Basic properties
| Modulus: | \(2153\) | |
| Conductor: | \(2153\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(538\) | 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.f
\(\chi_{2153}(4,\cdot)\) \(\chi_{2153}(28,\cdot)\) \(\chi_{2153}(30,\cdot)\) \(\chi_{2153}(38,\cdot)\) \(\chi_{2153}(39,\cdot)\) \(\chi_{2153}(62,\cdot)\) \(\chi_{2153}(64,\cdot)\) \(\chi_{2153}(66,\cdot)\) \(\chi_{2153}(69,\cdot)\) \(\chi_{2153}(72,\cdot)\) \(\chi_{2153}(74,\cdot)\) \(\chi_{2153}(81,\cdot)\) \(\chi_{2153}(82,\cdot)\) \(\chi_{2153}(83,\cdot)\) \(\chi_{2153}(116,\cdot)\) \(\chi_{2153}(118,\cdot)\) \(\chi_{2153}(137,\cdot)\) \(\chi_{2153}(159,\cdot)\) \(\chi_{2153}(170,\cdot)\) \(\chi_{2153}(173,\cdot)\) \(\chi_{2153}(179,\cdot)\) \(\chi_{2153}(196,\cdot)\) \(\chi_{2153}(200,\cdot)\) \(\chi_{2153}(210,\cdot)\) \(\chi_{2153}(213,\cdot)\) \(\chi_{2153}(214,\cdot)\) \(\chi_{2153}(221,\cdot)\) \(\chi_{2153}(225,\cdot)\) \(\chi_{2153}(233,\cdot)\) \(\chi_{2153}(254,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{269})$ |
| Fixed field: | Number field defined by a degree 538 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{367}{538}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2153 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{247}{269}\right)\) | \(e\left(\frac{367}{538}\right)\) | \(e\left(\frac{225}{269}\right)\) | \(e\left(\frac{457}{538}\right)\) | \(e\left(\frac{323}{538}\right)\) | \(e\left(\frac{153}{269}\right)\) | \(e\left(\frac{203}{269}\right)\) | \(e\left(\frac{98}{269}\right)\) | \(e\left(\frac{413}{538}\right)\) | \(e\left(\frac{381}{538}\right)\) |