Basic properties
Modulus: | \(4029\) | |
Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(104\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1343}(757,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cj
\(\chi_{4029}(100,\cdot)\) \(\chi_{4029}(196,\cdot)\) \(\chi_{4029}(223,\cdot)\) \(\chi_{4029}(247,\cdot)\) \(\chi_{4029}(304,\cdot)\) \(\chi_{4029}(433,\cdot)\) \(\chi_{4029}(457,\cdot)\) \(\chi_{4029}(484,\cdot)\) \(\chi_{4029}(733,\cdot)\) \(\chi_{4029}(757,\cdot)\) \(\chi_{4029}(763,\cdot)\) \(\chi_{4029}(808,\cdot)\) \(\chi_{4029}(994,\cdot)\) \(\chi_{4029}(1012,\cdot)\) \(\chi_{4029}(1045,\cdot)\) \(\chi_{4029}(1114,\cdot)\) \(\chi_{4029}(1171,\cdot)\) \(\chi_{4029}(1249,\cdot)\) \(\chi_{4029}(1351,\cdot)\) \(\chi_{4029}(1522,\cdot)\) \(\chi_{4029}(1681,\cdot)\) \(\chi_{4029}(1726,\cdot)\) \(\chi_{4029}(1759,\cdot)\) \(\chi_{4029}(1855,\cdot)\) \(\chi_{4029}(1879,\cdot)\) \(\chi_{4029}(1906,\cdot)\) \(\chi_{4029}(1963,\cdot)\) \(\chi_{4029}(2116,\cdot)\) \(\chi_{4029}(2185,\cdot)\) \(\chi_{4029}(2416,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{104})$ |
Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{5}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(757, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{49}{104}\right)\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{3}{104}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{5}{104}\right)\) | \(e\left(\frac{2}{13}\right)\) |