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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 968.bd
\(\chi_{968}(5,\cdot)\) \(\chi_{968}(37,\cdot)\) \(\chi_{968}(53,\cdot)\) \(\chi_{968}(69,\cdot)\) \(\chi_{968}(93,\cdot)\) \(\chi_{968}(125,\cdot)\) \(\chi_{968}(141,\cdot)\) \(\chi_{968}(157,\cdot)\) \(\chi_{968}(181,\cdot)\) \(\chi_{968}(213,\cdot)\) \(\chi_{968}(229,\cdot)\) \(\chi_{968}(301,\cdot)\) \(\chi_{968}(317,\cdot)\) \(\chi_{968}(333,\cdot)\) \(\chi_{968}(357,\cdot)\) \(\chi_{968}(389,\cdot)\) \(\chi_{968}(405,\cdot)\) \(\chi_{968}(421,\cdot)\) \(\chi_{968}(445,\cdot)\) \(\chi_{968}(477,\cdot)\) \(\chi_{968}(509,\cdot)\) \(\chi_{968}(533,\cdot)\) \(\chi_{968}(581,\cdot)\) \(\chi_{968}(597,\cdot)\) \(\chi_{968}(621,\cdot)\) \(\chi_{968}(653,\cdot)\) \(\chi_{968}(669,\cdot)\) \(\chi_{968}(685,\cdot)\) \(\chi_{968}(709,\cdot)\) \(\chi_{968}(741,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,485,849)\) → \((1,-1,e\left(\frac{21}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 968 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) |