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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1035.bv
\(\chi_{1035}(13,\cdot)\) \(\chi_{1035}(52,\cdot)\) \(\chi_{1035}(58,\cdot)\) \(\chi_{1035}(133,\cdot)\) \(\chi_{1035}(142,\cdot)\) \(\chi_{1035}(187,\cdot)\) \(\chi_{1035}(193,\cdot)\) \(\chi_{1035}(202,\cdot)\) \(\chi_{1035}(223,\cdot)\) \(\chi_{1035}(232,\cdot)\) \(\chi_{1035}(238,\cdot)\) \(\chi_{1035}(292,\cdot)\) \(\chi_{1035}(328,\cdot)\) \(\chi_{1035}(358,\cdot)\) \(\chi_{1035}(403,\cdot)\) \(\chi_{1035}(418,\cdot)\) \(\chi_{1035}(427,\cdot)\) \(\chi_{1035}(463,\cdot)\) \(\chi_{1035}(472,\cdot)\) \(\chi_{1035}(508,\cdot)\) \(\chi_{1035}(538,\cdot)\) \(\chi_{1035}(547,\cdot)\) \(\chi_{1035}(583,\cdot)\) \(\chi_{1035}(607,\cdot)\) \(\chi_{1035}(637,\cdot)\) \(\chi_{1035}(652,\cdot)\) \(\chi_{1035}(673,\cdot)\) \(\chi_{1035}(742,\cdot)\) \(\chi_{1035}(763,\cdot)\) \(\chi_{1035}(772,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((461,622,856)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1035 }(52, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) |