Basic properties
Modulus: | \(3040\) | |
Conductor: | \(3040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3040.fz
\(\chi_{3040}(187,\cdot)\) \(\chi_{3040}(347,\cdot)\) \(\chi_{3040}(403,\cdot)\) \(\chi_{3040}(427,\cdot)\) \(\chi_{3040}(587,\cdot)\) \(\chi_{3040}(643,\cdot)\) \(\chi_{3040}(747,\cdot)\) \(\chi_{3040}(803,\cdot)\) \(\chi_{3040}(883,\cdot)\) \(\chi_{3040}(1043,\cdot)\) \(\chi_{3040}(1203,\cdot)\) \(\chi_{3040}(1467,\cdot)\) \(\chi_{3040}(1707,\cdot)\) \(\chi_{3040}(1867,\cdot)\) \(\chi_{3040}(1923,\cdot)\) \(\chi_{3040}(1947,\cdot)\) \(\chi_{3040}(2107,\cdot)\) \(\chi_{3040}(2163,\cdot)\) \(\chi_{3040}(2267,\cdot)\) \(\chi_{3040}(2323,\cdot)\) \(\chi_{3040}(2403,\cdot)\) \(\chi_{3040}(2563,\cdot)\) \(\chi_{3040}(2723,\cdot)\) \(\chi_{3040}(2987,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,2661,1217,1921)\) → \((-1,e\left(\frac{7}{8}\right),-i,e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 3040 }(403, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{1}{72}\right)\) |