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.ie
\(\chi_{4033}(62,\cdot)\) \(\chi_{4033}(178,\cdot)\) \(\chi_{4033}(337,\cdot)\) \(\chi_{4033}(559,\cdot)\) \(\chi_{4033}(585,\cdot)\) \(\chi_{4033}(706,\cdot)\) \(\chi_{4033}(835,\cdot)\) \(\chi_{4033}(909,\cdot)\) \(\chi_{4033}(1039,\cdot)\) \(\chi_{4033}(1101,\cdot)\) \(\chi_{4033}(1103,\cdot)\) \(\chi_{4033}(1114,\cdot)\) \(\chi_{4033}(1246,\cdot)\) \(\chi_{4033}(1249,\cdot)\) \(\chi_{4033}(1473,\cdot)\) \(\chi_{4033}(1520,\cdot)\) \(\chi_{4033}(1653,\cdot)\) \(\chi_{4033}(2186,\cdot)\) \(\chi_{4033}(2245,\cdot)\) \(\chi_{4033}(2359,\cdot)\) \(\chi_{4033}(2483,\cdot)\) \(\chi_{4033}(2537,\cdot)\) \(\chi_{4033}(2574,\cdot)\) \(\chi_{4033}(2655,\cdot)\) \(\chi_{4033}(2667,\cdot)\) \(\chi_{4033}(3000,\cdot)\) \(\chi_{4033}(3038,\cdot)\) \(\chi_{4033}(3096,\cdot)\) \(\chi_{4033}(3203,\cdot)\) \(\chi_{4033}(3240,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{91}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1039, a) \) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{16}{27}\right)\) | \(-1\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(i\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{65}{108}\right)\) |