Basic properties
Modulus: | \(4334\) | |
Conductor: | \(2167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(98\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2167}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4334.z
\(\chi_{4334}(43,\cdot)\) \(\chi_{4334}(65,\cdot)\) \(\chi_{4334}(109,\cdot)\) \(\chi_{4334}(219,\cdot)\) \(\chi_{4334}(549,\cdot)\) \(\chi_{4334}(703,\cdot)\) \(\chi_{4334}(725,\cdot)\) \(\chi_{4334}(813,\cdot)\) \(\chi_{4334}(835,\cdot)\) \(\chi_{4334}(945,\cdot)\) \(\chi_{4334}(989,\cdot)\) \(\chi_{4334}(1011,\cdot)\) \(\chi_{4334}(1077,\cdot)\) \(\chi_{4334}(1121,\cdot)\) \(\chi_{4334}(1319,\cdot)\) \(\chi_{4334}(1363,\cdot)\) \(\chi_{4334}(1495,\cdot)\) \(\chi_{4334}(1517,\cdot)\) \(\chi_{4334}(1539,\cdot)\) \(\chi_{4334}(1583,\cdot)\) \(\chi_{4334}(1869,\cdot)\) \(\chi_{4334}(1979,\cdot)\) \(\chi_{4334}(2067,\cdot)\) \(\chi_{4334}(2133,\cdot)\) \(\chi_{4334}(2177,\cdot)\) \(\chi_{4334}(2419,\cdot)\) \(\chi_{4334}(2485,\cdot)\) \(\chi_{4334}(2507,\cdot)\) \(\chi_{4334}(2705,\cdot)\) \(\chi_{4334}(3101,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{49})$ |
Fixed field: | Number field defined by a degree 98 polynomial |
Values on generators
\((1971,199)\) → \((-1,e\left(\frac{39}{98}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 4334 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{98}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{59}{98}\right)\) | \(e\left(\frac{3}{49}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{38}{49}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{31}{49}\right)\) | \(e\left(\frac{37}{49}\right)\) |