Basic properties
Modulus: | \(1103\) | |
Conductor: | \(1103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1102\) | 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 1103.h
\(\chi_{1103}(5,\cdot)\) \(\chi_{1103}(7,\cdot)\) \(\chi_{1103}(10,\cdot)\) \(\chi_{1103}(11,\cdot)\) \(\chi_{1103}(13,\cdot)\) \(\chi_{1103}(14,\cdot)\) \(\chi_{1103}(15,\cdot)\) \(\chi_{1103}(19,\cdot)\) \(\chi_{1103}(20,\cdot)\) \(\chi_{1103}(21,\cdot)\) \(\chi_{1103}(22,\cdot)\) \(\chi_{1103}(26,\cdot)\) \(\chi_{1103}(28,\cdot)\) \(\chi_{1103}(30,\cdot)\) \(\chi_{1103}(31,\cdot)\) \(\chi_{1103}(33,\cdot)\) \(\chi_{1103}(38,\cdot)\) \(\chi_{1103}(39,\cdot)\) \(\chi_{1103}(40,\cdot)\) \(\chi_{1103}(42,\cdot)\) \(\chi_{1103}(44,\cdot)\) \(\chi_{1103}(45,\cdot)\) \(\chi_{1103}(52,\cdot)\) \(\chi_{1103}(56,\cdot)\) \(\chi_{1103}(57,\cdot)\) \(\chi_{1103}(59,\cdot)\) \(\chi_{1103}(60,\cdot)\) \(\chi_{1103}(62,\cdot)\) \(\chi_{1103}(63,\cdot)\) \(\chi_{1103}(66,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{551})$ |
Fixed field: | Number field defined by a degree 1102 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{907}{1102}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1103 }(1100, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{3}{551}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{907}{1102}\right)\) | \(e\left(\frac{212}{551}\right)\) | \(e\left(\frac{367}{1102}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{6}{551}\right)\) | \(e\left(\frac{223}{1102}\right)\) | \(e\left(\frac{111}{1102}\right)\) |