Basic properties
| Modulus: | \(3380\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3380.cn
\(\chi_{3380}(101,\cdot)\) \(\chi_{3380}(121,\cdot)\) \(\chi_{3380}(381,\cdot)\) \(\chi_{3380}(621,\cdot)\) \(\chi_{3380}(641,\cdot)\) \(\chi_{3380}(881,\cdot)\) \(\chi_{3380}(901,\cdot)\) \(\chi_{3380}(1141,\cdot)\) \(\chi_{3380}(1401,\cdot)\) \(\chi_{3380}(1421,\cdot)\) \(\chi_{3380}(1661,\cdot)\) \(\chi_{3380}(1681,\cdot)\) \(\chi_{3380}(1921,\cdot)\) \(\chi_{3380}(1941,\cdot)\) \(\chi_{3380}(2181,\cdot)\) \(\chi_{3380}(2201,\cdot)\) \(\chi_{3380}(2441,\cdot)\) \(\chi_{3380}(2461,\cdot)\) \(\chi_{3380}(2701,\cdot)\) \(\chi_{3380}(2721,\cdot)\) \(\chi_{3380}(2961,\cdot)\) \(\chi_{3380}(2981,\cdot)\) \(\chi_{3380}(3221,\cdot)\) \(\chi_{3380}(3241,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1691,677,1861)\) → \((1,1,e\left(\frac{35}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) |