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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2300.bt
\(\chi_{2300}(3,\cdot)\) \(\chi_{2300}(27,\cdot)\) \(\chi_{2300}(87,\cdot)\) \(\chi_{2300}(123,\cdot)\) \(\chi_{2300}(127,\cdot)\) \(\chi_{2300}(147,\cdot)\) \(\chi_{2300}(163,\cdot)\) \(\chi_{2300}(167,\cdot)\) \(\chi_{2300}(187,\cdot)\) \(\chi_{2300}(223,\cdot)\) \(\chi_{2300}(303,\cdot)\) \(\chi_{2300}(347,\cdot)\) \(\chi_{2300}(363,\cdot)\) \(\chi_{2300}(403,\cdot)\) \(\chi_{2300}(423,\cdot)\) \(\chi_{2300}(427,\cdot)\) \(\chi_{2300}(463,\cdot)\) \(\chi_{2300}(487,\cdot)\) \(\chi_{2300}(547,\cdot)\) \(\chi_{2300}(583,\cdot)\) \(\chi_{2300}(587,\cdot)\) \(\chi_{2300}(623,\cdot)\) \(\chi_{2300}(627,\cdot)\) \(\chi_{2300}(647,\cdot)\) \(\chi_{2300}(683,\cdot)\) \(\chi_{2300}(703,\cdot)\) \(\chi_{2300}(763,\cdot)\) \(\chi_{2300}(767,\cdot)\) \(\chi_{2300}(823,\cdot)\) \(\chi_{2300}(863,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((-1,e\left(\frac{1}{20}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 2300 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{41}{110}\right)\) |