Basic properties
| Modulus: | \(6272\) | |
| Conductor: | \(6272\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(672\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6272.do
\(\chi_{6272}(37,\cdot)\) \(\chi_{6272}(53,\cdot)\) \(\chi_{6272}(93,\cdot)\) \(\chi_{6272}(109,\cdot)\) \(\chi_{6272}(149,\cdot)\) \(\chi_{6272}(205,\cdot)\) \(\chi_{6272}(221,\cdot)\) \(\chi_{6272}(261,\cdot)\) \(\chi_{6272}(277,\cdot)\) \(\chi_{6272}(317,\cdot)\) \(\chi_{6272}(333,\cdot)\) \(\chi_{6272}(389,\cdot)\) \(\chi_{6272}(429,\cdot)\) \(\chi_{6272}(445,\cdot)\) \(\chi_{6272}(485,\cdot)\) \(\chi_{6272}(501,\cdot)\) \(\chi_{6272}(541,\cdot)\) \(\chi_{6272}(597,\cdot)\) \(\chi_{6272}(613,\cdot)\) \(\chi_{6272}(653,\cdot)\) \(\chi_{6272}(669,\cdot)\) \(\chi_{6272}(709,\cdot)\) \(\chi_{6272}(725,\cdot)\) \(\chi_{6272}(781,\cdot)\) \(\chi_{6272}(821,\cdot)\) \(\chi_{6272}(837,\cdot)\) \(\chi_{6272}(877,\cdot)\) \(\chi_{6272}(893,\cdot)\) \(\chi_{6272}(933,\cdot)\) \(\chi_{6272}(989,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{672})$ |
| Fixed field: | Number field defined by a degree 672 polynomial (not computed) |
Values on generators
\((4607,3333,4609)\) → \((1,e\left(\frac{25}{32}\right),e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6272 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{672}\right)\) | \(e\left(\frac{589}{672}\right)\) | \(e\left(\frac{71}{336}\right)\) | \(e\left(\frac{593}{672}\right)\) | \(e\left(\frac{193}{224}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{155}{168}\right)\) | \(e\left(\frac{61}{96}\right)\) | \(e\left(\frac{299}{336}\right)\) | \(e\left(\frac{253}{336}\right)\) |