Basic properties
Modulus: | \(6003\) | |
Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(77\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{667}(430,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.cm
\(\chi_{6003}(82,\cdot)\) \(\chi_{6003}(190,\cdot)\) \(\chi_{6003}(397,\cdot)\) \(\chi_{6003}(487,\cdot)\) \(\chi_{6003}(604,\cdot)\) \(\chi_{6003}(703,\cdot)\) \(\chi_{6003}(721,\cdot)\) \(\chi_{6003}(748,\cdot)\) \(\chi_{6003}(982,\cdot)\) \(\chi_{6003}(1225,\cdot)\) \(\chi_{6003}(1504,\cdot)\) \(\chi_{6003}(1531,\cdot)\) \(\chi_{6003}(1756,\cdot)\) \(\chi_{6003}(1963,\cdot)\) \(\chi_{6003}(2017,\cdot)\) \(\chi_{6003}(2026,\cdot)\) \(\chi_{6003}(2053,\cdot)\) \(\chi_{6003}(2170,\cdot)\) \(\chi_{6003}(2224,\cdot)\) \(\chi_{6003}(2431,\cdot)\) \(\chi_{6003}(2539,\cdot)\) \(\chi_{6003}(2548,\cdot)\) \(\chi_{6003}(2746,\cdot)\) \(\chi_{6003}(2791,\cdot)\) \(\chi_{6003}(2809,\cdot)\) \(\chi_{6003}(2953,\cdot)\) \(\chi_{6003}(3052,\cdot)\) \(\chi_{6003}(3061,\cdot)\) \(\chi_{6003}(3268,\cdot)\) \(\chi_{6003}(3475,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((668,3133,4555)\) → \((1,e\left(\frac{4}{11}\right),e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(2431, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{77}\right)\) | \(e\left(\frac{2}{77}\right)\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{18}{77}\right)\) | \(e\left(\frac{27}{77}\right)\) | \(e\left(\frac{4}{77}\right)\) |