Basic properties
Modulus: | \(83\) | |
Conductor: | \(83\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(41\) | 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 83.c
\(\chi_{83}(3,\cdot)\) \(\chi_{83}(4,\cdot)\) \(\chi_{83}(7,\cdot)\) \(\chi_{83}(9,\cdot)\) \(\chi_{83}(10,\cdot)\) \(\chi_{83}(11,\cdot)\) \(\chi_{83}(12,\cdot)\) \(\chi_{83}(16,\cdot)\) \(\chi_{83}(17,\cdot)\) \(\chi_{83}(21,\cdot)\) \(\chi_{83}(23,\cdot)\) \(\chi_{83}(25,\cdot)\) \(\chi_{83}(26,\cdot)\) \(\chi_{83}(27,\cdot)\) \(\chi_{83}(28,\cdot)\) \(\chi_{83}(29,\cdot)\) \(\chi_{83}(30,\cdot)\) \(\chi_{83}(31,\cdot)\) \(\chi_{83}(33,\cdot)\) \(\chi_{83}(36,\cdot)\) \(\chi_{83}(37,\cdot)\) \(\chi_{83}(38,\cdot)\) \(\chi_{83}(40,\cdot)\) \(\chi_{83}(41,\cdot)\) \(\chi_{83}(44,\cdot)\) \(\chi_{83}(48,\cdot)\) \(\chi_{83}(49,\cdot)\) \(\chi_{83}(51,\cdot)\) \(\chi_{83}(59,\cdot)\) \(\chi_{83}(61,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{41})$ |
Fixed field: | Number field defined by a degree 41 polynomial |
Values on generators
\(2\) → \(e\left(\frac{9}{41}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 83 }(30, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{41}\right)\) | \(e\left(\frac{33}{41}\right)\) | \(e\left(\frac{18}{41}\right)\) | \(e\left(\frac{38}{41}\right)\) | \(e\left(\frac{1}{41}\right)\) | \(e\left(\frac{31}{41}\right)\) | \(e\left(\frac{27}{41}\right)\) | \(e\left(\frac{25}{41}\right)\) | \(e\left(\frac{6}{41}\right)\) | \(e\left(\frac{11}{41}\right)\) |