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.fy
\(\chi_{3040}(53,\cdot)\) \(\chi_{3040}(317,\cdot)\) \(\chi_{3040}(477,\cdot)\) \(\chi_{3040}(637,\cdot)\) \(\chi_{3040}(717,\cdot)\) \(\chi_{3040}(773,\cdot)\) \(\chi_{3040}(877,\cdot)\) \(\chi_{3040}(933,\cdot)\) \(\chi_{3040}(1093,\cdot)\) \(\chi_{3040}(1117,\cdot)\) \(\chi_{3040}(1173,\cdot)\) \(\chi_{3040}(1333,\cdot)\) \(\chi_{3040}(1573,\cdot)\) \(\chi_{3040}(1837,\cdot)\) \(\chi_{3040}(1997,\cdot)\) \(\chi_{3040}(2157,\cdot)\) \(\chi_{3040}(2237,\cdot)\) \(\chi_{3040}(2293,\cdot)\) \(\chi_{3040}(2397,\cdot)\) \(\chi_{3040}(2453,\cdot)\) \(\chi_{3040}(2613,\cdot)\) \(\chi_{3040}(2637,\cdot)\) \(\chi_{3040}(2693,\cdot)\) \(\chi_{3040}(2853,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,2661,1217,1921)\) → \((1,e\left(\frac{7}{8}\right),i,e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3040 }(877, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{29}{72}\right)\) |