Basic properties
| Modulus: | \(2153\) | |
| Conductor: | \(2153\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2152\) | 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 2153.h
\(\chi_{2153}(3,\cdot)\) \(\chi_{2153}(5,\cdot)\) \(\chi_{2153}(6,\cdot)\) \(\chi_{2153}(10,\cdot)\) \(\chi_{2153}(11,\cdot)\) \(\chi_{2153}(12,\cdot)\) \(\chi_{2153}(13,\cdot)\) \(\chi_{2153}(17,\cdot)\) \(\chi_{2153}(20,\cdot)\) \(\chi_{2153}(21,\cdot)\) \(\chi_{2153}(22,\cdot)\) \(\chi_{2153}(23,\cdot)\) \(\chi_{2153}(24,\cdot)\) \(\chi_{2153}(26,\cdot)\) \(\chi_{2153}(27,\cdot)\) \(\chi_{2153}(34,\cdot)\) \(\chi_{2153}(35,\cdot)\) \(\chi_{2153}(40,\cdot)\) \(\chi_{2153}(42,\cdot)\) \(\chi_{2153}(43,\cdot)\) \(\chi_{2153}(44,\cdot)\) \(\chi_{2153}(45,\cdot)\) \(\chi_{2153}(46,\cdot)\) \(\chi_{2153}(47,\cdot)\) \(\chi_{2153}(48,\cdot)\) \(\chi_{2153}(52,\cdot)\) \(\chi_{2153}(53,\cdot)\) \(\chi_{2153}(54,\cdot)\) \(\chi_{2153}(57,\cdot)\) \(\chi_{2153}(61,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2152})$ |
| Fixed field: | Number field defined by a degree 2152 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{2152}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2153 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{955}{1076}\right)\) | \(e\left(\frac{1}{2152}\right)\) | \(e\left(\frac{417}{538}\right)\) | \(e\left(\frac{765}{2152}\right)\) | \(e\left(\frac{1911}{2152}\right)\) | \(e\left(\frac{244}{269}\right)\) | \(e\left(\frac{713}{1076}\right)\) | \(e\left(\frac{1}{1076}\right)\) | \(e\left(\frac{523}{2152}\right)\) | \(e\left(\frac{885}{2152}\right)\) |