Basic properties
| Modulus: | \(2738\) | |
| Conductor: | \(1369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(74\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1369}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2738.k
\(\chi_{2738}(73,\cdot)\) \(\chi_{2738}(147,\cdot)\) \(\chi_{2738}(221,\cdot)\) \(\chi_{2738}(295,\cdot)\) \(\chi_{2738}(369,\cdot)\) \(\chi_{2738}(443,\cdot)\) \(\chi_{2738}(517,\cdot)\) \(\chi_{2738}(591,\cdot)\) \(\chi_{2738}(665,\cdot)\) \(\chi_{2738}(739,\cdot)\) \(\chi_{2738}(813,\cdot)\) \(\chi_{2738}(887,\cdot)\) \(\chi_{2738}(961,\cdot)\) \(\chi_{2738}(1035,\cdot)\) \(\chi_{2738}(1109,\cdot)\) \(\chi_{2738}(1183,\cdot)\) \(\chi_{2738}(1257,\cdot)\) \(\chi_{2738}(1331,\cdot)\) \(\chi_{2738}(1405,\cdot)\) \(\chi_{2738}(1479,\cdot)\) \(\chi_{2738}(1553,\cdot)\) \(\chi_{2738}(1627,\cdot)\) \(\chi_{2738}(1701,\cdot)\) \(\chi_{2738}(1775,\cdot)\) \(\chi_{2738}(1849,\cdot)\) \(\chi_{2738}(1923,\cdot)\) \(\chi_{2738}(1997,\cdot)\) \(\chi_{2738}(2071,\cdot)\) \(\chi_{2738}(2145,\cdot)\) \(\chi_{2738}(2219,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | Number field defined by a degree 74 polynomial |
Values on generators
\(1371\) → \(e\left(\frac{33}{74}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2738 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{3}{74}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{33}{74}\right)\) | \(e\left(\frac{5}{74}\right)\) | \(e\left(\frac{17}{74}\right)\) | \(e\left(\frac{45}{74}\right)\) | \(e\left(\frac{15}{37}\right)\) |