Basic properties
Modulus: | \(8016\) | |
Conductor: | \(8016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bo
\(\chi_{8016}(35,\cdot)\) \(\chi_{8016}(59,\cdot)\) \(\chi_{8016}(83,\cdot)\) \(\chi_{8016}(131,\cdot)\) \(\chi_{8016}(155,\cdot)\) \(\chi_{8016}(227,\cdot)\) \(\chi_{8016}(323,\cdot)\) \(\chi_{8016}(347,\cdot)\) \(\chi_{8016}(371,\cdot)\) \(\chi_{8016}(443,\cdot)\) \(\chi_{8016}(587,\cdot)\) \(\chi_{8016}(611,\cdot)\) \(\chi_{8016}(635,\cdot)\) \(\chi_{8016}(659,\cdot)\) \(\chi_{8016}(683,\cdot)\) \(\chi_{8016}(707,\cdot)\) \(\chi_{8016}(779,\cdot)\) \(\chi_{8016}(803,\cdot)\) \(\chi_{8016}(827,\cdot)\) \(\chi_{8016}(875,\cdot)\) \(\chi_{8016}(971,\cdot)\) \(\chi_{8016}(995,\cdot)\) \(\chi_{8016}(1019,\cdot)\) \(\chi_{8016}(1043,\cdot)\) \(\chi_{8016}(1115,\cdot)\) \(\chi_{8016}(1163,\cdot)\) \(\chi_{8016}(1259,\cdot)\) \(\chi_{8016}(1307,\cdot)\) \(\chi_{8016}(1379,\cdot)\) \(\chi_{8016}(1403,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{332})$ |
Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,-i,-1,e\left(\frac{19}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(131, a) \) | \(-1\) | \(1\) | \(e\left(\frac{121}{332}\right)\) | \(e\left(\frac{42}{83}\right)\) | \(e\left(\frac{317}{332}\right)\) | \(e\left(\frac{13}{332}\right)\) | \(e\left(\frac{47}{83}\right)\) | \(e\left(\frac{129}{332}\right)\) | \(e\left(\frac{69}{83}\right)\) | \(e\left(\frac{121}{166}\right)\) | \(e\left(\frac{305}{332}\right)\) | \(e\left(\frac{133}{166}\right)\) |