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.jq
\(\chi_{4033}(139,\cdot)\) \(\chi_{4033}(176,\cdot)\) \(\chi_{4033}(280,\cdot)\) \(\chi_{4033}(506,\cdot)\) \(\chi_{4033}(521,\cdot)\) \(\chi_{4033}(707,\cdot)\) \(\chi_{4033}(802,\cdot)\) \(\chi_{4033}(805,\cdot)\) \(\chi_{4033}(842,\cdot)\) \(\chi_{4033}(1076,\cdot)\) \(\chi_{4033}(1077,\cdot)\) \(\chi_{4033}(1251,\cdot)\) \(\chi_{4033}(1298,\cdot)\) \(\chi_{4033}(1464,\cdot)\) \(\chi_{4033}(1584,\cdot)\) \(\chi_{4033}(1595,\cdot)\) \(\chi_{4033}(1871,\cdot)\) \(\chi_{4033}(1912,\cdot)\) \(\chi_{4033}(2002,\cdot)\) \(\chi_{4033}(2060,\cdot)\) \(\chi_{4033}(2065,\cdot)\) \(\chi_{4033}(2408,\cdot)\) \(\chi_{4033}(2463,\cdot)\) \(\chi_{4033}(2470,\cdot)\) \(\chi_{4033}(2520,\cdot)\) \(\chi_{4033}(2544,\cdot)\) \(\chi_{4033}(2630,\cdot)\) \(\chi_{4033}(2731,\cdot)\) \(\chi_{4033}(2890,\cdot)\) \(\chi_{4033}(3185,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{43}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1076, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(i\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{77}{108}\right)\) |