Basic properties
Modulus: | \(4002\) | |
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 \(\chi_{667}(397,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4002.bk
\(\chi_{4002}(25,\cdot)\) \(\chi_{4002}(49,\cdot)\) \(\chi_{4002}(169,\cdot)\) \(\chi_{4002}(223,\cdot)\) \(\chi_{4002}(397,\cdot)\) \(\chi_{4002}(487,\cdot)\) \(\chi_{4002}(547,\cdot)\) \(\chi_{4002}(625,\cdot)\) \(\chi_{4002}(703,\cdot)\) \(\chi_{4002}(721,\cdot)\) \(\chi_{4002}(745,\cdot)\) \(\chi_{4002}(877,\cdot)\) \(\chi_{4002}(1039,\cdot)\) \(\chi_{4002}(1051,\cdot)\) \(\chi_{4002}(1093,\cdot)\) \(\chi_{4002}(1225,\cdot)\) \(\chi_{4002}(1267,\cdot)\) \(\chi_{4002}(1531,\cdot)\) \(\chi_{4002}(1573,\cdot)\) \(\chi_{4002}(1591,\cdot)\) \(\chi_{4002}(1669,\cdot)\) \(\chi_{4002}(1705,\cdot)\) \(\chi_{4002}(1789,\cdot)\) \(\chi_{4002}(1843,\cdot)\) \(\chi_{4002}(1879,\cdot)\) \(\chi_{4002}(1921,\cdot)\) \(\chi_{4002}(1963,\cdot)\) \(\chi_{4002}(2017,\cdot)\) \(\chi_{4002}(2053,\cdot)\) \(\chi_{4002}(2083,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((2669,3133,553)\) → \((1,e\left(\frac{9}{11}\right),e\left(\frac{6}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
\( \chi_{ 4002 }(397, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{77}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{61}{77}\right)\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{76}{77}\right)\) | \(e\left(\frac{27}{77}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{58}{77}\right)\) |