Basic properties
Modulus: | \(4033\) | |
Conductor: | \(4033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.ir
\(\chi_{4033}(10,\cdot)\) \(\chi_{4033}(174,\cdot)\) \(\chi_{4033}(232,\cdot)\) \(\chi_{4033}(248,\cdot)\) \(\chi_{4033}(269,\cdot)\) \(\chi_{4033}(285,\cdot)\) \(\chi_{4033}(380,\cdot)\) \(\chi_{4033}(602,\cdot)\) \(\chi_{4033}(750,\cdot)\) \(\chi_{4033}(787,\cdot)\) \(\chi_{4033}(914,\cdot)\) \(\chi_{4033}(951,\cdot)\) \(\chi_{4033}(1025,\cdot)\) \(\chi_{4033}(1210,\cdot)\) \(\chi_{4033}(1268,\cdot)\) \(\chi_{4033}(1358,\cdot)\) \(\chi_{4033}(1617,\cdot)\) \(\chi_{4033}(1675,\cdot)\) \(\chi_{4033}(2024,\cdot)\) \(\chi_{4033}(2156,\cdot)\) \(\chi_{4033}(2193,\cdot)\) \(\chi_{4033}(2341,\cdot)\) \(\chi_{4033}(2468,\cdot)\) \(\chi_{4033}(2563,\cdot)\) \(\chi_{4033}(2579,\cdot)\) \(\chi_{4033}(2653,\cdot)\) \(\chi_{4033}(2674,\cdot)\) \(\chi_{4033}(2711,\cdot)\) \(\chi_{4033}(2764,\cdot)\) \(\chi_{4033}(2933,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{25}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{25}{108}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{23}{108}\right)\) |