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.bt
\(\chi_{1035}(2,\cdot)\) \(\chi_{1035}(32,\cdot)\) \(\chi_{1035}(77,\cdot)\) \(\chi_{1035}(128,\cdot)\) \(\chi_{1035}(167,\cdot)\) \(\chi_{1035}(173,\cdot)\) \(\chi_{1035}(248,\cdot)\) \(\chi_{1035}(257,\cdot)\) \(\chi_{1035}(302,\cdot)\) \(\chi_{1035}(308,\cdot)\) \(\chi_{1035}(317,\cdot)\) \(\chi_{1035}(338,\cdot)\) \(\chi_{1035}(347,\cdot)\) \(\chi_{1035}(353,\cdot)\) \(\chi_{1035}(407,\cdot)\) \(\chi_{1035}(443,\cdot)\) \(\chi_{1035}(473,\cdot)\) \(\chi_{1035}(518,\cdot)\) \(\chi_{1035}(533,\cdot)\) \(\chi_{1035}(542,\cdot)\) \(\chi_{1035}(578,\cdot)\) \(\chi_{1035}(587,\cdot)\) \(\chi_{1035}(623,\cdot)\) \(\chi_{1035}(653,\cdot)\) \(\chi_{1035}(662,\cdot)\) \(\chi_{1035}(698,\cdot)\) \(\chi_{1035}(722,\cdot)\) \(\chi_{1035}(752,\cdot)\) \(\chi_{1035}(767,\cdot)\) \(\chi_{1035}(788,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((461,622,856)\) → \((e\left(\frac{5}{6}\right),i,e\left(\frac{5}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1035 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) |