Basic properties
Modulus: | \(8016\) | |
Conductor: | \(668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{668}(323,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bn
\(\chi_{8016}(79,\cdot)\) \(\chi_{8016}(271,\cdot)\) \(\chi_{8016}(463,\cdot)\) \(\chi_{8016}(511,\cdot)\) \(\chi_{8016}(607,\cdot)\) \(\chi_{8016}(703,\cdot)\) \(\chi_{8016}(751,\cdot)\) \(\chi_{8016}(799,\cdot)\) \(\chi_{8016}(895,\cdot)\) \(\chi_{8016}(991,\cdot)\) \(\chi_{8016}(1039,\cdot)\) \(\chi_{8016}(1279,\cdot)\) \(\chi_{8016}(1327,\cdot)\) \(\chi_{8016}(1375,\cdot)\) \(\chi_{8016}(1471,\cdot)\) \(\chi_{8016}(1663,\cdot)\) \(\chi_{8016}(1711,\cdot)\) \(\chi_{8016}(2047,\cdot)\) \(\chi_{8016}(2095,\cdot)\) \(\chi_{8016}(2143,\cdot)\) \(\chi_{8016}(2191,\cdot)\) \(\chi_{8016}(2239,\cdot)\) \(\chi_{8016}(2335,\cdot)\) \(\chi_{8016}(2383,\cdot)\) \(\chi_{8016}(2575,\cdot)\) \(\chi_{8016}(2623,\cdot)\) \(\chi_{8016}(2767,\cdot)\) \(\chi_{8016}(2815,\cdot)\) \(\chi_{8016}(2959,\cdot)\) \(\chi_{8016}(3151,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,1,1,e\left(\frac{111}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(991, a) \) | \(1\) | \(1\) | \(e\left(\frac{111}{166}\right)\) | \(e\left(\frac{67}{166}\right)\) | \(e\left(\frac{37}{166}\right)\) | \(e\left(\frac{145}{166}\right)\) | \(e\left(\frac{73}{166}\right)\) | \(e\left(\frac{47}{166}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{28}{83}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{113}{166}\right)\) |