }(163, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) |