Basic properties
| Modulus: | \(223\) | |
| Conductor: | \(223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(74\) | 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 223.f
\(\chi_{223}(13,\cdot)\) \(\chi_{223}(26,\cdot)\) \(\chi_{223}(27,\cdot)\) \(\chi_{223}(52,\cdot)\) \(\chi_{223}(54,\cdot)\) \(\chi_{223}(59,\cdot)\) \(\chi_{223}(87,\cdot)\) \(\chi_{223}(91,\cdot)\) \(\chi_{223}(95,\cdot)\) \(\chi_{223}(103,\cdot)\) \(\chi_{223}(104,\cdot)\) \(\chi_{223}(108,\cdot)\) \(\chi_{223}(111,\cdot)\) \(\chi_{223}(118,\cdot)\) \(\chi_{223}(125,\cdot)\) \(\chi_{223}(141,\cdot)\) \(\chi_{223}(155,\cdot)\) \(\chi_{223}(157,\cdot)\) \(\chi_{223}(159,\cdot)\) \(\chi_{223}(163,\cdot)\) \(\chi_{223}(167,\cdot)\) \(\chi_{223}(174,\cdot)\) \(\chi_{223}(182,\cdot)\) \(\chi_{223}(189,\cdot)\) \(\chi_{223}(190,\cdot)\) \(\chi_{223}(191,\cdot)\) \(\chi_{223}(193,\cdot)\) \(\chi_{223}(195,\cdot)\) \(\chi_{223}(206,\cdot)\) \(\chi_{223}(207,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | Number field defined by a degree 74 polynomial |
Values on generators
\(3\) → \(e\left(\frac{1}{74}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 223 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{1}{74}\right)\) | \(e\left(\frac{32}{37}\right)\) | \(e\left(\frac{15}{74}\right)\) | \(e\left(\frac{33}{74}\right)\) | \(e\left(\frac{31}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{47}{74}\right)\) | \(e\left(\frac{33}{74}\right)\) |