Basic properties
Modulus: | \(8016\) | |
Conductor: | \(4008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4008}(2027,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bm
\(\chi_{8016}(23,\cdot)\) \(\chi_{8016}(71,\cdot)\) \(\chi_{8016}(119,\cdot)\) \(\chi_{8016}(407,\cdot)\) \(\chi_{8016}(647,\cdot)\) \(\chi_{8016}(791,\cdot)\) \(\chi_{8016}(887,\cdot)\) \(\chi_{8016}(983,\cdot)\) \(\chi_{8016}(1127,\cdot)\) \(\chi_{8016}(1271,\cdot)\) \(\chi_{8016}(1415,\cdot)\) \(\chi_{8016}(1607,\cdot)\) \(\chi_{8016}(1799,\cdot)\) \(\chi_{8016}(1847,\cdot)\) \(\chi_{8016}(1943,\cdot)\) \(\chi_{8016}(2039,\cdot)\) \(\chi_{8016}(2087,\cdot)\) \(\chi_{8016}(2135,\cdot)\) \(\chi_{8016}(2231,\cdot)\) \(\chi_{8016}(2327,\cdot)\) \(\chi_{8016}(2375,\cdot)\) \(\chi_{8016}(2615,\cdot)\) \(\chi_{8016}(2663,\cdot)\) \(\chi_{8016}(2711,\cdot)\) \(\chi_{8016}(2807,\cdot)\) \(\chi_{8016}(2999,\cdot)\) \(\chi_{8016}(3047,\cdot)\) \(\chi_{8016}(3383,\cdot)\) \(\chi_{8016}(3431,\cdot)\) \(\chi_{8016}(3479,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,-1,-1,e\left(\frac{99}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{99}{166}\right)\) | \(e\left(\frac{145}{166}\right)\) | \(e\left(\frac{33}{166}\right)\) | \(e\left(\frac{77}{83}\right)\) | \(e\left(\frac{9}{83}\right)\) | \(e\left(\frac{49}{83}\right)\) | \(e\left(\frac{7}{166}\right)\) | \(e\left(\frac{16}{83}\right)\) | \(e\left(\frac{38}{83}\right)\) | \(e\left(\frac{29}{166}\right)\) |