Basic properties
Modulus: | \(6012\) | |
Conductor: | \(1503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(498\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1503}(637,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.bc
\(\chi_{6012}(13,\cdot)\) \(\chi_{6012}(193,\cdot)\) \(\chi_{6012}(241,\cdot)\) \(\chi_{6012}(277,\cdot)\) \(\chi_{6012}(301,\cdot)\) \(\chi_{6012}(313,\cdot)\) \(\chi_{6012}(349,\cdot)\) \(\chi_{6012}(373,\cdot)\) \(\chi_{6012}(385,\cdot)\) \(\chi_{6012}(445,\cdot)\) \(\chi_{6012}(457,\cdot)\) \(\chi_{6012}(493,\cdot)\) \(\chi_{6012}(553,\cdot)\) \(\chi_{6012}(637,\cdot)\) \(\chi_{6012}(661,\cdot)\) \(\chi_{6012}(673,\cdot)\) \(\chi_{6012}(709,\cdot)\) \(\chi_{6012}(769,\cdot)\) \(\chi_{6012}(781,\cdot)\) \(\chi_{6012}(817,\cdot)\) \(\chi_{6012}(913,\cdot)\) \(\chi_{6012}(925,\cdot)\) \(\chi_{6012}(1057,\cdot)\) \(\chi_{6012}(1069,\cdot)\) \(\chi_{6012}(1093,\cdot)\) \(\chi_{6012}(1105,\cdot)\) \(\chi_{6012}(1141,\cdot)\) \(\chi_{6012}(1165,\cdot)\) \(\chi_{6012}(1237,\cdot)\) \(\chi_{6012}(1249,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{249})$ |
Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{7}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 6012 }(637, a) \) | \(-1\) | \(1\) | \(e\left(\frac{187}{498}\right)\) | \(e\left(\frac{160}{249}\right)\) | \(e\left(\frac{211}{249}\right)\) | \(e\left(\frac{337}{498}\right)\) | \(e\left(\frac{39}{166}\right)\) | \(e\left(\frac{37}{83}\right)\) | \(e\left(\frac{253}{498}\right)\) | \(e\left(\frac{187}{249}\right)\) | \(e\left(\frac{247}{249}\right)\) | \(e\left(\frac{32}{249}\right)\) |