Basic properties
Modulus: | \(4031\) | |
Conductor: | \(139\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(69\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{139}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4031.ba
\(\chi_{4031}(30,\cdot)\) \(\chi_{4031}(117,\cdot)\) \(\chi_{4031}(146,\cdot)\) \(\chi_{4031}(291,\cdot)\) \(\chi_{4031}(349,\cdot)\) \(\chi_{4031}(581,\cdot)\) \(\chi_{4031}(610,\cdot)\) \(\chi_{4031}(639,\cdot)\) \(\chi_{4031}(726,\cdot)\) \(\chi_{4031}(784,\cdot)\) \(\chi_{4031}(813,\cdot)\) \(\chi_{4031}(871,\cdot)\) \(\chi_{4031}(900,\cdot)\) \(\chi_{4031}(958,\cdot)\) \(\chi_{4031}(1132,\cdot)\) \(\chi_{4031}(1161,\cdot)\) \(\chi_{4031}(1190,\cdot)\) \(\chi_{4031}(1219,\cdot)\) \(\chi_{4031}(1248,\cdot)\) \(\chi_{4031}(1364,\cdot)\) \(\chi_{4031}(1538,\cdot)\) \(\chi_{4031}(1567,\cdot)\) \(\chi_{4031}(1596,\cdot)\) \(\chi_{4031}(1944,\cdot)\) \(\chi_{4031}(2089,\cdot)\) \(\chi_{4031}(2205,\cdot)\) \(\chi_{4031}(2379,\cdot)\) \(\chi_{4031}(2553,\cdot)\) \(\chi_{4031}(2669,\cdot)\) \(\chi_{4031}(2727,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 69 polynomial |
Values on generators
\((3337,697)\) → \((1,e\left(\frac{5}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(2553, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{69}\right)\) | \(e\left(\frac{67}{69}\right)\) | \(e\left(\frac{10}{69}\right)\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{43}{69}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{35}{69}\right)\) |