Basic properties
Modulus: | \(235\) | |
Conductor: | \(235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(92\) | 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 235.k
\(\chi_{235}(2,\cdot)\) \(\chi_{235}(3,\cdot)\) \(\chi_{235}(7,\cdot)\) \(\chi_{235}(8,\cdot)\) \(\chi_{235}(12,\cdot)\) \(\chi_{235}(17,\cdot)\) \(\chi_{235}(18,\cdot)\) \(\chi_{235}(27,\cdot)\) \(\chi_{235}(28,\cdot)\) \(\chi_{235}(32,\cdot)\) \(\chi_{235}(37,\cdot)\) \(\chi_{235}(42,\cdot)\) \(\chi_{235}(53,\cdot)\) \(\chi_{235}(63,\cdot)\) \(\chi_{235}(68,\cdot)\) \(\chi_{235}(72,\cdot)\) \(\chi_{235}(83,\cdot)\) \(\chi_{235}(97,\cdot)\) \(\chi_{235}(98,\cdot)\) \(\chi_{235}(102,\cdot)\) \(\chi_{235}(103,\cdot)\) \(\chi_{235}(108,\cdot)\) \(\chi_{235}(112,\cdot)\) \(\chi_{235}(118,\cdot)\) \(\chi_{235}(122,\cdot)\) \(\chi_{235}(128,\cdot)\) \(\chi_{235}(143,\cdot)\) \(\chi_{235}(147,\cdot)\) \(\chi_{235}(148,\cdot)\) \(\chi_{235}(153,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((142,146)\) → \((-i,e\left(\frac{9}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 235 }(143, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{92}\right)\) | \(e\left(\frac{7}{92}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{25}{92}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{61}{92}\right)\) | \(e\left(\frac{51}{92}\right)\) |