Basic properties
Modulus: | \(2366\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2366.bk
\(\chi_{2366}(53,\cdot)\) \(\chi_{2366}(79,\cdot)\) \(\chi_{2366}(235,\cdot)\) \(\chi_{2366}(261,\cdot)\) \(\chi_{2366}(417,\cdot)\) \(\chi_{2366}(443,\cdot)\) \(\chi_{2366}(599,\cdot)\) \(\chi_{2366}(625,\cdot)\) \(\chi_{2366}(781,\cdot)\) \(\chi_{2366}(807,\cdot)\) \(\chi_{2366}(963,\cdot)\) \(\chi_{2366}(989,\cdot)\) \(\chi_{2366}(1145,\cdot)\) \(\chi_{2366}(1171,\cdot)\) \(\chi_{2366}(1327,\cdot)\) \(\chi_{2366}(1509,\cdot)\) \(\chi_{2366}(1535,\cdot)\) \(\chi_{2366}(1717,\cdot)\) \(\chi_{2366}(1873,\cdot)\) \(\chi_{2366}(1899,\cdot)\) \(\chi_{2366}(2055,\cdot)\) \(\chi_{2366}(2081,\cdot)\) \(\chi_{2366}(2237,\cdot)\) \(\chi_{2366}(2263,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((339,2199)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{10}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 2366 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) |