Basic properties
Modulus: | \(1002\) | |
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 \(\chi_{501}(488,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1002.h
\(\chi_{1002}(11,\cdot)\) \(\chi_{1002}(29,\cdot)\) \(\chi_{1002}(47,\cdot)\) \(\chi_{1002}(65,\cdot)\) \(\chi_{1002}(77,\cdot)\) \(\chi_{1002}(89,\cdot)\) \(\chi_{1002}(107,\cdot)\) \(\chi_{1002}(137,\cdot)\) \(\chi_{1002}(173,\cdot)\) \(\chi_{1002}(179,\cdot)\) \(\chi_{1002}(185,\cdot)\) \(\chi_{1002}(191,\cdot)\) \(\chi_{1002}(203,\cdot)\) \(\chi_{1002}(209,\cdot)\) \(\chi_{1002}(215,\cdot)\) \(\chi_{1002}(221,\cdot)\) \(\chi_{1002}(233,\cdot)\) \(\chi_{1002}(239,\cdot)\) \(\chi_{1002}(251,\cdot)\) \(\chi_{1002}(263,\cdot)\) \(\chi_{1002}(275,\cdot)\) \(\chi_{1002}(281,\cdot)\) \(\chi_{1002}(293,\cdot)\) \(\chi_{1002}(299,\cdot)\) \(\chi_{1002}(311,\cdot)\) \(\chi_{1002}(317,\cdot)\) \(\chi_{1002}(329,\cdot)\) \(\chi_{1002}(341,\cdot)\) \(\chi_{1002}(353,\cdot)\) \(\chi_{1002}(359,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,673)\) → \((-1,e\left(\frac{10}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1002 }(989, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{145}{166}\right)\) | \(e\left(\frac{34}{83}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{71}{166}\right)\) | \(e\left(\frac{20}{83}\right)\) | \(e\left(\frac{95}{166}\right)\) | \(e\left(\frac{70}{83}\right)\) |