Basic properties
Modulus: | \(2209\) | |
Conductor: | \(2209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(47\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 2209.e
\(\chi_{2209}(48,\cdot)\) \(\chi_{2209}(95,\cdot)\) \(\chi_{2209}(142,\cdot)\) \(\chi_{2209}(189,\cdot)\) \(\chi_{2209}(236,\cdot)\) \(\chi_{2209}(283,\cdot)\) \(\chi_{2209}(330,\cdot)\) \(\chi_{2209}(377,\cdot)\) \(\chi_{2209}(424,\cdot)\) \(\chi_{2209}(471,\cdot)\) \(\chi_{2209}(518,\cdot)\) \(\chi_{2209}(565,\cdot)\) \(\chi_{2209}(612,\cdot)\) \(\chi_{2209}(659,\cdot)\) \(\chi_{2209}(706,\cdot)\) \(\chi_{2209}(753,\cdot)\) \(\chi_{2209}(800,\cdot)\) \(\chi_{2209}(847,\cdot)\) \(\chi_{2209}(894,\cdot)\) \(\chi_{2209}(941,\cdot)\) \(\chi_{2209}(988,\cdot)\) \(\chi_{2209}(1035,\cdot)\) \(\chi_{2209}(1082,\cdot)\) \(\chi_{2209}(1129,\cdot)\) \(\chi_{2209}(1176,\cdot)\) \(\chi_{2209}(1223,\cdot)\) \(\chi_{2209}(1270,\cdot)\) \(\chi_{2209}(1317,\cdot)\) \(\chi_{2209}(1364,\cdot)\) \(\chi_{2209}(1411,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{47})$ |
Fixed field: | Number field defined by a degree 47 polynomial |
Values on generators
\(5\) → \(e\left(\frac{45}{47}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2209 }(95, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{47}\right)\) | \(e\left(\frac{22}{47}\right)\) | \(e\left(\frac{35}{47}\right)\) | \(e\left(\frac{45}{47}\right)\) | \(e\left(\frac{16}{47}\right)\) | \(e\left(\frac{20}{47}\right)\) | \(e\left(\frac{29}{47}\right)\) | \(e\left(\frac{44}{47}\right)\) | \(e\left(\frac{39}{47}\right)\) | \(e\left(\frac{19}{47}\right)\) |