Basic properties
| Modulus: | \(8512\) | |
| Conductor: | \(8512\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | 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 8512.lm
\(\chi_{8512}(541,\cdot)\) \(\chi_{8512}(613,\cdot)\) \(\chi_{8512}(709,\cdot)\) \(\chi_{8512}(821,\cdot)\) \(\chi_{8512}(1005,\cdot)\) \(\chi_{8512}(1061,\cdot)\) \(\chi_{8512}(1605,\cdot)\) \(\chi_{8512}(1677,\cdot)\) \(\chi_{8512}(1773,\cdot)\) \(\chi_{8512}(1885,\cdot)\) \(\chi_{8512}(2069,\cdot)\) \(\chi_{8512}(2125,\cdot)\) \(\chi_{8512}(2669,\cdot)\) \(\chi_{8512}(2741,\cdot)\) \(\chi_{8512}(2837,\cdot)\) \(\chi_{8512}(2949,\cdot)\) \(\chi_{8512}(3133,\cdot)\) \(\chi_{8512}(3189,\cdot)\) \(\chi_{8512}(3733,\cdot)\) \(\chi_{8512}(3805,\cdot)\) \(\chi_{8512}(3901,\cdot)\) \(\chi_{8512}(4013,\cdot)\) \(\chi_{8512}(4197,\cdot)\) \(\chi_{8512}(4253,\cdot)\) \(\chi_{8512}(4797,\cdot)\) \(\chi_{8512}(4869,\cdot)\) \(\chi_{8512}(4965,\cdot)\) \(\chi_{8512}(5077,\cdot)\) \(\chi_{8512}(5261,\cdot)\) \(\chi_{8512}(5317,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((5055,6917,7297,3137)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{1}{3}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(709, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{144}\right)\) | \(e\left(\frac{25}{144}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{119}{144}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{43}{48}\right)\) |