Basic properties
Modulus: | \(60984\) | |
Conductor: | \(30492\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{30492}(22279,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 60984.xl
\(\chi_{60984}(103,\cdot)\) \(\chi_{60984}(367,\cdot)\) \(\chi_{60984}(1615,\cdot)\) \(\chi_{60984}(1879,\cdot)\) \(\chi_{60984}(2623,\cdot)\) \(\chi_{60984}(2887,\cdot)\) \(\chi_{60984}(3127,\cdot)\) \(\chi_{60984}(5911,\cdot)\) \(\chi_{60984}(7159,\cdot)\) \(\chi_{60984}(7423,\cdot)\) \(\chi_{60984}(8167,\cdot)\) \(\chi_{60984}(8431,\cdot)\) \(\chi_{60984}(8671,\cdot)\) \(\chi_{60984}(8935,\cdot)\) \(\chi_{60984}(11191,\cdot)\) \(\chi_{60984}(12703,\cdot)\) \(\chi_{60984}(12967,\cdot)\) \(\chi_{60984}(13711,\cdot)\) \(\chi_{60984}(13975,\cdot)\) \(\chi_{60984}(14215,\cdot)\) \(\chi_{60984}(14479,\cdot)\) \(\chi_{60984}(16735,\cdot)\) \(\chi_{60984}(16999,\cdot)\) \(\chi_{60984}(18247,\cdot)\) \(\chi_{60984}(18511,\cdot)\) \(\chi_{60984}(19255,\cdot)\) \(\chi_{60984}(19519,\cdot)\) \(\chi_{60984}(19759,\cdot)\) \(\chi_{60984}(20023,\cdot)\) \(\chi_{60984}(22279,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((15247,30493,54209,34849,57961)\) → \((-1,1,e\left(\frac{1}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{26}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 60984 }(22279, a) \) | \(1\) | \(1\) | \(e\left(\frac{269}{330}\right)\) | \(e\left(\frac{301}{330}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{13}{330}\right)\) |