Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(471,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.cq
\(\chi_{3549}(16,\cdot)\) \(\chi_{3549}(256,\cdot)\) \(\chi_{3549}(289,\cdot)\) \(\chi_{3549}(562,\cdot)\) \(\chi_{3549}(802,\cdot)\) \(\chi_{3549}(835,\cdot)\) \(\chi_{3549}(1075,\cdot)\) \(\chi_{3549}(1108,\cdot)\) \(\chi_{3549}(1348,\cdot)\) \(\chi_{3549}(1381,\cdot)\) \(\chi_{3549}(1621,\cdot)\) \(\chi_{3549}(1654,\cdot)\) \(\chi_{3549}(1894,\cdot)\) \(\chi_{3549}(1927,\cdot)\) \(\chi_{3549}(2167,\cdot)\) \(\chi_{3549}(2200,\cdot)\) \(\chi_{3549}(2440,\cdot)\) \(\chi_{3549}(2473,\cdot)\) \(\chi_{3549}(2713,\cdot)\) \(\chi_{3549}(2746,\cdot)\) \(\chi_{3549}(2986,\cdot)\) \(\chi_{3549}(3259,\cdot)\) \(\chi_{3549}(3292,\cdot)\) \(\chi_{3549}(3532,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2 |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{4}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(1654, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{39}\right)\) |