Basic properties
Modulus: | \(1339\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | 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 1339.bs
\(\chi_{1339}(4,\cdot)\) \(\chi_{1339}(17,\cdot)\) \(\chi_{1339}(49,\cdot)\) \(\chi_{1339}(82,\cdot)\) \(\chi_{1339}(231,\cdot)\) \(\chi_{1339}(238,\cdot)\) \(\chi_{1339}(264,\cdot)\) \(\chi_{1339}(316,\cdot)\) \(\chi_{1339}(335,\cdot)\) \(\chi_{1339}(342,\cdot)\) \(\chi_{1339}(407,\cdot)\) \(\chi_{1339}(517,\cdot)\) \(\chi_{1339}(543,\cdot)\) \(\chi_{1339}(556,\cdot)\) \(\chi_{1339}(634,\cdot)\) \(\chi_{1339}(647,\cdot)\) \(\chi_{1339}(654,\cdot)\) \(\chi_{1339}(673,\cdot)\) \(\chi_{1339}(686,\cdot)\) \(\chi_{1339}(771,\cdot)\) \(\chi_{1339}(784,\cdot)\) \(\chi_{1339}(842,\cdot)\) \(\chi_{1339}(862,\cdot)\) \(\chi_{1339}(907,\cdot)\) \(\chi_{1339}(946,\cdot)\) \(\chi_{1339}(979,\cdot)\) \(\chi_{1339}(1018,\cdot)\) \(\chi_{1339}(1024,\cdot)\) \(\chi_{1339}(1089,\cdot)\) \(\chi_{1339}(1122,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{38}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1339 }(1018, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{102}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{21}{34}\right)\) |