Basic properties
Modulus: | \(8016\) | |
Conductor: | \(4008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4008}(3101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bg
\(\chi_{8016}(41,\cdot)\) \(\chi_{8016}(377,\cdot)\) \(\chi_{8016}(425,\cdot)\) \(\chi_{8016}(473,\cdot)\) \(\chi_{8016}(521,\cdot)\) \(\chi_{8016}(569,\cdot)\) \(\chi_{8016}(665,\cdot)\) \(\chi_{8016}(713,\cdot)\) \(\chi_{8016}(905,\cdot)\) \(\chi_{8016}(953,\cdot)\) \(\chi_{8016}(1097,\cdot)\) \(\chi_{8016}(1145,\cdot)\) \(\chi_{8016}(1289,\cdot)\) \(\chi_{8016}(1481,\cdot)\) \(\chi_{8016}(1529,\cdot)\) \(\chi_{8016}(1577,\cdot)\) \(\chi_{8016}(1721,\cdot)\) \(\chi_{8016}(2009,\cdot)\) \(\chi_{8016}(2057,\cdot)\) \(\chi_{8016}(2105,\cdot)\) \(\chi_{8016}(2153,\cdot)\) \(\chi_{8016}(2201,\cdot)\) \(\chi_{8016}(2249,\cdot)\) \(\chi_{8016}(2393,\cdot)\) \(\chi_{8016}(2441,\cdot)\) \(\chi_{8016}(2489,\cdot)\) \(\chi_{8016}(2585,\cdot)\) \(\chi_{8016}(2777,\cdot)\) \(\chi_{8016}(2825,\cdot)\) \(\chi_{8016}(2873,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((1,-1,-1,e\left(\frac{59}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(1097, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{166}\right)\) | \(e\left(\frac{78}{83}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{9}{83}\right)\) | \(e\left(\frac{28}{83}\right)\) | \(e\left(\frac{19}{166}\right)\) | \(e\left(\frac{57}{83}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{26}{83}\right)\) | \(e\left(\frac{82}{83}\right)\) |