Basic properties
| Modulus: | \(755\) | |
| Conductor: | \(755\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | 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.bf
\(\chi_{755}(34,\cdot)\) \(\chi_{755}(39,\cdot)\) \(\chi_{755}(49,\cdot)\) \(\chi_{755}(69,\cdot)\) \(\chi_{755}(74,\cdot)\) \(\chi_{755}(99,\cdot)\) \(\chi_{755}(139,\cdot)\) \(\chi_{755}(144,\cdot)\) \(\chi_{755}(169,\cdot)\) \(\chi_{755}(194,\cdot)\) \(\chi_{755}(209,\cdot)\) \(\chi_{755}(239,\cdot)\) \(\chi_{755}(254,\cdot)\) \(\chi_{755}(289,\cdot)\) \(\chi_{755}(319,\cdot)\) \(\chi_{755}(324,\cdot)\) \(\chi_{755}(339,\cdot)\) \(\chi_{755}(344,\cdot)\) \(\chi_{755}(349,\cdot)\) \(\chi_{755}(364,\cdot)\) \(\chi_{755}(399,\cdot)\) \(\chi_{755}(439,\cdot)\) \(\chi_{755}(464,\cdot)\) \(\chi_{755}(474,\cdot)\) \(\chi_{755}(484,\cdot)\) \(\chi_{755}(489,\cdot)\) \(\chi_{755}(569,\cdot)\) \(\chi_{755}(574,\cdot)\) \(\chi_{755}(589,\cdot)\) \(\chi_{755}(609,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((152,6)\) → \((-1,e\left(\frac{56}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 755 }(609, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{79}{150}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{14}{75}\right)\) | \(e\left(\frac{77}{150}\right)\) | \(e\left(\frac{17}{150}\right)\) |