Basic properties
Modulus: | \(4029\) | |
Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(624\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1343}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.da
\(\chi_{4029}(31,\cdot)\) \(\chi_{4029}(40,\cdot)\) \(\chi_{4029}(73,\cdot)\) \(\chi_{4029}(88,\cdot)\) \(\chi_{4029}(124,\cdot)\) \(\chi_{4029}(130,\cdot)\) \(\chi_{4029}(160,\cdot)\) \(\chi_{4029}(163,\cdot)\) \(\chi_{4029}(184,\cdot)\) \(\chi_{4029}(190,\cdot)\) \(\chi_{4029}(241,\cdot)\) \(\chi_{4029}(250,\cdot)\) \(\chi_{4029}(262,\cdot)\) \(\chi_{4029}(277,\cdot)\) \(\chi_{4029}(286,\cdot)\) \(\chi_{4029}(313,\cdot)\) \(\chi_{4029}(352,\cdot)\) \(\chi_{4029}(367,\cdot)\) \(\chi_{4029}(388,\cdot)\) \(\chi_{4029}(397,\cdot)\) \(\chi_{4029}(415,\cdot)\) \(\chi_{4029}(439,\cdot)\) \(\chi_{4029}(445,\cdot)\) \(\chi_{4029}(487,\cdot)\) \(\chi_{4029}(490,\cdot)\) \(\chi_{4029}(499,\cdot)\) \(\chi_{4029}(505,\cdot)\) \(\chi_{4029}(547,\cdot)\) \(\chi_{4029}(550,\cdot)\) \(\chi_{4029}(589,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{624})$ |
Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{28}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{233}{312}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{203}{624}\right)\) | \(e\left(\frac{149}{624}\right)\) | \(e\left(\frac{25}{104}\right)\) | \(e\left(\frac{15}{208}\right)\) | \(e\left(\frac{473}{624}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{205}{208}\right)\) | \(e\left(\frac{77}{78}\right)\) |