Basic properties
| Modulus: | \(2300\) | |
| Conductor: | \(2300\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2300.bu
\(\chi_{2300}(63,\cdot)\) \(\chi_{2300}(67,\cdot)\) \(\chi_{2300}(83,\cdot)\) \(\chi_{2300}(103,\cdot)\) \(\chi_{2300}(203,\cdot)\) \(\chi_{2300}(227,\cdot)\) \(\chi_{2300}(247,\cdot)\) \(\chi_{2300}(263,\cdot)\) \(\chi_{2300}(267,\cdot)\) \(\chi_{2300}(283,\cdot)\) \(\chi_{2300}(287,\cdot)\) \(\chi_{2300}(327,\cdot)\) \(\chi_{2300}(383,\cdot)\) \(\chi_{2300}(387,\cdot)\) \(\chi_{2300}(447,\cdot)\) \(\chi_{2300}(467,\cdot)\) \(\chi_{2300}(503,\cdot)\) \(\chi_{2300}(523,\cdot)\) \(\chi_{2300}(527,\cdot)\) \(\chi_{2300}(563,\cdot)\) \(\chi_{2300}(567,\cdot)\) \(\chi_{2300}(603,\cdot)\) \(\chi_{2300}(663,\cdot)\) \(\chi_{2300}(687,\cdot)\) \(\chi_{2300}(723,\cdot)\) \(\chi_{2300}(727,\cdot)\) \(\chi_{2300}(747,\cdot)\) \(\chi_{2300}(787,\cdot)\) \(\chi_{2300}(803,\cdot)\) \(\chi_{2300}(847,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 2300 }(103, a) \) | \(-1\) | \(1\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{91}{220}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{7}{110}\right)\) |