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.bm
\(\chi_{2300}(11,\cdot)\) \(\chi_{2300}(111,\cdot)\) \(\chi_{2300}(171,\cdot)\) \(\chi_{2300}(191,\cdot)\) \(\chi_{2300}(291,\cdot)\) \(\chi_{2300}(411,\cdot)\) \(\chi_{2300}(431,\cdot)\) \(\chi_{2300}(471,\cdot)\) \(\chi_{2300}(511,\cdot)\) \(\chi_{2300}(571,\cdot)\) \(\chi_{2300}(631,\cdot)\) \(\chi_{2300}(711,\cdot)\) \(\chi_{2300}(871,\cdot)\) \(\chi_{2300}(891,\cdot)\) \(\chi_{2300}(911,\cdot)\) \(\chi_{2300}(931,\cdot)\) \(\chi_{2300}(971,\cdot)\) \(\chi_{2300}(1031,\cdot)\) \(\chi_{2300}(1091,\cdot)\) \(\chi_{2300}(1111,\cdot)\) \(\chi_{2300}(1171,\cdot)\) \(\chi_{2300}(1211,\cdot)\) \(\chi_{2300}(1331,\cdot)\) \(\chi_{2300}(1371,\cdot)\) \(\chi_{2300}(1391,\cdot)\) \(\chi_{2300}(1431,\cdot)\) \(\chi_{2300}(1491,\cdot)\) \(\chi_{2300}(1571,\cdot)\) \(\chi_{2300}(1631,\cdot)\) \(\chi_{2300}(1671,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 2300 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) |