Basic properties
| Modulus: | \(4719\) | |
| Conductor: | \(1573\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1573}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4719.dr
\(\chi_{4719}(7,\cdot)\) \(\chi_{4719}(19,\cdot)\) \(\chi_{4719}(28,\cdot)\) \(\chi_{4719}(46,\cdot)\) \(\chi_{4719}(85,\cdot)\) \(\chi_{4719}(106,\cdot)\) \(\chi_{4719}(145,\cdot)\) \(\chi_{4719}(184,\cdot)\) \(\chi_{4719}(193,\cdot)\) \(\chi_{4719}(271,\cdot)\) \(\chi_{4719}(292,\cdot)\) \(\chi_{4719}(310,\cdot)\) \(\chi_{4719}(349,\cdot)\) \(\chi_{4719}(358,\cdot)\) \(\chi_{4719}(370,\cdot)\) \(\chi_{4719}(409,\cdot)\) \(\chi_{4719}(436,\cdot)\) \(\chi_{4719}(448,\cdot)\) \(\chi_{4719}(514,\cdot)\) \(\chi_{4719}(535,\cdot)\) \(\chi_{4719}(574,\cdot)\) \(\chi_{4719}(613,\cdot)\) \(\chi_{4719}(622,\cdot)\) \(\chi_{4719}(700,\cdot)\) \(\chi_{4719}(721,\cdot)\) \(\chi_{4719}(739,\cdot)\) \(\chi_{4719}(778,\cdot)\) \(\chi_{4719}(787,\cdot)\) \(\chi_{4719}(799,\cdot)\) \(\chi_{4719}(865,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((1574,3511,4357)\) → \((1,e\left(\frac{7}{110}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4719 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{647}{660}\right)\) | \(e\left(\frac{317}{330}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{349}{660}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{571}{660}\right)\) |