Basic properties
Modulus: | \(83\) | |
Conductor: | \(83\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(82\) | 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 83.d
\(\chi_{83}(2,\cdot)\) \(\chi_{83}(5,\cdot)\) \(\chi_{83}(6,\cdot)\) \(\chi_{83}(8,\cdot)\) \(\chi_{83}(13,\cdot)\) \(\chi_{83}(14,\cdot)\) \(\chi_{83}(15,\cdot)\) \(\chi_{83}(18,\cdot)\) \(\chi_{83}(19,\cdot)\) \(\chi_{83}(20,\cdot)\) \(\chi_{83}(22,\cdot)\) \(\chi_{83}(24,\cdot)\) \(\chi_{83}(32,\cdot)\) \(\chi_{83}(34,\cdot)\) \(\chi_{83}(35,\cdot)\) \(\chi_{83}(39,\cdot)\) \(\chi_{83}(42,\cdot)\) \(\chi_{83}(43,\cdot)\) \(\chi_{83}(45,\cdot)\) \(\chi_{83}(46,\cdot)\) \(\chi_{83}(47,\cdot)\) \(\chi_{83}(50,\cdot)\) \(\chi_{83}(52,\cdot)\) \(\chi_{83}(53,\cdot)\) \(\chi_{83}(54,\cdot)\) \(\chi_{83}(55,\cdot)\) \(\chi_{83}(56,\cdot)\) \(\chi_{83}(57,\cdot)\) \(\chi_{83}(58,\cdot)\) \(\chi_{83}(60,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{41})$ |
Fixed field: | Number field defined by a degree 82 polynomial |
Values on generators
\(2\) → \(e\left(\frac{37}{82}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 83 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{82}\right)\) | \(e\left(\frac{20}{41}\right)\) | \(e\left(\frac{37}{41}\right)\) | \(e\left(\frac{15}{82}\right)\) | \(e\left(\frac{77}{82}\right)\) | \(e\left(\frac{25}{41}\right)\) | \(e\left(\frac{29}{82}\right)\) | \(e\left(\frac{40}{41}\right)\) | \(e\left(\frac{26}{41}\right)\) | \(e\left(\frac{34}{41}\right)\) |