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.hz
\(\chi_{4033}(56,\cdot)\) \(\chi_{4033}(59,\cdot)\) \(\chi_{4033}(72,\cdot)\) \(\chi_{4033}(91,\cdot)\) \(\chi_{4033}(314,\cdot)\) \(\chi_{4033}(494,\cdot)\) \(\chi_{4033}(498,\cdot)\) \(\chi_{4033}(832,\cdot)\) \(\chi_{4033}(957,\cdot)\) \(\chi_{4033}(967,\cdot)\) \(\chi_{4033}(975,\cdot)\) \(\chi_{4033}(1051,\cdot)\) \(\chi_{4033}(1189,\cdot)\) \(\chi_{4033}(1352,\cdot)\) \(\chi_{4033}(1428,\cdot)\) \(\chi_{4033}(1556,\cdot)\) \(\chi_{4033}(1578,\cdot)\) \(\chi_{4033}(1811,\cdot)\) \(\chi_{4033}(2222,\cdot)\) \(\chi_{4033}(2455,\cdot)\) \(\chi_{4033}(2477,\cdot)\) \(\chi_{4033}(2605,\cdot)\) \(\chi_{4033}(2681,\cdot)\) \(\chi_{4033}(2844,\cdot)\) \(\chi_{4033}(2982,\cdot)\) \(\chi_{4033}(3058,\cdot)\) \(\chi_{4033}(3066,\cdot)\) \(\chi_{4033}(3076,\cdot)\) \(\chi_{4033}(3201,\cdot)\) \(\chi_{4033}(3535,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{7}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(3076, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(1\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{59}{108}\right)\) |