Basic properties
| Modulus: | \(2704\) | |
| Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1352}(1309,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2704.cl
\(\chi_{2704}(9,\cdot)\) \(\chi_{2704}(185,\cdot)\) \(\chi_{2704}(217,\cdot)\) \(\chi_{2704}(393,\cdot)\) \(\chi_{2704}(425,\cdot)\) \(\chi_{2704}(601,\cdot)\) \(\chi_{2704}(633,\cdot)\) \(\chi_{2704}(809,\cdot)\) \(\chi_{2704}(841,\cdot)\) \(\chi_{2704}(1017,\cdot)\) \(\chi_{2704}(1049,\cdot)\) \(\chi_{2704}(1225,\cdot)\) \(\chi_{2704}(1257,\cdot)\) \(\chi_{2704}(1433,\cdot)\) \(\chi_{2704}(1465,\cdot)\) \(\chi_{2704}(1641,\cdot)\) \(\chi_{2704}(1673,\cdot)\) \(\chi_{2704}(1849,\cdot)\) \(\chi_{2704}(2057,\cdot)\) \(\chi_{2704}(2089,\cdot)\) \(\chi_{2704}(2265,\cdot)\) \(\chi_{2704}(2297,\cdot)\) \(\chi_{2704}(2473,\cdot)\) \(\chi_{2704}(2505,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,677,1185)\) → \((1,-1,e\left(\frac{11}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2704 }(633, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{2}{3}\right)\) |