Basic properties
Modulus: | \(4028\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(903,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.cq
\(\chi_{4028}(21,\cdot)\) \(\chi_{4028}(33,\cdot)\) \(\chi_{4028}(41,\cdot)\) \(\chi_{4028}(109,\cdot)\) \(\chi_{4028}(173,\cdot)\) \(\chi_{4028}(181,\cdot)\) \(\chi_{4028}(185,\cdot)\) \(\chi_{4028}(193,\cdot)\) \(\chi_{4028}(257,\cdot)\) \(\chi_{4028}(337,\cdot)\) \(\chi_{4028}(345,\cdot)\) \(\chi_{4028}(357,\cdot)\) \(\chi_{4028}(393,\cdot)\) \(\chi_{4028}(421,\cdot)\) \(\chi_{4028}(469,\cdot)\) \(\chi_{4028}(485,\cdot)\) \(\chi_{4028}(489,\cdot)\) \(\chi_{4028}(497,\cdot)\) \(\chi_{4028}(509,\cdot)\) \(\chi_{4028}(561,\cdot)\) \(\chi_{4028}(565,\cdot)\) \(\chi_{4028}(585,\cdot)\) \(\chi_{4028}(641,\cdot)\) \(\chi_{4028}(697,\cdot)\) \(\chi_{4028}(737,\cdot)\) \(\chi_{4028}(773,\cdot)\) \(\chi_{4028}(781,\cdot)\) \(\chi_{4028}(793,\cdot)\) \(\chi_{4028}(813,\cdot)\) \(\chi_{4028}(869,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{468})$ |
Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((2015,2757,2281)\) → \((1,e\left(\frac{17}{18}\right),e\left(\frac{1}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 4028 }(2917, a) \) | \(1\) | \(1\) | \(e\left(\frac{283}{468}\right)\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{49}{234}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{43}{234}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{253}{468}\right)\) | \(e\left(\frac{23}{36}\right)\) |