Basic properties
| Modulus: | \(121\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | 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 121.g
\(\chi_{121}(4,\cdot)\) \(\chi_{121}(5,\cdot)\) \(\chi_{121}(14,\cdot)\) \(\chi_{121}(15,\cdot)\) \(\chi_{121}(16,\cdot)\) \(\chi_{121}(20,\cdot)\) \(\chi_{121}(25,\cdot)\) \(\chi_{121}(26,\cdot)\) \(\chi_{121}(31,\cdot)\) \(\chi_{121}(36,\cdot)\) \(\chi_{121}(37,\cdot)\) \(\chi_{121}(38,\cdot)\) \(\chi_{121}(42,\cdot)\) \(\chi_{121}(47,\cdot)\) \(\chi_{121}(48,\cdot)\) \(\chi_{121}(49,\cdot)\) \(\chi_{121}(53,\cdot)\) \(\chi_{121}(58,\cdot)\) \(\chi_{121}(59,\cdot)\) \(\chi_{121}(60,\cdot)\) \(\chi_{121}(64,\cdot)\) \(\chi_{121}(69,\cdot)\) \(\chi_{121}(70,\cdot)\) \(\chi_{121}(71,\cdot)\) \(\chi_{121}(75,\cdot)\) \(\chi_{121}(80,\cdot)\) \(\chi_{121}(82,\cdot)\) \(\chi_{121}(86,\cdot)\) \(\chi_{121}(91,\cdot)\) \(\chi_{121}(92,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\(2\) → \(e\left(\frac{27}{55}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 121 }(60, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) |