Basic properties
Modulus: | \(1225\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | 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 1225.bq
\(\chi_{1225}(8,\cdot)\) \(\chi_{1225}(22,\cdot)\) \(\chi_{1225}(78,\cdot)\) \(\chi_{1225}(92,\cdot)\) \(\chi_{1225}(113,\cdot)\) \(\chi_{1225}(127,\cdot)\) \(\chi_{1225}(162,\cdot)\) \(\chi_{1225}(183,\cdot)\) \(\chi_{1225}(253,\cdot)\) \(\chi_{1225}(267,\cdot)\) \(\chi_{1225}(288,\cdot)\) \(\chi_{1225}(302,\cdot)\) \(\chi_{1225}(323,\cdot)\) \(\chi_{1225}(337,\cdot)\) \(\chi_{1225}(358,\cdot)\) \(\chi_{1225}(372,\cdot)\) \(\chi_{1225}(428,\cdot)\) \(\chi_{1225}(463,\cdot)\) \(\chi_{1225}(477,\cdot)\) \(\chi_{1225}(498,\cdot)\) \(\chi_{1225}(512,\cdot)\) \(\chi_{1225}(533,\cdot)\) \(\chi_{1225}(547,\cdot)\) \(\chi_{1225}(603,\cdot)\) \(\chi_{1225}(617,\cdot)\) \(\chi_{1225}(652,\cdot)\) \(\chi_{1225}(673,\cdot)\) \(\chi_{1225}(708,\cdot)\) \(\chi_{1225}(722,\cdot)\) \(\chi_{1225}(778,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{6}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(302, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{12}{35}\right)\) |