Basic properties
Modulus: | \(4033\) | |
Conductor: | \(4033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 4033.ig
\(\chi_{4033}(18,\cdot)\) \(\chi_{4033}(79,\cdot)\) \(\chi_{4033}(98,\cdot)\) \(\chi_{4033}(224,\cdot)\) \(\chi_{4033}(313,\cdot)\) \(\chi_{4033}(389,\cdot)\) \(\chi_{4033}(535,\cdot)\) \(\chi_{4033}(587,\cdot)\) \(\chi_{4033}(705,\cdot)\) \(\chi_{4033}(1021,\cdot)\) \(\chi_{4033}(1256,\cdot)\) \(\chi_{4033}(1456,\cdot)\) \(\chi_{4033}(1461,\cdot)\) \(\chi_{4033}(1467,\cdot)\) \(\chi_{4033}(1539,\cdot)\) \(\chi_{4033}(1611,\cdot)\) \(\chi_{4033}(1707,\cdot)\) \(\chi_{4033}(1909,\cdot)\) \(\chi_{4033}(2124,\cdot)\) \(\chi_{4033}(2326,\cdot)\) \(\chi_{4033}(2422,\cdot)\) \(\chi_{4033}(2494,\cdot)\) \(\chi_{4033}(2566,\cdot)\) \(\chi_{4033}(2572,\cdot)\) \(\chi_{4033}(2577,\cdot)\) \(\chi_{4033}(2777,\cdot)\) \(\chi_{4033}(3012,\cdot)\) \(\chi_{4033}(3328,\cdot)\) \(\chi_{4033}(3446,\cdot)\) \(\chi_{4033}(3498,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{31}{36}\right),e\left(\frac{67}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1539, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{19}{108}\right)\) | \(e\left(\frac{35}{108}\right)\) |