Basic properties
| Modulus: | \(28900\) | |
| Conductor: | \(7225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(680\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{7225}(77,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 28900.fa
\(\chi_{28900}(53,\cdot)\) \(\chi_{28900}(77,\cdot)\) \(\chi_{28900}(253,\cdot)\) \(\chi_{28900}(297,\cdot)\) \(\chi_{28900}(417,\cdot)\) \(\chi_{28900}(637,\cdot)\) \(\chi_{28900}(933,\cdot)\) \(\chi_{28900}(1073,\cdot)\) \(\chi_{28900}(1097,\cdot)\) \(\chi_{28900}(1273,\cdot)\) \(\chi_{28900}(1317,\cdot)\) \(\chi_{28900}(1413,\cdot)\) \(\chi_{28900}(1437,\cdot)\) \(\chi_{28900}(1613,\cdot)\) \(\chi_{28900}(1753,\cdot)\) \(\chi_{28900}(1777,\cdot)\) \(\chi_{28900}(1953,\cdot)\) \(\chi_{28900}(1997,\cdot)\) \(\chi_{28900}(2117,\cdot)\) \(\chi_{28900}(2337,\cdot)\) \(\chi_{28900}(2433,\cdot)\) \(\chi_{28900}(2633,\cdot)\) \(\chi_{28900}(2677,\cdot)\) \(\chi_{28900}(2773,\cdot)\) \(\chi_{28900}(2797,\cdot)\) \(\chi_{28900}(2973,\cdot)\) \(\chi_{28900}(3017,\cdot)\) \(\chi_{28900}(3113,\cdot)\) \(\chi_{28900}(3137,\cdot)\) \(\chi_{28900}(3453,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{680})$ |
| Fixed field: | Number field defined by a degree 680 polynomial (not computed) |
Values on generators
\((14451,24277,23701)\) → \((1,e\left(\frac{1}{20}\right),e\left(\frac{89}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 28900 }(77, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{680}\right)\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{3}{340}\right)\) | \(e\left(\frac{579}{680}\right)\) | \(e\left(\frac{73}{340}\right)\) | \(e\left(\frac{21}{340}\right)\) | \(e\left(\frac{117}{170}\right)\) | \(e\left(\frac{329}{680}\right)\) | \(e\left(\frac{9}{680}\right)\) | \(e\left(\frac{613}{680}\right)\) |