Basic properties
| Modulus: | \(1005\) | |
| Conductor: | \(335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{335}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1005.bv
\(\chi_{1005}(73,\cdot)\) \(\chi_{1005}(88,\cdot)\) \(\chi_{1005}(103,\cdot)\) \(\chi_{1005}(127,\cdot)\) \(\chi_{1005}(157,\cdot)\) \(\chi_{1005}(217,\cdot)\) \(\chi_{1005}(307,\cdot)\) \(\chi_{1005}(322,\cdot)\) \(\chi_{1005}(328,\cdot)\) \(\chi_{1005}(352,\cdot)\) \(\chi_{1005}(358,\cdot)\) \(\chi_{1005}(382,\cdot)\) \(\chi_{1005}(412,\cdot)\) \(\chi_{1005}(418,\cdot)\) \(\chi_{1005}(457,\cdot)\) \(\chi_{1005}(502,\cdot)\) \(\chi_{1005}(508,\cdot)\) \(\chi_{1005}(523,\cdot)\) \(\chi_{1005}(553,\cdot)\) \(\chi_{1005}(562,\cdot)\) \(\chi_{1005}(583,\cdot)\) \(\chi_{1005}(592,\cdot)\) \(\chi_{1005}(607,\cdot)\) \(\chi_{1005}(613,\cdot)\) \(\chi_{1005}(622,\cdot)\) \(\chi_{1005}(652,\cdot)\) \(\chi_{1005}(658,\cdot)\) \(\chi_{1005}(703,\cdot)\) \(\chi_{1005}(763,\cdot)\) \(\chi_{1005}(772,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((671,202,136)\) → \((1,-i,e\left(\frac{20}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1005 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{37}{66}\right)\) |