Basic properties
Modulus: | \(3089\) | |
Conductor: | \(3089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(193\) | 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 3089.f
\(\chi_{3089}(16,\cdot)\) \(\chi_{3089}(39,\cdot)\) \(\chi_{3089}(43,\cdot)\) \(\chi_{3089}(50,\cdot)\) \(\chi_{3089}(55,\cdot)\) \(\chi_{3089}(73,\cdot)\) \(\chi_{3089}(90,\cdot)\) \(\chi_{3089}(94,\cdot)\) \(\chi_{3089}(99,\cdot)\) \(\chi_{3089}(139,\cdot)\) \(\chi_{3089}(140,\cdot)\) \(\chi_{3089}(154,\cdot)\) \(\chi_{3089}(162,\cdot)\) \(\chi_{3089}(181,\cdot)\) \(\chi_{3089}(221,\cdot)\) \(\chi_{3089}(236,\cdot)\) \(\chi_{3089}(244,\cdot)\) \(\chi_{3089}(249,\cdot)\) \(\chi_{3089}(252,\cdot)\) \(\chi_{3089}(256,\cdot)\) \(\chi_{3089}(307,\cdot)\) \(\chi_{3089}(310,\cdot)\) \(\chi_{3089}(337,\cdot)\) \(\chi_{3089}(341,\cdot)\) \(\chi_{3089}(353,\cdot)\) \(\chi_{3089}(371,\cdot)\) \(\chi_{3089}(380,\cdot)\) \(\chi_{3089}(392,\cdot)\) \(\chi_{3089}(418,\cdot)\) \(\chi_{3089}(421,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{193})$ |
Fixed field: | Number field defined by a degree 193 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{122}{193}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 3089 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{92}{193}\right)\) | \(e\left(\frac{122}{193}\right)\) | \(e\left(\frac{184}{193}\right)\) | \(e\left(\frac{47}{193}\right)\) | \(e\left(\frac{21}{193}\right)\) | \(e\left(\frac{78}{193}\right)\) | \(e\left(\frac{83}{193}\right)\) | \(e\left(\frac{51}{193}\right)\) | \(e\left(\frac{139}{193}\right)\) | \(e\left(\frac{36}{193}\right)\) |