Basic properties
Modulus: | \(4029\) | |
Conductor: | \(4029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(624\) | 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 4029.cz
\(\chi_{4029}(5,\cdot)\) \(\chi_{4029}(11,\cdot)\) \(\chi_{4029}(20,\cdot)\) \(\chi_{4029}(44,\cdot)\) \(\chi_{4029}(92,\cdot)\) \(\chi_{4029}(95,\cdot)\) \(\chi_{4029}(167,\cdot)\) \(\chi_{4029}(194,\cdot)\) \(\chi_{4029}(209,\cdot)\) \(\chi_{4029}(248,\cdot)\) \(\chi_{4029}(269,\cdot)\) \(\chi_{4029}(320,\cdot)\) \(\chi_{4029}(329,\cdot)\) \(\chi_{4029}(335,\cdot)\) \(\chi_{4029}(347,\cdot)\) \(\chi_{4029}(431,\cdot)\) \(\chi_{4029}(437,\cdot)\) \(\chi_{4029}(479,\cdot)\) \(\chi_{4029}(500,\cdot)\) \(\chi_{4029}(524,\cdot)\) \(\chi_{4029}(566,\cdot)\) \(\chi_{4029}(572,\cdot)\) \(\chi_{4029}(584,\cdot)\) \(\chi_{4029}(602,\cdot)\) \(\chi_{4029}(626,\cdot)\) \(\chi_{4029}(641,\cdot)\) \(\chi_{4029}(668,\cdot)\) \(\chi_{4029}(674,\cdot)\) \(\chi_{4029}(677,\cdot)\) \(\chi_{4029}(683,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{624})$ |
Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{38}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(1229, a) \) | \(1\) | \(1\) | \(e\left(\frac{241}{312}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{295}{624}\right)\) | \(e\left(\frac{49}{624}\right)\) | \(e\left(\frac{33}{104}\right)\) | \(e\left(\frac{51}{208}\right)\) | \(e\left(\frac{589}{624}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{177}{208}\right)\) | \(e\left(\frac{7}{78}\right)\) |