Basic properties
Modulus: | \(103\) | |
Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | 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 103.h
\(\chi_{103}(5,\cdot)\) \(\chi_{103}(6,\cdot)\) \(\chi_{103}(11,\cdot)\) \(\chi_{103}(12,\cdot)\) \(\chi_{103}(20,\cdot)\) \(\chi_{103}(21,\cdot)\) \(\chi_{103}(35,\cdot)\) \(\chi_{103}(40,\cdot)\) \(\chi_{103}(43,\cdot)\) \(\chi_{103}(44,\cdot)\) \(\chi_{103}(45,\cdot)\) \(\chi_{103}(48,\cdot)\) \(\chi_{103}(51,\cdot)\) \(\chi_{103}(53,\cdot)\) \(\chi_{103}(54,\cdot)\) \(\chi_{103}(62,\cdot)\) \(\chi_{103}(65,\cdot)\) \(\chi_{103}(67,\cdot)\) \(\chi_{103}(70,\cdot)\) \(\chi_{103}(71,\cdot)\) \(\chi_{103}(74,\cdot)\) \(\chi_{103}(75,\cdot)\) \(\chi_{103}(77,\cdot)\) \(\chi_{103}(78,\cdot)\) \(\chi_{103}(84,\cdot)\) \(\chi_{103}(85,\cdot)\) \(\chi_{103}(86,\cdot)\) \(\chi_{103}(87,\cdot)\) \(\chi_{103}(88,\cdot)\) \(\chi_{103}(96,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1}{102}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 103 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{61}{102}\right)\) |