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.ia
\(\chi_{4033}(13,\cdot)\) \(\chi_{4033}(204,\cdot)\) \(\chi_{4033}(257,\cdot)\) \(\chi_{4033}(383,\cdot)\) \(\chi_{4033}(392,\cdot)\) \(\chi_{4033}(426,\cdot)\) \(\chi_{4033}(505,\cdot)\) \(\chi_{4033}(575,\cdot)\) \(\chi_{4033}(930,\cdot)\) \(\chi_{4033}(1053,\cdot)\) \(\chi_{4033}(1142,\cdot)\) \(\chi_{4033}(1241,\cdot)\) \(\chi_{4033}(1297,\cdot)\) \(\chi_{4033}(1367,\cdot)\) \(\chi_{4033}(1411,\cdot)\) \(\chi_{4033}(1720,\cdot)\) \(\chi_{4033}(1791,\cdot)\) \(\chi_{4033}(1835,\cdot)\) \(\chi_{4033}(2198,\cdot)\) \(\chi_{4033}(2242,\cdot)\) \(\chi_{4033}(2313,\cdot)\) \(\chi_{4033}(2622,\cdot)\) \(\chi_{4033}(2666,\cdot)\) \(\chi_{4033}(2736,\cdot)\) \(\chi_{4033}(2792,\cdot)\) \(\chi_{4033}(2891,\cdot)\) \(\chi_{4033}(2980,\cdot)\) \(\chi_{4033}(3103,\cdot)\) \(\chi_{4033}(3458,\cdot)\) \(\chi_{4033}(3528,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{55}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1411, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(1\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{47}{108}\right)\) |