Basic properties
| Modulus: | \(5635\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(77\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1127}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5635.cm
\(\chi_{5635}(36,\cdot)\) \(\chi_{5635}(71,\cdot)\) \(\chi_{5635}(141,\cdot)\) \(\chi_{5635}(211,\cdot)\) \(\chi_{5635}(351,\cdot)\) \(\chi_{5635}(386,\cdot)\) \(\chi_{5635}(561,\cdot)\) \(\chi_{5635}(771,\cdot)\) \(\chi_{5635}(841,\cdot)\) \(\chi_{5635}(876,\cdot)\) \(\chi_{5635}(946,\cdot)\) \(\chi_{5635}(1016,\cdot)\) \(\chi_{5635}(1051,\cdot)\) \(\chi_{5635}(1156,\cdot)\) \(\chi_{5635}(1191,\cdot)\) \(\chi_{5635}(1296,\cdot)\) \(\chi_{5635}(1366,\cdot)\) \(\chi_{5635}(1576,\cdot)\) \(\chi_{5635}(1646,\cdot)\) \(\chi_{5635}(1681,\cdot)\) \(\chi_{5635}(1751,\cdot)\) \(\chi_{5635}(1821,\cdot)\) \(\chi_{5635}(1856,\cdot)\) \(\chi_{5635}(1996,\cdot)\) \(\chi_{5635}(2101,\cdot)\) \(\chi_{5635}(2171,\cdot)\) \(\chi_{5635}(2381,\cdot)\) \(\chi_{5635}(2486,\cdot)\) \(\chi_{5635}(2556,\cdot)\) \(\chi_{5635}(2626,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((3382,346,2696)\) → \((1,e\left(\frac{2}{7}\right),e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 5635 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{31}{77}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{8}{77}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{62}{77}\right)\) |