Basic properties
| Modulus: | \(8016\) | |
| 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 \(\chi_{501}(200,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bi
\(\chi_{8016}(65,\cdot)\) \(\chi_{8016}(209,\cdot)\) \(\chi_{8016}(353,\cdot)\) \(\chi_{8016}(449,\cdot)\) \(\chi_{8016}(545,\cdot)\) \(\chi_{8016}(689,\cdot)\) \(\chi_{8016}(929,\cdot)\) \(\chi_{8016}(1217,\cdot)\) \(\chi_{8016}(1265,\cdot)\) \(\chi_{8016}(1313,\cdot)\) \(\chi_{8016}(1361,\cdot)\) \(\chi_{8016}(1457,\cdot)\) \(\chi_{8016}(1505,\cdot)\) \(\chi_{8016}(1553,\cdot)\) \(\chi_{8016}(1601,\cdot)\) \(\chi_{8016}(1697,\cdot)\) \(\chi_{8016}(1745,\cdot)\) \(\chi_{8016}(1841,\cdot)\) \(\chi_{8016}(1937,\cdot)\) \(\chi_{8016}(2033,\cdot)\) \(\chi_{8016}(2081,\cdot)\) \(\chi_{8016}(2177,\cdot)\) \(\chi_{8016}(2225,\cdot)\) \(\chi_{8016}(2321,\cdot)\) \(\chi_{8016}(2369,\cdot)\) \(\chi_{8016}(2465,\cdot)\) \(\chi_{8016}(2513,\cdot)\) \(\chi_{8016}(2561,\cdot)\) \(\chi_{8016}(2657,\cdot)\) \(\chi_{8016}(2705,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((1,1,-1,e\left(\frac{61}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(2705, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{166}\right)\) | \(e\left(\frac{60}{83}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{75}{166}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{43}{166}\right)\) | \(e\left(\frac{39}{83}\right)\) | \(e\left(\frac{123}{166}\right)\) | \(e\left(\frac{12}{83}\right)\) |