Basic properties
| Modulus: | \(2153\) | |
| Conductor: | \(2153\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(269\) | 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 2153.e
\(\chi_{2153}(7,\cdot)\) \(\chi_{2153}(16,\cdot)\) \(\chi_{2153}(18,\cdot)\) \(\chi_{2153}(29,\cdot)\) \(\chi_{2153}(49,\cdot)\) \(\chi_{2153}(50,\cdot)\) \(\chi_{2153}(65,\cdot)\) \(\chi_{2153}(67,\cdot)\) \(\chi_{2153}(102,\cdot)\) \(\chi_{2153}(110,\cdot)\) \(\chi_{2153}(112,\cdot)\) \(\chi_{2153}(115,\cdot)\) \(\chi_{2153}(120,\cdot)\) \(\chi_{2153}(126,\cdot)\) \(\chi_{2153}(135,\cdot)\) \(\chi_{2153}(143,\cdot)\) \(\chi_{2153}(146,\cdot)\) \(\chi_{2153}(152,\cdot)\) \(\chi_{2153}(156,\cdot)\) \(\chi_{2153}(158,\cdot)\) \(\chi_{2153}(163,\cdot)\) \(\chi_{2153}(171,\cdot)\) \(\chi_{2153}(178,\cdot)\) \(\chi_{2153}(183,\cdot)\) \(\chi_{2153}(203,\cdot)\) \(\chi_{2153}(206,\cdot)\) \(\chi_{2153}(218,\cdot)\) \(\chi_{2153}(239,\cdot)\) \(\chi_{2153}(242,\cdot)\) \(\chi_{2153}(248,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{269})$ |
| Fixed field: | Number field defined by a degree 269 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{239}{269}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2153 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{266}{269}\right)\) | \(e\left(\frac{239}{269}\right)\) | \(e\left(\frac{263}{269}\right)\) | \(e\left(\frac{184}{269}\right)\) | \(e\left(\frac{236}{269}\right)\) | \(e\left(\frac{82}{269}\right)\) | \(e\left(\frac{260}{269}\right)\) | \(e\left(\frac{209}{269}\right)\) | \(e\left(\frac{181}{269}\right)\) | \(e\left(\frac{81}{269}\right)\) |