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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1007.bg
\(\chi_{1007}(4,\cdot)\) \(\chi_{1007}(6,\cdot)\) \(\chi_{1007}(9,\cdot)\) \(\chi_{1007}(17,\cdot)\) \(\chi_{1007}(25,\cdot)\) \(\chi_{1007}(43,\cdot)\) \(\chi_{1007}(62,\cdot)\) \(\chi_{1007}(82,\cdot)\) \(\chi_{1007}(93,\cdot)\) \(\chi_{1007}(112,\cdot)\) \(\chi_{1007}(123,\cdot)\) \(\chi_{1007}(131,\cdot)\) \(\chi_{1007}(149,\cdot)\) \(\chi_{1007}(168,\cdot)\) \(\chi_{1007}(176,\cdot)\) \(\chi_{1007}(188,\cdot)\) \(\chi_{1007}(196,\cdot)\) \(\chi_{1007}(199,\cdot)\) \(\chi_{1007}(218,\cdot)\) \(\chi_{1007}(237,\cdot)\) \(\chi_{1007}(252,\cdot)\) \(\chi_{1007}(271,\cdot)\) \(\chi_{1007}(272,\cdot)\) \(\chi_{1007}(282,\cdot)\) \(\chi_{1007}(290,\cdot)\) \(\chi_{1007}(294,\cdot)\) \(\chi_{1007}(302,\cdot)\) \(\chi_{1007}(308,\cdot)\) \(\chi_{1007}(327,\cdot)\) \(\chi_{1007}(329,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{1}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1007 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{234}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{22}{39}\right)\) |