Basic properties
Modulus: | \(3021\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(234\) | 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)
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Galois orbit 3021.ck
\(\chi_{3021}(44,\cdot)\) \(\chi_{3021}(47,\cdot)\) \(\chi_{3021}(119,\cdot)\) \(\chi_{3021}(206,\cdot)\) \(\chi_{3021}(275,\cdot)\) \(\chi_{3021}(365,\cdot)\) \(\chi_{3021}(386,\cdot)\) \(\chi_{3021}(434,\cdot)\) \(\chi_{3021}(473,\cdot)\) \(\chi_{3021}(593,\cdot)\) \(\chi_{3021}(632,\cdot)\) \(\chi_{3021}(731,\cdot)\) \(\chi_{3021}(758,\cdot)\) \(\chi_{3021}(788,\cdot)\) \(\chi_{3021}(842,\cdot)\) \(\chi_{3021}(872,\cdot)\) \(\chi_{3021}(890,\cdot)\) \(\chi_{3021}(917,\cdot)\) \(\chi_{3021}(929,\cdot)\) \(\chi_{3021}(947,\cdot)\) \(\chi_{3021}(1031,\cdot)\) \(\chi_{3021}(1043,\cdot)\) \(\chi_{3021}(1049,\cdot)\) \(\chi_{3021}(1070,\cdot)\) \(\chi_{3021}(1073,\cdot)\) \(\chi_{3021}(1088,\cdot)\) \(\chi_{3021}(1106,\cdot)\) \(\chi_{3021}(1157,\cdot)\) \(\chi_{3021}(1202,\cdot)\) \(\chi_{3021}(1232,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,1750,2281)\) → \((-1,e\left(\frac{5}{9}\right),e\left(\frac{11}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 3021 }(1955, a) \) | \(-1\) | \(1\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{94}{117}\right)\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{7}{117}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{10}{117}\right)\) | \(e\left(\frac{19}{234}\right)\) | \(e\left(\frac{71}{117}\right)\) |