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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.jr
\(\chi_{4033}(61,\cdot)\) \(\chi_{4033}(106,\cdot)\) \(\chi_{4033}(246,\cdot)\) \(\chi_{4033}(301,\cdot)\) \(\chi_{4033}(387,\cdot)\) \(\chi_{4033}(647,\cdot)\) \(\chi_{4033}(758,\cdot)\) \(\chi_{4033}(799,\cdot)\) \(\chi_{4033}(846,\cdot)\) \(\chi_{4033}(1164,\cdot)\) \(\chi_{4033}(1337,\cdot)\) \(\chi_{4033}(1408,\cdot)\) \(\chi_{4033}(1626,\cdot)\) \(\chi_{4033}(1647,\cdot)\) \(\chi_{4033}(1719,\cdot)\) \(\chi_{4033}(1882,\cdot)\) \(\chi_{4033}(2050,\cdot)\) \(\chi_{4033}(2240,\cdot)\) \(\chi_{4033}(2383,\cdot)\) \(\chi_{4033}(2418,\cdot)\) \(\chi_{4033}(2609,\cdot)\) \(\chi_{4033}(2677,\cdot)\) \(\chi_{4033}(2703,\cdot)\) \(\chi_{4033}(2720,\cdot)\) \(\chi_{4033}(2862,\cdot)\) \(\chi_{4033}(2921,\cdot)\) \(\chi_{4033}(3017,\cdot)\) \(\chi_{4033}(3197,\cdot)\) \(\chi_{4033}(3572,\cdot)\) \(\chi_{4033}(3594,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{5}{36}\right),e\left(\frac{53}{54}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(106, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(i\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{17}{27}\right)\) |