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 \(\chi_{1503}(13,\cdot)\) | 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
\((3007,3341,4681)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{103}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6012 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{143}{498}\right)\) | \(e\left(\frac{137}{249}\right)\) | \(e\left(\frac{176}{249}\right)\) | \(e\left(\frac{287}{498}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{47}{498}\right)\) | \(e\left(\frac{143}{249}\right)\) | \(e\left(\frac{101}{249}\right)\) | \(e\left(\frac{127}{249}\right)\) |