Basic properties
Modulus: | \(3549\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(387,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.dw
\(\chi_{3549}(4,\cdot)\) \(\chi_{3549}(205,\cdot)\) \(\chi_{3549}(277,\cdot)\) \(\chi_{3549}(478,\cdot)\) \(\chi_{3549}(550,\cdot)\) \(\chi_{3549}(751,\cdot)\) \(\chi_{3549}(1024,\cdot)\) \(\chi_{3549}(1096,\cdot)\) \(\chi_{3549}(1297,\cdot)\) \(\chi_{3549}(1369,\cdot)\) \(\chi_{3549}(1570,\cdot)\) \(\chi_{3549}(1642,\cdot)\) \(\chi_{3549}(1843,\cdot)\) \(\chi_{3549}(1915,\cdot)\) \(\chi_{3549}(2116,\cdot)\) \(\chi_{3549}(2188,\cdot)\) \(\chi_{3549}(2461,\cdot)\) \(\chi_{3549}(2662,\cdot)\) \(\chi_{3549}(2734,\cdot)\) \(\chi_{3549}(2935,\cdot)\) \(\chi_{3549}(3007,\cdot)\) \(\chi_{3549}(3208,\cdot)\) \(\chi_{3549}(3280,\cdot)\) \(\chi_{3549}(3481,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{29}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1570, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{78}\right)\) |