Basic properties
Modulus: | \(6008\) | |
Conductor: | \(6008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(750\) | 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)
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Galois orbit 6008.ck
\(\chi_{6008}(29,\cdot)\) \(\chi_{6008}(69,\cdot)\) \(\chi_{6008}(101,\cdot)\) \(\chi_{6008}(133,\cdot)\) \(\chi_{6008}(141,\cdot)\) \(\chi_{6008}(205,\cdot)\) \(\chi_{6008}(213,\cdot)\) \(\chi_{6008}(253,\cdot)\) \(\chi_{6008}(277,\cdot)\) \(\chi_{6008}(293,\cdot)\) \(\chi_{6008}(317,\cdot)\) \(\chi_{6008}(349,\cdot)\) \(\chi_{6008}(365,\cdot)\) \(\chi_{6008}(381,\cdot)\) \(\chi_{6008}(389,\cdot)\) \(\chi_{6008}(413,\cdot)\) \(\chi_{6008}(421,\cdot)\) \(\chi_{6008}(453,\cdot)\) \(\chi_{6008}(501,\cdot)\) \(\chi_{6008}(509,\cdot)\) \(\chi_{6008}(517,\cdot)\) \(\chi_{6008}(533,\cdot)\) \(\chi_{6008}(541,\cdot)\) \(\chi_{6008}(565,\cdot)\) \(\chi_{6008}(573,\cdot)\) \(\chi_{6008}(629,\cdot)\) \(\chi_{6008}(645,\cdot)\) \(\chi_{6008}(653,\cdot)\) \(\chi_{6008}(661,\cdot)\) \(\chi_{6008}(677,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{375})$ |
Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((1,-1,e\left(\frac{577}{750}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6008 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{375}\right)\) | \(e\left(\frac{547}{750}\right)\) | \(e\left(\frac{209}{250}\right)\) | \(e\left(\frac{202}{375}\right)\) | \(e\left(\frac{43}{75}\right)\) | \(e\left(\frac{241}{750}\right)\) | \(e\left(\frac{749}{750}\right)\) | \(e\left(\frac{83}{750}\right)\) | \(e\left(\frac{511}{750}\right)\) | \(e\left(\frac{79}{750}\right)\) |