Basic properties
| Modulus: | \(1208\) | |
| Conductor: | \(151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(75\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{151}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1208.bo
\(\chi_{1208}(17,\cdot)\) \(\chi_{1208}(25,\cdot)\) \(\chi_{1208}(49,\cdot)\) \(\chi_{1208}(97,\cdot)\) \(\chi_{1208}(121,\cdot)\) \(\chi_{1208}(137,\cdot)\) \(\chi_{1208}(145,\cdot)\) \(\chi_{1208}(161,\cdot)\) \(\chi_{1208}(169,\cdot)\) \(\chi_{1208}(185,\cdot)\) \(\chi_{1208}(193,\cdot)\) \(\chi_{1208}(209,\cdot)\) \(\chi_{1208}(225,\cdot)\) \(\chi_{1208}(241,\cdot)\) \(\chi_{1208}(289,\cdot)\) \(\chi_{1208}(313,\cdot)\) \(\chi_{1208}(345,\cdot)\) \(\chi_{1208}(401,\cdot)\) \(\chi_{1208}(441,\cdot)\) \(\chi_{1208}(489,\cdot)\) \(\chi_{1208}(553,\cdot)\) \(\chi_{1208}(569,\cdot)\) \(\chi_{1208}(609,\cdot)\) \(\chi_{1208}(625,\cdot)\) \(\chi_{1208}(641,\cdot)\) \(\chi_{1208}(649,\cdot)\) \(\chi_{1208}(673,\cdot)\) \(\chi_{1208}(777,\cdot)\) \(\chi_{1208}(817,\cdot)\) \(\chi_{1208}(937,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\((303,605,761)\) → \((1,1,e\left(\frac{8}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1208 }(641, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{71}{75}\right)\) | \(e\left(\frac{11}{75}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{2}{75}\right)\) | \(e\left(\frac{28}{75}\right)\) | \(e\left(\frac{44}{75}\right)\) | \(e\left(\frac{14}{75}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{59}{75}\right)\) |