Basic properties
| Modulus: | \(223\) | |
| Conductor: | \(223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(37\) | 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 223.e
\(\chi_{223}(2,\cdot)\) \(\chi_{223}(4,\cdot)\) \(\chi_{223}(7,\cdot)\) \(\chi_{223}(8,\cdot)\) \(\chi_{223}(14,\cdot)\) \(\chi_{223}(15,\cdot)\) \(\chi_{223}(16,\cdot)\) \(\chi_{223}(17,\cdot)\) \(\chi_{223}(28,\cdot)\) \(\chi_{223}(30,\cdot)\) \(\chi_{223}(32,\cdot)\) \(\chi_{223}(33,\cdot)\) \(\chi_{223}(34,\cdot)\) \(\chi_{223}(41,\cdot)\) \(\chi_{223}(49,\cdot)\) \(\chi_{223}(56,\cdot)\) \(\chi_{223}(60,\cdot)\) \(\chi_{223}(64,\cdot)\) \(\chi_{223}(66,\cdot)\) \(\chi_{223}(68,\cdot)\) \(\chi_{223}(82,\cdot)\) \(\chi_{223}(98,\cdot)\) \(\chi_{223}(105,\cdot)\) \(\chi_{223}(112,\cdot)\) \(\chi_{223}(115,\cdot)\) \(\chi_{223}(119,\cdot)\) \(\chi_{223}(120,\cdot)\) \(\chi_{223}(128,\cdot)\) \(\chi_{223}(132,\cdot)\) \(\chi_{223}(136,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | Number field defined by a degree 37 polynomial |
Values on generators
\(3\) → \(e\left(\frac{21}{37}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 223 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{37}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{27}{37}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{5}{37}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{27}{37}\right)\) |