Basic properties
Modulus: | \(1225\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 1225.bu
\(\chi_{1225}(3,\cdot)\) \(\chi_{1225}(12,\cdot)\) \(\chi_{1225}(17,\cdot)\) \(\chi_{1225}(33,\cdot)\) \(\chi_{1225}(38,\cdot)\) \(\chi_{1225}(47,\cdot)\) \(\chi_{1225}(52,\cdot)\) \(\chi_{1225}(73,\cdot)\) \(\chi_{1225}(87,\cdot)\) \(\chi_{1225}(103,\cdot)\) \(\chi_{1225}(108,\cdot)\) \(\chi_{1225}(122,\cdot)\) \(\chi_{1225}(138,\cdot)\) \(\chi_{1225}(152,\cdot)\) \(\chi_{1225}(173,\cdot)\) \(\chi_{1225}(187,\cdot)\) \(\chi_{1225}(192,\cdot)\) \(\chi_{1225}(208,\cdot)\) \(\chi_{1225}(213,\cdot)\) \(\chi_{1225}(222,\cdot)\) \(\chi_{1225}(248,\cdot)\) \(\chi_{1225}(262,\cdot)\) \(\chi_{1225}(278,\cdot)\) \(\chi_{1225}(283,\cdot)\) \(\chi_{1225}(292,\cdot)\) \(\chi_{1225}(297,\cdot)\) \(\chi_{1225}(327,\cdot)\) \(\chi_{1225}(348,\cdot)\) \(\chi_{1225}(353,\cdot)\) \(\chi_{1225}(367,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{5}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(292, a) \) | \(1\) | \(1\) | \(e\left(\frac{313}{420}\right)\) | \(e\left(\frac{281}{420}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{67}{420}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{103}{105}\right)\) |