Basic properties
| Modulus: | \(1503\) | |
| Conductor: | \(501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{501}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1503.k
\(\chi_{1503}(17,\cdot)\) \(\chi_{1503}(26,\cdot)\) \(\chi_{1503}(35,\cdot)\) \(\chi_{1503}(53,\cdot)\) \(\chi_{1503}(71,\cdot)\) \(\chi_{1503}(80,\cdot)\) \(\chi_{1503}(125,\cdot)\) \(\chi_{1503}(134,\cdot)\) \(\chi_{1503}(143,\cdot)\) \(\chi_{1503}(161,\cdot)\) \(\chi_{1503}(197,\cdot)\) \(\chi_{1503}(206,\cdot)\) \(\chi_{1503}(269,\cdot)\) \(\chi_{1503}(278,\cdot)\) \(\chi_{1503}(287,\cdot)\) \(\chi_{1503}(296,\cdot)\) \(\chi_{1503}(305,\cdot)\) \(\chi_{1503}(323,\cdot)\) \(\chi_{1503}(332,\cdot)\) \(\chi_{1503}(368,\cdot)\) \(\chi_{1503}(377,\cdot)\) \(\chi_{1503}(386,\cdot)\) \(\chi_{1503}(404,\cdot)\) \(\chi_{1503}(413,\cdot)\) \(\chi_{1503}(440,\cdot)\) \(\chi_{1503}(476,\cdot)\) \(\chi_{1503}(485,\cdot)\) \(\chi_{1503}(494,\cdot)\) \(\chi_{1503}(521,\cdot)\) \(\chi_{1503}(575,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,172)\) → \((-1,e\left(\frac{53}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1503 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{166}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{56}{83}\right)\) | \(e\left(\frac{135}{166}\right)\) | \(e\left(\frac{15}{166}\right)\) | \(e\left(\frac{73}{166}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{157}{166}\right)\) | \(e\left(\frac{7}{83}\right)\) |