Basic properties
| Modulus: | \(8004\) | |
| Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2001}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.de
\(\chi_{8004}(5,\cdot)\) \(\chi_{8004}(125,\cdot)\) \(\chi_{8004}(149,\cdot)\) \(\chi_{8004}(245,\cdot)\) \(\chi_{8004}(341,\cdot)\) \(\chi_{8004}(497,\cdot)\) \(\chi_{8004}(557,\cdot)\) \(\chi_{8004}(701,\cdot)\) \(\chi_{8004}(845,\cdot)\) \(\chi_{8004}(941,\cdot)\) \(\chi_{8004}(1049,\cdot)\) \(\chi_{8004}(1169,\cdot)\) \(\chi_{8004}(1193,\cdot)\) \(\chi_{8004}(1253,\cdot)\) \(\chi_{8004}(1385,\cdot)\) \(\chi_{8004}(1397,\cdot)\) \(\chi_{8004}(1601,\cdot)\) \(\chi_{8004}(1745,\cdot)\) \(\chi_{8004}(1949,\cdot)\) \(\chi_{8004}(1985,\cdot)\) \(\chi_{8004}(2081,\cdot)\) \(\chi_{8004}(2213,\cdot)\) \(\chi_{8004}(2297,\cdot)\) \(\chi_{8004}(2333,\cdot)\) \(\chi_{8004}(2429,\cdot)\) \(\chi_{8004}(2777,\cdot)\) \(\chi_{8004}(2909,\cdot)\) \(\chi_{8004}(3125,\cdot)\) \(\chi_{8004}(3257,\cdot)\) \(\chi_{8004}(3281,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((1,-1,e\left(\frac{1}{22}\right),e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{85}{154}\right)\) | \(e\left(\frac{60}{77}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{58}{77}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{24}{77}\right)\) |