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.if
\(\chi_{4033}(52,\cdot)\) \(\chi_{4033}(165,\cdot)\) \(\chi_{4033}(205,\cdot)\) \(\chi_{4033}(357,\cdot)\) \(\chi_{4033}(425,\cdot)\) \(\chi_{4033}(446,\cdot)\) \(\chi_{4033}(668,\cdot)\) \(\chi_{4033}(698,\cdot)\) \(\chi_{4033}(723,\cdot)\) \(\chi_{4033}(745,\cdot)\) \(\chi_{4033}(1023,\cdot)\) \(\chi_{4033}(1129,\cdot)\) \(\chi_{4033}(1152,\cdot)\) \(\chi_{4033}(1271,\cdot)\) \(\chi_{4033}(1441,\cdot)\) \(\chi_{4033}(1532,\cdot)\) \(\chi_{4033}(1794,\cdot)\) \(\chi_{4033}(2013,\cdot)\) \(\chi_{4033}(2020,\cdot)\) \(\chi_{4033}(2239,\cdot)\) \(\chi_{4033}(2501,\cdot)\) \(\chi_{4033}(2592,\cdot)\) \(\chi_{4033}(2762,\cdot)\) \(\chi_{4033}(2881,\cdot)\) \(\chi_{4033}(2904,\cdot)\) \(\chi_{4033}(3010,\cdot)\) \(\chi_{4033}(3288,\cdot)\) \(\chi_{4033}(3310,\cdot)\) \(\chi_{4033}(3335,\cdot)\) \(\chi_{4033}(3365,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{71}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1152, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{83}{108}\right)\) | \(e\left(\frac{79}{108}\right)\) |