Basic properties
Modulus: | \(8016\) | |
Conductor: | \(2672\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2672}(1117,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bs
\(\chi_{8016}(61,\cdot)\) \(\chi_{8016}(85,\cdot)\) \(\chi_{8016}(133,\cdot)\) \(\chi_{8016}(157,\cdot)\) \(\chi_{8016}(181,\cdot)\) \(\chi_{8016}(205,\cdot)\) \(\chi_{8016}(229,\cdot)\) \(\chi_{8016}(397,\cdot)\) \(\chi_{8016}(421,\cdot)\) \(\chi_{8016}(517,\cdot)\) \(\chi_{8016}(565,\cdot)\) \(\chi_{8016}(589,\cdot)\) \(\chi_{8016}(613,\cdot)\) \(\chi_{8016}(733,\cdot)\) \(\chi_{8016}(757,\cdot)\) \(\chi_{8016}(805,\cdot)\) \(\chi_{8016}(853,\cdot)\) \(\chi_{8016}(877,\cdot)\) \(\chi_{8016}(901,\cdot)\) \(\chi_{8016}(949,\cdot)\) \(\chi_{8016}(997,\cdot)\) \(\chi_{8016}(1021,\cdot)\) \(\chi_{8016}(1117,\cdot)\) \(\chi_{8016}(1213,\cdot)\) \(\chi_{8016}(1285,\cdot)\) \(\chi_{8016}(1357,\cdot)\) \(\chi_{8016}(1429,\cdot)\) \(\chi_{8016}(1477,\cdot)\) \(\chi_{8016}(1525,\cdot)\) \(\chi_{8016}(1597,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{332})$ |
Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((1,-i,1,e\left(\frac{50}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(1117, a) \) | \(1\) | \(1\) | \(e\left(\frac{117}{332}\right)\) | \(e\left(\frac{97}{166}\right)\) | \(e\left(\frac{205}{332}\right)\) | \(e\left(\frac{99}{332}\right)\) | \(e\left(\frac{77}{83}\right)\) | \(e\left(\frac{63}{332}\right)\) | \(e\left(\frac{23}{166}\right)\) | \(e\left(\frac{117}{166}\right)\) | \(e\left(\frac{203}{332}\right)\) | \(e\left(\frac{18}{83}\right)\) |