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 \(\chi_{1183}(1010,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.cs
\(\chi_{3549}(100,\cdot)\) \(\chi_{3549}(172,\cdot)\) \(\chi_{3549}(373,\cdot)\) \(\chi_{3549}(445,\cdot)\) \(\chi_{3549}(646,\cdot)\) \(\chi_{3549}(718,\cdot)\) \(\chi_{3549}(919,\cdot)\) \(\chi_{3549}(1192,\cdot)\) \(\chi_{3549}(1264,\cdot)\) \(\chi_{3549}(1465,\cdot)\) \(\chi_{3549}(1537,\cdot)\) \(\chi_{3549}(1738,\cdot)\) \(\chi_{3549}(1810,\cdot)\) \(\chi_{3549}(2011,\cdot)\) \(\chi_{3549}(2083,\cdot)\) \(\chi_{3549}(2284,\cdot)\) \(\chi_{3549}(2356,\cdot)\) \(\chi_{3549}(2629,\cdot)\) \(\chi_{3549}(2830,\cdot)\) \(\chi_{3549}(2902,\cdot)\) \(\chi_{3549}(3103,\cdot)\) \(\chi_{3549}(3175,\cdot)\) \(\chi_{3549}(3376,\cdot)\) \(\chi_{3549}(3448,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1 |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{20}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(3376, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(1\) | \(e\left(\frac{25}{39}\right)\) |