Basic properties
| Modulus: | \(242\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 242.h
\(\chi_{242}(7,\cdot)\) \(\chi_{242}(13,\cdot)\) \(\chi_{242}(17,\cdot)\) \(\chi_{242}(19,\cdot)\) \(\chi_{242}(29,\cdot)\) \(\chi_{242}(35,\cdot)\) \(\chi_{242}(39,\cdot)\) \(\chi_{242}(41,\cdot)\) \(\chi_{242}(51,\cdot)\) \(\chi_{242}(57,\cdot)\) \(\chi_{242}(61,\cdot)\) \(\chi_{242}(63,\cdot)\) \(\chi_{242}(73,\cdot)\) \(\chi_{242}(79,\cdot)\) \(\chi_{242}(83,\cdot)\) \(\chi_{242}(85,\cdot)\) \(\chi_{242}(95,\cdot)\) \(\chi_{242}(101,\cdot)\) \(\chi_{242}(105,\cdot)\) \(\chi_{242}(107,\cdot)\) \(\chi_{242}(117,\cdot)\) \(\chi_{242}(123,\cdot)\) \(\chi_{242}(127,\cdot)\) \(\chi_{242}(129,\cdot)\) \(\chi_{242}(139,\cdot)\) \(\chi_{242}(145,\cdot)\) \(\chi_{242}(149,\cdot)\) \(\chi_{242}(151,\cdot)\) \(\chi_{242}(167,\cdot)\) \(\chi_{242}(171,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\(123\) → \(e\left(\frac{83}{110}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 242 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) |