Basic properties
| Modulus: | \(8640\) | |
| Conductor: | \(1728\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1728}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.ic
\(\chi_{8640}(11,\cdot)\) \(\chi_{8640}(131,\cdot)\) \(\chi_{8640}(371,\cdot)\) \(\chi_{8640}(491,\cdot)\) \(\chi_{8640}(731,\cdot)\) \(\chi_{8640}(851,\cdot)\) \(\chi_{8640}(1091,\cdot)\) \(\chi_{8640}(1211,\cdot)\) \(\chi_{8640}(1451,\cdot)\) \(\chi_{8640}(1571,\cdot)\) \(\chi_{8640}(1811,\cdot)\) \(\chi_{8640}(1931,\cdot)\) \(\chi_{8640}(2171,\cdot)\) \(\chi_{8640}(2291,\cdot)\) \(\chi_{8640}(2531,\cdot)\) \(\chi_{8640}(2651,\cdot)\) \(\chi_{8640}(2891,\cdot)\) \(\chi_{8640}(3011,\cdot)\) \(\chi_{8640}(3251,\cdot)\) \(\chi_{8640}(3371,\cdot)\) \(\chi_{8640}(3611,\cdot)\) \(\chi_{8640}(3731,\cdot)\) \(\chi_{8640}(3971,\cdot)\) \(\chi_{8640}(4091,\cdot)\) \(\chi_{8640}(4331,\cdot)\) \(\chi_{8640}(4451,\cdot)\) \(\chi_{8640}(4691,\cdot)\) \(\chi_{8640}(4811,\cdot)\) \(\chi_{8640}(5051,\cdot)\) \(\chi_{8640}(5171,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2431,3781,6401,3457)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{13}{18}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8640 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{67}{144}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{23}{144}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{47}{72}\right)\) |