Basic properties
| Modulus: | \(2153\) | |
| Conductor: | \(2153\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1076\) | 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.g
\(\chi_{2153}(2,\cdot)\) \(\chi_{2153}(8,\cdot)\) \(\chi_{2153}(9,\cdot)\) \(\chi_{2153}(14,\cdot)\) \(\chi_{2153}(15,\cdot)\) \(\chi_{2153}(19,\cdot)\) \(\chi_{2153}(25,\cdot)\) \(\chi_{2153}(31,\cdot)\) \(\chi_{2153}(32,\cdot)\) \(\chi_{2153}(33,\cdot)\) \(\chi_{2153}(36,\cdot)\) \(\chi_{2153}(37,\cdot)\) \(\chi_{2153}(41,\cdot)\) \(\chi_{2153}(51,\cdot)\) \(\chi_{2153}(55,\cdot)\) \(\chi_{2153}(56,\cdot)\) \(\chi_{2153}(58,\cdot)\) \(\chi_{2153}(59,\cdot)\) \(\chi_{2153}(60,\cdot)\) \(\chi_{2153}(63,\cdot)\) \(\chi_{2153}(73,\cdot)\) \(\chi_{2153}(76,\cdot)\) \(\chi_{2153}(78,\cdot)\) \(\chi_{2153}(79,\cdot)\) \(\chi_{2153}(85,\cdot)\) \(\chi_{2153}(89,\cdot)\) \(\chi_{2153}(98,\cdot)\) \(\chi_{2153}(100,\cdot)\) \(\chi_{2153}(103,\cdot)\) \(\chi_{2153}(105,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1076})$ |
| Fixed field: | Number field defined by a degree 1076 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1039}{1076}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2153 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{538}\right)\) | \(e\left(\frac{1039}{1076}\right)\) | \(e\left(\frac{173}{269}\right)\) | \(e\left(\frac{747}{1076}\right)\) | \(e\left(\frac{309}{1076}\right)\) | \(e\left(\frac{236}{269}\right)\) | \(e\left(\frac{519}{538}\right)\) | \(e\left(\frac{501}{538}\right)\) | \(e\left(\frac{17}{1076}\right)\) | \(e\left(\frac{611}{1076}\right)\) |