Basic properties
Modulus: | \(1007\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
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)
|
Galois orbit 1007.bh
\(\chi_{1007}(29,\cdot)\) \(\chi_{1007}(40,\cdot)\) \(\chi_{1007}(59,\cdot)\) \(\chi_{1007}(60,\cdot)\) \(\chi_{1007}(70,\cdot)\) \(\chi_{1007}(78,\cdot)\) \(\chi_{1007}(90,\cdot)\) \(\chi_{1007}(91,\cdot)\) \(\chi_{1007}(110,\cdot)\) \(\chi_{1007}(117,\cdot)\) \(\chi_{1007}(135,\cdot)\) \(\chi_{1007}(143,\cdot)\) \(\chi_{1007}(146,\cdot)\) \(\chi_{1007}(165,\cdot)\) \(\chi_{1007}(166,\cdot)\) \(\chi_{1007}(184,\cdot)\) \(\chi_{1007}(219,\cdot)\) \(\chi_{1007}(223,\cdot)\) \(\chi_{1007}(241,\cdot)\) \(\chi_{1007}(249,\cdot)\) \(\chi_{1007}(250,\cdot)\) \(\chi_{1007}(269,\cdot)\) \(\chi_{1007}(276,\cdot)\) \(\chi_{1007}(325,\cdot)\) \(\chi_{1007}(355,\cdot)\) \(\chi_{1007}(356,\cdot)\) \(\chi_{1007}(375,\cdot)\) \(\chi_{1007}(382,\cdot)\) \(\chi_{1007}(409,\cdot)\) \(\chi_{1007}(414,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{23}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1007 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{117}\right)\) | \(e\left(\frac{37}{117}\right)\) | \(e\left(\frac{77}{117}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{17}{117}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{25}{39}\right)\) |