Basic properties
| Modulus: | \(739\) | |
| Conductor: | \(739\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(41\) | 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 739.g
\(\chi_{739}(20,\cdot)\) \(\chi_{739}(37,\cdot)\) \(\chi_{739}(57,\cdot)\) \(\chi_{739}(64,\cdot)\) \(\chi_{739}(106,\cdot)\) \(\chi_{739}(125,\cdot)\) \(\chi_{739}(130,\cdot)\) \(\chi_{739}(133,\cdot)\) \(\chi_{739}(151,\cdot)\) \(\chi_{739}(191,\cdot)\) \(\chi_{739}(227,\cdot)\) \(\chi_{739}(270,\cdot)\) \(\chi_{739}(277,\cdot)\) \(\chi_{739}(283,\cdot)\) \(\chi_{739}(293,\cdot)\) \(\chi_{739}(367,\cdot)\) \(\chi_{739}(376,\cdot)\) \(\chi_{739}(383,\cdot)\) \(\chi_{739}(400,\cdot)\) \(\chi_{739}(401,\cdot)\) \(\chi_{739}(414,\cdot)\) \(\chi_{739}(416,\cdot)\) \(\chi_{739}(438,\cdot)\) \(\chi_{739}(443,\cdot)\) \(\chi_{739}(474,\cdot)\) \(\chi_{739}(478,\cdot)\) \(\chi_{739}(487,\cdot)\) \(\chi_{739}(495,\cdot)\) \(\chi_{739}(538,\cdot)\) \(\chi_{739}(541,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{41})$ |
| Fixed field: | Number field defined by a degree 41 polynomial |
Values on generators
\(3\) → \(e\left(\frac{17}{41}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 739 }(293, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{41}\right)\) | \(e\left(\frac{17}{41}\right)\) | \(e\left(\frac{33}{41}\right)\) | \(e\left(\frac{24}{41}\right)\) | \(e\left(\frac{13}{41}\right)\) | \(e\left(\frac{37}{41}\right)\) | \(e\left(\frac{29}{41}\right)\) | \(e\left(\frac{34}{41}\right)\) | \(e\left(\frac{20}{41}\right)\) | \(e\left(\frac{3}{41}\right)\) |