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 \(\chi_{1343}(607,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cy
\(\chi_{4029}(7,\cdot)\) \(\chi_{4029}(28,\cdot)\) \(\chi_{4029}(37,\cdot)\) \(\chi_{4029}(82,\cdot)\) \(\chi_{4029}(109,\cdot)\) \(\chi_{4029}(133,\cdot)\) \(\chi_{4029}(139,\cdot)\) \(\chi_{4029}(142,\cdot)\) \(\chi_{4029}(193,\cdot)\) \(\chi_{4029}(211,\cdot)\) \(\chi_{4029}(226,\cdot)\) \(\chi_{4029}(232,\cdot)\) \(\chi_{4029}(235,\cdot)\) \(\chi_{4029}(244,\cdot)\) \(\chi_{4029}(265,\cdot)\) \(\chi_{4029}(346,\cdot)\) \(\chi_{4029}(364,\cdot)\) \(\chi_{4029}(379,\cdot)\) \(\chi_{4029}(430,\cdot)\) \(\chi_{4029}(448,\cdot)\) \(\chi_{4029}(454,\cdot)\) \(\chi_{4029}(469,\cdot)\) \(\chi_{4029}(481,\cdot)\) \(\chi_{4029}(517,\cdot)\) \(\chi_{4029}(556,\cdot)\) \(\chi_{4029}(583,\cdot)\) \(\chi_{4029}(592,\cdot)\) \(\chi_{4029}(601,\cdot)\) \(\chi_{4029}(607,\cdot)\) \(\chi_{4029}(619,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{624})$ |
Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{7}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(607, a) \) | \(1\) | \(1\) | \(e\left(\frac{229}{312}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{391}{624}\right)\) | \(e\left(\frac{433}{624}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{75}{208}\right)\) | \(e\left(\frac{493}{624}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{89}{208}\right)\) | \(e\left(\frac{73}{78}\right)\) |