Basic properties
Modulus: | \(4011\) | |
Conductor: | \(4011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(570\) | 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 4011.ck
\(\chi_{4011}(17,\cdot)\) \(\chi_{4011}(26,\cdot)\) \(\chi_{4011}(59,\cdot)\) \(\chi_{4011}(68,\cdot)\) \(\chi_{4011}(80,\cdot)\) \(\chi_{4011}(194,\cdot)\) \(\chi_{4011}(206,\cdot)\) \(\chi_{4011}(215,\cdot)\) \(\chi_{4011}(236,\cdot)\) \(\chi_{4011}(269,\cdot)\) \(\chi_{4011}(299,\cdot)\) \(\chi_{4011}(311,\cdot)\) \(\chi_{4011}(320,\cdot)\) \(\chi_{4011}(353,\cdot)\) \(\chi_{4011}(395,\cdot)\) \(\chi_{4011}(416,\cdot)\) \(\chi_{4011}(425,\cdot)\) \(\chi_{4011}(446,\cdot)\) \(\chi_{4011}(467,\cdot)\) \(\chi_{4011}(479,\cdot)\) \(\chi_{4011}(500,\cdot)\) \(\chi_{4011}(551,\cdot)\) \(\chi_{4011}(593,\cdot)\) \(\chi_{4011}(677,\cdot)\) \(\chi_{4011}(731,\cdot)\) \(\chi_{4011}(773,\cdot)\) \(\chi_{4011}(782,\cdot)\) \(\chi_{4011}(815,\cdot)\) \(\chi_{4011}(824,\cdot)\) \(\chi_{4011}(836,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{17}{95}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(551, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{570}\right)\) | \(e\left(\frac{23}{285}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{23}{190}\right)\) | \(e\left(\frac{373}{570}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{103}{190}\right)\) | \(e\left(\frac{46}{285}\right)\) | \(e\left(\frac{248}{285}\right)\) | \(e\left(\frac{197}{570}\right)\) |