Basic properties
| Modulus: | \(1205\) | |
| Conductor: | \(1205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | 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.cq
\(\chi_{1205}(52,\cdot)\) \(\chi_{1205}(132,\cdot)\) \(\chi_{1205}(157,\cdot)\) \(\chi_{1205}(167,\cdot)\) \(\chi_{1205}(172,\cdot)\) \(\chi_{1205}(227,\cdot)\) \(\chi_{1205}(248,\cdot)\) \(\chi_{1205}(272,\cdot)\) \(\chi_{1205}(278,\cdot)\) \(\chi_{1205}(283,\cdot)\) \(\chi_{1205}(287,\cdot)\) \(\chi_{1205}(297,\cdot)\) \(\chi_{1205}(303,\cdot)\) \(\chi_{1205}(312,\cdot)\) \(\chi_{1205}(333,\cdot)\) \(\chi_{1205}(353,\cdot)\) \(\chi_{1205}(368,\cdot)\) \(\chi_{1205}(378,\cdot)\) \(\chi_{1205}(383,\cdot)\) \(\chi_{1205}(387,\cdot)\) \(\chi_{1205}(427,\cdot)\) \(\chi_{1205}(443,\cdot)\) \(\chi_{1205}(447,\cdot)\) \(\chi_{1205}(448,\cdot)\) \(\chi_{1205}(517,\cdot)\) \(\chi_{1205}(533,\cdot)\) \(\chi_{1205}(537,\cdot)\) \(\chi_{1205}(548,\cdot)\) \(\chi_{1205}(568,\cdot)\) \(\chi_{1205}(577,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((242,971)\) → \((-i,e\left(\frac{229}{240}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1205 }(1003, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{169}{240}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{23}{240}\right)\) |