Basic properties
Modulus: | \(6012\) | |
Conductor: | \(501\) | 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 \(\chi_{501}(131,\cdot)\) | 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 6012.r
\(\chi_{6012}(17,\cdot)\) \(\chi_{6012}(53,\cdot)\) \(\chi_{6012}(125,\cdot)\) \(\chi_{6012}(161,\cdot)\) \(\chi_{6012}(197,\cdot)\) \(\chi_{6012}(269,\cdot)\) \(\chi_{6012}(305,\cdot)\) \(\chi_{6012}(377,\cdot)\) \(\chi_{6012}(413,\cdot)\) \(\chi_{6012}(485,\cdot)\) \(\chi_{6012}(521,\cdot)\) \(\chi_{6012}(593,\cdot)\) \(\chi_{6012}(665,\cdot)\) \(\chi_{6012}(737,\cdot)\) \(\chi_{6012}(773,\cdot)\) \(\chi_{6012}(845,\cdot)\) \(\chi_{6012}(881,\cdot)\) \(\chi_{6012}(917,\cdot)\) \(\chi_{6012}(953,\cdot)\) \(\chi_{6012}(1025,\cdot)\) \(\chi_{6012}(1061,\cdot)\) \(\chi_{6012}(1097,\cdot)\) \(\chi_{6012}(1133,\cdot)\) \(\chi_{6012}(1349,\cdot)\) \(\chi_{6012}(1529,\cdot)\) \(\chi_{6012}(1637,\cdot)\) \(\chi_{6012}(1709,\cdot)\) \(\chi_{6012}(1781,\cdot)\) \(\chi_{6012}(1889,\cdot)\) \(\chi_{6012}(1997,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((1,-1,e\left(\frac{19}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 6012 }(1133, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{83}\right)\) | \(e\left(\frac{42}{83}\right)\) | \(e\left(\frac{117}{166}\right)\) | \(e\left(\frac{131}{166}\right)\) | \(e\left(\frac{47}{83}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{69}{83}\right)\) | \(e\left(\frac{19}{83}\right)\) | \(e\left(\frac{111}{166}\right)\) | \(e\left(\frac{25}{83}\right)\) |