Basic properties
Modulus: | \(1849\) | |
Conductor: | \(1849\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(301\) | 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 1849.m
\(\chi_{1849}(4,\cdot)\) \(\chi_{1849}(11,\cdot)\) \(\chi_{1849}(16,\cdot)\) \(\chi_{1849}(21,\cdot)\) \(\chi_{1849}(35,\cdot)\) \(\chi_{1849}(41,\cdot)\) \(\chi_{1849}(47,\cdot)\) \(\chi_{1849}(54,\cdot)\) \(\chi_{1849}(59,\cdot)\) \(\chi_{1849}(64,\cdot)\) \(\chi_{1849}(84,\cdot)\) \(\chi_{1849}(90,\cdot)\) \(\chi_{1849}(97,\cdot)\) \(\chi_{1849}(102,\cdot)\) \(\chi_{1849}(107,\cdot)\) \(\chi_{1849}(121,\cdot)\) \(\chi_{1849}(127,\cdot)\) \(\chi_{1849}(133,\cdot)\) \(\chi_{1849}(140,\cdot)\) \(\chi_{1849}(145,\cdot)\) \(\chi_{1849}(150,\cdot)\) \(\chi_{1849}(164,\cdot)\) \(\chi_{1849}(170,\cdot)\) \(\chi_{1849}(176,\cdot)\) \(\chi_{1849}(183,\cdot)\) \(\chi_{1849}(188,\cdot)\) \(\chi_{1849}(193,\cdot)\) \(\chi_{1849}(207,\cdot)\) \(\chi_{1849}(213,\cdot)\) \(\chi_{1849}(219,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{301})$ |
Fixed field: | Number field defined by a degree 301 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{99}{301}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1849 }(170, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{301}\right)\) | \(e\left(\frac{99}{301}\right)\) | \(e\left(\frac{110}{301}\right)\) | \(e\left(\frac{144}{301}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{165}{301}\right)\) | \(e\left(\frac{198}{301}\right)\) | \(e\left(\frac{199}{301}\right)\) | \(e\left(\frac{163}{301}\right)\) |