Basic properties
| Modulus: | \(968\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 968.bb
\(\chi_{968}(17,\cdot)\) \(\chi_{968}(41,\cdot)\) \(\chi_{968}(57,\cdot)\) \(\chi_{968}(73,\cdot)\) \(\chi_{968}(105,\cdot)\) \(\chi_{968}(129,\cdot)\) \(\chi_{968}(145,\cdot)\) \(\chi_{968}(193,\cdot)\) \(\chi_{968}(217,\cdot)\) \(\chi_{968}(249,\cdot)\) \(\chi_{968}(281,\cdot)\) \(\chi_{968}(305,\cdot)\) \(\chi_{968}(321,\cdot)\) \(\chi_{968}(337,\cdot)\) \(\chi_{968}(369,\cdot)\) \(\chi_{968}(393,\cdot)\) \(\chi_{968}(409,\cdot)\) \(\chi_{968}(425,\cdot)\) \(\chi_{968}(497,\cdot)\) \(\chi_{968}(513,\cdot)\) \(\chi_{968}(545,\cdot)\) \(\chi_{968}(569,\cdot)\) \(\chi_{968}(585,\cdot)\) \(\chi_{968}(601,\cdot)\) \(\chi_{968}(633,\cdot)\) \(\chi_{968}(657,\cdot)\) \(\chi_{968}(673,\cdot)\) \(\chi_{968}(689,\cdot)\) \(\chi_{968}(721,\cdot)\) \(\chi_{968}(745,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,485,849)\) → \((1,1,e\left(\frac{1}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 968 }(849, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) |