Basic properties
| Modulus: | \(941\) | |
| Conductor: | \(941\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(47\) | 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 941.g
\(\chi_{941}(34,\cdot)\) \(\chi_{941}(46,\cdot)\) \(\chi_{941}(93,\cdot)\) \(\chi_{941}(116,\cdot)\) \(\chi_{941}(118,\cdot)\) \(\chi_{941}(119,\cdot)\) \(\chi_{941}(161,\cdot)\) \(\chi_{941}(178,\cdot)\) \(\chi_{941}(180,\cdot)\) \(\chi_{941}(215,\cdot)\) \(\chi_{941}(234,\cdot)\) \(\chi_{941}(248,\cdot)\) \(\chi_{941}(282,\cdot)\) \(\chi_{941}(302,\cdot)\) \(\chi_{941}(323,\cdot)\) \(\chi_{941}(339,\cdot)\) \(\chi_{941}(341,\cdot)\) \(\chi_{941}(406,\cdot)\) \(\chi_{941}(413,\cdot)\) \(\chi_{941}(428,\cdot)\) \(\chi_{941}(437,\cdot)\) \(\chi_{941}(474,\cdot)\) \(\chi_{941}(480,\cdot)\) \(\chi_{941}(514,\cdot)\) \(\chi_{941}(538,\cdot)\) \(\chi_{941}(557,\cdot)\) \(\chi_{941}(623,\cdot)\) \(\chi_{941}(624,\cdot)\) \(\chi_{941}(630,\cdot)\) \(\chi_{941}(631,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{47})$ |
| Fixed field: | Number field defined by a degree 47 polynomial |
Values on generators
\(2\) → \(e\left(\frac{7}{47}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 941 }(716, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{47}\right)\) | \(e\left(\frac{39}{47}\right)\) | \(e\left(\frac{14}{47}\right)\) | \(e\left(\frac{28}{47}\right)\) | \(e\left(\frac{46}{47}\right)\) | \(e\left(\frac{10}{47}\right)\) | \(e\left(\frac{21}{47}\right)\) | \(e\left(\frac{31}{47}\right)\) | \(e\left(\frac{35}{47}\right)\) | \(e\left(\frac{1}{47}\right)\) |