Basic properties
Modulus: | \(3009\) | |
Conductor: | \(3009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(232\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3009.bh
\(\chi_{3009}(2,\cdot)\) \(\chi_{3009}(8,\cdot)\) \(\chi_{3009}(32,\cdot)\) \(\chi_{3009}(77,\cdot)\) \(\chi_{3009}(83,\cdot)\) \(\chi_{3009}(128,\cdot)\) \(\chi_{3009}(155,\cdot)\) \(\chi_{3009}(161,\cdot)\) \(\chi_{3009}(179,\cdot)\) \(\chi_{3009}(185,\cdot)\) \(\chi_{3009}(308,\cdot)\) \(\chi_{3009}(332,\cdot)\) \(\chi_{3009}(338,\cdot)\) \(\chi_{3009}(365,\cdot)\) \(\chi_{3009}(410,\cdot)\) \(\chi_{3009}(467,\cdot)\) \(\chi_{3009}(485,\cdot)\) \(\chi_{3009}(512,\cdot)\) \(\chi_{3009}(542,\cdot)\) \(\chi_{3009}(563,\cdot)\) \(\chi_{3009}(569,\cdot)\) \(\chi_{3009}(587,\cdot)\) \(\chi_{3009}(614,\cdot)\) \(\chi_{3009}(620,\cdot)\) \(\chi_{3009}(644,\cdot)\) \(\chi_{3009}(689,\cdot)\) \(\chi_{3009}(716,\cdot)\) \(\chi_{3009}(722,\cdot)\) \(\chi_{3009}(740,\cdot)\) \(\chi_{3009}(746,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{232})$ |
Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((1004,1771,1123)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{55}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 3009 }(155, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{116}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{131}{232}\right)\) | \(e\left(\frac{161}{232}\right)\) | \(e\left(\frac{11}{116}\right)\) | \(e\left(\frac{61}{232}\right)\) | \(e\left(\frac{77}{232}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{91}{232}\right)\) | \(e\left(\frac{23}{29}\right)\) |