Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.eg
\(\chi_{3549}(20,\cdot)\) \(\chi_{3549}(41,\cdot)\) \(\chi_{3549}(167,\cdot)\) \(\chi_{3549}(293,\cdot)\) \(\chi_{3549}(314,\cdot)\) \(\chi_{3549}(440,\cdot)\) \(\chi_{3549}(461,\cdot)\) \(\chi_{3549}(566,\cdot)\) \(\chi_{3549}(713,\cdot)\) \(\chi_{3549}(734,\cdot)\) \(\chi_{3549}(839,\cdot)\) \(\chi_{3549}(860,\cdot)\) \(\chi_{3549}(986,\cdot)\) \(\chi_{3549}(1007,\cdot)\) \(\chi_{3549}(1112,\cdot)\) \(\chi_{3549}(1133,\cdot)\) \(\chi_{3549}(1259,\cdot)\) \(\chi_{3549}(1280,\cdot)\) \(\chi_{3549}(1385,\cdot)\) \(\chi_{3549}(1406,\cdot)\) \(\chi_{3549}(1532,\cdot)\) \(\chi_{3549}(1553,\cdot)\) \(\chi_{3549}(1658,\cdot)\) \(\chi_{3549}(1679,\cdot)\) \(\chi_{3549}(1805,\cdot)\) \(\chi_{3549}(1826,\cdot)\) \(\chi_{3549}(1931,\cdot)\) \(\chi_{3549}(1952,\cdot)\) \(\chi_{3549}(2078,\cdot)\) \(\chi_{3549}(2099,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((-1,-1,e\left(\frac{85}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{155}{156}\right)\) |