Basic properties
| Modulus: | \(4675\) | |
| Conductor: | \(4675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 4675.ih
\(\chi_{4675}(58,\cdot)\) \(\chi_{4675}(267,\cdot)\) \(\chi_{4675}(313,\cdot)\) \(\chi_{4675}(333,\cdot)\) \(\chi_{4675}(422,\cdot)\) \(\chi_{4675}(588,\cdot)\) \(\chi_{4675}(653,\cdot)\) \(\chi_{4675}(702,\cdot)\) \(\chi_{4675}(823,\cdot)\) \(\chi_{4675}(928,\cdot)\) \(\chi_{4675}(972,\cdot)\) \(\chi_{4675}(1098,\cdot)\) \(\chi_{4675}(1527,\cdot)\) \(\chi_{4675}(1797,\cdot)\) \(\chi_{4675}(1983,\cdot)\) \(\chi_{4675}(2062,\cdot)\) \(\chi_{4675}(2077,\cdot)\) \(\chi_{4675}(2238,\cdot)\) \(\chi_{4675}(2578,\cdot)\) \(\chi_{4675}(2742,\cdot)\) \(\chi_{4675}(2748,\cdot)\) \(\chi_{4675}(2887,\cdot)\) \(\chi_{4675}(2902,\cdot)\) \(\chi_{4675}(3083,\cdot)\) \(\chi_{4675}(3338,\cdot)\) \(\chi_{4675}(3437,\cdot)\) \(\chi_{4675}(3567,\cdot)\) \(\chi_{4675}(3678,\cdot)\) \(\chi_{4675}(3848,\cdot)\) \(\chi_{4675}(4117,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4302,3401,3301)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{4}{5}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4675 }(3083, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{59}{80}\right)\) |