Basic properties
Modulus: | \(5635\) | |
Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(77\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1127}(876,\cdot)\) | 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
\((3382,346,2696)\) → \((1,e\left(\frac{1}{7}\right),e\left(\frac{1}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 5635 }(876, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{61}{77}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{53}{77}\right)\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{76}{77}\right)\) | \(e\left(\frac{45}{77}\right)\) |