Basic properties
| Modulus: | \(1862\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(519,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1862.cb
\(\chi_{1862}(43,\cdot)\) \(\chi_{1862}(85,\cdot)\) \(\chi_{1862}(169,\cdot)\) \(\chi_{1862}(225,\cdot)\) \(\chi_{1862}(253,\cdot)\) \(\chi_{1862}(309,\cdot)\) \(\chi_{1862}(351,\cdot)\) \(\chi_{1862}(365,\cdot)\) \(\chi_{1862}(435,\cdot)\) \(\chi_{1862}(519,\cdot)\) \(\chi_{1862}(575,\cdot)\) \(\chi_{1862}(617,\cdot)\) \(\chi_{1862}(631,\cdot)\) \(\chi_{1862}(701,\cdot)\) \(\chi_{1862}(757,\cdot)\) \(\chi_{1862}(841,\cdot)\) \(\chi_{1862}(897,\cdot)\) \(\chi_{1862}(967,\cdot)\) \(\chi_{1862}(1023,\cdot)\) \(\chi_{1862}(1051,\cdot)\) \(\chi_{1862}(1107,\cdot)\) \(\chi_{1862}(1149,\cdot)\) \(\chi_{1862}(1163,\cdot)\) \(\chi_{1862}(1233,\cdot)\) \(\chi_{1862}(1289,\cdot)\) \(\chi_{1862}(1317,\cdot)\) \(\chi_{1862}(1415,\cdot)\) \(\chi_{1862}(1429,\cdot)\) \(\chi_{1862}(1499,\cdot)\) \(\chi_{1862}(1555,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((1179,1275)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 1862 }(519, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) |