Basic properties
| Modulus: | \(1205\) | |
| Conductor: | \(1205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 1205.cn
\(\chi_{1205}(29,\cdot)\) \(\chi_{1205}(49,\cdot)\) \(\chi_{1205}(59,\cdot)\) \(\chi_{1205}(164,\cdot)\) \(\chi_{1205}(169,\cdot)\) \(\chi_{1205}(174,\cdot)\) \(\chi_{1205}(229,\cdot)\) \(\chi_{1205}(244,\cdot)\) \(\chi_{1205}(259,\cdot)\) \(\chi_{1205}(294,\cdot)\) \(\chi_{1205}(349,\cdot)\) \(\chi_{1205}(374,\cdot)\) \(\chi_{1205}(429,\cdot)\) \(\chi_{1205}(464,\cdot)\) \(\chi_{1205}(479,\cdot)\) \(\chi_{1205}(494,\cdot)\) \(\chi_{1205}(549,\cdot)\) \(\chi_{1205}(554,\cdot)\) \(\chi_{1205}(559,\cdot)\) \(\chi_{1205}(664,\cdot)\) \(\chi_{1205}(674,\cdot)\) \(\chi_{1205}(694,\cdot)\) \(\chi_{1205}(884,\cdot)\) \(\chi_{1205}(889,\cdot)\) \(\chi_{1205}(914,\cdot)\) \(\chi_{1205}(919,\cdot)\) \(\chi_{1205}(944,\cdot)\) \(\chi_{1205}(984,\cdot)\) \(\chi_{1205}(1009,\cdot)\) \(\chi_{1205}(1014,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((242,971)\) → \((-1,e\left(\frac{1}{120}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1205 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(i\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{107}{120}\right)\) |