Basic properties
Modulus: | \(3549\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(998,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.de
\(\chi_{3549}(88,\cdot)\) \(\chi_{3549}(121,\cdot)\) \(\chi_{3549}(394,\cdot)\) \(\chi_{3549}(634,\cdot)\) \(\chi_{3549}(667,\cdot)\) \(\chi_{3549}(907,\cdot)\) \(\chi_{3549}(940,\cdot)\) \(\chi_{3549}(1180,\cdot)\) \(\chi_{3549}(1213,\cdot)\) \(\chi_{3549}(1453,\cdot)\) \(\chi_{3549}(1486,\cdot)\) \(\chi_{3549}(1726,\cdot)\) \(\chi_{3549}(1759,\cdot)\) \(\chi_{3549}(1999,\cdot)\) \(\chi_{3549}(2032,\cdot)\) \(\chi_{3549}(2272,\cdot)\) \(\chi_{3549}(2305,\cdot)\) \(\chi_{3549}(2545,\cdot)\) \(\chi_{3549}(2578,\cdot)\) \(\chi_{3549}(2818,\cdot)\) \(\chi_{3549}(3091,\cdot)\) \(\chi_{3549}(3124,\cdot)\) \(\chi_{3549}(3364,\cdot)\) \(\chi_{3549}(3397,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{41}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(3364, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(-1\) | \(e\left(\frac{61}{78}\right)\) |