Basic properties
Modulus: | \(7605\) | |
Conductor: | \(7605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | 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 7605.hl
\(\chi_{7605}(187,\cdot)\) \(\chi_{7605}(382,\cdot)\) \(\chi_{7605}(463,\cdot)\) \(\chi_{7605}(772,\cdot)\) \(\chi_{7605}(853,\cdot)\) \(\chi_{7605}(967,\cdot)\) \(\chi_{7605}(1048,\cdot)\) \(\chi_{7605}(1357,\cdot)\) \(\chi_{7605}(1438,\cdot)\) \(\chi_{7605}(1552,\cdot)\) \(\chi_{7605}(1633,\cdot)\) \(\chi_{7605}(1942,\cdot)\) \(\chi_{7605}(2023,\cdot)\) \(\chi_{7605}(2137,\cdot)\) \(\chi_{7605}(2218,\cdot)\) \(\chi_{7605}(2527,\cdot)\) \(\chi_{7605}(2608,\cdot)\) \(\chi_{7605}(2722,\cdot)\) \(\chi_{7605}(3193,\cdot)\) \(\chi_{7605}(3307,\cdot)\) \(\chi_{7605}(3388,\cdot)\) \(\chi_{7605}(3697,\cdot)\) \(\chi_{7605}(3778,\cdot)\) \(\chi_{7605}(3892,\cdot)\) \(\chi_{7605}(3973,\cdot)\) \(\chi_{7605}(4282,\cdot)\) \(\chi_{7605}(4363,\cdot)\) \(\chi_{7605}(4477,\cdot)\) \(\chi_{7605}(4558,\cdot)\) \(\chi_{7605}(4867,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{31}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(i\) | \(e\left(\frac{7}{12}\right)\) |