Basic properties
| Modulus: | \(7803\) | |
| Conductor: | \(459\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{459}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7803.bp
\(\chi_{7803}(65,\cdot)\) \(\chi_{7803}(131,\cdot)\) \(\chi_{7803}(158,\cdot)\) \(\chi_{7803}(329,\cdot)\) \(\chi_{7803}(653,\cdot)\) \(\chi_{7803}(932,\cdot)\) \(\chi_{7803}(1091,\cdot)\) \(\chi_{7803}(1370,\cdot)\) \(\chi_{7803}(1694,\cdot)\) \(\chi_{7803}(1865,\cdot)\) \(\chi_{7803}(1892,\cdot)\) \(\chi_{7803}(1958,\cdot)\) \(\chi_{7803}(2063,\cdot)\) \(\chi_{7803}(2237,\cdot)\) \(\chi_{7803}(2387,\cdot)\) \(\chi_{7803}(2561,\cdot)\) \(\chi_{7803}(2666,\cdot)\) \(\chi_{7803}(2732,\cdot)\) \(\chi_{7803}(2759,\cdot)\) \(\chi_{7803}(2930,\cdot)\) \(\chi_{7803}(3254,\cdot)\) \(\chi_{7803}(3533,\cdot)\) \(\chi_{7803}(3692,\cdot)\) \(\chi_{7803}(3971,\cdot)\) \(\chi_{7803}(4295,\cdot)\) \(\chi_{7803}(4466,\cdot)\) \(\chi_{7803}(4493,\cdot)\) \(\chi_{7803}(4559,\cdot)\) \(\chi_{7803}(4664,\cdot)\) \(\chi_{7803}(4838,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2891,2026)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 7803 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{61}{144}\right)\) | \(e\left(\frac{107}{144}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{47}{144}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{49}{144}\right)\) | \(e\left(\frac{7}{18}\right)\) |