Basic properties
Modulus: | \(8016\) | |
Conductor: | \(2004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2004}(1727,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bk
\(\chi_{8016}(47,\cdot)\) \(\chi_{8016}(191,\cdot)\) \(\chi_{8016}(239,\cdot)\) \(\chi_{8016}(383,\cdot)\) \(\chi_{8016}(431,\cdot)\) \(\chi_{8016}(623,\cdot)\) \(\chi_{8016}(671,\cdot)\) \(\chi_{8016}(767,\cdot)\) \(\chi_{8016}(815,\cdot)\) \(\chi_{8016}(863,\cdot)\) \(\chi_{8016}(911,\cdot)\) \(\chi_{8016}(959,\cdot)\) \(\chi_{8016}(1295,\cdot)\) \(\chi_{8016}(1343,\cdot)\) \(\chi_{8016}(1535,\cdot)\) \(\chi_{8016}(1631,\cdot)\) \(\chi_{8016}(1679,\cdot)\) \(\chi_{8016}(1727,\cdot)\) \(\chi_{8016}(1967,\cdot)\) \(\chi_{8016}(2015,\cdot)\) \(\chi_{8016}(2111,\cdot)\) \(\chi_{8016}(2207,\cdot)\) \(\chi_{8016}(2255,\cdot)\) \(\chi_{8016}(2303,\cdot)\) \(\chi_{8016}(2399,\cdot)\) \(\chi_{8016}(2495,\cdot)\) \(\chi_{8016}(2543,\cdot)\) \(\chi_{8016}(2735,\cdot)\) \(\chi_{8016}(2927,\cdot)\) \(\chi_{8016}(3071,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,1,-1,e\left(\frac{76}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(1727, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{166}\right)\) | \(e\left(\frac{91}{166}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{26}{83}\right)\) | \(e\left(\frac{5}{166}\right)\) | \(e\left(\frac{101}{166}\right)\) | \(e\left(\frac{54}{83}\right)\) | \(e\left(\frac{69}{83}\right)\) | \(e\left(\frac{141}{166}\right)\) | \(e\left(\frac{151}{166}\right)\) |