Basic properties
Modulus: | \(1213\) | |
Conductor: | \(1213\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1212\) | 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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1213.l
\(\chi_{1213}(2,\cdot)\) \(\chi_{1213}(5,\cdot)\) \(\chi_{1213}(6,\cdot)\) \(\chi_{1213}(14,\cdot)\) \(\chi_{1213}(20,\cdot)\) \(\chi_{1213}(23,\cdot)\) \(\chi_{1213}(24,\cdot)\) \(\chi_{1213}(26,\cdot)\) \(\chi_{1213}(32,\cdot)\) \(\chi_{1213}(38,\cdot)\) \(\chi_{1213}(41,\cdot)\) \(\chi_{1213}(45,\cdot)\) \(\chi_{1213}(50,\cdot)\) \(\chi_{1213}(51,\cdot)\) \(\chi_{1213}(54,\cdot)\) \(\chi_{1213}(55,\cdot)\) \(\chi_{1213}(56,\cdot)\) \(\chi_{1213}(59,\cdot)\) \(\chi_{1213}(60,\cdot)\) \(\chi_{1213}(62,\cdot)\) \(\chi_{1213}(65,\cdot)\) \(\chi_{1213}(66,\cdot)\) \(\chi_{1213}(67,\cdot)\) \(\chi_{1213}(68,\cdot)\) \(\chi_{1213}(69,\cdot)\) \(\chi_{1213}(72,\cdot)\) \(\chi_{1213}(78,\cdot)\) \(\chi_{1213}(88,\cdot)\) \(\chi_{1213}(89,\cdot)\) \(\chi_{1213}(103,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1212})$ |
Fixed field: | Number field defined by a degree 1212 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1212}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1213 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{1212}\right)\) | \(e\left(\frac{232}{303}\right)\) | \(e\left(\frac{1}{606}\right)\) | \(e\left(\frac{209}{1212}\right)\) | \(e\left(\frac{929}{1212}\right)\) | \(e\left(\frac{64}{303}\right)\) | \(e\left(\frac{1}{404}\right)\) | \(e\left(\frac{161}{303}\right)\) | \(e\left(\frac{35}{202}\right)\) | \(e\left(\frac{331}{606}\right)\) |