Basic properties
| Modulus: | \(107\) | |
| Conductor: | \(107\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(53\) | 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 107.c
\(\chi_{107}(3,\cdot)\) \(\chi_{107}(4,\cdot)\) \(\chi_{107}(9,\cdot)\) \(\chi_{107}(10,\cdot)\) \(\chi_{107}(11,\cdot)\) \(\chi_{107}(12,\cdot)\) \(\chi_{107}(13,\cdot)\) \(\chi_{107}(14,\cdot)\) \(\chi_{107}(16,\cdot)\) \(\chi_{107}(19,\cdot)\) \(\chi_{107}(23,\cdot)\) \(\chi_{107}(25,\cdot)\) \(\chi_{107}(27,\cdot)\) \(\chi_{107}(29,\cdot)\) \(\chi_{107}(30,\cdot)\) \(\chi_{107}(33,\cdot)\) \(\chi_{107}(34,\cdot)\) \(\chi_{107}(35,\cdot)\) \(\chi_{107}(36,\cdot)\) \(\chi_{107}(37,\cdot)\) \(\chi_{107}(39,\cdot)\) \(\chi_{107}(40,\cdot)\) \(\chi_{107}(41,\cdot)\) \(\chi_{107}(42,\cdot)\) \(\chi_{107}(44,\cdot)\) \(\chi_{107}(47,\cdot)\) \(\chi_{107}(48,\cdot)\) \(\chi_{107}(49,\cdot)\) \(\chi_{107}(52,\cdot)\) \(\chi_{107}(53,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{53})$ |
| Fixed field: | Number field defined by a degree 53 polynomial |
Values on generators
\(2\) → \(e\left(\frac{12}{53}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 107 }(44, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{53}\right)\) | \(e\left(\frac{45}{53}\right)\) | \(e\left(\frac{24}{53}\right)\) | \(e\left(\frac{34}{53}\right)\) | \(e\left(\frac{4}{53}\right)\) | \(e\left(\frac{39}{53}\right)\) | \(e\left(\frac{36}{53}\right)\) | \(e\left(\frac{37}{53}\right)\) | \(e\left(\frac{46}{53}\right)\) | \(e\left(\frac{52}{53}\right)\) |