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.ii
\(\chi_{4033}(171,\cdot)\) \(\chi_{4033}(236,\cdot)\) \(\chi_{4033}(643,\cdot)\) \(\chi_{4033}(711,\cdot)\) \(\chi_{4033}(726,\cdot)\) \(\chi_{4033}(769,\cdot)\) \(\chi_{4033}(896,\cdot)\) \(\chi_{4033}(902,\cdot)\) \(\chi_{4033}(911,\cdot)\) \(\chi_{4033}(991,\cdot)\) \(\chi_{4033}(1213,\cdot)\) \(\chi_{4033}(1250,\cdot)\) \(\chi_{4033}(1361,\cdot)\) \(\chi_{4033}(1568,\cdot)\) \(\chi_{4033}(1679,\cdot)\) \(\chi_{4033}(1731,\cdot)\) \(\chi_{4033}(1784,\cdot)\) \(\chi_{4033}(2012,\cdot)\) \(\chi_{4033}(2021,\cdot)\) \(\chi_{4033}(2249,\cdot)\) \(\chi_{4033}(2302,\cdot)\) \(\chi_{4033}(2354,\cdot)\) \(\chi_{4033}(2465,\cdot)\) \(\chi_{4033}(2672,\cdot)\) \(\chi_{4033}(2783,\cdot)\) \(\chi_{4033}(2820,\cdot)\) \(\chi_{4033}(3042,\cdot)\) \(\chi_{4033}(3122,\cdot)\) \(\chi_{4033}(3131,\cdot)\) \(\chi_{4033}(3137,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{19}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(711, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{11}{108}\right)\) |