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.bc
\(\chi_{968}(13,\cdot)\) \(\chi_{968}(29,\cdot)\) \(\chi_{968}(61,\cdot)\) \(\chi_{968}(85,\cdot)\) \(\chi_{968}(101,\cdot)\) \(\chi_{968}(117,\cdot)\) \(\chi_{968}(149,\cdot)\) \(\chi_{968}(173,\cdot)\) \(\chi_{968}(189,\cdot)\) \(\chi_{968}(205,\cdot)\) \(\chi_{968}(237,\cdot)\) \(\chi_{968}(261,\cdot)\) \(\chi_{968}(277,\cdot)\) \(\chi_{968}(293,\cdot)\) \(\chi_{968}(325,\cdot)\) \(\chi_{968}(349,\cdot)\) \(\chi_{968}(365,\cdot)\) \(\chi_{968}(381,\cdot)\) \(\chi_{968}(413,\cdot)\) \(\chi_{968}(437,\cdot)\) \(\chi_{968}(453,\cdot)\) \(\chi_{968}(469,\cdot)\) \(\chi_{968}(501,\cdot)\) \(\chi_{968}(525,\cdot)\) \(\chi_{968}(541,\cdot)\) \(\chi_{968}(557,\cdot)\) \(\chi_{968}(589,\cdot)\) \(\chi_{968}(613,\cdot)\) \(\chi_{968}(629,\cdot)\) \(\chi_{968}(677,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,485,849)\) → \((1,-1,e\left(\frac{101}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 968 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) |