Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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 3549.dr
\(\chi_{3549}(101,\cdot)\) \(\chi_{3549}(173,\cdot)\) \(\chi_{3549}(374,\cdot)\) \(\chi_{3549}(446,\cdot)\) \(\chi_{3549}(647,\cdot)\) \(\chi_{3549}(719,\cdot)\) \(\chi_{3549}(920,\cdot)\) \(\chi_{3549}(1193,\cdot)\) \(\chi_{3549}(1265,\cdot)\) \(\chi_{3549}(1466,\cdot)\) \(\chi_{3549}(1538,\cdot)\) \(\chi_{3549}(1739,\cdot)\) \(\chi_{3549}(1811,\cdot)\) \(\chi_{3549}(2012,\cdot)\) \(\chi_{3549}(2084,\cdot)\) \(\chi_{3549}(2285,\cdot)\) \(\chi_{3549}(2357,\cdot)\) \(\chi_{3549}(2630,\cdot)\) \(\chi_{3549}(2831,\cdot)\) \(\chi_{3549}(2903,\cdot)\) \(\chi_{3549}(3104,\cdot)\) \(\chi_{3549}(3176,\cdot)\) \(\chi_{3549}(3377,\cdot)\) \(\chi_{3549}(3449,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{37}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(2630, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(1\) | \(e\left(\frac{17}{78}\right)\) |