Basic properties
| Modulus: | \(5635\) | |
| Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{245}(192,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5635.cq
\(\chi_{5635}(47,\cdot)\) \(\chi_{5635}(208,\cdot)\) \(\chi_{5635}(507,\cdot)\) \(\chi_{5635}(1013,\cdot)\) \(\chi_{5635}(1312,\cdot)\) \(\chi_{5635}(1473,\cdot)\) \(\chi_{5635}(1657,\cdot)\) \(\chi_{5635}(1818,\cdot)\) \(\chi_{5635}(2117,\cdot)\) \(\chi_{5635}(2278,\cdot)\) \(\chi_{5635}(2462,\cdot)\) \(\chi_{5635}(2623,\cdot)\) \(\chi_{5635}(3083,\cdot)\) \(\chi_{5635}(3267,\cdot)\) \(\chi_{5635}(3428,\cdot)\) \(\chi_{5635}(3727,\cdot)\) \(\chi_{5635}(3888,\cdot)\) \(\chi_{5635}(4072,\cdot)\) \(\chi_{5635}(4532,\cdot)\) \(\chi_{5635}(4693,\cdot)\) \(\chi_{5635}(4877,\cdot)\) \(\chi_{5635}(5038,\cdot)\) \(\chi_{5635}(5337,\cdot)\) \(\chi_{5635}(5498,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3382,346,2696)\) → \((i,e\left(\frac{31}{42}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 5635 }(5337, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) |