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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 235.l
\(\chi_{235}(13,\cdot)\) \(\chi_{235}(22,\cdot)\) \(\chi_{235}(23,\cdot)\) \(\chi_{235}(33,\cdot)\) \(\chi_{235}(38,\cdot)\) \(\chi_{235}(43,\cdot)\) \(\chi_{235}(52,\cdot)\) \(\chi_{235}(57,\cdot)\) \(\chi_{235}(58,\cdot)\) \(\chi_{235}(62,\cdot)\) \(\chi_{235}(67,\cdot)\) \(\chi_{235}(73,\cdot)\) \(\chi_{235}(77,\cdot)\) \(\chi_{235}(78,\cdot)\) \(\chi_{235}(82,\cdot)\) \(\chi_{235}(87,\cdot)\) \(\chi_{235}(88,\cdot)\) \(\chi_{235}(92,\cdot)\) \(\chi_{235}(107,\cdot)\) \(\chi_{235}(113,\cdot)\) \(\chi_{235}(117,\cdot)\) \(\chi_{235}(123,\cdot)\) \(\chi_{235}(127,\cdot)\) \(\chi_{235}(132,\cdot)\) \(\chi_{235}(133,\cdot)\) \(\chi_{235}(137,\cdot)\) \(\chi_{235}(138,\cdot)\) \(\chi_{235}(152,\cdot)\) \(\chi_{235}(163,\cdot)\) \(\chi_{235}(167,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((142,146)\) → \((-i,e\left(\frac{19}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 235 }(198, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{47}{92}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{51}{92}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{81}{92}\right)\) | \(e\left(\frac{73}{92}\right)\) |