Basic properties
| Modulus: | \(6012\) | |
| Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{167}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.u
\(\chi_{6012}(37,\cdot)\) \(\chi_{6012}(73,\cdot)\) \(\chi_{6012}(109,\cdot)\) \(\chi_{6012}(145,\cdot)\) \(\chi_{6012}(253,\cdot)\) \(\chi_{6012}(325,\cdot)\) \(\chi_{6012}(469,\cdot)\) \(\chi_{6012}(541,\cdot)\) \(\chi_{6012}(649,\cdot)\) \(\chi_{6012}(685,\cdot)\) \(\chi_{6012}(721,\cdot)\) \(\chi_{6012}(793,\cdot)\) \(\chi_{6012}(829,\cdot)\) \(\chi_{6012}(865,\cdot)\) \(\chi_{6012}(937,\cdot)\) \(\chi_{6012}(973,\cdot)\) \(\chi_{6012}(1045,\cdot)\) \(\chi_{6012}(1081,\cdot)\) \(\chi_{6012}(1153,\cdot)\) \(\chi_{6012}(1189,\cdot)\) \(\chi_{6012}(1261,\cdot)\) \(\chi_{6012}(1333,\cdot)\) \(\chi_{6012}(1405,\cdot)\) \(\chi_{6012}(1441,\cdot)\) \(\chi_{6012}(1513,\cdot)\) \(\chi_{6012}(1549,\cdot)\) \(\chi_{6012}(1585,\cdot)\) \(\chi_{6012}(1621,\cdot)\) \(\chi_{6012}(1693,\cdot)\) \(\chi_{6012}(1729,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((1,1,e\left(\frac{89}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6012 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{166}\right)\) | \(e\left(\frac{22}{83}\right)\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{37}{166}\right)\) | \(e\left(\frac{69}{166}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{35}{83}\right)\) | \(e\left(\frac{21}{83}\right)\) |