Basic properties
Modulus: | \(3549\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(417,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.ct
\(\chi_{3549}(79,\cdot)\) \(\chi_{3549}(235,\cdot)\) \(\chi_{3549}(352,\cdot)\) \(\chi_{3549}(625,\cdot)\) \(\chi_{3549}(781,\cdot)\) \(\chi_{3549}(898,\cdot)\) \(\chi_{3549}(1054,\cdot)\) \(\chi_{3549}(1171,\cdot)\) \(\chi_{3549}(1327,\cdot)\) \(\chi_{3549}(1444,\cdot)\) \(\chi_{3549}(1600,\cdot)\) \(\chi_{3549}(1717,\cdot)\) \(\chi_{3549}(1873,\cdot)\) \(\chi_{3549}(1990,\cdot)\) \(\chi_{3549}(2146,\cdot)\) \(\chi_{3549}(2263,\cdot)\) \(\chi_{3549}(2419,\cdot)\) \(\chi_{3549}(2692,\cdot)\) \(\chi_{3549}(2809,\cdot)\) \(\chi_{3549}(2965,\cdot)\) \(\chi_{3549}(3082,\cdot)\) \(\chi_{3549}(3238,\cdot)\) \(\chi_{3549}(3355,\cdot)\) \(\chi_{3549}(3511,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{2}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1600, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{9}{13}\right)\) |