Basic properties
Modulus: | \(6012\) | |
Conductor: | \(2004\) | 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 \(\chi_{2004}(1187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.w
\(\chi_{6012}(107,\cdot)\) \(\chi_{6012}(179,\cdot)\) \(\chi_{6012}(215,\cdot)\) \(\chi_{6012}(251,\cdot)\) \(\chi_{6012}(359,\cdot)\) \(\chi_{6012}(395,\cdot)\) \(\chi_{6012}(431,\cdot)\) \(\chi_{6012}(467,\cdot)\) \(\chi_{6012}(503,\cdot)\) \(\chi_{6012}(539,\cdot)\) \(\chi_{6012}(755,\cdot)\) \(\chi_{6012}(863,\cdot)\) \(\chi_{6012}(899,\cdot)\) \(\chi_{6012}(935,\cdot)\) \(\chi_{6012}(1079,\cdot)\) \(\chi_{6012}(1187,\cdot)\) \(\chi_{6012}(1223,\cdot)\) \(\chi_{6012}(1295,\cdot)\) \(\chi_{6012}(1331,\cdot)\) \(\chi_{6012}(1367,\cdot)\) \(\chi_{6012}(1511,\cdot)\) \(\chi_{6012}(1547,\cdot)\) \(\chi_{6012}(1619,\cdot)\) \(\chi_{6012}(1655,\cdot)\) \(\chi_{6012}(1691,\cdot)\) \(\chi_{6012}(1727,\cdot)\) \(\chi_{6012}(1763,\cdot)\) \(\chi_{6012}(2015,\cdot)\) \(\chi_{6012}(2051,\cdot)\) \(\chi_{6012}(2195,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((-1,-1,e\left(\frac{31}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 6012 }(1187, a) \) | \(1\) | \(1\) | \(e\left(\frac{145}{166}\right)\) | \(e\left(\frac{95}{166}\right)\) | \(e\left(\frac{38}{83}\right)\) | \(e\left(\frac{39}{83}\right)\) | \(e\left(\frac{49}{166}\right)\) | \(e\left(\frac{27}{166}\right)\) | \(e\left(\frac{81}{83}\right)\) | \(e\left(\frac{62}{83}\right)\) | \(e\left(\frac{87}{166}\right)\) | \(e\left(\frac{19}{166}\right)\) |