Basic properties
| Modulus: | \(668\) | |
| Conductor: | \(668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 668.g
\(\chi_{668}(3,\cdot)\) \(\chi_{668}(7,\cdot)\) \(\chi_{668}(11,\cdot)\) \(\chi_{668}(19,\cdot)\) \(\chi_{668}(27,\cdot)\) \(\chi_{668}(31,\cdot)\) \(\chi_{668}(47,\cdot)\) \(\chi_{668}(63,\cdot)\) \(\chi_{668}(75,\cdot)\) \(\chi_{668}(87,\cdot)\) \(\chi_{668}(99,\cdot)\) \(\chi_{668}(107,\cdot)\) \(\chi_{668}(115,\cdot)\) \(\chi_{668}(127,\cdot)\) \(\chi_{668}(147,\cdot)\) \(\chi_{668}(171,\cdot)\) \(\chi_{668}(175,\cdot)\) \(\chi_{668}(179,\cdot)\) \(\chi_{668}(183,\cdot)\) \(\chi_{668}(191,\cdot)\) \(\chi_{668}(195,\cdot)\) \(\chi_{668}(199,\cdot)\) \(\chi_{668}(203,\cdot)\) \(\chi_{668}(211,\cdot)\) \(\chi_{668}(215,\cdot)\) \(\chi_{668}(223,\cdot)\) \(\chi_{668}(231,\cdot)\) \(\chi_{668}(239,\cdot)\) \(\chi_{668}(243,\cdot)\) \(\chi_{668}(251,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,5)\) → \((-1,e\left(\frac{12}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 668 }(559, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{166}\right)\) | \(e\left(\frac{12}{83}\right)\) | \(e\left(\frac{93}{166}\right)\) | \(e\left(\frac{15}{83}\right)\) | \(e\left(\frac{91}{166}\right)\) | \(e\left(\frac{74}{83}\right)\) | \(e\left(\frac{39}{166}\right)\) | \(e\left(\frac{55}{83}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{54}{83}\right)\) |