Basic properties
| Modulus: | \(5635\) | |
| Conductor: | \(5635\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | 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 5635.cx
\(\chi_{5635}(34,\cdot)\) \(\chi_{5635}(314,\cdot)\) \(\chi_{5635}(419,\cdot)\) \(\chi_{5635}(454,\cdot)\) \(\chi_{5635}(559,\cdot)\) \(\chi_{5635}(594,\cdot)\) \(\chi_{5635}(664,\cdot)\) \(\chi_{5635}(769,\cdot)\) \(\chi_{5635}(839,\cdot)\) \(\chi_{5635}(1049,\cdot)\) \(\chi_{5635}(1119,\cdot)\) \(\chi_{5635}(1259,\cdot)\) \(\chi_{5635}(1364,\cdot)\) \(\chi_{5635}(1399,\cdot)\) \(\chi_{5635}(1539,\cdot)\) \(\chi_{5635}(1574,\cdot)\) \(\chi_{5635}(1644,\cdot)\) \(\chi_{5635}(1854,\cdot)\) \(\chi_{5635}(1924,\cdot)\) \(\chi_{5635}(2029,\cdot)\) \(\chi_{5635}(2064,\cdot)\) \(\chi_{5635}(2169,\cdot)\) \(\chi_{5635}(2274,\cdot)\) \(\chi_{5635}(2344,\cdot)\) \(\chi_{5635}(2379,\cdot)\) \(\chi_{5635}(2659,\cdot)\) \(\chi_{5635}(2729,\cdot)\) \(\chi_{5635}(2834,\cdot)\) \(\chi_{5635}(2869,\cdot)\) \(\chi_{5635}(2974,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((3382,346,2696)\) → \((-1,e\left(\frac{3}{14}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 5635 }(34, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{20}{77}\right)\) | \(e\left(\frac{60}{77}\right)\) | \(e\left(\frac{23}{154}\right)\) | \(e\left(\frac{103}{154}\right)\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{43}{77}\right)\) |