Basic properties
Modulus: | \(2678\) | |
Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{103}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.bi
\(\chi_{2678}(105,\cdot)\) \(\chi_{2678}(131,\cdot)\) \(\chi_{2678}(235,\cdot)\) \(\chi_{2678}(261,\cdot)\) \(\chi_{2678}(313,\cdot)\) \(\chi_{2678}(391,\cdot)\) \(\chi_{2678}(495,\cdot)\) \(\chi_{2678}(547,\cdot)\) \(\chi_{2678}(573,\cdot)\) \(\chi_{2678}(625,\cdot)\) \(\chi_{2678}(651,\cdot)\) \(\chi_{2678}(677,\cdot)\) \(\chi_{2678}(781,\cdot)\) \(\chi_{2678}(963,\cdot)\) \(\chi_{2678}(1093,\cdot)\) \(\chi_{2678}(1171,\cdot)\) \(\chi_{2678}(1327,\cdot)\) \(\chi_{2678}(1431,\cdot)\) \(\chi_{2678}(1457,\cdot)\) \(\chi_{2678}(1483,\cdot)\) \(\chi_{2678}(1561,\cdot)\) \(\chi_{2678}(1613,\cdot)\) \(\chi_{2678}(1665,\cdot)\) \(\chi_{2678}(1769,\cdot)\) \(\chi_{2678}(1873,\cdot)\) \(\chi_{2678}(1951,\cdot)\) \(\chi_{2678}(2055,\cdot)\) \(\chi_{2678}(2315,\cdot)\) \(\chi_{2678}(2419,\cdot)\) \(\chi_{2678}(2497,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((1,e\left(\frac{22}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 2678 }(105, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{6}{17}\right)\) |