Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.cr
\(\chi_{3549}(211,\cdot)\) \(\chi_{3549}(295,\cdot)\) \(\chi_{3549}(568,\cdot)\) \(\chi_{3549}(757,\cdot)\) \(\chi_{3549}(841,\cdot)\) \(\chi_{3549}(1030,\cdot)\) \(\chi_{3549}(1114,\cdot)\) \(\chi_{3549}(1303,\cdot)\) \(\chi_{3549}(1387,\cdot)\) \(\chi_{3549}(1576,\cdot)\) \(\chi_{3549}(1660,\cdot)\) \(\chi_{3549}(1849,\cdot)\) \(\chi_{3549}(1933,\cdot)\) \(\chi_{3549}(2122,\cdot)\) \(\chi_{3549}(2206,\cdot)\) \(\chi_{3549}(2395,\cdot)\) \(\chi_{3549}(2479,\cdot)\) \(\chi_{3549}(2668,\cdot)\) \(\chi_{3549}(2752,\cdot)\) \(\chi_{3549}(2941,\cdot)\) \(\chi_{3549}(3025,\cdot)\) \(\chi_{3549}(3214,\cdot)\) \(\chi_{3549}(3298,\cdot)\) \(\chi_{3549}(3487,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,1,e\left(\frac{31}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(3214, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{29}{39}\right)\) |