Basic properties
Modulus: | \(705\) | |
Conductor: | \(705\) | 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 705.u
\(\chi_{705}(23,\cdot)\) \(\chi_{705}(38,\cdot)\) \(\chi_{705}(62,\cdot)\) \(\chi_{705}(77,\cdot)\) \(\chi_{705}(92,\cdot)\) \(\chi_{705}(107,\cdot)\) \(\chi_{705}(113,\cdot)\) \(\chi_{705}(137,\cdot)\) \(\chi_{705}(152,\cdot)\) \(\chi_{705}(167,\cdot)\) \(\chi_{705}(182,\cdot)\) \(\chi_{705}(203,\cdot)\) \(\chi_{705}(218,\cdot)\) \(\chi_{705}(227,\cdot)\) \(\chi_{705}(233,\cdot)\) \(\chi_{705}(248,\cdot)\) \(\chi_{705}(257,\cdot)\) \(\chi_{705}(278,\cdot)\) \(\chi_{705}(287,\cdot)\) \(\chi_{705}(293,\cdot)\) \(\chi_{705}(302,\cdot)\) \(\chi_{705}(308,\cdot)\) \(\chi_{705}(317,\cdot)\) \(\chi_{705}(323,\cdot)\) \(\chi_{705}(362,\cdot)\) \(\chi_{705}(368,\cdot)\) \(\chi_{705}(398,\cdot)\) \(\chi_{705}(407,\cdot)\) \(\chi_{705}(428,\cdot)\) \(\chi_{705}(443,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((236,142,616)\) → \((-1,-i,e\left(\frac{17}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 705 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{65}{92}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{29}{92}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{15}{92}\right)\) | \(e\left(\frac{3}{23}\right)\) |