Basic properties
| Modulus: | \(8004\) | |
| Conductor: | \(8004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.cv
\(\chi_{8004}(35,\cdot)\) \(\chi_{8004}(71,\cdot)\) \(\chi_{8004}(167,\cdot)\) \(\chi_{8004}(179,\cdot)\) \(\chi_{8004}(515,\cdot)\) \(\chi_{8004}(647,\cdot)\) \(\chi_{8004}(671,\cdot)\) \(\chi_{8004}(731,\cdot)\) \(\chi_{8004}(767,\cdot)\) \(\chi_{8004}(863,\cdot)\) \(\chi_{8004}(995,\cdot)\) \(\chi_{8004}(1223,\cdot)\) \(\chi_{8004}(1343,\cdot)\) \(\chi_{8004}(1559,\cdot)\) \(\chi_{8004}(1691,\cdot)\) \(\chi_{8004}(1715,\cdot)\) \(\chi_{8004}(1775,\cdot)\) \(\chi_{8004}(2063,\cdot)\) \(\chi_{8004}(2267,\cdot)\) \(\chi_{8004}(2387,\cdot)\) \(\chi_{8004}(2603,\cdot)\) \(\chi_{8004}(2615,\cdot)\) \(\chi_{8004}(2819,\cdot)\) \(\chi_{8004}(2855,\cdot)\) \(\chi_{8004}(3107,\cdot)\) \(\chi_{8004}(3167,\cdot)\) \(\chi_{8004}(3203,\cdot)\) \(\chi_{8004}(3431,\cdot)\) \(\chi_{8004}(3551,\cdot)\) \(\chi_{8004}(3647,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((-1,-1,e\left(\frac{10}{11}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{53}{154}\right)\) | \(e\left(\frac{83}{154}\right)\) | \(e\left(\frac{45}{77}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{113}{154}\right)\) |