Basic properties
Modulus: | \(1849\) | |
Conductor: | \(1849\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(903\) | 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.o
\(\chi_{1849}(9,\cdot)\) \(\chi_{1849}(10,\cdot)\) \(\chi_{1849}(13,\cdot)\) \(\chi_{1849}(14,\cdot)\) \(\chi_{1849}(15,\cdot)\) \(\chi_{1849}(17,\cdot)\) \(\chi_{1849}(23,\cdot)\) \(\chi_{1849}(24,\cdot)\) \(\chi_{1849}(25,\cdot)\) \(\chi_{1849}(31,\cdot)\) \(\chi_{1849}(38,\cdot)\) \(\chi_{1849}(40,\cdot)\) \(\chi_{1849}(52,\cdot)\) \(\chi_{1849}(53,\cdot)\) \(\chi_{1849}(56,\cdot)\) \(\chi_{1849}(57,\cdot)\) \(\chi_{1849}(58,\cdot)\) \(\chi_{1849}(60,\cdot)\) \(\chi_{1849}(66,\cdot)\) \(\chi_{1849}(67,\cdot)\) \(\chi_{1849}(68,\cdot)\) \(\chi_{1849}(74,\cdot)\) \(\chi_{1849}(81,\cdot)\) \(\chi_{1849}(83,\cdot)\) \(\chi_{1849}(95,\cdot)\) \(\chi_{1849}(96,\cdot)\) \(\chi_{1849}(99,\cdot)\) \(\chi_{1849}(100,\cdot)\) \(\chi_{1849}(101,\cdot)\) \(\chi_{1849}(103,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{903})$ |
Fixed field: | Number field defined by a degree 903 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{730}{903}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1849 }(99, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{301}\right)\) | \(e\left(\frac{730}{903}\right)\) | \(e\left(\frac{92}{301}\right)\) | \(e\left(\frac{22}{903}\right)\) | \(e\left(\frac{124}{129}\right)\) | \(e\left(\frac{8}{129}\right)\) | \(e\left(\frac{138}{301}\right)\) | \(e\left(\frac{557}{903}\right)\) | \(e\left(\frac{160}{903}\right)\) | \(e\left(\frac{202}{301}\right)\) |