Basic properties
| Modulus: | \(1205\) | |
| Conductor: | \(1205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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.ck
\(\chi_{1205}(33,\cdot)\) \(\chi_{1205}(43,\cdot)\) \(\chi_{1205}(198,\cdot)\) \(\chi_{1205}(208,\cdot)\) \(\chi_{1205}(258,\cdot)\) \(\chi_{1205}(267,\cdot)\) \(\chi_{1205}(298,\cdot)\) \(\chi_{1205}(343,\cdot)\) \(\chi_{1205}(358,\cdot)\) \(\chi_{1205}(377,\cdot)\) \(\chi_{1205}(397,\cdot)\) \(\chi_{1205}(503,\cdot)\) \(\chi_{1205}(567,\cdot)\) \(\chi_{1205}(583,\cdot)\) \(\chi_{1205}(587,\cdot)\) \(\chi_{1205}(697,\cdot)\) \(\chi_{1205}(863,\cdot)\) \(\chi_{1205}(943,\cdot)\) \(\chi_{1205}(987,\cdot)\) \(\chi_{1205}(992,\cdot)\) \(\chi_{1205}(1037,\cdot)\) \(\chi_{1205}(1057,\cdot)\) \(\chi_{1205}(1067,\cdot)\) \(\chi_{1205}(1088,\cdot)\) \(\chi_{1205}(1102,\cdot)\) \(\chi_{1205}(1103,\cdot)\) \(\chi_{1205}(1112,\cdot)\) \(\chi_{1205}(1132,\cdot)\) \(\chi_{1205}(1148,\cdot)\) \(\chi_{1205}(1177,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((242,971)\) → \((-i,e\left(\frac{69}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1205 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(i\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{63}{80}\right)\) |