Basic properties
| Modulus: | \(1035\) | |
| Conductor: | \(1035\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 1035.bs
\(\chi_{1035}(7,\cdot)\) \(\chi_{1035}(43,\cdot)\) \(\chi_{1035}(67,\cdot)\) \(\chi_{1035}(88,\cdot)\) \(\chi_{1035}(97,\cdot)\) \(\chi_{1035}(103,\cdot)\) \(\chi_{1035}(112,\cdot)\) \(\chi_{1035}(148,\cdot)\) \(\chi_{1035}(157,\cdot)\) \(\chi_{1035}(178,\cdot)\) \(\chi_{1035}(247,\cdot)\) \(\chi_{1035}(268,\cdot)\) \(\chi_{1035}(283,\cdot)\) \(\chi_{1035}(313,\cdot)\) \(\chi_{1035}(337,\cdot)\) \(\chi_{1035}(373,\cdot)\) \(\chi_{1035}(382,\cdot)\) \(\chi_{1035}(412,\cdot)\) \(\chi_{1035}(448,\cdot)\) \(\chi_{1035}(457,\cdot)\) \(\chi_{1035}(493,\cdot)\) \(\chi_{1035}(502,\cdot)\) \(\chi_{1035}(517,\cdot)\) \(\chi_{1035}(562,\cdot)\) \(\chi_{1035}(592,\cdot)\) \(\chi_{1035}(628,\cdot)\) \(\chi_{1035}(682,\cdot)\) \(\chi_{1035}(688,\cdot)\) \(\chi_{1035}(697,\cdot)\) \(\chi_{1035}(718,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((461,622,856)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{19}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1035 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) |