Basic properties
Modulus: | \(4830\) | |
Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{805}(408,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4830.dn
\(\chi_{4830}(37,\cdot)\) \(\chi_{4830}(67,\cdot)\) \(\chi_{4830}(247,\cdot)\) \(\chi_{4830}(373,\cdot)\) \(\chi_{4830}(457,\cdot)\) \(\chi_{4830}(613,\cdot)\) \(\chi_{4830}(697,\cdot)\) \(\chi_{4830}(793,\cdot)\) \(\chi_{4830}(907,\cdot)\) \(\chi_{4830}(1003,\cdot)\) \(\chi_{4830}(1033,\cdot)\) \(\chi_{4830}(1213,\cdot)\) \(\chi_{4830}(1423,\cdot)\) \(\chi_{4830}(1537,\cdot)\) \(\chi_{4830}(1663,\cdot)\) \(\chi_{4830}(1717,\cdot)\) \(\chi_{4830}(1873,\cdot)\) \(\chi_{4830}(2137,\cdot)\) \(\chi_{4830}(2167,\cdot)\) \(\chi_{4830}(2503,\cdot)\) \(\chi_{4830}(2587,\cdot)\) \(\chi_{4830}(2683,\cdot)\) \(\chi_{4830}(2767,\cdot)\) \(\chi_{4830}(2797,\cdot)\) \(\chi_{4830}(2977,\cdot)\) \(\chi_{4830}(3007,\cdot)\) \(\chi_{4830}(3103,\cdot)\) \(\chi_{4830}(3133,\cdot)\) \(\chi_{4830}(3217,\cdot)\) \(\chi_{4830}(3553,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3221,967,2761,1891)\) → \((1,-i,e\left(\frac{1}{3}\right),e\left(\frac{7}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 4830 }(1213, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{5}{12}\right)\) |