Basic properties
| Modulus: | \(121\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | 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 121.h
\(\chi_{121}(2,\cdot)\) \(\chi_{121}(6,\cdot)\) \(\chi_{121}(7,\cdot)\) \(\chi_{121}(8,\cdot)\) \(\chi_{121}(13,\cdot)\) \(\chi_{121}(17,\cdot)\) \(\chi_{121}(18,\cdot)\) \(\chi_{121}(19,\cdot)\) \(\chi_{121}(24,\cdot)\) \(\chi_{121}(28,\cdot)\) \(\chi_{121}(29,\cdot)\) \(\chi_{121}(30,\cdot)\) \(\chi_{121}(35,\cdot)\) \(\chi_{121}(39,\cdot)\) \(\chi_{121}(41,\cdot)\) \(\chi_{121}(46,\cdot)\) \(\chi_{121}(50,\cdot)\) \(\chi_{121}(51,\cdot)\) \(\chi_{121}(52,\cdot)\) \(\chi_{121}(57,\cdot)\) \(\chi_{121}(61,\cdot)\) \(\chi_{121}(62,\cdot)\) \(\chi_{121}(63,\cdot)\) \(\chi_{121}(68,\cdot)\) \(\chi_{121}(72,\cdot)\) \(\chi_{121}(73,\cdot)\) \(\chi_{121}(74,\cdot)\) \(\chi_{121}(79,\cdot)\) \(\chi_{121}(83,\cdot)\) \(\chi_{121}(84,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{110}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 121 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) |