Basic properties
| Modulus: | \(2300\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2300.bq
\(\chi_{2300}(21,\cdot)\) \(\chi_{2300}(61,\cdot)\) \(\chi_{2300}(181,\cdot)\) \(\chi_{2300}(221,\cdot)\) \(\chi_{2300}(241,\cdot)\) \(\chi_{2300}(281,\cdot)\) \(\chi_{2300}(341,\cdot)\) \(\chi_{2300}(421,\cdot)\) \(\chi_{2300}(481,\cdot)\) \(\chi_{2300}(521,\cdot)\) \(\chi_{2300}(641,\cdot)\) \(\chi_{2300}(661,\cdot)\) \(\chi_{2300}(681,\cdot)\) \(\chi_{2300}(741,\cdot)\) \(\chi_{2300}(861,\cdot)\) \(\chi_{2300}(881,\cdot)\) \(\chi_{2300}(941,\cdot)\) \(\chi_{2300}(981,\cdot)\) \(\chi_{2300}(1121,\cdot)\) \(\chi_{2300}(1141,\cdot)\) \(\chi_{2300}(1161,\cdot)\) \(\chi_{2300}(1261,\cdot)\) \(\chi_{2300}(1321,\cdot)\) \(\chi_{2300}(1341,\cdot)\) \(\chi_{2300}(1441,\cdot)\) \(\chi_{2300}(1561,\cdot)\) \(\chi_{2300}(1581,\cdot)\) \(\chi_{2300}(1621,\cdot)\) \(\chi_{2300}(1661,\cdot)\) \(\chi_{2300}(1721,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{13}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 2300 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) |