Basic properties
| Modulus: | \(7018\) | |
| Conductor: | \(3509\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3509}(2817,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7018.bl
\(\chi_{7018}(67,\cdot)\) \(\chi_{7018}(265,\cdot)\) \(\chi_{7018}(353,\cdot)\) \(\chi_{7018}(419,\cdot)\) \(\chi_{7018}(441,\cdot)\) \(\chi_{7018}(573,\cdot)\) \(\chi_{7018}(705,\cdot)\) \(\chi_{7018}(903,\cdot)\) \(\chi_{7018}(991,\cdot)\) \(\chi_{7018}(1057,\cdot)\) \(\chi_{7018}(1079,\cdot)\) \(\chi_{7018}(1343,\cdot)\) \(\chi_{7018}(1541,\cdot)\) \(\chi_{7018}(1629,\cdot)\) \(\chi_{7018}(1717,\cdot)\) \(\chi_{7018}(1849,\cdot)\) \(\chi_{7018}(1981,\cdot)\) \(\chi_{7018}(2267,\cdot)\) \(\chi_{7018}(2333,\cdot)\) \(\chi_{7018}(2355,\cdot)\) \(\chi_{7018}(2487,\cdot)\) \(\chi_{7018}(2619,\cdot)\) \(\chi_{7018}(2817,\cdot)\) \(\chi_{7018}(2971,\cdot)\) \(\chi_{7018}(2993,\cdot)\) \(\chi_{7018}(3125,\cdot)\) \(\chi_{7018}(3257,\cdot)\) \(\chi_{7018}(3455,\cdot)\) \(\chi_{7018}(3543,\cdot)\) \(\chi_{7018}(3609,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2785,727)\) → \((e\left(\frac{5}{11}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 7018 }(2817, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{57}{154}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{19}{77}\right)\) |