Basic properties
| Modulus: | \(109\) | |
| Conductor: | \(109\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 109.l
\(\chi_{109}(6,\cdot)\) \(\chi_{109}(10,\cdot)\) \(\chi_{109}(11,\cdot)\) \(\chi_{109}(13,\cdot)\) \(\chi_{109}(14,\cdot)\) \(\chi_{109}(18,\cdot)\) \(\chi_{109}(24,\cdot)\) \(\chi_{109}(30,\cdot)\) \(\chi_{109}(37,\cdot)\) \(\chi_{109}(39,\cdot)\) \(\chi_{109}(40,\cdot)\) \(\chi_{109}(42,\cdot)\) \(\chi_{109}(44,\cdot)\) \(\chi_{109}(47,\cdot)\) \(\chi_{109}(50,\cdot)\) \(\chi_{109}(51,\cdot)\) \(\chi_{109}(52,\cdot)\) \(\chi_{109}(53,\cdot)\) \(\chi_{109}(56,\cdot)\) \(\chi_{109}(57,\cdot)\) \(\chi_{109}(58,\cdot)\) \(\chi_{109}(59,\cdot)\) \(\chi_{109}(62,\cdot)\) \(\chi_{109}(65,\cdot)\) \(\chi_{109}(67,\cdot)\) \(\chi_{109}(69,\cdot)\) \(\chi_{109}(70,\cdot)\) \(\chi_{109}(72,\cdot)\) \(\chi_{109}(79,\cdot)\) \(\chi_{109}(85,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{61}{108}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 109 }(85, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{95}{108}\right)\) |