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.cr
\(\chi_{1205}(7,\cdot)\) \(\chi_{1205}(13,\cdot)\) \(\chi_{1205}(37,\cdot)\) \(\chi_{1205}(42,\cdot)\) \(\chi_{1205}(62,\cdot)\) \(\chi_{1205}(68,\cdot)\) \(\chi_{1205}(78,\cdot)\) \(\chi_{1205}(92,\cdot)\) \(\chi_{1205}(112,\cdot)\) \(\chi_{1205}(127,\cdot)\) \(\chi_{1205}(137,\cdot)\) \(\chi_{1205}(142,\cdot)\) \(\chi_{1205}(163,\cdot)\) \(\chi_{1205}(173,\cdot)\) \(\chi_{1205}(202,\cdot)\) \(\chi_{1205}(207,\cdot)\) \(\chi_{1205}(228,\cdot)\) \(\chi_{1205}(292,\cdot)\) \(\chi_{1205}(293,\cdot)\) \(\chi_{1205}(307,\cdot)\) \(\chi_{1205}(327,\cdot)\) \(\chi_{1205}(372,\cdot)\) \(\chi_{1205}(373,\cdot)\) \(\chi_{1205}(398,\cdot)\) \(\chi_{1205}(408,\cdot)\) \(\chi_{1205}(412,\cdot)\) \(\chi_{1205}(413,\cdot)\) \(\chi_{1205}(468,\cdot)\) \(\chi_{1205}(513,\cdot)\) \(\chi_{1205}(528,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((242,971)\) → \((i,e\left(\frac{1}{240}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1205 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{227}{240}\right)\) |