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.jz
\(\chi_{4033}(69,\cdot)\) \(\chi_{4033}(167,\cdot)\) \(\chi_{4033}(316,\cdot)\) \(\chi_{4033}(449,\cdot)\) \(\chi_{4033}(483,\cdot)\) \(\chi_{4033}(503,\cdot)\) \(\chi_{4033}(531,\cdot)\) \(\chi_{4033}(648,\cdot)\) \(\chi_{4033}(753,\cdot)\) \(\chi_{4033}(819,\cdot)\) \(\chi_{4033}(890,\cdot)\) \(\chi_{4033}(1169,\cdot)\) \(\chi_{4033}(1236,\cdot)\) \(\chi_{4033}(1238,\cdot)\) \(\chi_{4033}(1393,\cdot)\) \(\chi_{4033}(1685,\cdot)\) \(\chi_{4033}(1700,\cdot)\) \(\chi_{4033}(1905,\cdot)\) \(\chi_{4033}(2128,\cdot)\) \(\chi_{4033}(2333,\cdot)\) \(\chi_{4033}(2348,\cdot)\) \(\chi_{4033}(2640,\cdot)\) \(\chi_{4033}(2795,\cdot)\) \(\chi_{4033}(2797,\cdot)\) \(\chi_{4033}(2864,\cdot)\) \(\chi_{4033}(3143,\cdot)\) \(\chi_{4033}(3214,\cdot)\) \(\chi_{4033}(3280,\cdot)\) \(\chi_{4033}(3385,\cdot)\) \(\chi_{4033}(3502,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{1}{36}\right),e\left(\frac{89}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(2333, a) \) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{31}{54}\right)\) | \(1\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(1\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{25}{108}\right)\) |