Basic properties
| Modulus: | \(3509\) | |
| Conductor: | \(3509\) | 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 3509.bk
\(\chi_{3509}(34,\cdot)\) \(\chi_{3509}(67,\cdot)\) \(\chi_{3509}(100,\cdot)\) \(\chi_{3509}(254,\cdot)\) \(\chi_{3509}(265,\cdot)\) \(\chi_{3509}(353,\cdot)\) \(\chi_{3509}(386,\cdot)\) \(\chi_{3509}(419,\cdot)\) \(\chi_{3509}(441,\cdot)\) \(\chi_{3509}(573,\cdot)\) \(\chi_{3509}(584,\cdot)\) \(\chi_{3509}(672,\cdot)\) \(\chi_{3509}(705,\cdot)\) \(\chi_{3509}(738,\cdot)\) \(\chi_{3509}(760,\cdot)\) \(\chi_{3509}(892,\cdot)\) \(\chi_{3509}(903,\cdot)\) \(\chi_{3509}(991,\cdot)\) \(\chi_{3509}(1024,\cdot)\) \(\chi_{3509}(1057,\cdot)\) \(\chi_{3509}(1079,\cdot)\) \(\chi_{3509}(1222,\cdot)\) \(\chi_{3509}(1310,\cdot)\) \(\chi_{3509}(1343,\cdot)\) \(\chi_{3509}(1376,\cdot)\) \(\chi_{3509}(1398,\cdot)\) \(\chi_{3509}(1530,\cdot)\) \(\chi_{3509}(1541,\cdot)\) \(\chi_{3509}(1629,\cdot)\) \(\chi_{3509}(1662,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2785,727)\) → \((e\left(\frac{1}{11}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3509 }(903, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{154}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{25}{77}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{75}{154}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{15}{22}\right)\) |