Basic properties
| Modulus: | \(2300\) | |
| Conductor: | \(2300\) | 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 2300.br
\(\chi_{2300}(19,\cdot)\) \(\chi_{2300}(79,\cdot)\) \(\chi_{2300}(159,\cdot)\) \(\chi_{2300}(319,\cdot)\) \(\chi_{2300}(339,\cdot)\) \(\chi_{2300}(359,\cdot)\) \(\chi_{2300}(379,\cdot)\) \(\chi_{2300}(419,\cdot)\) \(\chi_{2300}(479,\cdot)\) \(\chi_{2300}(539,\cdot)\) \(\chi_{2300}(559,\cdot)\) \(\chi_{2300}(619,\cdot)\) \(\chi_{2300}(659,\cdot)\) \(\chi_{2300}(779,\cdot)\) \(\chi_{2300}(819,\cdot)\) \(\chi_{2300}(839,\cdot)\) \(\chi_{2300}(879,\cdot)\) \(\chi_{2300}(939,\cdot)\) \(\chi_{2300}(1019,\cdot)\) \(\chi_{2300}(1079,\cdot)\) \(\chi_{2300}(1119,\cdot)\) \(\chi_{2300}(1239,\cdot)\) \(\chi_{2300}(1259,\cdot)\) \(\chi_{2300}(1279,\cdot)\) \(\chi_{2300}(1339,\cdot)\) \(\chi_{2300}(1459,\cdot)\) \(\chi_{2300}(1479,\cdot)\) \(\chi_{2300}(1539,\cdot)\) \(\chi_{2300}(1579,\cdot)\) \(\chi_{2300}(1719,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{15}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 2300 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) |