Basic properties
| Modulus: | \(755\) | |
| Conductor: | \(755\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | 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 755.bi
\(\chi_{755}(7,\cdot)\) \(\chi_{755}(12,\cdot)\) \(\chi_{755}(13,\cdot)\) \(\chi_{755}(48,\cdot)\) \(\chi_{755}(52,\cdot)\) \(\chi_{755}(63,\cdot)\) \(\chi_{755}(77,\cdot)\) \(\chi_{755}(82,\cdot)\) \(\chi_{755}(93,\cdot)\) \(\chi_{755}(102,\cdot)\) \(\chi_{755}(108,\cdot)\) \(\chi_{755}(112,\cdot)\) \(\chi_{755}(117,\cdot)\) \(\chi_{755}(133,\cdot)\) \(\chi_{755}(157,\cdot)\) \(\chi_{755}(158,\cdot)\) \(\chi_{755}(163,\cdot)\) \(\chi_{755}(202,\cdot)\) \(\chi_{755}(203,\cdot)\) \(\chi_{755}(207,\cdot)\) \(\chi_{755}(212,\cdot)\) \(\chi_{755}(222,\cdot)\) \(\chi_{755}(228,\cdot)\) \(\chi_{755}(233,\cdot)\) \(\chi_{755}(247,\cdot)\) \(\chi_{755}(253,\cdot)\) \(\chi_{755}(257,\cdot)\) \(\chi_{755}(262,\cdot)\) \(\chi_{755}(263,\cdot)\) \(\chi_{755}(268,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((152,6)\) → \((-i,e\left(\frac{91}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 755 }(718, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{91}{150}\right)\) | \(e\left(\frac{119}{300}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{2}{75}\right)\) | \(e\left(\frac{247}{300}\right)\) | \(e\left(\frac{37}{300}\right)\) |